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A limit theorem for a smooth class of semiparametric estimators


  • Pakes, Ariel
  • Olley, Steven


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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Suggested Citation

  • Pakes, Ariel & Olley, Steven, 1995. "A limit theorem for a smooth class of semiparametric estimators," Journal of Econometrics, Elsevier, vol. 65(1), pages 295-332, January.
  • Handle: RePEc:eee:econom:v:65:y:1995:i:1:p:295-332

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    References listed on IDEAS

    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
    3. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    4. Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, vol. 59(2), pages 307-345, March.
    5. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    6. Olley, G Steven & Pakes, Ariel, 1996. "The Dynamics of Productivity in the Telecommunications Equipment Industry," Econometrica, Econometric Society, vol. 64(6), pages 1263-1297, November.
    7. Stoker, Thomas M., 1991. "Smoothing bias in density derivative estimation," Working papers 3336-91., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    8. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    9. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    10. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
    11. Hotz, V.J. & Miller, R.A., 1991. "Conditional Choice Probabilities and the Estimation of Dynamic Models," GSIA Working Papers 1992-12, Carnegie Mellon University, Tepper School of Business.
    12. 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.
    13. Haerdle,Wolfgang & Stoker,Thomas, 1987. "Investigations smooth multiple regression by the method of average derivatives," Discussion Paper Serie A 107, University of Bonn, Germany.
    14. Newey, W.K., 1993. "Convergence Rates for Series Estimators," Working papers 93-10, Massachusetts Institute of Technology (MIT), Department of Economics.
    15. 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.
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    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms


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