My neighbour's neighbour is not my neighbour: Instrumentation and causality in spatial models

We analyse asymmetric spatial or network dynamics in a panel framework by first distinguishing them from stronger common effects. We eliminate pervasive influences by means of a de-factoring model and then uncover the weaker cross-sectional structures by identifying units with significant residual bivariate correlation. In order to assess the effect on a given unit i from shocks to ‘neighbouring' units, we make use of spatial econometric techniques. Given that the effects of these shocks can be directional, i.e. depend on factors such as a city's distance from other cities and their relative sizes appropriately defined, we measure network dependencies in terms of partial correlations instead. For this, we employ GMM and use the information in a regularised version of the residual correlation matrix to identify instruments which comply with the required relevance and exclusion restrictions for instrumentation. For the jth variable in the equation for the ith unit we select elements in the jth column of this correlation matrix that represent units that are correlated with the jth variable but are not correlated with the ith variable. Translating into the terminology of the spatial or networks literature, we focus on the effects of each unit's neighbours' neighbours that are not their neighbours. This approach is consistent with estimating a variant of a gravity model of idiosyncratic shocks to variables such as house prices.