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Revista Colombiana de Estadística

Print version ISSN 0120-1751

Rev.Colomb.Estad. vol.38 no.1 Bogotá Jan./July 2015

http://dx.doi.org/10.15446/rce.v38n1.48801 

http://dx.doi.org/10.15446/rce.v38n1.48801

Cointegration Vector Estimation by DOLS for a Three-Dimensional Panel

Estimación de un modelo de cointegración utilizando DOLS para un panel de tres dimensiones

LUIS FERNANDO MELO-VELANDIA1, JOHN JAIRO LEÓN2, DAGOBERTO SABOYÁ3

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


Abstract

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.


Resumen

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.


Texto completo disponible en PDF


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.         [ Links ]

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.         [ Links ]

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.         [ Links ]

4. Eilat, Y. & Einav, L. (2004), 'Determinants of international tourism: A three-dimensional panel data analysis', Applied Economics 36, 1315-1327.         [ Links ]

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.         [ Links ]

6. Hamilton, J. (1994), Time Series Analysis, Princeton University Press.         [ Links ]

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.         [ Links ]

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.         [ Links ]

9. Kremers, J., Ericsson, N. & Dolado, J. (1992), 'The power of cointegration tests', Oxford Bulletin of Economics and Statistics 54, 325-349.         [ Links ]

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.         [ Links ]

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.         [ Links ]

12. Phillips, P. & Loretan, M. (1991), 'Estimating long-run economic equilibria', Review of Economic Studies 58, 407-436.         [ Links ]

13. Phillips, P. & Moon, H. (1999), 'Linear regression limit theory for nonstationary panel data', Econometrica 67(5), 1057-1111.         [ Links ]

14. Saikkonen, P. (1991), 'Asymptotically efficient estimation of cointegration regressions', Econometric Theory 7, 1-21.         [ Links ]

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).         [ Links ]

16. Stock, J. & Watson, J. (1993), 'A simple estimator of cointegrating vectors in higher order integrated systems', Econometrica 61, 783-820.         [ Links ]

17. Sul, D., Phillips, P. & Choi, C. (2005), 'Prewhitening bias in HAC estimation', Oxford Bulletin of Economics and Statistics 67(4), 517-546.         [ Links ]

18. White, H. (2001), Asymptotic Theory for Econometricians, Academic Press. Revised Edition.         [ Links ]


[Recibido en septiembre de 2013. Aceptado en mayo de 2014]

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}
}