The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.
FEDERAL RESERVE BANK of ATLANTA
Inflation and Monetary Regimes
Gerald P. Dwyer and Mark Fisher
Working Paper 2009-26
September 2009
WORKING PAPER SERIES
FEDERAL RESERVE BANK o f ATLANTA
WORKING PAPER SERIES
Inflation and Monetary Regimes
Gerald P. Dwyer and Mark Fisher
Working Paper 2009-26
September 2009
Abstract: Correlations of inflation with the growth rate of money increase when data are averaged over
longer time periods. Correlations of inflation with the growth of money also are higher when high-inflation
as well as low-inflation countries are included in the analysis. We show that serial correlation in the
underlying inflation rate ties these two observations together and explains them. We present evidence that
averaging increases the correlation of inflation and money growth more when the underlying inflation rate
has higher serial correlation.
JEL classification: E31, E5
Key words: money and inflation, inflation, quantity theory
The authors have benefited from comments from participants in the conference Money and Monetary Policy, sponsored by the
Federal Reserve Bank of Atlanta and Fordham University. James R. Lothian and Paul D. McNelis provided helpful comments on
an earlier draft. Budina Naydenova provided helpful research assistance. The views expressed here are the authors’ and not
necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors’
responsibility.
Please address questions regarding content to Gerald P. Dwyer, Research Department, Federal Reserve Bank of Atlanta, 1000
Peachtree Street, N.E., Atlanta, GA 30309-4470, 404-498-7095, 404-498-8810 (fax), jerry@jerrydwyer.com, and University of Carlos
III, Madrid, Departamento de Economía de la Empresa, Calle Madrid, 126,28903 Getafe, Madrid, Spain, or Mark Fisher,
Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street, N.E., Atlanta, GA 30309-4470, 404-498-8757, 404498-8810 (fax), mark.fisher@atl.frb.org.
Federal Reserve Bank of Atlanta working papers, including revised versions, are available on the Atlanta Fed’s Web site at
www.frbatlanta.org. Click “Publications” and then “Working Papers.” Use the WebScriber Service (at www.frbatlanta.org) to
receive e-mail notifications about new papers.
1
Introduction
Is inflation related to money growth? Many have interpreted recent low correlations of money growth and inflation as evidence that inflation is not related
to money growth under all circumstances, perhaps especially in low-inflation
environments.
There is a large literature showing that money growth and inflation are related. The earliest papers in modern times were associated with the Money
and Banking workshop at the University of Chicago (Friedman 1956). While
Anderson and Jordan’s (1968) paper using quarterly data for the United States
was controversial, it clearly showed that money and inflation were related for
1952 to 1968. More recent papers suggest that such a relationship is not as
close or as informative since the decline in inflation in the U.S. in the 1980s.
Kishor and Kochin (2007) show that part if not all of the explanation for
the change in the importance of money growth in the United States is the
change in the importance attached to inflation in monetary policy. When
the monetary authority targets inflation using a control variable, the simple
relationship between inflation and the control variable will decline because
the control variable is changing to offset other influences on inflation. Kishor
and Kochin show that the evidence for the United States is quite consistent
with this analysis and an increasing emphasis on stabilizing inflation in U.S.
monetary policy.
Empirical results across countries are not unequivocal either. Lucas (1980),
Lothian (1985), Dwyer and Hafer (1988, 1999), McCandless and Weber (1995),
Rolnick and Weber (1997) and others find substantial correlations of money
growth and inflation across countries for different time periods. Moroney
(2002) and De Grauwe and Polan (2005) examine a common criticism of such
analyses, namely that the correlations are driven by the high inflation countries and there is little relationship between money growth and inflation for low
inflation countries. Moroney (2002) selects countries based on money growth
rates and finds a positive relationship between money growth and inflation in
low-money-growth countries, but the relationship is stronger and more striking when countries with higher money growth are included in the analysis. De
Grauwe and Polan present evidence that the correlations are close to zero or
zero for low inflation countries. Frain (2004), responding to the 2001 workingpaper version of De Grauwe and Polan’s paper, removes countries with visible,
documented data discontinuites or less than 25 years of data. He finds nonzero correlations of inflation and money growth relative to real income growth
for low inflation countries as well as high inflation countries. He also finds
regression coefficients for low inflation countries that are not different than
1
one at the five percent significance level. 1 Lothian and McCarthy (2009) proceed in a different way, comparing differences in growth rates across periods
with evident differences in inflation. Even though the mean inflation rate in
the high-inflation regime is less than ten percent, they find a close connection
between the increase in inflation to these low levels and an increase in the the
growth of money relative to real income.
The length of time over which growth rates are computed has an important
influence on the analysis as well. Dwyer and Hafer (1988, 1999) show that the
relationship across countries is not particularly obvious over periods as short
as a year and is unambiguous over five-year periods. McCandless and Weber
(1995) use data over 30 year periods to analyze the relationship and find clear
relationships. De Grauwe and Polan (2005) find a relationship when using all
countries over a 30-year period as does Frain (2004) for a 25-year period. While
interesting and possibly informative, if the only reliable relationship between
money growth and inflation is over a quarter of century, that certainly is very
long run.
2
Some Evidence on Money Growth and Inflation
Before proceeding to our analysis, we document the results discussed above,
including the importance of averaging over time and the implications of using
only low money-growth countries. First, there is a noticeably closer relationship between inflation and money growth over longer periods than shorter
periods. This is at least as strong a characteristic of the data as the other observation: countries with relatively high money growth show this relationship
more clearly and make a substantial contribution to the apparent relationship
across countries. We also summarize some empirical results about coefficients
in regressions of inflation on money growth.
Throughout this paper, we measure the nominal quantity of money and its
growth rate relative to real income. Adjusting the nominal quantity of money
in this manner is useful if the income elasticity of the demand for money is
unity or not too far from unity. While this is not a particularly important
adjustment when there is substantial variation in inflation relative to real
income growth, it is more important when inflation variation is on the order
of magnitude of the variation in inflation.
[Insert Figure 1 about here]
1
The standard errors are larger for low-inflation countries, but confidence intervals
include one and do not include zero.
2
The price level and money relative to real income are strikingly similar for both
of the two high inflation countries shown in Figure 1, Brazil from 1912 to 2006
and Chile from 1940 to 2006. The price level is the Gross Domestic Product
(GDP) deflator. The measure of money is the nominal quantity of money
divided by real GDP. All of the series are set to have average values of 100 for
the time periods covered. The vertical axis is a proportional scale, making it
possible to read growth rates from the slopes of the lines. The closeness of the
behavior of the price level and money in both graphs, including the decreases
in inflation toward the end of the periods, is striking.
