Estimación de un modelo SAR para datos panel con coeficientes espaciales específicos
Los modelos espaciales auto-regresivos permiten describir la dependencia espacial que surge cuando los valores que adopta una variable en una región o lugar están relacionados con las observaciones vecinas. Extensiones de estos modelos a estructuras de datos panel también han sido desarrolladas en l...
- Autores:
-
Delgado Contreras, David Fernando
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- Fecha de publicación:
- 2019
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- Universidad Nacional de Colombia
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- Matemáticas::Probabilidades y matemáticas aplicadas
spatial auto-regressive
panel data
linear models
development economics
Modelos espaciales auto-regresivos
datos panel
modelos lineales
desarrollo económico
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| dc.title.spa.fl_str_mv |
Estimación de un modelo SAR para datos panel con coeficientes espaciales específicos |
| dc.title.alternative.spa.fl_str_mv |
Estimation of a SAR model for panel data with spatial specific coefficients |
| title |
Estimación de un modelo SAR para datos panel con coeficientes espaciales específicos |
| spellingShingle |
Estimación de un modelo SAR para datos panel con coeficientes espaciales específicos Matemáticas::Probabilidades y matemáticas aplicadas spatial auto-regressive panel data linear models development economics Modelos espaciales auto-regresivos datos panel modelos lineales desarrollo económico |
| title_short |
Estimación de un modelo SAR para datos panel con coeficientes espaciales específicos |
| title_full |
Estimación de un modelo SAR para datos panel con coeficientes espaciales específicos |
| title_fullStr |
Estimación de un modelo SAR para datos panel con coeficientes espaciales específicos |
| title_full_unstemmed |
Estimación de un modelo SAR para datos panel con coeficientes espaciales específicos |
| title_sort |
Estimación de un modelo SAR para datos panel con coeficientes espaciales específicos |
| dc.creator.fl_str_mv |
Delgado Contreras, David Fernando |
| dc.contributor.advisor.spa.fl_str_mv |
Melo Martínez, Oscar Orlando |
| dc.contributor.author.spa.fl_str_mv |
Delgado Contreras, David Fernando |
| dc.subject.ddc.spa.fl_str_mv |
Matemáticas::Probabilidades y matemáticas aplicadas |
| topic |
Matemáticas::Probabilidades y matemáticas aplicadas spatial auto-regressive panel data linear models development economics Modelos espaciales auto-regresivos datos panel modelos lineales desarrollo económico |
| dc.subject.proposal.eng.fl_str_mv |
spatial auto-regressive panel data linear models development economics |
| dc.subject.proposal.spa.fl_str_mv |
Modelos espaciales auto-regresivos datos panel modelos lineales desarrollo económico |
| description |
Los modelos espaciales auto-regresivos permiten describir la dependencia espacial que surge cuando los valores que adopta una variable en una región o lugar están relacionados con las observaciones vecinas. Extensiones de estos modelos a estructuras de datos panel también han sido desarrolladas en la literatura espacial. El objetivo de este documento es presentar una propuesta que permita encontrar los estimadores de un modelo espacial auto-regresivo para datos panel con coeficientes espaciales específicos a través del método de máxima verosimilitud. La estrategia utilizada conlleva a obtener formas cerradas para la estimación de los parámetros asociados a las variables exógenas y a la varianza, mientras que resulta necesario el uso de métodos numéricos para calcular los coeficientes espaciales. Los resultados se aplican sobre un panel que tiene como objetivo explicar de forma lineal los componentes del IDH (Índice de Desarrollo Humano) dentro de una muestra intercontinental. Los experimentos dejaron notar que el cálculo de los coeficientes específicos resulta costoso computacionalmente, pero los resultados son significativamente diferentes a la especificación con un coeficiente espacial único y resulta en una mejor bondad de ajuste. En relación a la aplicación se resalta que mientras el modelo con único coeficiente espacial tiende a sobre-explicar el IDH por su componente de estándar de vida, el uso de esta propuesta atenúa la magnitud de tal parámetro asociado. |
