Robust Estimation and Inference for High-Dimensional Panel Data Models
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912230134513664 |
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| author | Gao, Jiti Liu, Fei Peng, Bin Yan, Yayi |
| author_facet | Gao, Jiti Liu, Fei Peng, Bin Yan, Yayi |
| contents | This paper provides the relevant literature with a complete toolkit for conducting robust estimation and inference about the parameters of interest involved in a high-dimensional panel data framework. Specifically, (1) we allow for non-Gaussian, serially and cross-sectionally correlated and heteroskedastic error processes, (2) we develop an estimation method for high-dimensional long-run covariance matrix using a thresholded estimator, (3) we also allow for the number of regressors to grow faster than the sample size.
Methodologically and technically, we develop two Nagaev--types of concentration inequalities: one for a partial sum and the other for a quadratic form, subject to a set of easily verifiable conditions. Leveraging these two inequalities, we derive a non-asymptotic bound for the LASSO estimator, achieve asymptotic normality via the node-wise LASSO regression, and establish a sharp convergence rate for the thresholded heteroskedasticity and autocorrelation consistent (HAC) estimator.
We demonstrate the practical relevance of these theoretical results by investigating a high-dimensional panel data model with interactive effects. Moreover, we conduct extensive numerical studies using simulated and real data examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07420 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Robust Estimation and Inference for High-Dimensional Panel Data Models Gao, Jiti Liu, Fei Peng, Bin Yan, Yayi Econometrics This paper provides the relevant literature with a complete toolkit for conducting robust estimation and inference about the parameters of interest involved in a high-dimensional panel data framework. Specifically, (1) we allow for non-Gaussian, serially and cross-sectionally correlated and heteroskedastic error processes, (2) we develop an estimation method for high-dimensional long-run covariance matrix using a thresholded estimator, (3) we also allow for the number of regressors to grow faster than the sample size. Methodologically and technically, we develop two Nagaev--types of concentration inequalities: one for a partial sum and the other for a quadratic form, subject to a set of easily verifiable conditions. Leveraging these two inequalities, we derive a non-asymptotic bound for the LASSO estimator, achieve asymptotic normality via the node-wise LASSO regression, and establish a sharp convergence rate for the thresholded heteroskedasticity and autocorrelation consistent (HAC) estimator. We demonstrate the practical relevance of these theoretical results by investigating a high-dimensional panel data model with interactive effects. Moreover, we conduct extensive numerical studies using simulated and real data examples. |
| title | Robust Estimation and Inference for High-Dimensional Panel Data Models |
| topic | Econometrics |
| url | https://arxiv.org/abs/2405.07420 |