Inflationary expectations and the term structure of interest rates

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Inflationary expectations and the term structure of interest rates
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INFLATIONARY EXPECTATIONS
AND THE
TERM STRUCTURE OF INTEREST RATES





BY

JAMES MCCALL TIPTON


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY


UNIVERSITY OF FLORIDA


1981
















Copyright 1981

by

James McCall Tipton















ACKNOWLEDGEMENTS


To my patient and confident adviser, Professor

William A. Bomberger, I would like to express my deepest

gratitude and sincerely say thank you very much for all

that you have done for me.

I also wish to thank Professors Leonall C. Andersen,

David A Denslow, H. Russell Fogler, and James T. McClave

for their reading and comments on this manuscript.

I am also grateful to Michael Conlon for his invalu-

able computer programming assistance and to Barbara Long

for her superb typing of the manuscript.

I wish to thank Patti Dunett of Action Graphics,

Waco, Texas for her excellent graphics work.

Finally, I would like to express my sincere apprecia-

tion for the understanding and support of three special

people: my wife, Barbara, my mother, and my father.


iii















TABLE OF CONTENTS



CHAPTER PAGE

ACKNOWLEDGEMENTS............... ................... iii

ABSTRACT................ ... ... ............ ...........

I INTRODUCTION.............................. 1

Background.................. ............... 2
The Term Structure of Interest Rates...... 4
Implications of Both Questions............ 6

II THEORETICAL MODEL......................... 7

Macroeconomic Model....................... 7
Other Variables............................ 14

III TESTING AND RESULTS...................... 19

Preliminary Step to the Test.............. 20
The Main Test.......... ................. .. 36
The Subperiod Test........................ 42
Notes................................... ... 43

IV ANALYSIS OF RESULTS....................... 49

The Term Structure of Inflationary Expec-
tations.................................. 49
Interest Rates and Inflationary Expec-
tations ............................... 52
Summary Statistics and Graphs............. 52
Maturity Matching......................... 56
Problems and Extensions................... 60

V CONCLUSIONS.............................. 64

BIBLIOGRAPHY............... ............... ..... ... 66

BIOGRAPHICAL SKETCH................................ 75















Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy


INFLATIONARY EXPECTATIONS
AND THE
TERM STRUCTURE OF INTEREST RATES

By

James McCall Tipton

March 1981

Chairman: William A. Bomberger
Major Department: Economics


Individuals find it to their advantage to gather

information about the sources of inflation. In this

study I assume they use this information by forming

rational forecasts based on the structure of the process

which precedes inflation. Individuals then are assumed

to use the most important variables of that process in

order to form more accurate forecasts of the future course

of inflation.

The stochastic processes which generate those patterns

of inflationary expectations for the different monthly

horizons were then matched with interest rates of different

monthly horizons. This was to test if the horizon of

inflationary expectations matched the horizon of the same

interest rate as the best explanatory variable for the









Fisher equation


e e
rt = Pt + T t tt (1)


The rt represents the nominal rate of interest at time

period t, pt represents the real rate of interest deter-

mined by the intersection of the supply and demand curves

(roughly speaking the net savings and net investment

curves) from the real section of the economy at time t,

Se represents the expected future price .appreciation at
t
time t, and ptne is the crossproduct which is of such

small magnitude that it is dropped.

Using this matching approach the paper investigates

the single idea that the expected real returns from hold-

ing debts to maturity of different terms are more similar

than the nominal returns. Therefore, as one examines the

structure of interest rates at a point in time, part or

all of that structure is a reflection of the underlying

structure of expected inflation.

This study shows, both in a main period, January 1959

to December 1978, and in an inflationary subperiod,

January 1965 to December 1978, the horizon of inflationary

expectations does not hold as the best explanatory vari-

able for the nominal interest rate of the same horizon.

Thus the underlying structure of expected inflation is

not completely reflected in the term structure of

interest rates.















CHAPTER I
INTRODUCTION



Perhaps as never before, today's financial economist

faces tremendous uncertainty in our present economy.

Each day seems to bring big surprises as interest rates

soar and fall and inflation spirals upward to previously

unheard of rates. Indeed, the uncertainty of the present

age seems to be the only thing we can be certain of.

One of the more interesting questions in the theory

of interest rates then becomes, "How does inflation affect

interest rates?" More specifically, "How does expected

inflation affect the nominal (market) rate of interest?"

It is rightly noted that expected inflation is not the

only argument in interest rate determination, but these

types of questions are important to economic theory

because it is through their assessment that we evaluate

the effect of inflation on the real cost of capital and

the real return to investors. These questions are quite

broad in scope and currently involve much disagreement

over the manner in which "expectations" of inflation are

formed as well as the actual number of determinants to be

used in their formulation.











The purpose of this study is to test a single idea:

the expected real returns from holding debts to maturity

of different terms are more similar than the nominal

returns. Therefore, as one examines the structure of

interest rates at a point in time, part or all of that

structure is a reflection of the underlying structure of

expected inflation.

An approach which would shed some light on these and

related issues of expectations theories would be to answer

the question, "Do different patterns which provide the

best predictors of inflation over a given horizon also

provide the best explanation of the movements of market

interest rates of comparable duration?" This then will

indicate the underlying expectations structure and its

relationship to the nominal interest rate structure.

Because we are studying the effects of expected

inflation on interest rates of different durations, we

are in effect studying the effects of expected inflation

on the term structure of interest rates. Alternatively

stated, the study becomes a study of the effect that

expectation of inflation has on the relationship among

different maturities of debt.


Background

Interest Rates and Inflation. Irving Fisher (1930)

was the first to formulate a systematic theory of the

business cycle. This theory involved money stock changes,











commodity price changes, and a disparity between money

interest rates and real interest rates induced by the

commodity price changes which then caused the cycle to

evolve.

It is from this work of Fisher, which drew upon the

earlier work of Henry Thornton (1802), that we obtain the

hypothesis that the nominal interest rate moves in the

opposite direction to changes in the value of money

(therefore, the same direction as price changes). This

proposition is generally presented in some form similar to


rt = + t + Pt (1)

where rt represents the nominal rate of interest at time

period t, pt represents the real rate of interest deter-

mined by the intersection of the supply and demand curves

(roughly speaking the net savings and net investment

curves) from the real section of the economy at time t, te

represents the expected future price appreciation at time

t, and p 7e is the crossproduct which is of such small
t t
magnitude that it is dropped.

