STRUCTURAL TRANSFORMATION FROM A MICROECONOMIC VIEW: EVIDENCE FROM SUB - SAHARAN AFRICAN COUNTRIES By Mayuko Kondo A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Agr icultural, Food, and Resource Economics Doctor of Philosophy 2020 ABSTRACT STRUCTURAL TRANSFORMATION FROM A MICROECONOMIC VIEW: EVIDENCE FROM SUB - SAHARAN AFRICAN COUNTRIES By Mayuko Kondo S tructural transformation and corresponding labor productivi ty growth are fundamentals of economic development. This dissertation, titled Structural Transformation from A Microeconomic View , explores the path of the str uctural transformation in Sub - Saharan Africa (SSA). In the last 20 years in SSA, structural trans formation was not always accompanied by overall labor productivity growth. The first essay of this dissertation , titled Education, Profitability , and Household Labor Allocation in Rural Uganda , explores the microeconomic factors that explain non - growing - pr oductivity structural change with a focus on the role of education . I jointly estimate household hourly profit (wage) and labor supply functions . The estimation result i s supportive of the hypothesis that the level of education, profitability of an activit y, and time allocation to that activity can be not positively correlated while education positively increases total household profit from the activity . To trigger structural transformation, the governments of SSA and donors have allocated a vast amount of resources into agricultural programs for over 20 years. Aggregate agriculture productivity, however, has shown little growth in the last 20 years. Yet the share of employment in agriculture has constantly decreased since 2000. Whether agriculture productivity growth advances the labor shift from the agriculture sector to the non - agriculture sector is still an open question and of great interes t for efficient investment in agriculture development and the economic growth of the countries. T he second essay , titled Land and Labor Bias of Farm Technology and t he Labor Allocation Decisions , explores the effect of land - and labor - labor decisions. I provide a theoretical model to describe the hous ehold responses to land - and labor - augmenting farm technical change . I classify agricultural households into six regimes based on the p articipation in on - and off - farm labor market s and the constraint of off - farm work opportunities . I derive propositions t o examine the behaviors of the households in each regime . In the empirical part of the study, I apply the model to microeconomic data from Tanzania to test the propositions. The estimation result s show that for Tanzanian maize farmers , the adoption of land - augmenting technology, that is organic fertilizer, inorganic fertilizer, or irrigation, increases on - farm labor and decreases off - farm labor while the adoption of labor - augmenting technology, including sprayer s , pesticide s , herbicide s , animal traction , or tractor s , decreases on - farm labor and increases off - farm labor when the elasticity of substitution between labor and land is sufficiently large. Taken together, these essays shed light on important policy implications for th e acceleration of str uctural transformation in SSA. The estimation result from the first essay suggests that the expansion of the industry in which higher levels of education increase profitability of work would pull labor er s from farming in to nonfarm acti vities . Relaxing the labor market constraints of individuals , especially from relatively less educated households , would shift hours of labor allocation from less profitable activities towards more profitable activities. Also, raising household income s or standard of living wo uld increase the preference of individuals for leisure relative to income, and increase the optimal marginal productivity of labor, and consequently the profitability of labor. The second essay provides evidence that depending on the c onditions of a countr y such as the level of elasticity of substitution between land and labor and the constraints around off - farm work opportunities, labor - augmenting agricultural technologies ha ve a good potential for speeding up the structural transformation . Copyright by MAYUKO KONDO 2020 v This dissertation is dedicated to my dear daughter and son , Emiko Kagwiria and Kotaro Muguna. vi ACKNOWLEDGEMENTS I would first like to express my sincere gratitude to my major professor, Thomas Reardon, for his i ncredible leadership, inspiration, and financial support over my years in my PhD program. His positive vibes and encouragement saved me fro m stopping my academic career many times. I am also grateful for the thoughtful feedback of professor David Tschirley , under whose supervision I worked for my third and fourth year of graduate school. I further express my thanks to advisory committee, prof essor Jeffrey Wooldridge and professor Songqing Jin, for precious time to comment on my studies and provide the techn ical advice. My sincere thanks also go to all the MSU communities, the graduate students, faculties, and staff. I am also grateful for the support I received from my friends John Olwande, Giri Aryal, Nahid Satter, Jina Yu, Leora Stutes, among othe rs. I truly value the time, struggle, efforts, and fun we shared together during our lives at MSU. The funding from Ito Foundation for International Education Exchange, the College of Agriculture and Natural Resource, and the Graduate School of Mi chigan State University made it possible to pursue my PhD degree. I deeply appreciate the financial support for my study at MSU . I would also like to extend my thanks to all my family members. When I came to the U.S. alone to start my PhD program, I had never imagined receiving such incredible support from all my families for my PhD career. My b rother a nd sister in law, Ronny Mburugu and Brandi impressed me deeply. My m other in law, Ajelica Kathure Murithi, and father in law, David Mburugu Murithi, took care of m y children in Kenya while I was staying in Michigan to vii continue my study. Their countless prayers for our family always comforted me. I thank my mot her and father, Chikako Kondo and Kikuo Kondo, for the tireless care from Japan for me and my family. In whi chever situation I am, their belie f in my ability helped me to keep going . This dissertation would not have been possible without the support of my husband, Eric Mutwiri Mburugu. He always encouraged me not to give up but to pursue whatever I want to achie ve in my life. I would also like to recognize m y late sister in law and best - ever friend, Lilly Kendi Mburugu, who brought me all such loving famili es in my life. In 2020, the COVID - 19 pandemic presented difficulties to complete this dissertation , but at the same time I received priceless help from many people to overcome the obstacles. I deeply appreciate Mercy Kagwiria and Yvonne Nkirote t o provide me with a space for working at their house in Meru, Kenya, when I had a problem to find a place to work under the strict curfew regulations. I also send my sincere gratitude to S i lvia Kanario and Annjoy Muthoni for taking care of my children and keeping them company during COVID - 19. My thanks are extended to Albert Naffy for giving me the great motivat ion in life during the final parts of writing my dissertation at the café in Nairobi, Kenya. Finally, I would like to send special apprecia tion to the professor emeritus, late Gustav Ranis, who gave me a chance to meet him in his office in New Hav en in February 2012. He stirred my enthusiasm about pursuing a PhD in development economics. My final motivation to complete this dissertation was t o keep my word to him. Thank you very, very much. viii TABLE OF CONTENTS LIST OF TABLES ................................ ................................ ................................ .......................... x LIST OF FIGURES ................................ ................................ ................................ ..................... xiii KEY TO ABBREVIA TIONS ................................ ................................ ................................ ...... xiv CHAPTER 1 ................................ ................................ ................................ ................................ ... 1 Education, Profitability, and Household Labor Allocation in Rural Uganda: Joint Estimation of Returns to Education and Labor Supply ................................ ................................ ......................... 1 1.1 Introduction ................................ ................................ ................................ ..................... 1 1.2 Data ................................ ................................ ................................ ................................ . 6 1.2.A Higher Education, Longer Hours, and Higher Per Hour Labor Productivity in Rural Nonfarm Activities Compared to Farming ................................ ................................ ............. 7 1.2.B Education Qualification Plays a Role in Sector Choice of Individual Labor Allocation ................................ ................................ ................................ .............................. 10 1.2. C Hourly Return and Hours of Labor Supply Negatively Correlated in All Activities 13 1.3 Model ................................ ................................ ................................ ............................ 16 ation Problem ................................ ............ 16 1.3.B Joint Estimation of Household Re turns to Education and Labor Allocation ............ 19 1.4 Model Specification and Validity Tests of Instrumental Variables .............................. 23 1.4.A Specification of Variables and Estimation Equations ................................ ............... 23 1.4.B Validity Tests of Instrumental Variables in Household Hourly Profit (Wage) and Labor Supply Estimations ................................ ................................ ................................ ..... 26 1.5 Estimation Re sults ................................ ................................ ................................ ........ 32 1.5.A Reduced and Two - Stage Estimates: Much Greater Returns to Education in Household Profit, Labor Participation, and Hours in Nonfarm Work than in Farm Work .. 32 1.5.B Joint Estimates: Education Does Not Significantly Increase Household Hourly Returns in Either Rural Nonfarm Activities or Farming ................................ ...................... 35 1.5.C Intra - Household Decision on Labor Allocation; Negative Correlation between Hourly Return and Labor Supp ly in Nonfarm Activities ................................ ...................... 45 1.6 Conclusion ................................ ................................ ................................ .................... 52 APPENDIX ................................ ................................ ................................ ............................... 55 REFERENCES ................................ ................................ ................................ ......................... 77 CHAPTER 2 ................................ ................................ ................................ ................................ . 81 Land and Labor Bias of Fa .... 81 2.1 Introduction ................................ ................................ ................................ ................... 81 2.2 Theoretical Study ................................ ................................ ................................ .......... 84 2.2.1 Theoretical Model ................................ ................................ ................................ ..... 84 2.2. 1.A Basic Model ................................ ................................ ................................ ...... 84 2.2.1.B Model with On - Farm Labor Market ................................ ................................ . 88 2.2.1.C Model with Binding Constraint on Off - Farm Job Opportunities ...................... 94 ix 2.2.2 Data and Strategy of Model Cal ibration ................................ ................................ ... 97 2.2.2.A Identification of the Household Regime and Summary of Propositions .......... 97 2.2.2.B Data ................................ ................................ ................................ ................... 99 2.2.2.C Parameter Values ................................ ................................ ............................ 102 2.2.3 Result of Model Calibration ................................ ................................ .................... 104 2.2.3.A Bias of Farm Technology and On - Farm Family Labor ................................ .. 104 2.2.3.B Bias of Farm Technology and On - F arm Hired Labor ................................ .... 107 2.2.4 Conclusio n ................................ ................................ ................................ .............. 109 2.3 Empirical Study ................................ ................................ ................................ .......... 110 2.3.1 Farm Technology and Labor Shift in Tanzania ................................ ...................... 110 2.3.2 Conceptual Model and Estimation Strategy ................................ ........................... 114 2.3.2 .A A Model of Biased Farm Technology and Labor Allocation ......................... 114 2.3.2.B Estimating the Elasticity of Substitution between Labor and Land ................ 117 2.3.2.C Test of Proposit ions ................................ ................................ ........................ 122 2.3.3 Data and Descriptive Statistics ................................ ................................ ............... 124 2.3.3.A Farming Technology, Gross Productivity, and Labor Shift ............................ 124 2.3.3.B Adoption Decision with Input Voucher and Yield Potential .......................... 129 2.3.4 Robustness Check ................................ ................................ ................................ ... 131 2.3.4.A Test of Propositions with Unobserved Separation ................................ .......... 131 2.3.4.B Test of Propositions with Observed Separation ................................ .............. 134 2.3.5 Estim ation Result ................................ ................................ ................................ .... 135 2.3.5.A Bias of Farm Technology and On - Farm Labor ................................ ............... 135 2.3.5.B Result of Robustness Check ................................ ................................ ............ 139 2.3.6 Conclusion ................................ ................................ ................................ .............. 142 APPENDIX ................................ ................................ ................................ ............................. 145 REFERENCES ................................ ................................ ................................ ....................... 148 x LIST OF TABLES Table 1.1 Education, hours of labor supply, hourly profit or wage, and characteristics of individuals by sector ................................ ................................ ................................ ............... 8 Table 1.2 Education qualification and sector choice of labor supply ................................ ........... 12 Table 1.3 Results of Vuong test ................................ ................................ ................................ .... 25 Table 1.4 Household education reduced form estimates (correlated random effects) .................. 28 Table 1.5 Validity tests of instrumental variables in the household hourly profit (wage) and labor equations ................................ ................................ ................................ ............................... 29 T able 1.6 Household hourly profit (wage) of non - migrants ................................ ......................... 31 Table 1.7 Validity tests of instrumental variables in the household profit equation .................... 32 Table 1.8 T he effect of education on the household profit reduced - form and two - stage estimates (correlated random effects) ................................ ................................ ................................ ... 33 Table 1.9 The effect of education on household labor supply reduced - form and two - stage estimates ................................ ................................ ................................ ................................ 34 Table 1.10 Household hourly profit (wage) joint estimates ................................ ......................... 36 Table 1.11 T est of instrumental variables in household self - employment labor supply .............. 39 Table 1.12 Household participation and hours of labor supply joint estimates ............................ 41 Table 1.13 The effect of education on hou sehold hourly returns and labor supply joint estimates ................................ ................................ ................................ ................................ ............... 43 ......................... 44 Table 1.15 Individual schooling reduced form estimates (c orrelated random effects) ................. 46 Table 1.16 Validity tests of instrumental variables in individu al hourly profit (wage) and labor supply equations ................................ ................................ ................................ .................... 47 Table 1.17 The effect of years of education on ind ividual hourly profit and labor supply joint estimates ................................ ................................ ................................ ................................ 48 xi Table 1.18 The effect of education qualification on individual hourly profit and labor supply joint estimates ................................ ................................ ................................ ....................... 48 Table 1.19 An additional .......................... 51 Table 1.A.1 Summary statistics of variables (household) ................................ ............................ 56 Table 1.A.2 Household hourly returns and profits of non - migrants (correlated random effects) 58 Table 1.A.3 Household profit (correlated random effects) ................................ ........................... 60 Table 1.A.4 Household profit (correlated random effects instrumental variable) ........................ 62 Table 1.A.5 Household average partial effect on probability of participation (poo led probit) .... 64 Table 1.A.6 Household hours of labor supply (Lognormal correlated random effects) ............... 66 Table 1.A.7 Household hours of labor supply (Lognormal correlated random effects instrumental variable) ................................ ................................ ................................ ................................ 68 Table 1.A.8 Summary statistics of variables (individual) ................................ ............................. 70 Table 1.A.9 Individual hourl y profit or wage (correlated random effects instrumental variable) 71 Table 1.A.10 Individual average partial effect on probability of participation (pooled probit) ... 73 Table 1.A.11 Individual hour s of labor supply (lognormal correlated random effects) ............... 75 Table 2.1 Classification of household regime ................................ ................................ ............... 98 Table 2.2 Household regime and optimal on - farm labor ................................ .............................. 98 Table 2.3 Number of households in each regime by year ................................ ............................. 99 Table 2.4 Household and district variables in 2012/2013 by household regime ........................ 101 Table 2.5 Calibration parameters ................................ ................................ ................................ 103 Table 2.6 Classification of categorical values and climate zones ................................ ............... 118 Table 2.7 Estimation of the production function and the elasticity of substitution between labor and land by climate zone (NLLS) ................................ ................................ ....................... 120 Table 2.8 Summary statistics of variables at plot level ................................ .............................. 125 Table 2.9 Summary statistics of variables at household level ................................ .................... 126 xii Table 2.10 Technology adoption, g ross productivity, and labor shift from farm to off - farm sectors ................................ ................................ ................................ ................................ . 128 Table 2.11 Targeting of the input voucher scheme ................................ ................................ ..... 130 Table 2.12 Adoption of farming technology by input voucher ................................ .................. 130 Table 2.13 Yield potential and technology adoption ................................ ................................ .. 131 Table 2.14 Test of propositions I: on - farm family labor ................................ ............................ 136 Table 2.15 Test of propositions II: on - farm hired labor ................................ ............................. 138 Table 2.16 Test of propositions III: on - farm family labor (switching regression) ..................... 140 Table 2.17 Test of propositions IV: off - farm labor (switching regression) ................................ 141 Table 2.A.1 Result of first stage estimations (pooled probit) ................................ ..................... 146 xiii LIST OF FIGURES Figure 1.1 Kernel density estimates of education by sector ................................ ......................... 10 Figure 1.2 M ultivariate kernel density estimates of education, hourly profit or wage, and hours of labor supply to farming ................................ ................................ ................................ ......... 14 Figure 1.3 Multivariate kernel density estimates of education, hourly profit or wage, and hours of labor supply to nonfarm sectors ................................ ................................ ............................ 15 Figure 2.1 Interior and corner solution of the basic model ................................ ........................... 87 Figure 2.2 Cases of solution with on - farm labor market ................................ .............................. 91 F igure 2.3 Cases of solution with binding constraint on off - farm work opportunities ................. 96 Figure 2.4 Relations of optimal on - farm family labor and other variables ................................ 105 Figure 2.5 Relations of optimal o n - farm hired labor and other variables ................................ ... 108 Figure 2.6 Climate zones in Tanzania ................................ ................................ ......................... 117 Figure 2.7 Bias of farm technology ................................ ................................ ............................ 127 xiv KEY TO ABBREVIATIONS AI Aridity Index CES Constant Elasticity of Substitution CRE Correlated Random Effects CV Coefficient of Variation EA Enumeration Area EOS Elasticity of Substitution FOC First Order Condition GDD Growing Degree Days GDP Gross Domestic Product GMM Generalized Metho d of Moments GYGA Global Yield Gap Atlas HH Household Head IMR Inverse Mills Ratio IV Instrumental Variable LIML Limited Maximum Likelihood LN Log - Normal MAE Mean Annual Potential Evapotr anspiration MAP Mean Annual Precipitation MLE Maximum Likeli hood Estimation MV Modified Variety NAIVS National Agricultural Input Voucher Scheme xv NLLS Non - Linear Least Squares PPP Purchasing Power Parity RE Random Effects SACCO Savings and Credit Co - Operative SD Standard Deviation 2SGMM Two - Stage Generalized Me thod of Moments 2SLS Two - Stage Least Squares SSA Sub - Saharan Africa TNPS Tanzania National Panel Survey TS Temperature Seasonality UNHS Uganda National Household Survey UNPS Uganda National Panel Survey USD United States Dollar VAT Value - Added Tax 1 CHAPTER 1 Education , Profitability , and Household Labor Allocation in Rural Uganda : Joint Estimati on of Returns to Education and Labor Supply 1.1 Introduction E conomic development is the process of structural transformation and corresponding increase i n per capita output in the economy. How farm households allocate more time away from farming and increase hourly return s is one of the important indicators of rural economic development. In the last 20 years structural transformation has occurred in Sub - Sa haran African countries; (World Bank , 2017) , and the share of agricultural employment fell during the 2000s by 10 percent (Barrett et al. , 2017) . The structural transformation was, however, not always accompanied by overall la bor productivity growth even with labor shift s from subsistence to non - subsistence sectors (McMillan & Headey , 2014 ; McMillan et al., 2014) . From a macroeconomic view point , a rev ealed comparative advantage in primary industry, overvalued cur rencies, and inflexible labor markets are the major factors inducing structural change with out overall labor productivity growth (McMillan et al., 2014) . This chapter explores non - growing - productivity structural change from a microeconomic perspective . I test the hypothesis that the level of education, prof itability of an activity , and time allocation to that activity can be not positively correlated while education positively increases total profit from the activity. T he estimation of either the household profit function or the labor supply function on its own provides the total effect of education on either h ousehold profit or 2 labor supply . This combines the direct effect that education has on household profit or labor supply with an indirect effect from the re - allocation of household labor induced by profi tability changes . Therefore, I jointly estimate the ho usehold hourly profit (wage) and labor supply functions to examine the impact of education on profitability of each activity and to determine whether the effect of education on household labor supply is associated with a difference in the education - induced profitability effects. S tudies on rural nonfarm activities in Sub - Saharan Africa emerged in the 1980s. The evidence from the field surveys in the late 1970s and 1980s changed a widespread view that rural Africans mainly farmed and undertook littl e activity off - farm , except when they left rural areas to migrate (Hill , 1982) . 20 studies from 10 Sub - rural inhabitants typically drive from 25 to 30 percent of their income from nonfarm sources, and nonagricultural income regularly accounts for from 30 to 50 percent of rural cash incomes (Haggblade et al., 1989) . In the 1990s em pirical studies explore d the systematic determinants and the eff ects of the rural off - farm activities of African farm households. Four - year panel data from Burkina Faso showed that shortfalls in cropping income push, while terms of trade pull, the househol ds towards nonfarm activities, but a land constraint does not dr ive the participation i n nonfarm activities (Reardon et al., 1992) . N onfarm activities are associated with higher and more stable income and consumption over years (Reardon et al., 1992) . A gricultural productivity growth was reinvesting nonfarm earnings into farming (Savadogo et al., 1994) . However, for those who lack access to off - farm activities, off - farm income increases inequality and fails to shield poor households against agroclimatic risks (Reardon & Taylor , 1996) . 3 By the end of the 1990s, e ducation captured the spotlight in rural nonfarm employment studies . A s new technologies developed, the relat ive impact of human capital on the marginal product of labor in farm and non - farm work changed, which determined t he allocation of an increment in human ca pital services between farm production and off - farm work (Huffman , 2001) . The experience of the Philippines during the Green Revo lution showed that because the adoption of modern varieties in rice farming increases the demand for labor in crop ping activities but does not increase the return to human capital as much as in nonfarm earnings, educated farm households tend to allocate mo re time away from farming to nonfarm employment (Estudillo & Otsuka , 1999) . The results from S SA are consistent in the positive effect of education on nonfarm earning and time allocation of rural farm households (Abdulai & Delgado , 1999; Abdulai & CroleRees , 2001) . Because a large share of nonfarm activities is in urban areas and in migration, an emphasis is put on the increase in access by the poor to assets . The latter include not only education but also information, financial capital, and infrastructure, all of which allow them to overcome non - farm entry barriers (Reardon et al. , 2000; Barrett et al., 2001) . For farm households, the returns to edu cation are not limited to educated individuals but include all household members because of the k nowledge spillover effects through both farm and off - farm activities (Yang , 1997) . Also, farm households reap rewards from schooling not only directly by enhancing pr ofitability of the ir activities but also indirectly by reallocating educated household labor from one activity to another in which the returns from schooling are high (Taylor & Y ú nez - Naude , 2000) . The data from rural Ghana showed that while direct effect of e ducation is positive and high in both farm and off - farm activities, the indirect effect of labor reallocation is negative in farming but positive in off - farm a ctivities . 4 Hence, in total, much of the value from increasing the educational attainmen t of farm households is found in its impact on off - farm activities, including the reallocation of time away from farm work (Jolliffe , 200 4) . For household - based nonfarm self - employment ventures, the household members jointly determine supply of labor given the shadow wage of the family activi ty where the shadow wage is unobservable . Th e joint estimation of the wage and labor supply equations incorporate s the effect of education on household earnings through the marginal productivity of labo r , labor allocation across activiti es , and its production externality effects (Laszlo , 2005, 2008) . Most of th e human capital literature estimate s the direct and indirect effect of education on profit and labor supply with the underlying assumption that the shadow wage and labor supply are positi vely correlated , but the labor supply functions are not jointly estim ated with endogenously determined shadow wage s . In developing countries, however, many households face strict constraints in the labor market , which can induce negative correlations betwe en the shadow wage and labor supply due to the allocative inefficienc y of labor . In this study, I jointly estimate the hourly profit (wage) and labor supply equations to incorporate the different channels through which education affects total prof it: profitability of hour s of labor , labor allocation across activiti es , and labor re - allocation through the education - induced profitability effects. I combine multiple models to overcome the difficulties of joint estimation. First, following Las zlo ( 2008) , because a marginal shadow wage is unobservable f or family self - employment, I us e an adequate instrument for the marginal shadow wage to estimate the effect of education on labor supply . Second, education itself is time - invariant for a majority of households and most likely to be c orrelated with unobserved heterogeneities because the decision on education is influenced by 5 family and community background . I exploit the variation of household person - year exposure to free primary education policy implemented by the Ugandan government a nd use it as an instrumental variable of education. Unlike t he season of birth (Angrist & Keueger , 1991) , sex of siblings (Butcher & Case , 1994) , policy int ervention (Harmon & Walker , 1995; Duflo, 200 1 ; Brunello et al., 2009) , and topological features (Cutler & Glaeser , 1997 ; Hoxby, 2000 ) , t his unique household variable explains both household and individual years of education and education qualification va riab les well, is perfectly exogenous, and does not directly explain hourly profit (wage) or labor supply. who are already married. Th ird, the hourly profit ( wage ) and labor supply equations are double censored. T he hour s of labor supply are censored at zero since observed hours of labor supply are always zero for those who are not participating in the ac tivity. Also, t he wage is observe d only when the household allocates positive hours of labor to the activity . To overcome this problem, I test the preeminence of the models and combine Double Hurdle and Type III structural Tobit models to appl y for the est imation. The structural feature of the model allows us to decompose the effect of education on profit into the direct effect of education on profitability , labor allocation across activities, and the indirect effect on re - allocation of labor through the ed ucation - i nduced profitability effect. The remainder of the paper is organized as follows. Section 1 .2 describes the data set and the preliminary findings from the descriptive analyses. Section 1 .3 explains the conceptual and estimation model s . Sec tion 1 .4 reports the model specification and the validity test of instrumental variables followed by the estimation result s of reduced form and two - stage 6 estimates, joint estimates, and intra - household estimates in Section 1 .5. Section 1 . 6 concludes with a summary of the key findings and discussion. 1.2 Data T he data used in this chapter come from the Uganda national panel survey (UNPS) 2009/2010, 2010/2011, and 2011/ 2012. UNPS is a nationwide household survey implemented by the Uganda Bureau of Statistics . The sample is implicitly stratified by geographic region. 322 Enumeration Areas (EAs) were selected out of the 783 EAs that had been visited by the Uganda National Househ old Survey (UNHS) in 2005/2006. They cover all 34 EAs visited by the UNHS 2005/2006 in Kampala District, and 72 EAs (58 rural and 14 urban) in each of the : (i) Central Region with the exception of Kampala District ; (ii) Eastern Region ; (iii) Western Region ; and (iv) Northern Region. UNHS featured 10 households selected randomly f rom each EA. The realized sample size was 2,975 households. From the full sample, I select all households in rural areas. Only the household members aged 20 to 65 are inclu ded in my sample. This selection criterion results in a sample of 2,195 households ( 5,813 individuals), among which 305 households (2,107 individuals) are in one - year panels, 347 households (1,045 individuals) are in two - year panels, and 1,543 households ( 2,661 individuals) form three - year panels. The average level of education of the poo led sample shows 5.55 years of completed education where seven years of education correspond to completion of primary school. 7 1 .2.A Higher Education, Longer Hours, and Higher Per Hour Labor Productivity in Rural Nonfarm Activities Compared to Farming L abor activities are classified into four sectors : own - farming, farm - wage - labor , nonfarm self - employment , and nonfarm wage - employment . Farming is defined as International Standard Industrial Classification (ISIC) code 1 and 2 , i.e., agriculture, hunting, forestry, and fishing. Nonfarm is defined as all other activities . The hour s of labor supply are defined as the time alloca tion of the main job and, if there is one , the second job in the last 12 months. In case the main or second job in the last seven day s is different from that in the last 12 months, the main or second job in the last seven days is also included. Hence, i f t he main and second jobs in the last 12 months and seven days are all different, a maximum of four jobs are considered per individual. The h our s of labor supply per week are computed based on the hour s of labor supply in the last 12 months and the average m onths per year and weeks per month of working days in the last 12 months. Therefore, it excludes the seasonality of the labor supply. Household non - labor income is the sum of the property income, interest , and dividends from investment s , pension s , and remi ttances. Table 1 .1 presents the education, hour s of labor supply, hourly profit s (wage s ) 1 , and characteristics of individual s in each secto r . In rural Uganda, in aggregate, around 40 percent of the hours of labor are supplied to nonfarm activities and 60 percent of the hours of labor are provided to farming. The individuals who provide positive hours of labor to nonfarm activit ies, on average, h ave higher education than those who provide positive hours of labor to farming . 