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Consider a regression model for $i=1,\cdots,N$ and $t= 1,\cdots,T$. I assume $N\rightarrow \infty$ while $T$ is a fixed finite number.

$$y_{it} = x_{it}\beta + \alpha_i + \alpha_t +\varepsilon_{it}, $$ where $x_{it}$ is observed data, $\alpha_i$ and $\alpha_t$ are fixed effects that are time invariant and individual invariant, respectively. $\varepsilon_{it}$ is a stochastic term, and I am interested in estimation $\beta$.

I see sometimes that people claim "I treat $\alpha_t$ as a parameter" What does it mean by treating as a parameter?

Does it mean that I create dummy NT by T matrix $D$ which takes 1 or 0 and estimates $\alpha_t$ for all $t$? I guess this is possible since I assume $N$ grows while $T$ is fixed; hence $\alpha_t$ can be estimated consistently.

And they cannot say "treat $\alpha_i$ as a parameter" because $alpha_i$ grows to infinity as $N$ grows to infinity?

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