UFDC Home  myUFDC Home  Help 



Full Text  
PAGE 1 1 ESSAYS ON CHILD LABOR, PRODUCTIVITY, AND TRADE By KRISTIAN ESTEVEZ A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILO SOPHY UNIVERSITY OF FLORIDA 2010 PAGE 2 2 2010 Kristian Estevez PAGE 3 3 To my family, for the love and support they provide PAGE 4 4 ACKNOWLEDGMENTS I would like to thank Elias Dinopoulos, whose guidance paved the way for this research. I would also like to than k Steven Slutsky, Richard Romano, Mark Rush, James Seale and the Department of Economics at the University of Florida for suggestions and advice that have proved to be invaluable. This research would also not have been possible were it not for the ground work laid by Kaushik Basu, Erik Edmonds, Nina Pavcnik, Kenneth Swinnerton, Carol Ann Rogers, and all others who have worked tirelessly to research ways to end child labor Lastly, I would like to thank my wife for reading this dissertation more times than is probably healthy. PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIG URES ................................ ................................ ................................ .......... 8 ABSTRACT ................................ ................................ ................................ ..................... 9 CHAPTER 1 THE ECONOMICS OF CHILD LABOR ................................ ................................ ..... 11 Sup ply of Child Labor ................................ ................................ .............................. 12 Demand for Child Labor ................................ ................................ .......................... 13 2 NUTRITIONAL EFFICIENCY WAGES AND CHILD LABOR ................................ .... 15 The Model ................................ ................................ ................................ ............... 16 Household Decision ................................ ................................ ......................... 17 Production ................................ ................................ ................................ ........ 22 Modern sector ................................ ................................ ............................ 23 Agrarian sector ................................ ................................ ........................... 24 Steady State Equilibrium ................................ ................................ .................. 27 Comparative Statics ................................ ................................ ................................ 29 Foreign Direct Investment ................................ ................................ ................ 29 Trade Sanctions ................................ ................................ ............................... 31 Education Improvements ................................ ................................ .................. 32 Migration ................................ ................................ ................................ ........... 33 Subsidies ................................ ................................ ................................ .......... 35 Child wage subsidies ................................ ................................ ................. 35 Education subsidies ................................ ................................ ................... 37 Conclusion ................................ ................................ ................................ .............. 39 3 CHILD LABOR AND FIRM HETEROGENEITY ................................ ........................ 41 The Basic Model ................................ ................................ ................................ ..... 43 Consumer Demand ................................ ................................ .......................... 44 Production ................................ ................................ ................................ ........ 45 Child Labor Demand ................................ ................................ ........................ 49 Firm Value ................................ ................................ ................................ ........ 50 Solving the Benchmark Case ................................ ................................ ........... 51 Aggregation ................................ ................................ ................................ ...... 52 Free Entry and Exit ................................ ................................ ........................... 54 Solving the Model when ................................ ................................ ................. 59 PAGE 6 6 Free Entry and Exit ................................ ................................ ........................... 60 Enforcement ................................ ................................ ................................ ..... 62 Traditional industry case ................................ ................................ ............ 63 Modern industry case ................................ ................................ ................. 64 Intra industry Trade ................................ ................................ ................................ 65 Free Entry and Exit ................................ ................................ ........................... 66 Trade Liberalization ................................ ................................ .......................... 69 Trade Liberalization in Traditional and Modern Sectors ................................ ... 71 Conclusion ................................ ................................ ................................ .............. 72 INCIDENCE OF CHILD LABOR IN A NORTH SOUTH MODEL OF TRADE ................ 73 The Model ................................ ................................ ................................ ............... 74 Consumption ................................ ................................ ................................ .... 75 Production in the North ................................ ................................ ..................... 76 Exporting Firms in the North ................................ ................................ ................... 81 North South Free Trade Equilibrium ................................ ................................ ....... 83 Production in the So uth ................................ ................................ .................... 83 Firm Value for Southern Firm ................................ ................................ ........... 85 Free Entry Condition for Northern Firms ................................ .......................... 86 Share of Firms ................................ ................................ ................................ .. 86 Incidence of Child Labor ................................ ................................ ................... 88 Comparative Statics ................................ ................................ ................................ 90 Increase in Child Labor Enforcement, ................................ .................. 90 One Time Increase in the Population in the South, ................................ ..... 91 Increase in the Rate of Imitation, ................................ ................................ 92 Trade Costs ................................ ................................ ................................ ...... 93 Conclu sion ................................ ................................ ................................ .............. 96 APPEN DIX A FIRST ORDER CONDITIONS ................................ ................................ .................. 98 B PROOF OF UNIQUE STEADY STATE EQUILIBRIUM ................................ ............ 99 C SIMULATION WITH ENDOGENOUS RATE OF IMITATION ................................ 101 LIST OF REFERENCES ................................ ................................ ............................. 102 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 105 PAGE 7 7 LIST OF TABLES Table page 2 1 Summary of Comparative Statics Results ................................ .......................... 38 PAGE 8 8 LIST OF FIGURES Figure page 2 1 Steady state equilibrium ................................ ................................ ..................... 28 2 2 Increase in FDI ................................ ................................ ................................ ... 30 2 3 Welfare among househ olds with an increase in FDI ................................ ........... 31 2 4 Welfare among households with trade sanctions ................................ ............... 32 2 5 Welfare of households with emigrati on of skilled workers ................................ .. 34 2 6 Child wage subsidies ................................ ................................ .......................... 36 3 1 Steady state equilibrium ................................ ................................ ..................... 56 3 2 Increase in enforcement when ................................ ................................ ... 63 3 3 Increase in enforcement when ................................ ................................ ... 64 3 4 Effect of trade in the steady state equilibrium ................................ ..................... 70 4 1 Autarky equilibrium ................................ ................................ ............................. 79 4 2 Trade equ ilibrium ................................ ................................ ................................ 83 4 3 Increase in enforcement ................................ ................................ ..................... 91 4 4 Increase in population ................................ ................................ ........................ 92 4 5 Price indices and trade costs ................................ ................................ .............. 95 4 6 Child labor and trade costs ................................ ................................ ................. 96 PAGE 9 9 Abstract of Dissertation Presented to the Graduate School of the Univ ersity of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ESSAYS ON CHILD LABOR, PRODUCTIVITY, AND TRADE By Kristian Estevez December 2010 Chair: Elias Dinopoulos Major: Economics The problem of children working around the world is not a new phenomenon, but rather a legacy of poverty that is slowly being eradicated as incomes inch up in developing economies. While the incidence of child labor has been on the decline, awareness of the issue has g rown in part due to globalization. This has led to debates as to the best way to cure the problem once and for all. Chapter 1 describes what leads to child labor briefly reviews the economic literature of the last 20 years, and summarizes the policy pre s criptions result ing from the research. Chapter 2 develops a dynamic, overlapping generations general equilibrium model of a small open economy where the demand and supply of child labor are analyzed. There are two goods: a modern good produced by skilled labor and capital, and an agrarian good produced by unskilled adult labor, child labor, and land. The model predicts that an increase in foreign direct investment (FDI) and improvements in education will decrease the incidence of child labor. Emigration of skilled (unskilled) workers will reduce (increase) the supply of child labor, while trade sanctions will reduce the demand for child labor. Child wage subsidies have an ambiguous effect on the incidence of child labor while education subsidies are eff e ctive in reducing child labor. PAGE 10 10 Chapter 3 examines the role of firm heterogeneity in the demand for child labor. productivity parameter affects the relative product ivity between adult and child workers. When the productivity elasticity of adult and child labor are equal, all firms choose the same proportion of child workers and only an increase in enforcement will reduce the demand for child labor. When the produc tivity elasticity of child labor is higher (lower) than that of adult labor, trade liberalization will result in a decrease (increase) in the demand for child labor. Last, Chapter 4 studies how international trade affects the incidence of child labor in a North South model of trade. Innovating firms in the North are heterogeneous and differ in their marginal costs, while imitating firms in the South are homogeneous and may use child labor in production. The incidence of child labor depend s not only on dom estic fa ctors such as the relative wage of adult and child labor in the South, but also on the endogenous rate of innovation in the North and the exogenous rate of imitation by Southern firms. Reductions in trade cost s decrease the number of Southern fir ms and will lower the demand for child labor. An increase in the exogenous rate of imitation by Southern firms will reduce the total number of varieties of the differentiated good and decrease the demand for child labor, while an increase in the populatio n in the South will increase the demand for child labor. PAGE 11 11 CHAPTER 1 THE ECONOMICS OF CHI LD LABOR Over the last decade, the incidence of child labor has been declin ing steadily worldwide However, the number of children classified as economically active ( over 191 million as of 2006) 1 is still too high and highly concentrated in the poorest nations. The number of economically active children accounts for 14% of the children in the world, but in sub Saharan Africa and Asia, the number is closer to 25% and 1 7%, respectively (ILO 2006b). Furthermore, m any of the children employed outside the agricultural sector work in unsafe and sometimes hazardous conditions. In recent years, the increase of globalization has raised awareness of the proble m of child labor in the industrialized world. The International Labo u r Organization (ILO) passed Convention 29 in 1930 which prohibit s all forms of forced and compulsory labor. In 1973, the ILO passed Convention 138 which set s a minimum age for children depending on t he type of work. L ight work, meant as work that does not significantly detract from schooling, is limited to children 13 years or older limited to children 18 and older. Many countries where child labor is most visible such as India, Nepal, and Thailand have national laws limiting or banning the use of child labor. Many others have compulsory education laws to ensure that children are receiving an education but that do not outlaw the use of ch ild labor outside compulsory scho oling. Unfortunately, laws outlawing child labor and compulsory education laws have shown to have a minimal effect in low income countries (Krueger 1996). The passage 1 See International Labor Organization (ILO) 2006a. For a comprehensive surve y of the child labor literature, see Basu (1999); Rogers and Swinnerton (2001); and Brown, Deardorff, and Stern (2003). PAGE 12 12 of compulsory education laws is endogenous to the current state of child labor, and it h as been shown that these laws are usually passed following a decline in child labor, not before it. Even programs that are meant to discourage child labor by providing incentive s to poor families to replace work with schooling have proved to be ineffectiv e due to the difficulty in monitoring compliance. Supply of Child Labor The main justification for government intervention to eliminat e child labor is that of externalities. The social returns to education have been shown to exceed private returns, so a s ituation in which children work rather than attend school is not socially optimal. In this case, eliminati ng child labor maximize s social welfare. The best way to achieve that objective eludes policymakers. Most economists would agree that economic grow th that reduces poverty is guaranteed to end child labor, but child labor in itself is what prevents economic growth in the poorest countries. Not surprisingly, Krueger (1996) found a strong correlation between a countr per capita GDP and the employmen t rate of 10 to 14 year olds. Most theoretical models make the assumption that parents are the sole decision make rs with regard to ies The education of children can thus be treated as an asset: a means of increasing futu re income at the expense of present consumption. Poverty is one of the causes of child labor, but not necessarily the main one. Basu and Van (1998) initiated the theoretical investigation in to the incidence of child labor when they assumed: 1) families would not send their children to adult labor and child labor were perfect substitutes in production. In the ir model, they proved the possible existence of multiple stabl e equilibri a : an equilibrium with low PAGE 13 13 wages where children worked and competed with unskilled adults and another with high wages and no child labor. The model suggests that a short term ban on child labor might be used effectively to jolt the economy to the favorable equilibrium with no child labor, but it will only be successful if th e ban increase s adult wages sufficiently Lately, a greater importance has been placed on the role of credit market imperfections in developing countries Baland and Robins on (2000) viewed child labor as a means f or low income households to transfer future income to the present when against the forgone income incurred from education. Ranjan (2 001) and Jafarey and Lahiri (2002) also focused on the lack of available credit as a reason why parents resort to sending their children to work Ranjan (2001) used an overlapping generations model where households differ in their talent level and found t hat the incidence of child labor increases as credit availability decreases and as income inequality increases. Jafarey and Lahiri (2002) also fou nd that the incidence of child labor decreases as access to credit markets increase s Demand for Child Labor In the developed world, it has been debated whether trade policies are effective at lowering the incentive for firms to use child labor. Staunch advocates against the use of child labor believe that countries with lax labor standards should be sanctioned Unfortunately, proof of the use of child labor in production is difficult to find and in those countries where chi ld labor is most rampant, existing laws against child labor often go unenforced. Some economist s worry that trade sanctions might increase the incidence of child labor by punishing unskilled adult work ers in the export sector, reducing the PAGE 14 14 income of low skilled households and possibly forcing children into more dangerous work (Maskus 1997) While studies have examined the supply of child lab or from households, t he demand for child labor has not received the same amount of attention. This is partly due to the lack of firm data which makes empirical research difficult The few empirical studies, such as Busse and Braun (2004), tend to use ma cro level data to find a relationship between child labor and trade openness. Busse and Braun find that an increase in trade openness is generally associated with a decrease in the incidence of child labor, but the effect disappears after controlling for income. This suggests that the method by which trade liberalization decreases child labor is through increasing parental incomes which then decreases the supply of child labor. The theoretical models that have examined the demand for child labor have foc used on the effects of trade liberalization, trade sanctions, and foreign direct investment. Gupta (2000 ) built a bargaining model with an efficiency wage function that determines the productivity of children given the wage paid to the child In that mod el, bargain with firms over the child wage and the efficiency wage that is paid to the child in the form of food. Dinopoulos and Zhao (2007) explored how trade liberali zation affects the demand for child labor in a model with efficiency wages They find that both trade liberalization and FDI that increases the output of the modern good decrease the incidence of child labor. PAGE 15 15 CHAPTER 2 NUTRITIONAL EFFICIENCY WAGES AND CHILD LABOR This chapter builds a theoretical model that examines both the supply and demand of child labor to examine the various policy options available to combat the problem Economists have mostly examined the issue of child labor and globalization t hrough the use of theoretical models due to the difficulty of acquiring data for empirical studies. The few published empirical papers have focused on household surveys in small regions in developing countries, but it is uncertain whether the ir results ar e applicable elsewhere For instance, Edmonds and Pavcnik (2005) found that globalization led to an increase in the price of rice in Vietnam, which decreased the incidence of child labor even though child labor is used heavily in the production of rice. On the other hand, Kruger (2007) found that globalization had the opposite effect, increasing the incidence of child labor in the coffee sector in Brazil even though globalization led to an increase in the price of coffee beans and in the wages in that sec tor. Gupta (2000 ) and Dinopoulos and Zhao (2007) published papers that focus predominately on the demand for child labor. Both studies use d child nutritional efficiency wages, a practice continued in this chapter which allows for the child wage to be fix ed. In Dinopoulos and Zhao (2007) market imperfections exist such that there is an underemployment of children and the income that guardians receive from sending their child to work is exogenous. Unfortunately, this assumption appears to be highly unre alistic, given that one of the main results in that paper the effect of subsidies, has been shown to have a significant impact on the supply of child labor. This paper endogenizes the decision that parents make about whether to educate or employ their ch ildren and thus allows for the supply of child labor to depend on the returns that PAGE 16 16 parents receive from sendi ng their children to work. T he premium that parents receive is endogenously determined and allows the model to analyze the effect that policies ha ve on both the supply and demand of child labor. The model shows that policies enacted to reduce the incidence of child labor must carefully explore both the supply and demand components of child labor. A policy like child wage subsidies, while meant to reduce the supply of child labor, will also increase the demand for child labor by reducing the cost of hiring one unit of child labor. This can result in an increase in the overall incidence of child labor. Education subsidies given to unskilled househo lds are a better policy that will reduce the supply of child labor without affecting demand. This result is supported by Schultz (2004) and Ravallion and Wodon (2000). Trade sanctions, which reduce the demand for products made with child labor, will redu ce the demand for child labor. Child wage subsidies, which in Dinopoulos and Zhao (2007) cause an increase in the incidence of child labor, ha ve an ambiguous effect when one accounts for the reduced supply of child labor. This chapter is organized as follo ws. Section 2 describes the dynamic general equilibrium model, starting with the characterization of the child schooling decision made by parents and concluding with a description of the two production sectors in the economy. Section 3 solves for the ste ady state equilibrium and S ection 4 analyzes the effect of domestic and international policies on the incidence of child labor. Simulations are also included to examine welfare and distributional effects of the various policies. Section 5 con cludes with some final remarks. The Model The model is a dynamic overlapping generations model that endogenizes the incidence of child labor. T he model has two homogen e ous goods: an agrarian good PAGE 17 17 that is produced using land and unskilled adult and child labor, and a modern good that uses skilled labor and capital in its production. The productivity of skilled workers depends on their innate ability which is assumed to differ among households. Perfect competition in the production sector guarantees that adult wor kers are paid their marginal revenue product of labor. The cost of one unit of child labor is split between the amount given to children in the form of meals which affects their productivity and the parental premium given to parents for the employment o f their child. This paper builds on two recent theoretical papers in the child labor literature. Ranjan (2001) uses differing talent levels to differentiate households, assuming that a talent remains constant across generations. This chapter assumes that households are differentiated by ability levels which determine s the skilled wage if the individual attended school as a child. It is also assumed that the ability of households is constant across generations. Dinopoulos and Zhao (2007) uti lize child nutritional efficiency wages to fix the child wage. This leads to the adult skilled wage being fixed and is used to derive the demand for child labor. A key difference between this paper and that of Dinopoulos and Zhao is that in this paper th e parental pre mium is endogenously determined by bargaining between parents and firms. Household Decision Household income is t he primary reason that parents resort to sending their child (1998) since educating a child is considered an unaffordable luxury to poor families. In this model, households are differentiated by their innate ability level which subsequently determines their adult wage if they attended school as children. PAGE 18 18 For not ational convenience, the population of each generation is normalized to 1. A family consists of one adult and one child, so the overall population in the economy is 2. The ability of each family follows a uniform distribution, where the range of abilitie s is their own. The assumption that parents and children have the same ability is for notational simplification, while the assumption that parents are ability is a plausible one. Children sent to work receive some form of education before they become old enough to work, whether it is in primary schooling or home schooling, ptitude in t hese early stages. It is assumed that parents care about the future well being of their children as well a standard one used in the child labor literature 2 Let at time : (2 1) where and good, respectively. For simplicity, it is assumed that all families have identical preferences. Writing Equation 2 1 in terms of prices and income gives the following indirect utility function: (2 2 ) 2 See Basu (1998), Ranjan (2001), and Jafarey and Lahiri (2001 ) PAGE 19 19 level, where income at time for any family is equal to: (2 3 ) where is the child wage paid in kind to child workers at time and is the parental income from sending his/her c hild to work at time where will be referr ed to as the parental premium. It will be assumed that children are fed at school if parents choose not send them to work, and if children are sent to work, th e firm will pay children in kind by providing them food. The amount of food that they provide will determine the productivity of the child as will be discussed in the production section in this chapter. To simplify the model and to allow for the supply o f child labor to be determined explicitly, a Cobb from current consumption 3 : (2 4 ) This leads to the following indirect utility function from Equation 2 2: (2 5 ) where and is the price index. It is necessary to examine in the steady state equilibrium both the child schooling decision of parents who are skilled workers a nd those who are unskilled. A household 3 The results of the model hold generally for any homothetic utility fu nction where income enters linearly. A possible extension of the model would be to incorporate a utility function in which the marginal utility of income decreases as income increases, which would allow for income effects in the determination of the suppl y of child labor. PAGE 20 20 is characterized by two factors: the parent which is constant across generations schooling dec ision to be written in the form where corresponds to whether the parent is skilled ( ) or unskilled ( ). schooling decision is summarized by the following equation: ( 2 6 ) where the first part he send s his child to school and the second part represents the he send s his child to work. To find the critical ability level that makes a skilled parent indifferent between sending the child to school versus work, we equalize Equation 2 6 using the Cobb Douglas specification in Equation 2 4: (2 7 ) (2 8 ) Let represent the critical ability level that solves Equation 2 8. F or all skilled households with parent s will chose to send their child to school. F or all skilled households with parents will opt to send their children to work. ( 2 9 ) PAGE 21 21 where the first part once again corresponds to the parent educating his/ her child and the second part to sending the child to work. Equalizing to find the critical ability level yields : (2 10) Using the Cobb Douglas specification, Equation 2 4, gives us the same equ ation as the one for skilled parents, Equation 2 8. Since Equation 2 8 represents the child schooling for both skilled and unskilled households, and the parent o educate his child or not is independent of whether the parent is educated himself The ability level that solves Equation 2 8 is represented by where critical