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Household and economy: Welfare economics of endogenous fertility
Book
reviews
209
Mark Nerlove, Assaf Razin and Efraim Sadka, Household and Economy: Welfare Economics of Endogenous Fertility (Academic Press, New York, 1987) pp. xii+ 155. This book provides a clear and uniform presentation of standard welfare economics, externalities and consumer theory; optimal population size; potential and actual market failures; and aspects of income distribution when fertility is a decision that is determined by utility maximizing parents. The authors adopt the view that the parents’ utility depends on both the number and welfare of their children. As such, current decisions are made when the future is optimally perceived by the parents. The focus of the book is on the implications of the above approach to endogenous fertility and population size for the optimal allocation of resources under different economic environments. The introduction immediately leads the reader to consider the most controversial and philosophical issue invoked by endogenous population the welfare criteria for the optimal size of population. Pareto optimality takes population size as given and therefore cannot be directly applied to analyze the question of optimal population size. A direct simple minded attempt to extend the Paretian criterion to varying population size fails, because an increase in the population by one member certainly increases the welfare of this individual, even if it decreases the welfare of all other existing members of society. Therefore, the two allocations are Pareto noncomparable and the criterion for optimal population (allocation) should be based on a more restrictive concept of optimality. The introduction presents four alternative concepts of optimality. The first is the classical Benthamite function in which the sum the utilities of all individuals in the economy is maximized. The second welfare function, due to Mill, is the maximum of the average utility over all members of the economy. The third utilitarian approach has been suggested more recently by Rawls. This criterion amounts to maximizing the welfare of the worst-off individual. The authors suggest an additional criterion which compares allocations according to Pareto efficiency restricted to the welfare of the current generation. Chapter 2 of the book presents a clear and elegant exposition of the concept of Pareto efficiency in an economy with a tinite number of individuals and a finite number of goods and services. The standard inefficiencies due to externalities in consumption and the existence of public goods, as well as the corrective pricing policies that support optimal allocation, are discussed in chapter 3. Chapter 4 briefly reviews the standard consumer theory. As such, the first part of the book reproduces microeconomic theory, using an extremely clear exposition, in a manner that is relevant for the following chapters. Chapter 5 expands the analysis by introducing both the number and
210
Book reviews
quality of children as arguments of individuals’ preferences. Following Becker and Lewis, quality is measured as the value of the expenditures per child and utility is obtained from the average quality per child. It is shown what types of preferences yield positive or negative income effects on the quality and/or the quantity of children. One of the problems that arises here and persists throughout the book is that the budget set is not convex; total expenditures on children are the product of two choice variables in the utility function. Therefore, the parents’ choice problem is not standard such that corner solutions (e.g., zero consumption and/or zero number of children) are more likely to exist and the comparative statics analysis is more complicated. Starting in chapter 6 the authors modify the utility of the parents by replacing the above definition of quality of children with the total value of the children’s own utility from their consumption; that is, the product of number of children and utility of each child. The only cost of fertility for the parent is the real bequest which is assumed to be equal across identical children. For simplicity it is assumed that parents live one period. However, parents correctly forecast their children’s future decisions, so that the parents’ bequest is evaluated given the optimal choices to be made in the future. In this way the current generation of parents internalizes all the consumption decisions in the future as long as the optimal bequest is positive. The laissezfaire allocation (LFA) is defined here as the interior solution for the above economy. Then, the allocations associated with the interior solutions of the social welfare criteria of Bentham (BOA) and Mill (MOA) are described. The comparison among these allocations implies that in the Benthamite allocation fertility is larger than the Millian allocation. However, the LFA of fertility may be larger or smaller than the fertility allocations in the Benthamite and the Millian solutions. Direct and indirect taxes and subsidies are considered in order to modify the LFA to that of the BOA and the MOA. The main finding is that it is necessary to use interest rate subsidies and child allowances (positive or negative) so that the LFA will obtain the optimal allocation. The economy with public goods and a fixed amount of land (Malthusian) is considered in chapter 7. It is shown that the LFA is optimal from the point of view of the initial generation. Hence, the inefficiency attributed to the presence of public goods, that is considered in chapter 3, disappears because public goods do not imply failure in allocation of fertility in a model where the current generation allocates resources as if it is a social planner. At this point the focus of the book is shifted to Samuelson’s overlapping generations model (OLG) where fertility is exogenous. The main result here is that the inclusion of the utility of children in parents’ utility implies that the competitive allocation is Pareto efficient. This result follows from the fact that the initial generation allocates resources as a planner would over the infinite-horizon economy. This is possible here due to the preference specification and because, in the competitive economy, bequests are not
Book reviews
211
