Question

A measure of real interest rates can be approximated by the Treasury Inflation-Indexed Security, or TIIS. Go to the St. Louis Federal Reserve FRED database, and find data on the five-year TIIS (FII5) and the personal consumption expenditure price index (PCECTPI), a measure of the price index. Choose “Quarterly” for the frequency setting of the TIIS, and download both data series. Convert the price index data to annualized inflation rates by taking the quarter-to-quarter percent change in the price index and multiplying it by $4$. Be sure to multiply by 100 so that your results are percentages.

a. Calculate the average inflation rate and the average real interest rate over the most recent four quarters of data available and the four quarters prior to that.

b. Calculate the change in the average inflation rate between the most recent annual period and the year prior. Then calculate the change in the average real interest rate over the same period.

c. Using your answers to part (b), compute the ratio of the change in the average real interest rate to the change in the average inflation rate. What does this ratio represent? Comment on how it relates to the Taylor principle.

Short answer

(A) The average inflation rate and the average real interest rate is $-0.36\mathrm{\%}$

(B) The average inflation rate between the most recent annual period is $-1.25\mathrm{\%}$

(c) The ratio of average real interest is$38$

Step-by-step solution

Step ; 1 Introduction

For the last eight quarters, the personal consumption expenditure price index

$\begin{array}{r}2019-04-01=109,835\\ 2019-07-01=110,141\\ 2019-10-01=110,612\\ 2020-01-01=110,958\\ 2020-04-01=110,505\\ 2020-07-01=111,507\\ 2020-10-01=111,928\\ 2021-01-01=112,989\\ 2021-04-01=114,775\end{array}$

Step :2 Price index into inflation rate  (part a)

Converting the price index into inflation rate:

$\begin{array}{r}2019-07-01=\frac{110,141-109,835}{109,835}\times 4\times 100=1.11\mathrm{\%}\\ 2019-10-01=\frac{110,612-110,141}{110,141}\times 4\times 100=1.71\mathrm{\%}\\ 2020-01-01=\frac{110,958-110,612}{110,612}\times 4\times 100=1.25\mathrm{\%}\end{array}$

$2020-04-01=\frac{110,505-110,958}{110,958}\times 4\times 100=-1.63\mathrm{\%}$

$\begin{array}{r}2020-07-01=\frac{111,507-110,505}{110,505}\times 4\times 100=3.62\mathrm{\%}\\ 2020-10-01=\frac{111,928-111,507}{111,507}\times 4\times 100=1.51\mathrm{\%}\end{array}$

$\begin{array}{r}2021-01-01=\frac{112,989-111,928}{111,928}\times 4\times 100=3.97\mathrm{\%}\\ 2021-04-01=\frac{114,775-112,989}{112,989}\times 4\times 100=6.32\mathrm{\%}\end{array}$

Step :3  The average real interest rate (part a)

To compute the average real interest rate from the given data, we'll use the TIIS data as a rough estimate.

$\begin{array}{r}2019-07-01=0.18\\ 2019-10-01=0.09\end{array}$

$\begin{array}{r}2020-01-01=-0.14\\ 2020-04-01=-0.49\\ 2020-07-01=-1.19\\ 2020-10-01=-1.32\\ 2021-01-01=-1.70\\ 2021-04-01=-1.71\end{array}$

The average of the real interest rate for the most recent four quarters:

$$\begin{gathered} =\frac{-1.71\mathrm{\%}+(-1.70\mathrm{\%})+(-1.32\mathrm{\%})+(-1.19\mathrm{\%})}{4} \\ =-1.48\mathrm{\%} \end{gathered}$$

The average of the real interest rate for the prior four quarters:

$$\begin{gathered} =\frac{-0.49\mathrm{\%}+(-0.14\mathrm{\%})+0.09\mathrm{\%}+0.18\mathrm{\%}}{4} \\ =-0.36\mathrm{\%} \end{gathered}$$

Step : 4Convert into inflation rate (part b)

b) First, because we have information about the price index, we have to convert it into inflation rate:

$\begin{array}{r}2018-01-01=108,318\\ 2019-01-01=109,922\\ 2020-01-01=111,225\end{array}$

Inflation$2019-01-01\text{:}$

$$\begin{gathered} \frac{109,922-108,318}{108,318}\times 100 \\ =1.48\mathrm{\%} \end{gathered}$$

Inflation $2020-01-01$

$$\begin{gathered} \frac{111,225-109,922}{109,922}\times 100 \\ =1.18\mathrm{\%} \end{gathered}$$

Step :5  The change of average inflation between 2019 and 2020 (part b) :

The change of average inflation between $2019$and $2020$:

Absolute change:

$1.48\mathrm{\%}-1.18\mathrm{\%}=0.3\mathrm{\%}$

Relative Change:

$$\begin{gathered} \frac{1.48\mathrm{\%}-1.18\mathrm{\%}}{1.18\mathrm{\%}}\times 100 \\ =25.42\mathrm{\%} \end{gathered}$$

Step :6 Real interest rate (part b)

The change of average real interest rate between $2019$and $2020$: (We have approximate values for the real interest rate)

$\begin{array}{c}2019-01-01=0,35\\ 2020-01-01=-0,79\end{array}$

Absolute change:

$$\begin{gathered} =-0.79\mathrm{\%}-0.35\mathrm{\%} \\ =1.14\mathrm{\%} \end{gathered}$$

Relative change:

$$\begin{gathered} =\frac{-0.79\mathrm{\%}+0.35\mathrm{\%}}{0.35}\times 100 \\ =-1.25\mathrm{\%} \end{gathered}$$

Step : 7 Divide the change in the real interest rate (part c)

Divide the change in the real interest rate by the change in the inflation rate.

$$\begin{gathered} \frac{1.14\mathrm{\%}}{0.03\mathrm{\%}} \\ =38 \end{gathered}$$

The risk premium should be higher than the rate of inflation. It means that the increase in the interest rate should be more than the increase in inflation. When real interest rates fall as inflation rises, hyperinflation may result.