Minimum distance estimation of the spatial panel autoregressive model

This paper contributes to the interface literature of new methodological foundation of analyzing historical data with space and spatio-temporal phenomena. In particular, I consider estimating the spatial panel autoregressive model using the minimum distance estimator. Spatial autoregression has important implications for economic system that typifies correlatedness across many spatial locations and which could evolve over long span of time. To overcome computational difficulties, I suggest a two-stage estimation procedure based on minimum distance estimators. A striking feature of the proposed model is that minimum distance estimates are derived under common slopes and complete equality of parameters across spatial units. Assumption of common slopes across spatial units is an empirical and theoretical plausibility as many spatial units are observed to share common trend and typology of changes occurring to the individual system under which equality of parameters are possibilities. The estimation strategy allows various restrictions on time-varying vector parameters. Moreover, those restrictions can easily be tested. I apply this procedure to the residential demand for water of 115 French municipalities over the biannual period 1988–1993. The primary contribution of the paper is to the methodological side of cliometrics while the empirical application (with shorter time period) has been presented for illustrative purpose although, it can nonetheless be readily applied to historical data with long-time horizon allowing for restrictions such as spatio-temporal common vector and structural break in parameter estimates.