Dinamik Panel Otoregresif Model için M-Tahmini Kullanan Dayanıklı Bir Yaklaşım

Abstract

Bu makale, otoregresif parametrenin yüksek süreklilik seviyeleri ve bireysel heterojenlik tarafından ortaya çıkan zorlukları ele alarak, birinci dereceden panel otoregresif modeller için dayanıklı bir M-tahmini yaklaşımını sunmaktadır. Dinamik panel modellerinde yaygın olarak kullanılan genelleştirilmiş momentler yöntemi tahmin edicileri, özellikle otoregresif parametre bire yaklaştıkça, zayıf araçlara karşı hassasiyet gösterir ve önemli miktarda sonlu örneklem yanlılıkları sergiler. Önerdiğimiz ağırlıklı M-tahmin edicisi, Huber’in kayıp fonksiyonundaki ölçek parametresi için bir kuvvet fonksiyonu kullanarak dayanıklı bir alternatif sunar. Optimal ayar parametresi aracılığıyla model parametrelerinin varyansını en aza indirerek, yöntemimiz parametre tahminlerinin etkinliğini ve dayanıklılığını artırır. Önerilen yaklaşımın üstünlüğünü, çeşitli Monte-Carlo simülasyonları ve hidroelektrik enerji üretim verilerine uygulama yoluyla göstererek, mevcut genelleştirilmiş momentler yöntemi tahmin edicileri ile kapsamlı karşılaştırmalar sunmaktayız.

Keywords

• Panel otoregresif modeller
• Dayanıklı tahmin
• M-tahmini
• Genelleştirilmiş momentler yöntemi

A Robust Approach using M-Estimation for Dynamic Panel Autoregressive Model

Abstract

This paper presents a robust M-estimation approach for first-order panel autoregressive models, addressing the challenges posed by high persistence levels of the autoregressive parameter and individual heterogeneity. Generalized method of moments estimators widely used in dynamic panel models exhibit substantial finite sample biases and are sensitive to weak instruments, particularly as the autoregressive parameter gets close to unity. Our proposed weighted M-estimator, which uses a power function for the scale parameter in Huber’s loss function, offers a robust alternative. By minimizing the variance of model parameters through an optimal tuning parameter, our method enhances the efficiency and robustness of parameter estimates. We demonstrate the superiority of the proposed approach through several Monte-Carlo simulations and an application to hydro-electric power output data, providing comprehensive comparisons with existing generalized method of moments estimators.

Keywords

• Panel autoregressive models
• Robust estimation
• M-estimation
• Generalized method of moments

References

1. Youssef, A. H. & Abonazel, M. R. (2017). Alternative GMM estimators for first-order autoregressive panel model: An improving efficiency approach. Communications in Statistics-Simulation and Computation, 46(4), 3112-3128.
2. Bun, M. J. G. & Kiviet, J. F. (2006). The effects of dynamic feedbacks on LS and MM estimator accuracy in panel data models. Journal of Econometrics, 132(2), 409-444.
3. Neyman, J. & Scott, E. L. (1948). Consistent estimates based on partially consistent observations. Econometrica, 16(1), 1-32.
4. Nickell, S. (1981). Biases in dynamic models with fixed effects. Econometrica, 49(6), 1417-1426.
5. Lancaster, T. (2002). Orthogonal parameters and panel data. Review of Economic Studies, 69(3), 647-666.
6. Hsiao, C., Pesaran, M. H. & Tahmiscioglu, A. K. (2002). Maximum likelihood estimation of fixed effects dynamic panel data models covering short time periods. Journal of Econometrics, 109(1), 107-150.
7. Binder, M., Hsiao, C. & Pesaran, M. H. (2005). Estimation and inference in short panel vector autoregressions with unit roots and cointegration. Econometric Theory, 21(4), 795-837.
8. Hayakawa, K. & Pesaran, M. H. (2015). Robust standard errors in transformed likelihood estimation of dynamic panel data models with cross-sectional heteroskedasticity. Journal of Econometrics, 188(1), 111-134.