1 Hourly wage is the weighted sum of wage within a sector using hours of labor supply of each job as weig ht. Hourly profit from self - employed activitie s is the total household profit divided by total hours of labor supply of all household members age 20 to 65 who are engaged in the activity. Total profit is the total value of output subtracted by the total va lue of input. The total values of output and i nput are the total quantity of output and input multiplied by the median prices of each at district - urban/rural level. In case there are less than 10 observations of prices, the larger locality level such as su b - region, region, or nation, is applied. 8 Table 1. 1 E ducation , hours of labor supply , hourly profit or wage, and characteristics of individuals by sector Own - f arming Farm - wage - labor Nonfarm s elf - employment Nonfarm wage - employment mean p50 cv mean p50 cv mean p50 cv mean p50 cv E ducation (year s ) 5.0 5.0 0.7 3.7 4.0 0.8 6.0 6.0 0.6 8.2 8.0 0.6 Labor supply (hour s / week) 21.3 19.4 0.7 15.1 6.8 1.4 32.3 23.1 0.9 3 5.4 31.6 0.8 Multiple sectors = 1 0.3 0.0 1.4 0.8 1.0 0.6 0.7 1.0 0.7 0.5 1.0 1.0 Hourly profit or wage ( USD /hour ) 1.6 0.4 12.3 1.7 0.7 2.7 5.3 0.7 16.4 3.2 1.1 4.6 E xperience (year s ) 21.4 20.0 0.6 9.3 7.0 1.1 9.3 6.0 1.0 7.6 4.0 1.1 A ge 37.9 37.0 0.3 36.9 36.0 0.3 38.0 37.0 0.3 35.8 35.0 0.3 F emale = 1 0. 6 1.0 0. 9 0. 5 0.0 1. 1 0.5 0.0 1.0 0.3 0.0 1.5 Household land holding s (acre s ) 4.8 2.5 2.4 4.4 2.0 2.5 4.2 2.0 2.6 4.4 1.9 3.5 Value of household farm asset (100 USD ) 0.7 0.2 2.5 0 .7 0.2 3.0 0.6 0.2 2.6 0.5 0.2 3.0 Household nonlabor income (100 USD /year) 0.6 0.0 5.8 0.3 0.0 4.8 1.9 0.1 3.7 1.4 0.0 6.2 Ownership = 1 0.2 0.0 1.9 - - - 0. 8 1.0 0. 6 - - - F ormal job = 1 0.0 2 0.0 0 6. 58 0.0 3 0.0 0 5. 89 0.0 4 0.0 0 4 . 99 0.2 5 0.0 0 1.7 4 Share of hours of labor supply 0.55 0.06 0.23 0.16 Number of obs. (individual - year pairs) 8149 1 286 2225 1393 Notes: USD used in the table is 2011 PPP USD . Experience of own - farming is the year of experience of the househol d. Multiple sectors mean having at least one additional job in another sector. F ormal job refers to having a formal job as the main job in the sector. A formal wage job is defined as the job for which the em ployer applies at least one of the following: pen sion or retirement funds, paid leaves, medical benefits, or income taxes. A formal self - employed job is defined as the business registered for VAT or subject to income tax. 9 T he average hour s of labor supply to own - farming are 21.3 hours per wee k, which is much shorter than 32.3 hours in nonfarm self - employment and 35.4 hours in nonfarm wage - employment. Although the hours of labor supply in farming are fewer than in t he nonfarm sectors, only 30 percent of individuals in own - farming allocate their time to multiple sectors while 70 percent in nonfarm self - employment and 50 percent in nonfarm wage - employment work in multiple sectors. T he hour s of labor supply in farm - wage - labor are 15.1 hours per week, which is shortest among all sectors, as 80 perce nt of individuals in farm - wage - labor are engaged in multiple sector s. The mean of hourly profit ( wage ) show s the largest value , 5.3 USD per hour, in nonfarm self - employment, followed by 3.2 USD per hour in nonfarm wage - employment, 1.7 USD per hour in farm - wage - labor, then 1.6 USD per hour in won - farming. The median of hourly profits (wages) is, however, higher in nonfarm wage - employment, that is 1.1 USD per ho ur, than in nonfarm self - employment, which shows 0.7 USD per hour. The variance of per hour profit is larger in nonfarm self - employment than in nonfarm wage - employment. Despite the longer years of average experience in farming than nonfarm activit ies, hourly profit (wage) suggests that rural nonfarm activities have the higher per hour labor pro ductivity than farming. The average age and share of female workers are not significantly different from the aggregate average age, 37, and the aggregate sha re of female, 53 percent, in all sectors except the share of female workers in nonfarm wage - employm ent, where only 30 percent of workers are female. The median of household land holdings indicates that individuals in own - farming, on average, have larger ho usehold land holdings than those in other sectors. There is no significant difference in medians of value of household farm assets and household nonlabor income across sectors. However, the highest 25 percent of household nonlabor income exhibits significa ntly 10 higher amounts of nonfarm activity than in farming, resulting in higher means of household non labor income in nonfarm sectors than in farming sectors. In terms of the ownership, 80 percent of workers in nonfarm self - employment own their busin ess while just 20 percent of workers in own - farming have the ownership. Most income generating acti vities are informal; just 2, 3, 4, and 25 percent of individuals in own - farming, farm - wage - labor, nonfarm self - employment, and nonfarm wage - employment respec tively have a formal job 2 as the main job. 1 .2.B Education Qualification Plays a Role in Sector Choice of Individual Labor Allocation Figure 1. 1 K ernel density estimates of education by sector 2 A formal wage job is defined as the job for which the employer applies at least one of pension or retirement funds, paid leaves, medical benefit s, or income taxes. A formal self - employed job is defined as the bus iness registered for VAT or subject to income tax. 11 Figure 1 .1 displays t he probability distribution of individual years of education in each sector. As shown in Table 1.1, the ave rage education is lowest in farm - wage - labor, followed by own - farming, nonfarm self - employment, and then nonfarm wage - employment. In Uganda, 7 and 13 years of education correspond to completion of primary school and secondary school respectively . T he probability distribution shows the different traits across sectors for the equal or lower than 7 years of education, between 7 and 13 years of education, and equal to or higher than 13 years of education. It suggests that not only years of education but also education qualification play some role in individual decisions on labor allocation. Table 1 .2 highlights t he sector choice of labor supply by education qualification. The values in the brackets show the share of number of observations and th e share of hours worked respectively. The share of hours of labor shows that those who have higher education qualificatio n allocate smaller share of time to own - farming or farm - wage - labor and larger share of time to nonfarm wage - employment. The share of ho urs worked in nonfarm self - employment, on the other hand, increases as education qualification increases for those whose education qualification is lower than some secondary but decreases as education increases for those whose education is higher than comp leted secondary. The gap between 1.00 and the sum of the shares of observations in all sectors and not working is the sha re of observations who are engaged in multiple sectors. Because some observations allocate hours of labor to more than two sectors, the share of observations in multiple sectors shows a little smaller value than the gap; 0.22, 0.26, 0.25, 0.21, 0.08, and 0 .31 for the education qualification of no primary, some primary, complete d primary, some secondary, completed secondary, and post - secon dary respectively. It implies that t he likelihood of income diversification shows a U - shaped form; individuals whose educ ation qualification is some primary, complete d primary or post - secondary show relatively higher 12 Table 1. 2 E ducation qualification and sector choice of labor supply Education q ualification Total Own - farming Farm - wage - labor Nonfarm s elf - employment Nonfarm wage - employment Not working No p rimary Obs. 2 , 071 1 , 529 330 246 107 342 ( 1.00 ) ( 0.74 ) ( 0.16 ) ( 0.12 ) ( 0.0 5 ) ( 0.17 ) Hours 47,523 34,764 4,846 5,722 2,192 0 (1.00) (0.73) (0.10) (0.12) (0.05) (0.00) Some Obs. 5 , 228 3 , 811 693 969 393 785 primary ( 1.00 ) ( 0.73 ) ( 0.13 ) ( 0.19 ) ( 0.08 ) ( 0.15 ) Hours 130,176 81,558 9,512 28,547 10,560 0 (1.00) (0.63) (0.07) (0.22) (0.08) (0.00) Completed Obs. 1 , 568 1 , 101 124 358 162 234 primary ( 1.00 ) ( 0.70 ) ( 0.08 ) ( 0.23 ) ( 0.10 ) ( 0.15 ) Hours 44,803 24,520 2,214 12,040 6,028 0 (1.00) (0.55) (0.05) (0.27) (0.13) (0.00) Some Obs. 2 , 419 1 , 370 111 504 423 558 secondary ( 1.00 ) ( 0.57 ) ( 0.05 ) ( 0.21 ) ( 0.17 ) ( 0.23 ) Hours 65,066 27,009 1,754 19,613 16,690 0 (1.00) (0.42) (0.03) (0.30) (0.26) (0.00) Completed Obs. 320 93 3 37 51 163 secondary ( 1.00 ) ( 0.29 ) ( 0.01 ) ( 0.12 ) ( 0.16 ) ( 0.51 ) Hours 5,280 1,512 195 1,351 2,22 3 0 (1.00) (0.29) (0.04) (0.26) (0.42) (0.00) Post - Obs. 394 175 6 70 219 51 secondary ( 1.00 ) ( 0.44 ) ( 0.02 ) ( 0.18 ) ( 0.56 ) ( 0.13 ) Hours 14,709 2,467 128 2,484 9,629 0 (1.00) (0.17) (0.01) (0.17) (0.65) (0.00) Total Obs. 12 , 000 8 , 082 1 , 267 2 , 185 1 , 356 2 , 134 ( 1.00 ) ( 0.67 ) ( 0.11 ) ( 0.18 ) ( 0.11 ) ( 0.18 ) Hours 307,556 171,829 18,649 69,756 47,322 307,556 (1.00) (0.56) (0.06) (0.23) (0.15) (1.00) Notes: The values in the brackets show the share of number of observations and the share of hours wo rked, respectively. Hour shows the total average weekly hours of work supplied to each sector based on the total hours of work supplied in a year. No primary refer s completing less than 1 primary grade or having never attended school. Some secondary includ es post primary specialized training. likelihood of income diversification than those whose education is no primary, some secondary, or completed secondary . The driver of income diversification would be different between those who did not proceed to sec ondary school and those who have post - secondary education. The share of observations of those not engaged in any income generating activities is also significant. The most common reason for not working for those who have not attended secondary school is si ckness or disability, which accounts for 16 percent of people who are not engaged in any 13 income generating activities. It is, then, followed by takin g care of house or family, which accounts for 8 percent. For those who attended secondary school but did no t proceed to post - secondary education, the most common reason for not working is attending school, which accounts for 33 percent, followed by taking care of house or family, which accounts for 10 percent. The reason for those who have post - secondary educat ion, is mainly looking for a job, which accounts for 24 percent of individuals who are not engaged in any income generating activities. 1 .2. C Hour ly Return and Hour s of Labor Supply Negatively Correlated in All Activities Figure 1 .2 and Figure 1 .3 illu strate the correlations between education, hourly profit ( wage ) , and hour s of labor supply in farming and in nonfarm activities respectively . The surface of the figure shows the multivariate kernel density estimates of the combinations of two variables . Th e figures show the relatively clear relations between hourly profit ( wage ) and hours of labor supply in all activities. Hourly returns and hours of labor supply are negatively correlated. From the multivariate kernel density estimates, both the education a nd hourly returns and education and hours of labor supply do not show explicit correlations in farming. Compared to farming, no nfarm activities display relatively higher probability in the area where higher education and higher hourly returns intersect and the area in which higher education and longer hours of labor supply intersect. However, the correlations between education and hourly return and education and hours of labor supply are not very distinct as some with high education show low hourly returns or short hours of labor supply in nonfarm activities. The figures suggest that separately estimating the effect of education on total profits instead of hourly profits and the effect of education on labor supply tends to overestimate the positive effect of education by masking the 14 Figure 1. 2 M ultivariate kernel density estimates of education, hourly profit or wage, and hours of labor supply to farming 15 Figure 1. 3 Multiv ariate kernel density estimates of education, hourly profit or wage, and hours of l abor supply to nonfarm sectors 16 negative relations between education, hourly returns, and hours of labor supply. To fully discern the outcomes, empirical analyses are requi re d. 1.3 Model To find out the joint determination of household hourly profit ( wage ) and hour s of labor supply, it is necessary to examine how education affects household profits , shadow wages, and labor supply in both farming and nonfarm activities . The agricultural household model, o riginally developed by Singh et. al. ( 1986) , is in the line of the joint determination studies. The household members share income within the household and jointly determine supply of labor given the shadow wage s of the on - farm and off - farm ac tivit ies (Jacoby , 1993; Newman & Gertler , 1994) . This approach allows estimation of the effect of education on household labor allocation through the shadow wage, that is , the hourly return of each activity. 1 .3.A The Farm H Utility Maximization P roblem Suppose that a unitary household maximizes the utility of all family members over consumption and leisure, subject to budget and time constraints. C onsumpti on is considered only on consu Y ) and leisure ( l ); U(Y,l; ) where is the set of exogenous factors which affect household preferences such as the number of adults and children and their gender . The utility func tion satisfies the standard assumptions : twice continuously differentiable and strictly qua si - concave. The h ousehold is endowed with hour s of labor and allocates endowed labor into M possible activities and leisure ( l ); . When h ousehold income ( Y ) comes from M activities and nonlabor income , t he farm household ut ility maximization problem can be stated as : 17 ( 1 . 1 ) where m easures profit, that is total expenditures subtracted from gross income; is education; represents household quasi - fixed assets required in each activity such as experience, landholding s , geographical situation , and capital stock; is a vector of prices of inputs; measures risk of earning profit s from the activity ; and is nonlabor in come. If activity m is wage work, then Y is the wage income earned by the family. I assume that family labor and hired labor are not perfect substitutes so tha t hired labor is determined just like the other variable inputs given the exogenous prices. Also, following Jolliffe ( 2004) , I assume that education cannot be purchased on the labor market, which means that the household cannot hir e a manager to make the decisions on household activities. The first order conditions to solve equation ( 1 .1) consist of non - negativity conditions of hour s of labor supply and uniformity of marginal product of labor in all activities: ( 1 . 2 ) The household does not participate in activity m income for leisure is greater than marginal return , or shadow wage, in activity m , evaluated at zero hours of labor in activity m . If the marginal return is greater, then the household provide hour s of labor to activity m so that the value of the marginal product of labor e quals t he marginal rate of substitution of income for leisure . To assure the possibility of an interior solution for wage work , which has constant marginal return to hour s of labor supply, the marginal rate of substitution must increase with hou r s of labor . Also, to assure that the household can be engaged 18 in multiple sectors, t he profit (wage income) functions must satisfy the positive and non - increasing marginal product of hour s of labor . Theoretically, i f all market s are complete , the wage rate is completely exogenous ly determined , and time is sufficient ly endowed such that the time constraint is not binding at the optimal solutions, the household suppl ies labor to wage work as we ll as self - employment activities up to the point where t he mar ginal rate of substitution of income for leisure equals t he price of leisure ( which is represented by the exogenous wage rate ) . In case the highest wage rate offered to the household is lower than the for le isure evaluated at zero hour s of labor, the household members allocate their time only to self - employment activities . However, market s are hardly complete especially in developing countries . M arket failures are rampant because of : (1) high transactio n cost s, which include distance from the market and poor infrastructure ; (2) high marketing margins due to merchants with local monopoly power ; (3) high search and recruitment costs due to imperfect information ; (4) high supervision and incentive costs on hired labor ; (5) s hallow local markets, which imply a high negative covariation between household supply and effective prices ; (6) p rice risk aversion , which influences the effective price used for decision making ; and (7) limited access to working capital credit (Sadoulet & d e Janvry , 1995) . With market failure, the corresponding good or factor becomes a non - tradable . Its price is no longer determined by the market but internally to the household as a shadow pri c e (Sadoulet & d e Janvry , 1995) . When labor markets are not complete , the shadow wage is given by the function of household characteristics and all factors that affect household pr ofit ( d e Janvry e t al., 1991) . A n allocation of household labor is , then, such that the marginal product of labor is 19 equated to an endogenously determined shadow wage, . T he solution to equation ( 1 . 2 ) is given as: ( 1 . 3 ) In this case, the optimal profit and the hourly profit are given as: ( 1 . 4 ) ( 1 . 5 ) Note that a market may fail only for some particular household s (Sadoulet & d e Janvry , 1995) . F or simplifying the estimation, and because the objective of this study is not to determine which households face the market failure, I assume that the labor market is incomplete for all households. As stated in section 1 .2. C, estimating equation ( 1 .4) to measure the effect of education on total profit from each activi ty tends to overestimate the positive returns to education in case there are negative correlations between education, hourly profit (wage), and hours of labor s upply. I will jointly estimate equation s ( 1 .3) and ( 1 .5) to reveal how hourly profit (wage) and labor allocation to off - farm work respectively contribute to the difficulties of joint estimation and how to overcome th e difficulties are explained in section 1 .3.B. 1 .3. B Joint Estimation of Household Returns to E ducation and Labor Allocation The aim of this chapter is to show increased by higher hourly profit (wage) or allocating more households labor into non farm work. In the latter case, it is possible that a labor shift from farming to nonfarm activities is not 20 accompan ied by an increase in the household hourly return s even if the total gain in household profit s is positive. T o separate out the effect of education on hourly profit (wage) and the effect of e ducation on hour s of labor supply , I jointly estimate household h ourly profit ( wage ) and household hours of labor supply. There are three obstacles to joint ly estimati ng household hourly profit (wage) and hours of labor supply . First, because hou sehold labor supply is not a function of the average return, but a function of the shadow wage, the estimation model necessarily includes the relation between marginal shadow wage and the hourly return. F or wage work, a marginal return is constant and equa l to hourly wage. However, f or family self - e mployment, a marginal shadow wage is not constant and unobservable . Second, education is time - invariant for most households and most likely to be correlated with the unobserved heterogeneities because the decisio n on education is influenced by family and c ommunity background. In the presence of endogeneity of education, estimations that do not tak e care of endogeneity result in inconsistent estimators of all parameters. Third, the hourly profit ( wage ) and labor su pply equations are double censored. T he hour s of labor supply are censored at zero since observed hours of labor supply are always zero for those who are not participating in the activity. Also, t he wage is observed only when the household allocates positi ve hours of labor to the activity . Three obstacles are overcome by combining multiple estimation models . Suppose that household hours of labor supply in equation ( 1 . 4 ) can be expressed as: ( 1 . 6 ) where is hours of labor supply; is marginal return to hour s of labor, that is shadow wage; represents the effect of education independent of its effect through the shadow wage; the vector includes household and regional exogenous variables affectin g hours worked; is a 21 stochastic disturbance term. For family self - employment, a marginal shadow wage is unobservable. However , by using an adequate instrumen t for , it is possible to estimate the effect of education on labor supply (Laszlo , 2008) . A household hourly profit ( wage ) equation ( 1 .5) is given as: ( 1 . 7 ) where is hou rly profit for family self - employment or hourly wage for wage employment; represents the hourly profit ( wage ) return to education ; and the vector includes demographic, market, and regional characteristics affecting hourly profit ( wage ) . For ho usehold self - employment activities, the vector must include a set of variables that is excluded from , which plays as instrumental variables for . The instrumental variables predict the marginal product of labor (shadow wage) but are ortho gonal to the error term in equation ( 1 . 6 ). Also, f or both wage employment and self - employment, years of schooling are potentially endogenous . I use a linear projection of education given as: ( 1 . 8 ) where is the vector which consists of the set of all exogenous variables in the hourly profit ( wage ) equation and instrumental variables for education . I exploit the variation of person - year expos ure of the household to the free primary educ ation program and use it as instrumental variable for the household average years of education . The detail of hypothesis tests of endogeneity and validity of instrumental variables are in section 1 .4.A. For simplicity of further mod eling, education is mode led as affecting hourly profit (wage) and labor supply linearly and with no interaction effects. However, as shown in section 1 .2.B, not only years of education but also education qualification plays some role in individual labor al location decisions. Ther efore, this restrictive assumption is eased in the intra - household estimations in section 1 .5. C . 22 To overcome the double censored problem of estimating equations ( 1 .6) and ( 1 .7) , I combine the two commonly used censored mode ls ; the Double H urdle an d Type III structural Tobit models. The Double H urdle model, which is often applied to the estimation of labor supply equation s , is a modified version of the Type I Tobit model (Cragg , 1971) . The 1 st stage of the Double H urdle model estimates the probability of participation, which is followed by the 2 nd stage estimation of the hours of labor suppl y given the probability of participation. While the Type I Tobit model imposes restrictions on the coefficients of first and second stage estimations, the Double H urdle model does not impose those restrictions. The preeminence of the model is tested by com paring the log - likelihood of both models (Vuong , 1989) . For the es timation of the wage equation, although the most widely used method is Heckit, which employs Type II Tobit model (Heckman , 1976) , the Type III Tobit model is preferred when not only participation status but also hours of labor supply data are available. The Type III Tobit mo del uses the residuals from the 1 st stage estimation instead of the Inverse Mil ls Ratio (IMR) (Amemiya , 1985) . Because residuals contain more information than IMR, there is e fficiency gain over the Type II Tobit model. Additionally, the Type III Tobit m odel relaxes the nonlinearity restriction of IMR imposed under the Type II Tobit model. First, I e stimate the reduced form labor supply equation as: ( 1 . 9 ) where is the vector of all exogenous vari ables in , , and . Then I obtain the IMRs from the 1 st stage and the residuals from the 2 nd stage estimation. Second, after estimating hourly profit ( wage ) equation ( 1 .7 ) and education equation ( 1 . 8 ) by adding the IMRs and the residuals a s the additional explanatory variables, I obtain fitted values of excluding the parts explained 23 by the IMR s and the residuals, which I denote as , and fitted values of , which I denote as , that I then use in a final stage where I estimate: ( 1 . 10 ) The estima te of in the hourly profit ( wage ) equation ( 1 .7 ) provides the hourly profit (wage) return to education , and the final stage estimate of i n equatio n ( 1 .10) give s the effect of education directly on labor supply . T he effect of education on hours through the (shadow) wage is estimated as in equation ( 1 .10) multiplied by in equation ( 1 .7) . 1.4 Model Specification and Validity Tests of Instrumenta l Variables 1 .4. A Specification of Variables and Estimation Equations The work is classified into four activities : own - farming, farm - wage - labor , nonfarm self - employment , and nonfarm wage - employment . After estimating the reduced form labor supply equati on ( 1 .9), I jointly estimate the hourly profit (wage) , equation ( 1 .7), the educati on equation ( 1 .8), and the labor supply equation ( 1 .10). The vector of includes time - variant and time - invariant household and district variables. also includes a vector of year dummies which represent year - specific change s of hourly profit ( wage ) and labor supply. The stochastic disturbance term, , consists of a stoch astic error term and unobserved household and district heterogeneities which are correlated with time - variant explanatory variables. For each activity, the estimation equations are spec ified as : ( 1 . 11 ) ( 1 . 12 ) ( 1 . 13 ) 24 ( 1 . 14 ) w here is the subscript for household ; is the subscript for district ; is the subscript for year ; an d are unobserved heterogeneities ; is a stochastic error term. The household average years of education of members 20 years of age and older serves as a measure of . The vector contains the vector of househol d composition ( ) suc h as the household average age, the number of children age d 0 - 6 and 7 - 12, the share of female workers, and the share of married workers, the vector of household quasi - fixed assets required in all activities ( ) such as year of experience in own - farmin g , farm - wage - labor , nonfarm self - employment , and nonfarm wage - employment , square of year s of experience, household landholding s , value of farm assets, distance to the nearest transport, and nonlabor income, and the vector of pri ces of inputs ( ) such as regional average hourly profit s in own - farming and nonfarm self - employment , the regional average hourly wage in farm - wage - labor and nonfarm wage - employment , the consumer price index of food products , and the land rental rate. The ve ctor is the vector which consists of the set of all exogenous variables in and instrumental variables for education . The vector include s all exogenous variables in . For own - farming, the value of farm assets is excluded from s o that the shadow wage is instrumented. For nonfarm self - employment , nonlabor income is excluded from to instrument the shadow wage. Whether the value of farm assets and nonlabor income are not directly explaining the household labor supply to each activity but explaining household labor supply through the shadow wage is tested in section 1 . 4.C . The vector consists of all exogenous variables in , , and . The summary statistics of the variables used for the estimations are reporte d in Table 1 .A.1 in the Appendix . Table 1.3 presents the results of the Vuong test for e stimat ing reduced form labor supply equation ( 1 . 11 ) by either the Type I T obit model or the Double H urdle model . The preeminence 25 Table 1. 3 R esults of Vuong test Activity Models tested Coefficient Preferred model Own - f arming Lognormal H urdle Type I Tobit 0. 255 *** (0.0 25 ) Lognormal H urdle Farm - wage - labor Lognormal H urdle Type I Tobit 1. 582 *** (0.05 7 ) Lognormal H urdle Nonfarm self - employment Lognormal H urdle Type I Tobit 1 . 047 *** (0.0 49 ) Lognormal H urdle Nonfarm wage - employment Lognormal H urdle Type I Tobit 1 . 116 *** (0.0 46 ) Lognormal H urdle Notes: Coefficient shows the mean of difference of log - likelihood ( Lognormal hurdle mo del minus Type I Tobit model) . Standard errors clustered at household level are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. of the model is tested by comparing the log - likelihood of both models (Vuong , 1989) . The coefficient shows the m ean of the difference of log - l ikelihood between Double Hurdle lognormal model and the Type I Tobit model. The result shows that in all activities, the Double H urdle lognormal model has statistically significantly higher log - likelihood at the one percent co nfidence level. Hence, I apply the Double H urdle lognormal model for the estimation of labor supply , equation ( 1 .11) and equation ( 1 .14). The endogeneity test of education confirms that there is no clear evidence that education is exogenously determined. T he detail of the test is repor ted in section 1 .4.B. I adopt two stage least square estimator (2SLS) for the estimation of hourly profit (wage) , equation ( 1 .12). Although fixed effect estimators of hourly profit (wage) , equation ( 1 .12) , and labor s upply , equation ( 1 .14) , are consistently estimated under less restrictive assumptions, I employ correlated random effect s (CRE) estimators because education is time - invariant for most households . Under (Mundlak , 1978) as: ( 1 . 15 ) where is a set of time means of the time - variant household or district explanatory variables in the corresponding eq uation. The heterogeneities are correlated with time - variant explanatory variables only through their time means. The consistency assumptions of Double H urdle and 26 Type III Tobit models (Wooldridge 2010) provide the consistency conditions: (1) ( ) is independent of ; (2) ; and (3) contains at least one element whose coefficient is different from zero that is not in . The estim ation procedure of the consistent estimators is as follows. Step 1. Est imate reduced form labor supply , equation ( 1 . 11 ) , by the Double H urdle lognormal model and get the IMRs from the 1 st stage and the residuals, , from the 2 nd stage estimations. Step 2. E stimate 2SLS CRE estimators of hourly profit ( wage ) , equation ( 1 . 12 ) , b y including IMRs and as the additional explanatory variables. Collect the fitted values, and from the estimations of the hourly prof it ( wage ) equation and the reduced form education equation where the p arts explained by IMRs and are extracted from the fitted values. Step 3. Estimate labor supply , equation ( 1 . 1 4) , using and as the explanatory variables by a Double H urdle lognormal model . 1 .4.B Validity Tests of Instrumental Variable s in Household Hourly Profit (Wage) and Labor Supply E stimations The government of Uganda abolished primary school fees on January 1, 1997 as part of a universal primary school policy. The policy was introduced for all primary grades simultaneously. The cost of textbooks was also abolished. The tuition fee in late 1996 was 5,000 Ugandan shillings per student per year for the first 3 grad es of schooling, and 8,100 Ugandan shillings for the 4 th to 7 th grades . In 1999, a teacher earned a monthly salary at a government - aided school of 75,000 shillings (Uganda , 1999) , and average household expen diture on food, 27 clothing, and living in rural Uganda was 86,700 shilling s per month (Uganda , 2001) . The policy resulted in a dramatic increase in net enrolment rate, from 57 percent in 1996 to 85 percent in 1997, and over 90 percent in 1999 (Uganda , 1999) . I exploit the variation of the sum of person - year s of exposure to free primary education across household s to explain household average years of education. In our sample, t he individuals who were exposed to free primary education are those aged 5 to 12 in 1997 ( 20 to 2 7 in 20 12 ) , that i s , 29.4 percent of individuals in our sample . The duration of exposure varies from one year to seven years depending on their birth years. By summing person - year s of exposure to free primary education within a household, the variation goes from one person - year to 40 person - years of exposure. In our sample, 47 percent of households were exposed to free primary education. To control the effect of the district environment on the policy, I utilize the information on the distance to the nearest market in the com munity in 1995. I matched the individual dis trict of birth data in UNPS with community - level service availability data from the Uganda demographic and health survey 3 (UDHS) 1995. The average individual distance to the nearest market in the community in 199 5 among household members aged 20 to 65 is used as another instrumental variable to explain household average years of education. T o instrument the household average education, it is necessary that instrumental variables be correlated with househ old average education while not directly de termining household hourly profit (wage) or labor allocation . The inclusion restriction is tested by estima ting the reduced form education , equation ( 1 . 13 ) . Because equation ( 1 . 1 s fo r the estimation of hourly profit ( wage ) equation, and all time - variant exogenous explanatory variables 3 UDHS was conducted by the M inistry of F inance and E conomic P lanning. 28 in the hourly profit (wage) equation are used as their own IVs in the reduced form education equation, I apply the CRE model rather than the pooled mode l to estimate equation ( 1 . 13 ). Table 1 . 4 reports the estimation result of the reduced form household education equation . The coefficients of person - year exposure to free primary education are all significant at the one percent confidence level . Th e coefficient of average distance to the nearest market in the district of birth in 1995 is also statistically significant, and it is significant at the five percent confidence level. T he signs of the coefficients are as expected; the person - year of exposu re to free primary education increases t he household average year s of education , and the average distance to the nearest market in the district of birth in 1995 negative ly affect s the household average year s of education . - statistics indicate instrumental variables ( IVs ) in the reduced form education equation are jointly significant at the one percent confidence level in both estimations . Table 1. 4 H ousehold education reduced form estimates ( correlated random effects ) Average years of schoolin g Average years of schooling Estimate Standard error Estimate Standard error Instrumental variables Person - y ear under free primary policy 0.065*** (0.014) 0.0 65* ** (0.014) Average di stance to nearest market in - 0.036** ( 0.017 ) - - district of birth in 1995 (km) - statistic a 28.4 1 *** 22.10*** (H 0 : IVs violate inclusion restriction) Number of observations 4,724 4,7 53 Number of households 2,008 2,014 R - squared 0.329 0. 