The hypothesis is then generally tested in some form

of a distributed lag equation as


r= p + Te
rt t + ~ (2)

Then the heroic assumption is made under the economic

theory of a long-run classical equilibrium that the real












rate is equal to some constant plus an error term, with

zero mean and finite variance,


Pt = "o + Et (3)


With statistical independence of the terms on the

righthand side in equation (2), the test equation

generally has become


rt = o + 7T + et (4)


where

m
TT= E aiPt-i (5)
i=o


That is, expectations of inflation are dependent on some

past series of inflation, and (Sargent 1973C) the weights

relating that influence sum to one:


T
Sai = 1 (6)
i=o


The Term Structure of Interest Rates

The theoretical relationship between interest rates

of different maturities likewise was being developed dur-

ing this and subsequent periods. This question of the

relationship between interest rates and maturity is com-

monly called the yield curve. Lutz (1940) restated this









5


classical relationship of the yield curve in terms of five

propositions from which we develop our modern theories.

He hypothesized that given three assumptions: that

everyone knows the future short-term rate, there are no

transactions cost, and there did not exist any constraints

on shifting investments for either the borrower or the

lender, that the relationship between the short-term and

long-term rates:

1. could be conceived of as the long-term rate
being an average of the future short-term rates,

2. that the long-term rate could never fluctuate as
widely as the short-term rate,

3. that it is possible that the long-term rate may
move temporarily opposite to the short rate,

4. that the current yield to redemption of a long-
term bond will be above the current short-term
rates up to the maturity date of the bond is
above the current short-term rate (and vice-
versa), and

5. that the return on an investment for a given
time is the same no matter in what form the
investment is made:

nominal interest rate + capital gains (or -capital loss)
purchasing price

The excitement then comes when the assumption of

certainty about future short-term rates is dropped.

Allowing for uncertainty then creates theories based on

expected future short-term rates being related to long-

term rates.












Implications of Both Questions

Until the recent article by Modigliani and Shiller

(1973) both bodies of economic theory, i.e., the question

of inflation and the interest rate and the question of

the term structure of interest rates, were being developed

in isolation. The Modigliani and Shiller article appears

to be the first attempt to combine the two questions into

one. Their article, as well as others, views only one

stochastic process as generating expectations for the debt

maturities studied.

If one believes the Fisher hypothesis to be true, the

fact that we observe different expected future short-term

rates and negative real rates, ex post, may be compatible

with the notion of more than one stochastic process

generating the expectation equation during periods of

transition from one long-run equilibrium to another long-

run equilibrium.















CHAPTER II
THEORETICAL MODEL



Macroeconomic Model

Sargent (1972b) has pointed out that if we wish to

study the relationship between inflationary expectations

and the nominal rate of interest it is most appropriate

to do so in the context of a macroeconomic system.

Of course, what is rational, or consistent, for the

individual to use in formulating his expectations is a

function of what one places within the model. The follow-

ing simplified IS-LM model is presented in order to talk

about possible different stochastic processes generating

inflationary expectations for different horizons.

Let the production sector be described by the follow-

ing IS curve:


Yt = Ft + o, + ai (rt-7) + vt (7)


where ao > 0 and al < 0, Yt is the log of real output, YF

is the log of real full-employment output, and vt is the

disturbance term.

The monetary sector is represented as the following

LM curve:











mt = Yt + B + (1rt + t (8)


where 81 < 0 and mt is defined as the log of real money

balances, i.e., log MSt log PLt, where MSt is the

nominal money supply and PLt is the price level and Et

represents the disturbance term.

The model's price adjustment equation represents an

intermediate position between the Keynesians and

Monetarists. Friedman (1970) described the price adjust-

ment equation as the crucial difference in the way they

close IS-LM models. Keynesians regard the money wage

rate as being exogenously determined and assume that firms

set prices equal to or proportional to marginal costs.

Assuming that short-run marginal cost are constant this

means constant prices and thus implies that PLt is exoge-

nous and that we need to solve for Yt and rt. Monetarists,

on the other hand, assume output, Yt, equals the exoge-
F
nously given full-employment level, Y., and treat rt and

PLt as endogenous variables.

This model assumes that the percentage change in

money wages can be represented by an expectational version

of the Phillips curve,


wt = a Ut + bt e (9)


where a < 0 and b = 1. In this equation, a defines the

short-run trade-off between the unemployment rate and the

rate of wage inflation, w, for a given t '_1, and b











measures the extent to which inflationary expectations are

reflected in current wage changes. The short-run capital

stock is fixed, Ko: thus real output is a function of the

other input factor, i.e., employment


Yt = f(Nt) (10)

where f'(Nt) > 0.

Assuming the unemployment rate is a linear function

about the full-employment level, N, then


Nt-Nt
U -= = k(Yt-YF) (11)
tt


where k < 0.

With the assumptions that prices are a constant

markup on unit labor costs, no technological change, and

constant labor productivity, then we may define the unit

of output to be such that


Pt = wt (12)

Substituting (12) and (11) into (9) and rearranging terms,

the Phillips Curve becomes


Y = F + Y(Pt t-l t (13)

where y > 0 and nt is the disturbance term. If in the

long run one held expectations based on some constant











level of past inflation, then (Pt-rel-) would equal zero

and


Yt = + (13a)


The three equations of the system


Yt = Yt + + al(rt-Te) + vt (7),


mt = Yt + o0 + 31rt + et (8), and


Y = yF + y (Pt-te) +t (13),
t t t t t-_1 t (1)

have four unknowns if .e is treated for the moment as
t
exogenous: mt, Yt, rt, and Pt. Thus the system is under-

determined. However, mt and Pt are related by the

identity


mt = Mt Pt + mt-1 (14)


where Mt represents the exponential growth rate for the

money supply i.e., log MSt log MSt_1, and Pt repre-

sents the exponential growth rate for inflation, i.e.,

log PLt PLtI. With these four equations then the

system can be solved in the sense that the four endogenous

variables may be expressed as linear functions of the pre-

determined variables and the disturbance terms. Let the

exponential growth rate for capacity output, log YF -

log Y -1, be defined as Gt. Continue to substitute for

the lagged endogenous variables in the solution for Pt











until the solution may be written as an infinite sum of

weighted past exogenous variables. The solution for Pt is


Pt = o + E ki mt-i + Z li Gt-i + Z ni t-it-l-i
1=o 1=o i=o


+ qivt-i + wit + t-i (15)
i=o i=o t 1 i=o sit-i


where jo, ki, li, ni' qi, wi, and si are simply removed

coefficients that are functions of ao, Bo, al, 01, and y

which can in principle be solved as well.

