L. Coppock, M. Poitras International Review of Economics and Finance 9 2000 181–192 185
The BI technique defines the weights according to [Eq. 3] w
i
5 min {1, at
i
}, 3
where a is a constant chosen to set the bound on the influence, and t
i
is a measure of the influence of observation i.
13
The two-step Welsch and iterative Krasker-Welsch techniques use somewhat different methods to measure the influence, t
i
. In either case, however, the definition of t
i
consists of a quadratic function dx
i
of the explana- tory variables that measures the “leverage” of observation i, multiplied by a standard-
ized measure of the estimated residual for observation i. Thus, we have [Eq. 4]
14
t
i
5 dx
i
|y
i
2 x
i
bˆs|. 4
The two-step procedure performs OLS in the first stage and weighted least squares in the second stage. The Krasker-Welsch iterative procedure updates the estimates
of b, w
i
, and s at each step. The procedure converges to a unique solution, and the resulting estimator is consistent and asymptotically normal. The Krasker-Welsch
estimator is also asymptotically efficient among BI estimators, given that an efficient BI estimator exists.
15
The BI technique does not provide a panacea for all possible econometric pathologies, but the method does yield inferences robust to small sample
changes and likely mitigates the effects of omitted variables and data reporting errors. Given the size of our sample, the BI technique insures that any subsample of meaning-
ful size should yield essentially the same inferences.
Columns III and IV of Table 1 display BI estimates of Eq. 1. In contrast to the OLS results, the BI estimates of b
lie significantly below one at the .01 level, indicating rejection of the Fisher hypothesis. The rejection is especially strong in light of the
fact that full adjustment with interest taxation implies b greater than one. The results
contradict those of Duck 1993, and demonstrate the importance of bounding the influence of the outliers in these data. While the results do not support a point-for-
point Fisher effect, the estimates do indicate a significant partial effect.
16
Table 2 lists the downweighted observations and the values of the weights, w
i
, for the squared residuals. The two techniques can generate different weights because
they define the influence differently. Note that the set of downweighted observations almost exclusively includes high-inflation countries; the two-step procedure down-
weights five of the six highest-inflation observations, and the iterative procedure downweights six of the nine highest. In particular, both methods strongly downweight
Brazil, suggesting that this observation does not conform to the same empirical model as do the bulk of the data.
In the following section we present a brief discussion of some leading theoretical explanations for the failure to observe a full Fisher effect. We then extend the empirical
model to examine a theory that attributes the source of partial adjustment to the liquidity properties of financial assets.
4. Sources of partial adjustment
As a theoretical proposition, the Fisher effect has considerable intuitive appeal. Researchers, however, cite several theories that can seemingly undermine the effect,
186 L. Coppock, M. Poitras International Review of Economics and Finance 9 2000 181–192
Table 2 Downweighted observations
a
Eq. 1 Eq. 5
Inflation Country
rank Two-step
Krasker-Welsch Two-step
Krasker-Welsch Brazil
1 0.04
0.01 0.03
0.02 Bolivia
2 0.03
1.00 0.03
1.00 Peru
3 0.16
1.00 0.06
0.06 Turkey
4 1.00
0.27 1.00
1.00 Iceland
5 0.61
0.93 1.00
1.00 Ecuador
6 0.87
0.27 NA
NA Columbia
7 1.00
0.19 1.00
0.34 Greece
9 1.00
0.85 1.00
1.00 Spain
14 1.00
1.00 1.00
0.71 Trinidad Tobago
17 1.00
1.00 1.00
0.73 Guatemala
18 1.00
0.69 NA
NA Denmark
29 1.00
0.97 1.00
1.00 Switzerland
39 1.00
1.00 1.00
0.99
a
Countries are ranked from highest 1 to lowest 40 level of inflation. The weights are those assigned to the squared residuals in least squares estimation.
even in the long-run. A number of authors invoke money illusion, but this explanation conflicts with the fundamental rationality assumption of modern theory. Some hypoth-
eses consistent with rationality state that inflation systematically reduces the real interest rate. Most frequently cited is the Mundell-Tobin effect, whereby inflation
causes substitution of capital for money, and the resulting increase in the capital stock reduces the real rate. The Mundell-Tobin effect, however, seems unlikely to have an
empirically significant effect on interest rates. Summers 1983 calculates that since money holding amounts to less than 2 of the value of the capital stock, substitution
of capital for money can reduce the real rate by no more than about 6 basis points.
