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?