This paper is concerned with inference about low-dimensional components of a high-dimensional parameter vector beta_0 which is identified through in- strumental 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 desparsi- fication 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 sta- tistical tests for single or low-dimensional components of beta_0 . In Monte-Carlo simulations we analyze the finite sample behavior of our estimator.
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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beta_0
\beta^0
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in- strumental
instrumental
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desparsi- fication
desparsification
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beta_0
\beta^0
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beta_0
\beta^0
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sta- tistical
statistical
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beta_0
\beta^0