Can the beta estimate from a fixed effects model be written as a function of the individual time-series betas?

[Runbo Li]

Suppose I have a time-series fixed effects model:

Yᵢ=αᵢ+βᵢXᵢt+uᵢt

where i denotes group and t denotes time period.

Can the beta estimate from the fixed effects model be written as a function of the individual time-series betas (i.e. the individual regressions run for each group i)?

Thanks in advance.

[Phil Bromiley]

You'll increase your chances of a a useful answer if you follow the FAQ on asking questions - provide Stata code in code delimiters, Stata output, and sample data.

I don't see the fixed effects in your equation. In general, I don't think you can calculate the beta you'd get from a xtreg,fe from a set of group reg's. They are estimating different models and minimizing different functions.