For many time periods and explanatory variables, constructing a full set of interactions can be tedious. First, estimate the restricted model by doing a pooled regression allowing for different time intercepts; this gives SSR_r. Then, run a regression for each of the, say, T time periods and obtain the sum of squared residuals for each time period. The unrestricted sum of squared residuals is obtained as SSR_ur = SSR_1 + SSR_2 + ... + SSR_T. If there are k explanatory variables (not including the intercept or the time dummies) with T time periods, then we are testing (T - 1)k restrictions, and there are T + Tk parameters estimated in the unrestricted model. So, if n = n_1 + n_2 + ... + n_T is the total number of observations, then the df of the F test are (T - 1)k and n - T - Tk. We compute the F statistic as usual: [(SSR_r - SSR_ur)/SSR_ur][(n - T - Tk)/(T - 1)k].