Further explorations of interactions between agricultural policy and regional growth in Western Europe - approaches to nonstationarity in spatial econometrics
The work discussed in Bivand and Brunstad (2003) was an attempt to throw light on apparent variability in regional convergence in relation to agriculture as a sector subject to powerful political measures, in Western Europe, 1989 1999. We tried to explore the possibility that some of the observed specification issues in current results are rooted in neglecting agricultural policy interventions, within the limitations imposed by data available. We also attempted to use this as a case setting for evaluating the appropriateness of geographically weighted regression (GWR) as a technique for assessing coef- ficient variability, over and above for instance country dummies, but possibly reflecting missing variables or other specification problems. The present study takes up a number of points made in conclusion in that paper. Since it is possible that the non-stationarity found there is related to further missing variables, including the inadequacy of the way in which agricultural subsidies are represented, we attempt to replace the agriculture variables with better estimates of producer subsidy equivalents for the base year. We also look at ways of handling changes in agricultural policy regime occurring between years and T. This raises the further challenge of looking at both spatial and temporal dimensions at the same time, which we will discuss, but are not likely to resolve satisfactorily. On the technical side, the tests on GWR estimates also need to be more firmly established. The GWR results also need to be tested for spatial autocorrelation, and re-worked in an adaptive weighting framework, although GWR does already involve a spatial weighting of the observations themselves. The paper is therefore also an account of the development of software contributed to the R project (R Development Core Team, 2004) as packages, in particular the spdep package for spatial econometrics, and the spgwr package for GWR fitting. In particular, specific issues regarding the handling of the Jacobian in fitting spatial simultaneous autoregressive (SAR) models, and in interpreting GWR output will be discussed. These will be set in the context of on-going work on semi-parametric spatial filtering, which it is hoped to add to spdep following contributions by Michael Tiefelsdorf, so that the weaknesses and strengths of alternative approaches can be compared. Concentrating on implementations in R is justified by the preliminary nature of many of these methods requiring open source and replicable statistical research approaches, so that others can, if they wish, see how results were calculated. One such technical issue is the representation of neighbours in the various approaches, and of the impact of symmetry requirements in conditional autoregressive (CAR) models typically used in MCMC estimation using Open- BUGS and elsewhere. Indeed, in many SAR models, symmetry is also required, or at least underlying symmetry, with the weights matrix in the rowstandardised weighting scheme typically being similar to a symmetric matrix. Using the Western European regional growth data augmented with agricultural policy variables, we will try to explore how far some as-yet unresolved technical questions impede progress with substantive interpretation. We will also try to show how these questions may be handled in other software settings, and how data can be moved between software platforms for analysis. In conclusion, the paper has two threads, one focussing on the analysis of the relationships between regional growth and agricultural policy, generating models needing testing, while the other attempts to meet the software demands generated in the first thread, and to incorporate on-going research in spatial data-analytic methods to respond adequately to the potential importance of the substantive research question.
