Properties of GMM estimators are sensitive to the choice of instruments. Usingmany instruments leads to high asymptotic asymptotic efficiency but can causehigh bias and/or variance in small samples. In this paper we develop and implementasymptotic mean square error (MSE) based criteria for...

There are many economic parameters that depend on nonparametric first steps. Examples include games, dynamic discrete choice, average exact consumer surplus, and treatment effects. Often estimators of these parameters are asymptotically equivalent to a sample average of an object referred to as...

Individual heterogeneity is an important source of variation in demand. Allowing for general heterogeneity is needed for correct welfare comparisons. We consider general heterogenous demand where preferences and linear budget sets are statistically independent. Only the marginal distribution of...

Many studies have estimated the effect of taxes on taxable income. To account for nonlinear taxes these studies either use instrumental variables approaches that are not fully consistent or impose strong functional form assumptions. None allow for general heterogeneity in preferences. In this...

The linear regression model is widely used in empirical work in Economics. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We give inference methods that allow for many covariates and heteroskedasticity. Our results are...

Many empirical studies estimate the structural effect of some variable on an outcome of interest while allowing for many covariates. We present inference methods that account for many covariates. The methods are based on asymptotics where the number of covariates grows as fast as the sample...

Often semiparametric estimators are asymptotically equivalent to a sample average. The object being averaged is referred to as the influence function. The influence function is useful in formulating primitive regularity conditions for asymptotic normality, in efficiency comparions, for bias...

Triangular systems with nonadditively separable unobserved heterogeneity provide a theoretically appealing framework for the modeling of complex structural relationships. However, they are not commonly used in practice due to the need for exogenous variables with large support for...

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...

Multidimensional heterogeneity and endogeneity are important features of models with multiple treatments. We consider a heterogeneous coefficients model where the outcome is a linear combination of dummy treatment variables, with each variable representing a different kind of treatment. We use...