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The Standard Errors of Persistence

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  • Morgan Kelly

Abstract

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 auto-correlation 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 auto-correlation 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

  • Morgan Kelly, 2019. "The Standard Errors of Persistence," Working Papers 201913, School of Economics, University College Dublin.
  • Handle: RePEc:ucn:wpaper:201913
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    File URL: http://hdl.handle.net/10197/10783
    File Function: First version, 2019
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    References listed on IDEAS

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    1. Sascha O. Becker & Ludger Woessmann, 2009. "Was Weber Wrong? A Human Capital Theory of Protestant Economic History," The Quarterly Journal of Economics, Oxford University Press, vol. 124(2), pages 531-596.
    2. Felipe Valencia Caicedo, 2019. "The Mission: Human Capital Transmission, Economic Persistence, and Culture in South America," The Quarterly Journal of Economics, Oxford University Press, vol. 134(1), pages 507-556.
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    4. Erik Hornung, 2014. "Immigration and the Diffusion of Technology: The Huguenot Diaspora in Prussia," American Economic Review, American Economic Association, vol. 104(1), pages 84-122, January.
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    Cited by:

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    2. Baranov, Victoria & de Haas, Ralph & Grosjean, Pauline, 2018. "Men. Roots and Consequences of Masculinity Norms," Discussion Paper 2018-041, Tilburg University, Center for Economic Research.
    3. Thomas Keywood & Jörg Baten, 0. "Elite violence and elite numeracy in Europe from 500 to 1900 CE: roots of the divergence," Cliometrica, Springer;Cliometric Society (Association Francaise de Cliométrie), vol. 0, pages 1-71.
    4. Sequeira, Tiago & Morão, Hugo, 2020. "Growth accounting and regressions: New approach and results," International Economics, Elsevier, vol. 162(C), pages 67-79.
    5. Cinnirella, Francesco & Naghavi, Alireza & Prarolo, Giovanni, 2020. "Islam and Human Capital in Historical Spain," CEPR Discussion Papers 14561, C.E.P.R. Discussion Papers.
    6. Schaff, Felix, 2020. "When ‘the state made war’, what happened to economic inequality? Evidence from preindustrial Germany (c.1400-1800)," LSE Research Online Documents on Economics 107046, London School of Economics and Political Science, LSE Library.
    7. Eric Schickler, 2020. "Causal inference and American political development: common challenges and opportunities," Public Choice, Springer, vol. 185(3), pages 501-511, December.
    8. James G. MacKinnon & Matthew D. Webb, 2020. "When and How to Deal with Clustered Errors in Regression Models," Working Paper 1421, Economics Department, Queen's University.
    9. Polugodina, Maria & Grigoriadis, Theocharis, 2020. "East Prussia 2.0: Persistent regions, rising nations," Discussion Papers 2020/8, Free University Berlin, School of Business & Economics.
    10. Bakker, Jan & Maurer, Stephan & Pischke, Jorn-Steffen & Rauch, Ferdinand, 2020. "Of mice and merchants: connectedness and the location of economic activity in the Iron Age," LSE Research Online Documents on Economics 103007, London School of Economics and Political Science, LSE Library.
    11. Michael Pollmann, 2020. "Causal Inference for Spatial Treatments," Papers 2011.00373, arXiv.org.
    12. Colella, Fabrizio & Lalive, Rafael & Sakalli, Seyhun Orcan & Thoenig, Mathias, 2019. "Inference with Arbitrary Clustering," IZA Discussion Papers 12584, Institute of Labor Economics (IZA).
    13. Tamanna Adhikari & Karl Whelan, 2019. "Do Business-Friendly Reforms Boost GDP?," Working Papers 201930, School of Economics, University College Dublin.
    14. Dean Eckles & Nikolaos Ignatiadis & Stefan Wager & Han Wu, 2020. "Noise-Induced Randomization in Regression Discontinuity Designs," Papers 2004.09458, arXiv.org, revised Sep 2020.
    15. Kersting, Felix & Wohnsiedler, Iris & Wolf, Nikolaus, 2020. "Weber Revisited: The Protestant Ethic and the Spirit of Nationalism," The Journal of Economic History, Cambridge University Press, vol. 80(3), pages 710-745, September.
    16. Gershman, Boris, 2020. "Witchcraft beliefs as a cultural legacy of the Atlantic slave trade: Evidence from two continents," European Economic Review, Elsevier, vol. 122(C).

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    Keywords

    Persistence; Deep origins; Spatial noise;

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