Up until now we have been treating r as a constant,

more specifically, t7-_l. This is justified on the basis

that the inflationary variable has been determined in the

prior period. We now wish to extend our model to future

periods. Thus with the longer-run extensions of the

model it becomes necessary to treat et as an endogenous

variable. Assume that the objective of the individual is

to forecast this variable minimizing the sum of errors in

the forecasting process, i.e., the individual is rational

if he minimizes the expected value of mean square forecast

error,


min E[e ] E[Pi t+i i=1,2, ...

(16)


This implies that if the forecast of inflation is to be

rational then











t+ = E(P t) i=1,2 ... (17)
t+1 t t+1

For example, from (15) we can derive the E(Pt+I) and thus

the function for t+1l

e 00 CO
t+lt = jo + Z kmt+li + E 1 Gt+l-i

S -i i mt+l-i + i i it+l-i +
i n1 7T=-i + qivtw=t1l+ +
ii=l qiit+--i i + i=l



iE si qt+l-i + ko E(mt+l) + 1o E(Gt+I) +
i=l


noE( T+l) + qo E(vt+l) + Wo E(et+l) + soE(nt+1).

(18)

To estimate equation (18) directly it is necessary

to have observations on all variables, including the

expected rates of inflation. Unfortunately, direct

observations on expectations for the various horizons are

not widely available. Therefore, a proxy variable needs

to be substituted for expected inflation. In the litera-

ture, the typical solution to this problem is to assume

that expectations are generated by a distributed lag on

past values of that variable which are observable. This

will be the procedure followed in this case. However,

the number of lagged variables will be restricted by use

of max X2 method for autoregressive schemes. The lag

structure generating expectations will follow an











extrapolation hypothesis that expected inflation equals a

weighted average of past rates of inflation together with

past rates of growth of the two other variables indicated

in equation (18). Then just what information becomes

important in the formation of rational expectations depends

upon the stochastic processes which generate the R.H.S.

variables, the assumptions we make about the error terms.

For example, suppose that after first differencing all of

the time series on the R.H.S. of (18) we approximate

"white noise." Then the best estimate for the future

value of the expected variable would be its present value

plus some error term. This then would have some weight

attached to it in the overall formulation of expecta-

tions. Likewise, if the time series did not convert to

"white noise," but instead showed some pattern which con-

tained information on the future value of its series, then

those observations would be included by their weight in

the formation of expectations.

Of course, the disturbance terms in (18) will be

proxied, as well as "full capacity" output. Expectations

themselves are unmeasurable and will require some proxy.

It is proposed that in terms of equation (18) expecta-

tions may be represented as a function of the past series

of monthly inflation rates, Consumer Price Index, monthly

growth rate of the money supply, MIA, and the growth rate

of monthly personal income, i.e.,












t+l t t' Pt-l' Pt-2' ** t' t-1' Mt-2' '

Yt' Yt-l' Yt-2' "'" ; rt' rt-l' rt-2' "').. (19)



where the interest rate series serves as a proxy for

E(Mt+ )

Let the exponential growth rate for expected infla-

tion one period (one month) forward, log PLt+1 log
e
PLt, be defined as t+lt. Likewise, let the exponential

growth rate for expected inflation two periods (two

months) forward, log PLt+2 log PLt, be defined as
e
t+27t. Continue this definitional pattern for expected
inflation forward for 60 periods. Thus the variable

t+60 represents the 5 year expected inflation rate as
of period t.


Other Variables

The theoretical model described above is not too

interesting if the only conclusion is a mathematical

manipulation, since virtually any result could be obtained

depending on what is included in the model. What makes

the "other variables" interesting is that they carry an

implication for different stochastic processes over time.

The economic interpretation of different processes for

the short-term with several variables versus the long-term

with only one variable has a very interesting explanation

in terms of information-processing by the market place.












It is suggested that additional variables are

necessary in the short-term equations because information

sources (data) on which investors form short-term infla-

tionary expectations are embedded with a high degree of

unreliability and possibly conflict. Short-term forecasts

of inflation are influenced by credit market conditions,

while medium and long-term forecasts are not, and investors

behave as though changes in fundamental economic relation-

ships in the short-term are highly unpredictable and use

several sources (different variables) of information to

reduce their uncertainty. Also, within a shorter time

period expectational effects occasioned by excluded vari-

ables, e.g., changes in the money stock, act to reduce

(increase) the real rate of interest temporarily. That

is, money is nonneutral in the short-term. This was

tested in the above mentioned model by adding additional

variables, e.g., money growth, etc., in the interest rate

determination equation as the variable Zt, i.e.,


rt =o + t+n + iZt + et i=2,3,4

(20)

This new formulation for short-term expectations

does not imply that the markets are not efficient. Rather,

the markets are efficient, i.e., all the currently avail-

able information is in the market place, but it implies

that our method of extracting the current information











about expected prices is inefficient if we restrict our-

selves to only one time series. Thus, the information of

how that series to be predicted will tend to move in the

future is a function not only of its own past, but also

of the indirect effects of other series, which act on

the future course of the price series itself.

Roughly speaking this implies that a change in cur-

rent personal income carries some information about the

future disturbance term. If income is rising toward full

employment income, it is valid to assume that this imparts

expectations about prices rising in the future. The

individual may even be said to expect prices to start

rising prior to YF, rather than have some clean break

assumption for price increase or decrease for Yt # YF.

Rapid changes in price levels may signal fear of escalat-

ing prices in the immediate future.

Likewise, current money supply changes may signal

the path of future prices over the next few months. This

information may or may not be reflected in the past price

series. Therefore, changes in the money supply were

included in the equation for the formation of expecta-

tions.

Finally, the last theoretical variable included in

the category "other variables," i.e., variables other

than the past series of prices, is the change in the











short-term interest rate, rt. This is included on the

grounds that it affects expectations of individuals

regarding the future monetary policy of the government.

This analysis provides a useful approach to the two

bodies of literature which analyze the role of inflation-

ary expectations. The first of these deals with the

question of the determinates in the formulation of infla-

tionary expectations. The second of these deals with the

question of testing Fisher's hypothesis that rt fully

adjusts to inflationary expectations, thus the sum of the

coefficients of lagged prices equals one. The majority of

the empirical studies yield estimates well below unity and

these are taken to reject the hypothesis (Yohe and

Karnosky 1969 and Gibson 1970). It is possible that the

reason the coefficients sum to less than unity is because

the specification of the formulation of expectations in

these studies is incorrect for the short-term interest

rates.