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2019 |
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2019-10-28 |
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2020-02-19T12:32:56Z |
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2020-02-19T12:32:56Z |
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Documento de trabajo |
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info:eu-repo/semantics/workingPaper |
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Anselin, L. (2001), ‘Spatial econometrics’, A companion to theoretical econometrics 310330. Anselin, L. (2013), Spatial Econometrics: Methods and Models, Vol. 4, Springer Science & Business Media Anselin, L. & Kelejian, H. H. (1997), ‘Testing for spatial error autocorrelation in the presence of endogenous regressors’, International Regional Science Review 20(1-2), 153–182 Anselin, L., Le Gallo, J. & Jayet, H. (2008), Spatial panel econometrics, in ‘The Econometrics of Panel Data’, Springer, pp. 625–660. Arellano, M. (2003), Panel data econometrics, Oxford University Press. Ayvar-Campos, F. J., Navarro-Chavez, J. C. L. & Giménez-García, V. M. (2017), ‘La eficiencia de la dimensión ingreso del IDH en México’, Ensayos. Revista de economía 36(2), 95–121. Baltagi, B. (2001), Econometric Analysis of Panel Data, John Wiley & Sons. Baltagi, B. H., Egger, P. & Pfaffermayr, M. (2013), ‘A generalized spatial panel data model with random effects’, Econometric Reviews 32(5-6), 650–685. Baltagi, B. H. & Li, D. (2006), ‘Prediction in the panel data model with spatial correlation: the case of liquor’, Spatial Economic Analysis 1(2), 175–185. Baltagi, B. H., Song, S. H. & Koh, W. (2003), ‘Testing panel data regression models with spatial error correlation’, Journal of Econometrics 117(1), 123–150. Baringhaus, L., Danschke, R. & Henze, N. (1989), ‘Recent and classical tests for normality-a comparative study’, Communications in Statistics-Simulation and Computation 18(1), 363–379. Barry, R. P. & Pace, R. K. (1999), ‘Monte carlo estimates of the log determinant of large sparse matrices’, Linear Algebra and its Applications 289(1-3), 41–54. Bibby, J., Kent, J. & Mardia, K. (1979), ‘Multivariate analysis’. Breusch, T. & Pagan, A. (1980), ‘The lagrange multiplier test and its applications to model specification in econometrics’, The Review of Economic Studies 47(1), 239–253. Brueckner, J. K. (2006), ‘Strategic interaction among governments’, A companion to urban economics 26, 332–347. Celemín, J. P. & Velázquez, G. A. (2017), ‘Spatial analysis of the relationship between a life quality index, HDI and poverty in the province of Buenos Aires and the Autonomous City of Buenos Aires, Argentina’, Social Indicators Research 17, 1–21. Chintagunta, P. K., Jain, D. C. & Vilcassim, N. J. (1991), ‘Investigating heterogeneity in brand preferences in logit models for panel data’, Journal of Marketing Research 1, 417–428. Cliff, A. D. & Ord, J. K. (1973), ‘Spatial autocorrelation, monographs in spatial environmental systems analysis’, London: Pion Limited 1. Doornik, J. A. & Hansen, H. (2008), ‘An omnibus test for univariate and multivariate normality’, Oxford Bulletin of Economics and Statistics 70, 927–939. Druska, V. & Horrace, W. C. (2004), ‘Generalized moments estimation for spatial panel data: Indonesian rice farming’, American Journal of Agricultural Economics 86(1), 185–198. Egger, P., Pfaffermayr, M. & Winner, H. (2005), ‘An