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Immigrant Workers and Technological Change: An Induced Innovation Perspective on Florida and U.S. Agriculture


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IMMIGRANT WORKERS AND TECHNOLOGICAL CHANGE: AN INDUCED INNOVATION PERSPECTIVE ON FLORIDA AND U.S. AGRICULTURE By ORACHOS NAPASINTUWONG A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2004

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Copyright 2004 by Orachos Napasintuwong

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To my parents: Pisal and Duangkmol Napasintuwong

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ACKNOWLEDGMENTS I am very grateful to have had the opportunity to work with my advisor, Dr. Robert D. Emerson. Working with him has taught me to be a good economist professionally, and to care for people and society. I would like to express my deep gratitude for his guidance, criticism, and encouragement in doing my research and dissertation. I also thank him for his understanding, patience, and support during difficult times in the process of writing my dissertation. I also would like to thank all of my committee members (Dr. Andrew Schmitz, Dr. Bin Xu, and Dr. Lawrence Kenny), who contributed significantly to the quality of my work. I also appreciate Dr. Xus suggestion of research topics that led to this research. Special thanks go to Eldon Ball, who put together the unpublished data from ERS, USDA specifically for this research. My thanks also go to all my friends and professors at the Food and Resource Economics Department. I appreciate my friends (Arturo Bocardo, Chris de Bodisco, and their families), who have been great companions during my years in Gainesville. I also want to thank Dr. Thomas Spreen, and the Florida Citrus Department, who sponsored my graduate assistantship during my first semester; and especially the Food and Resource Economics Department and the International Agricultural Trade and Policy Center for their material support during my Ph.D. program. I also thank Dr. Andrew Schmitz and Dr. Richard Kilmer, who gave me an opportunity to assist them in their research projects and classes; and Dr. Chris Andrew and Dr. Richard Weldon, who gave me a great opportunity to teach. iv

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My greatest gratitude goes to my parents, Pisal and Duangkmol Napasintuwong, who taught me to appreciate the importance of education and gave me the opportunity to explore education abroad. They always gave me love and support through some difficult times. Their understanding and encouragement make this journey possible. I also would like to thank my sister, Chanoknetr, for her love and encouragement; my cousins Varis, Kanat, and Karit; and their parents Guy and Krisna Ransibrahmanakul for their advice, love, and care here in the United States. My special thanks go to my family in Thailand, all my friends in Gainesville, Numpol Lawanyawatna, Nakarin Ruangpanit, and Pollajak Veerawetwatana for their moral support to accomplish this goal. v

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TABLE OF CONTENTS Page ACKNOWLEDGMENTS.................................................................................................iv TABLE OF CONTENTS...................................................................................................vi LIST OF TABLES.............................................................................................................ix LIST OF FIGURES.............................................................................................................x ABSTRACT......................................................................................................................xii CHAPTER 1 INTRODUCTION........................................................................................................1 Background...................................................................................................................1 Problem Statement........................................................................................................5 Research Objectives......................................................................................................6 Organization of Chapters..............................................................................................6 2 U.S. FARM LABOR MARKET, IMMIGRATION POLICY, AND FARM MECHANIZATION.....................................................................................................8 U.S. Farm Labor Market...............................................................................................8 U.S. Immigration Policy.............................................................................................10 Farm Mechanization in U.S. Agriculture...................................................................15 3 THEORETICAL AND ANALYTICAL FRAMEWORK.........................................21 Cost Minimization Model of Induced Innovation Theory..........................................21 Hicks-Ahmad Model of Induced Technological Change....................................23 Hayami and Ruttan Model of Induced Technological Change...........................25 Empirical Studies of Biases in U.S. Agricultural Technology............................29 Profit Function Model of Induced Innovation............................................................31 Rate of Technological Change and Biased Technological Change............................38 4 EMPIRICAL MODEL, DATA, AND ESTIMATION..............................................46 Empirical Model.........................................................................................................46 vi

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Model Specification.............................................................................................49 Model Restrictions...............................................................................................50 Laus Cholesky decomposition...........................................................................53 Wiley-Schmidt-Bramble decomposition......................................................54 Elasticity..............................................................................................................55 Price elasticity of output supply and variable input demand.......................55 Morishima elasticity of substitution.............................................................57 Data.............................................................................................................................60 Estimation...................................................................................................................67 Seemingly Unrelated Equations..........................................................................67 Imposing Restrictions for a Well-behaved Profit Function.................................70 Homogeneity................................................................................................70 Symmetry.....................................................................................................70 Continuity.....................................................................................................70 Curvature......................................................................................................70 Rate of Biased Technological Change................................................................74 Estimation of Elasticities.....................................................................................75 5 ECONOMETRIC RESULTS AND INTERPRETATION........................................76 Florida Results............................................................................................................76 Florida Rate of Technological Change and Biased Technological Change........79 Florida Own-Price Elasticity...............................................................................81 Florida Morishima Elasticity of Substitution......................................................81 The U.S. Results.........................................................................................................84 U.S. Rate of Technological Change and Biased Technological Change............85 U.S. Own-Price Elasticity....................................................................................88 U.S. Morishima Elasticity of Substitution...........................................................88 6 CONCLUSIONS, POLICY IMPLICATIONS, AND SUGGESTED FUTURE RESEARCH.............................................................................................................109 Summary and Conclusions.......................................................................................109 Theoretical Framework.....................................................................................110 Empirical Framework........................................................................................110 Data....................................................................................................................111 Empirical Findings............................................................................................111 Florida Results............................................................................................112 The U.S. Results.........................................................................................112 Concluding Remarks.........................................................................................113 Contributions............................................................................................................114 Policy Implications...................................................................................................116 Suggested Future Research.......................................................................................119 vii

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APPENDIX A PROOF OF PRICE ELASTICITY OF OUTPUT SUPPLY AND INPUT DEMAND.................................................................................................................122 B ELEMENTS IN MATRICES USED TO CALCULATE MORISHIMA ELASTICITY OF SUBSTITUTUTION..................................................................124 C FLORIDA BIASED AND RATE OF TECHNOLOGICAL CHANGE..................126 D U.S. BIASED AND RATE OF TECHNOLOGICAL CHANGE............................128 LIST OF REFERENCES.................................................................................................130 BIOGRAPHICAL SKETCH...........................................................................................137 viii

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LIST OF TABLES Table Page 2-1 Number of immigrants admitted as Immigration Reform and Control Act legalization...............................................................................................................20 5-1 Florida estimates with homogeneity and symmetry constraints..............................92 5-2 Florida estimates with homogeneity, symmetry, and convexity constraints............93 5-3 Florida biased technological change calculated at the means..................................94 5-4 Florida own-price elasticity and inverse price elasticity..........................................94 5-5 Florida average Morhishima elasticity of substitution.............................................95 5-6 U.S. estimates with homogeneity and symmetry constraints...................................96 5-7 U.S. estimates with homogeneity, symmetry, and convexity constraints................97 5-8 U.S. biased technological change calculated at the means.......................................98 5-9 U.S. own-price elasticity and inverse price elasticity..............................................98 5-10 U.S. average Morishima elasticity of substitution...................................................99 C-1 Florida biased technological change......................................................................126 C-2 Florida rate of technological change......................................................................127 D-1 U.S. biased technological change...........................................................................128 D-2 U.S. rate of technological change...........................................................................129 ix

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LIST OF FIGURES Figure Page 2-1 Percentage of hired farm workers by regions...........................................................18 2-2 Farm workers ethnicity and place of birth...............................................................19 2-3 Legal status of farm workers....................................................................................19 2-4 Percentage of deportable aliens located by border patrol who are Mexican agricultural workers..................................................................................................20 3-1 Ahmads induced innovation model........................................................................40 3-2 Induced technological change. A) Mechanical technology development. B) Biological technology development.........................................................................41 3-3 Innovation production possibility frontier and technological progress....................42 3-4 Technological progress and a change in prices........................................................43 3-5 Substitution and output effects of profit maximization............................................44 3-6 Induced innovation for profit maximizing technological change............................45 4-1 Florida price indices of outputs, variable inputs, and fixed inputs..........................65 4-2 Florida profit shares of outputs, variable inputs, and fixed inputs...........................65 4-3 U.S. Price Indices of outputs, variable inputs, and fixed inputs..............................66 4-4 U.S. profit shares of outputs, variable inputs, and fixed inputs...............................66 5-1 Florida biased technological change......................................................................100 5-2 Florida rate of technological change......................................................................100 5-3 Florida Morishima elasticity of substitution between variable inputs...................101 5-4 Florida Morishima elasticity of substitution between variable input and fixed input (fixed input price changes)............................................................................102 x

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5-5 Florida Morishima elasticity between fixed input and variable input (variable input price changes), and between fixed inputs.....................................................103 5-6 U.S. biased technological change...........................................................................104 5-7 U.S. biased technological change, other outputs and materials.............................104 5-8 U.S. rate of technological change...........................................................................105 5-9 U.S. Morishima elasticity of substitution between variable inputs........................106 5-10 U.S. Morishima elasticity of substitution between variable input and fixed input (fixed input price changes).....................................................................................107 5-11 U.S. Morishima elasticity between fixed input and variable input (variable input price changes), and between fixed inputs...............................................................108 xi

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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy IMMIGRANT WORKERS AND TECHNOLOGICAL CHANGE: AN INDUCED INNOVATION PERSPECTIVE ON FLORIDA AND U.S. AGRICULTURE By Orachos Napasintuwong May 2004 Chair: Robert D. Emerson Major Department: Food and Resource Economics Technological progress in agriculture is important for the industry to remain competitive in the world market. A major question is whether or not the advancement in farm mechanization is inhibited by the availability of inexpensive foreign workers. The Immigration Reform and Control Act (IRCA), designed to reduce the number of unauthorized foreign workers, was passed in 1986. My study analyzes the impacts of changes in immigration policies and in labor markets on the rate and direction of technological change in Florida and the U.S. by applying the theory of induced innovation. A new theoretical framework for profit-maximized induced innovation theory and definition of rates and biases of technological change are developed in this study. The profit function approach takes into account possible changes in output markets. The transcendental logarithmic profit function model is used for the econometric analysis. Homogeneity, symmetry, and curvature constraints are imposed. Curvature restrictions xii

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are imposed locally using the Wiley-Schmidt-Bramble reparameterization technique. The rate of technological change, bias of technological change, and Morishima elasticities of substitution are calculated from the parameter estimates. Farm wages are observed to increase at higher rates than the prices of other inputs after IRCA. Although labor became more expensive, the technology significantly became more self-employed labor-using in both Florida and the U.S., and more hired labor-using in the U.S. after the passage of IRCA. The technological change did not significantly increase adoption of farm mechanization in either area. My study suggests that a more stringent immigration policy does not necessarily decrease the incentive to use hired labor. The limited adoption of farm mechanization may be the result of an increase in the supply of illegal immigrant workers and the belief that immigration policy will create a greater flow of immigrant workers in the future. The more rapid adoption of farm mechanization would require policies reducing the supply of labor at a given wage to agriculture, most likely accomplished by limiting access to foreign workers, legal or illegal. xiii

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CHAPTER 1 INTRODUCTION Background One of the more controversial questions in U.S. agriculture is whether or not the recent slow pace of labor-saving innovation of new technology, specifically farm mechanization, is due to the availability of inexpensive foreign labor. Foreign workers are the major labor supply in U.S. agricultural employment, and a significant number of them are unauthorized. The National Agricultural Worker Survey (NAWS) reports that during 1997-1998, 52 % of hired farm workers were unauthorized. Unauthorized labor typically receives a lower hourly wage than do legal workers (Ise and Perloff 1995). The increasing flow of foreign workers, particularly unauthorized workers, can reduce farm wages below the level they would otherwise be, not only from an increased labor supply, but also because earnings of unauthorized workers have been shown to be lower than those of legal workers (Ise and Perloff 1995). As a result, it is argued that the availability of inexpensive unauthorized foreign workers reduces the incentive to develop and/or adopt labor-saving technology (Krikorian 2001). An example where labor-saving technology is available, but has not been adopted is dried-on-the-vine (DOV) production of raisins which started in the 1950s in Australia. This technology could save up to 85% of labor, but has not been widely adopted among California grape farmers, ostensibly because of the availability of workers from Mexico (Krikorian 2001). The implication of labor-saving technology on the income of U.S. farm workers differs from most other sectors. Since a large number of farm workers in the U.S. are 1

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2 unauthorized, the problem of displacement in the agricultural labor market due to labor-saving technology may hurt foreign workers more than native workers. If the reduction in labor demand from mechanization and more stringent immigration law and enforcement implies that immigrant workers are those who will lose jobs, labor-saving technology may not have a negative impact on domestic workers. In fact, a reduction of farm workers implies that the marginal productivity, and compensation, of the remaining workers will increase. The concern that the presence of foreign workers may inhibit the development of new agricultural technology occurs mostly in labor-intensive industries where there is a potential to develop mechanization technology, but it still has not materialized. In other cases, the technology may be available, but it has not been adopted. Florida, Texas, and California are among the states where agricultural production depends largely on foreign workers. Although the mechanical sugarcane harvester has been successfully adopted in Florida agriculture in the 1990s, the harvest of Floridas other major crops, nursery and greenhouse crops, vegetables, and citrus, is still highly labor-intensive. A premise of this research is that changes in the labor market or in immigration policy may have differing effects in labor-intensive and non-labor-intensive states due to differences in the potential substitutability between capital and labor. The problem of adopting farm mechanization is not limited to the availability of labor supply. The same technology that can be applied to some crops may not be feasible in other crops because of biological characteristics of the crops such as the lack of uniform maturity, or easy bruising of the product. For example, the harvest of potatoes, most other below ground vegetables, and all nuts (e.g., almonds, pecans, walnuts) except

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3 macadamia nuts, has been fully mechanized. In addition, over 50% of the acreage of grapes, plums, hot peppers, lima beans, parsley, pumpkin, tomatoes, carrots, sweet corn, and many other fruits and vegetables have been harvested mechanically (Sarig et al. 2000) The technology, however, cannot be readily replicated in apples, peaches, pears, nectarines, and many other crops. In some cases, the technology is not uniformly adopted in the same commodity produced for different markets because the damage from mechanical harvesting and the loss of post harvest quality may make the products unacceptable for export or fresh markets. For example, mechanical harvesting of tomatoes for the processing market has been successful, but it has not yet been successful for tomatoes destined for the fresh market due to unacceptable product damage and uneven ripening characteristics. There remain several opportunities for the development of farm mechanization in U.S. agriculture, particularly for fruits and vegetables. Not only does mechanization increase labor productivity, but it also stabilizes labor requirements, particularly in the production of seasonal crops. While low-income countries employ inexpensive labor, and other developed countries invent new machinery, U.S. fruit and vegetable production remains dependent largely on low-wage foreign labor. Establishing the competitiveness of American agriculture on the basis of foreign labor is a questionable policy approach. For instance, the labor cost of citrus production in Brazil is much lower than in Florida. It is estimated that during the 2000-2001 harvesting season, the costs for picking and loading of fruit into trailers ready for transport were $1.60 and $0.38 per box in Florida and Sa Paulo, respectively (Muraro et al. 2003) The estimated labor cost saved by the continuous canopy shake and catch harvester being tested by some harvesting companies

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4 is $0.56 per box ( Roka September 2001a ). The question implicitly being considered in the Florida citrus industry is whether it should adopt mechanical citrus harvesting, which is potentially less expensive and more productive than hand harvesting, in an effort to compete with Brazilian producers, or it should continue to depend on hand harvesting with a high presence of immigrant workers. Some analysts (Sarig et al. 2000) argue that mechanization will help the U.S. remain competitive in the world market. An example cited is Australia which has become the most mechanized in wine grape harvesting, while U.S. wine grape production relies on low-wage workers, and is still not the lowest cost wine producer (Sternberg et al. 1999) Another illustration is Holland, using mechanical technologies, which successfully exports cut flowers and green house tomatoes to North America (Mines 1999) The major purpose in analyzing technological change in this study is to determine the impacts of changes in farm wage rates due to changes in immigration policy on the direction and the rate of technological change. The induced innovation theory is adopted to examine the role of wage rates and other factor and output prices on the extent of bias in technological change, specifically whether it is labor-saving or capital-using technological change. Under the theory of induced innovation, a decrease in labor supply as a result of more stringent immigration policy resulting in higher farm wages would induce the adoption and innovation of additional farm mechanization. The implications resulting from changes in wage rates, prices and perhaps more importantly, changes in government policies on technological change will provide insights for the design of future economic policies.

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5 Problem Statement In a competitive world market, low-wage labor may not be a competitive advantage of U.S. agricultural production. While several developed countries utilize advanced technology (e.g., Australian wine grape harvesting), the U.S. continues to rely heavily on low-wage foreign workers. With relatively abundant land in the U.S, the development of farm mechanization can increase production by increasing labor productivity. However, due to readily available unauthorized farm labor, it is often argued that labor-saving technology has not been developed or adopted (Krikorian 2001). With readily available low-wage immigrant workers in U.S. agriculture, the incentive for producers to adopt new labor-saving technology is reduced. Although some farmers are concerned that a reduction of the supply of foreign workers will result in a shortage of farm workers, the success of the mechanized tomato harvester after the end of the Bracero program provides a counter-example to this concern. After September 11, 2001, there was a great uncertainty on foreign labor supply as the country became more aware of immigrants roles in the U.S. economy and security. A reduction in financial risk associated with labor uncertainty and stabilization in agricultural production are arguments in favor of farm mechanization. In addition, farm mechanization may also decrease government welfare expenditures on education and health care of foreign workers, and can conceivably strengthen national competitiveness in agricultural production. An increase in restrictions on illegal farm employment and a stringent border policy may stimulate the adoption of farm mechanization as labor becomes more expensive and not as readily available. The Immigration Reform and Control Act of 1986 (Public Law 99-603, hereafter, IRCA) was designed to reduce the flow and employment of unauthorized workers. The question of interest in this research is whether

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6 this change in immigration policy has increased the development of farm mechanization, typically labor-saving, capital-using technology, and whether the substitutability between capital and labor has changed. In order to address this question the model of induced innovation is adopted to analyze the change in factor prices on biased technological change. The results from this study will provide implications for immigration policy related to technological change. Research Objectives My primary purpose of this study was, to evaluate change in agricultural technology, and the impact of changes in farm wages along with other factor prices on the rate and direction of technological progress. Allowing potentially different results between a labor-intensive agricultural state and others, Florida and the U.S. were selected to be the study areas. Specific objectives include Estimating the rates of technological change between 1960 and 1999, and comparing them before and after the passage of IRCA. Estimating the bias in technological change of outputs and inputs during the study period, and evaluating the differences before and after the passage of IRCA Evaluating the impacts of changes in input and output prices on input use and output production by calculating the Morishima elasticity of substitution. Organization of Chapters The history and current situation of the farm labor market, immigration policy, and changes in technology, particularly farm mechanization in Florida and the U.S. are discussed first in the next chapter. The emphasis is on the relationship between farm mechanization and foreign workers. The theoretical concept of induced innovation theory used in this study is introduced in Chapter 3. The theory is extended to incorporate profit maximization rather than the more typical cost minimization case. The

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7 microeconomic model applying induced innovation theory, the bias and rate of technological change are introduced. In Chapter 4, the empirical model of the profit function approach of induced innovation is developed. The chapter explains the data, definitions of variables, and the restrictions on the transcendental profit function. The estimation techniques used to test and impose the curvature property, estimate the bias and rate of technological change, and estimate the Morishima elasticities conclude this chapter. The results of the econometric estimation and their economic interpretations are presented in Chapter 5. The final chapter summarizes the primary results of this study, provides policy implications and contributions of the study, and finally suggests future areas of research.

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CHAPTER 2 U.S. FARM LABOR MARKET, IMMIGRATION POLICY, AND FARM MECHANIZATION U.S. Farm Labor Market Agriculture was once the dominant component of the U.S. economy and culture. As the country became more industrialized, the number of agricultural workers declined, with farmers relocating to industrial work. In the early to mid-1880s, more than half of the U.S. population were farmers. In 1900, it was estimated that 38% of the labor force were farmers, but by 1990 farmers made up only 2.6% of the labor force. 1 Although self-employed workers are a majority of U.S. farm labor, a significant number of farm workers are hired and contract labor. In 1997, hired labor accounted for 34% of the production workforce in U.S. agriculture, and 12% of farms used contract labor (Runyan 2000). The estimates of the Economic Research Service, USDA, based on the Current Population Survey in 1997 show that about 33% of hired farm workers are non-U.S. citizens. Among non-U.S. citizens, hired farm workers are more likely to be male, Hispanic, and have less education. The distribution of hired farm workers depends on the geographic location of labor-intensive production. Figure 2-1 shows that the employment of hired farm workers occurs largely in the West and the South. The percentage of immigrant workers among hired workers also depends on geographic location. In some areas such as Florida, where citrus and vegetable harvesting is a major component of agricultural employment, immigrant workers account 1 A History of American Agriculture: Farmers and the Farm, ERS, USDA. 8

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9 for 75% of hired workers (Emerson and Roka 2002) while the national average is only 12% (Runyan 2000). A large number of immigrant workers are illegal: estimates of workers in the hired farm labor force lacking proper documents for work in the U.S. range from 25-75% (Effland and Runyan 1998). Although the number of undocumented workers in the hired farm work force is unknown, the Department of Labors National Agricultural Worker Survey (NAWS) initiated in 1988 reports extensive demographic information, including legal status of farm workers. The NAWS reported that Mexicans account for 77% of all farm workers in 1997-1998 (Figure 2-2); 52% of hired farm workers were unauthorized, 22% were citizens, 24% were legal permanent residents, and the rest were individuals with temporary work permits (Figure 2-3). The same survey also found that 19% of interviewed farm workers were employed by contractors, 61% work in fruits, nuts, and vegetables, and one-third of the jobs were in harvesting crops. On September 1, 1997, the federal minimum wage was increased to $5.15 per hour from $4.75, where it had been since October 1, 1996. The average farm wage during 1997-1998 was $5.94, and about 12% of farm workers received less than the minimum wage (Mehta et al. 2000). Those hired by farm labor contractors received a slightly lower wage ($5.80) than those hired directly by agricultural producers ($5.98) (Mehta et al. 2000). Although NAWS does not report the earnings by type of legal status, Ise and Perloff (1995) using NAWS data have shown that unauthorized workers received lower wages than legal workers. A large number of immigrant workers receive an income below the poverty line (29% of non-citizens as compared to 15% of U.S. citizens). Approximately 4.5 billion dollars are paid annually to 1.4 million immigrants through aid to families with dependent children (AFDC) or supplemental security income (SSI)

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10 (Larkin 1996). Even though illegal immigrants are not qualified for public assistance programs, except Medicaid, some may claim benefits by using fraudulent documents such as birth certificates or green cards. Moretti and Perloff (2000) examined the use of public and private assistance programs by families of farm workers. They found that families of unauthorized immigrants are more likely to use public medical assistance and less likely to use other public transfer programs than authorized immigrants and citizens. U.S. Immigration Policy In the previous section, it was apparent that foreign workers are a major source of the farm labor supply in the U.S. Consequently, changes in immigration policy may have a large impact on the farm labor market. The Immigration Act of 1917 was the first foreign worker program. The provision granted the entry to temporary workers from Western Hemisphere countries. In May 1917, the temporary farm worker program for unskilled Mexican workers was created. The temporary worker program, referred to as the first Bracero program, was established during World War I and ended in 1922 (Briggs 2004). The Bracero (person who works with arms or hands) program, also referred to as the Mexican Farm Labor Supply Program and the Mexican Labor Agreement, was established in July 1942 and ended in 1964. It was a bilateral program between the U.S. and Mexico to recruit Mexican workers for farm jobs. As a result of the Bracero program, there was a large increase in border migration. It is estimated that 4.6 million Mexicans were admitted to the United States as guest workers between 1942 and 1964. The number of Braceros increased over time: 13,000 Mexican immigrants were admitted between 1942 and 1944, and 146,000 were admitted between 1962 and 1964 (Martin 2001).

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11 In 1986, the Immigration Reform and Control Act (IRCA) was passed to reduce the flow of illegal immigrants, and to legalize illegal aliens already working in the U.S. IRCA established 3 ways to accomplish its objectives: employer sanctions, increased appropriations for enforcement, and amnesty provisions. The employer sanctions provision designated penalties for employers hiring unauthorized workers. It required all employers to verify the eligibility of each employee. Employers knowingly hiring unauthorized foreign workers became subject to fines ranging from $250 to $10,000 per incident, and employers persistently hiring unauthorized aliens risked a maximum of a 6-month prison sentence. Perishable agricultural crop producers who had relied heavily on an illegal labor supply, however, were exempt from this provision until December 1988, as were livestock producers. In order to assure that legal employees were not discriminated against on the basis of national origin, antidiscrimination provisions were also a component of the legislation. The Special Agricultural Worker program (SAW) granted amnesty to illegal workers who had at least 90 days of work in 1985-1986 in activities defined as seasonal agricultural services (SAS) in the agricultural sector. In addition, the Replenishment Agricultural Worker program (RAW) protected producers from experiencing a shortage of seasonal workers or the exit of legalized special agricultural workers. The RAW program was designed to allow a designated number of workers to enter the country, but they were required to find agricultural employment for at least 90 days per year for 3 years after entry. However, no shortage was ever formally determined. Consequently, no foreign workers were ever brought into the country under the RAW program.

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12 The H-2 temporary guest worker program established in the 1952 Immigration and Nationality Act was also retained under IRCA. The Immigration and Nationality Act (INA) as amended by IRCA authorized the new H-2A program for temporary foreign agricultural workers. It allowed agricultural employers who anticipated a shortage of domestic labor supply to apply for nonimmigrant alien workers to perform work of a seasonal or temporary nature. As a result of IRCA, nearly 2.7 million persons were ultimately approved for permanent residence (Rytina 2002), 75% of whom were Mexicans. By 2001, one-third of the IRCA lawful permanent residents had become naturalized. Table 2-1 shows the number of immigrants admitted as a result of IRCA. The number of total immigrants admitted under IRCA legalization, and the special agricultural workers declined during the 1990s, and slightly increased in the 2000s. The largest IRCA admission was in 1991. The U.S Citizenship and Immigration Services (USCIS) within the Department of Homeland Security (prior to November 2003, the Immigration and Naturalization Service (INS)) reported that deportable Mexican aliens working in agriculture and located by the border patrol were declining over the past decade. Although the number of legalized agricultural workers reported by INS and deportable Mexican farm workers declined after the passage of IRCA, the number of unauthorized farm workers is unknown. Although IRCA was designed to control illegal immigration to the U.S., and to provide sufficient labor for agricultural production, it did not eliminate the illegal employment of unauthorized farm workers. Heppel and Amendola (1992) distinguish between undocumented and fraudulently documented workers, indicating that the passage of IRCA decreased the number of undocumented farm workers, but the employment of

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13 fraudulent documented workers increased. The National Population Council of Mexico (Conapo) estimated that there were 8.3 million Mexican-born US residents in 2000, including 3 million unauthorized Mexicans, and another 14 million Mexican-Americans (Mexico: Bracero Lawsuit). On July 10, 2003 the Border Security and Immigration Reform Act of 2003 (S. 1387) proposed by Senator John Cornyn was introduced. This legislative bill would allow undocumented immigrants in the U.S. to apply for the guest worker program, applying for permanent residence status from their home country after participating 3 years in the program, open guest worker programs to any sector, and establish seasonal and non-seasonal guest worker programs. Seasonal workers are authorized to stay in the U.S. for a period of 9 months, and non-seasonal workers are authorized to stay in the U.S. for 1 year, but not to exceed 36 months. 2 On July 25, 2003, the Border Security and Immigration Improvement Act (S. 1461) was introduced by Senator John McCain. The proposed legislation would establish 2 new visa programs. One is entering a short term employment in the U.S., and the other is for undocumented workers currently residing in the U.S. The new program does not put a finite number on available visas, and allows free mobility across sectors. It is estimated that 6 to 10 million illegal aliens claiming residency in the U.S. would become legal guest workers. It would also allow new legal workers to get a visa authorizing them to work for 3 years, and then become eligible to apply for a temporary worker visa that may lead to legal permanent residency. 3 2 Border Security and Immigration Reform Act, Senator John Cornyn 3 Border Security and Immigration Improvement Act, John McCain

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14 Senator Larry Craig introduced AgJOBS legislation (S. 1645 and H.R. 3142) in November 2003. Unauthorized agricultural workers who had worked 100 or more days in 12 consecutive months during the 18-month period ending August 31, 2003 could apply for temporary resident status. If they perform at least 360 days of agricultural employment during the 6-year period ending on August 31, 2009, including at least 240 days during the first 3 years following adjustment, and at least 75 days of agricultural work during each of three 12-month periods in the 6 years following adjustment to temporary resident status, they may apply for permanent resident status. 4 The proposed legislation also modifies the existing H-2A temporary and seasonal foreign agricultural worker program. The H-2A foreign workers admitted for the duration of the initial job (not to exceed 10 months) may extend their stay if recruited for additional seasonal jobs (to a maximum continuous stay of 3 years). The H-2A foreign workers are authorized to be employed only in the job opportunity and by the employer for which they were admitted. On January 7, 2004, President Bush proposed immigration reform that would allow employers to bring guest workers from abroad if no American can fill the jobs, and also legalize as guest workers illegal immigrants who are already working in the U.S. The guest workers would receive 3-year renewable visas like those that would be issued to currently unauthorized workers in the U.S., but the new guest workers would not have to pay the registration fee of $1,000 to $2,000 charged to currently unauthorized workers in the U.S. As guest workers, they could travel in and out of the U.S. freely, and could apply for immigrant visas. However, no wage floor was proposed and that could create 4 AgJOBS Provision Issue Briefing, Larry Craig.

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15 an incentive for U.S. employers to recruit less expensive labor from abroad. Some critiques say that President Bush's proposal is more likely to ensure unauthorized workers who register their departure than their permanent residency due to a long waiting list before immigration visas become available for unskilled workers. On January 21, 2004, the Immigration Reform Act of 2004 (S. 2010) was introduced by Senators Chuck Hagel and Tom Daschle. The proposed legislation would allow illegal aliens who resided in the United States since January 21, 1999 to participate and become legal permanent residents. Although the potential impact of these proposals on the farm labor market is unknown, all allow foreign workers to work in the U.S. legally via guest worker programs. In conjunction with the new legislative proposals, apprehensions of illegal aliens have increased nationally by 10% to 11% over 2003, and apprehensions increased threefold in the San Diego area alone. 5 Farm Mechanization in U.S. Agriculture Mechanization has a long history in U.S. agriculture due to the abundant land and scarce labor endowments. Binswanger (1984) suggested that the most dramatic aspect of mechanization is the shift from one source of power to another. Several mechanical devices were developed from the usage of horsepower in place of hand power during 1862-1875, the first American agricultural revolution. 6 Mechanization was also developed for threshing as early as 1830, and by 1850 all grain threshing in the U.S. had been mechanized. Not long after small grain reapers became widely adopted in 1850, wheat harvesting moved to binders in the 1870s, followed by corn binders in the 1880s. 5 Illegal Immigration on the Rise since Bush Revealed Amnesty Plan: National Border Patrol Council News. 6 This paragraph draws heavily from A History of American Agriculture: Farm Machinery and Technology, ERS, USDA

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16 Before tractors became widely used after about 1926, the mechanization for tillage had been the substitution of animal power for human labor, and then steam engine and steel harrows. A change from horse power to tractors and the adoption of a group of technological practices characterized the second American agricultural revolution during 1945-1970. The termination of the Bracero program had a significant influence on the development of farm mechanization. One obvious example was the adoption of the mechanical tomato harvester in California. By 1968 it was expected that more than 80% of tomatoes grown in the U.S. for processing would be harvested by machine (Rasmussen 1975). In 1965 sugar beets became fully harvested by machinery, and 96% of cotton was harvested mechanically by 1968. Sarig et al. (2000) summarize the status of mechanical harvesters of fruits and vegetables in 1997. At least 20-25% of U.S. vegetable acreage and 40-45% of U.S. fruit acreage is still totally dependent on hand harvesting. Most fruits and vegetables harvested by machinery are used for processing. Mechanical harvesting usually requires a large capital investment, and can reduce the production flexibility to change from one crop to another. Included among the types of mechanical harvesting machinery are labor-aids, labor-saving, and robotic machines. Labor-saving harvesting machines are those that replace the work of hand harvesting such as shaking a tree or a bush, digging a row of below-ground vegetables, or cutting a row of above-ground vegetables. Examples of crops in which mechanical harvesters are widely used for the fresh market are almonds, pecans, walnuts, peanuts, potatoes, sweet corn, celery, carrots, and garlic. Crops destined for the processing market and that use mechanical harvesters include blackberries,

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17 grapes, papaya, plums, raspberries, cherries, celery, cucumbers, peppers, tomatoes, sweet corn, pumpkins, and peas. Mechanical citrus harvesters are currently being evaluated in Florida. Two primary types of mechanical citrus harvesters are being tested commercially (Roka 2001a). The first is the trunk, shake and catch system (TSC), and the second is the continuous canopy shake and catch system (CCSC). A TSC system includes 3 machines: a shaker, a receiver, and a field truck. A shaker and receiver are positioned at the tree where trunks are shaken for 5 to 10 seconds to remove the fruit. The receiver conveys fruits into a trailing bin, and a field truck (goat) hauls the fruit to a bulk trailer at the roadside. The trees need to have adequate clear trunk and skirt heights to allow the shaker and receiver units to position underneath the canopy. A set of CCSC includes a minimum of 4 machines: 2 harvesting units and 2 field trucks. Shaker heads rotate through the tree canopy to remove mature fruit. Trees must be skirted to allow fruit collection underneath the tree canopy. Both systems can recover about 90% of the available fruit. The citrus harvested mechanically is used only for processing due to damage during the harvesting. As labor became more expensive after the passage of IRCA, there have been many attempts to mechanize harvesting other crops such as fruits and vegetables during the past two decades. The impact of IRCA on farm mechanization was not uniform across the country. The study of changes in the labor intensity of agriculture by Huffman (2001) shows that the capital-labor ratio has increased 3% annually in Iowa, but decreased 4% annually in Florida and California. The material inputs-labor ratio also decreased in Florida and California after IRCA. This suggests that labor use increased following IRCA in some states, particularly Florida and California. In the absence of sector

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18 specific restrictions, legalized foreign workers would have little incentive to remain working in the agricultural sector. For example, the AgJOBS bill discussed above requires temporary resident farm workers to perform only 360 work days of agricultural employment to apply for permanent resident status. 7 The outflow of farm labor to other sectors is a continuing process. Mechanization is one way that production uncertainty due to farm worker availability may be mitigated. The impact of IRCA on the perishable crop industry in different states is discussed extensively in Heppel and Amendola (1992). 051015202530354045199019911992199319941995199619971998YearPercentage of Hired Farm Workers Northeast South Midwest West Figure 2-1. Percentage of hired farm workers by regions. Note: Data since 1994 are not directly comparable with data in 1993 and earlier due to changes of survey design. Source: ERS Calculation from Current Population Survey ( Runyan 2000 ). 7 AgJOBS Provision Issue Briefing, Larry Craig.

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19 Mexican-Born77%Other Foreign-Born1%Latin American Born2%US-Born White7%Asian Born1%Other US-Born2%US-Born African American1%US-Born Hispanic9% Figure 2-2. Farm workers ethnicity and place of birth. Source: National Agricultural Workers Survey, 1997-1998 (Mehta et al. 2000). Legal Pernament Resident24%Other2%Unauthorized52%Citizen22% Figure 2-3. Legal status of farm workers. Source: National Agricultural Workers Survey, 1997-1998 (Mehta et al. 2000).

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20 00.10.20.30.40.50.619921993199419951996199719981999200020012002YearPercentage Figure 2-4. Percentage of deportable aliens located by border patrol who are Mexican agricultural workers. ( USCIS table 60 ) Table 2-1. Number of immigrants admitted as Immigration Reform and Control Act legalization. Fiscal Year Resident Since 1982 Special Agricultural Workers Total IRCA Legalization 1991 214,003 909,159 1,123,162 1992 46,962 116,380 163,342 1993 18,717 5,561 24,278 1994 4,436 1,586 6,022 1995 3,124 1,143 4,267 1996 3,286 1,349 4,635 1997 1,439 1,109 2,548 1998 954 1 955 1999 4 4 8 2000 413 8 421 2001 246 17 263 2002 48 7 55 Total 293,632 1,036,324 1,329,956 Source: Statistical Yearbooks of the Immigration and Naturalization Service (U.S. Department of Justice)

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CHAPTER 3 THEORETICAL AND ANALYTICAL FRAMEWORK This chapter is divided into two parts. The first part provides an overview of the theory of technological change. The historical development of induced innovation theory based on cost minimization is illustrated. To my knowledge, the theoretical model of induced innovation based on profit maximization that is used in this study has not been developed before. The graphical profit maximization model of induced innovation theory of my own development is then introduced. The second part of this chapter gives the definition of technological change and biased technological change based on the induced innovation theory. Cost Minimization Model of Induced Innovation Theory In growth theory, a technological change that increases the productivity of capital, including human capital, is an indication of economic growth. Economists have developed several models to explain the sources of technological change. The theory of induced innovation is among the first set forth theoretically and empirically during the 1960s and 1970s. In the mid 1970s, Nelson and Winter (1973) developed an evolutionary theory that is an interpretation of the Schumpeterian process of economic development (Schumpeter 1934). In the late 1970s and 1980s, the path dependence theory was developed by Arthur (1989) and his colleagues. A more detailed discussion of each theory and its strengths and limitations is found in Ruttan (2001, p.117). Within the induced technological change theories, there are 3 major models that try to explain the rate and direction of technological change. First, a demand pull model 21

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22 emphasizes the role of the demand for technology on its supply. Griliches (1957) uses this model to determine the role of demand on the invention and diffusion of hybrid maize. Vernon (1966, 1979) also uses this model to study the invention and diffusion of consumer durable technologies. Second is a growth-theoretic model or a macroeconomic model. This model is based on the effects of factor endowments, their relative prices, and factor shares on the factor augmentation of a technological change. It is introduced by Kennedy (1964, 1966, 1967) and Samuelson (1965, 1966). However, the theory is criticized by Nordhaus (1973) for having an inadequate microeconomic foundation. Last, and the approach of this study, is a microeconomic model of induced innovation. The term induced innovation was first used by Hicks in his book Theory of Wages. A change in the relative prices of the factors of production is itself a spur to invention, and to invention of a particular kind-directed to economising the use of a factor which has become relatively expensiveIf, therefore, we are properly to appreciate the place of invention in economic progress, we need to distinguish two sorts of inventions. We must put on one side those inventions which are the result of a change in the relative prices of the factors; let us call these induced inventions. The rest we may call autonomous inventions. (Hicks 1932, p.124-125) Focusing on 2 types of factors, labor and capital, Hicks classified 3 types of inventions based on the changes in ratios of marginal products. Labour-saving inventions increase the marginal product of capital more than they increase the marginal product of labor; capital-saving inventions increase the marginal product of labour more than that of capital; neutral inventions increase both in the same proportion. (Hicks 1932, p.121-122) Even though Hicks first created the idea of induced innovation, the mechanism of how it would happen was not specified. As a result of the lack of an explanation, Salter (1960) criticized the Hicksian induced innovation hypothesis.

