Download Empirical Exchange Rate Equations for the Commodity Currencies

Commodity Currencies and Empirical Exchange Rate Equations
by
Yu-chin Chen (Harvard University)
and
Kenneth Rogoff (International Monetary Fund)
September 25, 2001
This paper was prepared for the November 15-16 Conference on Understanding Exchange
Rates in Amsterdam, The Netherlands. The authors are grateful to Andra Ghent, Tracy Chan,
and John Murray at the Bank of Canada, Faith Darling and Joseph Gagnon at the Board of
Governors of the Federal Reserve System, Ximena Cheetham, Hali Edison and Paul
Nicholson at the International Monetary Fund and to Anne-Marie Brook at the Reserve Bank
of New Zealand. The views expressed in this paper are the authors’ own and do not
necessarily represent those of the International Monetary Fund.
1. Introduction
While there do not appear to be any robust exceptions to the Meese-Rogoff (1983) result
for major OECD currencies (and certainly the advent of the euro has not changed that
assessment), there are some purported exceptions among some of the smaller OECD currencies.1
Researchers at the Bank of Canada have claimed for many years that in fact, not only do standard
empirical exchange rate equations fit out-of-sample, one can even use variants to successfully
predict the exchange rate, both unconditionally and in response to policy alternatives.2 A key
element of the Canadian equation involves augmenting the standard model by a terms of trade
variable reflecting the volatile movements in world prices of Canadian commodity exports,
particularly non-energy commodities. Researchers at the Reserve Bank of Australia have at
times been even more ebullient, finding that over the 1990’s, one could have earned a substantial
excess profit in trading on the Australian dollar by properly incorporating forecastable terms of
trade movements into exchange rate forecasts.3 Finally, a similar framework has also been
extended to the New Zealand dollar.4
It has long been recognized that if one could find a missing real shock that were
sufficiently volatile, one could potentially go a long ways towards resolving major empirical
exchange rate puzzles such as the Meese-Rogoff puzzle and the purchasing power parity (PPP)
puzzle.5 For most OECD economies, it is hard to know what that shock might be, much less
measure it.6 In Canada, Australia and New Zealand, however, because commodities constitute a
significant component of their export, world commodity price fluctuations – generally exogenous
to these small countries for all but a few goods – potentially explain a major component of their
terms of trade fluctuations.7 Therefore, for the three “commodity currencies,” a potential key
missing real shock is both easy to measure and to incorporate.
1
See Frankel and Rose (1995) for a comprehensive survey of the empirical research on exchange rates.
See, for example, Amano and van Norden (1993) and Djoudad, Murray, Chan and Dow (2000).
3
See, for example, Gruen and Kortian (1996).
4
See again Djoudad, Murray, Chan and Dow (2000); the connection is also explored in Brook (1994).
5
See, for example, Rogoff (1996) for a discussion of the PPP puzzle.
6
Oil prices certainly have the volatility and there is some evidence that they impact the terms of trade (Backus and
Crucini, 2000), but adding these variables to standard monetary equations does not seem to do the trick.
