The time series behavior of real interest rates A comment

Carnegie-Rochester North-Holland

Conference

Series on Public

Policy

24 (1986)

276-288

THE TIME SERIES BEHAVIOROF REAL INTEREST RATES A COMMENT 6.

WILLIAM

Graduate

School

of Management

University

of

I. The

Huizinga

changes

in

October,

1979

real

and

interest

signed Huizinga

October,

first

announced

rather

than

less

pronounced

when the

the

cause

in

behavior

results

the

they

the

seem too

good

enough their

series

behavior

regimes.

advocate, the

In

the

attempting Huizinga/Mishkin

*Support Rochester

is

from the gratefully

0 167-2231/86/$03.50

rest

of

Elsevier

Science

rates

after

sole

reliance

the

recent

period

paper but

are

are

seems

B.V.

Fed

supply

targets

Mishkin

find

a

1982,

on money behavior

supply of

real

World

War I

and they

find

a be-

techniques changes

play

the

about clear

Policy

(North-Holland)

and

used

in moderate

coincident

I will

in Government

Publishers

when the

thought-provoking

changes

questions it

de-

differently

following

large

that

or raise

are

process,

October,

amounts,

of

time.

relatively

this

results,

and

parameter

rates

qualify

on money

Huizinga

The statistical

small

Center for Research acknowledged.

0 1986

month

paper

be true.

interest

to

is the

by large

at that

indicate

real

that

the

rate

rates

detect

findings of

study

discount

to

behaved

of

Huizinga/Mishkin

to

have

was abandoning impressions

real

rates

in

behavior that

stochastic

the

Board

the

a

real

that

Reserve tests

of

primarily of

case

in

statistical

targets.

behavior

it

the

of

focusing

and Mishkin of

Federal changes

interest

rate

their

in

powerful

of

that

Huizinga increased

so

of

change

the

Of course,

interest

Fed

sizes,

of

before.

a strong

major

parameters

real

a new policy

in the The

in

than

nominal

rates,

change

not

1979

by

the

show that

presents

caused

a variety in

To corroborate

interest when

Through

Fed announced

targets.

1982

changes

and Mishkin

paper

"regimes"

in October,

detect

after

[1985]

policy

rates.

to

Rochester

INTRODUCTION

and Mishkin

monetary

SCHWERT*

the

are

sample

in

the

time

with

the

changes

role

of

Devil's

interpretation

that

even

Business

at

a skeptic

the

University

must

conclude

that

the

II,

To study (ex

post)

whether

monetary

interest

process

for

real

the

real

rate

rates,

xt,

(b)

the

current

shock"

variable,

Wilcox

[19831).

the

rate

direct

measures not

improve the

problem

of

two

rate

rate

in

rates

for

1926183, adjusted

so

Treasury

Bill the

as that

the

I use

average

of

Price

Index

1 contains

between of

the

of

C.P.I.

and

and of

the

inflation

real

interest

I was curious process and

as

for

real

Mishkin.

Ac-

and Mishkin,

equals

real

rates

has increased

the

ex post

It

is

real

loan is

are rates

inflation

rate)

apparent

from

in recent

between rates,

average

rate

variables

and the

1918-83.

[19841 time

inflation

the

from

Ibbotson

brokers'

rates

rates

276

for rate

sides

by Huizinga

from

All

rate

the

variable,

and

Huizinga

one-month

(CPI-U). a plot

to

variable.

The monthly

nominal

variables

model

both

nominal

studied

come

these

1926.

as

variable,

shock

stochastic

by

shock

rates

1918-26 during

percentage volatility

supply

interest

the

Figure

difference annual

use their

rate

inflation

from

[1977]), the

that

the

identical

of the

to

reached to

supply

behavior

of

similar

such

current

rate

and Schwert

conclusions data

between

Consumer

compounded. (the

Nelson

is

the

lagged

the

as (although

a predetermined

of

relation

specifications

not

rates

its

rates

The Huizinga/Mishkin

nominal

studied

and

discount

that

interest

rate.

the

I have States

of

the

(see

models). is

a regression rate,

a "supply energy

such

on real

believe

rate rate

inflation

interest

the

that

real

(c) of

Reserve

policy

their

inflation

variables

Federal

of

and

sto-

regression

(C.P.I.) price

of

the

consider it,

use

they

power

to

one-month

and

the

not

behavior

specify

lagged

rate,

do

interest

the

example,

I did for

analysis.

the

to

relative

monetary

(subtracting

alter

that

or

affects

(a)

the

16 indicates

the

I analyzed

Data

in

of

nominal

alternative

cordingly,

supply

equivalent

United

would

further

and Mishkin of

they

predictive

regression). the

(see,

except

footnote

inflation

whether

rates

in

is

necessary

interest

change

influence

nominal

of

real

the

forecasting

current

lags

money

of

the

shifts

first

Huizinga

nominal

forecasting

rate

deserve

regime is

as a function

lagged

current

of

real

on the

from

the

Since problem

the

to

of

discussion

the

it

Interestingly,

growth

discovered

policy

rates.

