Explain the Gauss-Markov assumptions required for unbiasedness and efficiency of the OLS estimator. Distinguish between the...

Explain the Gauss-Markov assumptions required for unbiasedness and efficiency of the OLS estimator. Distinguish between the assumptions for simple and multiple linear regressions. Provide examples of violations of each assumption. Under what circumstances are coefficient estimates from MLR and SLR identical?

Expert Solution

orchestra answered 2 years ago

Prove that the OLS estimator is efficient provided the Gauss Markov assumptions hold.

The Gauss Markov Theorem says a) Under the LS assumptions, the OLS estimator has the smallest...

The Gauss Markov Theorem says a) Under the LS assumptions, the OLS estimator has the smallest variance among all linear unbiased estimators b) Under the LS assumptions, the OLS estimator has the smallest variance among all linear estimators c) The OLS estimator has the smallest variance among all linear unbiased estimators d) Under the LS assumptions, the OLS estimator is the most consistent estimator of all linear unbiased estimators

. Under the Gauss-Markov assumptions, we know that the Ordinary Least Squares (OLS) estimator βˆ is...

. Under the Gauss-Markov assumptions, we know that the Ordinary Least Squares (OLS) estimator βˆ is unbiased, efficient, and consistent. However, if the assumption that E[ϵ 2 i |X] = σ 2 i = σ 2 is violated while the assumption of E[ϵi , ϵj ] = 0 , ∀i ̸= j holds, that the least squares estimator is unbiased but is no longer efficient. The Generalized Least Squares (GLS) estimator, in this case, may be unbiased, consistent, and efficient...

The Gauss-Markov theorem says that the OLS estimator is the best linear unbiased estimator.

The Gauss-Markov theorem says that the OLS estimator is the best linear unbiased estimator. Explain which assumptions are needed in order to verify Gauss-Markov theorem? Consider the Cobb-Douglas production function

What does the Gauss-Markov theorem claim? Explain the assumptions needed for the Gauss-Markov Theorem.

What does the Gauss-Markov theorem claim? Explain the assumptions needed for the Gauss-Markov Theorem. Are all the assumptions necessary to construct the OLS estimates of the intercept and slope coefficients.

Q1: Explain what homoscedasticity is. Why is heteroscedasticity a violation of the Gauss-Markov Assumptions. i.e. explain...

Q1: Explain what homoscedasticity is. Why is heteroscedasticity a violation of the Gauss-Markov Assumptions. i.e. explain why MLR.5 is necessary.

Question

Explain the Gauss-Markov assumptions required for unbiasedness and efficiency of the OLS estimator. Distinguish between the...

Solutions

Expert Solution

Related Solutions

Prove that the OLS estimator is efficient provided the Gauss Markov assumptions hold.

The Gauss Markov Theorem says a) Under the LS assumptions, the OLS estimator has the smallest...

. Under the Gauss-Markov assumptions, we know that the Ordinary Least Squares (OLS) estimator βˆ is...

The Gauss-Markov theorem says that the OLS estimator is the best linear unbiased estimator.

What does the Gauss-Markov theorem claim? Explain the assumptions needed for the Gauss-Markov Theorem.

Q1: Explain what homoscedasticity is. Why is heteroscedasticity a violation of the Gauss-Markov Assumptions. i.e. explain...

Explain what assumptions are needed in order for the OLS estimator to be unbiased in a crosss sectional environment.

Explain what assumptions are needed in order for the OLS estimator to be unbiased in a time series environment.

What are the Gauss Markov assumptions for the error term in a regression framework? Using these,...

A) What are the Gauss Markov assumptions for the error term in a regression framework? Using...