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23 When labour costs rise, any advance that reduces total costs is welcome, and whether this is achieved by saving labour or capital is irrelevant. There is no reason to assume that attention should be concentrated on labour-saving techniques, unless, because of some inherent characteristic of technology, labour-saving knowledge is easier to acquire than capital-saving knowledge. (Salter 1960, p.43). Following Salters criticism, Ahmad (1966) clarified the analytical basis of the induced bias innovation mechanism in the framework of a traditional comparative statics approach. His model is known as the Hicks-Ahmad model of induced technological change. Hicks-Ahmad Model of Induced Technological Change Ahmad assumed that the production function is linear and homogeneous. Each innovation is represented by a set of isoquants on labor and capital axes to represent a production function. If for any given output at each factor price ratio, the ratio of factor combinations of the new and old isoquants remains the same, innovation is neutral, assuming cost minimization by an entrepreneur. When a new isoquant indicates a lower ratio of labor to capital for the least cost combination, the innovation is labor-saving for a given output at a given factor price ratio. Similarly capital-saving innovation is defined in the same way. From Ahmads assumptions about the production function, the neutrality in his definition is equivalent to that of Hicks. He used the concept of the historical Innovation Possibility Curve (IPC) as an envelope of all alternative unit isoquants (representing a given output on various production functions) at a given time. Isoquants on the same IPC are a set of potential production processes, determined by a state of knowledge, which are available to be developed for a given amount of research and development expenditure. The elasticity of substitution of each isoquant is smaller than that of the IPC (the curvatures of the isoquants are greater than those of IPC). By assuming that IPC is smooth and convex, a

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24 point where the price line is tangent to IPC determines a production function. IPC is a result of technological knowledge, but the economic consideration is to choose a particular isoquant out of a set of various isoquants that belong to a particular IPC. He emphasized that the act of invention is the movement from one production function to another, while factor-substitution is just moving from one point to another on the same production function. The movement of a new isoquant closer to the origin is a cost-saving invention. Figure3-1 illustrates this model. At time period t, relative factor prices of P t P t were revealed, a cost minimizing production process I t was developed, and the corresponding IPC is IPC t Assuming that the same amount of expenditures are required to go from I t to any other technique on IPC t as to go from I t to any process on IPC t+1 no other process is developed in the same IPC t after I t is developed. The next period t+1, IPC t shifts inward to IPC t+1 indicating that there is a new set of technology. If the technological change is neutral (IPC t shifts neutrally to IPC t+1 ) and if the relative factor prices P t P t remain unchanged, a process I t+1 will be developed at time t+1. However, Ahmad indicated that IPC may shift nonneutrally even at constant relative factor prices, and biased technological change would occur. If at t+1, there is an increase in the relative price of labor corresponding to P t+1 P t+1 then the production process I t+1 is no longer optimal. If the IPC shifted neutrally, I t+1 becomes optimal, and it represents a relative labor-saving technology compared to I t If the innovation possibility is technologically unbiased, an increase in the relative price of labor will induce an innovation which is necessarily labor-saving. On the other hand, if the innovation possibility is biased in either direction, a change in the relative price of the factors will still induce technology to save the factor that has become

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25 relatively more expensive. Yet this inducement will be modified by the bias of the historical innovation possibility. With a 2-dimensional graph, it is difficult to demonstrate more than a 1 period model when the research expenditure does not remain fixed. A mathematical model facilitates analysis of the problem (Binswanger 1978, p.26-27). Hayami and Ruttan Model of Induced Technological Change Hayami and Ruttan have contributed greatly to the understanding of agricultural development. Their paper in the Journal of Political Economy in 1970 followed by the Agricultural Development book in 1971 emphasized the differences in agricultural development between Japan and the U.S. These 2 countries represent the 2 extreme resource endowments: Japan has abundant labor (L) and little land (A) while the U.S. has abundant land and little labor. 8 By partitioning the growth in output per worker (Y/L) into 2 components: land area per worker (A/L) and land productivity (Y/A), sources of technological change in the 2 countries can be identified. AYLALY 3.1 Given the relative factor price differences in 2 countries, growth of output per worker (Y/L) will be highly correlated to changes in land area per worker (A/L) in the U.S., and to changes in land productivity (Y/A) in Japan. In the U.S., land area per worker (A/L) rose much more rapidly than in Japan. The source of the increase in land area per worker would be explained by mechanical technology which allows farmers to operate on a larger land area. Mechanical technology replaces or supplements manpower with other sources of power that are economically 8 Their study in 1970 paper utilized the data for 1880-1960, and support of the U.S. data has been criticized by Olmstead and Rhode (1993).

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26 more efficient (animal, mechanical, electrical). Examples of mechanical innovation are the substitution of the self-raking reaper for the hand-rake reaper, and the substitution of the binder for the self-raking reaper that require more horses per worker. On the other hand, land productivity (Y/A) in Japan rose much more rapidly than in the U.S. The source of the increase in land area per worker was explained by biological technology that increased production per land area through fertilizer and yield-increasing improvements in varieties. They developed a 4-factor induced technological change model, similar to Ahmads model. In this model, land and mechanical power were regarded as complements, and were substitutes for labor. Biological technology and fertilizer were regarded as complements and were substitutes for land. Increases in land area per worker can be achieved through advances in technology. Graphical illustration of this model is shown in Figure 3-2a and 3-2b. Figure 3-2a represents a process of mechanical technology innovation. At time 0, I 0 represents the innovation possibility curve (IPC) 9 which is an envelope of less elastic unit land-labor isoquants, for example, to different types of harvesting machinery. If price ratio P 0 P 0 prevails, a technology (e.g., a reaper) i 0 is invented. Point P is a cost minimized equilibrium that determines the optimal combination of land, labor, and power requirements. Generally, technology that enables operating a large area per worker requires higher mechanical power. Land and power are represented by a combination line [A, M], which represents complementarity. At time period 1, assume that relative land rent to wage rate decreases as labor becomes more scarce; IPC 1 is represented by I 1 9 The concept of IPC was originally used as a metaproduction function in Hayami and Ruttan (1970). The differences in these 2 definitions are discussed in Binswanger (1978, p.46).

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27 A change in relative price from P 0 P 0 to P 1 P 1 induced a new technology (e.g., a combine) represented by i 1 Point Q represents a new optimal technology which allows farmers to use more land and less labor by using more power. In Figure 3-2b, a process of biological technology innovation is illustrated. Similar concepts of induced innovation can be explained by the increase in relative price of land to fertilizer. I* 0 represents IPC of different land-fertilizer isoquants, corresponding to different crop varieties such as i* 0 A shift of relative price P* 0 P* 0 to P* 1 P* 1 induced a new technology (e.g., a more fertilizer-responsive crop) represented by i* 1 is developed along I* 1 A linear combination [F, B] implies a complementary relationship between fertilizer and biological technology. In addition, land infrastructure and biological technology are assumed complementary since technology that substitutes fertilizer for land, for instance fertilizer responsive, high-yielding varieties, generally requires better control of water and land management such as irrigation and drainage systems. As the relative price of land to fertilizer increases, the optimal technology changes from P* to Q*. This indicates that the new crop variety allows farmers to use less land, and more fertilizers that require more land infrastructure. Hayami and Ruttan (1970, 1971) not only developed a theoretical model of induced innovation, but they also found empirical support of the theory in the U.S. and Japan. Agricultural growth in the U.S. and Japan during 1880-1960 can be viewed as a dynamic factor-substitution process. Long run trends of relative factor prices induce innovations that substitute for each other. In a fixed technology they assumed that elasticities of substitution among factors were small, that variations in factor proportions could be explained by changes in factor price ratios. If the variations in these factor proportions

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28 were consistently explained by the changes in factor price ratios, they argued that the innovations were induced. This test, however, was not a test of the induced innovation hypothesis. 10 Assuming that a production function is linear homogeneous, log-linear regressions of land-labor and power-labor ratios on the relative price of land to farm wage and the relative price of machinery to farm wage are examined. 11 The results showed that more than 80% of the variation in the land-labor ratio and in the power-labor ratio is explained by the changes in their price ratios. This indicated that the increases in land and power per worker in U.S. agriculture during 1880-1960 have been highly correlated with declines in prices of land, power and machinery relative to the farm wage rate. 12 It was also confirmed that land and machinery were complements by the negative signs. The regressions of fertilizer input per hectare of arable land on relative factor prices of fertilizer to land, labor to land, and machinery to land were also tested. The results showed that variations in fertilizer-land price ratio alone explained almost 90% of the variation of fertilizers. 13 The result also showed that fertilizer and land were substitutes. The same regressions were also tested for Japan but were excluded from this discussion. The comparison of the 2 countries indicated that changes in relative factor prices induced a dynamic factor substitution accompanying changes in the production surface. Labor 10 A test of induced innovation hypothesis would involve a test for nonneutral change in the production surface. 11 ln(A/L) = f(ln(r/w), ln(m/w)) where A=land area, L=worker, r=price of land, w=wage rate, m=price of machinery. Different definitions of land and labor are used in the original regressions. ln(M/L) = f(ln(r/w), ln(m/w)) where M= machinery. 12 Hayami and Ruttan (1970) Table 2. 13 Hayami and Ruttan (1970) Table 4.

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29 supply had been less elastic than land supply in the U.S. during this period. The price of labor relative to the price of land had been increasing; as a result, mechanical innovations of a labor-saving type were induced. A dramatic decrease in the price of fertilizer since 1930 had shifted mechanical innovations to biological innovations in the form of crop varieties highly responsive to the lower cost of fertilizer. Hayami and Ruttans 1970 paper has inspired many economists to develop both theoretical and empirical models of technological change. In the next part of this section, selected empirical studies of biased technological change in American agriculture are presented. Empirical Studies of Biases in U.S. Agricultural Technology Binswanger (1974b) developed a many-factor translog cost function model to analyze biased technological change. By applying Shephards lemma, factor share equations were estimated. He assumed 2 cases for the rate of biases: model A assumes variable rates of biases, and model B assumes constant rates over time. The parameter estimates from the models were used to demonstrate the direction of bias, and calculate Allen elasticities of substitution (Allen 1938) and cross elasticities of demand. This approach also allowed him to calculate the biases of technology in the absence of factor price changes. Cross-section data from 39 states or groups of states were used to estimate the share equations for the years 1949, 1954, 1959, and 1964. Time-series agricultural data from 1912-1968 were used to calculate the change in factor shares in the absence of price changes. The results showed a very strong bias toward fertilizer-using. While assuming that fertilizer prices were exogenous to agriculture, a rapid decrease in fertilizer price relative to output price demonstrated a consistent induced innovation model. The author also

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30 assumed an exogenous wage rate from agriculture since the price of labor was also governed by nonagricultural sectors. An increase in the price of labor in the existence of a labor-saving bias during the study period showed that the induced innovation hypothesis was consistent; the biased technological change alone explained about two-thirds of the decrease in labor share. Machine prices also increased during this period; however, technological change was machine-using. This means that a neutral innovation possibility could not have occurred, and it must be toward machine-using. Since land price was endogenous to agriculture, biases of land could not give much information. Antle (1984) utilized a translog profit function to measure the structure of U.S. agriculture during 1910-1978. He applied duality relations with a multifactor profit function to measure biased technological change, homotheticity, and estimate input demand and output supply elasticities. By applying Hotellings lemma to a profit function, input demand functions were estimated. Biased technological change of factor i, B i was defined as a rate of change of its production elasticity share over time. If the rate of change of the production elasticity is positive (negative), technological change is biased toward (against) that input. And if it is 0, a technological change is neutral. By estimating each profit-maximizing factor quantity equation, biased technological change can be calculated. This method has an advantage over Hicksian measurement based on marginal rates of technological substitution since biases can be calculated without measuring biases between every input pair. The estimation showed that during 1910-1946, the biases were primarily toward machinery and against land. These findings contradict Binswangers (1974b) results that technology was biased toward chemicals during the prewar period. However, the biases after the war (1947 to1978) were toward

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31 labor-saving and capitaland chemical-using similar to Binswangers results. The findings in Antles study were consistent with induced innovation theory since the wage rate relative to machinery and chemical price was declining during 1925 to 1940, and the bias during this period was toward labor. Shumway and Alexander (1988) estimated supply equations for 5 agricultural product groups and demand equations for 4 input groups in 10 regions of the U.S. By assuming a competitive market, they analyzed the impact of government intervention, changes in technology, and other market stimuli on agricultural production in different regions during 1951-1982. A profit function approach was used to derive input demand and output supply equations via the envelope theorem. A test of neutral technological change was conducted using the Hicksian neutrality definition. The results showed that disembodied technological change has taken place over the sample period, and it has not been Hicks-neutral in most regions. The authors suggested that technological change bias should be taken into account when modeling variable input demand ratios and output supply ratios. Weaver (1983) used a translog profit function to evaluate biases in technology of multi-input, multi-output production of U.S. wheat region. He defined a technological change as a derivative of the ratio of inputs with respect to technological knowledge. He found that the technology between 1950 and 1970 in the U.S. wheat region was labor-saving relative to capital and petroleum products. It was also fertilizer-using relative to capital, materials, and petroleum products. Profit Function Model of Induced Innovation Ahmads and Hayami and Ruttans theoretical framework of induced innovation model is based on cost minimization and assumed only 1 aggregate output. The change

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32 in technology is defined as the inward shift of the innovation possibility curve. Even though the definition of technological change based on cost minimization is closely linked to the theoretical definition of induced innovation and has been widely adopted, it ignores the changes in output combinations which become significantly important in agricultural development. The decrease in resource requirements to reduce the cost of production in induced innovation theory does not allow the analysis of the impact of changes in output since it is assumed to remain the same. Biological technology, for instance, has become increasingly important in American agriculture. In the Hayami and Ruttan definition, biological technology was defined as technology that increases output per unit of land. Recent developments of biological technology such as genetically modified crops do not aim only to increase output per unit of land via drought resistance, pesticide and herbicide resistance or virus resistance, but also to increase the market values of crops such as vitamin and protein enhanced grains and seedless fruits. The production of any new crop variety may change the optimal mixture of input requirements; therefore, it will fall outside the scope of cost minimizing induced innovation theory. In addition, the increasing international trade flow, changes in trade policy, and changes in trade agreements may change the demand for as well as the supply of different types of commodities. These changes in output combinations may also change the input requirements. The profit maximization approach of the induced innovation model is a more appropriate alternative in the study of multi-input, multi-output technology. It recognizes the simultaneous determination of output mix and variable inputs for given prices. The theoretical framework of this approach is now developed.

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33 At a given time period, the potential production processes are determined by the state of technology and the resource endowments. The Innovation Production Possibility Frontier (IPPF) is the envelope of all potential production processes that can be developed at a given time. Technological progress is defined as the upward shift of the IPPF, the envelope of production functions. The analogous innovation possibility frontier in the cost minimization model is the Innovation Possibility Curve (IPC) in the Hicks-Ahmad model of price-induced technological change and the Metaproduction Function (MPF) in Hayami and Ruttans model of induced innovation. Each potential production process is represented by a production function f(x). Figure 3-3 illustrates the concept of IPPF and technological change in a simple case of one output-one input technology. At time period 1, the innovation possibility frontier is represented by IPPF 1 the envelope of all less elastic production functions which are the potential technological processes at period 1. The isoprofit line, represents the profit for given input and output prices. Given that = py wx, 14 the profit function defined in y-x space can be written as y = /p + (w/p)*x. The slope of the isoprofit line is equal to w/p. If given prices in period 1 represent *, the most profitable technology available under IPPF 1 is Y 1 = f 1 (x) where the slope of the isoprofit line coincides with the slope of the production function, the first order condition of profit maximization. Assume that there is a technological progress (an upward shift of IPPF) represented by IPPF 2 in period 2, but prices remain unchanged so the slope of the isoprofit line remains constant, then the most profitable technological process in the second period is Y 2 = f 2 (x). Notice that the 14 = profit; y = output; x = input; p = output price; w = input price.

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34 intercept of the new isoprofit line, **, is higher than that of *; thus, the technological progress generates a higher profit at given prices. From Figure 3-3, the new most profitable technology produces more output and employs more input, but this is not necessarily the case. The new technology could also employ less or the same amount of the input at a higher output level for given prices Figure 3-3 represents the one-input, one-output production function, but if we assume a two-input, one-output technology, y = f(K,L), we can interpret Figure 3-3 as y = Y/L and x = K/L, and y = f(x) would be an intensive production function. Again, given that prices remain constant, technological progress may result in a higher, a lower, or a constant capital-labor ratio (biased or neutral technological change). Figure 3-4 represents technological progress from IPPF 1 to IPPF 2 and an increase in the price ratio from (w/p)* to (w/p). In period 1, represents the profit given (w/p)*, and the most profitable technological process is Y 1 = f 1 (x). After an increase of the relative factor price to output price to (w/p) reflected by an increase in the slope of the profit function to and before any innovation of new technology, the most profitable technological process is Y 1 = f 1 (x). An increase in w/p results in a decrease in output level and input requirement. If there is also a technological innovation in period 2 as a result of a change in w/p, there would be an increase in output from what it would have been without technological progress (from Y 1 to Y 2 ). In Figure 3-4, it is shown that technological progress also decreases the input requirement (from X 1 to X 2 ), but this may not be the case as will be discussed later. In sum, an increase in w/p will decrease the profit-maximizing output and input levels, but if this price change induces a new set of potential technological processes that increase profit, it will increase the output level

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35 and may or may not change the input requirement. The overall effects on output and input levels are ambiguous. In the case of more than one-input, one-output technology, it is unclear what a change in factor price or relative factor price will be on the output level. To illustrate, recall that the profit maximization solution is equal to the cost minimization solution if cost is minimized at the profit maximizing output level. 15 (p, w) = max y, x [py wx] 3.2 where x is a vector of many inputs. Let y* = y(p, w) be the profit maximizing output, (p, w) = py* min x [wx] 3.3 (p, w) = py* C(w, y*) 3.4 where C(w, y*) is the cost function at the given y*. Taking the first derivative with respect to w i we get iiw*)y,w(Cw 3.5 Utilizing Hotellings lemma and Shephards lemma, x i u (p, w) = x i c (w, y*). 3.6 The uncompensated factor demand, x i u (p, w), is the same as the compensated factor demand, x i c (w, y*), if the compensated factor demand is obtained from cost minimization at the profit maximizing output level, y*. Suppose that there is a change in a factor price w j Taking the derivative of Eq. 3.6 with respect to w j : jcijcijuiwyy*)y,w(xw*)y,w(xw)w,p(x 3.7 15 The profit function, the history of economic thought website

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36 If the price of factor j changes, factor demand changes may be decomposed into 2 effects: the substitution effect, represented by the first term on the right hand side of 3.7, and the output effect, represented by the second term on the right hand side. If output does not change, the direction of a change in cost minimizing input requirements due to the substitution effect (net effect) can be determined by whether the inputs are complements or substitutes. However, since there is an output effect which can counteract the substitution effect, the direction of a change in profit maximizing inputs as a result of changes in factor prices (gross effect) is ambiguous. Figure 3-5 illustrates changes in factor requirements as a result of substitution and output effects when there is a change in the factor price ratio in a profit maximization problem. As relative capital to labor prices increase from (r/w) 1 to (r/w) 2 a substitution effect will result in changes in compensated input demands due to cost minimization while holding output constant at Y 1. This results in a movement along isoquant I 1 from A to B which decreases the capital requirement from K 1 to K 1 and increases the labor requirement from L 1 to L 1 In addition, an increase in (r/w) also results in an output effect which may shift the isoquant inward to I 2 if output level decreases or to I 3 if output level increases. Gross changes in input requirements are ambiguous. As we can see from Figure 3-5, the gross effects of input requirements could be at C where K 2 and L 2 are lower than those before a price change or at D where K 3 and L 3 are higher than those before a price change. As a result of the ambiguity of the impact of changes in input prices on the direction of input change, I will explain the profit maximization approach of induced innovation theory as an upward shift in the IPPF induced by changes in relative input

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37 prices. The result of gross biased input requirement changes determines the direction of biased technological change. Since changes in input requirements could result from purely a substitution effect as a result of changes in prices, technological progress is defined as an increase in profit given that the output and input prices remain unchanged: /t > 0 for given ps and ws 3.8 An increase in profit could result from both an increase in output levels and a decrease in input requirements. Figure 3-6 gives the illustration of the profit maximizing induced innovation model for a two-input, one-output technology. The IPC is used to demonstrate the concept of induced innovation analogously to IPPF. An increase in relative factor prices from (r/w) 1 to (r/w) 2 results in a decrease in capital requirement and an increase in labor requirement by a substitution effect, a movement from A to B. A movement from technology at point A to point B does not require any innovation of new technology because they are both available under IPC 1 The IPC 1 could shift to IPC 1 or IPC 1 via the output effect resulting in a different profit maximized production process. Holding the output level constant (no output effect), an increase in relative capital to labor prices induces a new technology set IPC 2 which results in a further reduction of cost minimized input requirements. An increase in (r/w) could also induce a new set of technology that increases the output level, IPC 2 The gross effect of an increase in relative prices of capital to labor is ambiguous depending on whether the IPC curve shifts to IPC 2 or IPC 2 The example in Figure 3-6 is neutral technological progress which means that holding factor prices constant at (r/w) 2 the labor-capital ratio (L/K) remains constant as

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38 the IPCs shift. Biased technological progress can be defined as a gross change in (L/K) given that output prices, input prices and fixed input quantities remain unchanged. Rate of Technological Change and Biased Technological Change The development of definitions and mathematical derivations in this section is based heavily on Kohli (1991). A multi-output, multi-input variable profit function is defined as: }t,K|QZ{max)t,K,Z(Q for Z > 0 and K 0, where Z is a vector of N output and M variable input prices, and Q is a corresponding vector of quantities; K is a vector of L fixed inputs, R is a vector of fixed input prices, and t is a state of technology. Employing Eulers theorem, the linear homogeneity of the variable profit function in Z and K implies that jj2jii2iKtKZtZt 3.9 Define the semielasticity of the supply of output and the demand for variable inputs with respect to the state of technology as: tQlniit i = 1,, N+M 3.10 and the semielasticity of the inverse fixed input demand with respect to the state of technology as: tRlnjjt j = 1,, L 3.11 Dividing through by and using Hotellings Lemma and the marginal revenue of fixed input condition, Eq. 3.9 can be written as: jjtjiititln 3.12

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39 where is the rate of technological change, and i and j are profit shares of variable inputs and outputs, and those of fixed inputs, respectively. There is technological progress when the rate of technological change is positive. The rate of technological change is defined as the rate of growth in profit over time. It is also equal to an average of the rates of increase in outputs and decrease in variable inputs via changes in the state of technology weighted by profit shares, at given fixed input quantities, output and variable input prices. Alternatively, it can be expressed as a weighted average of the rates of increase in fixed input price via changes in the state of technology at given output and variable input prices and fixed input quantities. The bias of technology is defined as i = 1,, N+M 3.13 itiB jtjB j = 1,, L 3.14 A technological change is output i-producing if B i is positive, and it is output i-reducing if B i is negative. Similarly, a technological change is variable input i-using if B i is positive, and it is variable input i-saving if B i is negative. A technological change is fixed input j-using if B j is positive, and it is fixed input j-saving if B j is negative. If technological change is unbiased or neutral, B i = B j = 0, and J 1,..., j I; 1,..., i jtit 3.15

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40 IPC t IPC t IPCt+1 Pt Pt Pt Pt+1 It It It+1 I t+ 1 It+1 It+1 IPCt+1 Capital Pt Labor Figure 3-1. Ahmads induced innovation model. (Ahmad, Syed. On the Theory of Induced Invention. The Economic Journal 76(302) 1966, p.349)

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41 Lan d P 0 P 1 Mechanical Technology Labo r I0 I0 I1 I1 i0 i0 i1 [A, M] P 0 P 1 P Q i1 A Lan d P 0 P 1 Fertilize r [F, B] Biological Technology I*0 I*0 I*1 I*1 i*0 i*0 i*1 P 0 P 1 P Q* i*1 B Figure 3-2. Induced technological change. A) Mechanical technology development. B) Biological technology development. (Hayami and Ruttan. Factor Prices and Technological Change in Agricultural Development: The United States and Japan, 1880-1960. The Journal of Political Economy 78:5 (Sep. Oct. 1970), p.1126)

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42 IPPF1 IPPF2 ** X1 X2 Y1 Y2 Output Input Y2=f2(x) Y1=f1(x) Figure 3-3. Innovation production possibility frontier and technological progress.

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43 IPPF2 Y2=f2(x) IPPF1 Y1=f1(x) X1 X2 Y1 Y2 Y1 =f1 (x) X1 Y1 Output Input Figure 3-4. Technological progress and a change in prices.

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44 Labor I2 (r/w)2 (r/w)1 D I1 I3 AB C K1 K1 K2 K3 L1 L1 L2 L3 Capital Figure 3-5. Substitution and output effects of profit maximization. (Fonseca and Ussher. The Profit Function. The History of Economic Thought Website http://cepa.newschool.edu/het/essays/product/profit.htm#decomposition (April 13, 2004)

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45 I2 IPC1 I1 I1 IPC2 A (r/w)2 (r/w)1 B C D IPC1 IPC2 IPC1 I3 Labor Capital Figure 3-6. Induced innovation for profit maximizing technological change.

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CHAPTER 4 EMPIRICAL MODEL, DATA, AND ESTIMATION This chapter discusses the empirical model and the restrictions of the profit maximization approach of the induced innovation theory. Among other restrictions, curvature restriction will be discussed extensively. It also describes the data and the definition of each variable used in the model. Finally, estimation techniques of seemingly unrelated regression, imposing model restrictions, and the rate of biased technological change are discussed. Empirical Model Binswanger (1978) discussed issues in modeling induced technological change extensively in Induced Innovation. There are two approaches to modeling induced technological change: the production function approach, and the cost or profit function approach. Several authors, such as Kennedy (1964), use factor-augmenting coefficients in the production function in order to capture the change in technology. As discussed in Binswanger (1978), the method of factor augmentation has some disadvantages. If the production function is Cobb-Douglas, rates of change in augmenting coefficients of different factors will be neutral. Moreover, the change of technology embodied in one factor does not necessarily augment only that factor. For example, the quality improvement of workers who operate machine harvesters not only augments labor, but also machinery. Furthermore, a quality index is mistakenly used as factor augmentation. Changes in the quality of a factor (e.g. rate of human capital accumulation per worker) 46

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47 can neither be viewed nor measured as rates of augmentation in a factor-augmenting production function (Binswanger 1978). Much attention of technological change has been on endogenizing research and development in a firm decision since the 1960s. One disadvantage of this method is that technological advance is not perfectly correlated with research and development expenditures, and other omitted variables can result in a different specification of technological change (Lambert and Shonkwiler 1995). The effort to capture the stochastic trend on technological change has been done by Lambert and Shonkwiler (1995), but the trend also depends on research expenditures. However, understanding resource allocation, returns to investment, and technology transfer can be obtained by endogenizing the research and development expenditures decision in the model. Alternative approaches are the cost function and profit function approaches. There are several advantages of this over a production function approach (Binswanger 1974a). In a perfectly competitive market, output prices and factor prices are exogenous to producers decisions, while output and input quantities are endogenous. Using factor prices as independent variables in the estimation equation of the cost function or profit function approach is more appropriate than using input quantities in the production function approach, and the problem of multicollinearity is less among input prices than input quantities. Since the homogeneity property always holds in cost and profit functions, it is not necessary to impose the homogeneity property on a production function to derive the estimation equation for the cost or profit function approach. The cost minimization or profit maximization approaches are 2 alternatives for modeling microeconomic production models. The profit function provides more

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48 information than the cost function when multiple outputs are taken into account. The variable profit function is adopted in recognition of the simultaneous determination of output mix and variable inputs for given prices. This approach permits analysis of the impact of factor prices on the output mix. The transcendental logarithmic (translog) profit function is considered more appropriate than other functional forms for this study because of its flexibility, ease of interpretation, and ease of computation. A constant elasticity of substitution (CES) model is too restrictive for a many-factor profit function since all partial elasticities of substitution between all pairs of inputs must be constant. The translog function is a more generalized form of the Cobb-Douglas function since it is not restricted to unit elasticities of substitution. A translog profit function is a logarithmic Taylor series expansion to the second term of a twice-differentiable profit function around the variables evaluated at 1. Among other popular flexible functional forms, the translog is less restrictive than the generalized Leontief and normalized quadratic functions since these 2 functions pre-impose quasi-homotheticity expansion paths implying that the marginal rate of input substitution is independent of output levels. It is undesirable, for example, to restrict the input demand elasticities with respect to output to 1 as output increases. They also restrict marginal rates of substitution among any input pair to be independent of all input prices except those of the input pair, and they impose separability between inputs and outputs which implies that marginal rates of output transformation are independent of factor intensities or input prices (Lopez 1985). However, the advantage of using the normalized quadratic function is that it satisfies global curvature without additional

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49 constraints; whereas, the translog function does not. In this study, I impose the curvature constraints locally on the translog profit function. Model Specification Assuming that producers are price-takers and maximize short-run profit, a variable profit function of induced innovation theory is adopted. A state of technology influences the profit of production. Assume that outputs )Y,...,Y(YN1 use variable inputs and fixed inputs )X,...,X(XM1 )L ,...,K(KK1 The vectors of output prices, input prices and fixed input prices are denoted by )P,...,P(N1 P )W,...,W(M1 W and R = (R 1 ,, R L ), respectively. Let Q = (Q 1 ,,Q N+M ) be a vector of variable input and output quantities, and Z = (Z 1 ,, Z N+M ) be a corresponding price vector. A time variable, t, is used as a representative for technological knowledge even though it may leave much to be desired as an explanation of technological change. As Chambers (1994: 204) argues, time is a very economical variable for representing technological change; it has some definite advantages such as analytical and econometric tractability over some other approaches. The profit function is defined as: for Z > 0 and K 0. The translog variable profit function is written as }t,K|QZ{max)t,K,Z(Q t21ttKlntZln KlnZlnKlnKln21 ZlnZln21KlnZlnln2tttL1jjjtMN1iiitMN1iL1jjiijL1jL1kkjjkMN1iMN1hhiihjL1jjiMN1ii0 4.1

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50 Assuming that is twice continuously differentiable, it must satisfy Hotellings Lemma, /Z )K,W,P( i = Q i The differentiation of the variable profit function with respect to output (and variable input) prices yields profit maximizing output supplies (and variable input demands). Thus, /P i = Y i and /W j = X j and where Y i s and X i s are vectors of profit maximizing outputs and variable inputs, respectively. Recall that all output and variable input prices are positive; this implies that variable input quantities are negative. Utilizing the Hotellings Lemma, profit share equations can be derived from the derivatives of the log of profit with respect to the log of prices. MN1,...,i ZQZlnlniiii 4.2 where i > 0 if Z i is an output price, and i < 0 if Z i is a variable input price. The marginal revenue of a fixed input is equal to its cost under competitive conditions. Thus, the derivative of the variable profit function with respect to a fixed input quantity is equal to its cost, /K j = R j 0, and the derivatives of the logs yield profit share equations. L1,...,j KRKlnlnjjjj 4.3 In the case of the translog variable profit function, share equations are derived as follows: MN1,...,i t Kln ZlnZlnlnitL1jjijMN1hhihiii 4.4 L1,...,jt KlnZlnKlnlnjtkL1kjkiMN1iijjjj 4.5 Model Restrictions A well-defined nonnegative variable profit function for positive prices and nonnegative fixed input quantities satisfies the following restrictions: 1. Homogeneity

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51 A variable profit function is linearly homogeneous in prices of outputs and variable inputs and in fixed input quantities. It is defined as: (Z) = (Z), and (K) = (K), > 0. Eulers theorem states that the linear homogeneous function can be expressed as: )K(KK);Z(ZZjjjiii Thus, 1Klnln ;1Zlnlnjjii These are also known as adding-up conditions. The second and third summation terms and the last term in 4.4 and 4.5 contain variables that can take different values, the sum of share equations can only be restricted to 1 if these terms are restricted to 0. The homogeneity restrictions for the translog profit function are as follows: 00 1 ;1L1jjtMN1iitL1jijMN1iijL1kjkL1jjkMN1hihMN1iihL1jjMN1ii 4.6 2. Symmetry For a twice continuously differentiable profit function, Youngs theorem implies that the Hessian of the profit function is symmetric. In terms of the translog profit function, ; kjjkhiih 4.7 3. Curvature The convexity of a variable profit function in prices implies that the output supply and variable input demand functions are non-decreasing with respect to their own price. If i is a variable input (X i 0), an increase in its price reduces the quantity demanded,

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52 X i /W i 0. In other words, an increase in variable input price decreases its demand in absolute value. The concavity of a variable profit function in fixed inputs implies that the inverse demand equations are non-increasing with respect to their own quantities, R i /K i 0. The geometric property of the variable profit function (McFadden 1978, p.67) is defined as (Z, K, t) is convex over U iff )Z()1()Z( )Z)1(Z(2121 (Z, K, t) is concave over V iff )K()1()K( )K)1(K(2121 where U and V are convex subsets of R N ; and where Z 1 U, Z 2 U and K 1 V, K 2 V; 1 0. The algebraic properties of concavity and convexity can be expressed in terms of the signs of the Cholesky values of the function. The necessary and sufficient conditions for a convex (concave) profit function are that the Hessian of the profit function evaluated at output and variable input prices (fixed input quantities) is positive (negative) semidefinite or all principal minors are non-negative (non-positive). Lau introduced the concept of the Cholesky decomposition as an alternative to characterize the definiteness of the Hessian matrix. Laus Cholesky decomposition is favorable to the eigenvalue decomposition of the Hessian due to its fewer constraints (Lau 1978, Morey 1986). Wiley, Schmidt, and Bramble (1973) also propose alternative definiteness constraints which is the alternative used to impose the curvature property in this study. Both the Lau and Wiley-Schmidt-Bramble techniques can only impose curvature restrictions locally. While Gallant and Golub (1984), and Hazilla and Kopp (1985) suggested alternative methods of imposing curvature at multiple points, these methods still do not guarantee that the curvature will satisfy globally. Only at those points, although Gallant and

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53 Golubs technique does not limit to a finite number of points, are where the curvature will be satisfied. The Wiley-Schmidt-Bramble technique is used due to its consistency with the theory in contrast with alternatives which overly constrain the function and complicate the estimation, while not significantly improving the results. Morey (1986) suggests that there are 3 assumptions we can make before testing and imposing curvature properties. First is to assume that the true function and the estimated function have the same functional form, and they satisfy global curvature properties. Second, the estimated function and true function have the same functional form, but they do not possess the curvature property globally. And lastly, the estimated function is only a second-order approximation to the true function at some point. The translog function does not possess global curvature properties so we are left with 2 cases. To assume that the estimated function is a second-order approximation to the true function, we should know where the point of approximation is; otherwise, the test and imposition of curvature at a point are meaningless. As a result, I will assume that the estimated function and the true function have the same functional form. Laus Cholesky decomposition Every positive (negative) semidefinite matrix A has a Cholesky factorization A = LDL 4.8 where L is a unit lower triangular matrix, and D is a diagonal matrix. L is defined as a unit lower triangular matrix if L ii = 1, i and L ij = 0, j > i, i,j. D is defined as a diagonal matrix if D ij = 0, i, j, i j. The diagonal elements, D ii of D are called Cholesky values. A real symmetric matrix A is positive (negative) semidefinite if and only if its Cholesky values are non-negative (non-positive). For instance, a variable profit function is convex

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54 in variable input and output prices. Let A be the Hessian of the variable profit function with respect to 3 variable input and output prices. ,000000D ,101001L321323121 Thus, 4.9 323222311..3223121122211.311211133a..23a22a.13a12a11aA The A matrix is symmetric, as is the LDL matrix. All Cholesky values (s) must be non-negative for the Hessian of the variable profit function with respect to prices to be positive semidefinite. Similarly, if the A matrix is the Hessian of a variable profit function with respect to fixed input quantities, all Cholesky values must be non-positive. The Cholesky values from Laus definition can be calculated at each observation to detect if the curvature property is violated. I assume that the estimated profit function and the true function have the same functional form, but they do not posses the curvature property globally. In order to impose curvature restrictions by Laus technique, the inequality restrictions of the Cholesky values can be imposed; however, they cannot be imposed simultaneously at more than 1 point. Gallant and Golub (1984) have developed computationally intensive techniques to impose curvature simultaneously at multiple points. Wiley-Schmidt-Bramble decomposition A necessary and sufficient condition for a matrix A to be positive (negative) semidefinite is that it can be written as: A = (-)TT 4.10

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55 where T is a lower triangular matrix and Tij = 0, j > i, i,j. Due to the greater simplicity of the Wiley-Schmidt-Bramble decomposition than Laus decomposition, this technique is used to impose curvature in my model. For a translog variable profit function, the Hessian matrix of the profit function with respect to output and variable input prices, A II is positive semidefinite. 4.11 2MN,MN2MN1MN222MN112MN,111MN222MN1122222121211MN,1111211211MN2MNMN,MN2MN2,MN1MN1,MNMN2MN,2222222112MN1MN1211212111II... .........A The Hessian matrix of the profit function with respect to fixed input quantities, A JJ is negative semidefinite. 2L,L2L1L222L112L,111L222L1122222121211L,1111211211L2LL,L2MN2,L1L1,LL2L,2222222112L1L1211212111JJ*...******************** .........A 4.12 Elasticity Price elasticity of output supply and variable input demand The generalized input and output elasticities with respect to prices are (Appendix A)

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56 MN1,...,i 1-ZlnddlnQiiiiiiii 4.13 ji j; i, ZlnddlnQjiijJiij 4.14 Inputs i and j are gross substitutes if ij > 0, and gross complements if ij < 0; on the contrary, output i and j are gross substitutes if ij < 0, and gross complements if ij > 0. Following Kohli (1991, p.38), the matrix of price and quantity elasticities for the variable profit function is given by L,...,1k,jMN1,...,hi, .KlnRlnZlnRlnKlnQlnZlnQlnEEEEEkjhjkihiRKRZQKQZ 4.15 E QZ = { ih } are the price elasticities of output supply and variable input demand; E RK = { jk } are the quantity elasticities of inverse fixed input demands; E QK = { ij } capture the effects of changes in fixed inputs on variable input and output quantities; and E RZ = { ji } capture the effects of changes in prices of variable inputs and outputs on fixed input prices. The homogeneity of output supply and variable input demand functions, and of inverse fixed input demand functions requires that MNijiLjijLkjkMNhih1,1,0,0 Assuming that Q i = f(Z, K) and R j = g(Z, K), dKd K dQdZdZdQdQ KdKKlndQlndZdZZlndQlndQdQ K~ K ln d QlndZ~Zln d QlndQ~ 4.16

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57 where ~ is the relative change. Similarly, K~ K ln d RlndZ~Zln d RlndR~ 4.17 From Eq. 4.16 and Eq. 4.17, we can summarize the comparative statics of the variable profit function as K~Z ~ EEEER~Q ~ RKRZQKQZ 4.18 Morishima elasticity of substitution The extent of susbtitutability among inputs is the key concept in understanding the effects of factor and output price changes on technology, the demand for inputs, and the supply of outputs. The extensive studies of technological change in U.S. agriculture have primarily used the Allen-Uzawa elasticity of substitution (AES) as a measure of substitutability of inputs. The original concept of elasticity of substitution was introduced by Hicks (1932) to measure the effect of changes in the capital/labor ratio on the relative shares of labor and capital or the measurement of the curvature of the isoquant. However, as shown by Blackorby and Russell (1989), when there are more than 2 factors of production the AES is not the measure of the ease of substitution or curvature of the isoquant, provides no information about relative factor shares, and cannot be interpreted as a derivative of a quantity ratio with respect to the price ratio. In contrast, the Morishima elasticity of substitution (MES) does preserve the original Hicks concept. It measures the curvature, determines the effects of changes in price or quantity ratios on relative factor shares, and is the log derivative of a quantity ratio with respect to a marginal rate of substitution. To appropriately measure the ease of substitution, we calculate the MES among inputs.