constrained to be positive. The same is true in the appendix which extends the results to an economy with endogenous fertility, public goods and a fixed factor of production, land. As examples of ‘real market failures’ the authors consider two cases where bequests are not fully internalized by the initial parents. The first case is when marriage occurs across two families and each parent takes the bequest of the other family parametrically (Nash). Therefore, the effect of the bequest that is given by one family to the married couple is not internalized by the other family, Then, the bequests affect allocations as public goods do in chapter 3. The second example is a model of investment in children that may turn out to differ from each other in their future earning ability. As it turns out it is possible to get examples in which the optimal bequest is negative for the able child and positive for the less able child. It is argued that there is a market failure in a competitive system in which parents cannot impose debt on one child (negative bequest), while the other child inherits a positive bequest. The ‘old age security hypothesis’ is the view that children are a substitute for capital in the sense that having more children when parents are young increases the parents’ income at old age. The question is whether the existence of capital markets would decrease the quantity of children. The answer is negative. The reason is that capital markets would most likely increase the present value of income thus increasing the demand for children as well as the demand for second-period consumption. The last chapter considers the effect of unequal income distribution among families on the optimality of the ailocation. Here the authors choose the max-min social welfare function (Rawls) and show that child allowances are required in order to implement the optimal allocation as a competitive equilibrium. The epilog to the book contains several suggestions for extending the above model in order to analyze possible market failures and corrective policies. The book presents a general equilibrium demographic model and public finance analysis in an extremely clear and elegant style. As such, I strongly recommend it as an additional text for a graduate course on development, growth and demographic theory. The issue of the optimal allocation of resources when fertility and population growth are endogenous is central to the understanding of economic development. An important contribution of the book for the analysis of population issues is the introduction of the concept of optimality of the LFA in chapters 6 and 7. This concept is based on the assumed interior solution for the optimization problem of the initial generation. While the authors are aware of the fact that the non-convexity of the budget constraint implies that a corner solution is possible for a standard utility function, they do not investigate the conditions on preferences that guarantee the existence of such a solution. In the example of the LFA (p. 69)
212
Book reviews
the optimal number of children is positive but their consumption is zero. It seems that one would like rather to find conditions on preferences that exclude this type of optimal allocation. We could learn more if we knew the type of preferences that yield positive bequests and a positive number of children for each date. This is essential for the optimality of the LFA and for using the model as a positive theory of population growth. An important extension would be to characterize the dynamic allocation of the laissez-faire infinite horizon economy. To do that one would have to find restrictions on preferences that yield interior solutions. Furthermore, the condition for the non-negativitiy of bequests in an economy with heterogeneous population is important for optimality considerations as well as for analyzing the effectiveness of government debt policy [e.g., Abel (1987)]. The arguments that the authors give to support their unconstrained bequest (p. 92) are not convincing and require some additional analyses. In fact, chapter 8 imposes the restriction that does not allow parents to leave negative bequests (debt) to one child and positive bequests to another child of the same generation, thus implying a ‘real’ market failure. On the other hand, the authors argue that it is possible that one generation gets a positive bequest and another generation inherits debt. I am not convinced that these are reasonable assumptions for the same structure of the economy. One way to proceed in analyzing the dynamic model is to use a more restrictive form of endogenous fertility. For example, we may assume that only the number of children is an argument in parents’ preferences and that the costs of raising children is a given convex function of their number. This type of model together with land as a productive input, does not violate the optimality of the LFA in an OLG economy (the Pareto effecient result in chapter 7, p. 91, holds for this economy). Furthermore, this model has a standard budget set and the analysis proceeds in the same manner as in standard OLG models. In particular, the characterization of the dynamic allocation under different market structures is more manageable [see, for example, Eckstein and Wolpin (1985)]. In this type of model the current generation would not internalize the effect of public goods that are provided to the future generations. However, there is no reason to expect that in a Malthusian economy the LFA would be non-optimal. On the other hand, if one extends the endogenous fertility model of this book to a general dynastic economy a la Bernheim and Bagwel (1984), then the market failures suggested in chapter 8 may not be ‘real’ any more. The reason is that for such a dynastic economy one would expect the initial generation of parents to internalize the future decisions of all future families, including possible interaction among families. Hence, the degree of altruism that is assumed in the model has important implications for the optimality of the LFA. The search for the ‘most likely’ model is usually done by looking at the positive implications of alternative model specifications and comparing
Book reviews
213
them with actual or experimental data. Therefore, the most important extension of this book would be in characterizing the dynamic allocation under different specifications of preferences and technology. References Abel, Andrew B., 1977, Operative gift and bequest motives, American Economic Review 77, 1037-1047. Bernheim, B. Douglas and Kyle Bagwel, 1984, Is everything neutral? The implications of intergenerational altruism in an overlapping generations model with marriage, Mimeo. (Standford University, Stanford, CA). Eckstein, Zvi and I. Kenneth Wolpin, 1985, Endogenous fertility and optimal population size, Journal of Public Economics 27.93-106.
