Proceedings of World Business Research Conference
21 - 23 April 2014, Novotel World Trade Centre, Dubai, UAE, ISBN: 978-1-922069-48-1
Is the Fisher Hypothesis Inverted in the CIS Countries?
Razzaque H Bhatti
This paper examines the inverted Fisher hypothesis (HP) for five countries of the
Common Wealth of Independent States – Armenia, Georgia, Kazakhstan,
Kyrgyzstan and Moldova – using quarterly data on three-month Treasury bill
interest rates and consumer prices over the period 1995:01-2010:02. Results
based on regression analysis are strongly supportive of the inverted FH in all
cases, except for Kazakhstan. The regression estimates of the coefficient on
inflation rate are not only correctly significantly signed in all cases but they are also
very close unity. The results show that the proposition of a one-to-one
proportionality between real interest rates and inflation cannot be rejected in all
cases. One important implication that emerges from these results is that Treasury
bill markets in the CIS countries are unlikely to provide any hedge against inflation.
Another important implication is that monetary policy cannot be conducted
effectively to contain inflation by reducing interest rates.
I.
INTRODUCTION
The proposition embedded in the standard Fisher hypothesis (FH)1 that financial
assets – such as Treasury bills and common stocks – must provide a perfect hedge
against expected inflation has not been substantiated in the literature2. Notwithstanding
wide acceptance of this hypothesis, most studies have reported evidence that is generally
inconsistent with its proposition that there is one-to-one proportionality between nominal
return and expected inflation. In fact, Fisher (1930) himself was the first to note such an
anomaly in his empirical study of the relationship between interest and inflation rates. On
finding only the partial adjustment of the nominal interest rate to expected inflation, he
concluded his results as follows: “when prices are rising, the rate of interest tends to be
high but not so high as it should be to compensate for the rise; and when prices are falling,
the rate of interest tends to be low, but not so low as it should be to compensate for the
fall” (Fisher, 1930; p. 43).
Since the publication of the “Theory of Interest” in 1930, the tremendous amount of
work has been conducted to rationalize the failure of the nominal interest rate to adjust
fully to expected inflation. Mundell (1963) demonstrates that the nominal interest rate rises
by less than the rate of inflation, and as such there is a fall in the real rate of interest
during inflation. This conclusion is drawn on the ground that inflation reduces real money
balances, which in turn result in a fall in wealth and hence an increase in savings, thereby
putting a downward pressure on real interest rates. Tobin (1965; p.815) makes a similar
point by arguing that “because inflation reduces the demand for money balances, it
increases capital intensity, lowers the real rate of return and thus causes the nominal
interest to rise by less than the rate of inflation”. Darby (1975) argues that in efficient
markets with taxes on interest income, the nominal interest rate in equilibrium must
increase by more than the increase in expected inflation so as to compensate the lender
not only for a loss of principal due to inflation but also for a loss of return due to tax on
interest receipts from the principal3. Jaffe (1985) integrates Miller’s (1977) capital structure
___________________
Razzaque H Bhatti, Professor, Bang College of Business, Kazakhstan Institute of Management, Economics
and Strategic Research (KIMEP), 2 Abai Avenue Office #204, Dostyk Building, Almaty 050010, Kazakhstan,
Tel: +7(727) 2-70-44-40 Ext. 2114
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Proceedings of World Business Research Conference
21 - 23 April 2014, Novotel World Trade Centre, Dubai, UAE, ISBN: 978-1-922069-48-1
theorem with the theory of loanable funds to investigate the effect of inflation on both
interest rate and equity return. He derives the interest rate as well as the redistribution
effect to show that the responsiveness of the interest rate to the inflation rate is lower than
what is hypothesized by Darby (1975) whereas the redistribution effect may change this
responsiveness to either direction. Built on a more general case of a one-sector
neoclassical monetary growth model, in which personal and corporate income taxes exist,
Feldstein (1976) demonstrates that the nominal interest rate rises by more or less than
twice the rate of inflation4.
On the contrary, Carmichael and Stebbing (1983) demonstrate that the FH is
completely inverted if there is a relatively high degree of substitutability between money
and financial assets and if the government regulation precludes the payment of interest on
money. It is argued that a relatively high degree of substitutability between money and
financial assets will translate into a low variance of after-tax nominal interest rates relative
to the variance of the inflation rate, and as such the nominal interest on these assets may
be approximately constant over time, with the real interest rate moving inversely in a oneto-one proportionality with the rate of inflation. Using the data on Australia and the United
States, they were able to produce evidence which did not reject the inverted FH. The
results obtained were robust across time periods and maturities, lending strong support to
a one-to-one inverse relationship between after-tax real interest rates and inflation rates in
both countries. Subsequent studies, however, conducted, inter alia, by Amsler (1986),
Graham (1988), Choudhry (1997) and Choi (2002) produced mixed evidence on the
inverted FH. Amsler (1986) and Graham (1988) tested the inverted FH for the United
States, and Choudhry (1997) for Belgium, France and Germany. While results obtained by
Amsler (1986) were supportive of the inverted FH, those obtained by Graham (1988) were
not. Moazzami (1991) tested the FH and the inverted FH using quarterly data on threemonth Treasury bills and consumer prices for the United States and Australia over the
period 1953:1-1978:4 and produced evidence supportive of the FH in the long run,
although the nominal interest rate did not appear to move in one-to-one correspondence
with the inflation rate. The results also show that a valid error correction representation of
the FH exists in all cases.
