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Agricultural Commercialization and Food Security in Sub-Saharan Africa

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Title:
Agricultural Commercialization and Food Security in Sub-Saharan Africa
Creator:
Bolarinwa, Olufemi Daniel
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[Gainesville, Fla.]
Florida
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University of Florida
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english
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Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Food and Resource Economics
Committee Chair:
MOSS,CHARLES BRITT
Committee Co-Chair:
SCHMITZ,ANDREW
Committee Members:
SEALE,JAMES L,JR
PERZ,STEPHEN GEORGE
Graduation Date:
4/30/2016

Subjects

Subjects / Keywords:
Agricultural land ( jstor )
Agriculture ( jstor )
Commercial production ( jstor )
Commercials ( jstor )
Crop value ( jstor )
Farms ( jstor )
Food ( jstor )
Food security ( jstor )
Household income ( jstor )
Transaction costs ( jstor )
Food and Resource Economics -- Dissertations, Academic -- UF
africa -- agricultural -- commercialization -- food -- security -- sub-saharan
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bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Food and Resource Economics thesis, Ph.D.

Notes

Abstract:
Issues related to food security have been the focal point of policy debates, especially in sub Saharan Africa where the problem seems to be most severe. Also at the core of this debate is the choice of suitable agricultural policies that could enhance food security. There has been however, a lack of consensus on which alternative policy could provide a viable pathway to food security. The inconsistencies in the literature has been attributed to study designs and how agricultural commercialization has been measured. This study proposes a different approach that makes use of agricultural households preplanting production decision to stratify households based on production orientation. Specifically, the study estimates the probability that a farming household is commercially oriented based on their choice of hired labor and land rental. In addition, I estimated the effect of the latent variable for commercial farming on household food demand using the Workings model. Results show that the structural parameters of the underlying logit which estimates the probability that a farming household is involved in commercial agriculture are not individually significant. However, a joint likelihood ratio test on the structural parameters and the coefficient estimates of the variables in the logit are statistically significant at any conventional level. The comparison of the estimated probabilities with previous predictors using contingency tables shows some consistency of our estimates with previous measures. Specifically, the results show on the average that the estimated probabilities stratify households into the same production orientation class about 50 percent of the time. There is an implicit assumption that the probability of being a commercial farmer might be measured with error and this is likely to overstate the confidence level of the likelihood ratio test of the joint parameters. As an alternative approach, I calculated the elasticities of the probability for each equation and then used the delta method to compute the variance of the elasticities using the bootsrapped covariance matrix obtained from the initial model estimation. The results suggest that the elasticities are not significantly different from zero. This implies that market orientation may not be an important determinant of production input choices and household food demand. Lastly, results of the relative effect of commercial agriculture on the level of household food security suggest that commercial farming households employ a joint production initiative which entails some subsistence level of production along with commercial production in order to ensure household food security. In addition, commercial oriented households redistribute household income towards high valued and nutritious food relative to their subsistence counterparts who consume more of less nutritious food including food away from home. ( en )
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In the series University of Florida Digital Collections.
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Includes vita.
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Includes bibliographical references.
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Description based on online resource; title from PDF title page.
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This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (Ph.D.)--University of Florida, 2016.
Local:
Adviser: MOSS,CHARLES BRITT.
Local:
Co-adviser: SCHMITZ,ANDREW.
Statement of Responsibility:
by Olufemi Daniel Bolarinwa.

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Copyright Bolarinwa, Olufemi Daniel. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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AGRICULTURAL COMMERCIALIZATION AND FOOD SECURITY IN SUB SAHARAN AFRICA By OLUFEMI DANIEL BOLARINWA 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 2016

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© 2016 Olufemi Daniel Bolarinwa

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To the Almighty God

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4 ACKNOWLEDGMENTS I am eternally indebted to the Almighty God who has brought me this far in my academic pursuit. He gave me life and in turn hope; He has been my guide, my source and my refuge thus far. I am immensely grateful to Him. The tutelage over the years and insightful supervision of this dissertation by Dr. Ch arles B. Moss is much appreciated. Your drive for excellence has always urged me steps further than my perceived limit: thanks for your mentorship. My gratitude to my co advisors, D r. James Seale (jr) , Dr. Andrew Schmitz, and Dr. Stephen Perz for their gui dance and timely insights in the course of this research. Many thanks to my colleagues, and friends, Ayuba Asiedu and Di wash Neupane for their support while I researched and put together this dissertation. I will always remember your contributions towards the success of this piece. A world of gratitude to my jewel, Olapeju Bolarinwa: I may not have pulled this off without your love and all round support. Thank you for being there. For my son, Oluwalani, your magnetic smiles brightens my day more than your young mind can fathom. Thank you little one. I count myself lucky to be a part of the Bolarinwa family. Thanks Dad for your financial, moral and spiritual support all the way through my academic adventure. To my Siblings: Seyi, Tosin and Funmi, I am overwh elmed with your love in the course of this work. Thanks today and always. To my late Mum and my late Brother, your prayers, encouragement and support during your life time have helped thus far. I only wish you were here to share in my joy but I believe God knows best.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF TABLES ................................ ................................ ................................ ........................... 7 ABSTRACT ................................ ................................ ................................ ................................ ..... 8 1 INTRODUCTION ................................ ................................ ................................ .................. 10 Problem Statement ................................ ................................ ................................ .................. 11 Objecti ves of this Study ................................ ................................ ................................ .......... 13 2 LITERATURE REVIEW ................................ ................................ ................................ ....... 17 Overview of Transaction Cost ................................ ................................ ................................ 19 Transaction Cost Approach to Subsistence Orientation ................................ .................. 20 M easures and Impact of Agricultural Commercialization ................................ .............. 24 Theoretical Framework ................................ ................................ ................................ ........... 27 Workings Model ................................ ................................ ................................ ..................... 34 Contingency Tables ................................ ................................ ................................ ................ 35 Chapter Summary ................................ ................................ ................................ ................... 36 3 ECONOMETRIC SPECIFICATION ................................ ................................ ..................... 39 Generalized Method of Moment Framework ................................ ................................ ......... 39 Empirical Specification ................................ ................................ ................................ .......... 42 Estimation Procedure ................................ ................................ ................................ .............. 44 Boots trapping of Standard Errors ................................ ................................ ........................... 46 Chapter Summary ................................ ................................ ................................ ................... 47 4 DATA ................................ ................................ ................................ ................................ ..... 51 Study Area ................................ ................................ ................................ .............................. 51 Description of the Data Files ................................ ................................ ................................ .. 52 Data Preparation and Processing ................................ ................................ ............................ 53 Description of the Data ................................ ................................ ................................ ........... 54 5 RESULTS ................................ ................................ ................................ ............................... 62 6 CONCLUSION ................................ ................................ ................................ ....................... 78 Discussion ................................ ................................ ................................ ............................... 78 Future Work ................................ ................................ ................................ ............................ 82 APPENDIX: R CODE ................................ ................................ ................................ ................... 84

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6 LIST OF REFERENCES ................................ ................................ ................................ ............. 105 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 110

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7 LIST OF TABLES Table page 3 1 Estimates of the GMM for the Censored Labor Equation ................................ ................. 48 3 2 Estimates of the Tobit Model for the Labor Equation ................................ ....................... 49 3 3 Paired t test ................................ ................................ ................................ ........................ 50 4 1 Descri ptive Statistics of the Raw Data ................................ ................................ ............... 58 4 2 Descriptive Statistics of the Data after Excluding Extreme Outliers ................................ . 59 4 3 Descriptive Statistics of Variables ................................ ................................ ..................... 60 4 4 Budget Shares for Food ................................ ................................ ................................ ..... 61 5 1 Estimates of the Nonlinear Generalized Method of Moment ................................ ............ 67 5 2 Marginal Coefficients for the Whole Sample Based on Predicted Pr obability ................. 69 5 3 Wald Test Statistics ................................ ................................ ................................ ............ 70 5 4 Contingency Table for Agricultural Share of Household Income and probability ............ 71 5 5 Contingency Table for Commercialization Index and Predicted Probability .................... 72 5 6 Elasticities of the Probability ................................ ................................ ............................. 73 5 7 Per Adult Equivalent Expenditure for Subsistence Oriented Households ......................... 74 5 8 Per Capita Expenditure for Subsistence Oriented Households ................................ .......... 75 5 9 Per Adult Equivalent Expenditure for Commercial Oriented Households ........................ 76 5 10 Per Capita Expenditure for Commercial Oriented Households ................................ ......... 77

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8 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 AGRICULTURAL COMMERCIALIZATION AND FOOD SECURITY IN SUB SAHARAN AFRICA By Olufemi Daniel Bolarinwa May 2016 Chair: Charles B. Moss Major: Food and Resource Economics Issues related to food security have been the focal point of policy debates, especially in sub Saharan Africa where the problem seems to be most severe. Also at the core of this debate is the choice of suitable agricultural policies that could enhance foo d security. There has been however, a lack of consen sus on which alternative policy (subsistence or commercial agriculture) could provide a viable pathway to food security. The inconsistencies in the literature has been attributed to study designs and how agricultural commercialization has been measured. Th planting production decision to stratify households based on production orientation. Specifically, the study estimates the probability that a farming household is commerc ial ly o r iented based on their choice of hired labor and land rental. In addition, I estimate d the effect of the latent variable for com mercial farming on household food demand using the Working Leser model. Results show that the structural parameters of th e underlying logit which estimates the probability that a farming household is involved in commercial agriculture are not individually significant. However, a joint likelihood ratio test on the structural parameters and the coefficient estimates of the var iables in the logit are statistically significant at any conventional level. The comparison of the estimated probabilities with previous predictors using contingency tables

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9 shows some consistency of our estimates with previous measures. Specifically, t he r esults show on the average that the estimated probabilities stratify households into the same production orientation class about 50% of the time. T here is an implicit assumption that the probability of being a commercial farmer might be measured with erro r and this is likely to overstate the confidence level of the likelihood ratio test of the joint parameters. As an alternative approach, I calculated the elasticities of the probability for each equation and then used the delta method to compute the varian ce of the elasticities using the bootsrapped covariance matrix obtained from the initial model estimation. The results suggest that the elasticities are not significantly different from zero. This implies that market orientation may not be an important det erminant of production input choices and household food demand . Lastly, results of the relative effect of commercial agriculture on the level of household food security suggest that commercial farming households employ a joint production initiative which entails some subsistence level of production along with commercia l production in order to ensure household food security. In addition, commercial oriented households redistrib ute household income towards high valued and nutritious food relative to their subsistence counterparts who consume more of less nutritious food i ncluding food away from home.

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10 CHAPTER 1 INTRODUCTION Food insecurity has been a perennial global issue, as evident in the number of people suffering from hunger and malnutrition. Between the period of 2010 and 2012, about 870 million people across the world suffered from issues relating to hunger and malnutrition (FAO, 2012). Even though food insecurity is a global problem, the magnitude and nature of the problem vary between developing and developed economies. Magnitude refers to proportion of the affe cted population, while the nature has to do with the various aspects of food security, encompassing food access, availability and adequacy. The differences in the magnitude and nature might reflect differences in economic structure, which suggests that the problem of global food insecurity cannot be solved with a unified policy. For example, Mwaniki (2006) noted that developing economies unsuccessfully adopt food security strategies from developed economies, a phenomenon Mwaniki attributed to the unstable s ocial and political environment affecting various aspect of the economy, including economic growth. According to FAO, (2015 ), indicators of the various dimensions of food security show that Africa, especially sub Saharan Africa, ranks highest in terms of t he level of food insecurity. For example, sub Saharan Africa ranks highest (24.8%) in undernourishment prevalence (Clover, 2003) and is ranked second lowest (after south Asia) in terms of average dietary supply adequacy among developing countries. Sub Saha ran Africa also experienced the widest fluctuation in food supply price since 19 90, and Case (2005) notes that S ub Saharan Africa stands to be the only region where the level of hunger is projected to get worse over the next two decades if appropriate meas ures are not put in place. Barret (2002) notes that a successful long run strategy for ensuring food security should encompass three key elements: High labor productivity and stable employment that will ensure a

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11 regular stream of adequate income for susten ance; measures that facilitate consumption smoothening during periods of shocks to food supply and purchasing power which include access to credit, storage technologies and food markets; and provision of safety net opportunities ( such as transfers ) in case s where the economic system cannot alleviate adverse shocks. Falcon and Naylor (2005) have reiterated the importance of agriculture in providing sustained economic growth which is necessary to ensure food security of all citizens, including the poor. They stated that except for few countries that have exploitable natural resources like oil, agricultural development has been a major engine for growth in most of the low income countries. For example, Von Braun (1995), described commercial agriculture as viabl e pathway for rural economic growth through creation of more employment opportunities. Thus, t ransition to commercial agriculture is likely to provide a stable or more regular means of employment through on farm opportunities such as hired labor and off fa rm opportunities such as proces sing and marketing services. Problem Statement Issues related to food security have been the focal point of policy debates, especially in sub Saharan Africa where the problem seems to be most severe. Sub Saharan Africa continues to be predominantly rural (Awulachew et. al., 2008) with agriculture as a major source of livelihood for over 70 percent of the population (Boon, 2004; Awulachew et. al., 2008). Also at the core of this debate is the choice of suitable agricultu ral policies that could enhance food security. There has been, however, a lack of consensus on which alternative policy (subsistence or commercial agriculture) could provide a viable pathway to food security (Von Braun and Kennedy, 1994 ) . Subsistence agri et al., 2004). It presents the best alternative to famers, given all their constraints ( Von Braun and

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12 Kennedy, 1994). Nevertheless, it has been widely criticized: Gollin and Rogerson ( 2014) attribute the lack of development in sub Saharan Africa to its large dependence on subsistence Agriculture. Moreover, advocates of commercial agriculture continue to insist that commercial agriculture will increase income, ensure food security, and i mprove welfare and nutritional status of households (Von Braun and Kennedy, 1986). From an economic standpoint, output and input decisions of commercial agriculture are based on the principles of profit maximization and also help to reap the benefit of spe cialization (Pingali, 1997). results of previous studies addressing the effect of cash cropping on the food consumption of households and nutrition has been inconsistent. Vo n Braun and Kennedy (1986) attribute these inconsistencies to the design of these studies. For example, some of these studies that made use of cross sectional data did not take into account the condition of the household before that household adopted cash cropping. In addition, Jaleta et al., (2009) note that the literature is divergent in terms of measuring the degree of household commercialization. De Janvry et al., (1991) and Fafchamps, (1992) examine resource allocation within the household using the di chotomy between food and cash crops, while Von Braun et al, (1994) and Strasberg et al., (1999) make use of the ratio of the output sold or input purchased to the value of total agricultural production. Limitations of these approaches have been discussed b y Randolph, (1992) who described the ratio as a revealed marketing decision on the part of the household pertaining specifically to goods that can both be sold and consumed. Jaleta et al., (2009) however, argue that households can decide to sell goods that are not primarily produced for sale, a possibility that could result in a false conclusion.

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13 Objec tives of t his Study This study builds on previous studies using the concept of household separability as a means of stratifying agricultural households based on production orientation . This approach production and consumption decision of the household cannot be separated . Specifically, subsistence system are characterized i n such a way that production decisions are being influenced by their choice of consumption . On the other hand, commercial agriculture c onsumption decisio consumption decisions within the commercial agricultural system underscores the concept of separability in a gricultural household models . The concept of separability in household models ar e crucial to the stratification of agricultural households into subsistence and commercial farming households. While there is n o consensus on the yardstick for stratification, previous studies in the commercial agriculture literature have either used a dic hotomous variable of whether or not you plant cash crops, or use the ratio of the output sold or input purchased to the value of total agricultural production. In the last two decades, studies on commercial agriculture have employed the latter measure for stratification. However, the ratio of the output sold or input purchased to the value of total agricultural production does not really depict the production orientation of households because some households who initially planted crops for home consumption can change their decision to consume if prices at harvest increases. Thus, the use of ratio of the output sold or input purchased to the value of total agricultural production signifies an ex post decision making process. As a result, there is a need to em ploy an approach such that once you make a decision

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14 before the planting season to produce for consumption ( ex ante ), you will still be classified as a subsistence farmer irrespective of whether or not you change your decision at harvest. In order to stratify households based on the ex ante approach , this study will rely heavily on the transaction cost literature and literature on commercial agriculture for two reasons: First, households involved in commercial agriculture exhibit some certain characteristics. For example , a relevant characteristic of commercial farming households stated by Pingali (1997) is the substitution of nontraded inputs with purch ased input. Second, decision to participate in the market also signifies a decision tailored towards commercial production and such decision is determined by transaction cost . According to Vance and Geoghegan ( 2004 ), transaction cost approach to market ori entation suggests that households decides to be self sufficient when the transaction cost in participating in both inputs and output market are prohibitively high . Thus, relevant variables from both commercial agriculture and transaction cost literature ca n be used to predict the probability that a household will go into commercial agriculture. As a result, households who participates in the market by renting land, hiring labor, and purchasing other variable inputs used in their production process are more likely to be commercially oriented. Given this background on separability, t his study mod els the choice of input and consumer demand as a function of the traditional determinants and also the probability of adopting com mercial agriculture. Ultimately, thi s study will be able to assign to each household an ex ante probability of engaging in either a subsistence or commercial agriculture. Given the proposed improvement, the study also revisits questions about the impact of agricultural commercialization on t he living standard of agricultural households . Thus, t he broad of objective of this study is to re examine the effect of commercialization of smallholder farmers on the livelihood of rural households .

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15 This study has three central components. First, the de bate on whether or not agricultural commercialization do improve household living condition is crucial to agricultural economics and rural development especially in developing countries. As a result, a better understanding of household production and consu mption choices form an ex ante point of view will go a long way in helping to classify households bas ed on production orientation. In addition, results of the impact of agricultural commercialization on household living standards seems to be more reliable when this kind of approach is employed in the impact analysis . Second, the study reviews literature pertaining to the role of transaction cost in household production and consumption decisions, various measures of agricultural commercializat ion, and the impact of agricultural commercialization on household nutrition. Such a review is essential to have an idea of the various concepts and measures that have been used to measure agricultural commercialization before the introduction of the ex an te method of production orientation. The study also presents a theoretical and structural model on how agricultural households make production and consumption decisions. Third, the study estimates the different levels of market orientation using the ex ant e approach and also estimates the impact of commercial agriculture on household food demand. Results of earlier studies as regards the impact of agricultural commercialization on the livelihood of rural household s have been mixed. The mixed results is like ly due to the ex post household decision making approach adopted in previous studies. This dissertation is organized as follow s . Chapter II presents the relationship between agricultural commercialization and household food security. It also reviews litera ture on transaction cost app roach to production orientation, measures of agricultural commercia lization, and impact of agricultural commercialization on household welfare . Chapter II ends with a

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16 description of the theoretical model e contingency tables . Chap ter III presents the econometric specification, Chap ter I V discusses the data, Chapter V presents the results and Chapter V I concludes.