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58 The MES in the cost minimization is defined as )P/Pln()*X/*Xln(MESijjiij 4.19 where X* i s are the optimal cost minimizing inputs, and P j s are the input prices. Applying Shephards Lemma and homogeneity of the cost function, and assuming that the percentage change in the price ratio is only induced by P j )P,Y(C)P,Y(CP)P,Y(C)P,Y(CPMESjjjjiijjij 4.20 cjjcijijMES 4.21 where ij c (Y,P) is the constant-output cross-price elasticity of input demand. Inputs i and j are Morishima substitutes if MES ij > 0; that is if and only if an increase in P j results in an increase in the input ratio X* i /X* j and Morishima complements if MES ij < 0. The MES is not symmetric, and unlike the Allen elasticity of substitution, the sign of MES is not symmetric either (Chambers 1988, p.96-97). Thus, the classification of substitute and complement between 2 inputs depends critically on which price changes. Sharma (2002) applied the concept of the MES to the profit maximization approach. The following section is based largely on his development. The constant output elasticity of input demand, ij c can be calculated from 4.18. First, define Q* = (Y: R) and Z* = (P: K), then Eq. 4.18 can be written as: W~*Z ~ EEEEX~*Q ~ XW*XZW*Q*Z*Q 4.22 W ~ E*Z ~ E*Q ~ W*Q*Z*Q 4.23

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59 W ~ E*Z ~ EX ~ XW*XZ 4.24 From 4.23, W ~ EE*Q ~ E*Z ~ W*Q1*Z*Q1*Z*Q 4.25 Substitute Eq. 4.25 into Eq. 4.24, W ~ )EEEE(*Q ~ EEX ~ W*Q1*Z*Q*XZXW1*Z*Q*XZ 4.26 Equation 4.22 can be written as: 4.27 W~*Q~ EEEE EEEEEX~*Z~W*Q1-*Z*Q*XZXW1-*Z*Q*XZW*Q-1*Z*Q-1*Z*Q Holding the output level constant, W*Q1*Z*Q*XZXWEEEE W ~X ~ 4.28 The Morishima elasticity of substitution can be calculated by the definition in Eq. 4.21 where ij c = the ij element in Eq. 4.27. L ..., 2, 1, l ,jN ..., 2, 1, k i, ,KlnRlnPlnRlnKlnYlnPlnYlnEljkjliki*Z*Q 4.29 M ..., 2, 1, lL ..., 2, 1, j N; ..., 2, 1, i ,lnWlnRlnWlnYEljliW*Q 4.30 L ..., 2, 1, j N; ..., 2, 1, iM ..., 2, 1, l ,lnKlnXlnPlnXEjlil*XZ 4.31 M ..., 2, 1, l ,j ,WlnXlnEljXW 4.32 Note that all prices and quantities are positive, except for variable input quantities, Xs. Thus, ln(X)s imply ln(-X)s. The elements in each matrix can be calculated from the

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60 parameter estimates of the share equations in the same manner as the price elasticity of output supply and input demand (Appendix B). Data Data used in this study are provided by Eldon Ball, Economic Research Service (ERS), USDA. The construction of these data is similar to the published production account data available from ERS (Ball et al. 1997, 1999, 2001). The raw data include series of agricultural output and input price indices and their implicit quantities from 1960-1999. Price indices of these series are appropriate for this study since they are adjusted for quality change of each input category. More discussion of input quality is given by Jorgenson and Griliches (1967), and by Ball et al. (1997) for the USDA method. Quality change occurs when the rates of growth of quantities that have different marginal products within each input category are not the same, for instance, a demographic change of farm labor, a change in the composition of fertilizers used, or a change in types of machinery. Quality adjusted price indices or constant-quality price indices measure changes in the price of inputs while keeping the efficiency constant. It is important to use quality-adjusted data when analyzing induced technological change because using unadjusted quality indices will result in biased estimation of parameters in the induced innovation model. There are 2 sets of data: Florida and the U.S. Florida is chosen to compare with the U.S. in this study because its agricultural production is labor intensive, and a large number of workers are immigrants. In addition, there are major examples of farm mechanization in Florida during the study period such as the sugarcane mechanical harvester in the early 1990s and recent adoption of citrus mechanical harvester. There are 2 significant immigration policy changes during the study period. The first is the end

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61 of the Bracero program in 1964, and the second is the implementation of the 1986 Immigration Reform and Control Act. Theses 2 policies, as discussed in Chapter 2, are expected to have an impact on the supply of farm labor from immigrant labor, and on changes in farm mechanization. In the published ERS production account, input quantity indices are constructed based on the Tornqvist index number specification. Implicit price indices are constructed as the ratio of the value of the input aggregate to the corresponding quantity indices, and can be interpreted as unit values (expressed in millions of dollars) of the aggregates. A similar approach is used to generate this data set. First, the price indices are estimated, and the implicit quantity indices are then calculated as the ratio of value of the aggregate to the corresponding price indices. Hedonic regression techniques are used to construct chemical indices. Changes in characteristics of fertilizers (e.g. grades of nutrient) and of pesticides (e.g. persistence in the environment) will not change constant-quality price indices. The price index of labor input is constructed from the estimated average compensation per hour. The average compensation is estimated by constructing a compensation matrix based on characteristics (gender, age, education, and employment classes) of workers for each year and controlling it to compensation totals for annual compensation. The estimate of rental price indices for each capital stock is derived from the correspondence between purchase price and the discounted value of future service flow. The estimates of each capital stock are explained by Ball et al. (1997). The estimation of constant-quality land stock takes into account different land categories: irrigated and dry cropland, grazing land and other. Land area under Federal commodity

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62 program and Conservation Reserve is not included. A detailed discussion of data construction can be found in Ball et al. (1997, 1999). Data used in the analysis are aggregated into 2 outputs, 4 variable inputs, and 2 fixed inputs. Each price index is normalized to 1 in 1996. The outputs are aggregated into perishable crops and all other outputs using a Divisia price index. Perishable crops in Florida are aggregated from vegetables, fruits and nuts, and nursery products; perishable crops in the U.S. consist of vegetables, fruits and nuts, and horticultural products. Other outputs in Florida consist of livestock, grains, forage, industrial crops, potatoes, household consumption crops, secondary products, and other crops. Other outputs in the U.S. aggregate are the same output categories as those of Florida, except that grains are defined as cereals. Variable inputs are aggregated into hired labor, self-employed labor, chemicals, and materials. Hired labor includes direct-hired labor and contract labor. The wage of self-employed labor is imputed from the average wage of hired workers with the same demographics and occupational characteristics. Chemicals include fertilizers and pesticides. Materials include feed, seed, and livestock purchases. Fixed inputs are aggregated into land and capital inputs. Capital includes autos, trucks, tractors, other machinery, buildings, and inventories. Figures 4-1 to 4-4 illustrate the data by normalizing them to 1 in 1960 for ease of comparison. Figure 4-1 shows price indices for Florida outputs and inputs. All variables have an increasing trend. Both hired labor and self-employed labor wages changed in the same direction. While farm wages remain relatively constant in the 1960s and early 1970s, they increased significantly in the mid-1970s and thereafter. The wages also had greater variation in the 1990s. Chemicals, materials, perishable crops, and all other

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63 output price indices were relatively stable, with a slightly increasing trend. After the mid-1970s, land rent significantly increased over time, with exceptions in 1983, 1986, and the early 1990s. Capital price was stable until the mid 1970s, but increased significantly thereafter. Figure 4-2 illustrates shares of variable profits in Florida. Shares of all variable inputs are negative which means that the higher negative share implies higher profit share. Since perishable crops were major commodities in Florida, they had a larger share than all other crops combined. While the share of perishable crops remained constant over time with some fluctuations, all other outputs share was decreasing since the mid 1970s. Hired labor had larger shares than self-employed labor. Hired labor also had relatively stable shares, but it increased after 1964 until 1970 and from 1992 to 1996. Self-employed labor had a trend similar to hired labor. Profit shares of chemicals, materials, land, and capital were relatively stable over time with some fluctuations. Figure 4-3 reports the price indices of U.S. variables. Hired labor and self-employed labor wages had an increasing trend over time. They increased dramatically since the late 1970s. Capital rent was relatively stable in the 1960s and 1970s, but increased thereafter, except in 1982, 1983, 1986, and during 1989-1993. Chemicals, materials, perishable crops, and all other outputs prices slightly increased over time. Land price changed in the same pattern as that in Florida. Figure 4-4 shows the variable profit share of U.S. outputs and inputs. Profit share of perishable crops was stable over time and much smaller as compared to other products. Share of self-employed labor decreased since 1970, and remained stable from 1973 to 1990 when it started to increase. Share of hired labor was stable over time, except after

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64 the mid-1990s when it increased slightly. Capital share was relatively stable over time, but decreased in the early 1970s. It steadily decreased after the 1980s, but increased slightly after the mid-1990s.

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65 051015202519601962196419661968197019721974197619781980198219841986198819901992199419961998YearPrice Index Hired Self Chem Matl Land Capital Other Outputs Persh Crops Figure 4-1. Florida price indices of outputs, variable inputs, and fixed inputs. -1-0.500.511.5219601962196419661968197019721974197619781980198219841986198819901992199419961998YearProfit Share Hired Self Chem Matl Land Capital Other Outputs Persh Crops Figure 4-2. Florida profit shares of outputs, variable inputs, and fixed inputs.

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66 051015202519601962196419661968197019721974197619781980198219841986198819901992199419961998YearPrice Index Hired Self Chem Matl Land Capital Other Outputs Persh Crops Figure 4-3. U.S. Price Indices of outputs, variable inputs, and fixed inputs. -3-2-101234519601962196419661968197019721974197619781980198219841986198819901992199419961998YearProfit Share Hired Self Chem Matl Land Capital Other Out Persh Crop Figure 4-4. U.S. profit shares of outputs, variable inputs, and fixed inputs.

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67 Estimation Seemingly unrelated regression procedures were applied to the share equations and profit function using the Full Information Maximum Likelihood (FIML) procedure. 16 Least squares estimation methods with an iterated covariance matrix and seemingly unrelated regression methods were attempted prior to FIML, but the estimation was cumbersome, particularly as more restrictions were imposed. The FIML procedure facilitated convergence, although intervention was required in the iterative process by (i) reducing the number of parameters in the initial estimation and reintroducing them one at a time, and (ii) changing the starting values of parameters. Seemingly Unrelated Equations The translog profit function with linear homogeneity imposed and including an IRCA dummy variable is defined as uTt21t21tTt tKKlnTtKKlntZZlnTtZZln KKlnZZlnKKln21 ZZlnZZln21KKlnZZlnlnt022tt2tt22ttcapitalland22t1capitalland1t151imatli2it251imatli1itcapitallandmatli51i1i2capitalland1151i51hmatlhmatliihcapitalj1matli51ii0 4.33 where T 2 is a time dummy variable for years after the passage of IRCA in 1986. It is added to capture the potential difference in the biases and the rate of technological change. There are 2 outputs: perishable crops and other outputs; 4 variable inputs: hired labor, self-employed labor, chemicals, and materials; and 2 fixed inputs: land and capital. Linear homogeneity in prices is imposed by dividing through all prices by the price of 16 Time Series Processor (TSP) through the looking glass version 4.4 is used for statistical analysis.

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68 materials (the variable input equation dropped from the system), and linear homogeneity in fixed inputs is imposed by dividing fixed inputs by the quantity of capital (the fixed input equation dropped from the system). The profit shares are derived by taking the first derivative of the translog profit function with respect to the log of variable input and output prices and fixed input quantities. The system of share equations becomes 51,...,i utT t KKln ZZlnitit22it1capitalj1j51hmatlhihii 4.34 1j utT t KKln ZZlnjtlt22lt1capitalland1151imatliiljj 4.35 Although the translog profit function can be estimated directly, estimating the optimal, profit-maximizing input demand and output supply equations (or profit share equations) is more efficient (Berndt 1996, p.470). The profit function is assumed to be well-behaved; that is, it satisfies all the symmetry, homogeneity, and curvature conditions. A disturbance term, u i (u j ) is added to each equation, and each is assumed to be randomly distributed with 0 mean and scalar covariance matrix. Even though the translog profit function generates linear share equations in parameters with the same regressors, the equation-by-equation OLS (ordinary least square) estimates will not guarantee the symmetry constraints across equations. Moreover, the cross-equation constraints mean that the disturbances are correlated across equations, implying that the contemporaneous covariance matrix is nondiagonal. In this case, system estimation is more efficient. Zellner (1962) developed an efficient method of estimating seemingly unrelated equations known as Zellners seemingly unrelated estimator, ZEF, or seemingly unrelated regression estimator (SUR).

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69 Zellners seemingly unrelated estimator uses the covariance matrix of disturbances from equation-by-equation OLS as initial estimates, then performs feasible generalized least squares estimation. The iterative Zellner seemingly unrelated regression estimator, IZEF, updates the covariance matrix and iterates the Zellner procedure until the covariance matrix and the changes in estimated parameters are arbitrarily small. The estimates from IZEF are asymptotically equivalent to maximum likelihood estimates under the assumption of normality of the disturbance term. Recall that the (variable) profit is defined as total revenue minus total variable cost. At each observation, the sum of variable output and input shares is always equal to 1. This imposes an adding-up condition to the system. In addition, the profit function is linear homogeneous in variable input and output prices and linearly homogeneous in fixed input quantities. Thus, only N+M-1 variable input and output share equations are linearly independent, and only L-1 fixed input share equations are linearly independent. This also implies that the residual covariance matrix is singular. The singularity problem can be handled by dropping 2 share equations: 1 variable input and 1 fixed input share equation. The estimates from IZEF are invariant to the choice of which equation is deleted. The implied parameter estimates of the terms in Eq. 4.34 and Eq. 4.35 and the remaining parameter estimates in the omitted share equations can be obtained from the model restrictions. The system of share equations 4.34 and 4.35 is estimated jointly with the translog profit function 4.33 using the full information maximum likelihood procedure. Introducing the profit function is not typically done in empirical work, although it is likely to produce more efficient estimates (Kohli 1991, p.204). It is

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70 necessary to include it for the current specification since the rate of technological change includes parameters andthat cannot be estimated directly from the share equations. t tt Imposing Restrictions for a Well-behaved Profit Function Homogeneity 00 1 ;121j2jt21j1jt51i2it51i1it21jij51iij21kjk21jjk51hih51iih21jj51ii 4.36 Symmetry ; kjjkhiih 4.37 Continuity After introducing a dummy variable, the continuity at 1987 of the translog profit function requires that 0t21KKlnZZln872tt2tcapital87land872t151imatl87i872it 4.38 where Z 87 K 87 and t 87 represent the observed variables in 1987. Curvature The curvature properties of the estimated function can be checked at each observation in the sample. If curvature of the estimated function is satisfied locally in the neighborhood of every observation, we cannot reject that the true function is also locally satisfied over the region. The technique used to test and impose curvature restrictions is adopted from Kohli (1991). He showed that (Kohli 1991, p.109-110) the Hessian of the translog function can be evaluated in terms of the Allen elasticity of substitution matrix. He noted that it is also possible that the violation of convexity and concavity occurs at

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71 different observations. We want to ensure that the substitution matrix of variable inputs and outputs, II is positive semidefinite at some observation s, and the substitution matrix of fixed inputs, JJ is negative semidefnite at some observation r. Share equations 4.34 and 4.35 at each observation can be written as follows: s)-(tT s)-(t KKlnKKlnZZlnZZln sT sKKln ZZlnit22it1s,capitals,landt,capitalt,land1151hs,matlhst,matlhtihit22it1s,capitals,land1151hs,matlhsihiit r)-(tT r)-(t KKlnKKlnZZlnZZln r Tr KKlnZZln2jt21jtr,capitalr,landt,capitalt,land11r,matlirt,matlit51iij2jt21jtr,capitalr,land11r,matlir51iijjjt These can also be expressed as: s)-(tT s)-(t KKlnKKlnZZlnZZln~it22it1s,capitals,landt,capitalt,land1151hs,matlhst,matlhtihiit 4.39 r)-(tT r)-(t KKlnKKlnZZlnZZln~2jt21jtr,capitalr,landt,capitalt,land11r,matlirt,matlit51iijjjt 4.40 ~ where isi ~ and jrj are estimated profit shares of variable inputs and outputs at observation s and estimated profit shares of fixed inputs at observation r, respectively. The estimated substitution matrices are calculated from profit shares and can be expressed as:

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72 25525552525521515155252252222222121212I15115212112211211155/)(/)(/)(/)(/)(/)(/)(/)(/)( 4.41 2222222121212212112211211122*/*)*(**/*)*(**/*)*(*/*)*( 4.42 Note that the Allen substitution matrices are symmetric. The curvature property of the profit function is first checked by Laus Cholesky decomposition of the substitution matrix. At each observation, the Cholesky values derived from 4.41 should all be nonnegative, and those from 4.42 should all be nonpositive. The significance of the Cholesky values cannot be easily tested at each observation. However, as Lau noted, the significance of the Cholesky values can be examined by first normalizing the right hand side variables to 1 at a given observation, and normalize the time variable to 0 at the same observation. The observation where curvature is the most severely violated (the largest of Cholesky values in the absolute terms that have the wrong sign) is selected for normalization. Then reestimate the system by estimating the Cholesky values, s, in the diagonal matrix and the elements in the lower triangular matrix, s, using the Lau decomposition technique in place of the original parameters. The Lau decomposition, A = LDL, is shown below: 62666.....655652555....6446544542444...63365335433432333..622652254224322322222.6116511541143113211212111IIA

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73 ........4243324222411...4334232241311323222311..422412113223121122211.4113112111ILIDIL 4.43 626552644263326222611.6556454463533625226151152544253325222511644634336242261411544534335242251411633623226131153352322513116226121152251211611511 4.44 .***.***LDL.A222112111JJJ22222211212111JJ where A II is the Hessian of profit function with respect to variable inputs and outputs, and A JJ is the Hessian of profit function with respect to fixed input quantities. If the curvature is violated, the curvature restrictions can be imposed by using the Wiley-Schmidt-Bramble (W-S-B) reparameterization technique. The W-S-B technique still does not guarantee global curvature, but by imposing the curvature at a particular point, we can assure that the curvature is satisfied locally. Kohli found that it is often sufficient for the estimated function to satisfy the curvature for all observations when curvature restrictions are imposed at the point that seems to be the most seriously violated. The right hand side variables are normalized to 1 at the observation where curvature is to be imposed, and the time variable is normalized to 0 at the same observation. Using W-S-B reparameterization, the original parameters are replaced by a one to one correspondence between the Hessian, A II (A JJ ), and its W-S-B decomposition

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74 matrix, TT (-VV). T and V are lower triangular matrices of dimension 5x5 and 1x1, respectively. The reparameterization involves the following: 11 = 11 2 1 2 + 1 12 = 11 12 1 2 22 = 21 2 + 22 2 2 2 + 2 23 = 21 31 + 22 32 2 3 33 = 31 2 + 32 2 + 33 2 3 2 + 3 4.49 34 = 31 41 + 32 42 + 33 43 3 4 44 = 41 2 + 42 2 + 43 2 + 44 2 4 2 + 4 45 = 41 41 + 42 42 + 43 43 + 44 54 4 5 55 = 51 2 + 52 2 + 53 2 + 54 2 + 55 2 5 2 + 5 11 = 11 2 1 2 + 1 where the s and are elements in lower triangular matrices T and V, respectively. The remaining original parameter estimates are recovered using the homogeneity, symmetry, and continuity constraints. Rate of Biased Technological Change The rate of technological change by the definition in Chapter 3 and as derived from Eq. 4.33 is written as 22ttttcapitalland2t12capitalland1t151imatli2it251imatli1it22ttT*ttKKlnTKKlnZZlnTZZlnT* 4.46 After imposing the homogeneity, symmetry, and continuity restrictions, the rate of technological change can only be estimated by including the profit function with the system of share equations because t and tt are not obtainable from the share equations. The biased technological change of variable outputs and variable inputs as defined in the previous chapter and replicated here are calculated from the parameter estimates of the share equations.

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75 itiB 4.47 Following from Eq. 4.34, TtZQtQZtit22it12iiiii i = 1,, 6 4.48 solving for Q i /t from Eq. 4.48 and dividing by Q i tlnTtQQ1i2it21itiiit 4.49 i2it21ititT 4.50 Thus, i2it21itiTB i = 1,, 6 4.51 Similarly, the technological change of fixed inputs is calculated as j2jt21jtjTB j = 1, 2 4.52 Estimation of Elasticities The price elasticities of output supply and input demand can be calculated from the parameter estimates of the share equations. The price elasticities follow from Eq. 4.13 and Eq. 4.14. The Morishima elasticities of substitution are calculated using the definition in Eq. 4.21 where the constant-output cross-price elasticity of input demand, ij c can be derived from Eq. 4.27. The estimates of each matrix in Eq. 4.27 are found in Appendix B.

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CHAPTER 5 ECONOMETRIC RESULTS AND INTERPRETATION This chapter presents the econometric results and their interpretation. Estimates of the seemingly unrelated regression model with homogeneity and symmetry constraints imposed, the test for curvature property, the estimates after imposing the curvature restrictions, and the calculation of the rate of technological change, the biases, and the Morishima elasticities of substitution are reported. The chapter is divided into 2 sections: the results at the Florida level and those at the U.S. level. Each section also provides interpretation of the results. Florida Results The initial estimates of the seemingly unrelated regression model of the profit share equations and the translog profit function of Florida are presented in Table 5-1. These estimates are from the model that has only the homogeneity and symmetry restrictions imposed. Although the listed translog parameter estimates have no direct economic interpretation, they are the basis for the elasticity and the rate of technological change estimates. The interpretation of these estimates will be discussed after all restrictions are imposed. The estimates from this initial regression do not necessarily represent the well-behaved profit function since the curvature property may not have been satisfied. The curvature property is first analyzed by decomposing the matrices of the Allen elasticity of substitution (equivalent to the Hessian of the translog profit function), and checking the Cholesky values (s of the D matrix in Eq. 4.8). 76

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77 The Cholesky values of the Hessian with respect to the fixed inputs are negative at every observation. This means that the concavity property of the estimated profit function is not violated within the region of data for the fixed inputs. However, the Cholesky matrix of the Hessian with respect to the variable inputs and outputs has 1 negative Cholesky value at every observation. This means that the convexity property of the estimated profit function is violated at every point of the data among the outputs and variable inputs. The most negative Cholesky value, -3.1440, is found in 1998. Since only convexity is violated, subsequent curvature attention is given only to convexity. To further analyze the significance of the convexity violation, all the right hand side variables are normalized to 1, and the time variable is normalized to 0, in 1998, the observation with the smallest Cholesky value. Using data for all observations, below is the estimated Cholesky matrix of variable inputs and outputs after applying Laus reparameterization as in Eq. 4.43. The estimated standard errors are reported in the parentheses. (0.049)(0.108)(6.353)(1.462)(2.491)(-0.002)0.02550000000.13070000000.80370000000.72900000000.51280000000.0004-DIFL 5.1 There is one Cholesky value that has the wrong sign; however, it is insignificant at either the 0.05 or 0.10 significance level. This implies that although convexity may be violated, the indicator of the violation is not statistically significant given the observed

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78 data. Furthermore, it implies that imposing the convexity property to the profit function will be consistent with the data. The convexity is imposed using the Wiley-Schmidt-Bramble reparameterization technique as presented in Eq. 4.45. The right hand side variables are normalized to 1 and the time variable is normalized to 0 in 1998. This guarantees that convexity will be satisfied at this point. Instead of reporting the elements in the lower triangular matrix (T in 4.10), Table 5-2 presents the estimates transformed back to the original parameters of the translog profit function satisfying the regularity constraints, including convexity. As may be seen in Tables 5-1 and 5-2, the estimates differ, and for some parameters, the significance of the estimates changes after convexity is imposed. After convexity is imposed, the Cholesky values are calculated at each observation once again. Although the Cholesky values of the Hessian with respect to fixed inputs remain negative, 1 or more Cholesky values of the Hessian with respect to the variable inputs and outputs remain negative at all observations, except 1964 and 1998, 17 the latter year being the normalized observation. As a result, we can claim that convexity is not violated in 1964 and in 1998. The estimates at observations other than1964 and 1998 may not give correct economic interpretations because the convexity property is violated. To properly test the significance of violations at every observation would require an array of sequential statistical tests (Lau 1978b), while adding little to the ultimate results of the analysis. However, the Cholesky values estimated by the Lau reparameterization show that the violation in the absence of the convexity restriction is insignificant at the normalization point, i.e. the observation where the convexity appeared to be most 17 1 out of 6 Cholesky values are negative in 1998, but its magnitude is sufficiently small (-0.0000035) to be considered as a rounding error.

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79 seriously violated originally. The Wiley-Schmidt-Bramble reparameterization technique used to impose the curvature property in this study confirms that it does not guarantee global curvature, but it does ensure that the curvature property is satisfied locally at the point where curvature is imposed. A more restrictive procedure is likely to only bring demand or supply elasticities closer to 0 in cases where convexity is violated. Florida Rate of Technological Change and Biased Technological Change The estimates from Table 5-2 are used to calculate the rate of technological change, defined in Eq. 4.45, and biased technological change as defined in Eq. 4.51 and Eq. 4.52. Appendix C summarizes the rates and bias of technological change in Florida at each observation. Figure 5-1 depicts the biased technological change in Florida over time. Before 1986, point estimates of biases were significantly different than 0 at better than 0.01% for all inputs, except land and capital whose significance levels were larger than 80%. After 1986, other outputs and materials biases were significantly different than 0 at better than 0.01%, but biases of perishable crops and all other inputs were statistically insignificant. The estimated biases suggested that technological change in Florida was biased against all outputs and inputs, except for land (although insignificant), before 1986. Variable inputs were defined as negative outputs; as a result, the share-weighted sum of biases among variable inputs and outputs was 0. It is possible, as the results reveal, that biases among all outputs and variable inputs were negative. This is because the shares of variable inputs were negative. Table 5-3 reports the estimates of Florida biased technological change before and after the passage of IRCA, evaluated at the means of the explanatory variables for each subperiod. A test that the biases are jointly different between the 2 periods is highly

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80 significant as suggested by a Wald test statistic value of 47.06; the critical value for the is 21.95 at the .005 significance level. The individual differences of biases between the 2 periods and their standard errors suggest whether the changes are individually significant. After the passage of IRCA in 1986, the technology suggested significant bias toward more perishable crop-producing, but significantly bias against the production of other outputs. The technology became more self-employed labor-using, but the biases of hired labor and capital were not significantly different. The technology significantly used more chemical and less materials; whereas, the use of land did not change. The results suggest that although the technology significantly saved both types of labor before IRCA, it used more self-employed labor afterward. The IRCA did not change how much hired labor was employed nor stimulate the adoption of farm mechanized technology. The technology suggested an increase in the production of perishable crops. Instead of hiring more workers or adopting new mechanized technology, the technology apparently became more self-employed labor-using in the production of perishable crops in the labor intensive areas. Figure 5-2 compares the rate of technological change at observed prices and observed fixed inputs to the rate of technological change at constant prices and constant quantities. Both rates of technological change were significantly different than 0 at better than 0.01%, except in 1996 where their significance levels were less than 5%, and from 1997 to 1999 when their significance levels were larger than 80%. The rate of technological change at observed prices and observed fixed inputs declined from 17% to 0.08% from 1960 to1999, and the rate of technological change at constant prices and constant fixed inputs declined from 19% to 0.03% from 1960 to1999. The rate of

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81 technological change is defined as the rate of growth of profit. This means that while the technology was progressing (shifts of IPPF outward) at very high rates throughout the early years of the sample period, the rate significantly declined throughout the period. If prices and fixed inputs were held constant at their 1998 levels, the rate of technological progress would have been slightly higher in the beginning of the time period. Florida Own-Price Elasticity The own-price elasticities of both outputs were positive, and those of inputs were negative as expected at all observations. Table 5-4 summarizes the own-price elasticities of output supply and variable input demand and the inverse fixed input demand for selected years. The correct signs of the elasticities indicated that they were consistent with economic theory. The elasticities of land and for both types of labor were elastic, but those of the rest of inputs and outputs were inelastic. Florida Morishima Elasticity of Substitution The estimates of MESs among inputs at each observation in Florida are presented in Figures 5-3 to 5-5. Point estimation allows tracing the change over time. As defined in Eq. 4.21, the MES is not symmetric. A positive MES means that the 2 inputs are substitutes, and a negative MES means that they are complements. Figure 5-3 shows the MESs among variable inputs. The MESs among variable inputs were positive, except for the elasticity between self-employed labor and materials when material price changed. After 1986, the MES between materials and chemicals when chemical price changed and the MES between self-employed labor and chemicals when chemical price changed became negative, but only lasted for a few years. The elasticity between hired labor and self-employed labor, when returns to self-employed labor changed, was less elastic than the elasticity between these 2 types of labor when hired labor wages changed. This

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82 suggested that although hired and self-employed labor were substitutes, an increase in wages of hired labor created a larger incentive for self-employed producers to work longer hours than to hire more workers when returns to self-employed labor increased. Figure 5-4 illustrates the MESs among variable inputs and fixed inputs when fixed input prices change. Variable inputs and fixed inputs were substitutes when fixed input prices change throughout most of the period. However, the MESs were negative during the mid to late 1980s for chemicals and land when land price changed; self-employed labor and land when land price changed; and capital and hired labor when capital price changed. The substitution between self-employed labor and capital were more elastic than between hired labor and capital when capital price changed. Figure 5-5 shows the MESs among fixed inputs and variable inputs when variable input prices change, and among fixed inputs. The MESs were positive for all pairs of fixed inputs and variable inputs when variable input prices changed, and among fixed inputs, except for the MES between land and chemicals when chemicals price changed, and the MES between capital and chemicals when chemicals price changed in 1987 and 1988. The passage of IRCA in 1986 made MESs slightly more elastic for capital and labor when labor became more expensive; and between land and labor when labor was more expensive. However, the elasticities between land and chemicals when chemicals price changed, and between capital and chemicals when chemicals price changed, decline and became negative after IRCA, but only for 2 years. As we see from Figure 5-3 to 5-5, some of the MESs were highly variable over time. Table 5-5 summarizes the average MESs before and after the passage of IRCA. The test of differences in MESs between 2 periods is computationally problematic since

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83 the elasticities are obtained through a solution of matrix equations (Eq. 4.27), including the inverse of a matrix consisting of functions of the parameter estimates. As shown in Appendix B, the MESs are directly dependent on parameters that do not change throughout the sample period, and the expected profit shares which do change. The sources of changes in the expected profit shares are the parameters associated with the time dummy variable reflecting IRCA ( it2 and jt2 ), and changes in the observed values of the prices and fixed inputs. Holding the prices and fixed inputs constant, the joint test of the it2 and jt2 shift parameters is indicative of a significant difference in the MESs. The 2 (8) statistic of this test is 19.96, which means that the time dummy variables are statistically different than 0 at the 5% significance level. Although we cannot directly say that the differences in MESs reported in Table 5-5 are statistically significant, we can say that if prices and fixed inputs were to remain constant, changes in MESs would be a result of changes occurring under the period when IRCA was in force. The results reveal that hired labor and self-employed labor were substitutes in both periods. The MESs between the 2 types of labor increased after IRCA. As values of a type of labor changed, the increase of another type of labor became easier following IRCA. For instance, if hired workers became more expensive, self-employed labor would increase in efficiency units, either through increased quality, or through more hours, than before the passage of IRCA, and vice versa. Similarly, both types of labor and capital were substitutes for capital in both periods. The only MESs that switched signs are between self-employed labor and land, and between chemicals and land when land price changed. Self-employed labor and chemicals were substitutes for land when land price changed before IRCA. However, after IRCA, if land became more expensive,

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84 the use of chemicals would decrease and producers would work fewer hours. The passage of IRCA did not change the substitutability between labor and capital and between the 2 types of labor; however, the technological progress required less chemicals and self-employed labor when agricultural land area became more scarce. An example of a possible technological change is dripping pesticide and fertilizer applications. This technology allows the minimal use of chemicals while conserving the environment, and perhaps requiring less labor. As this technology was adopted, it increased land productivity without necessarily increasing the use of chemicals even when land price was increasing. The U.S. Results The preliminary U.S. estimates before imposing the curvature property are presented in Table 5-6. The Cholesky values of the Allen elasticity matrices were calculated at each observation, and it was found that all Cholesky values of the Hessian with respect to fixed inputs had the correct sign; however, at least 1 Cholesky value of the Hessian with respect to variable inputs and outputs was negative at all observations. The most negative Cholesky value was found in 1983, -163.53. The convexity property of the estimated profit function was therefore violated, whereas concavity was not. To check and impose convexity, the right hand side variables were normalized to 1 in 1983 and the time variable was normalized to 0 for the same year. The significance of the convexity violation was evaluated using Laus Cholesky decomposition to estimate the Cholesky values using data for all observations. The matrix in Eq. 5.2 shows the Cholesky values of the variable inputs and outputs with their estimated standard errors in parentheses.

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85 (0.339)(0.110)(0.196)(0.133)(0.058)(1.201)0.1900-0000000.06050000000.2007-0000000.1560-0000000.0837000000*2.4394-DIUS 5.2 There is one Cholesky value (-2.439) that was significantly negative at the 5% significance level, implying that the convexity property of the estimated U.S. profit function was significantly violated. Although it was undesirable to force the profit function to satisfy the convexity property when the data did not support it, convexity was imposed to maintain consistency with economic theory. Convexity was imposed using the Wiley-Schmidt-Bramble reparameterization technique. The original parameters were calculated and reported in Table 5-7. The curvature properties were once again evaluated by calculating the Cholesky values at each observation. After the convexity restriction was imposed, the Cholesky values remained negative at all observations, except in 1983 (the normalized year), when the Cholesky was negative, but close to 0 at -0.00006. Imposing local convexity property only guaranteed that it was satisfied at the point where convexity was imposed. As a result, the subsequent interpretations must be evaluated as tentative given the unsatisfactory curvature properties for the profit function for years other than the normalized year. U.S. Rate of Technological Change and Biased Technological Change Figures 5-6 to 5-8 illustrate the rate and bias of technological change in the U.S. over time. The detailed estimates are also presented in Appendix D. The rates of

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86 technological change and biased technological change were calculated from the estimates in Table 5-7. The estimates of biased technical change were significant at the 5% significance level for all variables at all observations, except for the biases of hired labor and chemicals after 1986 that were insignificant at larger than the 20% significance level. A graphical illustration of biased technological change is presented in Figure 5-6 and Figure 5-7. Except for capital, technological change was biased against all outputs and inputs prior to 1986. An explanation of biases against all outputs and variable inputs is the same as above in the Florida results. After 1986, the technology became perishable crops-producing, less self-employed labor-saving, and more land-saving. Although insignificant, the technology was less hired labor-saving and less chemical-saving, and the biases against other outputs increased after 1986. After 1986, the technology was dramatically biased against materials until 1991 when it became materials-using. Table 5-8 reports the average of U.S. biases before and after the passage of IRCA, and the differences between them. The technology was significantly biased against all outputs and inputs, except capital, before IRCA. After IRCA, the technology became significantly less hired and self-employed labor-saving; however, the use of capital was not significantly different. The technology became significantly more perishable crops-producing, but became significantly more other outputs-reducing. The technological bias shifted significantly in the direction of chemicals-using while there was no significant difference in the bias toward materials or land. Unlike Florida, the passage of IRCA coincided with a significant shift in technological bias toward employing more hired labor. Although the direction of bias toward land and capital did not change, it was significantly land-saving and capital-using in both periods.

