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High Dimensional Semiparametric Moment Restriction Models

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  • Dong, C.
  • Gao, J.
  • Linton, O.

Abstract

We consider nonlinear moment restriction semiparametric models where both the dimension of the parameter vector and the number of restrictions are divergent with sample size and an unknown smooth function is involved. We propose an estimation method based on the sieve generalized method of moments (sieve GMM). We establish consistency and asymptotic normality for the estimated quantities when the number of parameters increases modestly with sample size. We also consider the case where the number of potential parameters/covariates is very large, i.e., increases rapidly with sample size, but the true model exhibits sparsity. We use a penalized sieve GMM approach to select the relevant variables, and establish the oracle property of our method in this case. We also provide new results for inference. We propose several new test statistics for the over-identification and establish their large sample properties. We provide a simulation study that shows the performance of our methodology. We also provide an application to modelling the effect of schooling on wages using data from the NLSY79 used by Carneiro et al. [17].

Suggested Citation

  • Dong, C. & Gao, J. & Linton, O., 2018. "High Dimensional Semiparametric Moment Restriction Models," Cambridge Working Papers in Economics 1881, Faculty of Economics, University of Cambridge.
  • Handle: RePEc:cam:camdae:1881
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    Cited by:

    1. Connor, G. & Li, S. & Linton, O., 2020. "A Dynamic Semiparametric Characteristics-based Model for Optimal Portfolio Selection," Cambridge Working Papers in Economics 20103, Faculty of Economics, University of Cambridge.
    2. Dong, Chaohua & Gao, Jiti & Linton, Oliver, 2023. "High dimensional semiparametric moment restriction models," Journal of Econometrics, Elsevier, vol. 232(2), pages 320-345.
    3. Chaohua Dong & Jiti Gao & Oliver Linton, 2022. "Chaohua Dong, Jiti Gao and Oliver Linton’s contribution to the Discussion of ‘Assumption‐lean inference for generalised linear model parameters’ by Vansteelandt and Dukes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 707-708, July.
    4. Feng, Guohua & Gao, Jiti & Peng, Bin, 2022. "An integrated panel data approach to modelling economic growth," Journal of Econometrics, Elsevier, vol. 228(2), pages 379-397.

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    More about this item

    Keywords

    Generalized method of moments; high dimensional models; moment restriction; over-identification; penalization; sieve method; sparsity;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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