UFDC Home  myUFDC Home  Help 



Full Text  
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 Special thanks go to Eldon Ball, who put together the unpublished data from ERS, USDA specifically for this research.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 HicksAhmad 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 WileySchmidtBramble 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 Wellbehaved 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 nPrice 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. OwnPrice 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 21 Number of immigrants admitted as Immigration Reform and Control Act legalization. .......................................... ............................ 20 51 Florida estimates with homogeneity and symmetry constraints. ..........................92 52 Florida estimates with homogeneity, symmetry, and convexity constraints............93 53 Florida biased technological change calculated at the means................................94 54 Florida ownprice elasticity and inverse price elasticity .......................................94 55 Florida average Morhishima elasticity of substitution .......................... ..........95 56 U.S. estimates with homogeneity and symmetry constraints..............................96 57 U.S. estimates with homogeneity, symmetry, and convexity constraints ..............97 58 U.S. biased technological change calculated at the means...................................98 59 U.S. ownprice elasticity and inverse price elasticity. ...........................................98 510 U.S. average Morishima elasticity of substitution. .............................................99 Cl Florida biased technological change. ........................................ ............... 126 C2 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 21 Percentage of hired farm workers by regions .......................................................18 22 Farm workers ethnicity and place of birth. ....................................................19 23 L egal status of farm w workers ......................................................................... .... 19 24 Percentage of deportable aliens located by border patrol who are Mexican agricultural w orkers............. .... ............................................................. .. .... .... 20 31 Ahmad's induced innovation model. ............................................ ............... 40 32 Induced technological change. A) Mechanical technology development. B) Biological technology develop ent ............................................... ................... 41 33 Innovation production possibility frontier and technological progress ..................42 34 Technological progress and a change in prices....................................... ........... 43 35 Substitution and output effects of profit maximization ........................................44 36 Induced innovation for profit maximizing technological change. .........................45 41 Florida price indices of outputs, variable inputs, and fixed inputs ........................65 42 Florida profit shares of outputs, variable inputs, and fixed inputs.........................65 43 U.S. Price Indices of outputs, variable inputs, and fixed inputs. ..........................66 44 U.S. profit shares of outputs, variable inputs, and fixed inputs. ...........................66 51 Florida biased technological change. ........................................ ............... 100 52 Florida rate of technological change. ............ ............................. ...............100 53 Florida Morishima elasticity of substitution between variable inputs .................101 54 Florida Morishima elasticity of substitution between variable input and fixed input (fixed input price changes)....................................... ......................... 102 55 Florida Morishima elasticity between fixed input and variable input (variable input price changes), and between fixed inputs. ............. ..................................... 103 56 U .S. biased technological change.................................... .................................... 104 57 U.S. biased technological change, other outputs and materials. ..........................104 58 U .S. rate of technological change...................................... ......................... 105 59 U.S. Morishima elasticity of substitution between variable inputs........................106 510 U.S. Morishima elasticity of substitution between variable input and fixed input (fixed input price changes) ........... ...................................... 107 511 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 profitmaximized 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 WileySchmidtBramble 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 selfemployed laborusing in both Florida and the U.S., and more hired laborusing 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 laborsaving 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 19971998, 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 laborsaving technology (Krikorian 2001). An example where laborsaving technology is available, but has not been adopted is driedonthevine (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 laborsaving 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, laborsaving 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 laborintensive 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 laborintensive. A premise of this research is that changes in the labor market or in immigration policy may have differing effects in laborintensive and nonlaborintensive 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 lowincome countries employ inexpensive labor, and other developed countries invent new machinery, U.S. fruit and vegetable production remains dependent largely on lowwage 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 20002001 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 lowwage 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 laborsaving or capitalusing 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, lowwage 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 lowwage 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 laborsaving technology has not been developed or adopted (Krikorian 2001). With readily available lowwage immigrant workers in U.S. agriculture, the incentive for producers to adopt new laborsaving 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 counterexample 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 99603, 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 laborsaving, capitalusing 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 laborintensive 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 mid1880s, 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 selfemployed 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 nonU.S. citizens. Among nonU.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 laborintensive production. Figure 21 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 2575% (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 19971998 (Figure 22); 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 23). The same survey also found that 19% of interviewed farm workers were employed by contractors, 61% work in fruits, nuts, and vegetables, and onethird 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 19971998 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 noncitizens 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 19851986 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 H2 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 H2A 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, onethird of the IRCA lawful permanent residents had become naturalized. Table 21 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 Mexicanborn US residents in 2000, including 3 million unauthorized Mexicans, and another 14 million MexicanAmericans (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 nonseasonal guest worker programs. Seasonal workers are authorized to stay in the U.S. for a period of 9 months, and nonseasonal 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 18month period ending August 31, 2003 could apply for temporary resident status. If they perform at least 360 days of agricultural employment during the 6year 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 12month 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 H2A temporary and seasonal foreign agricultural worker program. The H2A 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 H2A 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 3year 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 18621875, 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 19451970. 