# Parental Priorities and Economic Inequality.

Review by Casey B. Mulligan. Chicago: University of Chicago Press,
1998. Pp. xvi, 377 $24.95.

Outside of economic history, it is rare for a recent Ph.D. in economics to publish a dissertation as a book and rarer still for the publisher to be one of the premier academic presses in economics. That said, Casey Mulligan's Parental Priorities and Economic Inequality compels attention because of the importance of the subject matter - the intergenerational transmission of inequality - and thoroughness of the analysis.

Parental Priorities is divided into an Introduction, Conclusion, and 12 substantive chapters arranged in 4 parts. The Introduction (Chapter 1) reviews the subject matter of the following chapters.

Chapter 2 begins the exposition with a simple two-period consumption-savings model borrowed from consumer theory. Households consist of a single parent and child. Utility is defined over the parent's current consumption and the child's future consumption. Thus, preferences are U([C.sub.p], [C.sub.c]), where p = parent and c = child and [p.sub.c] is 1/(1 +r). Because a period here is really a lifetime, r is defined across generations; hence, small, permanent changes in r can have a huge effect on p. Three characteristics of parental preferences are examined: the degree of altruism, moderation, and homotheticity. The indifference curves of a more altruistic parent are shifted toward the axis measuring the consumption of the child relative to those of a less altruistic parent. By moderation, Mulligan means the extent of substitutability between parental and child consumption. Leontief preferences, used extensively later in the book, imply maximum moderation (zero substitutability). Homotheticity means that, for any given value of r, [C.sub.c]/[C.sub.p] is independent of wealth, so that there is no regression to the mean in consumption across generations.

Chapter 3 reviews two previous models of intergenerational transmission, the permanent income (PI) model made famous by Robert Barro and the imperfect capital markets model. The key idea of the PI model is that income is fungible across generations, so that attempts to redistribute income by the government (such as social security) can be undone by families. In the first version of the model, earnings are taken as given, but Mulligan shows that basic predictions survive endogenous earnings. Since the permanent income model is focused on opportunities, there is no reason to make assumptions about preferences. If preferences are homothetic, consumption will not regress to the mean across generations, even if earnings does.

Unlike the PI model, the imperfect capital markets (ICC) model assumes that parents cannot incur debt that will be passed onto their offspring. At low levels of parental income, it may not be possible for parents to optimally invest in their children's human capital (optimal levels are defined by the PI model). Thus, even if preferences are homothetic, below the critical income level, the expansion path follows the earnings function; above the critical level, the expansion path is a straight line. Mulligan argues, however, that unique implications of the ICC model are very sensitive to assumptions, and hence the model is not very useful.

Chapter 4, the key analytical chapter, introduces the core idea of endogenous altruism. While the discussion in the text is clear (with many pretty diagrams), most economists, I think, will fast forward to the mathematical appendix. Parental utility is Leontief. Income is the present discounted value of parental and child earnings. Income is allocated to consumption plus child-oriented resources q, which, in turn, increases the amount of altruism (a) and, therefore, the optimal ratio of [C.sub.c]/[C.sub.p] according to an assumed function [Phi](a). Altruism can also be accumulated if parents spend time with their children. Mulligan makes several assumptions (such as diminishing returns to accumulating altruism) that ensure an interior solution.

Next, Mulligan addresses comparative statics, deriving a total resource effect and a substitution effect. The total resource effect refers to the impact of exogenous increases in parental income on altruism. Mulligan's assumptions ensure that altruism is a normal good, so rising income promotes altruism. However, rising income might occur because the value of parental time has gone up, which raises the price of accumulating altruism. Hence, there is no necessary reason for economic growth to alter the average degree of altruism the total resource effect of growth is (approximately) canceled out by the substitution effect. Mulligan also examines how interest rates affect altruism. An increase in the interest rate lowers the price of [C.sub.c] thereby increasing altruism (because q and C,. are complements).

