Many economic and non‐economic variables such as income, wealth, firm size, or city size often distribute Pareto in the upper tail. It is well established that Gibrat's law can explain this phenomenon, but Gibrat's law often does not hold. This note characterizes a class of processes, one that includes Gibrat's law as a special case, that can explain Pareto distributions. Of particular importance is a parsimonious generalization of Gibrat's law that allows size to affect the variance of the growth process but not its mean. This note also shows that under plausible conditions Zipf's law is equivalent to Gibrat's law.
We show that state non-separable preferences à la Epstein-Zin-Weil (EZW) provide a tractable and ‡exible framework to study the economics of health and longevity. This utility representation: (i) admits a preference for timing of resolution of uncertainty regarding mortality risks; (ii) links the marginal valuation of survival to the level of survival; (iii) can preserve homotheticity even for low degrees of intertemporal substitution without generating implausible predictions regarding the value of life; and (iv) adds needed ‡exibility to account for the empirical evidence on the value of life. We illustrate the implications of EZW preferences for the economic value of observed di¤erences in life expectancy across countries and over time, and for the value of life over the life cycle.
This paper builds a welfare measure encompassing household disposable income, unemployment and longevity, while using two different sets of "shadow prices" for non-income variables. The valuations of vital and unemployment risks estimated from life satisfaction data ("subjective shadow prices") and those derived from model-based approaches and calibrated utility functions ("model-based shadow prices") are shown to be broadly consistent once a number of conditions are fulfilled. Subjective shadow prices appear to be inflated by the downward bias on the income variable in life satisfaction regressions conducted at the individual level, while the latter bias is largely removed when running regressions at the country level. On the other hand, model-based shadow prices are typically underestimated as: (i) the valuation of the unemployment risk is assumed to take place under the veil of ignorance (i.e. for a representative agent that has no information on her current or future unemployment situation); (ii) the standard model relies on a constant relative risk aversion utility function, which has no specific relative risk aversion parameter for unemployment and vital risks; (iii) the value of statistical life that is used in standard calibration pertains to the adult lifespan, while life expectancy at birth covers the entire lifetime.
This paper provides a theory that explains the crosscountry distribution of average years of schooling, as well as the so called human capital premium puzzle. In our theory, credit frictions as well as di¤erences in access to public education, fertility and mortality turn out to be the key reasons why schooling di¤ers across countries. Di¤erences in growth rates and in wages are second order.
Extensive evidence from cross-sectional data reveals a robust negative relationship between family income and fertility. This paper argues that constraints to intergenerational transfers are crucial for understanding this relationship. If parents could legally impose debt obligations on their children as a way to recover the costs incurred in raising them, then fertility would be independent of parental income. In this case, if the present value of a child's future income exceeds the cost of raising the child, as the evidence suggests is the case, parents would have incentives to raise as many children as possible in order to maximize rents. A relationship between fertility and income arises when parents are unable to leave debts behind either because of legal, enforcement, or moral constraints. We also derive the conditions under which the fertility-income relationship is negative. Notably, an intergenerational elasticity of substitution larger than one is required. In this case, parental consumption is a good substitute for children's consumption making it optimal for income rich parents to have fewer children. Evidence from cross-sectional data reveals a negative relationship between family income and fertility. This paper argues that constraints to intergenerational transfers are crucial for understanding this relationship. If parents could legally impose debt obligations on their children to recover the costs incurred in raising them, then fertility would be independent of parental income. A relationship between fertility and income arises when parents are unable to leave debts because of legal, enforcement, or moral constraints. This relationship is negative when the intergenerational elasticity of substitution is larger than one, case in which parental consumption is a good substitute for children's consumption.There is extensive empirical evidence documenting a negative relationship between fertility and income. 1 For example, using cross-sectional individual data for the US, Becker (1960) …nds a negative fertility-income relationship in the 1910, 1940 and 1950 Censuses, and in the Indianapolis survey for the 1900s. More recently, Jones and Tertilt (2008) use US Census data as far back as the 1826 cohort to estimate an income elasticity of fertility of about 0:38. Their analysis is distinct in that they construct a more re…ned measure of lifetime income by using occupational income and education. Lifetime income and fertility are measured for several cross-sections of …ve-year birth cohorts from 1826-1830 to 1956-1960. They conclude that most of the observed fertility decline in the US can be explained by the negative fertility-income relationship estimated for each crosssection, together with the outward shift of the income distribution over time. The estimated income elasticity is robust to the inclusion of additional controls such as child mortality and the education i.e., the cost of raising the child is below the present value of the child's future income.Available data discussed in Section...
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