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Consider the simple regression model

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Answer #1

Zero Conditional Mean -The error u has an expected value of zero given any values of the independent variables.

Homoskedasticity - The conditional variance of the error term in a regression equation is constant for all values of the independent variables.

An estimator is unbiased if E(b) = $\beta$
That’s just saying if the expected value of estimator equals the parameter, then it’s an unbiased estimator.

Least Squares Assumptions 1 ·(XiÝ, ) are iid; random sampling 2. Large outliers are rare; If this condition fails, OLS estimator is not consistent. 3. E (u,|X)0; Conditional Mean Zero assumption. Xs are exogenous. This assumption fails if X and u are correalted No Perfect Multicolinearity Condition: The regressors are said to be perfectly multicollinear if one of the regressors is a perfect linear function of the other regressor(s) If all the assumptions are satisfied, the OLS estimates are unbiased and consistent.

a)

(holds

(holds) 81σ

Unbiased estimate

b)

(Does not hold

( 0) holds, variance ot constant

Biased estimate

c)

(holds)

(Does not hold)

Unbiased estimate

(Homoskedasticity is not required for unbiasedness of estimator)

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Answer 1

Zero Conditional Mean -The error u has an expected value of zero given any values of the independent variables.

Homoskedasticity - The conditional variance of the error term in a regression equation is constant for all values of the independent variables.

An estimator is unbiased if E(b) = $\beta$
That’s just saying if the expected value of estimator equals the parameter, then it’s an unbiased estimator.

Least Squares Assumptions 1 ·(XiÝ, ) are iid; random sampling 2. Large outliers are rare; If this condition fails, OLS estimator is not consistent. 3. E (u,|X)0; Conditional Mean Zero assumption. Xs are exogenous. This assumption fails if X and u are correalted No Perfect Multicolinearity Condition: The regressors are said to be perfectly multicollinear if one of the regressors is a perfect linear function of the other regressor(s) If all the assumptions are satisfied, the OLS estimates are unbiased and consistent.

a)

(holds

(holds) 81σ

Unbiased estimate

b)

(Does not hold

( 0) holds, variance ot constant

Biased estimate

c)

(holds)

(Does not hold)

Unbiased estimate

(Homoskedasticity is not required for unbiasedness of estimator)