Question

1. Suppose Melania borrows money from Jill for one year. They agree that the ex-ante real interest rate should be 1 percent.

(a) Suppose there is no zero lower bound. What nominal interest rate should Jill charge on the loan according to the Fisher equation, assuming the expected inflation rate is 5 percent? 2 percent? -2 percent? -5 percent?

(b) Now suppose there is a zero lower bound. How will this change your previous answers from part (a)?

(c) What is the ex-ante real interest rate implied by your answers to part (b), when the zero lower bound is binding?

Answer 1

a) Fisher Equation says that Nominal rate = real rate + expected inflation

Here real rate is 1

1) Expected inflation = 5

Nominal rate = real rate + expected inflation

= 1 + 5 = 6%

2) Expected inflation = 2

Nominal rate = real rate + expected inflation

= 1 + 2 = 3%

3) Expected inflation = - 5

Nominal rate = real rate + expected inflation

= 1 - 5 = -4%

4) Expected inflation = -2

Nominal rate = real rate + expected inflation

= 1 -2  = -1%

b) A zero lower bound means that the nominal rate cannot be below 0 percent. Then for cases 1 and 2 when the expected inflation is 5% and 2% there will be no change in the nominal rate as the nominal rate is well above 0%.

But for cases 3 and 4 when the expected inflation is -5% and -2% the nominal rate was negative. So because of the lower bound now, the nominal rate will be set to 0% in both cases unlike previously.

c) The ex-ante real interest rate when the zero lower bound is active will be calculated by using the Fisher equation and the given values of expected inflation and setting the nominal rate to 0. This will be done only for cases 3 and 4 when the expected inflation is -5% and -2% because the lower bound is active only in these.

3) Expected inflation = - 5

Nominal rate = real rate + expected inflation

0 = real rate  - 5

Real rate = 5%

4) Expected inflation = -2

Nominal rate = real rate + expected inflation

0 = real rate  - 2

Real rate = 2%

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