values will be denoted with a n asterisk In the steady state equilibrium, values of the endogenous variable s must remain constant. To solve for in the steady state equilibrium, we can use the corresponding value functions. In the steady state, it must be true that the first term in Equation 2 6 on problem since skilled workers are going to choose to educate their child. Likewise, the second term in Equation 2 9 must solve an steady state equilibrium: (2 11) ( 2 12) PAGE 22 22 Substituting Equations 2 11 and 2 12 into Equation 2 8 we can solve for the critical ability level that determines the supply of child labor: ( 2 13) Families with ability level educate their children while families with ability level send their children to work. Since a uniform distribution of abilitie s is assumed and the population of children is normalized to 1, the supply of child labor is equal to the critical ability level: ( 2 14) As the unskilled wage, their child to work, increases, the supply of child labor also increases. As the skilled wage, or the level of altruism, increases, the supply of child labor decreases. P roduction The production sector is characterized by perfect competition which ensures that factors are paid their marginal productivities. Capital complements skilled labor in the production of a modern good while land complements unskilled adult and ch ild labor in the production of an agrarian good. The production functions in both sectors are represented by constant returns to scale technologies of Cobb Douglas form. PAGE 23 23 Modern s ector Skilled labor and capital are used in the production of the modern good The productivity of a skilled worker will depend on his ability level. Using specific sector capital which is fixed in the modern sector allows for the analysis of foreign direct investment and its effect on the returns to education and the parental sc hooling decision. The production of the modern good is described by the following Cobb Douglas production function: ( 2 15) where 4 is the total human capital stock of s killed workers and is the productivity of a skilled worker given his ability. T he price of the modern good will act as the numeraire. The profit function for a firm producing the modern good is: ( 2 16) Firms maximize Equ ation 2 16 with respect to the employment of skilled workers and sector specific capital yielding the following first order conditions: ( 2 17) ( 2 18) 4 For an evaluation of the integral, see equation (33). PAGE 24 24 The wage paid to skilled workers and the rental of capital are given by Equations 2 17 and 2 18 Since a skilled worker with ability has productivity equal to his income will be equal to Agrarian s ector Output in the agrarian sector is determined by the amount of unskilled labor, both adult and child, and the amount of land available. Studies by the International Labor Organization (2006a) have found that the majority of children who forgo schooling tend to wo rk in rural settings, so the use of land as a complement to child labor is warranted. The use of nutritional efficiency wages, not unlike that used in Stiglitz (1976), describes how the productivity of child laborers is dependent on the amount of food giv en to them in the form of meals. The nutritional efficiency function which determines the productivity of children, is an increasing and concave function with respect to the consumption of food (the in kind child wage) and it is bounded from above ( i .e., there is a limit to how productive children can be and since it is assumed that child labor is always less productive than adult unskilled labor, ) Gupta (2000 ) developed a model where the producti ve efficiency of child labor depends on the amount of food their employer gives them He found that when employers maximize their profits, this leads to the common efficiency wage equation that fixes the child wage. Dinopoulos and Zhao (2007) utilize nut ritional efficiency wages for children along with efficiency wages for skilled adults to analyze the effects of globalization and domestic policies on the demand for child labor. The production of the agrarian good is determined by the following production function: PAGE 25 25 ( 2 19) where is the nutritional efficiency function of a child worker ; is a child equivalent scaling constant that equates how one unit of adult unskilled lab or corresponds with one unit of child labor ; is a productivity parameter; and and are the amount of child labor, adult unskilled labor, and land, respectively. Firms in the agrarian sector maximize their profit with respect to land, adult unskilled labor, child labor, and the child wage paid to children in the form of meals: ( 2 20) Although children are paid in the form of food, firms have to pay the premium, to parents which makes the total cost of one unit of child labor equal to Maximizing Equation 2 20 yields the following first order conditions: ( 2 21) ( 2 22) ( 2 23) ( 2 24) If we combine E quations 2 22 and 2 23 we get the standard result in the nutritional efficiency wage literature: ( 2 25) PAGE 26 26 Thi s leads to the child wage, being fixed in the steady state equilibrium for a given nutritional efficiency function. For agrarian firms to maximize profits, they must pay child workers a wage that equates their marginal producti vity of labor to their average productivity. Combining Equations 2 21, 2 22, and 2 25 solves for the adult unskilled wage in ( 2 26) To determin e the relationship between the fixed child wage and the rental of land, we combine Equations 2 21 and 2 24 to determine the relative rental of land in proportion to the unskilled adult wage: ( 2 27) Equations 2 21 and 2 27 lead to the zero profit condition in terms of the unskilled adult wage, the productivity parameter, and the price of the agrarian good, : ( 2 28) This zero profit condit ion, along with Equation 2 26 determines the rental of land: ( 2 29) A nd using Equation 2 27 the demand for child labor, : ( 2 30) PAGE 27 27 The demand for child labor is incre asing in the amount of land in the agrarian sector and the price of the agrarian good, and is decreasing in the amount of adult unskilled labor and in the parental premium. Substituting Equations 2 17 and 2 26 in the household schooling decision, Equation 2 14 the supply of child labor can be derived in terms of the parental premium and the parameters of the model: ( 2 31) The supply of child labor is increasing in the parental premium and in the supply of adult skilled work ers and is decreasing in the amount of capital in the modern sector and i n the price of the modern good. Steady State Equilibrium In the steady state equilibrium, for all The amount of child labor at any time has to be in the range Children who work become unskilled laborers in the next period while children who attend school become skilled laborers working in the modern sector. The supply of u nskilled workers is equal to the quantity of child labor in the previous generation, while the amount of skilled workers in efficiency units is: ( 2 32) Substituting these values into Equations 2 30 and 2 31 and writing the equations in terms of the inverse supply and demand of child labor in the steady state equilibrium yields: PAGE 28 28 ( 2 33) ( 2 34) These equations not only determine the incidence of child labor in the steady state equilibrium, but they also ensure an interior equilibrium, Figure 2 1. Steady state equilibrium As the demand for child labor goes t o infinity because the scarcity of unskilled labor drives the unskilled wage, and the parental premium, upward. The same holds as In this case, most of the population is employed in the agrarian sector and the marginal produc tivity of a unit of skilled labor goes to infinity. As shown in Figure 2 1, the parental premium and the incidence of child labor in the steady state are determined by the intersection of Equations 2 33 and 2 34. C 1 C D C C S PAGE 29 29 Comparative Statics I n this section, the c omparative statics are computed to show how globalization and domestic policies affect the incidence of child labor. The paper first examines how an increase in foreign direct investment can impact the incidence of child labor before exploring the effects of domestic policies. When applicable, simulations were conducted to analyze the effect of the different policies on welfare. The parameters used in the simulations were , , and 5 Using these figures, the incidence of child labor is roughly 21% of the child population and the parental premium, is 2, meaning that parents receive for sending their child to work, which is a little less than half of the adult unskilled wage. Foreign Direct Investment Globalization can impact an economy by allowing an additional influx of foreign schooling decision by increasing the marginal product of skilled labor. The increase in the skilled wage, shifts the supply of child labor leftward as shown in Figure 2 2. This results in a decrease in the incidence of child labor and an increase in the parental premium. 6 An interesting observa tion is that the increase in the parental premium not 5 Since the population is normalized to 1, the amount of land and capital can be thought of the land per capita and the capital per capita, respectfully. The values of K and L were calculated using statistics from the Philippines, where K is an approximation of the total capital divided by the population, and T is the amount of usable land (in square miles) divided by the population. The other values were arbitrarily assigned, but changes in these values do not qualitatively impact results. 6 Davis and Voy (2007) and Edmonds and Pavcnik (2005) have studied the relationship between FDI and trade openness with the incidence of child labor while controlling for endogenous factors. The y also find a negative relationship between child labor and foreign direct investment. PAGE 30 30 only increases the famil income from sending the child to work, but it also increases the adult unskilled wage through the relationship in Equation 2 26. Figure 2 2. Inc rease in FDI Consequently, an increase in foreign direct investment not only has the benefit of directly decreasing the incidence of child labor, it also increases the incomes of poor families. This result can better be seen by comparing the indirect ut ility of households, Equation 2 2, before and after the increase in foreign direct investment in Figure 2 3. The increase in capital reduces the incidence of child labor from 22% to 19% (since a uniform distribution of abilities is assumed) and all house holds are better off than previously Skilled households with the highest abilities benefit the most from an increase in foreign direct investment since the higher skilled wage benefits workers with the highest productivity. The results on the incidence of child labor depend on the fact C PAGE 31 31 that capital is used only to produce the modern good. If capital were used in the production of both goods, then the results would be ambiguous. Figure 2 3. Welfare among households with an increase in FDI Trade Sancti ons Internationally, trade sanctions have been recommended as a way of punishing countries that use child labor in the production of traded goods. By reducing the international demand for the good in question, trade sanctions attempt to lower the internat ional demand, which corresponds to a drop in the price of the agrarian good in the model. The fall in lowers the demand for child labor, Equation 2 33 and lowers the incidence of child labor in the steady state equilibrium. Ho wever, families with low ability may be punished because sanctions reduce nominal incomes by decreasing the parental premium and the adult unskilled wage. PAGE 32 32 Figure 2 4. Welfare among households with trade sanctions As shown in Figure 2 4, the effect of tr ade sanctions on unskilled household utility is ambiguous due to the fact that the lower agrarian price reduces the price level and can increase real income. Whether the decrease in the price of the agrarian good incomes depends on the relative demand for the agrarian good. Skilled nominal wages fall due to the increase in skilled workers, but real incomes may rise due to the decrease in the price of the agrarian good. Education Improvements One way governments ca n increase child enrollment in schools is to improve the efficiency of the education system which make s skilled workers more productive. By increasing the marginal productivity of skilled workers, the incomes of skilled workers and the returns to educati on will decrease the supply of child labor. This can be modeled by changing Equation 2 32 the amount of skilled adult labor in terms of efficiency units, to: PAGE 33 33 ( 2 35) where represents improvemen ts in education that increase the productivity of skilled workers. The supply of child labor then becomes: ( 2 36) which is unambiguously less than t he supply of child labor in Equation 2 31 Similar to the case of foreign direct investment, an increase in the education efficiency parameter, will shift the supply of child labor leftward, leading to an increase in the parental premium and a decrease in the incidence of child labor. Welfare effects are also similar, but there are greater gains for adult skilled households due to the increase in productivity. Migration Emigration of skilled workers is common in developing countries as wages for skilled workers are higher in developed economies. Here the paper examine s how this migration affects the incidence of child labor. First, assume that the skilled workers who migrate are those with the highest abilities since they would benefit the most from moving. Let represent the skilled worker with the lowest ability who decides to relocate. Therefore, the effect ive units of skilled labor in Equation 2 32 becomes: ( 2 37) which is unambiguously smaller than Equation 2 32 since Replacing Equation 2 37 in the supply of child labor equation yields : PAGE 34 34 ( 2 38) which is less than Equation 2 34 and represents a decrease in the supply of child labor in the steady state equilibrium. Like the case of foreign direct investment, emigration of skilled labor causes the supply of child labor to shift leftward, reducing the incidence of child labor in the steady state and increasing the current income of unskilled families. When skilled labor migrates, a v oid of skilled labor is left in the modern sector while the amount of capital remains fixed. This increases the marginal productivity of skilled workers and thus the skilled wage. The increase in the returns to education reduces the number of parents who are willing to forgo sending their child to school. As shown in Figure 2 5, the welfare of