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


Kozbur, Damian (2018). Inference in additively separable models with a high-dimensional set of conditioning variables. Working paper series / Department of Economics 284, University of Zurich.

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.

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.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Economics
Working Paper Series > Department of Economics
Dewey Decimal Classification:330 Economics
JEL Classification:C1
Uncontrolled Keywords:Additive nonparametric models, high-dimensional sparse regression, inference under imperfect model selection
Language:English
Date:April 2018
Deposited On:23 Apr 2018 15:56
Last Modified:24 Sep 2019 23:27
Series Name:Working paper series / Department of Economics
Number of Pages:48
ISSN:1664-7041
Additional Information:Revised version Auch erschienen in: arXiv: 1503.05436v5
OA Status:Green
Official URL:http://www.econ.uzh.ch/static/wp/econwp284.pdf
Related URLs:http://www.econ.uzh.ch/static/workingpapers.php

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