for

would

have

rates,

models

the

they

ALTERNATIVE STOCHASTIC PROCESSES FOR EX POSTREALRATESOF INTEREST

real

chastic

facts

years

of

the

calculated continuously of

interest expressed

this relative

graph to

-

-,

-60

-70

18

-

0

-50

-40

-30

-20

-10

10

20

30

50

23

28

33 March

38

Ex

Post

43 1918

I

Real

48 -

53 December

Rates

Figure of

58

1 Interest

1983

63

68

73

78

83

I

post-1953

the

much more

volatile

Figure interest of

than

is

suggested

tive

real

during

rates

1920.

behavior

This

is

raised

in

predicted

Mishkin. lowered

the

period discount real

ation

in

in real

the nor

real

To provide a model

for

interest

rate

the with

(“t

- “t-1)

that

inflation

on the

rate

This

is

due to the there

that

the

predicted during the

Federal changes

Huizinga

release

and

of

World

rate

and

substantial

not

vari-

explained

by

data

policy.

Huizinga/Mishkin

as

variable

inflation

is

is

Again,

more

by

CPI

that nega-

many other

studied the

method

shows

when

are

not

crude

dramatically

and Mishkin there

series

a first-order

of

1979.

much

rose

Nevertheless,

check

rate

generally

particular,

raised

in monetary

is

then

in mid-1946

rate

real good

around

rate

are

artificially

real

a further

and

Of course,

changes

is

plot

1953-70,

In

by Huizinga

rate.

predicted

by apparent

real

1919-20

rates

rates

rates. This

dramatically

rate.

which

real

from

period.

series

real

percentage

interest).

studied rate

measured

rose

predicted

from

of

[19841 as a relatively of stable

post-1979

its

controls

the

errors,

the

annual 12 monthly

rates

they

the

negative

The drop

II price

War

last

relatively

of

in

were

Reserve the

were

real

197Os, and

the

1953 than

real

the

the

behavior

period.

of

of

(or

rates

the

before

post-1979

by Fama and Gibbons

inflation

predicted

pre-1953

the

forecasts

on an average

forecasting

however,

in the

2 contains based

model

However,

experience.

a function

moving

I estimate

results, of

the

(MA(l))

average

current

nominal

process

for

the

errors,

where the

(mt-mt-I) change

and L is by Nelson est

is

in the the

= a

the

lag and

lagged

in

the

interest

operator

and Schwert

rates

change

nominal

(1)

+ e(i,-it-I)+(l-eL)E,,

Lkxt

(i.e.,

[1977] inflation.

monthly

rate,

e is

inflation

rate,

the

average

= xt-k).

to forecast It

moving

This

inflation

is

the

(it-it-I) same model

as a function

differs

from

the

is

parameter, of

used inter-

Huizinga/Mishkin

model,

=t =a+Bi because used

an exponentially in

Nevertheless, Table

(l),

whereas the

weighted only

1 contains

average

the

information estimates

(2)

+ ypmt-2 + Et’

t + Y2?-1

last set of

two

for

these

the

of

all

inflation

inflation

rates

two models

Nelson/Schwert

278

past is

model

are the

rates used

in

is (2).

same. in

(1) and the

18

-

-15

-

-

0

-10

-5

-

10

--

-

15

5-

-

20

25

23

28

33 March

38

Predicted

43 1919

48

Real

-

Figure

December

53

Rates

58

2 of

63 1983

Interest

68

73

78

83

Table

Alternative

Models (Standard

for the C.P.I. Inflation Errors in Parentheses)

A. (Ht-H+-,)

1

Rate

Nelson-Schwert

= a+B(i

t -i t-1

) + (l-9L)Et

(1)

F-Test Sample 4/18

Period

a

---L-

- 5/20

.OOl (.ool)

(11.4)

e

-

-I .a9

(Degrees

s(E)

.542

for

Stability of

Freedom)

.0125

t.1771 0.63 (3,111)

4118 l/53

.ooa

- 12127

.077 (2.02) .a94 c.163)

C.0004) .ooo

- g/79

(.ooool)

.531 c.080) . a97 c.026)

.0094 .0022 3.04 (3.366)

i/53

-

12183

,

.OOO

.714

(.00002)

8. Ht

Sample 4/18

Period - 5/20

0

= a + B it

-A!..003 C.015)

.a20 C.030)

f.133)

3.31 (4.45)

Huizinga + Y,H+,

- Mishkin +

Al-

r2nte2

22-

.252 C.199)