[Insert Figure 2 about here]
Figure 2 shows similar graphs for two countries with relatively low inflation,
Japan and the United States for the parts of the postwar period with consistent
data. The movements of the price level and money relative to real income are
similar, but definitely not as close as in the graphs for Brazil and Chile. As
earlier papers indicate, there is little obvious short-term relationship. In the
United States, money relative to income is low compared to the price level in
the 1990s. The fall in the price level in Japan from 1998 to 2006 is associated
with lower growth of money relative to income for those years, but there is no
corresponding fall in the level of money relative to income. Money relative to
income increases 0.8 percent per year from 1998 to 2006 while prices fall 1.3
percent per year.
[Insert Figure 3 about here]
Figure 3 shows average inflation rates and growth rates of money relative to
real income across countries. As does Frain (2004), we use the term “excess
money growth” instead of the more cumbersome “growth of money relative
to real income”. The upper left panel shows the relationship between the two
for all 166 countries for which we have data for twelve or more consecutive
years. We include data starting in 1985 or later through the end of the period.
Not all of the countries have data for the whole period, for example Albania’s
data begin in 1994. The upper right panel shows the relationship for countries
with an excess money growth rate less than 50 percent, 159 of the countries.
The lower left panel shows the relationship for countries with excess money
growth less than 20 percent, and the lower right panel shows the relationship
for countries with excess money growth less than 10 percent. We use the
growth of money relative to real income instead of the inflation rate to pick
countries with low inflation because regressions of inflation on money growth
have biased coefficients if countries are picked on the basis of the dependent
variable, the inflation rate. 2
2
Suppose that inflation and the growth of money relative to real income are related
with a coefficient of one and money growth is exogenous to inflation. If inflation is
used to pick countries, then the dependent variable is being used to select the
3
For all of the countries, there is a positive relationship between inflation and
excess money growth. We find a positive relationship for low inflation countries
which we define as those with excess money growth less than ten percent
per year. The correlation monotonically decrease with decreases in the cutoff
growth of excess money but it does not go to zero. The correlation is 0.47 even
for countries with the average growth of excess money less than ten percent.
Figure 3 also shows lines for regressions of inflation on excess money growth.
The slopes in these regressions also are used by some as a criteria for evaluating
the usefulness of money as a predictor of inflation, with coefficients close to one
being considered more supportive (Moroney, 2002; Frain, 2004; DeGrauwe and
Polan, 2005). As the data are cut off at lower growth rates of excess money, the
regression coefficients decrease, with the regression coefficients in this figure
decreasing from 1.01 for all the data, to 0.99 for countries with excess money
growth less than 50 percent, to 0.88 for countries with excess money growth
less than 20 percent and to 0.41 for countries with excess money growth less
than 10 percent.
The regression coefficient is substantially less than unity for lower growth rates
of excess money. Kisher and Kochin’s (2007) analysis suggests why this is so.
The correlation of inflation and excess money growth is zero if all deviations
from a constant target inflation rate are unpredictable. The fall in the correlation and the regression coefficient is consistent with their analysis if low
inflation countries have less variability of inflation targets and therefore less
correlation of inflation and excess money growth.
[Insert Figure 4 about here]
Figure 4 shows the relationship between inflation and money growth when
the data are averaged over successively shorter periods. The upper left panel
shows the relationship over all the years for which we have data on each
country, which is as much as 21 years and as few as twelve years. The upper
right panel shows the relationship with data averaged over the last ten years
for which we have data. The lower panels show the relationship with data
averaged over five years and one year. It is clear that the relationship becomes
weaker over shorter periods. This is consistent with averages presented over
five years and less presented by Dwyer and Hafer (1988, 1999).
Figure 4 also shows regression coefficients of inflation on excess money growth.
These coefficients also decrease as the data are averaged over shorter periods,
observations. Countries with inflation greater than 10 percent and growth of money
relative to real income less than 10 percent are excluded but countries with inflation
less than 10 percent and growth of money relative to real income greater than 10
percent are included. This selection biases the regression coefficient downward from
one.
4
from 1.01 for all the data to 0.46 for one year of data.
3
Money Growth and Inflation
Why are money growth and inflation more closely related when data are averaged over long time periods and when high inflation countries are included
in an analysis of inflation and money growth? In this section, we provide an
explanation based on variation of the underlying inflation rate relative to the
demand for money. This analysis predicts that higher serial correlation of the
underlying inflation rate is associated with a larger increase in the correlation between inflation and money growth as more years are averaged. We
also show that the size of the slope coefficient in a regression of inflation on
money growth is uninformative about whether the quantity theory holds. The
quantity theory is consistent with a slope coefficient of unity in a regression
of inflation on money growth and it is consistent with a slope coefficient less
than unity.
Suppose that the demand for money has unit income elasticity and no other
variables systematically affect demand. Then
μt − yt = π t + εt
(1)
where μt is the growth rate of the nominal quantity of money in period t, π t is
the inflation rate, yt is the growth rate of real income and εt is an error term
in the demand for money.
3.1 Inflation Targeting
Suppose that the monetary authority’s actions target the inflation rate, whether
this is intentional or not, and the target is π ∗t which varies over time. This relationship can be written
π t = π∗t + ηt ,
(2)
where η t is the error term in this equation. For simplicity, we suppress the
subscript t. Combining (1) and (2) results in
μ − y = π + ε = π ∗ + η + ε.
(3)
The correlation of the inflation rate (2) and excess money growth (3) is
ρ = Corr [π, μ − y] =
Cov [π ∗ + η, π ∗ + η + ε]
,
SD [π ∗ + η] SD [π ∗ + η + ε]
5
(4)
which equals
ρ=
Var [π ∗ + η] + Cov [ε, π ∗ + η]
SD [π ∗ + η] (Var [π ∗ + η] + 2Cov [ε, π ∗ + η] + Var [ε])1/2
.
(5)
At first glance, it is not obvious this is particularly helpful. Suppose, though,
that the error term in the demand for money is orthogonal to the target price
level and errors in hitting it, i.e. Cov [ε, π ∗ + η] = 0. Then the correlation of
the inflation rate and excess money growth simplifies to
ρ=
SD [π ∗ + η]
(Var [π ∗ + η] + Var [ε])1/2
(6)
.
This equation for the correlation can be interpreted in an informative way.
First off, suppose that the variance of the inflation target and errors in hitting
it are zero. Equation (6) states the obvious: the correlation of the inflation rate
with excess money growth is zero. If there is substantial variance in inflation
targets or errors in generating that inflation rate relative to the demand for
money, then the correlation will be closer to one. This is related to the analysis
by Kishor and Kochin (2007); it also provides a tenative explanation of Figure
3. For countries with similar inflation targets, i.e. little variance of inflation
targets or errors in hitting them, the correlation across countries of inflation
with excess money growth will be low if not zero. At the other end of the
range between zero and one, zero variance of the error term in the growth of
money demand implies
Corr [π, μ − y] = 1.