7
Simply incorporating the terms of trade as an explanatory variable would not be meaningful for most OECD
countries, since the terms of trade contain a large component that moves mechanically with the exchange rate (see
Obstfeld and Rogoff, 2000). This is most likely due to a combination of wage and price rigidities interacting with at
2
1
Our paper aims to address the following two questions. Is it true that commodity price
shocks explain a significant share of exchange rate movements for these currencies? And if so,
does the introduction of commodity prices more broadly “fix” standard monetary empirical
exchange rate models? Affirmative answers here might encourage researchers to try harder to
search for corresponding real shocks to the major currencies. In addition, understanding the
effects of commodity price shocks on exchange rates is also of broad interest to developing
countries, particularly as some open up their capital markets and adopt more flexible exchange
rates. If commodity prices can indeed be shown to be a consistent and empirically reliable factor
in empirical exchange rate equations, the finding would have important implications across a
variety of policy issues, not least concerning questions such as how to implement inflationtargeting in developing countries.8
The outline of this paper is as follows. In section 2 of the paper, we give a brief overview
of the economic environment in the three countries we are studying. We then proceed to give
some simple, but striking, evidence on just how closely movements in these currencies seem to
track the corresponding world price indices of their commodity exports. The strong correlations
come through not only for cross rates against the U.S. dollar, but also for cross rates against the
pound and against a broad index of non-US-dollar currencies. In section 3, we go on to see
whether the visual evidence stands up to closer scrutiny, focusing on the simplest empirical
models, not least because the data sample is limited and richer dynamic models would lack
credibility. We find that for New Zealand and Australia, the correlation between commodity
prices and exchange rates holds up remarkably well, and seems robust to alternative assumptions
about the underlying time series processes. Though there is some evidence of structural breaks,
especially at the time these countries switched to formal inflation targeting, the general size of
the contemporaneous correlation between commodity prices and exchange rates nevertheless
seems relatively consistent, both across time and across countries. The commodity price
elasticity estimate is roughly 0.5 for Australian and 1.0 for New Zealand. For Canada, the
least partial pass-through. Our main explanatory variable here is not the terms of trade but indices of world
commodity prices, which presumably do not move automatically with these small countries exchange rates.
8
There has been related work for developing countries that looks at cross-country panel data. For example,
Mendoza (1995) finds that terms of trade shocks account for a significant portion of variation in output in
developing countries, whereas Bidarkota and Crucini (2000) find a strong connection between shocks to commodity
prices and the terms of trade.
2
evidence is more mixed, with the correlation between exchange rates and commodity prices
much more sensitive to detrending. We go on in section 4 to ask whether the relationship might
result from the countries having market power in their commodities, and we find that this is not
the case. A structural interpretation of the estimates is offered in the appendix, in light of two
relatively standard exchange rate models. We argue that the quantitative size of our estimates is
quite plausible.
Having found a robust connection between commodity export prices and exchange rates,
we extends the analysis in section 5 to look at commodity price-augmented standard empirical
exchange rate equations. By controlling for this major source of real shocks, one might hope the
standard exchange rate equations - adjusted for commodity price shocks - might perform better
for "the commodity currencies" than they have been found to perform for the major currencies.
However, our results do not offer very strong encouragement for this point of view. The final
section concludes.
2. Background and Graphical Evidence
2.1. Background
From a macroeconomic perspective, Australia, Canada, and New Zealand are near perfect
examples of well-developed, small open economies. All three are highly integrated into global
capital markets and active participants in international trade. Moreover, to varying degrees, all
three countries can plausibly be described as “commodity economies”, given the large share
primary commodities occupy in their production and exports. For at least the past decade,
commodities have maintained a 60% share of Australia's total exports, with wool, wheat, and
various metals as examples of leading exports. In New Zealand, while the share has declined
from a hefty two-thirds in the late 1980s, commodities continue to account for more than half of
total exports in recent years. Canada, albeit having a larger industrial base, still has more than a
quarter of its exports in commodities such as base metals, forestry products, crude oil, and
natural gas.
3
Given the major role primary commodities play in generating export earnings for these
countries, it is perhaps no coincidence that, despite the relatively small size of their overall
economies, these countries hold significant market power for a few of their products. In New
Zealand, for instance, 46 million sheep cohabit with 3.8 million people. Not surprisingly, only
20 percent of its meat production are consumed domestically, and New Zealand supplies close to
half of the total world exports of lamb and mutton. Canada similarly dominates the world
market in forestry products, and Australia holds significant shares of the global exports in wool
and iron ore. However, while each country has some market power for a few key goods, they
are, on the whole, price takers in world markets for the vast majority of their commodity exports.