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17 CHAPTER 2 LITERATURE REVIEW World Food Summit in 1996 defined food security as a situation where everyone have both physical and economic access to food that are safe, sufficient, and nutritious enough to take care of the dietary requirements and food preferences for a healthy and life (Pinstrup Andersen, 2009). Although food security encompass e s food access, availability, sustainability, and adequacy, the problem of food insecurity cannot be solved with a unified policy. For example, developing economies could not successfully adopt food security strategies used in developed countries due to dif ferences in the social and political environment (Mwaniki, 2006). Thus, solution to problem of food security has to be region or country specific. According to Boon (2004), the problem of food insecurity in Africa is basically related to poverty which redu ces economic access to safe and nutritious food. Thus, policy interventions that will ensure food security should be tailored towards activities that increase the level of household income. According to Awulachew et. al. (2008), Sub Saharan Africa is pred ominantly rural and agriculture has been their major source of livelihood. As a result, policy interventions that will increase income and ensure food security need to focus on improving the profitability of agricultural production. Advocates of commercial agriculture has reiterated its potential to increase household income, ensure food security, and improve the welfare and nutritional status of agricultural household (Von Braun and Kennedy, 1986). The increase in household income as a result of increase i n profitability of commercial agricultural production may facilitate better economic access to high quality and nutritious food. For example, Von Braun (1995) stated that households may respond to increases in household income in different ways. These incl ude: purchase of more food, reduction in the amount of working hours in order to improve child care,

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18 reduction in exposure to infectious disease through improved sanitation and access to water of better quality, and effective demand for both preventive and curative health care. Apart from the economic access to food that can be provided through increased household income from commercial agricultural production, commercial agriculture could also provide other benefits to household food security. For example , the replacement of family labor as a source of energy with family labor as a source of knowledge (technical expertise) during the process of agricultural commercialization (Pingali, 1997) could increase the leisure time available to the household. The ex tra leisure obtained by households may be used to acquire more nutritional knowledge (Von Braun,1995) in order to enhance household food security. Thus agricultural commercialization has the potential to improve household food security both from economic a nd also nutrition stand point. Given the potential of commercial agriculture to provide better economic access to nutritious food through higher household income, actual evidence of its impact may be seen through a redistribution of household income toward s higher valued foods which could be taken as implicit indicator of the level food security . In recognition of this, Pingali and Rosegrant (1995), noted that the process of agricultural commercialization is accompanied with dietary transitions to higher valued foods such as meats, fruits and vegetables as household per capita income increase. Thus, one would expect per c apita expenditure of commercial ori ented households on high nutritious food to be higher relative to subsistence oriented households. Subsequently , per capita expenditure and per adult equivalent expenditure on various food groups will be computed for commercial and subsistence oriented hou seholds. Based on the cross sectional nature of the data used in this study, conclusions about the effect of commercial

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19 agriculture on household food security will depend on a comparison of households who are commercially oriented with those who are into subsistence farming. The next section presents the transaction cost approach to production orientation and also review relevant literature. Measures of agricultural commercialization and its impact on household income and nutrition are also discussed . The third section discusses the theoretical framework of production orientation using the transaction cost approach . The fourth and fifth section s present . T he final section concludes. O verview of Transaction Cost Agricultural households are usually classified based on their production orientation. However, there appears to be no general consensus on the mode of classification. For example, the concept of smallholder agriculture has been defined from the perspective of resource endowment, risk and vulnerability, and market orientation. However, Chamberlin (2007), indicate s that describing the concept of smallholder from a resource endowment or market orientation point of view is relatively easier than from that of risk and vulnerability. This is because of the difficulty in providing explicit quantitative indicators of risk and vulnerability. Even though the concept of smallholder agriculture can be described using the level of resource en dowment as an indicator, there is no unified threshold for classifying smallholder agriculture. For example, Ekboir et al. (2002) described a smallholder farmer in Ghana as a farmer cultivating less than 5 hectares of land while the lopment S trategy defines smallholder farmers as farmers cultivating less than 2 hectares of Land (World Bank, 2003). Given the shortcomings of risks and vulnerability and resource endowments as good indicators for describing smallholder agriculture, marke t orientation has been widely adopted as

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20 a working definition for smallholder agriculture (Chamberlin, 2007). Key et. al., (2000) attributes the differences in market orientation of agri cultural households to cost of market transactions. These costs, also known as transaction costs, refers to the set of barriers that prevents resource poor smallholder farmers fro m participating in the market (D e Janvry et al. 1991). Transaction Cost A pproach t o Subsistence Orientation De Janvry and Sadoulet (1994) present the transaction cost approach to subsistence orientation. They are able to show that transaction costs result in a price band bounded by the effective price obtained for goods sold and the effective price paid for goods purchased. Within the band, there u sually exists a range of factors and products for which there is equilibrium between demand and supply. In the transaction cost approach, the implicit price (shadow price) is bounded upward by the sale price and below by the purchase price. With this frame work, the concept of tradability or nontradability of a good and the subsistence or commercial orientation of a farm is based on internally (shadow) and externally determined prices and transaction costs which are specific to each household or decision uni t (Heidhues and Bruntrup, 2002). In this framework, the concept of separability is explained by the size of the price band. For example, if the width of the price band is narrow, the shadow price can be approximated using the market prices and, in this cas e, the production and consumption decisions are separable. Transaction costs are divided into two parts: proportional transaction costs which are costs associated with per unit costs of carrying out market transaction and fixed transaction costs which are costs associated with access to the market and are invariant to the quantity of goods traded. Examples of fixed transaction costs are search cost, cost of bargaining, screening, and enforcement while examples of proportional transaction cost include transp ortation cost (Alene et al., 2008; Key et. al. , 2000; Renkow et al., 2004).

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21 Goetz, ( 1992 ) employ s a switching regression model in order to separate the decision of whether or not to participate in the market from the level of participation in the market as a result of high level of fixed transaction cost that plagued most parts of sub Saharan Africa. Goetz however, take production as given and did not consider the effect of production shifters on marketable surplus. The results show that high transaction costs can significantly reduce market participation. Better access to information facilitates marke t participation while access to processing technology positively influence the level of market participation. Renkow et al. (2004) implement a framework for calculating the size of fixed transaction cost encountered by semi subsistence maize producing hou seholds in Kenya. Primary modes of village transport and distance to the nearest market are used as proxies for the degree of agricultural household market integration. They found that transaction costs prevents agricultural households from participating i n the maize market. Specifically, fixed transaction cost accounts for about 15.5% in terms of ad valorem tax equivalent. Alene et al . ( 2008 ) examine the effect of transaction cost on household market surplus and input use in Kenya using a selectivity model. Specifically, they examine the impact of fixed and variable transaction costs, assets, technology, and support services in stimulating the level of input use and creating marketable surplus. Similar to Goetz (1992), the results suggest that transaction costs have negative impact on market participation and the level of participation in the market. The results also reveal that output price on ly affects the intensity of market participation through increase in the level of supply by the sellers. Ouma et al. (2010) use data from Rwanda and Burundi to explore the role of transaction cost in market participation decision by households that buy and sell bananas. Three types of bananas were considered in the study: the cooking, beer making, and dessert types of bananas.

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22 They found that fixed transaction cost which include source of market information, and time required to travel to the nearest urban center did have significant negative impact on market participation and the level of market involvement by buyers and sellers. Also, differences in agro climatic conditions did influence market participation. Households living in areas that support growin g of beer bananas are likely to participate in markets as sellers when compared with households located in cooking banana growing zone. Literature abounds on the role of transaction cost in preventing smallholder farmers from participating in the market (A lene et al., 2008; Key et al., 2000; Renkow et al., 2004). However, smallholder farmers who are either in the transition stage of commercialization or engage in commercialized agricultural production are involved in va rious transaction cost reducing strate gies that has been of immense help during the process of commercialization or has helped them to remain as commercialized farming households. Omamo, (1998). Incorporates endogenous transaction costs into an integrated household model to analyze the respons e of agricultural households to increase in transaction cost associated with specialization. Using a numerical example, he found that specialization encourages trade and leads to gains from trade but smallholders however, diversify production as an optimal response to increasing transaction costs associated with high trading cost borne by the households and community as a whole. Bernard et al. (2008). Analyze the effect of marketing cooperatives a means of reducing transaction costs on commercialization of smallholder farming households that engage in cereal production in rural Ethiopia. They use propensity score matching as an approach to compare households that belong to a marketing coope rative with households that do not belong to any cooperative. The y found out households with cooperative membership secure higher output price

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23 relative to households that are non members of marketing cooperative. However, compared to non cooperative member households, households that have marketing cooperative membershi p do not on the average supply a larger fraction of their farm harvest to the market. Their results suggests a positive effect of collective action on agricultural commercialization through creation of better opportunities for marketing, better bargaining power and reduction in transaction costs. Fischer and Qaim, ( 2012 ) analyze the determinants and impacts of collective action through farmer organization among banana cultivating households in Kenya. Specifically they examine the effect of group participati on, a means of reducing transaction cost, on information access, input intensification, smallholder commercialization and household welfare. The results suggests that farmers who have group membership and also market their produce collectively did experien ce increase in household income. Thus, the extent of participation in group activities are crucial to reaping the benefits of collective action. Even though, studies abound that have reiterated the importance of collective actions in linking smallholders w ith market through reduction in transaction costs, (Bernard, and Taffesse, 2012) examined scenarios where this may not be true. They came up with three hypotheses in their conceptual model. First of which is that expansion in the marketing service initiati ve of cooperative could increase to a point where its transaction cost reducing strategy is matched with a corresponding rise in the cost of coordination. Second, the study also hypothesize that increase gative impact on their marketing performance. Lastly, they hypothesize that increasing heterogeneity in the cooperative is accompanied by the introduction of new activities that may be unrelated to the marketing initiative of the organization and thus, neg atively affect the performance of the cooperative. They found that

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24 significant increase in marketing services and scope of services offered by cooperatives could in the long run jeopardize their marketing service initiative. Measures and Impact o f Agricul tural Commercialization This section reviews some of the lite rature on different standards used in measuring the degree of commercialization and also the impact of a gricultural commercialization on income, health , and nutrition. Von Braun et al. (1994) pro pose three indices that can be used as a measure of agricultural commercialization at the household level depending on three different perspectives. Output and input side commercialization measures the proportion of agricultural output sold or input acquir ed to the total v alue of agricultural production. C ommercialization of the rural economy measures the ratio of the value of goods purchased form the market to th e total income of the household . T he degree of integration of the household into cash economy i s the ratio of the value of goods and services purchased through cash transactions to the total household income. Other measures of household agricultural commercialization include the household commercialization index (Govereh et al. 1999) which they calc ulate d as the ratio of the value of total crop sales per household per year to the value of total crop produced. Gabre Madhin et al. (2007) cited in Jaleta et al. (2009) explore four indices of commercialization which include sales to output ratio, sales to income ratio, net and absolute market positions (household that is either a net buyer, net seller, or self sufficient), and specialization index. The sales to output ratio refers to the value of gross agricultural sales relative to the gross value of to tal agricultural production. The sales to income ratio is the value of total gross sales relative to the total income obtained from crop production. Market positions are calculated as the ratio of the quantity of sales and quantity of purchases to the tota l quantity in stock. The total quantity in stock is obtained through the addition on quantity in storage form

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25 the previous year to the quantity produced in the current year. The specialization index is compu ted as the ratio of value of agricultural product s not produced by the household to the gross value of household agricultural production. The study of Kennedy and Cogill, (1987) is an example of dichotomous characterization of hou seholds into food and cash crop producers . Empirical evidence shows that ho useholds that switched from production of corn to sugarcane did earn higher income relative to the households that continue with the production of corn. They also show that preschool children from female headed households have better nutritional status rel ative to childre n from other types of household . A similar study by Bouis and Haddad, (1990) did not only reveal that sugarcane producing households earn higher income relative to their corn producing counterpart, it also shows that the increase in income did improve the nutrition of preschooler children. However, the study Dewey (1981) in rural Mexico provides evidence of negative association between dietary status (dietary diversity, dietary quality and nutritional status) of preschool children and increa sing dependence on purchased food. Tipraqsa, and Schreinemachers. (2009) explore the impact of agricultural commercialization through market integration on smallholder farming households in northern Thailand. They estimated the level of market integration, examined the determinants of market integration and analyzed the impact of market integra tion on farm productivity and household income. Similar to V on Braun and Kenney (1994), they came up with indices for household market integration: Integrat ions into variable input market, land market, fixed input market , nonfood consumption marke t, food consumption market, labor market, and farm output market . Input market integration is calculated as the ratio of the value of variable inputs acquired to the total val ue of variable input. Land market integration is evaluated using the ratio of the value of

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26 land rented to the imputed value of total farmland using the average annual rental price. Fixed input integration measures the ratio of the value of fixed input pur chas ed to the value of total fixed inputs. Nonfood consumption market integration corresponds to the ratio of total value of nonfood items that are purchased to the total value of nonfood items. The index for integration into food consumption market is com puted as the ratio of the value of purchased food items to the value of total food items. Labor market integration measures the ratio of net family income from market transactions to the total net family income. Lastly, output market integration is obtaine d through the division of gross farm output sales by the total gross farm output. They found that agricultural commercialization has a positive impact on farm productivity and household welfare. Muriithis and Matz (2015), examined the welfare effect of veg etable commercialization using Horticultural commercialization index (HCI) which is a variant of the commercialization index proposed by Von Braun et al., (1994). The first HCI was computed as the ratio of gross value of vegetables sold to the total househ old income. The second HCI was calculated as the ratio of the gross value of the vegetable sold to the total gro ss value of all crops sold. The third HCI is computed as the gross value of the vegetables sold divided by the gross value of all the vegetable crops that are produced. Using panel data which enable the authors to account for unobserved heterogeneity across household, they found that commercial vegetable production does have a positive effect on per Adult equivalent income for those households that use the export marketing channel while there was no evidence for a positive association with the per Adult equivalent asset holdings . On the other hand, depending on the HCI specification used, they found some limited evidence th at commercialized vegetable production for domestic market

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27 positively influence household welfare as measured by per Adult equivalent asset holdings and income. Theoretical Framework Production orientation has given rise to two broad classes of agricultura l household models based on the opportunities provided by the market: the separable model and the nonseparable model (Singh et. al, 1986). The separable approach is based on a functioning input and output markets which forms the basis for utility maximizin g behavior because a rational farmer can make production decision independently of consumption decision. However, the nonseparable approach is inconsistent with standard utility maximization and comes to play in the absence of market. According to (Singh, Squire, and Strauss 1986), the separable approach is also referred to as the recursive model. The recursive nature is based on the one way influence that household production decisions have on consumption and labor supply through farm profits which is an integral part of household income. The nonseparable model approach is inconsistent with profit maximizing behavior and this scenario arise when the cost associated with market exchange are prohibitively high enough to prevent households from participating in the market. The transaction cost approach suggests that households decide to be self suffici ent when the transaction cost of participating in both inputs and output market are prohibitively high (Vance and Geoghegan, 2004). On the other hand, some farmi ng households have been able to participate in the market through some transaction cost minimizing strategies. The strategies for on the role of formal organization as means of minimizing transaction costs through entrepreneurial coordination of economic activities (Coase, 1937). As noted by Pingali (1997), commercialization of agriculture is associated with increased market orientation where non -

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28 tradable inputs are s ubstituted with purchased inputs. As a result, the transaction cost approach can be used to explain the various scenarios where different types/levels of production orientation emerge. The transaction cost approach will be used in this study and it is base d on the theory of agricultural household model found in Strauss (1986) and was later modified by Key et al. (2000) to include the effect of fixed and proportional transaction costs. Similar to Alene et al. (2008), we apply the framework to both the input and consumer demand with slight modification. This study assumes a static model with the following household utility function Where refers to the household utility function and it is assumed to be monot onically increasing, concave, and it is twice continuously differentiable. The agricultural household maximizes a utility function subject to production and consumption . In addition, the household decides how much of each input ( used in producing good ) to acquire and the quantity of produced good to sell in the market. c an either be positive when it is a sale or negative when it is a purchase. On the other hand, can be either positive when it is a purchase or negative when it is a sale. The household maximizes utility subject to

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29 Where refers to the market price of output good , is the market price of input used in producing good , is an initial endowment of good i . refers to the exogenous transfers as well as other forms of income, represents the household production technology, and are exogenous shifters of the utility and production functions respectively which include individual and household characteristics . Thus, the households makes his production, consumption and trading decision jointly and this is subject to t he income constraint ( Equation 2 2), equilibrium quantities for input and outpu t ( Equation 2 3), p roduction technology ( Equation 2 4), a non n egativity constraint ( Equation 2 5). Equation s (2 1) to (2 5) depicts a conventional household maximization in the absence of transaction cost. For households that participate in the market, the income constraint will be altered by introducing transaction cost. This is because buyers and sellers will be faced with two types o f transaction costs; proportional transaction cost and the fixed transaction costs. However, this study will only introduce fixed transaction cost in the input market because output market participation is conditional on input market participation and once you pay the fixed transaction cost of participating in the input market in the first place, you do not need to pay another fixed transaction cost to access the output market. Implicitly, we assume that the input and output markets are the same which is a strong assumpti on. Although this assumption departs from the

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30 framework of Alene et al. (2008) and Key et al. (2000), it seems realistic because a farmer who intends to commercialize production through market participation would either enter into a form of contractua l agreement or join an organization such as a cooperative as a means of minimizing transaction costs. For example farmers planting crops due to regionalization would have some contractual agreement for input procurement and output marketing once they are locked into the contract. Also, once a farmer secures membership of a cooperative by fulfilling the terms of membership such as payment of dues (fixed transaction cost), the farmer is guaranteed full benefits of input procurement and output market ing. However, households who are sellers in the input market may still have to pay fixed transaction costs such as search cost in order to participate as buyers in the output market. From the proportional transaction cost perspective, b uyers effectively p ay the market price with an additional cost of transaction while sellers effectively receive the market price less the cost of transaction. Fixed and proportional transaction costs are unobservable but there are observable exogenous factors and that explains these costs. As a result , with the presence of fixed and proportional transaction costs, the income constraint can be modified as : The additional and in the superscripts above indicates the input and the output markets respectively. The households incurs a fixed costs of if the household sells good i in the input market and pays and extra if the household buys good i in the input market. On the other hand, the household does not need to incur a fixed cost if they sell in the output market but

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31 the buying households may need to incur an extra if they buy in the output market. Thus, in the presence of both the fixed and proportional transaction costs, the household m aximization becomes Equation s (2 1) and (2 3) to (2 6). For a trading household who faces both fixed and proportional transaction costs, the household demand and supply Equation s conditional on market participation is obtained from solving Equation (2 7) : Where and are the Langrage multipliers corresponding constraint, technology constraint and the income constraint respectively. Since fixed transaction costs creates discontinuities in the Langrang ian, the solution to Equation (2 7) has to be decomposed into two steps; first of wh ich is to obtain the optimal solution conditional on market participation and then choose the market participation regime that gives the greatest level of utility. The conditional supply and demand for which the system is optimal is obtained from the solut ion to the first order conditions (FOC). The first order condition for goods consumed is: F irst order condition for output is:

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32 F irst order condition for input is: and f irst ord er condition for traded goods in the input and the output markets are : The decision price Equation (2 includes proportional transaction costs. When the household decides not to trade, the decision price of the household is equivalent to the shadow price . The combination of the first order conditions with the decision price defined above ar e similar to the first order conditions of a separable producer and consumer pr oblem although (Key et al., 2000 ) notes that it is not actually separable because of the endogen eity of the decision price. This means it could be rewritten so that the first pa rt is profit maximization problem subject to production constraints and this leads to a system of output supply and input demand. The second part will be a utility maximization problem subject to the following income constraint:

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33 W hich gives rise to a system of consumer demand equation where denotes income and it is measured at the decision price. Finally, the decision of whether or not to participate in the market is contingent on the household utility obtained from the combination of each of the six regimes which can be represented by the indirect utility functions. The indirect utility functions are as follows: Describes the scenario of a commercialized farming household because commercialization of agriculture is associated with greater market orientation. Since this study is focused on agricultural commercialization, other combinations are not considered because those combi nations will result in intermediate cases which the literature considers as semi commercialized households. In Equation ( 2 14) is the household income at the decision price of the good produced after incorporating the transaction cost. For the input market, the optimal condition for the household to participate in the market is to buy when the price is below , remain autartkic when price is and sell when the price is above . Also, for the output market, the optimal condition for the household to participate in the market is to buy when the price is below , remain autarkic when price is and sell when the price is above . Taking these pieces together, the optimal condition for a

