Interpreting the intercept in the random-effects model

Consider the model

y_it = a + bX_it + c_i + e_it

Using a fixed effect model, the constant term a cannot be estimated. a is collinear with c_i. To break the collinearity, you need an additional restriction: xtreg, fe adds one restriction, reg another etc.. At the end, there's no way to separate a from c_i.

My question is if this holds true also in a random effect model. In a RE we impose that the mean of all c_i is equal to zero. Is this restriction sufficient to separately estimate a and c_i or not? More in general what is the interpretation of the constant term in a random effect model (xtreg, re)?

Thanks

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