All of these "other variables" would have a positive

effect on expectations of changes in prices at least in

the immediate term. Thus they would have an indirect

positive effect on the short-term interest rate.

With respect to the long-term interest rates, all

information about inflationary expectations would be con-

tained in a single variable time series, the price series.

That is, as the time horizon lengthens then the basis for












the formulation of expectations about inflation should be

reduced from an informational set of four series to one

series because all relevant information has passed from

the other series to the price series.

These different stochastic processes then answer

questions about the determination of the term structure

of interest rates. They imply that as the informational

set is unrestricted that the empirical conflict in the

literature will be reduced, as R. Craine and J. L. Pierce

(1978) claim. It almost seems counterintuitive to imply

that the agent is more certain about a five-year fore-

cast of inflation than about a two-year or three-year

forecast. But perhaps the individual knows the eventual

outcome of fundamental economic relationships, though

highly uncertain of the short-term timing for those events.















CHAPTER III
TESTING AND RESULTS



The hypothesis that the market rate of interest on

debt of different durations can best be explained by

inflationary expectations formed over different horizons

that correspond to those debt horizons is a joint hypoth-

esis. The first part, a test for the formulation of

expectations, is described below as the preliminary step.

The preliminary step is necessary since inflationary

expectations are constructed by statistical modeling.

The second part, a test matching the different maturities

of interest rates and inflationary expectations, is

designed to answer the question, "How much of the struc-

ture of interest rates is caused by the structure of

expected inflation?" The second part is designated below

as the main test.

Finally, a control is conducted for the main test

results by repeating the main test again for a subperiod

which has a different inflation rate. The control, des-

ignated below as the subperiod test, allows comparison

and contrast of two different inflation periods.












Preliminary Step to the Test

The preliminary step to the test is based on the

additional explanatory power yield by the additional

variables in the expected inflation equation. The

traditional linear autoregressive structure:


Pt = a + P- + 32 Pt-2 + .. + t (21)


is derived from a generalized polynomial function with

power terms for the various P's including time and its

powers as variables:

00 i oo co k
P = Z a.t + + E (22)
t i=o I k=l j=l j t-j+ t


under the assumption that the linear specification is

correct and will thus lead to an unbiased and efficient

forecast. The best prediction made at the end of the

current month for the next month t+l then becomes

e
t+l1t = a + bl Pt + b2 Pt-i + ... + 0 (23)


where the forecast error is


Et+l = (Pt+l t+lVt) (24)


The purpose of including additional autonomous vari-

ables is to reduce the size of the error term. For each

duration of actual inflation there exist several possible

autoregressive schemes. The best two, one a single












series model and the other a multiple series model, are

pitted against one another to select the better model in

terms of the minimum size error term.

Thus, consider the equations for expected inflation

one month hence tested for fit with the following two

autoregressive schemes:


(A) t+let = p(L)Pt-i i=0, 1, ... (25)


versus

e
(B) t+17T = (L)Pt-i + (L)Mti + Y(L)Yt-i +


S(L) t-i i=0, 1, ... (26)


where ( (L), 6 (L), (L), and 2 (L) represent the coeffi-

cients for each lagged polynomial, and the other vari-

ables are as described before.

The preliminary step should be considered as a set

of screening steps which, after Box-Jenkins (1976) identi-

fication for differencing requirements, divides the set

of possible autoregressive orders into those of an

efficient set and those of an inefficient set for both

the single series case and the multiple series case. This

division into subsets is accomplished for the single

series case by performing the max X2 operation on the

difference price series. The optimal lag list is then

used to construct the single series model. The multiple











series model requires that Pt be regressed onto Mt, Yt,

and rt


Pt = + 2Mt + a3 Yt + rt + Et (27)


by OLS regression and the residuals from the regression,

Et, be operated on by the max X2 procedure. Selection

is made then from the efficient set of that alternative

ARI order which, according to the max X2 method, mini-

mizes the residual variance for each case, i.e., the

single series case and the multiple series case. Finally,

one selects between alternatives, the single series

equation and the multiple series equation, the better

method of describing inflationary expectations for each

duration.

For example, the choice of the equation to represent

inflationary expectations one month hence, n=l, was

between the single series model:

e
t+lt = .31 Pt + .36 Pt-1 + .28 Pt-5 (28)
(.06) (.06) (.06)


with summary statistics:

-2
2 .78 DW 2.15
MSE 4.8E-6 Prob > F .0001


and the multiple series model:












t+T = .21 Pt + .30 Pt- + .24 Pt-5 + .10 Mt +
(.06) (.06) (.06) (.05)


.06 Mt-1 + .01 Mt-4 .00 Yt .01 Yt-1 +
(.05) (.05) (.03) (.03).


.06Y + .00 r + .00 r + .00 rt
(.00) (.00) (.00) (.00)

(29)

with summary statistics:

-2
R .80 DW 2.15
MSE 4.6E-6 Prob > F .0001


The values in parenthesis represent the standard
e
errors. The symbol t+l"t represents the expected infla-

tion rate, log PLt+l PLt. Likewise, Pt represents the

actual difference in the past log levels of the monthly

Consumer Price Index, log PLt log PLt-1, Pt-1 repre-

sents log PLt_1 log PLt_2, and Pt-5 represents log

PLt-5 PLt-6. The actual difference in the past log

levels of the monthly money supply (Ml, currency plus

demand deposits) is represented by Mt-l, where i=0, 1,

2, ... In equation 29, Mt represents log MSt log

MSt-1, Mt-1 represents log MSt_1 log MSt_2, and Mt-4

represents log MSt_4 log MSt_5. The symbol Yt-i'

where i=0, 1, 2, ... represents changes in the past

levels of monthly Personal Income. For example, Yt

represents log PIt log PItl, t-l represents log












PIt-1 log PIt-2, and Yt-4 represents log PIt4 log

PIt-5. Finally rti, where i=0, 1, 2, ... represents

the difference in the end of the month annualized bond-

equivalent yield of one month seasoned U.S. Government

Treasury Bills. In this case rt represents rt rtl,

rt-l represents rt-_ rt-2, and rt-4 represents rt_4 -

rt-5 1

In the above manner then one is able to select the

multiple series model as the better fit for expected

inflation one month forward, t+le', during the period

January 1959 to December 1978.

