Professor Joel L. Horowitz

This paper describes three methods for carrying out non-asymptotic inference on partially identified parameters that are solutions to a class of optimization problems.

We show the importance of Berkson errors for demand estimation with nonseparable unobserved heterogeneity.

The multinomial logit model with random coefficients is widely used in applied research. This paper is concerned with estimating a random coefficients logit model in which the distribution of each coefficient is characterized by finitely many parameters.

This paper describes a method for carrying out non-asymptotic inference on partially identified parameters that are solutions to a class of optimization problems. The optimization problems arise in applications in which grouped data are used for estimation of a model's structural parameters. The parameters are characterized by restrictions that involve the population means of observed random variables in addition to the structural parameters of interest. Inference consists of finding confidence intervals for the structural parameters. Our method is non-asymptotic in the sense that it provides a finite-sample bound on the difference between the true and nominal probabilities with which a confidence interval contains the true but unknown value of a parameter. We contrast our method with an alternative non-asymptotic method based on the median-of-means estimator of Minsker (2015). The results of Monte Carlo experiments and an empirical example illustrate the usefulness of our method.

e develop a consistent estimator using external information on the true distribution of prices. Examining the demand for gasoline in the U.S., accounting for Berkson errors is found to be quantitatively important for estimating price effects and for welfare calculations. Imposing the Slutsky shape constraint greatly reduces the sensitivity to Berkson errors.

This article explains the usefulness and limitations of the bootstrap in contexts of interest in econometrics.

This paper presents a simple method for carrying out inference in a wide variety of possibly nonlinear IV models under weak assumptions.

The multinomial logit model with random coefficients is widely used in applied research. This paper is concerned with estimating a random coefficients logit model in which the distribution of each coefficient is characterized by finitely many parameters.

Economic data are often generated by stochastic processes that take place in continuous time, though observations may occur only at discrete times.

This paper presents a simple non-asymptotic method for carrying out inference in IV models.

Economic theory often provides shape restrictions on functions of interest in applications, such as monotonicity, convexity, non-increasing (non-decreasing) returns to scale, or the Slutsky inequality of consumer theory; but economic theory does not provide finite-dimensional parametric models. This motivates nonparametric estimation under shape restrictions. Nonparametric estimates are often very noisy. Shape restrictions stabilize nonparametric estimates without imposing arbitrary restrictions, such as additivity or a single-index structure, that may be inconsistent with economic theory and the data. This paper explains how to estimate and obtain an asymptotic uniform confidence band for a conditional mean function under possibly nonlinear shape restrictions, such as the Slutsky inequality. The results of Monte Carlo experiments illustrate the finite-sample performance of the method, and an empirical example illustrates its use in an application.

We derive conditions under which a demand function with nonseparable unobserved heterogeneity in tastes can be estimated consistently by nonparametric quantile regression subject to the shape restriction from the Slutsky inequality.

A bootstrap method for constructing pointwise and uniform confidence bands for conditional quantile functions

Economic theory often provides shape restrictions on functions of interest in applications, such as monotonicity, convexity, non-increasing (non-decreasing) returns to scale, or the Slutsky inequality of consumer theory; but economic theory does not provide finite-dimensional parametric models. This motivates nonparametric estimation under shape restrictions. Nonparametric estimates are often very noisy. Shape restrictions stabilize nonparametric estimates without imposing arbitrary restrictions, such as additivity or a single-index structure, that may be inconsistent with economic theory and the data. This paper explains how to estimate and obtain an asymptotic uniform confidence band for a conditional mean function under possibly nonlinear shape restrictions, such as the Slutsky inequality. The results of Monte Carlo experiments illustrate the finite-sample performance of the method, and an empirical example illustrates its use in an application.

In this paper we propose a novel method to construct confidence intervals in a class of linear inverse problems.

This paper is concerned with inference about an unidentified linear functional, L(g), where g satisfies Y=g(X)+U; E(U|W)=0.

This paper presents a test for exogeneity of explanatory variables in a nonparametric instrumental variables (IV) model whose structural function is identified through a conditional quantile restriction. Quantile regression models are increasingly important in applied econometrics.

This paper explains how to estimate and obtain an asymptotic uniform confidence band for a conditional mean function under possibly nonlinear shape restrictions, such as the Slutsky inequality.

Models with high-dimensional covariates arise frequently in economics and other fields. This paper reviews methods for discriminating between important and unimportant covariates with particular attention given to methods that discriminate correctly with probability approaching 1 as the sample size increases.