Zvi Eckstein Tel Aviv University, Tel Aviv Boston University, Boston, MA John F. Due, Indirect Taxation in Developing Economies, Revised Edition (The Johns Hopkins University Press, Baltimore, MD, 1988) pp. x +246, $33.00. The shares of public sector expenditure and revenues in GNP have steadily increased in developing countries in the last 25 years. While this trend was regarded as only natural in the Keynesian-influenced growth strategies of the 60s and 70s it is now the subject of public and academic discussion. Since the beginning of the international debt crisis, the World Bank and the IMF have attached fairly strict requirements for fiscal reform to new loans. As a consequence, the public sector and especially taxation have become the subject of more extensive research, often initiated by the World Bank. This second, completely revised edition of Due’s Indirect Taxation in Developing Economies is one of numerous recent studies in this field. The structure of the book is straightforward. The author begins with a brief general assessment of the role of indirect taxation. The regression results relating per capita GNP and the relative reliance on indirect taxes, which generally show an inverse correlation of the two variables, are not surprising. In the poorest countries, such taxes account for up to 60 percent of total tax revenues. Due extends the analysis and shows that this inverse relationship is particularly marked for import duties. Traditionally, this phenomenon is explained by administrative ease of collection. Chapters 3 and 4 deal in some detail with small-revenue indirect taxes, such as all sorts of excises and customs duties. It may be surprising to find a discussion of the latter in a book on taxation, since tariffs are usually dealt with in the context of international trade. But the author makes a good case
reviews
209
Mark Nerlove, Assaf Razin and Efraim Sadka, Household and Economy: Welfare Economics of Endogenous Fertility (Academic Press, New York, 1987) pp. xii+ 155. This book provides a clear and uniform presentation of standard welfare economics, externalities and consumer theory; optimal population size; potential and actual market failures; and aspects of income distribution when fertility is a decision that is determined by utility maximizing parents. The authors adopt the view that the parents’ utility depends on both the number and welfare of their children. As such, current decisions are made when the future is optimally perceived by the parents. The focus of the book is on the implications of the above approach to endogenous fertility and population size for the optimal allocation of resources under different economic environments. The introduction immediately leads the reader to consider the most controversial and philosophical issue invoked by endogenous population the welfare criteria for the optimal size of population. Pareto optimality takes population size as given and therefore cannot be directly applied to analyze the question of optimal population size. A direct simple minded attempt to extend the Paretian criterion to varying population size fails, because an increase in the population by one member certainly increases the welfare of this individual, even if it decreases the welfare of all other existing members of society. Therefore, the two allocations are Pareto noncomparable and the criterion for optimal population (allocation) should be based on a more restrictive concept of optimality. The introduction presents four alternative concepts of optimality. The first is the classical Benthamite function in which the sum the utilities of all individuals in the economy is maximized. The second welfare function, due to Mill, is the maximum of the average utility over all members of the economy. The third utilitarian approach has been suggested more recently by Rawls. This criterion amounts to maximizing the welfare of the worst-off individual. The authors suggest an additional criterion which compares allocations according to Pareto efficiency restricted to the welfare of the current generation. Chapter 2 of the book presents a clear and elegant exposition of the concept of Pareto efficiency in an economy with a tinite number of individuals and a finite number of goods and services. The standard inefficiencies due to externalities in consumption and the existence of public goods, as well as the corrective pricing policies that support optimal allocation, are discussed in chapter 3. Chapter 4 briefly reviews the standard consumer theory. As such, the first part of the book reproduces microeconomic theory, using an extremely clear exposition, in a manner that is relevant for the following chapters. Chapter 5 expands the analysis by introducing both the number and
210
Book reviews
