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 propose a method for identifying exposure to changes in trade policy based on asset prices that has several advantages over standard measures: it encompasses all avenues of exposure, it is natively firm-level, it yields estimates for both goods and service producers, and it can be used to study reductions in difficult-to-quantify non-tariff-barriers in a way that controls naturally for broader macroeconomic shocks. Applying our method to two well-studied US trade liberalizations provides new insight into service-sector responses and reveals dramatically different outcomes among small versus large firms, even within narrow industries.
We propose a theory of gradualism in the implementation of good policies, suitable for environments featuring time consistency. We downplay the role of the initial period by allowing agents both to wait for future agents to start equilibrium play and to restart the equilibrium by ignoring past history. The allocation gradually transits toward one that weighs both short- and long-term concerns, stopping short of the Ramsey outcome but greatly improving upon Markovian equilibria. We use the theory to account for the slow emergence of both climate policies and the reduction of global tariff rates.
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 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.
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.
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.