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Cointegration Vector Estimation by DOLS for a Three-Dimensional Panel
Estimación de un modelo de cointegración utilizando DOLS para un panel de tres dimensiones
DOI:
https://doi.org/10.15446/rce.v38n1.48801Keywords:
Cointegration, Multidimensional, Panel Data (en)Cointegración, Modelos Panel, Multidimensional (es)
This paper extends the results of the dynamic ordinary least squares cointegration vector estimator available in the literature to a three-dimensional panel. We use a balanced panel of N and M lengths observed over T periods. The cointegration vector is homogeneous across individuals but we allow for individual heterogeneity using different short-run dynamics, individual-specific fixed effects and individual-specific time trends. We also model cross-sectional dependence using time-specific effects. The estimator has a Gaussian sequential limit distribution that is obtained by first letting T→∞ and then letting N→∞, M→∞. The Monte Carlo simulations show evidence that the finite sample properties of the estimator are closely related to the asymptotic ones.
Este documento extiende los resultados de los estimadores mínimos cuadrados dinámicos para series cointegradas disponible en la literatura a un panel de tres dimensiones. Se utiliza un panel balanceado de longitudes N y M para un periodo de tiempo de longitud T. El vector de cointegración es homogéneo a través de los individuos; sin embargo, el modelo permite cierto grado de heterogeneidad al usar diferentes dinámicas de corto plazo, efectos fijos y tendencias a niveles individuales. También se utilizan efectos en el tiempo para incluir dependencias cruzadas entre los individuos. El estimador tiene una distribución secuencial límite gausiana en la cual primero T->infinito y posteriormente N->infinito, M->infinito. Simulaciones Monte Carlo muestran evidencia de que las propiedades de muestra finita del estimador son cercanas a las asintóticas.
https://doi.org/10.15446/rce.v38n1.48801
1Banco de la República, Econometric Unit, Bogotá, Colombia. Senior Econometrician. Email: lmelovel@banrep.gov.co
2University of Maryland, Department of Economics, College Park, USA. PhD student. Email: leon@econ.umd.edu
3Universidad del Rosario, Department of Mathematics, Bogotá, Colombia. Professor. Email: dsaboyac@unal.edu.co
This paper extends the results of the dynamic ordinary least squares cointegration vector estimator available in the literature to a three-dimensional panel. We use a balanced panel of N and M lengths observed over T periods. The cointegration vector is homogeneous across individuals but we allow for individual heterogeneity using different short-run dynamics, individual-specific fixed effects and individual-specific time trends. We also model cross-sectional dependence using time-specific effects. The estimator has a Gaussian sequential limit distribution that is obtained by first letting T→∞ and then letting N→∞, M→∞. The Monte Carlo simulations show evidence that the finite sample properties of the estimator are closely related to the asymptotic ones.
Key words: Cointegration, Multidimensional, Panel Data.
Este documento extiende los resultados de los estimadores mínimos cuadrados dinámicos para series cointegradas disponible en la literatura a un panel de tres dimensiones. Se utiliza un panel balanceado de longitudes N y M para un periodo de tiempo de longitud T. El vector de cointegración es homogéneo a través de los individuos; sin embargo, el modelo permite cierto grado de heterogeneidad al usar diferentes dinámicas de corto plazo, efectos fijos y tendencias a niveles individuales. También se utilizan efectos en el tiempo para incluir dependencias cruzadas entre los individuos. El estimador tiene una distribución secuencial límite gausiana en la cual primero T→∞ y posteriormente N→∞, M→∞. Simulaciones Monte Carlo muestran evidencia de que las propiedades de muestra finita del estimador son cercanas a las asintóticas.
Palabras clave: cointegración, modelos panel, multidimensional.
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References
1. Banerjee, A., Hendry, D. & Smith, G. (1986), 'Exploring equilibrium relationships in econometrics through static models: some Monte Carlo evidence', Oxford Bulletin of Economics and Statistics 52, 92-104.
2. Davies, A. (2006), 'A framework for decomposing shocks and measuring volatilities derived from multi-dimensional panel data of survey forecasts', International Journal of Forecasting 22, 373-393.
3. Davies, A., Lahiri, K. & Sheng, X. (2011), Analyzing three-dimensional panel data of forecasts, 'The Oxford Handbook of Economics Forecasting', Oxford university Press, p. 473-556.
4. Eilat, Y. & Einav, L. (2004), 'Determinants of international tourism: A three-dimensional panel data analysis', Applied Economics 36, 1315-1327.
5. Eslava, M., Haltiwanger, J., Kugler, A. & Kugler, M. (2004), 'The effects of structural reforms on productivity and profitability enhancing reallocation: evidence from Colombia', Journal of Development Economics 75(2), 333-371.
6. Hamilton, J. (1994), Time Series Analysis, Princeton University Press.
7. Iregui, A., Melo, L. & Ramírez, M. (2007), 'Productividad regional y sectorial en Colombia: análisis utilizando datos de panel', Ensayos sobre Política Económica 25(53), 18-65.
8. Kao, C. & Chiang, M.-H. (2000), On the estimation and inference of a cointegrated regression in panel data, 'Advances in Econometrics: Nonstationary Panels, Panel Cointegration and Dynamic Panels', JAI Press.