To extend this process forward for t+n periods, we

make use of the general equation for single series fore-

casting:

e ( e) e e
t+nTt l(t+n-lt) + 2 (t+n-2t) + "- + n-l(t-n+1t) +


nPt-n + n+l Pt-n-l + .. (30)

which gives an optimal forecast in the sense of the

minimum extrapolation error (Mincer 1969).
e
For example where n=2, i.e., t+27t, substitute the

as yet unknown magnitude into the autoregression by its

extrapolated value. Thus the traditional formulation:

e
t+l1t = a + ~iPt + 2Pt-1 + ... (31)


is substituted into











e
t+2 T = a + 1Pt+l + 2Pt + 3t-l + (32)

for Pt+l, giving


t+2 = 0a + l(tt+1~ + Et+l) + 2Pt + 3Pt-l + *.. +


t+2 .(33)

Thus the mean squared error of extrapolation in predic-
e
ting t+21t, the two month expected inflation at time

period t, for the single series forecast is the variance

of (~ist+l + Et+2)-

Likewise, given that all the R.H.S. series of the

multivariate model have been whitened with constant

variance, the alternative formulation for the multi-

variate scheme is

e e P
t+2 t = + 1(t+lt + Et+l) + t2 Pt + 3Pt-l + +


1(t+iMe + E+1) + c2 Mt + 3Mt-1 + +

e Y
T e + + + + ...T
1(t+1 ) + 2 t + 3 t-1 + +

Sl(t+le + t+l) + 2rt + S23rt-l + + Et+2

(34)

Therefore, the mean squared error in predicting t+27t with

the multivariate model is the variance of ((~1t+l +

Olt+l + 1l +t+l + 1+1 +t+2)-












Renaming the coefficients to eliminate rewriting the

constants and bracketed terms, the choice is between


S= *(L)P i=, 1,
t+2Tt = *(L)Pt-i i=0, i,


(35)


and


t+2 = *(L)Pti + *(L)Mti + T*(L)Yt +


"*(L)rt-i i=0, 1, ...


(36)


for the two period forecast.

For the horizon n=2, the best single series model

was:


e
t+27t = .60 Pt +
(.11)


.57 Pt-i + .32 Pt-2 + .42 Pt-5
(.10) (.10) (.10)


(37)


with summary statistics:


-2
R .85
MSE 1.2E-5


DW 1.14
Prob > F .0001


The best of the multiple series models, and the better of

the single series versus multiple series models, was:


e
t+2t = .44 Pt +
(.10)


.17 Mt +
(.07)


.45 Pt-i +
(.10)


.11 M +
(.08)


.22 Pt-2 + .35 Pt-5 +
(.10) (.10)


.07 M .00 M +
(.07) (.07)


.01 Yt .00 Yt-1 .00 Yt-2 +
(.04) (.05) (.05)


.12 Yt-4 +
(.05)











.00 rt .00 rt .00 rt2 + .0008 rt4
(.00) (.00) (.00) (.0004)

(38)

with summary statistics:

-2
R2 .88 DW 1.12
MSE 1.1E-5 Prob > F .0001


In summary, the technique used to forecast the for-

ward one period rate of inflation for periods where n > 1

is that after the usual Box-Jenkins identification for

stationarity and the initial preliminary max X2 screen for

the optimal lag list, set up a two phase least squares

procedure. The lag list for the future values of the vari-

ables for time periods less than n from the first OLS

regression are then used as R.H.S. variables in the

estimation procedure of the second OLS regression. In

this manner, the estimation procedure steps the forecast

forward one step at a time giving the one period forward

rate of expected inflation for that duration and assures

approximately the same variance for each forward rate.

Thus by operating on the autoregressive schemes for-

ward, applying Wold's "chain principle of forecasting,"

replacing stochastic elements on the R.H.S. with their

prior lag last, expectations of inflation were derived

for different durations. Table 1 then shows the best

autoregressive scheme using the max X2 approach, and has

several interesting points for later discussion.

































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E-i 5












The Main Test

The best scheme for each horizon of expected infla-

tion having been formulated in the preliminary step,

interest rates of different maturities were then regressed

on the various annualized horizons of Table 1 using a

first order autoregressive scheme

e
rt = o + 3 t+nt + Et (39)


where


Et = t al t-l (40)


and pt is normally and independently distributed with

mean 0 and variance a2.2 We should expect the better fit

for inflation expectations to cause the estimated value

beta, 31, to approach in value the true value of beta.

If we expect the true value of beta to be one, then we

should observe the values of beta increasing towards the

value one as we substitute the better expectation fits

into the equation. The true value of beta is unknown.

It should be noted that it is possible for movement to

be away from the true value. Table 2 is the first order

autoregression of interest rates on the annualized infla-

tion schemes from Table 1.

Variables which were placed in the expectations

formulation are then placed into the interest rate equa-

tion as additional variables, zt, control variables. Thus











following the same procedure as described above,


rt = ao + 81 t+1" + t (41)


is compared with

e
rt = Co + 31 t+1 t + 2 Mt + 3 Yt + 4 rt-l + t

(42)

to conclude if any additional explanatory power can be

gained with the added determinates. The test is then

repeated for each interest rate. Table 3 gives the

results of equation (42) for a first order autoregression.

Thus the horizons are mixed according to the follow-

ing pattern.


Pattern A


rl t+1 t


t+2 t

S t+3 t


etc.


If the regressions show that the expected inflation for-

mulated for a given maturity best explains the interest

rate of that maturity, then the pattern for the highest

R2 observed would be that of the following,




















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"-4-

-4


H Z E-i W Z W E-4 E- W



































L ) (N r

N N N N






S L ) m n
(N (N (J (N





0 N N






N N Nm N









CN a) N


Sin 1 10 n H O
m n m m LO m rI

r- co Go n r- m co





N N N N N N N

n N (N N O cc r(
' v )r n v



' IT o L oN co co
N N N N










N (NN ( -4 -4H H-4

N N N N N N
- :. -, -. -. -i c. -








co cmi (N H H 0
Q0 Ao 00 ri r-i (Ni

LA LA cri 1 w) c (N






















N N N N N N N
1.0 I 1.C0 a) H 1.0 0








H-1 (M ci 'a 1


H












Pattern B

e
r---- t+l t

e



3 ----) t+3 t

etc.


rather than Pattern A, or some scheme similar to that of

Pattern A. Thus if Pattern B is observed we can con-

clude that the market rate of interest on debt of dif-

ferent durations could best be explained by inflationary

expectations over different horizons that correspond to

those debt horizons.


