What are the properties of estimators?

Properties of Good Estimator

• Unbiasedness. An estimator is said to be unbiased if its expected value is identical with the population parameter being estimated.
• Consistency.
• Efficiency.
• Sufficiency.

What are the OLS estimators?

OLS estimators are linear functions of the values of Y (the dependent variable) which are linearly combined using weights that are a non-linear function of the values of X (the regressors or explanatory variables).

What does the Gauss-Markov theorem tell us about the properties of the OLS estimators?

The Gauss-Markov theorem states that if your linear regression model satisfies the first six classical assumptions, then ordinary least squares (OLS) regression produces unbiased estimates that have the smallest variance of all possible linear estimators.

Why do we need OLS estimators?

In econometrics, Ordinary Least Squares (OLS) method is widely used to estimate the parameter of a linear regression model. OLS estimators minimize the sum of the squared errors (a difference between observed values and predicted values). The importance of OLS assumptions cannot be overemphasized.

What will be the properties of the OLS estimator in the presence of multicollinearity?

In fact, in the presence of near multicollinearity, the OLS estimator will still be consistent, unbiased and efficient.

Why is the Gauss Markov Theorem important?

The Gauss Markov assumptions guarantee the validity of ordinary least squares for estimating regression coefficients. They also allow us to pinpoint problem areas that might cause our estimated regression coefficients to be inaccurate or even unusable.

What is the implication of Gauss Markov Theorem?

In statistics, the Gauss–Markov theorem (or simply Gauss theorem for some authors) states that the ordinary least squares (OLS) estimator has the lowest sampling variance within the class of linear unbiased estimators, if the errors in the linear regression model are uncorrelated, have equal variances and expectation …