.0023

-.193 C.199)

(2)

+ et

S(E)

F-test for Stability (Degrees of Freedom)

.0102 8.47 (4,109)

4/18 l/53

- 12/27

.682

.532

.lOl

.0091

- 9/79

.06) .860

.094) .177

(.094) .214

.0022

.115)

.054)

C.055) 8.43 (4,364)

i/53

- 12183

.ooo

(.oMm Note:

.360 (.067)

.332 C.051)

.256 C.050)

nt

.0024

is the one-month nominal is the monthly C.P.I. inflation rate, it (either brokers’ time loans or Treasury Bills), and L is the lag operator, S(E) is the standard devia’tion of the residuals. The F-test for stability fit from the overall sample period with the fit from estimating coefficients after the changes in “regime” (either 6/20 or 10/79).

280

interest

rate

LkXt=Xtek. compares the before and

Huizinga/Mishkin and for

the

and

January

tests

for

the

these

results

above

8.0 stable

the

1953-83

models

Perhaps assumption nonstationary

the

the

to

random

in

terms

rate,

of

both

Plosser

of

about

properties

scope

of

cation

is

chastic

of

in

the

the

of

inflation

the

real

these

that

the of

errors

11976, Chapter

4]),

the

there varispecified

nominal

interest

As discussed on the

While of

is

is

it of

the

statisti-

is

beyond

which

change

sensitive

in

119821,

and White

effects

is

that

model

question

interest

these like

Schwert,

magnitude

in behave

processes.

difficult

of

an implicit

rate assumes

and

statistics.

the rate

in

one nonstationary

important

and test

clear

and

Nelson/Schwert

have

the

inflation model

stationary

resolve

and

similar

due to

Box and Jenkins

of

can

is

variables

and the

regression

hand, like

is

for

the

model

19781 and in Plosser,

it

in the

to

the

specifi-

the

sto-

assumed

specification. As a final

difference

point

between

Huizinga

change

rate,

the

in

periods.

Figure as While

virtually

it

1918-27 period

and the

argue of

that

these

policy

and

the

real

constant.

a plot

percentage rate

Figure

of

important are

is

the

nominal March,

dramatically

281

similar

note

a plot

Even terms of

different rate

one

in

behavior

quite

from

3b contains

to

1974-83 period.

associated

rate

rates

changes

is

episodes the

nominal

3a contains

annual the

clarification,

monetary

behavior

expressed

of

the

and Mishkin

major

1927.

Nelson/Schwert

other

to

process

model

stability

the

estimators

"best."

in

(see

paper

by Huizinga very

well.

substantial

stationarity

of

this

produced

in

statisti-

difference

equally

behave

highly

much

3.04

that

processes

[1977,

is

is

and

indicating

differences

which

and Schwert

assumptions cal

first

3.0

level

model

period

from

F-tests

models,

the

error

with

Nelson/Schwert

rate

On the

the

the

The Huizinga/Mishkin

regression

on another.

over

periods,

are

interest

walks.

unstable,

F-

seems

deviations

stationarity

nominal

It

Nelson/Schwert

F-test

half

sample

standard

data for

stochastic

a stationary

is

the

versus

the

than

and fit

about Both

less

the

is

the

the

1918-27 sample

the

asymptotic

Mishkin.

model

in

While residual

and

periods,

1918 - May 1920

contains

within

Huizinga

sample

April

1 also

whereas

.63

1953-83

in regime,

parameters

by

the

one reason

Huizinga/Mishkin

able

of

and

Table

model

periods,

is

that

Huizinga/Mishkin

non-nested

changes

1979.

period. it

Note

1918-27

Huizjnga/Mishkin

sample

significant,

similar

the the

F-tests

sample

the

performed the

both with

Mishkin.

of

tests that

in

models.

for

before

stability

the

more

the

(2)

1953 - September

to

the

in

subperiods

similar

cally

model

and the

the

major though of real

in

these

real

rate

1918 through December, in 1920, the nominal rate of

the

nominal

and real

a

•I

t

++ t ++ t / ++ + t --

t t t tf

k

t+ f

+Tt t

.

t t

+

t+ ‘t

t t

t

t t t

t

+

t

+ t

t

+t t

ft

t

++ t +++ +

t ++

t

sepd

ebquewed

282

pnuuv

f

.

t t t + + t + F t+ +

t

+

t

t

’ +$

t t

ft

t t+t

I P

T t

+t

+ ++ tt

t

t

t+

$ +++

t

ttt t

t:

+

t

t

t

4

t t %

t

t

t

*

t

I

I’I

283

I

t, I

rates

from

nominal

January,

rate

other

words,

tween

the

changes the nominal

is

due

behavior

of

nominal

rates.

of

rate

to

the

through

December,

as much or more

role

1918-27 period. period

1974

the

1983,

than

inflation

the

rate,

and

the

Almost

all

of

the

post-World

War I deflation.

rate

1979 is

real

real

rate,

the

since

it

appears

real

rate

in

which

is

the

is

dramatic

and

much more

rise

in

late

due

1979.

real

to

In be-

important

the

the

difference

On the

largely

that

in

rate

other high

the

in this hand,

the

and variable

III m THE RELATIONTO MONETARYPOLICY Even real

if

rates

one of

is

willing

interest

October,

1982),

do with

monetary of

timing

in

behavior.

monetary the

base

observed

such

or

in in

interest

rates

have

not

change.

