4
votes
Why is there omitted variable bias in my regression of uncorrelated regressors?
We show for the case of two regressors, that in the setup of the OP (two i.i.d Bernoullis as regressors, large sample), if the regression specification does not include a constant term, then the ...
- 59.9k
2
votes
Accepted
Struggling to prove that the Hessian is PSD for simple linear regression least squares method
This is an instance of the power mean inequality. A proof appears here on CV at Prove that $E(X^n)^{1/n}$ is non-decreasing for non-negative random variables, but since it is stated in terms of ...
- 329k
2
votes
Standardized regression coefficient
The standardized coefficient can be higher than 1, or lower than -1.
It's nothing to do with whether some of the variance in Y is still explained by the other predictors. It typically happens in the ...
- 18.6k
1
vote
Accepted
Simple OLS to measure correlation
I have taken the liberty to drop the subscripts and instead write
$$ Y = a + bX + u $$
$$ X = c + dY + v $$
Then, if we define $\beta = \frac{1}{1-bd} $
$$ Y = \underbrace{(a + bc)\frac{1}{1-bd}}_{\...
- 838
1
vote
Accepted
Does an endogenous variable bias the coefficient of the exogenous one?
The answer depends on whether x1 and x2 are correlated. If they are uncorrelated, endogeneity of x1 doesn't affect the expected value of beta2 because the equation for beta2 doesn't depend on x1 in ...
- 26
1
vote
How to prove an OLS estimator is inconsistent under simultaneity
Note that $Y_i = X_i - Z_i$ gives
\begin{align}
&X_i - Z_i = \beta_0 + \beta_1 X_i + \epsilon_i \\
\iff &(1 - \beta_1) X_i = \beta_0 + Z_i + \epsilon_i \\
\overset{\beta_1 \neq 1}{\iff} &...
- 6,355
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