9. Kremers, J., Ericsson, N. & Dolado, J. (1992), 'The power of cointegration tests', Oxford Bulletin of Economics and Statistics 54, 325-349.
10. Mark, N. & Sul, D. (2002), Appendix to cointegration vector estimation by panel dols and long-run money demand. Unpublished manuscript, available at http://www.nd.edu.
11. Mark, N. & Sul, D. (2003), 'Cointegration vector estimation by panel DOLS and long-run money demand', Oxford Bulletin of Economics and Statistics 65(5), 655-680.
12. Phillips, P. & Loretan, M. (1991), 'Estimating long-run economic equilibria', Review of Economic Studies 58, 407-436.
13. Phillips, P. & Moon, H. (1999), 'Linear regression limit theory for nonstationary panel data', Econometrica 67(5), 1057-1111.
14. Saikkonen, P. (1991), 'Asymptotically efficient estimation of cointegration regressions', Econometric Theory 7, 1-21.
15. Secretaría de Hacienda Distrital, (2003), 'Cambio tecnológico, productividad y crecimiento de la industria en Bogotá', Cuadernos de la Ciudad, Serie Productividad y Competividad(2).
16. Stock, J. & Watson, J. (1993), 'A simple estimator of cointegrating vectors in higher order integrated systems', Econometrica 61, 783-820.
17. Sul, D., Phillips, P. & Choi, C. (2005), 'Prewhitening bias in HAC estimation', Oxford Bulletin of Economics and Statistics 67(4), 517-546.
18. White, H. (2001), Asymptotic Theory for Econometricians, Academic Press. Revised Edition.
Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv38n1a03,
AUTHOR = {Melo-Velandia, Luis Fernando and León, John Jairo and Saboyá, Dagoberto},
TITLE = {{Cointegration Vector Estimation by DOLS for a Three-Dimensional Panel}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2015},
volume = {38},
number = {1},
pages = {45-73}
}
References
Banerjee, A., Hendry, D. & Smith, G. (1986), ‘Exploring equilibrium relationships in econometrics through static models: Some Monte Carlo evidence’, Oxford Bulletin of Economics and Statistics 52, 92–104.
Davies, A. (2006), ‘A framework for decomposing shocks and measuring volatilities derived from multi-dimensional panel data of survey forecasts’, International Journal of Forecasting 22, 373–393.
Davies, A., Lahiri, K. & Sheng, X. (2011), Analyzing three-dimensional panel data of forecasts, in M. Clements & D. Hendry, eds, ‘The Oxford Handbook of Economics Forecasting’, Oxford university Press, pp. 473–556.
Eilat, Y. & Einav, L. (2004), ‘Determinants of international tourism: A three-dimensional panel data analysis’, Applied Economics 36, 1315–1327.
Eslava, M., Haltiwanger, J., Kugler, A. & Kugler, M. (2004), ‘The effects of structural reforms on productivity and profitability enhancing reallocation: evidence from Colombia’, Journal of Development Economics 75(2), 333–371.
Hamilton, J. (1994), Time Series Analysis, Princeton University Press.
Iregui, A., Melo, L. & Ramírez, M. (2007), ‘Productividad regional y sectorial en Colombia: Análisis utilizando datos de panel’, Ensayos sobre Política Económica 25(53), 18–65.
Kao, C. & Chiang, M.-H. (2000), On the estimation and inference of a cointegrated regression in panel data, in B. Baltagi, ed., ‘Advances in Econometrics: Nonstationary Panels, Panel Cointegration and Dynamic Panels’, JAI Press.
Kremers, J., Ericsson, N. & Dolado, J. (1992), ‘The power of cointegration tests’, Oxford Bulletin of Economics and Statistics 54, 325–349.
Mark, N. & Sul, D. (2002), Appendix to cointegration vector estimation by panel dols and long-run money demand. Unpublished manuscript, available at http://www.nd.edu.
Mark, N. & Sul, D. (2003), ‘Cointegration vector estimation by panel DOLS and long-run money demand’, Oxford Bulletin of Economics and Statistics 65(5), 655–680.
Phillips, P. & Loretan, M. (1991), ‘Estimating long-run economic equilibria’, Review of Economic Studies 58, 407–436.
Phillips, P. & Moon, H. (1999), ‘Linear regression limit theory for nonstationary panel data’, Econometrica 67(5), 1057–1111.
Saikkonen, P. (1991), ‘Asymptotically efficient estimation of cointegration regressions’, Econometric Theory 7, 1–21.
Secretaría de Hacienda Distrital (2003), ‘Cambio tecnológico, productividad y crecimiento de la industria en Bogotá’, Cuadernos de la Ciudad, Serie Productividad y Competividad (2).
Stock, J. & Watson, J. (1993), ‘A simple estimator of cointegrating vectors in higher order integrated systems’, Econometrica 61, 783–820.
Sul, D., Phillips, P. & Choi, C. (2005), ‘Prewhitening bias in HAC estimation’, Oxford Bulletin of Economics and Statistics 67(4), 517–546.
White, H. (2001), Asymptotic Theory for Econometricians, Academic Press. Revised Edition.
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