328 Notes: In all estimations, all other exogenous variables in the profit or hourl y profit equations are included as explanatory variables but not reported in the table. All estimations used the correlated random effect s model. Clustered s tandard errors are in pare ntheses. *** p<0.01, ** p<0.05, * p<0.1. a - statistic show s the jo int significance of all IVs in the schooling reduced form equation. Table 1 . 5 presents the results of endogeneity and overidentification restriction tests . The result of hourly profit (wage) and 2 nd stage labor supply e stimations shows the estim ation results both with and without controlling selection bias. For the hourly profit (wage) e stimation , 29 Table 1. 5 Validity tests of instrumental variables in the household hourly profit (wage) and labor equations Own - f arming F arm - wage - labor Nonfarm self - employment Nonfarm wage - employment Endogeneity test a (H 0 : education is exogenous) Using two IVs Household hourly profit (wage) - 0.028**(0.014) 0.064**(0.029) 0.018(0.027) - 0.035(0.024) with selection bias cont rolled - 0.035**(0.014) 0.052*(0.028) - 0.004(0.026) - 0.048**(0.022) Household labor 1 st stage 36.46*** 37.32*** 15.90*** 28.57*** Household labor 2 nd stage - 0.045***(0.016) - 0.056(0.048) - 0.050*(0.028) - 0.044(0.029) with selection bias controlled - 0.03 8**(0.016) - 0.050(0.048) - 0.047*(0.028) - 0.031(0.030) Using one IV Household hourly profit (wage) - 0.028*(0.014) 0.066**(0.029) 0.015(0.027) - 0.033(0.024) with selection bias controlled - 0.034**(0.014) 0.052*(0.028) - 0.005(0.026) - 0.047**(0.021) Household labor 1 st stage 35.04*** 53.29*** 21.64*** 39.65*** Household labor 2 nd stage - 0.041***(0.016) - 0.060(0.048) - 0.043(0.028) - 0.046(0.029) with selection bias controlled - 0.034**(0.016) - 0.052(0.048) - 0.044(0.028) - 0.033(0.030) Overidentifying restriction test b (H 0 : IVs are jointly valid) Using two IVs Household hourly profit (wage) 5.52** 0.63 0.67 1.80 with selection bias controlled 7.04*** 1.06 0.73 4.19** Household labor 1 st stage 2.15 12.73*** 5.49** 10.88** Household labor 2 nd stage 4.54** 0.27 4.21* 14.82*** with selection bias controlled 3.84* 0.47 3.28* 10.79*** Notes: Household hourly profit (wage) and labor 2 nd stage estimations show correlated random effect s estimates . Household labor 1 st stage estimations us ed a pooled probit model with time means of all time - variant explanatory variables. Clustered s tandard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. a Household hourly profit (wage) and labor 2 nd stage show the significance of the coeffici ent of the residual from the reduce d form education equation . Household labor 1 st stage shows chi - square statistics of Wald test of exogeneity. b Household hourly profit (wage) and labor 2 nd stage show Sargan - Hansen statistics from two stage least squa re s estimations. Household labor 1 st stage shows Amemiya - Lee - Newey minimum chi - square statistics from probit two - stage instrumental variable estimations. selection bias is controlled by including the IMR and residual from estimating the 1 st stage reduce d - form labor supply estimation. For the 2 nd stage labor supply estimation, the IMR from the 1 st stage labor supply equation is included as an additional explanatory variable t o control for selection bias. The null hypothesis of the endogeneity test is that education is exogenously determined. T he result s of endogeneity test for household hourly profit (wage) and 2 nd stage labor supply e stimations show the significance of the coefficient of the residual from the reduced 30 form of education in the regression of the household hourly return or hour s of labor supply on all exogenous variables, education, and the residual from the reduced - form education e stimat ion using correlated random effects . The test result for the household 1 st stage labor supply e sti mation shows the - statistics of Wald test of exogeneity in the pooled probit two stage regression of the binary participation variable on all exogenous variables and education , which is instrumented by instrumental variables . The result of endogeneit y test s show s that for all equations the null hypothesis that education is exogenous is rejected at the 10 percent or less confidence level in at le ast one activity . Hence, there is no statistically significant evidence that education is exogenously determ ined. The null hypothesis of the overidentifying restriction test is that the multiple IVs are jointly valid in the estimations . The result of the o veridentifying restriction test for household hourly profit (wage) and 2 nd stage labor supply e stim ations shows Sargan - Hansen statistics from 2SLS CRE estimations. The result for 1 st stage labor supply e stimation shows Amemiya - Lee - Newey minimum - statistics from pooled probit two stage instrumental variable estimations. The results show that the nu ll hypothesis of joint validity of IVs are not rejected for more than half of the hourly profit (wage) e stimations . However, the null hypothesis of joint validity of IVs is rejected for more than half of 1 st and 2 nd stage labor supply e stim ations . Therefor e, in the further estimations, I use two IVs for the estimation of the household hourly profit (wage) but exclude the average distance to the nearest market in the district of birth in 1995 for the estimation of household labor supply. Because tho se in our sample were all born before 1997, there is no reasonable explanation that household person - year exposure to the free primary education directly explains household 31 hourly profit (wage) or labor supply. The potential concern to use household averag e distance to the nearest market in district of birth in 1995 is that it might correlate with the current household hourly profit (wage) if the household is non - migrant. To dispel the concern, I estimated the household hourly profit (wage) equation with a subsample of non - migrants by using average distance to the nearest market in the district of birth in 1995 and other exogenous variables as explanatory variables . Table 1 .6 shows the estimation results of hourly profit (wage) using a subsam ple of non - migra nts. The full set of parameter estimates are presented in Table 1.A.2 in the Appendix. The coefficients of the average distance to the nearest market in the district of birth in 1995 are all not statistically significantly different from zero. The estimati on result confirm s that there is no statistically significant evidence that the average distance to the nearest market in the district of birth in 1995 direc tly explains the current household hourly profit (wage) of non - migrants . Table 1. 6 Household hourly profit (wage) of non - migrants Dependent variable: Household hourly profit or wage ( USD / hour ) Own - f arming Farm - wage - labor Nonfarm self - employment Nonfarm wage - employment Explanatory variables CRE CRE CRE CRE With selection bi as controlled Average distance to nearest market in district 0.029 0.001 0.006 - 0.040 of birth in 1995 (0.020) (0.044) (0.037) (0.044) Observations (household - year pairs) 2,496 487 883 512 Number of households 1,275 386 596 379 R - squared 0.289 0.3 62 0.331 0.432 Notes: The full set of parameter estimates are presented in Table 1 . A.2. Clustered s tandard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. 32 1.5 Estimation Result s 1 .5.A Reduced and Two - Stage Estimates : Much Greater Return s to Education in Household Profit, Labor Participation, and Hours in Nonfarm Work than in Farm Work Fi rst , I estimate d the reduced - form and two stage instrumental variable estimat es of farm and non farm household profit and labor supply functions , equatio n s ( 1 .4) and ( 1 .3). All dependent variables are regressed on the same set of regressors which include household education, household composition variables, farm and nonfarm quasi - fixed assets , and input prices . H ousehold average years of education i s instr umented in the two - stage estimations . Table 1 .7 shows the result of validity tests of instrumental variables in the household profit equation. For the estimations with selection bias controlled, IMR and the residual from the reduced - form labor supply equat ion are also included as additional explanatory variables. Table 1. 7 Validity tests of i nstrumental variables in the household profit equation Own - f arming Farm - wage - labor Nonfarm self - employment Nonfarm wage - employment Endogen eity test a (H 0 : education is exogenous) Using two IVs Household profit - 0.125*(0.065) 0.0 07(0.033) - 0. 134(0.145) - 0.207**(0.094) with selection bias controlled - 0.133*(0.068) 0.030(0.030) - 0.115(0.151) - 0.203**(0.101) Using one IV H ousehold profit - 0.121*(0.065) 0.006(0.034) - 0.135(0.145) - 0.202**(0.092) with selection bias controlled - 0.131*(0.068) 0.031(0.031) - 0.117(0.152) - 0.197**(0.099) Overidentifying restriction test b (H 0 : IVs are jointly valid) Using two IVs Household profit 0.06 1.14 0.82 2.94* with selection bias controlled 0.01 1.26 1.13 2.16 Notes: Household profit estimation used correlated random effect s model. Clustered s tandard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. a The test result shows the significance of coefficient of the residual from reduced form education equation . b The test result shows Sargan - Hansen statistics from two stage least square estimation. 33 Similar to the result of the tests in the hou sehold hourly profit (wage) estimation, the coefficient is statistically significant in own - farming and nonfarm wage - employment. The null hypothesis of exogeneity of education is rejected in farm - wage - l abor and nonfarm self - employment, which shows that the re is no clear evidence that education is exogenously determined in the household profit function. The result of the overidentifying restriction test shows that instrumental variables are jointly valid in the household profit equation from any activity wit h selection bias controlled by IMR and residual from the reduced - from labor supply equation. Table 1. 8 The effect of education on the household profit reduced - form and two - st age estimates (correlated random effects) Dependent va riable Education not instrumented Education instrumented, 2SLS Household profit ( USD /week) Estimate Standard error Estimate Standard error Own - f arming 0.040* (0.022) 0.297 (0.216) with selection bias controlled 0.043* (0.024) 0.265 (0.310) Farm - w age - labor - 0.022 (0.019) 0.153 (0.105) with selection bias controlled - 0.018 (0.016) 0.019 (0.072) Nonfarm self - employment 0.132*** (0.048) 0.756* (0.404) with selection bias controlled 0.127** (0.052) 0.708 (0.433) Nonfarm wage - employment 0.20 0*** (0.068) 1.111*** (0.404) with selection bias controlled 0.218** (0.094) 1.121** (0.442) Notes: The full set of parameter estimates are presented in Table 1 . A.3 and Table 1.A.4. Household weekly profit is computed based on the gross income from t he activities and the cost of self - employed activities in a year. All estimations used the correlated ran dom effect s model. The 2SLS estimations used two instrumental variables : person - year exposure to free primary education and average distance to the nea rest market in the district of birth in 1995. Clustered standard errors are in parentheses. *** p<0.01, * * p<0.05, * p<0.1. Table 1.8 presents a summary of the reduced - form and two stage results by listing the impact of education on household p rofit from own - farming, farm - wage - labor , nonfarm self - employment , and nonfarm wage - employment, respectively. The full set of parameter estimates are presented in Table 1.A.3 and Table 1 .A.4 in the Appendix . The results show that the two - stage estimates hav e higher values than the reduced - form estimates in all estimations . 34 The estimates of both estimations are common in that nonfarm work has a much higher return to education than does farm work. The two - stage estimates show that an additional year o f the household average years of education increases profit from nonfarm self - employment and n onfarm wage - employment by 0.7 1 and 1.1 2 USD per week respectively , which are both greater than the return to education in farming activities . Table 1. 9 The effect of education on household labor supply reduced - form and two - stage estimates Dependent variable Education not instrumented Education instrumented, two stage Estimate Standard error Estimate Standard error Participation, poo led probit Own - farming 0.002 (0.002) 0.002 (0.002) Farm - wage - labor - 0.007*** (0.002) - 0.006*** (0.002) Nonfarm self - employment 0.006*** (0.002) 0.006*** (0.002) Nonfarm wage - employment 0.011*** (0.002) 0.012*** (0.002) Hours, lognormal CRE Own - f arming 0.005 (0.005) 0.014** (0.006) with selection bias controlled 0.004 (0.005) 0.009 (0.006) Farm - wage - labor 0.011 (0.016) 0.021 (0.020) with selection bias controlled - 0.001 (0.017) 0.018 (0.020) Nonfarm self - employment 0.044*** (0 .011) 0.056*** (0.013) with selection bias controlled 0.041*** (0.011) 0.054*** (0.013) Nonfarm wage - employment 0.073*** (0.011) 0.092*** (0.014) with selection bias controlled 0.060*** (0.012) 0.087*** (0.014) Notes: The full set of parameter estimates are presented in Table 1 . A.5, Table 1.A.6, and Table 1.A.7 . The result of pooled probit shows the average partial effect of schooling on the probability of participating in each activity. The instrumental variable estim ations used an instrumental variable ; person - year exposure to free primary education . Clustered standard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. Table 1 .9 presents the impact of education on household labor participation and hours worked by the reduced - form and two stage estimations in own - farming, farm - wage - labor , nonfarm self - employment , and nonfarm wage - employment respectively. The full set of parameter estimates are presented in Table 1 .A.5, 1 .A.6, and 1 .A.7 in the Appendix . Both reduced - form and two - stage results show that higher levels of schooling are associated with a higher level of household labor participat ion and hours of labor suppl ied in non farm activities. Two - stage estimates show that an additional year of household average years of educa tion 35 statistically significantly increases the probability of participating in nonfarm self - employment and nonfarm w age - employment by 0.6 percent and 1.2 percent respectively at the one percent confidence level. The estimates evaluated at mean household ho urs worked also show that an additional year of household average years of education statistically significantly inc reases the hours worked in nonfarm self - employment and nonfarm wage - employment by 2.23 and 3.74 (hour/week) respectively at the one percent confidence level. The results of reduced form and two - stage estimates are similar in that increased levels of educat ion increase nonfarm profit by a much greater amount than farm profit, and that the additional years of household education increase both th e probability of participation and hours of work in nonfarm activities relative to farming, corresponding to the res ults from Jolliffe (2004) . However, from the reduced - form or two stage results, it is not clear whether the large increases in nonfarm profit are due to more labor supply to those activities, or whether education improves the profitability of these activities. 1 . 5 . B Join t Estimates : Education Does Not Significantly Increase Household Hourly Return s in Either Rural Nonfarm Activities o r Farming Table 1 . 10 presents the full set of parameter estimates of household hourly profit (wage) with and without IMR s and residuals fro m labor supply estimations . The coefficients of the residual from the 2 nd stage labor supply e stimation are statistically significant in all activities at the one percent confidence level. It suggests that the selection bias of the participants of each act ivity exists , and it is controlled for by adding the residuals as an addi tional explanatory variable. The coefficient of IMR is statistically significant at the one percent confidence level in own - farming but not statistically significantly different from zero for all other activities. This is not due to the high correlations b etween the residual and IMR. The correlation s of the residual and IMR are 36 Table 1. 10 Household hourly profit (wage) joint estimates Dependent variable: Hou sehold hourly profit or wage ( USD / hour ) Own - f arming Own - f arming Farm - wage - labor Farm - wage - labor Nonfarm self - employment Nonfarm self - employment Nonfarm wage - employment Nonfarm wage - employment Explanatory variables CRE 2SLS CRE 2SLS CRE 2SLS CRE 2SLS CRE 2SLS C RE 2SLS CRE 2SLS CRE 2SLS Inverse mills ratio from 1 st stage labor - 0.151*** 0.033 - 0.043 - 0.085 equation (0.046) (0.102) (0.055) (0.104) Residuals from 2 nd stage labor equation - 0.302*** - 0.189*** - 0.287*** - 0.297*** (0.018) (0.030) (0.0 32) (0.046) Household education Average education (year s ) 0.002 - 0.019 - 0.126 - 0.104 0.070 0.069 0.080 0.067 (0.042) (0.041) (0.088) (0.073) (0.057) (0.055) (0.055) (0.056) Household member composition A verage a ge 0.002 0.001 - 0.019* * - 0.016** 0.001 0.001 0.007 0.007 (0.003) (0.003) (0.008) (0.007) (0.005) (0.005) (0.006) (0.005) Share of female workers - 0.083 - 0.107 0.006 0.036 - 0.024 - 0.039 - 0.007 - 0.003 (0.093) (0.089) (0.195) (0.170) (0.165) (0.164) (0.130) (0.110) Share of married workers - 0.021 - 0.026 0.252** 0.260** 0.009 - 0.004 0.196 0.204* (0.069) (0.066) (0.127) (0.118) (0.141) (0.140) (0.120) (0.105) Number of children aged 0 - 6 0.009 0.006 - 0.013 - 0.013 0.006 0.007 0.026 0.024 (0.010) (0.009) (0.024) (0.022) (0.0 23) (0.021) (0.023) (0.021) Number of children aged 7 - 12 - 0.013 - 0.015 0.052** 0.052** 0.045** 0.047** 0.026 0.029 (0.010) (0.010) (0.026) (0.026) (0.023) (0.021) (0.025) (0.021) Farming variables Land holdings (acres) 0.003** 0.003** - 0.004 - 0.003 0.003 0.003 0.004 0.004 (0.001) (0.001) (0.003) (0.003) (0.002) (0.002) (0.003) (0.003) Experience in own - farming (year s ) - 0.005* - 0.011*** 0.010 0.009 0.015** 0.014** 0.002 0.003 (0.003) (0.003) (0.007) (0.007) (0.006) (0.006) (0.007) (0.006) Square of experience in own - farmin g (year s ) 0.000 0.000** - 0.000 - 0.000 - 0.000 - 0.000 0.000 - 0.000 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Experience in farm - wage - labor (year s ) - 0.001 - 0.003 - 0.018* - 0.013 - 0.012 - 0.011 - 0.006 - 0 .010 (0.006) (0.006) (0.011) (0.018) (0.016) (0.016) (0.027) (0.027) Square of experience in farm - wage - labor 0.000 0.000 0.000* 0.000 0.000 0.000 0.001 0.001 (years) (0.000) (0.000) (0.000) (0.000) (0.001) (0.001) (0.001) (0.002) Value of farm asset (100 USD ) 0.055*** 0.057*** - 0.007 - 0.006 0.013 0.014 0.013 0.013 (0.016) (0.017) (0.019) (0.019) (0.022) (0.023) (0.023) (0.019) 37 T able 1 . 10 (c ) Farm ing prices Consumer Price Index of farm products - 0.002 - 0.002 0.001 0.001 - 0.002 - 0.003 0.008 0.008 (0.002) (0.002) (0.004) (0.004) (0.004) (0.004) (0.006) (0.005) Land rental rate (USD/acre/year) 0.002 0.003 0.015 0.013 0.005 0.006 - 0.000 - 0.007 (0.007) (0.007) (0.012) (0.011) (0.012) (0.011) (0.014) (0.013) Regional average farming ne t return 0.509*** 0.503*** 0.147 0.168 - 0.214 - 0.188 - 0.373 - 0.386 (USD/hour) (0.091) (0.086) (0.247) (0.226) (0.190) (0.183) (0.292) (0.264) Regional average farming wage (USD/hour) - 0.018 - 0.020 0.516** 0.529*** - 0.112 - 0.102 0.131 0.143 (0.070) (0. 065) (0.207) (0.194) (0.160) (0.154) (0.230) (0.207) Non farm variables Experience in nonfarm self - employment 0.006 0.009* 0.027** 0.026** 0.008 0.003 0.023 0.028* (year s ) (0.005) (0.005) (0.013) (0.013) (0.008) (0.010) (0.017) (0.015) Square o f experience in nonfarm self - 0.000 - 0.000 - 0.001 - 0.001 - 0.000 - 0.000 - 0.001 - 0.001 employment (year s ) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.001) (0.001) Experience in nonfarm wage - 0.009 0.019 0.020 0.015 - 0.037* - 0.036 0.024* 0.008 empl oyment (year s ) (0.015) (0.014) (0.026) (0.022) (0.022) (0.022) (0.015) (0.023) Square of experience in nonfarm wage - 0.000 - 0.000 - 0.001 - 0.001 0.001 0.001 - 0.001 - 0.000 employment (year s ) (0.000) (0.000) (0.001) (0.001) (0.001) (0.001) (0.000) (0.001) Nonlabor income (100 USD /year) 0.010* 0.010* - 0.032** - 0.030** 0.010*** 0.010*** 0.008*** 0.008*** (0.005) (0.006) (0.016) (0.014) (0.003) (0.003) (0.001) (0.002) Distance to nearest transport (km) - 0.002 - 0.002 0.011 0.010 - 0.002 - 0.002 0.004 0.006 ( 0.002) (0.002) (0.007) (0.007) (0.004) (0.004) (0.004) (0.004) Non farm prices Regional average nonfarm net return - 0.036 - 0.030 - 0.032 - 0.039 0.566*** 0.540*** - 0.093 - 0.087 (USD/hour) (0.040) (0.036) (0.084) (0.078) (0.105) (0.101) (0.129) (0. 118) Regional average nonfarm wage (USD/hour) 0.143 0.164* 0.130 0.178 0.271 0.300 0.424 0.426* (0.090) (0.084) (0.264) (0.245) (0.204) (0.195) (0.259) (0.248) Observations (household - year pairs) 3,981 3,981 765 765 1,546 1,546 907 907 Numbe r of households 1,802 1,802 573 573 954 954 645 645 R - squared 0.163 0.250 0.180 0.266 0.165 0.254 0.205 0.352 Notes: The value of profit from self - employment activities is censored at zero. T ime dummies, district dummies, time means of all time - variant e xplanatory variables are included in all estimations but not reported. USD used in the table is 2011 PPP USD . Clustered s tandard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. 38 0.004, 0.047, - 0.014, - 0.004 in own - farming, farm - wage - labor , nonf arm self - employment , and nonfarm wage - employmen t respectively. The coefficients of the value of farm asset s in own - farming and nonlabor income in nonfarm self - employment show that those variables satisfy the inclusion restriction to instrument shadow wage s . The result shows that the coefficients are al l statistically significant at the one percent confidence level, and the value of farm asset and nonlabor income meet the inclusion restrictions. The exclusion restriction of the instrumental variable is teste d by regressing the household labor supply on the fitted value of shadow wage, fitted value of education, instrumental variable of shadow wage, and all other exogenous variables. Table 1 . 11 shows the estimation result. The coefficient of the value of farm asset is not statistically si gnificant in both the 1 st stage and the 2 nd stage labor supply estimations of own - farming. Also, the coefficient of nonlabor income is not statistically significant in both the 1 st and 2 nd stage of labor supply estimations of n onfarm self - employment . The r esults verify that the value of farm assets and nonlabor income explains labor supply only through shadow wages. Test results show the robustness to use value of farm assets and nonlabor income as instrumental variable of shado w wage of own - farming and non farm self - employment respectively. Table 1.13 shows the estimation results of the effect of education on household hourly profit (wage) and labor supply. The table is made based on the result of estimations in Table 1. 10 and Table 1.12. The hourly profit (wage) functions were estim ated by CRE 2SLS using two instrumental variables: person - year exposure to free primary education and average distance to the nearest market in the district of birth in 1995. The fitted value of education in both 1 st stage and 2 nd stage labor supply are es timated by CRE using one instrumental variable: person - year exposure to free primary education. Although the average estimates show the negative effects of 39 Table 1. 11 Test of instrumental variables in household self - employment labor supply Dependent variable: Supply labor = 1 or Hours of labor supply (hours/week) Own - f arming Nonfarm self - employment Own - f arming Own - f arming Nonfarm self - employment Nonfarm self - empl oym ent Explanatory variables Pooled probit Pooled probit Pooled lognormal CRE lognormal Pooled lognormal CRE lognormal Fitted value of log of hourly profit ( USD /hour) - 0.039 0.090 1.377** 1.238* 0.299 0.177 (0.203) (0.080) (0.674) (0.677) (0.344) (0.3 40) Household education Fitted value of education (year s ) 0.001 - 0.001 0.043*** 0.041*** 0.033 0.043 (0.005) (0.007) (0.016) (0.016) (0.028) (0.028) Household member composition A verage a ge - 0.001 - 0.002* - 0.006*** - 0.006*** 0.001 - 0.003 (0.001) (0.001) (0.002) (0.002) (0.004) (0.004) Share of female workers 0.000 0.031 - 0.221** - 0.192* 0.019 0.073 (0.031) (0.028) (0.109) (0.109) (0.136) (0.137) Share of married workers 0.063*** 0.086*** 0.261*** 0.265*** 0.355** 0.299** (0.023) ( 0.028) (0.081) (0.082) (0.150) (0.148) Number of children age d 0 - 6 0.008** 0.006 0.041*** 0.040*** 0.030 0.029 (0.004) (0.005) (0.012) (0.013) (0.025) (0.025) Number of children age d 7 - 12 0.005 0.007 0.066*** 0.063*** 0.001 - 0.008 (0.005) (0.006) (0. 015) (0.016) (0.029) (0.029) Farming variables Land holding s (acre s ) 0.001 - 0.001 - 0.007*** - 0.006*** - 0.006* - 0.004 (0.001) (0.001) (0.002) (0.002) (0.003) (0.003) Experience in own - farming (year s ) 0.019*** - 0.007*** 0.060*** 0.055*** - 0.054*** - 0.048*** (0.002) (0.002) (0.008) (0.008) (0.008) (0.008) Square of experience in own - farming (year s ) - 0.000*** 0.000** - 0.001*** - 0.001*** 0.001*** 0.001*** (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Experience in farm - wage - labor (year s ) 0.000 - 0.012*** - 0.010 - 0.009 - 0.012 - 0.012 (0.002) (0.002) (0.007) (0.006) (0.021) (0.021) Square of experience in farm - wage - labor (year s ) - 0.000 0.000*** - 0.000 - 0.000 0.000 0.000 (0.000) (0.000) (0.000) (0.000) (0.001) (0.001) Value of farm asset (100 USD ) 0.005 0.006 - 0.038 - 0.026 0.043* 0.041 (0.012) (0.004) (0.041) (0.041) (0.026) (0.030) Farm ing prices Consumer Price Index of farm products - 0.001 - 0.002 0.011*** 0.010*** 0.000 - 0.000 (0.001) (0.001) (0.003) (0.003) (0.005) (0.005) 40 T able 1 . 11 (c ) Land rental rate ( USD /acre/year) 0.003 - 0.002 - 0.007 - 0.006 - 0.007 - 0.010 (0.003) (0.003) (0.008) (0.008) (0.017) (0.017) Regional average farming net return ( USD /hour) 0.023 0.007 - 1.003*** - 0.915*** 0.089 0.043 (0.107) (0.046) (0.350 ) (0.352) (0.211) (0.208) Regional average farming wage ( USD /hour) - 0.039 - 0.071* 0.161* 0.140* 0.107 0.104 (0.030) (0.038) (0.083) (0.083) (0.190) (0.191) Non farm variables Experience in nonfarm self - employment (year s ) - 0.006*** 0.075*** - 0.030 *** - 0.028*** 0.036*** 0.036*** (0.002) (0.003) (0.008) (0.008) (0.010) (0.010) Square of experience in nonfarm self - employment 0.000** - 0.002*** 0.000 0.000 - 0.001** - 0.001** (year s ) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Experience in nonf arm wage - employment (year s ) - 0.007 - 0.007 - 0.080*** - 0.073*** - 0.053** - 0.056** (0.005) (0.004) (0.016) (0.016) (0.027) (0.028) Square of experience in nonfarm wage - employment 0.000 0.000 0.001*** 0.001** 0.001 0.001 (year s ) (0.000) (0.000) (0.000) (0 .000) (0.001) (0.002) Nonlabor income (100 USD /year) - 0.000 - 0.002 - 0.014 - 0.012 0.003 0.004 (0.002) (0.002) (0.008) (0.009) (0.006) (0.006) Distance to nearest transport (km) - 0.001 - 0.001 0.003 0.002 - 0.004 - 0.005 (0.001) (0.001) (0.003) (0.003) (0 .005) (0.005) Non farm prices Regional average nonfarm net return ( USD /hour) - 0.018 - 0.017 - 0.030 - 0.025 - 0.327 - 0.271 (0.017) (0.048) (0.050) (0.050) (0.212) (0.213) Regional average nonfarm wage ( USD /hour) - 0.054 - 0.004 - 0.312** - 0.279* - 0.212 - 0.195 (0.054) (0.053) (0.156) (0.156) (0.248) (0.250) Observations (household - year pairs) 4,677 4,742 4,065 4,065 1,582 1,582 Number of households 1,981 2,006 1,852 1,852 962 962 Pseudo R - squared 0.350 0.413 - 0.210 - 0.286 Log pseudolikelih ood - 1270 - 1773 - 4591 - - 2151 - Notes: The estimate of pooled probit shows the average partial effect of education on the probability of participating in each activ ity. Time dummies, district dummies, and time means of all time - variant explanatory variabl es are included in all estimations but n ot reported. USD used in the table is 2011 PPP USD . Clustered s tandard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. 41 Table 1. 12 Household participation and hours of labor sup ply joint estimates Dependent variable: Supply hours of labor = 1 or log of hours Own - f arming Farm - wage - labor Nonfarm self - employment Nonfarm wage - employment Own - f arming Farm - wage - labor Nonfarm self - employment Nonfarm wage - employment Explanatory variables Pooled probit Pooled probit Pooled probit Pooled probit CRE lognormal CRE lognormal CRE lognormal CRE lognormal Fitted value of log of hourly return 0.034 0.142*** 0.116* 0.184*** 0.830*** 0.336 0.273 0.622* (USD/hour) (0.091) (0.044) (0.067) (0.066) ( 0.253) (0.364) (0.241) (0.335) Household schooling Fitted value of schooling (years) 0.003 0.010* - 0.002 - 0.002 0.032*** 0.060 0.036 0.046 (0.003) (0.005) (0.006) (0.005) (0.008) (0.048) (0.023) (0.029) Household composition A verage a ge - 0.001* 0.002* - 0.002* - 0.001 - 0.006*** 0.019** - 0.003 - 0.008 (0.001) (0.001) (0.001) (0.001) (0.002) (0.009) (0.004) (0.006) Share of female workers 0.008 - 0.069*** 0.032 - 0.049** - 0.235*** - 0.653*** 0.078 0.169 (0.024) (0.023) (0.029) (0.023) (0. 086) (0.175) (0.137) (0.180) Share of married workers 0.065*** - 0.079*** 0.082*** - 0.060** 0.256*** - 0.455** 0.303** - 0.027 (0.023) (0.026) (0.028) (0.027) (0.081) (0.202) (0.148) (0.191) Number of children aged 0 - 6 0.008* 0.001 0.006 - 0.003 0.043*** 0.086** 0.028 - 0.066* (0.004) (0.004) (0.005) (0.004) (0.012) (0.035) (0.025) (0.036) Number of children aged 7 - 12 0.006 - 0.007 0.006 - 0.009** 0.057*** - 0.004 - 0.013 - 0.013 (0.004) (0.005) (0.006) (0.005) (0.012) (0.041) (0.027) (0.037) Farming varia bles Land holdings (acres) 0.001 0.001 - 0.001 - 0.001 - 0.005*** - 0.003 - 0.004* - 0.012*** (0.001) (0.001) (0.001) (0.001) (0.001) (0.003) (0.002) (0.004) Experience in own - farming (years) 0.020*** - 0.003** - 0.007*** - 0.002* 0.050*** - 0.057*** - 0. 050*** - 0.029*** (0.001) (0.001) (0.002) (0.001) (0.005) (0.009) (0.007) (0.008) Square of experience in own - farming (years) - 0.000*** 0.000 0.000** - 0.000 - 0.001*** 0.001*** 0.001*** 0.000 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.00 0) Experience in farm - wage - labor (years) 0.000 0.049*** - 0.011*** 0.009*** - 0.011* 0.058*** - 0.011 - 0.003 (0.002) (0.003) (0.002) (0.004) (0.006) (0.013) (0.021) (0.034) Square of experience in farm - wage - labor - 0.000 - 0.001*** 0.000*** - 0.001*** - 0.00 0 - 0.001*** 0.000 - 0.002 (years) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.001) (0.003) Value of farm asset (100 USD ) - 0.007* 0.006 - 0.005 - 0.054* 0.040 - 0.042 - (0.004) (0.004) (0.004) - (0.030) (0.030) (0.037) 42 T able 1. 12 (c ) Farming prices Consumer Price Index of farm products - 0.001 - 0.002*** - 0.001 - 0.003*** 0.009*** - 0.009 - 0.000 - 0.004 (0.001) (0.001) (0.001) (0.001) (0.002) (0.006) (0.005) (0.006) Land rental rate (USD/acre/year) 0.003 - 0.002 - 0.0 03 0.004 - 0.005 - 0.021 - 0.011 0.028 (0.003) (0.003) (0.003) (0.003) (0.007) (0.021) (0.017) (0.018) Regional average farming return - 0.014 0.006 0.010 0.025 - 0.710*** - 0.439 0.064 0.271 (USD/hour) (0.059) (0.030) (0.045) (0.042) (0.152) (0.361) (0.204 ) (0.307) Regional average farming wage - 0.038 - 0.104** - 0.067* - 0.059* 0.131 - 0.397 0.113 - 0.030 (USD/hour) (0.030) (0.041) (0.038) (0.033) (0.081) (0.356) (0.189) (0.241) Off - farm variables Experience in nonfarm self - employment - 0.007*** - 0 .012*** 0.075*** - 0.012*** - 0.024*** - 0.010 0.036*** - 0.019 (years) (0.002) (0.003) (0.003) (0.003) (0.006) (0.019) (0.010) (0.022) Square of experience in nonfarm self - 0.000** 0.000** - 0.002*** 0.000*** 0.000 - 0.000 - 0.001** 0.000 employment (years) ( 0.000) (0.000) (0.000) (0.000) (0.000) (0.001) (0.000) (0.001) Experience in nonfarm wage - employment - 0.009*** - 0.008** - 0.006 0.075*** - 0.065*** - 0.043 - 0.053** 0.056*** (years) (0.003) (0.003) (0.004) (0.003) (0.010) (0.028) (0.026) (0.015) Square of experience in nonfarm wage - 0.000 0.000 - 0.000 - 0.002*** 0.001** 0.002** 0.001 - 0.002*** employment (years) (0.000) (0.000) (0.000) (0.000) (0.000) (0.001) (0.002) (0.001) Nonlabor income (100 USD /year) - 0.001 0.006*** - - 0.002** - 0.008 0.066*** - - 0.00 7* (0.001) (0.002) - (0.001) (0.006) (0.020) - (0.004) Distance to nearest transport (km) - 0.000 - 0.002*** - 0.001 - 0.001 0.002 0.001 - 0.005 - 0.003 (0.001) (0.001) (0.001) (0.001) (0.002) (0.012) (0.004) (0.007) Off - farm prices Regional avera ge nonfarm return - 0.016 0.011 - 0.032 - 0.024 - 0.037 - 0.056 - 0.322* 0.163 (USD/hour) (0.016) (0.017) (0.041) (0.019) (0.045) (0.137) (0.167) (0.137) Regional average nonfarm wage - 0.066 0.031 - 0.012 - 0.117** - 0.212* - 0.550 - 0.226 - 0.499 (USD/hour) (0.0 43) (0.043) (0.051) (0.052) (0.118) (0.377) (0.240) (0.329) Observations (household - year pairs) 4,677 4,699 4,742 4,725 4,065 891 1,582 1,038 Number of households 1,981 1,976 2,006 1,999 1,852 649 962 703 Log pseudolikelihood - 1270 - 1349 - 1776 - 1409 - - - - (Pseudo) R - squared 0.350 0.409 0.412 0.433 0.210 0.410 0.286 0.336 Notes: The estimate of pooled probit shows the average partial effect of education on the probability of participating in each activ ity. Time dummies, district dummies, and time means of all time - variant explanatory variables are included in all estimations but n ot reported. USD used in the table is 2011 PPP USD . Clustered s tandard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. 43 Table 1. 13 The effect of education on household hourly returns and labor supply joint estimates Dependent variable Average years of education Hourly profit or wage Estimate Standard error Estimate Standard error Hourly profit or wage, CRE 2SLS ( ) Own - farming - 0.019 (0.041) - - Farm - wage - labor - 0.104 (0.073) - - Nonfarm self - employment 0.069 (0.055) - - Nonfarm wage - employment 0.067 (0.056) - - Participation, pooled probit ( ) ( ) Own - farming 0.003 (0.003) 0.034 (0.091) Farm - wage - lab or 0.010* (0.005) 0.142*** (0.044) Nonfarm self - employment - 0.002 (0.006) 0.116* (0.067) Nonfarm wage - employment - 0.002 (0.005) 0.184*** (0.066) Hours, CRE lognormal ( ) ( ) Own - farming 0.032*** (0.008) 0.830*** (0.253) Farm - wage - labor 0.060 (0.048) 0.336 (0.364) Nonfarm self - employment 0.036 (0.023) 0.273 (0.241) Nonfarm wage - employment 0.046 (0.029) 0.622* (0.335) Notes: The full set of parameter estimates are presented in Table 1 . 10 and Table 1.12 . The pooled probit shows the average partial effect of education on the probability of participating in each activity. The 2SLS estimations used two instrumental variable s: per son - year exposure to free primary education and average distance to the nearest market in district of birth in 1995 . Fitted value of education in labor supply equations used one instrumental variable: person - year exposure to free primary education. Cluster ed standard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. education in farming and positive effects o f education in nonfarm activities, the estimates are not statistically significantly different from zero at the ten percent confidence level in any activity. In Table 1 . 1 4 , the effect of an additional year of education on household labor supply is calculated from the results in Table 1 .1 3 . By estimating the structural model of labor supply that includes profitability , it is possible to obtain a measure of the direct effect that education has on labor supply and the indirect effect that education ha s on labor supply through the education - induced profitability effect . By the equations ( 1 .12) and ( 1 .14), the effect of educ ation on household labor supply is divided into the direct effect of education and the indirect effect of education through the shad ow wag e. The effect of education on household hours of labor supply is written as: 44 ( 1 . 16 ) where is mean household hours worked . The mean household hours worked show 37. 7 , 19.1, 41. 3 , and 43.0 (hour s /week) in own - farming, farm - wage - labor, nonfarm self - employment, and nonfarm wage - employment respectively. Table 1. 14 y Effect of average years of education Direct effect Indirect effect Total effect Participation probability ( ) ( ) ( ) Own - farming 0.003 - 0.000 0.003 Farm - wage - labor 0.010 - 0.015 - 0.005 Nonfarm self - employment - 0.002 0.008 0.006 Nonfarm wage - employment - 0.002 0.012 0.010 Hours per week ( ) ( ) ( ) Own - farming 1.206 - 0.594 0. 