Estimating dynamic spatial panel data models with endogenous regressors using synthetic instruments

Abstract

The paper applies synthetic instruments, initially developed for cross-sectional regression, to estimate dynamic spatial panel data models. These have two main advantages. First, instruments correlated with endogenous variables and yet independent of the errors are difficult to find. Not only are synthetic instruments normally exogenous, but they are usually strongly correlated with endogenous variables, and thus help to avoid the problem of weak instruments. Secondly, they help to reduce instrumental variables proliferation, which is a common result of standard methods of avoiding endogeneity bias. As demonstrated by Monte Carlo simulation, instrument proliferation causes bias in the Sargan–Hansen J test statistic, which is an important indicator of instrument validity and hence estimation consistency. It is also associated with a downward bias in parameter standard error estimates. The paper shows the results of applying synthetic instruments across a variety of different specifications and data generating processes, and it illustrates the method with real data leading to more reliable inference of causal impacts on the level of employment across London districts.