Question

TRUE or FALSE and Explain why:

The assumption of normality of the error term is essential for the Gauss-Markov theorem (i.e. to show that the OLS estimator is BLUE (Best Linear Unbiased Estimator)).

Answer 1

TRUE

OLS Assumption : The error term has a population mean of zero

The error term accounts for the variation in the dependent variable that the independent variables do not explain. Random chance should determine the values of the error term. For your model to be unbiased, the average value of the error term must equal zero.

Suppose the average error is +7. This non-zero average error indicates that our model systematically underpredicts the observed values. Statisticians refer to systematic error like this as bias, and it signifies that our model is inadequate because it is not correct on average.

The Gauss-Markov Assumptions In Algebra

We can summarize the Gauss-Markov Assumptions succinctly in algebra, by saying that a linear regression modelrepresented by

y_i = x_i‘ β + ε_i

and generated by the ordinary least squares estimate is the best linear unbiased estimate (BLUE) possible if

• E{ε_i} = 0, i = 1, . . . , N
• {ε₁……ε_n} and {x₁…..,x_N} are independent
• cov{ε_i, ε_j} = 0, i, j = 1,…., N I ≠ j.
• V{ε₁ = σ², i= 1, ….N

The first of these assumptions can be read as “The expected value of the error term is zero.”. The second assumption is collinearity, the third is exogeneity, and the fourth is homoscedasticity.