Over the past four decades, the negative relationship between income and fertility in the United States has flattened. We document two additional patterns: fertility variation within income groups has increased, and the average preference for children among high income women has risen. We propose a novel channel through which heterogeneity in fertility preferences interacts with changes in the wage and price structures to reshape the income-fertility relationship as documented. To assess its quantitative importance, we develop an overlapping generations model with heterogeneity in productivity and fertility preferences, alongside existing mechanisms from the literature. The model reproduces the joint evolution of fertility rates, fertility variation, and fertility preferences, and shows that the proposed mechanism is important for changes in fertility behavior across the income distribution.
We develop a tractable general equilibrium model of cumulative innovation and growth to study the optimal combinations of three patent instruments: a patentability requirement to protect against future incremental innovation, a patent breadth to protect against current imitation, and the patent length governing the duration of its validity. New ideas strictly build upon frontier technologies, with the size of productivity improvements drawn from a stochastic distribution. The model features positive knowledge spillovers, and we discuss when this leads to under-investment in R&D in the market equilibrium relative to the social planner’s benchmark. We characterize analytically how each patent instrument affects research incentives, and further establish that the patentability requirement and patent breadth in the welfare-maximizing combination are each set at a strictly lower level than in the R&D-maximizing combination. Calibrating the model to aggregate data, the welfare-maximizing combination of instruments features a large patent breadth, a long patent duration, but a modest patentability requirement. The quantitative analysis points to sizeable welfare gains from these patent policies, while highlighting the importance of having multiple patent instruments.
This paper quantifies the effects of college expansion under purely merit-based, competitive admissions, endogenizing pre-labor-market conditions. We develop a heterogeneous-agent life-cycle model where parents invest in their children’s pre-college human capital at multiple stages to compete for limited college slots. Applying the framework to China—where admissions rely solely on score ranks and enrollment has grown tenfold over the past 25 years—we find that score-based admissions increase the importance of human capital at the college admission stage relative to initial endowments. Family resources therefore shape admission indirectly through parental investment in pre-college human capital. Expanding college access under this system reduces intergenerational mobility because higher-income families respond by disproportionately increasing pre-college investments, strengthening the link between child achievement and parental income. Counterfactuals show that mobility would improve with college expansion if endogenous parental investment responses were shut down.
This paper studies the impact of health on structural transformation and aggregate productivity in low-income economies through its effects on the gender-based division of labor across sectors. I develop a two-sector general equilibrium model in which returns to health are higher for men than for women in agriculture, implying that health improvements reallocate female labor toward nonagriculture. The model is calibrated to African economies. Quantitative results show that health improvements substantially reduce the agricultural employment share—particularly among women—and increase aggregate labor productivity. Over one-third of the productivity gains can be attributed to the gender-based division of labor. Policy experiments indicate that health subsidies are more effective than education subsidies in reducing women’s agricultural employment relative to men’s and in improving aggregate productivity and welfare.
The relationship between the human population size and per capita incomes has long been debated. Two competing forces feature prominently in these discussions. On the one hand, a larger population means that limited natural resources must be shared among more people. On the other hand, a larger population means more innovation and faster technological progress, other things equal. We study a flexible model that features both of these channels. This model delivers a sufficient statistic for the sign of the effect running from population to per capita income that depends on (i) the share of global income accruing to natural resource owners and (ii) the elasticity of TFP growth with respect to research inputs. Available evidence on these key parameters—most importantly, the small share of income that is paid to natural resource owners—suggests that, in the long run, (marginal) increases in population would likely lead to (marginal) increases in per capita incomes.
