Testing the Fisher Hypothesis: A Survey of Empirical … the Fisher Hypothesis: A Survey of Empirical Studies（Mitsuhiko Satake） R t≡E t r t＋E tπ t＋1 （, 1） where R t

Testing the Fisher Hypothesis: A Survey of Empirical Studies（Mitsuhiko Satake）

【論　説】

Testing the Fisher Hypothesis:

A Survey of Empirical Studies*

Mitsuhiko Satake**　　

1. Introduction

　In its simplest form, the Fisher hypothesis postulates a one-for-one relationship

between the nominal interest rate and the expected inflation rate, i.e. that the

nominal interest rate increases by 1% for every 1% increase in the expected

inflation rate. If the Fisher hypothesis holds true, then it has important practical

implications for the monetary policy, the super-neutrality of monetary policy, the

usefulness of interest rates as monetary policy targets and the predictability of

inflation rates using nominal interest rates. However, as is often the case with

applied economics, robust results on the empirical validity of the Fisher hypothesis

are difficult to find. There is a huge volume of both empirical and theoretical

work, starting with the original paper by Irving Fisher (1930), which found a one-

for-one relationship between nominal interest rates and inflation rates. Attempts

to replicate such results have led to a wide variety of studies using varying

techniques, time periods and data from a wide range of countries 1). This paper

＊　I would like to thank Garry MacDonald at Curtin University of Technology, Ken Hirayama at Kwansei Gakuin University and the members of Monetary Economics Workshop for helpful and insightful comments. However, the remaining errors are entirely the author’s responsibility.＊＊　Faculty of Economics, Doshisha University, Karasuma-Imadegawa, Kamigyo-ku, 602-8580. 　E-mail: [email protected]）　There are few surveys on testing the Fisher hypothesis, including Cooray (2003), a brief but

excellent survey.

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第 62巻　第 4号

attempts to summarize some of the results from this body of literature by focusing

on empirical testing methods, which have changed over time as econometric

techniques have changed and developed.

　The structure of this paper is as follows. Section 2 briefly discusses the meaning

and importance of the Fisher hypothesis. Sections 3 to 5 provide an overview of

testing the Fisher hypothesis according to the development of techniques. Section

3 looks at the original work of Fisher (1930) and various others who attempted

to extend and replicate his tests. Section 4 proceeds with the seminal work of

Fama (1975), which placed the testing of the Fisher hypothesis in the context

of efficient markets and rational expectations and marked a significant shift in

the methodology used to test the hypothesis. Section 5 focuses on more recent

attempts to test the hypothesis using modern time series techniques, in particular

those associated with the development of tests for nonstationarity (unit root)

and long-run relationships (cointegration). Section 6 discusses the results from a

large body of work (empirical and theoretical) that found no support for the Fisher

hypothesis and attempted to explain why the Fisher hypothesis was not supported.

The empirical literature reviewed in Sections 2 to 6 focuses largely on studies

based on US data; therefore, the final three sections of this chapter review briefly

the literature from Japan (Section 7), Australia (Section 8) and other countries (Section

9). Section 10 attempts to summarize the results discussed and puts them into

perspective.

2. The Meaning of the Fisher Hypothesis

　The Fisher hypothesis is based on the following identity, which simply states

that the nominal interest rate is the sum of the ex ante real interest rate and the

expected inflation rate.

56 （424）


　　　　Rt≡Et rt＋Etπt＋1 , （1）　　

where Rt is the nominal interest from t to (t＋1) and Et is the expectation

operator for period t ; therefore, Et rt is the real interest rate expected to hold

from period t to (t＋1) and Etπt＋1 is the expected inflation rate from period t to

(t＋1). This identity is called the Fisher equation after Irving Fisher, who originally

discussed the idea that, when the interest rate is considered, it is important to

distinguish between nominal and real rates. If we then suppose that the real

interest rate is constant (as determined by the rate of return on capital), equation

(1) clearly demonstrates a one-for-one relationship between nominal interest

rates and expected inflation rates. This concept is the Fisher hypothesis, or as it

is sometimes referred to, the Fisher effect. Economists typically use the phrase

‘Fisher effect’as shorthand for the potential effects of monetary policy on interest

rates in the context of equation (1). Thus, the Fisher effect tells us that when a

loose monetary policy causes an increase in the money supply, an increase in the

expected inflation rate due to this increase in the money supply will lead to an

increase in nominal interest rates, as suggested by the Fisher equation (1). Whilst

the implications of equation (1) are that, with constant real rates of return, any

increase in expected inflation will lead to a one-for-one increase in nominal interest

rates, this strict interpretation is sometimes dropped when economists refer to the

Fisher effect. Often, the Fisher effect is more loosely interpreted as the effect of a

1% increase in expected inflation rates on nominal interest rates that increase by α

%, where 0<α≤ 1.

　Before moving on to review at the empirical testing of the Fisher hypothesis, it

is worth briefly noting the importance of the hypothesis.

　First, as suggested by the discussion above, empirical support for the Fisher

hypothesis suggests the super-neutrality of money. As equation (1) suggests, the

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real rate of interest equals the nominal rate minus the expected inflation rate.

These move one for one; therefore, monetary policy changes to the money supply

affect nominal variables but not real variables. This is the key statement for

classical economics: support for the Fisher hypothesis implies the impotence of

monetary policy.

　The second implication is associated with the problem of the monetary policy

target, i.e. whether interest rates or a monetary aggregate are more adequate

as an instrument of monetary policy. The original theoretical discussion of this

problem was put forward by Poole (1970) in the context of a stochastic version of

the IS-LM model. Poole’s analysis clarified the choice to be made between interest

rates and quantity instruments and that the incorrect choice would lead to greater

output volatility. Gibson (1970b, 1970c) classified three effects of monetary policy

on nominal interest rates. For example, when a loose monetary policy increases

the supply of money, this increase in the money supply induces a decrease in

interest rates in the short run as a result of the liquidity effect. In the controversy

for the monetary policy target, economists thought that a loose monetary policy

decreases interest rates. Actually, a loose monetary policy increases interest rates

because of the income effect and the expected inflation effect (the Fisher effect) as

inflation occurs. In particular, the Fisher effect matters greatly during a period of

high inflation. A decrease in interest rates stimulates demand for investments and

so on, encouraging interest rates to increase through the income effect. Moreover,

an increase in expected inflation rates increases nominal interest rates more than

their original level in the long run. As a result, a loose monetary policy increases,

not decreases, interest rates. Consequently, the monetary authority cannot control

interest rates as an intermediate target for monetary policy 2). During the 1970s

in Japan and other OECD countries, with the above controversy, research for

2）　See Friedman (1968) and Sargent and Wallace (1975).

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monetary economics produced literature on testing the Fisher effect to assess the

adequacy of interest rates as a policy target. In the 1970s, policy management has

switched to making monetary aggregate more important than interest rates when

inflation accelerated. Therefore, with respect to controlling monetary policy, it

matters whether the Fisher effect holds or not, as do the size and adjustment rate

for the Fisher effect.

　Finally, an increase in money supply as a result of monetary policy does not affect

real interest rates, assuming that real interest rates are determined only by the

real sector. Therefore, in accordance with the Fisher hypothesis, a change in future

inflation rates, i.e. a change in expected inflation rates, causes the same change

in nominal interest rates. The one-for-one relationship between nominal interest

rates and expected inflation rates means that we can forecast future inflation rates

by observing movements in nominal interest rates because information on future

inflation is fully contained in such nominal interest rate movements.

　As the above suggests, the Fisher hypothesis embodies important implications

for macroeconomic policy. Thus, its empirical validity or otherwise has been the

subject of a large body of empirical work. The following sections provide a brief

survey of some of this evidence.

3. Initial Tests of the Fisher Hypothesis

　A. H. Gibson found evidence to suggest that a positive relationship exists

between nominal interest rates and price levels. John M. Keynes named the

relationship the Gibson Paradox 3). He referred to the finding as a paradox because

there should be a negative relationship between nominal interest rates and price

levels from the perspective of the theory at the time. According to Knut Wicksell 4),

3）　On the Gibson Paradox, J.M. Keynes referred to Gibson’s series of articles in Banker’s Magazine, in particular January 1923 and November 1926. See Keynes (1930, pp. 177-186).

4）　See Wicksell (1965).

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to attain the equilibrium that equates investment with saving in the real sector,

the ex ante interest rate is called the natural interest rate and is considered stable

over time. However, the actual rate, i.e. the market interest rate, tends to fluctuate

in the short run. If the market interest rate rises and becomes higher (lower) than

the natural rate, savings exceed (lag) investments. This leads to the development

of a deflationary (inflationary) gap and price levels fall (rise). Therefore, ‘Classical

Theory’ suggests a negative relationship between nominal interest rates and price

levels.

　Fisher (1930, Ch. 19, pp. 399-451) explained the Gibson Paradox by noting the

distinction between real interest rates and nominal interest rates; at equilibrium,

the nominal interest rate is the sum of the returns on real assets (the equilibrium

real interest rate) and the expected inflation rate. When the purchasing power

of money is stable, the real and nominal interest rates are constant. However,

the value of money changes over time. If fluctuations in the value of money are

perfectly foreseen and the purchasing power of money decreases by 1%, then

nominal interest rates become 1% higher than real interest rates. Therefore, the

inverse one-for-one relationship between the change in the purchasing power of

money and that of the nominal interest rate is clear and implies a positive one-

for-one relationship between nominal interest rates and inflation rates, since an

increase in inflation implies a decline in the value of money. However, in practice, it

is frequently the case that changes in the value of money are not perfectly foreseen

and agents make forecasts of expected changes. Expected inflation rates forecast a

change in the purchasing power of money, and Fisher argued that expected inflation

rates could be deduced from a distributed lag of prior inflation rates. This suggests

that a positive relationship exists between nominal interest rates and price levels

that are explained by the accumulation of lags in prior inflation rates.

　This idea formed the basis of the initial empirical work that was carried out by

60 （428）


Fisher, who estimated the correlation coefficient between the return on the long-

term bond and the expected inflation rate (proxied using a linear distributed lag of actual

inflation). His initial results showed that:

　• Using quarterly US data for the period 1890-1927, the maximum correlation

coefficient was 0.857 and used a lag length on inflation rates for the past 20

years.

　• Using quarterly UK data for the period 1898-1924, the maximum correlation

coefficient was 0.98, with a lag length of 28 years.

　Therefore, the Gibson Paradox, which is the positive relationship between long-

term bond returns and price levels, is interpreted as a response of the long-term

bond return to expected inflation rates. However, Fisher’s results suggested that

actual inflation rates affect expected inflation rates for a surprisingly long time,

with lags of 20 to 30 years, thus leading to the highest positive correlations in the

data.

　In summarizing his ideas in the final part of chapter 19 of Fisher’s (1930), The

Relation of Interest on Money and Price, he indicated that there is a remarkably high

correlation between inflation rates and interest rates. However, he also indicated

that changes in interest rates lag inflation rates for a long time and sometime for

a surprisingly long time. He concluded that interest rates change according to

changes in the real sector when the purchasing power of money is stable. On the

other hand, interest rates change according to a change in the purchasing power

of money when the purchasing power of money is unstable. It is perhaps worth

quoting some of his comments from the summary of chapter 19:

　　 ‘We have found evidence general and specific, from correlating P’ 5) with both bond yields

5）　Note that P’ means the inflation rate.

