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Application of Maximum Likelihood estimation (MLE) to the Generalized Least Square (GLS) model

I have the following regression $$y = X\beta +u$$ where $y$ and $u$ are $(n\times 1)$ and $X$ is a fixed $(n \times k)$ matrix with full column rank and $\beta$ is an unknown $(k\times 1)$ vector of ...
studentp's user avatar
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Is 2SLS asymptotically MLE?

$$y_i =\beta_0 +\beta_1 x_{1i}+\beta_2 x_{2i}+\varepsilon_i$$ Suppose $x_1$ is endogenous but $x_2$ is exogenous. We have two excluded instruments, $z_1$ and $z_2$. The first stage is: $$x_{1i} =\...
Michael Gmeiner's user avatar
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Incidental Parameters and Poisson Regression

Consider: $\ln(E[Y|X])=X_{it}'\beta+\alpha_i$ and thus $E[Y|X]=e^{X_{it}'\beta+\alpha_i}$. We can write this regression model as: $$Y_{it} =e^{X_{it}'\beta+\alpha_i}\eta_{it} $$ For which the ...
Michael Gmeiner's user avatar