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In biostatistics, fixed-effects may mean population-average effects. In econometrics, fixed-effects may represent the observed quantities in terms of explanatory variables that are treated as if the quantities were non-random.
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Projection vs fixed effects
Suppose I have $n$ observation indexed by $i$ and that each observation is part of a group $g$. I want to compare two regressions.
First regression:
$$
Y_i=\beta X_i + \alpha F_{g(i)}+\varepsilon_i
$$ …
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Orthogonalization vs fixed effects in instrumental variable estimation
Suppose that I have a set of observations indexed by $i$. Each observation belongs to a group $g$. Let's define by $\hat{Z}_i=Z_i - E\left[Z_i\vert g(i)\right]$ is the residual after projecting $Z$ on …