The standard errors of persistence

Many studies of historical persistence find that modern outcomes strongly reflect characteristics of the same places in the distant past. However they rely on data that often exhibit extreme spatial trends and autocorrelation, suggesting that their unusually large t-statistics may be due to inadequately controlling for spurious correlation. To analyze this we introduce a new regression procedure and two diagnostic tests of no treatment effect: (a) a placebo test where the treatment is replaced with spatial noise and (b) a synthetic outcomes test of the hypothesis that the outcome is generated by a trend plus a spatial noise process independent of the treatment. We then show how reliable regression results can be obtained by adding a low dimensional spatial basis to the regression of interest, and applying a large cluster standard error correction. Examining 30 persistence studies in leading journals we find that few approach significance at conventional levels. Our procedure applies to regressions with spatial observations more generally and is implemented in an open source package.