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Ill-posed Estimation in High-Dimensional Models with Instrumental Variables

Christoph Breunig, Enno Mammen, Anna Simoni

arXiv 2 Jun 2018 · Econometrics · publishedJournal of Econometrics (2020) · 3 citations (OpenAlex)

arXiv:1806.00666 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper is concerned with inference about low-dimensional components of a high-dimensional parameter vector $\beta^0$ 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 $\beta^0$ at a rate depending on the mapping properties of $M$ captured by a sparse link condition. Linear combinations of our estimator of $\beta^0$ 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 $\beta^0$. In Monte-Carlo simulations we analyze the finite sample behavior of our estimator.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1V. Chernozhukov, C. Hansen, and M. Spindler (2015) Post-selection and post-regularization inference in linear models with many controls and instruments0.87462100%
2N. Meinshausen and P. Bühlmann (2006) High-dimensional graphs and variable selection with the lasso0.81142100%
3S. van de Geer, P. Bühlmann, Y. Ritov, and R. Dezeure (2014) On asymptotically optimal confidence regions and tests for high-dimensional models0.74712542%
4E. Gautier, A. Tsybakov, and C. Rose (2011) High-dimensional instrumental variables regression and confidence sets0.73732100%
5X. Chen and D. Pouzo (2012) Estimation of nonparametric conditional moment models with possibly nonsmooth moments0.64422100%
6D. W. Andrews and X. Cheng (2012) Estimation and inference with weak, semi-strong, and strong identification0.64422100%
7X. Chen and T. M. Christensen (2018) Optimal sup-norm rates and uniform inference on nonlinear functionals of nonparametric iv regression0.58531100%
8P. Bühlmann and S. Van De Geer (2011) Statistics for high-dimensional data: methods, theory and applications0.5112250%
9S. Berry, J. Levinsohn, and A. Pakes (1995) Automobile prices in market equilibrium0.51121100%
10V. Chernozhukov, D. Chetverikov, M. Demirer, E. Duflo, C. Hansen, W.… (2018) Double/debiased machine learning for treatment and structural parameters0.51121100%

Showing the top 10 of 41 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Functional Spatial Autoregressive Models0.40511
2Ill-Conditioned Orthogonal Scores in Double Machine Learning0.40511