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34 commercialized farming household to maximize utility by participating in the input and output market will be to buy inputs when the price is below and to sell its produced goods when the price is above . This is because household utility is increasing as the decision price is increasing for sellers and household utility is increasing as the decision price is decreasing for buyers . Another interpretation is that households will go into commercial productio n if the expected utility associated with joint participation in the input and output markets as buyers and sellers respectively is greater than the expected utility associated with other n alternative combinations of input and output market orientations. Workings Model An important aspect of this study is to examine the impact of market orientation on household welfare. Household welfare can be represented as a utility function in standard economic theory. The outcome of utility maximization within the transaction cost framework developed in the previous section is the consumer demand for goods . From a duality theory, consumer decision can be expressed in terms of expenditure function . The expenditure function refers to the expenditure required to attain a given level of utility or welfare and one of its components are prices . The relationship between food expenditure and income can be attributed to the work of Engel who found that the percentage of income spent on food decreases as income increases (Unnevehr et. al, 2010; Moss et. al, 2015 ). However, a ccording to Moss et al. (2015 ) the specific the relationship between f ood expenditure and total expenditure can be represented as:

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35 w here is the expenditure on food and is the total expenditure. Leser (1963) extended the framework to include non linear relationship between the expenditure share on food and income. the Working Leser model which can be represented as follows: w he re is the share of food expenditure relative to the total consumer expenditure, is the total consumer expenditure, and are parameters to be estimated and is the residual term. Based on Working Leser formulation, and . There has been various extensions to the Working Leser model. Notable among the se extensions are the works of Kumar et. al (2008), and Mo ss et. al (2015 ). While developing a measure of poverty, Kumar et. al (2008) incorporated as to accommodate scenarios where the share of income spent on food first increases and later declines. Moss et. al (2015) marketing channel on the share of household expend iture on food. Similar to Moss et. al (2015) specification, this study intends to examine the impact of m arket orientation on the share of household budget on purchased food. The modified Working Leser model is expressed as: Where and are parameters to be estimated. Contingency T ables Based on the nature and the goals of this dissertation, it is important to compare the estimated probability ob tained from this study with other measures of agricultural commercialization that have been used in the literature. Two common measures that will be used

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36 as a basis for comparison are the household commercialization index and the agricultural share of hous ehold income. This will be done with the aid of contingency tables. The contingency tables will be computed in a two step process. First, the estimated probabilities, household commercialization index, and the agricultural share of household income are all converted into dummy variables using the 0.5 threshold for the first two measures and the mean agricultural share of household income for the threshold of the third . The dummies for the estimated probabilities, household commercialization index, and agric ultural share of household income equal one if these variables are greater than or equal to the threshold and zero otherwise. These dummy stratifications suggest that households tha t are equal to or above the threshold are classified into the commercial pr oduction category while those below the threshold belong to the subsistence class. Second, these dummies are then categorized into 2 major classes. The first class refers to the category where both the estimated probability and other predictor (commercial ization index or agricultural share of household income) predicts the households to be in the same production category. However, the second class refers to the category where the estimated probability and the other predictor predicts households into differ ent production categories. The level of consistency of the estimated probability is then measured as the percentage of the total observations that our estimates and the other predictor jointly predicts to be in the same production class. Chapter Summary T he literature review started with an overview of the relationship between commercial agriculture and food security. The next section review ed literature on indices used for classifying agricultural households based on production orientation. T hree main app roaches employe d for

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37 classifying agricultural households based on production orientation include the risk and vulnerability method, the resource endowment approach and the market orientation approach. Due to the difficulty in obtaining a reliable quantitat ive estimates for stratifying agricultural households in the risk and vulnerability approach, and the lack of consensus on a unified yard stick for stratifying agricultural households in the resource endowment approach, the market orientation approach beca me the obvious choice and has been widely used in the literature. The market orientation approach is based on the transaction cost theory which is premised on the fact that market participation both in the input and output sides are dependent on the level of transaction costs. High transaction costs can inhibit not only the decision to participate in the market but also the level of participation in the market. There are two types of transaction costs: fixed and proportional transaction costs. High fixed tr ansaction cost could inhibit market participation while proportional transaction cost (also known as per unit transaction cost) could inhibit the level of market participation. In addition to this, there was an extensive review of literature on the inhibit ive effect of transaction costs and the various approaches through which agricultural households have been able to mitigate the effect of high transaction costs. Subsequently, Chapter II reviews literature on the different measures that previous studies have used to classify agricultural household based on production orientation and also the impact of agricultural commercialization on household welfare. The review of literature on measures of agr icultural commercialization raises an important issue that is crucial to this study, most especially from a methodological stand point. The indices used to measure commercialization cannot eliminate households that actually produce for consumption but deci ded to sell their output due to price increase at harvest. This underscores the relevance of an

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38 ex ante input based transaction cost approach to re examine the question of whether or not commercialization of agriculture is the pathway to food security and better rural livelihood. It rules out subsistence oriented farmers who later changed their decision to consume based on price increase at harvest. Such a scenario might explain some of the negative effect of agricultural smallholder commercialization recor ded in previous studies. C hapter II ends with a n introduction to the Working Leser framework of consumer demand, and the contingency table.

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39 CHAPTER 3 E CONOMETRIC SPECIFICATION This chapter presents an overview of Generalized Method of Moment framework. The empirical model is a system of input and consumer demand equations which accounts for censoring in the input demand equation. Prior to estimation, estimates of the censored input demand equation were compared with corresponding estimates of the Tobit model in order to test how well the Generalized Method of Moment estimator fits the data . Finally, the system of equations are estimated using the nonlinear Generalized Method of Moments and standard errors of estimates are computed using the bootstrap pro cedure. Generalized Method of Moment Framework Based on the theoretical framework developed in C hapter II , I estimate a system of two This system of e quation will be estimated using a two stage nonlinear system of Generalized Method of Moments (GMM). Generalized Method of Moments (GMM) is a computationally convenient estimation procedure which permit specification of economic models without any distributional assumption on the errors (Hall, 2005). The estimation procedure accounts for heteroscedasticity of unknown form and can also be used to estimate nonlinear models with endogenous explanatory variables (Wooldridge, 2001). According to Hayashi (2000), joint estimation of e quation s within t he system GMM framework is asymptotically more efficient. Efficiency of system GMM estimator comes from two sources: the estimator accounts for cross e quation correlat ion and also takes into account general heteroscedasticity and correlation across observations (Cameron and Trivedi, 2005) .

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40 The system GMM framework for nonlinear models can be represented as follows: The dependent variable and error term specified in Equation (3 1) are vectors, is a column vector, and is a dimensional matrix which may be a block diagonal as specified in Equation (3 3) for the case of seemingly unrelated regression (SUR) . Since the number of parameters in each Equation can vary, . Similar to Cameron and Trivedi (2005), I assume that is independent across i . However, for a given i , components of can be correlated with variance and covariances that vary over i . In a situation where the vector of errors in the nonlinear model are additive, system estimation is similar to that of linear models. Thus, Equation (3 1) can be re written as: The matrix of instrument s are presented in Equation (3 4 ). is a dimensional matrix. However, since the number of instr uments in each of the Equation s can also vary, where is the total number of instruments in the system. Stacking Equation (3 2 ) over N households gives

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41 Equation (3 5 ) can be re written as Where and are vectors and is a matrix. Similarly, the matrix of instruments becomes a dimensional matrix. The GMM system estimation is based on the following moment condition: Equation (3 7 ) can be re written as T he vector of residual is a function of which is a vector parameters to be estimated . The orthogonality of the errors to the set of instruments in Equation (3 8 ) ensures that the parameter estimates are consistent. Based on the moment cond ition specified in Equation (3 8 ), the minimand for a system GMM specification can be written as found in (Cameron and Trivedi, 2005):

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42 is a weighting mat rix which is positive semi definite and converges in probability to a matrix of constants that is positive definite. Formally, the GMM estimator of can be expressed as Equation (3 10 ) suggests that the GMM estimator choose parameters in the parameter space that minimizes the function (Hall, 2005). The robust estimate of the asymptotic variance matrix can be expressed as: Where and With the assumption that is independent across observations with variance matrix , the choice of provides the most efficient estimator. Empirical Specification To achieve the goals of the research, the study estimates a system of factor input and consumer demand e quation s. In this study, o nce the household decides to participate in the market, their decision to participate in the input market as buyers or lessors in land and labor markets simultaneously represents a production orientation tailored towards commercial production . According to Pingali (1997), c ommercialization of agriculture is associated with greater market orientation in which nontraded inputs are substituted with purchased inputs. Since production orientation could be a signal for market participation, the econometric

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43 specification used in this study draws from empirical literature related to output supply and input selec regression models (Goetz, 1992; Alene et al. 2008). T he model adopted in this study is a lso a variant of the model . The choice of land rental and la bor hired is a function of input prices, household and household head characteristics, and a latent variable that signifies whether or not the household is into commercial agriculture which in itself is endogenous and should be modeled directly . In addition, the labor e quation includes a pseudo inverse m ills ratio which is necessary to control for potential baises that may arise from sample selectivity, and an extra term to account for possible censoring in cases where households did not hire labor. The consumer demand e quation is specified by incorporating the latent variable for commercial farming into the Working Lesser framework . Specifically, the model to be estimated in this study can be expressed as follows: Equation (3 1 3 ) is a system of three Equation s that will be estimated using the two stage nonlinear G eneralized M ethod of M oments (GMM). are constants, and are vectors of parameters corresponding to household characteristics, and are vectors of parameters corresponding to the characteristics of the head of household , and are parameter vectors of input prices, and are the coefficients of the log of expenditure, the probability of being a commercial farming household, and the interaction of the log of

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44 expenditure and probability o f being a commercial farming household respectively. is the probability that a household will go into commercial agriculture and it is specified as a logit in the model. is specified as a probit in order to account for censoring in the Labor e quation . The probit specification enters multiplicatively into the censored labor equation. Thus, if the dependent variable is zero, the probability from the probit tends to zero so tha t the multiplication of the probit specification with the other right hand side variables tends to zero. Since the is specified as the probability of being in commercial farming, and are restricted to be positive in the land and labor e quation s respectively. Restrictions of and to be positive are implicit conditions on the identification of the probability of being a commercial oriented household. The pseudo inverse mills ratio is calculated as in order to account for self selection in the labor e quation . is the probability density function, is the cumulative density function and is the parameter associated with the pseudo inverse mills ratio which will be estimated. Since rental price of land and the probability of being a commercial farming household are endogenous, the squ ared terms of the continuous variables in the model will be used as excluded instruments in the GMM estimation. Estimation P rocedure Prior to the GMM system estimation, I draw a random sample of 100 observations from my data set and estimated the censo red labor equation specified within the GMM as a single equation GMM. Using the same sample, I also estimate d the labor equation using the T obit specification. In order to compare the censored labor GMM estimates with the estimates f rom the T obit model, I constructed a paired t test for each of the coefficients. The results of the censored labor GMM, Tobit model and the paired t tests are presented in Tables (3 1), (3 2), and (3 3)

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45 respectively. The result s of the paired t test suggest that the estimates of the GMM are not significantly different from the estimates obtained from the Tobit model. Thus, there is some confidence that the system GMM is working at least as well as the Tobit specification. The parameters of the system GMM is computed in two stages. The first step estimates are constructed using the matrix of instruments as preliminary weights . With the assumption of the same number of instruments in each equation, the weighting matrix for the first stage can be expressed as: Where and are identity matrices with dimensions equal to the number of equations and instruments respectively. Estimates from the first stage is then used to compute the optimal weighting matrix that is used in the second stage of the estimation . T he optimal weighting matrix for the second stage is computed as follows: Where and denotes the kronecker product . The estimate of the optimal weighting matrix relies on the consistency of the parameter estimates from the first step. Numerical optimization routine will be employed to estimate the nonlinear GMM model. Specifically, the Br oyden Fletcher Goldfarb Shanno (BFGS) algorithm will be used in solving the nonlinear system o f equations. The BFGS algorithm method that utilizes the information from the gradient and hessian of the function that is bei ng optimized. Similar to other Newton like methods, it guarantees convergence when the function is

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46 quadratic. Given the Quadratic specification of the GMM estimator as expressed in Equation (3 9), the BFGS optimization routine seems appropriate. Accord ing to Cameron and Trivedi (2005 ), the Newton Raphson algorithm leads to quick convergence , most especially when the objective function is globally concave. Parameter estimates of the nonlinear GMM will be obtained using R© version 3.2.2 software. The R code used for estimation can be found in the Appendix. Bootstrapping of Standard E rrors Cameron and Trivedi (2005) expressed their concern about hypothesis t esting in nonlinear models. They stated that the size of the test may be wrong so that a 5% probability of rejecting the null hypothesis may be either more or less than 5%. Bootstrap method was the only remedy proposed to deal with size of the test . G iven the nonlinear system GMM estimation, I decided to construct a robust covariance matrix using the bootstrap method. Bootstrapping is a nonparametric approach which assumes that the sample used in the estimation procedure is representative of the population . As a result of this assumption, empirical distribution function obtained from the sample is a nonparametric estimate of the population distribution function (Guan, 2003). The boostrap procedure used will follow the standard bootstrap procedure. First, t he estimates of the model estimation are used to predict the dependent variable . Second, the predicted dependent variable is subtracted from the actual dependent variable from the dataset in order to obta in the residuals. Third, random samples with replacement are drawn repeatedly from the residuals obtained in the second step . Fourth, these randomly drawn errors are appended to in order to generate new set of dependent variables . Due to the censoring in the labor demand Equation , if the new dependent variable (amount of labor hired) generated in the

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47 previous step is negative, it is constrained to be zero . Lastly, the new set of dependent variables are used to re estimate the model and the new estimates are stored . The whole process is repeated in an iterative process in order to generate a sample distribution of the parameters. The standard errors are now computed as the standard deviati on of the sampling distribution for each of the parameters. Chapter Summary The chapter started with an overview of t he Generalized Method of Moment framework and the two stage estimation process which accounts for heteroscedasticity and cross equation correlation. Based on the theoretical framework in Chapter II, the chapter also presented the econometric framework for the empirical analysis. The resulting sys tem of input and consumer demand equations were estimated using a nonlinear Generalized Method of Moment (GMM). Prior to the system estimation, estimates of the censored labor equation within the system were compared with its Tobit counterpart in order to test the performance of the nonlinear GMM estimator. Part of the chapter was also dedicated to discussion on the choice of weighting matrix and numerical optimization routine used to obtain the estimates. The chapter ended with the presentation of the boot strap procedure used to obtain the standard errors of the coefficient estimates.

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48 Table 3 1. Estimates of the GMM for the Censored L abor Equation Estimates Std. err t value Constant 3.1421 20.8119 0.1510 Number of children in the household 0.3773 2.5861 0.1459 Gender of household head 0.5157 11.0869 0.0465 Education of the household head 0.2789 6.6291 0.0421 Price of land rent in by the household 0.0899 4.4809 0.0201 C oefficient of the probability 3.2787 23.8165 0.1377 C oefficient of inverse mills ratio for labor equation 1.4028 9.9365 0.1412

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49 Table 3 2. Estimates of the Tobit Model for the L abor Equation Estimate Std. error t value Constant 0.0655 0.1757 0.3730 Number of children in the household 0.0345 0.0508 0.6800 Gender of household head 0.1522 0.1298 1.1720 Education of the household head 0.1770 0.1193 1.4840 Price of land rent in by the household 0.0356 0.0608 0.5850 C oefficient of the probability 1.2620 1.0347 1.2200 C oefficient of inverse mills ratio for labor equation 0.6957 0.0905 7.6860

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50 Table 3 3 . Paired t test Paired t test Constant 0.2180 Number of children in the household 0.1874 Gender of household head 0.0464 Education of the household head 0.0972 Price of land rent in by the household 0.0171 C oefficient of the probability 0.1196

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51 CHAPTER 4 DATA Study Area The study makes use of the third integrated household living conditions survey (EICV3) d ata obtained from the National I nstitute of S tatistics of Rwanda. It is the third in the survey series that started in 2000/2001 and designed to keep track of the level of poverty and living conditions in the country of Rwanda. The survey started in November, 2010 and spans the period of one year in order to capture seasonal varia tions in household income an d consumption. A total of 14,308 households were sampled from 1,230 villages using a stratified two stage sample design. The first stage was the systematic sampling of villages within each stratum (district) using the ordered l ist of villages included in the sample frame. Villages in each of the districts were ordered according to the rate of urbanization (rural, mixed, and urban) and sampling was based on proportionate allocation across rural, mixed and urban households. The se cond stage was a systematic selection of 12 households in each of the rural villages in the provinces except for Kigali province where 9 households were selected per village. In order for the data to be representative of the population, weights or expansio n factors for each sampled household was included. However, these weights are not used because the focus of this study are sampled households. The data includes information on household demographics , education, health, migration, housing, economic activities, agricultural activities and non agricultural activities, household expenditure and subsistence farming, transfers of incomes, credit, durables and savings. However, only information on household demographics, education, migration, housing, econ omic activities, agricultural and non agricultural activities, household expenditure and subsistence farming were useful to this study .

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52 Description of th e D ata F iles The demographic aspect of the data include information on each member of the household suc h as age, gender , marital status, nationality, migration, and the relationship of household members with the head of household. Information available in education section of the data include educational qualifications, expenditure on education and probable barriers affecting education of household members. The migration section of the dataset contain information relating to whether or not a member of the household migrated and probable reasons for such migration. Information on the household dwelling includ e location and type of dwelling, occupancy status, length of occupancy, housing expenses, services and installations , and distance (in minutes) between the household and basic services or service centers such as schools, markets, all weather roads, and hea lth center. Household economic activities include information on farm and non farm activities, unemployment, and underemployment, occupation for members of household aged 6 and above who are employed, wages and salaries from farm and off farm employment, employment benefits, and domestic activities. Non agricultural activities section of the data contain information on the economic activities of household members that are self employed which include type of business, labor requirement and expenditure, inco me , and turnover from the business. The Agricultural section of the data include information on livestock, expenditure and income from livestock and livestock products, land and agricultural equipment . Other information in this section of the dataset inclu de expenditure and income from land and equipment, type of crop cultivated, expenditure and income from crop cultivation, and other sources of agricultural income. The data also have a section on household expenditure.

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53 Information in this section include e xpenditure on food and non food items as well as quantities and prices of subsistence production. Data P reparation and P rocessing The main task in the data processing is the aggregation of data into household level data using the household identification n umber. The re were a total of 14,308 households in the aggregated dataset. After the aggregation, useful columns were extracted and merged into a single file. Since the data included rural, peri urban and urban households, households that have their agricul tural share of household income equal to zero were excluded from the dataset. This reduced the number of households in the dataset from 14,308 to 14,258 households. Due to econometric reasons, households that reported zero price on land rental rates were a lso dropped from the sample. Inclusion of observations with zero price on land rental rate could potential bias the coefficient estimate of the rental price of land . This reduced the sample size from 14,258 to 4,806 households. Another variable that led to the reduction in sample size was income. Households that their income turned out to be negative were also excluded from the dataset. Total household income refers to the aggregate income obtained from salary, in kind payments, housing benefits, other income benefits , profit from business for those that are sole proprietors, income from renting out land and equipment, sharecropping, profit from crop sales, net transfers, and net miscellaneous income. Income from livestock product ion was not included in the computation of the aggregate household income because of data irregularities. Including the livestock income could have increased the number of households whose income turned out to be negative, further reducing the sample size. A common problem with the livestock data was insufficient information necessary to track livestock inventory over the period of survey. The exclusion of households with negative income reduced the sample size to 4,629 observations.

