Working Paper
Zhang, David Hao, and Paul Willen. Working Paper. “Do Lenders Still Discriminate? A Robust Approach for Assessing Differences in Menus”.Abstract

Motivated by the assessment of racial discrimination in mortgage pricing, we introduce a new methodology for comparing the menus of options borrowers face based on their choices. First, we show how standard regression based approaches for assessing discrimination in menus can lead to misleading and contradictory results. Second, we propose a new methodology that is robust these problems based on relatively weak economic assumptions. More specifically, we use pairwise dominance relationships in choices supplemented by restrictions on the range of plausible menus to define (1) a test statistic for equality in menus and (2) a difference in menus (DIM) metric for assessing whether one group of borrowers would prefer to switch to another group's menus. Our statistics are robust to arbitrary heterogeneity in borrower preferences across racial groups, are sharp in terms of identification, and can be efficiently computed using Optimal Transport methods. Third, we devise a new approach for inference on the value of Optimal Transport problems based on directional differentiation. Fourth, we use our methodology to estimate mortgage pricing differentials by race on a novel data set linking 2018--2019 Home Mortgage Disclosure Act (HMDA) data to Optimal Blue rate locks. We find robust evidence for mortgage pricing differentials by race, particularly among Conforming mortgage borrowers who are relatively creditworthy.

Gerardi, Kristopher, Paul Willen, and David Hao Zhang. Working Paper. “Mortgage Prepayment, Race, and Monetary Policy”.Abstract

Over the period 2005 to 2015, Black borrowers paid more than 40 basis points higher mortgage interest rates than Non-Hispanic white borrowers. We show that the main reason is that Non-Hispanic white borrowers are much more likely to exploit periods of falling interest rates by refinancing their mortgages or moving. Black and Hispanic white borrowers face challenges refinancing because, on average, they have lower credit scores, equity and income. But even holding those factors constant, Blacks and Hispanic white borrowers refinance less suggesting that other social factors are at play. Because they are more likely to exploit lower interest rates, white borrowers benefit more from monetary expansions. Policies that reduce barriers to refinancing for minority borrowers and alternative mortgage contract designs can significantly reduce racial mortgage rate inequality.

Wang, Jeffrey, and David Hao Zhang. Working Paper. “The Cost of Banking Deserts: Racial Disparities in Access to PPP Lenders and their Implications”.Abstract
Many government support programs for small businesses are designed to pass through banks and credit unions. However, this poses barriers for minority communities that are less connected to financial institutions for obtaining this support. Using the latest program for supporting small businesses, the Paycheck Protection Program (PPP), as an example, we show that there was a large disparity in both the presence and density of PPP enrolled lenders by racial composition of the neighborhood. This difference is both due to a lower number of lenders in those neighborhoods in general, and by the fact that the lenders that do operate there are small credit unions without a previous relationship with the Small Business Administration. More heavily Black neighborhoods have significantly lower take-up of PPP loans, particularly in lower population (more rural) areas where this disparity is most salient. Through an instrumental variables analysis, we show that the intensive margin of access to enrolled lenders can explain about 32% of the racial disparity in take up within the relevant areas. Our results suggest that government programs that provide ``support through banks'' can have undesirable distributional implications.
Liu, Tianwang, and David Hao Zhang. Working Paper. “Do Judge-Lawyer Relationships Influence Case Outcomes?”.Abstract
We examine whether law school alumni relationships between the lawyers and judges affect case outcomes. We show that in the context of medical malpractice lawsuits in Florida, the plaintiff lawyer sharing the same law school as the judge increases the chances of recovery by 2%. Furthermore, the effect is confined to younger lawyers who see a 4% increase in the likelihood of recovery from having been to the same law school as the judge, and is absent in older lawyers. We interpret our results as evidence that lawyers gain school-specific human capital from their law schools which helps in their interactions with judges that graduated from the same school, and that this school-specific human capital become less important further on in the lawyers' careers.
Zhang, David Hao. Working Paper. “Semi-Parametric Estimation of Counterfactuals in Dynamic Discrete Choice Models”.Abstract
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.
Journal Article
Ishii, Jun, and David Hao Zhang. 2017. “Options Compensation as a Commitment Mechanism in Oligopoly Competition”. Managerial and Decision Economics 38 (4):513–525. Publisher's VersionAbstract
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.
Shy, Oz, Rune Stenbacka, and David Hao Zhang. 2016. “History-based versus uniform pricing in growing and declining markets”. International Journal of Industrial Organization 48:88–117. Publisher's VersionAbstract
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.