Estimating Standard Errors with a Firm Effect OLS and Rogers Standard Errors
The author simulated a panel data set and then estimated the slope coefficient and its standard error. By doing this multiple times we can observe the true standard error as well as the average estimated standard errors. In the first version of the simulation, the author includes a fixed firm effect but no time effect in both the independent variable as well as in the residual. Across simulations it is assumed that the standard deviation of the independent variable and the residual were both constant at one and two respectively. Across different simulations, the fraction of the variance in the independent variable which is due to the firm effect is altered. This fraction ranged from zero to 75% in 25% percent increments. The same is done for the residual. This allows to demonstrate how the magnitude of the bias in the OLS standard errors varies with the strength of the firm effect in both the independent variable and the residual.