Abstract
Rainfall is a truly exogeneous variable and hence popular as an instrument for many outcomes. But by its very nature, rainfall in nearby areas tends to be correlated. I show theoretically that if there are also spatial trends in outcomes of interest, this may create spurious correlation. In panel data models where fixed features can be dummied out, the same problem can occur if time trends are spatially dependent. Using Monte Carlo analysis, I show that standard tests can reject true null hypotheses in up to 99% of cases. I also show that this feature is present in a study of the effect of precipitation on electoral turnout in Norway. Using precipitation on non-election days, I show that the distribution of parameter estimates is far away from the theoretical distribution. To solve the problem, I suggest controlling for spatial and spatio-temporal trends using multi-dimensional polynomial approximations.
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