(7)
The demand for money and the monetary authority’s inflation target may
well have different characteristics over time. Suppose that the inflation target
varies gradually over time and the demand for money varies more over short
periods of time. Then the relative variance of π ∗ + η and ε will change as data
are averaged over different time periods. Over short periods, the variance of
the demand for money will be larger relative to the variance in the supply;
over longer periods, the variance of the demand for money decreases relative
to the variance in the supply. In the limit, the variance in demand goes to
zero and the correlation of the inflation rate with excess money growth goes
to one.
Orthogonality of the error term in the demand for money and the error in the
supply of money and changes in the target inflation rate is sufficient for this
characterization of the correlations but is not necessary. The correlation can
be written
ρ=
1 + Cov [ε, π] /Var [π]
(1 + 2Cov [ε, π] /Var [π] + Var [ε] /Var [π])1/2
6
.
(8)
Even if Cov [ε, π] 6= 0, this correlation approaches one as Var [π] increases
relative to Cov [ε, π] and Var [ε] . In short, a higher correlation of inflation and
excess money growth is to be expected with a higher variance of the inflation
target and errors hitting it if the covariance of errors in the growth of money
demand with the inflation rate and the variance in errors in the demand for
money do not increase proportionately.
The regression coefficient from a regression of inflation on excess money growth
will not be unity even though the quantity theory holds in this setup. This
regression coefficient is
β π|μ−y =
Cov [π, μ − y]
,
Var [μ − y]
(9)
which can be rewritten as
β π|μ−y =
Var [π]
Cov [π, ε]
+
. (10)
Var [π] + 2Cov [ε, π] + Var [ε] Var [π] + 2Cov [ε, π] + Var [ε]
This does not obviously equal one, and it does not equal one in general. Even
if Cov [ε, π] = 0,
Var [π]
,
(11)
β π|μ−y =
Var [π] + Var [ε]
which is less than one unless Var [ε] is zero. 3 Stated more positively, β π|μ−y
approaches one as Var [ε] /Var [π] goes to zero but, with inflation targeting, the
coefficient does not equal one even if the covariance of errors in the growth of
money demand and the inflation rate is zero. This result does not hold under
all circumstances.
3.2 Control of Money Supply
Instead of being determined by the demand for money as it would be under
inflation targeting, suppose the supply of money is determined by
μ = π∗ + y + ζ,
(12)
where ζ is the error term and the demand for money is the same as equation
(1). The money supply is determined with a target inflation rate as the goal
but the growth rate of the nominal quantity of money is changed to effect the
3
The similarity of this formula and the one for regressions with errors in the
right-hand-side variables is not an accident. With inflation targeting, shocks to
the demand for money affect the growth of the nominal quantity of money but not
the inflation rate. This is similar to measurement error in a right-hand-side variable
that has no effect on a left-hand-side variable.
7
goal. The growth rate of real income is included in the equation for the supply
of money with a coefficient of one to reflect the growth of demand due to real
income. The central bank can achieve its target inflation rate by changing the
growth rate of the nominal quantity of money with the growth rate of real
income. This equation (12) can be rewritten
μ − y = π ∗ + ζ.
(13)
Equating the growth of the demand for the nominal quantity of money (1)
and the supply of the nominal quantity of money (13) yields
π = π ∗ + ζ − ε.
(14)
It follows that the correlation of the inflation rate and excess money growth
ρm is
ρm =
1 − Cov [ε, π ∗ + ζ] /Var [π ∗ + ζ]
(1 − 2Cov [π ∗ + ζ, ε] /Var [π ∗ + ζ] + Var [ε] /Var [π ∗ + ζ])1/2
.
(15)
If Cov [ε, π ∗ + ζ] = 0, then
ρm =
SD [π∗ + ζ]
(Var [π ∗ + ζ] + Var [ε])1/2
=
1
(1 + Var [ε] /Var [π ∗ + ζ])1/2
(16)
which approaches one as Var [ε] /Var [π ∗ + ζ] goes to one. This is the same
conclusion as above under inflation targeting.
The conclusion concerning regression coefficients does change though. The
coefficient from regressing the inflation rate on excess money growth is
β ∗π|μ−y =
Cov [π, μ − y] Var [π ∗ + ζ] − Cov [ε, π ∗ + ζ]
=
Var [μ − y]
Var [π∗ + ζ]
Cov [ε, π ∗ + ζ]
=1−
.
Var [π ∗ + ζ]
(17)
If Cov [ε, π ∗ + ζ] = 0, then β ∗π|μ−y = 1. This is not true if Cov [ε, π ∗ + ζ] 6= 0,
although β ∗π|μ−y approaches one as Cov [ε, π ∗ + ζ] /Var [π ∗ + ζ] goes to zero.
In sum, if the covariance of the errors in the demand for money and supply of
money is zero, the correlation of inflation and excess money growth increases
to one as the variance in the demand for money goes to zero relative to the
the variance in the supply for money. This conclusion concerning the correlation’s value holds whether the monetary regime is one of inflation targeting or
control of the money supply. The coefficient in a regression of inflation on the
excess money growth rate depends on how the nominal quantity of money is
determined.
8
4
Persistence in the Underlying Inflation Rate
In this section, we derive testable predictions concerning the evolution of the
underlying inflation rate and the correlation of excess money growth and inflation. We show that serial correlation of the underlying inflation rate is consistent with increases in the correlation of inflation and excess money growth
as data are averaged over longer periods, and higher serial correlation is consistent with a greater increase in the correlation.
Consistent with the argument above, suppose that errors in the demand for
money are serially uncorrelated but suppose that the underlying inflation rate,
or inflation target, evolves over time according to
π∗ = βπ ∗−1 + ν,
(18)
h
i
where ν is serially uncorrelated as well and 0 ≤ β < 1. Assume Cov π ∗−1 , ν =
0. If Cov [ε, π] = 0, the earlier analysis show that the one-period correlation
of inflation and excess money growth is
ρ=
SD [π]
(Var [π] + Var [ε])1/2
(19)
.
Let π2 = (π + π−1 ) /2 and ε2 = (ε + ε−1 ) /2. Given these definitions, the
correlation of two-period averages of inflation and excess money growth is
ρ2 =
SD [π2 ]
(Var [π 2 ] + Var [ε2 ])1/2
(20)
.
