In your macroeconomics class you learned about the quantity theory of money (QTM
ID: 1103301 • Letter: I
Question
In your macroeconomics class you learned about the quantity theory of money (QTM). This idea has been around for several hundred years actually. It states a simple relationship between money and prices. First, changes in the quantity of money have a positive effect on the general price level. Second, as an empirical matter, movements in the money stock should account for the major long run changes in the price level.
QTM has been written as the following relationship:
P Y = M V,
where M is the money supply, V is the velocity of money, P is the price level and Y is real output (income). Dividing both side by Y gives
P=MV/Y
If V and Y are constant, then changes in M result in equal changes in P . However, this version of the QTM
is too strict to hold in the real world. A less restrictive version can be written in terms of % changes:
P /P= M/M-Y /Y+V/V
Therefore, changes in money supply, income and velocity cause changes in the price level. Suppose we treat velocity of money as an unobserved error term. We can then express the QTM by the regression
(1)inf li = 0 + 1mgrowthi + 2ygrowthi + ui.
Note that inf li is simply P/P for country i, mgrowthi isM/M and ygrowthi is Y /Y. Finally, ut represents V/V for country i.
If the QTM holds, then 1 = 1 and 2 = 1. Use the money.csv data to this proposition. The data contains the following variables.
inf li = inflation of country i
mgrowthi = money growth of country i
ygrowthi = output growth of country i
Questions
(a)Estimate regression (1) and report the results. Are the point estimates consistent with the QTM?
(b)What is the R2 for your regression? What does it tell you?
(c)Test individually the hypotheses corresponding to the QTM; that is, individually test that 1 = 1 and
2 = 1. Are test results consistent with the QTM?
(d)
Evaluate the join hypothesis 1 = 1, 2 = 1 using an F-test. Are your results consistent with the the QTM? Does the joint test give the same result as the individual tests?
(e)Heteroskedasticity may be a concern. Can you test for the presence of heteroskedasticity using the two test we did in class - White or Breusch Pagan test?
Explanation / Answer
First of all copy the data and post it on the data editor on the STATA .
a) Now use command "reg inf li mgowthi ygrowthi"
Now check the signs of the coefficients of the variables mgrowth and ygrowth. If the sign for mgrowth and ygrowth is positive then point estimates are consistent with QTM.
b) R2 tells us the total variation in inf li explained by the variation in mgrowth and ygrowth.
c) Check for the following null hypothesis
First;
H0 =beta1 =1
H1: beta1!=1
Calculate t = (beta1(hat) -1)/SE(beta1(hat))
If t calculated above is greater than the critical t-value at given level of degrees of freedom and significance level . Then we reject the null hypothesis else not.
Second we will check for
H0: beta2 = -1
H1: beta 2!=0
If the t-value is greater than t- critical then we reject the null else we do not.
d) Now bhek
H0: beta1 = beta2 = 1 (joint significance)
H1 : beta1= beta2 != 1
Check the F- value given in the results from question 1 . If the F-value is ver high then reject the null else do reject the null.