Abstract
Theoretical models of strategic interaction between local governments are often implemented empirically using spatial econometric techniques. In order to empirically discriminate between different theoretical explanations for strategic interactions, it is important to ensure that the spatial weights matrix W reflects the theoretical mechanisms behind the interaction of interest. However, researchers do not usually have the information required to adequately define its elements in such a way. Here, we present a method for defining these elements that captures the interest of one jurisdiction’s inhabitants in the local politics of their neighboring jurisdictions even when this information is not directly available to the researcher. The method is suitable for use in empirical models of strategic interaction between local jurisdictions and can be used to define spatial weights matrices for spatial econometric models that will be used to test or control for yardstick competition across jurisdictions.
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Notes
This is a simplification. There are of course situations where inhabitants in jurisdiction \(j\) benefit from road expenditures in jurisdiction \(i\) even in the absence of direct road connections between the two jurisdictions.
In general, the definition of the elements in the spatial weights matrix (the definition of neighbors) is often neglected or at least not sufficiently discussed in spatial econometric analyses. This is quite surprising because the interpretation and sometimes the significance of the spatial effect depends on the definition of the spatial weights matrix.
That is, provided that we accept the relative populations of the two jurisdictions to be exogenous, which is reasonable in models of yardstick competition where migration is disregarded.
The covariance matrix for the empirical model developed from the responses was corrected to reflect the fact that answers from an individual respondent could not be considered to be independent from one another. The estimation was also weighted by the proportion of answers obtained from each municipality in relation to the municipality’s population.
The Umeå region consists of six municipalities including Umeå itself, and the Gothenburg region consists of 13 municipalities including Gothenburg itself. The Gothenburg area is the second largest metropolitan area in Sweden, with about 1.2 million inhabitants (about 500.000 of whom live in Gothenburg). The Umeå region represents a typical medium-sized Swedish region and has around 145.000 inhabitants (about 115.000 of whom live in Umeå). Almost 90 % of the Swedish population lives within areas of one of these two types, and around 35 % live in a major city region such as Gothenburg.
We also estimated a logarithmic version of Eq. (4) that gave basically identical results to those presented in the paper.
This is done based on the estimated probabilities from the ordered probit models. For the binomial models, the appropriate calculations would be \( w_{ij}=\Pr (y_{ij}=1)\), and \(w_{ij}=0\) if \(\Pr (y_{ij}=0)>\Pr (y_{ij}=1)\) while \(w_{ij}=1\) if \(\Pr (y_{ij}=1)>\Pr (y_{ij}=0)\).
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Acknowledgments
I’m grateful to the anonymous referee as well as the editor of this journal for constructive and useful comments. Special thanks also to Niklas Hanes, Chris Hudson, Anders Lidström, Sofia Lundberg, Elon Strömbäck, Emma Zetterdahl, Kerstin Westin, seminar participants at Umeå University and ERSA congress in Barcelona 2011 for valuable comments on previous versions of this paper. A research grant from Riksbankens Jubileumsfond is gratefully acknowledged.