The Mulligan (M) model has strong implications for intergenerational mobility. The basic prediction is regression towards the mean in consumption across generations. Suppose a parent has a low wage, perhaps because of discrimination or because he is an immigrant. This lowers the value of parental time, thus reducing the cost of accumulating altruism. Altruism goes up, the parent sacrifices for the sake of the child, and [C.sub.c]/[C.sub.p] is increased. Conversely, suppose that the parental wage is high; this will reduce altruism, and [C.sub.c]/[C.sub.p] goes down.

By this point, the text has become rather intricate, but there is a very useful table (Table 4.1) that summarizes the predications of the three models. By carefully reviewing this table, the reader can test his/her understanding and reread the text if necessary (as I did a few times). The chapter concludes with an extended comparison of the M model with a model of endogenous fertility due to Robert Barro and Gary Becker (BB). Mulligan argues that the BB model is not useful in a world where couples typically have one child. Chapter 5 considers how taxes might affect intergenerational altruism, concluding that the estate tax cannot have had much effect in the U.S. because so few people pay it.

Part Two is the empirical section of the book. Chapter 6 starts out with a simple regression

ln [y.sub.p] = [Alpha] + [Beta] ln [y.sub.c[ + [Epsilon].

Mulligan is interested in [Beta]. If it is less than one, we have regression to the mean across generations, a necessary, but not sufficient, condition for inequality (measured by the variance of In y) to decline over time. The chapter also reminds readers that inequality between groups might fall but overall inequality rises and that measurement error may cause an overstatement of the degree of regression to the mean. Chapter 6 also contains a review of the literature on the history of American inequality, relying heavily on the work of such scholars as Jeffrey Williamson, Peter Linden, James Smith, and Finis Welch, Evidence on cross-state, cross-region (in the U.S.), and cross-country inequality is also reviewed.

Chapter 7 explores the panel study of income dynamics (PSID). Mulligan constructs a sample with data on parents from 1967 to 1971 and children from the mid-1980s. Consumption expenditures are proxied by spending on food, housing, and property taxes. Ordinary least squares (OLS) estimates of [Beta] are similar for income, consumption, and wealth but are lower for earnings. Instrumental variables estimates, intended to correct for measurement error, show less regression to the mean than the OLS estimates. The chapter also reviews a variety of other studies, looking at schooling, occupation, and wealth mobility. On the basis of these studies, Mulligan concludes that intergenerational mobility within groups is about the same as across groups.

Chapter 8 contains tests of the ICC model using the PSID. The basic idea is that regression to the mean differs whether or not parents make financial transfers to children. Mulligan divides his sample into two groups: children who expect (in their 20s) to get an inheritance of at least $25,000 and those who do not. He finds very similar regression to the mean behavior for earnings and consumption regardless of expectations about inheritance, inconsistent with the ICC model. He does find that schooling is more dependent on parental income in families not expecting to make inheritances, but this does not affect the degree of regression to the mean in earnings. Consequently, Mulligan infers that the rich derive consumption value from education (such as from expensive private schools).

Part Three, composed of Chapters 9 and 10, is short. Chapter 9 considers the relationship between the Mulligan model and sociobiological perspectives in which genes are selected for fitness. Mulligan sketches an argument by which altruism is consistent with evolutionary reasoning. Chapter 10 examines what Adam Smith and John Rae thought about altruism and argues that his approach was anticipated by these authors.

The final three chapters (Part Four) explore extensions to the M model. Chapter 11 extends the endogenous altruism model to multiple offspring. Mulligan shows that it is possible to get unequal treatment within the family, even if preferences are equal across kids; that parents may not share unexpected increases in income with their children; and, perhaps most interestingly, that a noncustodial father might show more concern for children of a current marriage rather than a former. Chapter 12 extends the model to giving beyond the family, illuminating a variety of strategies by which charities influence altruistic behavior. Chapter 13 concerns the principal agent problem, arguing that principals can invest resources to instill loyalty in agents, which alters the optimal commission rate (makes it lower) in riskier environments. Chapter 14 ably sums up.