Is ρ2 > ρ? Because Var [π 2 ] = 12 Var [π] + 12 Cov [π, π −1 ] and Var [ε2 ] = 12 Var [ε] ,
"
Var [π] + Cov [π, π−1 ]
ρ2 =
Var [π] + Cov [π, π −1 ] + Var [ε]
#1/2
.
(21)
Given serially uncorrelated errors that are mutually uncorrelated, Cov [π, π −1 ] =
βVar [π ∗ ] and therefore
"
Var [π] + βVar [π ∗ ]
ρ2 =
Var [π] + βVar [π ∗ ] + Var [ε]
#1/2
.
(22)
The issue is whether
ρ2 R ρ.
This is equivalent to deciding whether
β
Var [π ∗ ] Var [ε]
R 0.
Var [π] Var [π]
9
(23)
(24)
Since this is positive by assumption, it follows that
(25)
ρ2 > ρ1 .
This algebra makes it clear that the correlation goes up with averaging as
∗ ] Var[ε]
β Var[π
increases. The parameter β represents the serial correlation in
Var[π] Var[π]
the underlying inflation rate. Increases in β increase the difference between
the one-period and two-period correlations. If β = 0, then ρ2 = ρ1 . If β > 0,
then ρ2 > ρ1 . The other terms represent the product of the variation in the
inflation target relative to the inflation rate and the variation in the demand
for money relative to the inflation rate, which affect the magnitude of the
increase in the correlation.
5
The Generalized Local Level Model
We can examine the relationship between the correlations and the serial correlation of the underlying inflation rate π ∗ in a state-space model in which
π ∗ is unobservable. We use a Bayesian analysis to derive the posterior distribution of the serial correlation parameter β and the relationship between β
and the correlation between inflation and excess money growth as the data
are averaged over longer periods.
The generalized local level model is a simple state-space model involving an
observation (measurement) equation and a state (transition) equation. 4 We
have T observations on inflation π = (π 1 , . . . , πT ). The state variable is the
underlying inflation rate π ∗ = (π ∗1 , . . . , π∗T ) which is not directly observed. The
observation and state equations are (for t = 1, . . . , T )
π t = π ∗t + η t
π ∗t = δ (1 − β) + β π ∗t−1 + ut ,
where
⎡
⎤
⎢η t ⎥ iid
⎣ ⎦∼
ut
N(0, Σ),
(26)
(27)
⎡
1
where Σ = h−1 ⎢
⎣
0
⎤
0⎥
⎦.
ψ
(28)
We impose the restriction −1 < β ≤ 1. The local level model itself as in Koop
(2003) is characterized by β = 1.
It is important to deal with the unobserved observation in period 0 in a clean
way. Let π ∗0 = δ + w, where w ∼ N(0, h−1 λ) and w is independent of the other
4
This model is a generalization of the local level model given in Koop (2003). The
generalization allows the unobserved state variable to be stationary.
10
disturbances. Eliminating π ∗0 from the state equation for π∗1 produces
π ∗1 = δ + β w + u1 .
(29)
Consequently, we see that π ∗1 ∼ N(δ, h−1 (β 2 λ + ψ)). (Note that if β = 0, then
λ does not appear in the distribution for π ∗1 .)
Given this setup, we now show that π follows a restricted ARMA(1,1) for
t ≥ 2. We can eliminate the unobserved state variable and obtain
⎧
⎨δ
+ β w + u1 + η1
πt = ⎩
δ (1 − β) + β π t−1 + ut + η t − β ηt−1
t=1
t ≥ 2.
(30)
Note E0 [w] = E0 [ut ] = E0 [η t ] = 0. Therefore, E0 [πt ] = δ for all t ≥ 1. Define
ω t := ut + ηt − β ηt−1 . Let γ ω (τ ) denote the autocovariance function for ω.
Then γ ω (0) = ψ h−1 + (1 + β 2 ) h−1 , γ ω (1) = −β h−1 , and γ ω (τ ) = 0 for τ ≥ 2.
This autocovariance function is characteristic of an MA(1). As such, we can
reexpress ω t as ωt = vt − ξ vt−1 , where |ξ| < 1. 5 We see that π is a restricted
ARMA(1,1) for t ≥ 2. If β = 1, then π is an IMA(1,1).
The posterior distribution for the unobservables conditional on the observable
series π is
p(π ∗ , h, φ|π) = p(π ∗ , h|π, φ) p(φ|π),
(31)
where
φ := (δ, β, λ, ψ).
(32)
The factorization on the right-hand side of (31) will prove convenient. The
posterior distribution (31) can be obtained from the joint distribution as follows:
p(π ∗ , h, φ|π) ∝ p(π, π ∗ , h, φ)
= p(π, π ∗ , h|φ) p(φ)
= p(π|π ∗ , h) p(π ∗ |h, φ) p(h|φ) p(φ).
(33)
According to this parameterization of ω, γ ω (0) = (1 + ξ 2 ) σ 2v and γ ω (1) = −ξ σ 2v .
Therefore,
q
1 + β 2 + ψ − (1 + β 2 + ψ)2 − 4 β 2
ξ=
2β
q
1 + β 2 + ψ + (1 + β 2 + ψ)2 − 4 β 2
2
.
σv =
2h
5
Thus the local level model imposes a restriction between ξ and β. Consequently
not all ARMA(1,1) processes can be expressed as a generalized local level model.
Moreover, β 6= ξ as long as β = 0. Therefore the problem of local non-identification
due to cancelation of common factors is absent.
11
The observation and state equations provide p(π|π ∗ , h) and p(π ∗ |h, φ) respectively. To complete the model we must specify the priors p(h|φ) and p(φ). We
defer consideration of p(φ) until later. Let the prior for h be independent of
φ: p(h|φ) = p(h), with p(h) given by the Gamma distribution: 6
h ∼ G(s−2 , ν).
(34)
This prior for h delivers analytical expressions for the conditional posterior
p(π ∗ , h|π, φ) and for the marginal likelihood p(π|φ).
In order to derive the aforementioned analytical expressions for the conditional
posterior and marginal likelihood, it is convenient to change the parametrization. As a preliminary, stack the observation equations as follows:
π = π∗ + η.
(35)
Using π ∗ = W θ, we can write (35) as
(36)
π = Wθ + η
where
⎡
θ :=
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎤
π ∗1
⎥
⎥
π∗2 − β π ∗1 ⎥
⎥
⎥
⎥
..
⎥
.
⎥
⎦
(37)
π ∗T − β π ∗T −1
and W is the T × T matrix such that
⎧
⎨β i−j
i≥j
otherwise.
