Introduction to econometrics II eco 356 faculty of social sciences course guide course Developers: Dr. Adesina-Uthman

INTRODUCTION TO ECONOMETRICS II

ECO 306

NOUN
61 This condition states that there should be no systematic association between the values of the disturbance term in any two observations. For example, just because the disturbance term is large and positive in one observation, there should be no tendency for it to be large and positive in the next (or large and negative, for that matter, or small and positive, or small and negative. The values of the disturbance term should be independent of one another. The condition implies that
μiμj
, the population covariance between μ
i
andμ
j
, is 0, because
μiμj
=E[(μ
i
– μu)(μ
j
– μu)] = E(μ
i
μ
j
) = E(μ
i
)E(μ
j
) = 0
…[2.29] where, u is a value in μ as shown in (
1
u
) of Figure 2.0 Note that the population means of μ
i
andμ
j
are 0, by the first Gauss–Markov condition, and that E(μ
i
μ
j
) can be decomposed as E(μ
i
)E(μ
j
) if μ
i
andμ
j
are generated independently. If this condition is not satisfied, OLS will again give inefficient estimates.
2.2.3.2.4 Gauss–Markov Condition 4: u Distributed Independently of the
Explanatory Variables
The final condition comes in two versions, weak and strong. The strong version is that the explanatory variables should be non-stochastic, that is, not have random components. This is very unrealistic for economic variables, and we will eventually switch to the weak version of the condition, where the explanatory variables are allowed to have random components provided that they are distributed independently of the disturbance term. However, the strong version is usually used because it simplifies the analysis of the properties of the estimators.
i
X
i
u
,*
i
X
(
i
X
)+*
i
u
+- (
i
X
i
X
) (
i
u
)
…[2.30]

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