Is the OLS estimator efficient?

Is the OLS estimator efficient?

The OLS estimator is one that has a minimum variance. An estimator that is unbiased but does not have the minimum variance is not good. An estimator that has the minimum variance but is biased is not good. An estimator that is unbiased and has the minimum variance of all other estimators is the best (efficient).

Why is OLS estimator widely used?

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.

Which is a property of the OLS estimator?

Statistical Properties of the OLS Slope Coefficient Estimator ¾ PROPERTY 1: Linearity of βˆ. 1 The OLS coefficient estimator can be written as a linear function of the sample values of Y, the Y. 1. βˆ. i (i = 1., N). Proof: Starts with formula (3) for βˆ. 1: because x 0.

Is the OLS estimator efficient under heteroscedasticity?

No, OLS is not efficient under heteroscedasticity. Efficiency of an estimator is obtained if the estimator has the least variance among other possible estimators. Statements about efficiency in OLS are made regardless of the limiting distribution of an estimator.

When does the variance of an OLS estimator converge?

Its variance converges to 0 as the sample size increases. Both these hold true for OLS estimators and, hence, they are consistent estimators. For an estimator to be useful, consistency is the minimum basic requirement. Since there may be several such estimators, asymptotic efficiency also is considered.

What are the finite sample properties of OLS regression?

So far, finite sample properties of OLS regression were discussed. These properties tried to study the behavior of the OLS estimator under the assumption that you can have several samples and, hence, several estimators of the same unknown population parameter.