In terms of monetary and exchange rate policies, all three countries have been operating
under a flexible exchange rate regime for a considerable length of time. Shortly after the
collapse of Bretton Woods, Canada began floating its currency, and as part of the economic
reform efforts to revitalize their economies, Australia and New Zealand abandoned their
exchange rate pegs in 1983 and 1985 respectively. In addition, Australia, Canada, and New
Zealand all adopted some variant of inflation targeting in the early 1990s.9
2.2. Graphical Evidence
[INSERT FIGURES 1a-c to 3a-c HERE]
Figures 1a through c show the Australian real exchange rate relative to three reference
currencies – the U.S. dollar, the British Pound, and a non-US-dollar currency basket – plotted
alongside the world price of Australia’s major non-energy commodities, aggregated using
Australian production weights. The corresponding graphs for Canada and New Zealand are
shown in Figures 2 and 3.
For all three countries, the sample period starts roughly a year after the float of the
particular home currency. To abstract away from the issue of non-stationarity in nominal prices,
we focus on real exchange rate behavior in this paper. The real exchange rates in these graphs
(and in all the subsequent analyses) are end-of-quarter nominal rates, expressed as the foreign
4
exchange values of the domestic currency, adjusted by the relevant CPIs. An increase in the real
rates thus represents a rise in the relative price of home goods or, a real appreciation for the
home country. The non-dollar basket is adopted from the Broad Index of the Federal Reserve. It
is a composite of over 30 non-US-dollar currencies, covering all major trading partners of the
United States each weighted by their respective trade shares.10 By measuring the relevant home
currencies against different anchors, especially the broad index covering many developing
countries, we hope to insulate our analysis from being driven by shocks to the U.S. economy and
the movements in the U.S. dollar.
The country-specific commodity price indices cover non-energy commodities only, and
they are fixed-weight geometric averages of the world market prices for the major commodities
produced in each country, weighted by their corresponding domestic production share.
Individual real commodity prices are quarterly averages of the world market transaction prices in
U.S. dollars, deflated by the U.S. CPI. The commodities included in each index and their
corresponding weights are listed in the data appendix.11
Looking at these sets of graphs, three features especially stand out. First, the correlations
between the various exchange rates and the commodity prices are strikingly apparent. Not only
do the series appear to mirror each other in movement, the magnitude of their swings are also
similar. In addition, the exchange rates, some more than others, appear to be highly persistent,
and possibly non-stationary. Lastly, the long-term decline of global commodity prices seems
clearly reflected in these country-specific series as well. In the following section, we explore
further just how strong and robust the apparent correlations are, and the role common trends may
play in explaining the co-movements of real exchange rates and commodity prices.
9
We refer the reader to Zettelmeyer (2000) for a more thorough discussion of the conduct of monetary policy in
these three countries in the 1990s.
10
It does not matter that the home-country currency appears in our non-dollar index (the New Zealand and Australia
weights are zero/very small), since it essentially factors out when we construct the exchange rate of the non-dollar
index against the home currency. There is no particular significance to using U.S. trade weights in our analysis; we
adopt the broad index of the Federal Reserve as a convenient check for the robustness of our results.
11
The weights for individual commodities are drawn from Djoudad, Murray, Chan, and Daw (2000) and represent
the average domestic production value of the commodity over the 1982-90 period. Certain commodities in the
original Djoudad et al indices are excluded as we were unable to extend the price series. The excluded commodities
amount to less then 5% of the original production weight in each instance (see the Data Appendix). However,
Australia and Canada, respectively, do hold significant global export market shares in barley and sulphur.
5
3. Some Empirical Evidence
We first focus extensively on testing very simple correlations, which seems an
appropriate starting point in light of earlier empirical failures. In subsequent sections, we will
explore richer dynamics, address potential endogeneity, and also test whether the inclusion of
commodity prices can help provide stronger empirical support for canonical exchange rate
models.
Results in Table 1 capture the simple contemporaneous correlations we observe in the
figures. The similarity of coefficient estimates across currency pairings is remarkable; a one
percent improvement in the world price of their commodity export is associated with an
appreciation of the home currency by around 40 to 50 basis points for all three countries,
regardless of the anchor currency.
