I am investigating the effects of migration on trade. My dataset contains approximately 120 countries and the 50 US states from 2013-2017, imports and exports. I am using a standard gravity equation with Fixed effects. I want to show the development of varying fixed effects as seen in “Gravity for Dummies and Dummies for Gravity Equations” by Baldwin and Taglioni(2006). I have run multiple regressions and was curious about the reasoning behind the results. IVS and DVs are logged so coefficients are interpreted as elasticities. Standard errors are clustered by state and country. When I include country, state, and year fixed effects the coefficient on migration stock is 0.1*** and 0.19*** for exports and imports respectively. When I include country-state pair FE and year FE the coefficient on migration stock becomes -.02* and .01 for exports and imports respectively (distance and contiguity dropped since time-invariant). My main question is why the large difference in elasticities?
From what I have gathered, fixed effects will subsume all unobserved time-invariant characteristics between the country and state in this case. I have also read from http://www.princeton.edu/~otorres/Panel101.pdf: “fixed-effects will not work well with data for which within-cluster variation is minimal or for slow changing variables over time”. This led me to examine the variation of the migration stock across the 5 years among country-state pairs. I calculated the coefficient of variation for each country-state pair and then took the average for the whole column. This was about 0.49 (49%) for imports and exports and was much higher than all other country and state variables (e.g. gdp, gsp, population) Trade was around 0.45 to 0.53. To me I do not know if this number is high. Could it also be that the number of dummies is so much higher, ca. around 3200 country-state FE categories which were generated in stata from using country-state FE?
I am not really sure how to interpret all this. Would really appreciate the input of the community.
Thanks.
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