INTRODUCTION TO ECONOMETRICS II ECO 306 NOUN 62 In addition to the Gauss–Markov
conditions, one usually assumes that the disturbance term is normally distributed. The reason is that if
u is
normally distributed, so will be the regression coefficients, and this is useful when performing tests of hypotheses and constructing
confidence intervals for and
using the regression results. The justification for the assumption depends on the Central Limit Theorem that, if a random variable is the composite result of the effects of a large number
of other random variables, it will have an approximately normal distribution even if its components do not, provided that none of them is dominant.
The disturbance term u is composed of a number of factors not appearing explicitly in the regression equation so, even if we know nothing about the distribution of these factors (or
even their identity, we are entitled to assume that they are normally distributed.
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