FE vs FD - not usual arguments

[Alexandre Kaisin]

Hi all!

First of all, I'd like to say I have read the standard econometric textbook sections on FE vs FD. Therefore, I am familiar with the relative efficiency of each of the methods depending on the assumptions on the serial correlation of the errors.

However, I have been suggested by my professor to estimate my FE model using FD but do not find any valid arguments for using one vs the other.



I am investigating the effect of drought shocks on agriculture production as well as on GDP using panel data for 120 countries for a timespan of around 40 years. The drought shocks are measured by a dummy variable that switches on if a country experiences drought. There are time fixed effects, country fixed effects, and country-specific time trends.
My model looks as follows in levels:

and like this in FD:

I am looking for arguments to go with the First Differenced regression rather than the regression in levels:

Some aspects I've considered are:

- Serial correlation and relative efficiency issues.
- Convenient interpretation of effect on growth rates
- Can estimating both FD and FE serve as some kind of robustness test if estimated coefficients BETA are similar?
- Considering drought is assumed to be transitory and contemporaneous, meaning the effect of the dummy being equal to 1 will be immediately translated to dependent variable effect will not have lagged effects.
- If my dependent variable is trending, could FD be better so as that my effect is not confounded with any trends?


I am really struggling to find strong arguments for FD. If anyone has any comments or suggestions they would be very welcomed.

Many thanks!

[Andrew Musau]

Why do you want to argue that one is better than the other? As the T dimension gets larger, and you have N>T, there will be little to differentiate between the coefficient estimates.