In the US, borrowers can choose to get lower interest rates on their mortgages by paying more discount points upfront. It is often observed that minority borrowers pay the same number of points as white borrowers controlling for the interest rate, but pay higher interest rates than white borrowers controlling for points. How can researchers tell if lenders charge minority borrowers more than observationally similar white borrowers? We show that the answer to this question involves a "menu problem," and intuitively appealing metrics of lender discrimination that are widely used in the literature can lead to false positives, false negatives, and contradictory results due to the existence of unobserved hetereogeneity in menus. This menu problem extends well beyond the mortgage market, but is often under-appreciated. To address this problem, we define (i) a new, robust, test statistic for equality in menus and (ii) a new difference in menus (DIM) metric for assessing whether one group of consumers would like to switch to another groups' menus, both based on pairwise dominance relationships in the data. We show how these metrics can be computed using methods from optimal transport, and devise a procedure for generating uniformly valid critical values in this class of problems based on directional differentiation. We implement our metrics on a new dataset matching 2018-2019 Home Mortgage Disclosure Act (HMDA) data to OptimalBlue rate locks. We find that Black and Hispanic borrowers were offered worse menus in terms of rates and points by lenders for conforming mortgages compared to Non-Hispanic White borrowers, and that the difference we detect can be largely explained by lender pricing differences across neighborhoods.

I develop a new method for estimating counterfactuals in dynamic discrete choice models, a widely used set of models in economics, without requiring a distributional assumption on utility shocks. Applying my method to the canonical Rust (1987) setting, I find that the typical logit assumption on utility shocks can lead the researcher to conclude that the agent's counterfactual choice probabilities are much more sensitive to policy changes than what a semi-parametric model would suggest. Therefore, my method may be useful to applied researchers in generating policy counterfactuals that are robust to such distributional assumptions.

We analyze how CEO stock options compensation can be used as a commitment device in oligopolistic competition. We develop a two-stage model where shareholders choose managerial compensation to commit their managers to being aggressive in equilibrium. Our results may explain why some shareholders appear to incentivize ‘excessive’ risk taking through stock options compensation. We analyze how our results are impacted by product quality, marginal cost, product differentiation, and industry concentration. As motivation for our research, we show that there exists positive empirical correlation between industry concentration and options compensation vega within a sample of firms, as suggested by our model.

We analyze the Markov Perfect Equilibria of an infinite-horizon overlapping generations model with consumer lock-in to compare the performance of history-based and uniform pricing in growing and declining markets. Under history-based pricing, firms charge higher prices to locked-in customers and lower prices to new customers. We show that a high exit rate of consumers (sufficiently declining market) constitutes a sufficient condition for history-based pricing to generate higher average prices than uniform pricing, thereby harming consumer welfare. In contrast, a high consumer entry rate (sufficiently growing market) ensures that history-based pricing intensifies competition compared with uniform pricing.

Households still pay rent primarily with paper methods, even though electronic methods are featured more prominently among high-income, high-education, and high-rent households. These patterns may be explained either by the lack of landlord acceptance of electronic methods or by the unwillingness of tenants to pay using these methods.
The dominant methods for paying rent are cash (22 percent), check (42 percent), and money order (16 percent). Electronic methods are still rarely used, at 8 percent for bank account number payment and 7 percent for online banking bill payment, and less than 2 percent for debit and credit cards.
Compared with other large bill payments of more than $200, rental payments are much more likely to be made with paper-based methods than with electronic methods, despite the recent attempts by start-ups to make it easier for landlords to accept electronic payments. They are also much less likely to be automatic.
Check and electronic methods are more frequently used for higher-value transactions and by those with higher income and education.