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54 Table (4 1) presents th e descriptive statistics of the 4,629 observations. The descriptive statistics suggests that the data is positively skewed because for most of the continuous variables, the mean is greate r than the median . Thus, using box plot techniques which assumes norm al distribution to get rid of outliers may be inappropriate and will significantly reduce the sample size. s test (Cook R. D. 1977) to get rid of the outliers. The data plot was used to exclude extreme outliers f rom the sample for each of the continuous variables specified in the model. This reduced the sample size from 4,629 to 4,248. Table (4 2) presents the descriptive statistics for the 4,248 observations. Based on the descriptive statistics, the distribution of the data is less skewed. other outliers from the sample. was done e quation by e quation and outliers in each e quation were dropped from the sample. Thus, out of the 14,308 household in the original data set , the effective sample used for this study is 3,754 . Variables related to prices and income are converted to United States Dollars using the average annual rate as at the time of data collection. Description of the D ata Descriptive statistics of the variables used in the nonlinear GMM estimation are presented in Table 4 3 . The dependent variables include the amount of land rented in, the quantity of labor hired by the household, and the share of purchased food relative to the total consumption expenditure of the household. Variables hypothesized in the logit specification t o explain decision of whether or not to engage in commercial production are guided by a combination of the theoretical framework, empirical studies related to market participation, and intuition. Transaction cost variables present in the logit specificatio n include membership of a cooperative, presence of a commercial merchant, distance to market, distance to all weather road,

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55 and planting crops due to regionalization. Membership of cooperative and presence of commercial merchant are expected to lower trans action costs and thus, increase market participation and the likelihood of going into commercial farming. Distance to market and distance to all weather road both serves as proxies for the state of road network and market access. Proximity to all weather r oads and markets offering good prices for inputs and outputs reduces transaction costs through reduction in the cost of market information and transportation and are likely to encourage households to participate in commercial agriculture. Crop regionalizat ion is expected to increase the likelihood of going into commercial production because it could facilitate establishment of crop specific processing facilities in these regions. This has the potential of reducing transaction costs through farmer processor contractual agreements. Other variables in t he logit specification include age of household head and d ummies indicating whether or not households incur expenditure on improve seeds, chemical fertilizers, and insecticides. Age of household head proxies farm ing experience and the role of human capital in reducing transaction cost. Square term for age of household head is also included. Dummy variables for improve seed, chemical fertilizer and insectici des are measure s of access to variable inputs which facili tates large scale production as well as timeliness of production operation during each production cycle. Access to these inputs is hypothesized to positively Apart from the probabilit y of going into commercial production, other explanatory variables in the land and labor demand e quation s are gender of the household head, number of children in the household, household head education dummy which is proxied by the ability of household hea d to read a short note, and rental price of land . Gender of household is included in

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56 the land and labor demand model because it can influence the amount of land and labor obtained in the market through its linkage to financial resources. Number of children in the household is expected to have a positive relationship with the amount of land rented in by the household and a negative relationship with the amount of labor hired. Education helps in acquisition of skills and this could increase the opportunity co st of labor outside agriculture. However, education could have either a positive or negative relationship with the volume of market transactions. For example, even though literate individuals are more involved in off farm work, education could have a posit ive impact on the volume of market transactions (land rented in or amount of labor hired) in cases where their involvement in commercial agriculture is through supervision and contribution of their managerial expertise which requires a small fraction of th eir time. Land rental price is expected to have a negative relationship with the amount of land rented. However, its relationship in the labor e quation depends on the relationship between land and labor in production mix. Variables in the probit specifica tion includes a constant, household expenditure on improved seed, expenditure on equipment rental, and expenditure on chemical fertilizer. These variables are included in the probit specification for censoring because households that do not participate in the land and labor markets are less likely to participate in the markets where these inputs are sold. Table 4 4 presents household share of expenditure on food; share of household production; and total household budget share on food relative to household expenditure. These shares were computed across various food categories which include grains, meat, fats and sugars, fruits and vegetables, legumes, starches, drinks, miscellaneous and food away from home. The table suggests that households purchase more o f grains , fruit and vegetables, and starches. Also,

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57 household food production is dominated by fruits and vegetables, legumes , starches, miscellaneous and drinks. The table suggests that a gricultural households augment purchased food with production of food crops.

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58 Table 4 1. Des criptive Statistics of the Raw D ata Minimum Q[0.25] Median Mean Q[0.75] Maximum Gender of household head 0.0000 1.0000 1.0000 0.7822 1.0000 1.0000 Number of children in the household 0.0000 1.0000 1.0000 1.3593 2.0000 5.0000 Education of household head 0.0000 0.0000 0.0000 0.3977 1.0000 1.0000 Dummy =1 if household plants improved seed 0.0000 0.0000 0.0000 0.2124 0.0000 1.0000 Expenditure on improved seed 0.0000 0.0000 0.0000 1.4282 0.0000 261.4286 Amount of labor hired 0.0000 0.0000 0.0000 68.8537 52.3646 6829.2150 Dummy =1 if household use s fertilizer 0.0000 0.0000 0.0000 0.3552 1.0000 1.0000 Expenditure on fertilizer 0.0000 0.0000 0.0000 6.3670 2.8571 822.8571 Dummy =1 if household use s insecticides 0.0000 0.0000 0.0000 0.3374 1.0000 1.0000 Expenditure on insecticides 0.0000 0.0000 0.0000 2.6589 0.7143 357.1429 Dummy =1 if commercial merchants are present 0.0000 0.0000 0.0000 0.0888 0.0000 1.0000 Membership of cooperative 0.0000 0.0000 0.0000 0.2039 0.0000 1.0000 Dummy =1 if household plant s crop due to regionalization 0.0000 0.0000 0.0000 0.2361 0.0000 1.0000 Amount of land rent in by household 0.0600 4.6600 10.5500 21.8058 23.3100 2500.0000 Price per acre of land rent in 0.0114 0.9628 2.1429 4.4752 4.7619 660.5726 Total household income 0.0071 28.3631 52.9702 88.1514 93.8393 7555.5420 Agricultural share of household income 0.0000 0.0000 0.0000 0.0593 0.0000 3.6295 Distance from home to market 0.0000 30.0000 60.0000 68.8907 90.0000 5990.0000 Distance from home to all weather road 0.0000 2.0000 5.0000 29.8911 15.0000 5980.0000 Age of household head 14.0000 31.0000 40.0000 42.5055 52.0000 98.0000 Total household expenditure 0.0000 72.5814 116.4229 801.8419 189.5314 1428728.0000 Total household expenditure on food 0.0000 0.0684 0.1207 0.1500 0.1990 0.9491 Agricultural commercialization index 0.0000 0.0611 0.1820 0.5578 0.3465 838.0828

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59 Table 4 2 . Des criptive Statistics of the Data after Excluding Extreme O utliers Minimum Q[0.25] Median Mean Q[0.75] Maximum Gender of household head 0.0000 1.0000 1.0000 0.7754 1.0000 1.0000 Number of children in the household 0.0000 1.0000 1.0000 1.3420 2.0000 5.0000 Education of household head 0.0000 0.0000 0.0000 0.3981 1.0000 1.0000 Du mmy =1 if household plants improve d seed 0.0000 0.0000 0.0000 0.2017 0.0000 1.0000 Expenditure on improved seed 0.0000 0.0000 0.0000 0.8384 0.0000 43.1429 Amount of labor hired 0.0000 0.0000 0.0000 38.1530 38.1825 498.5545 Dummy =1 if household use s fertilizer 0.0000 0.0000 0.0000 0.3322 1.0000 1.0000 Expenditure on fertilizer 0.0000 0.0000 0.0000 3.3360 2.1429 68.5714 Dummy =1 if household use s insecticides 0.0000 0.0000 0.0000 0.3166 1.0000 1.0000 Expenditure on insecticides 0.0000 0.0000 0.0000 1.2454 0.5714 38.5714 Dummy =1 if commercial merchants are present 0.0000 0.0000 0.0000 0.0840 0.0000 1.0000 Membership of cooperative 0.0000 0.0000 0.0000 0.1980 0.0000 1.0000 Dummy =1 if household plant s crop due to regionalization 0.0000 0.0000 0.0000 0.2314 0.0000 1.0000 Amount of land rent in by household 0.0600 4.5000 10.2400 17.4215 21.6050 158.0000 Price per acre of land rent in 0.0340 0.9572 2.0952 3.7348 4.5119 39.1865 Total household income 0.0071 28.1893 51.5461 81.3585 88.7039 7555.5420 Agricultural share of household income 0.0000 0.0000 0.0000 0.0545 0.0000 3.6295 Distance from home to market 0.0000 30.0000 60.0000 63.2481 90.0000 240.0000 Distance from home to all weather road 0.0000 2.0000 5.0000 13.3762 15.0000 140.0000 Age of household head 14.0000 31.0000 40.0000 42.5836 52.0000 98.0000 Total household expenditure 8.0360 70.7439 111.7257 151.2204 176.1082 1995.9690 Total household expenditure on food 0.0043 0.0707 0.1239 0.1537 0.2021 0.9491 Agricultural commercialization index 0.0000 0.0586 0.1736 0.2111 0.3240 0.9620

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60 Table 4 3 . Descriptive Statistics of V ariables Mean Std. Dev Minimum Maximum Gender of household head 0.7709 0.4203 0.0000 1.0000 Number of children in the household 1.3295 0.9810 0.0000 5.0000 Education of household head 0.4012 0.4902 0.0000 1.0000 Dummy =1 if household plants improved seed 0.1806 0.3847 0.0000 1.0000 Expenditure on improved seed 0.5524 2.1029 0.0000 27.4286 Amount of labor hired 22.5765 41.5752 0.0000 272.7322 Dummy =1 if household use s fertilizer 0.2978 0.4574 0.0000 1.0000 Expenditure on fertilizer 2.2905 6.0486 0.0000 68.5714 Dummy =1 if household use s insecticides 0.2805 0.4493 0.0000 1.0000 Expenditure on insecticides 0.9920 3.3562 0.0000 38.5714 Dummy =1 if commercial merchants are present 0.0666 0.2494 0.0000 1.0000 Membership of cooperative 0.1854 0.3887 0.0000 1.0000 Dummy =1 if household plant s crop due to regionalization 0.2184 0.4132 0.0000 1.0000 Amount of land rent in by household 14.2544 14.2817 0.0600 100.0000 Price per acre of land rent in 3.5984 4.3876 0.0340 39.1865 Total household income 77.8690 209.3737 0.0071 7555.5420 Agricultural share of household income 0.0502 0.1805 0.0000 3.6295 Distance from home to market 62.8935 43.3072 0.0000 240.0000 Distance from home to all weather road 13.4100 20.1978 0.0000 125.0000 Age of household head 42.3319 14.0394 14.0000 95.0000 Total household expenditure 139.6703 131.6699 10.6293 1995.9690 Total household expenditure on food 0.1549 0.1130 0.0043 0.8267 Agricultural commercialization index 0.1974 0.1753 0.0000 0.9620

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61 Table 4 4 . Budget Shares for Food Minimum Q[0.25] Median Mean Q[0.75] Maximum Purchased Food Grain 0.0000 0.0035 0.0111 0.0175 0.0238 0.3570 Meats 0.0000 0.0002 0.0029 0.0074 0.0095 0.1471 Fats and Sugar 0.0000 0.0036 0.0071 0.0098 0.0126 0.1098 Fruits and Vegetables 0.0000 0.0036 0.0088 0.0137 0.0178 0.2921 Legumes 0.0000 0.0009 0.0085 0.0180 0.0268 0.2484 Starches 0.0000 0.0033 0.0153 0.0265 0.0369 0.4662 Miscellaneous 0.0000 0.0016 0.0027 0.0034 0.0044 0.0388 Drinks 0.0000 0.0002 0.0033 0.0089 0.0117 0.1495 Away from Home 0.0000 0.0000 0.0001 0.0065 0.0062 0.2881 Food produced by Household Grain 0.0000 0.0000 0.0000 0.0157 0.0214 0.2770 Meats 0.0000 0.0000 0.0000 0.0051 0.0000 0.3903 Fats and Sugar 0.0000 0.0000 0.0000 0.0012 0.0000 0.1925 Fruits and Vegetables 0.0000 0.0170 0.0393 0.0529 0.0725 0.6030 Legumes 0.0000 0.0000 0.0388 0.0502 0.0752 0.5278 Starches 0.0000 0.0168 0.0466 0.0612 0.0870 0.4917 Miscellaneous 0.0000 0.0000 0.0000 0.0101 0.0000 0.6057 Drinks 0.0000 0.0000 0.0000 0.0077 0.0000 0.6159 Total Food Consumed Grain 0.0000 0.0095 0.0238 0.0332 0.0460 0.3570 Meats 0.0000 0.0003 0.0042 0.0125 0.0146 0.4103 Fats and Sugar 0.0000 0.0040 0.0077 0.0110 0.0139 0.1958 Fruits and Vegetables 0.0000 0.0303 0.0532 0.0667 0.0869 0.6102 Legumes 0.0000 0.0325 0.0562 0.0682 0.0894 0.5278 Starches 0.0000 0.0430 0.0740 0.0877 0.1163 0.5071 Miscellaneous 0.0000 0.0019 0.0032 0.0135 0.0061 0.6068 Drinks 0.0000 0.0003 0.0057 0.0165 0.0185 0.6179 Away from Home 0.0000 0.0000 0.0001 0.0065 0.0062 0.2881 Overall Budget Share Expenditure Share 0.0033 0.0537 0.0916 0.1117 0.1492 0.6563 Share of Home Production 0.0000 0.0973 0.1795 0.2040 0.2854 0.8822 Share of Food, including Home 0.0245 0.2051 0.2974 0.3157 0.4023 0.9375

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62 CHAPTER 5 RESULTS The pri mary objectives of this study we re to examine the effect of being a commercial farmer on the demand for two important inputs land and labor using an input based market participation approach. I estimate d the probability that each farming household was a commercial farmer based on their c hoice of hired labor and land rental. Estimates of the probability of going into commercial farming were compared with two measures of commercialization that have been used in the literature. In addition, I estimated the effect of the latent variable for c ommercial farming on food security using the Working Lesser model. The nonlinear Generalized Method of Moments (GMM) estimates for the three Equation system and the Wald test statistics are present ed in Table 5 1 and Table 5 3 respectively . Following the goals of this dissertation, we are particularly interested in the parameters of the underlying logit which estimates the probability that a farmer is involved in commercial agriculture. While the structural parameter of the logit speci ficat ion are not individually significant in each e quation , the joint likelihood ratio test of the structural parameter and the parameters of the independent variables in the logit are all statistically significant at any conventional level in all the three e qu ation s. Specifically, the results of the likelihood ratio tests for these joint parameters are 869.7412 , 996.1489 , and 890.7339 with corresponding 1% critical values of 26.22, 26.22, and 27.69 e quation s respectively. Nex t, we compare predictions from our probability estimates with other measures used in literature to stratify household s based on production orientation . The predictors previously used in the literature include the share of agricultural income relative to th e total household income and share of the value of total production that was actually sold in the market (commercialization index). The contingency table for the combination of the estimated probabilities and the

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63 agricultural share of household income is p resented in Table 5 4 . The results suggests that these two indices stratify households into the same cat egory 51% of the time. Table 5 5 report the results for the pair of predicted probabilities a nd the commercialization index. The estimated probabilities have a predictive power of about 50 %. The comparison of the estimated probabilitie s with previous predictors show some consistency of our estimates with previous measures . In order to examine each parameter individually, the marginal effect for each variable was computed. The margi nal effects are presented in Table 5 2 . The marginal effects corresponding to the variables in the logit model represents changes in probability of going into commercial production. Of particular interest is the result that members of cooperative have a greater likelihood of going into commercial production, with an average member being 152 % more likely to participate in commercial production than non members. Age exhibit a significant p ositive relationship with the probability of farming households going into c ommercial agricultural production . This result indicates that commercial production is associated with a reasonable amount of farming experience as younger household heads may lack the necessary skills and are less likely to adopt innovations that support market orientation. Consistent with expectation are the dummies that indicate household expenditure on chemical fertilizer and insecticides which are both significan t and positive. In addition, the results of the marginal effect suggest that households that plant crops due to crop regionalization are more likely to be market oriented. This implies that households responds to incentives and opportunities that accompan y crop regionalization. The presence of commercial merchant also turned out to have a positive effect on commercial production orientation of agricultural households. Presence of commercial merchants could signal low

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64 marketing cost to agricultural househol ds which could encourage them to produce on relatively large scale. However, the results of the marginal probability suggest that distance from household dwelling to the market increases the probability of being a commercial farming household which seems t o be counterintuitive. A plausible explanation might be that distance was measured with error. The proxy for distance to market used in this study is the duration of travel to the market which seems to be subjective because the rate of travel is likely to vary by age of household members. Given the estimates of these parameters , we are interested in the effect of the structural parameter (Logit coefficient) which represents the effect of being a commercial farmer on demands for additional land and hired lab or, and the effect of commercial farming on food security. C oefficient s of the variables in the logit specification and the structural parameter jointly influence the demand to rent in more acres of land. Specifically, the likelihood ratio test for the hyp othesis that all coefficients of these variables are equal to zero is 869.7412 . Similarly, the demand for hired labor is also influenced by the joint impact of the coefficients. Taken together, the joint likelihood ratio test for these parameters is 996.1489 which is statistically significant at 0.99 confidence level . In order to access the implications of commercial farming on food security, the commercially oriented and its interaction with the logarithm of expenditure. Although the coefficients are not individually significant, the joint likelihood ratio test for the coefficients of the two variables is 30.7867 which is statistically significant at any conventional conf idence level. In addition, I tested the hypothesis that two structural coefficients and those of the individual variables in the logit specification are equal to zero. The likelihood ratio test is

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65 890.7339 . Overall, t he results sugge orientation has implications for household food security. Although the results of the likelihood ratio tests suggests that the joint parameters are significant, their confidence level may be overstated because the probability of being a commercial farmer might be measured with error. As an alternative to the initial approach, I calculated the elasticities of the probability for each equation and then used the delta method to compute the variance of the elasticities using the bootsrapped covariance matrix obtained from the initial model estimation. The results are reported in Table 5 6. The results suggest that the elasticities are not significantly different from zero. This implies that market orientation may not be an important determinant of production input choices and household food security. Results of the relative effect of commercial agriculture on household food security are presented in Table 5 7, Table 5 8, Table 5 9, and Table 5 10. Table 5 7 and Table 5 8 reports per adult equivalent and per capita expenditures respectively for subsistence oriented households while Table 5 9 and Table 5 10 presents per adult equivalent and per capita expenditures respectively for commercial oriented households. Results of p er adult equivalent expenditure for purchased food shows that subsistence oriented farmers purchase more food across quartiles and across the various food categories relative to the commercial oriented households. However, results of per adult equivalent e xpenditures for household food production suggest that commercial oriented farmers produce more food across quartiles and across various food categories relative to subsistence oriented households. The results of per adult equivalent for total household fo od consumption reveals that commercial oriented households consume more high valued and more nutritious food relative to their subsistence counterparts. Specifically, per adult equivalent expenditure on meats, fruits and vegetables, and legumes are higher for

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66 commercial farming households relative to the subsistence farming households. On the other hand, per adult equivalent expenditure on grains, starches and food away from home are higher for subsistence oriented households when compared to the commercial oriented counterparts. These results suggest that commercial oriented households are better food secured relative to subsistence farming households given the fact that food accessibility, which depends greatly on income stability, is necessary to achieve food security. Similar explanations hold for the results of household per capita e xpenditure across quartiles and various food categories.

