The role of propensity score in the efficient estimation of the average treatment effects is examined. If the treatment is ignorable given some observed characteristics, it is shown that the propensity score is ancillary for estimation of the average treatment effects but not for estimation of average treatment effects on the treated. Efficient semiparametric estimators take the form of relevant sample averages of the data completed by the nonparametric imputation method. Projection on the propensity score is not necessary for efficient semiparametric estimation of the average treatment effects on the treated even if the propensity score is known.

February 01 2004 Functional Restriction and Efficiency in Causal Inference Jinyong Hahn Jinyong Hahn UCLA Search for other works by this author on: This Site Google Scholar Author and Article Information Jinyong Hahn UCLA Received: July 11 2001 Accepted: February 13 2003 Online Issn: 1530-9142 Print Issn: 0034-6535 © 2004 President and Fellows of Harvard College and the Massachusetts Institute of Technology2004 The Review of Economics and Statistics (2004) 86 (1): 73–76. https://doi.org/10.1162/003465304323023688 Article history Received: July 11 2001 Accepted: February 13 2003 Cite Icon Cite Permissions Share Icon Share MailTo Twitter LinkedIn Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Search Site Citation Jinyong Hahn; Functional Restriction and Efficiency in Causal Inference. The Review of Economics and Statistics 2004; 86 (1): 73–76. doi: https://doi.org/10.1162/003465304323023688 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAll JournalsThe Review of Economics and Statistics Search Advanced Search This content is only available as a PDF. © 2004 President and Fellows of Harvard College and the Massachusetts Institute of Technology2004 Article PDF first page preview Close Modal You do not currently have access to this content.

Fixed effects estimators of panel models can be severely biased because of the well-known incidental parameters problem. We show that this bias can be reduced by using a panel jackknife or an analytical bias correction motivated by large T. We give bias corrections for averages over the fixed effects, as well as model parameters. We find large bias reductions from using these approaches in examples. We consider asymptotics where T grows with n, as an approximation to the properties of the estimators in econometric applications. We show that if T grows at the same rate as n, the fixed effects estimator is asymptotically biased, so that asymptotic confidence intervals are incorrect, but that they are correct for the panel jackknife. We show T growing faster than n-super-1/3 suffices for correctness of the analytic correction, a property we also conjecture for the jackknife. Copyright The Econometric Society 2004.

The problem of when to control for continuous or high-dimensional discrete covariate vectors arises in both experimental and observational studies. Large-cell asymptotic arguments suggest that full control for covariates or stratification variables is always efficient, even if treatment is assigned independently of covariates or strata. Here, we approximate the behavior of different estimators using a panel-data-type asymptotic sequence with fixed cell sizes and the number of cells increasing to infinity. Exact calculations in simple examples and Monte Carlo evidence suggest this generates a substantially improved approximation to actual finite-sample distributions. Under this sequence, full control for covariates is dominated by propensity-score matching when cell sizes are small, the explanatory power of the covariates conditional on the propensity score is low, and/or the probability of treatment is close to 0 or 1. Our panel-asymptotic framework also provides an explanation for why propensity-score matching can dominate covariate matching even when there are no empty cells. Finally, we introduce a random-effects estimator that provides finite-sample efficiency gains over both covariate matching and propensity-score matching.

What is the weak-instruments (WI) problem and what causes it? Universal agreement does not exist on these questions. We define weak instruments by two features: (i) two-stage least squares (2SLS) analysis is badly biased toward the ordinary least-squares (OLS) estimate, and alternative “unbiased” estimators such as limited-information maximum likelihood (LIML) may not solve the problem; and (ii) the standard (first-order) asymptotic distribution does not give an accurate framework for inference. Thus, a researcher may estimate “bad results” and not be aware of the outcome. The cause of WI is often stated to be a low R or F statistic of the reduced-form equation, in the most commonly occurring situation of one right-handside endogenous variable. We find the situation is more complex with an additional factor, the correlation between the stochastic disturbances of the structural equation and the reduced form, that needs to be taken into account. We discuss in this paper a specification test (Hahn and Hausman, 2002a) for WI, a caution against using “no moments” estimators such as LIML in the WI situation, and suggestions for different estimators, an approach to inference of Frank Kleibergen (2002) for WI. We end with a caution of how “small biases” can become “large biases” in the WI situation. We begin with the limited-information structural model under the assumptions of Hausman (1983):