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and short term interest rates, that price changes do, generally and perceptibly, affect the

interest rate in the direction indicated by a priori theory. But since forethought is imperfect,

the effects are smaller than the theory requires and lag behind price movements, in some

periods, very greatly. When the effects of price changes upon interest rate are distributed over

several years, we have found remarkably high coefficients of correlation, thus indicating that

interest rates follow price changes closely in degree, though rather distantly in time.

　　　The final result, partly due to foresight and partly to the lack of it, is that price changes

do after several years and with the intermediation of change in profits and business activity

affect interest very profoundly. In fact, while the main object of this book is to show how

the rate of interest would behave if the purchasing power of money were stable, there have

never been any long period of time during which this condition has been even approximately

fulfilled. When it is not fulfilled, the money rate of interest, and still more the real rate of

interest, is more affected by the instability of money than by those more fundamental and

more normal causes connected with income impatience, and opportunity, to which this book

is chiefly devoted.’ (Fisher, 1930, p. 451, Chapter 19, Section 13 Summary)

　Thus, Fisher (1930) found surprisingly long distributed lags in estimating

expected inflation rates. Although he argued that the cause of the longer lags

was potentially the result of the incompleteness of both expectations and the

adjustment in the determination of expected inflation rates, the lag length of the

expected inflation rate in the empirical work was seen as troublesome and difficult

to justify in reality. Fisher (1930) did not test the size of the Fisher effect, but

simply estimated the correlation coefficient between nominal interest rates and

expected inflation rates and postulated that a 1% increase in expected inflation

rates leads to a 1% increase in nominal interest rates.

　Since the 1970s, when the major economies of the world started to experience

both higher and more volatile inflation rates, the literature on testing the Fisher

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effect focused on two key issues: the length of the lag and the size of the Fisher

effect. To confirm the results of Fisher (1930), papers such as Meiselman (1963),

Sargent (1969), Gibson (1970a), Yohe and Karnosky (1969) and Lahiri (1976)

forecasted expected inflation rates using a range of distributed lag models, tested

the Fisher hypothesis and estimated the size of the Fisher effect using the

following basic model structure.

　　　　Rt＝Et rt＋Etπt＋1 （2）　　

　　　　Rt＝α＋βEtπt＋1＋ε （3）　　

　Equation (2) simply recalls the original Fisher equation as denoted in Section 2.

Assuming that the ex ante real interest rate is a constant α, the Fisher hypothesis

is that β＝1 can be tested using equation (3).

　　　　Etπt＋1＝∑i

wiπt－i （4）　　

　　　　Rt＝r̄＋∑i

wiπt－i＋εt （5）　　

Expected inflation is estimated using the distributed lag model in (4). Putting the

estimated value of expected inflation rate from the regression model (4) into the

second term on the right-hand side of (3) can test whether the hypothesis that β

＝1 in (3) is supported or not. Most literature substitute equation (4) in equation (3)

and estimate model (5) to test whether the sum of the values of the coefficients in

the distributed lags is equal to or less than one. Note that the test using model (5)

could not identify the difference between the hypothesis β＝1 and the size of the

effect of the expected inflation rate from the distributed lag model. Basically, we

should test the Fisher hypothesis using model (3) with the expected inflation rate

derived from (4). However, we also summarize the testing in the literature based

on model (5).

　We first review some of the results in the context of the required length of the

distributed lags. Meiselman (1963), Sargent (1969) and Gibson (1970a), who employed

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several distributed lags, i.e. Koyck, geometric decreasing and unconditional

distributed lags respectively, found that by using data before World War II the

estimated length of distributed lag models was enough to support Fisher (1930).

　Meiselman (1963), using annual US data on returns on corporate bonds and WPI

for the period 1873-1960, applied the adaptive expectations and found a mean lag of

13 years, which supported the long lag length although the size of the Fisher effect

was very small before World War II. Sargent (1969), using annual US data for the

period 1902-1940, determined the effect on nominal interest rates of surprisingly

long distributed lags for price change variables, even while taking into account

the other monetary and real variables. Gibson (1970a) used annual short- and long-

term interest rate data for the period 1869-1963 and quarterly data for the period

1948-1963 and found the long-run effect of the expected inflation rate on nominal

interest rates, although the size of the effect is less than one.

　In another aspect of the literature, Yohe and Karnosky (1969), Feldstein and

Eckstein (1970), Carr and Smith (1972) and Lahiri (1976) showed that the length

of the lag required to capture the formation of the expected inflation rate was

shortened in the 1960s. Using monthly data from the US for the period 1952-1969,

Yohe and Karnosky (1969) analysed the relationship between nominal interest rates

and inflation. The yield on 3A corporate bonds was used as long-term rates, the

four to six month CP (Commercial Paper) rate was used as a short-term rate and the

inflation rate was measured using the CPI. Yohe and Karnosky (1969) conducted

regression analyses, in which the regressand was the nominal interest rate and

the distributed lags of prior inflation rates were regressors. Almon distributed

lag models 6) were adopted and three types of lag lengths, 24, 36 and 48 months,

were used to estimate the regression models. The results are summarized by

6）　The Almon distributed lag model is one of the distributed lag models and assumes that the shape of the distribution is polynomial, meaning that we can flexibly determine the shape.

64 （432）


two points. First, the maximum of the determination coefficients was 0.771,

using short-term interest rates in the case of the three-year lag length and 0.549,

using the long-term interest rates in the case of the four-year lag length. The

determination coefficients were rather large, although not as large as in the case

of Fisher (1930). Second, the duration of the effect of expected inflation on the

nominal interest rate is within two years and the latest period has the maximum

effect. Therefore, Yohe and Karnosky (1969) showed that the distribution lags

were not as long as Fisher (1930) insisted. This tendency appeared in Feldstein and

Eckstein (1970) and Carr and Smith (1972), which employed the Almon distributed

lag model. Polynomial distributed lag models are considered to have shorter lags

than monotonic decreasing distributed lags. Moreover, Lahiri (1976) found that the

some formations expect the inflation to adjust much faster.

　The reduction in the lag length of the distributed lags model depends not

only on the type of the model but also on the period during which the study was

undertaken. Dividing the sample periods between the 1950s and the 1960s, Yohe

and Karnosky (1969) and Gibson (1972) found that the adjustment rate accelerated

and the lag length shortened in the 1960s compared with the 1950s. Gibson

(1972) indicated that the expected inflation rate obtained from the Livingstone

survey data, which contain forecasts of future inflation rates for six or 12 month

in the future and could explain most of the variation in actual inflation during the

1960s. This suggests that the adjustment rate of the expected inflation effect on

nominal interest rates accelerated in the 1960s more than in the 1950s. Feldstein

and Eckstein (1970) and Carr and Smith (1972) conducted the analyses using data

mainly from the 1960s. It is believed that the adjustment rate of the effects of

expected inflation on the nominal interest rate accelerated. The reason might be

because agents needed to incorporate inflation expectations into the determination

of nominal variables more rapidly to insulate themselves from losses, considering

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that inflation was insistent in the 1960s.

　When researchers turned to analyse the size or magnitude of the Fisher effect,

they found evidence that it became larger in the 1960s than in the 1950s at the

same time that the lag length shortened. Thus far, the studies used the expected

inflation rate formulated by distributed lag models. However, we have a problem in

selecting distributed lag models because of the arbitrariness in selecting the shape

and lag length of such models. We need directly observed data, i.e. survey data to

make us escape from fear to determine whether we have a wrong price formation.

Although the frequency of such data is limited, the Livingstone survey data 7)

is available in the US since 1946. Using survey data, we can examine, without

doubting whether the price formation is correct, the magnitude of the Fisher

effect. We briefly summarize the literature using the survey data, i.e. Gibson (1972),

Pyle (1972), Cargill (1976), Lahiri (1976) and Cargill and Meyer (1980).

　Gibson (1972) used the Livingstone survey data as expected inflation rate instead

of the distributed lag model. Using US data between 1952 and 1970 and dividing

the entire period into two periods, i.e. the 1950s and 1960s, Gibson (1972) found

that the estimated coefficient of the expected inflation rate in the 1950s was less

than 0.5, while that estimated coefficient during the 1960s was nearly one. Yohe

and Karnosky (1969) indicated the same results. Using the Livingstone Survey

data, Cargill (1976) also tested the Fisher effect by dividing the sample period into

two periods, i.e. the 1950s and 1960s. He found that most of the results of the

estimation coefficients for the expected inflation rate were not significant in the

1950s, while the coefficients were almost significant and their size was supported

to be one in the 1960s. Therefore, the faster the inflation rate grew in the 1960s,

7）　The Livingstone Survey is produced by Joseph Livingstone, who was a nationally syndicated financial columnist. It has surveyed twice a year since 1946 from a group of business, government, labor and academic economists on their expectations of future values of macroeconomic variables including the consumer price index. See Gibson (1972).

66 （434）


the larger the effect on nominal interest rates. However, Cargill and Meyer (1980)

examined the Fisher effect, dividing the period into three subperiods, i.e. 1954-59,

1960-69 and 1970-75. As a result, the relationship between the nominal interest

rate and inflation is fairly unstable, which is inconsistent with the other two

studies.

　Although they did not divide the sample period, Pyle (1972) and Lahiri (1976)

examined the Fisher effect using the Livingstone survey data. Pyle (1972), using

US data for 1954-1969, obtained the results that the coefficient was nearly 1.0

when using 12-month forward data, while the result using six-month forward

data was less than one. For the 1952-1970 samples, Lahiri (1976) incorporated the

Livingstone survey data into four expectation formations and found that the size

of the effect was 0.7-0.9. The coefficient increased because both studies contained

data from the entire 1960s.

　As described above, the length of the distributed lags was shorten in the 1960s

and the result was accepted by researchers. Moreover, the magnitude of the Fisher

effect grew. However, this magnitude had been by and large less than one since

Yohe and Karnosky (1969). Therefore, it is conceivable that the Fisher hypothesis

is not fully supported in empirical studies.

　Since the seminal work of Fisher (1930), a large volume of literature has been

devoted to empirical work to test the Fisher effect. Research following Fisher

had two questions related to the results in Fisher (1930), i.e. far longer length of

distributed lags and the one-for-one relationship between the nominal interest rate

and inflation. Up to today, whilst the adjustment rate of the effect of the expected

inflation rate on nominal interest rates was very slow when inflation was stable

before the 1950s, it accelerated in the 1960s. Moreover, Fisher (1930) believed in

the one-for-one relationship. However, many studies following Fisher found that

the size of the Fisher effect was less than one, although it grew in the 1960s. We

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will follow the literature using new approaches from here on.

