Abstract
We develop threshold estimation methods for panel data models with two threshold variables and individual fixed specific effects covering short time periods. In the static panel data model, we propose least squares estimation of the threshold and regression slopes using fixed effects transformations; while in the dynamic panel data model, we propose maximum likelihood estimation of the threshold and slope parameters using first difference transformations. In both models, we propose to estimate the threshold parameters sequentially. We apply the methods to a 15-year sample of 565 U.S. firms to test whether financial constraints affect investment decisions.
-
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
-
Research funding: None declared.
-
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
Aivazian, V. A., Y. Ge, and J. Qiu. 2005. “The Impact of Leverage on Firm Investment: Canadian Evidence.” Journal of Corporate Finance 11 (1–2): 277–91. https://doi.org/10.1016/s0929-1199(03)00062-2.Search in Google Scholar
Bai, J. 1997. “Estimating Multiple Breaks One at a Time.” Econometric Theory 13 (3): 315–52. https://doi.org/10.1017/s0266466600005831.Search in Google Scholar
Barón, A., M. V. Landaberry, R. Lluberas, and J. Ponce. 2021. “Commercial and Banking Credit Network in Uruguay.” Latin American Journal of Central Banking 2 (3): 100034. https://doi.org/10.1016/j.latcb.2021.100034.Search in Google Scholar
Chan, K. S. 1993. “Consistency and Limiting Distribution of the Least Squares Estimator of a Threshold Autoregressive Model.” Annals of Statistics 21 (1): 520–33. https://doi.org/10.1214/aos/1176349040.Search in Google Scholar
Chen, H., T. Chong, and J. Bai. 2012. “Theory and Applications of TAR Model with Two Threshold Variables.” Econometric Reviews 31 (2): 142–70. https://doi.org/10.1080/07474938.2011.607100.Search in Google Scholar
Chong, T. 2003. “Generic Consistency of the Break-point Estimator under Specification Errors.” The Econometrics Journal 6 (1): 167–92. https://doi.org/10.1111/1368-423x.00106.Search in Google Scholar
Chong, T., and I. Yan. 2014. “Estimating and Testing Threshold Regression Models with Multiple Threshold Variables.” In MPRA Working Paper 54732. Also available at https://mpra.ub.uni-muenchen.de/54732/1/MPRA_paper_54732.pdf.Search in Google Scholar
Donayre, L., and I. Panovska. 2018. “U.S. Wage Growth and Nonlinearities: The Roles of Inflation and Unemployment.” Economic Modelling 68: 273–92. https://doi.org/10.1016/j.econmod.2017.07.019.Search in Google Scholar
Fazzari, S. M., R. Glenn Hubbard, and B. C. Petersen. 1988. “Financing Constraints and Corporate Investment.” Brookings Papers on Economic Activity 1988 (1): 141–95. https://doi.org/10.2307/2534426.Search in Google Scholar
Gonzáles, A., T. Terasvirta, and D. van Dijk. 2005. “Panel Smooth Transition Regression Models.” In Research Paper 165. Quantitative Finance Research Centre. Also available at https://www.uts.edu.au/sites/default/files/qfr-archive-02/QFR-rp165.pdf.Search in Google Scholar
Hansen, B. E. 1996. “Inference when a Nuisance Parameter Is Not Identified under the Null Hypothesis.” Econometrica 64 (2): 413–30. https://doi.org/10.2307/2171789.Search in Google Scholar
Hansen, B. E. 1997. “Inference in TAR Models.” Studies in Nonlinear Dynamics and Econometrics 2 (1): 1–14. https://doi.org/10.2202/1558-3708.1024.Search in Google Scholar
Hansen, B. E. 1999. “Threshold Effects in Non-dynamic Panels: Estimation, Testing and Inference.” Journal of Econometrics 93 (2): 345–68. https://doi.org/10.1016/s0304-4076(99)00025-1.Search in Google Scholar
Hansen, B. E. 2000. “Sample Splitting and Threshold Estimation.” Econometrica 68 (3): 575–603. https://doi.org/10.1111/1468-0262.00124.Search in Google Scholar
