# The properties of tests for spatial effects in discrete Markov chain models of regional income distribution dynamics

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## Abstract

Discrete Markov chain models (DMCs) have been widely applied to the study of regional income distribution dynamics and convergence. This popularity reflects the rich body of DMC theory on the one hand and the ability of this framework to provide insights on the internal and external properties of regional income distribution dynamics on the other. In this paper we examine the properties of tests for spatial effects in DMC models of regional distribution dynamics. We do so through a series of Monte Carlo simulations designed to examine the size, power and robustness of tests for spatial heterogeneity and spatial dependence in transitional dynamics. This requires that we specify a data generating process for not only the null, but also alternatives when spatial heterogeneity or spatial dependence is present in the transitional dynamics. We are not aware of any work which has examined these types of data generating processes in the spatial distribution dynamics literature. Results indicate that tests for spatial heterogeneity and spatial dependence display good power for the presence of spatial effects. However, tests for spatial heterogeneity are not robust to the presence of strong spatial dependence, while tests for spatial dependence are sensitive to the spatial configuration of heterogeneity. When the spatial configuration can be considered random, dependence tests are robust to the dynamic spatial heterogeneity, but not so to the process mean heterogeneity when the difference in process means is large relative to the variance of the time series.

## Keywords

Distributional dynamics Spatial dependence Growth Convergence## JEL classification:

R11 R15 C49## Notes

### Acknowledgments

This research was supported in part by National Science Foundation Grant SES-1421935.

## References

- Aghion P, Howitt P (1997) Endogenous growth theory. MIT Press, CambridgeGoogle Scholar
- Anselin L (1990) Some robust approaches to testing and estimation in spatial econometrics. Reg Sci Urban Econ 20(2):141–163CrossRefGoogle Scholar
- Anselin L, Rey S (1991) Properties of tests for spatial dependence in linear regression models. Geograph Anal 23(2):112–131CrossRefGoogle Scholar
- Barro RJ, Sala-i Martin X (1991) Convergence across states and regions. Brook Pap Econ Act 1:107–182CrossRefGoogle Scholar
- Bickenbach F, Bode E (2003) Evaluating the Markov property in studies of economic convergence. Int Reg Sci Rev 26(3):363–392CrossRefGoogle Scholar
- Bosker M, Krugell W (2008) Regional income evolution in South Africa after apartheid. J Reg Sci 48(3):493–523CrossRefGoogle Scholar
- Fingleton B (1997) Specification and testing of Markov chain models: an application to convergence in the European Union. Oxf Bull Econ Stat 59(3):385–403CrossRefGoogle Scholar
- Floden M (2008) A note on the accuracy of Markov-chain approximations to highly persistent AR (1) processes. Econ Lett 99(3):516–520CrossRefGoogle Scholar
- Galindev R, Lkhagvasuren D (2010) Discretization of highly persistent correlated AR(1) shocks. J Econ Dyn Control 34(7):1260–1276CrossRefGoogle Scholar
- Hammond GW (2004) Metropolitan/non-metropolitan divergence: a spatial Markov chain approach. Papers Reg Sci 83(3):543–563CrossRefGoogle Scholar
- Jones CI (1997) On the evolution of the world income distribution. J Econ Perspect 11(3):19–36CrossRefGoogle Scholar
- Kopecky KA, Suen RM (2010) Finite state Markov-chain approximations to highly persistent processes. Rev Econ Dyn 13(3):701–714CrossRefGoogle Scholar
- Kullback S, Kupperman M, Ku HH (1962) Tests for contingency tables and Markov chains. Technometrics 4(4):573–608Google Scholar
- Le Gallo J (2004) Space-time analysis of GDP disparities among European regions: a Markov chains approach. Int Reg Sci Rev 27(2):138–163CrossRefGoogle Scholar
- Le Gallo J, Chasco C (2008) Spatial analysis of urban growth in Spain, 1900–2001. Empir Econ 34(1):59–80CrossRefGoogle Scholar
- LeSage JP, Cashell BA (2015) A comparison of vector autoregressive forecasting performance: spatial versus non-spatial Bayesian priors. Ann Reg Sci 54(2):533–560CrossRefGoogle Scholar
- Liao FH, Wei YD (2012) Dynamics, space, and regional inequality in provincial China: a case study of Guangdong province. Appl Geogr 35(1–2):71–83CrossRefGoogle Scholar
- López-Bazo E, Vayá E, Mora AJ, Suriñach J (1999) Regional economic dynamics and convergence in the European Union. Ann Reg Sci 33(3):343–370CrossRefGoogle Scholar
- Lütkepohl H (2005) New introduction to multiple time series analysis. Springer, BerlinCrossRefGoogle Scholar
- Monasterio LM (2010) Brazilian spatial dynamics in the long term (1872–2000): “path dependency” or “reversal of fortune”? J Geogr Syst 12(1):51–67CrossRefGoogle Scholar
- Quah D (1993a) Empirical cross-section dynamics in economic growth. Eur Econ Rev 37(2):426–434CrossRefGoogle Scholar
- Quah D (1993b) Galton’s fallacy and tests of the convergence hypothesis. Scand J Econ 95(4):427–443CrossRefGoogle Scholar
- Quah DT (1996) Empirics for economic growth and convergence. Eur Econ Rev 40(6):1353–1375CrossRefGoogle Scholar
- Rey SJ (2001) Spatial empirics for economic growth and convergence. Geograph Anal 33(3):195–214CrossRefGoogle Scholar
- Rey SJ (2015) Discrete regional distribution dynamics revisited. J Reg Urban Econ 1/2:83–103Google Scholar
- Rey SJ, Gutiérrez MLS (2015) Comparative spatial inequality dynamics: the case of Mexico and the United States. Appl Geogr 61(July):70–80CrossRefGoogle Scholar
- Rey SJ, Le Gallo J (2009) Spatial analysis of economic convergence. In: Mills TC, Patterson K (eds) Palgrave handbook of econometrics, vol 2., Applied econometrics Palgrave Macmillan UK, London, pp 1251–1290CrossRefGoogle Scholar
- Schettini D, Azzoni CR, Paez A (2011) Neighborhood and efficiency in manufacturing in Brazilian regions: a spatial Markov chain analysis. Int Reg Sci Rev 34(4):397–418CrossRefGoogle Scholar
- Tauchen G (1986) Finite state Markov-chain approximations to univariate and vector autoregressions. Econ Lett 20(2):177–181CrossRefGoogle Scholar
- Tauchen G, Hussey R (1991) Quadrature-based methods for obtaining approximate solutions to nonlinear asset pricing models. Econometrica 59(2):371–396CrossRefGoogle Scholar
- Terry SJ, Knotek ES (2011) Markov-chain approximations of vector autoregressions: application of general multivariate-normal integration techniques. Econ Lett 110(1):4–6CrossRefGoogle Scholar
- Wolf LJ, Rey SJ (2015) On the lumpability of regional income convergence. Letters in spatial and resource sciences, pp 1–11Google Scholar