Table I
Commodity Price Elasticities of Real Exchange Rates
Dependent Variable: Log of Real Exchange Rate, relative to Different Anchor Currencies
ln(Real Exchange Rate)t = α + β*ln(Real Commodity Price)t + εt
Australia
National
Currency
vs.
U.S.
Dollar
vs.
British
Pound
Ln(Real
0.40 *
Commodity
Canada
vs.
U.S.
Dollar
vs.
British
Pound
0.51 *
vs.
NonDollar
Basket 1
0.36 *
0.40 *
(0.08)
(0.09)
(0.06)
0.39
0.55
0.51
New Zealand
vs.
U.S.
Dollar
vs.
British
Pound
0.50 *
vs.
NonDollar
Basket
0.36 *
0.53 *
0.61 *
vs.
NonDollar
Basket
0.41 *
(0.07)
(0.14)
(0.09)
(0.17)
(0.10)
(0.10)
0.56
0.34
0.34
0.30
0.45
0.36
Prices) 2
Adj. R2
N Obs.
70
114
62
Sample
Period
1984Q1 - 2001Q2
1973Q1 - 2001Q2
1986Q1 - 2001Q2
Note: * indicates significance at the 5% level. Newey-West heteroskedasticity and autocorrelation consistent
(HAC) standard errors in parentheses.
1. “Non-dollar Basket” is a U.S. trade-weighted average of over 30 currencies, excluding the U.S. dollar, of major
U.S. trading partners. It is based on the broad real index from the Federal Reserve.
2. Real commodity price index is the base country production-weighted average of world commodity prices in
U.S. dollars, deflated by the U.S. CPI. See the data appendix for country-specific production weights.
6
3.1. Detrending
The simple regressions in Table I are suggestive, but there is an issue of how best to
address a small sample of data with (near) unit-root behavior.12 Since our small sample size
precludes any meaningful test of stationarity, we instead rely on the considerable empirical
evidence suggesting that real exchange rates are stationary, possibly with a trend, as theory
would predict. (See Froot and Rogoff, 1995, who find that the half life of real exchange rate
shocks is roughly 3-4 years across a wide variety of historical data, at least in linear models.).
The same is arguably true for commodity prices.13 Ruling out non-stationarity/stochastic trends
a priori, detrending the data seems an appropriate strategy to consider next.14
We employ three different types of detrending methods – linear trend, Hodrick-Prescott
filter, and first differencing – to test the robustness of the positive correlations we observed
earlier.15 Since results based on different anchor currencies are very similar, to conserve space,
we only report results for the U.S. dollar exchange rates in this section. Table II shows the
commodity price elasticity estimates under these filters. For Australia and New Zealand, the
commodity price elasticity estimates show up slightly higher, but in general appear consistent
with the previous findings. The estimates also seem robust to the three detrending methods, even
first differencing, which admittedly would be more appropriate with non-cointegrated unit root
series. Results for the other anchor currencies are similar. For Canada, under the full sample
period of 1973 to 2001, detrending appears to render all previously observed correlations
12
In addition to the figures which hint at unit roots in these series, we cannot reject the null of non-stationarity using
the augmented Dickey-Fuller or the Phillips-Perron tests for the exchange rate and commodity price series. The null
of stationarity is rejected under the Kwiatkowski, Phillips, Schmidt, and Shen (1992) unit root test as well.
13
See Borensztein and Reinhart (1994) and Cashin, Liang and McDermott (2000). One might argue that even
though most real exchange rates appear to be stationary, the commodity currencies might be an exception if
commodity prices themselves have a unit root. However, it should be noted that over the very long run, countries
can substitute out of commodity production into manufactures if the relative price of commodities drifts too low.
Korea today exports primarily manufactured goods, but in 1960 almost 90% of exports were commodities.
