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Contribution Details

Type Working Paper
Scope Discipline-based scholarship
Title Inference in additively separable models with a high-dimensional set of conditioning variables
Organization Unit
  • Damian Kozbur
  • English
Institution University of Zurich
Series Name Working paper series / Department of Economics
Number 284
ISSN 1664-7041
Number of Pages 48
Date 2018
Abstract Text 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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Keywords Additive nonparametric models, high-dimensional sparse regression, inference under imperfect model selection, Modellwahl, Nichtparametrisches Verfahren, Regressionsanalyse, Konvergenz
Additional Information Revised version Auch erschienen in: arXiv: 1503.05436v5