Using Synthetic Variables in Instrumental Variable Estimation of Spatial Series Models

Identification of suitable instruments is a critical step for the implementation of instrumental variable (IV) estimation. A challenge is that, as the level of correlation between the instruments and the endogenous variable increases, so also do the chances that the instruments themselves will be correlated with the error terms. Contrariwise, when the correlation with the endogenous variable is low, the instruments may be weak and perform poorly. The objective of this paper is to explore the use of synthetic variables in IV estimation when the analysis is of spatial data series. The point of departure is the use of eigenvector analysis of the usual spatial weights matrix used in spatial statistics. Eigenvectors obtained from a transformed weights matrix are known to represent latent map patterns. Our proposal is to use these patterns to obtain synthetic variables for use as instruments in IV estimation. By their very nature, instruments based on synthetic variables are exogenous. Furthermore, they can provide relatively high levels of correlation with the endogenous variable. In this paper we consider two situations of interest: First, the case where there are no clear candidates for instrumentation and the instruments are comprised of purely synthetic variables; second, the case when there are substantive but weak instruments that can be enhanced by the addition of synthetic variables. The approach proposed is illustrated with an empirical example.