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

Author

Listed:
  • Christoph Breunig
  • Enno Mammen
  • Anna Simoni

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, CNRS - Centre National de la Recherche Scientifique)

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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Christoph Breunig & Enno Mammen & Anna Simoni, 2020. "Ill-posed estimation in high-dimensional models with instrumental variables," Post-Print hal-03089879, HAL.
    • Handle: RePEc:hal:journl:hal-03089879
    DOI: 10.1016/j.jeconom.2020.04.043
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    Cited by:

    1. Tadao Hoshino, 2024. "Functional Spatial Autoregressive Models," Papers 2402.14763, arXiv.org, revised Oct 2024.
    2. Lee, Chien-Chiang & Wang, Chih-Wei & Ho, Shan-Ju, 2022. "The dimension of green economy: Culture viewpoint," Economic Analysis and Policy, Elsevier, vol. 74(C), pages 122-138.
    3. Qingliang Fan & Zijian Guo & Ziwei Mei, 2022. "A Heteroskedasticity-Robust Overidentifying Restriction Test with High-Dimensional Covariates," Papers 2205.00171, arXiv.org, revised May 2024.

    More about this item

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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