4. The Influence of Fama (1975) on Tests of the Fisher Hypothesis

　A major change in the way in which applied studies approached the testing of

the Fisher hypothesis occurred with the publication of Fama’s seminal paper in

1975. Since Fisher (1930), regression models used to test the Fisher hypothesis

assumed that current nominal interest rates could be explained by the expected

inflation rate, which was estimated by some form of distributed lag model of past

inflation rates. Therefore, the implicit assumption was that causality flowed from

the inflation rate to nominal interest rates and that expectations were formed

adaptively, i.e. that agents were backward looking when forming expectations.

　Fama (1975) assumed that the market was forward looking and could correctly

forecast future inflation as a stochastic expected value. If the short-term financial

market is an ‘efficient market’, in the sense that it uses all available information

in the determination of the equilibrium short-term nominal interest rate, the

current nominal interest rate contains all of the information contained in the lags

of the actual inflation rate, making distributed lag models redundant. In this model,

current interest rates should therefore be good predictors of future inflation rates

and the causation runs from nominal interest rate to inflation rate. Fama (1975)

therefore incorporates two assumptions in the testing framework: that the market

is efficient (see Fama (1970)) and that agents are rational (see Muth (1960)).

　Fama (1975) estimated regression models in the form of equation (6), in which

the regressand is the one-period-ahead inflation rate and the regressor is the

current nominal interest rate.

　　　　πt＋1＝α＋βRt＋ut , （6）　　

where π is the inflation rate, R the nominal interest rate, α is a constant term

and equal to the minus real interest rate and ut is the error term. Whether or not

68 （436）


the market is efficient can be examined 1) by testing the hypothesis that β＝

1, which derives the constancy of the ex ante real interest rate and 2) by testing

the hypothesis that there is no serial correlation in the error term, which is

interpretable as reflecting market efficiency. When these hypotheses hold, the

Fisher hypothesis is completely supported and the nominal interest rate contains

complete information about past inflation under rational expectations and the

constant ex ante real interest rate.

　Using monthly US data between 1953 and 1971, with the reciprocal of the

rate of one-period changes in CPI as the change in purchasing power of money

and using one- to six-month Treasury Bills as the nominal interest rate, Fama’s

(1975) results suggested that the hypothesis that the coefficient of the nominal

interest rate is one could not be rejected. He calculated the autocorrelations of

inflation rates and real interest rates from one to twelve months and found a high

autocorrelation of inflation rates, showing that past inflation rates have information

on expected inflation rates. Moreover, he found no autocorrelation of real interest

rates, indicating that real interest rates are constant. Fama (1975) also estimated

the regression model in (6) augmented with the addition of a one-period lag of

the inflation rate as a regressor and found that the coefficient of the one-period

lag inflation rate was not significant. Fama (1975) argued that the current nominal

interest rate contains all of the information to predict one-period-ahead inflation.

Overall, Fama (1975) interpreted the results as supporting the notion that the

market was efficient, with the short-term interest rate fully incorporating all past

information on inflation, and that real rates were constant.

　Fama’s (1975) overwhelming empirical result induced a series of comments in

the American Economic Review in 1977, i.e. the comments by Carlson (1977), Joines

(1977) and Nelson and Schwert (1977) and the reply by Fama (1977). Essentially,

these papers attempted to find flaws in Fama’s analysis, usually by including other

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variables to test whether they had significant predictive power for inflation, thus

invalidating the idea that the current short-term interest rate fully incorporated all

information on past inflation.

　For example, Joines (1977) added the Wholesale Price Index and Hess and

Bricksler (1975) and Nelson and Schwert (1977) added the forecasting value of

inflation into Fama’s regression model. The coefficients of these variables turned

out to be significant. Carlson (1977) questioned Fama’s (1975) result that all

information in future expected inflation rate falls within the nominal interest rate

given that his finding of the addition of a variable measuring business cycle factors

into the Fama’s model is significant. Moreover, Carlson (1977) found that the real

interest rate is not constant using results based on his analysis of the Livingstone

survey data on the expected inflation rate.

　On the other hand, significant research (e.g. Shiller, Campbell, Schoenholtz and

Weiss (1982), Campbell and Shiller (1987) and so on) focused on the information in the

term structure of interest rates whether or not the relationship between interest

rates for different maturities can predict the future movement of the short-term

interest rate. Combining this idea with Fama’s (1975) approach, Mishkin (1990a)

proposed a method to examine the predictability of the term structure of nominal

interest rates on the future inflation rate. Mishkin (1990a) examined whether the

term structure of interest rates can predict the inflation rate and estimated the

relationship between the term structure of interest rates and the inflation spread

in the following model:

　　　　πtm－πt

n＝α＋β[Rtm－Rt

n ]＋et , （7）　　

where Rtm is the nominal interest rate of the m period matured, Rt

n is that of the

n period matured; therefore [ R tm－R t

n ] is the nominal interest spread matured

between the m period and the n period and [πtm－πt

n ] is the inflation spread

according to the nominal interest spread.

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　If β＝1 in equation (7), the nominal interest rate spread can completely forecast

the inflation spread in the sense that the change in the nominal interest rate

between different maturities, i.e. the term structure of nominal interest rates, is

fully reflected in the change in inflation at different periods; therefore, the complete

Fisher hypothesis holds. If 0＜β＜1, the nominal interest spread partly forecasts

the Fisher effect and the nominal interest spread contains the future inflation

rate. Equation (7) means the difference of the two equations in (6) with respect to

different maturities. Accordingly, the complete Fisher hypothesis is supported if

coefficient β in equation (7) is one. On the other hand, if β is less than one and

greater than zero, the Fisher effect is partly considered to be found.

　Mishkin (1990a) examined equation (7) for short-term TB rates in the US and

found that the coefficients of the nominal interest rates spreads were 0＜β＜

1, concluding that the nominal interest rates have the ability to predict future

inflation. Mishkin (1990b) also examined equation (7) for the longer terms in

the US, between one and five years. As a result, Mishkin (1990b) found that the

nominal interest rates spreads for longer terms contained information on future

inflation rates. Moreover, Jorion and Mishkin (1991) analysed data in the UK,

West Germany and Switzerland for the nominal interest rate maturing in one to

five years. The coefficients of the nominal interest rate spread were 0＜β＜1,

indicating that the nominal interest spread partly contained information on future

inflation rates. Moreover, the longer the maturity, the more information on inflation

was contained.

　Fama (1975) indicated the overwhelming result that the full Fisher effect was

supported by data in the US on one- to twelve-month TB rates and the CPI for

1953-1971, i.e. that nominal interest rates contain all information for one-period-

ahead inflation rate. Since Fama (1975), many studies have been conducted as

described above and studies examined the constancy of real interest rates, such

（439） 71


as Mishkin (1981), Fama and Gibbons (1982) and Huzinga and Mishkin (1986).

Moreover, a series of Mishkin’s studies were conducted to examine whether the

term structure of nominal interest rates contain information on future inflation. In

general, the results in this section also indicate that the size of the coefficient β in

both (6) and (7) is 0＜β＜1, indicating that the partial Fisher effect is obtained.

5. The Use of Modern Time Series Techniques to test the Fisher Hypothesis

　The next key development in testing the Fisher hypothesis was the utilization

of the framework of modern time series analysis, most particularly the unit root/

cointegration framework. The finding that most macroeconomic time series are

nonstationary I(1) processes and the development of techniques to deal with

the issues that arise from this have had implications for all applied work using

time series data. The literature on unit root and cointegration is very large and

the intent is not to survey this here. Equally, the literature on testing the Fisher

hypothesis using some variant of the techniques proposed in this literature is also

large and once again a full survey is not intended here. Rather, this section aims

to simply outline the nature of the tests used, the variants and problems that have

arisen and to summarize briefly the results for the US, with Sections 7 and 8 doing

the same for Japan and Australia.

　The Fisher hypothesis, as has been made clear, implies a one-for-one relationship

between the nominal interest rate and the inflation rate. In the context of recent

time series literature, this suggests that the applied researcher should first carry

out unit root tests on the nominal interest rate and the inflation rate. If the two

series are (as might be expected) nonstationary I(1) processes, then cointegration

tests are implemented. If the cointegrating vector is (1, －1) (evidence of cointegration

between the two series), then it is regarded that the one-for-one relationship between

the nominal interest rate and inflation rate, i.e. the Fisher hypothesis, is supported.

72 （440）


On the other hand, literature exists that simply tests the stationarity of the real

interest rate, arguing that support of the Fisher hypothesis is found in the case in

which the real interest rate is stationary.

　Table 1 below provides a perspective on a selection of studies between 1988

and 2008 that used some form of ‘modern’ time series approach to test the Fisher

hypothesis. As noted above, there are now a large number of variants of the basic

unit root and cointegration tests and the footnotes to the table provide a brief key to

the various methods used in these papers.

　Table 1 reveals a wide range of results, with some authors finding evidence in

favour of the Fisher hypothesis and others failing to do so. Two general points can

be made about the papers reported in Table 1.

　First, most studies using Johansen’s (1988) approach to test the relation

between the two variables support the Fisher hypothesis more than using Engle

and Granger’s (1987) approach. Some others approaches also tend to support the

Fisher hypothesis, for example, Lee, Clark and Ahn (1998), who applied methods

suggested by Ahn and Reinsel (1998), and Westerlund (2008), who applied the panel

cointegration test to 20 OECD countries.

　Second, all of the three studies, Lanne (2001), Mehra (1998) and Mishkin (1992),

divided their sample at the start of financial deregulation in 1979 and found that

the Fisher hypothesis holds true before, but not after, 1979. Referring to the

existing literature 8) , Mishkin indicated evidence of a lack of support for the

Fisher hypothesis in the pre-World War II data and the period after October 1979

until 1982, although the Fisher hypothesis is widely supported for the period

between 1951 and 1979. Mishkin (1992) observed that there are unit root in both

8）　Mishkin (1992) referred, for example, to Fama (1975), Mishkin (1981, 1988) and Fama and Gibbons (1982) as supporting evidence for the Fisher effect after the Fed-Treasury Accord in 1951 until the monetary regime shift in October 1979 and referred, for example, to Barsky (1987) and Huzinga and Mishkin (1986) as no supportive evidence existed before World War II and between 1979 and 1982.

