Persistence, Randomization, and Spatial Noise (revised paper)

Historical persistence studies and other regressions using spatial data commonly return severely inflated t statistics, and different standard error estimates that attempt to correct for this vary so widely as to be as to be of limited use in practice. This paper proposes a simple randomization inference procedure where the significance level of an explanatory variable is measured by its ability to outperform synthetic noise with the same estimated spatial structure. Spatial noise, in other words, acts as a treatment randomization in an artificial experiment based on correlated observational data. Examining twenty persistence studies, few perform substantially above the level of spatial noise.