Constant in a Fixed Effects Model

[Sidra Ilyas]

Hello Dear,

When we run xtreg fe command for a fixed effects model in Stata and obtain our output, we get a single value of constant. Can you please tell me whether that value of constant is an average of all individual fixed effects or something else by definition?

Many thanks.

[Carlo Lazzaro]

Sidra:
see https://www.stata.com/support/faqs/s...effects-model/.

[Andrew Musau]

You may also find the example in #12 of the following link useful.

https://www.statalist.org/forums/for...cts-with-xtreg

[Sidra Ilyas]

Thanks a lot Dear Carlo.

[Sidra Ilyas]

Dear Andrew,

Thanks a lot for your valuable input. I have been trying my best to go through and understand the information from the link you provided. In simple words, can I then say that the constant in xtreg, fe output is an addition of two terms i.e. a constant term and the average of all individual fixed effects? Please do correct me if I am getting it wrong. Thanks again.

[Andrew Musau]

Yes, because in the fixed effects model

$$ y_{it} = a + x_{it}b + \eta_{i} + e_{it} \;\; (i= 1, \cdots, N;\; t=1, \cdots, T)$$

you will not be able to get estimates of the \(a\) (the intercept) and \( \eta_{i} \) (the individual effects) without imposing some constraints on the system. So the resulting intercept is the average of \(a + \eta_{i} \) as shown in the link referenced in #3.

Also note that we can write the above equation as

$$ y_{it} = x_{it}b + \mu_{i} + e_{it} \;\; (i= 1, \cdots, N;\; t=1, \cdots, T)$$

by defining \(\mu_{i}= a+\eta_{i}\), and still refer to \(\mu_{i}\) as the fixed (time-invariant) effects, and thus xtreg's constant term as the average of the fixed effects.