unskilled households is unchanged, but the welfare of skilled households (assum ing ) increase s Figure 2 5. Welfare of households with emigration of skilled workers PAGE 35 35 Subsidies Last, the paper examine s how two different types of subsidies affect the employment of children in the economy. The first type analyze s financial assistance given directly to child workers in the form of meals (Din opoulos and Zhao, 2007) The second type, which has been empirically tested, deals with subsidies given directly to low income families to encourage them to send their children to school. Child wage s ubsidies The child wage subsidy is assumed to come from an exogenous source, which might include foreign aid from develop ed countries and aid from non governmental organizations. If the subsidy were financed by the government, we would then have to examine the scope of government and the way in which the subs idy is financed. A direct subsidy given to children in the form of meals effectively changes an agrarian profit maximizing problem, Equation 2 20 to: ( 2 39) where is the value of the wage su bsidy. When the agrarian firms maximize their profits with respect to the amount of child labor and the wage paid to child labor in terms of food, the standard nutritional efficiency wage equation becomes: ( 2 40) This ch ild wage subsidy increases the average productivity while decreasing the marginal productivity. This causes firms to lower the child wage that they pay in terms of food changing the steady state equations to: ( 2 41) PAGE 36 36 ( 2 42) The demand for child labor, Equation 2 41 increase s, while the supply of child labor, Equation 2 42 decrease s as shown in Figure 2 6. The effect of the child wage subsidies on the incidence of child labor is ambiguous since the increase in the parental premium is countered by a decrease in the child wage. Child wage subsidies lead to a decrease in the adult unskilled wage and its effect on the skilled wage depends on whether the level of child labor changes or not Figure 2 6. Child wage subsidies This result differs from that found in Dinopoulos and Zhao (2007). In that paper, the supply of child workers is perfectly elastic. This amounts to the supply of child labor being represented by a h orizontal line at the exogenous parental premium. The child wage subsidy would therefore only increase the demand for child labor, leading to an C PAGE 37 37 increase in child labor in the agrarian sector. With land instead of skilled labor in the agrarian sector and an endogenous supply of child labor, the opposite holds true. The increase in the average productivity of child laborers decreases the adult unskilled wage, which therefore increases the relative returns to education and decreases the supply of child lab or. This leads to an ambiguous change in the incidence of child workers. Education s ubsidies Some countries have used e ducation subsidies to reduce the incidence of child labor. Schultz (2004) examined a Mexican program called Progressa, in which househ olds in a randomly selected low income locality were given income subsidies if they sent their children to school. This resulted in an increase in average schooling for children in the localities that received the subsidy compared with similar localities that did not. Likewise Ravallion and Wodon (2000) examined a similar education subsidy in B angladesh and found that although increases in school enrollments came mostly at the expense of child leisure, the education subsidy did have a significant effect on reducin g the incidence of child labor. To incorporate an education subsidy in to the model, it is necessary to look back to the supply of child labor equation, Equation 2 13 and add the subsidy, that parents would receive if they send their child to school. The household maximization problem becomes: ( 2 43) PAGE 38 38 The education subsidy becomes an opportunity cost to parents who send their child to work. This changes the supply of child labor equatio n to: ( 2 44) An education subsidy will cause a leftward shift of the child labor supply curve and therefore will have an outcome similar to an increase in FDI. Unskilled family income will benefit twice: once through a direct i ncrease in household income caused by the education subsidy, and then through an indirect increase in the unskilled wage caused by the decrease in child workers. Table 2 1. Summary of Comparative Static s Results Supply of Child Labor Demand for Child Labor Incidence of Child Labor Welfare of Unskilled Households Domestic Policies Education Improvement Decreases Unchanged Decreases Increases Migration of Skilled Workers Decreases Unchanged Decreases Increases Child Wage Subsidie s Decrease s Increase s Ambiguous Increases Education Subsidies Decrease s Unchanged Decrease s Increases Trade Policies Foreign Direct Investment Decreases Unchanged Decreases Increases Trade Sanctions Unchanged Decrease s Decreases Ambi guous Table 2 1 summarizes the comparative static s results and the effect s that policies have on the welfare of unskilled households. As shown, most policies that reduce the incidence of child labor will lead to an increase in the welfare of unskille d households, even though some of these policies reduce the wage of unskilled workers. PAGE 39 39 Conclusion Child labor is a major problem in developing countries, but one that looks to be in decline around the world. Still, some forms of child labor might always exist as long as parents fail to sustain their family using only their income and as long as firms have access to this cheap form of labor. The only way to eradicate the problem truly is to ensure that families can s ustain adequate incomes without child labor earnings and that there are high rewards for schooling so that families can escape the vicious circle of poverty that plagues parts of the developing world. This paper develops a dynamic general equilibrium model of child labor that incorporates the parental schooling decision which determines the supply of child labor and the profit maximizing conditions of private firms which determine the demand for child labor. The use of child nutritional efficiency wages allows for the development of an act ive market for child labor that is dependent on the skilled and unskilled wages in both sectors, the amount of capital and land in the economy, and parental preferences toward educating their children. This allows us to study the impact of domestic and fo reign policy and its effect s on both the demand for and supply of child labor. Increases in foreign direct investment increase the returns to education and lead to a decrease in the incidence of child labor. In the long run, this increases the human capit al stock in future generations and leads to higher sustained economic growth. This finding is consistent with similar works by Dinopoulos and Zhao (2007). This paper differs from Dinopoulos and Zhao in regard to the impact of child wage subsidies. While Dinopoulos and Zhao find that child wage subsidies increase the incidence of child labor by increasing their complement of production in the agrarian sector, this paper finds that child wage subsidies increase the incomes of unskilled households but have an PAGE 40 40 ambiguous effect on the incidence of child labor. Finally, this paper shows that education subsidies can unambiguously decrease the incidence of child labor by giving families a monetary incentive to send their children to school. PAGE 41 41 CHAPTER 3 CHILD LAB OR AND FIRM HETEROGE NEITY The phenomenon of child labor is a stubborn problem that continues to plague the least developed countries and contributes to the perpetual cycle of poverty from which many nations have been unable to break free Although the inc idence of child labor has been steadily declining over the last decade, it still remains staunchly prevalent in the poorest nations. The r esearch on the causes of child labor has grown over the last twenty years but has been principally rooted in one side of the story, namely the decisions of households that determine the supply of child labor 7 Edmonds and Pavcnik (2005b), Dinopoulos and Zhao (2007), and Kis Katos (2007) are a few examples of recent theoretical papers that have examined child labor from t he demand side. This allows for the analysis of how trade liberalization, FDI, and other global factors affect the demand for child labor. These papers assume that children work in sectors that produce goods that are traded in an inter industry trade set ting. In doing so, they assume that the wages paid to children (or to the family of the children) reflect the productivity of the child worker. A study conducted by the International Labour Organization (2007) on child wages and productivity reveals that differences in adult and child wages are not reflected in their productivity difference s Even in sectors where children were nearly as productive as their adult counterparts, the child wage was anywhere from one sixth to one fourth the wage paid to adul t unskilled workers (ILO 2007). 7 Basu and Van (1998), Ranjan (2000), and Jafarey and Lahiri (2002) are just a few notable papers that have examined the supply of child labor from the household perspe ctive. For a comprehensive survey of the child labor literature, see Brown, Deardorff, and Stern (2003). PAGE 42 42 The aim of this paper is to analyze the short run demand for child labor in the presence of firm heterogeneity and intra industry trade. The model developed by Melitz (2003) will be used as the foundation for the model in this chapter which will endogenously determine the cutoff productivity level needed for a firm to enter an industry and the export cutoff productivity level that makes it profitable for a firm to export its good. As will be shown, sector characteristics particularly how firm productivity affects the relative productivity of child and adult workers, will determine whether trade liberalization can remedy or exacerbate the incidence of child labor. Intra industry trade, while not as prevalent in developing countries as in industrialized countries, is still a significant source of trade between similar developing nations and therefore must be examined with regard to child labor. 8 Heterogeneous firms engaging in intra industry trade in developing countries tend to be located in sectors characterized by significant amount s of child labor. Balassa (1998) examined the role of firm heterogeneity in developing countries. He looked at the level of intra industry trade in Latin America and noted that intra indust ry trade was prevalent among similar South American countries in sectors such as textiles ; fabricated metal goods ; and paper, clay, and glass products. Kucera (2002) concluded that child labor employ ed in the export sector was mostly located in textiles, apparel, craft production, and other light manufacturing in developing countries, most of the industries where intra industry trade is dominant in the developing economies studied by Balassa (1998). 8 Baland and Robinson (2000) note the need to consider firm heterogeneity before concluding that a ban on child labor will always lead to a Pareto imp rovement. Hummels and Klenow (2005) examine the extent of the extensive margin in 126 countries and show that in export variety makes up a large percentage of exports for large developing countries like China (.70) and India (.44). PAGE 43 43 Empirical work into the demand for child labor is relati vely lacking compared with the amount of work done on household factors. Unfortunately, the difficulty of acquiring firm level data on child labor is considerable and even if it were possible to obtai n these data would be questionable since firms have a notable disincentive to disclose information on their use of child labor and the wages paid to their workers. Using macro level data, Kucera (2002), Busse and Braun (2004), an d Davis and Voy (2007) have empirically found a relatively weak relationship between trade liberalization and child labor after accounting for changes in income. The u se of macro level data does not allow the demand for child labor to vary by sector whic h this paper examines It is therefore necessary to rely on theory to analyze the impacts of trade liberalization on the demand for child labor and to account for the fact that the relative prod uctivity of child workers differs among sectors. This chapte r is organized as follows. Section 2 outlines the closed model and solves the benchmark case where the productivity elasticity of adult and child labor are equalized. Section 3 describes how the model differs when adult labor and child labor differ in th eir productivity elasticity and shows how this might affect the ability of enforcement to reduce the demand for child labor. Section 4 introduces trade and shows how trade liberalization affects the demand for child labor in three cases. Last, Section 5 summarizes the policy implications and offers conclud ing remarks. The Basic Model The model presented below is based on Marc industry trade model. F or a firm to enter the market, it first incur s a fixed entry cost that allows it to conduct research and development (R&D) Once R&D has taken place firms discover PAGE 44 44 how productive they are in manufacturing a unique variety. Firms then choose the optimal amount of child labor (in proportion to the amount of adult workers) given their pro ductivity level by maximizing their expected firm value. The use of child labor in which increases the profits earned each period, but has the trade off of exposing the firm to additional risk each period. This t rade off results in an interior equilibrium where the proportion of child labor is greater than or equal to 0 but is bounded from above. Last, firms decide whether their expected firm value will be able to cover their fixed expected value exceeds its fixed production cost, then it then the firm will choose to exit the industry. In the steady state equilibrium, there exists a unique c utoff productivity level such that firms with productivity equal to or above that threshold will choose to produce and firms with productivity below the threshold will exit the market. Consumer Demand T he preferences of a representative consumer are given by a C.E.S. utility function over a continuum of goods, : ( 3 1) which will be maximized 9 Assuming that th is yields a demand function for each variety ,: 9 The Lagrangian and th e corresponding first order conditions are shown in Appendix A. PAGE 45 45 ( 3 2) where is the Lagrangian multiplier defined in Appendix A, and measures the elasticity of substitution between any two varieties. Total expenditure for a given variety