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Family Economics and Fertility Choice

"Is There "Too Much" Inequality in Health Spending Across Income Groups?" with Laurence Ales and Roozbeh Hosseini, March 2012.

In this paper we study the efficient allocation of health resources across individuals. We focus on the relation between health resources and income (taken as a proxy for productivity). In particular we determine the efficient level of the health care social safety net for the indigent. We assume that individuals have different life cycle profiles of productivity. Health care increases survival probability. We adopt the classical approach of welfare economics by considering how a central planner with an egalitarian (ex-ante) perspective would allocate resources. We show that, under the efficient allocation, health care spending increases with labor productivity, but only during the working years. Post retirement, everyone would get the same health care. Quantitatively, we find that the amount of inequality across the income distribution in the data is larger that what would be justified solely on the basis of production efficiency, but not drastically so. As a rough summary, in U.S. data top to bottom spending ratios are about 1.5 for most of the life cycle. Efficiency implies a decline from about 2 (at age 25) to 1 at retirement. We find larger inefficiencies in the lower part of the income distribution and in post retirement ages.

"Baby Busts and Baby Booms:  The Fertility Response to Shocks in Dynastic Models," with Alice Schoonbroodt, April 2016.

Economic demographers have long analyzed fertility cycles. This paper builds a foundation for these cycles in a model of fertility choice with dynastic altruism and aggregate shocks. It is shown that under reasonable parameter values, fertility is pro-cyclical and that, following a shock, fertility continues to cycle endogenously as subsequent cohorts enter retirement. Quantitatively, in the model, the Great Depression generates a large baby bust – between 38% and 63% of that seen in the U.S. in the 1930s – which is subsequently followed by a baby boom – between 53% and 92% of that seen in the U.S. in the 1950s.

"Optimal Contracting with Dynastic Altruism:  Family Size and Per Capita Consumption," with Roozbeh Hosseini and Ali Shourideh, Journal of Economic Theory, 2013, Vol. 148, 1806-1840.

We use a Barro-Becker model of endogenous fertility, in which parents are subject to idiosyncratic shocks that are private information (either to labor productivity or taste for leisure), to study the efficient degree of consumption inequality in the long run. The planner uses the trade off between family size and future consumption and leisure, in addition to the usual variables, to provide incentives for workers to reveal their shocks. We show that in this environment, the optimal dynamic contract no longer features immiseration in consumption. We also discuss the implications of the model on the long run properties of family size in the optimal contract and show that the long run trend in dynasty size can be either positive or negative depending on parameters.

"Risk Sharing, Inequality, and Fertility," with Roozbeh Hosseini and Ali Shourideh.   Supplementary Appendix.

We use an extended Barro-Becker model of endogenous fertility, in which parents are heterogeneous in their labor productivity, to study the efficient degree of consumption inequality in the long run. In our environment a utilitarian planner allows for consumption inequality even when labor productivity is public information. We show that adding private information does not alter this result. We also show that the informationally constrained optimal insurance contract has a resetting property -- whenever a family line experiences the highest shock, the continuation utility of each child is reset to a (high) level that is independent of history. This implies that there is a non-trivial, stationary distribution over continuation utilities and there is no mass at misery. The novelty of our approach is that the no-immiseration result is achieved without requiring that the objectives of the planner and the private agents disagree. Because there is no discrepancy between planner and private agents objectives, the policy implications for implementation of the efficient allocation differ from previous results in the literature. Two examples of these are: 1) estate taxes are positive and 2) there are positive taxes on family size.

"Fertility Theories:  Can They Explain the Negative Fertility-Income Relationship?" with Alice Schoonbroodt and Michele Tertilt,   NBER Working Paper No. 14266, August 2008. 

 There is overwhelming empirical evidence that fertility is negatively related to income in most countries at most times. Several theories have been proposed in the literature to explain this somewhat puzzling fact. The most common one is based on the opportunity cost of time being higher for individuals with higher earnings. Alternatively, people might differ in their desire to procreate and accordingly some people invest more in children and less in market-specific human capital and thus have lower earnings. We revisit these and other possible explanations. We find that these theories are not as robust as is commonly believed. That is, several special assumptions are needed to generate the negative relationship. Not all assumptions are equally plausible. Such findings will be useful to distinguish alternative theories.

"Complements versus Substitutes and Trends in Fertility Choice in Dynastic Models," with Alice Schoonbroodt, International Economic Review, 2010, Vol. 51, 671-699.   Appendix.

In this paper, we consider a variation on the Barro/Becker model of fertilty choice in which, contrary to what is usually assumed, family size and per capita utility are substitutes. We find that in reasonable, calibrated examples, most of the intuitions from the statistical
demography literature about the causes of the Fertility Transition are both qualitatively and quantitatively significant. This is in marked contrast to previous studies. Please click for larger image of graph.

"Efficiency with Endogenous Population Growth," joint with Mikhail Golosov and Michele Tertilt, Econometrica, 2007, Vol. 75, no. 4, 1039-1072.  Appendix.