Asymptotic justification of the bootstrap often takes the form of weak convergence of the bootstrap distribution to some limit distribution. Theoretical literature recognized that the weak convergence does not imply consistency of the bootstrap second moment or the bootstrap variance as an estimator of the asymptotic variance, but such concern is not always reflected in the applied practice. We bridge the gap between the theory and practice by showing that such common bootstrap based standard error in fact leads to a potentially conservative inference.

We study the asymptotic distribution of three-step estimators of a finite-dimensional parameter vector where the second step consists of one or more nonparametric regressions on a regressor that is estimated in the first step. The first-step estimator is either parametric or nonparametric. Using Newey's (1994) path-derivative method, we derive the contribution of the first-step estimator to the influence function. In this derivation, it is important to account for the dual role that the first-step estimator plays in the second-step nonparametric regression, that is, that of conditioning variable and that of argument.

This paper introduces an alternative estimator for the linear censored quantile regression model. The estimator also applies to cases where the censoring point is unknown. Since the objective function is globally convex and the estimator is a solution to a linear programming problem, a global minimizer is obtained in a finite number of simplex iterations. The estimator has a square root of n-convergence rate and is asymptotically normal. A Monte Carlo study performed shows that the suggested estimator has very desirable small sample properties.

It is shown that in a nonparametric nonseparable triangular system, the conditional moment restriction (CMR) does not identify the average structural function (ASF). The CMR identifies the ASF only if the model is structurally separable in observable covariates and unobservable random errors. This excludes, for instance, random coefficient models in which the CMR in general does not identify the average response. An implication of our results is that empirical researchers should use methods other than CMR if they want to estimate the average response in models that are not additively separable.

Ž. THE REGRESSION DISCONTINUITY RD data design is a quasi-experimental design with the defining characteristic that the probability of receiving treatment changes discontinuously as a function of one or more underlying variables. This data design arises frequently in economic and other applications but is only infrequently exploited as a source of identifying information in evaluating effects of a treatment. In the first application and discussion of the RD method, Thistlethwaite and Campbell Ž. 1960 study the effect of student scholarships on career aspirations, using the fact that awards are only made if a test score exceeds a threshold. More recently, Van der Klaauw Ž. 1997 estimates the effect of financial aid offers on students’ decisions to attend a particular college, taking into account administrative rules that set the aid amount partly on the basis of a discontinuous function of the students’ grade point average and SAT Ž. score. Angrist and Lavy 1999 estimate the effect of class size on student test scores, taking advantage of a rule stipulating that another classroom be added when the average Ž. class size exceeds a threshold level. Finally, Black 1999 uses an RD approach to estimate parents’ willingness to pay for higher quality schools by comparing housing prices near geographic school attendance boundaries. Regression discontinuity methods have potentially broad applicability in economic research, because geographic boundaries or rules governing programs often create discontinuities in the treatment assignment mechanism that can be exploited under the method. Although there have been several discussions and applications of RD methods in the literature, important questions still remain concerning sources of identification and ways of estimating treatment effects under minimal parametric restrictions. Here, we show that identifying conditions invoked in previous applications of RD methods are often overly strong and that treatment effects can be nonparametrically identified under an RD design by a weak functional form restriction. The restriction is unusual in that it requires imposing continuity assumptions in order to take advantage of the known discontinuity in the treatment assignment mechanism. We also propose a way of nonparametrically estimating treatment effects and offer an interpretation of the Wald estimator as an RD estimator.