is calculated by multiplying the demand for a variety by its price. Aggregating over all varieties nets total revenue which must equal total expen diture in the steady state equilibrium: (3 3 ) The price index, is a weighted average of the price of all varieties. Since total revenue equal s the aggregate quantity times the aggregate price, we can rewrite Equation 3 2 as: ( 3 4) The relative quantity demanded of two goods will therefore be dependent on their relative price: ( 3 5) Production Adult labor and child labor are assumed to be perfect substitutes in production, where is an adult scaling constant similar to the one used in Dinopoulos and PAGE 46 46 Zhao (2007). The supplies of both types of labor are assumed to be fixed an d perfectly inelastic in order to examine the short run demand for child labor. Although the relative to their productivity is less than that of adult labor, the trade off th at firms face of additional exposure to risk ensures that firms will not want to employ only children to produce the differentiated good. The quantity produced by each firm is a function of the : ( 3 6) where the amount of child labor, demanded by a firm is proportional to the amount of adult labor, : ( 3 7) The productivity elasticity for adult labor is equal to unity for all firms. A firm with a productivity parameter that is 10% greater than a rival firm will have adult labor that is also 10% more productive. For child labor, the productivity el asticity is equal to the parameter Since different sectors might have different s, whether is greater or less than unity will critical in how a policy will affect the incid ence of child labor When the relative productivity of adult and child workers will be constant for all firms. This will be referred to as the benchmark case to compare against the cases when is great er and less than unity. When referred to as the traditional industry case, child labor is relatively more productive compared with adult labor when working in firms with a higher productivity parameter. A traditional sector is one in which better technology simplifies work for all workers, thereby reducing any PAGE 47 47 productivity advantage that adult labor might have over child workers (e.g. certain textiles). Alternatively, when referred to as the mode rn industry case, better technology can lead to productivity gains that worsen the relative productivity of child laborers. This can be due to technology that complicates the production process resulting in a need for workers with greater ability and exp erience. In this scenario, child labor becomes less productive relative to adult labor in firms with higher productivity, and in extreme cases ( ) the productivity of children might actually decline when working for more firms wi th higher productivity. The wage of adult labor will act as the numeraire, and the child wage will be exogenously determined and equal to Empirical evidence conducted by the International Labour Organization (2007) shows that t he wage of child labor is generally not reflected by their productivity and is always less than the corresponding adult wage after accounting for productivity differences. T he total cost function for a firm is: ( 3 8) The m arginal cost, of a given firm depend s on the productivity parameter drawn by a firm, and the proportion of child labor, chosen: ( 3 9) Si nce empirical evidence (ILO 2007) has shown that the reason why firms employ child labor is that it is cheaper than adult labor after accounting for productivity differences, it will be assumed that: PAGE 48 48 ( 3 10) This assumpti on ensures that firms that use a higher proportion of child labor will have lower marginal costs 10 Maximizing per period profits Equation 3 11, with respect to price yields the standard profit maximizing price which is a constant marku rginal cost, Equation 3 12 : ( 3 11) ( 3 12) period pro fit and revenue marginal cost, the price index, and aggregate expenditure (equal to total revenue): ( 3 13) ( 3 14) The per period revenue and profit of a firm increase as the price index and total expenditure increase and as marginal cost, decreases. Since marginal cost is decreasing in the proportion of child labor and the productivity parameter, firms with higher productivity and/or higher proportion of child labor will earn higher per period 10 This assumption places a lower bound on the productivity elasticity of child labor, PAGE 49 49 revenue and profit. From Equation 3 5 th e price ratio of two firms depends on the relative quantities produced. We can rewrite it as: ( 3 15) All else equal, firms wit h lower marginal costs will produce more output Child Labor Demand The demand for child labo r, by a firm with productivity is det ermined by the : ( 3 16) ( 3 17) Taking the derivative of Equation 3 17 with respect t o yields: ( 3 18) The assumption in Equation 3 10 ensures that Equation 3 18 is positive for all firms. As the proportion of child laborers increases, the total amount of child labor hired by that firm also increases. This is due not just to the direct increase in the proportion of child labor, but also because the increase in the output produced. PAGE 50 50 Firm Value As in Melitz (2003), all firms face a probability of receiving a negative shock each period that might force the firm to exit. death, will depend on the proport ion of child labor employed by the firm: ( 3 20) where represents the strength of child labor enforcement and firms that hire no child labor face a probability of death equal to Firms that choose to employ a higher proportion of ch enforcement and are therefore more likely to face a negative shock. In this sense, strength of enforcement can not only represent government action to catch employers of child labor, but it may also incorpor ate the success of consumer groups advocating against the purchase of goods produced using child labor. period profit, divided by the probability of death fa ced each period and then subtracting a one time fixed production cost equal to : ( 3 21) Firms maximize their market value with respect to the proportion of child labor, taking aggregate revenue and a ggregate prices as given: ( 3 22) PAGE 51 51 ( 3 23) The optimal proportion of child labor, determined by Equation 3 23 and depend s roductivity parameter, and the exogenous parameters of the model: When the productivity parameter drops from both sides of 3 23 and the optimal proportion of child labor will be the sa me for all firms regardless of their productivity parameter: When (the traditional sector case), the RHS of Equation 3 23 becomes greater than the LHS as the productivity parameter inc reases. Therefore, the more productive firms will choose a higher proportion of child labor compared to firms with lower productivity. The inverse is true when (modern sector case). Firms with high productivity will not benefi t as much from child labor compared to firms with low productivity and therefore will choose a lower proportion of child labor. The rest of this section will detail the solution for the benchmark case ( ). Solving the Benchmark Ca se When the optimal proportion of the child labor equation becomes: ( 3 24) where is the proportion of child labor chosen by all firms which solves Equation 3 24 and i s therefore the average proportion of child labor in the industry. The marginal cost for a firm with productivity is : PAGE 52 52 ( 3 25) A n increase in the child wage, or the s trength of enforcement, reduces the optimal proportion of child labor that firms chose and increase s s Similarly, an increases in the elasticity of substitution, rai ses the optim al proportion of child labor and reduces the marginal cost s of all firms. Aggregation Aggregate price is equal to a weighted average of firm prices: ( 3 26) where is the mass of firms in the stead y state equilibrium and i s the ex ante distribution of the productivity parameter with the range Aggregate price can also be expressed as: ( 3 27) where The price index can be summarized as a function of the average productivity, : ( 3 28) and the mass of firms in the steady state equilibrium, : PAGE 53 53 ( 3 29) The rest of the aggregate variables are then calculated using Equation 3 29 Total quantity is equal to: ( 3 30) The relationship between the relative quantities of two firms in Equation 3 15 ca n be used to relate the quantity produced by any firm to the output of the firm with average productivity, : ( 3 31) Total revenue and aggregate per period profit, can sim ilarly be found as functions of the mass of firms and average productivity: ( 3 32) ( 3 33) Aggregate per period profit can also be used to solve for the average per period profit, define d by which is equal to the per period profit of the firm with average productivity: ( 3 34) The demand for child labor, derived in Equation 3 16 is simplified to: PAGE 54 54 ( 3 35) where depends on as shown in Equation 3 27 An increase in the proportion of child labor used by firms, will increase the demand for child labor by all firms Fr ee Entry and Exit For firms to enter the market, they first incur a fixed entry fee, needed to conduct R&D. Firms then draw a productivity parameter from a given distribution, with a continuous cumul ative distribution Let be the productivity parameter that corresponds to the firm whose firm value is equal to zero: ( 3 36) The expected value of firms with will be greater than zero so those firms will remain in the industry ; firms with will have a negative expected value and will choose to exit. The probability of successful entry is denoted by : ( 3 37) The average productivity in an industry will be a function of the cutoff productivity level, and the probability distribution, : ( 3 38) PAGE 55 55 An increase in the cutoff productivity level, will increase average productivity, since the least productive firms are forced to exit. The average firm value, equal to the value of the firm with average productivity, is equal to: ( 3 39) From Equation 3 36 the value of the cutoff firm must equal zero. We can substitute Equation 3 36 into Equation 3 39 to yield the average firm value in terms of the cutoff productivity level: ( 3 40) Equation 3 40 is the zero value cutoff condition (ZVC). It shows the relationship between the cutoff productivity level, and the average firm value, Potential entrants have the probability of obtaining a productivity parameter equal to or above the cutoff level The expected value of a potential entrant is: ( 3 41) Sett ing the expected firm value equal to the fixed entry cost yields the free entry condition (FE): ( 3 42) When the cutoff probability increases, it decreases the probability of successful entry. A higher average firm value is then necessary for the expected firm value to equal the fixed cost of entry. PAGE 56 56 Setting the free entry condition equal to the zero value cutoff condition will determine the cutoff productivity level and the average firm value in the steady state equilibr ium. As shown in Appendix B, this will result in a unique equilibrium. Since the ZVC and FE conditions are independent of the proportion of child labor, changes in the average proportion of child labor, Equation 3 23 have no effect on the cutoff productivity level and average productivity in the steady state equilibrium. Figure 3 1. Steady state equilibrium A ggregate variables must remain constant over time in the steady state equilibrium In t he steady state equilibrium, the mass of firms that exit each period is equal to the number of successful entrants, the cutoff productivity parameter and average firm value remain constant, and the incidence of child labor is unchanged in the long run. Th e number of successful entrants has to replace the number of firms exiting the market each period: FE ZVC PAGE 57 57 ( 3 43) where is equal to the number of potential entrants to the market. The total amount of a dult labor in the R&D sector, is then equal to the number of firms that attempt to enter each period, times the fixed entry cost, : ( 3 44) Tot al income of adult workers in the R&D sector is equal to the aggregate per period profit earned by firms. Total income received by all workers, which must be equal to total expenditure, is found by summing the income from all forms of labor: ( 3 45) Last, t otal revenue must equal total profits plus payments to the factors of production: ( 3 46) Average revenue can be written as a function of the average firm value solved in equilibrium by the fre e entry and zero value cutoff conditions: ( 3 47) As average firm value increases, so will average per period revenue. The mass of firms in the steady state equilibrium is found by dividing total revenue, equal to total income of all factors, by the revenue of the average firm. The mass of firms in equilibrium depend s on the endogenous demand for child labor, : ( 3 48) PAGE 58 58 The price index and aggregate quantity are e qual to: ( 3 49) ( 3 50) The amount of adult labor hired for R&D, adult labor hired for production, and child labor hired for production are equal to: ( 3 51) ( 3 52) ( 3 53) Equalizing Equations 3 48 and 3 53 will determine the mass of firms in the steady state equilibrium and the incidence of child labor: ( 3 54) ( 3 55) In the benchmark case, the incidence of child labor is determined solely by the parameters of the model ( and ) and the avera ge proportion of child labor determined by Equation 3 24 The derivative of Equation 3 55 with respect to is strictly greater than zero, so an increase in the average proportion of child labor in an industry will increase the i ncidence of child labor. PAGE 59 59 From Equation 3 48 the mass of firms, increases with the demand for child labor because child labor causes a rise in aggregate expenditure and revenue. A n increase in the number of firms though, incre ases the demand for adult labor to conduct R&D, removing adult labor from production and reducing the demand for child labor. These two opposing effects stabilize the demand for child labor in the steady state equilibrium in the benchmark case. Solving th e Model when This section will explore the steady state equilibrium when the productivity elasticity of child labor differs from that of adult labor. The equation that determines th e optimal level of child labor is rewritten bel ow for convenience: ( 3 56) Unlike the case where the optimal proportion of child labor for a firm will now depend on the productivity level of the firm. Similar to the benchmark case, an increase in the child wage or the strength of enforcement will reduce the optimal proportion of c hild labor chosen by all firm s When the productivity elasticity of child labor is greater than that of adult labor, i.e., firms