arXiv 11 Apr 2024 · Econometrics
arXiv:2404.08105 · PDF · DOI · OpenAlex · Extracted main text
We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and L1 estimation errors for the Lasso estimator of the slope parameters and the threshold parameter, accommodating heteroskedastic non-subgaussian error terms and non-subgaussian covariates. Next, we derive the asymptotic distribution of tests involving an increasing number of slope parameters by debiasing (or desparsifying) the Lasso estimator in cases with no threshold effect and with a fixed threshold effect. We show that the asymptotic distributions in both cases are the same, allowing us to perform uniform inference without specifying whether the model is a linear or threshold regression. Additionally, we extend the theory to accommodate time series data under the near-epoch dependence assumption. Finally, we identify statistically significant factors influencing cross-country economic growth and quantify the effects of military news shocks on US government spending and GDP, while also estimating a data-driven threshold point in both applications.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Adamek, R., S. Smeekes, and I. Wilms (2024, 04) (2024) Local Projection Inference in High Dimensions | 1.000 | 9 | 3 | 100% |
| 2 | van de Geer, S., P. Bühlmann, Y. Ritov, and R. Dezeure (2014) On asymptotically optimal confidence regions and tests for high-dimensional models | 0.941 | 6 | 4 | 83% |
| 3 | Lee, S., M. H. Seo, and Y. Shin (2016) The lasso for high dimensional regression with a possible change point | 0.894 | 28 | 5 | 71% |
| 4 | Durlauf, S. N. and P. A. Johnson (1995) Multiple regimes and cross-country growth behaviour | 0.874 | 5 | 2 | 100% |
| 5 | Chiang, H. D., J. Rodrigue, and Y. Sasaki (2023) Post-selection inference in three-dimensional panel data | 0.843 | 4 | 3 | 75% |
| 6 | Callot, L., M. Caner, A. B. Kock, and J. A. Riquelme (2017) Sharp threshold detection based on sup-norm error rates in high-dimensional models | 0.811 | 4 | 2 | 100% |
| 7 | Adamek, R., S. Smeekes, and I. Wilms (2023) Lasso inference for high-dimensional time series | 0.778 | 17 | 3 | 47% |
| 8 | Hansen, B. E (2000) Sample splitting and threshold estimation | 0.737 | 4 | 3 | 50% |
| 9 | Caner, M. and A. B. Kock (2018) Asymptotically honest confidence regions for high dimensional parameters by the desparsified conservative lasso | 0.693 | 9 | 3 | 33% |
| 10 | Ramey, V. A. and S. Zubairy (2018) Government spending multipliers in good times and in bad: evidence from us historical data | 0.693 | 9 | 1 | 100% |
Showing the top 10 of 43 scored citations.