612 Farm - wage - labor 1.149 - 0.669 0.480 Nonfarm self - employment 1.486 0.778 2.264 Nonfarm wage - employment 1.979 1.793 3.772 Notes: Results in this table are calculated from the results in Table 1.13, using equation (1.16) evaluated at mean household hou rs worked of estimation samples. Overall, education has a greater effect and a positive effect on participation and hours worked in nonfarm activities than in farming, which corresponds to the results by reduced form and two - stage estimates. Th e estimated positive effect of educa tion on participation in nonfarm activities is on average mostly from the indirect effect of education through the education - induced profitability effect. For the hours of household labor supply, education has a positive total effect on all activities, wit h a much larger effect on nonfarm activities. The direct effect of education on hours of labor supply is also larger than the indirect effect of education via profitability changes. The estimated total effects of educati on are larger than reduced form or t wo stage estimates. However, because the effect of education on the profitability of the activity is not statistically significant in any activity, the hypothesis that the level of education, 45 profitability of an activity , and time allocation to that activi ty can be not positively correlated, and that it positively increases total household profit from the activity, cannot be rejected by the estimations. There is a case that the labor shift is induced only by the direct ef fect of education on the labor alloc ation with no indirect profitability effect . 1 .5.C Intra - H ousehold Decision on Labor Allocation; Negative Correlation between Hourly Return and Labor Supply in Nonfarm Activities Throughout this chapter , the estimati on results have been presented at th e household and not the individual level. As illustrated in section 1.2.B and 1.2.C, however, the education qualification plays a role in determining labor allocation, and there we found negative correlations between hou rly profit (wage) and labor supply a t an individual level. Hence, I redo the estimations at individual level to explore whether there is any evidence to support the hypothesis that, within households, the years of education or education qualification, prof itability of each activity, and labo r allocation are not positively correlated . First, I test the validity of instrumental variables of education at individual level. I use years of education, a binary variable of completing primary school, and a binary variable of completing second ary school as the measures of education. The instrumental variable is the same as in the estimations at household level, household person - years exposure to free primary school education, because the individual education attainment is determined to maximize the returns given the household budget constraint, which is a function of household members composition. Table 1.15 presents the result of reduced form education estimations. Estimation results show that the co efficients of person - years e xposure to free primary school education are statistically significant at the one percent confidence level in all estimations. Although the coefficient of distance to the nearest market in the district of birth in 1995 is not st atistically 46 Table 1. 15 Individual schooling reduced form estimates (correlated random effects) Years of education Complete d primary=1 Complete d secondary=1 Instrumental variables Person - y ear under free primary school 0.0 26*** (0.008) 0.003*** (0.001) 0.003*** (0.001) D istance to nearest market in district - 0.018* (0.011) - 0.004** (0.002) - 0.001 (0.001) o f birth in 1995 (km) - statistic a 13.47*** 12.43*** 17.61*** (H 0 : IVs violate inclusion restriction) Number of observations 8,599 8,600 8,600 Number of individuals 4,433 4,433 4,433 R - squared 0.299 0.187 0.143 Notes: In all estimations, all other exogenous variables in the hourly profit equation are included as explanatory variables but not reported i n the table. All estimations used the correlated random effect s model. Clustered s tandard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. a - statistic s show the joint significance of all IVs in the reduced form education eq uation. significant in the regression of completing secondary school dummies, the - statistic shows that the combination of two instrumental variables are joint ly significant at the one percent confidence level in all estimations. Table 1 .16 shows the result of endogeneity and overidentifying restriction tests in individual hourly profit (wage) and labor supply estimations . The result shows that the null hypothesis that education is exogenous is rejected in at least one estimation f or both years of education and binary variables of completing primary school and completing secondary school. The results of overidentification tests do not reject the null hyp othesis of joint validity of instrumental variables in more than half of the est imations of individual hourly profit (wage), labor participation, and hours of labor allocation. Hence, I use two instrumental variables, household person - years exposure to fre e primary education and distance to the nearest market in the district of birth in 1995, to instrument both the individual years of education and education qualification dummies. 47 Table 1. 16 Validity tests of instrumental variabl es in individual hourly profit (wage) and labor supply equations Own - f arming Farm - wage - labor Nonfarm self - employment Nonfarm wage - employment Endogeneity test a (H 0 : education is exogenous) Years of education Individual hourly profit (wage) - 0.031***(0.010) 0.002(0.032) 0.004(0.024) - 0.074***(0.022) Individual labor 1 st stage 0.11 0.62 0.56 0.04 Individual labor 2 nd stage - 0.007(0.013) - 0.017(0.045) - 0.019(0.029) - 0.007(0.028) Education qualification Complete d primary = 1 Individu al hourly profit (wage) - 0.161***(0.056) - 0.068(0.173) - 0.134(0.125) - 0.205(0.192) Individual labor 1 st stage 5.09* 0.71 1.03 0.29 Individual labor 2 nd stage - 0.012(0.071) - 0.042(0.291) 0.069(0.169) - 0.251(0.232) Complete d secondary = 1 Individual h ourly profit (wage) - 0.151(0.166) 1.191**(0.564) - 0.281(0.315) - 0.697***(0.223) Individual labor 1 st stage 5.09* 0.71 1.03 0.29 Individual labor 2 nd stage - 0.083(0.190) 0.274(0.765) - 0.513(0.327) 0.087(0.205) Overidentifying restriction test b (H 0 : IVs are jointly valid) Years of education Individual hourly profit (wage) 0.59 0.01 1.53 2.28 Individual labor 1 st stage 4.98** 0.00 0.73 0.19 Individual labor 2 nd stage 0.26 0.11 15.65*** 1.01 Notes: The result of individual hourly profit (w age) and labor 2 nd stage equations show correlated random effect s estimates . Individual labor 1 st stage estimation used pooled probit model with time means of all time - variant explanatory variables. Clustered s tandard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. a Individual hourly profit (wage) and labor 2 nd stage show the significa nce of coefficient of the residual from reduced form education equation. Individual labor 1 st stage shows chi - square statistics of Wald test of exogeneity. b Individual wage and labor 2 nd stage show Sargan - Hansen statistics from correlated random effect s two stage least square estimations. Individual labor 1 st stage shows Amemiya - Lee - Newey minimum chi - square statistics from probit two stage instrumental vari able estimations. Table 1.17 and Table 1.18 summarize the results of the joint estimates of individual hourly profit (wage), labor participation, and hours of labor supply. The full set of the estimates are reported in Table 1.A.9, Table 1.A.10 , and Table 1.A.11 in the Appendix. The result is supportive of the hypothesis that there are no positive correlations which are statistically significant between education and hourly profit (wage) or hourly profit (wage) and labor supply in any activity. 48 Table 1. 17 The effect of years of education on individual hourly profit and labor supply joint estimates Dependent variable Average years of education Hourly profit or wage Estimate Standard error Estimate Standard error Ho urly profit or wage, CRE 2SLS ( ) Own - farming 0.012 (0.057) - - Farm - wage - labor - 0.004 (0.167) - - Nonfarm self - employment 0.052 (0.050) - - Nonfarm wage - employment - 0.018 (0.042) - - Participation, pooled probit ( ) ( ) Own - farming - 0.001 (0.001) - 0.072*** (0.025) Farm - wage - labor - 0.006* (0.003) 0.127 (0.716) Nonfarm self - employment 0.007*** (0.002) - 0.048** (0.023) Nonfarm wage - employment - 0.001 (0.003) - 0.336** (0.167) Hours, lognormal CRE ( ) ( ) Own - farming - 0.007** (0.004) 0.037 (0.069) Farm - wage - labor 0.014 (0.045) 9.753 (10.054) Nonfarm self - employment 0.015 (0.010) - 0.075 (0.080) Nonfarm wage - employment 0.007 (0.028) - 2.465* (1.368) Notes: The full set of parameter estimates are presented in Table 1 . A . 9, Table 1.A.10, and Table 1.A.11 . Th e pooled probit shows the average partial effect of schooling on the probability of participating in each activity. The 2SLS estimations used two instrumen tal variable s: household person - year exposure to free primary education and distance to the nearest m arket in district of birth in 1995 . Clustered standard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. Table 1. 18 The effect of education qualification on individual hourly profit and labor supply joint estimates Ed ucation qualification Complete d primary=1 Complete d secondary=1 Hourly profit ( wage ) Hourly profit or wage, CRE 2SLS ( ) ( ) Own - farming - 0.018(0.452) 0.027(1.260) - Farm - wage - labor 0.222(5.593) - 0.029(3.479) - Nonfarm self - employment - 0.367(1.178) 2.061(2.209) - Nonfarm wage - employment - 0.233(0.555) 0.002(0.398) - Labor p articipation, pooled probit ( ) ( ) ( ) Own - farming - 0.008(0.009) - 0.030(0.020) - 0.057***(0.022) Farm - wage - labor - 0.023(0.019) - 0.066***(0.022) - 0.062(0.068) Nonfarm self - employment 0.005(0.010) 0.115***(0.045) - 0.038**(0.015) Nonfarm wage - employment 0.025(0.019) 0.034**(0.017) - 0.022(0.067 ) Labor h ours, lognormal CRE ( ) ( ) ( ) Own - farming - 0.025(0.027) - 0.163*(0.085) 0.041(0.062) Farm - wage - labor 0.003(0.286) 0.542(0.602) - 0.722(1.133) Nonfarm self - employment - 0.032(0.071) 0.391(0.249) - 0.153**(0.077) Nonfarm wage - employment 0.199(0.231) 0.317***(0.110) - 0.829(0 .799) Notes: The full set of parameter estimates are presented in Table 1 . A . 9, Table 1.A.10, and Table 1.A.11 . The pooled probit shows the average partial effect of schooling on the probability of participating in each activity. The 2SLS estimations used two instrumental variable s: household person - year exposure to free primary education and distance to the neares t market in district of birth in 1995 . Clustered standard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. 49 Similar to the res ult from the household hourly profit (wage) estimations, all 12 estimates of the effect of years of education a nd the effect of education qualification on profitability are not statistically significantly different from zero. It suggests that there is stil l a very limited demand for highly educated labor in both farming and nonfarm activities due to the limited exp ansion of the industry in which higher levels of education increase s profitability of work in rural Uganda . Because not only completing primary s chool but also completing secondary school do no t show statistically significant effect on the profitability of any activity, i t is unlikely that the deterioration of quality of education under free primary education policy due to the rapid expansion of th e capacity of primary schools explains the reason of no statistically significant effect of education on the pr ofitability. The negative correlation between hourly profit (wage) and labor supply corresponds to the Figure 1.2 and Figure 1.3, which both illustrate the negative correlation of those variables at individual level. There are two possible explana tions of the reason why profitability is not positively affecting hours. The first view is that it is because of the allocative inefficiency of l abor in rural area s . Due to geographical and social disjuncture of the labor market, individuals face the const raints of job opportunities and taking job offers. It results in a gap between the predicted hourly return based on individual, household, and lo cal characteristics and the actual hourly return expected by the individual. It could be that a person has a hi gh predicted hourly return but is not working in the sector because of constraints. However, the individual - level result is not consiste nt with the result from household estimations. There is no statistically significant evidence that profitabilit y and labor supply are negatively correlated at the household level. It implies that those who are from relatively more educated households face less constraint in the labor market, which itself presents the potential 50 endogeneity of household and individua l education attainment. From the second point of view, if a person faces severe work opportunity constraints and is earning minimum income, the p erson has minimal preference for leisure instead of income. Hence, the lower the profitability is, the more of his or her time the person is likely to allocate to the work he or she has to meet the minimum income. Given the negative correlation between hou rly profit (wage) and labor supply, the direct effect of education on labor supply entails the preference of th e individual for working in the corresponding sector. The estimates show the strong preference in working off - farm for those who complet ed secondary school. The probability of participating in nonfarm self - employment and nonfarm wage - employment for those who completed secondary school is 11.5 and 3.4 percent higher than those who have competed neither primary school nor secondary school, a nd 11.0 and 0.9 percent higher than those who have completed only primary school . They also provide 11.3 and 4.2 (hour/week) more hour s to nonfarm wage - employment compared to those who have not completed primary education and those who completed only prima ry but have not completed secondary school respectively. Table 1 .19 presents the direct effect of an additional year of education and completing primary school or secondary school on household labor supply and the indirect effect through education - induced profitability effect, which are calculated from the results in Table 1.17 and Table 1.18. The total effect of education on labor participation and hours of labor supply is negative in farming and positive in nonfarm activities in all estimations e xcept the effect of completing secondary school on the ho urs of labor allocation to farm - wage - labor. It is consistent with earlier studies in SSA finding that education has positive effects on nonfarm earnings and time allocation of rural farm households t o nonfarm activities. The positive effect of completing 51 Table 1. 19 Effect of education, individual Direct effect Indirect effect Total effect Participation probability Years of schooling ( ) ( ) ( ) Own - f arming - 0.001 - 0.001 - 0.002 Farm - wage - labor - 0.006 - 0.001 - 0.007 Nonfarm self - employment 0.007 - 0.002 0.005 Nonfarm wage - employment - 0.001 0.006 0.005 Complete d primary=1 ( ) ( ) ( ) Own - farming - 0.008 0.001 - 0.007 Farm - wage - labor - 0.023 - 0.014 - 0.037 Nonfarm self - employment 0.005 0.014 0.019 Nonfarm wage - employment 0.025 0.005 0.030 Complete d secondary=1 ( ) ( ) ( ) Own - farming - 0.030 - 0.002 - 0.032 Farm - wage - labor - 0.066 0.002 - 0.064 Nonfarm self - emp loyment 0.115 - 0.078 0.037 Nonfarm wage - employment 0.034 - 0.000 0.034 Hours per week Years of schooling ( ) ( ) ( ) Own - farming - 0.150 0.010 - 0.140 Farm - wage - labor 0.203 - 0.565 - 0.362 Nonfarm self - employment 0.485 - 0.126 0.35 9 Nonfarm wage - employment 0.249 1.580 1.829 Complete d primary=1 ( ) ( ) ( ) Own - farming - 0.537 - 0.016 - 0.553 Farm - wage - labor 0.043 - 2.319 - 2.276 Nonfarm self - employment - 1.035 1.816 0.781 Nonfarm wage - employment 7.086 6.878 13.96 4 Complete d secondary=1 ( ) ( ) ( ) Own - farming - 3.504 0.024 - 3.480 Farm - wage - labor 7.843 0.303 8.146 Nonfarm self - employment 12.644 - 10.197 2.447 Nonfarm wage - employment 11.288 - 0.059 11.229 Notes: Results in this table are calc ulated from the results in Table 1 .17 and Table 1 .18, using equation ( 1 .16) evaluated at mean household hours worked. secondary on labor supply to farm - wage - labor is because they are engaged in wage work in the agriculture sector, but not engaged in sub sistence farming. However, the total effect veils the relations between the direct effect that education has on household profit or labor supply and the indirect effect through the re - allocation of househo ld labor induced by profitability changes. For those who complete d secondary school, the total 52 positive effects of education on labor supply in nonfarm activities are mostly derived from the direct effect of education on labor supply. The indirect effect o f education through the education - induced profitability effect is positive for workers who complete d primary school . However, it is positive because of the negative correlations between profitability and labor supply. A dditional education decreases the pro fitabili ty in nonfarm sectors , and the pro fitabilit y negatively affects both the participation and hour s of labor supply in nonfarm activities. 1.6 Conclusion This chapter explore d the non - growing - productivity structural change from a microeconomic persp ective . I test the hypothesis that the lev el of education, profitability of an activity, and time allocation to that activity may not be positively correlated while education positively increases total profit from the activity . Most of the human capital literature estimate the direct and indirect effect s of education on profit and labor supply with the assumption that the shadow wage and labor supply are positively correlated, but the labor supply functions have not yet jointly estimated with the endogenously determined shadow wages. In this study, I jointly estimate the hourly profit (wage) and labor supply equations to incorporate the different channels through which education affects total profit: profitability of hour s of labor , labor allocatio n across activities , and labor re - allocation through the education - induced profitability effects. I combine multiple models to overcome the difficulties of joint estimation. First, a marginal shadow wage of own - farming and nonfarm self - employment is instrumented by the value of farm asset s and nonl abor income , respectively. Second, I exploit the variation of household person - year exposure to free primary education policy implemented by the Ugandan government and use it as an instrumental variable of education. Third, the double - censored problem of hourly 53 profit ( wage ) and labor supply function s is overcome by combin ing the Double Hurdle and the Type III structural Tobit models. The structural feature of the model allows us to decompose the effect o f education on profit into the direct effect of educ ation on profitability, labor allocation across activities, and the indirect effect on re - allocation of labor through the education - induced profitability effect. The result of all of the reduced form, two stage, joint, and intra - household estimate s could not reject the hypothesis that the level of education, profitability of an activity, and time allocation to that activity can be not positively correlated while education positively increases total household profit from the activity . All t he estima tes have in common that the t otal effect of education on labor supply shows greater and positive effect on participation and hours worked in nonfarm activities than in farming . This latter is consistent with earlier studies in SSA . The estimations using ed ucation qualificati on variables also reveal that for those who complete d secondary school, the total positive effects of education on labor supply in nonfarm activities are mostly derived from the direct effect of education on labor supply. The indirect ef fect of education t hrough the education - induced profitability effect is positive for workers who complete d only primary school. However, the estimate is positive because of the negative correlations between education, profitability , and labor supply. All of 16 esti mates from joint and intra - household estimations of the effect of education on hourly profit (wage) are not statistically significantly different from zero. Education shows no statistically significant effect on the profitability of any activity. The bigge st difference between the results from household and individual estimations is the relation between profitability and labor supply. There is no statistically significant evidence that profitability and labor supply are negatively correla ted at household le vel. However, the individual - level estimations show the 54 evidence of negative correlations. This implies that those who are from relatively more educated household s face less constraints of labor market, which itself presents the potentia l endogeneity of ho usehold and individual education attainment. Therefore, the hypothesis that there are not positive correlations which are statistically significant between education and hourly profit (wage) or hourly profit (wage) and labor sup ply in any activity cannot be rejected. And this possible negative or nonpositive relation could explain the non - growing - productivity labor shift from subsistence to non - subsistence sectors. The expansion of the industry in which higher levels of education increase the profitability of work in rural Uganda would pull labor from farming in to nonfarm activities with a positive effect of education on the profitability of labor . Relaxing the labor market constraints of individuals esp ecially from relatively les s educated households would push the hour s of labor allocation from less profitable activities towards more profitable activities. Also, b oosting the bottom line of the household income or standard of living would increase the pr eference of individuals on leisure to income, and fundamentally increase the optimal marginal productivity of labor, and consequently the profitability of labor. 55 APPENDI X 56 Table 1.A. 1 Summary statistics of variables (household) Variable Obs. Mean C.v. Min. Max. Dependent Variables Hourly profit ( USD /hour) Own - f arming 4 , 579 2.0 10.0 - 261.5 952.8 Farm - wage - labor 874 2.2 2.5 0.0 113.6 Nonfarm self - employment 1 , 720 4.3 7.8 - 177.9 925.8 Nonfarm wage - employme nt 1 , 019 3.8 4.4 0.0 368.1 Supply positive hour of labor = 1 Own - f arming 5 , 628 0.83 0.5 0.0 1.0 Farm - wage - labor 5 , 628 0.18 2.1 0.0 1.0 Nonfarm self - employment 5 , 628 0.31 1.5 0.0 1.0 Nonfarm wage - employment 5 , 628 0.21 2.0 0.0 1 .0 Labor supply (hour/week) Own - f arming 5 , 628 30.8 1.0 0.0 370.7 Farm - wage - labor 5 , 628 3.4 3.7 0.0 138.4 Nonfarm self - employment 5 , 628 12.8 2.3 0.0 375.1 Nonfarm wage - employment 5 , 628 8.8 2.9 0.0 367.7 Explanatory Variables Household schooling Average e ducation (years) 5 , 616 5.1 0.6 0.0 17.0 Household composition Age 5 , 628 38.0 0.3 20.0 65.0 Share of female workers 5 , 628 0.56 0.5 0.0 1.0 Share of married workers 5 , 628 0.70 0.6 0.0 1.0 Number of children a ge d 0 - 6 5 , 628 1.5 0.9 0.0 9.0 Number of children age d 7 - 12 5 , 628 1.3 0.9 0.0 8.0 Farming variables Land holding s (acre s ) 5 , 502 4.1 2.7 0.0 340.0 Experience in own - farm ing (years) 5 , 325 18.8 0.7 0.0 68.0 Experience in farm - wage - labor (years) 5 , 325 1.7 3.0 0.0 55.0 Value of farm asset (100 USD ) 5 , 509 0.5 2.3 0.0 19.8 Farming prices CPI of farming products 5 , 628 200.1 0.2 164.5 273.4 Land rental rate ( USD /acre/year) 5 , 628 6.5 0.4 1.8 18.9 Average profit in own - farming (ln( USD /hour)) 5 , 457 0 .4 0.6 0.0 2.8 Average wage in farm - wage - labor (ln( USD /hour)) 5 , 628 0.7 0.3 0.3 1.8 Off - farm variables Experience in non far m s elf - employment (years) 5 , 325 2.5 2.2 0.0 46.0 Experience in nonfarm wage - employment (years) 5 , 325 1.3 2.9 0.0 37.0 Nonla bor income (100 USD /year) 5 , 628 0.9 5.9 0.0 267.8 Distance to nearest transport (km) 5 , 621 3.4 1.9 0.0 180.0 Off - farm prices Average net return in nonfarm self - employment (ln( USD /hour)) 5 , 430 0.6 0.6 0.0 3.1 Aver age wage in nonfarm wage - employment (ln( USD /hour)) 5 , 628 0. 8 0.2 0.2 1.3 Instrumental variables Average d istance to nearest market in 1995 in b irth district (km) 5 , 588 6.1 0.8 1.0 24.0 Person - year s e xposure to f ree p rimary e ducation 5 , 628 1.8 1.9 0.0 40.0 Notes: Observations pooled across years. USD used in the table is 2011 PPP USD . 57 58 Table 1.A. 2 Household hourly return s and profit s of non - migrants (correlated random effects) Dependent variable: Household hourly profit or wage ( USD / hour ) or profit (US D/week) Own - f arming Farm - wage - labor Nonfarm self - employment Nonfarm wage - employment Own - f arming Farm - wage - labor Nonfarm self - employment Nonfarm wage - employment Explanatory variables Hourly profit Hourly wage Hourly profit Hourly wage Profit Profit Profit Profit Inverse mills ra tio from 1 st stage labor - 0.171*** - 0.121 0.037 - 0.158 0.058 - 0.206 0.842 - 0.206 equation (0.061) (0.120) (0.067) (0.129) (0.497) (0.227) (0.552) (0.227) Residuals from 2 nd stage labor equation - 0.296*** - 0.184*** - 0.305*** - 0.29 4*** 0.168*** 0.275*** 0 .366*** 0.275*** (0.023) (0.033) (0.039) (0.035) (0.055) (0.054) (0.128) (0.054) Household education Average education (years) 0.015*** - 0.001 0.036*** 0.047*** 0.043 0.048*** 0.089* 0.048*** (0.006) (0.012) (0.012) (0 .010) (0.030) (0.018) (0 .049) (0.018) Instrumental variables Average distance to nearest market in 0.029 0.001 0.006 - 0.040 0.016 - 0.004 - 0.192 - 0.004 district of birth in 1995 (0.020) (0.044) (0.037) (0.044) (0.110) (0.128) (0.178) (0.128) Pe rson - year s exposure to p rimary - 0.009 - 0.007 0.001 0.013 - 0.011 0.069** 0.216** 0.069** education (0.006) (0.009) (0.012) (0.013) (0.029) (0.030) (0.106) (0.030) Household member composition A verage a ge 0.002 - 0.009** - 0.007 0.007 0.007 0.018** 0.014 0.018** (0.002) (0.004) (0.004) (0.005) (0.007) (0.009) (0.016) (0.009) Share of female workers - 0.100 0.144 0.145 0.019 - 0.065 0.270 1.197** 0.270 (0.069) (0.125) (0.135) (0.141) (0.139) (0.231) (0.606) (0.231) Share of married workers - 0.07 2 0.197 0.216 0.225* 0.4 17* 0.815* 1.625** 0.815* (0.081) (0.129) (0.151) (0.135) (0.252) (0.495) (0.758) (0.495) Number of children age d 0 - 6 0.005 - 0.018 - 0.026 0.025 0.109* 0.008 - 0.093 0.008 (0.011) (0.024) (0.030) (0.030) (0.064) (0.047) (0.086) ( 0.047) Number of childr en age d 7 - 12 - 0.015 0.035 0.087*** 0.034 0.102 0.056 0.240* 0.056 (0.012) (0.029) (0.027) (0.027) (0.064) (0.039) (0.132) (0.039) Farming variables Land holding s (acre s ) 0.004** - 0.005 0.002 0.018** 0.007 0.034 - 0.003 0. 034 (0.002) (0.007) (0 .005) (0.008) (0.008) (0.032) (0.019) (0.032) Experience in own - farming (years) - 0.011*** 0.002 0.017** 0.005 0.022 - 0.029 - 0.034 - 0.029 (0.004) (0.007) (0.008) (0.009) (0.022) (0.018) (0.027) (0.018) Square of experience in own - farming 0.000** - 0.000 - 0.000 - 0.000 - 0.001 0.000 0.000 0.000 (years) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.001) (0.000) Experience in farm - wage - labor (years) 0.000 - 0.021 - 0.018 - 0.038 - 0.033** - 0.068* - 0.078 - 0.068* (0.004) (0.020) (0. 019) (0.027) (0.016) (0. 039) (0.077) (0.039) 59 Table 1 .A.2 (c ) Square of experience in farm - wage - labor 0.000 0.001 0.000 0.002 0.001* 0.003 0.003 0.003 (years) (0.000) (0.001) (0.001) (0.002) (0.001) (0.003) (0.003) (0.003) Value of farm asset (100 USD ) 0.042** - 0.021 - 0. 012 0.007 0.099* - 0.013 0.040 - 0.013 (0.017) (0.018) (0.019) (0.023) (0.051) (0.038) (0.055) (0.038) Farm ing prices Consumer Price Index of farm products - 0.003 - 0.002 - 0.002 0.004 - 0.008 - 0.007 0.007 - 0.007 (0.002) (0 .004) (0.005) (0.005) (0 .015) (0.019) (0.021) (0.019) Land rental rate ( USD /acre/year) 0.006 0.007 0.009 - 0.011 0.018 - 0.007 - 0.033 - 0.007 (0.009) (0.012) (0.014) (0.015) (0.071) (0.024) (0.039) (0.024) Regional average farming net return 0.447*** 0.6 11* 0.013 - 0.319 - 0.677 - 0.294 0.541 - 0.294 ( USD /hour) (0.103) (0.333) (0.242) (0.328) (0.668) (1.292) (1.305) (1.292) Regional average farming wage - 0.053 0.502*** - 0.171 0.163 - 0.056 0.040 1.388 0.040 (USD/hour) (0.086) (0.179) (0.250) (0.235) (0.318 ) (0.501) (1.627) (0.501 ) Non farm variables Experience in nonfarm self - employment 0.010* 0.039*** 0.011 0.010 - 0.007 0.003 0.185* 0.003 (years) (0.006) (0.014) (0.013) (0.028) (0.028) (0.038) (0.109) (0.038) Square of experience in nonfarm sel f - - 0.000 - 0.001*** - 0.0 00 0.001 0.000 0.002 - 0.004 0.002 employment (years) (0.000) (0.000) (0.000) (0.003) (0.001) (0.003) (0.003) (0.003) Experience in nonfarm wage - 0.008 - 0.015 - 0.043* - 0.017 - 0.046 - 0.013 - 0.187*** - 0.013 employment (years) (0.00 8) (0.019) (0.022) (0.03 0) (0.039) (0.052) (0.063) (0.052) Square of experience in nonfarm wage - 0.000 0.000 0.002* 0.001 0.001 0.001 0.006* 0.001 employment (years) (0.000) (0.001) (0.001) (0.001) (0.002) (0.001) (0.004) (0.001) Nonlabor income (100 US D /year) 0.001 0.040 0.04 8*** 0.014 0.004 - 0.010 0.250* - 0.010 (0.005) (0.050) (0.010) (0.011) (0.023) (0.023) (0.143) (0.023) Distance to nearest transport (km) - 0.005* 0.015 - 0.002 - 0.000 - 0.009 0.005 0.008 0.005 (0.003) (0.010) (0.006) (0.007) (0.01 4) (0.013) (0.026) (0.01 3) Non farm prices Regional average nonfarm net return - 0.059 - 0.094 0.537*** - 0.136 - 0.333 - 0.559 1.162* - 0.559 ( USD /hour) (0.048) (0.092) (0.125) (0.123) (0.293) (0.555) (0.701) (0.555) Regional average nonfarm wage 0 .168 0.177 0.290 0.191 - 0.039 0.740 - 1.045 0.740 (USD/hour) (0.117) (0.265) (0.303) (0.322) (0.584) (0.940) (1.402) (0.940) Observations (household - year pairs) 2,496 487 883 512 2,365 508 840 508 Number of households 1,275 386 596 379 1,225 37 6 566 376 R - squared 0.2 89 0.362 0.331 0.432 0.0431 0.293 0.248 0.293 Notes: The value of profit from self - employment activities is censored at zero. T ime dummies, district dummies, time means of all time - variant explanatory variables are included in all estimations but not repo rted. USD used in the table is 2011 PPP USD . Clustered s tandard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. 60 Table 1.A. 3 Household profit (correlated random effects) Dependent variable: H ousehold profit from the activity ( USD /week) Own - f arming Own - f arming Farm - wage - labor Farm - wage - labor Nonfarm self - employment Nonfarm self - employment Nonfarm wage - employment Nonfarm wage - employment Explanatory variables CRE CRE CRE CRE CRE CRE CRE CRE Inv erse mills ratio from 1 s t stage labor - 0.048 - 0.311* - 0.450 0.734 equation (0.719) (0.168) (0.633) (1.229) Residuals from 2 nd stage labor equation 0.247*** 0.228*** 0.376*** 0.478*** (0.076) (0.046) (0.127) (0.102) Household education Average educat ion (years) 0.040* 0.043* - 0.022 - 0.018 0.132*** 0.127** 0.200*** 0.218** (0.022) (0.024) (0.019) (0.016) (0.048) (0.052) (0.068) (0.094) Household member composition A verage a ge - 0.002 - 0.001 0.010 0.010 - 0.016 - 0.012 0 .020* 0.016 (0.012) (0 .012) (0.013) (0.013) (0.014) (0.015) (0.011) (0.010) Share of female workers - 0.159 - 0.163 - 0.014 0.061 0.154 0.080 - 0.130 - 0.276 (0.233) (0.250) (0.102) (0.100) (0.992) (1.067) (0.368) (0.532) Share of married workers 0.325 0 .325 0.327* 0.380** - 0.0 78 - 0.441 - 0.015 - 0.112 (0.273) (0.277) (0.180) (0.188) (0.943) (1.069) (0.502) (0.564) Number of children age d 0 - 6 0.112** 0.111** - 0.048 - 0.050 - 0.158 - 0.151 0.003 0.003 (0.048) (0.048) (0.046) (0.044) (0.099) (0.104) (0.063) (0.057) Number of chil dren age d 7 - 12 0.056 0.063 0.076 0.079 0.113 0.085 - 0.000 - 0.010 (0.053) (0.057) (0.077) (0.075) (0.107) (0.112) (0.061) (0.059) Farming variables Land holding s (acre s ) - 0.005 - 0.006 - 0.005 - 0.005* - 0.009 - 0.006 0.004 0. 005 (0.008) (0.008) (0 .003) (0.003) (0.010) (0.008) (0.010) (0.010) Experience in own - farming (years) 0.005 0.001 - 0.027* - 0.025* - 0.007 - 0.002 - 0.029* - 0.035* (0.009) (0.031) (0.016) (0.014) (0.020) (0.022) (0.016) (0.019) Square of experience in ow n - farming (years) - 0.000 - 0.000 0.000* 0.000* 0.000 - 0.000 0.000 0.000 (0.000) (0.001) (0.000) (0.000) (0.000) (0.001) (0.000) (0.000) Experience in farm - wage - labor (years) - 0.019 - 0.019 - 0.003 - 0.049* 0.034 0.055 - 0.028 - 0.023 (0.014) (0.015) (0.010) (0.030) (0.065) (0.069) (0.045) (0.057) Square of experience in farm - wage - labor 0.001 0.001 - 0.000 0.001 - 0.001 - 0.002 0.002 0.001 (years) (0.000) (0.001) (0.000) (0.001) (0.002) (0.003) (0.003) (0.004) Value of farm asset (100 USD ) 0.210** 0.231** 0. 024 0.018 0.165 0.195 0.005 0.006 (0.095) (0.106) (0.016) (0.012) (0.154) (0.197) (0.043) (0.039) 61 Table 1 .A.3 (c ) Farm ing prices Consumer Price Index of farm products 0.000 - 0.002 0.013 0.014 0.003 0.009 - 0.021 - 0.018 (0.010) (0.011) (0.014) (0.015) (0. 021) (0.022) (0.018) (0.017) Land rental rate ( USD /acre/year) - 0.010 - 0.010 - 0.013 - 0.011 - 0.042 - 0.048 0.044 0.050 (0.050) (0.052) (0.031) (0.029) (0.046) (0.050) (0.039) (0.038) Regional average farming net return 0.140 - 0 .391 0.250 0.202 - 0.477 - 0. 603 - 0.535 - 0.460 (USD/hour) (0.438) (0.561) (0.358) (0.346) (1.377) (1.373) (1.180) (1.170) Regional average farm ing wage - 0.227 - 0.164 0.506* 0.523* 0.992 1.122 - 0.035 - 0.119 (USD/hour) (0.297) (0.319) (0.305) (0.304) (0.98 0) (1.026) (0.579) (0.530) Nonfarm variables Experience in nonfarm self - employment - 0.025 - 0.029 0.001 0.008 0.025 - 0.064 - 0.013 - 0.037 (years) (0.023) (0.022) (0.015) (0.014) (0.028) (0.118) (0.037) (0.060) Square of experience in nonfarm sel f - 0.001 0.001 - 0.000 - 0.00 0 - 0.000 0.002 - 0.000 0.000 employment (years) (0.001) (0.001) (0.001) (0.001) (0.001) (0.003) (0.002) (0.002) Experience in nonfarm wage - employment - 0.065** - 0.068** 0.004 0.012 - 0.166*** - 0.192*** 0.093** 0.242 (years) (0.0 30) (0.031) (0.017) (0.016) (0.047) (0.062) (0.042) (0.282) Square of experience in nonfarm wage - 0.002* 0.002 - 0.000 - 0.000 0.004** 0.007* - 0.003** - 0.007 employment (years) (0.001) (0.001) (0.001) (0.001) (0.002) (0.004) (0.001) (0.009) Nonlabor incom e (100 USD /year) 0.108 0.11 3 0.020 0.018 - 0.002 0.071 0.014*** 0.014*** (0.094) (0.098) (0.016) (0.016) (0.025) (0.051) (0.005) (0.004) Distance to nearest transport (km) - 0.015 - 0.014 0.023 0.024 0.010 0.012 0.005 0.004 (0.013) (0.013) (0.023) (0.022 ) (0.016) (0.017) (0.012) ( 0.012) Non farm prices Regional average nonfarm net return - 0.478* - 0.520* 0.044 0.042 0.525 0.515 - 0.110 - 0.179 (USD/hour) (0.263) (0.271) (0.116) (0.110) (0.580) (0.597) (0.506) (0.554) Regional average nonfarm wage ( USD /hour) 0.617 0.677 0.4 45 0.342 - 0.584 - 0.659 0.339 0.341 (0.565) (0.611) (0.457) (0.420) (1.148) (1.178) (0.673) (0.677) Observations (household - year pairs) 4,009 3,815 770 767 1,551 1,480 908 904 Number of households 1,810 1,761 577 575 955 919 645 643 R - squared 0.038 0.041 0.193 0.241 0.096 0.114 0.176 0.208 Notes: The value of profit from self - employment activities is censored at zero. Household weekly profit is computed based on the gross income from the activities and the cost of s elf - employed activities in a year. T ime dummie s, district dummies, time means of all time - variant explanatory variables are included in all estimations but not reported. All estimations used correlated random effect s model. USD used in the table is 2011 PP P USD . Clustered s tandard e rrors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. 