The objective of this paper is to examine whether the inverted FH holds in five CIS
countries - Armenia, Georgia, Kazakhstan, Kyrgyzstan and Moldova – using quarterly data
on interest rates on Treasury bills and consumer prices over the period 1995:1-2010:2.
The motivation for testing the inverted FH goes as follows. First, there is evidence
suggesting that the standard FH hypothesis does not work well for the underlying CIS
countries (see, for example, Bhatti et al, 2014). Second, while a number of studies have
been conducted on the inverted FH for developed countries, there is only little work for
transition economies of the CIS countries, which have recently experienced transition from
centrally planned economy to the one run on market basis. Since their independence from
the Soviet Union, most of these countries have experienced hyperinflation. Central banks
in each of these countries have undertaken measures to combat inflation, and switched
from exchange rate targeting to inflation targeting at one point or another. Active Treasury
bill markets exist in each of these countries, except for Moldova. Nominal interest rates on
Treasury bill have been very relatively higher in these countries since 1995. Third, inflation
rates seem to be more volatile than interest rates in these countries, creating an
environment more conducive to the inverted specification rather than the standard one.
This is confirmed by descriptive statistics, as reported in Table 1. The variability of the
inflation rate measured in terms of standard deviation and coefficient of variation is higher
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Proceedings of World Business Research Conference
21 - 23 April 2014, Novotel World Trade Centre, Dubai, UAE, ISBN: 978-1-922069-48-1
than that of the nominal interest rate in almost all cases. This implies that the inflation rate
is more volatile than the nominal interest rate.
The rest of the paper is structured as follows. Section II provides a brief description
of the standard and the inverted FH, while empirical results are presented in Section III.
Section IV concludes and discusses about policy implications of the results.
Table 1: Descriptive Statistics
Variable
Maximum Minimum Mean
Std.
Deviation
CV
Skewness Kurtosis
it
0.157
0.009
0.049
0.046
0.929 1.151
-0.103
pt 1
0.082
-0.086
0.010
0.038
3.847 -0.487
3.847
it
0.048
0.172
0.026
0.007
0.281 0.798
0.616
pt 1
0.144
-0.041
0.017
0.029
1.723 1.381
1.723
it
0.172
0.006
0.024
0.040
0.920 1.292
0.862
pt 1
0.155
-0.033
0.044
0.034
1.382 1.433
1.382
it
0.060
0.008
0.021
0.015
0.715 1.355
0.654
pt 1
0.085
-0.013
0.021
0.016
0.768 1.451
0.768
it
0.086
0.007
0.039
0.021
0.551 0.492
-0.487
pt 1
0.140
-0.034
0.031
0.032
1.033 0.769
1.710
Armenia
Georgia
Kyrgyzstan
Kazakhstan
Moldova
II.
THE STANDARD AND INVERTED FH
When applied to the money market, the FH in an approximate form is given by5
(1)
it  rte1  pte1
where i is the one-period nominal interest rate, pte1 is the expected change in the
logarithm of the domestic price index from time t to t+1 and rte1 is the ex ante real interest
rate realized from time t to t+1. The FH predicts that in an efficient capital market the
nominal interest rate rises by an amount equal to expected inflation, leaving the real
interest rate constant over the holding period. Therefore, the real interest rate rte1 is
2
Proceedings of World Business Research Conference
21 - 23 April 2014, Novotel World Trade Centre, Dubai, UAE, ISBN: 978-1-922069-48-1
commonly assumed to be constant, a , but subject to a stochastic term, u t , which is
uncorrelated with the anticipated inflation rate6. This is given by
(2)
rte1  a  ut
Substituting Equation (2) into Equation (1), we obtain
it  a  pte1  ut
(3)
Under the assumption that market agents efficiently process all available
information contained in the information set  t to predict the future inflation rate, then the
inflation rate realized from time t to t+1 will differ from the expected inflation rate by a
random term which is orthogonal to the past information. Formally, this is given by
(4)
pt 1  pte1  t 1
such that E t 1 |  t   0 and Et 1t 1i   0i  0 . Substituting Equation (4) into Equation
(3) and rewriting the resultant one in a stochastic regression form we obtain
(5)
it   0  1pt 1   t 1
where  0  a and  t 1  ut  t 1 is an error term. For a strong-form Fisher hypothesis to
hold the twin restriction that  0 , 1   0,1 and the error term  t 1 is stationary should not
be rejected.