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87 IRCA coincided not only with U.S. producers failing to shift to a more labor-saving technology, but rather with a shift toward more labor-using technology at the same time that the presence of illegal foreign workers was increasing (Mehta et al. 2000). In addition, the change in the adoption of mechanized technology was insignificant in the post-IRCA period as compared to pre-IRCA. However, the passage of IRCA coincided with greater profitability in the production of perishable crops and reduced profitability in the production of the other outputs category at the U.S. level. The production of perishable crops increasingly involved the employment of foreign workers (Mehta et al. 2000), and the bias in favor of these commodities suggested that producers adopted technologies favoring both perishable commodities and more hired labor. As the technology became more perishable crops-producing and more other outputs-reducing with IRCA, the technology became significantly more chemicals-using. The agricultural land-saving characteristic of technology did not significantly change with IRCA. Rates of technological change were estimated both at observed prices and fixed input quantities, and at constant prices and fixed input quantities. The rate of technological change at observed prices and fixed input quantities was significantly different than 0 at 5% significance level from 1960 to 1994; from 1995 to 1999 they were insignificant at greater than the 30% level. The rate of technological change at constant prices and fixed input quantities was significant at the 0.01% level from 1960 to 1990. It became significant at the 5% level for the remaining years, except for 1992 to 1994 when it was insignificant. Figure 5-8 shows that the rate of technological change at observed prices and observed fixed inputs declined from 16% to -0.9%. The rate of technological

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88 change at constant prices and constant fixed inputs declined from 21% to -7.8%; however, it declined more rapidly after 1986, with the implementation of IRCA. U.S. Own-Price Elasticity Price elasticities of output supply, variable input demand, and inverse fixed input demand in the U.S. are presented in Table 5-9 for selected years. Input demand elasticities were negative for all inputs at all observations, except for materials from 1986 to 1990. Hired labor demand was elastic throughout the sample period. Price elasticities of perishable crops were positive as expected, but those of other outputs became negative after 1986. The elasticity of other outputs declined from being positively elastic to negatively elastic throughout the period. The price elasticities of the other variables were relatively stable. U.S. Morishima Elasticity of Substitution Point estimates of MESs in the U.S. are summarized in Figures 5-9 to Figure 5-11. The MESs between variable inputs in U.S. agriculture are illustrated in Figure 5-9. Before 1986, they were relatively stable around 0, except for 1961, 1975, and 1979; all pairs of variable inputs were substitutes, except for chemicals and materials with changes in materials price. After 1986 and until the mid-1990s, they were highly variable. The MESs between hired labor and self-employed labor were positive at almost all observations, and did not change the trend after 1986. This means that hired and self-employed labor were substitutes. After 1986, hired labor, self-employed labor, and materials were complements for chemicals when chemicals price changed. Figure 5-10 depicts the MESs between variable inputs and fixed inputs when fixed input prices change. Before 1986, variable inputs and fixed inputs were substitutes when fixed input prices changed, and the MESs among them were relatively stable (except in

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89 1961 and 1975). The results implied that all variable inputs were substitutable with fixed inputs prior to the passage of IRCA. After 1986 (except for 1989 to 1991), MESs were negative between hired labor and capital when capital price changed; between self-employed labor and capital when capital price changed; between materials and capital when capital price changed; and between land and chemicals when land price changed. Figure 5-11 illustrates the MESs between fixed inputs and variable inputs when the variable input prices changed, and between fixed inputs. Except for the MES between land and capital (when capital price changed) that remained negative throughout the period, all other MESs were positive before 1986 (except in 1965, 1975, and 1979). After 1986 (except during 1989 to 1991), MESs between land and chemicals when chemicals price changed; between capital and self-employed labor when returns to self-employed labor changed; and between capital and land when land price changed, were negative. Capital was substituted for labor before 1986 with increases in the hired wage rate. After 1986, capital was a complement to labor with increases in the hired wage rate, but capital and hired labor again became substitutes with increases in the hired labor wage rate after the mid-1990s. The average MESs are calculated for the preand post-IRCA periods and summarized in Table 5-10. We can see that some of the MESs are dramatically different between the 2 periods. This is because of high volatility during the mid-1980s to the mid-1990s, and in 1961, 1975, and 1979. Although additional work can be done to separate these effects, the comparison of averages between 2 periods will give some idea of the changes. Similarly to Florida, the differences of MESs between the 2 periods are implicitly tested by jointly testing the shift parameters (parameters of the time dummy

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90 variables in the profit share equations). The 2 (8) statistic of the test is 46.73. This means that the shift parameters are jointly significantly different than 0 at the 1% significance level. This implies that the differences in the MESs are significantly different in the pre-IRCA and the IRCA periods. Similarly to the Florida results, the MESs between hired labor and self-employed labor are positive, suggesting that they are substitutes. Capital and both types of labor are also substitutes in both periods. The results show that the substitutability of self-employed labor for hired labor when hired wages changed became easier after IRCA. By contrast, the substitutability of hired labor for self-employed labor when returns to self-employed labor changed decreased. The MES between capital and hired labor was greater than MES between capital and self-employed labor when the respective prices of labor changed in both periods. Following the passage of IRCA, the adoption of mechanized technology was even more sensitive to changes in the value of labor, particularly to hired labor wages. This could imply that the passage of IRCA and implementation of new regulations resulted in considerable uncertainty about hiring in a labor market acknowledged to have large numbers of illegal workers. With an increase in the hired labor wage, the impact of on the ease of adoption of farm mechanization would be greater following IRCA than before IRCA. Hired labor was also more sensitive to the change of capital price than self-employed labor. After IRCA, the ease of substitution of hired labor for capital increased while the ease of substitution of self-employed labor for capital decreased with capital price changes. If mechanized technology became less expensive, the adoption of mechanized technology would reduce the employment of hired labor more than the work of self-employed labor. After IRCA, producers may have found mechanization more

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91 appealing than to risk a different set of potential hiring and employment difficulties with illegal workers. If the new mechanized technology became simultaneously readily available and less expensive, the adoption of mechanized technology would greatly decrease the need for labor, presumably including illegal labor, more than before the passage of IRCA, while the need for self-employed labor would decrease less than before the passage of IRCA. Land and chemicals were also found to be substitutes in both periods. After IRCA, the substitution between land and chemicals became more elastic. This implies that if land price rose, the application of chemicals increased more than before the passage of IRCA, and vice versa. Unlike in Florida after the passage of IRCA, as U.S. agricultural land became more scarce, an increasing price of land would create greater use of chemicals. This difference could result from the U.S. being relatively more agricultural land abundant than Florida. Following IRCA, there was increased ease of technology adoption to save land and the use of chemicals with an increase in land price in less land-intensive areas such as Florida, but the same technology was not adopted in land-abundant areas.

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92 Table 5-1. Florida estimates with homogeneity and symmetry constraints. Parameter Estimate Parameter Estimate Parameter Estimate 0 14.6744* (0.0673) hlc -0.2184* (0.0307) pt1 -0.0143* (0.0032) oout 0.9061* (0.0365) hlm -0.3680* (0.0640) pt2 0.0179* (0.0063) persh 1.6899* (0.0365) slsl 0.0653 (0.0817) hlt1 0.0120* (0.0020) hired -0.5267* (0.0258) slc 0.0269 (0.0265) hlt2 -0.0071* (0.0029) self -0.1815* (0.0120) slm 0.1225* (0.0544) slt1 0.0069* (0.0014) chem -0.2814* (0.0107) cc -0.0821* (0.0237) slt2 -0.0071* (0.0019) matl -0.6065* (0.0263) cm -0.0463 (0.0384) ct1 0.0043* (0.0011) land 0.3599* (0.0378) mm -0.3969* (0.1077) ct2 -0.0054* (0.0016) capital 0.6401* (0.0378) ol -0.0429 (0.0734) mt1 0.0117* (0.0026) oo 0.1772 (0.1336) pl 0.1159 (0.0740) mt2 -0.0124* (0.0044) op -0.9880* (0.0713) hll 0.0544 (0.0610) ll -0.3051* (0.0878) ohl 0.3533* (0.0558) sll -0.1233* (0.0333) lk 0.3051* (0.0878) osl 0.0841 (0.0589) cl -0.1028* (0.0242) kl 0.3051* (0.0878) oc 0.0686 (0.0407) ml 0.0988 (0.0550) kk -0.3051* (0.0878) om 0.3049* (0.0990) ok 0.0429 (0.0734) lt1 -0.0002 (0.0033) pp -0.2051 (0.1228) pk -0.1159 (0.0740) lt2 0.0011 (0.0068) phl 0.4688* (0.0516) hlk -0.0544 (0.0610) kt1 0.0002 (0.0033) psl 0.0891* (0.0352) slk 0.1233* (0.0333) kt2 -0.0011 (0.0068) pc 0.2513* (0.0290) ck 0.1028* (0.0242) t 0.0383* (0.0068) pm 0.3838* (0.0764) mk -0.0988 (0.0550) t2 -0.0148 (0.0113) hlhl 0.1523 (0.1405) ot1 -0.0206* (0.0035) tt -0.0044* (0.0004) hlsl -0.3880* (0.1006) ot2 0.0140* (0.0042) tt2 -0.0007 (0.0024) Note: Estimated standard errors are in parentheses. o=other outputs, p=perishable crops, hl=hired labor, sl=self-employed labor, c=chemicals, m=materials, l=land, k=capital. Significant at the 0.05 level.

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93 Table 5-2. Florida estimates with homogeneity, symmetry, and convexity constraints. Parameter Estimate Parameter Estimate Parameter Estimate 0 14.9548* (0.0709) hlc -0.2270* (0.0300) pt1 -0.0129* (0.0033) oout 0.7824* (0.0387) hlm -0.3627* (0.0643) pt2 0.0152* (0.0055) persh 1.5541* (0.0407) slsl 0.0933 (0.0735) hlt1 0.0113* (0.0021) hired -0.4307* (0.0272) slc 0.0155 (0.0250) hlt2 -0.0060* (0.0025) self -0.1364* (0.0109) slm 0.1659* (0.0449) slt1 0.0059* (0.0009) chem -0.2372* (0.0113) cc -0.0805* (0.0230) slt2 -0.0065* (0.0017) matl -0.5321* (0.0290) cm -0.0323 (0.0376) ct1 0.0035* (0.0011) land 0.3829* (0.0465) mm -0.4065* (0.0744) ct2 -0.0043* (0.0013) capital 0.6171* (0.0465) ol -0.0140 (0.0723) mt1 0.0097* (0.0027) oo 0.2792* (0.0613) pl 0.1440* (0.0736) mt2 0.0144* (0.0048) op -0.9916* (0.0703) hll 0.0567 (0.0627) ll -0.3022* (0.0893) ohl 0.3463* (0.0553) sll -0.1386* (0.0330) lk 0.3022* (0.0893) osl 0.0461 (0.0339) cl -0.1075* (0.0239) kl 0.3022* (0.0893) oc 0.0682 (0.0378) ml 0.0594 (0.0556) kk -0.3022* (0.0893) om 0.2519* (0.0642) ok 0.0140 (0.0723) lt1 0.0007 (0.0034) pp -0.2016 (0.1245) pk -0.1440* (0.0736) lt2 0.0023 (0.0060) phl 0.4601* (0.0528) hlk -0.0567 0.0627 kt1 -0.0007 (0.0034) psl 0.0932* (0.0352) slk 0.1386* (0.0330) kt2 -0.0023 (0.0060) pc 0.2561* (0.0288) ck 0.1075* (0.0239) t 0.0236* (0.0068) pm 0.3838* (0.0762) mk -0.0594 (0.0556) t2 -0.0165 (0.0133) hlhl 0.1973 (0.1416) ot1 -0.0175* (0.0029) tt -0.0044* (0.0004) hlsl -0.4140* (0.1010) ot2 -0.0128* (0.0036) tt2 -0.0024 (0.0024) Note: Estimated standard errors are in parentheses; convexity imposed in 1998. o=other outputs, p=perishable crops, hl=hired labor, sl=self-employed labor, c=chemicals, m=materials, l=land, k=capital. Significant at the 0.05 level.

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94 Table 5-3. Florida biased technological change calculated at the means. Pre-IRCA Post-IRCA Difference Other Outputs -0.0173* (0.0024) -0.0341* (0.0039) -0.0168* (0.0030) Persh Crops -0.0089* (0.0020) 0.0016 (0.0052) 0.0105* (0.0039) Hired Labor -0.0260* (0.0035) -0.0138 (0.0099) 0.0122 (0.0074) Self-employed -0.0342* (0.0034) 0.0052 (0.0181) 0.0394* (0.0161) Chemicals -0.0160* (0.0037) 0.0035 (0.0094) 0.0195* (0.0069) Materials -0.0153* (0.0034) -0.0379* (0.0065) -0.0225* (0.0059) Land 0.0018 (0.0092) 0.0075 (0.0200) 0.0057 (0.0152) Capital -0.0011 (0.0055) -0.0050 (0.01314) -0.0039 (0.0100) Note: Estimated standard errors are in parentheses. significant at 0.05 level. Table 5-4. Florida own-price elasticity and inverse price elasticity. 1960 1970 1980 1987 1998* Other Outputs 0.2884 0.3398 0.2458 0.2326 0.1392 Perish Crop 0.2148 0.2677 0.3531 0.0838 0.4244 Hired Labor -1.8973 -1.8883 -1.8886 -2.0371 -1.8887 Self-employed -1.6794 -1.6972 -1.7463 -2.1786 -1.8203 Chemicals -0.8529 -0.8827 -0.8138 -0.5499 -0.8980 Materials -0.8785 -0.9953 -1.0146 -1.1299 -0.7681 Land -2.0361 -1.5132 -1.1346 -1.2255 -1.4064 Capital -0.6335 -0.8150 -1.0751 -0.9963 -0.8726 Normalized year

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95 Table 5-5. Florida average Morhishima elasticity of substitution. Pre-IRCA Post-IRCA MEShlsl 2.6867 3.2241 MEShlc 1.7065 1.0805 MEShlm 0.9742 0.9981 MESslhl 4.2290 5.5092 MESslc 1.0441 0.1358 MESslm -0.4193 -0.9324 MESchl 2.8108 2.7913 MEScsl 1.6221 1.8495 MEScm 0.4551 0.4445 MESmhl 2.2169 2.2881 MESmsl 1.5234 1.8712 MESmc 1.2236 0.6231 MEShll 0.4624 0.2950 MEShlk 0.2956 0.1379 MESsll 0.2175 -0.0522 MESslk 1.0542 1.0753 MEScl 0.6754 -0.0583 MESck 0.5621 0.7086 MESml 0.6469 0.4660 MESmk 0.5147 0.4873 MESlhl 1.8694 1.9718 MESlsl 1.6428 2.0206 MESlc 1.3093 0.5030 MESlm 0.7503 0.7452 MESkhl 1.7862 1.8262 MESksl 1.9344 2.2591 MESkc 1.2763 0.7263 MESkm 0.5592 0.5686 MESlk 0.5537 0.4951 MESkl 0.5694 0.3555

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96 Table 5-6. U.S. estimates with homogeneity and symmetry constraints. Parameter Estimate Parameter Estimate Parameter Estimate 0 11.083* (0.0605) hlc -0.0978* (0.0234) pt1 -0.0040 (0.0036) oout 3.1440* (0.1208) hlm -0.4611* (0.0987) pt2 0.0099* (0.0033) persh 0.5860* (0.0195) slsl -1.0149* (0.1353) hlt1 0.0152* (0.0026) hired -0.3128* (0.0145) slc -0.1551* (0.0345) hlt2 -0.0088* (0.0024) self -0.6186* (0.0293) slm -0.4750* (0.1681) slt1 0.0489* (0.0052) chem -0.3052* (0.0126) cc -0.1428* (0.0299) slt2 -0.0129* (0.0049) matl -1.4934* (0.0873) cm -0.2830* (0.0958) ct1 0.0102* (0.0024) land 0.5849* (0.0366) mm -3.8984* (0.5311) ct2 -0.0078* (0.0022) capital 0.4151* (0.0366) ol -1.6553* (0.3384) mt1 0.0843* (0.0138) oo -6.5753* (0.8974) pl 0.0090 (0.0611) mt2 -0.0338* (0.0136) op -0.9277* (0.1668) hll 0.0305 (0.0451) ll -0.8587* (0.1539) ohl 0.7924* (0.1212) sll -0.0159 (0.0900) lk 0.8587* (0.1539) osl 1.4956* (0.2314) cl 0.2489* (0.0402) kl 0.8587* (0.1539) oc 0.5337* (0.1142) ml 1.3828* (0.2450) kk -0.8587* (0.1539) om 4.6813* (0.6614) ok 1.6553* (0.3384) lt1 -0.0125 (0.0073) pp 0.2308* (0.0607) pk -0.0090 (0.0611) lt2 0.0091 (0.0071) phl 0.0227 (0.0419) hlk -0.0305 (0.0451) kt1 0.0120 (0.0073) psl 0.0931 (0.0501) slk 0.0159 (0.0900) kt2 -0.0091 (0.0071) pc 0.1449* (0.0315) ck -0.2489* (0.0402) t 0.0894* (0.0068) pm 0.4362* (0.1395) mk -1.3828* (0.2450) t2 -0.0327 (0.0195) hlhl -0.3128* (0.1476) ot1 -0.1545* (0.0194) tt -0.0049* (0.0006) hlsl 0.0565 (0.1333) ot2 0.0533* (0.0192) tt2 -0.0035 (0.0039) Note: Estimated standard errors are in parentheses. o=other outputs, p=perishable crops, hl=hired labor, sl=self-employed labor, c=chemicals, m=materials, l=land, k=capital. Significant at the 0.05 level.

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97 Table 5-7. U.S. estimates with homogeneity, symmetry, and convexity constraints. Parameter Estimate Parameter Estimate Parameter Estimate 0 10.8014* (0.0335) hlc -0.0823* (0.0227) pt1 -0.0130* (0.0017) oout 2.9035* (0.0676) hlm -0.4311* (0.0573) pt2 0.0200* (0.0040) persh 0.2969* (0.0107) slsl -0.4318* (0.0849) hlt1 0.0187* (0.0014) hired -0.1732* (0.0085) slc -0.1048* (0.0257) hlt2 -0.0154* (0.0031) self -0.3610* (0.0182) slm -0.4249* (0.0687) slt1 0.0453* (0.0025) chem -0.2163* (0.0085) cc -0.1204* (0.0283) slt2 -0.0254* (0.0065) matl -1.4499* (0.0495) cm -0.3028* (0.0746) ct1 0.0153* (0.0015) land 0.6213* (0.0345) mm -3.3660* (0.2358) ct2 -0.0153* (0.0029) capital 0.3787* (0.0345) ol -2.4437* (0.3145) mt1 0.1042* (0.0064) oo -5.2432* (0.3361) pl -0.2692* (0.0745) mt2 0.1379* (0.0279) op -0.9694* (0.0619) hll 0.1951* (0.0552) ll -0.6090* (0.2563) ohl 0.6966* (0.0607) sll 0.1151 (0.1005) lk 0.6090* (0.2563) osl 0.9922* (0.0876) cl 0.4519* (0.0522) kl 0.6090* (0.2563) oc 0.4794* (0.0725) ml 1.9507* (0.2701) kk -0.6090* (0.2563) om 4.0442* (0.2580) ok 2.4437* (0.3145) lt1 -0.0223* (0.0078) pp 0.2510* (0.0260) pk 0.2692* (0.0745) lt2 -0.0180 (0.0126) phl -0.0127 (0.0382) hlk -0.1951* (0.0552) kt1 0.0223* (0.0078) psl 0.1193* (0.0290) slk -0.1151 (0.1005) kt2 0.0180 (0.0126) pc 0.1309* (0.0263) ck -0.4519* (0.0522) t 0.0924* (0.0057) pm 0.4809* (0.0560) mk -1.9507* (0.2701) t2 0.0208* (0.0052) hlhl -0.0205 (0.1116) ot1 -0.1705* (0.0080) tt -0.0053* (0.0007) hlsl -0.1500 (0.0915) ot2 -0.1017* (0.0213) tt2 -0.0067* (0.0022) Note: Estimated standard errors are in parentheses; convexity imposed in 1983. o=other outputs, p=perishable crops, hl=hired labor, sl=self-employed labor, c=chemicals, m=materials, l=land, k=capital. Significant at the 0.05 level.

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98 Table 5-8. U.S. biased technological change calculated at the means. Pre-IRCA Post-IRCA Difference Other Outputs -0.0466* (0.0019) -0.2436* (0.1006) -0.1970* (0.0988) Persh Crops -0.0362* (0.0044) 0.0128* (0.0051) 0.0490* (0.0086) Hired Labor -0.0659* (0.0042) -0.0113 (0.0101) 0.0547* (0.0125) Self-employed -0.0628* (0.0031) -0.0337* (0.0109) 0.0291* (0.0129) Chemicals -0.0662* (0.0055) -0.0000 (0.0095) 0.0661* (0.0123) Materials -0.0584* (0.0033) 0.4999 (0.3260) 0.5583 (0.3231) Land -0.0426* (0.0147) -0.0688* (0.0184) -0.0262 (0.0230) Capital 0.0466* (0.0168) 0.0969* (0.0239) 0.0503 (0.0290) Note: Estimated standard errors are in parentheses. significant at 0.05 level. Table 5-9. U.S. own-price elasticity and inverse price elasticity. 1960 1970 1983* 1987 1999 Other Outputs 2.0037 1.4601 0.0977 -1.9283 -14.8275 Perish Crops 0.0517 0.0911 0.1422 0.0321 0.0557 Hired Labor -1.3122 -1.2296 -1.0546 -1.0982 -1.3100 Self-employed -1.5728 -1.3360 -0.1649 -0.4590 -1.0762 Chemicals -0.5845 -0.7132 -0.6597 -0.5265 -0.9473 Materials -1.3871 -0.8936 -0.1283 6.1984 -2.2283 Land -2.4932 -2.2333 -1.3589 -1.9088 -1.3299 Capital -1.2470 -1.3570 -2.2295 -1.5531 -2.2905 *Normalized year

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99 Table 5-10. U.S. average Morishima elasticity of substitution. Pre-IRCA Post-IRCA MEShlsl 1.1864 0.0945 MEShlc 1.7332 4.5103 MEShlm 0.9196 32.4579 MESslhl 1.4237 1.8077 MESslc 1.7718 3.6345 MESslm 0.9735 31.5179 MESchl 2.1919 4.3232 MEScsl 1.1166 3.7097 MEScm -0.3587 25.2069 MESmhl 1.2903 17.9664 MESmsl 0.8532 19.8773 MESmc 1.4537 -16.3489 MEShll 1.1736 0.2944 MEShlk 0.1593 0.5028 MESsll 0.7292 0.8402 MESslk 0.2739 0.0597 MEScl 1.6660 4.8223 MESck 0.5562 -0.2021 MESml 1.3001 22.0507 MESmk 0.2747 -5.6854 MESlhl 1.4522 1.6115 MESlsl 0.2884 0.2624 MESlc 1.8532 3.8601 MESlm 1.6747 32.2925 MESkhl 1.2286 2.7393 MESksl 0.8045 1.5934 MESkc 1.6385 2.7073 MESkm 0.7560 28.9412 MESlk -0.0965 -0.1665 MESkl 0.7445 1.8788

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100 -0.06-0.05-0.04-0.03-0.02-0.0100.010.0219601962196419661968197019721974197619781980198219841986198819901992199419961998YearBiased Technological Change Other outputs bias Perish crops bias Hired labor bias Self-employed bias Chem bias Matl bias Land bias Capital bias Figure 5-1. Florida biased technological change. 00.050.10.150.20.2519601962196419661968197019721974197619781980198219841986198819901992199419961998YearRate of Technological Change mu at constant prices and constant fixed inputs Figure 5-2. Florida rate of technological change.

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101 -4-2024681019601962196419661968197019721974197619781980198219841986198819901992199419961998YearMES MEShlsl MEShlc MEShlm MESslhl MESslc MESslm MESchl MEScsl MEScm MESmhl MESmsl MESmc Figure 5-3. Florida Morishima elasticity of substitution between variable inputs. Note: hl=hired labor, sl=self-employed labor, c=chemicals, m=materials.

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102 -3-2-101234519601962196419661968197019721974197619781980198219841986198819901992199419961998YearMES MEShll MEShlk MESsll MESslk MEScl MESck MESml MESmk Figure 5-4. Florida Morishima elasticity of substitution between variable input and fixed input (fixed input price changes). Note: hl=hired labor, sl=self-employed labor, c=chemicals, m=materials, l=land, k=capital.

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103 -2-10123456719601962196419661968197019721974197619781980198219841986198819901992199419961998YearMES MESlhl MESlsl MESlc MESlm MESkhl MESksl MESkc MESkm MESlk MESkl Figure 5-5. Florida Morishima elasticity between fixed input and variable input (variable input price changes), and between fixed inputs. Note: hl=hired labor, sl=self-employed labor, c=chemicals, m=materials, l=land, k=capital.

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104 -0.15-0.1-0.0500.050.10.150.20.250.30.3519601962196419661968197019721974197619781980198219841986198819901992199419961998YearBiased Technological Change Perish crops bias Hired labor bias Self-employed bias Chem bias Land bias Capital bias Figure 5-6. U.S. biased technological change. -6-4-2024619601962196419661968197019721974197619781980198219841986198819901992199419961998YearBiased Technological Change Other outputs bias Matl bias Figure 5-7. U.S. biased technological change, other outputs and materials.

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105 -0.1-0.0500.050.10.150.20.2519601962196419661968197019721974197619781980198219841986198819901992199419961998YearRate of Technological Change mu at constant prices and constant fixed inputs Figure 5-8. U.S. rate of technological change.

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106 -100-80-60-40-2002040608010019601962196419661968197019721974197619781980198219841986198819911993199519971999YearMES MEShlsl MEShlc MEShlm MESslhl MESslc MESslm MESchl MEScsl MEScm MESmhl MESmsl MESmc Figure 5-9. U.S. Morishima elasticity of substitution between variable inputs. Results in 1990 are excluded due to scaling. Note: hl=hired labor, sl=self-employed labor, c=chemicals, m=materials.

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107 -20-100102030401960196219641966196819701972197419761978198019821984198619881992199419961998YearMES MEShll MEShlk MESsll MESslk MEScl MESc k MESml MESm k Figure 5-10. U.S. Morishima elasticity of substitution between variable input and fixed input (fixed input price changes). Results in 1990 and 1991 are excluded due to scaling. Note: hl=hired labor, sl=self-employed labor, c=chemicals, m=materials, l=land, k=capital.

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108 -30-20-1001020304050601960196219641966196819701972197419761978198019821984198619881992199419961998YearMES MESlhl MESlsl MESlc MESlm MESkhl MESksl MESkc MESkm MESlk MESkl Figure 5-11. U.S. Morishima elasticity between fixed input and variable input (variable input price changes), and between fixed inputs. Result in 1990 and 1991 are excluded due to scaling. Note: hl=hired labor, sl=self-employed labor, c=chemicals, m=materials, l=land, k=capital.

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CHAPTER 6 CONCLUSIONS, POLICY IMPLICATIONS, AND SUGGESTED FUTURE RESEARCH This chapter summarizes the essence of this study and draws conclusions from empirical findings. The results from the study in Florida and the U.S. provide implications for immigration and agricultural policy related to technological change that can be applied to other states and countries with similar issues in the labor market and socioeconomic characteristics. The development of the theoretical framework in the profit maximization model of induced innovation, and estimation techniques can be adopted in other applied production economics. Summary and Conclusions As international trade becomes increasingly important in the worlds economy, several developing countries are taking advantage of their inexpensive labor while developed countries rely on technological advancement to remain competitive. Agricultural industries in the U.S. still depend largely on inexpensive immigrant labor that not only creates welfare and social costs to the U.S. economy, but is also believed to slow the development of labor-saving technology. The issue of foreign workers in the agricultural sector is addressed in this study. The research provides suggestions that may be used for immigration and agricultural policies. In order to evaluate the influence of changes in the labor market on the innovation of labor-saving technology, particular economic variables are analyzed. Specific objectives include: (i) estimating the rates of technological change, (ii) estimating the biased technological change of outputs and inputs, and (iii) estimating the Morishima 109

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110 elasticity of substitution at each time period, and evaluating changes before and after the passage of IRCA. Theoretical Framework The profit maximization model of the induced innovation theory is developed by extending the concept from the original cost minimization model. In the profit maximization approach, the impact of changes in input prices on both outputs and inputs is taken into consideration unlike the cost minimization approach where output is exogenous. The rate of technological change, is defined as the rate of growth of profits over time. There is technological progress if the rate of technological change, is positive. The bias of technological change, B i is defined as the semielasticity of the supply of output (the demand for the variable input) with respect to time, less the rate of technological change. A technological change is output i-producing if B i is positive, and it is output i-reducing if B i is negative. Similarly, a technological change is variable input i-using if B i is positive, and it is variable input i-saving if B i is negative. The bias of technological change in fixed inputs, B j is defined as the semielasticity of the inverse fixed input demand with respect to time, less the rate of technological change. A technological change is fixed input j-using if B j is positive, and it is fixed input j-saving if B j is negative. Neutral technological change occurs when all B i = B j = 0. Empirical Framework A seemingly unrelated regression model of the system of the translog profit function and profit share equations is estimated using the full information maximum likelihood method. Due to singularity of the covariance matrix of disturbances, two profit share equations are dropped. The homogeneity, symmetry, and curvature restrictions are imposed. The remaining parameters of the deleted equations are

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111 calculated from the model restrictions. Laus Cholesky decomposition is first used to test the curvature property, and the Wiley-Schmidt-Bramble reparameterization technique is subsequently used to impose the curvature restrictions. Parameter estimates of the profit function are used to calculate the rate of technological change, the bias in technological change, and the Morishima elasticities of substitution. Data Data used in this study were provided by Eldon Ball, Economic Research Service, USDA. They include quality-adjusted price indices and implicit quantity indices of agricultural outputs and inputs. Quality adjusted data take into account changes in quality and characteristics so that they reflect constant efficiency and quality. In the absence of adjustments in the data for quality changes, changes in the nature of the inputs become confounded with quantity changes in the inputs and changes in technology. Two major outputs are defined: perishable crops and all other outputs; 4 variable inputs: hired labor (direct hired and contract labor), self-employed labor, chemicals, and materials; and 2 fixed inputs: land and capital. Empirical Findings The tests of parameter estimates from the model with homogeneity and symmetry restrictions using Laus Cholesky decomposition reveal violation of curvature properties at each observation. The violation is not statistically significant in the Florida model, but it is significant in the U.S. model. Curvature restrictions are imposed locally using the Wiley-Schmidt-Bramble reparameterization techniques in both models. After imposing the curvature restrictions, the curvature properties are satisfied only at the point of restriction in both U.S. and Florida.

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112 Florida Results The rate of technological change at observed prices and fixed inputs declined from 17% to 0.08% from 1960 to1999, and the rate of technological change at constant prices and fixed inputs declined from 19% to 0.03% from 1960 to1999. The technology in Florida was significantly biased against all outputs and inputs, except for land (only the biases of land and capital were insignificant), before IRCA. After IRCA, the technology was perishable crops-producing, but other outputs-reducing. It also used more hired and self-employed labor, but the use of capital remained no different after the passage of IRCA. The estimates of own-price demand elasticities of outputs were positive and those of inputs were negative as expected. Morishima elasticities of substitution showed that hired and self-employed labor were substitutes; labor (hired and self-employed) and capital were also substitutes both before and after IRCA. Chemicals and land were substitutes when chemical prices changed in both periods, but after IRCA they became complements when land prices changed. The U.S. Results From 1960 to 1999, the rate of technological change at observed prices and observed fixed inputs declined from 16% to -0.9%, and the rate of technological change at constant prices and constant fixed inputs declined from 21% to -7.8%; however, they were significant only up to 1992. The technology was significantly biased against all outputs and inputs, except for capital before IRCA. After IRCA, the technological progress produced more perishable crops and less other outputs. It also increased the use of both types of labor and chemicals while the use of materials, land, and capital were not significantly different after IRCA.

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113 Own-price demand elasticities of inputs were negative, except that of materials from 1986 to 1990. Own-price elasticities of outputs were positive as expected, except for the price elasticity of other outputs after 1986. The Morishima elasticity between hired labor and self-employed labor showed that they were substitutes in both periods. Both types of labor and capital also remained substitutes after IRCA. Land and chemicals were also substitutes in both periods, and the MESs between land and chemicals became even more elastic after IRCA. Concluding Remarks The estimation of a translog profit function using the full information maximum likelihood method provides efficient parameter estimates. However, the estimates are most useful when they are consistent with economic theory. The production theory states that a well-behaved profit function must satisfy homogeneity, symmetry, curvature, and monotonicity constraints. This study found that estimates of the profit model before and after imposing curvature constraints differ. As a result, the estimators from the model that satisfy the curvature property are preferred. The Wiley-Schmidt-Bramble repararameterization technique used in this study only guarantees the curvature property at the point of imposition. During 1960 to 1999, there was significant technological progress in U.S. and Florida agriculture. The rates of technological change at observed prices and quantities declined from about 17% to about 0% in both Florida and the U.S. The rate of technological change at constant prices and quantities in Florida was higher than the rate at the observed prices and quantities. The rate of technological change at constant prices and quantities declined from about 19% to 0% from 1960 to 1999, and it declined slightly faster after 1986. Before 1976, the rate of technological change at constant prices and

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114 quantities in the U.S. was higher than the rate at the observed prices and quantities. The rate of technological change at constant prices and quantities declined much more rapidly and became lower than the rate at observed prices and quantities after 1986. The directions of biased technological change were somewhat similar between Florida and the U.S. The technology was biased against both types of outputs before IRCA, but changed to produce more perishable crops and less other outputs after IRCA in both areas. The technology was also biased against both types of labor before IRCA, but increased the use of both types of labor after IRCA; however, the increasing use of hired labor was insignificant in Florida. The technology was capital-using in the U.S., and did not change after IRCA. The technology in Florida was capital-reducing, but was not significant in either period. The technology was also biased against chemicals in the pre-IRCA period, and significantly increased the use of it in both areas after IRCA. The own-price demand elasticities were negative for the inputs and positive for the outputs in both Florida and the U.S. as expected. Exceptions for the U.S. were the material elasticity from 1986 to 1990, and other output elasticity after 1986, which had the wrong signs. The substitutability among inputs measured by the Morishima elasticity of substitution was also similar between Florida and the U.S. Hired labor and self-employed labor were substitutes, and they were also substitutes for capital in Florida and the U.S. Land and chemicals were also substitutes before and after IRCA, but they became complements in Florida with changes in land prices. Contributions The theory of induced innovation has been adopted in a significant number of studies of technological change in U.S. agriculture. This study not only uses more recent data, but also uses data that have been carefully adjusted for quality changes. Very

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115 limited quality adjustment was done in the original Hayami and Ruttan (1970) work. Binswangers subsequent work (1974a, 1974b) introduced more extensive quality adjustments. However, the subsequent extensive work by Ball (1997, 1999, 2001) at ERS, USDA in developing quality adjusted input measures is a major advance, and utilized in the present research. This study develops a profit maximization framework of the induced innovation theory that has not previously been discussed in the literature. The cost minimization approach ignores the influence of factor prices on changes in the output mix. The profit maximization framework is more appropriate when analyzing technological change that can influence both input and output combinations. The study of induced innovation has not previously been applied to the relationship between farm labor and immigration issues on changes in technology, particularly farm mechanization, in the U.S. or at any state level. This study provides a comparison between the labor-intensive agricultural production state of Florida, and the more diverse labor intensity production for the U.S. as a whole. It also disaggregates labor into self-employed, and hired and contract labor to more fully understand the technology effects in both types of labor markets. Imposing the curvature property has been ignored in most studies assuming the translog functional form because of its difficulty. This study recognizes the importance of valid estimates that must be consistent with economic theory. As a result, the curvature property has been taken into account in the estimation. Most studies of technological change evaluate the ease of substitution by calculating the Allen substitution elasticity. As pointed out earlier, the Allen elasticity is

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116 not an appropriate measure of substitutability. The Morishima elasticity is used in the economic analysis of this study instead, and provides estimates with a standard economic interpretation of substitutability. The preceding contributions collectively provide defensible estimates of the extent of bias in technological change, but more importantly, they provide a strong basis for determining the implications for immigration, labor, and agricultural policies. Policy Implications The significant rate of technological progress, although declining, in the U.S. and Florida agriculture over 1960-1999 suggests that there remain opportunities for further development. Similarly to the developments in other sectors of the economy, technological advancement in agriculture allows the industry and country to remain competitive. It is apparent from earlier studies such as Hayami and Ruttan (1970) and Binswanger (1974a, 1974b), and confirmed in this study, that the direction of technological change is influenced by economic scarcity. Depending on policy objectives, different implications and suggestions for policy changes can be obtained from the empirical findings of this study. Recognizing that immigrant farm labor creates social and economic costs such as welfare benefits of unauthorized workers (Simcox et al. 1994) and may inhibit the advancement of mechanical technology, the following implications focus on the labor-saving technological change. In the U.S. where the supply of foreign workers may not have been as widely available over much of the sample period, the technology was biased toward the use of capital. Unlike the U.S., the technology was not significantly capital-using in Florida where the production was still labor intensive. Although the technology was biased against the use of both hired and self-employed labor in both Florida and the U.S., it

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117 became significantly more hired labor-using in the U.S. after the passage of IRCA, but did not change in Florida. This suggests that even if the passage of IRCA to reduce the number of unauthorized foreign workers made hiring legal foreign labor become more expensive, the incentives remained to use more labor, presumably much of it foreign, in the broader, less labor intensive U.S. production. The increasing use of hired labor could be the result of an increasing availability of inexpensive undocumented immigrant workers. In a more labor-intensive area, the availability of undocumented immigrants may not have changed as a result of IRCA. Correspondingly, there was no significant evidence of the adoption of new mechanized technology or decrease in the use of hired labor. Although the technology remained biased toward the use of capital in the U.S., IRCA did not have a significant impact on the adoption of mechanized technology in either area. The lack of incentive to adopt mechanized technology could be the result of the availability of inexpensive undocumented immigrant workers, not enough research investment from the private sector, and the lack of political interests to promote the development of a more affordable mechanized technology. The success of the mechanical tomato harvester after the end of the Bracero program tells us that when the financial and production risks associated with hiring foreign workers became considerable, the incentive was created to adopt mechanized technology that was already available, but unused. If the technology was not available or still economically unaffordable, foreign labor would still be an alternative solution. This suggests that a more stringent immigration policy may not reduce incentives to use foreign workers, particularly in the areas where undocumented immigrant labor

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118 becomes increasingly available. The policy promoting mechanical technological progress would also require the development of producer expectations that there would not be an increased flow of either immigrant workers or undocumented workers in the future. In order to see more adoption of farm mechanization, it is necessary that the technology is readily available when there is any change in immigration policy. For instance, in production where labor is the only necessary factor (e.g., hand harvesting of fresh market products), a more stringent immigration policy will not lead to more adoption of mechanized technology until the specialized technology is developed. This implies that the technological development in farm mechanization also requires coordinated support from both private and government sectors. If reducing the flow of immigrant workers in agriculture is the objective of immigration policy, this also needs other supportive policies in promoting the development of technology to replace immigrant workers. The impact of IRCA on the choice of output is similar in Florida and the U.S. The technology became perishable crops-producing and more other outputs-reducing in both areas. Following IRCA, the production of labor-intensive industries apparently became more attractive at the same time as the technology became more hired labor-using in the U.S. Thus, coinciding with IRCA was more profitable labor-intensive production that was hired labor-using. The guest worker programs associated with IRCA and other recent immigration proposals also have potential impacts on the rate of technological change. An increase in legal foreign workers (although temporary) would decrease the farm wage rate below what it would otherwise be. The (negative) estimates of this change in wage rate as a

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119 result of IRCA on the rate of technological change, hlt2 suggest that an increase in farm wage rate after the passage of IRCA slowed down the technological progress in both Florida and the U.S. Although the impact of guest workers on biases through the wage rate is unclear, the hlt2 estimates suggest that they may inhibit overall technological progress. Suggested Future Research The attempt has been made in this study to provide valid policy implications that come from estimates consistent with economic theory. The restrictions imposed on the translog profit function model assure that the results will satisfy properties of a well-behave function. The estimated model in this study satisfies homogeneity, symmetry, and local curvature properties, but there are other properties that can be pursued further. The monotonicity property of the profit function implies that the profit function is non-decreasing in output price and non-increasing in input prices. Although the monotonicity property can be verified by checking the sign of expected profit shares, I did not impose monotonicity restrictions in this model. Significant time and effort were devoted to locally impose the curvature property in this study. However, as the results reveal, it is only guaranteed at the point of restriction. Empirically imposing global curvature constraints is another subject for further research. Nevertheless, the loss of flexibility and necessity of any additional constraints should be taken into account before the imposition. Recognizing that there is no variable perfectly correlated with changes in technology, a time variable is used in this study. The time variable may capture effects other than technology or input and output prices influencing changes in profit or profit

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120 shares. Other studies (e.g., Huffman and Evenson, 1992) have used different variables such as research and development expenditures to capture the state of technology, but the technology index still merits further exploration. There has been increasing emphasis in economics on the institutional and socioeconomic factors that have impacts on changes in the economy. For the empirical study of induced innovation on biased technological change, the research that incorporates those factors is still lacking. Napasintuwong and Emerson (2003) quantify some socioeconomic and institutional variables in a cost function approach of the induced innovation model. The number of deportable aliens located was used to represent the number of illegal workers, serving as an indicator for immigration control. Future research may consider verifying socioeconomic variables that better represent the social and institutional characteristics and applying them in the profit maximization framework. The primary objective of this study was to evaluate the impact of changes in farm wages (due to changes in immigration policy) along with other factor prices on the rate and direction of technological progress. The IRCA of 1986 is the immigration policy of interest. After the passage of IRCA, although it is believed that the policy decreased the incentive for labor mobility across the border, it is still unclear how the policy actually influenced the supply of unauthorized workers. To evaluate the immigrant worker problem in the context of technological change, more than one immigration policy should be analyzed. Specifically, if changes in the immigrant labor market resulting from immigration policy changes can be identified, it will help in understanding the actual impacts of immigrant workers on technological progress. The desired rates and directions of biased technological change could be a more specific goal for policy design.

