Abstract
This paper studies the variable selection problem in threshold model with a covariate-dependent threshold, in which the threshold is modeled by a function of candidate variables that affect the separation of regimes. To simultaneously select explanatory variables and the variables that affect the threshold, we develop a variable selection procedure via mixed integer optimization in the \(l_0\)-penalization framework. Monte Carlo simulations are conducted to assess the performance of the suggested variable selection procedure, and the simulation results indicate that the variable selection procedure works well in finite samples. The empirical usefulness of the proposed approach is illustrated with an application to the famous growth–debt nexus.
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Notes
A natural choice of \(({\underline{p}}, {\overline{p}})\) is \((0, 2 p_x+p_z)\). When \(2 p_x+p_z\) is very large, we can choose a small \({\overline{p}}\) to speed up computations in practice.
We thank an anonymous referee to raise this point to us.
It is worth noting that Hidalgo et al. (2019) find that the US data would be better fitted with a multiple threshold model, and conclude that the low threshold they find (17.2%) is not necessarily invalidating the Reinhart-Rogoff hypothesis. We thank an anonymous referee to raise this point to us.
A further investigate on the post-selection inference in the framework is worthwhile, but it will not be pursued in this paper. We intend to study this in the future. As the selected model (omitting debt in the first regime) does not nest the classical threshold model, we include debt in the first regime in conducting inference in the paper.
We thank the anonymous referees to raise this point to us.
We thank an anonymous referee to raise this point to us.
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Acknowledgements
The author acknowledges the financial support from the National Natural Science Foundation of China (Grant No. 72273059). The author thanks anonymous referees and the editor for very valuable comments and suggestions on previous versions of the paper. Remaining errors are my own.
Funding
This study is supported by the National Natural Science Foundation of China (Grant No. 72273059).
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Yang, L. Variable selection in threshold model with a covariate-dependent threshold. Empir Econ 65, 189–202 (2023). https://doi.org/10.1007/s00181-022-02340-3
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DOI: https://doi.org/10.1007/s00181-022-02340-3
Keywords
- Variable selection
- Threshold model
- Covariate-dependent threshold
- Monte Carlo simulations
- Growth–debt nexus