Interpretation of Structural Parameters for Models with Spatial Autoregression


  • Michał Bernard Pietrzak Nicolaus Copernicus University in Torun



spatial econometrics, measures of average impact, SAR model, SDM model, spatial autocorrelation


The main purpose of the article is to consider a important issue of spatial econometrics, which is a proper interpretation of structural parameters of econometric models with spatial autoregression. The problem will be considered basing on the example of the spatial SAR model. Another purpose of the article is to make an overview of measures of average spatial impact proposed by the subject literature (see Lesage and Pace 2009). The analysis will include such measures as Average Total Impact to an Observation, Average Total Impact from an Observation, Average Indirect Impact to an Observation, Average Indirect Impact from an Observation and Average Direct Impact. Having considered the above issues, I will introduce a set of three original measures that allow the interpretation of the strength of the impact of the explanatory processes within the spatial SAR model, which take the forms of average direct impact, average indirect impact and average induced impact. The use of this set of measures will be illustrated with the example of the analysis of the unemployment rate in Poland. It must be emphasized that the presented set of measures may also be designated for other spatial models. With the knowledge of the empirical form of the model and of the spatial weight matrix, the set of measures introduced simplifies significantly the complex procedure of the interpretation of the structural parameters for spatial models to the use of merely three values.


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Abreu M.H., de Groot L.H., Florax J.G.M. (2005), Space and growth: a survey of empirical evidence and methods, ?Région et Développement?, Vol. 21. DOI:
Anselin L. (1988), Spatial Econometrics: Methods and Models, Kluwer Academic, Dordrecht.
Anselin L., Florax. J.G.M. (1995), New Directio,n in Spatial Econometrics, Springer- Verlag, Berlin Heidelberg.
Anselin L. (2003), Spatial Externalities, Spatial Multipliers, And Spatial Econometrics, ?International Regional Science Review", Vol. 26. DOI:
Anselin L., Florax J.G.M., Rey S.J. (eds.), (2004), Advances in Spatial Econometrics. Methodology, Tools and Applications, Berlin, Springer-Verlag.
Arbia G. (1989), Spatial Data Configuration in Statistical Analysis of Regional Economics and Related Problems, Kluwer Academic Publisher, Dordrecht.
Arbia G. (2006), Spatial Econometrics: Statistical Foundations and Applications to Regional Convergence, Springer-Verlag, Berlin Heidelberg.
Bivand R.S., Pebesma E.J., Gómez-Rubio V. (2008), Applied Spatial Data Analyses with R, Springer, New York.
Cliff A.D., Ord J.K. (1973), Spatial Autocorrelation, Pion, London.
Cliff A.D., Ord J.K. (1981), Spatial Processes: Models and Applications, Pion, London.
Cressie N.A.C. (1993), Statistics for Spatial Data, Wiley & Sons, New York. DOI:
Fischer M.M., Getis A. (eds.) (2004), Recent Developments in Spatial Analysis: Spatial Statistics, Behavioural Modelling, and Computational Intelligence, Springer-Verlag, Berlin Heidelberg.
Getis A., Mur J., Zoller H.G. (eds.) (2004), Spatial Econometrics and Spatial Statistics, Palgrave Macmillan, New York.
Griffith D.A. (1988), Advanced Spatial Statistics, Kluwer Academic Publisher, Dordrecht.
Griffith D.A. (2003), Spatial Autocorrelation and Spatial Filtering: Gaining Understanding Through Theory and Scientific Visualization, Springer-Verlag, Berlin Heidelberg.
Haining R. (1990), Spatial data analysis in the social and environmental sciences, Cambridge University Press, Cambridge.
Haining R. (2003), Spatial Data Analysis: Theory and Practice, Cambridge University Press, Cambridge.
Kelejian H.H., Murrell P., Shepotylo O. (2008), Spatial Spillovers in the Development of Institutions, Working Papers DOI:
Klaassen L.H., Paelinck H.P., Wagenaar S. (1979), Spatial Systems: a general introduction, Saxon House, Farnborough.
LeSage J., Pace R.K. (eds.) (2004), Advances in Econometrics: Spatial and Spatiotemporal Econometrics, Elsevier Ltd, Amsterdam.
LeSage J., Pace R.K. (2009), Introduction to Spatial Econometrics, FL: Chapman & Hall/CRC, Boca Raton. Paelinck J.H.P., Nijkamp P. (1975), Operational theories and method in regional analysis, Saxon House, Farnborough.
Paelinck J.H.P., Klaassen L.H. (1979), Spatial Econometrics, Saxon House, Farnborough. DOI:
Ripley B.D. (1981), Spatial Statistics, Wiley & Sons, New York.
Schabenberger, O., Gotway C.G. (2005), Statistical Methods for Spatial Data Analysis, Chapman & Hall/CRC, Boca Raton.
Ward M.D., Kristian S.G. (2008), Spatial Regression Models, CA: Sage, Thousand Oaks.




How to Cite

Pietrzak, M. B. (2013). Interpretation of Structural Parameters for Models with Spatial Autoregression. Equilibrium. Quarterly Journal of Economics and Economic Policy, 8(2), 129–155.