The Standard Errors of Persistence

47 Pages Posted: 11 Jun 2019 Last revised: 29 Jul 2019

See all articles by Morgan Kelly

Morgan Kelly

University College Dublin (UCD) - Department of Economics

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Date Written: June 2019


A large literature on persistence finds that many modern outcomes strongly reflect characteristics of the same places in the distant past. However, alongside unusually high t statistics, these regressions display severe spatial autocorrelation in residuals, and the purpose of this paper is to examine whether these two properties might be connected. We start by running artificial regressions where both variables are spatial noise and find that, even for modest ranges of spatial correlation between points, t statistics become severely inflated leading to significance levels that are in error by several orders of magnitude. We analyse 27 persistence studies in leading journals and find that in most cases if we replace the main explanatory variable with spatial noise the fit of the regression commonly improves; and if we replace the dependent variable with spatial noise, the persistence variable can still explain it at high significance levels. We can predict in advance which persistence results might be the outcome of fitting spatial noise from the degree of spatial autocorrelation in their residuals measured by a standard Moran statistic. Our findings suggest that the results of persistence studies, and of spatial regressions more generally, might be treated with some caution in the absence of reported Moran statistics and noise simulations.

Suggested Citation

Kelly, Morgan, The Standard Errors of Persistence (June 2019). CEPR Discussion Paper No. DP13783, Available at SSRN:

Morgan Kelly (Contact Author)

University College Dublin (UCD) - Department of Economics ( email )

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