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Testing Exclusion Restrictions in Nonseparable Triangular Models

  • Joeri Smits
  • Jeffrey S. Racine

In recent years, estimators for nonseparable models have been developed that rely on (an) instrumental variable(s) for identification. The exclusion restriction in triangular models can be reformulated and causally decomposed under the Settable Systems extension to the Pearl Causal Model due to Chalak & White (2012). We propose two new ways of testing the exclusion restriction, one based on testing conditional independence nonparametrically and one based on multivariate conditional mutual information. Unlike existing tests for overidentifying restrictions, the proposed tests are applicable in the just identified case. An important field of application is randomized trials with partial compliance, since for that case, the exclusion restriction is not only refutable, but also confirmable. The first approach, conditional independence testing, is illustrated by the application of the nonparametric test of equality of conditional densities of Li, Maasoumi & Racine (2009) to examples from medicine and economics.

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File URL: http://socserv.mcmaster.ca/econ/rsrch/papers/archive/2013-02.pdf
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Paper provided by McMaster University in its series Department of Economics Working Papers with number 2013-02.

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Length: 31 pages
Date of creation: Jan 2013
Date of revision:
Handle: RePEc:mcm:deptwp:2013-02
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  1. Karim Chalak & Halbert White, 2011. "Viewpoint: An extended class of instrumental variables for the estimation of causal effects," Canadian Journal of Economics, Canadian Economics Association, vol. 44(1), pages 1-51, February.
  2. Huber, Martin & Mellace, Giovanni, 2011. "Testing instrument validity for LATE identification based on inequality moment constraints," Economics Working Paper Series 1143, University of St. Gallen, School of Economics and Political Science.
  3. Markus Frölich & Blaise Melly, 2013. "Unconditional Quantile Treatment Effects Under Endogeneity," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 346-357, July.
  4. Andrew Chesher, 2010. "Instrumental Variable Models for Discrete Outcomes," Econometrica, Econometric Society, vol. 78(2), pages 575-601, 03.
  5. Matz Dahlberg & Eva Mork & Per Tovmo, 2008. "Power properties of the Sargan test in the presence of measurement errors in dynamic panels," Applied Economics Letters, Taylor & Francis Journals, vol. 15(5), pages 349-353.
  6. Susanne Schennach & Halbert White & Karim Chalak, 2007. "Local Indirect Least Squares and Average Marginal Effects in Nonseparable Structural Systems," Boston College Working Papers in Economics 680, Boston College Department of Economics, revised 26 Dec 2009.
  7. Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
  8. Li, Qi & Maasoumi, Esfandiar & Racine, Jeffrey S., 2009. "A nonparametric test for equality of distributions with mixed categorical and continuous data," Journal of Econometrics, Elsevier, vol. 148(2), pages 186-200, February.
  9. Oliver Linton & Pedro Gozalo, 1996. "Conditional Independence Restrictions: Testing and Estimation," Cowles Foundation Discussion Papers 1140, Cowles Foundation for Research in Economics, Yale University.
  10. repec:taf:jnlbes:v:30:y:2012:i:2:p:275-287 is not listed on IDEAS
  11. Karim Chalak & Halbert White, 2008. "Causality, Conditional Independence, and Graphical Separation in Settable Systems," Boston College Working Papers in Economics 689, Boston College Department of Economics, revised 04 Jul 2010.
  12. Markus Frölich, 2008. "Parametric and Nonparametric Regression in the Presence of Endogenous Control Variables," International Statistical Review, International Statistical Institute, vol. 76(2), pages 214-227, 08.
  13. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, 01.
  14. Su, Liangjun & White, Halbert, 2008. "A Nonparametric Hellinger Metric Test For Conditional Independence," Econometric Theory, Cambridge University Press, vol. 24(04), pages 829-864, August.
  15. 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.
  16. C. W. Granger & E. Maasoumi & J. Racine, 2004. "A Dependence Metric for Possibly Nonlinear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 649-669, 09.
  17. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
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