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What are the possible problems, regarding the estimation of your standard errors, when you cluster the standard errors at the ID level? And how does one test the necessity of clustered errors?

When you have panel data, with an ID for each unit repeating over time, and you run a pooled OLS in Stata, such as:

reg y x1 x2 z1 z2 i.id, cluster(id)

Or a fixed-effects model:

xtreg y x1 x2 z1 z2, fe cluster(id)

How does one test the accuracy of using clustered errors?

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Stata provides an estimate of rho in the xtreg output. Rho is the intraclass correlation coefficient, which tells you the percent of variance in the dependent variable that is at the higher level of the data hieracrchy (here the individual). If that value is anywhere north of .01, that's a good indication that you should be concerned about clustering. As for problems, I don't know that there are any.

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  • $\begingroup$ In a FE model where you have $y_{it}=x'\beta + \alpha_{i}+\varepsilon_{it}$, $\rho$ is the share of the estimated variance of the overall error accounted for by the individual effect $\alpha_i$, or $\frac{\sigma_{\alpha}^2}{\sigma_{\alpha}^2+\sigma_{\varepsilon}^2}$. Clustering is about $Cov(\varepsilon_{it},\varepsilon_{it'}) \ne 0$. Could you elaborate on why $\rho$ reveals anything about the need to cluster? $\endgroup$
    – dimitriy
    Commented Oct 28, 2015 at 1:20
  • $\begingroup$ In modeling clustered data, many have pointed out that the proportion of variance at the between level relative to the total variance (between + within) is a very good indicator of the severity of the clustering effect on the outcome. Higher ICCs are indicative of a stronger influence of the higher level unit on the lower level level units, as it relates to variance in the DV of interest. I would recommend looking at any number of good books on multilevel modeling to get more information and elaboration on this, including, Raudenbush and Bryk, Rabe-Hesketh and Skrondal, and many others. $\endgroup$
    – Erik Ruzek
    Commented Oct 28, 2015 at 3:23
  • $\begingroup$ I have read the RBS book, but I cannot find a discussion of why you can interpret $\rho$ this way. From Cameron, Miller, and Gelbach's JBES paper, I thought that when the primary source of clustering is due to group-level common shocks, a useful approximation is that the OLS standard errors for variable $x$ from ignoring the clustering are inflated by factor $1 + \rho_{x} \cdot \rho_u \cdot (\bar N_g − 1),$ $\endgroup$
    – dimitriy
    Commented Oct 28, 2015 at 18:41
  • $\begingroup$ where $\rho_{x}$ is the within cluster correlation of x, $\rho_{u}$ is the within cluster error correlation, and $\bar N_g$ is the average cluster size. Thus it seems that the $\rho$ reported by Stata is not sufficient to determine that errors are off. $\endgroup$
    – dimitriy
    Commented Oct 28, 2015 at 18:41
  • $\begingroup$ Good point, Dimitry. I realize that I was addressing the question of whether fixed (or random) approaches were needed in my explanation, not whether they were off. I'm not sure why the original poster would think the use of cluster correction/modeling methods were inaccurate unless the rho value was very small (say <.01). $\endgroup$
    – Erik Ruzek
    Commented Oct 29, 2015 at 2:40

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