Assumptions Concerning the Disturbance Term

INTRODUCTION TO ECONOMETRICS II

ECO 306

NOUN
60 It is thus obvious that the properties of the regression coefficients depend critically on the properties of the disturbance term. Indeed the latter has to satisfy four conditions, known as the Gauss–Markov conditions, if ordinary least squares regression analysis is to give the best possible results. If they are not satisfied, the user should be aware of the fact. If remedial action is possible, he or she should be capable of taking it. If it is not possible, he or she should be able to judge how seriously the results may have been affected.
2.2.3.2.1 Gauss–Markov Condition 1: E(μ
i
) = 0 for All Observations
The first condition is that the expected value of the disturbance term in any observation should be 0. Sometimes it will be positive, sometimes negative, but it should not have a systematic tendency in either direction. If an intercept is included in the regression equation, it is usually reasonable to assume that this condition is satisfied automatically since the role of the intercept is to pickup any systematic but constant tendency in Y not accounted for by the explanatory variables included in the regression equation.
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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