This

regimes."

have raises

Certainly

occurred

have

change

such

that

in policy

wonder

growth

directly

to

the

caused

reasonably

as the

to

rate

account

of for

As noted

by Huizinga

and Mishkin,

explaining

the

of

real

show

that

in

Huizinga growth,

apparent

discount

rates

analogous

to that

fell

the

behavior

and or

Mishkin

inflation,

change

time

are

of of

not

1918-83.

Accord, could

that

question

these

in

equally

series

what

what

the

the

or

nominal

behavior

meant

of

and

be

identified

the

1920 and 1979 episodes.

With

the

conanon rates.

experience in

both

of periods,

Of course,

this

real

end

a

number for

the

without

real

rates

caused

that

in policy

in monetary and

policy

of

the

of in of

that to

in

a manner

I

hindsight, the

inflation

an accompanying

equivalent

that Federal

changes

study

benefit

1920 and 1979 is is

of

factors by a "change

changes

beginning Twist,"

well

behavior

specific

is

only

The

"Operation

dramatically interest

evidence

no understanding

between

Reserve-Treasury

rates

the

possibly

this

vigorously

could

be used

monetary

explain

we have

but-we

rate

cannot rate.

useful

about

cannot

variables

In addition,

studies.

In effect,

nominal

been

uncertainty

changed,

believe

real

the

of

1979.

in

have

policy

1920 (and

in

argue

that

behavior

What does

a skeptic

rate

the

stochastic

question:

evidence

discount

the

and Mishkin

striking

monetary of

previous

changes rates

of the

obvious

Nevertheless,

behavior

variables

rates

is

measures

the Huizinga

policy?

that

1979, and possibly

in

remains

the

why direct

conclude

changed

there

coincidence change

to

saying

drop that

in real

rose. From

this

perspective,

I do

not

284

think

we

have

gained

much

in

our

understanding of

of

interest.

high

ti

monetary

We remain

and

variable

papers

in

such

as the

the

behavior

puzzled

long

after

references

of

budget

of

policy

deficit

real

affects

about the

the

but

behavior

why nominal

inflation

none

had

the

that

rate

remained

Many

analyze

can help

a reliable

real

rates

fallen.

paper

factors

has found

of

interest

rate

Huizinga/Mishkin

as possible

rates,

the

of

the

variables

to explain

explanation

the

for

this

phenomenon. It by

is

also

Huizinga

Plosser

and

[1982]

associated

with that

monetary

policy

by

analyzing

to

money

or

from

September, the

1982 real

nominal

related

to

period to

March,

there

are supply

about

twice

havior

Huizinga/Mishkin

of

the

the

October,

tary

policy

real 1979

to

of

real

behavior

is

impressive

this that

paper),

the

remains this

of and

rates.

evidence

deserves

versus

prices supply

rate

During

for

goods

interest

Bills)

(de-

does

not

re-

September,

the

1979,

October,

significant

announcements,

Cornell

announcements

of

1977 to

as that

I979

to

responses

although

of

the

change

about

the

in

CONCLUSIONS important It

1982 that

(although

mechanism

of

raises

While

a mystery.

rates.

future

statistically

interest.

October,

"regimes,"

behavior

rates

paper

rate

no evidence

are

as large.

IV. The

he interprets

real

1984.

puzzle.

spending

in nominal

October,

rate

which

to money

goods

real

discussed

He finds

expected from

not

government

daily

Bills

price

money

in

the

rates,

of

the

relative

1982

is

response

studies

on

to changes

and Treasury that

light

is reduced.

announcements

rates rate

the find

the

supply

October,

expected

are

etc.) They

spond

shed

related

interest

rate

study

are

increases

interest

variables

fined

may

in nominal

real

1977-84.

there

unexpected

decreases

silver,

that

that

that

[19851

gold,

between

Mishkin

the

French

(e.g.,

noting

finds

evidence and

worth

which

argues,

period this

the

had

further

analysis.

285

too

a substantial

qualified links

perhaps

was an important

statistical

As I indicated

questions

by some of monetary in

the

strongly, change

that in mone-

influence

evidence

for the

policy introduction,

be-

on

the

a change

in

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