Shrinkage for categorical regressors

Phillip Heiler and Jana Mareckova

Journal of Econometrics, 2021, vol. 223, issue 1, 161-189

Abstract: This paper introduces a flexible regularization approach that reduces point estimation risk of group means stemming from e.g. categorical regressors, (quasi-)experimental data or panel data models. The loss function is penalized by adding weighted squared ℓ2-norm differences between group location parameters and informative first stage estimates. Under quadratic loss, the penalized estimation problem has a simple interpretable closed-form solution that nests methods established in the literature on ridge regression, discretized support smoothing kernels and model averaging methods. We derive risk-optimal penalty parameters and propose a plug-in approach for estimation. The large sample properties are analyzed in an asymptotic local to zero framework by introducing a class of sequences for close and distant systems of locations that is sufficient for describing a large range of data generating processes. We provide the asymptotic distributions of the shrinkage estimators under different penalization schemes. The proposed plug-in estimator uniformly dominates the ordinary least squares estimator in terms of asymptotic risk if the number of groups is larger than three. Monte Carlo simulations reveal robust improvements over standard methods in finite samples. Real data examples of estimating time trends in a panel and a difference-in-differences study illustrate potential applications.

Keywords: Categorical regressors; Regularization; Smoothing kernels; Model averaging (search for similar items in EconPapers)
JEL-codes: C25 C51 C52 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304407620303407
Full text for ScienceDirect subscribers only

Related works:
Working Paper: Shrinkage for Categorical Regressors (2019)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:223:y:2021:i:1:p:161-189

DOI: 10.1016/j.jeconom.2020.07.051

Access Statistics for this article

Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

More articles in Journal of Econometrics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().