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High Dimensional Sparse Econometric Models: An Introduction

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  • Alexandre Belloni
  • Victor Chernozhukov

Abstract

In this chapter we discuss conceptually high dimensional sparse econometric models as well as estimation of these models using L1-penalization and post-L1-penalization methods. Focusing on linear and nonparametric regression frameworks, we discuss various econometric examples, present basic theoretical results, and illustrate the concepts and methods with Monte Carlo simulations and an empirical application. In the application, we examine and confirm the empirical validity of the Solow-Swan model for international economic growth.

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  • Alexandre Belloni & Victor Chernozhukov, 2011. "High Dimensional Sparse Econometric Models: An Introduction," Papers 1106.5242, arXiv.org, revised Sep 2011.
    • Handle: RePEc:arx:papers:1106.5242
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    1. Joshua D. Angrist & Alan B. Keueger, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(4), pages 979-1014.
    2. Joshua Angrist & Victor Chernozhukov & Iván Fernández-Val, 2006. "Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure," Econometrica, Econometric Society, vol. 74(2), pages 539-563, March.
    3. A. Belloni & D. Chen & V. Chernozhukov & C. Hansen, 2012. "Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain," Econometrica, Econometric Society, vol. 80(6), pages 2369-2429, November.
    4. Levine, Ross & Renelt, David, 1992. "A Sensitivity Analysis of Cross-Country Growth Regressions," American Economic Review, American Economic Association, vol. 82(4), pages 942-963, September.
    5. Hansen, Christian & Hausman, Jerry & Newey, Whitney, 2008. "Estimation With Many Instrumental Variables," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 398-422.
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