that draw a higher productivity parameter will choose a higher proportion of child labor, so Alternatively, when the productivity elasticity of child labor is less than that of adult labor, i.e., firms that draw a higher productivity parameter will choose a lower proportion of child labor, and PAGE 60 60 ( 3 57) where Equation 3 10 ensures that for all firms. The price index is still equal to the weighted average price of all producing firms: ( 3 58) where average marginal cost, is equal to: ( 3 59) The aggregate equations from the benchmark case, Equations 3 30 through 3 33 remain unchanged. Free Entry and Exit The value of the firm with average productivity, is equal to: ( 3 60) while the value of the cutoff firm is equal to zero: ( 3 61) Combining Equations 3 60 and 3 61 yields the zero value cutoff condition (ZVC): PAGE 61 61 ( 3 62) which depends solely on the cutoff productivity level, The free entry condition (FE) is the same as in the benchmark case: ( 3 63) Firms that enter the market and draw a productivity parameter less than will choose to exit the market. Equalizing the free entry and zero value cutoff condition s determines the cutoff productivity level and the average firm value in the steady state equilibri um. The average proportion of child labor is a function of the cutoff productivity level: ( 3 64) In the traditional industry case, where the average proportion of child labor increases as the cuto ff productivity level increases, so ; the inverse is true in the modern industry case, and Aggregate variables must once again be constant in the steady state equilibrium so the number of successful ent rants must equal the num ber of firms exiting the market. The rest of the aggregate variables are the same as in the benchmark case. The demand for child labor is equal to: ( 3 65) PAGE 62 62 Equations 3 48 and 3 65 determine the mass of firms and the incidence of child labor in the steady state equilibrium: ( 3 66) ( 3 6 7) Since and an increase in the average propor tion of child labor will always lead to an increase in the incidence of child labor, and Enforcement The parameter measures the risk of using child labor in production. Firms that use a high proportio n of child labor are more likely to draw suspicion from authorities or face repercussion s from consumers ; as a result these firms face greater risk compared with those that use little to no child labor 11 In the benchmark case, the proportion of child labor, decreased as the strength of enforcement increased. The derivative of the total demand for child labor, Equation 3 55, with respect to was always greater than zero, so that a decrease in always reduce d the incidence of child labor. The case is more complicated when Equation 3 64 determines the relationship between the cutoff productivity level, and the average proportion of child labor, This is shown in Figure 3 2 for the traditional industry case ( ). The 11 public backlashes due to their connections with firms that employ children. In all cases, the large multinational corporations severed ties with the subcontracted firm accused of employing child labor. PAGE 63 63 relationship between the average proportion of child labor, and the incidence of child labor in Equation 3 67 has also been added to Figure 3 2. Traditional industry case Figure 3 2. Increase in enforcement when An increase in the level of child la bor enforcement, decreases for all firms (except those where ). More enforcement also shifts the zero value FE ZVC PAGE 64 64 condition curve upward, increasing the cutoff productivity level. Increasing enforcement in a traditional sector will therefore have ambiguous effects on the average proportion of child labor, and on the incidence of child labor, Modern industry case Figure 3 3. Increase in enforcement when In the modern industry example, an increase in enforcement, not only increases the zero value cutoff condition, lead ing to an increase in the cutoff productivity level, but it also decreases the proportion of child labor used by all firms. FE ZVC PAGE 65 6 5 The increase in the cutoff productivity level causes the least productive firms to exit which reduces the average proportion of ch ild labor. Both effects lower the demand for child labor i n the steady state equilibrium. Intra industry Trade This section introduces trade in to the basic model. Firms have the option of exporting their good to identical coun tries ( T herefore the total number of countries is equal to ). If a firm exports, it face s an additional fixed cost of production equal to for each country to which it export s and incur s an iceberg per unit trade cost equal to Per period profit from exporting to each country is: ( 3 68) Maximizing per period profit with respect to price yields the profit maximizing price for an exported good: ( 3 69) The revenue from exporting to each country is proportional to the revenue earned from selling domestically : ( 3 70) where is the revenue from selling to t he domestic market and is determined by Equation 3 14 The combined revenue of a firm that exports is: ( 3 71) PAGE 66 66 Similarly, the p rofit from expor ting to each country will also be proportional to domestic profits : ( 3 72) and com bined per period profit is equal to: ( 3 73) An exporting firm will have the following firm value: ( 3 74) As in the closed model, firms will maximize thei r expected value with respect to the proportion of child labor which yields the same equation as in Equation 3 23 Thus, a its child labor decision. Free Entry and Exit Setting firm value equal to zero yields the zero value cutoff for an exporting firm: ( 3 75) The productivity level ensuring that Equation 3 75 holds is The zero value cutoff for a firm that only sells domestically is derived from Equatio n 3 61 : ( 3 76) where the productivity level ensuring that Equation 3 76 holds is Substituting Equation 3 76 into Equation 3 75 yields the following relationship between and : PAGE 67 67 ( 3 77) The probability of successful entry is equal to The probability that a firm has a productivity level that will make it profitable to export is: ( 3 78) The mass of exporting firms is equal to so the total mass of varieties available to consumers in any country, is equal to the number of domestic firms plus the numb er of exporting firms : ( 3 79) The weighted average productivity of firms that export is: ( 3 80) and the weighted average productivity of all firms is: ( 3 8 1) The aggregate variables are the same as those in the closed case, only substituting total average productivity, Average per period profit, revenue, and firm value are: ( 3 82) ( 3 83) PAGE 68 68 ( 3 84) We can compare the firm revenue that meets the dome stic cutoff productivity level with the firm revenue that meets the export cut off productivity level : ( 3 8 5) This expresses the export cutoff productivity level, as a function of the domestic cutoff productivity level, : ( 3 86) Due to the added costs of exporting, the export cutoff productivity parameter will always be greater than the domestic cutoff productivity parameter. Therefore, only the most productive firms will export. The average firm value, Equation 3 84 can be described completely in terms of the domestic cuto ff level. Setting this equal to zero defines the zero value cutoff condition (ZVC): ( 3 87) The a verage productivity of exporting firms, is a function of the export cutoff level, while is itself a function of ( from Equation 3 86 ) The free entry condition (FE) is the same as in the autarky case: ( 3 88) PAGE 69 69 The intersection of the ZVC and FE conditions determine s the average firm value and the cutoff productivity level in the steady state equilibrium. The mass of incumbent firms each period is equal to: ( 3 89) and the incidence of child labor is denoted by: ( 3 90 ) Similar to the autarky case, the incidence of child labor increases only if there is a rise in the average proportion of child labor, which still depend s on the cutoff productivity level, ( with the exception of the benchmark case ) Trade Liberalization Trade liberalization can be shown through an increase in the number of trading partners, ; a decrease in the fixed cost of export ing ; or a reduction in iceberg trade costs, All three methods of showing trade liberalization, although they affect the mass of firms and varieties differently have the same effect on the incidence of child labor in the steady state equilibrium. Trade liberalization has no imp act on the free entry condition, Equation 3 88, but it will shift the zero value condition, Equation 3 87 upwar d, shown in Figure 3 4. As in the Melitz (2003) model, trade liberalizati on will always cause an increase in the domestic cutoff productivity level, forcing the least productive firms to exit and increasing the average firm value, In the benchmark case, an increase in the cutoff productivity level does not affect the child labor decision of firms and therefore PAGE 70 70 does not have any impact on the average proportion of child labor. The increase in the average firm value will decrease the mass of firm s in the steady state equilibrium ; however, from Equation 3 90, trade liberalization will have no effect on the incidence of child labor. Figure 3 4. Effect of trade in the steady state equilibrium The sectoral allocation of adult labor in R&D and production remain s the same since the number of potential entrants, is constant in all cases even though the mass of firms in the steady state equilibrium, falls Since the cu toff productivity level increases with trade liberalization, the probability of successful entry decreases. The price level, which is a weighted average of the prices of producing firms, decreases after trade liberalization since the firms that charge the highest prices are forced to exit. The least productive firms have the highest marginal costs and charge the highest prices due to price being a constant mark up over marginal cost. As in Melitz (2003), a FE ZVC PAGE 71 71 decrease in the price level increases the r eal w age of adult and child labor. Since trade liberalization increases the ex ante firm value of a potential entrant, this raises the demand for adult workers in the R&D sector and leads to an increase in the relative wage. Trade Liberalization in Traditional and Modern Sectors When trade liberalization will affect the average proportion of child labor. Since the mass of potential entrants, remains fixed, the number of adult workers in the R&D sector, an d thus the number of adult workers in production, will also remain unchanged. The incidence of child labor, which is proportional to the amount of adult labor in production, will then depend solely on how trade liberalization a ffects the average proportion of child labor, In the traditional sector case, trade liberalization causes the exit of low productivity firms which rely the least on child labor. It also increase s th e quantity produced by productive firm s Both effects will increase the average proportion of child labor that firms use The decrease in the price index increase s real wage s which in a more general model, would affect the supply of child labor ambiguo usly Th is ambiguity (see Basu and Van 1998) result s from opposing income and substitution effects derived from the parental choice of sending one s child to work. In the modern industry case, trade liberalization reduc es the demand for child labor. Unlike in a traditional industry, the more productive firms use relatively little child labor in production. Trade liberalization, by increasing the cutoff productivity level, forces the least productive firms to exit the industr y. This will decrease the average proportion of child labor and reduce the incidence of child labor. As in the traditional PAGE 72 72 sector case, trade liberalization i ncrease s real wages, whose effects the child labor supply depend on the corresponding substituti on and income effects. Conclusion Although the incidence of child labor has been declining around the world over the last half century (ILO 2006), the percentage of child laborers in many of the poorest countries remain high. The culprit, as many economis ts will agree, is extreme poverty opportunity to educate its children However, it is important to recognize that firms employ ing cheap child labor to earn higher profits also play a large role. While completely eliminating the demand for child labor is not realistic, demand in sectors exposed to trade may be reduced via targeted trade policies that take into account the relationship between child labor and productivity In industries where the productivity gap between adult work ers and child labor decreases as productivity increases, trade liberalization can increase the demand for child labor. Trade sanctions, which increase trade costs and are generally accompanied by negative welfare effects, can lower the cutoff productivity level which can reduce the demand for child labor in the steady state equilibrium. Trade liberalization can be successful in industries where the more productive firms see little use in employing child labor since the gap between adult and child workers is large. A reduction in trade costs in this case will result in an exit of firms whose workforce is largely composed of child ren, which can reduce the incidence of child labor in the steady state equilibrium PAGE 73 73 CHAPTER 4 INCIDENCE OF CHILD LABOR IN A NOR T H SOUTH MODEL OF TRADE Supporters of globalization argue that increased exposure to trade increases incomes of low skilled households, thereby reduc ing the incidence of child labor when insufficient income is the main cause. T rade liberalization opponents in developing countries argue that globalization opens the doors for foreign firms to take advantage of cheap labor, increasing the demand for and incidence of child labor. While household factors such as insufficient income, lack of access to credit mar kets, and effectiveness of schooling have been examined and empirically researched, less work has explained the relationship between trade liberalization and the incidence of child labor. Davis and Voy (2007) and Busse and Braun (2004) are two examples of recent works that empirically examine the relationship between foreign direct investment and the incidence of child labor. Davis and Voy (2007) use openness to trade, defined by a or C ontrolling for a host of country factors they find a significant negative relationship between child labor and globalization ; however, this relationship vanishes once they control for income. This suggests that when globalization is able to increase the income of low skilled households, it can reduce the incidence of