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121 Napasintuwong and Emerson (2002) simulated different biased technological change scenarios to provide the demand for labor at different rates of technological change, and to provide changes in wage and labor supply scenarios that influence technological progress. However, the simulation is hypothetical and does not suggest a specific immigration policy. Future research could determine institutional and political changes that would provide alternatives for technological progress.

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APPENDIX A PROOF OF PRICE ELASTICITY OF OUTPUT SUPPLY AND INPUT DEMAND Applying Hotellings Lemma, MN1,...,i ZQZlnlniiii A.1 MN 1,...,i ZQiii A.2 lnlnZ-lnlnQiii A.3 i 1-lnln1lnlnQiiiiiiZZ A.4 i 1-iiiiii A.5 where ii is the own-price elasticity of output supply or input demand ji j; i, lnln1lnlnQijjiijZZ A.6 i j; i, jijjiij A.7 where ij is the cross-price elasticity of output supply or input demand. In the case of variable inputs, while the prices are positive, their quantity and shares, j are negative. Thus, M1,...,j 0 WXjjj A.8 lnlnW-)ln(-)ln(-Xjj j A.9 122

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123 j 1-ln)(ln1ln)ln(-XjjjjjjWW A.10 j 1-iiiiii A.11 Similarly, i M;1,...,j i, jijjiij A.12

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APPENDIX B ELEMENTS IN MATRICES USED TO CALCULATE MORISHIMA ELASTICITY OF SUBSTITUTUTION N1,...,i PYPlnlniiii B.1 lnlnP-lnlnYiii B.2 kiNPkiikk;,...,1k i, lnlnYi B.3 N,...,1i 1PlnlnYiiiiii B.4 LlNKliill,...,1;,...,1 i lnlnYi B.5 L,...,1l;N,...,1i WlnlnYliilli B.6 M1,...,j WXWlnlnjjjj B.7 M1,...,j 0 WXjjj B.8 lnlnW-)ln(-)ln(-Xjj j B.9 For a convenient notation, all Xs from here on are Xs to make them positive. ljMWljjll;,...,1 l j, lnlnXj B.10 MWjjjjj,...,1 j 1lnlnXj B.11 124

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125 NiMPillii,...,1;,...,1 l lnlnXl B.12 LjMKjlljj,...,1;,...,1 l lnlnXl B.13 L1,...,j KRKlnlnjjjj B.14 lnlnK-lnlnRjjj B.15 N,...,1k;L,...,1 j PlnlnRkjkjkj B.16 L,...,1 lj, KlnlnRljjllj B.17 L,...,1 j 1KlnlnRjjjjjj B.18 M,...,1l;L,...,1 j WlnlnRljljlj B.19

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APPENDIX C FLORIDA BIASED AND RATE OF TECHNOLOGICAL CHANGE Table C-1. Florida biased technological change. Year Other outputs Perish crops Hired labor Self-employed Chem Matl Land Capital 1960 -0.0173 -0.0095 -0.0294 -0.0307 -0.0162 -0.0167 0.0028 -0.0009 1961 -0.0178 -0.0089 -0.0270 -0.0298 -0.0157 -0.0164 0.0029 -0.0009 1962 -0.0161 -0.0089 -0.0244 -0.0290 -0.0140 -0.0155 0.0031 -0.0009 1963 -0.0203 -0.0089 -0.0297 -0.0318 -0.0176 -0.0176 0.0027 -0.0009 1964 -0.0243 -0.0088 -0.0338 -0.0319 -0.0206 -0.0195 0.0025 -0.0009 1965 -0.0180 -0.0085 -0.0247 -0.0291 -0.0150 -0.0162 0.0027 -0.0009 1966 -0.0160 -0.0088 -0.0239 -0.0299 -0.0141 -0.0153 0.0026 -0.0009 1967 -0.0151 -0.0085 -0.0216 -0.0297 -0.0130 -0.0143 0.0025 -0.0009 1968 -0.0190 -0.0087 -0.0268 -0.0297 -0.0166 -0.0169 0.0021 -0.0010 1969 -0.0166 -0.0089 -0.0253 -0.0276 -0.0151 -0.0159 0.0021 -0.0010 1970 -0.0162 -0.0091 -0.0254 -0.0324 -0.0154 -0.0152 0.0019 -0.0010 1971 -0.0185 -0.0092 -0.0302 -0.0360 -0.0176 -0.0158 0.0018 -0.0011 1972 -0.0188 -0.0095 -0.0323 -0.0348 -0.0185 -0.0165 0.0017 -0.0011 1973 -0.0154 -0.0100 -0.0273 -0.0425 -0.0166 -0.0148 0.0017 -0.0011 1974 -0.0137 -0.0094 -0.0227 -0.0344 -0.0138 -0.0134 0.0017 -0.0011 1975 -0.0139 -0.0090 -0.0212 -0.0350 -0.0132 -0.0134 0.0017 -0.0011 1976 -0.0149 -0.0084 -0.0208 -0.0362 -0.0135 -0.0131 0.0016 -0.0011 1977 -0.0166 -0.0082 -0.0222 -0.0366 -0.0148 -0.0134 0.0016 -0.0012 1978 -0.0178 -0.0088 -0.0267 -0.0334 -0.0166 -0.0151 0.0015 -0.0012 1979 -0.0185 -0.0096 -0.0314 -0.0430 -0.0196 -0.0158 0.0014 -0.0013 1980 -0.0169 -0.0092 -0.0268 -0.0430 -0.0178 -0.0143 0.0014 -0.0013 1981 -0.0161 -0.0093 -0.0257 -0.0432 -0.0167 -0.0142 0.0014 -0.0013 1982 -0.0167 -0.0085 -0.0236 -0.0328 -0.0152 -0.0145 0.0015 -0.0013 1983 -0.0184 -0.0087 -0.0262 -0.0369 -0.0173 -0.0150 0.0014 -0.0013 1984 -0.0197 -0.0085 -0.0260 -0.0402 -0.0176 -0.0158 0.0014 -0.0013 1985 -0.0217 -0.0085 -0.0287 -0.0390 -0.0189 -0.0166 0.0014 -0.0013 1986 -0.0206 -0.0088 -0.0291 -0.0407 -0.0183 -0.0164 0.0014 -0.0013 1987 -0.0324 0.0019 -0.0211 0.0075 0.0054 -0.0341 0.0067 -0.0054 1988 -0.0333 0.0017 -0.0168 0.0093 0.0047 -0.0342 0.0070 -0.0052 1989 -0.0346 0.0017 -0.0176 0.0072 0.0045 -0.0361 0.0072 -0.0051 1990 -0.0293 0.0016 -0.0141 0.0040 0.0033 -0.0337 0.0076 -0.0049 1991 -0.0345 0.0017 -0.0180 0.0053 0.0040 -0.0375 0.0072 -0.0051 1992 -0.0381 0.0017 -0.0171 0.0069 0.0042 -0.0391 0.0072 -0.0051 1993 -0.0324 0.0016 -0.0133 0.0046 0.0033 -0.0376 0.0078 -0.0048 1994 -0.0325 0.0015 -0.0121 0.0051 0.0031 -0.0372 0.0080 -0.0048 1995 -0.0331 0.0015 -0.0116 0.0043 0.0029 -0.0377 0.0079 -0.0048 1996 -0.0321 0.0014 -0.0101 0.0036 0.0026 -0.0372 0.0084 -0.0046 1997 -0.0343 0.0015 -0.0111 0.0047 0.0029 -0.0402 0.0080 -0.0048 1998 -0.0387 0.0015 -0.0123 0.0047 0.0031 -0.0452 0.0078 -0.0048 1999 -0.0414 0.0015 -0.0122 0.0059 0.0032 -0.0473 0.0076 -0.0049 126

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127 Table C-2. Florida rate of technological change. Year 2 1960 0.1697 0.1916 1961 0.1674 0.1872 1962 0.1645 0.1828 1963 0.1587 0.1783 1964 0.1541 0.1739 1965 0.1535 0.1695 1966 0.1495 0.1651 1967 0.1471 0.1607 1968 0.1412 0.1562 1969 0.1382 0.1518 1970 0.1333 0.1474 1971 0.1276 0.1430 1972 0.1232 0.1385 1973 0.1196 0.1341 1974 0.1191 0.1297 1975 0.1158 0.1253 1976 0.1132 0.1209 1977 0.1092 0.1164 1978 0.1031 0.1120 1979 0.0961 0.1076 1980 0.0946 0.1032 1981 0.0907 0.0988 1982 0.0894 0.0943 1983 0.0842 0.0899 1984 0.0796 0.0855 1985 0.0750 0.0811 1986 0.0705 0.0767 1987 0.0779 0.0820 1988 0.0725 0.0752 1989 0.0649 0.0684 1990 0.0590 0.0616 1991 0.0516 0.0548 1992 0.0463 0.0480 1993 0.0393 0.0412 1994 0.0336 0.0344 1995 0.0285 0.0276 1996 0.0230 0.0207 1997 0.0150 0.0139 1998 0.0071 0.0071 1999 0.0008 0.0003 Note: the rate of technological change at observed prices and observed fixed inputs; the rate of technological change at constant prices and fixed inputs.

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APPENDIX D U.S. BIASED AND RATE OF TECHNOLOGICAL CHANGE Table D-1. U.S. biased technological change. Year Other outputs Perish crops Hired labor Self-employed Chem Matl Land Capital 1960 -0.0402 -0.0355 -0.0509 -0.0452 -0.0777 -0.0511 -0.0667 0.0334 1961 -0.0418 -0.0367 -0.0534 -0.0469 -0.0849 -0.0538 -0.0727 0.0321 1962 -0.0422 -0.0379 -0.0546 -0.0478 -0.0817 -0.0548 -0.0634 0.0343 1963 -0.0420 -0.0356 -0.0536 -0.0483 -0.0807 -0.0534 -0.0548 0.0375 1964 -0.0414 -0.0323 -0.0513 -0.0466 -0.0766 -0.0525 -0.0513 0.0393 1965 -0.0434 -0.0372 -0.0565 -0.0486 -0.0810 -0.0571 -0.0639 0.0341 1966 -0.0458 -0.0426 -0.0628 -0.0516 -0.0881 -0.0619 -0.0890 0.0297 1967 -0.0423 -0.0337 -0.0543 -0.0478 -0.0680 -0.0547 -0.0523 0.0387 1968 -0.0421 -0.0308 -0.0529 -0.0477 -0.0610 -0.0543 -0.0464 0.0428 1969 -0.0436 -0.0355 -0.0583 -0.0506 -0.0626 -0.0574 -0.0533 0.0382 1970 -0.0445 -0.0394 -0.0628 -0.0535 -0.0658 -0.0585 -0.0589 0.0358 1971 -0.0436 -0.0335 -0.0586 -0.0537 -0.0611 -0.0552 -0.0451 0.0440 1972 -0.0495 -0.0385 -0.0708 -0.0627 -0.0744 -0.0654 -0.0672 0.0333 1973 -0.0541 -0.0562 -0.0932 -0.0775 -0.0868 -0.0734 -0.0926 0.0293 1974 -0.0509 -0.0505 -0.0854 -0.0776 -0.0677 -0.0659 -0.0533 0.0382 1975 -0.0460 -0.0366 -0.0679 -0.0684 -0.0540 -0.0565 -0.0341 0.0640 1976 -0.0446 -0.0359 -0.0664 -0.0673 -0.0537 -0.0536 -0.0330 0.0683 1977 -0.0425 -0.0297 -0.0587 -0.0629 -0.0489 -0.0498 -0.0275 0.1173 1978 -0.0489 -0.0339 -0.0720 -0.0736 -0.0580 -0.0603 -0.0372 0.0555 1979 -0.0502 -0.0365 -0.0782 -0.0834 -0.0599 -0.0606 -0.0361 0.0580 1980 -0.0473 -0.0358 -0.0749 -0.0858 -0.0543 -0.0546 -0.0303 0.0836 1981 -0.0486 -0.0328 -0.0746 -0.0929 -0.0550 -0.0553 -0.0277 0.1134 1982 -0.0450 -0.0293 -0.0647 -0.0762 -0.0482 -0.0513 -0.0241 0.2913 1983 -0.0587 -0.0437 -0.1082 -0.1255 -0.0706 -0.0719 -0.0358 0.0588 1984 -0.0583 -0.0376 -0.0971 -0.1138 -0.0693 -0.0714 -0.0318 0.0743 1985 -0.0531 -0.0321 -0.0799 -0.0908 -0.0631 -0.0635 -0.0278 0.1111 1986 -0.0661 -0.0375 -0.1096 -0.1146 -0.0970 -0.0867 -0.0396 0.0509 1987 -0.1454 0.0179 -0.0165 -0.0452 0.0000 -0.5493 -0.0897 0.0730 1988 -0.1528 0.0169 -0.0152 -0.0445 0.0000 -0.7443 -0.0739 0.0883 1989 -0.1574 0.0156 -0.0136 -0.0387 0.0000 -1.2327 -0.0698 0.0950 1990 -0.1649 0.0153 -0.0129 -0.0352 0.0000 -5.2852 -0.0738 0.0884 1991 -0.1771 0.0134 -0.0116 -0.0343 0.0000 3.8475 -0.0652 0.1050 1992 -0.2096 0.0131 -0.0116 -0.0342 0.0000 0.8334 -0.0688 0.0970 1993 -0.2425 0.0130 -0.0114 -0.0332 0.0000 0.4903 -0.0708 0.0932 1994 -0.2545 0.0125 -0.0107 -0.0314 0.0000 0.4044 -0.0647 0.1065 1995 -0.3676 0.0116 -0.0104 -0.0319 0.0000 0.2743 -0.0672 0.1003 1996 -0.4539 0.0118 -0.0103 -0.0313 0.0000 0.2298 -0.0679 0.0987 1997 -0.4829 0.0109 -0.0095 -0.0301 0.0000 0.2187 -0.0620 0.1148 1998 -0.7372 0.0101 -0.0090 -0.0286 0.0000 0.1833 -0.0636 0.1095 1999 -1.4187 0.0099 -0.0089 -0.0286 0.0000 0.1620 -0.0646 0.1066 128

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129 Table D-2. U.S. rate of technological change. Year 2 1960 0.1570 0.2133 1961 0.1525 0.2080 1962 0.1507 0.2028 1963 0.1514 0.1975 1964 0.1556 0.1923 1965 0.1487 0.1870 1966 0.1405 0.1818 1967 0.1509 0.1765 1968 0.1512 0.1712 1969 0.1435 0.1660 1970 0.1382 0.1607 1971 0.1407 0.1555 1972 0.1246 0.1502 1973 0.1082 0.1450 1974 0.1105 0.1397 1975 0.1230 0.1344 1976 0.1260 0.1292 1977 0.1339 0.1239 1978 0.1179 0.1187 1979 0.1114 0.1134 1980 0.1130 0.1082 1981 0.1104 0.1029 1982 0.1231 0.0976 1983 0.0924 0.0924 1984 0.0977 0.0871 1985 0.1111 0.0819 1986 0.0960 0.0766 1987 0.0755 0.0654 1988 0.0703 0.0535 1989 0.0635 0.0415 1990 0.0558 0.0296 1991 0.0535 0.0177 1992 0.0436 0.0057 1993 0.0323 -0.0062 1994 0.0286 -0.0182 1995 0.0141 -0.0301 1996 0.0065 -0.0420 1997 0.0089 -0.0540 1998 -0.0026 -0.0659 1999 -0.0099 -0.0779 Note: the rate of technological change at observed prices and observed fixed inputs; the rate of technological change at constant prices and fixed inputs.

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LIST OF REFERENCES Ahmad, Syed. On the Theory of Induced Invention. The Economic Journal 76:302 (1966): 344-357. Allen, Roy George Douglas. Mathematical Analysis for Economists. London: Macmillan and Co., 1938. Antle, John M. The Structure of U.S. Agricultural Technology, 1910-78. American Journal of Agricultural Economics 66 (1984): 414-421. Arthur, W. Brian. Competing Technologies, Increasing Returns, and Lock-in by Historical Events. The Economic Journal 99 (1989): 116-131. Ball, V. Eldon, Jean-Pierre Butault, and Richard Nehring. U.S. Agriculture, 1960-96: A Multilateral Comparison of Total Factor Productivity. Washington DC: U.S. Department of Agriculture, ERS. Technical Bulletin Number 1895, May 2001. http://www.ers.usda.gov/publications/tb1895/tb1895.pdf (December 2003). Ball, V. Eldon, Frank M. Gollop, Alison Kelly-Hawke, and Gregory P. Swinand. Patterns of State Productivity Growth in the U.S. Farm Sector: Linking State and Aggregate models. American Journal of Agricultural Economics 81 (1999): 164-179. Ball, V. Eldon, Jean-Christophe Bureau, Richard Nehring, and Agapi Somwaru. Agricultural Productivity Revisited. American Journal of Agricultural Economics 79 (1997): 1045-1063. Berndt, Ernst R. The Practice of Econometrics: Classic and Contemporary. Massachusetts: Addison-Wesley Publishing Company, 1996. Binswanger, Hans P. A Cost Function Approach to the Measurement of Elasticities of Factor Demand and Elasticities of Substitution. American Journal of Agricultural Economics 56 (1974a): 377-386. Binswanger, Hans P. The Measurement of Technical Change Biases with Many Factors of Production. The American Economic Review 64: 6 (1974b): 964-976. Binswanger, Hans P. Induced Technical Change: Evolution of Thought. Induced Innovation, Technology, Institutions and Development, H.P. Binswanger and V.W. Ruttan, eds., pp.13 43. Baltimore, MD: Johns Hopkins University Press, 1978. 130

PAGE 144

131 Binswanger, Hans P. Agricultural Mechanization: A Comparative Historical Perspective. Working Paper Number 673, World Bank, Washington DC, 1984. Blackorby, Charles and Robert Russell. Will the Real Elasticity of Substitution Please Stand Up? (A Comparision of the Allen/Uzawa and Morishima Elasticities). The American Economic Review 79:4 (1989): 882-888. Briggs, Vernon. Guestworker Programs: Lessons from the Past and Warnings for the Future. Backgrounders. Center for Immigration Studies, March 2004. http://www.cis.org/articles/2004/back304.pdf (April 2004). Chambers, Robert G. Applied Production Analysis: A Dual Approach. Cambridge: Cambridge University Press, 1994. (First edition 1988) Cornyn, John. The Border Security and Immigration Reform Act. Washington DC http://cornyn.senate.gov/reform/files/GuestProspectus.pdf (April 2004). Effland, Anne B. W. and Jack L. Runyan. Hired Farm Labor in U.S. Agriculture. Washington DC: U.S. Department of Agriculture, ERS. Agricultural Outlook, October 1998. http://www.ers.usda.gov/Publications/Agoutlook/oct1998/ao255f.pdf (February 2004). Emerson, Robert D. and Fritz Roka. Income Distribution and Farm Labour Markets. The Dynamics of Hired Farm Labour. Jill Findeis, ed., pp. 137-149. New York: CABI Publishing, November 2002. Fonseca, Gonalo and Leanne Ussher. The Profit Function. The History of Economic Thought Website http://cepa.newschool.edu/het/essays/product/profit.htm (April 2004). Gallant, A. Ronald and Gene H. Golub. Imposing Curvature Restrictions on Flexible Functional Forms. Journal of Econometrics 26 (1984): 295-321. Griliches, Zvi. Hybrid Corn: An Exploration of the Economics of Technical Change. Econometrica 25 (1957): 501-522. Hayami, Yujiro and Vernon W. Ruttan. Factor Prices and Technical Change in Agricultural Development: The United States and Japan, 1880-1960. The Journal of Political Economy 78:5 (1970): 1115-1141. Hayami, Yujiro and Vernon W. Ruttan. Agricultural Development: An International Perspective. Baltimore, MD: Johns Hopkins University Press, 1985. (First edition 1971) Hazilla, Michael and Raymond J. Kopp. Imposing Curvature Restrictions on Flexible Functional Forms. Resources for the Future Discussion Paper QE85-04, Washington DC, January 1985.

PAGE 145

132 Heppel, Monica L. and Sandra L. Amendola. Immigration Reform and Perishable Crop Agriculture: Compliance or Circumvention? The Center for Immigration Studies. Lanham: University Press of America, 1992. Hicks, John R. Theory of Wages. London: Macmillan, 1935. (First edition 1932) Huffman, Wallace E. Changes in the Labour Intensity of Agriculture: A Comparison of California, Florida and the USA. The Dynamics of Hired Farm Labour. Jill Findeis, ed., New York: CABI Publishing, November 2002. Huffman, Wallace E. and Evenson, R.E. Contributions of Public and Private Science and Technology to United States Agricultural Productivity. American Journal of Agricultural Economics 74:3 (1992): 751-756. Ise, Sabrina and Jeffrey M. Perloff. Legal Status and Earnings of Agricultural Workers. American Journal of Agricultural Economics 77 (1995): 375-386. Jorgenson, D. W. and Z. Griliches. The Explanation of Productivity Change. The Review of Economic Studies 34:3 (1967): 249-283. Kennedy, Charles. Induced Bias in Innovation and the Theory of Distribution. The Economic Journal 74 (1964): 541-547. Kennedy, Charles. Samuelson on Induced Innovation. Review of Economics and Statistics 48 (1966): 442-444. Kennedy, Charles. On the Theory of Induced Innovation-A Reply. The Economic Journal 77 (1967): 958-960. Kohli, Ulrich., ed. Technology, Duality, and Foreign Trade: The GNP Function Approach to Modeling Imports and Exports. Hong Kong: Harvester Wheatsheaf, 1991. Krikorian, Mark. Guestworker Programs: A Threat to American Agriculture. Backgrounders. Center for Immigration Studies, June 2001. http://www.cis.org/articles/2001/back801.pdf (March 2004). Lambert, David K. and J.S. Shonkwiler. Factor Bias under Stochastic Technical Change. American Journal of Agricultural Economics 77 (1995): 578-590. Larkin, Marry Ann. Immigrants and Welfare. Research Perspective on Migration 1:1, 1996. http://www.ceip.org/files/projects/imp/rpm/rpml.pdf (February 2001). Lau, Lawrence J. Testing and Imposing Monotonicity, Convexity and Quasi-Convexity Constraints. Production Economics: A Dual Approach to Theory and Applications Volume1. Melvyn Fuss and Daniel McFadden, eds., pp. 409-453. New York: North-Holland Publishing Company, 1978.

PAGE 146

133 Lopez, Ramon. Structural Implications of a Class of Flexible Functional Forms for Profit Functions. International Economic Review 26:3 (1985): 593-601. Martin, Philip. There Is Nothing More Permanent than Temporary Foreign Workers. Backgrounders. Center for Immigration Studies, April 2001. http://www.cis.org/articles/2001/back501.pdf (March 2004). McCain, John. McCain Introduces Comprehensive Immigration Reform. Press Release August 25, 2003. http://mccain.senate.gov/index.cfm?fuseaction=Newscenter.ViewPressRelease&Content_id=1148 (April 2004). McFadden, Daniel. Cost, Revenue, and Profit Function Production Economics: A Dual Approach to Theory and Applications Volume1, Melvyn Fuss and Daniel McFadden eds., pp. 3-109. New York: North-Holland Publishing Company, 1978. Mehta, Kala, Susan M. Gabbard, Vanessa Barrat, Melissa Lewis, Daniel Carroll, and Richard Mines. Findings from National Agricultural Worker Survey (NAWS) 1997-1998: A Demographic and Employment Profile of U.S. Farm Workers. Research Report Number 8, U.S. Department of Labor, March 2000. http://www.dol.gov/asp/programs/agworker/report_8.pdf (June 2003). Mexico: Bracero Lawsuit. Rural Migration News 8:1 (2002). http://migration.ucdavis.edu/rmn/more.php?id=565_0_4_0 (February 2004). Mines, Richard, Susan M. Gabbard, and Anne Steirman. Profile of U.S. Farm Workers: Demographic, Household Composition, Income, and Use of Services. Based on Data from NAWS Survey 1997. Office of Program Economics Research Report #6. U.S. Department of Labor. http://www.dol.gov/asp/programs/agworker/report/main.htm (June 2003). Mines, Richard. What Kind of Transition Is Necessary to Secure the Future of U.S. Fruit, Vegetable, and Horticultural Agriculture? Labor Management Decisions 8:1, 1999. http://are.berkeley.edu/APMP/pubs/lmd/html/wintspring_99/LMD.8.1.transition.html (February 2004). Moretti, Enrico and Jeffrey M. Perloff. Use of Public Transfer Programs and Private Aid by Farm Workers. Industrial Relations 39(1) (2000): 26-47. Morey, Edward R. An Introduction to Checking, Testing, and Imposing Curvature Properties: The True Function and the Estimated Function. The Canadian Journal of Economics 19:2 (1986): 207-35.

PAGE 147

134 Muraro, Ronald P., Thomas H. Spreen, and Marcos Pozzan. Comparative Costs of Growing Citrus in Florida and Sao Paulo (Brazil) for the 2000-01 Season. Department of Food and Resource Economics, Florida Cooperative Extension Service, Institute of Food and Agricultural Sciences, University of Florida. Electronic Data Information Source: FE 364. (February 2003). Napasintuwong, Orachos and Robert D. Emerson. Induced Innovation and Foreign Workers in U.S. Agriculture. Selected paper for presentation at the American Agricultural Economics Association Annual Meeting, Long Beach, California, July 2002. Napasintuwong, Orachos and Robert D. Emerson. Farm Mechanization and the Farm Labor Market: A Socioeconomic Model of Induced Innovation. Selected paper for presentation at the Southern Agricultural Economics Association Annual Meeting, Mobile, Alabama, February 2003. Nelson, Richard R. and Sidney G. Winter. Toward an Evolutionary Theory of Economic Capabilities. American Economic Review 63 (1973): 440-119. Nordhaus, William D. Some Skeptical Thoughts on the Theory of Induced Innovation. The Quarterly Journal of Economics 87 (1973): 209-19. Olmstead, Alan L. and Paul Rhode. Induced Innovation in American Agriculture: A Reconsideration. The Journal of Political Economy 101 (1993): 100-118. Rasmussen, Wayne D., ed. Agriculture in the United States: A Documentary History. New York: Random House, 1975. Roka, Fritz. Immokalee Report: Outlook on Mechanical Citrus Harvester. Citrus and Vegetable Magazine, September 2001a. http://www.citrusandvegetable.com/home/archive/2001_SeptImmokalee.html (February 2004). Roka, Fritz. Labor Requirement in Florida Citrus. Department of Food and Resource Economics, Florida Cooperative Extension Service, Institute of Food and Agricultural Sciences, University of Florida. Electronic Data Information Source: FE 304, September 2001b. http://edis.ifas.ufl.edu/pdffiles/FE/FE30400.pdf (February 2004). Runyan, Jack L. Profile of Hired Farmworkers, 1998 Annual Average. Washington DC: U.S. Department of Agriculture, ERS, AER No.790, November 2000. http://www.ers.usda.gov/Publications/AER790/ (February 2004). Ruttan, Vernon W. Technical and Institutional Innovation. Technology, Growth, and Development: An Induced Innovation Perspective. Vernon W. Ruttan, ed., pp.100-146. New York: Oxford University Press, 2001.

PAGE 148

135 Rytina, Nancy. IRCA Legalization Effects: Lawful Permanent Residence and Naturalization through 2001. Office of Policy and Planning, U.S. Immigration and Naturalization Service, presented paper at the Effect of Immigrant Legalization Programs on the United States, October 2002. Salter, W.E.G. Productivity and Technical Change, 1 st edition. Cambridge: Cambridge University Press, 1960. Samuelson, Paul A. A Theory of Induced Innovation along Kennedy-Weizsacker Lines. Review of Economics and Statistics 47 (1965): 343-356. Samuelson, Paul A. Rejoinder: Agreements, Disagreements, Doubts and the Case of Induced Harrod-Neutral Technical Change. Review of Economics and Statistics 48 (1966): 444-448. Sarig, Yoav, James F. Thompson, and Galen K. Brown. Alternatives to Immigrant Labor? The Status of Fruit and Vegetable Harvest Mechanization in the United States. Backgrounders. Center for Immigration Studies, December 2000. http://cis.org/articles/2000/back1200.pdf (March 2004). Schumpeter, Joseph A. The Theory of Economic Development: An Inquiry into Profits, Capital, Credit, Interest, and the Business Cycle. Cambridge, MA: Harvard University Press, 1934. Sharma, Subhash. The Morishima Elasticity of Substitution for the Variable Profit Function and the Demand for Imports in the United States. International Economic Review 43:1 (2002): 115-135. Shumway, C. Richard and William P. Alexander. Agricultural Product Supplies and Input Demand: Regional Comparisons. American Journal of Agricultural Economics 80 (1988): 153-161. Simcox, David, John L. Martin, and Rosemary Jenks. The Cost of Immigration: Assessing a Conflicted Issue. Backgrounders. Center for Immigration Studies, September 1994. http://www.cis.org/articles/1994/back294.htm (March 2004). U.S. Citizenship and Immigration Services. Table 60: Principal Activities and Accomplishments of the Border Patrol 1992-2002. Washington DC. http://uscis.gov/graphics/shared/aboutus/statistics/enf02yrbk/table60.xls (April 2004). U.S. Department of Justice, Immigration and Naturalization Service. Statistical Yearbook of the Immigration and Naturalization Service 1996-2001. Washington DC. http://uscis.gov/graphics/shared/aboutus/statistics/ybpage.htm (April 2004). Vernon, Raymond. International Investment and International Trade in the Product Cycle. Quarterly Journal of Economics 80 (1966): 190-207.

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136 Vernon, Raymond. The Product Cycle Hypothesis in a New International Environment. Oxford Bulletin of Economics and Statistics 40 (1979): 255-267. Weaver, Robert D. Multiple Input, Multiple Output Production Choices and Technology in the U.S. Wheat Region. American Journal of Agricultural Economics 65:1 (1983): 45-56. Wiley, David E., William H. Schmidt, and William J. Bramble. Studies of a Class of Covariance Structure Models. Journal of the American Statistical Association 68:342 (1973): 317-323. Zellner, Arnold. An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias. Journal of the American Statistical Association 57:298 (1962): 348-68.

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BIOGRAPHICAL SKETCH Orachos Napasintuwong was born in 1974, in Bangkok. She pursued a bachelor of science in biotechnology at Mahidol University, Thailand, and graduated with the second class honor in 1995. Her senior project was on Isolation and Purification of Chephalosporin C Acylase. She first came to the United States, in 1996, to continue her education. She received a master of business administration (with the concentration in marketing and international business) from Louisiana State University in 1998. In the fall of 1998, she joined Food and Resource Economics Department at the University of Florida to pursue her Ph.D. degree. She received a graduate research assistantship in the fall of 1998 from the Economic and Market Research Department, Florida Department of Citrus at University of Florida. She continued to receive a graduate research assistantship and graduate teaching assistantship from Food and Resource Economics Department throughout her Ph.D. program, where she had the opportunity to work with Dr. Emerson, Dr. Schmitz, and Dr. Kilmer on their research projects and classes. In the summer of 2001, she taught a class in Principle of Food and Resource Economics. During her last two years in the program, she received financial support from the International and Agricultural Trade Center. She completed her Ph.D. degree in May 2004. 137


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IMMIGRANT WORKERS AND TECHNOLOGICAL CHANGE:
AN INDUCED INNOVATION PERSPECTIVE ON
FLORIDA AND U.S. AGRICULTURE













By

ORACHOS NAPASINTUWONG


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2004

































Copyright 2004

by

Orachos Napasintuwong

































To my parents: Pisal and Duangkmol Napasintuwong















ACKNOWLEDGMENTS

I am very grateful to have had the opportunity to work with my advisor, Dr. Robert

D. Emerson. Working with him has taught me to be a good economist professionally,

and to care for people and society. I would like to express my deep gratitude for his

guidance, criticism, and encouragement in doing my research and dissertation. I also

thank him for his understanding, patience, and support during difficult times in the

process of writing my dissertation. I also would like to thank all of my committee

members (Dr. Andrew Schmitz, Dr. Bin Xu, and Dr. Lawrence Kenny), who contributed

significantly to the quality of my work. I also appreciate Dr. Xu's suggestion of research

topics that led to this research. Special thanks go to Eldon Ball, who put together the

unpublished data from ERS, USDA specifically for this research.

My thanks also go to all my friends and professors at the Food and Resource

Economics Department. I appreciate my friends (Arturo Bocardo, Chris de Bodisco, and

their families), who have been great companions during my years in Gainesville. I also

want to thank Dr. Thomas Spreen, and the Florida Citrus Department, who sponsored my

graduate assistantship during my first semester; and especially the Food and Resource

Economics Department and the International Agricultural Trade and Policy Center for

their material support during my Ph.D. program. I also thank Dr. Andrew Schmitz and

Dr. Richard Kilmer, who gave me an opportunity to assist them in their research projects

and classes; and Dr. Chris Andrew and Dr. Richard Weldon, who gave me a great

opportunity to teach.









My greatest gratitude goes to my parents, Pisal and Duangkmol Napasintuwong,

who taught me to appreciate the importance of education and gave me the opportunity to

explore education abroad. They always gave me love and support through some difficult

times. Their understanding and encouragement make this journey possible. I also would

like to thank my sister, Chanoknetr, for her love and encouragement; my cousins Varis,

Kanat, and Karit; and their parents Guy and Krisna Ransibrahmanakul for their advice,

love, and care here in the United States. My special thanks go to my family in Thailand,

all my friends in Gainesville, Numpol Lawanyawatna, Nakarin Ruangpanit, and Pollajak

Veerawetwatana for their moral support to accomplish this goal.
















TABLE OF CONTENTS

Page

A C K N O W L E D G M E N T S ................................................................................................. iv

T A B L E O F C O N T E N T S ................................................. ............................................ vi

LIST O F TA B LE S .................. .......... .. ............................. ....... ....... ix

LIST OF FIGURES ............................... ... ...... ... ................. .x

ABSTRACT .............. ..................... .......... .............. xii

CHAPTER

1 IN TR OD U CTION ............................................... .. ......................... ..

B a c k g ro u n d ................................................................................................... 1
Problem Statem ent ........................................................ ...... .. ......... .. .. .5
R research O bjectives.......... ..................................................................... ....... .... .6
O organization of C chapters .......................................................... ..............6

2 U.S. FARM LABOR MARKET, IMMIGRATION POLICY, AND FARM
M ECH A N IZA TION ............................................................... .................8

U .S. F arm L abor M arket...................................................................... ....... ........... 8
U .S. Im m migration P policy ............................................................................. ... ........10
Farm M echanization in U .S. Agriculture ....................................... ............... 15

3 THEORETICAL AND ANALYTICAL FRAMEWORK .......................................21

Cost Minimization Model of Induced Innovation Theory ................ .....................21
Hicks-Ahmad Model of Induced Technological Change............................. 23
Hayami and Ruttan Model of Induced Technological Change ...........................25
Empirical Studies of Biases in U.S. Agricultural Technology..........................29
Profit Function M odel of Induced Innovation................................. ...... ............ ...31
Rate of Technological Change and Biased Technological Change.........................38

4 EMPIRICAL MODEL, DATA, AND ESTIMATION ...........................................46

E m p irical M o d el ..................................................... ................ 4 6









M odel Specification..................... ......... ............................... 49
M o d el R estriction s....................................................................... ..................50
Lau's Cholesky decom position ........................................ ....................... 53
Wiley-Schmidt-Bramble decomposition...................... ............... 54
Elasticity ....................................... ....... .. .. .. .. ........... ............... 55
Price elasticity of output supply and variable input demand .....................55
M orishim a elasticity of substitution .................. ..................... ......... 57
D ata ............... ............................ .............................................. .6 0
Estimation ............. .......... .... ......... ..... ............. ......... 67
Seemingly Unrelated Equations ............................. ..... ..............67
Imposing Restrictions for a Well-behaved Profit Function..............................70
H om ogeneity ................................................................... 70
S y m m etry ................................................... ................ 7 0
C o n tin u ity ........................................... .. ................................................ 7 0
Curvature ................................ ............................... 70
Rate of Biased Technological Change ..................................... .................74
E stim ation of E lasticities ...................... .. .. ......... ..................... ............... 75

5 ECONOMETRIC RESULTS AND INTERPRETATION .......................................76

F lorida R esu lts ................. ...................................................................... 76
Florida Rate of Technological Change and Biased Technological Change........79
Florida O w n-Price Elasticity .................................................... ............... 81
Florida Morishima Elasticity of Substitution ............................................... 81
T he U .S R results ............................... ................. ... .. ............ ................ 84
U.S. Rate of Technological Change and Biased Technological Change ............85
U.S. Own-Price Elasticity......................... ....... ............................ 88
U.S. Morishima Elasticity of Substitution.........................................................88

6 CONCLUSIONS, POLICY IMPLICATIONS, AND SUGGESTED FUTURE
R E SE A R C H ........................................... .......... ................. 109

Sum m ary and Conclusions ......................................................... .............. 109
Theoretical Fram ew ork ......................................................... .............. 110
E m pirical F ram ew ork .................................................................................. 110
D ata ........................................................ 1 1 1
Em pirical Findings ............................................ .. ........ .... ............ .. 111
Florida Results.................. ............................ ...... .. ................ 112
The U .S. R results .................. .................................. .. .. ................ 112
Concluding R em arks .......................................................... ............... 113
C o n trib u tio n s .................................................................. ..................................1 14
Policy Im plications ..................................... ........ ............ .. ........ .. 116
Suggested Future R research .................................................................. ............... 119









APPENDIX

A PROOF OF PRICE ELASTICITY OF OUTPUT SUPPLY AND INPUT
D EM A N D ............................................................... .... ..... ......... 122

B ELEMENTS IN MATRICES USED TO CALCULATE MORISHIMA
ELASTICITY OF SUBSTITUTUTION ............................................................... 124

C FLORIDA BIASED AND RATE OF TECHNOLOGICAL CHANGE................ 126

D U.S. BIASED AND RATE OF TECHNOLOGICAL CHANGE............................128

L IST O F R E F E R E N C E S ...................................................................... ..................... 130

BIOGRAPHICAL SKETCH ............................................................. ............... 137
















LIST OF TABLES


Table Page

2-1 Number of immigrants admitted as Immigration Reform and Control Act
legalization. .......................................... ............................ 20

5-1 Florida estimates with homogeneity and symmetry constraints. ..........................92

5-2 Florida estimates with homogeneity, symmetry, and convexity constraints............93

5-3 Florida biased technological change calculated at the means................................94

5-4 Florida own-price elasticity and inverse price elasticity .......................................94

5-5 Florida average Morhishima elasticity of substitution .......................... ..........95

5-6 U.S. estimates with homogeneity and symmetry constraints..............................96

5-7 U.S. estimates with homogeneity, symmetry, and convexity constraints ..............97

5-8 U.S. biased technological change calculated at the means...................................98

5-9 U.S. own-price elasticity and inverse price elasticity. ...........................................98

5-10 U.S. average Morishima elasticity of substitution. .............................................99

C-l Florida biased technological change. ........................................ ............... 126

C-2 Florida rate of technological change. ............................. ...............127

D -1 U .S. biased technological change.................................... .................................... 128

D -2 U .S. rate of technological change...................................... ......................... 129
















LIST OF FIGURES


Figure Page

2-1 Percentage of hired farm workers by regions .......................................................18

2-2 Farm workers ethnicity and place of birth. ....................................................19

2-3 L egal status of farm w workers ......................................................................... .... 19

2-4 Percentage of deportable aliens located by border patrol who are Mexican
agricultural w orkers............. .... ............................................................. .. .... .... 20

3-1 Ahmad's induced innovation model. ............................................ ............... 40

3-2 Induced technological change. A) Mechanical technology development. B)
Biological technology develop ent ............................................... ................... 41

3-3 Innovation production possibility frontier and technological progress ..................42

3-4 Technological progress and a change in prices....................................... ........... 43

3-5 Substitution and output effects of profit maximization ........................................44

3-6 Induced innovation for profit maximizing technological change. .........................45

4-1 Florida price indices of outputs, variable inputs, and fixed inputs ........................65

4-2 Florida profit shares of outputs, variable inputs, and fixed inputs.........................65

4-3 U.S. Price Indices of outputs, variable inputs, and fixed inputs. ..........................66

4-4 U.S. profit shares of outputs, variable inputs, and fixed inputs. ...........................66

5-1 Florida biased technological change. ........................................ ............... 100

5-2 Florida rate of technological change. ............ ............................. ...............100

5-3 Florida Morishima elasticity of substitution between variable inputs .................101

5-4 Florida Morishima elasticity of substitution between variable input and fixed
input (fixed input price changes)....................................... ......................... 102









5-5 Florida Morishima elasticity between fixed input and variable input (variable
input price changes), and between fixed inputs. ............. ..................................... 103

5-6 U .S. biased technological change.................................... .................................... 104

5-7 U.S. biased technological change, other outputs and materials. ..........................104

5-8 U .S. rate of technological change...................................... ......................... 105

5-9 U.S. Morishima elasticity of substitution between variable inputs........................106

5-10 U.S. Morishima elasticity of substitution between variable input and fixed input
(fixed input price changes) ........... ...................................... 107

5-11 U.S. Morishima elasticity between fixed input and variable input (variable input
price changes), and betw een fixed inputs ........................................... .................108















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

IMMIGRANT WORKERS AND TECHNOLOGICAL CHANGE:
AN INDUCED INNOVATION PERSPECTIVE ON
FLORIDA AND U.S. AGRICULTURE

By

Orachos Napasintuwong

May 2004

Chair: Robert D. Emerson
Major Department: Food and Resource Economics

Technological progress in agriculture is important for the industry to remain

competitive in the world market. A major question is whether or not the advancement in

farm mechanization is inhibited by the availability of inexpensive foreign workers. The

Immigration Reform and Control Act (IRCA), designed to reduce the number of

unauthorized foreign workers, was passed in 1986. My study analyzes the impacts of

changes in immigration policies and in labor markets on the rate and direction of

technological change in Florida and the U.S. by applying the theory of induced

innovation.