unbalanced spatial panel data approach to us state tax competition’, Economics Letters 88(3), 329–335. Elhorst, J. P. (2003), ‘Specification and estimation of spatial panel data models’, International Regional Science Review 26(3), 244–268. Frazier, C. & Kockelman, K. (2005), ‘Spatial econometric models for panel data: incorporating spatial and temporal data’, Transportation Research Record: Journal of the Transportation Research Board (1902), 80–90. Goldfeld, S. M. & Quandt, R. E. (1965), ‘Some tests for homoscedasticity’, Journal of the American Statistical Association 60(310), 539–547. Greene, W. (2000), Econometric analysis, International edition, Pearson US Imports & PHIPEs Hausman, J. A. (1975), ‘An instrumental variable approach to full information estimators for linear and certain nonlinear econometric models’, Econometrica: Journal of the Econometric Society 43, 727–738. Hausman, J. A. (1978), ‘Specification tests in econometrics’, Econometrica: Journal of the Econometric Society 46, 1251–1271 Henze, N. & Zirkler, B. (1990), ‘A class of invariant consistent tests for multivariate normality’, Communications in Statistics-Theory and Methods 19(10), 3595–3617. Kao, C. (1999), ‘Spurious regression and residual-based tests for cointegration in panel data’, Journal of Econometrics 90(1), 1–44 Kapoor, M., Kelejian, H. H. & Prucha, I. R. (2007), ‘Panel data models with spatially correlated error components’, Journal of Econometrics 140(1), 97–130. Kmenta, J. & Rafailzadeh, B. (1997), Elements of econometrics, University of Michigan Press. Kumar, S. (2014), ‘Eigenvalue statistics for the sum of two complex wishart matrices’, EPL (Europhysics Letters) 107(6), 60002. Lax, P. D. & Lax, P. (2007), Linear Algebra and its Applications, Wiley-Interscience. Lee, L.-F. (2004), ‘Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models’, Econometrica 72(6), 1899–1925. Lee, L.-f. & Yu, J. (2010a), ‘Estimation of spatial autoregressive panel data models with fixed effects’, Journal of Econometrics 154(2), 165–185. Lee, L.-f. & Yu, J. (2010b), ‘Some recent developments in spatial panel data models’, Regional Science and Urban Economics 40(5), 255–271. LeSage, J. & Pace, R. K. (2009), Introduction to spatial econometrics, Chapman and Hall/CRC. Letkoviˇcov´a, H. et al. (2014), ‘Spatial distribution and relationship between sustainable development measures in EU countries’, Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis 53(3), 87–94 Maddala, G. S. (1987), ‘Limited dependent variable models using panel data’, Journal of Human Resources 22. Maddala, G. S. & Wu, S. (1999), ‘A comparative study of unit root tests with panel data and a new simple test’, Oxford Bulletin of Economics and Statistics 61, 631–652. Magnus, J. R. & Neudecker, H. (1988), ‘Matrix differential calculus with applications in statistics and econometrics’, Wiley Series in Probability and Mathematical Mtatistics . Mardia, K. V. (1970), ‘Measures of multivariate skewness and kurtosis with applications’, Biometrika 57(3), 519–530. Moran, P. A. (1950), ‘Notes on continuous stochastic phenomena’, Biometrika 37(1/2), 17–23. Mutl, J. & Pfaffermayr, M. (2008), The spatial random effects and the spatial fixed effects model: the hausman test in a cliff and ord panel model, Technical report, Reihe Okonomie/Economics Series, Institut f¨ur H¨ohere Studien (IHS). Ord, K. (1975), ‘Estimation methods for models of spatial interaction’, Journal of the American Statistical Association 70(349), 120–126. Pace, R. K. & Barry, R. (1997), ‘Quick computation of spatial autoregressive estimators’, Geographical analysis 29(3), 232–247. Pawitan, Y. (2001), In all likelihood: statistical modelling and inference using likelihood, Oxford University Press. Pesaran, M. H. & Smith, R. (1995), ‘Estimating long-run relationships from dynamic heterogeneous panels’, Journal of Econometrics 68(1), 79–113. Qiu, Q., Sung, J., Davis, W. & Tchernis, R. (2018), ‘Using spatial factor analysis to measure human development’, Journal of Development Economics 132, 130–149. Shaker, R. R. (2015), ‘The spatial distribution of development in Europe and its underlying sustainability correlations’, Applied Geography 63, 304–314. Wooldridge, J. M. (2010), Econometric analysis of cross section and panel data, MIT press. |
