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Testing Conditional Independence via Rosenblatt Transforms

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Author Info
Kyungchul Song () (Department of Economics, University of Pennsylvania)
Abstract

This paper investigates the problem of testing conditional independence of Y and Z given λθ(X) for some unknown θ ∈ Θ ⊂ Rd, for a parametric function λθ(·). For instance, such a problem is relevant in recent literatures of heterogeneous treatment effects and contract theory. First, this paper finds that using Rosenblatt transforms in a certain way, we can construct a class of tests that are asymptotically pivotal and asymptotically unbiased against √n-converging Pitman local alternatives. The asymptotic pivotalness is convenient especially because the asymptotic critical values remain invariant over different estimators of the unknown parameter θ. Even when tests are asymptotically pivotal, however, it is often the case that simulation methods to obtain asymptotic critical values are yet unavailable or complicated, and hence this paper suggests a simple wild bootstrap procedure. A special case of the proposed testing framework is to test the presence of quantile treatment effects in a program evaluation data set. Using the JTPA training data set, we investigate the validity of nonexperimental procedures for inferences about quantile treatment effects of the job training program.

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Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 07-026.

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Length: 52 pages
Date of creation: 05 Sep 2007
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Handle: RePEc:pen:papers:07-026

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Related research
Keywords: Conditional independence asymptotic pivotal tests Rosenblatt transforms wild bootstrap

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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing

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  2. Joseph G. Altonji & Rosa L. Matzkin, 2005. "Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 73(4), pages 1053-1102, 07. [Downloadable!] (restricted)
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    Other versions:
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  6. Donald W. K. Andrews, 1997. "A Conditional Kolmogorov Test," Econometrica, Econometric Society, vol. 65(5), pages 1097-1128, September.
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  7. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June. [Downloadable!]
  8. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, 07. [Downloadable!] (restricted)
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  9. Heckman, James J & Smith, Jeffrey, 1997. "Making the Most Out of Programme Evaluations and Social Experiments: Accounting for Heterogeneity in Programme Impacts," Review of Economic Studies, Blackwell Publishing, vol. 64(4), pages 487-535, October. [Downloadable!] (restricted)
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  11. Alberto Abadie & Joshua Angrist & Guido Imbens, 2002. "Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings," Econometrica, Econometric Society, vol. 70(1), pages 91-117, January. [Downloadable!] (restricted)
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  12. Jeffrey A. Smith & Petra E. Todd, 2001. "Reconciling Conflicting Evidence on the Performance of Propensity-Score Matching Methods," American Economic Review, American Economic Association, vol. 91(2), pages 112-118, May. [Downloadable!] (restricted)
  13. Heckman, James J & Ichimura, Hidehiko & Todd, Petra E, 1997. "Matching as an Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme," Review of Economic Studies, Blackwell Publishing, vol. 64(4), pages 605-54, October. [Downloadable!] (restricted)
  14. A. Smith, Jeffrey & E. Todd, Petra, 2005. "Does matching overcome LaLonde's critique of nonexperimental estimators?," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 305-353. [Downloadable!] (restricted)
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  15. Rajeev H. Dehejia & Sadek Wahba, 1998. "Causal Effects in Non-Experimental Studies: Re-Evaluating the Evaluation of Training Programs," NBER Working Papers 6586, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  17. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
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  18. Whang, Yoon-Jae, 2000. "Consistent bootstrap tests of parametric regression functions," Journal of Econometrics, Elsevier, vol. 98(1), pages 27-46, September. [Downloadable!] (restricted)
  19. Joshua D. Angrist & Guido M. Kuersteiner, 2004. "Semiparametric Causality Tests Using the Policy Propensity Score," NBER Working Papers 10975, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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