Publications

Here we provide our solutions to the First Proof questions. We also discuss the best responses from publicly available AI systems that we were able to obtain in our experiments prior to the release of the problems on February 5, 2025. We hope this discussion will help readers with the relevant domain expertise to assess such responses.

I estimate the effect of trade on local labor market concentration and its implications for wages using employer-employee linked data and tariff shocks from Brazil’s trade liberalization. Trade increased concentration by 7%, an effect driven by firm exit and worker flows to surviving import-competing firms. Increased concentration reduced wage take-home shares—estimated at 50 cents on the dollar pre-shock—enough to offset small wage gains from reallocation, but did not meaningfully reduce wages on net. Most of the wage declines attributed to Brazil’s trade liberalization resulted instead from reductions in the marginal revenue product of labor. Incorporating informality reveals substantial regional heterogeneity.

We develop a new approach to estimating earnings, job, and employment dynamics using subjective expectations data from the NY Fed Survey of Consumer Expectations. These data provide beliefs about future earnings offers and acceptance probabilities, offering direct information on counterfactual outcomes and enabling identification under weaker assumptions. Our framework avoids biases from selection and unobserved heterogeneity that affect models using realized outcomes. First-step fixed-effects regressions identify risk, persistence, and transition effects; second-step GMM recovers the covariance structure of unobserved heterogeneities such as ability, mobility, and match quality. We find lower risk and persistence of the individual productivity component than in prior work, but greater heterogeneity in ability and match quality. Simulations show that reduced-form estimates overstate persistence and volatility on individual-level productivity due to job transitions and sorting. After accounting for heterogeneity, volatility declines and becomes flat across the earnings distribution. These results underscore the value of expectations data.

In this paper, we propose a triple (or double-debiased) Lasso estimator for inference on a low-dimensional parameter in high-dimensional linear regression models. The estimator is based on a moment function that satisfies not only first- but also second-order Neyman orthogonality conditions, thereby eliminating both the leading bias and the second-order bias induced by regularization. We derive an asymptotic linear representation for the proposed estimator and show that its remainder terms are never larger and are often smaller in order than those in the corresponding asymptotic linear representation for the standard double Lasso estimator. Because of this improvement, the triple Lasso estimator often yields more accurate finite-sample inference and confidence intervals with better coverage. Monte Carlo simulations confirm these gains. In addition, we provide a general recursive formula for constructing higher-order Neyman orthogonal moment functions in Z-estimation problems, which underlies the proposed estimator as a special case.

We study optimization problems in which a linear functional is maximized over probability measures that are dominated by a given measure according to an integral stochastic order in an arbitrary dimension. We show that the following four properties are equivalent for any such order: (i) the test function cone is closed under pointwise minimum, (ii) the value function is affine, (iii) the solution correspondence has a convex graph with decomposable extreme points, and (iv) every ordered pair of measures admits an order-preserving coupling. As corollaries, we derive the extreme and exposed point properties involving integral stochastic orders such as multidimensional mean-preserving spreads and stochastic dominance. Applying these results, we generalize Blackwell's theorem by completely characterizing the comparisons of experiments that admit two equivalent descriptions—through instrumental values and through information technologies. We also show that these results immediately yield new insights into information design, mechanism design, and decision theory.