Dependence of spatial effects on the level of regional aggregation, weights matrix, and estimation method

Researchers have repeatedly noted that the results in spatial-econometric studies depend significantly on the level of regional aggregation (Jacobs-Crisioni et al., 2014; Kang et al., 2014, Baltagi, Li, 2014). Currently, hierarchical models can contribute a lot to the studies of spatial effects since they take into account nested structure of regions (Dong, Harris, 2014). In addition, some studies say that econometric results also depend on the choice of the weights matrix W and the estimation method used (Elhorst, Vega, 2013; Kukenova, 2008). In different studies Monte-Carlo method with specially generated data is used to justify the selection of models or estimation method and to test the goodness-of-fit criteria (Kukenova, 2008, Piras, 2012). There are not so many studies that use real data. In this work we try to fill this gap by using different models for economic growth in the Russian regions. The data for 75 Russian regions within the period between 2005 and 2011years are used. We also include two levels of data aggregation: into 12 economic regions and into 8 federal districts. We are testing three main hypotheses: H1: The estimation results of spatial-econometric models depend on the level of regional aggregation. H2: The estimation results of spatial-econometric models depend on the choice of the method of estimation. H3: The estimation results of spatial-econometric models depend on the choice of the weighs matrix. To test these hypotheses SAR models are estimated with and without hierarchical regional structure. As a dependent variable in these models we use the GRP growth in analyzing spatial units. As the spatial weighs matrix we use the binary contiguity matrix, matrix of boundaries lengths and matrix of inverse distance between the capitals of the regions by road. Methods of estimation used are ML, difference GMM and system GMM. According to the results obtained from estimated models we get the empirical support for the first and second hypotheses. This means that the level of regional aggregation and the choice of estimation method significantly influence the results of spatial analysis. Our third hypothesis has been rejected for the vast majority of cases, except for those, where system GMM and difference GMM provide different results in the significance level of the coefficients in accordance to the weights matrix used. Thus, obtained results provided by the data on Russian regions largely confirm the findings of the articles cited above (Elhorst, 2013), (Kukenova, 2008), (Piras, 2012), and other studies related to the importance of choosing the right level of aggregation, model specification and estimation method when working with spatial data. However, all of estimated models show the stable positive spatial effect at any level of aggregation, any specification and estimation method used.