Wij = ⎩
0
(38)
(Note |W | = 1.) As long as we condition on φ, we can treat β–and hence
W –as known. The advantage of the new parametrization appears in the state6
We adopt the parametrization of the Gamma distribution given by Koop (2003,
p. 326): If z ∼ G(δ, ν), then the density of z is given by
(
¡ −ν z ¢
ν−2
2 exp
c−1
0<z<∞
G z
2δ
fG (z|δ, ν) =
0
otherwise,
where
cG =
µ
2δ
ν
¶ν
2
Γ
³ν ´
2
is independent of z and Γ(·) is the Gamma function. Note E[z] = δ and Var[z] =
2 δ 2 /ν.
12
dynamics:
⎧
⎨δ
+ β w + u1
θt = ⎩
δ (1 − β) + ut
t=1
t > 1.
(39)
The distributions for π and θ implied by (36) and (39) are
³
π | (θ, h, φ) ∼ N W θ, h−1 IT
³
´
θ | (h, φ) ∼ N θ, h−1 V ,
where
⎡
θ=
⎤
δ
⎢
⎥
⎢
⎥
⎢
⎥
⎢δ (1 − β)⎥
⎢
⎥
⎢
⎥
..
⎢
⎥
.
⎢
⎥
⎣
⎦
´
(40a)
(40b)
⎡
⎤
2
>
⎢β λ + ψ 0T −1 ⎥
and V = ⎣
⎦.
0T −1 ψ IT −1
δ (1 − β)
(41)
Equation (36) can be interpreted as a normal linear regression model for which
(40b) and (34) form a natural conjugate prior:
(θ, h)|φ ∼ NG(θ, V , s−2 , ν).
(42)
Given the conjugacy of the prior (42) with respect to the likelihood (40a), the
posterior inherits the form of the prior; namely,
(θ, h) | (π, φ) ∼ NG(θ, V , s−2 , ν),
(43)
where 7
³
θ = V V −1 θ + W > y
³
V = V −1 + W > W
ν =ν +T
³
´
(44)
´−1
´> ³
(45)
´
³
´>
³
´
(46)
V −1 θ − θ .
(47)
p(π ∗ |π, h, φ) = p(θ|π, h, φ)|θ=W −1 π∗
= N(W −1 π ∗ | θ, h−1 V ) = N(π ∗ | π ∗ , h−1 V π∗ ),
(48)
ν s2 = ν s2 + y − W θ
y − Wθ + θ − θ
The conditional posterior for π ∗ is given by
where π∗ = W θ and V π∗ = W V W > . Thus we have established the posterior
distribution for π ∗ and h conditional on φ:
(π ∗ , h) | (π, φ) ∼ NG(π∗ , V π∗ , s−2 , ν).
7
See Koop (2003, p. 187).
13
(49)
We now turn to the posterior for φ. The marginal posterior for φ can be
expressed as
p(φ|π) ∝ p(π|φ) p(φ).
(50)
The marginal likelihood of φ is 8
p(π|φ) =
ZZ
p(π, θ, h|φ) dθ dh = c
where
³
Γ(ν/2) ν s2
Ã
|V |
|V |
!1/2
³
ν s2
´−ν/2
,
(51)
´ν/2
.
(52)
Γ(ν/2) π T /2
(Note c is free of φ.) The first equality in (51) is identically true while the second equality follows from the specific functional forms given in (34) and (40).
c=
The parameter space for φ = (δ, β, λ, ψ) is
Φ = (−∞, ∞) × (−1, 1] × (0, ∞) × (0, ∞).
(53)
We adopt the following prior:
p(φ) = (2 π)−1 e−( 2 δ
1 2
+λ+ψ)
.
(54)
In addition, values for (s2 , ν) must be specified. We adopt a noninformative
prior, setting ν = 0 and setting s2 to an arbitrary value (since s2 enters the
posterior only via the product ν s2 ).
We can make draws of φ from p(φ|π) via the symmetric random-walk Metropolis MCMC algorithm. The algorithm produces a sequence of draws {φ(r) }R
r=1
. Given φ(r) one computes φ(r+1) as follows: Draw φ0 ∼ N(φ(r) , Ω) and u ∼
U(0, 1), and then set
(r+1)
φ
⎧
⎨φ0
= ⎩ (r)
φ
p(φ0 |π)
p(φ(r) |π)
≥u
otherwise.
(55)
Equation (55) shows that if the proposal φ0 is “uphill” from the current point
φ(r) in the sense that p(φ0 |π) ≥ p(φ(r) |π), then it is always accepted (i.e., added
to the output sequence); by contrast, if the proposal is “downhill” from the
current point, then it is accepted with a probability that is proportional to the
likelihood ratio. (If the proposal is out of bounds, i.e. if φ0 6∈ Φ, then p(φ0 |π) = 0
and the proposal is never accepted.) Note that if the proposal is not accepted,
then the current point φ(r) is placed again in the output sequence, which
(among other things) induces serial correlation in the sequence of draws. To
make the algorithm operational, one chooses a starting value φ(0) ∈ Φ and the
8
See Koop (2003, p. 189)
14
covariance matrix Ω. (The covariance matrix provides a scale for the randomwalk step size.) One must also specify the number of burn-in draws to discard
and the amount of thinning to do (if any) after the burn-in period. 9
6
Our Estimates
We have a dataset with 166 countries, each of which has continuous annual
data for twelve or more years. The number of observations on inflation in each
country ranges from twelve to 21. While it would be even better to compare
across monetary regimes within a country, the paucity of observations implied
by such a strategy leads us to examine the data across countries.
6.1 Estimates of the Serial Correlation
Let φi denote the parameters for the i-th country. The parameter of interest
is {β i }. We make draws of φi from p(φi |π i ) via the symmetric random-walk
Metropolis MCMC algorithm. For each country we make two runs, using the
results of the first to calibrate the second. For the first run, we adopt a starting
(0)
value of φi = (0, .5, 1, 1) and we use Ω = diag(10−4 , 10−2 , 10−2 , 10−2 ) as the
covariance matrix for the scale of the step size. We make 104 burn-in draws and
then make 105 draws, keeping every one in 102 . Next we compute the mean
and covariance of the 103 draws produced by the first run. For the second run,
(0)
we set φi to the computed mean (from the first run) and we set Ω to .2 times
the computed covariance matrix. We make 104 burn-in draws for the second
run and then make 105 draws, keeping every one in 102 . This produces a total
of 103 draws for each country to approximate the posterior distribution of
φi . The draws are not independent and the average first-order autocorrelation
across all parameters and all countries is .13. There are only four countries
for which the maximum autocorrelation for any of the four parameters in φi
is above .5. An approximation for the effective number of independent draws
is given by
1−ρ
e ≈R
,
(56)
n
1+ρ
where R is the number of draws and ρ is the first-order autocorrelation. In
e averages about 790 and is not less than 340.
our case R = 103 . For β, n
The posterior means and the 90% highest posterior density regions for β i are
shown in Figure 5. The point estimates for all but 12 countries are positive
and the regions do not include zero for 96 of the 166 countries.
