European Spatial Research and Policy


The aim of the paper is to investigate the relationship between socio-economic factors and the level of health of citizens of selected European countries. Disability-adjusted life years (DALYs) were used as the measure of health. The author applied dynamic spatial panel data models with fixed effects and spatial autocorrelation of the error term. The models were estimated using a novel, modified quasi maximum likelihood method based on M-estimators. The approach is resistant to deviations from the assumptions on the distribution of initial observations. The estimation of initial observations is a severe weakness of standard methods based on the maximization of the quasi-likelihood function in the case of short panels. M-estimators are consistent and asymptotically normally distributed. The empirical analysis covers the specification, estimation, and verification of the models.


dynamic spatial panel data models, M-estimation, fixed effects, short panels, DALYs – disability-adjusted life years, the level of health, socio-economic factors




ANAND, S. and HANSON, K. (1997), ‘Disability-adjusted lost years – a critical review’, Journal of Health Economics, 16, pp. 685‒702.

ANAND, S. and HANSON, K. (1998), ‘DALYs: efficiency versus equity’, World Development, 26 (2), pp. 307‒310.

ANSELIN, L. (1988), Spatial Econometrics: Methods and Models, The Netherlands: Kluwer Academic Press.

ANSELIN, L. (2001), ‘Spatial Econometrics’, [in:] BALTAGI, B. H. (eds.), A companion to theoretical econometrics, Massachusetts: Blackwell Publishers Ltd., pp. 310‒330.

ANSELIN, L., LE GALLO, J. and JAYET, J. (2008), ‘Spatial panel econometrics’, [in:] MATYAS, L., SEVESTRE, P. (eds.), The Econometrics of Panel Data: Fundamentals and Recent Developments in Theory and Practice, Berlin-Heidelberg: Springer-Verlag, pp. 625‒660.

BARKER, C. and GREEN, A. (1996), ‘Opening the Debate on DALYs’, Health Policy and Planning, 11, pp. 179‒183.

BERMAN, S. (1995), ‘Otitis media in developing countries’, Pediatrics, 96, pp. 126‒131.

BINDER, M., HSIAO, C. and PESARAN, M. H. (2005), ‘Estimation and inference in short panel vector autoregressions with unit roots and cointegration’, Econometric Theory, 21, pp. 795‒837.

BUN, M. J. and CARREE, M. A. (2005), ‘Bias-corrected estimation in dynamic panel data models’, Journal of Business and Economic Statistics, 23, pp. 200‒210.

DAŃSKA-BORSIAK, B. (2011), Dynamiczne modele panelowe w badaniach ekonomicznych, Łódź: Wydawnictwo Uniwersytetu Łódzkiego.

DESJARLAIS, R., EISENBERG, L., GOOD, B., and KLEINMAN, A. (1995), World mental health: problems and priorities in low income countries, New York: Oxford University Press.

DEVLEESSCHAUWER, B., HAVELAAR, A. H., MAERTENS DE NOORDHOUT, C., HAAGSMA J. A., PRAET, N., DORNY, P., DUCHATEAU, L., TORGERSON, P. R., VAN OYEN H. and SPEYBROECK, N. (2014), ‘DALY calculation in practice: a stepwise approach’, International Journal of Public Health, 59 (3), pp. 571‒574.

ELHORST, J. P. (2005), ‘Unconditional maximum likelihood estimation of linear and loglinear dynamic models for spatial panels’, Geographical Analysis, 37, pp. 85‒106.

ELHORST, J. P. (2010a), ‘Spatial Panel Data Models’, [in:] FISCHER, M. M., GETIS, A., (eds), Handbook of Applied Spatial Analysis, Springer, Berlin.

ELHORST, J. P. (2010b), ‘Applied spatial econometric: raising the bar’, Spatial Economic Analysis, 5 (1), pp. 9‒28.

ELHORST, J. P. (2010c), ‘Dynamic panels with endogenous interaction effects when T is small’, Regional Science and Urban Economics, 40, pp. 272‒282.


GOURIEROUX, C. and PHILLIPS, P. C. B., YU, J. (2010), ‘Indirect inference for dynamic panel models’, Journal of Econometrics, 157, pp. 68‒77.

HSIAO, C., PESARAN, M. H. and TAHMISCIOGLU, A. K. (2002), ‘Maximum likelihood estimation of fixed effects dynamic panel data models covering short time periods’, Journal of Econometrics, 109, pp. 107‒150.

HUBER, P. J. (1981), Robust Statistics. New York: Wiley.

KORNIOTIS, G. M. (2010), ‘Estimating panel models with internal and external habit formation’, Journal of Business and Economic Statistics, 28, pp. 145‒158.

