We derive general, yet simple, sharp bounds on the size of the omitted variable bias for a broad class of causal parameters that can be identified as linear functionals of the conditional expectation function of the outcome. Such functionals encompass many of the traditional targets of...

In this paper, we provide a suite of tools for empirical market design, including optimal nonlinear pricing in intensive-margin consumer demand, as well as a broad class of related adverse-selection models. Despite significant data limitations, we are able to derive informative bounds on demand...

This paper analyzes difference-in-differences designs with a continuous treatment. We show that treatment effect on the treated-type parameters can be identified under a generalized parallel trends assumption that is similar to the binary treatment setup. However, interpreting differences in...

Inverse problems can be described as functional equations where the value of the function is known or easily estimable but the argument is unknown. Many problems in econometrics can be stated in the form of inverse problems where the argument itself is a function. For example, consider a...

This chapter reviews recent advances in nonparametric and semiparametric estimation, with an emphasis on applicability to empirical research and on resolving issues that arise in implementation. It considers techniques for estimating densities, conditional mean functions, derivatives of...

This paper develops linear estimators for structural and causal parameters in nonparametric,nonseparable models using panel data. These models incorporate unobserved, time-varying, individual heterogeneity, which may be correlated with the regressors. Estimation is based on an approximation of...