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 2025% of U.S. vegetable acreage and 4045% 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, laborsaving, and robotic machines. Laborsaving harvesting machines are those that replace the work of hand harvesting such as shaking a tree or a bush, digging a row of belowground vegetables, or cutting a row of aboveground 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 capitallabor ratio has increased 3% annually in Iowa, but decreased 4% annually in Florida and California. The material inputslabor 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 21. 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. MexicanBor 77% Latin American Born 2% Other USBorn 2% USBor African American 1% USBor Hispanic 9% USBom White 7% S Asian Bom 1% Other Foreign Bom 1% Figure 22. Farm workers ethnicity and place of birth. Source: National Agricultural Workers Survey, 19971998 (Mehta et al. 2000). Citizen 22% Unauthorized 52% Other 2% / Legal Pemament Resident 24% Figure 23. Legal status of farm workers. Source: National Agricultural Workers Survey, 19971998 (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 24. Percentage of deportable aliens located by border patrol who are Mexican agricultural workers. (USCIS table 60) Table 21. 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 growththeoretic 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 kinddirected 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. "..."Laboursaving" inventions increase the marginal product of capital more than they increase the marginal product of labor; "capitalsaving" inventions increase the marginal product of labour more than that of capital; "neutral" inventions increase both in the same proportion." (Hicks 1932, p.121122) 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 laboursaving techniques, unless, because of some inherent characteristic of technology, laboursaving knowledge is easier to acquire than capitalsaving 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 HicksAhmad model of induced technological change. HicksAhmad 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 laborsaving for a given output at a given factor price ratio. Similarly capitalsaving 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 factorsubstitution 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 costsaving invention. Figure31 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 laborsaving 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 laborsaving. 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 2dimensional 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.2627). 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 18801960, 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 selfraking reaper for the handrake reaper, and the substitution of the binder for the selfraking 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 yieldincreasing improvements in varieties. They developed a 4factor 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 32a and 32b. Figure 32a 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 landlabor 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 32b, 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 landfertilizer 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 fertilizerresponsive 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, highyielding 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 18801960 can be viewed as a dynamic factorsubstitution 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, loglinear regressions of landlabor and powerlabor 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 landlabor ratio and in the powerlabor 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 18801960 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 fertilizerland 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 laborsaving 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 manyfactor 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. Crosssection data from 39 states or groups of states were used to estimate the share equations for the years 1949, 1954, 1959, and 1964. Timeseries agricultural data from 19121968 were used to calculate the change in factor shares in the absence of price changes. The results showed a very strong bias toward fertilizerusing. 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 laborsaving 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 machineusing. This means that a neutral innovation possibility could not have occurred, and it must be toward machineusing. 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 19101978. 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 profitmaximizing 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 laborsaving and capital and chemicalusing 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 19511982. 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 Hicksneutral 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 multiinput, multioutput 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 fertilizerusing 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 multiinput, multioutput 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 HicksAhmad model of priceinduced 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 33 illustrates the concept of IPPF and technological change in a simple case of one outputone 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 yx 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 33, 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 33 represents the oneinput, oneoutput production function, but if we assume a twoinput, oneoutput technology, y = f(K,L), we can interpret Figure 33 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 capitallabor ratio (biased or neutral technological change). Figure 34 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 34, 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 profitmaximizing 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 oneinput, oneoutput 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 35 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 35, 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 36 gives the illustration of the profit maximizing induced innovation model for a twoinput, oneoutput 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 36 is neutral technological progress which means that holding factor prices constant at (r/w)2, the laborcapital 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 multioutput, multiinput 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 iproducing if Bi is positive, and it is output i reducing if Bi is negative. Similarly, a technological change is variable input iusing if Bi is positive, and it is variable input isaving if Bi is negative. A technological change is fixed input jusing if Bj is positive, and it is fixed input jsaving 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 31. 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 32. 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, 18801960." 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 33. Innovation production possibility frontier and technological progress. Output Y1 Y1'=fi' Yi=fi(x) Figure 34. Technological progress and a change in prices. IPPF2 IPPF1 X2 X1' X1 Input Labor L 3 .......... Li' L ........... L1 L 2 .......... Figure 35. 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 36. 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 factoraugmenting 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 CobbDouglas, 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 factoraugmenting 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 manyfactor 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 CobbDouglas 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 twicedifferentiable 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 quasihomotheticity 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 pricetakers and maximize shortrun 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 11 k1 Model Restrictions A welldefined 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 addingup 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 11 ji 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 nondecreasing 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 nonincreasing 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 nonnegative (nonpositive). 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 WileySchmidtBramble 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 WileySchmidtBramble 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 secondorder 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 secondorder 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 nonnegative (nonpositive). 