In contrast, the inverted FH postulates that in a world in which there is some
regulation of interest rates (a minimum degree of regulation being the nonpayment of
interest on money balances) and there is a high degree of substitutability between money
and financial assets, after tax nominal interest rates on financial assets may be
approximately constant over time, with the real interest rate moving in one-to-one
proportionality with the rate of inflation. To derive the inverted FH in an empirically testable
form, Carmichael and Stebbing (1983) assume rational expectations so that the expected
inflation is an unbiased predictor of the actual inflation rate, as represented by Equation
(4). They also assume that since it is known at all times, the net nominal interest equals a
constant value b plus a random error  , and as it is defined as follows
(6)
it  b  
Substituting equations (5) and (6) into equation (3) and assuming rational expectations so
that the expected real interest rate equals its ex post value realized at time t+1 plus a
random error  t 1 , we obtain
(7)
rt 1  b  pt 1    t 1   t 1
where  and  t 1 are independent random terms by assumption, and, for equation (7),  t 1
is also independent of the inflation rate, pt 1 . In a general stochastic testable regression
form, equation (8) can be rewritten as follows:
rt 1   0  1pt 1  t
(8)
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Proceedings of World Business Research Conference
21 - 23 April 2014, Novotel World Trade Centre, Dubai, UAE, ISBN: 978-1-922069-48-1
where  0  b and t    t 1   t 1 . The inverted FH holds if the restriction 1  1 is not
rejected.
III.
DATA AND EMPIRICAL RESULTS
The empirical testing of the standard Fisher and inverted FH is carried out on the
basis of equations (5) and (8) respectively. For this purpose, quarterly data are used on
three-month Treasury bill rates and consumer prices for five CIS countries7 – Armenia,
Georgia, Kazakhstan, Kyrgyzstan, and Moldova – covering the period 1995q1-2010q2.
Data were obtained from the IMF CD-ROM.
Prior to deciding whether to employ regression analysis or cointegration technique to
testing the inverted FH, as represented by equations (8), the variables underlying both
equations are tested for a unit root. Results based on the Dickey-Fuller (1979) and
Phillips-Perron (1988) tests of unit root, as reported in Table 2, indicate that real interest
and inflation rates are I(0) in level in all cases.
Table 2: Testing for Unit Root
Variable
Level
ADF
First Difference Level
Armenia
it
-1.87
pt 1
-4.98*
rt 1
Georgia
it
-0.70
-12.02*
-4.05*
-2.66
-11.81*
-2.45
pt 1
-10.02*
-12.50*
rt 1
Kyrgyzstan
it
-8.06*
-6.14*
pt 1
-4.81*
-4.81*
rt 1
Kazakhstan
it
-4.58*
-4.55*
-6.55*
-10.79*
pt 1
-3.52*
-4.23*
rt 1
Moldova
it
-15.12*
-11.03*
-4.73*
-4.56*
pt 1
-4.52*
-4.42*
rt 1
-5.24*
-5.22*
-2.19
-2.66
-1.12
PP
First Difference
-6.97*
-7.45*
-7.46*
-2.21
4
-11.45*
-8.11*
Proceedings of World Business Research Conference
21 - 23 April 2014, Novotel World Trade Centre, Dubai, UAE, ISBN: 978-1-922069-48-1
The only exception here is the real interest rate in Armenia which is I(1) when the
Dickey-Fuller test is used rather than when the Phillips-Perron test is used. Consequently,
we use regression analysis to the inverted FH. Results based on regression analysis, as
presented in Table 3, lend strong support to the inverted FH in all countries except for
Kazakhstan. This is because the OLS estimates are correctly singed in cases, except
Kazakhstan. However, these estimates are not reliable because they do not pass
diagnostic tests, in particular the test for serial correlation. Therefore, the error terms from
regression must be corrected for serial correlation to obtain efficient estimators of the
inverted Fisher hypothesis. For this purpose, the inverted Fisher hypothesis is tested
again for four cases (except for Kazakhstan in which case there is no evidence for serial
correlation) by applying the Corchrane-Orcutt method to correct the regression errors for
serial correlation. The OLS results obtained, as reported in Table 3, are strongly
consistent with the inverted Fisher hypothesis in all cases, since the coefficients on
inflation are not only correctly signed in all cases but they are close to unity. The results
also show that the proposition of a one-to-one proportionality between real interest rates
and inflation rates cannot be rejected in the cases.
