Essays in Dynamic Macroeconomics and Economic Theory
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Economics
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This thesis consists of three chapters studying population change and technology. The first chapter studies fertility in places with location-specific housing prices and education resources. Using a general equilibrium model with endogenous fertility, neighborhood choice, and child skill development, I quantify the impact of changing school financing from a system where education funding is location-specific and is funded by local property taxes, to a system where funding is shared across locations. After calibrating the model using U.S. data, I find that the policy increases fertility by 1.64 percent. Additionally, the model predicts that raising the child subsidy from $1000 per child per year to $2000 increases fertility by 0.85 percent. The second chapter studies how fertility policies can be set optimally. I present a tractable model for the analysis of optimal pronatalist policies where the consequence of a declining population is its negative impact on economic growth. The closed-form solutions yield qualitative principles for the design of pronatalist policies. The model highlights the importance of jointly considering fertility and education decisions when setting pronatalist policies, and demonstrates that the replacement rate may not necessarily be the optimal population growth rate. The third chapter, based on joint work with Eduardo M. Azevedo, José Luis Montiel Olea, and Amilcar Velez, studies firm experimentation. A risk-neutral firm can perform a randomized experiment to learn about the effects of implementing an idea of unknown quality. The firm's goal is to decide the experiment's sample size and whether the idea should be implemented after observing the experiment's outcome. We show that when the distribution for idea quality is Gaussian and there are linear costs of experimentation, there are exact formulae for the firm's optimal implementation decisions, the value of obtaining more data, and optimal experiment sizes. The formulae---which assume that companies use randomized experiments to maximize expected profits---provide simple alternatives to the standard rules-of-thumb of power calculations for determining the sample size of an experiment, and to ad hoc thresholds based on statistical significance to interpret the outcome of an experiment.