02850cam a22003017 4500001000700000003000500007005001700012008004100029100002100070245015700091260006600248490004200314500001900356520138800375530006101763538007201824538003601896690006201932690011001994690018602104700002202290700002102312700002102333710004202354830007702396856003802473856003702511w15760NBER20160208164305.0160208s2010 mau||||fs|||| 000 0 eng d1 aBarrios, Thomas.10aClustering, Spatial Correlations and Randomization Inferenceh[electronic resource] /cThomas Barrios, Rebecca Diamond, Guido W. Imbens, Michal Kolesar. aCambridge, Mass.bNational Bureau of Economic Researchc2010.1 aNBER working paper seriesvno. w15760 aFebruary 2010.3 aIt is standard practice in empirical work to allow for clustering in the error covariance matrix if the explanatory variables of interest vary at a more aggregate level than the units of observation. Often, however, the structure of the error covariance matrix is more complex, with correlations varying in magnitude within clusters, and not vanishing between clusters. Here we explore the implications of such correlations for the actual and estimated precision of least squares estimators. We show that with equal sized clusters, if the covariate of interest is randomly assigned at the cluster level, only accounting for non-zero covariances at the cluster level, and ignoring correlations between clusters, leads to valid standard errors and confidence intervals. However, in many cases this may not suffice. For example, state policies exhibit substantial spatial correlations. As a result, ignoring spatial correlations in outcomes beyond that accounted for by the clustering at the state level, may well bias standard errors. We illustrate our findings using the 5% public use census data. Based on these results we recommend researchers assess the extent of spatial correlations in explanatory variables beyond state level clustering, and if such correlations are present, take into account spatial correlations beyond the clustering correlations typically accounted for. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web. 7aC01 - Econometrics2Journal of Economic Literature class. 7aC1 - Econometric and Statistical Methods and Methodology: General2Journal of Economic Literature class. 7aC31 - Cross-Sectional Models • Spatial Models • Treatment Effect Models • Quantile Regressions • Social Interaction Models2Journal of Economic Literature class.1 aDiamond, Rebecca.1 aImbens, Guido W.1 aKolesar, Michal.2 aNational Bureau of Economic Research. 0aWorking Paper Series (National Bureau of Economic Research)vno. w15760.4 uhttp://www.nber.org/papers/w1576041uhttp://dx.doi.org/10.3386/w15760