（441） 73


Table 1　 The Literature on Testing the Fisher Hypothesis Using Time Series Analyses without Consideration of Structural Break in the United States

Literaturea Period Frequency Approachb Resultc

Atkins (1989)* 1965-1981 Quarterly COINT(JOH), ECM FH: Supported

Atkins and Coe (2002)* 1953-1999 Monthly ARDL Bounds TestFH: Supported before-tax rate,Not after-tax rate

Atkins and Serletis (2003)* 1880-1985 Annual ARDL Bounds Test FH: Not Supported

Bekdache (1999) 1961-1991 MonthlyMS Model, Time Varying Parameter Model

r: Shifted Twice, FH: Not Supported

Bonham (1991) 1955-1990 Monthly COINT(EG) FH: Supported in consideration for r

Choudhry (1996) 1879-1913 Annual COINT(JOH) FH: Supported

Crowder and Hoffman (1996) 1952-1991 Quarterly COINT(JOH), ECMFH: Supported in the longrun, considering tax

Crowder and Wohar(1999) 1950-1995 Annual COINT(Several) FH: Supported

Daniels, Nourzad, and Toukoushian (1996)

1952-1992 Quarterly COINT(JOH), ECM FH: Supported

Engsted (1995)* 1962-1993 Quarterly VAR with PVM Constraint FH: Not Supported

Ghazali and Ramlee (2003)* 1974-1996 MonthlyARFIMA Models, Fractional COINT Test

FH: not Supported

Kasman, Kasman, and Turgutlu (2006)*

1964-2004 Monthly Fractional COINT Test FH:Supported

Koustas and Serletis (1999)* 1957-1995 QuarterlyVAR with King=Watson's (1997) Method

FH: Not Supported

Lai (1997) 1965-1994 Monthly UNIT(DF-GLS) r: Stationary, FH: Supported

Lanne (2001) 1953-1990 Monthly Near UNIT(CES) TechniqueFH: Supported until 1979, Not after 1979

Lee, Clark and Ahn (1998) 1953-1990 Monthly COINT, ECM FH: Supported

MacDonald and Murphy(1989)*

1955-1986 Quarterly COINT(EG)FH: Not Supported, except Fixed Exchange Rate Sytem

Mehra (1998) 1961-1996 Quarterly COINT(JOH), ECMFH: Supported until 1979, Not after 1979

Mishkin (1992) 1953-1990 Monthly COINT(EG)FH: Supported until 1979, Not after 1979

Moazzami (1991)* 1953-1978 Quarterly UNIT, ECM FE: Partial

Peláez (1995) 1959-1993 Quarterly COINT(EG, JOH) FH: Not Supported

Peng (1995)* 1957-1994 Quarterly COINT(JOH) FH: Not Supported

Rapach and Weber (2004)* 1957-2000 Monthly UNIT, COINT(Several) π~I(0), R~ I(1), FH:Not Supported

74 （442）


the nominal interest rate and the inflation rate for the monthly US data during the

periods between 1953 and 1979 and between 1953 and 1990. He also observed a

cointegrating relationship between them, making it clear that the there is a Fisher

effect in the long run in these periods and not in other periods. Therefore, Mishkin

(1992) argued that the Fisher effect occurred only when a stochastic trend in both

the nominal interest rate and the inflation rate was present. As Mishkin (1992)

indicated, nominal interest rates and inflation rates have had a common trend since

World War II and until 1979. Therefore, it could be credible that the cointegration

relationship between such variables can be found and they have a common trend.

Mishkin’s findings were echoed by a number of other papers that found evidence

of support for the Fisher hypothesis over certain spans of data but not others.

Some papers, such as Bonham (1991), attempted to relate these sorts of findings

to factors influencing the economy and to determine whether the nature of the

exchange rate affected the results of the Fisher equation by dividing the sample

into periods of fixed and floating exchange rate regimes in the US. As a result,

Rose (1988)*Annual:1892-1970，1901-1950, Monthly: 1947-1986

UNITπ~I(0), R~ I(1), r~I(1),FH: Not Supported

Strauss and Terrell (1995) 1973-1989 Quarterly COINT (JOH) FH: Supported

Wallece and Warner (1993) 1948-1990 Quarterly COINT(JOH) FH: Supported

Westerlund (2008)* 1980-2004 Quarterly Panel COINT Test FH: Supported

Yuhn (1996)* 1979-1993 Quarterly COINT( JOH) FH: Supported in the lon run

(Notes)a Literature attached * tests in multiple countries including the US. The result is shown in the US only.b UNIT is Unit Root Test, COINT is Cointegration test, EG is Engle and Granger Test, JOH is Johansen

test, ECM is Error Correction Model. MS model means Markov Switching Model. ARDL Bound Test is Autoregressive Distributed Lag Bound test, that does not require the standard univariate time series of the data. The ARFIMA model is Autoregressive Fractional Moving Average model. CES is Cavanagh, Elliot and Stock's (1995) method, which has the advantage to be asymptotically valid whether the variable is I(1) or I(0), or near unit root based on ECM.

c R is nominal interest rate, r is real interest and π is infaltion rate. FH is the Fisher Hypothesis, which is a one-for-one long-run relationship between R and π. FE is the Fisher effect, whose size is classified into full, partial and non. 'full' means the support for the Fisher hypothesis.

（443） 75


there is evidence supporting the Fisher effect in consideration of ex ante real

interest rates regardless of sample periods.

　The results in Table 1 suggest the potential for structural breaks and changes to

impact the results of the Fisher hypothesis tests. The finding that structural breaks

can impact the results of unit root and cointegration tests is now well known. The

results in Table 1 are limited to papers that tested the Fisher hypothesis using

time series analysis without consideration for structural breaks in the US.

　Clearly, Fisher hypothesis tests should consider the possibility of structural

breaks in the series and the relationship between nominal interest rates and

inflation. Table 2 provides a selection of papers that have re-tested the Fisher

hypothesis, allowing for breaks.

　We can classify the literature into the following three groups with respect to the

different techniques used:

　• unit root and cointegration tests that have been modified to allow for the

consideration of structural breaks;

　• threshold models such as the Threshold Autoregressive (TAR) models and

Smooth Transition Autoregressive (STAR) models; and

　•Markov Switching (MS) models.

　First, the Fisher hypothesis test was conducted mainly using the unit root test

for the real interest rate, with consideration for structural breaks. The stationarity

of the real interest rate with break shifts is found in the US by Bai and Perron

(2003), Caporale and Grier (2000), Lai (2004) and Million (2003), supporting the

Fisher hypothesis. While Rapach and Wohar (2005) found the stationarity of real

interest rates with structural breaks in 13 OECD countries, they also found that

breaks in the inflation rate negatively corresponded to those in the real interest

rate, indicating less support for the Fisher hypothesis. The study by Klug and

76 （444）


Nadav (1999) is the only one to reject the Fisher hypothesis and they applied

Mishkin’s (1990) formula in constructing the structural break. Silvapulle and

Hewarathna (2002) applied Gregory and Hansen’s (1996) cointegration test, with

one structural break in the nominal interest rate and inflation rate in Australia and

found cointegration supportive of the Fisher effect. Atkins and Chan (2004) and

Malliaropulos (2000) found a trend-stationarity in the nominal interest rate and

inflation rate with a break shift in the US. They applied the VAR approach to the

detrended data and found evidence supportive of the Fisher effect. As a result of

the unit root and cointegration tests with break shifts, we find that every study

except for Klug and Nadav (1999), whose formulation is different from others,

supported the Fisher hypothesis when considering structural breaks, while Atkins

and Chan (2004) only obtained a partial Fisher effect.

　Second, Bajo-Rubio, Díaz-Roldán and Esteve (2005), Lanne (2006), Maki

(2005) and Million (2004) all use nonlinear threshold models mainly applied to

cointegration tests, which used threshold models to examine the residuals derived

from cointegrating regression. All of these studies found supportive evidence for

the Fisher hypothesis, except that Bajo-Rubio, Diaz-Roldan and Esteve (2005)

found the partial Fisher effect. Another approach using nonlinear models was

conducted by Choi (2002) and Christopoulos and León-Ledesma (2007). They

constructed nonlinear models to take two regimes into account and found evidence

supportive of the Fisher hypothesis. The literature using nonlinear models

indicated strong evidence that supports the Fisher hypothesis by allowing for the

existence of nonlinearities in the Fisher relation.

　Finally, the Markov switching model, another approach to considering multiple

regimes instead of threshold models, was adopted by Evans and Lewis (1995) and

Garcia and Perron (1996). Evans and Lewis (1995) applied the Markov switching

model to obtain the expected inflation rate to test the relationship between nominal

（445） 77


Table 2　 The Literature on Testing the Fisher Hypothesis Using Time Series Analyses Allowing for Structural Breaks

Literature Coutries Periods Frequancy Approacha Resultsb

Atkins and Chan (2004) US,Canada 1950-2000 QuarteryUNIT with SB, ARDL Bounds Test

FE: Partial

Bai and Perron (2003) US 1961-1986 Quartery UNIT(BP) r: I(0) with SB, FH: Supported

Bajo-Rubio, Díaz-Roldán and Esteve (2005)

Spain 1963-2002 Annual TAR COINT Test Partial FE

Caporale and Grier (2000) US 1961-1992 Quartery UNIT(BP)r: I(0) with SB, FH: Supported, shifts in response to Political Changes

Choi (2002) US 1947-1997 Monthly TAR ModelIFH: Supported in low infaltion, FH: Supported in high inflation

Christopoulos and Léon-Ledesma (2007)

US 1960-2004 Quarterly STAR Model FH: Supported Volker-Greenspan ear

Evans and Lewis (1995) US 1947-1987 Monthly MS Model FH: Supported

Garcia and Perron (1996) US 1961-1986 Quarterly MS Model FH: Supported with SB

Klug and Nadav (1999) US 1920-1940 Monthly Mishkin with SB FH: Not Supported

Lai (2004) US 1978-2002 Monthly UNIT (VP, BLS)Real Interest Rate: Stationary with SB, FH: Supported

Lanne (2006) US 1953-2004 QuarterlyVECM incorporating TAR model into EC term

FH: Supported

Maki (2005) Japan 1963-2002 Quarterly TAR COINT test FH: Supported

Malliaropulos (2000) US 1960-1995 Quarterly IRF from VAR using Detrended Data with Trend Stationary

FH: Supported

Million (2003) US 1951-1999 MonthlyNear UNIT Test with SB

FH: Supported

Million (2004) US 1951-1999 MonthlyCOINT(GH), apply STAR Model to Residual as r

r: I(0) with SB, FH: Supported

Rapach and Wohar (2005)OECD 13 Countries

1960-1998 Quarterly UNIT (BP)r: I(0) with SB, π:I(0)with SB in accodance with r, FH: Not Supported

Silvapulle and Hewarathna (2002)

Australia 1968-1998 Quarterly COINT (GH) Test FH: Supported

(Notes)a SB is structural break. UNIT is unit root test including Bai and Perron (1998) (BP), Vogelsang and

Perron (1998)(VP) and Barnejee, Lamsdane and Stock (1992)(BLS). COINT is cointegration test. GH is Garegory and Hansen (1996) coitegration test. MS model is Markov Switching model. TAR and STAR models means Threshold Autoregressive and Smooting Trasition Autoregressive models. IRF is Impulse Response Function. VECM is Vector Erroe Correction Model. ARDL Bound test is the same as Table 1.

b R is nominal interest rate, r is real interest and π is infaltion rate. FE is the Fisher effect, FH is the Fisher hypothesis, and SB is structural break. IFH is the Inverted Fisher Hypothesis.

78 （446）


interest rates and inflation rates. Garcia and Perron (1996) applied the Markov

switching model directly to ex post real interest rates. Both of the two studies

supported the Fisher hypothesis.

　Mishkin (1992) indicates that the Fisher effect appears only when both the

nominal interest rate and the inflation rate have stochastic trends. Therefore,

many studies that have applied linear models to the analysis, do not support the

Fisher hypothesis in long-term samples. However, once the nonlinear models, that

considers multiple regimes and the unit root test and cointegration tests with the

consideration of the structural breaks, applies, i.e. once breaks are allowed for in

the test procedure, the literature gets more supportive for the Fisher hypothesis.

