Yu-Chin Hsu

Improving the Power of Tests of Stochastic Dominance

We extend Hansens (2005) recentering method to a continuum of inequality constraints to construct new Kolmogorov–Smirnov tests for stochastic dominance of any pre-specified order. We show that our tests have correct size asymptotically, are consistent against fixed alternatives and are unbiased against some N−1/2 local alternatives. It is shown that by avoiding the use of the least favorable configuration, our tests are less conservative and more powerful than Barrett and Donalds (2003) and in some simulation examples we consider, we find that our tests can be more powerful than the subsampling test of Linton et al. (2005). We apply our method to test stochastic dominance relations between Canadian income distributions in 1978 and 1986 as considered in Barrett and Donald (2003) and find that some of the hypothesis testing results are different using the new method.

Incorporating Covariates in the Measurement of Welfare and Inequality: Methods and Applications

Methods for comparing social welfare and inequality across populations typically involve the entire distribution of economic wellbeing. Conditional analysis requires an estimate of the entire distribution conditional on a large set of covariates. In this paper, we present methods for estimating conditional distributions including flexible parametric, semiparametric and non‐parametric approaches. We demonstrate how to use the statistical properties of the estimators to conduct inference for welfare and inequality comparisons conditional on covariates. Further, we consider how to use the results to perform counterfactual analysis.

Testing the Unconfoundedness Assumption via Inverse Probability Weighted Estimators of (L)ATT

We propose inverse probability weighted estimators for the local average treatment effect (LATE) and the local average treatment effect for the treated (LATT) under instrumental variable assumptions with covariates. We show that these estimators are asymptotically normal and efficient. When the (binary) instrument satisfies one-sided noncompliance, we propose a Durbin–Wu–Hausman-type test of whether treatment assignment is unconfounded conditional on some observables. The test is based on the fact that under one-sided noncompliance LATT coincides with the average treatment effect for the treated (ATT). We conduct Monte Carlo simulations to demonstrate, among other things, that part of the theoretical efficiency gain afforded by unconfoundedness in estimating ATT survives pretesting. We illustrate the implementation of the test on data from training programs administered under the Job Training Partnership Act in the United States. This article has online supplementary material.

Estimating Conditional Average Treatment Effects

We consider a functional parameter called the conditional average treatment effect (CATE), designed to capture the heterogeneity of a treatment effect across subpopulations when the unconfoundedness assumption applies. In contrast to quantile regressions, the subpopulations of interest are defined in terms of the possible values of a set of continuous covariates rather than the quantiles of the potential outcome distributions. We show that the CATE parameter is nonparametrically identified under unconfoundedness and propose inverse probability weighted estimators for it. Under regularity conditions, some of which are standard and some are new in the literature, we show (pointwise) consistency and asymptotic normality of a fully nonparametric and a semiparametric estimator. We apply our methods to estimate the average effect of a first-time mother’s smoking during pregnancy on the baby’s birth weight as a function of the mother’s age. A robust qualitative finding is that the expected effect becomes stronger (more negative) for older mothers.

Cyclical Co-Movement Between Output, the Price-Level, and the Inflation Rate

In this chapter, we examine the relationship between the cyclical components of output, the price level and the inflation rate. During the post-war period, there is a negative correlation between output and the price level and a positive correlation between output and the inflation rate. A phase shift in the cyclical component between output and the price level can account for these two facts. The phase shift is consistent with movements in the price level Granger causes movements in output. In addition, we consider time-varying correlations between the two pairs of series. Spectral analysis suggest the price and output have different wavelengths, but the difference is not statistically significant.

Robust Hypothesis Tests for M-Estimators with Possibly Non-differentiable Estimating Functions

We propose a new robust hypothesis test for (possibly nonlinear) constraints on Mestimators with possibly non-differentiable estimating functions. The proposed test employs a random normalizing matrix computed from recursive M-estimators to eliminate the nuisance parameters arising from the asymptotic covariance matrix. It does not require consistent estimation of any nuisance parameters, in contrast with the conventional heteroskedasticity autocorrelation consistent (HAC)-type test and the KVB-type test of Kiefer, Vogelsang, and Bunzel (2000). Our test reduces to the KVB-type test in simple location models with OLS estimation, so the error in rejection probability of our test in a Gaussian location model is OIP(T−1 log T). We discuss robust testing in quantile regression, and censored regression models in details. In simulation studies, we find that our test has better size control and better finite sample power than the HAC-type and KVB-type tests.

A Stochastic Frontier Model with Endogenous Treatment Status and Mediator

Government policies are frequently used to promote productivity. Some policies are designed to enhance production technology, while others are meant to improve production efficiency. An important issue to consider when designing and evaluating policies is whether a mediator is required or effective in achieving the desired final outcome. To better understand and evaluate the policies, we propose a new stochastic frontier model with a treatment status and a mediator, both of which are allowed to be endogenous. The model allows us to decompose the total program (treatment) effect into technology and efficiency components, and to investigate whether the effect is derived directly from the program or indirectly through a particular mediator. Supplementary materials for this article are available online.

Model Selection Tests for Conditional Moment Restriction Models

We propose a Vuong (1989)-type model-selection test for models defined by conditional moment restrictions. The moment restrictions that define the models can be standard equality restrictions that point-identify the model parameters, or moment equality or inequality restrictions that partially identify the model parameters. The test uses a new average generalized empirical likelihood criterion function designed to incorporate full restriction of the conditional model. We also introduce a new adjustment to the test statistic that makes it asymptotically pivotal whether the candidate models are nested or nonnested. The test uses simple standard normal critical values and is shown to be asymptotically similar, to be consistent against all fixed alternatives, and to have nontrivial power against n−1=2-local alternatives. Monte Carlo simulations demonstrate that the finite sample performance of the test is in accordance with the theoretical prediction. This article is protected by copyright. All rights reserved