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 INFLATION is the growth rate of the general price level, MONEY GROWTH is the growth rate of the money supply, and OUTPUT GROWTH is the growth rate of national output. According to theory we should observe that \(\beta_{1}=0, \beta_{2}=1\), and \(\beta_{3}=-1\). Use the data file brumm. It consists of 1995 data on 76 countries. We wish to 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 \(\beta_{3}=-1\)

a. It is argued that OUTPUT GROWTH may be endogenous. Four instrumental variables are proposed, INITIAL = initial level of real GDP, SCHOOL = a measure of the population's educational attainment, \(I N V=\) average investment share of GDP, and POPRATE = average population growth rate. Using these instruments, obtain instrumental variables (2SLS) estimates of the inflation equation.

b. Test the strong and weak hypotheses using the IV estimates.

c. Compute the IV/2SLS residuals, \(\hat{e}_{I V}\). Identify the observation with the largest absolute residual, \(\left|\hat{e}_{I V}\right|\). How does it compare to the next smallest residual?

d. Let us examine the effect of the observation with the largest residual. Drop the corresponding observation from the data, reestimate the model using IV/2SLS, and carry out the tests of the strong and weak hypotheses. How much do things change, if any?

e. Obtain the IV/2SLS residuals from part (d), \(\tilde{e}_{I V}\). Regress \(\tilde{e}_{I V}^{2}\) on MONEY. Calculate the heteroskedasticity test statistic \(N R^{2}\). Compare it to the 95th percentile of the \(\chi_{(1)}^{2}\) distribution. Is there evidence of heteroskedasticity?

f. Using the 75 remaining observations from (d) obtain the IV/2SLS estimates with heteroskedasticity robust standard errors. Carry out the tests of the strong and weak hypotheses. How to the test results compare to those in (d)?

g. Using the remaining 75 observations from (d), estimate the first-stage equation and test the joint significance of the IV. Repeat the tests robust to heteroskedasticity. Is there evidence that the instruments are strong?

h. Regress \(\tilde{e}_{I V}\) against the four IV and MONEY. Are any of the coefficients significant? If the IV are valid, do we expect any significant coefficients in this regression? Explain.

Transcribed Image Text:

INFLATION = B + BMONEY GROWTH + BOUTPUT GROWTH + e