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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Characterizing selection bias using experimental data

This paper develops and applies semiparametric econometric methods to estimate the form of selection bias that arises from using nonexperimental comparison groups to evaluate social programs and to test the identifying assumptions that justify three widely-used classes of estimators and our extensions of them: (a) the method of matching; (b) the classical econometric selection model which represents the bias solely as a function of the probability of participation; and (c) the method of difference-in-differences. Using data from an experiment on a prototypical social program combined with unusually rich data from a nonexperimental comparison group, we reject the assumptions justifying matching and our extensions of that method but find evidence in support of the index-sufficient selection bias model and the assumptions that justify application of a conditional semiparametric version of the method of difference-in-difference. Fa comparable people and to appropriately weight participants and nonparticipants a sources of selection bias as conveniently measured. We present a rigorous defin bias and find that in our data it is a small component of conventially meausred it is still substantial when compared with experimentally-estimated program impa matching participants to comparison group members in the same labor market, givi same questionnaire, and making sure they have comparable characteristics substan the performance of any econometric program evaluation estimator. We show how t analysis to estimate the impact of treatment on the treated using ordinary obser

Characterizing Selection Bias Using Experimental Data

(2002). Wavelet Methods for Time Series Analysis. Journal of the American Statistical Association: Vol. 97, No. 457, pp. 362-363.

Wavelet Methods for Time Series Analysis

In the last ten years, there has been increasing interest and activity in the general area of partially linear regression smoothing in statistics. Many methods and techniques have been proposed and studied. This monograph hopes to bring an up-to-date presentation of the state of the art of partially linear regression techniques. The emphasis of this monograph is on methodologies rather than on the theory, with a particular focus on applications of partially linear regression techniques to various statistical problems. These problems include least squares regression, asymptotically efficient estimation, bootstrap resampling, censored data analysis, linear measurement error models, nonlinear measurement models, nonlinear and nonparametric time series models.
We hope that this monograph will serve as a useful reference for theoretical and applied statisticians and to graduate students and others who are interested in the area of partially linear regression. While advanced mathematical ideas have been valuable in some of the theoretical development, the methodological power of partially linear regression can be demonstrated and discussed without advanced mathematics.
This monograph can be divided into three parts: part one–Chapter 1 through Chapter 4; part two–Chapter 5; and part three–Chapter 6. In the first part, we discuss various estimators for partially linear regression models, establish theo- retical results for the estimators, propose estimation procedures, and implement the proposed estimation procedures through real and simulated examples.
The second part is of more theoretical interest. In this part, we construct several adaptive and efficient estimates for the parametric component. We show that the LS estimator of the parametric component can be modified to have both Bahadur asymptotic efficiency and second order asymptotic efficiency. In the third part, we consider partially linear time series models. First, we propose a test procedure to determine whether a partially linear model can be used to fit a given set of data. Asymptotic test criteria and power investigations are presented. Second, we propose a Cross-Validation (CV) based criterion to select the optimum linear subset from a partially linear regression and estab- lish a CV selection criterion for the bandwidth involved in the nonparametric kernel estimation. The CV selection criterion can be applied to the case where the observations fitted by the partially linear model (1.1.1) are independent and identically distributed (i.i.d.). Due to this reason, we have not provided a sepa- rate chapter to discuss the selection problem for the i.i.d. case. Third, we provide recent developments in nonparametric and semiparametric time series regression.
This work of the authors was supported partially by the Sonderforschungs- bereich373“QuantifikationundSimulationO konomischerProzesse”.Thesecond author was also supported by the National Natural Science Foundation of China and an Alexander von Humboldt Fellowship at the Humboldt University, while the third author was also supported by the Australian Research Council. The second and third authors would like to thank their teachers: Professors Raymond Car- roll, Guijing Chen, Xiru Chen, Ping Cheng and Lincheng Zhao for their valuable inspiration on the two authors’ research efforts. We would like to express our sin- cere thanks to our colleagues and collaborators for many helpful discussions and stimulating collaborations, in particular, Vo Anh, Shengyan Hong, Enno Mam- men, Howell Tong, Axel Werwatz and Rodney Wolff. For various ways in which they helped us, we would like to thank Adrian Baddeley, Rong Chen, Anthony Pettitt, Maxwell King, Michael Schimek, George Seber, Alastair Scott, Naisyin Wang, Qiwei Yao, Lijian Yang and Lixing Zhu.
The authors are grateful to everyone who has encouraged and supported us to finish this undertaking. Any remaining errors are ours.

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Partially Linear Models

In this paper, we develop several consistent tests in the context of a nonparametric regression model. These include tests for the significance of a subset of regressors and tests for the specification of the semiparametric functional form of the regression function, where the latter covers tests for a partially linear and a single index specification against a general nonparametric alternative. One common feature to the construction of all these tests is the use of the Central Limit Theorem for degenerate U-statistics of order higher than two. As a result, they share the same advantages over most of the corresponding existing tests in the literature: (a) They do not depend on any ad hoc modifications such as sample splitting, random weighting, etc. (b) Under the alternative hypotheses, the test statistics in this paper diverge to positive infinity at a faster rate than those based on ad hoc modifications.

Qi Li

Papers

Consistent model specification tests : Omitted variables and semiparametric functional forms