# Cluster-robust standard errors in panel data analysis

In a simple panel data analysis with data on 64 firms over 8 years, I use cluster-robust standard errors (at the firm level) to evaluate significance of coefficients. I observe important differences between clustered and non-clustered standard errors.

1) Does these differences necessarily mean that there is indeed serial correlations at the firm level in my data?

2) How could I test for serial correlation at the firm level to evaluate whether clustered standard errors are needed?

3) Say we observe that there is no serial correlation at the firm level, what is the impact of using clustered standard errors instead of non-clustered standard errors?

If, for each firm, time periods are independent then cluster-robust standard errors and standard errors without clustering will estimate the same thing (the same population standard deviation), but will use different strategies to do so. The standard errors without clustering will use more information (they don't have to infer that auto-correlations are zero from the data) and are expected to be a slightly better estimator. For large panels this will not make much of a difference but $$N = 64$$ is fairly small.