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GMM Efficiency and IPW Estimation for Nonsmooth Functions

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  • Ot�vio Bartalotti

    ()
    (Department of Economics, Tulane University)

Abstract

In a GMM setting this paper analyzes the problem in which we have two sets of moment conditions, where two sets of parameters enter into one set of moment conditions, while only one set of parameters enters into the other, extending Prokhorov and Schmidt's (2009) redundancy results to nonsmooth objective functions, and obtains relatively efficient estimates of interesting parameters in the presence of nuisance parameters. One-step GMM estimation for both set of parameters is asymptotically more efficient than two-step procedures. These results are applied to Wooldridge's (2007) inverse probability weighted estimator (IPW), generalizing the framework to deal with missing data in this context. Two-step estimation of beta_0 is more efficient than using known probabilities of selection, but this is dominated by one-step joint estimation. Examples for missing data quantile regression and instrumental variable quantile regression are provided.

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File URL: http://econ.tulane.edu/RePEc/pdf/tul1301.pdf
File Function: First Version, January 2013
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Bibliographic Info

Paper provided by Tulane University, Department of Economics in its series Working Papers with number 1301.

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Length: 29 pages
Date of creation: Jan 2013
Date of revision:
Handle: RePEc:tul:wpaper:1301

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Keywords: generalized method of moments; nonsmooth objective functions; inverse probability weighting; missing data; quantile regression;

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  1. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, 09.
  2. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(03), pages 295-313, December.
  3. Wooldridge, Jeffrey M., 2007. "Inverse probability weighted estimation for general missing data problems," Journal of Econometrics, Elsevier, vol. 141(2), pages 1281-1301, December.
  4. Newey, W.K., 1991. "The Asymptotic Variance of Semiparametric Estimators," Working papers 583, Massachusetts Institute of Technology (MIT), Department of Economics.
  5. Chernozhukov, Victor & Hansen, Christian, 2008. "Instrumental variable quantile regression: A robust inference approach," Journal of Econometrics, Elsevier, vol. 142(1), pages 379-398, January.
  6. Chernozhukov, Victor & Hansen, Christian, 2006. "Instrumental quantile regression inference for structural and treatment effect models," Journal of Econometrics, Elsevier, vol. 132(2), pages 491-525, June.
  7. Artem Prokhorov & Peter Schmidt, 2008. "GMM Redundancy Results for General Missing Data Problems," Working Papers 08003, Concordia University, Department of Economics.
  8. Moshe Buchinsky, 1998. "Recent Advances in Quantile Regression Models: A Practical Guideline for Empirical Research," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 88-126.
  9. Newey, Whitney K., 1984. "A method of moments interpretation of sequential estimators," Economics Letters, Elsevier, vol. 14(2-3), pages 201-206.
  10. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  11. Qian, Hailong & Schmidt, Peter, 1999. "Improved instrumental variables and generalized method of moments estimators," Journal of Econometrics, Elsevier, vol. 91(1), pages 145-169, July.
  12. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
  13. Hitomi, Kohtaro & Nishiyama, Yoshihiko & Okui, Ryo, 2008. "A Puzzling Phenomenon In Semiparametric Estimation Problems With Infinite-Dimensional Nuisance Parameters," Econometric Theory, Cambridge University Press, vol. 24(06), pages 1717-1728, December.
  14. Cattaneo, Matias D., 2010. "Efficient semiparametric estimation of multi-valued treatment effects under ignorability," Journal of Econometrics, Elsevier, vol. 155(2), pages 138-154, April.
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