6. Explanations for Non-Support of the Fisher Hypothesis

　Before reviewing the empirical literature on the Fisher hypothesis in Japan,

Australia and other countries, it is worth briefly considering the impact on the

literature of the large number of studies that found no support for the Fisher

hypothesis. Justifications for the empirical failure of the Fisher hypothesis

generally fall into three categories:

　•the inverted Fisher hypothesis.

　•asset effects (the Mundell–Tobin effect).

　•tax effects (the Darby–Feldstein effect).

　Carmichael and Stebbing (1983) turned the Fisher hypothesis on its head by

arguing that the nominal interest rate is constant and that the real interest rate

responds inversely one-for-one to the inflation rate. This hypothesis became

known in the literature as, for obvious reasons, ‘the inverted Fisher hypothesis’.

According to Carmichael and Stebbing (1983), people hold money because it has

implicit returns like liquidity, although the nominal interest rate on money is

（447） 79


zero. The implicit return is almost constant and equal to the nominal return on

financial assets when there is high substitutability between monetary assets and

money. Therefore, the real interest rate inversely responds one-for-one to the

inflation rate. Carmichael and Stebbing (1983) found initial support for an inverted

Fisher effect with their results that showed a negative one-for-one relationship

between the real interest rate and the inflation rate using data from 1953–1978 in

the US and from 1965-1981 in Australia. Barth and Bradley (1988) re-examined the

inverted Fisher hypothesis, extending the period used by Carmichael and Stebbing

(1983). They found that the inverted Fisher hypothesis was not supported and that

the value of the coefficient used to test the hypothesis decreased to much less than

one in the sample from 1953 to 1984. In interpreting their results, they argued

that a structural break in the Fisher relationship occurred after 1979. After the

1990s, the inverted Fisher hypothesis was tested by Inder and Silvapulle (1993) in

Australia and Choudhry (1997) in Belgium, France and Germany. They found that

the inverted Fisher hypothesis was rejected. However, Choi (2002) found that the

inverted Fisher hypothesis was supported when inflation is low and stable and that

the Fisher hypothesis was supported when inflation persists, using the threshold

autoregressive model (TAR model) with two regimes. Similar to the original Fisher

hypothesis, it appears that evidence on its inverted version is mixed.

　The second variation on this theme is the so-called Mundell-Tobin effect (see

Mundell (1963) and Tobin (1965)), which argues that real money balances decrease

with increases in inflation, resulting in a fall in the real asset holding of agents.

Therefore, agents increase their savings and the real interest rate decreases. As

a result, a 1% increase in the inflation rate leads to a less than 1% increase in the

nominal interest rate. Many authors used the idea of the Mundell–Tobin effect to

justify the finding that the Fisher effect is less than one-for-one. For example, see

Woodward (1992), Crowder and Hoffman (1996) and Coppock and Poitras (2000).

80 （448）


　Finally, as originally formulated in the Fisher equation, the nominal interest rate

that agents consider as the signal for deciding the level of their investment is the

after-tax rate. Therefore, the effect of a change in the expected inflation rate on

the before-tax nominal interest rate, which is frequently used in applied studies,

could be greater than one. This theoretical argument was first suggested by Darby

(1975) and Feldstein (1976). Following their theoretical argument, empirical studies

were conducted. Although Peek (1981) strongly supported the Darby-Feldstein

effect, most empirical studies, for example Tanzi (1980), Cargill (1977) and Carr,

Pesando and Smith (1976), found that the Fisher effect was equal to or less than

one, rejecting the Darby-Feldstein effect. Yun (1984) and Crowder and Wohar (1999),

using both taxable and tax-exempt bond rates, found that the coefficient for the

former rate was greater than that for the latter, supporting the Darby-Feldstein

effect. As it is hard to distinguish one effect, such as the Darby-Feldstein effect,

from others, such as the Mundell-Tobin effect, the evidence is mixed.

7. The Fisher Hypothesis in Japan

　This section reviews the literature on testing the Fisher hypothesis in Japan in

more detail. The literature on testing the Fisher hypothesis in Japan has grown

rapidly since the late 1970s, when the inflation rate rose substantially and became

quite volatile. Table 3 lists some of the key papers in the area and, once again, it

seems sensible to divide these papers into three categories.

　　1. Papers that use the traditional methods of analysis to calculate the expected

inflation rate using distributed lag models.

　　2. Papers that apply the testing methods suggested by Fama (1975) and

Mishkin (1990a).

　　3. Papers that use ‘modern’ time series methods.

（449） 81


Table 3　The Results in the Tests on the Fisher Hypothesis in Japan

Literature Periods Frequency Interest Ratea Inflation Rateb Methodc Resultsd

Shimizu (1978) 1966-1976 Monthly Long & Short CPI Fama FE: Partial

Oritani (1979) 1967-1978 Monthly Short WPI TraditionalFE: Partial, Lags:within 2 years

Kama(1981) 1967-1978 Monthly Long CPI, WPI TraditionalFE: Partial, Lags: within 3 years

Tatsumi (1982) 1955-1975 Monthly Short CPI, WPI Fama FE: Partial

Kuroda (1982)1977-1980 Cross, Time & Panel

Quarterly Long WPI：Expected Fama FE: Partaial

Miyagawa(1983)

1969-1978 Quarterly Long & Short WPI, CPI TraditionalFE: Partial, Lags: within 3 years

Furukawa(1985)

1965-1982 Quarterly Long & ShortWPI, CPI, GNP deflator

TraditionalFE: Partial, Lags:within 2 years

Yamada (1991) 1979-1989 Monthly Long & Short CPI Fama, Mishkin FE: Partaial

Bank of Japan (1994)

1971-1994 Monthly Long & Short CPI Mishkin FE: Partaial

Engsted(1995) 1974-1992 Quarterly Long CPIVAR with PVM constraint

FH: Supported

Satake (1997) 1972-1995 Quarterly Long WPIVAR with PVM constraint

FE: Partaial

Kamae (1999) 1977-1995 Monthly Long CPI: Expected COINT FH: Supported

Ito (2005) 1990-1999 Monthly Long & Short CPI1) Mishkin,2) COINT

1)FE: Partial,2)FH: Supported

Maki (2005) 1963-2002 Quarterly Short CPI TAR COINT test FH: Supported

Satake(2005a) 1971-2002 Quarterly Short CPI COINT etc FH: Not Supported

Satake (2005b) 1971-2002 Quarterly Short CPI IRF with SB FE: Partaial

Satake (2006) 1971-2002 Quarterly Short CPI TAR modelFE: Partial, IFE: Patial, But larger than Linear Model

(Notes)a Interest rate is classified into two categories, i.e. Short and Long. 'Long' contains NTT coupon and

Government bonds, and Short does Call , Gensaki and CD Rate.b Expected means to use expected infaltion rate derived from ARMA or Kalman filter model.c Traditional is the approach using Distributed Lag Models. Fama and Mishkin is the approach using (6) and

(7) respectively. COINT is Cointegration analysis. PVM is Present Value Model. SB is Structural Break. IRF is Impuls Respense Function. TAR is Thoreshold Autoregresion.

d FE is Fisher Effect, FH is the Fisher Hypothesis, and IFE is the inverted Fisher Effect. Lags is the lags of distributed lag models.

82 （450）


7.1 Literature Related to Monetary Policy Target: Traditional Testing Methods

　Oritani (1979), Kama (1981), Miyagawa (1983) and Furukawa (1985) conducted

Fisher hypothesis tests to discuss the potential role of an interest-rate target as

a monetary policy objective and all use some variant of the ‘traditional’ method of

testing the Fisher effect with some form of distributed lag to proxy for expected

inflation. Oritani (1979) examines the magnitude of the Fisher effect to calculate

the expected inflation rate using time series models as well as distributed lag

models. The empirical work in this paper uses the three-month Gensaki 9) rate as

the nominal interest rate and the wholesale price index (WPI) as the price level

for monthly Japanese data from February 1967 to December 1978. An Almon

lag model with three degrees and 24-month lags is adopted. It was found that

inflation fluctuation lags two years earlier affect current nominal interest rates.

The estimation by the Koyck lag model indicates that the coefficient of the one-

period nominal interest rate is 0.85 and that of the inflation rate is 0.17, therefore

finding that the effect continues about two years and its size is less than one as

same as the case of Almon lag model, so that the lag length of the effect is not as

long as the result of Fisher (1930). In the analysis using ARMA models to estimate

the expected inflation rate, Oritani (1979) found that the coefficient of the expected

inflation rate was significant but less than 0.25, contrary to the result of 1.0 (for US

data) in Feldstein, Summers et al. (1978).

　Kama (1981), Miyagawa (1983) and Furukawa (1985) conducted the traditional

approach of deriving the expected inflation rate from Almon lag models for almost

the same period as Oritani (1979). They found that the lag length of the Almon lag

models is less than three years, quite shorter than the evidence in Fisher (1930)

and that the size of the Fisher effect is far less than one.

　To test the Fisher effect, Kama (1981) estimated the Almon lag models using

9）　Gensaki means repurchase agreements.

（451） 83


the return on NTT coupon bonds as the long-term interest rate, the call rate as

the short-term interest rate and the WPI and CPI to calculate the inflation rate

during the period from October 1967 to December 1978. The lag lengths of 18, 24

and 30 months and three or six polynomial degrees are adopted. The results are

as follows: 1) as the significance of the coefficients of the lagged inflation rates

disappeared by the thirtieth lag, it is considered that the inflation rate three years

prior does not affect the nominal interest rate. Therefore, the effect from the long

lag length as in Fisher (1930) could not be found. 2) The sum of the coefficients of

lagged variables is far less than one, converted at the annual rate, indicating that

the Fisher effect is partial. Moreover, 3) the lag length and the size of the Fisher

effect in the case of WPI are larger than in the case of CPI and the lag length of the

long-term interest rate is shorter than that of the short-term interest rate. As the

serial correlation in the residual term is substantially high, Kama (1981) indicates

the possibility of missing explanatory variables. Therefore, Kama (1981) conducted

the estimation adding real income (to test the income effect) and real money supply

(to test the liquidity effect) as regressors into the equations. It is found that 1) the

coefficient of the real money supply is only significant in the case of the long-term

interest rate and that 2) there is no difference in the effect of the expected inflation

rate both with and without adding two other regressors.

　Miyagawa (1983) conducted a test of the Fisher effect, estimating the Almon

lag models with three polynomial degrees and thirty months of lag for monthly

Japanese data. The monthly change rates of WPI and CPI were adopted as the

inflation rate, the return on NTT coupon bonds were used as the long-term

interest rate and the call rate was used as the short-term interest rate, similar

to Kama (1981), between January 1969 and December 1978. Finding that the

signs of the coefficients were all significantly positive and the coefficient of the

determination was more than 0.9, Miyagawa (1983) insisted that the results show

84 （452）


evidence to support the Fisher hypothesis while not mentioning that the size

of the effect, which considers the sum of the coefficients of the distributed lags

converted at the annual rate, was far less than one. Although the coefficients of lag

lengths up to thirty months are significant, a lagged inflation rate longer than thirty

months does not affect the nominal interest rate. As described above, the result of

Miyagawa (1981) was very similar to that of Kama (1981).