14
Note that this assumption notwithstanding, the methodologies discussed in this section do cover the econometric
techniques appropriate for I(1) processes, namely first-differencing and dynamic OLS.
15
We recognize the limitation and potential problems associated with each of these filters. For example, should the
series be difference-stationary, linear detrending will result in spurious cycles. While the HP filter does not assume
a stable trend process over time, it suffers from the well-documented end-point problem, as well as the drawback
mentioned in Cogley and Nason (1991) should the exchange rate and commodity price series be cointegrated. First
difference filter removes long term trend but also potentially important information contained in the levels of the
series; it is mainly relevant when commodity prices and real exchange rates are non-cointegrated I(1) series.
7
between real commodity prices and the Canadian real exchange rates insignificantly different
from zero, and in several cases, it produces negative commodity price elasticity estimates.
We note that one cannot entirely dismiss the significance of the common long-term trend
between the Canadian dollar and commodity export prices. Indeed, the downward drift in both
series may be intimately connected; we simply cannot statistically demonstrate any such
connection here. In addition, we suspect the elusiveness of this correlation for Canada may be
related to its ambiguous status as a “true commodity economy”. After all, commodities are
clearly the minority in its export base, compared to the case of New Zealand and Australia.
However, structural breaks occurring somewhere over the thirty year period is certainly another
possibility.16 Indeed, looking at the Canadian-U.S. rates since mid-1980s (as we do for Australia
and New Zealand), we obtain significant positive coefficient estimates of around 0.3 under the
linear and the hp filters. However, perhaps not surprisingly, such significant correlation
disappears when its exchange rate is measured relative to the other two anchor currencies. We
will return to the issue of parameter stability later.
Table II: Detrending Series
Dependent Variable: Log of Real Exchange Rate, vs. U.S. Dollar
Detrended ln(Real Exchange Rate)t = α + β*Detrended ln(Real Commodity Price)t + εt
Australia
Detrending
Filter:
Ln(Real
Linear
HP
0.81 *
Commodity
Canada
st
New Zealand
Linear
HP
0.09
1
Difference
0.05
1.10 *
0.73 *
1st
Difference
0.59 *
(0.15)
(0.07)
(0.06)
(0.32)
(0.20)
(0.26)
0.05
0.03
-0.00
0.27
0.25
0.10
Linear
HP
0.58 *
1
Difference
0.47 *
0.21
(0.12)
(0.12)
(0.14)
0.53
0.37
0.07
st
Prices)
Adj. R2
N Obs.
Sample Period
70
114
62
1984Q1 - 2001Q2
1973Q1 - 2001Q2
1986Q1 - 2001Q2
Note: * indicates significance at the 5% level. Newey-West heteroskedasticity and autocorrelation consistent
(HAC) standard errors in parentheses.
16
It is important to emphasize that we focus here only on non-energy commodities. In gross terms at least, Canada
is a significant exporter of coal and natural gas. Our explorations with including energy prices separately did not
significantly change our results for the Canadian dollar, but the issue needs to be investigated more thoroughly than
we take up here.
8
As different detrending techniques seem to yield similar results, we will continue the rest
of our analysis with the linear trend. Figures 4 through 6 show the linearly detrended data.
Again, note how closely the detrended commodity price and exchange rate series seem to track
each other.