9
Koop (2003, Section 5.5) provides a detailed summary of the Metropolis MCMC.
15
[Insert Figure 5 about here]
6.2 Relation to Correlations
We are interested in the relation across countries between the posterior means
of the autoregressive coefficients and the correlations of the inflation rate and
the growth rate of exces money. Let β i denote the posterior mean of β i and ρis
denote the sample correlation between the inflation rate and the excess money
growth rate for country i over s periods. We summarize the relationship by
the correlation between β = (β 1 , . . . , β n ) and ρs = (ρ1s , . . . , ρns ) by the simple
correlation rs .
Figure 6 shows scatterplots for ρis versus β i for s ∈ {1, 3, 5}. The top row
shows plots for all 166 countries, while the bottom row shows plots for only
those 119 countries for which we have at least 20 observations. Twenty observations would be considered a small sample for estimating a serial correlation
coefficient in most contexts, but requiring 20 observations eliminates over a
quarter of these countries.
[Insert Figure 6 about here]
To estimate the posterior distribution of rs , we apply the Bayesian bootstrap
to rs , producing {rs(m) }M
m=1 . The Bayesian bootstrap works as follows. Make a
(m)
draw w
from the flat Dirichlet distribution and compute rs(m) using w(m) as
probabilities:
c(m)
rs(m) = q (m) (m)
(57)
vβ vρs
from
(m)
mβ
=
n
X
(m)
wi
βi
(m)
vβ
=
i=1
mρ(m)
=
s
n
X
n
X
(m)
wi
i=1
(m)
wi
ρis
i=1
vρ(m)
=
s
c(m) =
n
X
(m)
wi
i=1
n
X
t=1
(m)
wi
³
´
(m) 2
β i − mβ
³
ρis − mρ(m)
s
³
(m)
β i − mβ
´2
´³
´
ρis − mρ(m)
.
s
Figure 7 shows the estimated posterior distributions of the correlations between the serial correlation coefficients and the correlations of inflation and
money growth different time spans. All of the rs are positive, indicating that
the posterior means of the serial correlation coefficients and the correlation of
money growth and inflation clearly are positive.
[Insert Figure 7 about here]
16
(m)
(m)
Next we compare r1 with r3 and r5 . In particular, we compute d3 := r3 −
(m)
(m)
(m)
(m)
r1 and d5 := r5 − r1 . The results are shown in Figure 8. We find the
(m)
(m)
fraction of d3 that is positive is about .91 while the fraction of d5 that is
positive is about .66. If we use only countries that have at least 20 observations,
then the fractions increase to about .99 and .93, respectively.
These distributions are evidence in favor of the proposition that an increase
in the serial correlation coefficient leads to an increase in the correlation of
money growth and inflation.
[Insert Figure 8 about here]
7
Conclusion
The relationship between inflation and excess money growth still is controversial. We find a positive correlation across all countries. The correlation falls as
countries with higher excess money growth are excluded, but the correlation
is 0.47 across countries with excess money growth of ten percent or less. We
show that the lower correlation for low inflation countries is not surprising if
low inflation countries have lower variation in unpredictable changes in the
supply of money relative to unpredictable changes in the demand for money.
We also show that the size of a regression coefficient of inflation on excess
money growth is uninformative about the quantity theory. If errors in the
supply of money are uncorrelated with errors in the demand for money, then
a regression of inflation on the growth rate of money will have a slope coeffient
of unity. On the other hand, if this correlation is not zero, as it is with explicit
or implicit inflation targeting, the nominal quanity of money is endogenous
and a regression of inflation on money growth will not deliver a coefficient
of unity. This is perfectly consistent with the quantity theory holding. While
regression coefficients equal to unity may seem like a plausible way to evaluate
the quantity theory, the quantity theory is consistent with coefficients less than
one as well as equal to one.
Higher correlations between money growth and inflation when data are averaged over time is consistent with this same analysis. We show that positive
serial correlation of the underlying inflation rate is consistent with higher
correlations of excess money growth with inflation as the growth rates are
computed over longer time periods. We also show that monetary regimes with
more sustained deviations of inflation from its mean will show greater increases
in the correlation of excess money growth and inflation as the growth rates
are computed over longer time periods.
17
We then test these implications. We find substantial variation in serial correlation of underlying inflation rates and we find this variation is positively
related to the increase in correlations as data are averaged over longer periods.
Our results indicate that sustained excess money growth is positively correlated with inflation. The greater apparence of that relationship when data are
averaged over time and when countries with sustained deviations of inflation
from its mean inflation are quite consistent with the quantity theory holding.
18
8
Data Appendix
We analyze annual data for the United States and for 182 countries. The
data across countries include available data for 1985 and subsequent years.
These data are from the World Development Indicators website, the March
2008 CD for International Financial Statistics, and from Haver. Haver is the
source of the data on Taiwan. The nominal and real Gross Domestic Product
(GDP) data primarily are from World Development Indicators. These data
are supplemented by data from International Financial Statistics when these
IFS data are more complete or consistent. 10 We use the data on money plus
quasimoney from IFS except when the WDI data cover a longer period or
have more significant digits. 11 The price index is the Gross Domestic Product
deflator and nominal income is GDP. Table A1 in the Appendix lists all the
countries and the periods over which we have GDP and money data.
Data for some individual countries are from Haver or country-specific sources.
Data for Taiwan are from Haver because these data are not available in either
WDI or IFS.
Inspection of some series suggested discontinuities in the underlying data from
WDI and IFS. As it turned out, all of the issues concerned the nominal quantity of money. When collecting data from an individual central bank’s website,
we collected the monetary series emphasized by the central bank. The nominal quanity of money for Belgium is M3 from the National Bank of Belgium’s
website. The quantity of money for Canada is M2 from Haver. The quantity
of money for Japan is M2 including certificates of deposit from the Bank of
Japan’s website. Earlier and later series are spliced by the average monthly
ratio of 0.995519 in the overlapping period April 1998 to March 1999. The
quantity of money for New Zealand is M3 from the Bank of New Zealand.
The growth rate of the nominal quantity of money for Macedonia is M2 from
the Central Bank. The nominal quantity of money for the United Kingdom
is M4 from the Bank of England. All data for the United States are from
the Federal Reserve Bank of St. Louis’s website and the nominal quantity of
money is M2.
