# Clustered standard errors and time dummies in panel data

Assume a simple linear regression model, I have $$i$$ firms and $$t=17$$ periods

$$Y_{it}=\alpha + \beta_2 T_2 + \beta_3 T_3 + \cdots + \beta_{16} T_{16} + \gamma_i + \varepsilon_{it}$$

In this case, $$t=1$$ is the base period and $$T_t$$ are dummies for each other periods. $$\gamma_i$$ represents firm fixed effects.

When I run this regression using clustered standard errors at the firm level, the 95% confidence interval (CI) of the estimates of the coefficients of the time dummies increases with $$t$$, i.e. CI of $$\beta_3$$ is higher than CI of $$\beta_2$$, CI of $$\beta_4$$ is higher than CI of $$\beta_3$$, and it keeps on increasing until 16. Which is not the case when I don't cluster the standard errors, the CI intervals remain similar for the different $$\beta$$s.

I suspect this is logical, but could it be possible to have a simple explanation for this behaviour of the clustered standard errors?

• Any piece of information would be useful! – user6441253 Jul 13 '19 at 8:39

First, this seems to be somehow data-dependent. If I consider instead of $$Y_{i,t}$$ a random variable, I do not get an increasing pattern over time with clustered and robust standard errors.
Hence, I would guess this implies some meaningful increase in variance over time. Maybe you have selected some units at time $$T_1$$, and their path is progressively diverging regarding variable $$Y_{i,t}$$?
• I do not observe an increase in dispersion, but I observe in my data that the mean of $Y_{i,t}$ increases over time. Could it explain the increase of the clustered standard errors? – user6441253 Jul 18 '19 at 7:50