5 - Missing Variable_Short

# 5 - Missing Variable_Short - The "missing...

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Unformatted text preview: The "missing variables" groblem (1) Yi = a + 131x1i + b2X2i + b3x3i + 134x4i + (2) Yi=a+in+Ui (3) *=a+bX*+U* Y. =a+in +ui - Y* =a+bX* +U* (4) yi = bxi + ui (5) yi i = bxi2 + uixi (6) Zyi i = b inz + Zuix. (7) gym: b + Zu.x. 2);; 2i; (3) b" = Zyixi I inz (9) b" = b + Zu.xl (averaging over all values) (lower-case = deviations from means) So the key question about the "missing-variables" problem has to do with whether the missing variable (the U of equation (2)) is or is not correlated with the included variable, X: - If U and X are u_ncorrelated, then the OLS estimate of the coefficient on X — in other words, b" — will be unbiased. - If U and X are positively correlated, then the OLS estimate of b will be upward-biased. - If U and X are negatively correlated, then the OLS estimate of b will be downward-biased. Example: (10) Y=a+bE+U where Y = earnings, E = education, U = unobservables. What if “ability” (“|Q,” etc.) isn’t (or can’t be) measured? Then it is included in U. So long as ability and education are positively correlated, E and U are positively correlated — So that the OLS estimate of b (the estimate of the coefficient on E) will be upward-biased. Now consider the multivariate regression (11) Yi = a + b1X1i + b2x2i + b3X3i + b4X4i + Ui where the variables X1 through X4 are measured, and where U refers to omitted variables. Suppose we are interested in the estimate of the coefficient b1. Then - If U and X1 are moorrelated (with all other included variables — X2, X3, and X4 — held constant), then the OLS estimate of the coefficient on X1 — in other words, of b1 — will be unbiased. - If U and X are positively correlated (with all other included variables — X2, X3, and X4 — held constant), then the OLS estimate of b1 will be upward-biased. - If U and X are negatively correlated (with all other included variables — X2, X3, and X4 — held constant), then the OLS estimate of b1 will be downward-biased ...
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## This note was uploaded on 09/29/2011 for the course ECON 364 taught by Professor Killingsworth during the Fall '11 term at Rutgers.

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5 - Missing Variable_Short - The "missing...

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