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Derechos reservados - Universidad Nacional de Colombia |
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Atribución-NoComercial-SinDerivadas 4.0 InternacionalDerechos reservados - Universidad Nacional de ColombiaAcceso abiertohttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Melo Martínez, Oscar Orlandod6076907-84aa-404d-bc43-eed399528397-1Delgado Contreras, David Fernandoce0b8d19-b2b2-4470-a7e9-9c6fd228170e2020-02-19T12:32:56Z2020-02-19T12:32:56Z2019-10-28https://repositorio.unal.edu.co/handle/unal/75644Los modelos espaciales auto-regresivos permiten describir la dependencia espacial que surge cuando los valores que adopta una variable en una región o lugar están relacionados con las observaciones vecinas. Extensiones de estos modelos a estructuras de datos panel también han sido desarrolladas en la literatura espacial. El objetivo de este documento es presentar una propuesta que permita encontrar los estimadores de un modelo espacial auto-regresivo para datos panel con coeficientes espaciales específicos a través del método de máxima verosimilitud. La estrategia utilizada conlleva a obtener formas cerradas para la estimación de los parámetros asociados a las variables exógenas y a la varianza, mientras que resulta necesario el uso de métodos numéricos para calcular los coeficientes espaciales. Los resultados se aplican sobre un panel que tiene como objetivo explicar de forma lineal los componentes del IDH (Índice de Desarrollo Humano) dentro de una muestra intercontinental. Los experimentos dejaron notar que el cálculo de los coeficientes específicos resulta costoso computacionalmente, pero los resultados son significativamente diferentes a la especificación con un coeficiente espacial único y resulta en una mejor bondad de ajuste. En relación a la aplicación se resalta que mientras el modelo con único coeficiente espacial tiende a sobre-explicar el IDH por su componente de estándar de vida, el uso de esta propuesta atenúa la magnitud de tal parámetro asociado.Spatial auto-regressive models allow to describe spatial dependence underlying when regional values are related to the neighbor observations. Extensions of this models to data panel structures have been developed in recent spatial literature, too. This paper has as objective to present a proposal that allows to find the estimators of a spatial auto-regressive model for panel data with specific spatial coefficients through the maximum likelihood methodology. Implemented strategy leads to obtain closed expressions for the parameter estimators associated to non-distance explanatory variables, and variance, while it is necessary the use numeric methodologies to compute the spatial coefficients. Results were applied over a panel which has as objective explaining in a linear way the HDI (Human Development Index) com- ponents within an intercontinental sample. Experiments let to see that estimation of specific coefficients is very computing expensive, but the results are statistically different respect to the unique spatial coefficient specification and leads a better goodness-of-fit. Regarding to the application, we highlight the over-accounting in living standard component by the unique coefficient proposal, parameter attenuated using specific coefficients model.Magister en Ciencias - Estadística. Línea de Investigación: Modelos Lineales para datos