　Furukawa (1985) conducted an estimation of the Fisher effect for quarterly

Japanese data from 1965 to 1982 using the return on NTT coupon bonds as the

long-term interest rate, the call rate and the Gensaki rate as short-term interest

rates and the WPI, the CPI and the GNP deflator as price indices. The results are

as follows. 1) The effect of the lags continues for one year in the case of the GNP

deflator and for two years in the case of the WPI. It is shorter than that of Fisher

(1930). 2) The sum of the lag coefficients is far less than one, indicating that the

Fisher effect is incomplete. 3) The size of the sum of the coefficients is larger than

the Gensaki rate, the call rate and the return on the NTT Bond, in that order. The

effect of long-term interest rates is less than that of short-term interest rates.

This result is consistent with Yohe and Karnosky (1969), Gibson (1970a, 1972) and

Cargill and Meyer (1980). Furukawa (1985) , as well as Kama (1981), conducted an

estimation of the equation with real money supply and real income as additional

regressors. He found that, compared with the estimation of the model without

additional explanatory variables, 1) the sign conditions were both satisfied and the

coefficient of determination rose, 2) the liquidity effect disappeared over a short

period while the income effect was persistent and 3) the results with additional

explanatory variables were not different from those without them, similar to Kama

(1981).

　Essentially then, the results in this section suggest that the size of the Fisher

effect is less than one and that lag lengths of up to three years are required to

（453） 85


capture the impact of inflation.

7.2 Empirical Studies of the Fisher Hypothesis Using the Methods of Fama and

Mishkin

　Fama’s (1975) approach was adopted by Shimizu (1978), Tatsumi (1982), Kuroda

(1982) and Yamada (1991). Fama (1975) estimated the regression of the nominal

interest rate on the inflation rate in equation (6) and tested whether or not the

coefficient β is one.

　Shimizu (1978) was the first to apply Fama’s (1975) approach to Japanese data.

Using the call rate as the short-term interest rate and the CPI as the price index,

he found that 1) there is a serial correlation in the residual term, while the

hypothesis β＝1 in equation (6) was not rejected and 2) the coefficient of the one-

period lagged inflation rate was significant. Therefore, the efficiency in the call

market was rejected.

　Tatsumi (1982) also tested Fama’s (1975) efficient market hypothesis for whether

the coefficient β in equation (6) is one by estimating the regression model of the

nominal interest rate on the inflation rate using monthly Japanese data for the full

and sub samples during the period from 1955 to 1975, with the call rate and the

Gensaki rate as the short-term interest rate and the CPI and WPI as the inflation

rate. The efficient market hypothesis was basically rejected and supported for

the only period when interest rates moved freely. This did not support the Fisher

hypothesis. However, as there are many cases in which the hypothesis β＝0 is

rejected, we could construe that the nominal interest rate has partial information

on future inflations.

　Kuroda (1982) used quarterly Japanese data from 1977 to 1980, with government

bond (listed, compounded, yield to maturity) returns as the long-term interest rate

and the WPI as the inflation rate. Kuroda (1982) calculates the expected inflation

86 （454）


rate at each maturity according to the government bond return from forecasting

values estimated by ARMA models. The examinations are grouped into three

categories: 1) the time series data at each maturity, 2) the cross-sectional data at

each forecasting period of the inflation rate and 3) the panel data congregating the

time series and the cross section data. The results were as follows: 1) the size of

the Fisher effect was between 0.3 and 0.4 in the panel data set and 2) in the case of

the time series data, the results of the longer maturity show a larger Fisher effect,

although the size at maturity during year nine was the largest at 0.77.

　As described above, an examination of the hypothesis based on Fama’s (1975)

approach suggests that the Fisher hypothesis and the efficient market hypothesis

are not supported by short-term financial markets in Japan, contrary to most of

the results for the US. The size of the Fisher effect in Japan is smaller than that

in the US. Evidence shows that the efficient market hypothesis is supported for

the period during which the interest rate was deregulated, but not supported for

regulated periods. Therefore, the assertion that the short-term financial market in

Japan was inefficient is basically true.

　The interest rate, described above, was regulated for most of the period of the

empirical studies in Japan. Yamada (1991) applied Fama’s (1975) approach to recent

data when the interest rate was deregulated from May 1979 to January 1989, using

the one- to twelve-month matured interest rate. He found that 1) the hypothesis β

＝0 in equation (6) was rejected for one- to twelve-month interest rate maturities,

indicating that the nominal interest rate contains information on the future inflation

rate and 2) the hypothesis β＝1 was not rejected for shorter maturities, e.g. one

month and three months, but was rejected for six and twelve month maturities. It

is generally considered that the interest rate partially contains information on the

future inflation rate, implying that the partial Fisher effect was detected in Japan.

　Studies applying Mishkin’s (1990a) approach can be found in Japan in Yamada

（455） 87


(1991), the Bank of Japan (1994) and Ito (2005). Yamada (1991) estimated equation (7)

to test the size of the coefficient of the spread of nominal interest rates for different

maturities, for the period from May 1979 to January 1989. The results show that

1) the hypothesis β＝0 is rejected only in the case of the short-term spread in

nominal interest rates from one month to three month and 2) the hypothesis β

＝1 is rejected in all cases. Therefore, the Fisher hypothesis was not supported.

However, it can be suggested that the nominal interest rate within a one-year

maturity in Euro-Yen data partly contains the information on future inflation and

not in the long term. Applying Mishkin’s (1990a) approach, the Bank of Japan (1994)

also investigated whether the nominal interest rate spread can be an effective

indicator for forecasting future inflation rates for the term structures of nominal

interest rates from one month to ten years, including for maturities longer than

two years. The result was that, in the case of the spread between the overnight

call rate and the three-month Gensaki rate, both hypotheses β＝0 and β＝1 were

rejected, suggesting that 0＜β＜1. As described above, the Fisher hypothesis was

not supported in the relationship between the term structure of nominal interest

rates and the inflation rate spread in Japan. However, the results suggest that the

term structure of nominal interest rates contains information on future inflation

only for a very short-term.

　Ito (2005) applied Mishkin’s (1990a) approach to the monthly Japanese data for

the Euro-Yen LIBOR rate from one month to twelve months and the yen swap

rate with two-year to seven-year maturity during the period from February 1990

to August 1999. Basically, the term structure was found to have information on

future inflation in most of the term structures. The coefficient of determination in

the estimation results for short-term relationships was noted to be lower and the

higher the coefficient of determination approached a one-for one in the response to

the inflation rate spread the longer the maturity becomes. The result in Ito (2005)

88 （456）


is different from those in Yamada (1991) and the Bank of Japan (1994) with respect

to maturity.

7.3 Empirical Results from Time Series Analyses Testing in Japan

　In accordance with the development of recent time series analyses, the testing

method of the Fisher hypothesis was conducted mainly by cointegration analysis

and the VAR (Vector Autoregression) approach. Studies in Japan were undertaken

by Engsted (1995), Satake (1997), Kamae (1999), Ito (2005), Maki (2005) and Satake

(2005a, 2005b, 2006).

　Kamae (1999) applied the cointegration test by Engel and Granger’s (1987)

method to monthly Japanese data from June 1977 to June 1995 to examine the

Fisher hypothesis using the expected inflation rates derived from the time series

model by the Kalman filter method. It was found that the Fisher hypothesis was

supported in most cases.

　Ito (2005) conducted the Engle and Granger cointegration test using monthly

Japanese data for the one-month to ten-year nominal interest rate and the CPI in

the 1990s. Ito (2005) supports the Fisher hypothesis, consistent with the results of

Kamae (1999). However, the cointegration relationship does not hold for short-term

maturities.

　Satake (2005a) used quarterly Japanese data for the CPI and CD rates during

the period from 1971 to 2002 and examined the Fisher hypothesis by using two

cointegration tests, i.e. the Engle and Granger test and the Johansen (1988) test.

The analysis was conducted for the full sample and the two subsamples after a high

inflation period for oil shocks. As a result, there is no cointegration relationship

between the nominal interest rate and the inflation rate in most cases, while the

Fisher hypothesis was supported in some Johansen test cases, as opposed to

Kamae (1999) and Ito (2005). This may be the result of the difference in the data and

（457） 89


the sample periods.

　Engsted (1995) also applied the long-run Fisher hypothesis by testing the

constraints on the present value model for Japan. He found that the long-term

nominal interest rate reflects the long-term expected inflation rate using quarterly

data for the long-term interest rate and CPI for the period from 1974 to 1992,

suggesting that the Fisher hypothesis is supported. Satake (1997) examined the

robustness of the results in Engsted (1995) using the WPI instead of the CPI in

Japan. It was also suggested that the long-term nominal interest rate reflects

the long-term expected inflation rate, while the parameters’ constraints on the

present value model was not supported.

　Recently, approaches considering structural breaks on time series analyses like

unit root and cointegration tests were developed. In testing the Fisher hypothesis,

two types of approaches were basically applied; one is the cointegration test in

consideration of structural breaks and the other is to apply a nonlinear model to

the analysis to take multiple regimes into account.

　Using quarterly Japanese data for the period from 1971 to 2002, Satake (2005b)

confirmed that the nominal interest rate and the inflation rate are trend-stationary

with one structural break and applied the Malliaropulos’ (2000) approach to the

data, removing the trends from the variables that considered the structural break

to test the Fisher hypothesis. He found that the partial Fisher effect was detected.

Maki (2005) implemented the cointegration test incorporating the nonlinear TAR

(Threshold Autoregressive) model, which divided the period into two regimes, into

the Japanese nominal interest rate and inflation rate and found the cointegration

between the two and supported the Fisher hypothesis.

　Subject to Choi’s (2002) method, Satake (2006) examined whether the Fisher

hypothesis or the inverted Fisher hypothesis was supported by using the TAR

model, which is the nonlinear model to divide the sample period into two regimes,

90 （458）


one in which the inflation rate was high and volatile and the other in which it

was stable. Whether the Fisher hypothesis or the inverted Fisher hypothesis in

each regime was supported was tested. Results showed that the partial Fisher

and partial inverted Fisher effects are detected in each regime. It was also found

that the inverted Fisher effect when the inflation rate is stable is larger than the

estimate of the linear model.

　The results described above can be summarized as follows. 1) The partial

Fisher effect, which means that the increase in the expected inflation rate partially

induces an increase in the nominal interest rate, was mainly detected. 2) few

studies support the Fisher hypothesis in that a one-for-one relationship exists

between the variables. However, 3) Kamae (1999) and Ito (2005) conducted the

cointegration tests and found support for the Fisher hypothesis.

8. Summary of Test Results in Australia for the Fisher Hypothesis

　There are several empirical studies on testing the Fisher hypothesis in Australia.

