**Auction for Double Wide Ads:**

https://arxiv.org/abs/2207.04172

We propose an auction for online advertising where each ad occupies either one square or two horizontally-adjacent squares of a grid of squares. Our primary application are ads for products shown on retail websites such as Instacart or Amazon where the products are naturally organized into a grid. We propose efficient algorithms for computing the optimal layout of the ads and pricing of the ads. The auction is a generalization of the generalized second-price (GSP) auction used by internet search engines (e.g. Google, Microsoft Bing, Yahoo!).

Credible Inference for Heterogeneous Returns to Schooling

Credible Inference for Heterogeneous Returns to Schooling

**–**

**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)**

**–**

**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**

**–**

**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.