# Clustered standard errors - Why are SE smaller or bigger than OLS depending on cluster level?

I am analyzing some data using an OLS model. Data represent managers working for US cities. Within each city, we surveyed more than one manager (max 5). Multiple cities per state were surveyed.

I'd like to use clustered standard errors to account for possible clusters at the city or at the state level (state policies might be relevant in our study). Some researchers (e.g., Cameron & Miller, 2015) suggest clustering at the highest level (the state level, in my case). As a check, I tried to estimate clustered SE at both levels and:

1. When I use clustered SE at the city level, standard errors become slightly larger, but overall they are very similar to OLS results.
2. When I use clustered SE at the state level, standard errors become much smaller, leading to quite different results than the OLS model.

What are the possible reasons for such differences? What estimates should I consider? The fact that the standard errors change more when I look at the state-level, would this be a suggestion that state-level clusterization is more important?

My sample contains 2250 observations, grouped in 487 cities (average cluster size = 4, but some cluster size = 1) and 49 states (average cluster size = 30).

• Okay, so then the next question is, if clustering changes the SE size, say making it smaller, is that a problem because it creates model dependence? – Sharif Amlani Sep 8 '20 at 19:29

The variance inflation equation (6) on page six (adjusted for unequal cluster size below) in the Cameron and Miller paper you linked contains the intuition. If you have positive correlation in either the regressor of interest or the errors within cities (the two $$\rho$$s), but a negative correlation within states, that could explain the pattern of what you are seeing. This could be amplified by the unequal cluster size multiplying the $$\rho$$s at the two levels of clustering. You can estimate these to confirm this.