This paper considers two-sided tests for the parameter of an endogenous variable in an instrumental variable (IV) model with heteroskedastic and autocorrelated errors. We develop the finite-sample theory of weighted-average power (WAP) tests with normal errors and a known long-run variance. We...

This paper considers the problem of testing many moment inequalities where the number of moment inequalities, denoted by p, is possibly much larger than the sample size n. There are variety of economic applications where the problem of testing many moment in- equalities appears; a notable...

This paper examines the asymptotic behavior of the posterior distribution of a possibly nondifferentiable function g(theta), where is a finite dimensional parameter. The main assumption is that the distribution of the maximum likelihood estimator theta_n, its bootstrap approximation, and the...

This paper makes several contributions to the literature on the important yet difficult problem of estimating functions nonparametrically using instrumental variables. First, we derive the minimax optimal sup-norm convergence rates for nonparametric instrumental variables (NPIV) estimation of...

This paper considers the problem of testing many moment inequalities where the number of moment inequalities, denoted by p, is possibly much larger than the sample size n. There are a variety of economic applications where the problem of testing many moment in- equalities appears; a notable...

This paper examines the asymptotic behavior of the posterior distribution of a possibly nondifferentiable function g(theta), where theta is a finite-dimensional parameter of either a parametric or semiparametric model. The main assumption is that the distribution of a suitable estimator theta_n,...

We show that the identification results of finite mixture and misclassification models are equivalent in a widely-used scenario except an extra ordering assumption. In the misclassification model, an ordering condition is imposed to pin down the precise values of the latent variable, which are...

This chapter presents key concepts and theoretical results for analyzing estimation and inference in high-dimensional models. High-dimensional models are characterized by having a number of unknown parameters that is not vanishingly small relative to the sample size. We first present results in...

This paper develops a specification test for instrument validity in the heterogeneous treatment effect model with a binary treatment and a discrete instrument. The strongest testable implication for instrument validity is given by the condition for nonnegativity of point-identifiable complier's...

This paper is concerned with inference about an unidentified linear functional, L(g), where the function g satisfies the relation Y=g(x) + U; E(U/W) = 0. In this relation, Y is the dependent variable, X is a possibly endogenous explanatory variable, W is an instrument for X, and U is an...