Correlation within SNCF administrative regions among track segment maintenance cost equation residuals of a country-wide model

Using as reference a recent France-wide model of rail infrastructure maintenance cost where regression model residuals associated to track segments are assumed to be similarly correlated among themselves within the 23 administrative regions of the national firm (SNCF), we attempt to explain the presence of the strong positive and stationary correlation coefficient estimated in this manner and to probe the extent to which the assumption of a common correlation coefficient across administrative regions might be refined and interpreted. We first find that country-wide within-region correlation among residuals is not weakened if regional dummy variables are added to the model in the hope of finding interpretative clues, notably of the presence of climate effects unaccounted for in the model specification. The implicit region-specific weather effects indirectly so represented turn out to be extremely weak, if present at all, and do not affect the strength of extant within-region correlation or the need to make sense of it. We then explore differences in correlation coefficient estimates among regions and show that, within the reference maintenance cost model, two large geographic groupings of regions, each comprising in the East or in the North about 15% of total available track segments, in fact have own residuals that are uncorrelated among themselves, in contrast to the more numerous 70% of segment residuals remaining in the rest of regions, which as a group remain robustly and positively correlated, and in a stationary manner. As the two groupings with uncorrelated residuals closely match the networks of regional firms merged into the SNCF conglomerate in 1938, we hypothesize, faute de mieux and in the absence for the moment of refined local climate variables to pursue unpromising missing variable tests, that within-firm accounting traditions might have survived centralized management control of the assignment of track surveillance, maintenance and repair invoices to track sections centrally defined for accounting management purposes.