Question: Suppose that the population model determining y is and this model satisifies Assumptions MLR.1 through MLR.4. However, we estimate the model that omits x3. Let

Suppose that the population model determining y is

and this model satisifies Assumptions MLR.1 through MLR.4. However, we estimate the model that omits x3. Let ea pi and 02 be the OLS estimators from the regression of y on xt and)0.

Snow that the expected value 01 31 (given the values of the independent variables in the sample)

where the rf1 are the OLS residuals from the regression of x1 on x2. [Hint: The formula for 61 comes from equation. Plug y. = 60 + 61xii + 82x12 + 63x13 + U. into this equation. Alter some algebra, take the expectation treating x13 and ri 1 as nonrandom.]

y = 30 +31x1 + 32X2 +33X3+ u, E(B)-B,+B, - =

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