**Working Papers:**

**The Impact of Grants on Schools and Students**

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**Latest Version**

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**Presentation Slides**

This article estimates the causal impact of additional government funding on school choice. I construct a structural equilibrium model of the application-admission-scholarship-enrollment game between students and schools. I show how to estimate the causal impact in the presence of omitted variable bias and measurement error. A jump in Cal Grant aid at a GPA threshold serves as a shift in net tuition that is independent from omitted variables. I find that the vast majority of California Cal Grant recipients would have enrolled in-state even without the Cal Grant. I predict that removing the Cal Grant would decrease in in-state enrollment by one-tenth, and the majority of this decrease leads to non-enrollment.

**Credible Inference for Heterogeneous Returns to Schooling**

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**Latest Version**

This article estimates the heterogeneous returns to education by place-of-birth for males born between 1930 and 1940. We form intervals of credibility from the posterior distribution of our estimate. Instead of assuming the two-stage least squares estimate is distributed normal, we simulate draws from the posterior distribution of our two-stage estimate. When using weak priors, we obtain the same point estimates as the standard IV-2SLS methods, but we have much larger 95% credible intervals. When using the "best" priors as determined from cross-validation, we find that we are 95% sure that the returns to education are positive for only four out of nine regions, whereas the standard IV-2SLS approach would yield "significant" results for all nine geographic regions.

**Economic Impact Evaluation of the City of Pasadena's Minimum Wage Ordinance (co-authored with Professor Edward E. Leamer and Mengshan Cui)**

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**Latest Version**

We analyze the impact of the minimum-wage change in Pasadena, California, in a three-phase project. First, we compare Pasadena with surrounding cities to design the geographic structure of a data set to study local competition and heterogenous effects. Second, we identify low wage industries as having the greatest increase in earnings. Furthermore, we use a novel approach to show that only half of the impact of minimum wage on earnings occurs within the first quarter. We find significant impacts of the minimum wage on employment in limited service industries and establishments in hair/nail salons in recent time periods.

Preliminary Work:

**Updating the Update Rule in Reinforcement Learning**

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**Latest Version**

Games with many actions can become intractable. Reinforcement learning simulates a sequence of moves to estimate a policy function that maximizes the probability of winning. Here I provide a corrected update rule that trains the parameters of a policy function such that the correct objective is maximized.