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High dimensional semiparametric moment restriction models

Author

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  • Chaohua Dong

    (Institute for Fiscal Studies and Southwestern University of Finance and Economics, China)

  • Jiti Gao

    (Institute for Fiscal Studies)

  • Oliver Linton

    (Institute for Fiscal Studies and University of Cambridge)

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-identi fication 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.

Suggested Citation

  • Chaohua Dong & Jiti Gao & Oliver Linton, 2018. "High dimensional semiparametric moment restriction models," CeMMAP working papers CWP69/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:69/18
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    References listed on IDEAS

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    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. Guohua Feng & Jiti Gao & Bin Peng, 2019. "An Integrated Panel Data Approach to Modelling Economic Growth," Papers 1903.07948, arXiv.org.

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    More about this item

    Keywords

    Generalized method of moments; high dimensional models; moment restriction; over-identi fication; 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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