The long-term data for Brazil and Chile are from Rolnick and Weber (1997)
10 We
use some or all IFS data for Anguilla, Aruba, Barbados, Cambodia, Cape
Verde, Fiji, Kuwait, Libya, the Maldives, Montserrat, Qatar and San Marino.
11 The WDI data available to us often contain more significant digits when there are
large changes in the quantity of money. We use WDI data for Argentina, Bolivia,
Brazil, Chile, the Democratic Republic of the Congo, Cyprus, Ethiopia, Ghana,
Guinea, Lao People’s Democratic Republic, Lebanon, Malta, Nicaragua, Peru,
Romania, Samoa, San Marino, Slovenia, Sudan, Turkey, Turkmenistan, Uganda,
Uruguay and Zimbabwe.
19
updated by World Development Indicators. 12 The monetary variable from
Rolnick and Weber’s data is their M2. The data are updated by spliced data
from the World Development Indicators for 1986 through 2006.
12 Rolnick
and Weber (1995) provide the data sources in their Data Appendix. We
thank Warren Weber for providing the data.
20
Anderson, L. C., Jordan, J. L. 1968. Monetary and Fiscal Actions: A Test of
Their Relative Importance in Economic Stabilization. Federal Reserve Bank
of St. Louis Review 50 (11), 11-24.
De Grauwe, P., Polan, M. 2005. Is Inflation Always and Everywhere a Monetary Phenomenon? Scandinavian Journal of Economics 107 (2), 239-59.
Dwyer, Jr., G. P., Hafer, R. W. 1999. Are Inflation and Money Growth Still
Related? Federal Reserve Bank of Atlanta Economic Review 84 (2), 32-43.
Dwyer, Jr., G. P., Hafer, R. W. 1988. Is Money Irrelevant? Federal Reserve
Bank of St. Louis Review 70 (3), 1-17.
Estrella, A., Mishkin, F. S. 1997. Is There a Role for Monetary Aggregates
in the Conduct of Monetary Policy? Journal of Monetary Economics 40 (2),
279-304.
Frain, J. Inflation and Money Growth: Evidence from a Multi-Country Dataset. Economic and Social Review 35 (3), 251-66.
Friedman, M. 1956. Studies in the Quantity Theory of Money. Chicago: University of Chicago Press.
Kishor, N. K., Kochin, L. A. 2007. The Success of the Fed and the Death of
Monetarism. Economic Inquiry 45(1), 56-70.
Koop, G. 2003. Bayesian Econometrics. Chichester, England: John Wiley &
Sons Ltd.
Lothian, J. R. 1985. Equilibrium Relationships between Money and Other
Economic Variables. American Economic Review 75 (4), 828-35.
Lothian, J. R. 1976. The Demand for High-Powered Money. American Economic Review 66 (1), 56-68.
Lothian, J. R., McCarthy, C. 2009. The Behavior of Money and Other Economic Variables: Two Natural Experiments. Journal of International Money
and Finance, this issue.
Lucas, Jr., R. E. 1980. Two Illustrations of the Quantity Theory of Money.
American Economic Review 70 (5), 1005-14.
McCandless, Jr., G. T., Weber, W. E. 1995. Some Monetary Facts. Federal
Reserve Bank of Minneapolis Quarterly Review 19 (3), 2-11.
Moroney, J. R. 2002. Money Growth, Output Growth and Inflation: Estimation of a Modern Quantity Theory. Southern Economic Journal 69 (4),
21
398-413.
Rolnick, A. J., Weber, W. E. 1995. Money, Inflation and Output Under Alternative Monetary Standards. Staff Report 175, Federal Reserve Bank of
Minneapolis.
Rolnick, A. J., Weber, W. E. 1997. Money, Inflation and Output under Fiat
and Commodity Standards. Journal of Political Economy 105 (6), 1308-21.
22
Figure 1
Money and Prices in Brazil and Chile
Brazil 1912 to 2006
1000
100
Chile 1940 to 2006
Price level
Money relative to real income
100
Percentage of period average
10
10
1
0.1
1
0.01
0.001
0.1
0.0001
1e-005
0.01
1e-006
1e-007
0.001
1e-008
1e-009
0.0001
1e-010
1e-011
1e-005
1e-012
1900
1920
1940
1960
Year
1980
2000
1940
1970
Year
2000
Figure 2
Money and Prices in the U.S. and Japan
Japan 1967 to 2007
United States 1959 to 2007
Percentage of period average
2
Price level
Money relative to real income
2
102
9
8
102
9
7
8
6
7
5
6
4
5
3
4
2
3
101
2
1970
1990
Year
2010
1971
1982
1993
Year
2004
Figure 3
Inflation and Excess Money Growth for Lower Growth Rates of Excess Money
Note: The slope indicated in the figure is the slope of the regression line. The solid line in the
figure is the regression line. The dotted line is a regression from the origin with a slope of one.
100
Inflation Rate
100
All countries
correlation 0.979
slope
1.006
80
80
60
60
40
40
20
20
0
0
0
Inflation Rate
100
Excess money growth less than 50 percent
correlation 0.951
slope
0.992
20
40
60
80
100
0
40
60
80
100
Excess money growth less than 10 percent
correlation 0.465
slope
0.411
Excess money growth less than 20 percent
correlation 0.853
slope
0.883
80
20
8
60
4
40
20
0
0
0
20
40
60
80
100
Growth Rate of of Excess Money
0
2
4
6
8
10
Growth Rate of of Excess Money
Figure 4
Inflation and Excess Money Growth over Shorter Time Periods
Note: The slope indicated in the figure is the slope of the regression line. The solid line in the
figure is the regression line. The dotted line is a regression from the origin with a slope of one.
80
Inflation Rate
100
All years
correlation 0.979
slope
1.006
80
Ten years
correlation 0.972
slope
0.844
60
60
40
40
20
20
0
0
0
40
60
80
0
100
Five years
correlation 0.916
slope
0.773
Inflation Rate
120
20
200
20
40
60
80
One year
correlation 0.807
slope
0.460
150
80
100
40
50
0
0
0
40
80
120
Growth Rate of of Excess Money
0
50
100
150
200
Growth Rate of of Excess Money
Figure 5. Posterior means and 90% highest posterior density regions for
βi for 166 countries (sorted by mean).
1.0
0.5
0.0
-0.5
-1.0
0
50
100
150
Figure 6. Scatterplots of ρis versus β i for s ∈ {1, 3, 5}. The sample
correlations rs are shown.
