2. According to Irving Fisher’s theory of interest, the real rate of interest eq
ID: 1250943 • Letter: 2
Question
2. According to Irving Fisher’s theory of interest, the real rate of interest equal the nominal rate of interest minus the expected rate of inflation; since the expected rate of inflation is likely to be highly correlated with the actual rate of inflation, the latter is often used as proxy for the former. To test this theory, the nominal rate of interest on three-month treasury bills (RTRS) was regressed against the rate of change in the implicit price deflator (INF) using annual data for the period 1948 to 1983. The result of the regression is:^
RTRS = 1.658 + 0.785 INF
(0.793) (0.161)
where figures in parentheses are the corresponding, estimated standard errors.
Use these results to test the following hypothesis:
a. The nominal rate of interest increases as the rate of inflation increases.
b. The nominal rate of interest increases by 1 percent for each 1 percent increase in the rate of inflation.
c. The real rate of interest (i.e., the nominal rate of interest when INF = O) is positive.
Explanation / Answer
We use a statistical t test with degrees of freedom 30. (since we have 36 years of data and t tables give 30 and 40; we use 30 to be conservative).
a) Ho:B1=0
Ha : B1>0 (Coefficient of INF is positive)
t= 0.785/.161= 4.87 P value is less than .0005 so we can conclude that B1>0 and there is a positive relattionship between the inflation rate and nominal rate of interest.
b) Ho: B1=1
Ha: B1 =/1
t= (0.785-1)/.161= -1.33
P value .05<p<.10 so we reject the null hypothesis (at the .05 level of significance) that the nominal rate of interest increases 1% (it's actually slightly less) for every 1% increase in the rate of inflation.
c)Ho: Bo =0 (The coefficient of the y intercept is equal to zero so the nominal interest rate is zero when the rate of inflation is 0).
Ha: Bo>0
t=1.658/.793= 2.09
.02<p<.025 so we reject the null hypothesis and conclude that Bo>0 that the nominal rate of interest is positive when the rate of inflation is 0.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.