In this paper, we generalize the notion of Pareto-efficiency to make it applicable to environments with endogenous populations. Two different efficiency concepts are proposed, P-efficiency and A-efficiency. The two concepts differ in how they treat people that are not born. We show how these concepts relate to the notion of Pareto efficiency when fertility is exogenous. We then prove versions of the first welfare theorem assuming that decision making is efficient within the dynasty. Finally, we give two sets of sufficient conditions for non-cooperative equilibria of family decision problems to be efficient. These include the Barro and Becker model as a special case.

"An Economic History of Fertility in the U.S.:  1826-1960," with Michele Tertilt, Frontiers of Family Economics, Volume 1, Peter Rupert, ed., Emerald Group Publishing, 2008, 165-209.

Endo Figure 4
In this paper, we use data from the US census to document the history of therelationship between fertility choice and key economic indicators at the individual level for women born between 1826 and 1960. We find that this data suggests several new facts that should be useful for researchers trying to model fertility.  Please click here for a larger view of the graph.
  1. The reduction in fertility known as the Demographic Transition (or the FertilityTransition) seems to be much sharper based on cohort fertility measures compared to usual measures like Total Fertility Rate;
  2. The baby boom was not quite as large as is suggested by some previous work;
  3. We find a strong negative relationship between income and fertility for all cohorts and estimate an overall income elasticity of about -0.38 for the period;
  4. We also find systematic deviations from a time invariant, isoelastic, relationship between income and fertility. The most interesting of these is an increase in the income elasticity of demand for children for the 1876- 1880 to 1906-1910 birth cohorts. This implies an increased spread in fertility by income which was followed by a dramatic compression.
"Why are Married Women Working So Much," with Rodolfo E. Manuelli and Ellen R. McGrattan.

This paper studies the large observed changes in labor supply by married women in the United States over the period from 1950 to 1990, a period when labor supply by single females has hardly changed at all. We investigate the effects of changes in the gender wage gap, technological improvements in the production of non-market goods and potential inferiority of these goods on understanding this change. To this end we use a dynamic general equilibrium model which distinguishes between single and married households. We find that small decreases in the gender wage gap can explain simultaneously the significant increases in the average hours worked by married females and the relative constancy in the hours worked by single females, as well the invariance of male hours over the 1950-1990 period.

The two main features of the model that account for the ability of changes to the gender wage gap to match the hours data are:
endogenous specialization among married couples and human capital accumulation. We also find that technological improvements in the household have ---for
realistic values--- too small an impact on married female hours and the relative wage of females to males. Some specifications of the inferiority of home goods do match the hours patterns, but have counterfactual predictions for wages and expenditure patterns.


To the right, you see a figure showing a comparison between the model and data from the U.S. economy over the 1950 to 2000 period when the 'Wage Gap' between men and women is exogenously narrowed following what happened in the data. Shown are the time paths for labor supply from the model for Women and Men, both Single and Married, along with a host of other predicted relationships from the model.  Please click to see a larger version of the graph.



"Fertility and Social Security," with Michele Boldrin and Mariacristina De Nardi.

In this paper, we study the effects of differential sizes of governmentally provided pension funds on the incentives for parents to have children in two different models of endogenous fertility These two models are the Barro and Becker model of children as consumption and the Caldwell model of children as investments for old age as developed in Boldrin and Jones.

We find that changing the size of a PAYGO Social Security System has only a very small effect on fertility in the B&B model, but that the effects are large, and quantitatively significant in the Caldwell version. For example, in the calibrated version of the Caldwell model that we use as our base case, we find that increasing the size of a PAYGO Social Security System from a tax rate of 10% to 25% gives rise to a fertility reduction of about 60% of the observed fertility differential between the U.S. and the Southern European countries.

Shown in the graph is a time series of the entire fertility history of the U.S. from 1850 to now along with the predicted path of fertility from the Caldwell model discussed above. The chart is prepared using steady state to steady state movements of fertility in the model over time when the only changes are the actual changes in young adult mortality and changes in the size of the Social Security System from U.S. data.
  Please click for a larger version of the graph.



"Mortality, Fertility, And Saving Decisions in a Malthusian Economy," with Michele Boldrin, Review of Economic Dynamics, Vol. 5, 2002, 775-814.

In this paper, we develop and analyze a simple model of fertility choice by utility maximizing households. Following the work of Barro and Becker, our model is based on an explicit notion of intergenerational external effects. In contrast to the Barro and Becker model however, we assume that the external effects run from children to parents. That is, parents consumption when old directly enters the utility function of the children. This gives rise to a fundamentally different reason for bearing of children. This is that parents expect to be cared for, at least partially, by their children in their old age when their labor productivity is low. Thus, children are an investment in own old age consumption from the point of view of parents. We take infant mortality rates as the key exogenous variable and endogeneize the size of the transfer from children to parents by linking it to the endogenous savings and fertility choice of the parents. This generates a simple dynamic model of economic growth and of fertility transition.