182 L. Coppock, M. Poitras International Review of Economics and Finance 9 2000 181–192
to changes in expected inflation. This evidence leads many authors to conclude that financial markets suffer from money illusion.
1
Since studies typically focus only on the short-run, their inability to detect a full Fisher effect is perhaps not surprising; as Fisher himself emphasized, the adjustment
of nominal rates can be expected to occur only in the long-run Fisher, 1930. Recently, however, a number of studies have undertaken to test the hypothesis in the long-run,
and have found support for a full Fisher effect. In particular, Duck 1993 finds evidence of a full Fisher effect by using long-term averages of inflation and interest
rates for a cross section of countries.
2
In this article, we reexamine the Fisher effect in long-term cross-country averages. Our analysis employs bounded-influence estimation to limit the effects of influential
outliers and obtain results that are robust to small changes in the sample used for estimation. In particular, the bounded-influence techniques serve to limit the effects
on the parameter estimates of hyperinflation countries such as Brazil and Peru. In contradiction to the results in Duck 1993, our estimates reject the hypothesis that
government bond rates display a point-for-point Fisher effect; we find instead only partial adjustment of interest rates.
Section 2 describes the data and the empirical techniques. Among other things, we argue that testing the Fisher effect by using long-term averages might adhere more
closely to economic theory than do commonly used long-run techniques such as cointegration analysis. Section 3 presents the results, and section 4 extends the empiri-
cal model to test a hypothesis about the source of partial adjustment. Specifically, we find that the interest rate response depends on the riskiness of the bonds; the tests
reject a full Fisher effect only for those countries with sovereign ratings of investment grade. The result concurs with the Fried and Howitt 1983 theory that financial assets
feature a liquidity premium that increases with expected inflation.
Finally, in section 5 we offer concluding remarks. In particular, we note that our results imply that increasing the liquidity of government securities can lead to greater
stability of interest rates in the face of fluctuating inflationary expections.
2. Data and econometric issues
The data consist of 13-year averages of annual rates of inflation and interest from 1976–1988 for a cross-section of 40 countries.
3
The empirical model takes the form r
i
5 a 1 b p
i
1 b
1
VP
i
1 e
t
. 1
For country i, p
i
represents the average annual inflation rate, measured by the gross national product GNP or the gross domestic product GDP deflator; r
i
is the average short-term or medium-term rate on government debt; and VP
i
is the variability of inflation, measured by the standard deviation of the annual inflation rate.
The model includes VP
i
as a proxy for inflation uncertainty. Models of asset pricing such as Lucas 1978 and Stulz 1986 generally predict a negative effect of inflation
uncertainty on interest rates. This effect follows from Jensen’s inequality: a nominal bond’s expected real return increases as inflation becomes more variable because the
L. Coppock, M. Poitras International Review of Economics and Finance 9 2000 181–192 183
bond’s real maturity value is a convex function of the price level. Hence, to maintain the equilibrium real return, the nominal rate must decline. Less formally, Friedman
and Schwartz 1982 argue that inflation variability can erode yields by impairing capital market efficiency and thus lowering average real productivity.
4
For the purpose of testing the Fisher effect, long-term cross-country averages offer some distinct advantages. First, the Fisher effect cannot be expected to hold in the
short-term because typical short-run macroeconomic models determine the inflation rate and the nominal interest rate endogenously. Hence, the observed short-term
correlation between inflation and interest rates depends on the paths of the exogenous variables forcing the system. For instance, temporary productivity shocks might induce
positive correlation between inflation and interest rates, but liquidity shocks would tend to cause negative correlation.
5
Only in the long-run can theory make clear predictions about the response of nominal rates to changes in inflation because the
long-term inflation rate can be treated as exogenous with respect to interest rates. Conventional time series studies that test only for short-term correlations have there-
fore no direct relevance to Fisher’s hypothesis.
