Hello,
This may be a rookie question, but if I run the xtreg without specifying an fe, re, be, or pa estimator, what does it default to? Is it a GLM?

I'm running a super simple model where we have panel data for a set of markets over time and we've divided the markets into 2 groups. We want to test the difference in y by group and we're interested in the magnitude and the significance, so hence not running an ANOVA. It is panel data and we expect the panel variable (market) is correlated with the error term, and a Breusch-Pagan test rejected H0 so pooled OLS wouldn't be appropriate. But our explanatory variable is time-constant, so a fixed effects estimator also isn't useful. So my second question is if using xtreg without fe/re/be/pa, would we include the market dummies (only 29 markets)? Here are the two model options

Code:
xtreg y x i.market month, vce(cluster market)
xtreg y x month, vce(cluster market)
Where the x variable is 0 or 1 but is constructed from market, so should be collinear but isn't dropping out of the regression, and I'm trying to understand the underlying model to figure out why not.

It's so simple that we keep questioning the method.

Thanks so much for the explanation and any recommendations!
-Kate