The Subperiod Test

A subsequent test was performed for the time period

January 1965 to December 1978 using the autoregressive

schemes developed from the main period, January 1959 to

December 1978. The subperiod testing allowed the inclu-

sion of seven to eleven month T-bills in the output

results in addition to the purpose of studying the

results for consistency during a period of rapid infla-

tion. The yearly mean inflation rate was larger in the

subsequent period, changing fromran arithmetic mean of 4.3

in the whole period to an arithmetic mean of 5.7 in the

subperiod.












Tables 4 and 5 contain the results for the sub-

period January 1965 to December 1978 using the infla-

tionary expectations formulation indicated on Table 1 for

Tables 2 and 3.

From initial data screens on the subperiod it was

obvious that this was a period where formulation of

inflationary expectations had changed. Thus some simi-

larity of results in a period with different auto-

regressive orders and rapid inflation would be taken as

additional confidence in the original results.


Notes

1. Data for Gross Personal Income and Money Supply, Ml,
are seasonally adjusted monthly observations from the
November 1979 CITIBASE tape compiled and updated by
Citicorp National Bank, New York, and supplied
courtesy of the Bureau of Business and Economic
Research, University of Florida, Gainesville. Data
for Consumer Price Index was supplied courtesy of the
Bureau of Labor Statistics, Department of Commerce,
Washington, D.C. Data for T-bills are discount yields
(bid yields) as of the end of the preceding month
from Salomon Brothers quote sheets. The bid yields
are converted to bond equivalents by the following
calculation



r(semiannual) = 2[( 1 )365/2t -
1-dxt
360


where the discount rate on a 360-day T-bill is con-
verted to a semiannual compounded rate based on a
365-day year, r represents the semiannual interest
rate, d represents the annual discount rate, and t
represents the time in days til maturity. Bond data
are beginning of the month series of yields of United















44























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a, 0 m m 0 0- w o




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6' ~ ~ I 1N ( N ( N 0 10 (N co aN ( N
0 0








E--i (a U) ii ii
(N ~ ~ c (N ( (N ( (N N N N N (N ( N -



0(N




W d N NI N N N N N N N N
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(N (N (N N (N (N (N (N (N (N (N r.4( N

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4 U N N N N (N (N (N SN -4 r- -


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No No fN N N/ N^ N Nf N N N


o a o 0 0 0 0 0 0 0 0 0
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N O PN O SO N N N N BD N







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N N N N N N 1N N N



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States securities read from monthly yield curves pre-
pared by Saloman Brothers. Whenever there is a choice
of coupons, the curves follow the yields of higher
coupon issues in the longer maturities.

2. The annualized interest rates were given, and the
inflationary patterns of Table 1 were annualized by
compounding each to one year as in the following
example of the monthly expectation


12
e e
t+lt(A) = r (1 + t+lt) 1
k=l


likewise to annualize te
t+2 t

6
e e
t+2't(A) = (1 + t+2"t) 1
k=l


Thus Table 1 was annualized and regressed against
annualized interest rates. Missing observations, due
to differencing the data for equation fit in Table 1,
were generated by the expectation equation for the
respective horizon. Thus expectations values for
longer horizons were "filled" in for the later years
of the data set under the assumption that expectation
were formulated in the same manner. Thus sample sizes
are equal.















CHAPTER IV
ANALYSIS OF RESULTS



The Term Structure of Inflationary Expectations

Table 1 indicates a limited number of different

inflationary patterns. The actual number of different

lag patterns to be matched is six. The spread between

the patterns and the change in loading patterns in Table 1

implies that individuals formulate, at a minimum, two

distinct sets of inflationary expectations.

Two sets are isolated primarily by the statistical

significance of the lagged inflation variables at a .10

level. In the first set, lagged values of price changes

(inflation) plus various combinations of additional vari-

ables generate expectations. The second set of expecta-

tions, horizons twenty-four to fifty months, shall be

called long-term expectations. In the second set, lagged

values of money supply growth plus various combinations

of additional variables generate expectations.

The term structure of inflationary expectations has

an upward drift and indicates a four year cycle. Thus

the lag pattern is unique in most of the first eight

periods and tries to correct itself with additional












information from past inflation. It adjusts itself for

the remainder of the term structure to the eight month lag

pattern.

The relatively short pattern of lagged values is

taken to indicate that individuals anticipate the longer-

run impacts of changing economic conditions much quicker

than in previous periods of stable monetary growth. The

use of additional information from the other time series

and the more active inflation rates after 1965 are offered

as explanations for the change from past formations of

long lag patterns.

Table 1 indicates the question, "Do changes in the

inflation rate cause changes in interest rates?" is

justified only as a reflection of the primary determinate

of expected inflation. In the study of short-term

interest rates there exists more than the one determinate,

past and current price changes, for the formation of

expected inflation. The study of long-term interest rates,

however, is the study of the movement of both interest

rates and inflation responding primarily to changes in the

growth rate of the money supply.

This observation from Table 1 of the different load-

ing patterns of short-term and long-term interest rates

described above is weakened when the business cycle repeats

itself. The various alternating upswings and downswings of

varied length and intensity occur at slightly less than












forty-eight months. The observation also is weakened at

turning points, directional changes, within the business

cycle. -This marked difference in loading on interest

rates at turning points suggests a new way to forecast

phases of the cycle.

For example, the twenty-four month inflationary

expectations are influenced not only by the growth rate

of the money supply, but are influenced also by the past

change in one month interest rates. Expectations for the

fourth year repeat the business cycle and are influenced

by income changes, as well as, money supply growth.

Determinates for the five year forecast are a similar

combination of the four year determinates and the one year

determinates. This is taken to indicate that the indi-

vidual is forecasting that five years from the present

time of forecast the business cycle will be one year into

repeating another second cycle.

Table 1 shows the assumption made in Chapter 2 con-

cerning the convergence of information to a single series,

the price series, is unjustified.

The following conclusions concerning expectations

formulation were reached. There exist two distinctly

different sets of inflationary expectations. Each set of

expectations is generated by a different stochastic process.

Expectations of inflation are influenced by the use of

information other than the price series. The market place











takes into consideration not only the current and past

values of inflation to Dredict the future course of infla-

tion, but also uses information concerning the rate of

growth of personal income, the growth rate of the money

supply, and past changes in the one-month interest rate.


Interest Rates and Inflationary Expectations

To answer the question, "How much of the structure of

interest rates is caused by the structure of expected

inflation?" two types of evidence are presented. First,

an examination of summary statistics and graphs is pre-

sented to determine whether there is a structure to

expected inflation which is in some way comparable tothe

structure of interest rates. Second, the major results

of matching interest rate maturities and expectations

horizons are presented for the different time periods and

different interest rate equations to determine the match-

ing with the highest explanatory power.


