Econometric Inference for High Dimensional Predictive Regressions

59 Pages Posted: 12 Nov 2024

See all articles by Zhan Gao

Zhan Gao

University of Southern California

Ji Hyung Lee

affiliation not provided to SSRN

Ziwei Mei

The Chinese University of Hong Kong (CUHK) - Department of Economics

Zhentao Shi

Department of Economics, the Chinese University of Hong Kong

Abstract

LASSO introduces shrinkage bias into estimated coefficients, which can adversely affect the desirable asymptotic normality and invalidate the standard inferential procedure based on the t-statistic. The desparsified LASSO has emerged as a well-known remedy for this issue. In the context of high dimensional predictive regression, the desparsified LASSO faces an additional challenge: the Stambaugh bias arising from nonstationary regressors. To restore the standard inferential procedure, we propose a novel estimator called IVX-desparsified LASSO (XDlasso). XDlasso eliminates the shrinkage bias and the Stambaugh bias simultaneously and does not require prior knowledge about the identities of nonstationary and stationary regressors. We establish the asymptotic properties of XDlasso for hypothesis testing, and our theoretical findings are supported by Monte Carlo simulations. Applying our method to real-world applications from the FRED-MD database — which includes a rich set of control variables — we investigate two important empirical questions: (i) the predictability of the U.S. stock returns based on the earnings-price ratio, and (ii) the predictability of the U.S. inflation using the unemployment rate.

Keywords: Forecast, Data-rich Environment, Hypothesis testing, Shrinkage, Unit root

Suggested Citation

GAO, ZHAN and Lee, Ji Hyung and Mei, Ziwei and Shi, Zhentao, Econometric Inference for High Dimensional Predictive Regressions. Available at SSRN: https://ssrn.com/abstract=5017781 or http://dx.doi.org/10.2139/ssrn.5017781

ZHAN GAO

University of Southern California ( email )

2250 Alcazar Street
Los Angeles, CA 90089
United States

Ji Hyung Lee

affiliation not provided to SSRN ( email )

No Address Available

Ziwei Mei (Contact Author)

The Chinese University of Hong Kong (CUHK) - Department of Economics ( email )

Shatin, N.T.
Hong Kong

Zhentao Shi

Department of Economics, the Chinese University of Hong Kong ( email )

Shatin, N.T.
Hong Kong

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