# Fairly elementary OLS w/ fixed effects question

Good afternoon. I'm have a coefficient interpretation question. I have two tables that all have the same outcome variables. Table 1 has no county fixed effect and table 2 has a county fixed effect. The estimates are of the percentage of a census tract that identify as a specific demographic. Subsequently, they can only take on values between 0 and 100.

Table 1:

          Outcome_1   Outcome_2

Level_1   0.116       2.31

Level_2   2.39        1.29

Constant  0.282       0.290



Table 2:

          Outcome_1   Outcome_2
Level_1   -2.091      -0.210

Level_2   -3.502       -3.410

Constant  0.456       2.12


For table 1, I assume that the mean estimate for Level_1 and Outcome_1 is 0.116+0.282 and thus the mean estimate for Level_1 without a fixed effect is 0.398. For table 2, however, I add the county fixed effect and the mean estimate is negative. How should I interpret this?

• Further information is needed please. The question seems to be along the lines of "why does the estimate for a fixed effect become negative after adding an additional covariate as a fixed effect?" Is that what you are asking/thinking ? There could be several reasons but without more it's hard to be confident, but first thing that springs out to me is that the added covariate is a confounder. If you could edit the question to show a summary of both models, that would help a lot. If working with R then use summary(my_model). Commented Dec 2, 2023 at 19:23