Publications

We propose a new adaptive hypothesis test for inequality (e.g., monotonicity, convexity) and equality (e.g., parametric, semiparametric) restrictions on a structural function in a nonparametric instrumental variables (NPIV) model. Our test statistic is based on a modified leave-one-out sample analog of a quadratic distance between the restricted and unrestricted sieve two-stage least squares estimators. We provide computationally simple, data-driven choices of sieve tuning parameters and Bonferroni adjusted chi-squared critical values. Our test adapts to the unknown smoothness of alternative functions in the presence of unknown degree of endogeneity and unknown strength of the instruments. It attains the adaptive minimax rate of testing in L². That is, the sum of the supremum of type I error over the composite null and the supremum of type II error over nonparametric alternative models cannot be minimized by any other tests for NPIV models of unknown regularities. Confidence sets in L² are obtained by inverting the adaptive test. Simulations confirm that, across different strength of instruments and sample sizes, our adaptive test controls size and its finite-sample power greatly exceeds existing non-adaptive tests for monotonicity and parametric restrictions in NPIV models. Empirical applications to test for shape restrictions of differentiated products demand and of Engel curves are presented.

A signal is privacy‐preserving with respect to a collection of privacy sets if the posterior probability assigned to every privacy set remains unchanged conditional on any signal realization. We characterize the privacy‐preserving signals for arbitrary state space and arbitrary privacy sets. A signal is privacy‐preserving if and only if it is a garbling of a reordered quantile signal. Furthermore, distributions of posterior means induced by privacy‐preserving signals are exactly mean‐preserving contractions of that induced by the quantile signal. We discuss the economic implications of our characterization for statistical discrimination, the revelation of sensitive information in auctions and price discrimination.

We develop a new equilibrium model in which households’ labour supply choices form the link between sorting on the marriage market and sorting on the labour market. We first show that in theory, the nature of home production—whether partners’ hours are complements or substitutes—shapes equilibrium labour supply as well as marriage and labour market sorting. We then estimate our model using German data to empirically assess the nature of home production, and find that spouses’ home hours are complements. We investigate to what extent complementarity in home hours drives sorting and inequality. We find that home production complementarity strengthens positive marriage sorting and reduces the gender gap in hours and in labour sorting. This puts significant downward pressure on the gender wage gap and on within-household income inequality, but fuels between-household inequality. Our estimated model sheds new light on the sources of inequality in today’s Germany, and—by identifying important shifts in home production technology toward more complementarity—on the evolution of inequality over time.

This paper studies school choice and information frictions in Haiti. Through a randomized control trial, we assess the impact of disclosing school-level test score information on learning outcomes, prices, and market shares. We find evidence that in markets where information was disclosed, students attending private schools increased test scores. The results also suggest private schools with higher baseline test scores increased their market share as well as their fees when the disclosure policy is implemented. While prices and test scores were not significantly correlated in the baseline survey, they exhibited a significant and positive correlation in treatment markets after information disclosure. These results underscore the potential of information provision to enhance market efficiency and improve children’s welfare in context such as Haiti.

We analyze representativeness in a COVID-19 serological study with randomized participation incentives. We find large participation gaps by race and income when incentives are lower. High incentives increase participation rates for all groups but increase them more among under-represented groups. High incentives restore representativeness on race and income and also on health variables likely to be correlated with seropositivity, such as the uninsured rate, hospitalization rates, and an aggregate COVID-19 risk index.

Poor entrepreneurs must frequently choose between business investment and children's education. To examine this trade-off, we exploit experimental variation in short-run microenterprise growth among a sample of Indian households and track schooling and business out-comes over eleven years. Treated households, who experience higher initial microenterprise growth, are on average one-third more likely to send children to college. However, educational investment and schooling gains are concentrated among literate-parent households, whose enterprises eventually stagnate. In contrast, illiterate-parent households experience long-run business gains but declines in children's education. Our findings suggest that microenterprise growth has the potential to reduce relative intergenerational educational mobility.

A principal incentivizes a group of agents to work by choosing a monitoring structure and a scheme of performance-contingent rewards. The monitoring structure partitions the set of agents into monitoring teams, each delivering a signal of joint performance. We show that unlike under partial implementation, the principal always exhausts her monitoring capacity to optimally implement work as a unique outcome. Optimal monitoring teams are homogeneous between them: equally sized and with agents allocated in an anti-assortative fashion. Higher-effort-cost agents receive lower rents, and they tend to be monitored more closely than lower-effort-cost agents when the principal's allocation is constrained.