The results are summarized in Table 4. In summary, the results from this set of

papers seems to find evidence of a Fisher effect, with the hypothesis that 0＜β＜

1 in (6) is on the whole supported, while the hypothesis that β＝1 in (6), i.e. a ‘full’

Fisher effect, found little support in Australia. We should make three points on the

existing literature in Australia.

　First, although three of the studies in Australia insisted on rejecting the long run

Fisher hypothesis, i.e. Carmichael and Stebbing (1983), Inder and Silvapulle (1993)

and Engsted (1995), these results were interpreted as supportive of a partial Fisher

effect. While Carmichael and Stebbing (1983) found the evidence supportive of

the inverted Fisher hypothesis, Moazzami (1991) supported a partial Fisher effect

using the same data as Carmichael and Stebbing (1983) with a unit root test and

error correction models. Inder and Silvapulle (1993) showed that the real interest

（459） 91


rate decreases 0.5% in response to a 1% increase in inflation rate, concluding

the rejection for the Fisher hypothesis. However, it is construable that a partial

Fisher effect exists. Engsted (1995) tested the restriction of the Fisher hypothesis

from the present value model, which is the test that β＝1. As the alternative

hypothesis, β≠1 contains the possibility that 0＜β＜1 in this test and we cannot

reject a partial Fisher effect.

　Second, although Atkins (1989) and Mishkin and Simon (1995) supported the

Fisher hypothesis in the long run, Olekalns (1996, 2001) and Hawtrey (1997) found

mixed evidence for the Fisher hypothesis within subperiods. They showed that

the Fisher hypothesis is not supported in the period before financial deregulation

in 1983, but supported after the deregulation. Therefore, financial liberalization

makes the Fisher hypothesis supportive, although we mainly have evidence for a

Table 4　The Results in the Tests on the Fisher Hypothesis in Australia

Literature Perioda Interest Rateb Methodc Resultsd

Carmichael and Stebbing (1983) 1965-1981 Long & Short OLS IFH: Supported

Atkins(1989) 1965-1981 Short COINT(EG) FH: Supported

Moazzami (1991) 1965-1981 Long & Short UNIT, ECM FE: Partial

Inder and Silvapulle(1993) 1964-1990 Short Several COINT tests FH: Not Supported

Mishkin and Simon (1995) 1962-1993 Short COINT(EG) FH: Supported

Engsted (1995) 1969-1993 Long VAR with PVM Constraint FH: Not Supported

Olekalns(1996) 1969-1993 Short VAR(Keating, 1990) FH: Supportted(Post), Not(Pre)

Hawtrey(1997) 1969-1994 Long & Short COINT(JOH) FH: Supportted(Post), Not(Pre)

Olekalns(2001) 1969-2001 Short VAR(Keating, 1990), SB test FH: Supportted(Post), Not(Pre)

Silvapulle and Hewarathna (2002) 1968-1998 Short COINT with SB FH: Supported

(Notes)a The frequency of the data is quatrerly in all studies.b Interest rate is classified into two categories, i.e. Short and Long. 'Long' contains 10 years corporate bond

and 10 years government bond, and 'Short' does 3 month Bank Accepted Bill and Treasury Bill rates.c UNIT is Unit Root test. COINT is Cointegration test, EG is Engle and Granger test, and JOH is Johansen

test. PVM is Present Value Model. SB means Structural Breaks. ECM is Error Correction Model.d FE is Fisher Effect, FH is the Fisher Hypothesis, and IFE is the Inverted Fisher Effect. Pre is pre-

deregulation period, and Post is post deregulation period.

92 （460）


partial Fisher effect.

　Finally, using a cointegration test with consideration for a structural break,

Silvapulle and Hewarathna (2002) stated that there was a structural break in the

first quarter of 1980 and that the Fisher hypothesis is supported for all of the

samples from 1968 to 1998.

　As described above, the results for testing the long-run Fisher hypothesis are

clear. Although in Olekalns (1996) and Hawtrey (1997), the hypothesis that β＝1

in (6) is only supported after the deregulation period, as well as the partial Fisher

hypothesis that 0＜β＜1 is almost supported, a recent study by Silvapulle and

Hewarathna (2002) supported the Fisher hypothesis regardless of sample periods.

9. Summary of Test Results on the Fisher Hypothesis in Other Countries

9.1 Results for Other Developed (OECD) Countries

　Table 5 summarizes some of the key papers essentially from OECD countries.

The literature reviewed here is categorized into two techniques, i.e. Fama’s or

Mishkin’s methods and time series analyses as unit root and cointegration tests

and VAR models.

　The main studies on developed (OECD) countries using regression analyses

for Fama’s or Mishkin’s models are put forward by Caporale and Pitts (1998),

Gerlach (1997), Jorion and Mishkin (1991), Koedijk and Kool (1995), Mishkin (1984)

and Mishkin (1991), all which found evidence for a partial Fisher effect, except for

Caporale and Pitts (1998), which insisted on rejecting the Fisher effect because of

the rejection of the hypothesis β＝1 in (7).

　Miskin (1984) examined the Fisher hypothesis by testing the constancy of the

real interest rate in the Euro deposit market using seven OECD quarterly data

for the period from 1967 to 1979. Mishkin (1984) found that the constancy of

real interest rates was rejected and a negative correlation between real interest

（461） 93


Literature Countires Period Frequency Approacha Results

Andrade and Clare (1994)

UK 1969-1991 QuarterlyKalman Filter, COINT (JOH)

FH: Not Supported

At k i n s a n d C o e (2002)

US, Canada 1953-1999 Monthly ARDL Bounds TestFH: Supported in the long run before-tax rate not after-tax rate

Berument and Jelassi (2002)

12 Developed Countries

-1998 Monthly COINT Regression FH: Supported in 9 of 12 Countries

Caporale and Pittis (1998)

OECD 8 countries 1981-1992 Monthly Miskin FE: Non, Not reject β =0 in (7)

Choudhry (1997)Belgium, France, German

1955-1994 Quarterly COINT Regression FE: Partial, IFH: Rejected

Crowder (1997) Canada 1960-1991 Quarterly COIT(JOH), VECM FH: Supported

D u t t a n d G h o s h (1995)

Canada 1960-1993 Quarterly COINT(JOH, FM-OLS) FH: Not Supported

Engsted (1995) OECD 13 countries 1962-1993 QuarterlyVAR with PVM Constraints

FH: three groups, supportive, less supportive, not supportive

Gerlach (1997) German 1967-1995 Monthly Miskin FE: almost Full

Ghazali and Ramlee (2003)

G7 Countries 1974-1996 Monthly Fractional COINT Test FH: Not Supported

Jorion and Mishkin (1991)

US, UK, Germany, Switzerland

1973-1989 Monthly MiskinFE: Par t ia l for L ong Ter m Maturities

Kasman, Kasman and Turgutlu (2006)

33 countries -2004 Monthly Fractional COINT Test FH:Supported

Koedijk and Kool (1995)

OECD 7 Countries1982(1976)-1991

Monthly MiskinFE: Partial for Short Maturity, Full for Long Maturity, Not in Belgium, France and Germany

Koustas and Serletis (1999)

OECD 11 countriesUS:1957-1995

QuarterlyKing=Watson's (1997) VAR Method

FH: Not Supported

MacDonald and Murphy (1993)

US, UK, Canada , Bergium

1955-1986 Quarterly COINT(EG)FH: Not Supported, except Fixed Exchange Rate Sytem in US & Canada

Mishkin (1984) OECD 7 countries 1967-1979 QuarterlyRegression of π on Ex Ante r

FH: Not Supported, Rejected Constanacy of r

Mishkin (1991) OECD 10 countries 1973-1986 Monthly Miskin FE: Partial

Nievas (1998) EU 10 countries 1980-1996 Quarterly COINT(JOH)FH: Supported in France, Italy and the UK before EMU, Not after EMU

Peng (1995)Fr a n c e , U K , U S , German, Japan

1957(1960)-1994

Quarterly COINT(JOH) FH: Not Supported

Table 5　The Literature on Testing the Fisher Hypothesis in OECD countries

94 （462）


rates and expected inflation appeared for all seven countries. This showed that

short-term bonds are a poor inflation hedge not only in the US but also in other

countries. Mishkin (1991) tested the forecastability of the term structure of interest

rates on inflation in 10 OECD countries using equation (7) by Mishkin (1990a) and

found evidence for a partial Fisher effect. In Gerlach (1997), Jorion and Mishkin

(1991), Koedijk and Kool (1995) and Woodward (1992), the literature applying

Mishkin’s method found evidence for a stronger Fisher effect for a longer maturity

of government bonds for OECD countries, although Koedijk and Kool (1995)

found weak evidence for the Fisher effect in Belgium, France and Germany. We

have mixed evidence using Mishkin’s method, although by and large we obtained

evidence for 0＜β＜1, which is the coefficient for the size of the Fisher effect in

equation (7).

　The main studies on developed (OECD) countries using cointegration tests were

put forward by Andrade and Clare (1994), Berment and Jelassi (2002), Choudhry

(Notes)a R is nominal interest rate, r is real interest and π is infaltion rate. Fama and Mishkin is the approach

using (6) and (7) respectively. UNIT is unit root test, COINT is Cointegration analysis, EG is Engle and Granger Test, JOH is Johansen test, VECM is Vector Error Correction Model. PVM is Presen Value Model. TAR is Thoreshold Autoregresion. ARDL Bound test is the same as Table 1.

b R is nominal interest rate, r is real interest and π is infaltion rate. FE is Fisher Effect, FH is the Fisher Hypothesis, and IFH is Inverted Fisher Hypothesis.

Rapach and Weber (2004)

OECD 16 Countries 1957-2000 Monthly UNIT, COINT(Several)π~I(0), R~ I(1), FH: Not Supported

Rose (1988) US, OECD18 countries

US:1892-1970, 1901- 1950(Annual)1947-86 (Monthly), OECD:1957-(Quarterly)

UNITπ~I(0), R~ I(1), r~I(1), FH: Not Supported

Westerlund (2008)20 OECD coutries' Panel Data

1980-2004 Quarterly Panel COINT Test FH: almost Supported

Woodward (1992) UK 1982-1990 MonthlyFama, using Eπderived from Indexed Bond.

FE: Partial for Short Maturity, Full for Long Maturity

Yuhn (1996)US, UK, Japan, German, Canada

1979(1982)-1993

Quarterly COINT( JOH)FH: Supported in the long run in the US, German and Japan

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(1997), Crowder (1997), Dutt and Ghosh (1995), Ghazali and Ramlee (2003), Kasman,

Kasman and Turgutlu (2003), MacDonald and Murphy (1993), Nievas (1998), Peng

(1995), Westerlund (2008) and Yuhn (1996).

　The literature has several issues with respect to testing the Fisher hypothesis,

i.e. monetary policy changes, a regime change for exchange rate systems and the

initiation of the European Monetary Unit (EMU).

　For the first issue, for example, Peng (1995) tested the Fisher hypothesis using

Johansen cointegration test in the US, UK, France, Germany and Japan for the

period between 1957 and 1994. He found strong evidence for the cointegration

relationship between the nominal interest rate and inflation in the US, the UK and

France, while there was weak evidence in Germany and Japan and guessed that

the strong anti-inflation policy in Germany and Japan weakened the Fisher effect.

