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BOUNDED SUPPORT IN LINEAR RANDOM COEFFICIENT MODELS: IDENTIFICATION AND VARIABLE SELECTION

Published online by Cambridge University Press:  26 March 2024

Philipp Hermann  and
Hajo Holzmann
Philipp Hermann
Affiliation:
Philipps-Universität Marburg
Hajo Holzmann*
Affiliation:
Philipps-Universität Marburg
*
Address correspondence to Hajo Holzmann, Department of Mathematics and Computer Science, Philipps-Universität Marburg, Marburg, Germany, holzmann@mathematik.uni-marburg.de.
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Abstract

We consider linear random coefficient regression models, where the regressors are allowed to have a finite support. First, we investigate identification, and show that the means and the variances and covariances of the random coefficients are identified from the first two conditional moments of the response given the covariates if the support of the covariates, excluding the intercept, contains a Cartesian product with at least three points in each coordinate. We also discuss identification of higher-order mixed moments, as well as partial identification in the presence of a binary regressor. Next, we show the variable selection consistency of the adaptive LASSO for the variances and covariances of the random coefficients in finite and moderately high dimensions. This implies that the estimated covariance matrix will actually be positive semidefinite and hence a valid covariance matrix, in contrast to the estimate arising from a simple least squares fit. We illustrate the proposed method in a simulation study.

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ARTICLES
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Econometric Theory , Volume 41 , Issue 4 , August 2025 , pp. 947 - 976
Copyright
© The Author(s), 2024. Published by Cambridge University Press

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