Problem implenting a DiD with contiguous region pairs

[Titir Bhattacharya]

Hello,

I'm trying to implement a DiD using contiguous regions as control group, like in Dube et al and Cortes et al


The specification used by Cortes for comparing contiguous region pairs is the following:

Here V_iopt is outcome variable for i-th county part of p-th county pair, in o-th occupation, at time period t. The fixed effect `gamma' links the i-th county to its pair in p-th contiguous county pair.

I tried to implement this estimation, however, when I add the fixed effects, I lose all observations. Following is the simplified version of what I have tried:

areg y i.frontier_county##i.after i.x1 x2 i.county_A i.county_B i.county_C i.county_D i.county_E, absorb(x3) cluster(cluster)

which gives following error

no observations
r(2000);

Here frontier_county is the counties in the policy state that are at the frontier. These counties are A,B,C,D,E. The fixed effect county_A is 1 county A, 0 if observation is in its paired contiguous county. Similarly for rest of the fixed effects.

I have alternatively tried the following:

areg y i.county_A##i.after i.county_B##i.after i.county_C##after i.county_D##i.after i.county_E##after i.x1 x2, absorb(x3) cluster(cluster)

and have gotten the same error.

The way I see it, for each observation belonging to a county, there will be a fixed effect corresponding to that county pair, but I'm not able to figure out how to work this into the estimation code.

I'm not sure how to work out this problem and would appreciate any help.

Thanks!