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.

ols Inflation const Money Output

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

restrict

 b[1] = 0

 b[2] = 1

 b[3] = -1

end restrict

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

series resid=$uhat

gnuplot  resid_sq Money

modtest --white

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?

ols Inflation const Money Output –robust

Conclusion does not change – they are jointly not equal to the theoretical parameters

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).

First stage:

ols Output const initial poprate school invest Money

series Output_hat=$yhat

Second stage:

ols Inflation const Money Output_hat

f)       Are the instruments strong? Only invest predicts the Output significantly, other variables
are weak instruments.  The theoretical parameters are again jointly rejected. The impact of output
on the inflation is now lower than before.