INTRODUCTION TO ECONOMETRICS II
ECO 306
NOUN
81 15 29 76+ u
6 1
1 5 Let [2.40] be the true relationship, that is
…[2.63]
Suppose that there is a linear relationship between and
:
…[2.64]
and suppose that X
2 increases by one unit in each observation. X
3
will increase by two units, and Y by approximately five units as indicated in Table 3.1. Applying the linear relationship between X
2 andX
3
in manipulating [2.40] will result indifferent conclusions for Y. In such a situation it is impossible for regression analysis, or any other technique for that matter, to distinguish between these possibilities. You would not even be able to calculate the regression coefficients because both the numerator and the denominator of the regression coefficients would collapse to 0. This willbe demonstrated with the general two- variable case. Suppose
…[2.65]
And
…[2.66]
Substituting for in [3.58] gives
(
) (
) (,
- ) (
,
- )
(
) (
) , (
,
-)-
=
(
) (
) (
) (
)
(
) (
) , (
-)-
…[2.67] From Variance Rule 4, the additive in the variances can be dropped. A similar rule could be developed for covariances, since an additive does not affect them either.
INTRODUCTION TO ECONOMETRICS II ECO 306 NOUN 82 Therefore, ( ) ( ) ( ) ( ) ( ) ( ) , ( -)- …[2.68] Share with your friends: |
