Diff-in-Diff Coefficient Sign Flip with Time Fixed-Effects?

[Stephen Ch]

I have a panel data set which records entity-level transactions on a given date.

One can think of hospitals purchasing medical equipment (e.g. MRI machine).

The panel data looks something like:



I am interested in running a difference-in-difference regression based on a policy change that impacted only a certain group of hospitals on their equipment purchase price.

In Stata, I perform one with hospital-level FE and one with hospital- and year-level FE models using the command -xtreg, fe-.

 reghdfe y i.policy, absorb(id) vce(cluster id)
reghdfe y i.policy, absorb(id county) vce(cluster id)
reghdfe y i.policy, absorbe(date id) vce(cluster id)
reghdfe y i.policy i.date, absorb(id) vce(cluster id)
reghdfe y i.policy, absorb(date id county) vce(cluster id)

The coefficients for the (1) and (2) are positive.
But, for the rest where I include the time fixed-effects, the coefficients are negative.

My questions:

(i) Is it possible that inclusion of the time fixed-effects can flip the sign, and if so, why? If it doesn't, why?

(ii) In my case, how can I detect the cause of the flip of the sign?

(iii) How is (1) and (2) different each other?

(iv) How are (3), (4), and (5) different from each other?

[Carlo Lazzaro]

Stephen:
1) it is possible, if -i.year- is responsible for most of the within-panel variation, other things being equal.
2) If adding -i.year- creates that change in results, probably -i.year- is the cause (please note that -timevar- should be included by default in the right-hand side of the -fe- regression);
3) the second code included the fixed efefct of county, too (that is probably time-invariant);
4) the differ for the fixed effects that you want to estimate;
5) last but not least, you're nit using -xtreg,fe- as far as I can see, but the community-contributed command (as FAQ kindly request you to mention) -reghdfe-.

[Stephen Ch]

Hi Carlo,

Thanks for the comments.

It would be strange to think that the within panel variation is coming from time, but I would have to check.

-xtreg, fe- produce similar results.

Stephen:
1) it is possible, if -i.year- is responsible for most of the within-panel variation, other things being equal.
2) If adding -i.year- creates that change in results, probably -i.year- is the cause (please note that -timevar- should be included by default in the right-hand side of the -fe- regression);
3) the second code included the fixed efefct of county, too (that is probably time-invariant);
4) the differ for the fixed effects that you want to estimate;
5) last but not least, you're nit using -xtreg,fe- as far as I can see, but the community-contributed command (as FAQ kindly request you to mention) -reghdfe-.

[Carlo Lazzaro]

Stephen:
When you have eliminated the impossible, whatever remains, however improbable, must be the truth. - philosiblog