Table 3: OLS Estimates of the Inverted Fisher Hypothesis ( rt 1   0  1pt 1  t )
0
1
R2
DW
LM(4)
HT(1)
FF(2)
NT(1)
Armenia
-540
(0.007)
-0.85
(0.159)
0.33
Georgia
0.029
(0.002)
-0.91
(0.071)
0.74
Kazakhstan
-0.009
(0.000)
0.67
(0.233)
0.12
Kyrgyzstan
0.034
(0.006)
-0.47
(0.014)
0.17
Moldova
0.035
(0.005)
-0.71
(0.109)
0.43
0.13
51.71*
2.57
7.57*
0.28
0.41
36.46*
0.36
134.42*
0.20
0.98
2.74
23.15*
1323.2*
22.65*
0.49
34.96*
0.01
2.92
7.82*
0.30
40.00*
3.19
7.28*
0.38
OLS Estimates with Corrected Errors Based on Cochrane-Orcutt Method
0
1
R2
t1 1
V.
0.035
(0.043)
-0.99
(0.041)
0.93
0.0235
(0.003)
-0.98
(0.020)
0.97
0.037
(0.028)
-0.94
(0.064)
0.84
0.031
(0.010)
-0.97
(0.038)
0.92
-0.24
-1.00
-1.56
-0.79
CONCLUSION
This paper aims to test the inverted FH for five CIS. Quarterly data are used on
three month Treasury bill rates and consumer prices covering the sample period from
1995q1 to 2010q2. Before testing the validity of the FH, tests are conducted based on the
Dickey-Fuller and Phillips-Perron test statistics to determine the order of integration of the
underlying time series. Results obtained show that real interest and inflation rates are
stationary in all cases when assessed based on Phillips-Perron tests. Consequently,
regression analysis was used to test the inverted FH for all CIS countries. The results lend
strong support to the inverted FH all cases except Kazakhstan because the proposition
5
Proceedings of World Business Research Conference
21 - 23 April 2014, Novotel World Trade Centre, Dubai, UAE, ISBN: 978-1-922069-48-1
that there is one-to-one correspondence between real interest rate and inflation could not
be rejected.
One implication that emerges from these results is that Treasury bill markets in the
CIS countries do not provide any hedge against inflation. Another important implication is
that monetary policy cannot be conducted effectively to contain inflation by reducing
interest rates.
6
Proceedings of World Business Research Conference
21 - 23 April 2014, Novotel World Trade Centre, Dubai, UAE, ISBN: 978-1-922069-48-1
Notes
1
2
3
It is arguable that Fisher (1930) was the first economist to develop the standard
hypothesis relating the nominal interest with expected inflation and real interest
rates. Humphrey (1983; pp.2-6) argues that the proposition that the nominal interest
rate equals the real interest rate plus the expected inflation rate has a long history
that can be traced back more than 240 years in the writings of William Douglass,
Henry Thornton, John Stuart Mill, Jacob de Hass, Alfred Marshall and J B Clark. It
is argued that the notion that the nominal interest adjusts fully to anticipated
inflation is disproved by Fisher (1896) himself when he makes it clear that he was
by no means the first to present that analysis.
See Moosa and Bhatti (1997; pp. 97-106) and Bhatti et al (2014) for a
comprehensive review of the previous work on the FH.
In fact, Fisher’s conclusion that there is one-to-one correspondence between
nominal return and expected inflation (that is, di / dpt 1  1) corresponds to the special
case in which there are no taxes on interest income, and the demand for real
money balances is interest insensitive. However, if the lender pays income tax on
the nominal interest receipts at the rate  , then the after-tax return is 1   1  i 
times the amount lent. Similarly, if the borrower is allowed to deduct tax payment
from gross income, the net payment by the borrower is 1   1  i  times the amount
borrowed. Therefore, given the tax on interest income, the strong-form FH can be
written as
it 
1 e
1
1 e e
r 
e 
r 
1
1
1
where the coefficient of expected inflation is greater than unity.
4.
The difference between Darby’s (1975) and Feldstein’s (1976) formulation is that it
is the income tax on individuals’ income which matters in the former formulation,
while it is the corporate tax which matters in the latter.
5.
When applied to stock market return (see, for example, Nelson, 1976; Gultekin,
1983; Solnik, 1983; and Bhatti and Pak, 2013) the FH hypothesis implies that the
one-period expected nominal return on a portfolio of common stocks must reflect
fully expected inflation such that that the ex ante real return on the portfolio remains
constant over the holding period.
6.
See Sargent (1972).
7.
The only exception is Georgia for which data on three-month deposit rates is used.
Moreover, the reason for picking up only five CIS countries is that sufficient data
were not available on the other CIS countries.
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Proceedings of World Business Research Conference
21 - 23 April 2014, Novotel World Trade Centre, Dubai, UAE, ISBN: 978-1-922069-48-1
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