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A Limit Theorem for a Smooth Class of Semiparametric Estimators

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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.

Suggested Citation

  • Ariel Pakes & Steven Olley, 1994. "A Limit Theorem for a Smooth Class of Semiparametric Estimators," Cowles Foundation Discussion Papers 1066, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1066
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    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.
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    More about this item

    Keywords

    Semiparametric m-estimators; selection and simultaneity biases in production functions;

    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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