To examine the quantity theory of money, Brumm \({ }^{15}\) specifies the equation

where INFLAT is the growth rate of the general price level, MONEY is the growth rate of the money supply, and OUTPUT is the growth rate of national output. According to theory we should observe that \(\beta_{1}=0, \beta_{2}=1\), and \(\beta_{3}=-1\). The data in the data file brumm are on 76 countries for the year 1995 .

a. Using a \(5 \%\) significance level, test i. the strong joint hypothesis that \(\beta_{1}=0, \beta_{2}=1\), and \(\beta_{3}=-1\).
ii. the weak joint hypothesis \(\beta_{2}=1\) and \(\beta_{3}=-1\).

b. Using the DFFITS criterion, find the four most influential observations.

c. Repeat the two tests with the four most influential observations omitted. Does omission of these four observations change the test outcome?

d. Moroney \({ }^{16}\) has argued that \(\beta_{2}\) is likely to be different for different countries. Suppose that \(\beta_{2}=\alpha_{1}+\alpha_{2} M O N E Y+\alpha_{3}\) OUTPUT. Substitute this equation into the original model and, omitting the same four influential observations, estimate the new model.

e. Repeat the two tests for the model estimated in (d) for a hypothetical country with the sample median values \(M O N E Y=16.35\) and \(O U T P U T=2.7\).

Transcribed Image Text:

INFLATB + BMONEY + 3OUTPUT + e