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A test of the conditional independence assumption in sample selection models

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Abstract

Identi?cation in most sample selection models depends on the independence of the regressors and the error terms conditional on the selection probability. All quantile and mean functions are parallel in these models; this implies that quantile estimators cannot reveal any? per assumption non-existing? heterogeneity. Quantile estimators are nevertheless useful for testing the conditional independence assumption because they are consistent under the null hypothesis. We propose tests of the Kolmogorov-Smirnov type based on the conditional quantile regression process. Monte Carlo simulations show that their size is satisfactory and their power su¢ cient to detect deviations under realistic data generating processes. We apply our procedures to female wage data from the 2011 Current Population Survey and show that homogeneity is clearly rejected.

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Bibliographic Info

Paper provided by Brown University, Department of Economics in its series Working Papers with number 2012-11.

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Date of creation: 2012
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Handle: RePEc:bro:econwp:2012-11

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Postal: Department of Economics, Brown University, Providence, RI 02912

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Keywords: sample selection; quantile regression; independence; test;

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  1. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, Elsevier, vol. 58(1-2), pages 3-29, July.
  2. Huber, Martin & Melly, Blaise, 2011. "Quantile Regression in the Presence of Sample Selection," Economics Working Paper Series, University of St. Gallen, School of Economics and Political Science 1109, University of St. Gallen, School of Economics and Political Science.
  3. Sokbae Lee, 2004. "Endogeneity in Quantile Regression Models: A Control Function Approach," Econometric Society 2004 North American Summer Meetings, Econometric Society 521, Econometric Society.
  4. Michael Lechner & Blaise Melly, 2010. "Partial Idendification of Wage Effects of Training Programs," Working Papers, Brown University, Department of Economics 2010-8, Brown University, Department of Economics.
  5. Pedro Carneiro & Sokbae 'Simon' Lee, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP01/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. Chen, Songnian & Khan, Shakeeb, 2003. "Semiparametric Estimation Of A Heteroskedastic Sample Selection Model," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 19(06), pages 1040-1064, December.
  7. Victor Chernozhukov & Ivan Fernandez-Val & Blaise Melly, 2009. "Inference on counterfactual distributions," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP09/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  8. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, American Economic Association, vol. 15(4), pages 143-156, Fall.
  9. Donald, Stephen G., 1995. "Two-step estimation of heteroskedastic sample selection models," Journal of Econometrics, Elsevier, Elsevier, vol. 65(2), pages 347-380, February.
  10. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, Elsevier, vol. 32(1), pages 143-155, June.
  11. Chernozhukov, Victor & Hansen, Christian, 2006. "Instrumental quantile regression inference for structural and treatment effect models," Journal of Econometrics, Elsevier, Elsevier, vol. 132(2), pages 491-525, June.
  12. Blundell, Richard & Powell, James L., 2007. "Censored regression quantiles with endogenous regressors," Journal of Econometrics, Elsevier, Elsevier, vol. 141(1), pages 65-83, November.
  13. Huber, Martin & Mellace, Giovanni, 2011. "Sharp bounds on causal effects under sample selection," Economics Working Paper Series, University of St. Gallen, School of Economics and Political Science 1134, University of St. Gallen, School of Economics and Political Science.
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Cited by:
  1. Machado, Cecilia, 2012. "Selection, Heterogeneity and the Gender Wage Gap," IZA Discussion Papers 7005, Institute for the Study of Labor (IZA).

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