It is my first time working with IV regression and I need some help with understanding the process. Specifically, I am looking at the effect of female presidents/prime ministers on health/education expenditure. Following a paper by Chen(2020), I use the electoral rule as an instrumental variable for the the gender of the leader. The problem is, when I run the baseline regression in Stata:
xtivreg2 educationexpenditurelag (male=majoritarianrule) i.year, fe robust first
the p-value of the F test of excluded instruments is not significant (first stage) , but once I include my control variables it becomes significant.
Does that mean that my instrument is not appropriate since the baseline regression has a not significant relationship between instrumental and instrumented variable?
Validity refers to exogeneity (not directlt testable) and relevance (related to the strenght of the first stage).
Your main model is the long one and using fixed-effects, so I would not worry about the smaller correlation without controls and fixed-effects. The opposite would be much more problematic.
Thank you so much for your answer! So, would I then not show the baseline results and just show the results from the other models in my Master thesis?
I am not sure. If, for instance, the problem appears without the fixed-effects, you can show the results directly with them. In any case, you should show results wihout the IV.
You could show the results of several specifications with different set of covariates without the IV and then a complete specification with IV.
Tecnically, my view is that there is no problem in what you mention. A weak isntrument when controlling for more variables would be a more serious concern...
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