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?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.