quality of children as arguments of individuals’ preferences. Following Becker and Lewis, quality is measured as the value of the expenditures per child and utility is obtained from the average quality per child. It is shown what types of preferences yield positive or negative income effects on the quality and/or the quantity of children. One of the problems that arises here and persists throughout the book is that the budget set is not convex; total expenditures on children are the product of two choice variables in the utility function. Therefore, the parents’ choice problem is not standard such that corner solutions (e.g., zero consumption and/or zero number of children) are more likely to exist and the comparative statics analysis is more complicated. Starting in chapter 6 the authors modify the utility of the parents by replacing the above definition of quality of children with the total value of the children’s own utility from their consumption; that is, the product of number of children and utility of each child. The only cost of fertility for the parent is the real bequest which is assumed to be equal across identical children. For simplicity it is assumed that parents live one period. However, parents correctly forecast their children’s future decisions, so that the parents’ bequest is evaluated given the optimal choices to be made in the future. In this way the current generation of parents internalizes all the consumption decisions in the future as long as the optimal bequest is positive. The laissezfaire allocation (LFA) is defined here as the interior solution for the above economy. Then, the allocations associated with the interior solutions of the social welfare criteria of Bentham (BOA) and Mill (MOA) are described. The comparison among these allocations implies that in the Benthamite allocation fertility is larger than the Millian allocation. However, the LFA of fertility may be larger or smaller than the fertility allocations in the Benthamite and the Millian solutions. Direct and indirect taxes and subsidies are considered in order to modify the LFA to that of the BOA and the MOA. The main finding is that it is necessary to use interest rate subsidies and child allowances (positive or negative) so that the LFA will obtain the optimal allocation. The economy with public goods and a fixed amount of land (Malthusian) is considered in chapter 7. It is shown that the LFA is optimal from the point of view of the initial generation. Hence, the inefficiency attributed to the presence of public goods, that is considered in chapter 3, disappears because public goods do not imply failure in allocation of fertility in a model where the current generation allocates resources as if it is a social planner. At this point the focus of the book is shifted to Samuelson’s overlapping generations model (OLG) where fertility is exogenous. The main result here is that the inclusion of the utility of children in parents’ utility implies that the competitive allocation is Pareto efficient. This result follows from the fact that the initial generation allocates resources as a planner would over the infinite-horizon economy. This is possible here due to the preference specification and because, in the competitive economy, bequests are not
Book reviews
211
constrained to be positive. The same is true in the appendix which extends the results to an economy with endogenous fertility, public goods and a fixed factor of production, land. As examples of ‘real market failures’ the authors consider two cases where bequests are not fully internalized by the initial parents. The first case is when marriage occurs across two families and each parent takes the bequest of the other family parametrically (Nash). Therefore, the effect of the bequest that is given by one family to the married couple is not internalized by the other family, Then, the bequests affect allocations as public goods do in chapter 3. The second example is a model of investment in children that may turn out to differ from each other in their future earning ability. As it turns out it is possible to get examples in which the optimal bequest is negative for the able child and positive for the less able child. It is argued that there is a market failure in a competitive system in which parents cannot impose debt on one child (negative bequest), while the other child inherits a positive bequest. The ‘old age security hypothesis’ is the view that children are a substitute for capital in the sense that having more children when parents are young increases the parents’ income at old age. The question is whether the existence of capital markets would decrease the quantity of children. The answer is negative. The reason is that capital markets would most likely increase the present value of income thus increasing the demand for children as well as the demand for second-period consumption. The last chapter considers the effect of unequal income distribution among families on the optimality of the ailocation. Here the authors choose the max-min social welfare function (Rawls) and show that child allowances are required in order to implement the optimal allocation as a competitive equilibrium. The epilog to the book contains several suggestions for extending the above model in order to analyze possible market failures and corrective policies. The book presents a general equilibrium demographic model and public finance analysis in an extremely clear and elegant style. As such, I strongly recommend it as an additional text for a graduate course on development, growth and demographic theory. The issue of the optimal allocation of resources when fertility and population growth are endogenous is central to the understanding of economic development. An important contribution of the book for the analysis of population issues is the introduction of the concept of optimality of the LFA in chapters 6 and 7. This concept is based on the assumed interior solution for the optimization problem of the initial generation. While the authors are aware of the fact that the non-convexity of the budget constraint implies that a corner solution is possible for a standard utility function, they do not investigate the conditions on preferences that guarantee the existence of such a solution. In the example of the LFA (p. 69)
212
Book reviews
