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The Factor-Lasso And K-Step Bootstrap Approach For Inference In High-Dimensional Economic Applications

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  • Hansen, Christian
  • Liao, Yuan

Abstract

We consider inference about coefficients on a small number of variables of interest in a linear panel data model with additive unobserved individual and time specific effects and a large number of additional time-varying confounding variables. We suppose that, in addition to unrestricted time and individual specific effects, these confounding variables are generated by a small number of common factors and high-dimensional weakly dependent disturbances. We allow that both the factors and the disturbances are related to the outcome variable and other variables of interest. To make informative inference feasible, we impose that the contribution of the part of the confounding variables not captured by time specific effects, individual specific effects, or the common factors can be captured by a relatively small number of terms whose identities are unknown. Within this framework, we provide a convenient inferential procedure based on factor extraction followed by lasso regression and show that the procedure has good asymptotic properties. We also provide a simple k-step bootstrap procedure that may be used to construct inferential statements about the low-dimensional parameters of interest and prove its asymptotic validity. We provide simulation evidence about the performance of our procedure and illustrate its use in an empirical application.

Suggested Citation

  • Hansen, Christian & Liao, Yuan, 2019. "The Factor-Lasso And K-Step Bootstrap Approach For Inference In High-Dimensional Economic Applications," Econometric Theory, Cambridge University Press, vol. 35(3), pages 465-509, June.
  • Handle: RePEc:cup:etheor:v:35:y:2019:i:03:p:465-509_00
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    6. Philippe Goulet Coulombe, 2020. "The Macroeconomy as a Random Forest," Papers 2006.12724, arXiv.org, revised Mar 2021.
    7. Vogt, M. & Walsh, C. & Linton, O., 2022. "CCE Estimation of High-Dimensional Panel Data Models with Interactive Fixed Effects," Janeway Institute Working Papers 2218, Faculty of Economics, University of Cambridge.
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    9. Vogt, M. & Walsh, C. & Linton, O., 2022. "CCE Estimation of High-Dimensional Panel Data Models with Interactive Fixed Effects," Cambridge Working Papers in Economics 2242, Faculty of Economics, University of Cambridge.
    10. Michael Vogt & Christopher Walsh & Oliver Linton, 2022. "CCE Estimation of High-Dimensional Panel Data Models with Interactive Fixed Effects," Papers 2206.12152, arXiv.org.

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    JEL classification:

    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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