Is It Persistence Over Time? Or Over Space?

[From the article “The standard errors of persistence” by Morgan Kelly, published at Vox – CEPR Policy Portal]
“Does the slave trade continue to affect trust between people in Africa? Does a country’s prosperity depend on the genetic diversity of its population? Do arbitrary colonial boundaries continue to drive poverty in Peru and internal conflict in Africa? These and other questions are part of a substantial literature on persistence, or deep origins, which finds that many modern outcomes strongly reflect the characteristics of the same place in the more or less distant past.”
“While a judicious choice of variables or time periods might coax a t statistic towards 1.96, there would seem to be no way that the t statistics of four, five, or even higher that appear routinely in this literature could be the result of massaging regressions …”
“Such persistence results must instead reflect … the enduring legacies of the past. However, alongside unusually high t statistics, persistence regressions usually display extreme levels of spatial autocorrelation of residuals.”
“Figure 1 gives the basic idea. I generate two spatial noise series – where areas with high values are coloured yellow and those with low values purple – and take their values at the white dots which correspond to towns. I will call one noise series the ‘modern’ outcome (say, GDP per capita or attitudes toward immigrants), and the other I label the ‘historical’ variable (say, deaths in the Thirty Years’ War or duration of rule by the Ottoman Empire).”
“If you regressed one variable on the other without knowing that they are both artificial noise, you would probably conclude from Figure 1 that the ‘historical’ variable exerts an overwhelming impact on the ‘modern’ outcome.”
“…there turns out to be a reliable indicator to caution us that our findings may be specious, and that indicator is the Moran statistic. The Moran statistic is the standard test for spatial autocorrelation in regression residuals … No study that I examine below reports Moran statistics.”
“I analyse the results of 28 persistence papers that have appeared in the American Economic Review, Econometrica, Journal of Political Economy, and Quarterly Journal of Economics to assess their robustness to spatial noise. The approach is to replicate the first substantive regression of the paper …”
“The Z scores of Moran statistics for each regression are shown in Figure 2 and we can see that, with some exceptions, the spatial autocorrelation in these results is extreme.”
“…we have seen that a standard Moran statistic serves as a useful warning light for potential trouble with spatial noise. My results suggest that in cases where this statistic is not reported the findings of persistence studies (and regressions using spatial data more generally) should be treated with some caution.”
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