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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) (lowercase = deviations from means) So the key question about the "missingvariables" 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 upwardbiased.  If U and X are negatively correlated, then the OLS estimate of b will
be downwardbiased. 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 upwardbiased. 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 upwardbiased.  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
downwardbiased ...
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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.
 Fall '11
 killingsworth

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