A new theoretical framework for profit-maximized induced innovation theory and

definition of rates and biases of technological change are developed in this study. The

profit function approach takes into account possible changes in output markets. The

transcendental logarithmic profit function model is used for the econometric analysis.

Homogeneity, symmetry, and curvature constraints are imposed. Curvature restrictions









are imposed locally using the Wiley-Schmidt-Bramble reparameterization technique.

The rate of technological change, bias of technological change, and Morishima

elasticities of substitution are calculated from the parameter estimates.

Farm wages are observed to increase at higher rates than the prices of other inputs

after IRCA. Although labor became more expensive, the technology significantly

became more self-employed labor-using in both Florida and the U.S., and more hired

labor-using in the U.S. after the passage of IRCA. The technological change did not

significantly increase adoption of farm mechanization in either area. My study suggests

that a more stringent immigration policy does not necessarily decrease the incentive to

use hired labor. The limited adoption of farm mechanization may be the result of an

increase in the supply of illegal immigrant workers and the belief that immigration policy

will create a greater flow of immigrant workers in the future. The more rapid adoption of

farm mechanization would require policies reducing the supply of labor at a given wage

to agriculture, most likely accomplished by limiting access to foreign workers, legal or

illegal.














CHAPTER 1
INTRODUCTION

Background

One of the more controversial questions in U.S. agriculture is whether or not the

recent slow pace of labor-saving innovation of new technology, specifically farm

mechanization, is due to the availability of inexpensive foreign labor. Foreign workers

are the major labor supply in U.S. agricultural employment, and a significant number of

them are unauthorized. The National Agricultural Worker Survey (NAWS) reports that

during 1997-1998, 52 % of hired farm workers were unauthorized. Unauthorized labor

typically receives a lower hourly wage than do legal workers (Ise' and Perloff 1995). The

increasing flow of foreign workers, particularly unauthorized workers, can reduce farm

wages below the level they would otherwise be, not only from an increased labor supply,

but also because earnings of unauthorized workers have been shown to be lower than

those of legal workers (Ise' and Perloff 1995). As a result, it is argued that the

availability of inexpensive unauthorized foreign workers reduces the incentive to develop

and/or adopt labor-saving technology (Krikorian 2001). An example where labor-saving

technology is available, but has not been adopted is dried-on-the-vine (DOV) production

of raisins which started in the 1950s in Australia. This technology could save up to 85%

of labor, but has not been widely adopted among California grape farmers, ostensibly

because of the availability of workers from Mexico (Krikorian 2001).

The implication of labor-saving technology on the income of U.S. farm workers

differs from most other sectors. Since a large number of farm workers in the U.S. are









unauthorized, the problem of displacement in the agricultural labor market due to labor-

saving technology may hurt foreign workers more than native workers. If the reduction

in labor demand from mechanization and more stringent immigration law and

enforcement implies that immigrant workers are those who will lose jobs, labor-saving

technology may not have a negative impact on domestic workers. In fact, a reduction of

farm workers implies that the marginal productivity, and compensation, of the remaining

workers will increase.

The concern that the presence of foreign workers may inhibit the development of

new agricultural technology occurs mostly in labor-intensive industries where there is a

potential to develop mechanization technology, but it still has not materialized. In other

cases, the technology may be available, but it has not been adopted. Florida, Texas, and

California are among the states where agricultural production depends largely on foreign

workers. Although the mechanical sugarcane harvester has been successfully adopted in

Florida agriculture in the 1990s, the harvest of Florida's other major crops, nursery and

greenhouse crops, vegetables, and citrus, is still highly labor-intensive. A premise of this

research is that changes in the labor market or in immigration policy may have differing

effects in labor-intensive and non-labor-intensive states due to differences in the potential

substitutability between capital and labor.

The problem of adopting farm mechanization is not limited to the availability of

labor supply. The same technology that can be applied to some crops may not be feasible

in other crops because of biological characteristics of the crops such as the lack of

uniform maturity, or easy bruising of the product. For example, the harvest of potatoes,

most other below ground vegetables, and all nuts (e.g., almonds, pecans, walnuts) except









macadamia nuts, has been fully mechanized. In addition, over 50% of the acreage of

grapes, plums, hot peppers, lima beans, parsley, pumpkin, tomatoes, carrots, sweet corn,

and many other fruits and vegetables have been harvested mechanically (Sarig et al.

2000). The technology, however, cannot be readily replicated in apples, peaches, pears,

nectarines, and many other crops. In some cases, the technology is not uniformly

adopted in the same commodity produced for different markets because the damage from

mechanical harvesting and the loss of post harvest quality may make the products

unacceptable for export or fresh markets. For example, mechanical harvesting of

tomatoes for the processing market has been successful, but it has not yet been successful

for tomatoes destined for the fresh market due to unacceptable product damage and

uneven ripening characteristics.

There remain several opportunities for the development of farm mechanization in

U.S. agriculture, particularly for fruits and vegetables. Not only does mechanization

increase labor productivity, but it also stabilizes labor requirements, particularly in the

production of seasonal crops. While low-income countries employ inexpensive labor,

and other developed countries invent new machinery, U.S. fruit and vegetable production

remains dependent largely on low-wage foreign labor. Establishing the competitiveness

of American agriculture on the basis of foreign labor is a questionable policy approach.

For instance, the labor cost of citrus production in Brazil is much lower than in Florida.

It is estimated that during the 2000-2001 harvesting season, the costs for picking and

loading of fruit into trailers ready for transport were $1.60 and $0.38 per box in Florida

and Sa6 Paulo, respectively (Muraro et al. 2003). The estimated labor cost saved by the

continuous canopy shake and catch harvester being tested by some harvesting companies









is $0.56 per box (Roka September 2001a). The question implicitly being considered in

the Florida citrus industry is whether it should adopt mechanical citrus harvesting, which

is potentially less expensive and more productive than hand harvesting, in an effort to

compete with Brazilian producers, or it should continue to depend on hand harvesting

with a high presence of immigrant workers. Some analysts (Sarig et al. 2000) argue that

mechanization will help the U.S. remain competitive in the world market. An example

cited is Australia which has become the most mechanized in wine grape harvesting, while

U.S. wine grape production relies on low-wage workers, and is still not the lowest cost

wine producer (Sternberg et al. 1999). Another illustration is Holland, using mechanical

technologies, which successfully exports cut flowers and green house tomatoes to North

America (Mines 1999).

The major purpose in analyzing technological change in this study is to determine

the impacts of changes in farm wage rates due to changes in immigration policy on the

direction and the rate of technological change. The induced innovation theory is adopted

to examine the role of wage rates and other factor and output prices on the extent of bias

in technological change, specifically whether it is labor-saving or capital-using

technological change. Under the theory of induced innovation, a decrease in labor supply

as a result of more stringent immigration policy resulting in higher farm wages would

induce the adoption and innovation of additional farm mechanization. The implications

resulting from changes in wage rates, prices and perhaps more importantly, changes in

government policies on technological change will provide insights for the design of

future economic policies.









Problem Statement

In a competitive world market, low-wage labor may not be a competitive advantage

of U.S. agricultural production. While several developed countries utilize advanced

technology (e.g., Australian wine grape harvesting), the U.S. continues to rely heavily on

low-wage foreign workers. With relatively abundant land in the U.S, the development of

farm mechanization can increase production by increasing labor productivity. However,

due to readily available unauthorized farm labor, it is often argued that labor-saving

technology has not been developed or adopted (Krikorian 2001). With readily available

low-wage immigrant workers in U.S. agriculture, the incentive for producers to adopt

new labor-saving technology is reduced. Although some farmers are concerned that a

reduction of the supply of foreign workers will result in a shortage of farm workers, the

success of the mechanized tomato harvester after the end of the Bracero program

provides a counter-example to this concern. After September 11, 2001, there was a great

uncertainty on foreign labor supply as the country became more aware of immigrants'

roles in the U.S. economy and security. A reduction in financial risk associated with

labor uncertainty and stabilization in agricultural production are arguments in favor of

farm mechanization. In addition, farm mechanization may also decrease government

welfare expenditures on education and health care of foreign workers, and can

conceivably strengthen national competitiveness in agricultural production.

An increase in restrictions on illegal farm employment and a stringent border

policy may stimulate the adoption of farm mechanization as labor becomes more

expensive and not as readily available. The Immigration Reform and Control Act of

1986 (Public Law 99-603, hereafter, IRCA) was designed to reduce the flow and

employment of unauthorized workers. The question of interest in this research is whether









this change in immigration policy has increased the development of farm mechanization,

typically labor-saving, capital-using technology, and whether the substitutability between

capital and labor has changed. In order to address this question the model of induced

innovation is adopted to analyze the change in factor prices on biased technological

change. The results from this study will provide implications for immigration policy

related to technological change.

Research Objectives

My primary purpose of this study was, to evaluate change in agricultural

technology, and the impact of changes in farm wages along with other factor prices on

the rate and direction of technological progress. Allowing potentially different results

between a labor-intensive agricultural state and others, Florida and the U.S. were selected

to be the study areas. Specific objectives include

* Estimating the rates of technological change between 1960 and 1999, and comparing
them before and after the passage of IRCA.

* Estimating the bias in technological change of outputs and inputs during the study
period, and evaluating the differences before and after the passage of IRCA

* Evaluating the impacts of changes in input and output prices on input use and output
production by calculating the Morishima elasticity of substitution.

Organization of Chapters

The history and current situation of the farm labor market, immigration policy, and

changes in technology, particularly farm mechanization in Florida and the U.S. are

discussed first in the next chapter. The emphasis is on the relationship between farm

mechanization and foreign workers. The theoretical concept of induced innovation

theory used in this study is introduced in Chapter 3. The theory is extended to

incorporate profit maximization rather than the more typical cost minimization case. The









microeconomic model applying induced innovation theory, the bias and rate of

technological change are introduced. In Chapter 4, the empirical model of the profit

function approach of induced innovation is developed. The chapter explains the data,

definitions of variables, and the restrictions on the transcendental profit function. The

estimation techniques used to test and impose the curvature property, estimate the bias

and rate of technological change, and estimate the Morishima elasticities conclude this

chapter. The results of the econometric estimation and their economic interpretations are

presented in Chapter 5. The final chapter summarizes the primary results of this study,

provides policy implications and contributions of the study, and finally suggests future

areas of research.














CHAPTER 2
U.S. FARM LABOR MARKET, IMMIGRATION POLICY,
AND FARM MECHANIZATION

U.S. Farm Labor Market

Agriculture was once the dominant component of the U.S. economy and culture.

As the country became more industrialized, the number of agricultural workers declined,

with farmers relocating to industrial work. In the early to mid-1880s, more than half of

the U.S. population were farmers. In 1900, it was estimated that 38% of the labor force

were farmers, but by 1990 farmers made up only 2.6% of the labor force.1

Although self-employed workers are a majority of U.S. farm labor, a significant

number of farm workers are hired and contract labor. In 1997, hired labor accounted for

34% of the production workforce in U.S. agriculture, and 12% of farms used contract

labor (Runyan 2000). The estimates of the Economic Research Service, USDA, based on

the Current Population Survey in 1997 show that about 33% of hired farm workers are

non-U.S. citizens. Among non-U.S. citizens, hired farm workers are more likely to be

male, Hispanic, and have less education. The distribution of hired farm workers depends

on the geographic location of labor-intensive production. Figure 2-1 shows that the

employment of hired farm workers occurs largely in the West and the South.

The percentage of immigrant workers among hired workers also depends on

geographic location. In some areas such as Florida, where citrus and vegetable

harvesting is a major component of agricultural employment, immigrant workers account


1 A History of American Agriculture: Farmers and the Farm, ERS, USDA.









for 75% of hired workers (Emerson and Roka 2002) while the national average is only

12% (Runyan 2000). A large number of immigrant workers are illegal: estimates of

workers in the hired farm labor force lacking proper documents for work in the U.S.

range from 25-75% (Effland and Runyan 1998). Although the number of undocumented

workers in the hired farm work force is unknown, the Department of Labor's National

Agricultural Worker Survey (NAWS) initiated in 1988 reports extensive demographic

information, including legal status of farm workers. The NAWS reported that Mexicans

account for 77% of all farm workers in 1997-1998 (Figure 2-2); 52% of hired farm

workers were unauthorized, 22% were citizens, 24% were legal permanent residents, and

the rest were individuals with temporary work permits (Figure 2-3). The same survey

also found that 19% of interviewed farm workers were employed by contractors, 61%

work in fruits, nuts, and vegetables, and one-third of the jobs were in harvesting crops.

On September 1, 1997, the federal minimum wage was increased to $5.15 per hour

from $4.75, where it had been since October 1, 1996. The average farm wage during

1997-1998 was $5.94, and about 12% of farm workers received less than the minimum

wage (Mehta et al. 2000). Those hired by farm labor contractors received a slightly

lower wage ($5.80) than those hired directly by agricultural producers ($5.98) (Mehta et

al. 2000). Although NAWS does not report the earnings by type of legal status, Ise' and

Perloff (1995) using NAWS data have shown that unauthorized workers received lower

wages than legal workers. A large number of immigrant workers receive an income

below the poverty line (29% of non-citizens as compared to 15% of U.S. citizens).

Approximately 4.5 billion dollars are paid annually to 1.4 million immigrants through aid

to families with dependent children (AFDC) or supplemental security income (SSI)









(Larkin 1996). Even though illegal immigrants are not qualified for public assistance

programs, except Medicaid, some may claim benefits by using fraudulent documents

such as birth certificates or green cards. Moretti and Perloff (2000) examined the use of

public and private assistance programs by families of farm workers. They found that

families of unauthorized immigrants are more likely to use public medical assistance and

less likely to use other public transfer programs than authorized immigrants and citizens.

U.S. Immigration Policy

In the previous section, it was apparent that foreign workers are a major source of

the farm labor supply in the U.S. Consequently, changes in immigration policy may have

a large impact on the farm labor market. The Immigration Act of 1917 was the first

foreign worker program. The provision granted the entry to temporary workers from

Western Hemisphere countries. In May 1917, the temporary farm worker program for

unskilled Mexican workers was created. The temporary worker program, referred to as

the first Bracero program, was established during World War I and ended in 1922 (Briggs

2004).

The Bracero (person who works with arms or hands) program, also referred to as

the Mexican Farm Labor Supply Program and the Mexican Labor Agreement, was

established in July 1942 and ended in 1964. It was a bilateral program between the U.S.

and Mexico to recruit Mexican workers for farm jobs. As a result of the Bracero

program, there was a large increase in border migration. It is estimated that 4.6 million

Mexicans were admitted to the United States as guest workers between 1942 and 1964.

The number of Braceros increased over time: 13,000 Mexican immigrants were admitted

between 1942 and 1944, and 146,000 were admitted between 1962 and 1964 (Martin

2001).









In 1986, the Immigration Reform and Control Act (IRCA) was passed to reduce the

flow of illegal immigrants, and to legalize illegal aliens already working in the U.S.

IRCA established 3 ways to accomplish its objectives: employer sanctions, increased

appropriations for enforcement, and amnesty provisions. The employer sanctions

provision designated penalties for employers hiring unauthorized workers. It required all

employers to verify the eligibility of each employee. Employers knowingly hiring

unauthorized foreign workers became subject to fines ranging from $250 to $10,000 per

incident, and employers persistently hiring unauthorized aliens risked a maximum of a 6-

month prison sentence. Perishable agricultural crop producers who had relied heavily on

an illegal labor supply, however, were exempt from this provision until December 1988,

as were livestock producers. In order to assure that legal employees were not

discriminated against on the basis of national origin, antidiscrimination provisions were

also a component of the legislation.

The Special Agricultural Worker program (SAW) granted amnesty to illegal

workers who had at least 90 days of work in 1985-1986 in activities defined as seasonal

agricultural services (SAS) in the agricultural sector. In addition, the Replenishment

Agricultural Worker program (RAW) protected producers from experiencing a shortage

of seasonal workers or the exit of legalized special agricultural workers. The RAW

program was designed to allow a designated number of workers to enter the country, but

they were required to find agricultural employment for at least 90 days per year for 3

years after entry. However, no shortage was ever formally determined. Consequently,

no foreign workers were ever brought into the country under the RAW program.









The H-2 temporary guest worker program established in the 1952 Immigration and

Nationality Act was also retained under IRCA. The Immigration and Nationality Act

(INA) as amended by IRCA authorized the new H-2A program for temporary foreign

agricultural workers. It allowed agricultural employers who anticipated a shortage of

domestic labor supply to apply for nonimmigrant alien workers to perform work of a

seasonal or temporary nature.

As a result of IRCA, nearly 2.7 million persons were ultimately approved for

permanent residence (Rytina 2002), 75% of whom were Mexicans. By 2001, one-third of

the IRCA lawful permanent residents had become naturalized. Table 2-1 shows the

number of immigrants admitted as a result of IRCA. The number of total immigrants

admitted under IRCA legalization, and the special agricultural workers declined during

the 1990s, and slightly increased in the 2000s. The largest IRCA admission was in 1991.

The U.S Citizenship and Immigration Services (USCIS) within the Department of

Homeland Security (prior to November 2003, the Immigration and Naturalization Service

(INS)) reported that deportable Mexican aliens working in agriculture and located by the

border patrol were declining over the past decade. Although the number of legalized

agricultural workers reported by INS and deportable Mexican farm workers declined

after the passage of IRCA, the number of unauthorized farm workers is unknown.

Although IRCA was designed to control illegal immigration to the U.S., and to provide

sufficient labor for agricultural production, it did not eliminate the illegal employment of

unauthorized farm workers. Heppel and Amendola (1992) distinguish between

undocumented and fraudulently documented workers, indicating that the passage of

IRCA decreased the number of undocumented farm workers, but the employment of









fraudulent documented workers increased. The National Population Council of Mexico

(Conapo) estimated that there were 8.3 million Mexican-born US residents in 2000,

including 3 million unauthorized Mexicans, and another 14 million Mexican-Americans

(Mexico: Bracero Lain ,i/i).

On July 10, 2003 the Border Security and Immigration Reform Act of 2003 (S.

1387) proposed by Senator John Cornyn was introduced. This legislative bill would

allow undocumented immigrants in the U.S. to apply for the guest worker program,

applying for permanent residence status from their home country after participating 3

years in the program, open guest worker programs to any sector, and establish seasonal

and non-seasonal guest worker programs. Seasonal workers are authorized to stay in the

U.S. for a period of 9 months, and non-seasonal workers are authorized to stay in the U.S.

for 1 year, but not to exceed 36 months.2 On July 25, 2003, the Border Security and

Immigration Improvement Act (S. 1461) was introduced by Senator John McCain. The

proposed legislation would establish 2 new visa programs. One is entering a short term

employment in the U.S., and the other is for undocumented workers currently residing in

the U.S. The new program does not put a finite number on available visas, and allows

free mobility across sectors. It is estimated that 6 to 10 million illegal aliens claiming

residency in the U.S. would become legal guest workers. It would also allow new legal

workers to get a visa authorizing them to work for 3 years, and then become eligible to

apply for a temporary worker visa that may lead to legal permanent residency.3




2 Border Security and Immigration Reform Act, Senator John Coryn.

3 Border Security and Immigration Improvement Act, John McCain.









Senator Larry Craig introduced AgJOBS legislation (S. 1645 and H.R. 3142) in

November 2003. Unauthorized agricultural workers who had worked 100 or more days

in 12 consecutive months during the 18-month period ending August 31, 2003 could

apply for temporary resident status. If they perform at least 360 days of agricultural

employment during the 6-year period ending on August 31, 2009, including at least 240

days during the first 3 years following adjustment, and at least 75 days of agricultural

work during each of three 12-month periods in the 6 years following adjustment to

temporary resident status, they may apply for permanent resident status.4 The proposed

legislation also modifies the existing H-2A temporary and seasonal foreign agricultural

worker program. The H-2A foreign workers admitted for the duration of the initial job

(not to exceed 10 months) may extend their stay if recruited for additional seasonal jobs

(to a maximum continuous stay of 3 years). The H-2A foreign workers are authorized to

be employed only in the job opportunity and by the employer for which they were

admitted.

On January 7, 2004, President Bush proposed immigration reform that would allow

employers to bring guest workers from abroad if no American can fill the jobs, and also

legalize as guest workers illegal immigrants who are already working in the U.S. The

guest workers would receive 3-year renewable visas like those that would be issued to

currently unauthorized workers in the U.S., but the new guest workers would not have to

pay the registration fee of $1,000 to $2,000 charged to currently unauthorized workers in

the U.S. As guest workers, they could travel in and out of the U.S. freely, and could

apply for immigrant visas. However, no wage floor was proposed and that could create


4 AgJOBS Provision Issue Briefing, Larry Craig.









an incentive for U.S. employers to recruit less expensive labor from abroad. Some

critiques say that President Bush's proposal is more likely to ensure unauthorized workers

who register their departure than their permanent residency due to a long waiting list

before immigration visas become available for unskilled workers.

On January 21, 2004, the Immigration Reform Act of 2004 (S. 2010) was

introduced by Senators Chuck Hagel and Tom Daschle. The proposed legislation would

allow illegal aliens who resided in the United States since January 21, 1999 to participate

and become legal permanent residents. Although the potential impact of these proposals

on the farm labor market is unknown, all allow foreign workers to work in the U.S.

legally via guest worker programs. In conjunction with the new legislative proposals,

apprehensions of illegal aliens have increased nationally by 10% to 11% over 2003, and

apprehensions increased threefold in the San Diego area alone.5

Farm Mechanization in U.S. Agriculture

Mechanization has a long history in U.S. agriculture due to the abundant land and

scarce labor endowments. Binswanger (1984) suggested that the most dramatic aspect of

mechanization is the shift from one source of power to another. Several mechanical

devices were developed from the usage of horsepower in place of hand power during

1862-1875, the first American agricultural revolution.6 Mechanization was also

developed for threshing as early as 1830, and by 1850 all grain threshing in the U.S. had

been mechanized. Not long after small grain reapers became widely adopted in 1850,

wheat harvesting moved to binders in the 1870s, followed by corn binders in the 1880s.

5 Illegal Immigration on the Rise since Bush Revealed Amnesty Plan: National Border Patrol Council
News.
6 This paragraph draws heavily from A History of American Agriculture: Farm Machinery and Technology,
ERS, USDA









Before tractors became widely used after about 1926, the mechanization for tillage had

been the substitution of animal power for human labor, and then steam engine and steel

harrows. A change from horse power to tractors and the adoption of a group of

technological practices characterized the second American agricultural revolution during

1945-1970.

The termination of the Bracero program had a significant influence on the

development of farm mechanization. One obvious example was the adoption of the

mechanical tomato harvester in California. By 1968 it was expected that more than 80%

of tomatoes grown in the U.S. for processing would be harvested by machine (Rasmussen

1975). In 1965 sugar beets became fully harvested by machinery, and 96% of cotton was

harvested mechanically by 1968.

Sarig et al. (2000) summarize the status of mechanical harvesters of fruits and

vegetables in 1997. At least 20-25% of U.S. vegetable acreage and 40-45% of U.S. fruit

acreage is still totally dependent on hand harvesting. Most fruits and vegetables

harvested by machinery are used for processing. Mechanical harvesting usually requires

a large capital investment, and can reduce the production flexibility to change from one

crop to another. Included among the types of mechanical harvesting machinery are labor-

aids, labor-saving, and robotic machines. Labor-saving harvesting machines are those

that replace the work of hand harvesting such as shaking a tree or a bush, digging a row

of below-ground vegetables, or cutting a row of above-ground vegetables. Examples of

crops in which mechanical harvesters are widely used for the fresh market are almonds,

pecans, walnuts, peanuts, potatoes, sweet corn, celery, carrots, and garlic. Crops destined

for the processing market and that use mechanical harvesters include blackberries,









grapes, papaya, plums, raspberries, cherries, celery, cucumbers, peppers, tomatoes, sweet

corn, pumpkins, and peas.

Mechanical citrus harvesters are currently being evaluated in Florida. Two primary

types of mechanical citrus harvesters are being tested commercially (Roka 2001a). The

first is the trunk, shake and catch system (TSC), and the second is the continuous canopy

shake and catch system (CCSC). A TSC system includes 3 machines: a shaker, a

receiver, and a field truck. A shaker and receiver are positioned at the tree where trunks

are shaken for 5 to 10 seconds to remove the fruit. The receiver conveys fruits into a

trailing bin, and a field truck (goat) hauls the fruit to a bulk trailer at the roadside. The

trees need to have adequate clear trunk and skirt heights to allow the shaker and receiver

units to position underneath the canopy. A set of CCSC includes a minimum of 4

machines: 2 harvesting units and 2 field trucks. Shaker heads rotate through the tree

canopy to remove mature fruit. Trees must be skirted to allow fruit collection underneath

the tree canopy. Both systems can recover about 90% of the available fruit. The citrus

harvested mechanically is used only for processing due to damage during the harvesting.

As labor became more expensive after the passage of IRCA, there have been many

attempts to mechanize harvesting other crops such as fruits and vegetables during the past

two decades. The impact of IRCA on farm mechanization was not uniform across the

country. The study of changes in the labor intensity of agriculture by Huffman (2001)

shows that the capital-labor ratio has increased 3% annually in Iowa, but decreased 4%

annually in Florida and California. The material inputs-labor ratio also decreased in

Florida and California after IRCA. This suggests that labor use increased following

IRCA in some states, particularly Florida and California. In the absence of sector







18


specific restrictions, legalized foreign workers would have little incentive to remain

working in the agricultural sector. For example, the AgJOBS bill discussed above

requires temporary resident farm workers to perform only 360 work days of agricultural

employment to apply for permanent resident status.7 The outflow of farm labor to other

sectors is a continuing process. Mechanization is one way that production uncertainty

due to farm worker availability may be mitigated. The impact of IRCA on the perishable

crop industry in different states is discussed extensively in Heppel and Amendola (1992).


45

40

35

0
30 -



420 -
0
15

S10

5

0
1990 1991 1992 1993 1994 1995 1996 1997 1998
Year

--Northeast -- South Midwest --West

Figure 2-1. Percentage of hired farm workers by regions. Note: Data since 1994 are not
directly comparable with data in 1993 and earlier due to changes of survey
design. Source: ERS Calculation from Current Population Survey (Runyan
2000).


AgJOBS Provision Issue Briefing, Larry Craig.










Mexican-Bor
77%


Latin American
Born
2%
Other US-Born
2%
US-Bor African
American
1%
US-Bor
Hispanic
9%


US-Bom White
7%


S Asian Bom
1%

Other Foreign-
Bom
1%


Figure 2-2. Farm workers ethnicity and place of birth. Source: National Agricultural
Workers Survey, 1997-1998 (Mehta et al. 2000).


Citizen
22%


Unauthorized
52%


Other
2%


/ Legal
Pemament
Resident
24%


Figure 2-3. Legal status of farm workers. Source: National Agricultural Workers
Survey, 1997-1998 (Mehta et al. 2000).










0.6


0.5


0.4


S0.3


0.2


0.1


0
0 -----------------------------------
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 200
Year

Figure 2-4. Percentage of deportable aliens located by border patrol who are Mexican
agricultural workers. (USCIS table 60)

Table 2-1. Number of immigrants admitted as Immigration Reform and
Control Act legalization.
Fiscal Resident Since Special Agricultural Total IRCA
Year 1982 Workers Legalization


1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
Total


214,003
46,962
18,717
4,436
3,124
3,286
1,439
954
4
413
246
48
293,632


909,159
116,380
5,561
1,586
1,143
1,349
1,109
1


1,036,324


1,123,162
163,342
24,278
6,022
4,267
4,635
2,548
955
8
421
263
55
1,329,956


Source: Statistical Yearbooks
Department of Justice)


of the Immigration and Naturalization Service (U.S.


2














CHAPTER 3
THEORETICAL AND ANALYTICAL FRAMEWORK

This chapter is divided into two parts. The first part provides an overview of the

theory of technological change. The historical development of induced innovation theory

based on cost minimization is illustrated. To my knowledge, the theoretical model of

induced innovation based on profit maximization that is used in this study has not been

developed before. The graphical profit maximization model of induced innovation theory

of my own development is then introduced. The second part of this chapter gives the

definition of technological change and biased technological change based on the induced

innovation theory.

Cost Minimization Model of Induced Innovation Theory

In growth theory, a technological change that increases the productivity of capital,

including human capital, is an indication of economic growth. Economists have

developed several models to explain the sources of technological change. The theory of

induced innovation is among the first set forth theoretically and empirically during the

1960s and 1970s. In the mid 1970s, Nelson and Winter (1973) developed an

evolutionary theory that is an interpretation of the Schumpeterian process of economic

development (Schumpeter 1934). In the late 1970s and 1980s, the path dependence

theory was developed by Arthur (1989) and his colleagues. A more detailed discussion

of each theory and its strengths and limitations is found in Ruttan (2001, p. 117).

Within the induced technological change theories, there are 3 major models that try

to explain the rate and direction of technological change. First, a demand pull model









emphasizes the role of the demand for technology on its supply. Griliches (1957) uses

this model to determine the role of demand on the invention and diffusion of hybrid

maize. Vernon (1966, 1979) also uses this model to study the invention and diffusion of

consumer durable technologies.

Second is a growth-theoretic model or a macroeconomic model. This model is

based on the effects of factor endowments, their relative prices, and factor shares on the

factor augmentation of a technological change. It is introduced by Kennedy (1964, 1966,

1967) and Samuelson (1965, 1966). However, the theory is criticized by Nordhaus

(1973) for having an inadequate microeconomic foundation.

Last, and the approach of this study, is a microeconomic model of induced

innovation. The term "induced" innovation was first used by Hicks in his book "Theory

of Wages".

"...A change in the relative prices of the factors of production is itself a spur to
invention, and to invention of a particular kind-directed to economising the use of a
factor which has become relatively expensive... If, therefore, we are properly to
appreciate the place of invention in economic progress, we need to distinguish two
sorts of inventions. We must put on one side those inventions which are the result
of a change in the relative prices of the factors; let us call these "induced"
inventions. The rest we may call "autonomous" inventions." (Hicks 1932, p.124-
125)

Focusing on 2 types of factors, labor and capital, Hicks classified 3 types of

inventions based on the changes in ratios of marginal products.

"..."Labour-saving" inventions increase the marginal product of capital more than
they increase the marginal product of labor; "capital-saving" inventions increase
the marginal product of labour more than that of capital; "neutral" inventions
increase both in the same proportion." (Hicks 1932, p.121-122)

Even though Hicks first created the idea of induced innovation, the mechanism of

how it would happen was not specified. As a result of the lack of an explanation, Salter

(1960) criticized the Hicksian induced innovation hypothesis.









"When labour costs rise, any advance that reduces total costs is welcome, and
whether this is achieved by saving labour or capital is irrelevant. There is no
reason to assume that attention should be concentrated on labour-saving techniques,
unless, because of some inherent characteristic of technology, labour-saving
knowledge is easier to acquire than capital-saving knowledge." (Salter 1960, p.43).

Following Salter's criticism, Ahmad (1966) clarified the analytical basis of the

induced bias innovation mechanism in the framework of a traditional comparative statics

approach. His model is known as the Hicks-Ahmad model of induced technological

change.

Hicks-Ahmad Model of Induced Technological Change

Ahmad assumed that the production function is linear and homogeneous. Each

innovation is represented by a set of isoquants on labor and capital axes to represent a

production function. If for any given output at each factor price ratio, the ratio of factor

combinations of the new and old isoquants remains the same, innovation is neutral,

assuming cost minimization by an entrepreneur. When a new isoquant indicates a lower

ratio of labor to capital for the least cost combination, the innovation is labor-saving for a

given output at a given factor price ratio. Similarly capital-saving innovation is defined in

the same way. From Ahmad's assumptions about the production function, the neutrality

in his definition is equivalent to that of Hicks.

He used the concept of the historical Innovation Possibility Curve (IPC) as an

envelope of all alternative unit isoquants (representing a given output on various

production functions) at a given time. Isoquants on the same IPC are a set of potential

production processes, determined by a state of knowledge, which are available to be

developed for a given amount of research and development expenditure. The elasticity of

substitution of each isoquant is smaller than that of the IPC (the curvatures of the

isoquants are greater than those of IPC). By assuming that IPC is smooth and convex, a









point where the price line is tangent to IPC determines a production function. IPC is a

result of technological knowledge, but the economic consideration is to choose a

particular isoquant out of a set of various isoquants that belong to a particular IPC.

He emphasized that the act of invention is the movement from one production

function to another, while factor-substitution is just moving from one point to another on

the same production function. The movement of a new isoquant closer to the origin is a

cost-saving invention. Figure3-1 illustrates this model.

At time period t, relative factor prices of PtPt were revealed, a cost minimizing

production process It was developed, and the corresponding IPC is IPCt. Assuming that

the same amount of expenditures are required to go from It to any other technique on IPCt

as to go from It to any process on IPCt+i, no other process is developed in the same IPCt

after It is developed. The next period t+1, IPCt shifts inward to IPCt+1 indicating that

there is a new set of technology. If the technological change is neutral (IPCt shifts

neutrally to IPCt+i), and if the relative factor prices PtPt remain unchanged, a process It+l

will be developed at time t+1. However, Ahmad indicated that IPC may shift

nonneutrally even at constant relative factor prices, and biased technological change

would occur. If at t+1, there is an increase in the relative price of labor corresponding to

Pt+1Pt+l, then the production process It+l is no longer optimal. If the IPC shifted neutrally,

I't+1 becomes optimal, and it represents a relative labor-saving technology compared to It.

If the innovation possibility is technologically unbiased, an increase in the relative

price of labor will induce an innovation which is necessarily labor-saving. On the other

hand, if the innovation possibility is biased in either direction, a change in the relative

price of the factors will still induce technology to save the factor that has become









relatively more expensive. Yet this inducement will be modified by the bias of the

historical innovation possibility.

With a 2-dimensional graph, it is difficult to demonstrate more than a 1 period

model when the research expenditure does not remain fixed. A mathematical model

facilitates analysis of the problem (Binswanger 1978, p.26-27).

Hayami and Ruttan Model of Induced Technological Change

Hayami and Ruttan have contributed greatly to the understanding of agricultural

development. Their paper in the Journal of Political Economy in 1970 followed by the

Agricultural Development book in 1971 emphasized the differences in agricultural

development between Japan and the U.S. These 2 countries represent the 2 extreme

resource endowments: Japan has abundant labor (L) and little land (A) while the U.S. has

abundant land and little labor.8 By partitioning the growth in output per worker (Y/L)

into 2 components: land area per worker (A/L) and land productivity (Y/A), sources of

technological change in the 2 countries can be identified.

Y AY
Y AY 3.1
L LA
Given the relative factor price differences in 2 countries, growth of output per

worker (Y/L) will be highly correlated to changes in land area per worker (A/L) in the

U.S., and to changes in land productivity (Y/A) in Japan.

In the U.S., land area per worker (A/L) rose much more rapidly than in Japan. The

source of the increase in land area per worker would be explained by mechanical

technology which allows farmers to operate on a larger land area. Mechanical technology

replaces or supplements manpower with other sources of power that are economically

8 Their study in 1970 paper utilized the data for 1880-1960, and support of the U.S. data has been criticized
by Olmstead and Rhode (1993).









more efficient (animal, mechanical, electrical). Examples of mechanical innovation are

the substitution of the self-raking reaper for the hand-rake reaper, and the substitution of

the binder for the self-raking reaper that require more horses per worker. On the other

hand, land productivity (Y/A) in Japan rose much more rapidly than in the U.S. The

source of the increase in land area per worker was explained by biological technology

that increased production per land area through fertilizer and yield-increasing

improvements in varieties.

They developed a 4-factor induced technological change model, similar to

Ahmad's model. In this model, land and mechanical power were regarded as

complements, and were substitutes for labor. Biological technology and fertilizer were

regarded as complements and were substitutes for land. Increases in land area per worker

can be achieved through advances in technology. Graphical illustration of this model is

shown in Figure 3-2a and 3-2b.

