2.2.3.2.2 Gauss–Markov Condition 2: Population Variance of μ
i
Constant for All
Observations
The second condition is that the population variance of the disturbance term should be constant for all observations. Sometimes the disturbance term will be greater, sometimes smaller, but there should not be any a priori reason for it to be more erratic in some observations than in others. The constant is usually denoted by
, often abbreviated to
, and the condition is written as,
Since E(μ
i
)is 0, the population variance of μ
i
is equal to
(
), so the condition can also be written
(
)
, of course is unknown. One of the tasks of regression analysis is to estimate the standard deviation of the disturbance term. If this condition is not satisfied, the OLS regression coefficients will be inefficient, but you should be able to obtain more reliable results by using a modification of the regression technique.
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