62 Table 1.A. 4 Household profit (correlated random effect s instrumental variable) Dependent variable: Household profit from the activity ( USD /week) Own - f arming Own - f arm ing Farm - wage - labor Farm - wage - labor Nonfarm self - employment Nonfarm self - employment Nonfarm wage - employment Nonfarm wage - employment Explanatory variables CRE 2SLS CRE 2SLS CRE 2SLS CRE 2SLS CRE 2SLS CRE 2SLS CRE 2SLS CRE 2SL S Inverse mills ratio from 1 st stage labor 0.206 - 0.350* - 0.702 - 0.141 equation (0.981) (0.183) (0.672) (0.700) Residuals from 2 nd stage labor equation 0.251*** 0.221*** 0.178 - 0.253 (0.079) (0.048) (0.177) (0.262) Household educatio n Average educatio n (years) 0.297 0.265 0.153 0.019 0.756* 0.708 1.111*** 1.121** (0.216) (0.310) (0.105) (0.072) (0.404) (0.433) (0.404) (0.442) Household member composition A verage a ge 0.017 0.016 0.024 0.013 0.031 0.036 0.087** 0.08 9** (0.017) (0.025) (0.01 9) (0.013) (0.036) (0.040) (0.041) (0.042) Share of female workers 0.195 0.142 0.278 0.137 1.121 0.828 0.313 0.354 (0.425) (0.534) (0.211) (0.147) (1.462) (1.500) (0.793) (0.798) Share of married workers 0.434 0.432 0.383* 0 .394** 0.358 - 0.283 0.196 0 .207 (0.293) (0.298) (0.214) (0.192) (1.186) (1.207) (0.721) (0.728) Number of children age d 0 - 6 0.128*** 0.124*** - 0.048 - 0.049 - 0.109 - 0.093 0.035 0.022 (0.045) (0.043) (0.050) (0.045) (0.107) (0.113) (0.123) (0.125) Numb er of children age d 7 - 12 0. 051 0.059 0.080 0.081 0.128 0.084 - 0.018 - 0.009 (0.057) (0.061) (0.082) (0.076) (0.114) (0.118) (0.140) (0.139) Farming variables Land holding s (acre s ) - 0.005 - 0.006 - 0.000 - 0.004 - 0.009 - 0.005 - 0.006 - 0.006 (0.008) (0.009) (0.004) (0.003) (0 .013) (0.011) (0.024) (0.024) Experience in own - farming (years) 0.010 0.013 - 0.033* - 0.026* - 0.003 0.004 - 0.008 - 0.005 (0.010) (0.041) (0.018) (0.014) (0.025) (0.027) (0.038) (0.039) Square of experience in own - farming - 0.00 0 - 0.000 0.000** 0.000** 0. 000 0.000 0.000 0.000 (years) (0.000) (0.001) (0.000) (0.000) (0.001) (0.001) (0.001) (0.001) Experience in farm - wage - labor (years) 0.018 0.011 0.014 - 0.051 0.108 0.138 0.227 0.218 (0.042) (0.054) (0.012) (0.034) (0.086) (0.0 92) (0.145) (0.156) Square of experience in farm - wage - labor - 0.000 - 0.000 - 0.000 0.001 - 0.002 - 0.004 - 0.005 - 0.004 (years) (0.001) (0.001) (0.000) (0.001) (0.003) (0.003) (0.007) (0.007) Value of farm asset (100 USD ) 0.173* 0.194* 0.032 0.021* 0.076 0. 083 - 0.148 - 0.154 (0.097) (0.116) (0.020) (0.012) (0.167) (0.203) (0.125) (0.132) 63 T able 1 .A.4 (c ) Farm ing prices Consumer Price Index of farm products 0.002 - 0.001 0.011 0.014 0.001 0.007 0.013 0.016 (0.010) (0.010) (0.014) (0 .015) (0.023) (0.024) (0.03 3) (0.034) Land rental rate ( USD /acre/year) - 0.014 - 0.012 - 0.020 - 0.014 - 0.056 - 0.058 0.053 0.046 (0.051) (0.053) (0.034) (0.030) (0.051) (0.054) (0.063) (0.063) Regional average farming return 0.134 - 0.473 0.299 0.213 - 0.63 2 - 0.696 - 1.555 - 1.660 (US D/hour) (0.440) (0.496) (0.391) (0.347) (1.375) (1.364) (1.754) (1.785) Regional average farming wage - 0.196 - 0.119 0.343 0.500 1.067 1.132 0.999 1.051 (USD/hour) (0.298) (0.308) (0.289) (0.320) (1.008) (1.049) (1.060) (1.105) Non farm variables Experience in nonfarm self - employment - 0.042* - 0.047* - 0.009 0.007 0.022 - 0.105 - 0.123 - 0.122 (years) (0.022) (0.024) (0.020) (0.013) (0.034) (0.123) (0.083) (0.092) Square of experience in nonfarm self - 0.001* 0.001** - 0.00 0 - 0.000 0.000 0.003 0.006 0.006 employment (years) (0.001) (0.001) (0.001) (0.001) (0.001) (0.003) (0.004) (0.004) Experience in nonfarm wage - employment - 0.153** - 0.151 - 0.038 0.006 - 0.358*** - 0.383** - 0.066 - 0.104 (years) (0.069) (0.106) (0.033) (0.0 21) (0.137) (0.156) (0.072) (0.141) Square of experience in nonfarm wage - 0.004** 0.004 0.001 - 0.000 0.007 0.010* 0.001 0.002 employment (years) (0.002) (0.003) (0.001) (0.001) (0.004) (0.006) (0.002) (0.005) Nonlabor income (100 USD /year) 0.104 0.110 0 .016 0.015 - 0.006 0.065 0.0 15* 0.014 (0.094) (0.099) (0.022) (0.018) (0.027) (0.051) (0.009) (0.009) Distance to nearest transport (km) - 0.014 - 0.014 0.020 0.023 0.010 0.012 - 0.012 - 0.012 (0.013) (0.013) (0.024) (0.022) (0.016) (0.017) (0.025) (0.026) Non farm prices R egional average nonfarm return - 0.494* - 0.542** 0.004 0.036 0.410 0.377 - 0.235 - 0.210 (USD/hour) (0.266) (0.261) (0.127) (0.113) (0.619) (0.640) (0.627) (0.645) Regional average nonfarm wage 0.625 0.692 0.753 0.395 - 0.512 - 0. 535 - 0.822 - 0.861 (USD/hou r) (0.577) (0.623) (0.557) (0.430) (1.188) (1.233) (1.340) (1.399) Observations (household - year pairs) 3,981 3,790 765 762 1,546 1,475 907 903 Number of households 1,802 1,754 573 571 954 918 645 643 R - squared 0.025 0.030 0.103 0.231 0.055 0.0 70 0.097 0.094 Notes: The value of profit from self - employment activities is censored at zero. Household weekly profit is computed based on the gross income from the activities and the cost of self - employed activities in a year. T ime dummies, district dum mies, time means of all time - variant explan atory variables are included in all estimations but not reported. All estimations used the correlated random effect s model. The 2SLS estimations used two instrumental variables: total ye ars under free primary educ ation and average distance to the nearest m arket in the birth district in 1995. USD used in the table is 2011 PPP USD . Clustered s tandard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. 64 Table 1.A. 5 Household aver age partial effect on probability of participation (pooled probit) Dependent variable: Supply hours of labor = 1 Own - f armin g Own - f arming Far m - wage - labor Farm - wage - labor Nonfarm self - employment Nonfarm self - employment Nonfarm wage - employment Nonfarm wage - em ployment Explanatory variables Reduced Two stage Reduced Two stage Reduced Two stage Reduced Two stage Household education Average education (years) 0.002 - 0.007*** 0.006*** 0.011*** (0.002) (0.002) (0.002) (0 .002) Fitted value of edu cation (year s ) 0.002 - 0.006*** 0.006*** 0.012*** (0.002) (0.002) (0.002) (0.002) Household composition A verage a ge - 0.001* - 0.001* - 0.001 - 0.001 - 0.001* - 0.001* 0.000 0.000 (0.001) (0.001) (0.001) (0.001) (0 .001) (0.001) (0.001) (0.00 1) Share of female workers 0.004 0.005 - 0.067*** - 0.067*** 0.027 0.028 - 0.049** - 0.047** (0.021) (0.021) (0.023) (0.023) (0.028) (0.028) (0.023) (0.023) Share of married workers 0.063*** 0.064*** - 0.040* - 0.043* 0.081*** 0.0 86*** - 0.022 - 0.021 (0.02 2) (0.022) (0.022) (0.023) (0.028) (0.028) (0.023) (0.023) Number of children age d 0 - 6 0.008** 0.008** - 0.001 - 0.001 0.007 0.007 0.001 0.001 (0.004) (0.004) (0.004) (0.004) (0.005) (0.005) (0.004) (0.004) Number of children a ge d 7 - 12 0.006 0.006 0.001 0.001 0.011** 0.012** - 0.004 - 0.004 (0.004) (0.004) (0.004) (0.004) (0.005) (0.005) (0.004) (0.004) Farming variables Land holding s (acre s ) 0.001 0.001 0.000 0.000 - 0.001 - 0.001 0.000 0.000 (0.001) (0.001) (0.001) ( 0.001) (0.001) (0.001) (0.0 01) (0.001) Experience in own - farming (years) 0.019*** 0.019*** - 0.001 - 0.001 - 0.005*** - 0.005*** - 0.002 - 0.002 (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) Square of experience in own - farming - 0.000*** - 0 .000*** - 0.000 - 0.000 0.000 * 0.000* - 0.000 - 0.000 (years) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Experience in farm - wage - labor (years) 0.000 0.000 0.047*** 0.047*** - 0.013*** - 0.013*** 0.007** 0.007** (0.002) (0.002) (0.003) (0 .003) (0.002) (0.002) (0.00 3) (0.003) Square of experience in farm - wage - labor - 0.000 - 0.000 - 0.001*** - 0.001*** 0.000*** 0.000*** - 0.001*** - 0.001*** (years) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Value of farm asset (100 USD ) 0.003 0.002 0.005 0.006* 0. 008* 0.007 - 0.003 - 0.003 (0.006) (0.006) (0.003) (0.003) (0.004) (0.004) (0.004) (0.004) Farming prices Consumer Price Index of farm products - 0.001 - 0.001 - 0.002*** - 0.002*** - 0.002* - 0.002* - 0.001 - 0.001 (0.001) ( 0.001) (0.001) (0.001) (0.0 01) (0.001) (0.001) (0.001) 65 T able 1 .A.5 (c ) Land rental rate ( USD /acre/year) 0.003 0.003 - 0.000 - 0.000 - 0.002 - 0.002 0.003 0.003 (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) Regional average farming r eturn 0.003 0.003 0.032 0. 030 - 0.011 - 0.009 - 0.046 - 0.045 (USD/hour) (0.037) (0.037) (0.030) (0.030) (0.043) (0.043) (0.035) (0.035) Regional average farming wage - 0.038 - 0.038 - 0.030 - 0.028 - 0.079** - 0.080** - 0.033 - 0.032 (USD/hour) (0.030) (0.030) ( 0.033) (0.033) (0.038) (0.0 38) (0.032) (0.032) Non farm variables Experience in nonfarm self - employment - 0.007*** - 0.007*** - 0.008*** - 0.008*** 0.076*** 0.075*** - 0.007*** - 0.007*** (years) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) Square of experie nce in nonfarm self - 0.000** 0.000** 0.000 0.000 - 0.002*** - 0.002*** 0.000 0.000 employment (years) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Experience in nonfarm wage - employment - 0.008*** - 0.008*** - 0.0 05* - 0.005* - 0.010*** - 0.01 1*** 0.076*** 0.076*** (years) (0.002) (0.002) (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) Square of experience in nonfarm wage - 0.000 0.000 0.000 0.000 0.000 0.000 - 0.002*** - 0.002*** employment (years) (0.000) (0.000) (0 .000) (0.000) (0.000) (0.00 0) (0.000) (0.000) Nonlabor income (100 USD /year) - 0.000 - 0.000 - 0.000 0.001 0.001 - 0.001 - 0.000 - 0.001 (0.000) (0.001) (0.001) (0.001) (0.001) (0.002) (0.001) (0.001) Distance to nearest transport (km) - 0.000 - 0.000 - 0.001 - 0.001 - 0.001 - 0.001 0.000 0 .000 (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) Non farm prices Regional average nonfarm return - 0.017 - 0.017 0.006 0.005 0.031 0.032* - 0.040** - 0.040** (USD/hour) (0.016) (0.016) (0.017) (0.017) (0.019) (0.019) (0.017) (0 .017) Regional average nonfarm wage - 0.060 - 0.061 0.056 0.057 0.023 0.022 - 0.039 - 0.039 (USD/hour) (0.040) (0.040) (0.043) (0.043) (0.047) (0.047) (0.041) (0.041) Observations (household - year pairs) 4,677 4,677 4,69 9 4,699 4,742 4,742 4,725 4 ,725 Number of households 1,981 1,981 1,976 1,976 2,006 2,006 1,999 1,999 Pseudo R - squared 0.350 0.350 0.408 0.407 0.412 0.413 0.433 0.432 Pseudo likelihood - 1270 - 1270 - 1352 - 1354 - 1776 - 1774 - 1410 - 1413 Notes: The two stage estimations instrumented a verage years of schooling by an instrumental variable , total years under free primary education . Time dummies, district dummies, and time means of all time - variant explanatory variables are included in all estimations but not rep orted. USD u sed in the tabl e is 2011 PPP USD . Clustered s tandard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. 66 Table 1.A. 6 Household hours of labor supply (Lognormal correlated random effects) Dependent variabl e: Log of hours worked (hou rs/week) Own - f arming Own - f arming Farm - wage - labor Farm - wage - labor Nonfarm self - employment Nonfarm self - employment Nonfarm wage - employment Nonfarm wage - employment Explanatory variables CRE CRE CRE CRE CRE CRE CRE CRE Inverse mill s ratio from 1 st stage labo r - 0.279* 0.398** - 0.220 - 0.451*** equation (0.166) (0.201) (0.155) (0.166) Household education Average education (years) 0.005 0.004 0.011 - 0.001 0.044*** 0.041*** 0.073*** 0.060*** (0.005) (0.005) (0.016) (0.017) (0.011) (0.011) (0. 011) (0.012) Household composition A verage a ge - 0.006*** - 0.005** 0.012** 0.010 - 0.004 - 0.003 - 0.005 - 0.003 (0.002) (0.002) (0.006) (0.006) (0.004) (0.004) (0.006) (0.006) Share of female workers - 0.334*** - 0.351*** - 0.667*** - 0.774*** 0.056 0 .038 0.152 0.232 (0.079) (0.079) (0.174) (0.185) (0.136) (0.136) (0.179) (0.183) Share of married workers 0.238*** 0.197** - 0.373** - 0.435** 0.289* 0.256* 0.086 0.130 (0.081) (0.083) (0.181) (0.184) (0.148) (0.147) (0.180) (0.183) Number of children age d 0 - 6 0.048*** 0.048*** 0.080** 0.079** 0.029 0.028 - 0.055 - 0.057* (0.012) (0.012) (0.034) (0.034) (0.025) (0.025) (0.034) (0.034) Number of children age d 7 - 12 0.046*** 0.046*** 0.015 0.012 0.000 - 0.005 0.007 0.013 (0.01 2) (0.012) (0.036) (0.036) (0.024) (0.025) (0.035) (0.035) Farming variables Land holding s (acre s ) - 0.003** - 0.004*** - 0.004 - 0.004 - 0.003 - 0.003 - 0.010*** - 0.010*** (0.001) (0.001) (0.003) (0.003) (0.002) (0.002) (0.003) (0.003) Experience in own - farming (years) 0.042* ** 0.032*** - 0.054*** - 0.057*** - 0.046*** - 0.043*** - 0.028*** - 0.025*** (0.004) (0.007) (0.008) (0.008) (0.007) (0.007) (0.008) (0.008) Square of experience in own - farming - 0.001*** - 0.001*** 0.001*** 0.001*** 0.001*** 0.001* ** 0.000 0.000 (years) (0. 000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Experience in farm - wage - labor (years) - 0.015** - 0.015** 0.051*** 0.112*** - 0.015 - 0.008 - 0.010 - 0.023 (0.006) (0.006) (0.011) (0.031) (0.021) (0.022) (0.034) (0.036) Square of experience in f arm - wage - labor 0.000 0.000 - 0.001*** - 0.003*** 0.000 0.000 - 0.002 - 0.001 (years) (0.000) (0.000) (0.000) (0.001) (0.001) (0.001) (0.003) (0.003) Value of farm asset (100 USD ) 0.042*** 0.038*** 0.057* 0.063** 0.046 0.041 - 0.034 - 0.029 (0.015) (0.015) ( 0.030) (0.030) (0.029) (0.029) (0.040) (0.039) Farming prices Consumer Price Index of farm products 0.008*** 0.008*** - 0.009 - 0.011* - 0.001 - 0.000 0.002 0.002 (0.002) (0.002) (0.006) (0.006) (0.005) (0.005) (0.006) (0 .006) 67 Table 1 .A.6 (c ) Land rental rate ( USD /acre/year) - 0.002 - 0.003 - 0.016 - 0.017 - 0.009 - 0.009 0.024 0.023 (0.007) (0.007) (0.021) (0.021) (0.018) (0.018) (0.018) (0.018) Regional average farming return - 0.289*** - 0.375*** - 0.368 - 0.313 - 0.006 0.008 0.042 0.037 (USD/ho ur) (0.083) (0.107) (0.353) (0.355) (0.201) (0.202) (0.266) (0.262) Regional average farming wage 0.110 0.135 - 0.205 - 0.263 0.084 0.115 0.043 0.076 (USD/hour) (0.081) (0.082) (0.300) (0.302) (0.188) (0.188) (0.236) (0.237) No nfarm variables Ex perience in nonfarm self - employment - 0.017*** - 0.014*** - 0.001 - 0.012 0.037*** 0.002 - 0.000 0.011 (years) (0.005) (0.005) (0.016) (0.017) (0.010) (0.026) (0.019) (0.020) Square of experience in nonfarm self - 0.000 0.000 - 0.000 - 0.000 - 0.001** 0.000 - 0.0 01 - 0.001 employment (years) (0.000) (0.000) (0.000) (0.000) (0.000) (0.001) (0.001) (0.001) Experience in nonfarm wage - employment - 0.046*** - 0.043*** - 0.034 - 0.041 - 0.058** - 0.054** 0.066*** - 0.024 (years) (0.009) (0.009) (0 .027) (0.027) (0.025) (0.02 5) (0.014) (0.036) Square of experience in nonfarm wage - 0.001* 0.001 0.002* 0.002** 0.001 0.001 - 0.002*** 0.001 employment (years) (0.000) (0.000) (0.001) (0.001) (0.002) (0.002) (0.001) (0.001) Nonlabor income (100 USD /year) - 0.003 - 0.003 0.056*** 0.0 54*** 0.005 0.005 - 0.000 - 0.000 (0.004) (0.004) (0.014) (0.013) (0.005) (0.005) (0.003) (0.003) Distance to nearest transport (km) - 0.000 - 0.001 0.004 0.004 - 0.005 - 0.005 - 0.000 - 0.001 (0.002) (0.002) (0.011) (0.011) (0.004) (0.004) (0.006) (0.006) N onfarm prices Regional average nonfarm return - 0.060 - 0.056 - 0.067 - 0.062 - 0.175* - 0.189* 0.117 0.160 (USD/hour) (0.045) (0.045) (0.135) (0.136) (0.096) (0.097) (0.134) (0.133) Regional average nonfarm wage - 0.078 - 0 .061 - 0.506 - 0.389 - 0.130 - 0.146 - 0.239 - 0.215 (USD/hour) (0.110) (0.111) (0.364) (0.366) (0.234) (0.234) (0.286) (0.286) Observations (household - year pairs) 4,065 3,989 891 891 1,582 1,582 1,038 1,037 Number of households 1,852 1,819 649 649 962 962 703 702 R - squared 0.208 0.211 0.409 0.412 0.286 0.287 0.335 0.338 Notes: Time dummies, district dummies, and time means of all time - variant explanatory variables are included in all estimations but not reported. USD used in the table is 2011 PPP USD . Standard errors cluste red at household level are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. 68 Table 1.A. 7 Household hours of labor supply (Lognormal correlated random effects instrumental variable) Dependent variabl e: Log of hours worked (hou rs/week) Own - f arming Own - f arming Farm - wage - labor Farm - wage - labor Nonfarm self - employment Nonfarm self - employment Nonfar m wage - employment Nonfarm wage - employment Explanatory variables CRE 2SLS CRE 2SLS CRE 2SLS CRE 2SLS CRE 2SLS CRE 2SLS CRE 2SLS CRE 2SLS Inverse mills ratio from 1 st stage labor - 0.808*** - 0.257 - 0.510*** - 0.820*** equation (0.151) (0.180) (0.146) (0.155) Household education Fitted value of education (years) 0.014** 0.009 0.021 0.018 0.056*** 0 .054*** 0.092*** 0.087*** (0.006) (0.006) (0.020) (0.020) (0.013) (0.013) (0.014) (0.014) Household member composition A verage a ge - 0.005** - 0.003 0.013** 0.013** - 0.003 0.001 - 0.003 0.002 (0.002) (0.002) (0.006) (0.006) (0.004) (0.004) (0.00 6) (0.006) Share of female workers - 0.326*** - 0.363*** - 0.649*** - 0.594*** 0.067 0.041 0.175 0.292 (0.079) (0.079) (0.175) (0.182) (0.136) (0.138) (0.182) (0.185) Share of married workers 0.233*** 0.140* - 0.368** - 0.324* 0.301** 0.236 0.099 0.165 (0 .081) (0.081) (0.181) (0.18 5) (0.148) (0.149) (0.180) (0.185) Number of children age d 0 - 6 0.048*** 0.042*** 0.080** 0.079** 0.031 0.030 - 0.048 - 0.043 (0.012) (0.012) (0.034) (0.034) (0.025) (0.025) (0.034) (0.033) Number of children age d 7 - 12 0.045*** 0.042*** 0.014 0.014 - 0.000 - 0.012 0.002 0.017 (0.012) (0.012) (0.036) (0.036) (0.024) (0.024) (0.036) (0.035) Farming variables Land holding s (acre s ) - 0.003** - 0.004*** - 0.004 - 0.004 - 0.004 - 0.003 - 0.009*** - 0.008** (0.001) (0.001) (0.003) ( 0.003) (0.002) (0.002) (0.0 03) (0.003) Experience in own - farming (years) 0.041*** 0.012* - 0.054*** - 0.053*** - 0.046*** - 0.042*** - 0.027*** - 0.022*** (0.004) (0.006) (0.008) (0.008) (0.007) (0.007) (0.008) (0.008) Square of experience in own - farming - 0 .001*** - 0.000** 0.001*** 0 .001*** 0.001*** 0.001*** 0.000 0.000 (years) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Experience in farm - wage - labor (years) - 0.014** - 0.014** 0.052*** 0.012 - 0.013 0.001 - 0.011 - 0.028 (0.006) (0.006) ( 0.011) (0.028) (0.021) (0.0 22) (0.034) (0.037) Square of experience in farm - wage - labor - 0.000 0.000 - 0.001*** - 0.000 0.000 - 0.000 - 0.002 0.000 (years) (0.000) (0.000) (0.000) (0.001) (0.001) (0.001) (0.003) (0.003) Value of farm asset (100 USD ) 0.044** * 0.037** 0.055* 0.052* 0.0 43 0.031 - 0.030 - 0.028 (0.015) (0.015) (0.030) (0.029) (0.030) (0.028) (0.034) (0.031) Farming prices Consumer Price Index of farm products 0.008*** 0.008*** - 0.009 - 0.008 - 0.001 0.001 0.001 0.002 (0.002) (0.002) (0 .006) (0.006) (0.005) (0.00 4) (0.006) (0.006) 69 Table 1.A.7 (c ) Land rental rate ( USD /acre/year) - 0.003 - 0.004 - 0.016 - 0.017 - 0.009 - 0.009 0.024 0.021 (0.007) (0.007) (0.021) (0.021) (0.017) (0.017) (0.018) (0.019) Regional average farming return - 0.293*** - 0.385*** - 0.371 - 0.423 0.016 0.082 0.026 0.015 (USD/hour) (0.082) (0.107) (0.354) (0.354) (0.201) (0.202) (0.271) (0.266) Regional average farming wage 0.111 0.158* - 0.212 - 0.158 0.086 0.164 0.065 0.123 (USD/hour) (0.081) (0.082) (0.300) (0. 300) (0.188) (0.187) (0.239 ) (0.238) Nonfarm variables Experience in nonfarm self - employment - 0.017*** - 0.008 - 0.001 0.006 0.036*** - 0.043* - 0.001 0.020 (years) (0.005) (0.005) (0.016) (0.017) (0.010) (0.024) (0.019) (0.020) Square of experien ce in nonfarm self - 0.000 - 0.000 - 0.000 - 0.001 - 0.001** 0.001* - 0.001 - 0.001 employment (years) (0.000) (0.000) (0.000) (0.000) (0.000) (0.001) (0.001) (0.001) Experience in nonfarm wage - employment - 0.049*** - 0.039*** - 0.037 - 0.028 - 0.063** - 0.058** 0.0 57*** - 0.109*** (years) (0 .009) (0.009) (0.027) (0.028) (0.025) (0.025) (0.015) (0.035) Square of experience in nonfarm wage - 0.001* 0.001 0.002** 0.002* 0.001 0.001 - 0.002*** 0.003*** employment (years) (0.000) (0.000) (0.001) (0.001) (0.001) (0.001) ( 0.001) (0.001) Nonlabor in come (100 USD /year) 0.001 - 0.000 0.056*** 0.057*** 0.005 0.003 - 0.003 - 0.003 (0.005) (0.005) (0.018) (0.018) (0.005) (0.005) (0.003) (0.003) Distance to nearest transport (km) - 0.000 - 0.001 0.004 0.005 - 0.005 - 0.005 0.000 - 0.0 02 (0.002) (0.002) (0.011 ) (0.011) (0.004) (0.004) (0.006) (0.006) Nonfarm prices Regional average nonfarm return - 0.061 - 0.057 - 0.070 - 0.087 - 0.175* - 0.208** 0.097 0.185 (USD/hour) (0.045) (0.045) (0.135) (0.136) (0.095) (0.098) (0.131) (0.1 30) Regional average nonfa rm wage - 0.075 - 0.031 - 0.492 - 0.579 - 0.146 - 0.190 - 0.212 - 0.115 (USD/hour) (0.110) (0.111) (0.364) (0.368) (0.234) (0.234) (0.286) (0.283) Observations (household - year pairs) 4,065 3,964 891 885 1,582 1,576 1,038 1,0 36 Number of households 1, 852 1,814 649 644 962 960 703 702 R - squared 0.209 0.221 0.410 0.411 0.286 0.294 0.334 0.356 Notes: Time dummies, district dummies, and time means of all time - variant explanatory variables are included in all estimations but not reported. USD used in the table is 2011 PPP USD . Standard errors clustered at household level are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. 70 Table 1.A. 8 Summary statistics of variables (individual) Variable Obs. Mean C.v. Min. Max. Dependent V ariables Hourly profit ( USD /hour) Own - f arming 10,382 4.2 27.4 - 261.5 6598.8 Farm - wage - labor 1,293 1.7 2.7 0.0 113.6 Nonfarm self - employment 4,229 10.9 14.7 - 177.9 3863.6 Nonfarm wage - employment 1,398 3.2 4.5 0.0 368.1 Supp ly positive hour s of labor = 1 Own - f arming 12,180 0.67 0.7 0.0 1.0 Farm - wage - labor 12,180 0.11 2.9 0.0 1.0 Nonfarm self - employment 12,180 0.18 2.1 0.0 1.0 Nonfarm wage - employment 12,180 0.11 2.8 0.0 1.0 Labor supply (hour s /wee k) Own - f arming 12,180 14.2 1.1 0.0 145.0 Farm - wage - labor 12,180 1.6 5.1 0.0 125.4 Nonfarm self - employment 12,180 5.9 3.0 0.0 219.4 Nonfarm wage - employment 12,180 4.0 3.7 0.0 148.4 Explanatory Varia bles Individual schooli ng E ducation (years) 11,994 5.5 0.7 0.0 17.0 Individual characteristics Age 12,180 37.0 0.3 20.0 65.0 Female = 1 12,180 0.53 0.9 0.0 1.0 Married = 1 12,166 0.70 0.6 0.0 1.0 Number of children age d 0 - 6 12,180 1.6 0.8 0.0 9.0 Number of child ren age d 7 - 12 12,180 1.3 0.9 0.0 8.0 Farming variables Land holding s (acre s ) 11,871 4.8 2.7 0.0 340.0 Experience in own - farm ing (years) 10,447 18.4 0.8 0.0 114.0 Experience in farm - wage - labor (years) 10,447 1.5 3.6 0.0 55.0 Value of farm asset s ( 100 USD ) 11,545 0.6 2.3 0.0 27.1 Farming prices CPI of farming products 12,180 202.3 0.2 164.5 273.4 Land rental rate ( USD /acre/year) 12,180 6.6 0.4 1.8 18.9 Average profit in own - farming (ln( USD /hour)) 12,180 0.4 0.6 0.0 2.8 Average wage in far m - wage - labor (ln( USD /hour)) 12,180 0.7 0.3 0.3 1.8 Non farm variables Experience in non far m self - employment (years) 10,447 2.4 2.6 0.0 59.0 Experience in nonfarm wage - e mployment (years) 10,447 1.2 3.6 0.0 47.0 Nonlabor i ncome (100 USD /year) 12,180 1.0 5.5 0.0 267.8 Distan ce to nearest transport (km) 12,166 3.4 1.9 0.0 180.0 Nonfarm prices Average net return in nonfarm self - employment (ln( USD /hour)) 12,180 0.6 0.6 0.0 3.1 Aver age wage in nonfarm wage - employment (l n( USD /hour)) 12,180 0.8 0.2 0.2 1.3 Instrumental variabl es Distance to nearest market in 1995 in birth district (km) 11,975 6.3 0.8 1.0 26.3 Person - year s under free primary education 12,180 3.2 1.6 0.0 40.0 Notes: Observations pooled across years. USD used in the table is 2011 PPP USD . 71 Tabl e 1.A. 9 Individual hourly profit or wage (correlated random effects instrumental variable) Dependent variable: Hourly profit or wage ( USD /week) Own - f arming Own - f arming Farm - wage - la bor Farm - wage - labor Nonfarm self - employment Non farm self - employment Nonfarm wage - employment Nonfarm wage - employment Explanatory variables CRE 2SLS CRE 2SLS CRE 2SLS CRE 2SLS CRE 2SLS CRE 2SLS CRE 2SLS CRE 2SLS Individual education Education (years) 0.012 - 0.004 0.052 - 0.018 (0.057) (0.167) (0.050) (0.042) Complete d primary school = 1 - 0.018 0.222 - 0.367 - 0.233 (0.452) (5.593) (1.178) (0.555) Complete d secondary school = 1 0.027 - 0.029 2.061 0.002 (1.260) (3.479) (2.209) (0.398) Individual characteristics Age 0.005 0.003 - 0.006 - 0.005 0.003 - 0.002 0.004 0.004 (0.003) (0.002) (0.012) (0.018) (0.004) (0.005) (0.004) (0.005) Married = 1 0.011 - 0.018 0.117 0.116 0.121 0.109 0.173** 0.181** (0.031) (0.0 64) (0.080) (0.106) (0.087) (0.145) (0.077) (0. 086) Female = 1 0.014 - 0.031 0.097 0.152 - 0.023 - 0.109 - 0.028 - 0.033 (0.073) (0.046) (0.279) (1.047) (0.118) (0.168) (0.080) (0.078) Number of children age d 0 - 6 0.017 0.014 - 0.009 - 0.007 - 0.000 0.001 0.021 0.020 (0.012) (0.012) (0.023) (0.029) (0.021 ) (0.029) (0.022) (0.024) Number of children age d 7 - 12 - 0.015 - 0.014 0.043 0.040 0.031 0.048* - 0.021 - 0.021 (0.010) (0.011) (0.030) (0.030) (0.021) (0.025) (0.021) (0.022) Farming variables Land h olding s (acre s ) 0.004** 0.003** 0.006 0.005 0.0 02 0.003 0.001 0.001 (0.002) (0.001) (0.005) (0.029) (0.002) (0.002) (0.003) (0.003) Experience in own - farming (years) - 0.004 - 0.005** 0.012*** 0.013** 0.017*** 0.008* 0.010* 0.009 (0.007) (0.003) (0.005) (0.006) (0.005) (0.005) (0.005) (0.006) Squar e of experience in own - farming 0.000 0.000 - 0.000** - 0.000 - 0.000*** - 0.000 - 0.000* - 0.000 (years) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Experience in farm - wage - labor (years) - 0.00 1 - 0.000 - 0.006 - 0.009 0.023 0.007 0.022 0.018 (0.007) (0.009) (0.020) (0.052) (0.015) (0.018) (0.029) (0.031) Square of experience in farm - wage - labor 0.000 - 0.000 0.000 0.000 - 0.001* - 0.000 - 0.001 - 0.000 (years) (0.000) (0.000) (0.000) (0.001) (0.000 ) (0.000) (0.001) (0.001) Value of farm asset (100 USD ) 0.039** 0.059*** 0.007 0.009 0.020 0.049* 0.044*** 0.044*** (0.017) (0.016) (0.019) (0.036) (0.024) (0.027) (0.016) (0.016) 72 T able 1 .A.9 (c ) Farm ing prices Consum er Price Index of farm products - 0.005*** - 0.00 4** 0.002 0.001 0.002 - 0.002 - 0.002 - 0.001 (0.002) (0.002) (0.005) (0.008) (0.003) (0.005) (0.004) (0.004) Land rental rate ( USD /acre/year) 0.004 0.002 0.005 0.004 - 0.001 0.006 - 0.002 - 0.000 (0.007) (0.00 7) (0.014) (0.048) (0.012) (0.017) (0.013) (0.0 14) Regional average farming return 0.490*** 0.446*** - 0.045 - 0.026 0.012 - 0.042 0.119 0.141 (USD/hour) (0.089) (0.090) (0.297) (0.600) (0.163) (0.209) (0.218) (0.226) Regional average farming wage - 0.060 - 0.050 0.495** 0.474 0.099 - 0.083 0.024 0.006 (USD/hour) (0.058) (0.061) (0.250) (0.730) (0.171) (0.221) (0.209) (0.227) Non farm variables Experience in nonfarm self - employment 0.004 0.007* 0.014 0.017 - 0.022 - 0.000 0.080*** 0.082*** (years) (0.005) (0.004) (0.015) (0.069) (0.014) (0.009) (0.024) (0.026) Square of experience in nonfarm self - - 0.000 - 0.000 - 0.000 - 0.000 0.001 0.000 - 0.002* - 0.002* employment (years) (0.000) (0.000) (0.000) (0.002) (0.000) (0.000) (0.001) (0.001) Experience i n nonfarm wage - employment 0.018 0.019 0.017 0. 010 0.013 - 0.034 - 0.006 - 0.005 (years) (0.021) (0.023) (0.052) (0.220) (0.022) (0.027) (0.022) (0.021) Square of experience in nonfarm wage - - 0.000 - 0.001 - 0.001 - 0.001 - 0.001 0.000 0.000 0.000 employment ( years) (0.000) (0.000) (0.001) (0.006) (0.001) (0.001) (0.001) (0.001) Nonlabor income (100 USD /year) 0.015* 0.013 - 0.016 - 0.021 0.007 0.009 0.010** 0.010** (0.008) (0.010) (0.027) (0.102) (0.009) (0.014) (0.004) (0.005) Distance to nearest transport ( km) - 0.002 - 0.002 0.011 0.011 - 0.002 - 0.004 0.0 07* 0.007* (0.002) (0.002) (0.008) (0.012) (0.004) (0.005) (0.004) (0.004) Non farm prices Regional average nonfarm return - 0.051 - 0.058* - 0.009 - 0.019 0.393*** 0.453*** - 0.074 - 0.069 (USD/hour) ( 0.032) (0.033) (0.067) (0.136) (0.076) (0.093) (0.078) (0.082) Regional average nonfarm wage 0.142* 0.162* 0.089 0.149 0.033 0.056 0.725*** 0.736*** (USD/hour) (0.075) (0.089) (0.402) (1.324) (0.178) (0.277) (0.244) (0.253) Observations (indi vidual - year pairs) 6,870 7,679 1,048 1,054 1,94 2 3,158 1,185 1,190 Number of individuals 3,719 4,002 833 837 1,338 2,108 872 876 R - squared 0.274 0.273 0.305 0.284 0.258 0.118 0.226 0.221 Notes: The value of profit from self - employment activities is cens ored at zero. T ime dummies, district dummies, d ummies of negative net return, IMR and residuals from reduced form labor supply estimation, and time means of all time - variant explanatory variables are included in all estimations but not reported. All estima tions used correlated random effect s model. Th e 2SLS estimations used an instrumental variable: total years under free primary educatio n . USD used in the table is 2011 PPP USD . Clustered s tandard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. 73 Table 1.A. 10 In dividual average partial effect on probability of participation (pooled probit) Dependent variable: Supply hours of labor = 1 Own - f arming Own - f arming Farm - wage - labor Farm - wage - labor Nonfarm self - employment No nfarm self - empl o yment Nonfarm wage - employment N onfarm wage - employment Explanatory variables Probit Probit Probit Probit Probit Probit Probit Probit Fitted value of log of hourly return - 0.072*** - 0.057*** 0.127 - 0.062 - 0.048** - 0.038** - 0.336** - 0.022 (USD/hour) (0.025) (0.022) (0.716) (0.068) (0.0 23) (0.015) (0.167) (0.067) Individual education Fitted value of education (year s ) - 0.001 - - 0.006* - 0.007*** - - 0.001 - (0.001) - (0.003) - (0.002) - (0.003) - Fitted value of complete d primary = 1 - - 0.008 - - 0.023 - 0.005 - 0.025 - (0.00 9) - (0.019) - (0.010) - (0.019) Fitted value of complete d secondary = 1 - - 0.030 - - 0.066*** - 0.115*** - 0.034** - (0.020) - (0.022) - (0.045) - (0.017) Individual characteristics Age - 0.002*** - 0.002*** 0.001 0.000 0.001 0.000 0.001* - 0.000 (0.001) (0.001) (0.004) (0.000) (0.000) (0.000) (0.001) (0.000) Female = 1 0.040*** 0.038*** - 0.025 - 0.022*** - 0.002 - 0.007 - 0.029*** - 0.031*** (0.007) (0.007) (0.017) (0.006) (0.006) (0.006) (0.005) (0. 006) Married = 1 0.032*** 0.030*** - 0.025 - 0. 018** 0.031*** 0.030*** 0.055* - 0.001 (0.009) (0.009) (0.032) (0.007) (0.008) (0.008) (0.029) (0.015) Number of children age d 0 - 6 0.007** 0.006** - 0.002 - 0.004 - 0.001 - 0.000 0.005 - 0.002 (0.003) (0.003) ( 0.007) (0.003) (0.003) (0.003) (0.004) (0.003) Number of children age d 7 - 12 - 0.000 - 0.000 - 0.006 0.002 0.001 0.002 - 0.010** - 0.003 (0.003) (0.003) (0.031) (0.004) (0.003) (0.003) (0.004) (0.003) Farming variables Household land holding s (acre s ) - 0.000 - 0.000 - 0.000 0.001 0.000 0.000 0.001* ** 0.001** (0.000) (0.000) (0.004) (0.001) (0.000) (0.000) (0.000) (0.000) Experience in own - farming (years) 0.017*** 0.017*** - 0.005 - 0.002** - 0.005*** - 0.006*** - 0.001 - 0.004*** (0.001) (0.001) (0.009) (0.001) (0.001) (0.001) (0.002) (0.001) Square of experience in own - farming - 0.000*** - 0.000*** 0.000 0.000 0.000*** 0.000*** - 0.000 0.000*** (years) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Experience in farm - wage - labor (years) - 0.007*** - 0.007*** 0.030*** 0.029*** - 0.011*** - 0.012*** 0.001 - 0.006*** (0.001) (0.001) (0.004) (0.002) (0.002) (0.002) (0.004) (0.002) Square of experience in farm - wage - labor 0.000*** 0.000*** - 0.001*** - 0.001*** 0.000*** 0.000*** - 0.000 0.000** (y ears) (0.000) (0.000) (0.000) (0.000) (0.000) ( 0.000) (0.000) (0.000) 74 Table 1 .A.10 (c ) Value of farm asset (100 USD ) - - - 0.001 0.001 0.003 0.004* 0.008 - 0.006 - - (0.005) (0.002) (0.002) (0.002) (0.008) (0.005) Farming prices Consumer Price Index of farm products 0.000 0.0 00 - 0.002 - 0.002*** - 0.001 - 0.001* - 0.001** - 0.001 (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.000) Land rental rate ( USD /acre/year) 0.005** 0.005** - 0.001 0.000 - 0.002 - 0.002 0.002 0.002 ( 0.002) (0.002) (0.004) (0.002) (0.002) (0.002) (0.002) (0.002) Regional average farming return 0.040 0.030 0.011 0.005 - 0.029 - 0.030 0.033 - 0.004 (USD/hour) (0.030) (0.029) (0.037) (0.018) (0.025) (0.025) (0.027) (0.021) Regional average farming wage 0.002 0.003 - 0.120 - 0.031 - 0.047** - 0.054** - 0. 002 - 0.010 (USD/hour) (0.023) (0.023) (0.353) (0.039) (0.023) (0.023) (0.020) (0.020) Non farm variables Experience in nonfarm self - employment - 0.013*** - 0.013*** - 0.009 - 0.006*** 0.048*** 0.049*** 0.014 - 0.011** (years) (0.001) (0.001) (0.010) (0.002) (0.002) (0.001) (0.013) (0.006) Square of experience in nonfarm self - 0.000*** 0.000*** 0.000 0.000*** - 0.001*** - 0.001*** - 0.000 0.000 employment (years) (0.000) (0.000) (0.000) (0.000) (0.000) (0. 000) (0.000) (0.000) Experience in nonfarm wag e - employment - 0.016*** - 0.016*** - 0.011 - 0.008*** - 0.017*** - 0.019*** 0.037*** 0.039*** (years) (0.002) (0.002) (0.012) (0.002) (0.002) (0.002) (0.002) (0.002) Square of experience in nonfarm wage - 0.000*** 0.000*** 0.000 0.000** 0.000*** 0.000*** - 0.00 1*** - 0.001*** employment (years) (0.000) (0.000) (0.001) (0.000) (0.000) (0.000) (0.000) (0.000) Nonlabor income (100 USD /year) 0.001 0.000 0.001 - 0.002 - - 0.004** 0.000 (0.001) (0.001) (0.012) (0.002) - - (0.002) (0.001) Distance to nearest transpo rt (km) - 0.000 - 0.000 - 0.001 0.001 - 0.001 - 0.001 0.003*** 0.001* (0.001) (0.001) (0.008) (0.001) (0.001) (0.001) (0.001) (0.001) Non farm prices Regional average nonfarm return - 0.019* - 0.018* - 0.0 09 - 0.011 0.018 0.016 - 0.024 - 0.001 (USD/hour) (0.010) (0.010) (0.012) (0.010) (0.014) (0.013) (0.015) (0.009) Regional average nonfarm wage 0.005 0.004 0.057 0.078*** 0.027 0.028 0.203* - 0.024 (USD/hour) (0.033) (0.033) (0.071) (0.029) (0.031) (0.031) (0.123) (0.054) Observations (indiv idual - year pairs) 8,595 8,596 8,482 8,483 8,576 8,577 8,550 8,551 Number of individuals 4,429 4,429 4,367 4,367 4,412 4,412 4,405 4,405 Pseudo R - squared 0.427 0.427 0.476 0.475 0.509 0.508 0.551 0.548 Log p seudolikelihood - 2339 - 2339 - 1662 - 1664 - 2260 - 2262 - 1545 - 1557 Notes: The estimate of pooled probit shows the average partial effect of schooling on the probability of participating in each activ ity. Time dummies, district dummies, and time means of all time - variant explanatory variables are included in all estimations but n ot reported. USD used in the table is 2011 PPP USD . Clustered s tandard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. 75 Table 1.A. 11 Individual hours of labor supply (lognormal correlated ra ndom effect s) Dependent variable: Log of hours worked (hour s /week) Own - f arming Own - f arming Farm - wage - labor Farm - wage - labor Nonfarm self - employment Nonfarm self - employment Nonfarm wage - employment Nonfarm wage - e mployment Explanatory variables LN CRE LN CRE LN CRE LN CRE LN CRE LN CRE LN CRE LN CRE Fitted value of log of hourly return 0.037 0.041 9.753 - 0.722 - 0.075 - 0.153** - 2.465* - 0.829 (USD/hour) (0.069) (0.062) (10.054) (1.133) (0.080) (0.077) (1.368) (0. 799) Individual education Fitted valu e of education (year s ) - 0.007** - 0.014 - 0.015 - 0.007 - (0.004) - (0.045) - (0.010) - (0.028) - Fitted value of complete d primary = 1 - - 0.025 - 0.003 - - 0.032 - 0.199 - (0.027) - (0.286) - (0.071) - (0 .231) Fitted value of complete d secondary = 1 - - 0.163* - 0.542 - 0.391 - 0.317*** - (0.085) - (0.602) - (0.249) - (0.110) Individual characteristics Age - 0.002 - 0.002 0.064 0.007 - 0.005 - 0.006** 0.004 - 0.003 (0.001) (0.001) (0.057) (0.006) (0.003) (0.003) (0.007) (0.005) Female = 1 0.1 46*** 0.144*** - 1.366 - 0.133 0.220** 0.229** 0.652** 0.378** (0.040) (0.040) (1.199) (0.158) (0.101) (0.103) (0.260) (0.185) Married = 1 - 0.020 - 0.015 - 1.574 - 0.498** - 0.113 - 0.136 0.084 0.130 (0.046) (0 .046) (1.001) (0.198) (0.110) (0.110) (0.122) ( 0.119) Number of children age d 0 - 6 0.010 0.010 0.114 0.021 0.005 0.005 0.008 - 0.026 (0.009) (0.009) (0.095) (0.029) (0.021) (0.021) (0.040) (0.032) Number of children age d 7 - 12 0.012 0.012 - 0.411 0.034 0.0 02 0.008 - 0.049 - 0.017 (0.009) (0.009) (0.431 ) (0.056) (0.021) (0.021) (0.043) (0.035) Farming variables Household land holding s (acre s ) - 0.001 - 0.001 - 0.057 0.005 - 0.003 - 0.003 - 0.008 - 0.011* (0.001) (0.001) (0.059) (0.009) (0.003) (0.003) ( 0.006) (0.006) Experience in own - farming (year s) 0.022*** 0.022*** - 0.174 - 0.045*** - 0.048*** - 0.048*** - 0.021 - 0.037*** (0.003) (0.003) (0.123) (0.016) (0.005) (0.005) (0.015) (0.009) Square of experience in own - farming - 0.000*** - 0.000*** 0.003 0.00 1* 0.001*** 0.001*** 0.000 0.001** (years) (0. 000) (0.000) (0.002) (0.000) (0.000) (0.000) (0.000) (0.000) Experience in farm - wage - labor (years) - 0.018*** - 0.018*** 0.083 0.023** - 0.019 - 0.020 - 0.049 - 0.083** (0.004) (0.004) (0.059) (0.012) (0.014) (0. 