panelMaestría96application/pdfspaMatemáticas::Probabilidades y matemáticas aplicadasspatial auto-regressivepanel datalinear modelsdevelopment economicsModelos espaciales auto-regresivosdatos panelmodelos linealesdesarrollo económicoEstimación de un modelo SAR para datos panel con coeficientes espaciales específicosEstimation of a SAR model for panel data with spatial specific coefficientsDocumento de trabajoinfo:eu-repo/semantics/workingPaperinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_8042Texthttp://purl.org/redcol/resource_type/WPDepartamento de EstadísticaUniversidad Nacional de Colombia - Sede BogotáAnselin, L. (2001), ‘Spatial econometrics’, A companion to theoretical econometrics 310330.Anselin, L. (2013), Spatial Econometrics: Methods and Models, Vol. 4, Springer Science & Business MediaAnselin, L. & Kelejian, H. H. (1997), ‘Testing for spatial error autocorrelation in the presence of endogenous regressors’, International Regional Science Review 20(1-2), 153–182Anselin, L., Le Gallo, J. & Jayet, H. (2008), Spatial panel econometrics, in ‘The Econometrics of Panel Data’, Springer, pp. 625–660.Arellano, M. (2003), Panel data econometrics, Oxford University Press.Ayvar-Campos, F. J., Navarro-Chavez, J. C. L. & Giménez-García, V. M. (2017), ‘La eficiencia de la dimensión ingreso del IDH en México’, Ensayos. Revista de economía 36(2), 95–121.Baltagi, B. (2001), Econometric Analysis of Panel Data, John Wiley & Sons.Baltagi, B. H., Egger, P. & Pfaffermayr, M. (2013), ‘A generalized spatial panel data model with random effects’, Econometric Reviews 32(5-6), 650–685.Baltagi, B. H. & Li, D. (2006), ‘Prediction in the panel data model with spatial correlation: the case of liquor’, Spatial Economic Analysis 1(2), 175–185.Baltagi, B. H., Song, S. H. & Koh, W. (2003), ‘Testing panel data regression models with spatial error correlation’, Journal of Econometrics 117(1), 123–150.Baringhaus, L., Danschke, R. & Henze, N. (1989), ‘Recent and classical tests for normality-a comparative study’, Communications in Statistics-Simulation and Computation 18(1), 363–379.Barry, R. P. & Pace, R. K. (1999), ‘Monte carlo estimates of the log determinant of large sparse matrices’, Linear Algebra and its Applications 289(1-3), 41–54.Bibby, J., Kent, J. & Mardia, K. (1979), ‘Multivariate analysis’.Breusch, T. & Pagan, A. (1980), ‘The lagrange multiplier test and its applications to model specification in econometrics’, The Review of Economic Studies 47(1), 239–253.Brueckner, J. K. (2006), ‘Strategic interaction among governments’, A companion to urban economics 26, 332–347.Celemín, J. P. & Velázquez, G. A. (2017), ‘Spatial analysis of the relationship between a life quality index, HDI and poverty in the province of Buenos Aires and the Autonomous City of Buenos Aires, Argentina’, Social Indicators Research 17, 1–21.Chintagunta, P. K., Jain, D. C. & Vilcassim, N. J. (1991), ‘Investigating heterogeneity in brand preferences in logit models for panel data’, Journal of Marketing Research 1, 417–428.Cliff, A. D. & Ord, J. K. (1973), ‘Spatial autocorrelation, monographs in spatial environmental systems analysis’, London: Pion Limited 1.Doornik, J. A. & Hansen, H. (2008), ‘An omnibus test for univariate and multivariate normality’, Oxford Bulletin of Economics and Statistics 70, 927–939.Druska, V. & Horrace, W. C. (2004), ‘Generalized moments estimation for spatial panel data: Indonesian rice farming’, American Journal of Agricultural Economics 86(1), 185–198.Egger, P., Pfaffermayr, M. & Winner, H. (2005), ‘An unbalanced spatial panel data approach to us state tax competition’, Economics Letters 88(3), 329–335.Elhorst, J. P. (2003), ‘Specification and estimation of spatial panel data models’, International Regional Science Review 26(3), 244–268.Frazier, C. & Kockelman, K. (2005), ‘Spatial econometric models for panel data: incorporating spatial and temporal