The second edition of this acclaimed graduate text provides a unified treatment of two methods used in contemporary econometric research, cross section and data panel methods. By focusing on assumptions that can be given behavioral content, the book maintains an appropriate level of rigor while emphasizing intuitive thinking. The analysis covers both linear and nonlinear models, including models with dynamics and/or individual heterogeneity. In addition to general estimation frameworks (particular methods of moments and maximum likelihood), specific linear and nonlinear methods are covered in detail, including probit and logit models and their multivariate, Tobit models, models for count data, censored and missing data schemes, causal (or treatment) effects, and duration analysis. Econometric Analysis of Cross Section and Panel Data was the first graduate econometrics text to focus on microeconomic data structures, allowing assumptions to be separated into population and sampling assumptions. This second edition has been substantially updated and revised. Improvements include a broader class of models for missing data problems; more detailed treatment of cluster problems, an important topic for empirical researchers; expanded discussion of "generalized instrumental variables" (GIV) estimation; new coverage (based on the author's own recent research) of inverse probability weighting; a more complete framework for estimating treatment effects with panel data, and a firmly established link between econometric approaches to nonlinear panel data and the "generalized estimating equation" literature popular in statistics and other fields. New attention is given to explaining when particular econometric methods can be applied; the goal is not only to tell readers what does work, but why certain "obvious" procedures do not. The numerous included exercises, both theoretical and computer-based, allow the reader to extend methods covered in the text and discover new insights.

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Econometric Analysis of Cross Section and Panel Data

Propensity score matching (PSM) has become a popular approach to estimate causal treatment effects. It is widely applied when evaluating labour market policies, but empirical examples can be found in very diverse fields of study. Once the researcher has decided to use PSM, he is confronted with a lot of questions regarding its implementation. To begin with, a first decision has to be made concerning the estimation of the propensity score. Following that one has to decide which matching algorithm to choose and determine the region of common support. Subsequently, the matching quality has to be assessed and treatment effects and their standard errors have to be estimated. Furthermore, questions like 'what to do if there is choice-based sampling?' or 'when to measure effects?' can be important in empirical studies. Finally, one might also want to test the sensitivity of estimated treatment effects with respect to unobserved heterogeneity or failure of the common support condition. Each implementation step involves a lot of decisions and different approaches can be thought of. The aim of this paper is to discuss these implementation issues and give some guidance to researchers who want to use PSM for evaluation purposes.

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Some practical guidance for the implementation of propensity score matching

This paper considers whether it is possible to devise a nonexperimental procedure for evaluating a prototypical job training programme. Using rich nonexperimental data, we examine the performance of a two-stage evaluation methodology that (a) estimates the probability that a person participates in a programme and (b) uses the estimated probability in extensions of the classical method of matching. We decompose the conventional measure of programme evaluation bias into several components and find that bias due to selection on unobservables, commonly called selection bias in econometrics, is empirically less important than other components, although it is still a sizeable fraction of the estimated programme impact. Matching methods applied to comparison groups located in the same labour markets as participants and administered the same questionnaire eliminate much of the bias as conventionally measured, but the remaining bias is a considerable fraction of experimentally-determined programme impact estimates. We test and reject the identifying assumptions that justify the classical method of matching. We present a nonparametric conditional difference-in-differences extension of the method of matching that is consistent with the classical index-sufficient sample selection model and is not rejected by our tests of identifying assumptions. This estimator is effective in eliminating bias, especially when it is due to temporally-invariant omitted variables.

Matching As An Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme

When estimating causal effects using observational data, it is desirable to replicate a randomized experiment as closely as possible by obtaining treated and control groups with similar covariate distributions. This goal can often be achieved by choosing well-matched samples of the original treated and control groups, thereby reducing bias due to the covariates. Since the 1970's, work on matching methods has examined how to best choose treated and control subjects for comparison. Matching methods are gaining popularity in fields such as economics, epidemiology, medicine, and political science. However, until now the literature and related advice has been scattered across disciplines. Researchers who are interested in using matching methods-or developing methods related to matching-do not have a single place to turn to learn about past and current research. This paper provides a structure for thinking about matching methods and guidance on their use, coalescing the existing research (both old and new) and providing a summary of where the literature on matching methods is now and where it should be headed.