014) (0.044) (0.037) Square of experience in f arm - wage - labor 0.000* 0.000* - 0.002 - 0.000 0.000 0.000 0.001 0.002 (years) (0.000) (0.000) (0.002) (0.000) (0.000) (0.000) (0.002) (0.001) 76 Table 1 .A.11 (c ) Value of farm asset (100 USD ) - - - 0.034 0.039** 0.015 0.022 0.059 - 0.010 - - ( 0.070) (0.020) (0.019) (0.019) (0.065) (0.042) Farming prices Consumer Price Index of farm products 0.009*** 0.009*** - 0.021 - 0.005 - 0.002 - 0.002 - 0.002 0.001 (0.002) (0.002) (0.017) (0.006) (0.004 ) (0.004) (0.005) (0.005) Land rental rate (US D/acre/year) 0.003 0.003 - 0.053 - 0.004 - 0.005 - 0.003 0.020 0.022 (0.006) (0.006) (0.051) (0.020) (0.014) (0.014) (0.016) (0.016) Regional average farming return - 0.330*** - 0.327*** 0.479 0.059 0.172 0.159 0.282 0.097 (USD/hour) (0.083) (0.080) (0.511) (0.311) (0.174) (0.175) (0.272) (0.249) Regional average farming wage 0.139** 0.136** - 4.744 0.432 - 0.106 - 0.131 - 0.078 - 0.126 (USD/hour) (0.065) (0.065) (5.018) (0.598) (0.165) (0.166) (0.236) (0.238) No n farm variables Experience in nonfarm self - employment - 0.023*** - 0.024*** - 0.166 - 0.012 0.036*** 0.038*** 0.103 - 0.030 (years) (0.004) (0.004) (0.145) (0.025) (0.007) (0.007) (0.111) (0.069) Square of experience in nonfarm self - 0.000** 0.000** 0.003 0.000 - 0.001*** - 0.001*** - 0.003 0.001 employment (years) (0.000) (0.000) (0.002) (0.001) (0.000) (0.000) (0.003) (0.002) Experience in nonfarm wage - employment - 0.062*** - 0.060*** - 0.203 - 0.039 - 0.055** - 0.060*** 0.046*** 0.054*** (years) (0.007 ) (0.008) (0.178) (0.038) (0.023) (0.023) (0.01 2) (0.010) Square of experience in nonfarm wage - 0.001*** 0.001*** 0.011 0.001 0.001 0.001 - 0.001 - 0.001*** employment (years) (0.000) (0.000) (0.010) (0.001) (0.001) (0.001) (0.001) (0.000) Nonlabor income (100 USD /year) - 0.001 - 0.001 0.208 0.036 - - 0 .028* 0.012 (0.004) (0.004) (0.169) (0.035) - - (0.016) (0.010) Distance to nearest transport (km) - 0.002 - 0.002 - 0.106 0.007 0.004 0.003 0.018* 0.007 (0.002) (0.002) (0.110) (0.017) (0.006) (0.006) (0.01 0) (0.007) Non farm prices Regional av erage nonfarm return - 0.065** - 0.066** - 0.001 - 0.105 - 0.078 - 0.037 - 0.146 - 0.027 (USD/hour) (0.033) (0.033) (0.147) (0.108) (0.089) (0.092) (0.136) (0.107) Regional average nonfarm wage - 0.142 - 0.140 - 1.57 7 - 0.597 - 0.324 - 0.315 1.591 0.414 (USD/hour) (0.090) (0.090) (0.968) (0.382) (0.197) (0.197) (1.059) (0.649) Observations (individual - year pairs) 7,031 7,032 1,048 1,048 1,952 1,952 1,187 1,187 Number of individuals 3,822 3,822 833 833 1,347 1,347 874 874 R - squared 0.154 0.154 0.443 0.44 1 0.299 0.299 0.403 0.404 Notes: The estimate of pooled probit shows the average partial effect of schooling on the probability of participating in each activ ity. 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Education and off - farm work. Economic D evelopment and C ultural C hange , 45 (3 ), 613 - 632. 81 CHAPTER 2 Land and Labor Bias of F arm Technology and the Labor Allocation Decisions 2.1 Introduction For over 250 years, since the first industrialization, the growth path and the preconditions of economic growth have been of great interest for many scholars. The early schola rs tried to understand the process of economic development by i solating the facto rs that trigger structural transformation. The early studies include the observations of a process of structural transformati on : the fall of the share of agriculture in employ ment (Petty , 1690; Clark , 1951; Lewis , 1954 ; Kuznets, 1957 ) ; agricultural productivity growth as the precondition of structural transformation (Rosenstein - Rodan , 1943; Schul tz, 1953; Rostow , 1959; Nurkse, 1966 ) ; and the bi - sectoral economic model to desc ribe the labor shift from rural agriculture to urban industries (Lewis , 1954; Ranis & Fei , 1961; Jorgenson , 1961; Johnston & Mellor , 1961) . In the 2010s some countries in Sub - Saharan Africa (SSA ) achieved structural tran sformation and economic growth. In spite of the stagnation of agricultural land productivity growth, the share of empl oyment in agriculture has constantly decreased sin ce the 2000s, from 82.5 percent in 2000 to 66.4 percent in 2018 (World Bank , 2019) . Whether agriculture productivi ty growth advances the labor shift from the agricu lture sector to the non - agriculture sector is still an open question and of great intere st for efficient investment in agriculture development and economic growth of the countries in SSA. From a ma croeconomic view, on the one hand, the growth in a gricultural productivity raises income per capita, which generates demand for manufactur ing goods, and the higher demand for manufactures generates a reallocation of labor away from agriculture ( Baumol, 1967; 82 Murphy et al., 1989; Kongsamut et al., 2001; Gollin et al., 2002; Ngai & Pissarides , 2007; Gollin et al., 2007) . Also, productivity growth in agriculture allows labor that w as otherwise used to produce food to b e released to other activities if productivity gro wth in agriculture is faster than in manufacturing and these goods ar e complements in consumption (Baumol , 1967; Ngai & Pissarides , 2007) . On the other hand, the increase in agricultural output lead s to an increase in agricul tural labor demand, resulting in the crowd ing - out of non - agricultural employment (Field , 1978; Wright , 1979; Corden & Neary, 1982; Krugman, 1987; Matsuyama , 1992; Mokyr , 1977, 2013) . Bustos et. al. ( 2016) show that the effects of agricultur al productivity growth on the labor shift depend on the factor - bia s of farm technology and whether land productivity or labor productivity increases. While the adoption of land - augmenting technology and land productivity growth in agriculture leads to a hi gher share of ag riculture employment at the expense of the manufac turing sector, the adoption of labor - augmenting technology and increase in labor productivity in agriculture lead to a higher share of the manufacturing sector. McGowan and Vasilakis ( 2019) find that improving land productivity in agriculture causes a relocation of the workforce not only from manufacturing but from tradable services as well. From a microeconomic view, as ne w technologies d product of l abor in farm and non - farm work change s , which determine s the household allocation of an increment in human capital services between farm production and off - farm work (Huffman , 2001) . The experience of the Philippines d uring the Green Revolution showed that because the adoption of mod ern varieties in rice farming increases the demand for labor in crop ping but does not increase the return to human capital as much as in nonfarm earnings, educated farm households tend to al locate more time away from farming to nonfarm employment (Estudillo & Otsuka , 1999) . How technology develops in farming is the essential 83 determinant of explore the relations of far m technology, fa rm productivity, and the ion, I borrow the concept of biased technology, labor - augmenting and land - augmenting technologies, from Bustos et . al. (2016) , and construct a model which explai ns how a allocation decisions are affected by labor - and land - au gmenting technological change . This chapt er consists of a theoretical part and an empirical part. In the theoretical part, I present a model to describe the hou sehold labor allocation responses to land - and labor - augmenting technical change in far ming. The model is based on the agricultural house hold model developed by Singh et. al. ( 1986) . I derive the propositions of the effects of the land - and labor - augmenting technical change from allocations . The model is then calibrated usin g microdata from the Tanzania National Panel Surve y (TNPS) in 2012/2013. The results of the calibrations satisfy all the propositions derived in the theoretical model. In the empirical part, I apply th e theoretical model to empirically test the re lations between land and labor augmenting technica l change on labor allocation between on - farm and off - farm labor suppl y, and the demand for on - farm labor. The empirical study provides micro evidence of the effect of land - and labor - augmenting technology c hange allocation s using microeconomic data from Tanzania. I exploit the variation of the adoption of land - and labor - augmenting technologies among Tanzanian maize farme rs during the input voucher program from 2008 to 2 013 and the gap of the potential yield before and after the adoption of technologies for the estimation of the effect o f land - and labor - allocation between on - farm and off - farm activities as well as the deman d of on - farm labor. 84 The remainder of the paper is organized as follows. In the theoretical part, section 2.2. 1 illustrates the theoretical model and derives propositions of the relations of the la nd - and labor - augmenting technical changes and the data and strategy of the model calibration to compute the rel ations of the household variables and the optimal on - farm family and hired labor derive d from the theoretical model. Section 2.2.3 presen ts the result s of the model calibrations. Section 2.2.4 summarizes the key findings of the theoretical study and discussions. The empirical part begins with an explanation of the background of farming techn ology and labor shift in Tanzania in section 2.3.1 . Section 2.3. 2 describes a conceptual model and estimation strategy. Section 2.3.3 illustrates the data and descriptive statistics. Section 2.3.4 presents the conceptual and empirical model as a robustness check, followed by the result s of the estimations in section 2. 3.5. Section 2.3.6 concludes with the summary of the key findings of the empirical study and discussions. 2.2 Theoretical Study 2.2.1 Theoretical Model 2.2.1.A Basic Model Suppose that a unitary house hold maximizes the utility of all family members over consumption a nd leisure, subject to budget and time constraints. Consumption is considered only as consumption of money, and the Y ) and leisure ( l ); U(Y, l; ) where are the exogenous factors which affect household preferences such as the number of adults and children. The utility function satisfies the standard assumptions : twice continuously differentiable and strictly quasi - concave. 85 F arm production is assumed to have a CES form with two inputs, labor ( L ) and land ( A ). Apart from the two inputs, a vector of regional and the household exogenous factors ( ) such as rainfall, crop disease , and the e l evel of farm production. The production function is specified as: (2. 17 ) where represents the Hicks - neutral tec hnical change, and and indicate labor - augmenting and land - augmenting technical change respectively; is elasticity of substitution between labor and land; is a parameter taking between 0 and 1. This function is not very restrictive bec ause the usual Cobb - Douglas form is included as the limit case; . F arm production satisfies the diminishing marginal product of each input and the compl e ment arity of labor and land; and where the first partial derivative of the production function with respect to labor is written as: (2. 18 ) Now assume that the off - farm labor market is flexible enough to set no constraint on that the farm labor market and land market are not functioning in remote areas . These conditions a re relaxed in section B and C below. The h ouseh old is endowed with time and land and allocates endowed time to on - farm labor ( L ), off - farm work ( O ), and leisure ( l ); . Hence, the household income ( Y ) comes from three sources : farm production, off - farm work, and non - labor income as: (2. 19 ) 86 where is the competitive price of the farm product; is wage rate of off - farm work; is non - labor income. Substituting equation (2.3) into the utility function yields: (2. 20 ) The h ousehold maximizes its utility by choosing L and l . The optimal choices, L* and l* solve the following first order conditions (FOC): (2. 21 ) (2. 22 ) The interpretation of these conditions is intuitive. By equation (2.5), the household determines the amount of on - farm labor ( L* ) so that t he value of the marginal product of labor ( ) equals the market off - farm wage ( ). By equation (2.6), the household chooses time allocated to leisure so that the marginal rate of substitution of leisure for income ( ) equals t he competitive price of leisure, which is represented by the off - farm wage rate ( ). Given the form of the marginal product of labor ( ) in equation (2.2) and FOC of equation (2.5), we have the interior solution of on - farm labor as: (2. 23 ) Figure 2.1 shows the interior and corner solutions of farm labor supply. If the interior solution of far m labor ( ) is smaller than the endowed time deduct ing the optimal time on leisure ( ), the optimal farm labor ( ) satisfies the interior solution. In this case, the household provides positive hours of labor ( ) to of f - farm work ( O ). If the interior solution ( ) is larger than the endowed time deduct ing the optimal time on leisure ( ), the optimal farm labor ( ) takes a corner solution, which equals . In this case, the household does not provide labor 87 Figure 2. 1 Interior and corner solution of the basic model to off - farm work. The optimal farm labor takes a corner solution when the endowed time, that is, the number of adults of working age is small, the preference for leisure to income is high, or the off - farm wage rate is low. The optimal farm labor is summarized as: (2. 24 ) By equation (2.7) and equation (2.8), under flexible off - farm work opportunities and no n - functioning farm labor or land market, if the household provides positive hours to off - farm work, the optimal farm labor ( ) increases as the endowed land ( ) increases while it decreases as the real off - farm wage ( ) increases. As for technical change, both Hicks - neutral technical change ( ) and land - augmenting technical change ( ) increase the optimal level of farm labor. Labor - augmenting technical change ( ), on the other hand, decreases the optimal on - farm labor un less the elasticity of substitution between labor and land ( ) is sufficiently small. Interior solution Corner solution Y Y L L Slope = Slope = 88 If the household does not provide time to off - farm work, optimal farm labor ( ) increases as endowed time ( ), that is, the number of adults of working age, increases. It also depends on household characteristics which determine the household preference for income and leisure. These relations are summarized in the proposition 2 .1. Proposition 2.1 Under flexible off - farm work opportunities and non - funct ioning farm labor or land market, (a). if the household provides positive hours to off - farm work, (i). the optimal farm labor increases as the land endowment increases while it decreases as the real off - farm wage increases; (ii). land - augmenting technical cha nge increases optimal farm labor; (iii). labor - augmenting technical change increases or decreases opti mal on - farm labor depending on the elasticity of substitution between labor and land. (b). If the household does not provide time to off - farm work, (i). optima l farm labor increases as the number of adults of working age increases; (ii). optimal farm labor depe nds on household characteristics which determine the for income and leisure. 2.2.1.B Model with On - F arm Labor Market In this section, I r ela x the assumption of a no n - functioning farm labor market. Assume that there is no constraint on hiring in on - farm labor or supplying labor to off - farm work. Also, assume that family labor and hired labor are perfect substitutes but have different levels of efficiency so that the off - farm wage rate is different from the wage rate of on - farm hired labor. I adopt the concept of the effective labor input, introduced by D eolalikar and Vijverberg ( 1987) , in which effective 89 farm labor ( L ) is given as an increasing linear function of family labor ( F ) and hired labor ( H ); and where and are the first partial derivatives of effective farm labor with respect to family labor and hired labor , respectively. Same as the basic model, the household income ( Y ) comes from three sources : far m production, off - farm work, and non - labor incom e: (2. 25 ) where is wage rate of on - farm hired labor . In equation (2.9), the net income from farm production equa ls the gross income from farm production ( ) deduct ing the payment to the hired labor ( ). Substituting equation (2.9) into the utility function yields: (2. 26 ) The h ousehold maximizes its utility by choosing F , H , and l . The optimal choices, F* , H* , and l* , solve the following FOCs: (2. 27 ) (2. 28 ) (2. 29 ) Equation (2.11) and (2.12) indicate that the household determines the amount of effective farm labor ( L* ) for farm product ion so that the value of the marginal product of family labor ( ) and hired labor ( ) equal the market off - farm wage ( ) and hired - in wage ( ) respectively. By equation (2.13), the household allocates optimal time to leisur e so t hat the marginal rate of substitution of leisure for income ( ) equals the off - farm wage ( ). Given the form of the marginal product of labor ( ) in equation (2.2) and FOCs of equations (2.11) and (2.12), we have the interior so lutions o f on - f arm labor as: 90 (2. 30 ) (2. 31 ) Figure 2.2 shows the possible cases of optimal on - farm family and hired labor. When , the optimal on - farm hired labor ( ) satisfies the second interior solution ( ), and the household does not provide on - farm family labor because the hired la bor is cheaper than family labor. In this case, the household provides the endowed time deduct ing the optimal time on leisure ( ) to off - farm work. When , there are three subcases. If the second interior solution ( ) is larger than the endowed time deduct ing the optimal time on leisure ( ), the optimal on - farm family labor ( ) takes the corn er solution, which equals while the optimal on - farm hired labor ( ) takes the second interior solution deduct ing the optimal on - farm family labor ( . In this case, the household does not provide labor to off - farm work . If the endowed time deduct ing the optimal time on leisure ( ) is between the second and first interior solutions, the optimal on - farm f amily labor ( ) again takes the corner solution, which equals . In this case, the household d oes not hire on - farm labor because family labor is cheaper than hired - in labor. Also, because the endowed time is constrained, the household does not provide labor to off - farm work. If the endowed time deduct ing the optimal time on leisure ( ) is larger than the first interior solution ( ), the optimal on - farm family labor ( ) takes the first interior solution ( ), and the household does not hire on - farm labor because family labor is cheaper than hired - in labor. In this case, th e household provides positive hours of labor ( ) to 91 Figure 2. 2 Cases of solution with on - farm l abor market off - farm work. The optimal on - farm family labor ( ) and hired labor ( ) are summarized as: (2. 32 ) Case 1. Case 2. and Y L L Slope = Slope = Case 3. and Case 4. and Y L L Slope = Slope = Y Y Slope = Slope = 92 (2. 33 ) By equation (2.14) and (2.16), under flexible off - farm work opport unities with on - farm labor market and no land market, if the household provides positive hours of labor to both on - farm and off - farm work, the optimal family labor ( ) increases as the endowed land ( ) increases while it decreases as the real off - f arm wage ( ) increases. Both Hicks - neutral technical change ( ) and land - augmenting technical change ( ) increase the optimal level of f amily labor ( ). Labor - augmenting technical change ( ), on the other hand, decreases the optimal family labor unless the elasticity of substitution between labor and land ( ) is sufficiently small. If the household does not provide labor to off - farm work, the optimal family labor ( ) increases as the endowed time ( ), that is, the nu mber of adults of working age, increases. It also depends on household characteristics which determines the household preference for income and leisure. By eq uation (2.15), and (2.17), under flexible off - farm work opportunities with on - farm labor market and no land market, if the household provides positive hours of labor to off - farm work and hires in on - farm labor, the optimal on - farm hired labor ( ) increas es as the endowed land ( ) increases while it decreases as the real on - farm hired - in wage ( ) increases. Both Hicks - neutral technical change ( ) and land - augmenting technical change ( ) increase the optimal on - farm hire d labor ( ). Labor - augm enting technical change ( ), on the other hand, decreases the optimal hired labor unless the elasticity of substitution between labor and land ( ) is sufficiently small. If the household does not provide labor to off - farm work, the optimal on - farm hire d labor ( ) decreases as the endowed time ( ), that is, the number of adults of working 93 age, increases. It also depends on household characteristics which determines the household preference for income and leisure. Th ese relations are summarized in the propositions 2.2 and 2.3. Proposition 2.2. Under flexible off - farm work opportunities wi th on - farm labor market and no n - functioning land market, (a). if the household provides positive hours of labor to both on - farm a nd off - farm work, (i). the optimal on - farm family labor increases as the endowed land increases; it decreases as the real off - farm wage increases; (ii). land - augmenting technical change increases the optimal on - farm family labor; (iii). labor - augmenting technical change increases o r decreases the optimal on - farm family labor depending on the elasticity of substitution between labor and land. (b). If the household does not provide labor to off - farm work, (i). the optimal on - farm family labor increases as the number of adults of working age increases; (ii). the optimal on - farm family labor depends on household characteristics which determine the preference for income and leisure. Proposition 2.3. Under flexible off - farm work opportunities with on - farm labor market and no n - function ing land market, (a). if the household provides positive hours of labor to off - farm work and hires in on - farm labor, (i). the optimal on - farm hired labor increases as the endowed land increases; it decreases as the real on - farm hired - in wage incre ases; (ii). l and - augmenting technical change increases the optimal on - farm hired labor; 94 (iii). labor - augmenting technical change increases or decreases the optimal on - farm hired labor depending on the elasticity of substitution between labor and land. (b). If th e househol d does not provide labor to off - farm work, (i). the optimal on - farm hired labor decreases as the number of adults of working age increases; (ii). the optimal on - farm hired labor depends on household characteristics which determine the preference for i ncome and leisure. 2.2.1.C Model with Binding Constraint on Off - F arm Job Opportunities H eterogeneous households choose the optimal time allocation by maximizing their utilities with or without facing a binding constraint on the off - farm work opportunities. In th is section, assume that the off - farm work opportunities are limited and binding at . Then, the time spent on leisure is given as . The corresponding household income and utility function are written as: (2. 34 ) (2. 35 ) The h ousehold maximizes its utility ( U ) with respect to family labor ( F ) and hired labor ( H ) . Th e optimal level of family labor ( ) and hired labor ( ) satisfy the following FOCs: (2. 36 ) (2 . 37 ) Equation (2.20) and (2.21) show that the household determines effective farm labor ( L* ) for farm production so that the value of the marginal product of family labor ( ) and hired labor ( ) 95 equal the mar gin al rate of substitution of leisure for income ( ) and on - farm hired - in wage ( ) respectively. Given the form of the marginal product of labor ( ) in equation (2.2) and FOCs of equations (2.20) and (2.21), we have the interior sol utions of on - farm labor as: (2. 38 ) (2. 39 ) Figure 2.3 shows the cases of solution of optimal on - farm family and hired labor. When , the household does not provide on - farm f ami ly labor because hired labor is cheaper than family labor. In this case, the optimal on - farm family labor ( ) take s the second interior solution ( ). When , the household does not hire on - farm labor because family labor is chea per than hired labor. In this case, the optimal on - farm family labor ( ) takes the third interior solution ( ) . The optimal on - farm family labor ( ) and hired - in labor ( ) are summarized as: (2. 40 ) (2. 41 ) By equation (2.22) and (2.24), under binding constraint s o n off - farm work o ppo rtunities, if the household provides positive hours to on - farm family labor, the optimal family labor ( ) depends on the household characteristics which determine the preference for income and leisure. If the household hires on - farm labor, the opti m al on - farm hired labor ( ) increases as the 96 Figure 2. 3 Cases of solution with binding constraint on off - farm work opportunities endowed land ( ) increa ses while it decreases as the real on - farm hired - in wage ( ) increases. Both Hicks - neutral technical change ( ) and land - augmenting technical change ( ) increase the optimal on - farm hired labor ( ). Labor - augmenting technical chang e ( ), on the other hand, decreases the optimal hired labor unless the elasticity of substitution between labor and land ( ) is sufficiently small. These relations are summarized in the propositions 2.4. and 2.5. Proposition 2.4. Under binding con str aint s o n off - farm work opportunities and a no n - functioning land market, if the household provides positive hours to on - farm labor, (i). the optimal on - for inc ome and leisure. Propo sition 2.5. Under binding constraint s o n off - farm work opportunities and a no n - funct i oning land market, if the household hires on - farm labor, Slope = L Slope = Q L Y Case 1. Case 2. L Q L Y Slope = 97 (i). the optimal on - farm hired labor increases as the endowed land increases; it decrease s a s the real on - farm hir ed - in wage increases; (ii). land - augmenting technical change increases the optimal on - farm hired labor; (iii). labor - augmenting technical change increases or decreases the optimal on - farm hired labor depending on the elasticity of substi tut ion between labor and land. 2.2.2 Data and Strategy of Model Calibration 2.2.2.A Identification of the Household Regime and Summary of Propositions H eterogeneous households choose optimal time allocations by maximizing their utilities. Each household choose s th e inte rior or corner solutions of the on - farm family labor supply and hired labor demand given the exogenous household and regional variables. With the existence of the on - farm labor market, the interior and corner solutions of the optimal on - farm famil y l abor s upply and hired labor demand present six cases. According to the six solution cases, the households are classified into six regimes, which are interpreted a ccording to the two observable and one unobservable criteria: whether the household spends pos itive hours on off - farm work , whether the household hires in positive hours of on - farm labor, and whether the constraints o n off - farm work opportunities are binding. Table 2.1. shows the classification of the household regimes. Each regime corresponds to a case in Figure 2.2 or Figure 2.3. The corresponding case to each regime is presented in the table. The optimal choices of on - farm family labor ( ) and hired labor ( ) in each regime are given by the functions of the different set of variables. Those relations correspond to the propositions 2.2, 2.3, 2.4, and 2.5. Table 2.2. summarizes the relations. 98 Table 2. 1 C lassification of household regime The h ousehold regime Regime I Regime II Regime III Regime IV Regime (i) Regime (ii) Regime (iii) Regime (iv) Regime (v) Regime (vi) Observable criteria Spend positive hours on off - far m work Yes Yes Y es Yes No No Hire in positive hours of on - farm labor Yes Yes No No No Yes Unobservable criteria Off - farm job constraint is binding No Yes No Yes No No Case no. in Figure 2.2 Case 1 - Case 4 - Case 3 Case 2 Case no. in Fi gure 2.3 - Case 1 - Case 2 - - Table 2. 2 Household regime and optimal on - farm labor The h ousehold regime Optimal on - farm family labor ( ) Proposition Optimal on - farm hired labor ( ) Proposition Regime (i) - Proposition 2.3.(a) Regime (ii) 0 - Proposition 2.5 Regime (iii) Proposition 3.2.(a) - Regime (iv) Pro position 3.4 - Regime (v) Proposition 3.2.(b) - Regime (vi) Proposition 3.2.(b) Proposition 2.3.(b) Notes: The specifications of , , and are giv en in equations (2.14), (2.15), and (2.22) respectively. is the set of variables which determine the - labor income, and meso - variables. 99 2.2.2.B Data I c alibrate the m ode l using data from the Tanzania National Panel Survey (TNPS 4 ) and show the relations of the household variables and the optimal on - farm family labor supply and hired labor demand . The relations correspond to the propositions in section 2.2.1. I use data fro m household, agriculture, and community questionnaires in mainland for the h ouseholds who cultivate maize. Among 3,021 households in the mainland, 2,892 households cultivate mai ze. Table 2. 3 Number of households in each regim e b y year 2008/2009 2010/2011 2012/2013 Regime Obs. Share Obs. Share Obs. Share Regime I a 189 0.11 296 0.15 434 0.18 Regime II b 297 0.18 547 0.28 709 0.29 Regime III c 723 0.43 726 0.38 759 0.31 Regime IV d 471 0.28 359 0.19 525 0.22 Total 16 80 1.00 1928 1.00 2427 1.00 Notes: a The h ousehold spends time on off - farm work and hires in on - farm labor. b The h ousehold spends time on off - farm work and does not hire in on - farm labor. c The h ousehold does not spend time on off - farm w ork or hire in on - farm labor. d The h ousehold does not spend time on off - farm work but hires in on - farm labor. Table 2.3 displays the number of households in each regime by year. Because we cannot identify whether the household faces a bindin g c onstraint o n off - farm work opportunities by the observable variables, in Table 2.3 the households are classified into 4 regimes by two observable criteria. Table 2.3 shows that the number o f households who spend time on off - farm work , that is the number of households in regime I and II, constantly increases from 2008/2009 to 2012/2013. Although just 29 percent of hou seholds spend time on off - farm work in 2008/2009, 47 percent of households spend time on off - farm work in 2012/2013. Also, the share of hous eho lds who hire in on - farm labor, that is the number of households in regime I and IV, increases from 39 percent in 4 TNPS was implemented by the Tanzania N ational B ureau of S tatistics . 100 2008/2009 to 40 percent in 2012/ 2013. For the balancing of the number of households in each regime, I use the data from 2012/2013 for the m ode l calibrations. Table 2.4 shows summary statistics of the household and district variables in 2012/2013 by household regime. Although in the theoretical model the households in the first (I) regime do not do on - farm work (Figure 2.2 , Case 1), i n p ractice (beyond the theoretical model) they spend time on on - farm work. This would be because the expected off - fa rm wage varies across the household members, and for some members the expected off - farm wage could be lower than the on - farm wage even if th e h ousehold average expected off - farm wage among all members i s higher than the household average expected on - farm w age. For those who face a lower expected off - farm wage than the on - farm wage, there exists the incentive to spend time on on - farm work. In t erm s of the solutions of the optimal on - farm family labor, the households in regime II take the interior solution of the optimal on - farm family labor while the households in regime III and IV take the corner solution of the optimal on - farm family labor (Fi gur e 2.2 , Case s 2, 3, and 4). The household s in regime II, as described by the theoretical model, ha ve mo re adult s of working age, that is , a larger time endowment. The household s in regime II also ha ve more children age d from 0 to 3 than the household s in re gime III and IV. This corresponds to the theoretical model if the household with more infants and todd lers has a higher preference for money to leisure. The off - farm wage and on - farm hired - in wage at the household level also coincide with the model. The av erage off - farm wage of the households in regime I is higher than that of the households in regime II ( Figure 2.2 , Case s 1 and 4) while the average on - farm hired - in wage is higher for the households in regime IV than for the household in regime I (Figure 2. 2 , Case s 1 and 2). In case the household is facing a binding constraint o n the off - farm work opportuni ties (Figure 2.3), the level of the constraint is likely to be tighter for the households in regime II than for the 101 Table 2. 4 Household and district variables in 2012/2013 by household regime Regime I a Regime II b Regime III c Regime IV d Mean P50 Sd Mean P50 Sd Mean P50 Sd Mean P50 Sd Household variable Labor allocation On - farm family lab or (day) 123.5 82.5 139.1 117.8 82.0 112.7 127.7 94.0 135.0 116.0 82.0 127.2 On - farm hired labor (day) 32.9 14.0 60.6 0.0 0.0 0.0 0.0 0.0 0.0 31.5 16.0 43.8 Off - farm labor (day) 193.3 84.0 258.5 131.9 55.8 171.4 0.0 0.0 0.0 0.0 0.0 0.0 H ousehold characteristics Land holding s (acre s ) 10.8 4.4 35.4 5.6 2.9 11.7 6.9 4.0 9.8 10.6 5.2 23.6 Number of adult s age d 15 - 65 3.3 3.0 1.9 3.1 3.0 1.6 2.9 2.0 1.9 2.6 2.0 1.8 Number of child ren age d 0 - 3 0.8 1.0 0.9 0.8 1.0 0.9 0.7 1.0 1.1 0.7 0.0 1.0 Number of child ren age d 3 - 6 0.5 0.0 0.7 0.5 0.0 0.7 0.5 0.0 0.7 0.5 0.0 0.7 Number of child ren age d 7 - 14 1.3 1.0 1.3 1.3 1.0 1.3 1.3 1.0 1.3 1.2 1.0 1.3 1=HH is female 0.20 0.00 0.40 0.23 0.00 0.42 0.24 0.00 0.4 2 0.26 0.00 0.44 s ) 6.0 7.0 4.3 5.2 7.0 3.3 4.4 6.0 3.2 4.7 6.0 3.5 1=member belongs to SACCO 0.14 0.00 0.34 0.04 0.00 0.18 0.02 0.00 0.14 0.04 0.00 0.20 Wage at household level Off - farm wage ( USD /hour) 4.0 1.4 19.4 3.7 1 .5 8.0 - - - - - - On - farm wage ( USD /hour) 1.3 0.9 1.9 - - - - - - 1.4 0.9 1.8 District variable Off - farm wage ( USD /hour) 1.3 1.1 0.5 1.2 1.1 0.5 1.3 1.2 0.6 1.3 1.2 0.6 On - farm wage ( USD /day) 5.2 4.8 1.4 5.2 4 .9 1.4 5.2 4 .9 1.2 5.3 4.9 1.3 Local price of maize ( USD /kg) 1.0 1.0 0.2 0.9 1.0 0.2 0.9 1.0 0.2 0.9 1.0 0.2 Observations 434 709 759 525 Notes: USD used in the table is 2011 PPP USD . The mean and median of wages at househ old level are computed by using only positive values of wages. SACCO refers to Savings and Credit Co - Operative . a The h ousehold spends time on off - farm work and hires in on - farm labor. b The h ousehold spends time on off - farm work and does not hire in on - farm labo r. c The h ousehold does not spend time on off - farm work or hire in on - farm labor. d The h ousehold does not spend time on off - farm work but hires in on - farm labor. 102 households in regime I. The share of households who have a female househo ld head is la rger, the r who belongs to Savings and Credit Co - Operative ( SACCO ) is lower in regime II than in regime I. In fact, the households in regime I provide 193.3 days to off - farm work , which is greater than 131.9 days provided by those in regime II. 2.2.2.C Parameter Values Table 2.5 presents the values of the calibration parameters and a brief explanation of how the value of each parameter is selected. The weighted mean of each var iable among the households in each regime is selected as the parameter value if the variable is available in TNPS 2012/2013. The values of share parameter ( ) and EOS (elasticity of substitution) between land and labor ( ) are taken from my estimates of the CES production function. The detail of the estimation of the CES production function is in section 2.3.2.B. The land - and labor - augmenting technical cha nge ( and ), Hicks - neutral technical change ( ), and the efficiency of hired labor ( ) are normalized at one unless the variable is used as the indefinite number in the model calibration. The value of efficiency of family labor ( ), 2.54, is collected from the estimate by Deolalikar and Vijverberg ( 1987) , who introduced the concept of effective farm labor that I applied in the theoretical model . The strategy of the calibration exercise is to restrict the values of the farm production variables ( ) to match the observations of on - farm family and hired labor ( F and H ) variables from TNPS 2012/2013. The model is then calibrated to show the relations of the optimal on - farm family and hired labor and other variables to correspond to the prop ositions in section 2.2.1. For the households in regime I, I used equation (2.14) to set the farm production variables ( ) by 103 Table 2. 