6
Additionally, short-run empirical models face the difficulty of measuring expected inflation. Numerous studies employ actual inflation as a proxy for expected inflation,
but as Honohan 1985 and Graham 1988 demonstrate, this approach can create substantial errors-in-variables bias. Measurement error does not pose the same prob-
lem when the data consist of long-term averages: the Law of Large Numbers implies that short-term errors tend to cancel out when computing long-term averages.
7
Several recent studies of the Fisher effect shift focus to the long-run by employing cointegration analysis.
8
This approach, however, requires the assumption that inflation and nominal rates follow unit root processes. The unit root assumption contradicts
economic theory since virtually the entire spectrum of macroeconomic models specifies or predicts a covariance stationary inflation rate.
9
Nor can empiricism alone settle the issue, since tests for unit roots have essentially zero power against plausible alternatives
Cochrane, 1991. By contrast, the analysis in this article requires no assumption of unit roots. In fact, the method of long-term averages has the advantage of remaining
valid in the both the unit root and no unit root cases.
10
The foregoing considerations favor the use of long-term averages to test the Fisher effect. A cause for concern, however, is that the empirical model in Eq. 1 might
suffer from bias due to omitted variables. Many factors can cause real interest rates to vary across countries.
11
Here, we mention three possible omitted factors that could cause bias if they correlate with inflation. First, some countries impose controls on
interest rates, causing observed rates to deviate from market-clearing rates. Second, tax rates on interest income vary across countries, and a higher tax rate implies a
greater marginal effect of inflation on the interest rate. Finally, government bonds of various nations possess differing liquidity and risk characteristics. Liquidity can influ-
ence not only real yields, but also the marginal effect of inflation through a Fried- Howitt effect, as discussed below. For this reason, we extend the empirical model in
section 4 to account for variation in risk and liquidity.
Another cause for concern involves a small number of hyperinflation countries
184 L. Coppock, M. Poitras International Review of Economics and Finance 9 2000 181–192
Table 1 Estimates of Eq. 1
1 II
III IV
Variable OLS
OLS, omit Brazil Two-step BI
Krasker-Welsch BI Inflation
1.01 0.667
0.784 0.633
0.09 0.059
0.089 0.053
Inflation variance 20.328
20.136 20.294
20.105 0.101
0.056 0.174
0.050 Intercept
2.65 5.36
4.88 5.54
1.21 0.69
0.81 0.59
R
2
0.851 0.880
0.713 0.898
ow
i
40 39
36.72 36.18
Parentheses contain standard errors. The reported R
2
applies to the weighted dependent variable. Indicates significant difference from zero at the 0.01 level.
Indicates significant difference from zero at the 0.05 level.
such as Brazil, Bolivia, and Peru; these extreme observations are likely candidates for outliers since empirical regularities that exist under conditions of moderate inflation
may break down under conditions of hyperinflation. The magnitude of the hyperinfla- tion observations could permit them in a small sample to exert considerable leverage
on the parameter estimates. The results in Table 1 show that individual observations can in fact have a pivotal effect on the estimates.
The first two columns of Table 1 present Ordinary Least Squares OLS estimates of Eq. 1. The estimates in column I use the full data set, while those in column II
omit Brazil, the highest inflation country. The results using the full data set support those of Duck 1993. The point estimate of b
, the marginal effect of inflation, lies quite close to one, and we cannot reject the hypothesis of a point-for-point Fisher
effect. In contrast, column II shows that omitting Brazil reduces the estimate of b significantly below one at the .01 level. Hence, the statistical inference on the Fisher
hypothesis hinges on whether the sample includes Brazil. Other high inflation countries also exert substantial influence on the estimates.
12
To limit the effects of influential outliers, we want to apply a formal technique rather than to arbitrarily discard observations. The bounded-influence BI techniques
presented by Welsch 1980, and Krasker and Welsch 1982, implement a weighting scheme to yield estimates that do not pivot on a small subset of the data. Welsch
1980 demonstrates a two-step BI technique, while Krasker and Welsch 1982 present an iterative procedure. To explore the robustness of results across techniques, the
next section presents both two-step and iterated BI estimates.
3. Bounded-influence methods and results
