Adjusting for aggregation bias in house price indices: A clustered trajectory approach

This paper explores how the íprice index problemî has a fundamentally spatial component to it in the context of housing because houses in different sub-regions change in value at different rates. The problem, we argue, is essentially one of how to group small areas on the basis of similar price trajectories, and then how to apply the appropriate weighting when computing price indices. We aim to demonstrate that, without such adjustment, significant biases can occur in index computation that frustrate meaningful cross-regional comparisons because different regions are likely to experience different degrees of aggregation bias due to different degrees of housing market segmentation. Our solution is to use clustered p-splines to group areas on the basis of similar price trajectories which has the effect of identifying groups of areas that have stable price relatives and can thereforeóaccording to the Composite Commodity Theoremólegitimately be entered as a single ícommodityî into a price index. We find that the proposed method produces significant reductions in aggregation biasóthe Ten Cluster Fisher Index computed using our clustered geography is almost indistinguishable from the All Areas Fisher Index derived from every individual small area being entered separately into the index calculation.