the optimal number of children is positive but their consumption is zero. It seems that one would like rather to find conditions on preferences that exclude this type of optimal allocation. We could learn more if we knew the type of preferences that yield positive bequests and a positive number of children for each date. This is essential for the optimality of the LFA and for using the model as a positive theory of population growth. An important extension would be to characterize the dynamic allocation of the laissez-faire infinite horizon economy. To do that one would have to find restrictions on preferences that yield interior solutions. Furthermore, the condition for the non-negativitiy of bequests in an economy with heterogeneous population is important for optimality considerations as well as for analyzing the effectiveness of government debt policy [e.g., Abel (1987)]. The arguments that the authors give to support their unconstrained bequest (p. 92) are not convincing and require some additional analyses. In fact, chapter 8 imposes the restriction that does not allow parents to leave negative bequests (debt) to one child and positive bequests to another child of the same generation, thus implying a ‘real’ market failure. On the other hand, the authors argue that it is possible that one generation gets a positive bequest and another generation inherits debt. I am not convinced that these are reasonable assumptions for the same structure of the economy. One way to proceed in analyzing the dynamic model is to use a more restrictive form of endogenous fertility. For example, we may assume that only the number of children is an argument in parents’ preferences and that the costs of raising children is a given convex function of their number. This type of model together with land as a productive input, does not violate the optimality of the LFA in an OLG economy (the Pareto effecient result in chapter 7, p. 91, holds for this economy). Furthermore, this model has a standard budget set and the analysis proceeds in the same manner as in standard OLG models. In particular, the characterization of the dynamic allocation under different market structures is more manageable [see, for example, Eckstein and Wolpin (1985)]. In this type of model the current generation would not internalize the effect of public goods that are provided to the future generations. However, there is no reason to expect that in a Malthusian economy the LFA would be non-optimal. On the other hand, if one extends the endogenous fertility model of this book to a general dynastic economy a la Bernheim and Bagwel (1984), then the market failures suggested in chapter 8 may not be ‘real’ any more. The reason is that for such a dynastic economy one would expect the initial generation of parents to internalize the future decisions of all future families, including possible interaction among families. Hence, the degree of altruism that is assumed in the model has important implications for the optimality of the LFA. The search for the ‘most likely’ model is usually done by looking at the positive implications of alternative model specifications and comparing
Book reviews
213
them with actual or experimental data. Therefore, the most important extension of this book would be in characterizing the dynamic allocation under different specifications of preferences and technology. References Abel, Andrew B., 1977, Operative gift and bequest motives, American Economic Review 77, 1037-1047. Bernheim, B. Douglas and Kyle Bagwel, 1984, Is everything neutral? The implications of intergenerational altruism in an overlapping generations model with marriage, Mimeo. (Standford University, Stanford, CA). Eckstein, Zvi and I. Kenneth Wolpin, 1985, Endogenous fertility and optimal population size, Journal of Public Economics 27.93-106.
Zvi Eckstein Tel Aviv University, Tel Aviv Boston University, Boston, MA John F. Due, Indirect Taxation in Developing Economies, Revised Edition (The Johns Hopkins University Press, Baltimore, MD, 1988) pp. x +246, $33.00. The shares of public sector expenditure and revenues in GNP have steadily increased in developing countries in the last 25 years. While this trend was regarded as only natural in the Keynesian-influenced growth strategies of the 60s and 70s it is now the subject of public and academic discussion. Since the beginning of the international debt crisis, the World Bank and the IMF have attached fairly strict requirements for fiscal reform to new loans. As a consequence, the public sector and especially taxation have become the subject of more extensive research, often initiated by the World Bank. This second, completely revised edition of Due’s Indirect Taxation in Developing Economies is one of numerous recent studies in this field. The structure of the book is straightforward. The author begins with a brief general assessment of the role of indirect taxation. The regression results relating per capita GNP and the relative reliance on indirect taxes, which generally show an inverse correlation of the two variables, are not surprising. In the poorest countries, such taxes account for up to 60 percent of total tax revenues. Due extends the analysis and shows that this inverse relationship is particularly marked for import duties. Traditionally, this phenomenon is explained by administrative ease of collection. Chapters 3 and 4 deal in some detail with small-revenue indirect taxes, such as all sorts of excises and customs duties. It may be surprising to find a discussion of the latter in a book on taxation, since tariffs are usually dealt with in the context of international trade. But the author makes a good case