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Inference in additively separable models with a high-dimensional set of conditioning variables

Author

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  • Damian Kozbur

Abstract

This paper studies nonparametric series estimation and inference for the effect of a single variable of interest x on an outcome y in the presence of potentially high-dimensional conditioning variables z. The context is an additively separable model E[y|x, z] = g0(x) + h0(z). The model is high-dimensional in the sense that the series of approximating functions for h0(z) can have more terms than the sample size, thereby allowing z to have potentially very many measured characteristics. The model is required to be approximately sparse: h0(z) can be approximated using only a small subset of series terms whose identities are unknown. This paper proposes an estimation and inference method for g0(x) called Post-Nonparametric Double Selection which is a generalization of Post-Double Selection. Standard rates of convergence and asymptotic normality for the estimator are shown to hold uniformly over a large class of sparse data generating processes. A simulation study illustrates finite sample estimation properties of the proposed estimator and coverage properties of the corresponding confidence intervals. Finally, an empirical application estimating convergence in GDP in a country-level crosssection demonstrates the practical implementation of the proposed method.

Suggested Citation

  • Damian Kozbur, 2013. "Inference in additively separable models with a high-dimensional set of conditioning variables," ECON - Working Papers 284, Department of Economics - University of Zurich, revised Apr 2018.
  • Handle: RePEc:zur:econwp:284
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    File URL: https://www.zora.uzh.ch/id/eprint/151161/1/econwp284.pdf
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    References listed on IDEAS

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    Cited by:

    1. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Christian Hansen & Kengo Kato, 2018. "High-dimensional econometrics and regularized GMM," CeMMAP working papers CWP35/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Christian Hansen & Damian Kozbur & Sanjog Misra, 2016. "Targeted undersmoothing," ECON - Working Papers 282, Department of Economics - University of Zurich, revised Apr 2018.
    3. Damian Kozbur, 2017. "Testing-Based Forward Model Selection," American Economic Review, American Economic Association, vol. 107(5), pages 266-269, May.
    4. Philipp Bach & Sven Klaassen & Jannis Kueck & Martin Spindler, 2020. "Estimation and Uniform Inference in Sparse High-Dimensional Additive Models," Papers 2004.01623, arXiv.org, revised Apr 2024.
    5. Byunghoon Kang, 2019. "Inference in Nonparametric Series Estimation with Specification Searches for the Number of Series Terms," Papers 1909.12162, arXiv.org, revised Feb 2020.

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    More about this item

    Keywords

    Additive nonparametric models; high-dimensional sparse regression; inference under imperfect model selection;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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