79 In looking for the simple Keynesian multiplier you regres

7.9. In looking for the simple Keynesian multiplier, you regress the GNP on in- vestment and find that there is some relationship. Now, thinking that it can not hurt much, you include the \"irrelevant\" variable \"state and local taxes To your surprise, the investment variable loses its significance. How can an irrelevant variable do this?

Solution

When we regress GNP on investment we can expect to find a positive relation. That is an increase in investment brings about an increase in GNP. Now if we include the state and local tax variable then there will be some degree of correlation between this and investment and this will thus create a multicolinearity problem. This will inflate the standard errors of the investment variable and so will mean that the t stat of the investment variable is small and so the investment variable will be insignificant. Thus it is the multicolinearity between taxes and the investment variable which renders the investment variable insignificant. We can expect that a rise in state and local taxes will reduce investment and so they can be correlated.