5 Calibration parameters Parameter Value Explanations Regime I a Regime II b Regim e III c Regime IV d Household parameters Land holding s (acre s ) 8.04 4.94 5.87 9.07 Weighted mean from TNPS 2012/2013 Number of adult s age d 15 - 65 3.09 2.94 2.71 2.37 Weighted mean from TNPS 2012/2013 Time endowment (day) 1127.85 1073.1 989.15 865.05 Number of adult s multiplied by 365 Off - farm labor (day) 172.54 127.63 0.00 0.00 Weighted mean from TNPS 2012/2013 Farming parameters On - farm family labor (day) 119.17 110.27 124.82 108.58 Weighted mean from TNPS 2012/2013 On - farm hired labor (day) 28.52 0.00 0.00 32.91 Weighted mean from TNPS 2012/2013 Share parameter 0.82 0.80 0.82 0.85 e EOS between land and labor 0.67 0.70 0.69 0.65 e Farm production variables 10.30 2.61 - 21.18 Set to equalize right and left - hand sides f Efficiency of family labor - 2.54 - - From Deolalikar and Vijverberg ( 1987) Efficiency of hired labor 1.00 - - 1.00 Normalization Land - augmenting technical change 1.00 1.00 1.00 1.00 Normalization Labor - augmenting technical change 1.00 1.00 1.00 1.00 Normalization Hicks - neutral technical change 1. 00 1.00 1.00 1.00 Normalization District parameters Off - farm wage ( USD /hour) 1.24 1.15 1.28 1.27 Weighted mean from TNPS 2012/2013 On - farm wage ( USD /day) 5.23 5.25 5.29 5.34 Weighted mean from TNPS 2012/2013 Local market price of maize 0.96 0.95 0.91 0.96 Weighted mean from TNPS 2012/2013 ( USD /kg) Observations 434 709 759 525 Number of households Notes: USD used in the table is 2011 PPP USD . a The h ousehold spends time on off - farm work and hires in on - farm labor. b The h ousehold spends time on off - farm work and does not hire in on - farm labor. c The h ousehold does not spend time on off - farm work or hire in on - farm labor. d The h ousehold does not spend time on off - farm work but hires in on - farm labor. e Th e detail of the estimation of share parameters ( ) and EOS ( ) is in section 2.3.2.B. f The detail of setting production variables is explained in section 2.2.2.C. 104 equalizing the right and left - hand sides of the equation. For the households in regime II and IV, equation (2.23) is used to set the farm production variables ( ) while the observed on - farm family labor ( F ) is used as the value of the endowed time deduct ing the optimal time on leisure ( ) for the households in regime IV because the households in regime IV does not spend time on off - farm work. By using set values of the farm production variables ( ), the model is calibrated by changing endowed land, off - farm or on - farm wage, land - augmenting technical change , la bor - augmenting technical change , and EOS between land and labor respectively to derive the relations of those variables and the optimal on - fa rm family and hired labor. Those relations correspond to the propositions in section 2.2.1. 2.2.3 Result of Model Calibr ation 2.2.3.A Bias of Farm Technology and On - F arm Family Labor Figure 2.4 shows the relations of optimal on - farm family labor and the household variables. Panel A, B, C, and D of Figure 2.4 correspond to propositions 2.2.a.(i), (i), (ii), and (iii) respective ly. The calibration was done by using the weighted mean of the variables of the households in regime II. The figures show that the relations of the household variables and optimal on - farm family labor all satisfy the propositions. In panel A and C, the lan d h olding s and the land - augmenting technical change both show positive correlations with the optimal on - farm family labor regardle ss of the value of the EOS between land and labor. In panel B, the off - farm wage is negatively correlated with the optimal on - far m family labor at any value of the EOS. In panel D, on the other side, labor - augmenting technical change displays both positive and negative correlations with the optimal on - farm family labor depending on the value of the EOS between land and labor. 105 Figure 2. 4 Relations of optimal on - farm family labor and other variables 106 The calibration results show that an additional one acre of landholding s increases the optimal on - farm family labor by 22.3 person - da y s from 110.3 person - day s to 132.6 per son - day s at the weighted mean of landholding s , 4.94 acre s , and EOS between land and labor, 0.70. The effect of additional land holding s increases as the EOS increases. The increase in one dollar per hour off - farm wag e i s accompanied by the decrease in the o ptimal on - farm family labor by 70.2 person - day s when off - farm wage and EOS take the weighted means, 1.15 USD per hour and 0.70 respectively. The effect of off - farm wage increases as the EOS between land and labor in cre ases or off - farm wage decreases. Since the optimal on - farm family labor is the multiplication of the land - augmenting technical change and other variables, one percent increase in land - augmenting technical change is associated with one percent increase i n t he optimal on - farm family labor. Hence , when EOS takes the weighted mean, 0.70, 10 percent land - augmenting technical change from 1.0 to 1.1 increases the optimal on - farm family labor by 10 percent from 110.3 person - day s to 121.3 person - day s . The effect of the land - augmenting technical change increases as the EOS between land and labor increases. The labor - augmenting technical change , on the other side, increases and decreases the optimal on - farm family labor depending on the values of the EO S between lan d a nd labor. When the EOS is greater than 0.56, labor - augmenting technical change is positively correlated with the optimal on - farm family labor at any value of labor - augmenting technical change between 0 and 1. When labor - augmenting technical change is sm all er than 0.23, the EOS is negatively correlated with the optimal on - farm family labor at any value of the EOS between 0 and 1. When EOS takes the weighted mean, 0.70, the increase in labor - augmenting technical change from 1.0 to 1.1 results in the increa se in the optimal on - farm family labor by 4.5 person - day s from 110.3 person - day s to 114.8 person - day s . The effect of labor - augmenting technical change is positive because EOS takes 0.70, which is greater than 0.23. 107 2.2.3.B Bias of Farm Technology and On - F arm H ired L abor Figure 2.5 shows the relations of optimal on - farm hired labor and the household variables. Panel A, B, C, and D of Figure 2.5 correspond to propositions 2.3.a.(i) and 2.5.(i), 2.3.a.(i) and 2.5.(i), 2.3.a.(ii) and 2.5.(ii), and 2.3.a.(iii) and 2.5.(i ii) respectively. The calibration was done by using the weighted mean of the variables of the households in regime I. The figure shows that the propositions are all satisfied by the relations of the household variables and the optimal on - farm hired l abor. In panel A and C, the land holding s and the land - augmenting technical change both show the positive correlations with the optimal on - farm hired labor regardless of the value of the EOS between land and labor. In panel B, the off - farm wage is negative ly cor related with the optimal on - farm hired labor at any value of the EOS. In pan el D, on the other side, labor - augmenting technical change displays both positive and negative correlations with the optimal on - farm hired labor depending on the value of the EOS b etween land and labor. The calibration results show that an additional one acre of landholding s increases the optimal on - farm hired labor by 3.5 person - day s from 28.5 person - day s to 32.1 person - day s at the weighted mean of landholding s , 8.04 acre s , and EOS between land and labor, 0.67. The effect of additional land holding s increases as the EOS increases. Additional one dollar per hour on - farm hired - in wage decreases the optimal on - farm family labor by 10.1 person - day s when on - farm hired - in w age an d EOS take the weighted means, 5.23 USD per day and 0.67 respectively. The effect of on - farm hired - in wage increases as the EOS between land and labor increases or on - farm wage decreases. Similar to the optimal on - farm family labor, one percent incre ase in land - augmenting technical growth is accompa nied by one percent increase in the optimal on - farm 108 Figure 2. 5 Relations of optimal on - farm hired labor and other variables 109 hired labor. Hence, when EOS takes th e weig hted mean, 0.67, 10 percent land - augmenting technical growth from 1.0 to 1.1 increases the optimal on - farm hired labor by 10 percent from 28.5 person - day s to 31.4 person - day s . The effect of the land - augmenting technical change increases as the EOS be tween land and labor incr eases. The labor - augmenting technical change , on the other side, increases and decreases the optimal on - farm hired labor depending on the values of the EOS between land and labor. When the EOS is greater than 0.39, labor - augmenting techn ical change is posi tively correlated with the optimal on - farm hired labor at any value of labor - augmenting technical change between zero and one . When labor - augmenting technical change is smaller than 0.65, the EOS is negatively correlated with the o ptimal on - farm family lab or at any value of the EOS between zero and one . When the EOS takes the weighted mean, 0.67, the increase in labor - augmenting technical change from 1.0 to 1.1 results in the increase in the optimal on - farm hired labor by 3.5 person - day s from 28.5 person - da y s to 32.0 person - day s . The effect of labor - augmenting technical change is positive because EOS takes 0.67, which is greater than 0.39. 2.2.4 Conclusion This study provides a theoretical model to explain how land and labor - augmenting t echnic al changes - farm family and hired labor. The model is based on the agricultural household model, which was developed by Singh et. al. ( 1986) . I derive the propositions of the effects of land and labor - augmenting technical change on the ho decisions on labor. The model calibration results satisfy all the propositions derived in the theoretical model. The calibrations are done by using microdata from Tanzania National Panel Survey (TNPS) in 2012/2013. The households are, as de scribe d in the theoretical model, 110 classified into regimes by whether they face a binding constraint o n the off - farm work opportunities and whether they are in off - farm or on - farm labor markets. The results show that labor - and land - augmenting tec hnical changes could have the the EOS takes the weighted mean, the land - augmenting technical change from 1.0 to 1 .1 increases the optimal on - farm family labor from 110.3 person - day s to 121.3 pers on - day s and the optimal on - farm hired labor from 28.5 person - day s to 31.4 person - day s . L abor - augmenting technical change , on the other side, increases and decreases the optimal on - farm family labor depending on the values of the EOS between land and labor. L abor - augmenting technical change is negatively correlated with the optimal on - farm family labor and on - farm hired labo r for at least some value of labor - augmenting technical change between 0 and 1 when EOS is smaller than 0.56 and 0.39 respectively. When the E OS takes the weighted mean, the increase in labor - augmenting technical change from 1.0 to 1.1 results in the incre ase in the optimal on - farm family labor by 4.5 person - day s from 110.3 person - day s to 114.8 person - day s and the optimal on - farm hired lab or by 3.5 person - day s from 28.5 person - day s to 32.0 person - day s . The results suggest that depending on the con ditions of a country such as the level of EOS between land and labor and the constraints on off - farm work opportunities, labor - augmentin g farm technologies ha ve a good potential for accelerating structural transformation in SSA countries. 2.3 Empirical Study 2.3.1 Farm Technology and Labor Shift in Tanzania In Tanzania, the agriculture sector has long been identified as the key driver for econ omic 111 d evelopment . Since the Tanzania Development Vision 2025 5 raised the priority of agricultural sector d evelopment for the acceleration of the economic growth and poverty reduction in 1999, the government has allocated a lot of resources into agricultura l prog rams. In 2003, the government of Tanzania agreed to allocate a minimum of 10 percent of its budget t o the agricultural and rural sector, which was reaffirmed through the C omprehensive Africa A gricultural D evelopment P rogram (CAADP) in 2010. From 2008 to 20 13, the government invested approximately 300 million US D including a concessional loan of 160 milli on US D from the World Bank to provid e small - scale maize and rice farmers with input vouchers of fertilizer and improved seeds (World Bank , 2014) . rowth, aggregate productivity has shown little growth in the last 20 years, which remains only 20 to 30 percent of potential yield s (World Bank , 2009) . Yet, in terms of the labor reallocation in the development process, the share of employment (measuring in terms of sh are of number of persons doing some farming) in agriculture has constantly decreased since 2000, from 82.5 percent in 2000 to 66.4 percent in 2018, in Tanzania (Worl d Bank , 2019) . Whether agriculture productivity growth advances the labor shift from agriculture sector to the non - agriculture sector is still an open question and of great inte rest for efficient investment in agriculture development and economic growth o f the country. Following the success of high - yielding varieties (MVs) of rice and wheat in Latin American and Asian countries in the mid - 1960s, large numbers of MVs were released in Sub - 5 Tanzania Development Vision 2025 was first adopted in 2000 wit h the goal of transforming the country into a strong and competitive middle income economy by 2015. During the first five ye ar plan, the government ty in the agriculture sector, increase the num ber of skilled laborers, and enhanced the business environment within the coun try (Tanzania Invest, 2019) . 112 Saharan African countries in the 1960s and 1970s (Evenson & Gollin , 2003) . In spite of the release of the MVs, few farmers adopted MVs in the 1960s an d 1970s in Sub - Saharan Afric a . Because MVs respond to fertilizer better than t raditi onal varieties, the diffusion of MVs has been always considered jointly with the application of the fertilizer. In Tanzania, the government operated the input sub sidy program in the 1970s and early 1980s to promote the adoption of fertilize r and improved seeds. The program was, however, criticized for being costly, inefficient, overwhelmingly beneficial to large farmers, and detrimental to the private sector (Carter et al., 2013) . Because of the criti ques , input subsidies were phased out du ring a gricultural market liberalization in 1990s (Putterman , 1995) . Ten years later, the government instituted a transport subsidy for fertilizer, which was replaced with a voucher - based subsidy called the national agricultural input voucher scheme (NAIVS) in 2008. In 2008, the adoption rate of i mprove d seeds and fertilizer w as still low; improved seeds were adopted by eight percent of maize farmers, and only three percent of farmers applied fertilizer ( National Breau of Statistics , 2012) . NAIVS was started in 56 pilot districts in 2008 and extended to 65 dist ricts in 2009 as part of a thr ee - year program until 2013. Learning from the inefficiency of the past universal price subsidy programs, N AIVS was targeted to the high - potential small - scale farms (Druilhe & Barreiro - Hurlé , 2012) . The eligible households are those who (1) are able to top up the price of inputs purchased with the voucher; (2) are literate; (3) do not c ultivate more than 1 ha of maize or rice; with priority to be given to female headed households who have used little or no modern inputs on maize or rice in the prior five years (Pan & Christiaensen , 2012) . The program resulted in an increase in maize yields by an average of 433 kg per acre among farmers receiving subsidized maize seed and fertilizer. 47 percent of the farmers wh o had 113 never tried improved inp uts prior to the NAIVS continued to purchase seed on their own, and 19 percent continued to purchase fertilizer (World Bank , 2014) . However, because of the targeting structure of the program and the reported operational problems and fraud, the number of farmers who were benefitted by the program was limited. A ggre gate productivity of maize displayed almost no growth from 1990 to 2012 in Tanzania (World Bank , 2014) . The productivity remains only 20 to 30 percent of potential yield (World Bank , 2009) . Compared to improved seeds and fe rtilizer, the government has put little effort in to promot ing other farming technologies such as irrigation, spray er, pe sticide, herbicide, animal traction, or tractor uses . Given the fact that the average size of the land holdings remains small, ranging f rom 0.2 to 2 .0 hectares, and only 26 percent of potentially arable land is currently farmed in Tanzania (World Bank , 2014) , there is much potential for increasing labor productivit y by increasing f arm si ze and the adoption of labor - augmenting technologies. Also, in terms of structural transformation, that is the labor shift from the farming sector to the non - farm sector, labor productivity growth in agriculture sector contributes to the lab or shi ft more than land productivity growth (Bust os et al., 2016) . Because the share of employment in agriculture has constantly decreased since the 2000s, from 82.5 percent in 2000 to 66.4 percent in 2018 ( World Bank , 2019) in spite of the st agnation of the agricultural land productivity growth, the relation between the adoption of land or labor - augmenting technology, agricultural productivity, and the labor shift from farming sector to non - farm sector is s till a n open question. In the followi ng sections I estimate the effect of land - and labor - augmenting technolog ies on the household decisions on labor allocation by exploiting the variation in the potential yield increase by the adoption of farm technologie s . 114 2.3.2 C onceptual Model and Estimation Strategy 2.3.2.A A Model of Biased Farm Technology and Labor Allocation I assume that a unitary household maximizes income ( Y ) given the endowment of labor ( ) and cultivated land ( ). The h ousehold allocates the endowed labor between on - farm family labor ( F ) and off - farm labor ( O ). Suppose that land market is not functioning in rural area s but t h e h ousehold faces a perfect farm labor market where the hou sehold hires in farm labor at a given wage without restrictions. The h duction and off - farm activity. It is written as: (2. 42 ) where i s the competitive price of the farm product; is farm production which is determined by two inputs, labor ( L ) and land ( A ), and the vector of exogenous variables ( ) such as rainfall, crop disease , and the is on - farm hired labor; is wage rate of on - farm hired labor ; is wage rate of off - farm labor . F arm production is assumed to have CES form which is specified as: (2. 43 ) where represents Hicks - neutral technical change, and and indicate labor - augmenting and land - augmenting technical changes respectively; is the elasticity of substitution between labor and land; is a parameter taking between 0 and 1. This function is not very restrictive because the usual Cobb - Douglas form is included as the limit case; . F arm production satisfies the diminishing marginal product of each input and the compl e ment f eature of labor and land; and where the first derivative of the production function with respect to labor is written as: 115 (2. 44 ) Assume that family labor and hired labor are perfect substitutes but have different efficienc ies . The off - farm wage rate is, therefore, different from th e wage rate of on - farm hired labor. I adopt the concept of effective labor input introduced by Deolalikar and Vijverberg ( 19 87) , in which effective farm labor ( L ) is given as an increasing linear function of family labor and hired labor; and where and are the first partial derivatives of effective farm labor with respect to family labor and hired labor respectively. The optimal on - farm family labor ( ) and on - farm hired labor ( ) solve the following FOCs: (2. 45 ) (2. 46 ) Equation (2.29) and (2.30) indicate that the household determines the amount of effective farm labor for farm production so that the value of the marginal product of family labor ( ) and hired labor ( ) equal the market off - farm wage ( ) and hired - in wage ( ) respectively. Given the fo rm of the marginal product of labor ( ) in equation (2.28) and FOCs of equation (2.29) and equation (2.30), we have t he interior solutions of on - farm family and hired labor as: (2. 47 ) (2. 48 ) 116 By equation (2.31) and (2.32) , when interior solutions exist, the optimal on - farm family labor ( ) increases as t he endowed cultivated land ( ) increases. It decreases as the off - farm wage relative to the price of farm production ( ) increases. As for technical changes, both Hicks - neutral technical change ( ) and land - augmenting technical change ( ) increase the optimal family labor. Labor - augmenting technical change ( ), on the other hand, decreases the optimal on - farm family labor unless the elasticity of substitution between labor and land ( ) is sufficie ntly small. Similarly, the o ptimal on - farm hired labor ( ) increases as the endowed land ( ) increases. It decreases as the hired - in wage relative to the price of farm production ( ) increases. Hicks - neutral technical change and land - augmenting tech nical change incr ease the optimal on - farm hired labor. Labor - augmenting technical change decreases the optimal hired - in labor unless the elasticity of substitution between labor and land is sufficiently small. These relations are summarized in the proposit ion 2.6. Proposi tion 2.6. Under an unrestricted labor market with a no n - functioning land market, a) the optimal on - farm family labor increases as the endowed cultivated land increases; it decreases as off - farm wage relative to production price increases; b) land - augmenting te chnical change increases the optimal on - farm family labor; c) labor - augmenting technical change decreases the optimal on - farm family labor unless the elasticity of substitution between labor and land is sufficiently small; d) the optimal on - farm hired labor incr eases as the endowed land increases; it decreases as on - farm hired - in wage relative to produ ction price increases; e) land - augmenting technical change increases the optimal on - farm hired labor; f) labor - augmenting technical change decreases the optimal on - farm h ired labor unless the elasticity of substitution between labor and land is sufficiently smal l. 117 2.3.2.B Estimating t he Elasticity of Substitution between Labor and Land Proposition 2.6 presents that the effect of labor augmenting technical change on optimal on - far m family and hired labor depends on the elasticity of substitution (EOS) between labor and l and ( ). In this section I estimate the EOS between labor and land by estimating the CES farm production function. I present the estimations by climate zone using plot level data. Figure 2.6 shows the climate zones in Tanzania from the Global Y ield G ap A tlas (GYGA , 2019) . The climate zone consists of three categorical values: growing d egree days (GDD), annual aridity Figure 2. 6 Climate zones in Tanzania Notes: The z oning map is s ourced from GYGA (2019) . 118 Table 2. 6 Classification of categorical values and climate zone s (1) (2) (3) GDD Climate zone AI Climate zone TS Climate zone 5950 - 7111 6000 2696 - 3893 100 0 - 3832 01 7112 - 8564 7000 3894 - 4791 200 3833 - 8 355 02 8565 - 9311 8000 4792 - 5689 300 >8356 03 5690 - 6588 400 6589 - 7785 500 7786 - 8685 600 8686 - 10181 700 Notes: Classifications are cited from GYGA (2019) . index (AI), and temperature seasonality (TS). GDD and AI are calculated as: (2. 49 ) (2. 50 ) where is temperature ( ) for each time period, MAP is mean annual precipitation (100 mm), and MAE is mean annual potential evapotranspiration (100 mm). TS is calculated as the standard deviation of the 12 mean monthly temperatures (10 ). The data of temperature, precipitation, and temperature seasonality are taken from University of East Anglia Climate Research Unit (CRU , 2019) , CGIAR Consortium for Spatial Information (CGIAR , 2019) , and World Clim Global Climate Data (World Clim , 2019) respectively. The classification of three categorical values and the climate zones a re summarized in Table 2.6. To estimate the production function by climate zone, for each estimation I include all the observations in the regions which hav e the climate zone in the region. I assume the EOS does not change over time. By taking the log of e quation (2.27), we have the CES production function as: (2. 51 ) 119 where is parameter formed by EOS ( ): (Kumar & Gapins ki , 1974) nonlinear least square (NLLS) estimator using pooled data. The specification of the estim ation is: (2. 52 ) where subscripts , , and represent plot, household, and ti me respectively; is total kg of harvested maize; is total days of on - farm labor; is total acre s of the plot; is the vector of exogenous household and plot characteristics which affect the level of production a s well as the total value of farm assets and total expenses on input s ; and are plot and household unobserved heterogeneities. The vector of exogenous variables ( ) include perienced d r o ught or flood, crop disease , price decrease of the crop, price rise of the input, water shortage in a year, whether the plot is with title or not, and the year s since the household acquired the plot. Unobserved heterogeneities are controlled b y the obser ved time - household head is female, type and quality of the soil, and slope of the plot. Table 2.7 presents the result of the estimations of production function and the EOS by climate zone. The estimates of the EOS rang e from 0.303 to 1.258. All the estimates are statistically significant at from one to ten percent confidence levels. 120 Table 2. 7 Estimation of the production function and the elasticity of subst itution between labor and land by climate zone (NLLS) Dependent variable: Climate zone Ln(harvested maize (kg)) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Explanatory variables 7101 7201 7301 6501 8301 8401 7601 7501 7701 7401 Household variables HH education (year s ) 0.067*** 0.005 0.014 0.062*** 0.018 0.042* 0.027 0.085*** 0.039* 0.032** (0.024) (0.017) (0.016) (0.023) (0.018) (0.023) (0.027) (0.024) (0.023) (0.016) HH age (year s ) - 0.018*** - 0.012*** - 0.000 - 0.003 - 0.018*** - 0.014*** - 0.021* ** 0.011* - 0.005 - 0.002 (0.006) (0.003) (0.003) (0.005) (0.004) (0.005) (0.005) (0.005) (0.006) (0.003) 1 = HH is female - 0.007 - 0.109 - 0.082 0.038 - 0.101 0.233 - 0.059 - 0.127 - 0.007 - 0.141 (0.184) (0.137) (0.123) (0.162) (0.145) (0.157) (0.180) (0.191 ) (0.173) (0.119) 1 = experience d draught or - 0.365** - 0.412*** - 0.434*** - 0.356** - 0.339** - 0.282 - 0.149 - 0.350** - 0.519*** - 0.515*** flood (0.163) (0.104) (0.115) (0.154) (0.136) (0.172) (0.206) (0.167) (0.171) (0.112) 1 = experience d crop 0.105 - 0.00 2 - 0.147 0.099 - 0.136 - 0.032 0.044 - 0.539*** 0.113 - 0.646*** disease (0.157) (0.113) (0.128) (0.168) (0.160) (0.180) (0.153) (0.156) (0.170) (0.097) 1 = experience d price 0.306* 0.320** 0.290** 0.101 - 0.155 - 0.021 - 0.169 0.262 0.049 0.199* decrease of c rop (0.179) (0.124) (0.114) (0.152) (0.132) (0.200) (0.154) (0.208) (0.166) (0.106) 1 = experience d price rise of 0.0642 - 0.103 - 0.194 0.195 0.075 - 0.222 0.304** 0.205 0.178 - 0.035 input (0.211) (0.138) (0.132) (0.135) (0.153) (0.185) (0.142) (0.175) (0.1 37) (0.096) 1 = exp erienced water 0.066 - 0.046 - 0.025 - 0.108 - 0.037 0.387** - 0.266* - 0.546*** 0.022 - 0.014 shortage (0.193) (0.116) (0.131) (0.173) (0.146) (0.156) (0.147) (0.178) (0.153) (0.114) 1 = rural - 0.019 0.082 - 0.629*** - 0.440*** 0.098 - 0.209 - 0.101 - 0.538*** - 0.381*** 0.052 (0.226) (0.206) (0.177) (0.128) (0.171) (0.182) (0.175) (0.162) (0.142) (0.150) Plot variables 1 = soil is sandy 0.368** 0.023 - 0.106 - 0.169 - 0.428*** - 0.076 - 0.310** - 0.126 - 0.339** - 0.166 (0.155) (0.126) (0 .125) (0.153) (0.147) (0.133) (0.129) (0.157) (0.171) (0.110) 1 = soil is clay - 0.072 - 0.138 - 0.294* - 0.253 - 0.311** 0.231 0.014 - 0.556*** - 0.237 - 0.230** (0.248) (0.126) (0.159) (0.165) (0.143) (0.221) (0.178) (0.155) (0.168) (0.108) 1 = soil is good quality 0.292* 0.321*** 0.324*** 0.329*** 0.202* 0.0150 0.098 0.458*** 0.062 0.395*** (0.155) (0.103) (0.104) (0.116) (0.111) (0.130) (0.123) (0.142) (0.108) (0.081) 121 T able 2.7 (c ) 1 = soil is bad quality - 0.081 0.095 0.163 - 0.321 - 0.13 5 0.005 - 0.311 - 0.233 - 0.570** - 0.244* (0.277) (0.172) (0.132) (0.257) (0.331) (0.190) (0.245) (0.237) (0.265) (0.139) 1 = plot is sloped 0.169 0.079 - 0.025 0.101 - 0.053 - 0.645*** 0.243** - 0.119 0.159 - 0.211*** (0.150) (0.099) (0.099) (0.111) (0.123) (0.185) (0.111) (0.121) (0.102) (0.079) 1 = plot is steep 1.001*** - 0.026 - 0.259 - 0.130 0.226 - 0.339 0.266 0.141 - 0.182 - 0.312 (0.331) (0.185) (0.634) (0.246) (0.180) (0.603) (0.310) (0.262) (0.248) (0.218) 1 = have problem of 0.271 0.104 - 0.133 0.018 0.178 0.157 - 0.091 - 0.331* - 0.162 - 0.183* erosion (0.166) (0.106) (0.131) (0.160) (0.186) (0.311) (0.178) (0.179) (0.170) (0.107) 1 = plot with title - 0.106 0.160 0.025 - 0.281 - 0.166 - 0.065 0.359 - 0.358 0.054 - 0.099 (0.189) (0.134) (0.149) (0.199) (0.1 83) (0.306) (0.230) (0.273) (0.260) (0.118) Year since acquired land - 0.001 0.001 0.001 - 0.002 0.006*** - 0.000 0.001 - 0.002 - 0.003 - 0.001 (0.003) (0.002) (0.002) (0.002) (0.002) (0.002) (0.003) (0.003) (0.002) (0.001) Parameters Rho ( ) 0.3 68 1.033* 0.642* 0.108 - 0.125 - 0.205 - 0.185 2.303 - 0.196 0.976*** (0.465) (0.553) (0.378) (0.291) (0.214) (0.308) (0.353) (1.737) (0.303) (0.359) Delta ( ) 0.782*** 0.972*** 0.932*** 0.583** 0.422* 0.385 0.415 0.999*** 0.249 0.967*** (0.293) (0.051) (0.083) (0.290) (0.220) (0.314) (0.300) (0.004) (0.229) (0.044) EOS ( ) 0.731*** 0.492*** 0.609*** 0.903*** 1.143*** 1.258** 1.227** 0.303* 1.244*** 0.506*** (0.249) (0.134) (0.140) (0.237) (0.280) (0.488) (0.532) (.159) (0.469) (0.092) Ob servations 767 2301 1642 879 1038 670 580 1098 651 2667 Adjusted R - squared 0.197 0.145 0.186 0.197 0.149 0.038 0.313 0.203 0.267 0.180 Notes: Time dummies are included in all estimations but not reported. Standard errors are in parentheses. *** p<0.01, * * p<0.05, * p<0.1. 122 2.3.2.C Test of Propositions To empirically test the proposition 2.6, I specify the reduced form empirical model as: (2. 53 ) where the subscripts h, j, and t represe nt household, region, and time respectively; is total days of on - farm family labor; is the vector of household characteristics which affect the is total area of plots; and are dum my variables of technological growth which takes 1 if the household applies land - augmenting technology, if the household applies labor - augmenting technology, and takes otherwise; is the estim ated EOS between labor and land from equation (2.36); and are wage rate of off - farm labor and on - farm hired labor relative to the producer price of maize , respectively; and are household and regional unobserved heter ogeneities. The vector of exogenous prod uction variables ( ) include whether the household experienced dr o ught or flood, crop disease , price decrease of the crop, price rise of the input, and water shortage in a year and whether the household h as a plot with title. Because on - farm hired labor is zero for 3,742 among 5,967 observations, I apply the Tobit model for the on - farm hired labor. The reduced form empirical model is specified as: (2. 54 ) where is total days of on - farm hired labor. The hypotheses I t est from the proposition 2.6 are as follows. Under the existence of the interior solutions, the optimal on - farm fam ily and hired labor increase as total farm area increases ( and ). Both optimal on - farm labor and hired labor increase as lan d - 123 augmenting technological change increases ( and ). They both decrease as land - augmenting technological change increases unless the EOS between land and labor is sufficiently small ( and ). The optimal on - farm famil y labor decreases as the off - farm wage relative to the producer price of maize increases ( ). The optimal on - farm hired labor decreases as the on - farm hired - in wage relative to the producer price of maize increases ( ). The decision on whet her to apply farm technology is normally dependent on the various characteristics of the plot and the household. Those characteristics include water availability and land quality (Caswell & Zilberman , 1985; Caswell & Zilberman , 1986; Green et al. , 1996; Moreno & Sunding , 2005) , the network in which the household is involved (Foster & Rosenzweig , 1995; Munshi , 2004; Conley & Udry , 2010) , and the resource endowment and scarcit y in the location (Hayami & R uttan , 1971; Matsuyama , 1992) . I, the refore, present the fixed effect estimation to eliminate the effect of unobserved household and regional heterogeneities as well as two stage estimations to test and control for the endogeneity of the adoption of far ming technologies. For the two stage est imations, the first stage estimations of the adoption of farming technologies are specified as: (2. 55 ) where is the vector of instrumental variables which include dummy variables of the re ceipt of input voucher and the potential yield gain from the adoption of farming technology. For the two step estimations of on - farm hired labor, I apply the Type II Tobit, tha t is the Heckman selection model (Heckman 1976) , to control for the selection bias as well as the endogeneity of the adoption of farming technology. The h ousehold heterogeneities are controlled by the time - 124 female or not, and whether household member belongs to Savings and Credit Co - Operative ( SACCO ) or not. Similarly, is contro lled by the EOS in all estimations. 2.3.3 Data and Descriptive Statistics I use data from the Tanzania National Panel Survey (TNPS) wave 1 to 3; 2008/ 2009, 2010/2011, and 2012/2013. It is a part of World Bank Living Standards Measurement Study (LSMS) dataset. I use data from household, agriculture, and community questionnaires in the mainland for the households who cultivate maize. Among 3,021 household s and 6,561 plots in the mainland, 2,892 households cultivate maize in 5,598 plots. Among 9,266 plot observati ons, 3,171 plots form a 3 - year panel, 1,186 plots form a 2 - year panel, and 1,241 plots are a 1 - year panel. Table 2.8 and Table 2.9 report the summary statistics of variables at plot level and at household level respectively. 2.3.3.A Farming Technology, Gross P rod uctivity, and Labor Shift Figure 2.7 shows the change in the labor to land ratio and area of land to yield one ton of maize by applying each farming technology. A technology is called a land - augmenting technology when it reduces relatively more land th an labor to yield one ton of maize because farmers gain area to cultivate additional maiz e by applying that technology. For example, by applying inorganic fertilizer, the farmer saves 10 acres to yield one ton of maize, so inorganic fertilizer augments lan d b y 10 acres. Similarly, a technology is called labor - augmenting technology when it redu ces relatively more labor than land to yield one ton of maize because farmers gain labor to cultivate additional maize by applying that technology. In F igure 2.7, I us e t he labor to land ratio rather than labor to examine the labor bias of technology becau se the simple labor productivity, 125 Table 2. 8 Summary statistics of variables at plot level Variable Obs Mean Sd Min Max Panel A. TNPS - Agr icu lture Questionnaire Total area under maize (acre s ) 8477 2.01 4.00 0.00 150.00 Total cultivated area (acre s ) 8477 3.34 9.58 0.00 600.00 Harvested maize (kg) 8477 460.93 1195.12 0.00 50000.00 Total on - farm labor (person*day) 8477 88.28 92.85 0.00 11 70.00 1 = apply organic fertilizer 8477 0.14 0.35 0.00 1.00 1 = apply inorganic fertilizer 8477 0.15 0.36 0.00 1.00 1 = apply improved seed 8477 0.23 0.42 0.00 1.00 1 = apply irrigation 8477 0.02 0.13 0.00 1.00 1 = apply pesticide or herbicide 8477 0. 