Another explanation for partial adjustment, the so-called Wicksell effect, maintains that redistribution caused by monetary expansion systematically reduces the real rate
Wicksell, 1907; Cagan, 1980. Our calculations indicate that, like the Mundell-Tobin effect, the Wicksell effect cannot account for significant reductions in real rates because
of the relatively large size of the existing capital stock.
A more plausible explanation uses the idea that low-risk financial assets such as government bonds yield non-pecuniary liquidity returns. Fried and Howitt 1983
show that if money and bonds substitute in the production of liquidity, and each offers positive but diminishing marginal liquidity, then inflation-induced substitution of bonds
for money increases the liquidity premium on bonds and lowers the pecuniary real rate. Hence, the Fried-Howitt effect implies that the Fisher effect might hold for
illiquid, but not liquid, assets. The result has implications for cross-country tests of the Fisher effect since the liquidity of government bonds varies across countries. U.S.
Treasury securities have immense trading volume and are thus highly liquid, but sovereign debt issues of many nations trade in relatively thin markets and might lack
L. Coppock, M. Poitras International Review of Economics and Finance 9 2000 181–192 187
Table 3 Estimates of Eq. 5
I II
III IV
Variable OLS
OLS, omit Brazil Two-step BI
Krasker-Welsch BI Inflation
1.18 0.737
1.04 0.961
0.10 0.070
0.10 0.095
Inflation 20.427
20.178 20.366
20.316 Variance
0.097 0.055
0.152 0.068
Grade 7.67
1.72 5.17
4.51 2.99
1.63 1.68
1.59 Grade · inflation
20.528 20.151
20.399 20.332
0.177 0.097
0.106 0.102
Intercept 20.85
4.83 1.58
2.20 2.44
1.37 1.45
1.38 R
2
0.899 0.925
0.872 0.929
Rw
i
35 34
32.12 31.85
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.
liquidity. In some nations, precious metals or U.S. dollar-denominated assets might supersede sovereign debt as a substitute for money balances in times of inflation.
To control for liquidity differences, we define a dummy variable GRADE taking the value 1 for countries with Moody’s bond risk ratings of investment grade Baa
or higher and zero otherwise. Strictly speaking, risk and liquidity are not identical; nonetheless, sovereign risk ratings should provide a useful proxy since low risk typically
characterizes highly liquid assets.
The extended empirical model takes the form r
i
5 a 1 b p
i
1 b
1
VP
i
1 b
2
GRADE
i
1 b
3
GRADE · p
i
1 e
t
. 5
To allow for a Fried-Howitt effect, the interaction term GRADE · p
i
permits the marginal effect of inflation on investment grade debt, b
1 b
3
, to differ from that on non-investment grade debt, b
. The specification also includes the dummy variable GRADE
to permit a fixed effect, b
2
, of risk or liquidity on yields. Table 3 displays estimates of Eq. 5.
17
The estimates indicate a significant shift in the marginal effect of inflation across bond grade categories. The OLS estimates in
column I suggest that the marginal effect falls short of one for investment grade sovereigns, and exceeds one for non-investment grade sovereigns. As column II shows,
however, dropping the Brazil observation again causes a considerable reorientation of the estimated regression. In response, we obtain BI estimates of Eq. 5. Columns
III and IV show that the point estimate of the marginal effect of inflation for non- investment grade sovereigns lies remarkably close to one for both the two-step and
iterative BI techniques. In contrast, the point estimates of 0.64 and 0.63 for investment grade bonds lie significantly below one at the 0.01 level. The result suggests rejection
188 L. Coppock, M. Poitras International Review of Economics and Finance 9 2000 181–192
of the hypothesis of a full Fisher effect for liquid, but not illiquid, sovereigns, which concurs with the Fried-Howitt hypothesis.
18
5. Conclusions
