Income convergence in Japan: A Bayesian spatial Durbin model approach Hajime Seya a, ⁎, Morito Tsutsumi b , Yoshiki Yamagata a a Center for Global Environmental Research, National Institute for Environmental Studies, 305-8506, Onogawa 16-2, Tsukuba, Ibaraki, Japan b Graduate School of Systems and Information Engineering, University of Tsukuba, 305-8573, Tennodai 1-1-1, Tsukuba, Ibaraki, Japan abstract article info JEL classification: C21 D31 018 Keywords: Income convergence Bayesian spatial Durbin model β-convergence σ-convergence With the collapse of the bubble economy in the early 1990s, economic disparities among both people and regions have arisen in Japan. Although developments in spatial econometrics have provided regional convergence studies with highly effective tools to explicitly consider spatial dependence and heterogeneity, there has as yet been no significant research on Japan's economic disparity using spatial econometrics. Moreover, most conventional regional convergence studies on Japan study the post-war high economic growth period before the economic bubble. Hence, the objective of this study is to analyze regional income disparities in Japan in the period after the bubble burst. We use the Bayesian spatial Durbin model, which can consider both spatial dependence and heterogeneity. The data used in this research are annual data collected at the municipality level during 1989– 2007. To the best of our knowledge, no research has been conducted to analyze Japan's regional income disparities at the municipality level, though some research has been done at the prefecture level. First, the study suggests that σ-convergence does not hold whether or not spatial dependence is considered. Second, it analyzes regional income convergence by applying the simplified Bayesian spatial Durbin model to the β -convergence approach. The results show that β-convergence holds over 1990–2007. © 2010 Elsevier B.V. All rights reserved. 1. Introduction With the collapse of the bubble economy in the early 1990s, economic disparities among both people and regions have arisen in Japan, and have now become a major social issue. One of the popular approaches to analyzing economic disparities is testing the β- and σ- convergence hypothesis. With regard to these approaches, many studies on economic growth/disparities have suggested the impor- tance of considering spatial effects (e.g., Rey and Montouri, 1999; Abreu et al., 2004; López-Bazo et al., 2004; Vayá et al., 2004; Bivand and Brunstad, 2006; Egger and Pfaffermayr, 2006; Fingleton and López-Bazo, 2006; Rey and Dev, 2006; Ertur and Koch, 2007; Basile, 2008; Battisti and De Vaio, 2008; Le Gallo and Dall'erba, 2008; Pfaffermayr, 2009; Rey and Le Gallo, 2009; Tsutsumi et al., 2009; Arbia et al., 2010; Fischer, 2010). However, it is notable that Fingleton and López-Bazo (2006) demonstrated that many of the empirical researches on regional growth employing spatial econometrics have modeled spatial dependence in a rather ad hoc manner. They discussed this problem from the perspective of economic theory (i.e., endogenous growth theory and economic geography) with the model introduced by López-Bazo et al. (2004) and suggested that their theoretical model was very similar to the specifications of the spatial Durbin model (SDM) (e.g., Anselin, 1988; LeSage and Pace, 2009) in spatial econometrics. In relation to this, Pfaffermayr (2009) system- atically suggests that the local knowledge spillover model of Egger and Pfaffermayr (2006) leads to the empirical equation of a spatial cross-regressive model (SCM) (Florax and Folmer, 1992) and the global knowledge spillover model by Ertur and Koch (2007) also leads to the empirical equation of the SDM. The differences in these two theoretically derived SDM models pertain to the question of whether or not the spatial lag of explanatory variables is included (i.e., structural variables and control variables; needless to say, the spatial lag of initial output per worker variable is included in both models). That is, the model of López-Bazo et al. (2004) leads to the model without a spatial lag of explanatory variables, while the model by Ertur and Koch (2007) leads to the model with a spatial lag of explanatory variables (Basile, 2008). Including the spatial lag of explanatory variables is a very effective way of controlling spatial effects; however, the model often suffers from multi-collinearly among the variables and/or biased estimates (e.g., Kakamu, 2009). Hence, our study is based on the model by López-Bazo et al. (2004) and similar work by Vayá et al. (2004); VLMS hereafter). This study slightly extends the VLMS model theoretically, and applies it to the analysis of the regional per capita income disparities at the municipality level in Japan after the bubble burst. The data employed in this research are annual data collected at the municipality level during 1989–2007. To the best of our knowledge, no research has been conducted to analyze Japan's regional income disparities at the municipality level except for our early draft, Tsutsumi et al. (2009); however, there have been several works on Japan's regional income Economic Modelling 29 (2012) 60–71 ⁎ Corresponding author. E-mail addresses: seya.hajime@nies.go.jp (H. Seya), tsutsumi@sk.tsukuba.ac.jp (M. Tsutsumi), yamagata@nies.go.jp (Y. Yamagata). 0264-9993/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.econmod.2010.10.022 Contents lists available at ScienceDirect Economic Modelling journal homepage: www.elsevier.com/locate/ecmod