/pdf/matching-methods-for-causal-inference-a-review-and-a-look-1133erv7vp.pdf

Matching Methods for Causal Inference: A Review and a Look Forward

This paper considers causal inference and sample selection bias in nonexperimental settings in which (i) few units in the nonexperimental comparison group are comparable to the treatment units, and (ii) selecting a subset of comparison units similar to the treatment units is difficult because units must be compared across a high-dimensional set of pre-treatment characteristics. We discuss the use of propensity score-matching methods, and implement them using data from the National Supported Work experiment. Following LaLonde (1986), we pair the experimental treated units with nonexperimental comparison units from the CPS and PSID, and compare the estimates of the treatment effect obtained using our methods to the benchmark results from the experiment. For both comparison groups, we show that the methods succeed in focusing attention on the small subset of the comparison units comparable to the treated units and, hence, in alleviating the bias due to systematic differences between the treated and compariso...

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Propensity score-matching methods for nonexperimental causal studies

This paper develops the method of matching as an econometric evaluation estimator. A rigorous distribution theory for kernel-based matching is presented. The method of matching is extended to more general conditions than the ones assumed in the statistical literature on the topic. We focus on the method of propensity score matching and show that it is not necessarily better, in the sense of reducing the variance of the resulting estimator, to use the propensity score method even if propensity score is known. We extend the statistical literature on the propensity score by considering the case when it is estimated both parametrically and nonparametrically. We examine the benefits of separability and exclusion restrictions in improving the efficiency of the estimator. Our methods also apply to the econometric selection bias estimator. Matching is a widely-used method of evaluation. It is based on the intuitively attractive idea of contrasting the outcomes of programme participants (denoted Y1) with the outcomes of "comparable" nonparticipants (denoted Y0). Differences in the outcomes between the two groups are attributed to the programme. Let 1 and 11 denote the set of indices for nonparticipants and participants, respectively. The following framework describes conventional matching methods as well as the smoothed versions of these methods analysed in this paper. To estimate a treatment effect for each treated person iecI, outcome Yli is compared to an average of the outcomes Yoj for matched persons je10 in the untreated sample. Matches are constructed on the basis of observed characteristics X in Rd. Typically, when the observed characteristics of an untreated person are closer to those of the treated person ieI1, using a specific distance measure, the untreated person gets a higher weight in constructing the match. The estimated gain for each person i in the treated sample is

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Matching As An Econometric Evaluation Estimator

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.

https://faculty.smu.edu/millimet/classes/eco7377/papers/hahn et al 00.pdf

Identification and estimation of treatment effects with a regression-discontinuity design

https://ir.lib.uwo.ca/cgi/viewcontent.cgi?article=1037&context=economicscibc

Does matching overcome LaLonde's critique of nonexperimental estimators?

Semiparametric methods are developed to estimate the bias that arises from using nonexperimental comparison groups to evaluate social programs and to test the identifying assumptions that justify matching, selection models, and the method of difference-in-differences. Using data from an experiment on a prototypical social program and data from nonexperimental comparison groups, we reject the assumptions justifying matching and our extensions of it. The evidence supports the selection bias model and the assumptions that justify a semiparametric version of the method of difference-in-differences. We extend our analysis to consider applications of the methods to ordinary observational data.

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Petra E. Todd

Papers

Matching As An Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme

Matching As An Econometric Evaluation Estimator

Identification and estimation of treatment effects with a regression-discontinuity design

Does matching overcome LaLonde's critique of nonexperimental estimators?

Characterizing selection bias using experimental data