child labor. What has not been examined, due to the complexity of gathering sufficient data, is how trade liberalization affects the demand for child labor from domestic and foreign fir ms. North South trade models have been used to explain many facets of trade but have not been used to analyze the trade implications on child labor. These models explain the product cycle of manufactured goods, where they are first innovated and produced in the North, but over time production shifts to the imitating South. As such, PAGE 74 74 the South exogenously absorbs innovation from firms in the North. Reductions in trade costs tend to increase the rate of innovation in the North and increase the total number of varieties. For a summary on the North South trade literature, see Chui et al. (2002). The model in this paper incorporates firm heterogeneity, as in Melitz (2003) and Melitz and Ottaviano (2008) in a standard North South trade model. Firms in the Nor th will differ in the ir marginal cost s The free entry condition in the North will then endogenize the rate of innovation. Southern firm s are assumed to be homogeneous, but their costs will depend on their use of child labor in production. Child labor, while off of increasing the probability of receiving a negative shock. This paper is organized as follows : Section 2 solves for the autarky equilibrium in the North, characterizing the critical cost paramet er necessary for a firm to enter the market. Section 3 expands the model to allow Northern firms to export to the South. Section 4 develops the traditional North South trade model where Southern firms imitate products from the North and can use child lab or in production to reduce their costs. Section 5 shows the comparative statics and describes how changes in the exogenous rate of imitation, population increases in the South, and increases in trade costs and enforcement affect the incidence of child lab or The paper then presents concluding remarks. The Model This model assumes that firm s are heterogeneous in the North while firms in the South that imitate Northern products share a common marginal cost that depend s on the use of child labor in productio n. This allow s for the examination of how trade liberalization affects the demand for child labor in the South. As in Krugman (1979), the PAGE 75 75 rate of imitation is assumed to be exogenous so that the model can be solved explicitly, but simulations that endoge nize this variable are shown to reinforce the results of the model. Consumption Consumer utility will be base d on a quadratic utility model, similar to that found in Melitz and Ottaviano (2008), where utility depend s on the consumption of an agricultural g ood, and differentiated varieties of a manufactured good, where : ( 4 1) A representative consumer maximizes utility subject to a budget constrai nt: ( 4 2) This leads to the following Lagra n gian and its corresponding first order conditions: ( 4 3) ( 4 4) ( 4 5) ( 4 6) where and the price of the agricultural good is the numeraire. This leads to the following inverse demand function for a differentiated variety: when ( 4 7) PAGE 76 76 Aggregati ng over all symmetric consumers leads to the following market demand function for a specific variety: ( 4 8) where is the number of consumed varieties, is the number of consumers, and is the average price, or the price index, equal to: ( 4 9) The maximum price that a firm can charge is the price such that demand is driven to zero, ( 4 10) Production in the North Production of the numeraire good, follows a constant return s to scale production function and differs in the North and South. In the North production of the numeraire good is equal to the amount of adult labor, in that sector : ( 4 11) This leads to a unitary wage in the North, In the South, the nume raire good is produced using only adult labor : ( 4 12) where is assumed to be less than 1. Therefore, the wage of adult labor in the South is equal to and less than the adult wage in the North, The rest of this section will solve for the autarky steady s tate equilibrium in the North. PAGE 77 77 Firms in the differentiated good sector incur a fixed entry cost to conduct research and development Once R&D is conducted, firms discover part of their marginal cost of producing the good, Adult l abor is the only factor used in the production of this manufactured good and is equal to : ( 4 13) wh ere the random cost is found after the R&D process The marginal cost of a firm is The profit of a firm with cost parameter is : ( 4 14) Maximizing Equation 4 14 with respect to quantity yields the profit maxim izing quantity produced by this firm : ( 4 15) Let be the cutoff cost level that corresponds to the maximum possible price that drives the quantity demanded to zero: ( 4 16) This cutoff cost level is a function of the parameters of the model and the average price in the differentiated goods market. Firms with earn pos itive profits and remain in the market while firms with earn negative profits and exit the industry. As the average price, increases, the cutoff cost level, will also incr ease The quantity, price, revenue, and per period profit of a firm with productivity are function s : PAGE 78 78 ( 4 17) ( 4 18) ( 4 19) ( 4 20) ( 4 21) Firms in the North are assumed to face an exogenous probability of death, so that a is equal to: ( 4 22) I n the steady state equilibrium the expected firm value from conducting research and development must be equal to the fixed cost of R&D. This is the fr ee entry condition in the North: ( 4 23) This equation determines the cutoff cost level in the steady state equilibrium, which then determines the price index, from Equat ion 4 16 This can best be illustrated in Figure 4 1 which show s the necessary so that the expected firm value equal s the fixed entry cost: PAGE 79 79 Figure 4 1. Autarky equilibrium If the cutoff cost level is above the probability of entry is high and the ex a nte firm value exceed s the fixed entry cost This induce s firms to enter, lowering the price index and driving out firms with high marginal costs until the cutoff cost leve l converges to If the cutoff cost level is below t he ex ante firm value is not large enough to cover the fixed cost of entry. This reduce s the number of firms willing to enter the market until the c utoff marginal cost rises to To simplify the analysis, a uniform distribution of the cost parameter is assumed. T he cumulative distribution and probability distribution functions are: ( 4 24) ( 4 25) where Solvin g the free entry condition, Equation 4 23 for the cutoff cost level yields: f E Cost parameter E (V) c Expe cted Firm Value, Entry Cost PAGE 80 80 ( 4 26) To ensure an interior solution, it is assumed that the population is large enough so that the following condition holds : ( 4 27) With th e cutoff cost determined by Equation 4 27 the price index and the average marginal cost in the North are equa l to : ( 4 28) ( 4 29) The number of firms in this autarky equilibrium in the North can then be derived from Equation 4 16 : ( 4 30) Note that the derivative of E quation 4 30 with respect to is negative, so that an increase in the cutoff cost variable will decrease the number of firms in the steady state equilibrium. Average per period profit is equal to : ( 4 31) PAGE 81 81 The number of new firms each period has to equal the number of firms exiting in the steady state equilibrium : ( 4 32) Welfare in the North, shown by Equation 4 1 [Do you mean utility? 4 1 is defined as utility.] can be written in terms of indirect utility: ( 4 33) A decrease in the cutoff cost level, reduce s the price level and increase s the number of varieties available to consumers. Both these e ffects mean that per capita welfare rises as falls Exporting Firms in the North This section analyze s the steady state equilibrium when Northern firms have the option to export their goods to the South. It will be assumed that t he demand s for the agricultural and differentiated good s are identical in both the North and South The population in the North is the population in the South is and is the world population. Firms that trade incur an additional iceberg trade cost of The per period profit from exporting to the South for a Northern firm with is: ( 4 34) The c utoff export cost level can be defined as a function of the domestic cutoff cost level : ( 4 35) PAGE 82 82 F irms with a low cost parameter will export to the South and produce for the d omestic market, firms with will produce solely for the domestic market, and f irms with will not produce for either market The firm value of an exporting firm is: ( 4 36) A potential entrant into the market has to take into account the probability that it will have a cost parameter low enough that will allow it to be an exporter The free entry condition will then determine the cutoff cost level: ( 4 37 ) The extreme fre e trade case occurs when and result s in where all Northern fi rms choose to export. The larger the trade cost, the smaller the chance that a firm will have a cost parameter low enough to allow it to export and the lower the per period profits from exporting. An a utarky case occurs when I f no firms in the North have an incentive to export to the South. Figure 4 2 compa res the steady state equilibrium in the autarky case, denoted by E A and the free trade steady state equilibrium when denoted by E T : PAGE 83 83 Figure 4 2. Trade equilibrium As trade costs are reduced, the ex ante firm value from entering the market increases This will decrease the cutoff cost level, while simultaneously increasing the cutoff export cost level, Compared with the autarky case, by reducin g trade raises the welfare of Northern consumers by lowering the average price of differentiated goods and increasing the number of varieties available for purchase. North South Free Trade Equilibrium This secti on examines the equilibrium where Southern firms can imitate Northern products. Southern firms are assumed to be homogeneous and face a probability of death that depend s on their use of child labor in production. T his section assume s no trade costs, or Production in the South Similar to firms in the North the profit of a Southern firm is : f E Cost Parameter E A (V) c *A E T (V) c *T Expected Value, Entry Cost PAGE 84 84 ( 4 38) where represents the proportion of child labor used in production. The derivative of a Note that if a Southern firm chooses not to use any child labor, its marginal cost equal s the adult wage which is Therefore, Southern firms always have a cost advantage over Northern firms even if they choose not to employ children T he profit maximizing quantity and price charged by a Southern firm is a function of the cutoff cost level in the North determine d by Equation 4 16 : ( 4 39) ( 4 40) Since Southern firms imitate products produced by the North, the lowest price that Northern firms can charge is equal to its marginal cost. If the wage g ap between the North and South is small, this will force firms in the South to charge a price slightly lower To assure a high wage gap that will result in Southern firms choosing their monopolist price, the monopoli st price for a Southern firm has to be less than the smallest marginal cost for a Northern firm. Therefore, a sufficient condition to ensure that a high wage gap exists is that This means that the North South wage gap, has to be greater than the cutoff marginal cost level in the North : PAGE 85 85 ( 4 41 ) The larger the combined populations of the North and South, the lower the wage gap has to be so th at Southern firms can charge their monopolist price s The per period profit of a Southern firm is then equal to: ( 4 42 ) Firm Value for Southern Firm Firms in the South maximize their firm value with respect to the optimal quantity of child labor, : ( 4 43 ) where receiving a negative shock that will put it out of business. As proportion of child labor employed increases, the so called probability of death for the firm also increases. The optimal proportion of child labor is found by taking the derivative of Equation 4 42 with respect to and setting it equal to zero: ( 4 44 ) ( 4 45 ) PAGE 86 86 Since while and assuming that the second order derivatives are and ,there exists a unique so that Equation 4 44 holds for a given Note that an increase in increase s the first term in Equation 4 44 which decrease s the proportion of child labor used by all Southern firms, or Free Entry Condition for Northern Firms The free entry condition for Northern firms like in the autarky case, will determine the cutoff cost level: ( 4 46) ( 4 47 ) where Northern firms face an exogenous probability of imitation, in a ddition to the Northern probability of death, With a fixed probability of imitation, the number of Southern firms depend s on the number of Northern firms in the steady state equilibrium. As such, firms in the South act as oligopolists which is why they can charge their monopolist price s Share of Firms The total number of firms (and varieties), is equa l to the total number of firms in the North, plus the total number of firms in the South, Let represent the share of varieties located in the North: PAGE 87 87 ( 4 48 ) T he share of Southern varieties is then : ( 4 49 ) In the steady state equilibrium, the number of Northern firms that are imitated each period must equal the number of new Southern firms. This must also equal the number of Southern firms exit ing each period The number of Northern firms that are imitated each period is equal to: ( 4 5 0 ) while the number of Southern firms that exit each period is equal to: ( 4 5 1 ) In the steady state equilibrium, the number of Northern firms that have their product imitated must equal the number of new Southern entrants, which itself must equal the number of Southern firms that exit each period: ( 4 5 2 ) Therefore, in the steady state equilibrium the share of Northern firms must be: ( 4 5 3 ) This depend s on the endogenous rate of death in the South which comes from the child labor decision of Southern firms Equation 4 44 and the exogenous rate of imitation, PAGE 88 88 The price index depend s on the shares of firms located in the North and South T he price of Northern products comes from Equati on 4 28 and the price of Southern varieties is determined by Equation 4 40 : ( 4 5 4 ) The cutoff cost level, and the share of firms located in the North, determine the price index in the steady state equilibrium. A n increase in will increase the price index, but b y an amount less than the change in : ( 4 5 5 ) Note that with the assumption of a high wage gap between the North and South, the average price charged by firms in the North will always be