Figure 3-2a represents a process of mechanical technology innovation. At time 0,

Io represents the innovation possibility curve (IPC)9 which is an envelope of less elastic

unit land-labor isoquants, for example, to different types of harvesting machinery. If

price ratio PoPo prevails, a technology (e.g., a reaper) io is invented. Point P is a cost

minimized equilibrium that determines the optimal combination of land, labor, and power

requirements. Generally, technology that enables operating a large area per worker

requires higher mechanical power. Land and power are represented by a combination

line [A, M], which represents complementarity. At time period 1, assume that relative

land rent to wage rate decreases as labor becomes more scarce; IPCi is represented by Ii.

9 The concept of IPC was originally used as a "metaproduction function" in Hayami and Ruttan (1970).
The differences in these 2 definitions are discussed in Binswanger (1978, p.46).









A change in relative price from PoPo to PiP1 induced a new technology (e.g., a combine)

represented by ii. Point Q represents a new optimal technology which allows farmers to

use more land and less labor by using more power.

In Figure 3-2b, a process of biological technology innovation is illustrated. Similar

concepts of induced innovation can be explained by the increase in relative price of land

to fertilizer. I*0 represents IPC of different land-fertilizer isoquants, corresponding to

different crop varieties such as i*o. A shift of relative price P*oP*o to P*iP*i induced a

new technology (e.g., a more fertilizer-responsive crop) represented by i*' is developed

along I*1. A linear combination [F, B] implies a complementary relationship between

fertilizer and biological technology. In addition, land infrastructure and biological

technology are assumed complementary since technology that substitutes fertilizer for

land, for instance fertilizer responsive, high-yielding varieties, generally requires better

control of water and land management such as irrigation and drainage systems. As the

relative price of land to fertilizer increases, the optimal technology changes from P* to

Q*. This indicates that the new crop variety allows farmers to use less land, and more

fertilizers that require more land infrastructure.

Hayami and Ruttan (1970, 1971) not only developed a theoretical model of induced

innovation, but they also found empirical support of the theory in the U.S. and Japan.

Agricultural growth in the U.S. and Japan during 1880-1960 can be viewed as a dynamic

factor-substitution process. Long run trends of relative factor prices induce innovations

that substitute for each other. In a fixed technology they assumed that elasticities of

substitution among factors were small, that variations in factor proportions could be

explained by changes in factor price ratios. If the variations in these factor proportions









were consistently explained by the changes in factor price ratios, they argued that the

innovations were induced. This test, however, was not a test of the induced innovation

hypothesis.10

Assuming that a production function is linear homogeneous, log-linear regressions

of land-labor and power-labor ratios on the relative price of land to farm wage and the

relative price of machinery to farm wage are examined." The results showed that more

than 80% of the variation in the land-labor ratio and in the power-labor ratio is explained

by the changes in their price ratios. This indicated that the increases in land and power

per worker in U.S. agriculture during 1880-1960 have been highly correlated with

declines in prices of land, power and machinery relative to the farm wage rate.12 It was

also confirmed that land and machinery were complements by the negative signs. The

regressions of fertilizer input per hectare of arable land on relative factor prices of

fertilizer to land, labor to land, and machinery to land were also tested. The results

showed that variations in fertilizer-land price ratio alone explained almost 90% of the

variation of fertilizers.13 The result also showed that fertilizer and land were substitutes.

The same regressions were also tested for Japan but were excluded from this discussion.

The comparison of the 2 countries indicated that changes in relative factor prices induced

a dynamic factor substitution accompanying changes in the production surface. Labor


10 A test of induced innovation hypothesis would involve a test for nonneutral change in the production
surface.

1 ln(A/L) = f(ln(r/w), ln(m/w)) where A=land area, L=worker, r=price of land, w=wage rate, m=price of
machinery. Different definitions of land and labor are used in the original regressions.

ln(M/L) = f(ln(r/w), ln(m/w)) where M= machinery.

12 Hayami and Ruttan (1970) Table 2.

13 Hayami and Ruttan (1970) Table 4.









supply had been less elastic than land supply in the U.S. during this period. The price of

labor relative to the price of land had been increasing; as a result, mechanical innovations

of a labor-saving type were induced. A dramatic decrease in the price of fertilizer since

1930 had shifted mechanical innovations to biological innovations in the form of crop

varieties highly responsive to the lower cost of fertilizer.

Hayami and Ruttan's 1970 paper has inspired many economists to develop both

theoretical and empirical models of technological change. In the next part of this section,

selected empirical studies of biased technological change in American agriculture are

presented.

Empirical Studies of Biases in U.S. Agricultural Technology

Binswanger (1974b) developed a many-factor translog cost function model to

analyze biased technological change. By applying Shephard's lemma, factor share

equations were estimated. He assumed 2 cases for the rate of biases: model A assumes

variable rates of biases, and model B assumes constant rates over time. The parameter

estimates from the models were used to demonstrate the direction of bias, and calculate

Allen elasticities of substitution (Allen 1938) and cross elasticities of demand. This

approach also allowed him to calculate the biases of technology in the absence of factor

price changes. Cross-section data from 39 states or groups of states were used to estimate

the share equations for the years 1949, 1954, 1959, and 1964. Time-series agricultural

data from 1912-1968 were used to calculate the change in factor shares in the absence of

price changes.

The results showed a very strong bias toward fertilizer-using. While assuming that

fertilizer prices were exogenous to agriculture, a rapid decrease in fertilizer price relative

to output price demonstrated a consistent induced innovation model. The author also









assumed an exogenous wage rate from agriculture since the price of labor was also

governed by nonagricultural sectors. An increase in the price of labor in the existence of

a labor-saving bias during the study period showed that the induced innovation

hypothesis was consistent; the biased technological change alone explained about two-

thirds of the decrease in labor share. Machine prices also increased during this period;

however, technological change was machine-using. This means that a neutral innovation

possibility could not have occurred, and it must be toward machine-using. Since land

price was endogenous to agriculture, biases of land could not give much information.

Antle (1984) utilized a translog profit function to measure the structure of U.S.

agriculture during 1910-1978. He applied duality relations with a multifactor profit

function to measure biased technological change, homotheticity, and estimate input

demand and output supply elasticities. By applying Hotelling's lemma to a profit

function, input demand functions were estimated. Biased technological change of factor

i, Bi, was defined as a rate of change of its production elasticity share over time. If the

rate of change of the production elasticity is positive (negative), technological change is

biased toward (against) that input. And if it is 0, a technological change is neutral. By

estimating each profit-maximizing factor quantity equation, biased technological change

can be calculated. This method has an advantage over Hicksian measurement based on

marginal rates of technological substitution since biases can be calculated without

measuring biases between every input pair. The estimation showed that during 1910-

1946, the biases were primarily toward machinery and against land. These findings

contradict Binswanger's (1974b) results that technology was biased toward chemicals

during the prewar period. However, the biases after the war (1947 tol978) were toward









labor-saving and capital- and chemical-using similar to Binswanger's results. The

findings in Antle's study were consistent with induced innovation theory since the wage

rate relative to machinery and chemical price was declining during 1925 to 1940, and the

bias during this period was toward labor.

Shumway and Alexander (1988) estimated supply equations for 5 agricultural

product groups and demand equations for 4 input groups in 10 regions of the U.S. By

assuming a competitive market, they analyzed the impact of government intervention,

changes in technology, and other market stimuli on agricultural production in different

regions during 1951-1982. A profit function approach was used to derive input demand

and output supply equations via the envelope theorem. A test of neutral technological

change was conducted using the Hicksian neutrality definition. The results showed that

disembodied technological change has taken place over the sample period, and it has not

been Hicks-neutral in most regions. The authors suggested that technological change

bias should be taken into account when modeling variable input demand ratios and output

supply ratios.

Weaver (1983) used a translog profit function to evaluate biases in technology of

multi-input, multi-output production of U.S. wheat region. He defined a technological

change as a derivative of the ratio of inputs with respect to technological knowledge. He

found that the technology between 1950 and 1970 in the U.S. wheat region was labor-

saving relative to capital and petroleum products. It was also fertilizer-using relative to

capital, materials, and petroleum products.

Profit Function Model of Induced Innovation

Ahmad's and Hayami and Ruttan's theoretical framework of induced innovation

model is based on cost minimization and assumed only 1 aggregate output. The change









in technology is defined as the inward shift of the innovation possibility curve. Even

though the definition of technological change based on cost minimization is closely

linked to the theoretical definition of induced innovation and has been widely adopted, it

ignores the changes in output combinations which become significantly important in

agricultural development. The decrease in resource requirements to reduce the cost of

production in induced innovation theory does not allow the analysis of the impact of

changes in output since it is assumed to remain the same. Biological technology, for

instance, has become increasingly important in American agriculture. In the Hayami and

Ruttan definition, biological technology was defined as technology that increases output

per unit of land. Recent developments of biological technology such as genetically

modified crops do not aim only to increase output per unit of land via drought resistance,

pesticide and herbicide resistance or virus resistance, but also to increase the market

values of crops such as vitamin and protein enhanced grains and seedless fruits. The

production of any new crop variety may change the optimal mixture of input

requirements; therefore, it will fall outside the scope of cost minimizing induced

innovation theory. In addition, the increasing international trade flow, changes in trade

policy, and changes in trade agreements may change the demand for as well as the supply

of different types of commodities. These changes in output combinations may also

change the input requirements.

The profit maximization approach of the induced innovation model is a more

appropriate alternative in the study of multi-input, multi-output technology. It recognizes

the simultaneous determination of output mix and variable inputs for given prices. The

theoretical framework of this approach is now developed.









At a given time period, the potential production processes are determined by the

state of technology and the resource endowments. The Innovation Production Possibility

Frontier (IPPF) is the envelope of all potential production processes that can be

developed at a given time. Technological progress is defined as the upward shift of the

IPPF, the envelope of production functions. The analogous innovation possibility

frontier in the cost minimization model is the Innovation Possibility Curve (IPC) in the

Hicks-Ahmad model of price-induced technological change and the Metaproduction

Function (MPF) in Hayami and Ruttan's model of induced innovation. Each potential

production process is represented by a production function f(x). Figure 3-3 illustrates the

concept of IPPF and technological change in a simple case of one output-one input

technology.

At time period 1, the innovation possibility frontier is represented by IPPF1, the

envelope of all less elastic production functions which are the potential technological

processes at period 1. The isoprofit line, 7t, represents the profit for given input and

output prices. Given that n7 = py wx,14 the profit function defined in y-x space can be

written as y = 7T/p + (w/p)*x. The slope of the isoprofit line is equal to w/p. If given

prices in period 1 represent 7*, the most profitable technology available under IPPF1 is

Y1 = fi(x) where the slope of the isoprofit line coincides with the slope of the production

function, the first order condition of profit maximization. Assume that there is a

technological progress (an upward shift of IPPF) represented by IPPF2 in period 2, but

prices remain unchanged so the slope of the isoprofit line remains constant, then the most

profitable technological process in the second period is Y2 = f2(x). Notice that the


14 7 = profit; y = output; x = input; p = output price; w = input price.









intercept of the new isoprofit line, 7t**, is higher than that of 7*; thus, the technological

progress generates a higher profit at given prices. From Figure 3-3, the new most

profitable technology produces more output and employs more input, but this is not

necessarily the case. The new technology could also employ less or the same amount of

the input at a higher output level for given prices

Figure 3-3 represents the one-input, one-output production function, but if we

assume a two-input, one-output technology, y = f(K,L), we can interpret Figure 3-3 as y =

Y/L and x = K/L, and y = f(x) would be an intensive production function. Again, given

that prices remain constant, technological progress may result in a higher, a lower, or a

constant capital-labor ratio (biased or neutral technological change).

Figure 3-4 represents technological progress from IPPF1 to IPPF2, and an increase

in the price ratio from (w/p)* to (w/p)'. In period 1, 7t* represents the profit given (w/p)*,

and the most profitable technological process is Yi = fi(x). After an increase of the

relative factor price to output price to (w/p)' reflected by an increase in the slope of the

profit function to 7', and before any innovation of new technology, the most profitable

technological process is Yi'= fi'(x). An increase in w/p results in a decrease in output

level and input requirement. If there is also a technological innovation in period 2 as a

result of a change in w/p, there would be an increase in output from what it would have

been without technological progress (from Yi' to Y2). In Figure 3-4, it is shown that

technological progress also decreases the input requirement (from XI' to X2), but this

may not be the case as will be discussed later. In sum, an increase in w/p will decrease

the profit-maximizing output and input levels, but if this price change induces a new set

of potential technological processes that increase profit, it will increase the output level









and may or may not change the input requirement. The overall effects on output and

input levels are ambiguous.

In the case of more than one-input, one-output technology, it is unclear what a

change in factor price or relative factor price will be on the output level. To illustrate,

recall that the profit maximization solution is equal to the cost minimization solution if

cost is minimized at the profit maximizing output level.15

7T(p, w) = max y, x[py wx] 3.2

where x is a vector of many inputs. Let y* = y(p, w) be the profit maximizing output,

7x(p, w) = py* minx [wx] 3.3

7T(p, w) = py* C(w, y*) 3.4

where C(w, y*) is the cost function at the given y*. Taking the first derivative with

respect to wi, we get

S C(w, y*) 3.5
aw, aw,

Utilizing Hotelling's lemma and Shephard's lemma,

xi,(p, w)= xic(w, y*). 3.6

The uncompensated factor demand, xiU(p, w), is the same as the compensated factor

demand, xic(w, y*), if the compensated factor demand is obtained from cost minimization

at the profit maximizing output level, y*.

Suppose that there is a change in a factor price wj. Taking the derivative of Eq. 3.6

with respect to wj:

ax,"(p,w) caxlC(w,y*) caxlC(w,y*) y
w y 3.7
Cwj wj -y aw i


15 The profit function, the history of economic thought website.









If the price of factor j changes, factor demand changes may be decomposed into 2

effects: the substitution effect, represented by the first term on the right hand side of 3.7,

and the output effect, represented by the second term on the right hand side. If output

does not change, the direction of a change in cost minimizing input requirements due to

the substitution effect (net effect) can be determined by whether the inputs are

complements or substitutes. However, since there is an output effect which can

counteract the substitution effect, the direction of a change in profit maximizing inputs as

a result of changes in factor prices (gross effect) is ambiguous.

Figure 3-5 illustrates changes in factor requirements as a result of substitution and

output effects when there is a change in the factor price ratio in a profit maximization

problem. As relative capital to labor prices increase from (r/w)1 to (r/w)2, a substitution

effect will result in changes in compensated input demands due to cost minimization

while holding output constant at Y1. This results in a movement along isoquant Ii, from

A to B which decreases the capital requirement from K1 to Ki' and increases the labor

requirement from L1 to Li'. In addition, an increase in (r/w) also results in an output

effect which may shift the isoquant inward to 12 if output level decreases or to 13 if output

level increases. Gross changes in input requirements are ambiguous. As we can see from

Figure 3-5, the gross effects of input requirements could be at C where K2 and L2 are

lower than those before a price change or at D where K3 and L3 are higher than those

before a price change.

As a result of the ambiguity of the impact of changes in input prices on the

direction of input change, I will explain the profit maximization approach of induced

innovation theory as an upward shift in the IPPF induced by changes in relative input









prices. The result of gross biased input requirement changes determines the direction of

biased technological change. Since changes in input requirements could result from

purely a substitution effect as a result of changes in prices, technological progress is

defined as an increase in profit given that the output and input prices remain unchanged:

x/8at > 0 for given p's and w's 3.8

An increase in profit could result from both an increase in output levels and a

decrease in input requirements. Figure 3-6 gives the illustration of the profit maximizing

induced innovation model for a two-input, one-output technology. The IPC is used to

demonstrate the concept of induced innovation analogously to IPPF.

An increase in relative factor prices from (r/w)1 to (r/w)2 results in a decrease in

capital requirement and an increase in labor requirement by a substitution effect, a

movement from A to B. A movement from technology at point A to point B does not

require any innovation of new technology because they are both available under IPC1.

The IPC1 could shift to IPC1' or IPC1" via the output effect resulting in a different profit

maximized production process. Holding the output level constant (no output effect), an

increase in relative capital to labor prices induces a new technology set IPC2 which

results in a further reduction of cost minimized input requirements. An increase in (r/w)

could also induce a new set of technology that increases the output level, IPC2'. The

gross effect of an increase in relative prices of capital to labor is ambiguous depending on

whether the IPC curve shifts to IPC2 or IPC2'

The example in Figure 3-6 is neutral technological progress which means that

holding factor prices constant at (r/w)2, the labor-capital ratio (L/K) remains constant as









the IPCs shift. Biased technological progress can be defined as a gross change in (L/K)

given that output prices, input prices and fixed input quantities remain unchanged.

Rate of Technological Change and Biased Technological Change

The development of definitions and mathematical derivations in this section is

based heavily on Kohli (1991). A multi-output, multi-input variable profit function is

defined as: r(Z, K, t) = maxQ Z'Q | K, t}for Z > 0 and K> 0, where Z is a vector of N

output and M variable input prices, and Q is a corresponding vector of quantities; K is a

vector of L fixed inputs, R is a vector of fixed input prices, and t is a state of technology.

Employing Euler's theorem, the linear homogeneity of the variable profit function in Z

and K implies that

-= Z = KJ 3.9
at a 8tSZ1 tOKJ

Define the semielasticity of the supply of output and the demand for variable inputs

with respect to the state of technology as:

8ln Q1
it nQ i 1,...,N+M 3.10
8t

and the semielasticity of the inverse fixed input demand with respect to the state of

technology as:

8lnR
t n j = 1,...,L 3.11

Dividing through by rT, and using Hotelling's Lemma and the marginal revenue of

fixed input condition, Eq. 3.9 can be written as:

ln 3.12
C1= = -- : nE, = l~t~ 7: 2 3.12
1 J









where / is the rate of technological change, and 7ni and tcj are profit shares of variable

inputs and outputs, and those of fixed inputs, respectively. There is technological

progress when the rate of technological change is positive.

The rate of technological change is defined as the rate of growth in profit over time.

It is also equal to an average of the rates of increase in outputs and decrease in variable

inputs via changes in the state of technology weighted by profit shares, at given fixed

input quantities, output and variable input prices. Alternatively, it can be expressed as a

weighted average of the rates of increase in fixed input price via changes in the state of

technology at given output and variable input prices and fixed input quantities.

The bias of technology is defined as

B, E;t i = 1,...,N+M 3.13

B1 s j = 1,..., L 3.14

A technological change is output i-producing if Bi is positive, and it is output i-

reducing if Bi is negative. Similarly, a technological change is variable input i-using if Bi

is positive, and it is variable input i-saving if Bi is negative. A technological change is

fixed input j-using if Bj is positive, and it is fixed input j-saving if Bj is negative. If

technological change is unbiased or neutral, Bi = Bj = 0, and

S= t = t Vi = 1,...,I; V j = ,...,J 3.15







40



Capital



IPCt
IPCt+,




S i 't+1 +
Pt I\ It

Pt





It+l




Labor
Pt+ Pt Pt

Figure 3-1. Ahmad's induced innovation model. (Ahmad, Syed. "On the Theory of
Induced Invention." The Economic Journal 76(302) 1966, p.349)











Labor


Io
Po j
t io


Io P*l


Q
Sii


Land


[A, M


Mechanical Technology


Figure 3-2.


Biological Technology


Induced technological change. A) Mechanical technology development. B)
Biological technology development. (Hayami and Ruttan. "Factor Prices and
Technological Change in Agricultural Development: The United States and
Japan, 1880-1960." The Journal of Political Economy 78:5 (Sep. Oct.
1970), p.1126)


Q*
1 1*


- I*1


Fertilizer





[F, B]


Land










Output


IPPF2


IPPF1


Yi=fi(x)


Xi X2 Input


Figure 3-3. Innovation production possibility frontier and technological progress.













Output









Y1


Y1'=fi'


Yi=fi(x)


Figure 3-4. Technological progress and a change in prices.


IPPF2


IPPF1


X2 X1' X1 Input











Labor


L 3 ..........







Li'

L ...........
L1
L 2 ..........










Figure 3-5.


K2 Ki' K1 K3 Capital


Substitution and output effects of profit maximization. (Fonseca and Ussher.
"The Profit Function." The History of Economic Thought Website
http://cepa.newschool.edu/het/essays/product/profit.htm#decomposition
(April 13, 2004)











Labor


IPC2


IPC1,
IPC1


Capital


Figure 3-6. Induced innovation for profit maximizing technological change.














CHAPTER 4
EMPIRICAL MODEL, DATA, AND ESTIMATION

This chapter discusses the empirical model and the restrictions of the profit

maximization approach of the induced innovation theory. Among other restrictions,

curvature restriction will be discussed extensively. It also describes the data and the

definition of each variable used in the model. Finally, estimation techniques of

seemingly unrelated regression, imposing model restrictions, and the rate of biased

technological change are discussed.

Empirical Model

Binswanger (1978) discussed issues in modeling induced technological change

extensively in "Induced Innovation". There are two approaches to modeling induced

technological change: the production function approach, and the cost or profit function

approach. Several authors, such as Kennedy (1964), use factor-augmenting coefficients

in the production function in order to capture the change in technology. As discussed in

Binswanger (1978), the method of factor augmentation has some disadvantages. If the

production function is Cobb-Douglas, rates of change in augmenting coefficients of

different factors will be neutral. Moreover, the change of technology embodied in one

factor does not necessarily augment only that factor. For example, the quality

improvement of workers who operate machine harvesters not only augments labor, but

also machinery. Furthermore, a quality index is mistakenly used as factor augmentation.

Changes in the quality of a factor (e.g. rate of human capital accumulation per worker)









can neither be viewed nor measured as rates of augmentation in a factor-augmenting

production function (Binswanger 1978).

Much attention of technological change has been on endogenizing research and

development in a firm decision since the 1960s. One disadvantage of this method is that

technological advance is not perfectly correlated with research and development

expenditures, and other omitted variables can result in a different specification of

technological change (Lambert and Shonkwiler 1995). The effort to capture the

stochastic trend on technological change has been done by Lambert and Shonkwiler

(1995), but the trend also depends on research expenditures. However, understanding

resource allocation, returns to investment, and technology transfer can be obtained by

endogenizing the research and development expenditures decision in the model.

Alternative approaches are the cost function and profit function approaches. There

are several advantages of this over a production function approach (Binswanger 1974a).

In a perfectly competitive market, output prices and factor prices are exogenous to

producers' decisions, while output and input quantities are endogenous. Using factor

prices as independent variables in the estimation equation of the cost function or profit

function approach is more appropriate than using input quantities in the production

function approach, and the problem of multicollinearity is less among input prices than

input quantities. Since the homogeneity property always holds in cost and profit

functions, it is not necessary to impose the homogeneity property on a production

function to derive the estimation equation for the cost or profit function approach.

The cost minimization or profit maximization approaches are 2 alternatives for

modeling microeconomic production models. The profit function provides more









information than the cost function when multiple outputs are taken into account. The

variable profit function is adopted in recognition of the simultaneous determination of

output mix and variable inputs for given prices. This approach permits analysis of the

impact of factor prices on the output mix.

The transcendental logarithmic (translog) profit function is considered more

appropriate than other functional forms for this study because of its flexibility, ease of

interpretation, and ease of computation. A constant elasticity of substitution (CES)

model is too restrictive for a many-factor profit function since all partial elasticities of

substitution between all pairs of inputs must be constant. The translog function is a more

generalized form of the Cobb-Douglas function since it is not restricted to unit elasticities

of substitution. A translog profit function is a logarithmic Taylor series expansion to the

second term of a twice-differentiable profit function around the variables evaluated at 1.

Among other popular flexible functional forms, the translog is less restrictive than the

generalized Leontief and normalized quadratic functions since these 2 functions pre-

impose quasi-homotheticity expansion paths implying that the marginal rate of input

substitution is independent of output levels. It is undesirable, for example, to restrict the

input demand elasticities with respect to output to 1 as output increases. They also

restrict marginal rates of substitution among any input pair to be independent of all input

prices except those of the input pair, and they impose separability between inputs and

outputs which implies that marginal rates of output transformation are independent of

factor intensities or input prices (Lopez 1985). However, the advantage of using the

normalized quadratic function is that it satisfies global curvature without additional










constraints; whereas, the translog function does not. In this study, I impose the curvature

constraints locally on the translog profit function.

Model Specification

Assuming that producers are price-takers and maximize short-run profit, a variable

profit function of induced innovation theory is adopted. A state of technology influences

the profit of production. Assume that outputs Y = (Y,,..., Y,) use variable inputs

X = (X,,..., X,) and fixed inputs K = (K,,...,KL). The vectors of output prices, input

prices and fixed input prices are denoted by P = (P,,..., P), W = (W,,..., WM), and R =

(R1,..., RL), respectively. Let Q = (Qi,...,QN+M) be a vector of variable input and output

quantities, and Z = (Zi,..., ZN+M) be a corresponding price vector.

A time variable, t, is used as a representative for technological knowledge even

though it may leave much to be desired as an explanation of technological change. As

Chambers (1994: 204) argues, time is a very economical variable for representing

technological change; it has some definite advantages such as analytical and econometric

tractability over some other approaches. The profit function is defined as:

7(Z, K, t) = maxQ {Z'Q | K, t} for Z > 0 and K > 0. The translog variable profit function is


written as

N+M L 1 N+MN+M
ln7r = o+ Ol InZ, +1jflnK1 + Yh lnZ,lnZh
1=1 =1 2 =1 h=1
L L N+M L

S=l k=l 1=1 =l 4.1
N+M L
+ 6 t InZt+ t InK t+ Pt+ -tt2
1=1 j=l 2









Assuming that 47(P, W, K) is twice continuously differentiable, it must satisfy

Hotelling's Lemma, &//OZi = Qi. The differentiation of the variable profit function with

respect to output (and variable input) prices yields profit maximizing output supplies (and

variable input demands). Thus, On7/Pi = Yi, and i/OtWj = Xj, and where Yi's and Xi's

are vectors of profit maximizing outputs and variable inputs, respectively. Recall that all

output and variable input prices are positive; this implies that variable input quantities are

negative. Utilizing the Hotelling's Lemma, profit share equations can be derived from

the derivatives of the log of profit with respect to the log of prices.

tln Q1Z,
= 7, i 1,...,N+M 4.2
8lnZ, n7
where 7ti > 0 if Zi is an output price, and 7ti < 0 ifZi is a variable input price.

The marginal revenue of a fixed input is equal to its cost under competitive

conditions. Thus, the derivative of the variable profit function with respect to a fixed

input quantity is equal to its cost, &/O/8Kj = Rj > 0, and the derivatives of the logs yield

profit share equations.

tln R1K
-=1 j = 1,...,L 4.3
OlnK 7r
In the case of the translog variable profit function, share equations are derived as follows:

SIn 7 N+M L
7t,-- = a y + hlnZh + 6lnKJ+6tt i=1,...,N+M 4.4
SIn Z h=1 j=1
ln r N+M L
7J = nK + 61 lnZ jk l + k lnKk t j =,...,L 4.5
OlnK 1 1-1 k-1
Model Restrictions

A well-defined nonnegative variable profit function for positive prices and

nonnegative fixed input quantities satisfies the following restrictions:

1. Homogeneity










A variable profit function is linearly homogeneous in prices of outputs and variable

inputs and in fixed input quantities. It is defined as: 7i(XZ) = hkt(Z), and 7t(kK) = Xkj(K),

k > 0. Euler's theorem states that the linear homogeneous function can be expressed as:


S Z, 7rt(Z); K 7t(K)
OBZ, OKJ
ln ln X
Thus, = 1; Y = 1 These are also known as adding-up conditions.
1 lnZ, alnK1

The second and third summation terms and the last term in 4.4 and 4.5 contain variables

that can take different values, the sum of share equations can only be restricted to 1 if

these terms are restricted to 0. The homogeneity restrictions for the translog profit

function are as follows:

N+M L
Z=1 = 1; '= 1
1-1 j-i
N+M N+M L L N+M L
ZYih lZY h = Z jk = jk= y61 =Z6, =0 4.6
1i1 h=1 ]=1 k=1 1=1 ]=1
N+M L
Y6lt t= 1t =0
1=1 -=1
2. Symmetry

For a twice continuously differentiable profit function, Young's theorem implies

that the Hessian of the profit function is symmetric. In terms of the translog profit

function,

Ylh = Yhi; jk = kj 4.7

3. Curvature

The convexity of a variable profit function in prices implies that the output supply

and variable input demand functions are non-decreasing with respect to their own price.

If i is a variable input (Xi < 0), an increase in its price reduces the quantity demanded,









0Xi/8Wi > 0. In other words, an increase in variable input price decreases its demand in

absolute value. The concavity of a variable profit function in fixed inputs implies that the

inverse demand equations are non-increasing with respect to their own quantities, RRi//Ki

<0.

The geometric property of the variable profit function (McFadden 1978, p.67)

is defined as

7t(Z, K, t) is convex over U iff 7r(kZ1 + (1- k)Z2)< kT (Z1) + (1- k)7(Z2).
7t(Z, K, t) is concave over V iff 7(1K' + (1 k)K2)> k2(K1) + (1 X)7(K2),
where U and V are convex subsets of RN; and where Z1 U, Z2E U and K e V,
K2 V; 0 1 <1.

The algebraic properties of concavity and convexity can be expressed in terms of

the signs of the Cholesky values of the function. The necessary and sufficient conditions

for a convex (concave) profit function are that the Hessian of the profit function

evaluated at output and variable input prices (fixed input quantities) is positive (negative)

semidefinite or all principal minors are non-negative (non-positive). Lau introduced the

concept of the Cholesky decomposition as an alternative to characterize the definiteness

of the Hessian matrix. Lau's Cholesky decomposition is favorable to the eigenvalue

decomposition of the Hessian due to its fewer constraints (Lau 1978, Morey 1986).

Wiley, Schmidt, and Bramble (1973) also propose alternative definiteness constraints

which is the alternative used to impose the curvature property in this study. Both the Lau

and Wiley-Schmidt-Bramble techniques can only impose curvature restrictions locally.

While Gallant and Golub (1984), and Hazilla and Kopp (1985) suggested alternative

methods of imposing curvature at multiple points, these methods still do not guarantee

that the curvature will satisfy globally. Only at those points, although Gallant and









Golub's technique does not limit to a finite number of points, are where the curvature will

be satisfied. The Wiley-Schmidt-Bramble technique is used due to its consistency with

the theory in contrast with alternatives which overly constrain the function and

complicate the estimation, while not significantly improving the results.

Morey (1986) suggests that there are 3 assumptions we can make before testing and

imposing curvature properties. First is to assume that the true function and the estimated

function have the same functional form, and they satisfy global curvature properties.

Second, the estimated function and true function have the same functional form, but they

do not possess the curvature property globally. And lastly, the estimated function is only

a second-order approximation to the true function at some point. The translog function

does not possess global curvature properties so we are left with 2 cases. To assume that

the estimated function is a second-order approximation to the true function, we should

know where the point of approximation is; otherwise, the test and imposition of curvature

at a point are meaningless. As a result, I will assume that the estimated function and the

true function have the same functional form.

Lau's Cholesky decomposition

Every positive (negative) semidefinite matrix A has a Cholesky factorization

A = LDL' 4.8

where L is a unit lower triangular matrix, and D is a diagonal matrix. L is defined as a

unit lower triangular matrix if Li = 1, Vi and Lij = 0, j > i, Vi,j. D is defined as a diagonal

matrix if Dij = 0, Vi, j, i #j. The diagonal elements, Dii, of D are called Cholesky values.

A real symmetric matrix A is positive (negative) semidefinite if and only if its Cholesky

values are non-negative (non-positive). For instance, a variable profit function is convex









in variable input and output prices. Let A be the Hessian of the variable profit function

with respect to 3 variable input and output prices.

1 0 0 6, O 0
L- L2 1 0 D 0 6 0 ,
-31 k 32 1 0 0 63
Thus,

a a al 1 1 21 1 31
A= a22 a23 1 21 22+2 1 2 31 2 32 4.9
a33 6 1 312+ 2 322 +3
The A matrix is symmetric, as is the LDL' matrix. All Cholesky values (6s) must

be non-negative for the Hessian of the variable profit function with respect to prices to be

positive semidefinite. Similarly, if the A matrix is the Hessian of a variable profit

function with respect to fixed input quantities, all Cholesky values must be non-positive.

The Cholesky values from Lau's definition can be calculated at each observation to

detect if the curvature property is violated. I assume that the estimated profit function

and the true function have the same functional form, but they do not posses the curvature

property globally. In order to impose curvature restrictions by Lau's technique, the

inequality restrictions of the Cholesky values can be imposed; however, they cannot be

imposed simultaneously at more than 1 point. Gallant and Golub (1984) have developed

computationally intensive techniques to impose curvature simultaneously at multiple

points.

Wiley-Schmidt-Bramble decomposition

A necessary and sufficient condition for a matrix A to be positive (negative)

semidefinite is that it can be written as:

A =(-)TT' 4.10










where T is a lower triangular matrix and Tij = 0, j > i, V i,j. Due to the greater simplicity

of the Wiley-Schmidt-Bramble decomposition than Lau's decomposition, this technique

is used to impose curvature in my model. For a translog variable profit function, the

Hessian matrix of the profit function with respect to output and variable input prices, AIn,

is positive semidefinite.

2
Y11 +a -a Y12 + a 1 2 .. Y1N+M + 1 N+M
2
Y+i y. y+c, c+a -a y.N M +a M
A = 12 ((2 Y22 2 (2 ... Y2,N+M 2 (2(N+M
11: : :

YN+M,1 + (N+M YN+M,2 +(N+M 2 YN+MN+M + N+M N+M 4.11
2
'Z11 'C 1C12 '1'1C,N+M
2 2
11 1' 2 "12 22 .. '12 1N+M + 22 2N+M

2 2
11 1IN+M 'C121 N+M + 1C22c2N+M 'CI N+M "1N+M,N+M


The Hessian matrix of the profit function with respect to fixed input quantities, Ajj,

is negative semidefinite.


11 12 1 12 1+PP2 ... IL +PPL
S +12 P132 +22+ P22 32 ... L +P2PL
AM=
JJ: : .

L, L+P LP1 ,2 +PNMP2 LLPL+P-PL 4.12
T*2 4* .12
t11 22 'Cii 'tiL
1 1 1 9 92 11 1,L *
1 12 2 2 g2 12 1L 22 2


,11 1,L 12 1L 22 2L 1 1L 2 --'" LL 2


Elasticity

Price elasticity of output supply and variable input demand

The generalized input and output elasticities with respect to prices are (Appendix









dlnQ1 y,1
E = -l-+-, i=1...N+M
dlnZ1 1 4.13


dlnQ1 Y
S+dlZ Vi j;ij 4.14
dlnZ- 71

Inputs i andj are gross substitutes if ij > 0, and gross complements if ij < 0; on the

contrary, output i and j are gross substitutes if s < 0, and gross complements if s > 0.

Following Kohli (1991, p.38), the matrix of price and quantity elasticities for the

variable profit function is given by

E =EQZ EQK1 7 alnQl/alnZh alnQ1/alnKk i,h=,...,N+M 4.1
ERZ ERK _LanRJ/alnZh alnRJ/alnKk] j,k= ,...,L

EQZ = {gih} are the price elasticities of output supply and variable input demand;

ERK = {Sjk} are the quantity elasticities of inverse fixed input demands; EQK = {ij}

capture the effects of changes in fixed inputs on variable input and output quantities; and

ERZ = {sji} capture the effects of changes in prices of variable inputs and outputs on fixed

input prices. The homogeneity of output supply and variable input demand functions,

and of inverse fixed input demand functions requires that

N+M L L N+M
I1h = 0, oi ;jk =0, ,j =1,=, =1
h k

Assuming that Qi = f(Z, K) and Rj = g(Z, K),

dQ= dQdZ+dQdK
dZ dK

dQ dlnQ dZ dlnQ dK
Q dlnZ Z dlnK K

Q dnQZ+ 4.16
dInZ dlnK









where is the relative change.


Similarly, R dlnRZ+dlnR 4.17
dInZ dlnK

From Eq. 4.16 and Eq. 4.17, we can summarize the comparative statics of the variable

profit function as

Q L EQz EQK Z 4.18
R ERZ ERK K

Morishima elasticity of substitution

The extent of susbtitutability among inputs is the key concept in understanding the

effects of factor and output price changes on technology, the demand for inputs, and the

supply of outputs. The extensive studies of technological change in U.S. agriculture have

primarily used the Allen-Uzawa elasticity of substitution (AES) as a measure of

substitutability of inputs. The original concept of elasticity of substitution was

introduced by Hicks (1932) to measure the effect of changes in the capital/labor ratio on

the relative shares of labor and capital or the measurement of the curvature of the

isoquant. However, as shown by Blackorby and Russell (1989), when there are more

than 2 factors of production the AES is not the measure of the ease of substitution or

curvature of the isoquant, provides no information about relative factor shares, and

cannot be interpreted as a derivative of a quantity ratio with respect to the price ratio. In

contrast, the Morishima elasticity of substitution (VMES) does preserve the original Hicks

concept. It measures the curvature, determines the effects of changes in price or quantity

ratios on relative factor shares, and is the log derivative of a quantity ratio with respect to

a marginal rate of substitution. To appropriately measure the ease of substitution, we

calculate the MES among inputs.










The MES in the cost minimization is defined as

J ln(X /X*)
MES, = 4.19
t ln(P /P,)

where X*i's are the optimal cost minimizing inputs, and Pj's are the input prices.

Applying Shephard's Lemma and homogeneity of the cost function, and assuming that

the percentage change in the price ratio is only induced by Pj,

PjCj (Y, P) PC, (Y, P)
MES = 4.20
C,(Y,P) Cj(Y,P)

MESj = sl C 4.21

where sij(Y,P) is the constant-output cross-price elasticity of input demand. Inputs i and

j are Morishima substitutes if MESj > 0; that is if and only if an increase in Pj results in

an increase in the input ratio X*i/X*j, and Morishima complements if MESj < 0. The

MES is not symmetric, and unlike the Allen elasticity of substitution, the sign of MES is

not symmetric either (Chambers 1988, p.96-97). Thus, the classification of substitute and

complement between 2 inputs depends critically on which price changes. Sharma (2002)

applied the concept of the MES to the profit maximization approach. The following

section is based largely on his development.

The constant output elasticity of input demand, sij, can be calculated from 4.18.

First, define Q* = (Y: R)' and Z* = (P: K)', then Eq. 4.18 can be written as:


Q* E xz E xw Z*
Q* EQ** EQQ*W J 4.22
X Ex Exw


Q* E*zZ7 +EQW 4.23









X = ExZ*+ExW 4.24

From 4.23, Z* = EQ* 1Q* -EQ,*z EQW 4.25

Substitute Eq. 4.25 into Eq. 4.24,

X = Ex*EQ*Z* Q *+(Ex ExEQ,, EQw)W. 4.26

Equation 4.22 can be written as:

-11
Z* E*Z*I I EXW EQZ* E* Q*W 427
S Ex*EQ*z*- E Xw ExzEQz, E Q, W

Holding the output level constant,

OX
O=E -EE 'E 4.28
O = EXW -EXZ*Q*Z* EQ*W 4.28
aW

The Morishima elasticity of substitution can be calculated by the definition in Eq.

