I am running what is essentially a difference in differences regression on a large dataset with a lot of fixed effects. Bizarrely (maddeningly, even), I get a slightly different coefficient on my main treatment effect depending on the order I provide the list of independent variables. The regression has individual level data, with county fixed effects, month fixed effects, and state-specific trends. The variable "treatment" is equal to 1 if a state-level policy has gone into effect in the person's state as of the current month. There is a separate set of trends for New York City, as NYC implemented its own policy.

Here's my code and output

Code:
. local conditions if month<=695 & state_cd <= 56 & birthyear_last!=.

. qui xtreg success_14 treated i.month  i.state#c.open_dt 1.NYC#c.open_dt i.state#c.open_dt#c.open_dt 1.NYC#c.open_dt#c.open_dt i.state#c.open_dt#c.open_dt#c.open_dt 1.NYC#c.open_dt#c.open_dt#c.open_dt sc RACE Hispanic EDUCATION Median_income i.bankrank birthyear_last `conditions' , fe vce(cluster state_cd)

. disp _b[treated]
.0064373

. qui xtreg success_14 treated  sc RACE Hispanic EDUCATION Median_income i.bankrank i.month  i.state#c.open_dt 1.NYC#c.open_dt i.state#c.open_dt#c.open_dt 1.NYC#c.open_dt#c.open_dt i.state#c.open_dt#c.open_dt#c.open_dt 1.NYC#c.open_dt#c.open_dt#c.open_dt  birthyear_last `conditions' , fe vce(cluster state_cd)

. disp _b[treated]
.00803661
I realize those are long regression commands, but if you look closely you'll see that they both have the same list of variables, just in a difference order. Both versions drop a few factor levels of i.month for collinearity, but they both drop the same ones. I get the same result using areg instead of xtreg. The regressions each take more than an hour to run, so trying different variations is cumbersome. The problem doesn't replicate if I use a random 0.5% subsample of my data. I'm running out of ideas here--anyone know what's going on? Really just want to know which version is more likely to be the "right" coefficient.

I'm running Stata/MP 15.1 on a Linux server with Red Hat 6.