All 166 Countries
r1 = 0.38
r3 = 0.44
r5 = 0.40
1.0
1.0
1.0
0.5
0.5
0.5
0.0
0.0
0.0
-0.5
-0.5
-0.5
-1.0
-1.0
-0.5
0.0
0.5
1.0
-1.0
-1.0
-0.5
0.0
0.5
1.0
-1.0
-1.0
-0.5
0.0
0.5
1.0
119 countries with at least 20 observations
r1 = 0.37
r3 = 0.49
r5 = 0.47
1.0
1.0
1.0
0.5
0.5
0.5
0.0
0.0
0.0
-0.5
-0.5
-0.5
-1.0
-1.0
-0.5
0.0
0.5
1.0
-1.0
-1.0
-0.5
0.0
0.5
1.0
-1.0
-1.0
-0.5
0.0
0.5
1.0
Figure 7. Bayesian bootstrap distributions of rs .
n = 166 and s = 1
n = 166 and s = 3
n = 166 and s = 5
6
6
6
5
5
5
4
4
4
3
3
3
2
2
2
1
1
1
0
0.0
0
0.0
0.2
0.4
0.6
0.8
1.0
n = 119 and s = 1
0.2
0.4
0.6
0.8
1.0
0
0.0
n = 119 and s = 3
6
6
5
5
5
4
4
4
3
3
3
2
2
2
1
1
1
0
0.0
0
0.0
0.4
0.6
0.8
1.0
0.2
0.4
0.6
0.8
0.4
0.6
0.8
1.0
n = 119 and s = 5
6
0.2
0.2
1.0
0
0.0
0.2
0.4
0.6
0.8
1.0
Figure 8. Differences d3 (thick) and d5 .
All 166 Countries
119 Countries with T ³ 20
10
10
8
8
6
6
4
4
2
2
0
0
-0.2
-0.1
0.0
0.1
0.2
0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
Table 1
Countries and Years
Country
First Year
Last Year
Albania
1994
2006
Algeria
1985
Anguilla
Country
First Year
Last Year
Brazil
1985
2006
2006
Bulgaria
1991
2006
1990
2005
Burkina Faso
1985
2006
Antigua and
Barbuda
1985
2006
Burundi
1985
2006
Argentina
1985
2006
Cambodia
1993
2006
Armenia
1992
2006
Cameroon
1985
2006
Aruba
1991
2004
Canada
1985
2006
Australia
1985
2006
Cape Verde
1985
2006
Austria
1985
1997
Central African
Republic
1985
2006
Azerbaijan
1992
2006
Chad
1985
2006
Bahamas, The
1985
2002
Chile
1985
2006
Bahrain
1985
2005
China
1985
2006
Bangladesh
1985
2006
Colombia
1990
2006
Barbados
1985
2004
Comoros
1985
2006
Belarus
1994
2006
Costa Rica
1985
2006
Belgium
1985
1998
Cote d'Ivoire
1985
2006
Belize
1985
2006
Croatia
1993
2006
Benin
1985
2006
Cyprus
1985
2006
Bhutan
1985
2006
Czech Republic
1993
2006
Bolivia
1985
2006
Denmark
1985
2006
Botswana
1985
2006
Djibouti
1990
2006
Dominica
1985
2006
Haiti
1985
2006
Dominican Republic
1985
2006
Honduras
1985
2006
Ecuador
1985
2006
Hong Kong
1991
2006
Egypt
1985
2006
Hungary
1985
2006
El Salvador
1985
2006
Iceland
1985
2006
Equatorial Guinea
1985
2006
India
1985
2006
Estonia
1991
2006
Indonesia
1985
2006
Country
First Year
Last Year
Ethiopia
1985
2006
Euro Area
1995
Fiji
Country
First Year
Last Year
Iran
1986
2006
2007
Israel
1985
2006
1985
2006
Italy
1985
1997
Finland
1985
1997
Jamaica
1985
2006
France
1985
1997
Japan
1985
2006
Gabon
1985
2006
Jordan
1985
2006
Gambia, The
1985
2006
Kazakhstan
1993
2006
Germany
1985
1997
Kenya
1985
2006
Ghana
1985
2006
Kuwait
1992
2006
Grenada
1985
2006
Laos
1987
2006
Guatemala
1985
2006
Latvia
1993
2006
Guinea
1989
2005
Lebanon
1988
2006
Guinea-Bissau
1986
2006
Lesotho
1985
2006
Guyana
1985
2006
Liberia
1991
2006
Libya
1985
2006
Netherlands
1985
1997
Lithuania
1993
2006
New Zealand
1985
2006
Macao
1985
2006
Nicaragua
1985
2006
Macedonia
1992
2006
Niger
1985
2006
Madagascar
1985
2006
Nigeria
1985
2005
Malawi
1985
2006
Norway
1985
2003
Malaysia
1985
2006
Oman
1985
2005
Maldives
1985
2006
Pakistan
1985
2006
Mali
1985
2006
Panama
1985
2006
Malta
1985
2006
Papua New Guinea
1985
2006
Mauritania
1985
2003
Paraguay
1985
2006
Mauritius
1985
2006
Peru
1985
2006
Mexico
1985
2006
Philippines
1985
2006
Moldova
1991
2006
Poland
1990
2006
Mongolia
1991
2006
Portugal
1985
1997
Country
First Year
Last Year
Montserrat
1985
2005
Morocco
1985
Mozambique
Country
First Year
Last Year
Qatar
1985
2006
2006
Republic of the
Congo
1985
2006
1988
2006
Romania
1985
2006
Myanmar
1985
2005
Russia
1993
2006
Namibia
1990
2006
Rwanda
1985
2005
Nepal
1985
2006
Saint Kitts and
Nevis
1985
2006
Saint Lucia
1985
2006
Taiwan
1985
2007
Saint Vincent and
the Grenadines
1985
2005
Tanzania
1988
2006
Samoa
1985
2006
Thailand
1985
2006
Saudi Arabia
1985
2006
Togo
1985
2006
Senegal
1985
2006
Tonga
1985
2006
Seychelles
1985
2006
Trinidad and
Tobago
1985
2006
Sierra Leone
1985
2006
Tunisia
1985
2006
Singapore
1985
2006
Turkey
1985
2006
Slovakia
1993
2006
Uganda
1985
2006
Slovenia
1991
2006
Ukraine
1992
2006
Solomon Islands
1985
2006
United Arab
Emirates
1985
2005
South Africa
1985
2006
United Kingdom
1985
2006
South Korea
1985
2006
United States
1985
2006
Spain
1985
1997
Uruguay
1985
2006
Sri Lanka
1985
2005
Vanuatu
1985
2006
Sudan
1985
2006
Venezuela
1985
2006
Suriname
1985
2006
Yemen
1990
2006
Swaziland
1985
2006
Zambia
1993
2006
Sweden
1985
2006
Zimbabwe
1985
2005
Switzerland
1985
2006
Syria
1985
2006
@FedFRASER