09 0.29 0.00 1.00 1 = apply sprayer 8477 0.07 0.26 0.00 1.00 1 = apply animal traction 8477 0.13 0.34 0.00 1.00 1 = apply tractor use 8477 0.03 0.18 0.00 1.00 1 = receive input voucher 8477 0.09 0.28 0.00 1.00 Year since acquired plot (year s ) 8477 20. 88 26.13 0.00 113.00 1 = plot with title 8477 0.11 0.31 0.00 1.00 1 = soil is sandy 8477 0.17 0.38 0.00 1.00 1 = soil is clay 8477 0.17 0.37 0.00 1.00 1 = soil is good quality 8477 0.48 0.50 0.00 1.00 1 = soil is bad quality 8477 0.06 0.24 0.00 1.0 0 1 = plot is sloped 8477 0.33 0.47 0.00 1.00 1 = plot is steep 8477 0.04 0.19 0.00 1.00 1 = have problem of erosion 8477 0.14 0.34 0.00 1.00 Panel B. TNPS - Household Questionnaire 1 = experience d dr o ught or flood 8477 0.32 0.46 0.00 1.00 1 = exp erience d crop disease 8477 0.28 0.45 0.00 1.00 1 = experience d price decrease of crop 8477 0.32 0.47 0.00 1.00 1 = experience d price rise of input 8477 0.32 0.47 0.00 1.00 1 = experience d water shortage 8477 0.27 0.45 0.00 1.00 1 = rural 8477 0.87 0 .34 0.00 1.00 Panel C. GYGA and FAO - Agromaps Potential yield gain from input (ton/acre) 8477 5.01 1.24 1.54 7.41 Notes: Observations pooled across years. 126 Table 2. 9 Summary statistics of variables at household level V ari able Obs Mean Sd Min Max Panel A. TNPS - Agriculture Questionnaire On - farm family labor (person*day) 5967 123.02 132.60 2.00 1400.00 On - farm hired labor (person*day) 5967 11.02 32.40 0.00 661.00 Off - farm labor (person*day) 5967 55.12 132.34 0.0 0 2 064.00 Total cultivated area (acre s ) 5967 4.86 8.03 0.01 150.00 On - farm hired in wage ( USD /day) 5967 4.90 1.47 1.87 10.24 1 = apply land augmenting technology 5967 0.31 0.46 0.00 1.00 1 = apply labor augmenting technology 5967 0.24 0.43 0.00 1.00 1 = have plot title 5966 0.12 0.33 0.00 1.00 1 = receive input voucher 5967 0.07 0.25 0.00 1.00 Panel B. TNPS - Household Questionnaire HH education (year s ) 5927 4.79 3.51 0.00 19.00 1= HH is female 5967 0.24 0.42 0.00 1.00 1 = household member be lon gs to SACCO 5967 0.05 0.22 0.00 1.00 Off - farm wage ( USD /hour) 5967 1.60 1.18 0.31 11.56 Number of adult s age d 15 - 65 5967 2.87 1.73 0.00 25.00 Number of child ren age d 0 - 3 5967 0.74 0.91 0.00 14.00 Number of child ren age d 4 - 6 5967 0.53 0.70 0.00 6.00 Number of child ren age d 7 - 14 5967 1.28 1.28 0.00 10.00 1 = experience d dr o ught or flood 5967 0.32 0.47 0.00 1.00 1 = experience d crop disease 5967 0.27 0.45 0.00 1.00 1 = experience d price decrease of crop 5967 0.30 0.46 0.00 1.00 1 = experience d price rise of inp ut 5967 0.30 0.46 0.00 1.00 1 = experience d water shortage 5967 0.28 0.45 0.00 1.00 1 = rural 5967 0.87 0.34 0.00 1.00 Panel C. TNPS - Community Questionnaire Local market price of maize ( USD /kg) 5967 0.84 0.20 0.44 1.62 Panel D. GYGA and FAO - Agr omaps Potential yield gain by input (ton/acre) 5967 5.02 1.29 1.54 7.41 Notes: Observations pooled across years. USD used in the table is 2011 PPP USD . 127 Figure 2. 7 Bias of farm technology the labor used to yiel d o ne ton of maize, entails the change in the area of land to yield one ton of maize. Hence, by using the labor to land ratio rather than labor, I determine d the net labor bias of the technology. The values in the figure are computed by taking the differen ce of the means of each variable of the plots to which the household applied the technology and the plots to which the household did not apply the technology. Based on the result of the calculations, I classif ied organic fertilizer, inorganic fertilizer, a nd irriga tion into land - augmenting technology, and sprayer, pesticide, herbicide, animal traction , and tractor use into labor - augmenting technology. This classification is used for the empirical test of propositions. Table 2.10 shows the change o f a doption of farming technologies, gross productivity of maize, and the labor shift from farming sector to off - farm sector from 2008 to 2013. The table shows that the adoption of technology, change in land and labor productivity, and the labor shift from far ming sector to off - farm sector are not exactly corresponding to each other. The adoption 128 Table 2. 10 Technology adoption, gross productivity, and labor shift from farm to off - farm sectors 2008/2009 2010/2011 2012/2013 Mean Sd Mean Sd Mean Sd Plot variables Land - augmenting technology Organic fertilizer 0.14 0.35 0.13 0.34 0.15 0.36 Inorganic fertilizer 0.13 0.33 0.15 0.36 0.14 0.34 Irrigation 0.02 0.14 0.02 0.13 0.01 0.12 Neutral technology Improved s eed 0.15 0.36 0.11 0.31 0.39 0.49 Labor - augmenting technology Pesticide or herbicide 0.10 0.30 0.08 0.28 0.08 0.28 Sprayer 0.08 0.28 0.06 0.24 0.08 0.26 Animal traction 0.13 0.33 0.13 0.34 0.16 0.37 Tractor 0.00 0.06 0.04 0.20 0.05 0.22 Gross p roductivity of m aize Land productivity (kg/acre) 227.06 375.42 280.71 407.07 261.76 443.02 Land labor ratio (person*day/acre) 78.90 163.73 64.12 111.13 68.70 107.43 Labor productivity (kg/person*day) 6.36 10.26 7.52 10.10 6.60 10.24 Household var iables On - farm labor (person*day) 140.36 162.63 128.41 127.62 134.17 130.51 1 = supply off - farm labor 0.29 0.45 0.44 0.50 0.47 0.50 Off - farm labor (person*day) 33.16 72.59 53.34 131.22 71.67 159.97 Notes: On - farm labor is sum of on - farm family la bor and hired la bor. rate of the most land biased technology, that is inorganic fertilizer, increased from 0.13 to 0.14 from 2008/2009 to 2012/2013 having the highest adoption rate, 0.15, in 2010/2011. It is corresponding to the increase in the gross lan d productivity, which increased from 227.06 kg per acre in 2008/2009 to 261.76 kg per acre in 2012/2013, and has the highest land productivity, 280.71 kg per acre, in 2010/2011. While the adoption rate of labor augmenting technologies all increased from 20 10/2011 to 2012/ 2013, gross labor productivity hit the highest value, 7.52 kg per person - da y, in 2010/2011, and the land labor ratio shows the smallest value, 64.12 person - day s per acre, in 2010/2011. In terms of the labor shift from farm sector to non - far m sector, the ra te of households who supply off - farm labor and the days supplied to the off - farm activities both constantly increased from 2008/2009 to 2012/2013. The rate of households who supply off - 129 farm labor increased from 0.29 in 2008/2009 to 0.47 in 2012/2013, and t he supply of off - farm labor increased from 33.16 person - day s in 2008/2009 t o 71.67 person - day s in 2012/2013. To further examine the effect of the adoption of biased farming technologies on the labor allocation of the household s , we need t o estimat e empiric al models. 2.3.3.B Adoption Decision with Input Voucher and Yield Potential Tabl e 2.11 shows the comparison of household characteristics by the receipt of the input voucher. Except from whether household head is female or not, all other varia bles correspond to the targeting criteria explained in section 2.3.1. The household who receiv ed input voucher cultivates less area for maize; is more likely to belong to SACCO; and has a household head with higher education. The difference s of those varia bles are statistica lly significant. Although the input voucher was provided to subsidize inorg anic fertilizer or improved seeds, it affected the adoption of other technologies. Table 2.12 displays the difference s of the adoption rate of farming technology between households who received input voucher s and who did not. Except f or animal traction and tractor use , for all other farming technologies the households who received input voucher s have higher adoption rate s than the households who did not. The differ ence of the adoptio n rates is statistically significant at the one percent confidence level ex cept for irrigation. Although the input voucher ha d a strong effect on the adoption of farming technologies, because only 10.75 percent of maize farmers received input voucher at le ast once between 2008 and 2013, the overall adoption rates did not change drastically over years (see Table 2.10). The potential yield gain from the adoption of the technology also determines the technology adoption. I generated the data of potent ial yield gain by taking the difference between 130 Table 2. 11 Targeting of the input voucher scheme (1) (2) (3) Not received input voucher Received input voucher Total t - test Mean Sd Mean Sd Mean Sd (1)=(2) Total area under maize (acre s ) 2.01 4.00 1.70 2.41 1.98 3.90 ** Household head education (year s ) 4.79 3.51 6.01 2.94 4.89 3.49 *** 1 = household head is female 0.23 0.42 0.18 0.38 0.23 0.42 *** 1 = belongs to SACCO 0.05 0.22 0.13 0.34 0.06 0.24 *** N otes: *** p<0.01, * * p<0.05, * p<0.1. Table 2. 12 Adoption of farming technology by input voucher (1) (2) (3) Farming technology Not receive input voucher Receive input voucher Total t - test (1) < (2) Organic fertilizer 0.14 0.19 0.14 *** Inor ganic fertilizer 0.09 0.65 0.14 *** Improved seed 0.23 0.30 0.23 *** Irrigation 0.02 0.02 0.02 Pesticide or herbicide 0.08 0.18 0.09 *** Sprayer 0.07 0.11 0.07 *** Animal traction 0.14 0.14 0.14 Tractor 0.04 0.02 0.04 Notes: ** * p<0.01, ** p<0.05 , * p<0.1. the simulated yield potential of maize and the actual yield in 2001, when the farming technologies were hardly adopted by farmers in Tanzania. Simulated yield potential and the actual yield in 2001 are collected from GYGA (GYGA , 2019) and FAO - Agromaps (FAO , 2019) respectively. Table 2.13 shows the means of computed potential yield gain s of household who adopted the farming technology and who did not. Except for irri gation, for all other farming technologies, the households who adopted technology have higher potential yield gain than the household who did not. The potential yield gain is u nobservable for the farmers, but it affects their decision on the adoption of te chnology. The households who adopted irrigation have smaller potential yield gain s than those who did not because the simulated yield potential is 131 Table 2. 13 Yield potential and technology adoption Potential yield gain (ton/acre ) (1) (2) t - test Farming technology Not ad o pted Ad o pted (1)=(2) Organic fertilizer 4.97 5.03 Inorganic fertilizer 4.95 5.18 *** Improved seed 4.98 4.98 Irrigation 4.98 4.76 ** Pesticide or herbicide 4.95 5.25 *** Sprayer 4.97 5.09 ** Animal tract ion 4.95 5.19 *** Tractor 4.96 5.46 *** generated by rainfed maize data, hence, it takes smaller values if the household faces limited rain. And households with limited water availability are more likely to adopt the irrigation. 2.3.4 Robustness Check 2.3.4.A T est of Propositions with Unobserved Separation H eterogeneous household s choose the ir optimal labor allocation s by maximizing their income from farm production and off - farm activities. The household does or does not face a binding constraint o n off - farm la bor opportunities. When a household faces a binding constraint, the application of farm technology does not aff ect the on - farm family labor, but has an effect on on - farm hired labor. Suppose the off - farm opportunity is constrained and binding at . Th en, the on - farm family labor is given as . Assume again there is no land market, and the on - farm labor ma rket is perfectly competitive. The corresponding household income is, then, given as: (2. 56 ) The h ousehold maximizes its income with respect to hired labor ( H ) . The optimal hired labor ( ) satisfies the FOC which is equivalent to equation (2.30). The interior solution of on - farm 132 hired labor is, therefore, given as equation (2.32), which is equivalent to the case of no binding constraint o n off - farm labor. The o n - farm family labor is, on the other hand, determined by , the number of adults of working age in the household, and , the level of off - farm labor binding constraint. The adoption of farming technology also has a different effect on the optimal level of off - farm labor when the household faces a binding constraint o n off - farm labor. Without a binding constraint, the optimal off - farm labor is given as . Hence, the land endow ment , adoption of land - and labor - augmenting farming technologies, and off - farm wage relative to production price all have opposite effects on off - farm labor compared with the effects on the optimal on - farm family labor . When the off - farm constraint is binding, the off - farm labor is determined by the level of a binding constr aint, which is determined by regional and household exogenous factors. These relations are summarized in the proposition 2.7. Proposition 2.7. Un der an unrestricted labor market with no land market, a) if the household does not face a binding constraint o n off - farm labor, the optimal on - farm family labor holds a), b), and c) of Proposition 2.6; b) if the household faces a binding constraint o n off - farm l abor, the optimal on - farm family labor increases as th e number of adults of working age increases; it depends on household and regional exogenous variables which determines the level of binding constraint o n off - farm labor; c) if the household does not face a binding constraint o n off - farm labor, the optimal off - farm labor increases as the number of adults of working age increases; it decreases as the endowed land increases; it increases as off - farm wage relative to production price increases; land - augmenting technical change decreases the optimal off - farm labor; 133 labor - augmenting technical change increases the optimal off - farm labor unless the elasticity of substitution between labor and land is sufficiently small; d) if the household faces a binding constraint of off - farm labor, the optimal off - farm labor depends on household and regional exogenous variables which determines the level of binding constraint o n off - farm labor. For the test of the proposition 2.7, I apply a switching regression model with un observed sample separation (Maddala , 1986) because whether the off - farm constraint is b inding is unobservable. The estimation model is specified as: (2. 57 ) where represents the - farm family labor or off - farm labor; the vector of explanatory variables, , consists of number of adult s age d 15 - 65 in the household ( ), a vector of ), total area of plots ( ), dummy variables of biased technological growth ( and ), an interaction term of the du mmy va riable of labor - augmenting technology and the EOS between labor and land ( ), the off - farm wage relative to the producer price of maize ( ), and the vector of variables which determine the level of binding constraint o n off - f arm labor ( ); and are household and regional heterogeneities; is independent and identically distributed by normal distribution with zero means where variance of is standardized at one , and a nd hav e same variance, . While is observed, , , and are unobserved latent variables. Whether we observe or depends on the value of the latent variable, . 134 Since the idiosyncratic error term, , is distributed by the standard normal distribution, the probability of observing is given as , and the probability to observe is written as . The p robability density function of observed labor allocation is, therefore, expressed as: (2. 58 ) where and are the probability density function of and . Using equation (2.42), the likelihood function of a sample of N observations is written as: (2 . 59 ) By maximizing equation (2.43) with respect to , I estimate the maximum li kelihood estimators. Following Vakis et al. ( 2004) , I apply the E - M method (Dempster et al., 1977) after deciding on the in itial values of the parameters by pre - estimation procedure (Kiefer , 1978) . For the estimations, and are represented by the time - invariant household and region variables as the proxies of the unobserved heterogeneities. 2.3.4.B Test of Propositions with Observed Separation The switching regression with unobserved separation uses all observa tio ns and the estima ted probability of a household . In this section, I present the estimations by assigning households into two separate regimes using the ex - post observed information. Followi ng Hartley ( 1978) , I assign a household as with a binding constraint if the conditional expectation of the latent variable ( ) is equal or greater than zero, , and as a household without a binding constraint if the 135 conditional expectation of the latent variable is smaller than zero, . By assigning households to two regimes, I present fixed ef fec t estimations using the observations in each r egime separately. The conditional expectation is computed by observed variables as: (2. 60 ) The reduced form estimations are specified as: (2. 61 ) For the estimations, the ex - post computed conditional expectation of the latent variable is included as one of the explanatory variables to control for selection bias of each regime. 2.3.5 Est imation Result 2.3.5.A Bias of Farm Technology and On - Farm Labor Table 2.14 presents the results of the estimations of on - farm family labor to test Proposition 2.6 a), b), and c). The table shows that the signs of the estimates by the fixed effect, two sta ge lea st square s (2SLS), two stage generalized method of moment s (2SGMM), and limited maximum likelihood estimations all satisfy the p ropositions. The total area of plots and the adoption of land - augmenting technology both show positive effects on on - farm family labor while the interaction term of the adoption of labor - augmenting technology and EOS between land and 136 Table 2. 14 Test of propositions I: on - farm family labor Dependent variable: (1) (2) (3) (4) On - farm family labor ( person *day) Fixed effect 2SLS a 2 stage LIML a Explanatory variables Vector GMM a Technology adoption 1 = ad o pt land augmenting technology 14.50** 11.43 36.87** 23.10 (5.901) (18.86) (16.15) (28.03) 1 = ad o pt labor augmenting technology 40.44* 93.84 68.41 132.8 (21.94) (78.65) (78.05) (97.93) Interaction term: (labor tech=1)*(EOS) - 112.0*** - 235.6 - 356.2** - 34 8.2 (43.27) (146.2) (138.8) (224.6) Household variables Total area of plot with maize (acre s ) A 3.370*** 4.869*** 6.678*** 5.161*** (0.878) (1.023) (0.760) (1.256) Local variables Real off - farm wage ( USD /hour) - 4.755*** - 2.638** - 1.492 - 2.442* (1.145) (1.269) (1.192) (1.419) Real hired in wage ( USD /day) - 0.0117 - 0.587 - 0.941 - 0.868 (0.971) (0.746) (0.731) (0.895) Control variables Time invariant household variable NO YES YES YES Time invariant regiona l variable NO YES YES YES Time variant production variable YES YES YES YES Hypothesis Tests Chi sq. from endogeneity test - 15.38*** 15.38*** 15.38*** (H 0 : technology is exogenous) Chi sq. from overidentifying restric tion test - 7.12** 7.12** 6.64** (H 0 : IVs are not jointly valid) Observations 5966 5926 5926 5926 Log likelihood - 34273 - 36883 - 37675 - 37191 Adjusted R - squared 0.096 0.150 - 0.110 0.057 Notes: Time dummies are included in all estimation s but not reported. USD used in the table are 2011 PPP USD . Standard errors clustered at household level are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. a Technology adoption is instrumented by dummy variable s of input voucher receipt, potential yi eld gain from applying input s , fitted values of probabilities of ad o pting labor - and land - augmenting technology respectively from the first stage probit estimation, and the fitted value of probability of ad o pting labor - augmenting technology multiplied by t he EOS. labor displays negative effects. The real off - farm wage also shows the negative effects on on - farm family labor. The fixed effect and 2SGMM estimates are statistically signifi cant at five percent confidence level for both adoption of land - augment ing technology and the interaction term of labor - augmenting technology and the EOS between land and labor. On average, the 137 adoption of land - augmenting technology increases 21.5 person - d ay s of on - farm family labor. Because the EOS between land and labor tak es the values between 0.303 and 1.258 (see Table 2.7), the effect of labor - augmenting technology ranges from 4.2 person - day s to - 247.0 person - day s on average. The effect of the adoption of labor - augmenting technology is negative unless the EOS between land and labor is smaller than 0.319. For the two - step estimations, the technology adoptions are instrumented by the dummy variable of input voucher receipt, potential yield gain from apply ing input, fitted values of probabilities of ad o pting labor - and land - a ugmenting technology respectively from the first stage probit estimations, and the fitted value of the probability of ad o pting labor - augmenting technology multiplied by the EOS between land and labor. The exogeneities of the adoption of land - and labor - aug menting technologies are both rejected at the one percent confidence level in all estimations. The instrumental variables also pass the overidentifying restriction test at five percent confidence level in all estimations. The results of the first stage pro bit estimations of the adoption of land - and labor - augmenting technologies are reported in column (1) and (2) of Table 2.A.1. Table 2.15 displays the results of t he estimations of on - farm hired labor to test Proposition 2.1 d), e), and f). Again, all the signs of the coefficients satisfy the propositions. The total area of plots and land - augmenting technological change both have the positive effects on on - farm hire d labor while the interaction term of the labor - augmenting technological change and E OS between labor and land shows a negative effect. The real on - farm hired - in wage also has negative effects. The land - augmenting technology increases on - farm hired labor b y on average 5.23 person - day s . Because the EOS between land and labor takes the value s between 0.303 and 1.258 (see Table 2.2), the effect of adoption of labor - augmenting technology takes the values between 25.81 person - day s and - 26.93 person - day s . The eff ect is negative if the EOS 138 Table 2. 15 Test of proposition s II: on - farm hired labor Dependent variable: (1) (2) (3) (4) On - farm hired labor (person*day) Tobit Heckman Heckman Heckman Explanatory variables Vector RE 2SLS a 2SGMM a LIML a Technology adoption 1 = ad o pt land augmenting technology 5.746*** 5.103 4.672 5.379 (2.107) (4.241) (3.667) (6.537) 1 = ad o pt labor augmenting technology 13.35** 39.02 75.55*** 42.24 (6.451) (43.37) (28.04) (55.21) Interaction term: (labor tech=1)*(EOS) - 13.91* - 37.78 - 126.9*** - 42.31 (8.216) (76.94) (46.01) (110.6) Household variables Total area of plot with maize (acre s ) A 1.764*** 1.004*** 1.124*** 1.000*** (0.112) (0.193) (0.185) (0.248) Local variables Real off - farm wage ( USD /hour) - 0.402 - 0.677* - 0.719** - 0.695* (0.619) (0.363) (0.302) (0.357) Real hired in wage ( USD /day) - 2.037*** - 0.621*** - 0.662*** - 0.634** (0.408) (0.187) (0.134) (0.251) Control variables Inverse mills ratio from probit - 15.79*** 15.63*** 15.81*** - (0 .595) (0.542) (0.629) Time invariant household variable YES YES YES YES Time invariant regional variable YES YES YES YES Time variant production variable YES YES YES YES Hypothesis Tests Chi sq from endogeneity test - 8.36** 8.36** 8.36** (H 0 : technology is exogenous) Chi sq from overidentifying restriction test - 6.16** 6.16** 6.15** (H 0 : IVs are not jointly valid) Observations 5926 5926 5926 5926 Log likelihood - 13746 - 28269 - 28860 - 28285 Adjusted R - squared - 0.223 0.052 0.219 Notes: Time dummies are included in all estimations but not reported. USD used in the table is 2011 PPP USD . Standard errors clustered at household level are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. a Tec hnology adoptions are instrumented by dummy variable of input voucher receipt, potential yield gain from applying input, fitted values of probabilities of ad o pting labor and land augmenting technology respectively from the first stage probit estimation, an d fitted value of probability of ad o pting labor augmenting technology multiplied by EOS. between labor and land is greater than 0.770. For the two stage estimations, I apply the same instrumental variables as the estimations of the on - farm family labo r. The endogeneity test rejected the exogeneity of the technology adoptions at the five percent confidence level in all 139 estimations. The instrumental variables pass the overidentifying restriction at the five percent confidence level in all estimations. Fo r t he Heckman estimations, I use the inverse mills ratio taken from the probit estimation of the binary variable of whether the household hires on - farm labor as the additional explanatory variable in the estimations of the test of propositions. The coeffic ien t of the inverse mills ratio is statistically significant at the one percent confidence level in all estimations. It indicates that selection bias exists and is controlled in the estimations. The result of the first stage probit estimation of the binary va riable of whether household hires on - farm labor is reported in the column (3) of Table 2.A.1 2.3.5.B Result of Robustness Check Table 2.16 shows the results of switching regressions of on - farm family labor to test Proposition 2.2 a) and b). For estimation wi th the observed separation, ex - post assignment of the regimes classifies 1,801 households into those who do not face a binding constraint o n off - farm labor, and it classifies 4,125 households into those who face a binding constraint. The households without bi nding constraints satisfy the proposition 2.2 a) except the total area of plot by a switching regression with observed sepa ration. The land - augmenting technology increases on - farm family labor by an average of 30.99 person - day s . Taking the range of the EOS into account, the effect of labor - augmenting technology on on - farm family labor ranges from 21.63 person - day s to - 149.98 person - day s . It takes a negative value unless the EOS between land and labor is less than 0.423. The real off - farm wage decreases o n - f arm family labor. For the households with a binding off - farm constraint, the number of adults age d 15 - 65 has a positive effect on on - farm family labor. The effect of the number of children is, however, not clearly different between the households with a bi nding constraint and those without. Hence, proposition 140 Table 2. 16 Test of p ropositions III: on - farm family labor ( switching regression ) Dependent variable: Unobserved separation Observed separation On - farm family labor (p ers on*day) (ex - post predicted) Not binding Binding Not binding Binding Explanatory variables Vector Pooled MLE Pooled MLE Fixed effect Fixed effect Technology adoption 1 = ad o pt land augmenting technology 24.167 - 2.094 37.819*** 7.863 (29.314) (2.825) (12.793) (5.209) 1 = ad o pt labor augmenting technology 146.085* - 23.047** 6.072 - 9.479 (76.870) (9.865) (42.440) (15.848) Interaction term: (labor tech=1)*(EOS) - 348.05 7*** 29.341** - 11.333 - 20.768 (100.448) (12.975) (82.183) (72.484) Household variables Total area of plot with maize (acre s ) A 4.687*** 3.858*** - 0.697 5.116*** (1.600) (0.512) (0.701) (0.613) Number of adult s age d 15 - 65 M 27.660*** 15.082*** 34.064*** 21.084*** (8.930) (1.082) (6.893) (2.355) Number of child ren age d 0 - 3 - 13.185 - 0.262 - 6.148 2.709 (14.568) (1.807) (11.078) (3.328) Number of child ren age d 4 - 6 - 14.204 0.736 10.525 - 1.735 (17.798) (1.984) (9.048) (3.655) Number of child ren age d 7 - 14 - 33.649*** 2.775** 41.154*** 3.788 (9 .207) (1.206) (9.167) (3.448) Local variables Real off - farm wage ( USD /hour) - 5.425 - 0.152 - 7.565*** - 4.954*** (10.633) (0.463) (2.771) (1.028) Control variables Time invariant household variable YES YES NO NO Time i nvariant regional variable YES YES NO NO Time variant production variable YES YES YES YES Observations 5926 5926 1801 4125 Log likelihood - 35628 - 35628 - 9630 - 21595 Adjusted R - squared 0.095 0.150 0.371 0.211 Notes: Time dummies are included in all estimations but not reported. USD used in the table is 2011 PPP USD . Standard errors clustered at household level are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. 141 Table 2. 17 Test of propositions I V: off - farm labor (switching regression) Dependent variable: Unobserved separation Observed separation On - farm family labor (person*day) (ex - post predicted) Not binding Binding Not binding Binding Explanatory variables Vector Pooled MLE Pooled M LE Fixed effect Fixed effect Technology adoption 1 = ad o pt land augmenting technology - 25.340 2.757 - 16.753* 13.283 (23.166) (2.269) (9.991) (8.374) 1 = ad o pt labor augmenting technology 62.584 - 26.163*** 13.286 12.955 (66.343) (7.721) (33.407) (25.561) Interaction term: (labor tech=1)*(EOS) - 121.138* 25.565** 182.376 76.062 (71.894) (10.605) (141.397) (108.134) Household variables Total area of plot with maize (acre s ) A 3.021 - 0.534*** 0.4 91 - 0.539 (2.190) (0.102) (0.454) (0.342) Number of adult s age d 15 - 65 M 43.980*** 8.510*** 4.282 14.919*** (8.788) (0.849) (3.624) (3.927) Number of child ren age d 0 - 3 - 34.265*** - 2.732** 4.628 - 3.604 (9.629) (1.183) (5.954) (4.93 6) Number of child ren age d 4 - 6 21.054 0.035 - 10.451 - 3.672 (16.643) (1.396) (6.853) (6.232) Number of child ren age d 7 - 14 - 1.505 - 1.864** - 3.778 0.188 (8.348) (0.821) (5.049) (3.986) Local variables Real off - farm wage ( US D /hour) - 26.124*** - 2.589*** 2.223 - 1.761 (9.727) (0.531) (1.980) (2.009) Control variables Time invariant household variables YES YES NO NO Time invariant regional variable YES YES NO NO Time variant production va riables YES YES YES YES Observations 5926 5926 1,815 4,111 Log likelihood - 35466 - 35466 - 9090 - 23014 Adjusted R - squared 0.382 0.121 0.064 0.054 Notes: Time dummies are included in all estimations but not reported. USD used in the table is 2011 PPP USD . Standard errors clustered at household level are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. 142 2.2 b) may hold, but the number of children is not likely the exogenous variable to determine the level of a binding constraint o n off - farm work opportunities . Table 2.17 shows the results of estimations to test Proposition 2.2 c) and d). Using the off - farm labor as the dependent variable, the ex - post assignment of the regimes classifies 1,815 households into those without a bin ding constraint and 4,111 households into those with a binding constraint. The number of households assigned in each regime corresponds to the case of on - farm family labor. Although the results are not as obvious to satisfy the propositions as on - farm fami ly labor or hired labor, for the households without a binding constraint, the land - augmenting technology has a negative effect on off - farm labor. The adoption of land - augmenting technology decreases off - farm labor by an average 21.05 person - day s . The effec t of labor - augmenting technology, on the other hand, i s positive on off - farm labor. The effects range from 47. 21 person - day s to 76.45 person - day s . The number of adult s also has a positive effect on off - farm labor. For the households with a binding constrai nt, the land - augmenting technology does not have a statistically significant effect in both estimations. Again , the effect of the number of children is not clearly different between the households with a binding constraint and those without, and it is not likely the exogenous variable determine s the level of a binding constraint of off - farm work opportunities. 2.3.6 Co nclusion This study provides micro economic evidence of the effect of land - and labor - augmenting farming technologies on household s labor allocations . I use data of Tanzanian maize farmers from the Tanzanian N ational P anel S urvey wave s 1 to 3. I exploit the variation of the adoption of farming technologies during the input voucher scheme implemented in the 143 country from 2008 to 2013. T he estimations of the farm production function provide the estimates of the elasticity of substitution b etween land and labor by climate zone. The estimated values range from 0.303 to 1.258. By comparing the change in the labor to land ratio and area of la nd to yield one ton of maize among the farming technologies, I classify organic fertilizer, inorganic fe rtilizer, and irrigation into land - augmenting technologies, and sprayer, pesticide, herbicide, animal traction , and tractor use into labor - augmenting te chnologies. Estimation results show that the labor - and land - augmenting technologies c an have allocation . The adoption of land - augmenting technology increases on - farm family labor and on - farm hired labor by a n average 30.99 person - day s and 5.23 person - day s respectively and decreases off - farm la bor by a n average of 21.05 person - day s . The adoption of labor - augmenting technology, on the other hand, decreases on - farm family labor by a n average 85. 91 person - day s when the elasticity of substitution between land and labor is less than 0.423 and on - farm hired labor by 21.24 person - day s when the elasticity of substitution between land and labor is less than 0.770. It increases off - farm labor by on avera ge 65.58 person - day s . The results suggest depending on the conditions of a country such as the level of elasticity of substitution between land and labor, which is partly determined by the land availability and constraints on the land market, th at labor - augmenting agricultural technologies ha ve a good potential for accelerating structural transformation . Considering that the average size of the smallholder farm holdings in Tanzania remains small, and only 26 percent of 50 million hectares of potent ially arable land are currently farmed (World Bank , 2014) , Tanzania still has much potential of the growth of agricultural labor productivity by scaling up the land h oldings and the adoption of labor - augmenting technologies. However , it depends on the land and other market 144 constraints, labor - augmenting technologies, which have been less e mphasized in the history of the agricultural policies in Tanzania, may play import ant roles in the development of the agricultural sector and economic growth in the country. 145 APPENDI X 146 Table 2.A. 1 Result of first stage estimations (pooled probit) Dependent variable: (1) (2) (3) 1 = ad o pt technology or 1 = hire labor Land - augmenting Labor - augmenting On - farm Explanatory variables technology technology hired labor Instrumental variables 1 = receive input voucher 0.540*** 0.120*** 0.067** (0.023) (0.025) (0.026) Yield potential by input (ton/acre) 0.030*** 0.051*** - 0.001 (0.006) (0.005) (0.006) Technology ad o ption 1 = ad o pt land augmenting technology - - 0.162*** - - (0.044) 1 = ad o pt labor augmenting technology - - 0.052*** - - (0.015) Interaction term: (labor tech=1)*(EOS) - - - 0.047 - - (0.060) Household variables Total area of plot with Maize (acre s ) 0.001 0.008*** 0.009*** (0.001) (0.001) (0.001) Number of adult s age d 15 - 65 0.014*** 0.029*** - 0.024*** (0.004) (0.004) (0.005) Number of child ren age d 0 - 3 - 0.012 0.008 0.007 (0.007) (0.007) (0.008) Number of child ren age d 4 - 6 - 0.008 0.006 - 0.006 (0.009) (0.008) (0.010) Number of child ren age d 7 - 14 0.015 *** 0.025*** - 0.015** (0.005) (0.005) (0.006) HH education (year s ) 0.014*** 0.003 0.010*** (0.002) (0.002) (0.002) 1 = HH is female - 0.028 - 0.057*** 0.014 (0.017) (0.016) (0.017) 1 = member belong to SACCO 0.066** 0.055** 0.206*** (0.028) (0.025 ) (0.029) Local variables Real off - farm wage ( USD /hour) - 0.016*** 0.008** 0.001 (0.004) (0.003) (0.004) Real hired in wage ( USD /day) 0.007*** - 0.003 - 0.013*** (0.002) (0.002) (0.003) Production variables 1 = have plot with title 0.057*** - 0. 004 0.042** (0.018) (0.016) (0.019) 1 = experience d dr o ught or flood - 0.062*** - 0.004 0.038*** (0.013) (0.011) (0.014) 1 = experience d crop disease 0.010 0.016 0.008 (0.014) (0.013) (0.015) 1 = experience d price decrease of crop - 0.022 0.037*** - 0 .012 (0.014) (0.014) (0.016) 147 T able 2.A.1 (c ) 1 = experience d price rise of input 0.117*** 0.059*** 0.018 (0.015) (0.014) (0.016) 1 = experience d water shortage - 0.044*** - 0.016 0.005 (0.014) (0.013) (0.015) 1 = rural - 0.015 0.087*** - 0. 147*** (0.020) (0.016) (0.022) Observations 5,926 5,926 5,926 Log likelihood - 3157.9177 - 2777.4589 - 3651.1058 Notes: Time dummies are included in all estimations but not reported. 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