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1 vote
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Derivation of sample variance of OLS estimator

The conditioning is on $x$, where $x$ represents all independent variables for all observations. Thus $x$ is treated as a constant throughout the derivation. This is the standard method of deriving ...
3 votes
Accepted

Measurement Error - Multivariate Case

To derive this you'll want to use the Frisch-Waugh-Lovell theorem. Using the true variable, $x_2$, let $\widetilde{x_2}$ be the residual from a regression of $x_2$ on $x_1$, $$x_2 = \delta_0 +\delta_1 ...
1 vote
Accepted

Do Economists use Newey-West/Robust Standard Errors with GLS or GLM?

Newey-West/Robust are methods to calculate standard errors. OLS/GLS/GLM are methods to estimate coefficients. I think typically econometricians first choose a method to estimate coefficients (GLS/OLS/...
0 votes

How is the standard error of the discontinuity calculated when using local regression in a discontinuous regression?

Functions of your original independent variables just yield new independent variables. Yes, you might know particular interpretations of the transformations, but the math neither knows nor cares. If ...
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4 votes

Unbiasedness and OLS Regression

They are not equivalent. In the linear regression model (matrix notation), $$ y = X\beta + u,$$ the OLS estimator for $\beta$ is $$\hat \beta_{OLS} = \beta + (X'X)^{-1}X'u.$$ Then $$\mathbb E\left(\...
4 votes

Unbiasedness and OLS Regression

The idea is that $E[\hat{b}|X]$ could possibly be a function of $X$. For example, we might have an estimator for which $E[\hat{b}|X] = b +f(X)$. This would mean our estimator is only unbiased for the ...

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