KRUINIGER, H. (2013), ‘Quasi ML estimation of the panel AR(1) model with arbitrary initial conditions’, Journal of Econometrics, 173, pp. 175‒188.

LAURELL, A. C. and ARELLANO, L. O. (1996), ‘Market commodities and poor relief: The World Bank proposal for health’, Journal of Health Economics, 26 (1), pp. 1‒18.

LEE, L. F. and YU, J. (2010a), ‘Estimation of spatial autoregressive panel data model a with fixed effects’, Journal of Econometrics, 154(2), pp. 165‒185.

LEE, L. F. and YU, J. (2010b), Estimation of spatial panels: random components vs. fixed effects, Manuscript, Ohio State University.

LEE, L. F. and YU, J. (2010c), ‘Some recent developments in spatial panel data models’, Regional Science and Urban Economics, 40, pp. 255‒271.

LEE, L. F. and YU, J. (2010d), ‘A spatial dynamic panel data model with both time and individual fixed effects’, Econometric Theory, 26, pp. 564‒597.

LOZANO, R., MURRAY, C. J. L., FRENK, J. and BOBADILLA, J. L. (1995), ‘Burden of diseases assessment and health system reform: results of a study in Mexico’, Journal of International Development, 7 (3), pp. 555–564.

MARTENS, W. J., NIESSEN, L. W., ROTMANS, J., JETTEN, T. H. and McMICHAEL A.J. (1995), ‘Potential impact of global climate change on malaria risk’, Environmental Health Perspectives, 103 (5), pp. 458–64.

MURRAY, C. J. L. (1994), ‘Quantifying the burden of disease: the technical basis for disability-adjusted life years’, Bulletin of the World Health Organization, 72 (3), pp. 429–445.

MURRAY, C. J. L. (1996), ‘Rethinking DALYs’, [in:] MURRAY, C. J. L., LOPEZ, A. D., The Global Burden of Disease and Injury Series, Harvard School of Public Health, World Health Organization, World Bank, Boston, 1, pp. 1–98.

MURRAY, C. J. L. and LOPEZ, A. D. (1994), Global comparative assessments in the health sector: disease burden, expenditures and intervention packages., Geneva, World Health Organization.

MURRAY, C. J. L. and LOPEZ, A. D. (1996a), ‘A comprehensive assessment of mortality and disability from diseases, injuries, and risk factors in 1990 and projected to 2020’, The Global Burden of Disease and Injury Series. The Global Burden of Disease, 1, Harvard School of Public Health, World Bank, World Health Organization.

MURRAY, C. J. L. and LOPEZ, A. D. (1996a), ‘A compendium of incidence, prevalence and mortality estimates for over 200 conditions’, The Global Burden of Disease and Injury Series.The Global Burden of Disease, 2, Harvard School of Public Health, World Bank, World Health Organization.

MURRAY, C. J. L., SALOMON, J. A., MATHERS, C. D. and D. LOPEZ A. D. (2002), Summary measures of population health – concepts, ethics, measurement and applications. Geneva, World Health Organization.

ROBINE, J. M. (2006), ‘Summarizing Health Status’ [in:] PENCHEON, D., GUEST, C., MELZER, D. and GRAY, J. A. M., Oxford Handbook of Public Health Practice, Oxford University Press.

SU, L. and YANG, Z. (2015), ‘QML estimation of dynamic panel data models with spatial errors’, Journal of Econometrics, 185, pp. 230‒258.

TRZPIOT, G. and ORWAT-ACEDAŃSKA, A. (2016), ‘Spatial quantile regression in analysis of healthy life years in the European Union countries’, Comparative Economic Research, 19 (5), pp. 179‒199.

VAN DER VAART, A. W. (1998), Asymptotic Statistics.Cambridge University Press.

WRÓBLEWSKA, W. (2008), ‘Sumaryczne miary stanu zdrowia populacji’, Studia Demograficzne, pp. 153‒154.

YANG, Z. (2018), ‘Unified M-Estimation of Fixed-Effects Spatial Dynamic Models with Short Panels’, Journal of Econometrics, 205, pp. 423‒447.

YANG, Z., LI, C. and TSE, Y. K. (2006), ‘Functional form and spatial dependence in dynamic panels’, Economics Letters, 91, pp. 138‒145.

YU, J., DE JONG, R. and LEE, L. F. (2008), ‘Quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and T are large’, Journal of Econometrics, 146, pp. 118‒134.

YU, J. and LEE, L. F. (2010), ‘Estimation of unit root spatial dynamic panel data models’, Econometric Theory, 26, pp. 1332‒1362.

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