Spatial Regression: The Curious Case of Negative Spatial Dependence

Positive spatial dependence is predominant in the spatial data. Therefore, it is not surprising that most of the methodological papers are concerned with the positive spatial dependence (either in terms of spatial lag, spatial error, or both) when evaluating estimation, testing and forecasting procedures [For example, see Anselin, Bera, Florax, and Yoon (1996) and Baltagi, Song, and Koh (2003) for testing spatial dependence.] However, prevalence of negative spatial dependence is not uncommon as evidenced in many applied papers; just to mention a few: the studies of welfare competition or federal grants competition among local governments [Saavedra (2000) and Boarnet and Glazer (2002)]; the studies of regional employment [Filiztekin (2009) and Pavlyuk (2011)]; the cross-border lottery shopping [Garrett and Marsh (2002)]; foreign direct investment in OECD countries [Garretsen and Peeters (2009)] and locations of Turkish manufacturing industry [Basdas (2009)]. Griffith and Arbia (2010) investigated empirical situations in which negative spatial dependence may occur and situations in which it may be masked by positive spatial autocorrelation. In particular, they presented examples of negatively spatial autocorrelated phenomena based on the geographic competition for land surface, for territory, and for market area. The literature of theoretic explanation for the presence of negative spatial dependence is still growing slowly. Some attempts have been made in economic theory recently, especially in trade and growth theory. For example, Frank and Botolf (2007) suggest that Myrdal’s backwash effect [Myrdal (1957)] can be