AppliedMultiple choice

The variable you left out · Part 2 of 3

The true model is $y = x_1 + 2x_2 + \varepsilon$ , with $\operatorname{Var}(x_1) = \operatorname{Var}(x_2) = 1$ and $\varepsilon$ independent of both regressors. The sample is large enough that estimates sit at their probability limits.

Now suppose instead that $\operatorname{Cov}(x_1, x_2) = -0.5$ . What does the short regression of $y$ on $x_1$ estimate?

A2, the same size of bias as before
B0, so x₁ looks useless even though its true effect is 1
C1, because a negative covariance cannot bias an estimate upward
D−1, reversing the sign of the true effect

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Identification: endogeneity, instruments and panel methods

Now suppose instead that Cov⁡(x1,x2)=−0.5\operatorname{Cov}(x_1, x_2) = -0.5Cov(x1​,x2​)=−0.5. What does the short regression of yyy on x1x_1x1​ estimate?

More regression and econometrics questions

Now suppose instead that $\operatorname{Cov}(x_1, x_2) = -0.5$ . What does the short regression of $y$ on $x_1$ estimate?