A monotone function interval is the set of monotone functions that lie pointwise between two fixed monotone functions. We characterize the set of extreme points of monotone function intervals and apply this to a number of economic settings. First, we leverage the main result to characterize the set of distributions of posterior quantiles that can be induced by a signal, with applications to political economy, Bayesian persuasion, and the psychology of judgment. Second, we combine our characterization with properties of convex optimization problems to unify and generalize seminal results in the literature on security design under adverse selection and moral hazard.

A monopolist platform uses data to match heterogeneous consumers with multiproduct sellers. The consumers can purchase the products on the platform or search off the platform. The platform sells targeted ads to sellers that recommend their products to consumers and reveals information to consumers about their match values. The revenue- optimal mechanism is a managed advertising campaign that matches products and preferences efficiently. In equilibrium, sellers offer higher qualities at lower unit prices on than off platform. The platform exploits its information advantage to increase its bargaining power vis-à-vis the sellers. Finally, privacy-respecting data-governance rules can lead to welfare gains for consumers.

We study noisy aggregation of dispersed information in financial markets without imposing parametric restrictions on preferences, information, and return distributions. We provide a general characterization of asset returns by means of a risk-neutral probability measure that features excess weight on tail risks. Moreover, we link excess weight on tail risks to observable moments such as forecast dispersion and accuracy, and argue that it provides a unified explanation for several prominent cross-sectional return anomalies. Simple calibrations suggest the model can account for a significant fraction of empirical returns to skewness, returns to disagreement, and interaction effects between the two.

A buyer procures a good owned by a group of sellers whose heterogeneous cost of trade is private information. The buyer must either buy the whole good or nothing, and sellers share the transfer in proportion to their share of the good. We characterize the optimal mechanism: trade occurs if and only if the buyer's benefit of trade exceeds a weighted average of sellers' virtual costs. These weights are endogenous, with sellers who are ex ante less inclined to trade receiving higher weight. This mechanism always outperforms posted-price mechanisms. An extension characterizes the entire Pareto frontier.

We derive a small open economy (SOE) as the limit of an economy as the number or size of its trading partners goes to infinity and trade costs also go to infinity. We obtain this limit in the Armington, Eaton–Kortum, Krugman, and Melitz models. In all cases, the trade of the SOE with the foreign countries approaches a finite limit, and the domestic expenditure share for the SOE approaches a limit that is not zero or unity. The foreign countries can be either infinitely many SOEs, or alternatively, one or many large countries with domestic expenditure shares that approach unity. We illustrate the usefulness of this framework by obtaining a formula for the optimal tariff in the SOE – depending on the elasticity of domestic wages with respect to the tariff – that is consistent with all models.

Globally, preschool enrollment has surged, but its quality is often poor. We evaluate strategies to improve quality of public preschools in Colombia. The first, designed by the government and rolled out nationwide, provided extra funding, mainly earmarked for hiring teaching assistants. The second also offered low-cost training for existing teachers. The first intervention had no effect on child development, while the second improved children’s cognitive development, especially for more disadvantaged children. This pattern can be explained by the interventions affecting teachers' behavior differently. The first led teachers to reduce their classroom time, including learning activities, while additional training offset the adverse effect on learning activities and improved teaching quality.

The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a number of applications to models of individual and group decision-making. These include a representation of stationary monotone time preferences, extending the work of Fishburn and Rubinstein (1982) to time lotteries. This extension offers a new perspective on risk attitudes toward time, as well as on the aggregation of multiple discount factors. We also offer a novel class of non-expected utility preferences over gambles which satisfy invariance to background risk as well as betweenness, but are versatile enough to capture mixed risk attitudes.

We study the welfare and human capital impacts of colleges’ (non)participation in Chile’s centralized higher-education platform, leveraging administrative data and two policy changes: the introduction of a large scholarship program and the inclusion of additional institutions, which raised the number of on-platform slots by approximately 40%. We first show that the expansion of the platform raised on-time graduation rates. We then develop and estimate a model of college applications, offers, wait lists, matriculation, and graduation. When the platform expands, welfare increases, and welfare, enrollment, and graduation rates are less sensitive to off-platform frictions. Gains are larger for students from lower-socioeconomic-status backgrounds.