Hansen, B. E. 2011. “Threshold Autoregression in Economics.” Statistics and Its Interface 4 (2): 123–7. https://doi.org/10.4310/sii.2011.v4.n2.a4.Search in Google Scholar
Hsiao, C., M. Pesaran, and K. Tahmiscioglu. 2002. “Maximum Likelihood Estimation of Fixed Effects Dynamic Panel Data Models Covering Short Time Periods.” Journal of Econometrics 109 (1): 107–50. https://doi.org/10.1016/s0304-4076(01)00143-9.Search in Google Scholar
Hu, X., and F. Schiantarelli. 1998. “Investment and Capital Market Imperfections: a Switching Regression Approach Using U.S. Firm Panel Data.” The Review of Economics and Statistics 80 (3): 466–79. https://doi.org/10.1162/003465398557564.Search in Google Scholar
Hubbard, H. 1998. “Capital-market Imperfections and Investment.” Journal of Economic Literature 36 (1): 193–225.Search in Google Scholar
Kapetanios, G. 2008. “A Bootstrap Procedure for Panel Data Sets with Many Cross-Sectional Units.” The Econometrics Journal 11 (2): 377–95.10.1111/j.1368-423X.2008.00243.xSearch in Google Scholar
Lancaster, T. 2000. “The Incidental Parameter Problem since 1948.” Journal of Econometrics 95 (2): 391–413. https://doi.org/10.1016/s0304-4076(99)00044-5.Search in Google Scholar
Nickell, S. J. 1981. “Biases in Dynamic Models with Fixed Effects.” Econometrica 49 (6): 1417–26. https://doi.org/10.2307/1911408.Search in Google Scholar
Ramírez-Rondán, N. R. 2020. “Maximum Likelihood Estimation of Dynamic Panel Threshold Models.” Econometric Reviews 39 (3): 260–76. https://doi.org/10.1080/07474938.2019.1624401.Search in Google Scholar
Seo, M. H., and Y. Shin. 2016. “Dynamic Panels with Threshold Effect and Endogeneity.” Journal of Econometrics 195 (2): 169–86. https://doi.org/10.1016/j.jeconom.2016.03.005.Search in Google Scholar
Schiantarelli, F. 1996. “Financial Constraints and Investment: Methodological Issues and International Evidence.” Oxford Review of Economic Policy 12 (2): 70–89. https://doi.org/10.1093/oxrep/12.2.70.Search in Google Scholar
Tong, H. 2007. “Birth of the Threshold Time Series Model.” Statistica Sinica 17 (1): 8–14.Search in Google Scholar
Yanquen, E., G. Livan, R. Montañez-Enriquez, and S. Martinez-Jaramillo. 2022. “Measuring Systemic Risk for Bank Credit Networks: A Multilayer Approach.” Latin American Journal of Central Banking 3 (2): 100049. https://doi.org/10.1016/j.latcb.2022.100049.Search in Google Scholar
Supplementary Material
The online version of this article offers supplementary material (https://doi.org/10.1515/snde-2020-0048).
© 2022 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Research Articles
- On determination of the number of factors in an approximate factor model
- Clean energy consumption and economic growth in China: a time-varying analysis
- Panel data models with two threshold variables
- What will drive global economic growth in the digital age?
- On the nonlinear relationships between shadow economy and the three pillars of sustainable development: new evidence from panel threshold analysis
- Tail behaviours of multiple-regime threshold AR models with heavy-tailed innovations
- Stock price prediction using multi-scale nonlinear ensemble of deep learning and evolutionary weighted support vector regression
Articles in the same Issue
- Frontmatter
- Research Articles
- On determination of the number of factors in an approximate factor model
- Clean energy consumption and economic growth in China: a time-varying analysis
- Panel data models with two threshold variables
- What will drive global economic growth in the digital age?
- On the nonlinear relationships between shadow economy and the three pillars of sustainable development: new evidence from panel threshold analysis
- Tail behaviours of multiple-regime threshold AR models with heavy-tailed innovations
- Stock price prediction using multi-scale nonlinear ensemble of deep learning and evolutionary weighted support vector regression