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# To examine the quantity theory of money, Brumm (2005) ["Money Growth, Output Growth, and Inflation:

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:

Inflat = ????1 + ????2MONEY + ????3OUTPUT + ????

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 the theory we should observe that ????1 = 0, ????2 = 1 ????3 = −1. The data are in the excel file As3_q2.xlsx, it consists of 1995 data on 76 countries. (a) Estimate the model by least squares, and test

(i) The strong joint hypothesis that ????1 = 0, ????2 = 1 and ????3 = −1

(ii) The weak joint hypothesis ????2 = 1 ????3 = 1

(b) Examine the least squares residuals for the presence of heteroskedasticity related to the variable MONEY.

(c) Obtain robust standard errors for the model and compare them to the least squares standard errors.

(d) 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, INV=average investment share of GDP, and POPRATE=average population growth rate. Using these instruments, obtain instrumental variables (2SLS) estimates of the inflation equation.

(e) Test the strong and weak hypothesis listed in (a) using the IV estimates.

(f) Use the Hausman test to check the endogeneity of OUTPUT. Because the regression errors may be heteroskedastic, use robust standard errors when estimating the auxiliary regression.