Explain: OLS is BLUE under some assumptions. What assumptions and why?

Expert Solution

OLS is BLUE under the following assumptions:

1)The linear regression model is “linear in parameters.”

2)The error term has a population mean of zero.

3)There is a random sampling of observations.

4)There is no multi-collinearity (or perfect collinearity).

5)There is homoscedasticity and no auto-correlation.

According to the Gauss-Markov Theorem, under these assumptions of the linear regression model, the OLS estimatorsare the Best Linear Unbiased Estimators (BLUE).

Why these assumptions are important?

Explanation:

If these assumptions hold true, the OLS procedure creates the best possible estimates. In statistics, estimators that produce unbiased estimates that have the smallest variance are referred to as being “efficient.” Efficiency is a statistical concept that compares the quality of the estimates calculated by different procedures while holding the sample size constant. OLS is the most efficient linear regression estimator when these assumptions hold true.

Another benefit of satisfying these assumptions is that as the sample size increases to infinity, the coefficient estimates converge on the actual population parameters.

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Rahul Sunny answered 2 years ago

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