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67 Table 5 1 . Estimates of the Nonlinear Generalized Method of Moment Variable Names Coefficient Estimates Logit variables Logit constant 98.5906 *** (25.3301) Membership of a cooperative 234.2072 ** (117.3236) Dummy=1 if Household plants improved seed 91.7805 (83.2029) Age of household head 256.5768 *** (74.4318) Square (Age of household head) 36.1111 (37.9749) Dummy=1 if Household incurs expenditure on fertilizer 1207.2830 *** (120.7974) Dummy=1 if Household incurs expenditure on insecticides 486.0718 *** (133.9987) Planting crop due to regionalization 122.9866 *** (30.3037) Distance (in minutes) to market by household 264.4194 * (152.3907) Distance (in minutes) to All weather road by household 135.5457 (137.3275) Presence of commercial merchant 315.8115 *** (128.2109) Linear part of the Land equation Constant 0.9938 *** (0.2238) Number of children in the household 3.2226 (3.0983) Gender of household head 1.2913 (1.2519) Education of the household head 57.3966 (121.8564) Price of land rent in by the household 1.1249 *** (0.2963) C oefficient of the probability 0.0000 (0.2046)

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68 Table 5 1. Continued Variable Names Coefficient Estimates Linear part of the Labor equation Constant 7.2597 (21.0225) Number of children in the household 814.1081 *** (230.5545) Gender of household head 1068.5960 *** (154.0071) Education of the household head 435.0432 (292.4887) Price of land rent in by the household 111.4996 (170.2204) Coefficient of the probability 8.8859 (6.8182) Coefficient of inverse mills ratio for labor equation 19.6087 * (11.9416) Workings Model Constant 1.5220 ** (0.6681) Log of expenditure 0.8068 *** (0.3274) Logit probability 0.3045 (0.4254) Log(Expenditure)*Logit 0.3180 (0.2831) Probit part of the censored Labor equation Constant 2.3501 *** (0.1332) Household expenditure on improved seed 0.7939 *** (0.1570) Household expenditure on equipment rental 0.4086 (1.1671) Household expenditure on chemical fertilizer 2.2525 *** (0.2305) Numbers in parenthesis denotes standard errors. *, **, and *** denotes statistical significance at 0.10, 0.05, and 0.01 levels of significance respectively

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69 Table 5 2 . Marginal Coefficients for the Whole Sample B ased on Predicted P robability Variable name Coefficient Estimates Membership of a cooperative 1.5252 ** ( 0.7640 ) Dummy=1 if Household plants improved seed 0.5977 ( 0.5418 ) Age of household head 1.6709 *** ( 0.4847 ) Square (Age of household head) 0.2352 ( 0.2473 ) Dummy=1 if Household incurs expenditure on fertilizer 7.8621 *** ( 0.7867 ) Dummy =1 if Household incurs expenditure on insecticides 3.1654 *** ( 0.8726 ) Planting crop due to regionalization 0.8009 *** ( 0.1973 ) Distance (in minutes) to market by household 1.7220 * ( 0.9924 ) Distance (in minutes) to All weather road by household 0.8827 ( 0.8943 ) Presence of commercial merchant 2.0566 ** ( 0.8349 ) Numbers in parenthesis denotes standard errors. *, **, and *** denotes statistical significance at 0.10, 0.05, and 0.01 levels of significance respectively

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70 Table 5 3 . Wald Test Statistics Equation Wald Statistics Degrees of freedom Land 869.7412 12 Labor 996.1489 12 Workings Model 890.7339 13 Workings Model(Structural coefficients) 30.7867 2 System 1006.9087 15

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71 Table 5 4 . Contingency T able for Agricultural S hare of Household I ncome and probability Pairs Counts Agricultural share=1, Probability=1 295 Agricultural share=1, Probability=0 179 Agricultural share=0, Probability=1 1676 Agricultural share=0, Probability=0 1604

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72 Table 5 5 . Contingency T able for C ommercialization I ndex and Predicted P robability Pairs Counts Commercialization Index=1, Probabilit y =1 164 Commercialization Index=1, Probabilit y =0 95 Commercialization Index=0, Probabilit y =1 1807 Commercialization Index=0, Probabilit y =0 1688

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73 Table 5 6. Elasticities of the P robability Equation Estimate Land 0.0234 (0.2073) Labor 0.1488 (6.1477) Workings 0.2776 (0.6315)

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74 Table 5 7. Per Adult Equivalent E xpenditure for Subsistence Oriented Households Minimum Q[0.25] Median Mean Q[0.75] Maximum Purchased Food Grain 0.0000 0.0940 0.3145 0.5614 0.6922 20.9679 Meats 0.0000 0.0061 0.0745 0.2904 0.2895 8.9102 Fats and Sugar 0.0000 0.0804 0.1806 0.3266 0.3791 5.2429 Fruits and Vegetables 0.0000 0.1029 0.2524 0.4770 0.5879 5.3948 Legumes 0.0000 0.0563 0.2820 0.4531 0.6351 10.1863 Starches 0.0000 0.1520 0.4738 0.6932 0.9579 7.8936 Miscellaneous 0.0000 0.0433 0.0664 0.0924 0.1131 0.8786 Drinks 0.0000 0.0036 0.0725 0.3006 0.3194 11.9610 Away from Home 0.0000 0.0000 0.0018 0.2532 0.1390 29.4462 Food produced by Household Grain 0.0000 0.0000 0.0000 0.3601 0.4516 6.7797 Meats 0.0000 0.0000 0.0000 0.1454 0.0000 15.1250 Fats and Sugar 0.0000 0.0000 0.0000 0.0291 0.0000 5.7528 Fruits and Vegetables 0.0000 0.3659 0.8479 1.2524 1.6671 17.9339 Legumes 0.0000 0.0000 0.8529 1.2223 1.7120 11.4844 Starches 0.0000 0.3350 1.0484 1.4000 1.9271 33.3333 Miscellaneous 0.0000 0.0000 0.0000 0.2854 0.0000 12.9643 Drinks 0.0000 0.0000 0.0000 0.1403 0.0000 29.7030 Total Food Consumed Grain 0.0000 0.2000 0.5672 0.9215 1.2466 20.9679 Meats 0.0000 0.0089 0.1008 0.4358 0.4462 16.2093 Fats and Sugar 0.0000 0.0873 0.1955 0.3557 0.4195 5.8389 Fruits and Vegetables 0.0006 0.7224 1.3016 1.7294 2.1964 18.6015 Legumes 0.0000 0.7323 1.2879 1.6754 2.1230 13.6492 Starches 0.0000 1.1177 1.7518 2.0932 2.6506 34.0731 Miscellaneous 0.0000 0.0477 0.0764 0.3779 0.1507 13.1486 Drinks 0.0000 0.0046 0.1112 0.4409 0.4596 29.8001 Away from Home 0.0000 0.0000 0.0018 0.2532 0.1390 29.4462

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75 Table 5 8. Per Capita E xpenditure for Subsistence Oriented Households Minimum Q[0.25] Median Mean Q[0.75] Maximum Purchased Food Grain 0.0000 0.0922 0.2940 0.5191 0.6302 20.9679 Meats 0.0000 0.0057 0.0726 0.2673 0.2610 7.0034 Fats and Sugar 0.0000 0.0771 0.1689 0.3009 0.3494 5.2429 Fruits and Vegetables 0.0000 0.1005 0.2361 0.4388 0.5510 5.3948 Legumes 0.0000 0.0530 0.2777 0.4252 0.6033 11.5309 Starches 0.0000 0.1467 0.4448 0.6478 0.8925 8.0514 Miscellaneous 0.0000 0.0411 0.0624 0.0859 0.1010 0.8786 Drinks 0.0000 0.0033 0.0740 0.2766 0.2943 9.7457 Away from Home 0.0000 0.0000 0.0014 0.2354 0.1410 29.4462 Food produced by Household Grain 0.0000 0.0000 0.0000 0.3327 0.4286 5.5786 Meats 0.0000 0.0000 0.0000 0.1365 0.0000 15.1250 Fats and Sugar 0.0000 0.0000 0.0000 0.0268 0.0000 5.6952 Fruits and Vegetables 0.0000 0.3478 0.8179 1.1668 1.5403 18.7857 Legumes 0.0000 0.0000 0.8098 1.1375 1.6000 11.3596 Starches 0.0000 0.3214 1.0000 1.3021 1.8085 24.7500 Miscellaneous 0.0000 0.0000 0.0000 0.2659 0.0000 12.9643 Drinks 0.0000 0.0000 0.0000 0.1333 0.0000 30.0000 Total Food Consumed Grain 0.0000 0.1988 0.5349 0.8519 1.1533 20.9679 Meats 0.0000 0.0086 0.0947 0.4038 0.4310 16.2093 Fats and Sugar 0.0000 0.0835 0.1844 0.3277 0.3778 5.7805 Fruits and Vegetables 0.0007 0.6959 1.2360 1.6057 2.0459 19.0888 Legumes 0.0000 0.7075 1.1946 1.5627 1.9424 15.4509 Starches 0.0000 1.0546 1.6736 1.9499 2.4271 25.2993 Miscellaneous 0.0000 0.0446 0.0754 0.3518 0.1427 13.1486 Drinks 0.0000 0.0043 0.1024 0.4099 0.4159 30.0981 Away from Home 0.0000 0.0000 0.0014 0.2354 0.1410 29.4462

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76 Table 5 9 . Per Adult Equivalent E xpenditure for Commercial Oriented Households Minimum Q[0.25] Median Mean Q[0.75] Maximum Purchased Food Grain 0.0000 0.0754 0.2574 0.5268 0.6139 12.6786 Meats 0.0000 0.0040 0.0620 0.2487 0.2363 6.7844 Fats and Sugar 0.0000 0.0801 0.1674 0.2997 0.3422 4.5802 Fruits and Vegetables 0.0000 0.0676 0.1985 0.3817 0.4460 8.6602 Legumes 0.0000 0.0130 0.1751 0.3934 0.5581 6.3474 Starches 0.0000 0.0567 0.3352 0.5687 0.8073 11.0400 Miscellaneous 0.0000 0.0418 0.0636 0.0856 0.1030 1.9270 Drinks 0.0000 0.0043 0.0937 0.3045 0.3451 16.8129 Away from Home 0.0000 0.0000 0.0026 0.2121 0.1968 19.5171 Food produced by Household Grain 0.0000 0.0000 0.0361 0.5551 0.7673 11.2995 Meats 0.0000 0.0000 0.0000 0.2051 0.0000 42.8571 Fats and Sugar 0.0000 0.0000 0.0000 0.0494 0.0000 18.6344 Fruits and Vegetables 0.0000 0.5301 1.0717 1.5884 1.9674 71.5238 Legumes 0.0000 0.3027 1.1850 1.5577 2.0619 27.7857 Starches 0.0000 0.6198 1.3323 1.6289 2.2803 20.0602 Miscellaneous 0.0000 0.0000 0.0000 0.3260 0.0000 18.7740 Drinks 0.0000 0.0000 0.0000 0.2836 0.0000 15.2381 Total Food Consumed Grain 0.0000 0.2384 0.6660 1.0819 1.3891 13.1309 Meats 0.0000 0.0072 0.0986 0.4538 0.4295 44.8254 Fats and Sugar 0.0000 0.0856 0.1827 0.3490 0.3852 18.9513 Fruits and Vegetables 0.0000 0.7889 1.4109 1.9701 2.3796 71.9905 Legumes 0.0000 0.8798 1.4859 1.9511 2.3965 28.5375 Starches 0.0000 1.2127 1.8592 2.1976 2.7703 23.0256 Miscellaneous 0.0000 0.0448 0.0741 0.4116 0.1469 18.8079 Drinks 0.0000 0.0084 0.1834 0.5881 0.6411 16.8129 Away from Home 0.0000 0.0000 0.0026 0.2121 0.1968 19.5171

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77 Table 5 10. Per Capita E xpenditure for Commercial Oriented Households Minimum Q[0.25] Median Mean Q[0.75] Maximum Purchased Food Grain 0.0000 0.0741 0.2555 0.5027 0.5967 13.1686 Meats 0.0000 0.0039 0.0609 0.2346 0.2338 6.1686 Fats and Sugar 0.0000 0.0786 0.1623 0.2838 0.3257 5.0154 Fruits and Vegetables 0.0000 0.0675 0.1915 0.3630 0.4260 8.2271 Legumes 0.0000 0.0125 0.1675 0.3754 0.5480 6.0300 Starches 0.0000 0.0565 0.3240 0.5464 0.7871 11.0400 Miscellaneous 0.0000 0.0404 0.0617 0.0814 0.0997 1.7343 Drinks 0.0000 0.0043 0.0963 0.2902 0.3291 16.8129 Away from Home 0.0000 0.0000 0.0025 0.2035 0.1907 19.5171 Food produced by Household Grain 0.0000 0.0000 0.0357 0.5260 0.7372 9.3786 Meats 0.0000 0.0000 0.0000 0.1943 0.0000 38.5714 Fats and Sugar 0.0000 0.0000 0.0000 0.0475 0.0000 17.2554 Fruits and Vegetables 0.0000 0.5043 1.0493 1.5141 1.8571 64.3714 Legumes 0.0000 0.3157 1.1582 1.4696 2.0000 25.2000 Starches 0.0000 0.6000 1.3136 1.5532 2.2229 19.0571 Miscellaneous 0.0000 0.0000 0.0000 0.3106 0.0000 16.3333 Drinks 0.0000 0.0000 0.0000 0.2721 0.0000 13.7143 Total Food Consumed Grain 0.0000 0.2364 0.6506 1.0287 1.3421 14.4440 Meats 0.0000 0.0069 0.0969 0.4289 0.4306 40.3429 Fats and Sugar 0.0000 0.0850 0.1800 0.3313 0.3649 17.5489 Fruits and Vegetables 0.0000 0.7776 1.3687 1.8771 2.2992 64.7914 Legumes 0.0000 0.8813 1.4536 1.8450 2.2657 26.2171 Starches 0.0000 1.1754 1.7987 2.0997 2.6696 21.8743 Miscellaneous 0.0000 0.0439 0.0749 0.3920 0.1406 16.3629 Drinks 0.0000 0.0076 0.1805 0.5623 0.6079 16.8129 Away from Home 0.0000 0.0000 0.0025 0.2035 0.1907 19.5171

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78 CHAPTER 6 CONCLUSION Di scussion Agricultural commercialization has the potential to increase household income, ensure food security and improve household welfare. However, results from studies that have examined the impact of commercial agriculture on household welfare have been mixed. T he inconsistencies in the literature has been attributed to study designs and how agricultural commercialization has been measured. It was based on this premise that this study was conceived. This study re examines the impact of commercialization of smallh older farmers on the livelihood of agricultural households. Contrary to previous studies that have measured the level of agricultural commercialization using either a dichotomy between food and cash crops or proxies that depict a revealed marketing decisio n (a form of ex post production decision), this study models the level of agricultural commercialization from an ex ante point of view. Market orientation of households was modelled from an input based stand point. This methodology rules out subsistence or iented farmers who later changed their decision to consume based on price increase at harvest. Using nonline ar Generalized Method of Moment , the study estimates a s ystem of input demand and consumer demand e quation s . It hypothesize s that production orientation influences input and consumption decision and hence should be taken into consideration when modell ing agricultural household decision making process. The probability of being a commercial farming household was modelled as a fun ction of some household characteristics, production characteristics, and variables of transaction costs. Predicted probabilities was used to stratify households into subsistence oriented and commercial oriented farming households.

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79 E stimated probabilities w ere compared with other measures of agricultural commercialization used in the literature using contingency tables. The results of the first contingency table shows that the predicted probability from the logit and agricultural share of household income te nd to stratify households into the same category (either sub sistence or commercial) about 51 % of the time. The predicted probability however, under predicts th e agricultural share of income 4 .7% of the time and over predicts the agricultural share of incom e 44.7 % of the time. The second contingency tables suggests that our estimated probability and the commercialization index tend to stratify households into similar class of production orientation ab out 50 % of the time. Our estimated probability under pred icts the commercialization index 2.5 % of the time and over predicts the commercialization index 48.1 percent of the time. While the over prediction is relatively high in the both contingency table s , it is important to note that agricultural share of inco me and commercialization index may not be good proxies for agricultural commercialization. Pingali (1997) and Pingali and Rosegrant (1995) notes that as opportunity costs of time of household members increase as a result of growth in off farm opportunities , the share of agricultural income decreases, nontraded inputs are substituted with traded inputs, and expenditure of energy by household members is replaced by technical expertise, management, and supervision. In addition, Martey et al. (2012) affirms in their study that increase off farm income serves as a source of income that can be invested in farm technology to boost marketed output. Thus, although the predicted probabilities seem to overestimate the agricultural share of income and commercialization index , the predicted probabilities may be taking into account households who engage in off farm activities in order to increase the capital they invest in commercial agriculture.

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80 On the other hand, the under prediction of the agricultural share of income could be as a result of poverty in households that belong to this category. For example, poor households whose major source of income comes from agriculture will on the average have their household agricultural share of income greater than the mean share o f the sample. This example further strengthens the argument that agricultural share of household income may not be a good proxy for agricultural commercialization. The results of the second contingency table supports the argument that led to this study. Th e dummy obtained from our estimated probability unde r predicts the commercialization index about 2.5 % percent of the time. This 2.5 % category are the subsistence oriented households that are classified into commercial farming households when commercializat ion index is used as a measure of agricultural commercialization. This supports the argument that commercialization index does not rule out subsistence oriented farmers who participate in output market to take advantage of price increases . While the perce ntage of the category that represents the subsistence oriented class seems relatively small in this study, a higher percentage of this group in other related studies could greatly bias the effect agricultural commercialization on various indices used as pr oxies for rural household welfare. Given the results of the estimated probabilities, we explored the marginal effects of these variables on the probability of households going into commercial farming. Consistent with our expectations, Households that belong to a cooperative , have access to marketing channels, and also incur expenditure on inputs such as chemical fertilizer and insecticides are more likely to engage in commercial production. The results also suggests that commercial production requires skills and expertise which is only acquired over time . However, contrary to expectation , households that live relatively far away from the market are more likely to go into commercial

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81 production. This counterintuitive result might be due to two reasons. Fi rst, distance from household dwelling to the market might not be a good proxy for marketing cost because farmers are more likely to convey their produce directly from the farm to market . Second, the proxy for distance to market is measured as the duration between the household and the market which seems to be a subjective measure because travel time will vary across household members based on their age. Based on the results of the estimated probabilities, the study also explored the effect of commercial agr The results appear to be consistent with prior expectation as the coefficient on the natural logarithm of household expenditure is negative. A comparison of my estimates with that of Moss et al. (2015) s hows that estimate of t heir constant is somewhat lower than my estimate, and the estimate of the coefficient of the logarithm of their expenditure is somewhat less negative than the coefficient of the logarithm of expenditure obtained in this study. These discrepancy may be due to the differences in the sample used. Moss et al. (2015) only focused on regions where coffee are grown while this study is concerned with the cropping system as a whole. The ity that a household is commercially oriented and its interaction with the logarithm of expenditure. Individually, the coefficients on commercial farming (proxied by the probability of going into commercial agriculture) and that of its interaction with the logarithm of expenditure are not st atistically significant. However, a joint likelihood ratio test for the two coefficients and the coefficients of all the variables in the logit specification suggest that we may not reject the significance of the commerc ial agriculture variable on the share of household food expenditure.

