Perhaps the last thing I’ll ever post on multilevel models vs. clustered standard errors

Ban Chuan Cheah writes: “This paper may be relevant to a recent entry on your blog.” Here’s the abstract:

Multilevel models are used to revisit Moulton’s (1990) work on clustering. Moulton showed that when aggregate level data is combined with micro level data, the estimated standard errors from OLS estimates on the aggregate data are too small leading the analyst to reject the null hypothesis of no effect. Simulations using similar data suggest that even when corrected for clustering, the null hypothesis is over-rejected compared to the estimates obtained from multilevel models. The relationship between survey sampling and Moulton’s correction is also explored. The parallel between these two areas is extended into multiway clustering. Simulations using a data set with students clustered within classrooms and classrooms within schools suggest that the over-rejection rate from multilevel models is smaller than those corrected for clustering. This is particularly true when the number of clusters (classrooms) is small. The results suggest that modeling the clustering of the data using a multilevel methods is a better approach than fixing the standard errors of the OLS estimate.