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Clustering, Spatial Correlations, and Randomization Inference

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Author Info

  • Thomas Barrios
  • Rebecca Diamond
  • Guido W. Imbens
  • Michal Koles�r

Abstract

It is a standard practice in regression analyses to allow for clustering in the error covariance matrix if the explanatory variable of interest varies at a more aggregate level (e.g., the state level) than the units of observation (e.g., individuals). Often, however, the structure of the error covariance matrix is more complex, with correlations not vanishing for units in different clusters. Here, we explore the implications of such correlations for the actual and estimated precision of least squares estimators. Our main theoretical result is that with equal-sized clusters, if the covariate of interest is randomly assigned at the cluster level, only accounting for nonzero covariances at the cluster level, and ignoring correlations between clusters as well as differences in within-cluster correlations, leads to valid confidence intervals. However, in the absence of random assignment of the covariates, ignoring general correlation structures may lead to biases in standard errors. We illustrate our findings using the 5% public-use census data. Based on these results, we recommend that researchers, as a matter of routine, explore the extent of spatial correlations in explanatory variables beyond state-level clustering.

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File URL: http://hdl.handle.net/10.1080/01621459.2012.682524
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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Journal of the American Statistical Association.

Volume (Year): 107 (2012)
Issue (Month): 498 (June)
Pages: 578-591

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Handle: RePEc:taf:jnlasa:v:107:y:2012:i:498:p:578-591

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Cited by:
  1. Hugh Gravelle & Rita Santos & Luigi Siciliani & Rosalind Goudie, 2012. "Hospital Quality Competition Under Fixed Prices," Working Papers 080cherp, Centre for Health Economics, University of York.
  2. Breinlich, Holger & Ottaviano, Gianmarco & Temple, Jonathan, 2013. "Regional Growth and Regional Decline," CEPR Discussion Papers 9568, C.E.P.R. Discussion Papers.
  3. John Gibson & Bonggeun Kim & Susan Olivia, 2010. "Can We Trust Cluster-Corrected Standard Errors? An Application of Spatial Autocorrelation with Exact Locations Known," Working Papers in Economics 10/07, University of Waikato, Department of Economics.
  4. Brewer, Mike & Crossley, Thomas F. & Joyce, Robert, 2013. "Inference with Difference-in-Differences Revisited," IZA Discussion Papers 7742, Institute for the Study of Labor (IZA).
  5. F. Coelli & P. Manasse, 2014. "The impact of floods on firms' performance," Working Papers wp946, Dipartimento Scienze Economiche, Universita' di Bologna.

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