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82 Although the coefficients of probability are jointly significant, the confidence level for these variables of interest might be overstated because of the underlying assumption that the p robability of being a commercial farmer might be measured with error. As a result, I calculated the elasticity for the probability of being a commercial farmer and also employed the delta method to compute the corresponding variance from the bootstrapped c ovariance matrix obtained from the GMM estimates . The computed elasticity is not significantly different from zero. Thus, production orientation does not seem to affect the relationship between the relative share of food expenditure to the household total expenditures and the logarithm of household expenditures. Results of the relative effect of commercial agriculture on the level of household food security suggest that commercial farming households purchase relatively less food across quartiles and various food groups when compared to subsistence farming households. However, commercial farming households seem to produce more of the f ood that they consume relative to their subsistence counterpart. This is consistent with the findings of Von Braun (1995) who noted that smallholder producers continue to maintain some level of subsistence production along with the ir commercial level of pr oduction . He referred to the joint production initiative as a form of insurance policy for farm households against risky income environment. In addition, the results also suggest that commercial oriented farmers shift their diets towards high valued and nu tritious food relative to their subsistence counterparts who consume more of less nutritious food including food away from home. Future Work This study contributes to the commercial agriculture literature from two stand point. First, it models the decision to participate in the market from an input stand point. This methodology rules out subsistence oriented households who change their decision to participate in the market

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83 due to price increases at harvest. Seco nd, given the estimates of the probability of being a commercial farmer, I went ahead to examine the effect of production orientation on food security using the workings model. Despite the contributions of this study, there are still opportunities for futu re work in this area. First, household decision to commercialize production is synonymous with market participation . As a result, most of the variables included in the estimated model are guided by the market participation literature. However, due to data limitation, variables that could improve the predictive power of the probability of being a commercial farmer were not included in the model. Such variables include access to extension worker, a good proxy for marketing cost such as distance from farm to m arket, formal credit access, input and output prices. From food security stand point, this study considered expenditure on food as a whole. However, disaggregating food expenditure based on nutrient composition may be a better path way to examine the impac t of agriculture commercialization. This is because increased income from agricultural commercialization may likely lead to the redistribution of expenditure shares towards more nutritious food components which may not be pronounced when expenditure on var ious classes of food are lumped together.

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84 APPENDIX A R CODE ############################################################################### # Olufemi GMM code # # Olufemi Bolarinwa bolarinw@ufl.edu # # disserationGMM.R # ############################################################################### # This program demonstrates a system instrumental variable approach to # # motivate nonlinear generalize method of moments estimation. # ############################################################################### # Data dtafinal.dta # # dta[,1] Household ID # # dta[,2] Household head migratio n dummy # # dta[,3] Gender of household head # # dta[,4] Household head b eing a seasonal worker # # dta[,5] Household sends at least of of their children to a private school # # dta[,6] Number of children in the ho usehold # # dta[,7] Presence of domestic worker in the household # # dta[,8] Education of the household head # # dta[,9] Home ownership # # dta[,10] Dummy that shows if Houshold plants improved seed # # dta[,11] Household expenditure on improved seed # # dta[,12] Dummy that Household incures expenditure on equipment rental # # dta[,13] Household expenditure on equipment rental # # dta[,14] Dummy that Household incures expenditure on hired labor # # dta[,15] Amount of labor hired by the Household # # dta[,16] Dummy that Household incures expenditure on chemical fertilizer # # dta[,17] Household expenditure on chemical fertilizer # # dta[,18] Dummy that Household incures expenditure on insecticides # # dta[,19] Household expenditure on insecticides # # dta[,20] Dummy that Household incu res expenditure on irrigation # # dta[,21] Household expenditure on irrigation # # dta[,22] Presence of commercial merchant, coo perative to sell ag produce #

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85 # dta[,23] Membership of a cooperative # # dta[,24] Access to or Ownership of equipment (plough) # # dta[,25] Planting of new crops due to regionalization # # dta[,26] Amount of land rent in by the household # # dta[,27] Price of land rent in by the household # # dta[,28] Household Income from Salary # # dta[,29] Household in kind payment # # dta[,30] Household housing benefits # # dta[,31] Other houshold work benefits (transportation) # # dta[,32] Household VUP income benefit # # dta[,33] Non agricultural business labor expenditure by household # # dta[,34] Non agricultural business non labor expenditure by household # # dta[,35] Non agricultural business turnover by household # # dta[,36] Non agricultural business profit by household # # dta[,37] Revenue from Land rented out by household # # dta[,38] Revenue from sharecropping by household # # dta[,39] Revenue from renting out Farm equipment # # dta[,40] Monthly Revenue from small scale crop production # # dta[,41] Monthly Revenue from large scale crop production # # dta[,42] Monthly Revenue from other Agricultural activities # # dta[,43] Expenditure on agricultural activities # # dta[,44] Profit from crop production # # dta[,45] Monthly Total transfers sent out by the household # # dta[,46] Monthly Total transfers received by the household # # dta[,47] Net tranfers by household per month # # dta[,48] Public income Support # # dta[,49] Other household expenses # # dta[,50] Household net miscellaneous income # # dta[,51] Total household income # # dta[,52] Agricultural share of Household income # # dta[,53] Distance (in minutes) to market by household # # dta[,54] Distance (in minutes) to board transport by household # # dta[,55] Distance (in minutes) to All weather road by household #

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86 # dta[,56] Age of household head # # dta[,57] value of food grown by household # # dta[,58] value of food bought by household # # dta[,59] value of NON food items bought by household frequently in a year # # dta[,60] value of NON food items bought by household rarely in a year # # dta[,61] value of NON food items bought by household last 4 weeks # # dta[,62] share of value of total food produced to total consumed # # dta[,63] share of value of total food consumed to total hh expenditure # # dta[,64] total household expenditure # # dta[,65] share of value of total food bought to total hh expenditure # # dta[,66] income dummy # # dta[,67] Constant # # dta[,68] Dummy==1 if you rentin land # # dta[,69] Dummy==1 if you rentin labor # # dta[,70] Dummy==1 if you rentin land and labor # # dta[,71] Value of grain produced by the household # # dta[,72] value of meat produced by thw household # # dta[,73] value of oil and sugar produced by the household # # dta[,74] value of fruit and vegetables g rown by the household # # dta[,75] value of legumes grown by the household # # dta[,76] value of starchy foods produced by the household # # dta[,77] value of miscellaneus food products produced by the household # # dta[,78] value of drinks produced by the household # # dta[,79] value of grains bought by the household # # dta[,80] value of meat bought by the household # # dta[,81] value of oil and sugar bought by the household # # dta[,82] value of fruits and vegetables bought by the household # # dta[,83] value of legumes bought by the households # # dta[,84] value of starchy foods bought by the household # # dta[,85] value of miscellaneous products bought by the household # # dta[,86] value of drinks bought by the household # # dta[,87] value of food away from home bought by the household # # dta[,88] total value of small crops sold #

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87 # dta[,89] total value of small crops produced # # dta[,90] total value of large crops sold # # dta[,91] total value of large crops produced # # dta[,92] commercialization index # # dta[,93] newly computed income dummy form new ag share # # dta[,94] cooks test for land # # dta[,95] cooks test for labor # # dta[,96] nonlinear cooks test for the workings model # ############################################################################### # library(foreign) # load the fore ign package# library(Matrix) library(optimx) library(numDeriv) setwd("C:/Users/bolarinw/Desktop/test1") dta = read.dta("dtafinal.dta") # read from .dta file mn < sapply(dta,mean,na.rm=TRUE) md < sapply(dta,median,na.rm=TRUE) sd < sapply(dta,sd,na.rm= TRUE) mi < sapply(dta,min,na.rm=TRUE) mx < sapply(dta,max,na.rm=TRUE) print(t(rbind(mn,sd,mi,mx))) x1 < dta[,23]/10 x2 < dta[,10]/10 x3 < dta[,56]/((sd(dta[,56]))*10) x4 < (dta[,56]^2)/((sd(dta[,56]^2))*100) x5 < dta[,16]/100 x6 < dta[,20] x7 < dta[,18]/10

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88 x8 < dta[,24]/10 x9 < dta[,53]/((sd(dta[,53]))*100) x10< dta[,55]/((sd(dta[,55]))*100) x11< dta[,22]/10 x12< dta[,6]/((sd(dta[,6]))*100) x13< dta[,3]/10 x14< dta[,8]/1000 x15< dta[,27]/((sd(dta[,27]))*10) x16< dta[,6]/((sd(dta[,6]))*1000) x17< dta[,3]/100 x18< dta[,8]/100 x19< dta[,27]/((sd(dta[,27]))*100) x20< dta[,11]/((sd(dta[,11]))*100) x21< dta[,13]/((sd(dta[,13]))*100) x22< dta[,17]/((sd(dta[,17]))*1000) x23< dta[,19]/((sd(dta[,19]))*100) x24< dta[ ,5] x25< dta[,11]/((sd(dta[,11]))*10) x26< dta[,13]/((sd(dta[,13]))*100) x27< dta[,17]/((sd(dta[,17]))*10) x28< dta[,21] x29< dta[,2] x30< dta[,12] x31< dta[,25]/1000 x32< dta[,7] x33< dta[,6]^2/((sd(dta[,6]^2))*10000) x34< dta[,8]^2 x35< dta[,5 3]^2/((sd(dta[,53]^2))*100) x36< dta[,55]^2/((sd(dta[,55]^2))*10000) x37< dta[,11]^2/((sd(dta[,11]))*100) x38< dta[,13]^2/((sd(dta[,13]^2))*10000) x39< dta[,17]^2/((sd(dta[,17]^2))*10000) x40< dta[,21]^2

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89 x41< dta[,62] x42< dta[,64]/(sd(dta[,64])) dta$nagshare < ifelse(dta[,52]>=mean(dta[,52]),1,0) y1 < dta[,26]/(sd(dta[,26])) y2 < dta[,15]/(sd(dta[,15])) y3 < dta[,93] y4 < dta[,68] y5 < dta[,69] y6 < dta[,65]/(sd(dta[,65])) #Starting values logitst < glm(y3 ~ x1+x2+x3+x4+x5+x7+x31+x9+x1 0+x11, family="binomial") probitst2 < glm(y5 ~ x25+x26+x27, family=binomial(link="probit")) pp < (1/(1+exp( ( 3.2216320+1.1711367*x1+2.9505105*x2+3.2282952*x3 8.2330578*x4+8.192804*x5+3.5389377*x7+6.650707*x31+9.209349*x9+4.9988177*x10+2.8679171*x11)) )) rr < pnorm( 0.3634663+1.4800611*x25+9.861813*x26+3.1449886*x27) rr1< dnorm( 0.3634663+1.4800611*x25+9.861813*x26+3.1449886*x27) rr2< rr1/rr land < lm(y1 ~ x12+x13+x14+x15+pp) labor < lm(y2 ~ x16+x17+x18+x19+pp+rr2) int1 < log(x42)*pp lne < log(x42)

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90 work < lm(y6 ~ lne+pp+int1) wt < diag(1,nrow=69,ncol=69) obj < function(b) { err < matrix(0,nrow=nrow(dta),ncol=3) pp < (1/(1+exp( (b[1]+b[2]*x1+b[3]*x2+b[4]*x3+b[5]*x4+b[6]*x5+b[7]*x7+b[8]*x31+b[9]*x9+b[10]*x10+b[11]*x11)))) rr < pnorm(b[29]+b[30]*x25+b[31]*x26+b[32]*x27) rr1< dnorm(b[29]+b[30]*x25+b[31]*x26+b[32]*x27) rr2< rr1/rr err[,1] < y1 ((b[12]+b[13]*x12+b[14]*x13+b[15]*x14+b[16]*x15+b[17]^2*pp)) err[,2] < y2 ((b[18]+b[19]*x16+b[20]*x17+b[21]*x18+b[22]*x19+b[ 23]^2*pp+b[24]*rr2)*(rr)) err[,3] < y6 (b[25]+b[26]*log(x42)+b[27]*pp+b[28]*(pp*log(x42))) qt < 0 for (i in 1:nrow(dta)) { zz < rbind(cbind(x1[i],x2[i],x3[i],x4[i],x5[i],x7[i],x31[i],x9[i],x10[i],x11[i],x12[i],x13[i],x14[i],x4[i],x20[i ],x21[i],x22[i],x23[i],x35[i],x36 [i],x37[i],x38[i],x39[i],matrix(0,nrow=1,ncol=46)), cbind(matrix(0,nrow=1,ncol=23),x1[i],x2[i],x3[i],x4[i],x5[i],x7[i],x31[i],x9[i],x10[i],x11[i],x16[i],x17[i],x18[i],x4[i],x23[ i],x25[i],x2 6[i],x27[i],x35[i] ,x36[i],x37[i],x38[i],x39[i],matrix(0,nrow=1,ncol=23)), cbind(matrix(0,nrow=1,ncol=46),x1[i],x2[i],x3[i],x4[i],x5[i],x7[i],x31[i],x9[i],x10[i],x11[i],x16[i],x17[i],x18[i],x4[i],x23[ i],x25[i],x2 6[i],x27[i],x35[i],x36[i],x37[i],x38[i],(log(x4 2[i])))) qt < qt + err[i,]%*%zz%*%wt%*%t(zz)%*%err[i,] }

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91 return(qt[1,1]) } gra < function(b){ dq = matrix(0,nrow=32,ncol=1) for (i in 1:nrow(dta)){ pp < (1/(1+exp( (b[1]+b[2]*x1[i]+b[3]*x2[i]+b[4]*x3[i]+b[5]*x4[i]+b[6]*x5[i]+b[7]*x7[i]+b[8]*x31[i]+b[9]*x9[i]+b[10]*x10[i]+b[11]*x11[i])))) rr < pnorm(b[29]+b[30]*x25[i]+b[31]*x26[i]+b[32]*x27[i]) rr1< dnorm(b[29]+b[30]*x25[i]+b[31]*x26[i ]+b[32]*x27[i]) rr2< rr1/rr err < rbind((y1[i] ((b[12]+b[13]*x12[i]+b[14]*x13[i]+b[15]*x14[i]+b[16]*x15[i]+b[17]^2*pp))), (y2[i] ((b[18]+b[19]*x16[i]+b[20]*x17[i]+b[21]*x18[i]+b[22]*x19[i]+b[23]^2*pp+b[24]*rr2)*(rr))), (y6[i] (b[25]+b[26]*log(x42[i])+b[27]*pp+b[28]*(pp*log(x42[i]))))) p1 < (exp(b[1]+b[2]*x1[i]+b[3]*x2[i]+b[4]*x3[i]+b[5]*x4[i]+b[6]*x5[i]+b[7]*x7[i]+b[8]*x31[i]+b[9]*x9[i]+b[10]*x10[i]+b[11]*x11[i]) ) p2 < (1+(exp(b[1]+b[2]*x1[i]+b[3]*x 2[i]+b[4]*x3[i]+b[5]*x4[i]+b[6]*x5[i]+b[7]*x7[i]+b[8]*x31[i]+b[9]*x9[i]+b[10]*x10[i]+b[11]*x11[ i])))^2 p < (p1/p2) r1 < dnorm(b[29]+b[30]*x25[i]+b[31]*x26[i]+b[32]*x27[i]) r2 < pnorm(b[29]+b[30]*x25[i]+b[31]*x26[i]+b[32]*x27[i]) rr3 < ((( (b[29]+b[30]*x25[i]+b[31]*x26[i]+b[32]*x27[i]))*((exp(( (1/2))*((b[29]+b[30]*x25[i]+b[31]*x26[i]+b[32]*x27[i])^2)))))/((44/7)^(1/2))) r3 < ((r2*rr3 (r1^2))/r2^2) r < dnorm(b[29]+b[30]*x25[i]+b[31]*x26[i]+b[32]*x27[i])

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92 ss < (b[12]+b[13]*x12[i]+b[14]*x13[i]+b[15]*x14[i]+b[16]*x15[i]+b[17]^2*pp) tt < (b[18]+b[19]*x16[i]+b[20]*x17[i]+b[21]*x18[i]+b[22]*x19[i]+b[23]^2*pp+b[24]*rr2) zz < rbind(cbind(x1[i],x2[i],x3[i],x4[i],x5[i],x7[i],x31[i],x9[i],x10[i],x11 [i],x12[i],x13[i],x14[i],x4[i],x20[i],x21[i],x22[i],x23[i],x35[i],x36 [i],x37[i],x38[i],x39[i],matrix(0,nrow=1,ncol=46)), cbind(matrix(0,nrow=1,ncol=23),x1[i],x2[i],x3[i],x4[i],x5[i],x7[i],x31[i],x9[i],x10[i],x11[i],x16[i],x17[i],x18[i],x4[i ],x23[i],x25[i],x2 6[i],x27[i],x35[i],x36[i],x37[i],x38[i],x39[i],matrix(0,nrow=1,ncol=23)), cbind(matrix(0,nrow=1,ncol=46),x1[i],x2[i],x3[i],x4[i],x5[i],x7[i],x31[i],x9[i],x10[i],x11[i],x16[i],x17[i],x18[i],x4[i],x23[ i],x25[i],x2 6[i],x27[i] ,x35[i],x36[i],x37[i],x38[i],(log(x42[i])))) dq[1]=dq[1] + cbind(2*(b[17]^2)*( (p)),2*(rr)*(b[23]^2)*( (p)),2*( (p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[2]=dq[2] + cbind(2*(b[17]^2)*( (x1[i]*p)),2*(rr)*(b[23]^2)*( (x1[i ]*p)),2*( (x1[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[3]=dq[3] + cbind(2*(b[17]^2)*( (x2[i]*p)),2*(rr)*(b[23]^2)*( (x2[i]*p)),2*( (x2[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[4]=dq[4] + cbind(2*( b[17]^2)*( (x3[i]*p)),2*(rr)*(b[23]^2)*( (x3[i]*p)),2*( (x3[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[5]=dq[5] + cbind(2*(b[17]^2)*( ((x4[i])*p)),2*(rr)*(b[23]^2)*( ((x4[i])*p)),2*( (x4[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz )%*%wt%*%t(zz)%*%(err) dq[6]=dq[6] + cbind(2*(b[17]^2)*( (x5[i]*p)),2*(rr)*(b[23]^2)*( (x5[i]*p)),2*( (x5[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[7]=dq[7] + cbind(2*(b[17]^2)*( (x7[i]*p)),2*(rr)*(b[23]^2)*( (x7[i]*p)),2*( (x7[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[8]=dq[8] + cbind(2*(b[17]^2)*( (x31[i]*p)),2*(rr)*(b[23]^2)*( (x31[i]*p)),2*( (x31[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[9]=dq[9] + cbind(2*(b[17]^ 2)*( (x9[i]*p)),2*(rr)*(b[23]^2)*( (x9[i]*p)),2*( (x9[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err)

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93 dq[10]=dq[10] + cbind(2*(b[17]^2)*( (x10[i]*p)),2*(rr)*(b[23]^2)*( (x10[i]*p)),2*( (x10[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%w t%*%t(zz)%*%(err) dq[11]=dq[11] + cbind(2*(b[17]^2)*( (x11[i]*p)),2*(rr)*(b[23]^2)*( (x11[i]*p)),2*( (x11[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[12]=dq[12] + cbind(2*( (1)),0,0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[13]=dq[ 13] + cbind(2*( (x12[i])),0,0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[14]=dq[14] + cbind(2*( (x13[i])),0,0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[15]=dq[15] + cbind(2*( (x14[i])),0,0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[16]=dq[16] + cbind(2*( (x15[i])),0,0)%*%(zz) %*%wt%*%t(zz)%*%(err) dq[17]=dq[17] + cbind(2*2*b[17]*( (pp)),0,0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[18]=dq[18] + cbind(0,2*(rr)*( (1)),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[19]=dq[19] + cbind(0,2*(rr)*( (x16[i])),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[20]=dq[20] + cbind(0,2*(rr)*( (x17[i])),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[21]=dq[21] + cbind(0,2*(rr)*( (x18[i])),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[22]=dq[22] + cbind(0,2*(rr)*( (x19[i])),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[23]=dq[23] + cb ind(0,2*2*b[23]*(rr)*( (pp)),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[24]=dq[24] + cbind(0,2*(rr)*( (rr2)),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[25]=dq[25] + cbind(0,0, 2)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[26]=dq[26] + cbind(0,0, 2*(log(x42[i])))%*%(zz)%*%wt %*%t(zz)%*%(err) dq[27]=dq[27] + cbind(0,0, 2*pp)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[28]=dq[28] + cbind(0,0, 2*(pp*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[29]=dq[29] + cbind(0, 2*(((tt)*(r))+(((r2*b[24]*(r2*rr3 (r1^2))/r2^2)))),0)%*%(zz)%*%wt %*%t(zz)%*%(err) dq[30]=dq[30] + cbind(0, 2*(((tt)*(r)*(x25[i]))+(((r2*b[24]*(r2*rr3*(x25[i]) (r1^2)*(x25[i]))/r2^2)))),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[31]=dq[31] + cbind(0, 2*(((tt)*(r)*(x26[i]))+(((r2*b[24]*(r2*rr3*(x26[i]) (r1^2)*(x26[i]))/r2^ 2)))),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[32]=dq[32] + cbind(0, 2*(((tt)*(r)*(x27[i]))+(((r2*b[24]*(r2*rr3*(x27[i]) (r1^2)*(x27[i]))/r2^2)))),0)%*%(zz)%*%wt%*%t(zz)%*%(err) } return(dq) }