data’, Transportation Research Record: Journal of the Transportation Research Board (1902), 80–90.Goldfeld, S. M. & Quandt, R. E. (1965), ‘Some tests for homoscedasticity’, Journal of the American Statistical Association 60(310), 539–547.Greene, W. (2000), Econometric analysis, International edition, Pearson US Imports & PHIPEsHausman, J. A. (1975), ‘An instrumental variable approach to full information estimators for linear and certain nonlinear econometric models’, Econometrica: Journal of the Econometric Society 43, 727–738.Hausman, J. A. (1978), ‘Specification tests in econometrics’, Econometrica: Journal of the Econometric Society 46, 1251–1271Henze, N. & Zirkler, B. (1990), ‘A class of invariant consistent tests for multivariate normality’, Communications in Statistics-Theory and Methods 19(10), 3595–3617.Kao, C. (1999), ‘Spurious regression and residual-based tests for cointegration in panel data’, Journal of Econometrics 90(1), 1–44Kapoor, M., Kelejian, H. H. & Prucha, I. R. (2007), ‘Panel data models with spatially correlated error components’, Journal of Econometrics 140(1), 97–130.Kmenta, J. & Rafailzadeh, B. (1997), Elements of econometrics, University of Michigan Press.Kumar, S. (2014), ‘Eigenvalue statistics for the sum of two complex wishart matrices’, EPL (Europhysics Letters) 107(6), 60002.Lax, P. D. & Lax, P. (2007), Linear Algebra and its Applications, Wiley-Interscience.Lee, L.-F. (2004), ‘Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models’, Econometrica 72(6), 1899–1925.Lee, L.-f. & Yu, J. (2010a), ‘Estimation of spatial autoregressive panel data models with fixed effects’, Journal of Econometrics 154(2), 165–185.Lee, L.-f. & Yu, J. (2010b), ‘Some recent developments in spatial panel data models’, Regional Science and Urban Economics 40(5), 255–271.LeSage, J. & Pace, R. K. (2009), Introduction to spatial econometrics, Chapman and Hall/CRC.Letkoviˇcov´a, H. et al. (2014), ‘Spatial distribution and relationship between sustainable development measures in EU countries’, Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis 53(3), 87–94Maddala, G. S. (1987), ‘Limited dependent variable models using panel data’, Journal of Human Resources 22.Maddala, G. S. & Wu, S. (1999), ‘A comparative study of unit root tests with panel data and a new simple test’, Oxford Bulletin of Economics and Statistics 61, 631–652.Magnus, J. R. & Neudecker, H. (1988), ‘Matrix differential calculus with applications in statistics and econometrics’, Wiley Series in Probability and Mathematical Mtatistics .Mardia, K. V. (1970), ‘Measures of multivariate skewness and kurtosis with applications’, Biometrika 57(3), 519–530.Moran, P. A. (1950), ‘Notes on continuous stochastic phenomena’, Biometrika 37(1/2), 17–23.Mutl, J. & Pfaffermayr, M. (2008), The spatial random effects and the spatial fixed effects model: the hausman test in a cliff and ord panel model, Technical report, Reihe Okonomie/Economics Series, Institut f¨ur H¨ohere Studien (IHS).Ord, K. (1975), ‘Estimation methods for models of spatial interaction’, Journal of the American Statistical Association 70(349), 120–126.Pace, R. K. & Barry, R. (1997), ‘Quick computation of spatial autoregressive estimators’, Geographical analysis 29(3), 232–247.Pawitan, Y. (2001), In all likelihood: statistical modelling and inference using likelihood, Oxford University Press.Pesaran, M. H. & Smith, R. (1995), ‘Estimating long-run relationships from dynamic heterogeneous panels’, Journal of Econometrics 68(1), 79–113.Qiu, Q., Sung, J., Davis, W. & Tchernis, R. (2018), ‘Using spatial factor analysis to measure human development’, Journal of Development Economics 132, 130–149.Shaker, R. R. (2015), ‘The spatial distribution of development in Europe and its underlying sustainability correlations’, Applied Geography 63, 304–314.Wooldridge, J. M. 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