In a book of such complexity and length about a central topic of economics, there are bound to be points of strong disagreement and criticism. In terms of style, the book reads like a dissertation. Some material - for example, the discussion of the Becker-Barro model - reads as if it were included originally in order to satisfy advisors. Certain chapters, notably those in Pan Three (as well as Chapter 13), are not well integrated into the text and perhaps could have been dispensed with in the interest of producing a tighter volume. In the Introduction, Mulligan expresses the hope that the book will achieve a wide readership outside of economics, and he claims to have tailored the style (heavy on graphs, light on math) to maximize his audience. Hope springs eternal, but I am unconvinced. To truly understand much (if not most) of the text (and, more importantly, to appreciate it), one needs to be a professional economist (or well on one's way to becoming one). And professionals are apt to become weary of those portions of the text that introduce elementary concepts (such as indifference curves).

Some readers will be unimpressed by the model. At a formal level, there is no technical advance. Child-oriented resources enter the utility function in a particular way (by influencing the marginal rate of substitution between [C.sub.c] and [C.sub.p]), but there is nothing in the ordinary theory of consumer behavior - certainly as amended by standard household production models - that rules out such a formulation. Mindful of this point, Mulligan interprets his model as a theory of endogenous taste formation, in the manner of rational addiction models. In an attempt to deflect criticism, Chapter 4 presents an example of an M-type model involving ski equipment and ski trips. Imagine, dear reader, that you, a nonskier, buy expensive ski equipment and subsequently go skiing frequently. When friends query you about your new-found hobby, you reply "I want to get my money's worth" (p. 90). Mulligan's theory presumes that ski trips and ski equipment are complements, so that your willingness to pay for ski trips has gone up (and you knew it would, in advance). But "getting your money's worth" is an odd rationale because the skis are a sunk cost at that point. There can be many (fungible) reasons why you choose to go skiing more frequently, none of which has to do with the possible effects of owning a durable good (the skis) on tastes.

Whether one accepts the M model or not, I think, may have a lot to do with one's own preferences about how to model preferences. In Mulligan's world, the ICC and PI models are about budget constraints so that, in the absence of any evidence to the contrary, preferences should he assumed homothetic and exogenous. But preferences might be nonhomothetic and exogenous. To really know whether endogenous altruism has value as an analytical concept, we need an experiment that allows altruism to accumulate (with no depreciation). Suppose, for example, that the parental wage were to rise over some period and then decline to its original value. In a (suitably dynamic) M model, altruism would change and, if altruism were putty-clay, would change permanently. In a model with nonhomothetic preferences, this would not be the case. Unfortunately, there seem to be no experiments of this type in the book. Indeed, much of the (original) empirical work in the book does not really test a model per se but rather is directed at establishing the magnitude of [Beta] for different economic variables. As a result, the facts uncovered by Mulligan's regressions can be contemplated independently of any particular model, which perhaps is not what Mulligan intended.

Being an economic historian, my immediate familiarity with the PSID is limited to what I read in the papers, so to speak. I will leave it to others more expert on these data to evaluate Mulligan's contribution except to note that his points about measurement error are well taken and that the econometric analysis seems thoughtful. But his review of the history of American inequality will not impress specialists. Mulligan relies too heavily on Williamson and Lindert, whose findings have been challenged repeatedly. His treatment of black-white differences is somewhat misleading. Mulligan notes that the black-to-white wage ratio has converged over the 1940 to 1980 period and that the rate of convergence is what one might expect from his model. While true, this ignores the period from 1900 to 1940, which witnessed virtually no convergence. Why does the M model apply to one period and not another? The point is not that intergenerational altruism plays no role in black-white convergence indeed, greater familiarity with the economic history literature would have provided Mulligan with both anecdotal and quantitative evidence in favor of his argument but rather that the history of inequality is very complex, perhaps too complex for a single model. Here, again, the book's origins as a dissertation come into play. Like a proud parent, there is a natural tendency to cherish the models in one's thesis, protect them from harm's way, and promote them as more insightful than they really are. (I wonder if Mulligan knew this would happen before he embarked on his project.)

Criticisms aside, Parental Priorities is a very important book. I urge all economists with an interest in inequality to read it.

