Ill-posed estimation in high-dimensional models with instrumental variables

Christoph Breunig, Enno Mammen and Anna Simoni

Journal of Econometrics, 2020, vol. 219, issue 1, 171-200

Abstract: This paper is concerned with inference about low-dimensional components of a high-dimensional parameter vector β0 which is identified through instrumental variables. We allow for eigenvalues of the expected outer product of included and excluded covariates, denoted by M, to shrink to zero as the sample size increases. We propose a novel estimator based on desparsification of an instrumental variable Lasso estimator, which is a regularized version of 2SLS with an additional correction term. This estimator converges to β0 at a rate depending on the mapping properties of M. Linear combinations of our estimator of β0 are shown to be asymptotically normally distributed. Based on consistent covariance estimation, our method allows for constructing confidence intervals and statistical tests for single or low-dimensional components of β0. In Monte-Carlo simulations we analyze the finite sample behavior of our estimator. We apply our method to estimate a logit model of demand for automobiles using real market share data.

Keywords: Instrumental Variables; Sparsity; Central limit theorem; Lasso; Linear model; Desparsification; Ill-posed estimation problem (search for similar items in EconPapers)
JEL-codes: C18 C26 C55 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Related works:
Working Paper: Ill-posed Estimation in High-Dimensional Models with Instrumental Variables (2020)
Working Paper: Ill-posed estimation in high-dimensional models with instrumental variables (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:219:y:2020:i:1:p:171-200

DOI: 10.1016/j.jeconom.2020.04.043

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