_10.Suppose that X₁ is measured with error. Y_i = $\beta$₀ + $\beta$₁X_1i + $\varepsilon$_i X_i = X*_1i + $\varepsilon$_i Which of the following is most accurate? A) The estimate of $\beta$₁hat will be larger than it should be. B) The estimate of $\beta$₁hat will be smaller than it should be. C) $\beta$₁hat will be biased toward zero. D) We know $\beta$₁hat will be biased, but do not know which direction.

Question

Quizplus · Accepted Answer

The error term in the equation for Y is not independent of X_1i, which means that the OLS estimate of F1F1F1S1F1F1F10₁ will be biased. Specifically, it will be biased toward zero because the second term in the equation for Y will tend to cancel out some of the effect of the first term, making it look like X_1i is less important in predicting Y than it really is.

10 Suppose That X1 Is Measured with Error β\betaβ 0

₁₀Suppose That X₁ Is Measured with Error $\beta$ ₀