Summary Statistics and Graphs

The information presented in Table 6 and Figure 1 is

designed to answer the following two questions: "Do the

Te's vary as much across the horizons as the r's vary

across maturities?" and "Does the expectation "yield

curve" bend up and down when the interest rate curve does?"

Going vertically down Table 6 the mean r's rise and

the variances of the r's fall. This is as expected. The












same is true of the 7e's at least for the variances; the

means behave slightly different by having only a general

upward trend. However, the behavior of the mean re's does

not damage the theory. Only if the variances indicated a

different trend pattern would the theory be damaged.


Hori
in mo


Table 6
Summary Statistics for
Interest Rates and Inflationary Expectations
1/59 to 12/78

Standard St
zon r mean Deviation re mean De
>nths Prt Va r2 e e
t t


4.61
4.70
4.90
4.90
4.98
5.04
5.21
5.44
5.56
5.64
5.69


1.78
1.68
1.67
1.67
1.67
1.66
1.75
1.63
1.58
1.55
1.55


4.50
4.54
4.56
4.56
4.56
4.57
4.53
4.56
4.56
4.58
4.59


andard
aviation
4-


2.73
2.66
2.61
2.61
2.64
2.60
2.56
2.13
2.01
1.97
1.95


Figure 1 helps to highlight the results of Table 6.

It adds evidence that the two structures are comparable.

The Te's do vary as much across horizons as the r's vary

across maturities. As the expectations "yield curve"

bends up the interest rate curve bends up, and as the

expectations "yield curve" bends down the interest rate

curve does also. Interesting is the observation of

increased frequency after 1968 of the times the portion




























s 67 69 71 13 75 77 79


Figure 1 A.


The Term Structure of Interest Rates


mms 6 63 s w 6 n 73 in 7 7


Figure 1 B. The Term Structure of Inflationary
Expectations













































28


12 !
1969 61 63 65 67 69 71 73 75 77 79








Figure 1 C. Inflationary Expectation and the Term
Structure of Interest Rates












of short-term expectations curve lies above the interest

rate curve. This is interpreted as the result of the

increased inflation activity and more rapid information

processing by the market place.

The above results from Table 6 and Figure 1 shows

the structure of expected inflation is comparable to the

structure of interest rates.


Maturity Matching

Tables 2 and 4 represent the various interest rates

regressed on the different inflation horizons with an

adjustment for first order serial correlation for the

Fisher equation. Tables 3 and 5 show the same results

for the multivariate regression model. Therefore the

result of the existence of at least two distinct horizon

was not model sensitive. However, the results of the

loading patterns were sensitive to the rate of inflation,

i.e., the main period or the subperiod, and the specifica-

tion of a single variable or multiple variable interest

rate equation. The results below show the highest load-

ings during the main period. Thus if horizons do matter,

the pattern of loadings exhibited in the main period

imply that the horizons of the interest rates does not

match that of the expected inflation rate as a unique

set.














Interest Rates
(monthly maturities)

1


Inflationary Expectations
Table 2 Table 3
(annualized horizon)


6,7
6
6
6
6
6
6
5
3
3,4
3


6,6
1,3,4,5,6
3,4


Likewise the loading patterns for the subperiod of

more rapid inflation indicate


Interest Rates
(monthly maturities)

1
2
3
4
5
6
7
8
9
10
11
12
24
36
48
60


Inflationary Expectations
Table 2 Table 3
(annualized horizons)

7 8,9
7 7,8
7 8
7 7,8
7 7
7 7
7 7
7 7
7 7
7 7
7 7
7,8,9,10,11,12 7,8,9,10,11,12
5,6 5,6
5,6 3,4,5,6
5,6 3,5
3,4,5,6 3,4,5,6


Again if horizons do matter, i.e., the small changes

in the R2 values are thought to imply some significance,

then the pattern of loadings does not support the Fisher

hypothesis.












Information processing by the market place concerning

inflationary expectations shows little if any real dif-

ference between matches in short-term rates or the long-

term rates. The major difference in loading patterns

appears to be between the two groups short and long rates.

It appears that individuals forecast the 6 month and

7 month inflation rate very well, and that they use these

two durations as the basis for most of the interest rate

equations.

At no time with the use of any of the different models

did the nominal interest rate fully adjust to expected

inflation. The sign of the price expectations influence

was always positive and slightly sensitive to the use of a

single series or a multiple series expectation formulation.

This is not taken as a rejection of the Fisher hypothesis.

It is taken as an indication that the Fisher equation will

hold only during periods that occasion conditions of long-

run classical equilibrium. Therefore, if the data are dur-

ing periods of transition, the Fisher hypothesis is not

expected to empirically hold for the duration of debt instru-

ments used. The more rapid the rate of price increase, the

weaker will be the Fisher relationship between expected

inflation and nominal interest rates. This is easily seen

in the comparison of Table 2 of the main period, 1/59 to

12/78, to Table 4 of the subperiod, 1/65 to 12/78.












Likewise, the comparison of Table 3 to Table 5, the

more rapid the rate of price increase the more valuable

the change in the money supply became in explaining the

nominal interest rate. The negative sign and strength of

money indicates the strong influence the "liquidity effect"

(Friedman 1968) had on nominal interest rates during the

period of rapid inflation for interest rates with a 11

month or less horizon.

The statistical loss of significance for the "real

output" proxy, personal income, from the intermediate and

long-term interest rates, from Table 3 to Table 5 is

interpreted as a result of the disturbance from monetary

sources, Mt.

The increase in parameter values of t+n e from

Tables 2 and 4 to Tables 3 and 5, respectively, and the
-2
increase in R2 value is taken to imply the correct speci-

fication of interest rate determinates in Tables 2 and 4

had been relegated to the disturbance term. That is, a

multivariate model is more desirable in explaining nominal

interest rates than a single variable model. This speci-

fication was sensitive to the duration of the rates. Thus

both the determinates of the interest rate and the results

of the Fisher equation "test" are sensitive to sample

period choice and duration of rates chosen.

It is interesting that the general matching pattern

increases in maturity as the subperiod loadings are












compared to the main period. Thus individuals would need

to extend their expectations horizon during periods of

rapid inflation in order to better explain interest rate

movements. This maturity extension, due to the increased

uncertainty of the holding (opportunity) cost of money,

implies expected inflation will underestimate actual

inflation. The six month T-bill should have reflected

within its "price" the seven month expected inflation

instead of the six month expectations. Interest rate fore-

cast with matched horizons will also tend to be nonoptimal.

