(Yi, X1i, X2i) satisfy the assumptions of the attachment. You are interestedin β1, the causal effect of X1 on Y. Suppose that X1 and X2 are uncorrelated.You estimate β1 by regressing Y onto X1 (so that X2 is not included in theregression). Does this estimator suffer from omitted variable bias? Explain. The Least Squares Assumptions In the MultipleRegression ModelY; = B + BIXli + BX2i + -. + BXki + Ui, i = 1, ...,n,where1. u; has conditional mean zero given Xi, X7;, ..., X, that is,E(u;|Xlis Xis ..., X) = 02. (X, X ..., X Y;), i = 1, ...,n, are independently and identically distrib-uted (i.i.d.) draws from their joint distribution.3. Large outliers are unlikely: X ..., Xị and Y; have nonzero finite fourthmoments.4. There is no perfect multicollinearity.

Regression analysis is an important technique of forecasting in the field of econometrics. It…

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ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

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(Y_i, X_1i, X_2i) satisfy the assumptions of the attachment. You are interested
in β₁, the causal effect of X₁ on Y. Suppose that X₁ and X₂ are uncorrelated.
You estimate β₁ by regressing Y onto X₁ (so that X₂ is not included in the
regression). Does this estimator suffer from omitted variable bias? Explain.

The Least Squares Assumptions In the Multiple
Regression Model
Y; = B + BIXli + BX2i + -. + BXki + Ui, i = 1, ...,n,
where
1. u; has conditional mean zero given Xi, X7;, ..., X, that is,
E(u;|Xlis Xis ..., X) = 0
2. (X, X ..., X Y;), i = 1, ...,n, are independently and identically distrib-
uted (i.i.d.) draws from their joint distribution.
3. Large outliers are unlikely: X ..., Xị and Y; have nonzero finite fourth
moments.
4. There is no perfect multicollinearity.

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