Outside of economic history, it is rare for a recent Ph.D. in economics to publish a dissertation as a book and rarer still for the publisher to be one of the premier academic presses in economics. That said, Casey Mulligan's Parental Priorities and Economic Inequality compels attention because of the importance of the subject matter - the intergenerational transmission of inequality - and thoroughness of the analysis.

Parental Priorities is divided into an Introduction, Conclusion, and 12 substantive chapters arranged in 4 parts. The Introduction (Chapter 1) reviews the subject matter of the following chapters.

Chapter 2 begins the exposition with a simple two-period consumption-savings model borrowed from consumer theory. Households consist of a single parent and child. Utility is defined over the parent's current consumption and the child's future consumption. Thus, preferences are U([C.sub.p], [C.sub.c]), where p = parent and c = child and [p.sub.c] is 1/(1 +r). Because a period here is really a lifetime, r is defined across generations; hence, small, permanent changes in r can have a huge effect on p. Three characteristics of parental preferences are examined: the degree of altruism, moderation, and homotheticity. The indifference curves of a more altruistic parent are shifted toward the axis measuring the consumption of the child relative to those of a less altruistic parent. By moderation, Mulligan means the extent of substitutability between parental and child consumption. Leontief preferences, used extensively later in the book, imply maximum moderation (zero substitutability). Homotheticity means that, for any given value of r, [C.sub.c]/[C.sub.p] is independent of wealth, so that there is no regression to the mean in consumption across generations.

Chapter 3 reviews two previous models of intergenerational transmission, the permanent income (PI) model made famous by Robert Barro and the imperfect capital markets model. The key idea of the PI model is that income is fungible across generations, so that attempts to redistribute income by the government (such as social security) can be undone by families. In the first version of the model, earnings are taken as given, but Mulligan shows that basic predictions survive endogenous earnings. Since the permanent income model is focused on opportunities, there is no reason to make assumptions about preferences. If preferences are homothetic, consumption will not regress to the mean across generations, even if earnings does.

Unlike the PI model, the imperfect capital markets (ICC) model assumes that parents cannot incur debt that will be passed onto their offspring. At low levels of parental income, it may not be possible for parents to optimally invest in their children's human capital (optimal levels are defined by the PI model). Thus, even if preferences are homothetic, below the critical income level, the expansion path follows the earnings function; above the critical level, the expansion path is a straight line. Mulligan argues, however, that unique implications of the ICC model are very sensitive to assumptions, and hence the model is not very useful.

Chapter 4, the key analytical chapter, introduces the core idea of endogenous altruism. While the discussion in the text is clear (with many pretty diagrams), most economists, I think, will fast forward to the mathematical appendix. Parental utility is Leontief. Income is the present discounted value of parental and child earnings. Income is allocated to consumption plus child-oriented resources q, which, in turn, increases the amount of altruism (a) and, therefore, the optimal ratio of [C.sub.c]/[C.sub.p] according to an assumed function [Phi](a). Altruism can also be accumulated if parents spend time with their children. Mulligan makes several assumptions (such as diminishing returns to accumulating altruism) that ensure an interior solution.

Next, Mulligan addresses comparative statics, deriving a total resource effect and a substitution effect. The total resource effect refers to the impact of exogenous increases in parental income on altruism. Mulligan's assumptions ensure that altruism is a normal good, so rising income promotes altruism. However, rising income might occur because the value of parental time has gone up, which raises the price of accumulating altruism. Hence, there is no necessary reason for economic growth to alter the average degree of altruism the total resource effect of growth is (approximately) canceled out by the substitution effect. Mulligan also examines how interest rates affect altruism. An increase in the interest rate lowers the price of [C.sub.c] thereby increasing altruism (because q and C,. are complements).

The Mulligan (M) model has strong implications for intergenerational mobility. The basic prediction is regression towards the mean in consumption across generations. Suppose a parent has a low wage, perhaps because of discrimination or because he is an immigrant. This lowers the value of parental time, thus reducing the cost of accumulating altruism. Altruism goes up, the parent sacrifices for the sake of the child, and [C.sub.c]/[C.sub.p] is increased. Conversely, suppose that the parental wage is high; this will reduce altruism, and [C.sub.c]/[C.sub.p] goes down.