The final point to be noted is the reduction in MSE of

the interest rate with the use of the multivariable model.

If the MSE is considered as a proxy for the variance, and

the variance is the appropriate measure of risk for the

purchase of an investment (or a portfolio of investments),

then the reduction in risk, and the measure of performance

by a risk manager, can be improved with the additional

variables in the interest rate equation, especially during

periods of rapid inflation.


Problems and Extensions

Any empirical study within the field of economics can

be said to have problems, either with theory or measurement.

This study is certainly no exception.

The two major problems concern the development of

Table 1. First, serial correlation in the forward rates












makes use of summary statistics typically used for OLS

comparison very suspect, i.e., the t statistic, the F

statistic, and the MSE. Likewise, the lagged values of

the L.H.S. variable on the R.H.S. invalidates the D.W.

statistic except as a measure of direction for the increase

or decrease of correlation. Second, the decrease in the

sample size in order to fit the various expectations

horizons with the actual difference price series makes

the stability of the parameters and comparison across

sample sizes suspect. Generating values for missing data

was justified with the assumption that for the observa-

tions lost at the end of the dataset the formation of the

expectations did not change.

Timing of the data is suspect when using the C.P.I.

and end-of-month interest rates to generate Fisher equa-

tions. The regressions were adjusted forward and lagged

back by one month to test sensitivity. The results showed

that timing did not statistically matter.

The concern with developing and analyzing an inte-

grated macromodel, rather than with any detailed discussion

of particular expenditure functions, caused the omission

of devotion to detailed consumption, investment, govern-

ment, or money demand functions. Thus the theoretical

model is simple and permits inflationary expectations to

enter into the system only through the investment function

and the price adjustment process and overlooks the











elasticity with respect to the demand for money (Friedman

1956) and the proportion of government expenditure financed

by increasing the monetary base (Christ 1968) and taxes.

It is suggested that if the variable on the R.H.S.

meant to capture future government anticipations in the

credit market were altered to using a listing of future

debt sales of the government that the model could be

improved.

A very interesting observation is the movement of the

real rate ao. The real rates for Tables 2, 3, 4 and 5,

with the exception of the twelve month rates, increased

slightly in value as the maturity of-the debt increased.

Because the equation was not controlled for the various

effects on the real rate (Mundell 1963 and Phillips 1958

and Darby 1975 and Friedman 1977 and Feldstein and Summers

1978), the various movements in the real rate from Table 2

'to Table 3, and along the horizon on the same Table 2 or

3, and the comparison with the subperiod Tables 4 and 5,

must have offered as an explanation of occurrence being

due to statistical modeling. However, several interesting

questions arise. Does the real rate remain constant, or

increase with the horizon? Does price uncertainty,

measured by the variance of the forecast, cause the real

rate to rise during periods of rapid inflation? Does the

real rate approach a constant for the longer maturity

horizons, e.g., 5 year bonds? What are the determinates











for the real rate of interest, i.e., should it be con-

sidered as a variable in the Fisher hypothesis when test-

ing during transition periods,


rt = Pt + 17 + St (43)


Did the increase in the savings to disposable income ratio

during the subperiod, from 6.2% to 6.5% shift the net sav-

ings curve to the right by a smaller dynamic growth than

the shift to the right in the government deficit training,

thus causing the real rate to rise? There are many pos-

sible economic and statistical answers that could be

offered for the movement of the real rate. It is hoped

that additional study will answer these questions.















CHAPTER V
CONCLUSIONS



The results of this study show that for the main

period, 1/59 to 12/78, that the use of a multivariate

model to forecast inflation both reduces the MSE of the
-2
forecast and gives a better R (explanatory fit) for the

interest rate. Moreover, the different stochastic pro-

cesses underlying the term structure of inflationary

expectations, as indicated by both the different lag

patterns and the different loading patterns, suggest

segmentation of the expectations curve.

The analysis of the structure of inflationary

expectations and the structure of interest rates indicates

the two structures are comparable. A slight difference

was observed between the short-term and long-term relation-

ships. This difference in relationships was much more

pronounced during periods of rapid inflation.

It was shown that in both the main period, 1/59 to

12/78, and the subperiod, 1/65 to 12/78, the horizons of

the same length of interest rates and inflationary expec-

tations did not yield a unique match. It was suggested

that the Fisher hypothesis applies only to equilibrium

periods thus the study was not taken to be inconsistent

with the long-run theory.












The main conclusion of the study has to be that if

horizons are thought to be important, then the Fisher

hypothesis stated with the duration of the interest rate

matching the duration of expected inflation does not hold

for the different durations along the yield curve.

In addition to using a multivariable expectation

forecast, the results show an interest rate which includes

additional variables as determinates provides a better fit

and a smaller MSE than those equations without the addi-

tional variables. Finally, the real rate of interest is

noted as not being constant across different horizons,

but the explanation is left to question because the

equation was not adequately controlled to discuss move-

ments in the real rate.















BIBLIOGRAPHY


Bomberger, W. A. and W. J. Frazer, Jr., "Interest Rates,
Uncertainty and the Livingston Data," Working Paper,
May 1980.

Box, G.E.P. and G. M. Jenkins, Time Series Analysis,
San Francisco, CA: Holden-Day, Inc., 1976.

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BIOGRAPHICAL SKETCH


I was born July 20, 1948, to James Reed and Lois

McCall Tipton in Knox County, Tennessee. I grew up and

attended public schools in Chattanooga, Tennessee,

graduating from Brainerd Senior High School in 1966.

I graduated from the University of Tennessee,

Knoxville, with a Bachelor of Science in Economics in

1970. Then after spending three years as a regular Army

officer, I served an internship with the Chicago North-

western Transportation Company as a Treasury Analyst.

Entering the University of Florida in September 1974, I

graduated with a Master of Business Administration, con-

centrating in Finance in 1976. I married Barbara Ann

Miller in June 1976. I then received a Master of Arts

in Economics in 1978. I have accepted a joint appoint-

ment in both Finance and Economics from Baylor University,

Waco, Texas beginning August 1980.










I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.





William A. Bomberger, Chairman
Professor of Economics





I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.





David A. Denslow
Professor of Economics





I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.





Jamr T. McClave
Professor of Statistics











I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.





H. Russell Foglet
Professor of Management




This dissertation was submitted to the Graduate Faculty of
the Department of Economics in the College of Business
Administration and to the Graduate Council, and was
accepted as partial fulfillment of the requirements for
the degree of Doctor of Philosophy.






Dean for Graduate Study and
Research