4.21 where sj = the ij element in Eq. 4.27.

SlinY, (lnY
E | lnPk OlnK1) i, k =, 2,..., N 4.29
Q*z* lnRj) OlnRj j, =1,2,...,L
OlnPk OlnK1


E lnY (l1nR i =1,2,...,N; j = 1,2,..., L
E '" 4.30
W L1OlnW) 1OlnWj I = 1,2,...,M


E xz lnX, (lnX1 = 1,2,...,M
,, inP1j 1lnKj' i= 1, 2,..., N; j= 2,..., L


Exw = j,l =1,2,..., M 4.32
c lnW1 ..

Note that all prices and quantities are positive, except for variable input quantities, X's.

Thus, ln(X)'s imply ln(-X)'s. The elements in each matrix can be calculated from the









parameter estimates of the share equations in the same manner as the price elasticity of

output supply and input demand (Appendix B).

Data

Data used in this study are provided by Eldon Ball, Economic Research Service

(ERS), USDA. The construction of these data is similar to the published production

account data available from ERS (Ball et al. 1997, 1999, 2001). The raw data include

series of agricultural output and input price indices and their implicit quantities from

1960-1999. Price indices of these series are appropriate for this study since they are

adjusted for quality change of each input category. More discussion of input quality is

given by Jorgenson and Griliches (1967), and by Ball et al. (1997) for the USDA method.

Quality change occurs when the rates of growth of quantities that have different marginal

products within each input category are not the same, for instance, a demographic change

of farm labor, a change in the composition of fertilizers used, or a change in types of

machinery. Quality adjusted price indices or constant-quality price indices measure

changes in the price of inputs while keeping the efficiency constant. It is important to use

quality-adjusted data when analyzing induced technological change because using

unadjusted quality indices will result in biased estimation of parameters in the induced

innovation model.

There are 2 sets of data: Florida and the U.S. Florida is chosen to compare with the

U.S. in this study because its agricultural production is labor intensive, and a large

number of workers are immigrants. In addition, there are major examples of farm

mechanization in Florida during the study period such as the sugarcane mechanical

harvester in the early 1990s and recent adoption of citrus mechanical harvester. There

are 2 significant immigration policy changes during the study period. The first is the end









of the Bracero program in 1964, and the second is the implementation of the 1986

Immigration Reform and Control Act. Theses 2 policies, as discussed in Chapter 2, are

expected to have an impact on the supply of farm labor from immigrant labor, and on

changes in farm mechanization.

In the published ERS production account, input quantity indices are constructed

based on the Tornqvist index number specification. Implicit price indices are constructed

as the ratio of the value of the input aggregate to the corresponding quantity indices, and

can be interpreted as unit values (expressed in millions of dollars) of the aggregates. A

similar approach is used to generate this data set. First, the price indices are estimated,

and the implicit quantity indices are then calculated as the ratio of value of the aggregate

to the corresponding price indices. Hedonic regression techniques are used to construct

chemical indices. Changes in characteristics of fertilizers (e.g. grades of nutrient) and of

pesticides (e.g. persistence in the environment) will not change constant-quality price

indices. The price index of labor input is constructed from the estimated average

compensation per hour. The average compensation is estimated by constructing a

compensation matrix based on characteristics (gender, age, education, and employment

classes) of workers for each year and controlling it to compensation totals for annual

compensation. The estimate of rental price indices for each capital stock is derived from

the correspondence between purchase price and the discounted value of future service

flow. The estimates of each capital stock are explained by Ball et al. (1997). The

estimation of constant-quality land stock takes into account different land categories:

irrigated and dry cropland, grazing land and other. Land area under Federal commodity









program and Conservation Reserve is not included. A detailed discussion of data

construction can be found in Ball et al. (1997, 1999).

Data used in the analysis are aggregated into 2 outputs, 4 variable inputs, and 2

fixed inputs. Each price index is normalized to 1 in 1996. The outputs are aggregated

into perishable crops and all other outputs using a Divisia price index. Perishable crops

in Florida are aggregated from vegetables, fruits and nuts, and nursery products;

perishable crops in the U.S. consist of vegetables, fruits and nuts, and horticultural

products. Other outputs in Florida consist of livestock, grains, forage, industrial crops,

potatoes, household consumption crops, secondary products, and other crops. Other

outputs in the U.S. aggregate are the same output categories as those of Florida, except

that grains are defined as cereals. Variable inputs are aggregated into hired labor, self-

employed labor, chemicals, and materials. Hired labor includes direct-hired labor and

contract labor. The wage of self-employed labor is imputed from the average wage of

hired workers with the same demographics and occupational characteristics. Chemicals

include fertilizers and pesticides. Materials include feed, seed, and livestock purchases.

Fixed inputs are aggregated into land and capital inputs. Capital includes autos, trucks,

tractors, other machinery, buildings, and inventories.

Figures 4-1 to 4-4 illustrate the data by normalizing them to 1 in 1960 for ease of

comparison. Figure 4-1 shows price indices for Florida outputs and inputs. All variables

have an increasing trend. Both hired labor and self-employed labor wages changed in the

same direction. While farm wages remain relatively constant in the 1960s and early

1970s, they increased significantly in the mid-1970s and thereafter. The wages also had

greater variation in the 1990s. Chemicals, materials, perishable crops, and all other









output price indices were relatively stable, with a slightly increasing trend. After the

mid-1970s, land rent significantly increased over time, with exceptions in 1983, 1986,

and the early 1990s. Capital price was stable until the mid 1970s, but increased

significantly thereafter.

Figure 4-2 illustrates shares of variable profits in Florida. Shares of all variable

inputs are negative which means that the higher negative share implies higher profit

share. Since perishable crops were major commodities in Florida, they had a larger share

than all other crops combined. While the share of perishable crops remained constant

over time with some fluctuations, all other outputs share was decreasing since the mid

1970s. Hired labor had larger shares than self-employed labor. Hired labor also had

relatively stable shares, but it increased after 1964 until 1970 and from 1992 to 1996.

Self-employed labor had a trend similar to hired labor. Profit shares of chemicals,

materials, land, and capital were relatively stable over time with some fluctuations.

Figure 4-3 reports the price indices of U.S. variables. Hired labor and self-

employed labor wages had an increasing trend over time. They increased dramatically

since the late 1970s. Capital rent was relatively stable in the 1960s and 1970s, but

increased thereafter, except in 1982, 1983, 1986, and during 1989-1993. Chemicals,

materials, perishable crops, and all other outputs prices slightly increased over time.

Land price changed in the same pattern as that in Florida.

Figure 4-4 shows the variable profit share of U.S. outputs and inputs. Profit share

of perishable crops was stable over time and much smaller as compared to other products.

Share of self-employed labor decreased since 1970, and remained stable from 1973 to

1990 when it started to increase. Share of hired labor was stable over time, except after






64


the mid-1990s when it increased slightly. Capital share was relatively stable over time,

but decreased in the early 1970s. It steadily decreased after the 1980s, but increased

slightly after the mid-1990s.






































O NM 'IT .0O oo o NM 'IT .0O oo o 04 'IT DO oo o 04 'T" DO oo
.O .O .O .O .O I(. I(. I- I- I OO OO OO OO OO T) T) T) T) 0)

Year
-*- Hired Self Chem Matl --- Land -- Capital -e-- Other Outputs -- Persh Crops

Figure 4-1. Florida price indices of outputs, variable inputs, and fixed inputs.


2 0.5
l"


C-1------------------------
-0.5



-1
C O ( O C) .O ( O O C) CO ( O O C) CO 0O
CO CO CO CO CO IN IN IN IN- I OO CO O O O 0T CT C T) 0T)
0) 0) 0) 0) 0) 0) 0) 0) 0) 0) 0) 0) 0) 0) 0) 0) 0') 0') 0') 0')

Year

-*-- Hired -- Self Chem Matl --- Land Capital -e-- Other Outputs Persh Crops

Figure 4-2. Florida profit shares of outputs, variable inputs, and fixed inputs.













25



20



S 15



10



5



0
C (N 'I CO 0O O (N 'I- CO 0O O (N 'IT CO 0O O (4N 'T CO O0
CO CO CO CO CO 1- 1- 1- 1- N- 00 00 00) 00) 0) 0T) 07)
0T) 0T) 0T) 0T) 0T) 0T) 0T) 0T) 0T) 0T) 0T) 0T) 0T) 0T) 0T) 0T) 0T) 0T) 0T) 0T)

Year

-*- Hired -- Self Chem Matl --- Land -- Capital --- Other Outputs -- Persh Crops

Figure 4-3. U.S. Price Indices of outputs, variable inputs, and fixed inputs.


0 CN '" CO oC 0 CN '" CO oC 0 CN '" CO o 0 CD N 'T CO o0
CO CO CO CO CO I- IN- IN- IN- IN- OC O0 O0 O0 O0O ) M) M M)

Year

-*- Hired -- Self Chem Matl -X Land Capital -- Other Out Persh Crop

Figure 4-4. U.S. profit shares of outputs, variable inputs, and fixed inputs.









Estimation

Seemingly unrelated regression procedures were applied to the share equations and

profit function using the Full Information Maximum Likelihood (FIML) procedure.16

Least squares estimation methods with an iterated covariance matrix and seemingly

unrelated regression methods were attempted prior to FIML, but the estimation was

cumbersome, particularly as more restrictions were imposed. The FIML procedure

facilitated convergence, although intervention was required in the iterative process by (i)

reducing the number of parameters in the initial estimation and reintroducing them one at

a time, and (ii) changing the starting values of parameters.

Seemingly Unrelated Equations

The translog profit function with linear homogeneity imposed and including an

IRCA dummy variable is defined as

5 Z K l 5 Z Zh
ln7r= c+-a In '1 +, In +-_ Yhln- In h-
1-1 Zmatl Kcapital 2 11 h 1 Zmatl Zmati

11 land 56n land
2 Kcapital 1=1 Zmatl Kcapital
5 Z Zl Kland
+-iltn ln t+ T261t2 ln t t++41ltn d 2T2 n Kland t 4.33
1=1 Zmat 1 1 Zmati Kcapital Kcapital
11
+ Ptt +3t2tT2 +- ttt2 +-Ittt2T2 +uOt
2 2
where T2 is a time dummy variable for years after the passage of IRCA in 1986. It is

added to capture the potential difference in the biases and the rate of technological

change. There are 2 outputs: perishable crops and other outputs; 4 variable inputs: hired

labor, self-employed labor, chemicals, and materials; and 2 fixed inputs: land and capital.

Linear homogeneity in prices is imposed by dividing through all prices by the price of


16 Time Series Processor (TSP) through the looking glass version 4.4 is used for statistical analysis.









materials (the variable input equation dropped from the system), and linear homogeneity

in fixed inputs is imposed by dividing fixed inputs by the quantity of capital (the fixed

input equation dropped from the system).

The profit shares are derived by taking the first derivative of the translog profit

function with respect to the log of variable input and output prices and fixed input

quantities. The system of share equations becomes


=a,+ZYlhln Zh +1l6ln K 1 +6t+Tz26tt+Ult i=1,...,5 4.34
h=l Zmatl Kcapital
5 Z K
7tj = + 61, In Z +,, In land + t1t + T2At2t +ut j= 1 4.35
1=1 Zmatl capital
Although the translog profit function can be estimated directly, estimating the

optimal, profit-maximizing input demand and output supply equations (or profit share

equations) is more efficient (Berndt 1996, p.470). The profit function is assumed to be

well-behaved; that is, it satisfies all the symmetry, homogeneity, and curvature

conditions. A disturbance term, ui (uj) is added to each equation, and each is assumed to

be randomly distributed with 0 mean and scalar covariance matrix. Even though the

translog profit function generates linear share equations in parameters with the same

regressors, the equation-by-equation OLS (ordinary least square) estimates will not

guarantee the symmetry constraints across equations. Moreover, the cross-equation

constraints mean that the disturbances are correlated across equations, implying that the

contemporaneous covariance matrix is nondiagonal. In this case, system estimation is

more efficient. Zellner (1962) developed an efficient method of estimating seemingly

unrelated equations known as Zellner's seemingly unrelated estimator, ZEF, or seemingly

unrelated regression estimator (SUR).









Zellner's seemingly unrelated estimator uses the covariance matrix of disturbances

from equation-by-equation OLS as initial estimates, then performs feasible generalized

least squares estimation. The iterative Zellner seemingly unrelated regression estimator,

IZEF, updates the covariance matrix and iterates the Zellner procedure until the

covariance matrix and the changes in estimated parameters are arbitrarily small. The

estimates from IZEF are asymptotically equivalent to maximum likelihood estimates

under the assumption of normality of the disturbance term.

Recall that the (variable) profit is defined as total revenue minus total variable cost.

At each observation, the sum of variable output and input shares is always equal to 1.

This imposes an adding-up condition to the system. In addition, the profit function is

linear homogeneous in variable input and output prices and linearly homogeneous in

fixed input quantities. Thus, only N+M-1 variable input and output share equations are

linearly independent, and only L-1 fixed input share equations are linearly independent.

This also implies that the residual covariance matrix is singular. The singularity problem

can be handled by dropping 2 share equations: 1 variable input and 1 fixed input share

equation. The estimates from IZEF are invariant to the choice of which equation is

deleted.

The implied parameter estimates of the terms in Eq. 4.34 and Eq. 4.35 and the

remaining parameter estimates in the omitted share equations can be obtained from the

model restrictions. The system of share equations 4.34 and 4.35 is estimated jointly with

the translog profit function 4.33 using the full information maximum likelihood

procedure. Introducing the profit function is not typically done in empirical work,

although it is likely to produce more efficient estimates (Kohli 1991, p.204). It is










necessary to include it for the current specification since the rate of technological change

includes parameters P, and tt that cannot be estimated directly from the share equations.

Imposing Restrictions for a Well-behaved Profit Function

Homogeneity

5 2

1=1 j=1
5 5 2 2 5 2
ih = h = Yih Z k = Z jk = = 6?= 0 4.36
1=1 h=l J=1 k=l 1=1 J=1
5 5 2 2
6t1 = 6,t2 1Z Jtl Z jt2 = 0
=1 1=1 J=1 J=1
Symmetry

Y1h = Yhl; 4jk = k k 4.37
Continuity

After introducing a dummy variable, the continuity at 1987 of the translog profit

function requires that


5 Z87 8787 =0 4.38
1=1 Z matl K capital 2

where Z87, K87, and t87 represent the observed variables in 1987.

Curvature

The curvature properties of the estimated function can be checked at each

observation in the sample. If curvature of the estimated function is satisfied locally in the

neighborhood of every observation, we cannot reject that the true function is also locally

satisfied over the region. The technique used to test and impose curvature restrictions is

adopted from Kohli (1991). He showed that (Kohli 1991, p. 109-110) the Hessian of the

translog function can be evaluated in terms of the Allen elasticity of substitution matrix.

He noted that it is also possible that the violation of convexity and concavity occurs at









different observations. We want to ensure that the substitution matrix of variable inputs

and outputs, 11n, is positive semidefinite at some observation s, and the substitution

matrix of fixed inputs, Yjj, is negative semidefnite at some observation r. Share

equations 4.34 and 4.35 at each observation can be written as follows:

5 Z Kland
t l a + Ylhln Zhs +611 in ads +tlS + T26,t2s
h=1 Zmatl,s capital,s

+ ih Zht Zhs 1, Kland,t In lands
+hYl in irl mnatlsrTI 2 In--4r
h= matl,t matls captal,t captal,s
+ 6,tl (t s) + T21lt2 (t s)
5 Z K
71t =jp + 6J In zr +,, In land + tlr +T2 jt2
1 Zmatl,r K capital,r

+ 6 In z lt In zr + In land,t In land,r
1=1 Zmatl,t Zmatr K capital,t Kcapital,r
+ jtl (t- r) + 2(jt2 (t2 r)
These can also be expressed as:

5t = l h Zht Zhs 11 land K lands
h= Zmatl,t Zmatls Kcapital,t Kcapitals 4.39
+ ,t (t s) + T26t2 (t s)
5 ZZ K K
7Jt = I t In r 11 + landt In land
1=1 matl,t Zmatr K capital,t K capitalr 4.40
+ (jt (t- r) + 2jt2 (t- r)
where 1a = tS and pj = fjr are estimated profit shares of variable inputs and outputs at

observation s and estimated profit shares of fixed inputs at observation r, respectively.

The estimated substitution matrices are calculated from profit shares and can be

expressed as:









(Y,1+ ft1 2- 1 )/ftI2 (Y12+ft1f)/i2 .. (Y715+ ftift5)/fii 1
(Y12 + ft21)l/ft21 (Y22 +Y 22 -ft2)/ft22 (Y25 + f 2f5) / 441
S- 4.41

(Y15 + f5f1)/ 15f1 (Y52 + f5 2)/ 5 2 (Y55 + f52 f5)/f52
(11 +f 1, )2 1*) 2 (.2 +t4 *2") 2
(22 + *, 2* ~, *)/, *", (2 + ft2 *2 -f2*) / 2 *2

Note that the Allen substitution matrices are symmetric.

The curvature property of the profit function is first checked by Lau's Cholesky

decomposition of the substitution matrix. At each observation, the Cholesky values

derived from 4.41 should all be nonnegative, and those from 4.42 should all be

nonpositive. The significance of the Cholesky values cannot be easily tested at each

observation. However, as Lau noted, the significance of the Cholesky values can be

examined by first normalizing the right hand side variables to 1 at a given observation,

and normalize the time variable to 0 at the same observation. The observation where

curvature is the most severely violated (the largest of Cholesky values in the absolute

terms that have the wrong sign) is selected for normalization. Then reestimate the system

by estimating the Cholesky values, 6s, in the diagonal matrix and the elements in the

lower triangular matrix, Xs, using the Lau decomposition technique in place of the

original parameters. The Lau decomposition, A = LDL', is shown below:


Y1 11 2-l 12+ 12c2 Y13+cc3 Y14+cL4 715+cc5 716+cL6
Y22+22-2 23+c2c3 24+24 725+c2c5 726+c2c6
A -33+23 -3 34+(34 Y35+3c5 Y36+3Y6
S44+24 -4 745+ 45 46+46
2
Y55+2-5 5 '56+56
Y66+'62 -'6









1 1 21 6131 6141
1 212 + 2 6121 31 62k32 61 21 41 62 42
LD L= 1 31 32 3 1 3141+ 232 42+ 343
61 412 2642 2+ 63432+ 4


615 1 61 5261
61'2 5 1+625 2 61'2 16 1+a62
613 iL 1+562 +353 2 353 6 1+621+3 26 363 4.43
614 5 1+624 52+634 353+64 54 4 6 1+6324 62+634 363+644
6135 +63 52 +6532 64354 +5 6135 b61+63 562+635363+643 45 64+6 565
2 2 2 2 2
161k2 +2 622 +83632 4k642 5652 +6
A 11 + p12 1 +P12 +PIP2
C22 +P2 2 4.44
6* 6 1*21
L L 1 1 k 21"
J = [ 61 *1 21* + 2 *
where All is the Hessian of profit function with respect to variable inputs and outputs, and

Ajj is the Hessian of profit function with respect to fixed input quantities.

If the curvature is violated, the curvature restrictions can be imposed by using the

Wiley-Schmidt-Bramble (W-S-B) reparameterization technique. The W-S-B technique

still does not guarantee global curvature, but by imposing the curvature at a particular

point, we can assure that the curvature is satisfied locally. Kohli found that it is often

sufficient for the estimated function to satisfy the curvature for all observations when

curvature restrictions are imposed at the point that seems to be the most seriously

violated. The right hand side variables are normalized to 1 at the observation where

curvature is to be imposed, and the time variable is normalized to 0 at the same

observation. Using W-S-B reparameterization, the original parameters are replaced by a

one to one correspondence between the Hessian, All (Ajj), and its W-S-B decomposition










matrix, TT' (-VV'). T and V are lower triangular matrices of dimension 5x5 and lx1,

respectively.

The reparameterization involves the following:
2 2
Y11 = T112 -a12 + O
Y12= THT12 (ai(a2

2 2 2
Y22= T21 + T222- (22 + a2
Y23 = T21T31 + T22T32 (2a3

Y33 = T312 + T322 T332 32 + 3 4.49
Y34 = T31T41 + T32T42 + T33T43 ( 43(-4

Y44 = 41 + T42 + T43 + T442- (42 + (4
Y45 = T41T41 + T42T42 + T43T43 + T44T54 (4(-5
2 2 2 2 2 2
55 = T512 + T52 + T53 + T54 + T552 -52 + a5
)11 V112 12+ 1

where the zs and v are elements in lower triangular matrices T and V, respectively. The

remaining original parameter estimates are recovered using the homogeneity, symmetry,

and continuity constraints.

Rate of Biased Technological Change

The rate of technological change by the definition in Chapter 3 and as derived from

Eq. 4.33 is written as

5 Kand Kand
t=Pt +t2 *T2 + 6t1In +T21t2ln Z t In +T2t2n Kland tt+t2t*T2 4.46
1=1 Zmatl 1-1 Zmatl Kcapital Kcapital
After imposing the homogeneity, symmetry, and continuity restrictions, the rate of

technological change can only be estimated by including the profit function with the

system of share equations because Pt and tt are not obtainable from the share equations.

The biased technological change of variable outputs and variable inputs as defined in the

previous chapter and replicated here are calculated from the parameter estimates of the

share equations.









4.47


B, E, t

Following from Eq. 4.34,


Q,
TI Z Q1
0 _, t Q1Z1 0 7T26lt2
S- = 7 7 =2 at +T2 it2

solving for QQi/ct from Eq. 4.48 and dividing by Qi,

1 Q, ,t + T26t2 9 ln2 r
t Q, t a, 7t


Et = +T2 6t2 +
E, T +C


4.48


4.49


4.50



4.51


Thus, B,= 61 T2t2


Similarly, the technological change of fixed inputs is calculated as


B, = tl T jt2 j 1, 2


4.52


Estimation of Elasticities

The price elasticities of output supply and input demand can be calculated from

the parameter estimates of the share equations. The price elasticities follow from Eq.

4.13 and Eq. 4.14. The Morishima elasticities of substitution are calculated using the

definition in Eq. 4.21 where the constant-output cross-price elasticity of input demand,

sije, can be derived from Eq. 4.27. The estimates of each matrix in Eq. 4.27 are found in

Appendix B.














CHAPTER 5
ECONOMETRIC RESULTS AND INTERPRETATION

This chapter presents the econometric results and their interpretation. Estimates of

the seemingly unrelated regression model with homogeneity and symmetry constraints

imposed, the test for curvature property, the estimates after imposing the curvature

restrictions, and the calculation of the rate of technological change, the biases, and the

Morishima elasticities of substitution are reported. The chapter is divided into 2 sections:

the results at the Florida level and those at the U.S. level. Each section also provides

interpretation of the results.

Florida Results

The initial estimates of the seemingly unrelated regression model of the profit share

equations and the translog profit function of Florida are presented in Table 5-1. These

estimates are from the model that has only the homogeneity and symmetry restrictions

imposed. Although the listed translog parameter estimates have no direct economic

interpretation, they are the basis for the elasticity and the rate of technological change

estimates. The interpretation of these estimates will be discussed after all restrictions are

imposed.

The estimates from this initial regression do not necessarily represent the well-

behaved profit function since the curvature property may not have been satisfied. The

curvature property is first analyzed by decomposing the matrices of the Allen elasticity of

substitution (equivalent to the Hessian of the translog profit function), and checking the

Cholesky values (6s of the D matrix in Eq. 4.8).









The Cholesky values of the Hessian with respect to the fixed inputs are negative at

every observation. This means that the concavity property of the estimated profit

function is not violated within the region of data for the fixed inputs. However, the

Cholesky matrix of the Hessian with respect to the variable inputs and outputs has 1

negative Cholesky value at every observation. This means that the convexity property of

the estimated profit function is violated at every point of the data among the outputs and

variable inputs. The most negative Cholesky value, -3.1440, is found in 1998. Since

only convexity is violated, subsequent curvature attention is given only to convexity. To

further analyze the significance of the convexity violation, all the right hand side

variables are normalized to 1, and the time variable is normalized to 0, in 1998, the

observation with the smallest Cholesky value. Using data for all observations, below is

the estimated Cholesky matrix of variable inputs and outputs after applying Lau's

reparameterization as in Eq. 4.43. The estimated standard errors are reported in the

parentheses.

-0.0004 0 0 0 0 0
(-0.002)
0 0.5128 0 0 0 0
(2.491)
0 0 0.7290 0 0 0
DFL (1.462)
0 0 0 0.8037 0 0
(6.353)
0 0 0 0 0.1307 0
(0.108)
0 0 0 0 0 0.0255
0 (0.049)
There is one Cholesky value that has the wrong sign; however, it is insignificant at

either the 0.05 or 0.10 significance level. This implies that although convexity may be

violated, the indicator of the violation is not statistically significant given the observed









data. Furthermore, it implies that imposing the convexity property to the profit function

will be consistent with the data.

The convexity is imposed using the Wiley-Schmidt-Bramble reparameterization

technique as presented in Eq. 4.45. The right hand side variables are normalized to 1 and

the time variable is normalized to 0 in 1998. This guarantees that convexity will be

satisfied at this point. Instead of reporting the elements in the lower triangular matrix (T

in 4.10), Table 5-2 presents the estimates transformed back to the original parameters of

the translog profit function satisfying the regularity constraints, including convexity. As

may be seen in Tables 5-1 and 5-2, the estimates differ, and for some parameters, the

significance of the estimates changes after convexity is imposed.

After convexity is imposed, the Cholesky values are calculated at each observation

once again. Although the Cholesky values of the Hessian with respect to fixed inputs

remain negative, 1 or more Cholesky values of the Hessian with respect to the variable

inputs and outputs remain negative at all observations, except 1964 and 1998,17 the latter

year being the normalized observation. As a result, we can claim that convexity is not

violated in 1964 and in 1998. The estimates at observations other than1964 and 1998

may not give correct economic interpretations because the convexity property is violated.

To properly test the significance of violations at every observation would require an array

of sequential statistical tests (Lau 1978b), while adding little to the ultimate results of the

analysis. However, the Cholesky values estimated by the Lau reparameterization show

that the violation in the absence of the convexity restriction is insignificant at the

normalization point, i.e. the observation where the convexity appeared to be most

1 1 out of 6 Cholesky values are negative in 1998, but its magnitude is sufficiently small (-0.0000035) to
be considered as a rounding error.









seriously violated originally. The Wiley-Schmidt-Bramble reparameterization technique

used to impose the curvature property in this study confirms that it does not guarantee

global curvature, but it does ensure that the curvature property is satisfied locally at the

point where curvature is imposed. A more restrictive procedure is likely to only bring

demand or supply elasticities closer to 0 in cases where convexity is violated.

Florida Rate of Technological Change and Biased Technological Change

The estimates from Table 5-2 are used to calculate the rate of technological change,

[t, defined in Eq. 4.45, and biased technological change as defined in Eq. 4.51 and Eq.

4.52. Appendix C summarizes the rates and bias of technological change in Florida at

each observation. Figure 5-1 depicts the biased technological change in Florida over

time. Before 1986, point estimates of biases were significantly different than 0 at better

than 0.01% for all inputs, except land and capital whose significance levels were larger

than 80%. After 1986, other outputs and materials biases were significantly different

than 0 at better than 0.01%, but biases of perishable crops and all other inputs were

statistically insignificant. The estimated biases suggested that technological change in

Florida was biased against all outputs and inputs, except for land (although insignificant),

before 1986. Variable inputs were defined as negative outputs; as a result, the share-

weighted sum of biases among variable inputs and outputs was 0. It is possible, as the

results reveal, that biases among all outputs and variable inputs were negative. This is

because the shares of variable inputs were negative.

Table 5-3 reports the estimates of Florida biased technological change before and

after the passage of IRCA, evaluated at the means of the explanatory variables for each

subperiod. A test that the biases are jointly different between the 2 periods is highly









significant as suggested by a Wald test statistic value of 47.06; the critical value for the

S2(8) is 21.95 at the .005 significance level. The individual differences of biases between

the 2 periods and their standard errors suggest whether the changes are individually

significant. After the passage of IRCA in 1986, the technology suggested significant bias

toward more perishable crop-producing, but significantly bias against the production of

other outputs. The technology became more self-employed labor-using, but the biases of

hired labor and capital were not significantly different. The technology significantly used

more chemical and less materials; whereas, the use of land did not change. The results

suggest that although the technology significantly saved both types of labor before IRCA,

it used more self-employed labor afterward. The IRCA did not change how much hired

labor was employed nor stimulate the adoption of farm mechanized technology. The

technology suggested an increase in the production of perishable crops. Instead of hiring

more workers or adopting new mechanized technology, the technology apparently

became more self-employed labor-using in the production of perishable crops in the labor

intensive areas.

Figure 5-2 compares the rate of technological change at observed prices and

observed fixed inputs to the rate of technological change at constant prices and constant

quantities. Both rates of technological change were significantly different than 0 at better

than 0.01%, except in 1996 where their significance levels were less than 5%, and from

1997 to 1999 when their significance levels were larger than 80%. The rate of

technological change at observed prices and observed fixed inputs declined from 17% to

0.08% from 1960 to1999, and the rate of technological change at constant prices and

constant fixed inputs declined from 19% to 0.03% from 1960 to1999. The rate of









technological change is defined as the rate of growth of profit. This means that while the

technology was progressing (shifts of IPPF outward) at very high rates throughout the

early years of the sample period, the rate significantly declined throughout the period. If

prices and fixed inputs were held constant at their 1998 levels, the rate of technological

progress would have been slightly higher in the beginning of the time period.

Florida Own-Price Elasticity

The own-price elasticities of both outputs were positive, and those of inputs were

negative as expected at all observations. Table 5-4 summarizes the own-price elasticities

of output supply and variable input demand and the inverse fixed input demand for

selected years. The correct signs of the elasticities indicated that they were consistent

with economic theory. The elasticities of land and for both types of labor were elastic,

but those of the rest of inputs and outputs were inelastic.

Florida Morishima Elasticity of Substitution

The estimates of MES's among inputs at each observation in Florida are presented

in Figures 5-3 to 5-5. Point estimation allows tracing the change over time. As defined

in Eq. 4.21, the MES is not symmetric. A positive MES means that the 2 inputs are

substitutes, and a negative MES means that they are complements. Figure 5-3 shows the

MES's among variable inputs. The MES's among variable inputs were positive, except

for the elasticity between self-employed labor and materials when material price changed.

After 1986, the MES between materials and chemicals when chemical price changed and

the MES between self-employed labor and chemicals when chemical price changed

became negative, but only lasted for a few years. The elasticity between hired labor and

self-employed labor, when returns to self-employed labor changed, was less elastic than

the elasticity between these 2 types of labor when hired labor wages changed. This









suggested that although hired and self-employed labor were substitutes, an increase in

wages of hired labor created a larger incentive for self-employed producers to work

longer hours than to hire more workers when returns to self-employed labor increased.

Figure 5-4 illustrates the MES's among variable inputs and fixed inputs when fixed

input prices change. Variable inputs and fixed inputs were substitutes when fixed input

prices change throughout most of the period. However, the MES's were negative during

the mid to late 1980s for chemicals and land when land price changed; self-employed

labor and land when land price changed; and capital and hired labor when capital price

changed. The substitution between self-employed labor and capital were more elastic

than between hired labor and capital when capital price changed.

Figure 5-5 shows the MES's among fixed inputs and variable inputs when variable

input prices change, and among fixed inputs. The MES's were positive for all pairs of

fixed inputs and variable inputs when variable input prices changed, and among fixed

inputs, except for the MES between land and chemicals when chemicals price changed,

and the MES between capital and chemicals when chemicals price changed in 1987 and

1988. The passage of IRCA in 1986 made MES's slightly more elastic for capital and

labor when labor became more expensive; and between land and labor when labor was

more expensive. However, the elasticities between land and chemicals when chemicals

price changed, and between capital and chemicals when chemicals price changed, decline

and became negative after IRCA, but only for 2 years.

As we see from Figure 5-3 to 5-5, some of the MES's were highly variable over

time. Table 5-5 summarizes the average MES's before and after the passage of IRCA.

The test of differences in MES's between 2 periods is computationally problematic since









the elasticities are obtained through a solution of matrix equations (Eq. 4.27), including

the inverse of a matrix consisting of functions of the parameter estimates. As shown in

Appendix B, the MES's are directly dependent on parameters that do not change

throughout the sample period, and the expected profit shares which do change. The

sources of changes in the expected profit shares are the parameters associated with the

time dummy variable reflecting IRCA (6it2 and jt2), and changes in the observed values

of the prices and fixed inputs. Holding the prices and fixed inputs constant, the joint test

of the 6it2 and jt2 shift parameters is indicative of a significant difference in the MES's.

The X2(8) statistic of this test is 19.96, which means that the time dummy variables are

statistically different than 0 at the 5% significance level. Although we cannot directly

say that the differences in MES's reported in Table 5-5 are statistically significant, we

can say that if prices and fixed inputs were to remain constant, changes in MES's would

be a result of changes occurring under the period when IRCA was in force.

The results reveal that hired labor and self-employed labor were substitutes in both

periods. The MES's between the 2 types of labor increased after IRCA. As values of a

type of labor changed, the increase of another type of labor became easier following

IRCA. For instance, if hired workers became more expensive, self-employed labor

would increase in efficiency units, either through increased quality, or through more

hours, than before the passage of IRCA, and vice versa. Similarly, both types of labor

and capital were substitutes for capital in both periods. The only MES's that switched

signs are between self-employed labor and land, and between chemicals and land when

land price changed. Self-employed labor and chemicals were substitutes for land when

land price changed before IRCA. However, after IRCA, if land became more expensive,









the use of chemicals would decrease and producers would work fewer hours. The

passage of IRCA did not change the substitutability between labor and capital and

between the 2 types of labor; however, the technological progress required less chemicals

and self-employed labor when agricultural land area became more scarce. An example of

a possible technological change is dripping pesticide and fertilizer applications. This

technology allows the minimal use of chemicals while conserving the environment, and

perhaps requiring less labor. As this technology was adopted, it increased land

productivity without necessarily increasing the use of chemicals even when land price

was increasing.

The U.S. Results

The preliminary U.S. estimates before imposing the curvature property are

presented in Table 5-6. The Cholesky values of the Allen elasticity matrices were

calculated at each observation, and it was found that all Cholesky values of the Hessian

with respect to fixed inputs had the correct sign; however, at least 1 Cholesky value of

the Hessian with respect to variable inputs and outputs was negative at all observations.

The most negative Cholesky value was found in 1983, -163.53. The convexity property

of the estimated profit function was therefore violated, whereas concavity was not. To

check and impose convexity, the right hand side variables were normalized to 1 in 1983

and the time variable was normalized to 0 for the same year. The significance of the

convexity violation was evaluated using Lau's Cholesky decomposition to estimate the

Cholesky values using data for all observations. The matrix in Eq. 5.2 shows the

Cholesky values of the variable inputs and outputs with their estimated standard errors in

parentheses.









-2.4394* 0 0 0 0 0
(1.201)
0 0.0837 0 0 0 0
(0.058)
0 0 -0.1560 0 0 0
DUS (0.133) 5.2
0 0 0 -0.2007 0 0
(0.196)
0 0 0 0 0.0605 0
(0.110)
0 0 0 0 0 -0.1900
(0.339)
There is one Cholesky value (-2.439) that was significantly negative at the 5%

significance level, implying that the convexity property of the estimated U.S. profit

function was significantly violated. Although it was undesirable to force the profit

function to satisfy the convexity property when the data did not support it, convexity was

imposed to maintain consistency with economic theory.

Convexity was imposed using the Wiley-Schmidt-Bramble reparameterization

technique. The original parameters were calculated and reported in Table 5-7. The

curvature properties were once again evaluated by calculating the Cholesky values at

each observation. After the convexity restriction was imposed, the Cholesky values

remained negative at all observations, except in 1983 (the normalized year), when the

Cholesky was negative, but close to 0 at -0.00006. Imposing local convexity property

only guaranteed that it was satisfied at the point where convexity was imposed. As a

result, the subsequent interpretations must be evaluated as tentative given the

unsatisfactory curvature properties for the profit function for years other than the

normalized year.

U.S. Rate of Technological Change and Biased Technological Change

Figures 5-6 to 5-8 illustrate the rate and bias of technological change in the U.S.

over time. The detailed estimates are also presented in Appendix D. The rates of









technological change and biased technological change were calculated from the estimates

in Table 5-7. The estimates of biased technical change were significant at the 5%

significance level for all variables at all observations, except for the biases of hired labor

and chemicals after 1986 that were insignificant at larger than the 20% significance level.

A graphical illustration of biased technological change is presented in Figure 5-6 and

Figure 5-7. Except for capital, technological change was biased against all outputs and

inputs prior to 1986. An explanation of biases against all outputs and variable inputs is

the same as above in the Florida results. After 1986, the technology became perishable

crops-producing, less self-employed labor-saving, and more land-saving. Although

insignificant, the technology was less hired labor-saving and less chemical-saving, and

the biases against other outputs increased after 1986. After 1986, the technology was

dramatically biased against materials until 1991 when it became materials-using.

Table 5-8 reports the average of U.S. biases before and after the passage of IRCA,

and the differences between them. The technology was significantly biased against all

outputs and inputs, except capital, before IRCA. After IRCA, the technology became

significantly less hired and self-employed labor-saving; however, the use of capital was

not significantly different. The technology became significantly more perishable crops-

producing, but became significantly more other outputs-reducing. The technological bias

shifted significantly in the direction of chemicals-using while there was no significant

difference in the bias toward materials or land. Unlike Florida, the passage of IRCA

coincided with a significant shift in technological bias toward employing more hired

labor. Although the direction of bias toward land and capital did not change, it was

significantly land-saving and capital-using in both periods.









IRCA coincided not only with U.S. producers failing to shift to a more labor-saving

technology, but rather with a shift toward more labor-using technology at the same time

that the presence of illegal foreign workers was increasing (Mehta et al. 2000). In

addition, the change in the adoption of mechanized technology was insignificant in the

post-IRCA period as compared to pre-IRCA. However, the passage of IRCA coincided

with greater profitability in the production of perishable crops and reduced profitability in

the production of the other outputs category at the U.S. level. The production of

perishable crops increasingly involved the employment of foreign workers (Mehta et al.

2000), and the bias in favor of these commodities suggested that producers adopted

technologies favoring both perishable commodities and more hired labor. As the

technology became more perishable crops-producing and more other outputs-reducing

with IRCA, the technology became significantly more chemicals-using. The agricultural

land-saving characteristic of technology did not significantly change with IRCA.

Rates of technological change were estimated both at observed prices and fixed

input quantities, and at constant prices and fixed input quantities. The rate of

technological change at observed prices and fixed input quantities was significantly

different than 0 at 5% significance level from 1960 to 1994; from 1995 to 1999 they were

insignificant at greater than the 30% level. The rate of technological change at constant

prices and fixed input quantities was significant at the 0.01% level from 1960 to 1990. It

became significant at the 5% level for the remaining years, except for 1992 to 1994 when

it was insignificant. Figure 5-8 shows that the rate of technological change at observed

prices and observed fixed inputs declined from 16% to -0.9%. The rate of technological