Choosing model specification: region*time FEs vs. country-specific time trends

[Alexandre Kaisin]

Hello!

I am trying to find the effect of drought on agricultural production using a model of the following form:

I have panel data of the form:

Country	Continent	Year	agprod	drought
ABW	LAC	1972	13413513	0
ABW	LAC	1973	15213523	1
ABW	LAC	1974	13513513	1
ADO	WEOFF	1972	353413	0
ADO	WEOFF	1973	234233	0

I have tried several specifications and progressively including country FEs, time FEs etc.

These are the results I get:

I am now hesitating between model (4) and model (5).
Model (4) is a regression of ln_agprod on my drought indicator and adding country FEs and continent-year FEs. Model (5) is a regression of ln_agprod on my drought indicator with a linear country-specific time trend and both country FEs and year FEs.

My coefficient of interest is significant in both regressions I am thus hesitating which model to choose as my baseline. I am tempted to say model 4 is more simple and still accounts for unobserved heterogeneity and the fact that year effects may be different across regions.

Any thoughts?

[Andrew Musau]

The estimation of the equation that you show is model 3 (country and year fixed effects). This is the standard specification in large \(N\) and small \(T\) panels, and here your coefficient is not significant. This indicates that your results are not robust. If I were a referee, I would insist on seeing the results of this specification before you try to sell me some other intricate models with linear and higher-order time trends and region-specific time effects.

[Carlo Lazzaro]

Alexandre:
as an aside to Andrew's wise recommendation, in models B-E you have sky-rocketing R-sqs with one predictor only (-spei_05-).
If I were a reviewer, I would ask for a detailed clarification about the role of -spei_05- and about your model specification.
Eventually, I would recommend you to take a comprehensive look at the literature in your research field and see how others deal with the very similar research topic in the past.