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A limit theorem for a smooth class of semiparametric estimators

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  • Pakes, Ariel
  • Olley, Steven

Abstract

We consider an econometric model based on a set of moment conditions which are indexed by both a finite dimensional parameter vector of interest, and an infinite dimensional parameter, h, which in turn depends upon both and another infinite dimensional parameter, tau. The model assumes that the moment conditions equal zero at the true value of all unknown parameters. Estimators of are obtained by forming nonparametric estimates of h and tau, substituting them into the sample analog of the moment conditions, and choosing that value of that makes the sample moments as "close as possible" to zero. Using independence and smoothness assumptions the paper provides consistency, root{n} consistency, and asymptotic normality proofs for the resultant estimator. As an example, we consider Olley and Pakes' (1991) use of semiparametric techniques to control for both simultaneity and selection biases in estimating production functions. This example illustrates how semiparametric techniques can be used to overcome both computational problems, and the need for strong functional form restrictions, in obtaining estimates from structural models. We also provide two additional sets of empirical results for this example. First we compare the estimators of theta obtained using different estimators for the nonparametric components of the problem, and then we compare alternative estimators for the estimated standard errors of those estimators.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 65 (1995)
Issue (Month): 1 (January)
Pages: 295-332

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Handle: RePEc:eee:econom:v:65:y:1995:i:1:p:295-332

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Web page: http://www.elsevier.com/locate/jeconom

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  1. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November.
  2. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July.
  3. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-82, November.
  4. V. Joseph Hotz & Robert A. Miller, 1992. "Conditional Choice Probabilities and the Estimation of Dynamic Models," Working Papers 9202, Harris School of Public Policy Studies, University of Chicago.
  5. Donald W.K. Andrews, 1988. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Cowles Foundation Discussion Papers 874R, Cowles Foundation for Research in Economics, Yale University, revised May 1989.
  6. Zvi Griliches, 1967. "Production Functions in Manufacturing: Some Preliminary Results," NBER Chapters, in: The Theory and Empirical Analysis of Production, pages 275-340 National Bureau of Economic Research, Inc.
  7. G. Steven Olley & Ariel Pakes, 1992. "The Dynamics of Productivity in the Telecommunications Equipment Industry," NBER Working Papers 3977, National Bureau of Economic Research, Inc.
  8. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
  9. Haerdle,Wolfgang & Stoker,Thomas, 1987. "Investigations smooth multiple regression by the method of average derivatives," Discussion Paper Serie A 107, University of Bonn, Germany.
  10. Ariel Pakes, 1991. "Dynamic Structural Models: Problems and Prospects. Mixed Continuous Discrete Controls and Market Interactions," Cowles Foundation Discussion Papers 984, Cowles Foundation for Research in Economics, Yale University.
  11. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
  12. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  13. Stoker, Thomas M., 1991. "Smoothing bias in density derivative estimation," Working papers 3336-91., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  14. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  15. Newey, W.K., 1993. "Convergence Rates for Series Estimators," Working papers 93-10, Massachusetts Institute of Technology (MIT), Department of Economics.
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