Exercise 7


To examine the quantity theory of money, Brumm (2005) [‘‘Money Growth, Output Growth, and
Inflation: A Reexamination of the Modern Quantity Theory’s Linchpin Prediction,’’ Southern Economic
Journal, 71(3), 661–667] 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  and . The data used in this paper is contained in the file brumm.gdt. It consists of 1995
year data on 76 countries.

a)      Estimate the model by OLS and interpret all the parameters.

b)   Test the joint hypothesis that  and . What do you conclude?

c)      Examine the least squares residuals for the presence of heteroskedasticity related to the
variable Money.

d)      Obtain robust standard errors for the model and compare them to the OLS standard errors.
Does your conclusion change in part (b) after using robust standard errors?

e)      It is argued that Output may be endogenous. Four instrumental variables are proposed,
INITIAL = initial level of real GDP, SCHOOL = a measure of the population’s educational attainment,
INVEST = average investment as a share of GDP, and POPRATE = average population growth rate. Using
these instruments, obtain instrumental variables (2SLS) estimates of the inflation equation (do the
two stage procedure).

f)       Are the instruments strong?