Larry E. Jones

Family Economics and Fertility Choice

Complements versus Substitutes and Trends in Fertility Choice in Dynastic Models joint with Alice Schoonbroodt, March 2008.

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.

"Efficiency with Endogenous Population Growth" joint with Mikhail Golosov and Michèle Tertilt. Appendix (forthcoming, Econometrica).

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, The Handbook of Family Economics , Peter Rupert, Ed., forthcoming.

In this paper, we use data from the US census to document the history of the
relationship 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.

The reduction in fertility known as the Demographic Transition (or the Fertility
Transition) seems to be much sharper based on cohort fertility measures compared to usual measures like Total Fertility Rate;

The baby boom was not quite as large as is suggested by some previous work;

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;

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.

"Baby Busts and Baby Booms: The Fertility Response to Shocks in Dynastic Models," Larry Jones and Alice Schoonbroodt August 2007.

After the fall in fertility during the demographic transition, many developed countries experienced a baby bust, followed by the baby boom and subsequently a return to low fertility (BBB event). Demographers have linked these large fluctuations in fertility to the series of ‘economic shocks' that occurred with similar timing – the Great Depression, World War II (WWII), the economic expansion that followed and then the productivity slow down of the 1970s. This paper is an attempt to formalize a more general link between fluctuations in output and fertility decisions, in simple versions of stochastic growth models with endogenous fertility. First, we develop initial tools to address the effects of ‘temporary' shocks to productivity on fertility choices. These tools are based on a production function, where labor is the only input. Second, we analyze calibrated versions of these models. We can then answer several qualitative and quantitative questions: Is there ‘catching-up' in fertility after a period of particularly low fertility? Under what conditions is fertility pro- or counter-cyclical? How large are these effects? Qualitatively, results show that there is no ‘catching-up' in this model and that under reasonable parameter values fertility is pro-cyclical. Using the U.S. BBB event as a laboratory, we find that the elasticity of fertility to shocks lays between 1 and 2 and, finally, that in these simple models, productivity shocks capture about 70 percent of the pre-WWII baby bust in the U.S.. For the post-WWII baby boom, the predictions of this simple model are small and happen late compared to the data.

" Why Are Married Women Working So Much? " joint 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.

"Fertility and Social Security," with M. Boldrin and M. 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.

" Mortality, Fertility and Saving Decisions, in a Malthusian Economy"
with Michele Boldrin, Review of Economic Dynamics , 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.

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April 17, 2008