Hello everyone,


I have a question on the various specifications of a fixed effect model. I always thought that within estimators using areg, xtreg, or reghdfe should (be able to) provide identical results as using simple dummies within your reg specification. In other words, that within estimators are identical to least squares dummy variables (LSDV).

In the mock example below, I want to regress impshare on uncertainty. Both vary only in time (quarter). Now say I would want to include quarter fixed effects. This should absorb all variation in impshare and uncertainty, and thus result in no output for uncertainty. Indeed, that's what I get when I use areg.
However, when I regress impshare on uncertainty and include quarter dummies (which again, I thought was identical to using the areg option), I do get an output for uncertainty, which puzzles me. Why is uncertainty now not perfectly collinear with quarter dummies and how do I interpret the uncertainty coefficient in this case?


See data and code below. please ignore that it's an oversimplified database, resulting in the omission of standard errors etc. It's because I collapsed a panel dataset to this time series format for simplification. The coefficients and results regarding areg or dummies are the same.

Code:
* Example generated by -dataex-. To install: ssc install dataex
clear
input long quarter double impshare float uncertainty
201501 .08978211473287988    35
201502  .0908441642096677    35
201503 .09298928428359604    35
201504 .09066902977290353    35
201601  .0975096476492042    35
201602 .09609810364723077    35
201603 .09644018437561988 37.86
201604 .09476250311679726 38.13
201701 .09643089107585387 38.13
201702 .09585398951901894 35.82
201703    .09537700327528 38.89
201704 .09612222201218018 38.64
201801 .09723944204344515 38.54
201802 .09668838998878439 36.94
201803 .09647264244667098 43.23
201804  .0966329961359868 53.52
201901 .09828297726092321 56.51
201902 .09214517032365498 49.93
201903 .09308704924572131 54.45
end

Code:
 areg impshare uncertainty, absorb(quarter)  // uncertainty omitted due to collinearity with quarter; as expected

reg impshare uncertainty i.quarter // a coefficient of 0.000169 for uncertainty, despite the inclusion of quarter fixed effects. how to interpret??