INTRODUCTION TO ECONOMETRICS II ECO 306 NOUN 66 where and are parameters and
u is a disturbance term. You
might further hypothesize that, apart from the effects of the disturbance term, price inflation is equal to wage inflation. Under these circumstances you would say that the hypothesis that you are going to test, known as your
nullhypothesis and
denoted H0, is that
is equal to 1. We also define an alternative hypothesis, denoted
H1
, which represents your conclusion if the experimental
test indicates that H0
is false. In the present case
H1,
is simply that
is not equal to 1. The two hypotheses are stated using the notation
H0 H1
In this particular case, if we believe that price inflation is equal to wage inflation, we are trying to establish the credibility of
H0
by subjecting it to the strictest possible test and hoping that it emerges intact. In practice, however, it is more usual to setup a null hypothesis and attack it with the objective of establishing the alternative hypothesis as the correct conclusion. For example, consider
the simple earnings function …[2.42]
Where
EARNINGS is hourly earnings in dollars and
S is years of schooling. On very reasonable theoretical grounds, you expect earnings to be dependent on schooling, but your theory is not strong enough to enable you to specify a particular value for
You can nevertheless establish the dependence of earnings on schooling by the inverse procedure in which you take as your null hypothesis the
assertion that earnings does not depend on schooling, that is, that
is 0. Your alternative hypothesis is that
is not equal to 0, that is, that schooling doesaffect earnings. If you can reject the null hypothesis, you have
established the relationship, at least in general terms. Using the conventional notation, your null and alternative hypotheses are
H0 H1
, respectively. The following discussion uses the simple regression model
