Suppose the conditional mean function is Y = Bo + B1X + B2X² + B3X3 + U where E[U|X]3D0. By mistake, a researcher omitted X^2 and X^3 terms in the regression and ran regression of Y on X and an intercept only. It turns out that covariance between X and B2X +B3X is nonzero. Is the OLS estimator researcher computed consistent for beta_1? Yes, since the omitted variables are just functions of X. O Yes, since the covariance between X and B2X2 + B3X° is nonzero No, since the covariance between X and B2X4 + B3X is nonzero No, since the omitted variables are negligibly small.

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Suppose the conditional mean function is
Y = Bo + BiX + B2X² + B3X3 + U
%3D
where E[U]X]3D0. By mistake, a researcher omitted X^2 and X^3 terms in the
regression and ran regression of Y on X and an intercept only. It turns out that
covariance between X and B2X2 + B3X° is nonzero. Is the OLS estimator
researcher computed consistent for beta 1?
Yes, since the omitted variables are just functions of X.
Yes, since the covariance between X and B2X2 + B3X is nonzero
No, since the covariance between X and B2X4 + B3X° is nonzero
No, since the omitted variables are negligibly small.
Transcribed Image Text:Suppose the conditional mean function is Y = Bo + BiX + B2X² + B3X3 + U %3D where E[U]X]3D0. By mistake, a researcher omitted X^2 and X^3 terms in the regression and ran regression of Y on X and an intercept only. It turns out that covariance between X and B2X2 + B3X° is nonzero. Is the OLS estimator researcher computed consistent for beta 1? Yes, since the omitted variables are just functions of X. Yes, since the covariance between X and B2X2 + B3X is nonzero No, since the covariance between X and B2X4 + B3X° is nonzero No, since the omitted variables are negligibly small.
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