higher than that charged by South ern firms Therefore, an increase in the share of Northern firms, all else equal, will increase the price index. T he last step is then to calculat e the total number of varieties: ( 4 56) Incidence of Child Labor The quantity produced by a Southern firm is equal to: ( 4 57 ) so the number of children being emp loyed by each Southern firm, is equal to: PAGE 89 89 ( 4 58 ) where is an adult scaling constant, so that one unit of child labor produces the same amount as units of adult labor. is therefore the proportion of output produced using child labor. The total incidence of child labor, is computed by multiplying Equation 4 58 by the total number of Souther n firms, : ( 4 59 ) The demand for child labor with respect to the cutoff cost level then has the following property: ( 4 60 ) The derivative of Equation 4 59 will depend on the si gn of the following equation: ( 4 61 ) Note that wh en all firms are located in the North the sign of Equation 4 61 becomes : ( 4 62 ) When the sign of Equation 4 61 becomes : ( 4 63 ) PAGE 90 90 Since and Equation 4 63 is less than zero as well. Since an increase in increases the price index, an i ncrease in will always mono tonically reduce Equation 4 61 Therefore, an increase in the cutoff marginal cost level will all else equal, reduce the incidence of child labor, or Comparative Statics Th is section examine s how changes in some of the parameter values affect the incidence of child labor. Graphs showing the results of simulations with an endogenous rate of imitation are shown when applicable, but they reinforce the results of the closed m od el. See A ppendix C for more details on the simulation. Increase in Child Labor Enforcement, An increase in child labor enforcement is a policy that increases for all Using a probability of death formula : ( 4 64 ) an increase in child labor enforcement is characterized by an increase in the parameter From Equation 4 44 this decrease s the proportion of child labor that every Southern firm choose s but does not affect the cutoff cost level in the North. Although is not affected, the fall in raises the marginal cost of Southern firms, wh ich increase s the price they charge An increase in enforcement affect s the allocation of firms between the North and South. The total number of firms decrease s but the share of firms located in the North rises PAGE 91 91 Figure 4 3. Increase in enforcement Th e decrease in the number of firms in the South reduces the incidence of child labor A n increase in child labor enforcement raises the average price for the differentiated goods and lowers the number of varieties available in both the North and South, red ucing welfare in both countries. The reduction of welfare in the South, at least in the short run, can partially explain the reluctance of officials in developing countries to clamp down on child labor. One Time Increase in the Population in the South, An increase in the population raises the ex ante value of all firms by increasing the profit earned each period The increased competition for resources decrease s the cutoff cost level in the North. This cause s the high c ost firms to exit, reduce s the price level and increase s the total number of firms in the steady state equilibrium Since the allocation of firms between the North and South remain s unchanged, t he number of Southern firms increase s, which also raises the incidence of child labor The lower price level and the increase in total varieties increase s welfare in both the North and South PAGE 92 92 Figure 4 4. Increase in p opulation Increase in the Rate of Imitation, An increase in the exog enous rate of imitation by Southern firms decrease s the ex ante firm value for Northern firms from Equation 4 47 increasing The increase in the exogenous rate of imit ation also reduces the share of firms located in the North : (4 65) The number of firms in both the North and South decrease s with the increase in the cutoff cost level from Equation 4 56 reducing the total number of firms in the steady state equilibrium : (4 66) The derivative of Equation 4 66 with respect to the exogenous rate of imitation is less than zero, since and From Equation 4 60, the increase in the cutoff co st level reduce s the incidence of child labor due to the decrease in the PAGE 93 93 total number of Southern firms in the steady state equilibrium Social welfare of households in both the North and South falls due to the increase in the p rice index and the lower number of varieties. Trade Costs T his section assume s that all firms face iceberg trade costs, equal to when exporting their product s The per period profit from exporting, expected firm value, and fr ee entry condition for firms in the North are shown in the previous section The exporting profit for a South ern firm is : ( 4 67 ) The profit maximizing quantity, price, and profit for a Southern firm from exporting are: ( 4 68 ) ( 4 69 ) ( 4 70 ) Total profit and expected firm value for a Southern firm are then: ( 4 71) ( 4 72 ) All other equations remain the same as those in the free trade case. Compared with free trade ( ), the addition of trade costs decreases per period profits and the firm value of both Northern and Southern firms. As shown in the previous section the addition of trade costs for North ern firms splits them into those that PAGE 94 94 produce domestically and export and those that produce for the domestic market only The export marginal cost cutoff level for firms in the North is equal to: ( 4 73 ) and the expected firm value for a Northern firm is equal to: ( 4 74 ) Setting Equation 4 74 equal to the fixed cost of entry and solving for determines the cutoff cost level for Northern firms. A n increase in trade costs, increase s the cutoff marginal cost level and decrease s the cutoff export cost level. Trade costs create a price divergence in the North and South. Unlike thei r Northern counterparts, all Southern firms choose to export their good s and pass on their trade costs. The price index in the North is: ( 4 75 ) while the price index in the South is: ( 4 76 ) where is the number of exporting Northern firm s, equal to and represents the share of Northern firms that export relative to the total number of firms, PAGE 95 95 An interesting result of this model is that while a n increase in trade costs raises the price index in the North, the price index in the South also rises but to a much lesser extent due to a shift in consumption to ward domestic goods The increase in trade c osts raises the cutoff cost level and reduces the export cutoff level in the North. It also increases the price charged by Southern firms. Figure 4 5. Price indices and trade costs The total number of firms in the North increase s but the share of tota l firms that exports to the South, decreases. Therefore, the South consume s a greater proportion of goods produced domestically, but the goods they import fro m the North are more costly. PAGE 96 96 Figure 4 6. Child labor and trade cos ts A rise in trade costs not only shift s the production of goods to the South relative to the North, but it also increase s the mass of firms in the South. The quantity produced by each firm also increase s due to the higher cutoff cost level, so the incide nce of child labor rises The numbers of available products in the North and South increases, but higher prices limit any welfare gains in the North. Conclusion This paper examines how trade liberalization affects the incidence of child labor in a North South model of trade. Since the supply of child labor is assumed to be perfectly elastic, the demand for child labor will determine the number of children working in the steady state equilibrium. Firms in the North are assumed to differ in their cost of producing a differentiated good which endogenizes the rate of innovation in the North, whi le the cost of Southern firms depends on the ir use of child labor in production. The rate of innovation in the North along with the exogenous rate of imitation in the South determine s how the share of output is allocated between the North and South PAGE 97 97 A rise in the cost cutoff level, caused by a decrease in the size of the population in either the North or South or by an increase in trade costs, increase s the numbe r of firms located in the South and raises the output produced by each firm. Since the increase in the cost cutoff level does not affect the proportion of child labor that Southern firms employ, the demand for child labor increase s A reduction in trade costs can therefore help lower the incidence of child labor in the steady state equilibrium. An increase in the exogenous rate of imitation by Southern firms can similarly work to decreas e the incidence of child labor by reducing the total number of firms located in the South. PAGE 98 98 APPENDIX A FIRST ORDER CONDITIONS The utility optimization problem of the representative consumer is given by: (A 1) which result s in the following first order conditions: (A 2) (A 3) (A 4) PAGE 99 99 APPENDIX B PROOF OF UNIQUE STEADY STATE EQUILIBRIUM The intersection of the zero value condition and the free entry condition results in a unique equilibrium. From Equati ons 3 40 and 3 42: ZVC: (B 1) FE: (B 2) Setting the two conditions equal yields : (B 3) To prove a unique equilibrium, we need to show that the RHS is mon otonic and always downward sloping so that it intersects the LHS once. The derivative of the RHS with respect to the cutoff productivity level is: (B 4) This equation simplifies to: (B 5) Since this equation is always negative, the RHS in (B3) is always downward sloping. Furthermore, the RHS goes to infinity as the cutoff productivity goes to zero, and since it PAGE 100 100 is always downward sloping and does not converge to a positive number, it must inters ect only once with the LHS of Equation B 3. PAGE 101 101 APPENDIX C SIMULATION WITH ENDOGENOUS RATE OF IMITATION The simulations conducted assume that the rate of imitation is determined endogenously by the free entry conditions in the North and South. It is necessar y to add an exogenous probability of successfully imitating a product, Therefore, the ex ante firm value in the South is equal to: (C 1) The free entry condition in the South will actually determ ine the cutoff cost level in the North: (C 2) The free entry condition in the North will then determine the endogenous cost of imitation: (C 3) The rest of the equations are the same as those in Chapter 4. For the simulations, the following values are given for the exogenous parameters: , and An increase in the cutoff cost level, in the steady state equilibrium, which decreases the demand for child labor, will increase the endogenous rate of imitation, all else equal. PAGE 102 102 LIST OF REFERENCES Antoniades, Alexis. 2008. Working Paper. Baland, Jean Mimeo Baland, Jean Marie, and James Robinson. 200 Journal of Political Economy, 108(4): 662 679. Basu, Kaushik 1999. nce, and Cure, with Remarks on Journal of Economic Literature, 37( 3 ): 1083 1119. Basu Kaush ik, and Pham Hoang Van. 1998. American Economic Review, 88( 3 ): 412 427. Brown, Drusilla K., Alan V. Deardorff, and Robert M. Stern. 2003. International Labor Standards: H isto ry, T heory, and P olicy O ption ed. Kaushik Basu, et al. Oxford: Blackwell Publishing 195 241 Busse, Matthias, and Sebastian Braun. 2004. Journal of Economic Integration 19(4): 804 829. Chui, Michael, Paul Lev ine, S. Mansoob Murshed, and Joseph Pearlman. 2002. Journal of Economics Surveys 16(2): 123 143. Davis, Ronald B., and Annie Voy. 2007. IIIS Discussion Paper, No. 215 Dinop o ulos, Elias, and Bulent Unel. 2009. Working Paper Dinop oulos, Elias, and Laixun Zhao. 2007. Journal of Labor Economics, 25( 3 ): 553 579. Edmon ds, Eric V., and Nina Pavcnik. 2005. Journal of International Economics, 65: 401 419. Flam, Harry, and Elhanan Helpman. 1987. American Economic Review 77( 5): 810 822. Mimeo. u International Labour Review 134(2): 187 203. Gupta, Manash R. 2000 Review of Development Economics, 4( 2 ): 219 228. PAGE 103 103 Helpman, Elhanan. 2006. Journal of Economi c Literature 44: 589 630. Helpman, Elhanan, Marc J. Melitz, and Stephen R. Yeaple. 2004. The American Economic Review 94( 1 ): 300 316. Jaf arey, Saqib, and Sajal Lahiri. 2001. Theory, Policy an World Economics 2( 1 ): 69 93 Jaf arey, Saqib, and Sajal Lahiri. 2002. The Journal of Development Economics, 68( 1 ): 137 156. International Labor Organization 2006a. The End of Child Labour: Within Reach. Geneva: ILO. International Labor Organization 2006b. Global Child Labour Trends: 2000 2004. Geneva: ILO. International Labo r Organization. 2007. Child Labour Wages and Productivity: Results from Demand Side Surveys Genev a: ILO. Kis Katos, Krisztina. 2007. The Journal of International Trade and Economic Development, 16( 1 ): 71 92. Krueger, Alan. 1996. Annual World Bank Conference on De velopment Economics eds. Michael Bruno and Boris Pleskovic. Washington: The World Bank, 281 302. Kruger, Diana I. 2007. Journal of Economic Development 82( 2 ): 448 463. Krugma n, Pa ul R. 1979. Journal of Political Economy 87(2): 256 266. World Bank D evelopment Research Group Policy Research Working Paper No. 1817. Mimeo Melitz, Marc J. 2003. Industry Reallocations and Aggregate Industry Produc Econometrica 71( 6 ): 1695 1725. Melitz, Marc J. and Giancarlo I. P. Ottaviano. 2008. Review of Economic Studies 75: 295 316. PAGE 104 104 a nd Journal of Population Economics 10(4): 387 405. Journal of Population Economics 10(4): 377 386. alysis of Child Labor in Peru and Pakistan: A Comparative Journal of Population Economics 13(1): 3 19. Ranjan, Priya. 2001. Journal of Development Economics, 64: 81 102. Ravalli on, Martin, and Quentin Wodon. 2000. The Economic Journal 110 : C158 C175. Rogers, Carol A nn, and Kenneth A. Swinnerton. 2001. Child Labor Unpublished Manuscript Schultz, Paul T. 2004. Journal of Developmental Economics 74: 199 250. Stiglitz, Joseph E. 1976. sis, Surplus Labor, and the Oxford Economic Papers 28( 2 ): 185 207. The Journal of Political Economy 112(4): 939 94 6. Yeapl e, Stephen R. 2005. Journal of International Economics 65: 1 20. PAGE 105 105 BIOGRAPHICAL SKETCH Kristian Est vez was born in Miami, Florida to a Cuban father and Ecuadoran mother. H e grew up in Little Havana and graduated from G. Holmes Braddock Senior High School in 2001. He received his Bachelor of Science degree in e conomics from the University of Florida in 2005 and earned his Ph.D. in e conomics in 2010 His fields of specializ ation are international trade, public economics, and game t heory, and his research focuses on trade policies income inequality, and other issues affecting developing countries 