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94 b0 < c( 3.221632,1.171137,2.950510,3.228295, 8.23305 8,8.192804,3.538938,6.650707,9.209349,4.998818,2.867917,0.91882159,1.25303168,2.19975052, 8.18120401, 1.24302468, 0.01642444,1.877659, 5.863361,6.983298, 1.522744, 1.175778,0.492106, 1.513499,1.3212831, 0.9166935, 0.7457179,1.8540787, 0.3634663,1.4800611,9 .8618132,3.1449886) mygrad = gra(b0) numgrad = grad(obj, b0) cbind(mygrad,numgrad) res < optim(par=b0, fn=obj,gr=gra,method ="BFGS",hessian=FALSE, control=list(maxit=10000)) res #second stage err < matrix(0,nrow=nrow(dta),ncol=3) phat < (1/(1+exp( (res$par[1]+res$par[2]*x1+res$par[3]*x2+res$par[4]*x3+res$par[5]*x4+res$par[6]*x5+res$par[7]*x7+res$par[8]*x31+res$par[9]*x 9+res$par[10]*x10+res$par[11]*x11)))) rrhat < pnorm(res$par[29]+res$par[30]*x25+res$par[31]*x26+res$par[32]*x27) rrhat1< dnorm(res$par[29]+res$par[30]*x25+res$par[31]*x26+res$par[32]*x27) rrhat2< rrhat1/rrhat err[,1] < y1 ((res$par[12]+res$par[13]*x12+res$par[14]*x13+res$par[15]*x14+res$par[16]*x15+res$par[17]^2*phat)) err[,2] < y2 ((res$par[18]+res$par[19]*x16+res$par [20]*x17+res$par[21]*x18+res$par[22]*x19+res$par[23]^2*phat+res$par[24]*rrhat2)*(rrhat) ) err[,3] < y6 ((res$par[25]+res$par[26]*log(x42)+res$par[27]*phat+res$par[28]*(phat*log(x42)))) vhat < (1/nrow(err))*t(err)%*%err wt < solve(vhat)%x%matrix(1,23,23)

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95 obj2 < function(b) { err < matrix(0,nrow=nrow(dta),ncol=3) pp < (1/(1+exp( (b[1]+b[2]*x1+b[3]*x2+b[4]*x3+b[5]*x4+b[6]*x5+b[7]*x7+b[8]*x31+b[9]*x9+b[10]*x10+b[11]*x11)))) rr < pnorm(b[29]+b[30]*x25+b[31]*x26+b[32]*x27) rr1< dnorm(b[29]+b[3 0]*x25+b[31]*x26+b[32]*x27) rr2< rr1/rr err[,1] < y1 ((b[12]+b[13]*x12+b[14]*x13+b[15]*x14+b[16]*x15+b[17]^2*pp)) err[,2] < y2 ((b[18]+b[19]*x16+b[20]*x17+b[21]*x18+b[22]*x19+b[23]^2*pp+b[24]*rr2)*(rr)) err[,3] < y6 (b[25]+b[26]*log(x42)+b[27]* pp+b[28]*(pp*log(x42))) qt < 0 for (i in 1:nrow(dta)) { zz < rbind(cbind(x1[i],x2[i],x3[i],x4[i],x5[i],x7[i],x31[i],x9[i],x10[i],x11[i],x12[i],x13[i],x14[i],x4[i],x20[i],x21[i],x22[i],x2 3[i],x35[i],x36 [i],x37[i],x38[i],x39[i],matrix(0,nrow=1,ncol=46)), cbind(matrix(0,nrow=1,ncol=23),x1[i],x2[i],x3[ i],x4[i],x5[i],x7[i],x31[i],x9[i],x10[i],x11[i],x16[i],x17[i],x18[i],x4[i],x23[i],x25[i],x2 6[i],x27[i],x35[i],x36[i],x37[i],x38[i],x39[i],matrix(0,nrow=1,ncol=23)), cbind(matrix(0,nrow=1,ncol=46),x1[i],x2[i],x3[i],x4[i],x5[i],x7[i],x31[i],x 9[i],x10[i],x11[i],x16[i],x17[i],x18[i],x4[i],x23[i],x25[i],x2 6[i],x27[i],x35[i],x36[i],x37[i],x38[i],(log(x42[i])))) qt < qt + err[i,]%*%zz%*%wt%*%t(zz)%*%err[i,] } return(qt[1,1]) } gra2 < function(b){ dq = matrix(0,nrow=32,nc ol=1)

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96 for (i in 1:nrow(dta)){ pp < (1/(1+exp( (b[1]+b[2]*x1[i]+b[3]*x2[i]+b[4]*x3[i]+b[5]*x4[i]+b[6]*x5[i]+b[7]*x7[i]+b[8]*x31[i]+b[9]*x9[i]+b[10]*x10[i]+b[11]*x11[i])))) rr < pnorm(b[29]+b[30]*x25[i]+b[31]*x26[i]+b[32]*x27[i]) rr 1< dnorm(b[29]+b[30]*x25[i]+b[31]*x26[i]+b[32]*x27[i]) rr2< rr1/rr err < rbind((y1[i] ((b[12]+b[13]*x12[i]+b[14]*x13[i]+b[15]*x14[i]+b[16]*x15[i]+b[17]^2*pp))), (y2[i] ((b[18]+b[19]*x16[i]+b[20]*x17[i]+b[21]*x18[i]+b[22]*x19[i]+ b[23]^2*pp+b[24]*rr2)*(rr))), (y6[i] (b[25]+b[26]*log(x42[i])+b[27]*pp+b[28]*(pp*log(x42[i]))))) p1 < (exp(b[1]+b[2]*x1[i]+b[3]*x2[i]+b[4]*x3[i]+b[5]*x4[i]+b[6]*x5[i]+b[7]*x7[i]+b[8]*x31[i]+b[9]*x9[i]+b[10]*x10[i]+b[11]*x11[i]) ) p2 < (1+(exp(b[1]+b[2]*x1[i]+b[3]*x2[i]+b[4]*x3[i]+b[5]*x4[i]+b[6]*x5[i]+b[7]*x7[i]+b[8]*x31[i]+b[9]*x9[i]+b[10]*x10[i]+b[11]*x11[ i])))^2 p < (p1/p2) r1 < dnorm(b[29]+b[30]*x25[i]+b[31]*x26[i]+b[32]*x27[i]) r2 < pnorm(b[29]+b[30]*x25[i]+b[31]*x26[i]+b[32]*x27[i]) rr3 < ((( (b[29]+b[30]*x25[i]+b[31]*x26[i]+b[32]*x27[i]))*((exp(( (1/2))*((b[29]+b[30]*x25[i]+b[31]*x26[i]+b[32]*x27[i])^2)))))/((44/7)^(1/2))) r3 < ((r2*rr3 (r1^2))/r2^2) r < dnorm(b[ 29]+b[30]*x25[i]+b[31]*x26[i]+b[32]*x27[i]) ss < (b[12]+b[13]*x12[i]+b[14]*x13[i]+b[15]*x14[i]+b[16]*x15[i]+b[17]^2*pp) tt < (b[18]+b[19]*x16[i]+b[20]*x17[i]+b[21]*x18[i]+b[22]*x19[i]+b[23]^2*pp+b[24]*rr2)

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97 zz < rbind(cbind(x1[ i],x2[i],x3[i],x4[i],x5[i],x7[i],x31[i],x9[i],x10[i],x11[i],x12[i],x13[i],x14[i],x4[i],x20[i],x21[i],x22[i],x23[i],x35[i],x36 [i],x37[i],x38[i],x39[i],matrix(0,nrow=1,ncol=46)), cbind(matrix(0,nrow=1,ncol=23),x1[i],x2[i],x3[i],x4[i],x5[i],x7 [i],x31[i],x9[i],x10[i],x11[i],x16[i],x17[i],x18[i],x4[i],x23[i],x25[i],x2 6[i],x27[i],x35[i],x36[i],x37[i],x38[i],x39[i],matrix(0,nrow=1,ncol=23)), cbind(matrix(0,nrow=1,ncol=46),x1[i],x2[i],x3[i],x4[i],x5[i],x7[i],x31[i],x9[i],x10[i],x11[i ],x16[i],x17[i],x18[i],x4[i],x23[i],x25[i],x2 6[i],x27[i],x35[i],x36[i],x37[i],x38[i],(log(x42[i])))) dq[1]=dq[1] + cbind(2*(b[17]^2)*( (p)),2*(rr)*(b[23]^2)*( (p)),2*( (p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[2]=dq[2] + cbind(2*(b[17]^2)*( (x1[i]*p)),2*(rr)*(b[23]^2)*( (x1[i]*p)),2*( (x1[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[3]=dq[3] + cbind(2*(b[17]^2)*( (x2[i]*p)),2*(rr)*(b[23]^2)*( (x2[i]*p)),2*( (x2[i]*p))*((b[27])+b[28]*log(x42[i]))) %*%(zz)%*%wt%*%t(zz)%*%(err) dq[4]=dq[4] + cbind(2*(b[17]^2)*( (x3[i]*p)),2*(rr)*(b[23]^2)*( (x3[i]*p)),2*( (x3[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[5]=dq[5] + cbind(2*(b[17]^2)*( ((x4[i])*p)),2*(rr)*(b[23]^2)*( ((x4[i ])*p)),2*( (x4[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[6]=dq[6] + cbind(2*(b[17]^2)*( (x5[i]*p)),2*(rr)*(b[23]^2)*( (x5[i]*p)),2*( (x5[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[7]=dq[7] + cbind(2* (b[17]^2)*( (x7[i]*p)),2*(rr)*(b[23]^2)*( (x7[i]*p)),2*( (x7[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[8]=dq[8] + cbind(2*(b[17]^2)*( (x31[i]*p)),2*(rr)*(b[23]^2)*( (x31[i]*p)),2*( (x31[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz )%*%wt%*%t(zz)%*%(err) dq[9]=dq[9] + cbind(2*(b[17]^2)*( (x9[i]*p)),2*(rr)*(b[23]^2)*( (x9[i]*p)),2*( (x9[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[10]=dq[10] + cbind(2*(b[17]^2)*( (x10[i]*p)),2*(rr)*(b[23]^2)*( (x10[i]*p)) ,2*( (x10[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[11]=dq[11] + cbind(2*(b[17]^2)*( (x11[i]*p)),2*(rr)*(b[23]^2)*( (x11[i]*p)),2*( (x11[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[12]=dq[12] + cbind( 2*( (1)),0,0)%*%(zz)%*%wt%*%t(zz)%*%(err)

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98 dq[13]=dq[13] + cbind(2*( (x12[i])),0,0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[14]=dq[14] + cbind(2*( (x13[i])),0,0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[15]=dq[15] + cbind(2*( (x14[i])),0,0)%*%(zz)%*%wt%*%t(zz)%*%( err) dq[16]=dq[16] + cbind(2*( (x15[i])),0,0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[17]=dq[17] + cbind(2*2*b[17]*( (pp)),0,0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[18]=dq[18] + cbind(0,2*(rr)*( (1)),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[19]=dq[19] + cbind(0,2*(rr)*( (x16[i])),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[20]=dq[20] + cbind(0,2*(rr)*( (x17[i])),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[21]=dq[21] + cbind(0,2*(rr)*( (x18[i])),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[22]=dq[22] + cb ind(0,2*(rr)*( (x19[i])),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[23]=dq[23] + cbind(0,2*2*b[23]*(rr)*( (pp)),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[24]=dq[24] + cbind(0,2*(rr)*( (rr2)),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[25]=dq[25] + cbind(0,0, 2)%*%(zz)%*% wt%*%t(zz)%*%(err) dq[26]=dq[26] + cbind(0,0, 2*(log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[27]=dq[27] + cbind(0,0, 2*pp)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[28]=dq[28] + cbind(0,0, 2*(pp*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[29]=dq[29] + cbind(0, 2*(((tt)*(r))+(((r2*b[24]*(r2*rr3 (r1^2))/r2^2)))),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[30]=dq[30] + cbind(0, 2*(((tt)*(r)*(x25[i]))+(((r2*b[24]*(r2*rr3*(x25[i]) (r1^2)*(x25[i]))/r2^2)))),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[31]=dq[31] + cbi nd(0, 2*(((tt)*(r)*(x26[i]))+(((r2*b[24]*(r2*rr3*(x26[i]) (r1^2)*(x26[i]))/r2^2)))),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[32]=dq[32] + cbind(0, 2*(((tt)*(r)*(x27[i]))+(((r2*b[24]*(r2*rr3*(x27[i]) (r1^2)*(x27[i]))/r2^2)))),0)%*%(zz)%*%wt%*%t(zz)%*%(err) } return(dq) } mygrad = gra(res$par) numgrad = grad(obj2, res$par) cbind(mygrad,numgrad) res2 < optim(par=res$par, fn=obj2,gr=gra2,method ="BFGS",hessian=FALSE, control=list(maxit=10000))

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99 res2 #Bootstrapping err2 < matrix(0,nrow=nrow(dta),ncol=3) phat2 < (1/(1+exp( (res2$par[1]+res2$par[2]*x1+res2$par[3]*x2+res2$par[4]*x3+res2$par[5]*x4+res2$par[6]*x5+res2$par[7]*x7+res2$par[8]*x31+res 2$par[9]*x9+res2$par[10]*x10+res2$par[11]*x11)))) rrb < pnorm(res2$par[29]+res 2$par[30]*x25+res2$par[31]*x26+res2$par[32]*x27) rrb1< dnorm(res2$par[29]+res2$par[30]*x25+res2$par[31]*x26+res2$par[32]*x27) rrb2< rrb1/rrb yhat2 < cbind(((res2$par[12]+res2$par[13]*x12+res2$par[14]*x13+res2$par[15]*x14+res2$par[16]*x15+res2$par[17]^2 *phat2)), ((res2$par[18]+res2$par[19]*x16+res2$par[20]*x17+res2$par[21]*x18+res2$par[22]*x19+res2$par[23]^2*phat2+res2$par[24]*rrb2 )*(rrb)), ((res2$par[25]+res2$par[26]*log(x42)+res2$par[27]*phat2+res2$par[28]*(phat2*log(x42)) ))) err2[,1] < y1 ((res2$par[12]+res2$par[13]*x12+res2$par[14]*x13+res2$par[15]*x14+res2$par[16]*x15+res2$par[17]^2*phat2)) err2[,2] < y2 ((res2$par[18]+res2$par[19]*x16+res2$par[20]*x17+res2$par[21]*x18+res2$par[22]*x19+res2$par[23]^2*phat2+res2$par[24 ]*rrb2 )*(rrb)) err2[,3] < y6 ((res2$par[25]+res2$par[26]*log(x42)+res2$par[27]*phat2+res2$par[28]*(phat2*log(x42)))) vhat2 < (1/nrow(err2))*t(err2)%*%err2 wt < solve(vhat2)%x%matrix(1,23,23) print(vhat) print(vhat2) for (i in 1:200) { indx < sampl e.int(nrow(yhat2),replace = TRUE)

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100 yt < yhat2 + err2[indx,] yt[yt[,2] < 0] < 0 obj3 < function(b) { err < matrix(0,nrow=nrow(dta),ncol=3) pp < (1/(1+exp( (b[1]+b[2]*x1+b[3]*x2+b[4]*x3+b[5]*x4+b[6]*x5+b[7]*x7+b[8]*x31+b[9]*x9+b[10]*x10+b[11]*x11)))) rr < pnorm(b[29]+b[30]*x25+b[31]*x26+b[32]*x27) rr1< dnorm(b[29]+b[30]*x25+b[31]*x26+b[32]*x27) rr2< rr1/rr err[,1] < yt[,1 ] ((b[12]+b[13]*x12+b[14]*x13+b[15]*x14+b[16]*x15+b[17]^2*pp)) err[,2] < yt[,2] ((b[18]+b[19]*x16+b[20]*x17+b[21]*x18+b[22]*x19+b[23]^2*pp+b[24]*rr2)*(rr)) err[,3] < yt[,3] (b[25]+b[26]*log(x42)+b[27]*pp+b[28]*(pp*log(x42))) qt < 0 for (i in 1:nrow(dta)) { zz < rbind(cbind(x1[i],x2[i],x3[i],x4[i],x5[i],x7[i],x31[i],x9[i],x10[i],x11[i],x12[i],x13[i],x14[i],x4[i],x20[i],x21[i],x22[i],x2 3[i],x35[i],x36 [i],x37[i],x38[i],x39[i],matrix(0,nrow=1,ncol=46)), cb ind(matrix(0,nrow=1,ncol=23),x1[i],x2[i],x3[i],x4[i],x5[i],x7[i],x31[i],x9[i],x10[i],x11[i],x16[i],x17[i],x18[i],x4[i],x23[i] ,x25[i],x2 6[i],x27[i],x35[i],x36[i],x37[i],x38[i],x39[i],matrix(0,nrow=1,ncol=23)), cbind(matrix(0,nrow=1,ncol=46 ),x1[i],x2[i],x3[i],x4[i],x5[i],x7[i],x31[i],x9[i],x10[i],x11[i],x16[i],x17[i],x18[i],x4[i],x23[i],x25[i],x2 6[i],x27[i],x35[i],x36[i],x37[i],x38[i],(log(x42[i])))) qt < qt + err[i,]%*%zz%*%wt%*%t(zz)%*%err[i,] } return(q t[1,1]) }

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101 gra3 < function(b){ dq = matrix(0,nrow=32,ncol=1) for (i in 1:nrow(dta)){ pp < (1/(1+exp( (b[1]+b[2]*x1[i]+b[3]*x2[i]+b[4]*x3[i]+b[5]*x4[i]+b[6]*x5[i]+b[7]*x7[i]+b[8]*x31[i]+b[9]*x9[i]+b[10]*x10[i]+b[11]*x11[i])))) rr < pnorm(b[29]+b[30]*x25[i]+b[31]*x26[i]+b[32]*x27[i]) rr1< dnorm(b[29]+b[30]*x25[i]+b[31]*x26[i]+b[32]*x27[i]) rr2< rr1/rr err < rbind((yt[i,1] ((b[12]+b[13]*x12[i]+b[14]*x13[i]+b[15]*x14[i]+b[16]*x15[i]+b[17]^2*pp))), (yt[i,2] ((b[18]+b[19]*x16[i]+b[20]*x17[i]+b[21]*x18[i]+b[22]*x19[i]+b[23]^2*pp+b[24]*rr2)*(rr))), (yt[i,3] (b[25]+b[26]*log(x42[i])+b[27]*pp+b[28]*(pp*log(x42[i]))))) p1 < (exp(b[1]+b[2]*x1[i]+b[3]*x2[i ]+b[4]*x3[i]+b[5]*x4[i]+b[6]*x5[i]+b[7]*x7[i]+b[8]*x31[i]+b[9]*x9[i]+b[10]*x10[i]+b[11]*x11[i])) p2 < (1+(exp(b[1]+b[2]*x1[i]+b[3]*x2[i]+b[4]*x3[i]+b[5]*x4[i]+b[6]*x5[i]+b[7]*x7[i]+b[8]*x31[i]+b[9]*x9[i]+b[10]*x10[i]+b[11]*x11[ i])))^2 p < (p1 /p2) r1 < dnorm(b[29]+b[30]*x25[i]+b[31]*x26[i]+b[32]*x27[i]) r2 < pnorm(b[29]+b[30]*x25[i]+b[31]*x26[i]+b[32]*x27[i]) rr3 < ((( (b[29]+b[30]*x25[i]+b[31]*x26[i]+b[32]*x27[i]))*((exp(( (1/2))*((b[29]+b[30]*x25[i]+b[31]*x2 6[i]+b[32]*x27[i])^2)))))/((44/7)^(1/2))) r3 < ((r2*rr3 (r1^2))/r2^2) r < dnorm(b[29]+b[30]*x25[i]+b[31]*x26[i]+b[32]*x27[i]) ss < (b[12]+b[13]*x12[i]+b[14]*x13[i]+b[15]*x14[i]+b[16]*x15[i]+b[17]^2*pp) tt < (b[18]+b[19 ]*x16[i]+b[20]*x17[i]+b[21]*x18[i]+b[22]*x19[i]+b[23]^2*pp+b[24]*rr2)

