Zhan Gao, Ji Hyung Lee, Ziwei Mei, Zhentao Shi
arXiv 16 Sep 2024 · Statistics — Methodology
arXiv:2409.10030 · PDF · DOI · OpenAlex · Extracted main text
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.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Zhang, Cun-Hui and Zhang, Stephanie S (2014) Confidence intervals for low dimensional parameters in high dimensional linear models | 1.000 | 7 | 3 | 100% |
| 2 | Campbell, John Y and Yogo, Motohiro (2006) Efficient tests of stock return predictability | 1.000 | 5 | 3 | 100% |
| 3 | Phillips, Peter CB and Lee, Ji Hyung (2016) Robust econometric inference with mixed integrated and mildly explosive regressors self | 0.928 | 5 | 3 | 80% |
| 4 | Lee, Ji Hyung and Shi, Zhentao and Gao, Zhan (2022) On LASSO for predictive regression self | 0.928 | 4 | 3 | 100% |
| 5 | Fukang Zhu and Zongwu Cai and Liang Peng (2014) Predictive regressions for macroeconomic data | 0.928 | 4 | 3 | 100% |
| 6 | Chernozhukov, Victor and Chetverikov, Denis and Demirer, Mert and Du… (2018) Double/debiased machine learning for treatment and structural parameters | 0.811 | 4 | 2 | 100% |
| 7 | Kostakis, Alexandros and Magdalinos, Tassos and Stamatogiannis, Mich… (2015) Robust econometric inference for stock return predictability | 0.794 | 8 | 4 | 50% |
| 8 | Phillips, Peter CB and Magdalinos, Tassos (2009) Econometric inference in the vicinity of unity | 0.737 | 10 | 3 | 40% |
| 9 | Mei, Ziwei and Shi, Zhentao (2024) On LASSO for high dimensional predictive regression self | 0.737 | 3 | 3 | 67% |
| 10 | Adamek, Robert and Smeekes, Stephan and Wilms, Ines (2023) Lasso inference for high-dimensional time series | 0.737 | 3 | 2 | 100% |
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