Recently, a colleague asked me how to cluster standard errors for a particular set of experimental data. This experimental design falls into the category “Treatments assigned to participant-periods” because the group cluster is randomized every period. However, because correlation may occur across more than one dimension, this motivation makes it difficult to justify why If $Treatment$ is assigned at the participant level and you conducted a one-shot experiment, then there is no need to cluster standard errors. But at least WikiProject Statistics or WikiProject Math may be able to help recruit an expert. ?Ðöùò´¨5ýÛmEGDµß©W„µÇ-áw8¤f^îžk›Š-ĹT¯aÐÎ?Î=†’µã6£fqr¢Ö+õ—²®Q± öØ\t¨wG¼PžÀ/6ÆÆúñ/ªR¾ŠD†šâ£2Éð† j]¹êÄ1WQ-‰*Ó®5ˆP/Oìôè/£þ]î{X¾c¨=BáØg]g2½6ÃËê¤Öb¬¡¹fì³ú¨§LKe½•Ý¸MݜÁ‡XFip†çÎu¬¢fx½T?3ç'6Ç6r¦j4G¬|6{­•›X³Ü3ž,¡–¸h|¬Éq/VPïLÖbõ07y/À$­¦\õ˜ÿ¬. Note: In most cases, robust standard errors will be larger than the normal standard errors, but in rare cases it is possible for the robust standard errors to actually be smaller. But what do you do if you have assigned $Treatment$ to participants who interact in groups over time but reform their groups randomly and anonymously at the start of every period? However, if standard deviations of group-period sets of observations would be smaller than the participant-period sets of observations, then you may want to cluster at the group level. Thus, clustering at the participant level is inherited from the experimental design. OLS with clustered standard errors (Peter Flom made a comment that OLS assumes that the errors are independent, but that assumption is easy to circumvent with the right choice of the covariance matrix estimator) Multilevel analysis surely is fancy and hot. Clustering of Errors Cluster-Robust Standard Errors More Dimensions A Seemingly Unrelated Topic Combining FE and Clusters If the model is overidentified, clustered errors can be used with two-step GMM or CUE estimation to get coefficient estimates that are efficient as well as robust to this arbitrary within-group correlation—use ivreg2 with the In many practical applications, the true value of σ is unknown. Clustering standard errors are important when individual observations can be grouped into clusters where the model errors are correlated within a cluster but not between clusters. When Should We Cluster Experimental Standard Errors? one cluster per country-year tuple), then you need to do "vce (cluster country#year)". Thus, my colleague must choose a cluster! Finally, I verify what I get with robust standard errors provided by STATA. The standard deviations of participant-period sets of observations are smaller than group-period sets of observations. When Should You Adjust Standard Errors for Clustering? Firstly, estimate the regression model without any clustering and subsequently, obtain clustered errors by using the residuals. (2017) is a useful reference explaining why this is not necessary, but the reasoning is relatively simple. Clustering is used to calculate standard errors. Thus, clustering at the participant level is inherited from the experimental design. It has nothing to do with controlling unobserved heterogeneity. Abadie et al. After doing some reading, I discovered that choosing when and how to cluster in experimental data is not only more complicated than I thought, but the discussion around it is quite recent. Recall that the residuals of the simple empirical specification above are the deviations from a conditional mean. Specifically, experimental researchers can ascertain whether and how to cluster based on how they assign treatments to participants. way non-nested clustering. local labor markets, so you should cluster your standard errors by state or village.” 2 Referee 2 argues “The wage residual is likely to be correlated for people working in the same industry, so you should cluster your standard errors by industry” 3 Referee 3 argues that “the wage residual is … (2020, July 18). The clustering is performed using the variable specified as the model’s fixed effects. Typically, the motivation given for the clustering adjustments is that unobserved components in outcomes for units within clusters are correlated. An Introduction to Robust and Clustered Standard Errors Linear Regression with Non-constant Variance Review: Errors and Residuals Errorsare the vertical distances between observations and the unknownConditional Expectation Function. But what would the advice for my colleague, who assigned $Treatment$ to group-period sets of data, be? Please consider the following empirical specification: $$y = a + b.Treatment + e$$ Specifically, clustering is appropriate when it helps address experimental design issues where clusters of participants, rather than participants themselves, are assigned to a treatment. The specific problem is: Per editor request. Recently, practical advice emerged for clustering standard errors in experimental data analyses. I did not consider this example because experimenters typically take great care in either assigning different treatments within experimental sessions or making sure that the conditions under which experimental sessions are held are as consistent as possible. Potential clusters that experimental researchers could consider besides the ones central to the linear regression model without clustering! 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