By this point, the text has become rather intricate, but there is a very useful table (Table 4.1) that summarizes the predications of the three models. By carefully reviewing this table, the reader can test his/her understanding and reread the text if necessary (as I did a few times). The chapter concludes with an extended comparison of the M model with a model of endogenous fertility due to Robert Barro and Gary Becker (BB). Mulligan argues that the BB model is not useful in a world where couples typically have one child. Chapter 5 considers how taxes might affect intergenerational altruism, concluding that the estate tax cannot have had much effect in the U.S. because so few people pay it.

Part Two is the empirical section of the book. Chapter 6 starts out with a simple regression

ln [y.sub.p] = [Alpha] + [Beta] ln [y.sub.c[ + [Epsilon].

Mulligan is interested in [Beta]. If it is less than one, we have regression to the mean across generations, a necessary, but not sufficient, condition for inequality (measured by the variance of In y) to decline over time. The chapter also reminds readers that inequality between groups might fall but overall inequality rises and that measurement error may cause an overstatement of the degree of regression to the mean. Chapter 6 also contains a review of the literature on the history of American inequality, relying heavily on the work of such scholars as Jeffrey Williamson, Peter Linden, James Smith, and Finis Welch, Evidence on cross-state, cross-region (in the U.S.), and cross-country inequality is also reviewed.

Chapter 7 explores the panel study of income dynamics (PSID). Mulligan constructs a sample with data on parents from 1967 to 1971 and children from the mid-1980s. Consumption expenditures are proxied by spending on food, housing, and property taxes. Ordinary least squares (OLS) estimates of [Beta] are similar for income, consumption, and wealth but are lower for earnings. Instrumental variables estimates, intended to correct for measurement error, show less regression to the mean than the OLS estimates. The chapter also reviews a variety of other studies, looking at schooling, occupation, and wealth mobility. On the basis of these studies, Mulligan concludes that intergenerational mobility within groups is about the same as across groups.

Chapter 8 contains tests of the ICC model using the PSID. The basic idea is that regression to the mean differs whether or not parents make financial transfers to children. Mulligan divides his sample into two groups: children who expect (in their 20s) to get an inheritance of at least $25,000 and those who do not. He finds very similar regression to the mean behavior for earnings and consumption regardless of expectations about inheritance, inconsistent with the ICC model. He does find that schooling is more dependent on parental income in families not expecting to make inheritances, but this does not affect the degree of regression to the mean in earnings. Consequently, Mulligan infers that the rich derive consumption value from education (such as from expensive private schools).

Part Three, composed of Chapters 9 and 10, is short. Chapter 9 considers the relationship between the Mulligan model and sociobiological perspectives in which genes are selected for fitness. Mulligan sketches an argument by which altruism is consistent with evolutionary reasoning. Chapter 10 examines what Adam Smith and John Rae thought about altruism and argues that his approach was anticipated by these authors.

The final three chapters (Part Four) explore extensions to the M model. Chapter 11 extends the endogenous altruism model to multiple offspring. Mulligan shows that it is possible to get unequal treatment within the family, even if preferences are equal across kids; that parents may not share unexpected increases in income with their children; and, perhaps most interestingly, that a noncustodial father might show more concern for children of a current marriage rather than a former. Chapter 12 extends the model to giving beyond the family, illuminating a variety of strategies by which charities influence altruistic behavior. Chapter 13 concerns the principal agent problem, arguing that principals can invest resources to instill loyalty in agents, which alters the optimal commission rate (makes it lower) in riskier environments. Chapter 14 ably sums up.

