Growth and Demographic Change
Michele Boldrin
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 "The Two Transitions, Demographic and Industrial "
with Aubhik Khan and Larry E. Jones

"Mortality, Fertility, and Intergenerational Transfers: A Long Run Perspective"
  with Larry E. Jones

From Busts to Booms in Babies and Goodies  NEW!
with Larry E. Jones and Alice Schoonbroodt
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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. Received wisdom from the Demography literature links these large fluctuations in fertility to the series of Economics 'shocks' that occurred with similar timing - the Great Depression, WWII, the economic expansion that followed and then the productivity slow down of the 1970's. To economists, this line of argument suggests a more general link between fluctuations in output and fertility decisions, of which the Baby Bust-Boom-Bust event (BBB) is a particularly stark example. Surprisingly, little has been done to formally address this link in a stochastic model of optimal fertility choice. This paper is an attempt to formalize the conventional wisdom 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. Second, we analyze calibrated versions of these models. We can then answer several qualitative and quantitative questions: Under what conditions is fertility pro- or countercyclical? How large are these effects and how is this related to the 'persistence' of the shocks? How much of the BBB can be accounted for by the kinds of medium run productivityfluctuations described as computed from the data?

Three Equations Generating an Industrial Revolution?  NEW!
With Aubhik Khan and Larry E. Jones
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In this paper we evaluate quantitatively the relationship between economic and demographic growth. We use simple models of endogenous growth, featuring human capital investment at the individual level in conjunction with either of two models of fertility choice, the B&B dynastic motive, and the B&J lateage-security motive. We find that exogenous improvements in agespecific survival probabilities, lead to increases in the rate of return to human capital investment. This, in turn, engenders an increase in the growth rate of output per capita much like what is typically seen when countries go through industrialization. In the models implemented so far, we also find that this is accompanied either by a permanent increase in the growth rate of population (for the B&B), or by too much late age consumption and a rate of return on capital that is too high relative to available data (for the B&J). Historical records show that the increase in the growth rate of population during the takeoff was temporary, and that the transition eventually lead to a stationary population; it is unclear if a different version of the B&B model can be built that generates this crucial stylized facts. On the other hand, preliminary work shows that more realistic variations of the B&J model should eliminate the unrealistic predictions about old age consumption and rate of return on capital while maintaining the ability of the model to generate an IR and a DT.

Public Education and Capital Accumulation NEW!
Research in Economics 59 (2005), 85-109
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I study an overlapping generations model where physical and human capitals are inputs of production that can be accumulated by withholding resources from current consumption. Human capital is the output of a schooling system which can be financed either by private expenditures, or by taxes, or by a combination of both. In a political equilibrium with majority voting, public school financing turns out to be an instrument to solve a ``free rider problem''. By improving the skills of next period's workers it increases the expected return on physical capital, something which cannot be achieved by means of private expenditure in education only. When financed by a uniform income tax, public schools are also an instrument for intergenerational redistribution. Depending on initial conditions, the model predicts either a poverty trap (poor societies invest too little in education) or persistent growth driven by the accumulation of human capital. The introduction of public financed education shrinks the set of initial conditions leading to the poverty trap. I characterize the global dynamics of the model, which delivers a number of testable hypotheses on the relation between income growth, capital accumulation and the development of public education. All throughout the paper I concentrate on specific functional forms allowing for a closed form solution, nevertheless, all the important results carry over to fairly general utility and production functions.

Fertility and  Social Security NEW!
with Larry E. Jones and Maria Cristina DeNardi.
First version October 2003, this version March 2005.
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The data show that an increase in government provided old-age pensions is strongly correlated with a reduction in fertility. What type of model is consistent with this finding? We explore this question using two models of fertility, the one by Barro and Becker (1989), and the one inspired by Caldwell and developed by Boldrin and Jones (2002). In the Barro and Becker model parents have children because they perceive their children's lives as a continuation of their own. In the Boldrin and Jones' framework parents procreate because the children care about their old parents' utility, and thus provide them with old age transfers. The effect of increases in government provided pensions on fertility in the Barro and Becker model is very small, and inconsistent with the empirical findings. The effect on fertility in the Boldrin and Jones model is sizeable and accounts for between 55 and 65\% of the observed Europe-US fertility differences both across countries and across time and over 80\% of the observed variation seen in a broad cross-section of countries. Another key factor affecting fertility the Boldrin and Jones model is the access to capital markets, which can account for the other half of the observed change in fertility in developed countries over the last 70 years.

Mortality, Fertility and Saving in a Malthusian Economy

with Larry E. Jones
Review of Economic Dynamics   5 (2002), 775-814.
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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 that performs better, qualitatively and quantitatively, than previous models of which we are aware.

Chaotic Equilibrium Dynamics in Endogenous Growth Models
with K. Nishimura, T. Shigoka and M. Yano
Journal of Economic Theory , 96 (2001), 97-132
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We study a class of two-sector endogenous growth models in the presence of a positive external effect. The class of models exhibits global indeterminacy of equilibria. The qualitative properties of a set of examples are analyzed by means of analytical and numerical methods. We also construct robust examples of both topological and ergodic chaos.

Growth Cycles and Market Crashes
with David K. Levine
Journal of Economic Theory , 96 (2001), 13-39.
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Stock market booms are often followed by dramatic falls. This is often viewed as a bad thing, and evidence of investor irrationality. To explain this from a fundamentalist point of view requires an asymmetry in the underlying technology shocks driving the market. Here we argue that a straightforward model of technological progress leads to clear asymmetries and these asymmetries may be also the source of growth cycles. In a simple optimization model with a representative consumer, if traders are not too risk averse, we show that the stock market will generally rise, punctuated by occasional dramatic falls. This is first best. Surprisingly, if consumers are very risk averse, the gradual rise in the market will be broken by dramatic increases in stock prices on the occasion of bad news. Bad news do not correspond to a contraction of the production possibility set but, rather, to a decrease in the rate at it expands. For this reason, this economy provides a model of endogenous growth in which the timing of recoveries and recessions is dictated by the pace at which technological innovations are adopted.

Growth Under Perfect Competition
with David K. Levine
mimeo.  First version: October 1997; this version June 2005.
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We construct an abstract, dynamic general equilibrium model of innovation and growth, in the spirit of Schumpeter's Theory of Theory of Economic Development. Despite the existence of infinitely many commodities and activities, the use of which may vary over time, we give a characterization of equilibrium using the standard first and second welfare theorems, and a standard transversality condition. We consider a series of examples characterizing the dynamic properties of equilibria and show that many results discussed in the "endogenous growth" literature can be obtained as special cases of the model we propose. Next we study the role of initial conditions in the process of economic growth and show that most kinds of "path dependence" discussed in the literature may arise under conditions of perfect competition and in the absence of any external effect.

November 11, 2006