On the other hand, Yuhn (1996) reported that the Fisher hypothesis was supported

in the US, Germany and Japan, and not in the UK and Canada for the period from

1979 to 1993, and that the results were robust to policy changes, contrary to

Mishkin (1992).

　The second issue with respect to testing the Fisher hypothesis was whether

the nature of the exchange rate regime used in countries impacted the empirical

testing of the hypothesis. For example, MacDonald and Murphy (1989) analysed the

Fisher hypothesis in the US, the UK, Canada and Belgium for the period from 1955

to 1986. Results indicated that the cointegration relationship was detected in the

US and Canada for the period of the fixed exchange regime, but not in all countries

with a floating exchange regime. The results for the US were consistent with

Bonham (1991). It is conceivable that inflation was not constrained from monetary

policy, although monetary policy was not free during the fixed exchange rate

regime.

　Finally, Nievas (1998) tested the Fisher hypothesis to examine the effects of the

96 （464）


initiation of the EMU in 1989 for the impact of the inflation rate and the German

interest rate on the interest rate of other European countries. He found that the

Fisher effect disappeared in the three countries after initiation, while German

interest rates affect the interest rates of other EU countries because interest rates

in EU countries are controlled by German monetary policy.

　With respect to other studies using modern time series analyses, as shown in

Table 5, mixed evidence exists and it is very hard to find a clear message. As we

have referred to these papers in Section 5, when reviewing them in the US, we do

not argue about it.

9.2 Results for Other Developing Countries

　A number of studies test the Fisher hypothesis in developing countries. Table

6 summarizes some of the key papers that essentially come from Latin American

and South-East Asian economies.

　Most Latin American countries experienced high inflation and, therefore,

as might be expected we have clearer evidence that the Fisher hypothesis is

supported. Tests that rely on the cointegration framework tend to find evidence

of a common trend in nominal interest rates and inflation rates, where interest

rates adjusting promptly to keep real interest rates constant in response to high

and volatile inflation. The literature on Latin America includes papers by Boschen

and Newman (1987), Carneiro, Divino and Rocha (2003), Choudhly (2001), Garcia

(1993), Mendoza (1992), Phylaktis and Blake (1993) and Thornton (1996). Berument

and Jelassi (2002) test the Fisher hypothesis in a cross-section of 26 countries

containing six Latin American countries and Kasman, Kasman and Turgutlu (2006)

tested 19 developing countries, which included seven Latin American countries.

　Phylaktis and Blake (1993) examined the Fisher hypothesis for three Latin

American countries, i.e. Argentina, Brazil and Mexico, using monthly data from the

（465） 97


1970s and 1980s. Using the unit root and cointegration tests, Phylaktis and Blake

Table 6　The Literature on Testing the Fisher Hypothesis in Developing Countries

Literature Countires Period Frequency Approacha Resultsb

Berument and Jelassi (2002)

26 Countries -1998 Monthly COINT RegressionF H : S u p p o r t e d i n 7 o f 1 4 Developing Countries

Boschen and Newman (1987)

Argentina 1976-1982 MonthlyRegression of E π on r derived from Indexed Bond

Negative Relation, FH: Not Supported

Carneiro, Divino and Rocha (2002)

Argentina, Brazil, Mexico

1980-1997 Monthly COINT(JOH)FH: Supported in Argentine and Brazil, Not in Mexico

Choudhry (2001)Argentina, Chile, Mexico, Venezuela

1981(1985)-1998

MonthlyUNIT, Regression of π on Stock Return

FH: Supported in Argentina and Chile, Not in Mexico and Venezuela

Cooray (2002) Sri Lanka1952-1998(Annual),1978-1998 (Quarterly),1990-1998(Monthly)

COINT(EG), Regression of Eπderived from AE & RE on R

FH: Suppor ted only in the Annual Full Sample

Garcia (1993) Brazil 1973-1990 Monthly Regression of Eπ & R on r FH: Supported

Kandel, Ofer and Sarig (1996)

Israel 1984-1992 MonthlyRegression of r derived from Bond Price on π

Negative Relation found, FH: Rejected, but FE: Partial

Kasman, Kasman and Turgutlu (2006)

1 9 D e v e l o p i n g Countries

-2004 Monthly Fractional COINT TestFH: Suppor ted in 15 o f 19 Countries, But Partial FE

Kutan and Aksoy (2003)

Turkey 1985-2000 MonthlyRegression of πon R using Stock Returns

FH: Supported only for Stock Return in Financial Sector

Mendoza (1992) Chili 1986-1990 MonthlyRegression using Indexed Bond

FH: Supported

Payne and Ewing (1997)

Argentina, Fiji, India, Ma l ays i a , N iger, Pakistan, Singapore, Sri Lanka, Thailand

1970s-1990s Quarterly UNIT, COINT(JOH)FH: Supported in Sri Lanka, Malaysia, Singapore and Pakistan, Not in Other Countries

Phylaktis and Blake (1993)

Argentina, Brazil, Mexico

1970s-1990s Quarterly UNIT, COINT(JOH), ECM FH: Supported in all countries

Thornton (1996) Mexico 1978-1994 Quarterly UNIT, COINT(JOH) FH: Supported

(Notes)a UNIT is Unit Root Test, COINT is Cointegration test, EG is Engle and Granger Test, JOH is Johansen

test, ECM is Error Correction Model. R is nominal interest rate, r is real interest and π is infaltion rate. AE is Adaptive Exprectations, and RE is Rational Expections.

b FH is the Fisher Hypothesis, which is a one-for-one long-run relationship between R and π. FE is the Fisher effect, whose size is classified into full, partial and non. 'full' means the support for the Fisher hypothesis.

98 （466）


(1993) found a long-run relationship between nominal interest rates and inflation in

the three countries, supporting the Fisher hypothesis.

　Berument and Jelassi (2002) applied cointegration regression to six Latin

American countries and found that the Fisher hypothesis was supported in four

out of the six, i.e. Chile, Mexico, Uruguay and Venezuela and but not Brazil and

Costa Rica. Kasman, Kasman and Turgutlu (2006) use the fractional cointegration

test, which allowed for the time series property subject to I(d), where 0＜d＜1 and

tends to support the Fisher hypothesis. They obtained supportive evidence for all

countries except for Costa Rica. Other supportive evidence can be found in Garcia

(1993) for Brazil, in Mendoza (1992) for Chile and in Thornton (1996) for Mexico.

Mixed evidence can be found in Carneiro, Divino and Rocha (2003), who conducted

Johansen’s cointegration test and found that the Fisher hypothesis is supported

for Argentina and Brazil but not for Mexico and in Choudhly (2001), who used

stock returns to find evidence supporting Argentina and Chile but not Mexico and

Venezuela. Boschen and Newman (1987) applied regression analysis of expected

inflation on real interest rates derived from indexed bonds to Argentina data and

found a negative relationship between real interest rates and inflation, insisting a

rejection of the Fisher hypothesis.

　Payne and Ewing (1997) conducted unit root and cointegration tests for nine

developing countries, including six Asian countries, i.e. India, Malaysia, Pakistan,

Singapore, Sri Lanka and Thailand. They found cointegration relationships in

Malaysia, Pakistan, Singapore and Sri Lanka and supported the Fisher relation in

these countries except for Singapore. Berument and Jelassi (2002) conducted a

Fisher hypothesis test in four Asian countries, i.e. India, Kuwait, the Philippines

and Turkey and found supportive evidence in Turkey. Kasman, Kasman and

Turgutlu (2006) conducted the test in eight Asian countries, i.e. China, India,

Indonesia, Malaysia, Pakistan, the Philippines, Thailand and Turkey and found

（467） 99


nonsupportive evidence only in Malaysia and the Philippines. Cooray (2002)

applied cointegration analysis and regression on expected inflation derived from

adaptive and rational expectations of nominal interest rates to Sri Lanka and found

weak evidence to support the Fisher hypothesis, as opposed to the evidence of

Payne and Ewing (1997). Kutan and Askoy (2003) conducted a Fisher hypothesis

test using stock returns as the nominal interest rate in Turkey and found limited

support using financial sector returns. Kandel, Ofer and Sarig (1996) examined

the relationship between ex ante real interest rates derived from bond prices

on expected inflation and found a negative relationship between them, insisting

that weak evidence existed on the Fisher effect. In Asian countries, a Fisherian

relationship is, as in most developed economies, inconclusive.

10. Conclusions

　This paper provided a brief review of the literature pertaining to the empirical

tests of the Fisher hypothesis. For convenience, the survey of the literature in the

US, Australia, Japan and the rest of the world was divided into three parts, each

pertaining to a different general testing methodology, including:

　• The ‘traditional’ approach, which Fisher (1930) originally suggested and which

formed the basis for much of the initial work.

　• Tests based on the methods suggested by two seminal papers, those of Fama

(1975) and Mishkin (1990a).

　• Tests based on ‘modern’ time series methods associated with unit root and

cointegration tests.

　Drawing conclusions from such diverse literature is difficult. However, some

general conclusions can be drawn.

　Fisher’s original results have not held up to the scrutiny of further empirical

100 （468）


work. Few studies find evidence in favour of the ‘strong form’ of the Fisher

hypothesis with an adjustment in interest rates and inflation being one-for-one.

In following Fisher, a number of authors found that after inflation rates started

to increase and became more persistent in the late 1960s, the distributed lag

structure that Fisher found to be rather lengthy began to shorten, suggesting

that agents were building in inflationary expectations more rapidly as the costs of

inflation rose. In the second wave of the literature, applying the Fama and Mishkin

approaches, the focus of the testing became whether the Fisher effect was full,

partial, or zero. Although the evidence is mixed in that it differs from period to

period and from country to country, it is conceivable that the evidence is, by and

large, in favour of a partial Fisher effect. Finally, the literature applying time series

analysis also shows mixed evidence. Tests using Johansen’s cointegration approach

tend to find some support for the hypothesis in the US, in particular that evidence

is stronger in cases in which the research considers the impact of structural breaks

and in the application of nonlinear models to detect structural changes.

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The Doshisha University Economic Review Vol.62 No.4

Abstract

Mitsuhiko SATAKE, Testing the Fisher Hypothesis: A Survey of Empirical Studies

　　This paper provides a brief review of the literature pertaining to the

empirical tests of the Fisher hypothesis. The survey of the literature in the US,

Japan, Australia, and the rest of the world has been divided into three parts,

each pertaining to a different general testing methodology. These include (1) the

“traditional” approach, which was originally suggested by Fisher (1930) and was

the basis of much of the initial works; (2) tests based on the methods suggested

by the seminal papers of Fama (1975) and Mishkin (1990a); and (3) tests based on

“modern” time series methods associated with unit root and co-integration tests.

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Testing the Fisher Hypothesis: A Survey of Empirical … the Fisher Hypothesis: A Survey of Empirical Studies（Mitsuhiko Satake） R t≡E t r t＋E tπ t＋1 （, 1） where R t