9. Bun M. J. G., Carree, M. A. & Juodis, A. (2017). On Maximum likelihood estimation of dynamic panel data models. Oxford Bulletin of Economics and Statistics, 79(4), 463-494.
10. Alvarez, J. & Arellano, M. (2022). Robust likelihood estimation of dynamic panel data models. Journal of Econometrics, 226(1), 21-61.
11. Hansen, L. P. (2010). Generalized method of moments estimation. In: Macroeconometrics and Time Series Analysis, Durlauf, S. N., Blume, L. E. (eds), Palgrave Macmillan, London, p. 105-118.
12. Cochrane, J. H. (2001). Asset pricing. Princeton University Press, Princeton, New Jersey.
13. Arellano, M. (2003). Panel data econometrics. Oxford University Press, New York.
14. Hall, A. R. (2005). Generalized method of moments. Oxford University Press, New York
15. Singleton, K. J. (2006). Empirical dynamic asset pricing: Model specification and econometric assessment. Princeton University Press, Princeton, New Jersey.
16. Anderson, T. W. & Hsiao, C. (1982). Formulation and estimation of dynamic models using panel data. Journal of Econometrics, 18(1), 47-82.
17. Holtz-Eakin, D., Newey, W. & Rosen, H. S. (1988). Estimating vector autoregressions with panel data. Econometrica, 56(6), 1371-1395.
18. Arellano, M. & Bond, S. (1991). Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Review of Economic Studies, 58(2), 277-297.
19. Blundell, R. & Bond, S. (1998). Initial conditions andmoment restrictions in dynamic panel data models. Journal of Econometrics, 87(1), 115-143.
20. Alonso-Borrego, C. & Arellano, M. (1999). Symmetrically normalized instrumental variable estimation using panel data. Journal of Business & Economic Statistics, 17(1), 36-49.
21. Han, C., Phillips, P. C. B. & Sul, D. (2014). X-differencing and dynamic panel model estimation. Econometric Theory, 30(1), 201-251.
22. Arellano, M. & Bover, O. (1995). Another look at the instrumental variable estimation of error components models. Journal of Econometrics, 68(1), 29-51.
23. Ahn, S. C. & Schmidt, P. (1995). Efficient estimation of models for dynamic panel data. Journal of Econometrics, 68(1), 5-27.
24. Bun, M. J. G. & Windmeijer, F. (2010). The weak instrument problem of the system GMM estimator in dynamic panel data models. Econometrics Journal, 13(1), 95-126.
25. Hayakawa, K. (2007). Small sample bias properties of the system GMM estimator in dynamic panel data models. Economics Letters, 95(1), 32-38.
26. Han, C. & Philips, P. (2010). GMM estimation for dynamic panels with fixed effects and strong instruments at unity. Econometric Theory, 26(1), 119-151.
27. Callens, A., Wang, Y. G., Fu, L. & Liquet, B. (2021). Robust estimation procedure for autoregressive models with heterogeneity. Environmental Modeling & Assessment, 26, 313-323.
28. Wang, Y. G., Lin, X., Zhu, M. & Bai, Z. (2007). Robust estimation using the Huber function with a data-dependent tuning constant. Journal of Computational and Graphical Statistics, 16(2), 468-481.
29. Wang, N., Wang, Y. G., Hu, S., Hu, Z. H., Xu, J., Tang, H. & Jin, G. (2018). Robust regression with data-dependent regularization parameters and autoregressive temporal correlations. Environmental Modeling & Assessment, 23, 779-786.
30. Alvarez, J. & Arellano, M. (2003). The time series and cross-section asymptotics of dynamic panel data estimators. Econometrica, 71(4), 1121-1159.
31. Windmeijer, F. (2005). A finite sample correction for the variance of linear efficient two-step GMM estimators. Journal of Econometrics, 126(1), 25-51.
32. Box, G. E. P. & Hill, W. J. (1974). Correcting inhomogeneity of variance with power transformation weighting. Technometrics, 16(3), 385-389.
33. Croux, C. (1994). Efficient high-breakdown M-estimators of scale. Statistics and Probability Letters, 19(5), 371–379.
34. Bianco, A., Boente, G. & Di Rienzo, J. (2000). Some results for robust GM-based estimators in heteroscedastic regression models. Journal of Statistical Planning and Inference, 89(1-2), 215-242.