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102 zz < rbind(cbind(x1[i],x2[i],x3[i],x4[i],x5[i],x7[i],x31[i],x9[i],x10[i],x11[i],x12[i],x13[i],x14[i],x4[i],x20[i],x21[i],x22[i],x2 3[i],x35[i],x36 [i],x37[i],x38[i],x3 9[i],matrix(0,nrow=1,ncol=46)), cbind(matrix(0,nrow=1,ncol=23),x1[i],x2[i],x3[i],x4[i],x5[i],x7[i],x31[i],x9[i],x10[i],x11[i],x16[i],x17[i],x18[i],x4[i],x23[ i],x25[i],x2 6[i],x27[i],x35[i],x36[i],x37[i],x38[i],x39[i],matrix(0,nrow=1,ncol=2 3)), cbind(matrix(0,nrow=1,ncol=46),x1[i],x2[i],x3[i],x4[i],x5[i],x7[i],x31[i],x9[i],x10[i],x11[i],x16[i],x17[i],x18[i],x4[i],x23[ i],x25[i],x2 6[i],x27[i],x35[i],x36[i],x37[i],x38[i],(log(x42[i])))) dq[1]=dq[1] + cbind(2*(b[17 ]^2)*( (p)),2*(rr)*(b[23]^2)*( (p)),2*( (p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[2]=dq[2] + cbind(2*(b[17]^2)*( (x1[i]*p)),2*(rr)*(b[23]^2)*( (x1[i]*p)),2*( (x1[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[3]=dq[3] + cbind(2*(b[17]^2)*( (x2[i]*p)),2*(rr)*(b[23]^2)*( (x2[i]*p)),2*( (x2[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[4]=dq[4] + cbind(2*(b[17]^2)*( (x3[i]*p)),2*(rr)*(b[23]^2)*( (x3[i]*p)),2*( (x3[i]*p))*((b[27] )+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[5]=dq[5] + cbind(2*(b[17]^2)*( ((x4[i])*p)),2*(rr)*(b[23]^2)*( ((x4[i])*p)),2*( (x4[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[6]=dq[6] + cbind(2*(b[17]^2)*( (x5[i]*p) ),2*(rr)*(b[23]^2)*( (x5[i]*p)),2*( (x5[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[7]=dq[7] + cbind(2*(b[17]^2)*( (x7[i]*p)),2*(rr)*(b[23]^2)*( (x7[i]*p)),2*( (x7[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[8]=dq[8] + cbind(2*(b[17]^2)*( (x31[i]*p)),2*(rr)*(b[23]^2)*( (x31[i]*p)),2*( (x31[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[9]=dq[9] + cbind(2*(b[17]^2)*( (x9[i]*p)),2*(rr)*(b[23]^2)*( (x9[i]*p)),2*( (x9[i]*p))*((b [27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[10]=dq[10] + cbind(2*(b[17]^2)*( (x10[i]*p)),2*(rr)*(b[23]^2)*( (x10[i]*p)),2*( (x10[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[11]=dq[11] + cbind(2*(b[17]^2)*( (x 11[i]*p)),2*(rr)*(b[23]^2)*( (x11[i]*p)),2*( (x11[i]*p))*((b[27])+b[28]*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err)

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103 dq[12]=dq[12] + cbind(2*( (1)),0,0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[13]=dq[13] + cbind(2*( (x12[i])),0,0)%*%(zz)%*%wt%*%t(zz)%*%(er r) dq[14]=dq[14] + cbind(2*( (x13[i])),0,0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[15]=dq[15] + cbind(2*( (x14[i])),0,0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[16]=dq[16] + cbind(2*( (x15[i])),0,0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[17]=dq[17] + cbind( 2*2*b[17]*( (pp)),0,0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[18]=dq[18] + cbind(0,2*(rr)*( (1)),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[19]=dq[19] + cbind(0,2*(rr)*( (x16[i])),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[20]=dq[20] + cbind(0,2*(rr)*( (x17[i])),0 )%*%(zz)%*%wt%*%t(zz)%*%(err) dq[21]=dq[21] + cbind(0,2*(rr)*( (x18[i])),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[22]=dq[22] + cbind(0,2*(rr)*( (x19[i])),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[23]=dq[23] + cbind(0,2*2*b[23]*(rr)*( (pp)),0)%*%(zz)%*%w t%*%t(zz)%*%(err) dq[24]=dq[24] + cbind(0,2*(rr)*( (rr2)),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[25]=dq[25] + cbind(0,0, 2)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[26]=dq[26] + cbind(0,0, 2*(log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[27]=dq[27] + cbind(0,0, 2*pp)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[28]=dq[28] + cbind(0,0, 2*(pp*log(x42[i])))%*%(zz)%*%wt%*%t(zz)%*%(err) dq[29]=dq[29] + cbind(0, 2*(((tt)*(r))+(((r2*b[24]*(r2*rr3 (r1^2))/r2^2)))),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[30]= dq[30] + cbind(0, 2*(((tt)*(r)*(x25[i]))+(((r2*b[24]*(r2*rr3*(x25[i]) (r1^2)*(x25[i]))/r2^2)))),0)%*%(zz)%*%wt%*%t(zz)%*%(err) dq[31]=dq[31] + cbind(0, 2*(((tt)*(r)*(x26[i]))+(((r2*b[24]*(r2*rr3*(x26[i]) (r1^2)*(x26[i]))/r2^2)))),0)%*%(zz)%*%wt%*%t(z z)%*%(err) dq[32]=dq[32] + cbind(0, 2*(((tt)*(r)*(x27[i]))+(((r2*b[24]*(r2*rr3*(x27[i]) (r1^2)*(x27[i]))/r2^2)))),0)%*%(zz)%*%wt%*%t(zz)%*%(err) } return(dq) } resd < optim(par=res2$par, fn=obj3,gr=gra3,method ="BFGS",hessian=FALSE, control=list(maxit=10000)) if (i==1) rbeta < t(resd$par) else rbeta < rbind(rbeta,t(resd$par)) }

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104 rbeta[,17]< (rbeta[,17])*(rbeta[,17]) rbeta[,23]< (rbeta[,23])*(rbeta[,23]) res2$pa r[17] < res2$par[17]*res2$par[17] res2$par[23] < res2$par[23]*res2$par[23] ebeta < rbeta matrix(1,nrow=nrow(rbeta),ncol=1)%*%t(res2$par) vbeta < t(ebeta)%*%ebeta/nrow(ebeta) print(cbind(res2$par,sqrt(diag(vbeta)),res2$par/sqrt(diag(vbeta)),1 pnorm( abs(res2$par/sqrt(diag(vbeta))))))

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105 LIST OF REFERENCES Alene, A. D., Manyong, V. M., Omanya, G., Mignouna, H. D., Bokanga, M., and Odhiambo, G. (2008). Smallholder market participation under transactions costs: Maize supply and fertilizer demand in Kenya. Food Policy , 33 (4), 318 328. Awulachew, S. B., Sal ly, H., Bahri, A., Molden, D., and Giordano, M. (2008). Water security for food security: gaps, needs and potential for growth in Sub Saharan Africa. First African celerating Water Security for Socio Economic Development of , 26 28. Banks, J., Blundell, R., and Lewbel, A. (1997). Quadratic Engel curves and consumer demand. Review of Economics and Statistics , 79 (4), 527 539. Barrett, C. B. (2002) . Food security and food assistance programs. Handbook of agricultural economics , 2 , 2103 2190. Bernard, T., and Taffesse, A. S. (2012). Returns to Scope? Smallholders' Commercialisation through Multipurpose Cooperatives in Ethiopia. Journal of African economies , ejs002. Bernard, T., Taffesse, A. S., and Gabre Madhin, E. (2008). Impact of cooperatives on smallholders' commercialization behavior: evidence from Ethiopia. Agricultural Economics , 39 (2), 147 161. Boon, E. K. (2004). Food security in Africa: challenges and prospects. An Overview of Sustainable Development in Africa. Oxford, UK: Encyclopedia of Life Support Systems (EOLSS)/UNESCO, Eolss Publishers . Bouis , H . E . and Haddad , L . J. ( 1990 ) . Effects of agricultural commercialization on land tenure, househol d resource allocation, and nutrition in the Philippines. Research Report 79. IFPRI (International Food Policy Research Institute), Washington, DC, USA. Case , B. A. (2005). Food Security and Agricltural Development in Sub Saharan Africa http://www.sarpn.org/documents/d0001583/FAO2005_mainreport.pdf Cameron, A. C., & Trivedi, P. K. (2005). Microeconometrics: methods and applications . Cambridge university press. Chamberlin, J. (2007). Defining smallholder agriculture in Ghana: Who are smallholders, what do they do and how are they linked with markets? Prepared as part of the Ghana Strategy Support Program and submitted for consideration as an IFPRI Discussion Paper. Clover, J. ( 2003). Food security in sub Saharan Africa. African Security Studies , 12 (1), 5 15. Coase, R. H. (1937). The nature of the firm. economica , 4 (16), 386 405. Cook, R. D.. (1977). Detection of Influential Observation in Linear Regression. Technometrics , 19 (1), 15 18.

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106 De Janvry, A., Fafchamps, M., and Sadoulet, E. (1991). Peasant household behaviour with missing markets: some paradoxes explained. The Economic Journal , 1400 1417. De Janvry, A. and Sadoulet, E. (1994). Structural Adjustment under Transaction Cost, in Heidhues, F. and Knerr, B. (eds.), Food and Agricultural policies under Structural Adjustment, Peter Lang: Frankfurt, 137 165. Dewey, K. G. (1981). Nutritional conseque nces of the transformation from subsistence to commercial agriculture in Tabasco, Mexico. Human Ecology , 9 (2), 151 187. Ekboir, J., Boa, K., and Dankyi, A. A. (2002). Impact of no till technologies in Ghana . CIMMYT, International Maize and Wheat Improvement Center. Fafschamps, M. (1992). Cash crop production, food price volatility, and rural market integration in the third world. American Journal of Agricultural Economics 74(1):90 99. Falcon, W. P., and Naylor, R. L. (2005). Rethinking food security for the twenty first century. American Journal of Agricultural Economics , 87 (5), 1113 1127. FAO (2012) The State of Food Insecurity in the World 2012: Economic growth is necessary but not sufficient to accelerate reduction of hunger and malnutrition. FAO, Rome . (A vailable at http://www.fao.org/docrep/016/i3027e/i3027e.pdf ). FAO (2015 ). FAO Statistics Division (FAOSTAT) data, (Available at http://faostat3.fao.org/browse/D/FS/E ). Fischer, E., and Qaim, M. (2012). Linking smallholders to markets: determinants and impacts of farmer collective action in Kenya. World Development , 40 (6), 1255 1268. Foster, J. E. (1983). An axiomatic characterization of the Theil measure of income inequality Journal of Economic Theory , 31 (1), 105 121. G abre Madhin, E. Z., Dawit, A., and Dejene, S. (2007). From farmer to market: Smallholder commercialization of food crops in Ethiopia . Draft ESSP Working Paper (Unpublished). Goetz, S. J. (1992). A selectivity model of household food marketing behavior in sub Saharan Africa. American Journa l of Agricultural Economics , 74 (2), 444 452. Gollin, D., and Rogerson, R. (2014). Productivity, transport costs and subsistence agriculture. Journal of Development Economics , 107 , 38 48. Govereh J, Jayne T.S., and Nyoro J. (1999). Smallholder commercializ ation, interlinked markets and food crop productivity: Crosscountry evidence in eastern and southern Africa. http://fsg.afre.msu.edu/ag_transformation/atw_govereh.PDF Guan, W. (2003). From the help desk: bootstrapped standard errors. The Stata Journal , 3 (1), 71 80.

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107 Gudeman, S. (1978). The demise of a rural economy. From Subsistence to Capitalism in a Latin American Village . Hall, A. R. (2003). Generalized method of moments. A Co mpanion to Theoretical Econometrics , 230 255. Hall, A. R. (2005). Generalized Method of Moments. Advanced Texts in Econometrics Series. Hayashi, F. (2000). Econometrics. 2000. Pr inceton University Press. Heckman, J. J. (1976). The common structure of statistical models of truncation, sample selection and limited dependent variables and a simple estimator for such models. In Annals of Economic and Social Measurement, Volume 5, number 4 (pp. 475 492). NBER. Heidhues, F. R. A. N. Z., and Brüntrup, M. (2002). Subsistence agriculture in development: Its role in processes of structural change. Subsistence agriculture in Central and Eastern Europe: How to break the vicious circle , 1 27. Jaleta, M., Gebremedhin, B., and Hoekstra, D. (2009). Sm allholder commercialization: Processes, determinants and impact. Kennedy E and Cogill B. ( 1987 ) . Income and nutritional effects of the commercialization of agriculture in southwestern Kenya. Research Report No. 63. IFPRI (International Food Policy Research Institute), Washington, DC, USA. Key, N., Sadoulet, E., and De Janvry, A. (2000). Transactions costs and agricultural household supply response. American journal of agricultural economics , 82 (2), 245 259. Kumar, T. K., Holla, J., and Guha, P. (2008). Enge l curve method for measuring poverty. Economic and Political Weekly , 115 123. Leser, C. E. V. (1963). Forms of Engel functions. Econometrica: Journal of the Econometric Society , 694 703. Martey, E., Al Hassan, R. M., and Kuwornu, J. K. (2012). Commercialization of smallholder agriculture in Ghana: A Tobit regression analysis. African Journal of Agricultural Research , 7 (14), 2131 2141. Mishra, A. K., Moss, C. B., and Erickson, K. W. (2006). Farm wealth inequality within and across states in the United States. Agricultural and resource economics review , 35 (2), 251. Moss, C.B., Oehmke, J.F., and Lyambabaje, A. (2015) . Food Security, Subsistence Agriculture, and s Model. In Food Security in an Uncertain World: An International Perspective Eds Schmitz, A., Kennedy, P.L., and Schmitz, T.G.; Emerald Publishing Gr oup, Boston Massachusetts, USA , 19 32.

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108 Muriithi, B. W., and Matz, J. A. (2015). Welfare effects of vegetable commercialization: Evidence from smallholder producers in Kenya. Food Policy , 50 , 80 91. Mwaniki, A. (2006). Achieving food security in Africa: Challenges and issues. UN Office of the Special Advisor on Africa (OSAA) http://www. un. org/ africa/osaa/reports/Achieving% 20Food% 20Security% 20in% 20Africa Challen ges% 20and% 20Issues.pdf (Last accessed on May 9, 2010) . Omamo, S. W. (1998). Transport costs and smallholder cropping choices: An application to Sia ya District, Kenya. American Journal of Agricultural Economics , 80 (1), 116 123. Ouma , E., Jagwe, J., Obare, G. A., and Abele, S. (2010). Determinants of smallholder farmers' participation in banana markets in Central Africa: the role of transaction costs. Agricultural Economics , 41 (2), 111 122. Pasha, H. A. (2002, December). Pro poor policies. In Fourth Global Forum on Citizens . Pingali, P. L. (1997). From subsistence to commercial production systems: The transformation of Asian agriculture. American Journa l of Agricultural Economics , 628 634. Pingali, P. L., and Rosegrant, M. W. (1995). Agricultural commercialization and diversification: processes and policies. Food policy , 20 (3), 171 185. Pinstrup Andersen, P. (2009). Food security: definition and measurement. Food security , 1 (1), 5 7. Randolph, T. F. (1992). The impact of agricultural commercialization on child nutrition: a case study of smallholder households in Malawi . Cornell University, May. Renkow, M., Hallstrom, D. G., and Karanja, D. D. (2004). Rural infrastructure, transactions costs and market participation in Kenya. Journal of development economics , 73 (1), 349 367. Robles, M., Torero, M., and Cuesta, J. (2010). Understanding the Impact of High Food Prices in Latin Ameri ca [with Comment]. Economia , 117 164. Runge, C. F., Senauer, B., Pardey, P. G., and Rosegrant, M. W. (2004). Ending hunger in Africa prospects for the small farmer (No. 16). International Food Policy Research Institute (IFPRI). Singh, I., Squire, L., and S trauss, J. (1986). Agricultural household models: extensions, applications, and policy . Johns Hopkins University Press. Strasberg, P. J., Jayne, T. S., Yamano, T., Nyoro, J. K., Karanja, D. D., and Strauss, J. (1999). Effects of agricultural commercialization on food crop input use and productivity in Kenya (No. 54675).Michigan State University, Department of Agricultural, Food, and Resource Economics.

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109 Strauss, J., (1986). The Theory and Comparative Statics o f Agricultural Household Models: A General Approach. IJ Singh, l. Squire and J. Strauss, eds. Agricultural Household Models: Extensions, Applications and Policy. Baltimore: Johns Hopkins University Oress . Tipraqsa, P., and Schreinemachers, P. (2009). Agricultural commercialization of Karen Hill tribes in northern Thailand. Agricultural Economics , 40 (1), 43 53. Unnevehr, L., Eales, J., Jensen , H., Lusk, J., McCluskey, J., and Kinsey, J. (2010). Food and consumer economics. American Journal of Agricultural Economics , 92 (2), 506 521. Vance, C., and Geoghegan, J. (2004). Modeling the determinants of semi subsistent and commercial land uses in an agricultural frontier of southern Mexico: a switching regression approach. International Regional Science Review , 27 (3), 326 347. Von Braun, J., and Kennedy, E. (1986). Commercialization of subsistence agriculture: Income and nutritional effects in developing countries . Washington. DC: International Food Policy Research Institute. Von Braun, J., and Kennedy, E. (1994). Agricultural commercialization, economic development, and nutrition . Johns Hopkins University Press. Von Braun J., Bouis H., and Kennedy, E. (1994). Conceptual framework. In: Von Braun J and Kennedy E (eds), Agricultural commercialization, economic development, and nutrition . Johns Hopkins University Press. Von Braun, J. (1995). Agricultural commercialization: impacts on income and nutrition and implications for policy. Food policy , 20 (3), 187 202. Wooldridge, J. M. (2001). Applications of Generalized Method of M oments estimation. Journal of Economic perspectives , 87 100. World Bank. (2003). Reaching the rural poor: A renewed strategy for rural development. Washington, DC.

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110 BIOGRAPHICAL SKETCH Olufemi Bolarinwa was born in Oyo town in Niger ia. He completed his Bachelor of Agriculture at the Federal University of Agriculture Abeokuta, Ogun State, Nigeria and his Master of Science from the Department of Applied Economics and Statistics at the University of Delaware in 2011. He completed his doctorate in food and resource e con omics at the University of Florida in 2015. Olufemi area of research includes Agricultural and development economics. After completion of his doctoral degree, Olufemi intends to pursue a career in teaching and research.