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 nonnegative 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 nonpositive. 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. WileySchmidtBramble 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 WileySchmidtBramble 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+PPL 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 AllenUzawa 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 constantoutput crossprice 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.9697). 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 19601999. 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 constantquality price indices measure changes in the price of inputs while keeping the efficiency constant. It is important to use qualityadjusted 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 constantquality 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 constantquality 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 directhired labor and contract labor. The wage of selfemployed 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 41 to 44 illustrate the data by normalizing them to 1 in 1960 for ease of comparison. Figure 41 shows price indices for Florida outputs and inputs. All variables have an increasing trend. Both hired labor and selfemployed labor wages changed in the same direction. While farm wages remain relatively constant in the 1960s and early 1970s, they increased significantly in the mid1970s 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 mid1970s, 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 42 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 selfemployed labor. Hired labor also had relatively stable shares, but it increased after 1964 until 1970 and from 1992 to 1996. Selfemployed 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 43 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 19891993. 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 44 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 selfemployed 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 mid1990s 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 mid1990s. 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 41. Florida price indices of outputs, variable inputs, and fixed inputs. 2 0.5 l" C1 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 42. 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 43. 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 44. 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 11 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, selfemployed 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, profitmaximizing input demand and output supply equations (or profit share equations) is more efficient (Berndt 1996, p.470). The profit function is assumed to be wellbehaved; 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 equationbyequation OLS (ordinary least square) estimates will not guarantee the symmetry constraints across equations. Moreover, the crossequation 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 equationbyequation 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 addingup 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+M1 variable input and output share equations are linearly independent, and only L1 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 Wellbehaved 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. 109110) 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 In4r 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 2l 12+ 12c2 Y13+cc3 Y14+cL4 715+cc5 716+cL6 Y22+222 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+25 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 WileySchmidtBramble (WSB) reparameterization technique. The WSB 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 WSB reparameterization, the original parameters are replaced by a one to one correspondence between the Hessian, All (Ajj), and its WSB 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 11 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 constantoutput crossprice 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 51. 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 WileySchmidtBramble 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 52 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 51 and 52, 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 WileySchmidtBramble 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 52 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 51 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 53 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 cropproducing, but significantly bias against the production of other outputs. The technology became more selfemployed laborusing, 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 selfemployed 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 selfemployed laborusing in the production of perishable crops in the labor intensive areas. Figure 52 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 OwnPrice Elasticity The ownprice elasticities of both outputs were positive, and those of inputs were negative as expected at all observations. Table 54 summarizes the ownprice 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 53 to 55. 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 53 shows the MES's among variable inputs. The MES's among variable inputs were positive, except for the elasticity between selfemployed labor and materials when material price changed. After 1986, the MES between materials and chemicals when chemical price changed and the MES between selfemployed labor and chemicals when chemical price changed became negative, but only lasted for a few years. The elasticity between hired labor and selfemployed labor, when returns to selfemployed 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 selfemployed labor were substitutes, an increase in wages of hired labor created a larger incentive for selfemployed producers to work longer hours than to hire more workers when returns to selfemployed labor increased. Figure 54 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; selfemployed labor and land when land price changed; and capital and hired labor when capital price changed. The substitution between selfemployed labor and capital were more elastic than between hired labor and capital when capital price changed. Figure 55 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 53 to 55, some of the MES's were highly variable over time. Table 55 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 55 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 selfemployed 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, selfemployed 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 selfemployed labor and land, and between chemicals and land when land price changed. Selfemployed 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 selfemployed 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 56. 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 WileySchmidtBramble reparameterization technique. The original parameters were calculated and reported in Table 57. 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 56 to 58 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 57. 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 56 and Figure 57. 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 cropsproducing, less selfemployed laborsaving, and more landsaving. Although insignificant, the technology was less hired laborsaving and less chemicalsaving, and the biases against other outputs increased after 1986. After 1986, the technology was dramatically biased against materials until 1991 when it became materialsusing. Table 58 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 selfemployed laborsaving; however, the use of capital was not significantly different. The technology became significantly more perishable crops producing, but became significantly more other outputsreducing. The technological bias shifted significantly in the direction of chemicalsusing 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 landsaving and capitalusing in both periods. IRCA coincided not only with U.S. producers failing to shift to a more laborsaving technology, but rather with a shift toward more laborusing 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 postIRCA period as compared to preIRCA. 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 cropsproducing and more other outputsreducing with IRCA, the technology became significantly more chemicalsusing. The agricultural landsaving 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 58 shows that the rate of technological change at observed prices and observed fixed inputs declined from 16% to 0.9%. The rate of technological 