Measurement

This paper derives conditions under which preferences and technology are nonparametrically identified in hedonic equilibrium models, where products are differentiated along more than one dimension and agents are characterized by several dimensions of unobserved heterogeneity.

We propose a bootstrap-based calibrated projection procedure to build confidence intervals for single components and for smooth functions of a partially identified parameter vector in moment (in)equality models. The method controls asymptotic coverage uniformly over a large class of data generating processes.

Econometrics has traditionally revolved around point identication. Much effort has been devoted to finding the weakest set of assumptions that, together with the available data, deliver point identification of population parameters, finite or infinite dimensional that these might be. And point identification has been viewed as a necessary prerequisite for meaningful statistical inference. The research program on partial identification has begun to slowly shift this focus in the early 1990s, gaining momentum over time and developing into a widely researched area of econometrics.

To perform Bayesian analysis of a partially identified structural model, two distinct approaches exist: standard Bayesian inference, which assumes a single prior for the structural parameters, including the non-identified ones; and multiple-prior Bayesian inference, which assumes full ambiguity for the non-identified parameters. The prior inputs considered by these two extreme approaches can often be a poor representation of the researcher’s prior knowledge in practice.

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.

There exists a useful framework for jointly implementing Durbin-Wu-Hausman exogeneity and Sargan-Hansen overidentication tests, as a single articial regression. This note sets out the framework for linear models and discusses its extension to non-linear models. It also provides an empirical example and some Monte Carlo results.

In a randomized control trial, the precision of an average treatment effect estimator and the power of the corresponding t-test can be improved either by collecting data on additional individuals, or by collecting additional covariates that predict the outcome variable. To design the experiment, a researcher needs to solve this tradeoff subject to her budget constraint. We show that this optimization problem is equivalent to optimally predicting outcomes by the covariates, which in turn can be solved using existing machine learning techniques using pre-experimental data such as other similar studies, a census, or a household survey. In two empirical applications, we show that our procedure can lead to reductions of up to 58% in the costs of data collection, or improvements of the same magnitude in the precision of the treatment effect estimator.

In this paper we investigate panel regression models with interactive fixed effects. We propose two new estimation methods that are based on minimizing convex objective functions.

We propose to combine smoothing, simulations and sieve approximations to solve for either the integrated or expected value function in a general class of dynamic discrete choice (DDC) models.

Efron's elegant approach to g-modeling for empirical Bayes problems is contrasted with an implementation of the Kiefer-Wolfowitz nonparametric maximum likelihood estimator for mixture models for several examples. The latter approach has the advantage that it is free of tuning parameters and consequently provides a relatively simple complementary method.

This paper examines the asymptotic behavior of the posterior distribution of a possibly nondifferentiable function g(θ), where θ is a finite-dimensional parameter of either a parametric or semiparametric model. The main assumption is that the distribution of a suitable estimator θ^n, its bootstrap approximation, and the Bayesian posterior for θ all agree asymptotically.

I develop a model of a randomized experiment with a binary intervention and a binary outcome. Potential outcomes in the intervention and control groups give rise to four types of participants. Fixing ideas such that the outcome is mortality, some participants would live regardless, others would be saved, others would be killed, and others would die regardless. These potential outcome types are not observable. However, I use the model to develop estimators of the number of participants of each type.

We propose a new specification test for assessing the validity of fuzzy regression discontinuity designs (FRD-validity). We derive a new set of testable implications, characterized by a set of inequality restrictions on the joint distribution of observed outcomes and treatment status at the cut-off.

The LATE monotonicity assumption of Imbens and Angrist (1994) precludes "defiers," individuals whose treatment always runs counter to the instrument, in the terminology of Balke and Pearl (1993) and Angrist et al. (1996). I allow for defiers in a model with a binary instrument and a binary treatment.

This paper provides inference methods for best linear approximations to functions which are known to lie within a band. It extends the partial identification literature by allowing the upper and lower functions dening the band to carry an index, and to be unknown but parametrically or non-parametrically estimable functions.

This paper is concerned with learning decision makers' (DMs) preferences using data on observed choices from a finite set of risky alternatives with monetary outcomes.

The particular concern of this paper is the construction of a confidence region with pointwise asymptotically correct size for the true value of a parameter of interest based on the generalized Anderson-Rubin (GAR) statistic when the moment variance matrix is singular.

The Wald development of statistical decision theory addresses decision making with sample data. Wald's concept of a statistical decision function (SDF) embraces all mappings of the form [data => decision]. An SDF need not perform statistical inference; that is, it need not use data to draw conclusions about the true state of nature. Inference-based SDFs have the sequential form [data => inference => decision]. This paper offers remarks on the use of statistical inference in statistical decisions.

In a model with endogenous regressors, heteroskedastic and autocorrelated (HAC) errors and weak instruments, tests that depend on the data only through the Anderson-Rubin (AR) and Lagrange Multiplier (LM) statistics ignore important information on the regression coefficients. This is in contrast to the homoskedastic case, where these statistics, together with the rank statistic, are one-to-one with the maximal invariant. The information loss with heteroskedastic and/or autocorrelated errors can be so extreme that the LM and conditional quasi-likelihood ratio (CQLR) tests have power close to size when it is trivial to distinguish the null from the alternative hypothesis. The severe loss of power can occur if the Hermitian part of the reduced-form covariance matrix has eigenvalues of opposite signs.

This paper studies inference in randomized controlled trials with covariate-adaptive randomization when there are multiple treatments. More specically, we study in this setting inference about the average effect of one or more treatments relative to other treatments or a control.