In a book of such complexity and length about a central topic of economics, there are bound to be points of strong disagreement and criticism. In terms of style, the book reads like a dissertation. Some material - for example, the discussion of the Becker-Barro model - reads as if it were included originally in order to satisfy advisors. Certain chapters, notably those in Pan Three (as well as Chapter 13), are not well integrated into the text and perhaps could have been dispensed with in the interest of producing a tighter volume. In the Introduction, Mulligan expresses the hope that the book will achieve a wide readership outside of economics, and he claims to have tailored the style (heavy on graphs, light on math) to maximize his audience. Hope springs eternal, but I am unconvinced. To truly understand much (if not most) of the text (and, more importantly, to appreciate it), one needs to be a professional economist (or well on one's way to becoming one). And professionals are apt to become weary of those portions of the text that introduce elementary concepts (such as indifference curves).

Some readers will be unimpressed by the model. At a formal level, there is no technical advance. Child-oriented resources enter the utility function in a particular way (by influencing the marginal rate of substitution between [C.sub.c] and [C.sub.p]), but there is nothing in the ordinary theory of consumer behavior - certainly as amended by standard household production models - that rules out such a formulation. Mindful of this point, Mulligan interprets his model as a theory of endogenous taste formation, in the manner of rational addiction models. In an attempt to deflect criticism, Chapter 4 presents an example of an M-type model involving ski equipment and ski trips. Imagine, dear reader, that you, a nonskier, buy expensive ski equipment and subsequently go skiing frequently. When friends query you about your new-found hobby, you reply "I want to get my money's worth" (p. 90). Mulligan's theory presumes that ski trips and ski equipment are complements, so that your willingness to pay for ski trips has gone up (and you knew it would, in advance). But "getting your money's worth" is an odd rationale because the skis are a sunk cost at that point. There can be many (fungible) reasons why you choose to go skiing more frequently, none of which has to do with the possible effects of owning a durable good (the skis) on tastes.

Whether one accepts the M model or not, I think, may have a lot to do with one's own preferences about how to model preferences. In Mulligan's world, the ICC and PI models are about budget constraints so that, in the absence of any evidence to the contrary, preferences should he assumed homothetic and exogenous. But preferences might be nonhomothetic and exogenous. To really know whether endogenous altruism has value as an analytical concept, we need an experiment that allows altruism to accumulate (with no depreciation). Suppose, for example, that the parental wage were to rise over some period and then decline to its original value. In a (suitably dynamic) M model, altruism would change and, if altruism were putty-clay, would change permanently. In a model with nonhomothetic preferences, this would not be the case. Unfortunately, there seem to be no experiments of this type in the book. Indeed, much of the (original) empirical work in the book does not really test a model per se but rather is directed at establishing the magnitude of [Beta] for different economic variables. As a result, the facts uncovered by Mulligan's regressions can be contemplated independently of any particular model, which perhaps is not what Mulligan intended.

Being an economic historian, my immediate familiarity with the PSID is limited to what I read in the papers, so to speak. I will leave it to others more expert on these data to evaluate Mulligan's contribution except to note that his points about measurement error are well taken and that the econometric analysis seems thoughtful. But his review of the history of American inequality will not impress specialists. Mulligan relies too heavily on Williamson and Lindert, whose findings have been challenged repeatedly. His treatment of black-white differences is somewhat misleading. Mulligan notes that the black-to-white wage ratio has converged over the 1940 to 1980 period and that the rate of convergence is what one might expect from his model. While true, this ignores the period from 1900 to 1940, which witnessed virtually no convergence. Why does the M model apply to one period and not another? The point is not that intergenerational altruism plays no role in black-white convergence indeed, greater familiarity with the economic history literature would have provided Mulligan with both anecdotal and quantitative evidence in favor of his argument but rather that the history of inequality is very complex, perhaps too complex for a single model. Here, again, the book's origins as a dissertation come into play. Like a proud parent, there is a natural tendency to cherish the models in one's thesis, protect them from harm's way, and promote them as more insightful than they really are. (I wonder if Mulligan knew this would happen before he embarked on his project.)

Criticisms aside, Parental Priorities is a very important book. I urge all economists with an interest in inequality to read it.

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Author: | Margo, Robert A. |
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Publication: | Southern Economic Journal |

Article Type: | Book Review |

Date: | Oct 1, 1998 |

Words: | 2446 |

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