[ INSERT FIGS 4-6 HERE]
3.2. Serial Correlation
Given the persistence of the series, it is perhaps no surprise that even with the inclusion
of a linear trend, the error structure in the linear regressions still exhibit significant serial
correlation.17 We will examine more fully in section 5 how this serial correlation may reflect the
nature of the missing shocks. In this section, we focus on correcting the biased standard errors
estimates under serial correlation. Up to this point, we have been reporting the kernel-based
nonparametric GMM estimator of Newey-West (1987). Because such non-parametric estimators
are known to have poor small sample properties, we now also consider a parametric specification
where the error terms are assumed to follow a first order autoregressive process. As can be seen
from Table III, the AR(1) specifications effectively bring the Durbin-Watson statistics back
towards 2, and while lowering the coefficients slightly, still give elasticity estimates of around
0.5, consistent with our earlier findings.18
Alternatively, if these series were non-stationary, the estimates and significance tests
performed above based on classical statistical methods would be invalid. As a robustness check,
we consider the alternative assumption that real exchange rates and real commodity prices are
cointegrated I(1) series.19 In Table III, we present results from the dynamic OLS specifications
of Stock and Watson (1993), where leads and lags of the first-differenced log commodity prices
17
The Durbin-Watson statistics for the regressions presented in Table 1 and 2 are all well below 2, and
autocorrelograms show clear evidence of autoregressive error structures. (Note the HAC consistent GMM standard
errors reported in these tables account for this serial correlation.)
18
The autocorrelation coefficient estimates are in the range of 0.88 to 0.96, broadly similar to what we see in PPP
regressions (See Froot and Rogoff 1995). This is suggestive of why it is unlikely that commodity prices will indeed
be the panacea for the monetary models, despite being able to explain a significant portion of the exchange rate
volatility for these countries. We will come back to this point in Section 5.
19
We are aware of the inference problem put forth by Elliott (1998), that applying cointegration methods on nearunit root processes may introduce biases and inefficiencies. Here, we are simply using it as a robustness check.
9
are included in the regressions as well. Under the alternative assumption that real exchange rates
and real commodity prices are cointegrated I(1) processes, the dynamic OLS approach produces
the correct standard errors for the “superconsistent” point estimates which are robust to the
presence of endogeneity.20 As evident in Table III, our small sample sizes notwithstanding, the
elasticity estimates for Australia and New Zealand from the dynamic OLS are not far off from
those obtained under the assumption of stationarity, and still produce estimates significantly
different from zero.21 As in Table I, the elasticity estimate for the Canadian-U.S. real exchange
rate shows up as significant under dynamic OLS, likely reflecting the common trend discussed
earlier.22
As the coefficient estimates appear robust to these alternative assumptions on the
underlying data generating process, we will continue with the Newey-West standard error
correction procedure, in accordance with our view that these series are stationary.
20
See Hamilton (1994), Ch. 19.
While asymptotically, the Stock-Watson dynamic OLS procedure yields the same parameter estimates as
conventional OLS, this may not be the case in finite samples. We experimented with longer lead and lag lengths,
and the estimation results are similar.
22
Stock (1987) shows that OLS estimators for cointegrating parameters converge faster than parameter estimates in
OLS models using stationary variables, as the effect of common trend dominates that of the stationary component.
21
10
Table III: Alternative Specifications
Dependent Variable: Log of Real Exchange Rate, vs. U.S. Dollar
Australia
Ln(Real
Comm Prices)
NeweyWest 1
0.81*
AR(1)
(0.12)
AR(1) root
Durbin-
2
Canada
NeweyWest
0.21
AR(1)
0.54 *
Dynamic
OLS 3
0.39 *
(0.14)
(0.06)
(0.15)
New Zealand
NeweyWest
1.10 *
AR(1)
0.04
Dynamic
OLS
0.40 *
0.51 *
Dynamic
OLS
0.58 *
(0.07)
(0.03)
(0.32)
(0.21)
(0.09)
0.88 *
0.96 *
0.95 *
(0.05)
(0.03)
(0.05)
0.36
2.15
0.57
0.86
0.10
1.92
0.06
0.96
0.19
1.99
0.37
0.90
Watson stat
Adj. R2
Sample Period
0.36
1984Q1 - 2001Q2
0.56
1973Q1 - 2001Q2
0.40
1986Q1 - 2001Q2
Note: * indicates significance at the 5% level.
1.
ln(Real Exchange Rate)t = α + β*t + γ*ln(Real Commodity Price)t + εt
2.
using non-parametric GMM Newey-West approach to correct for the biased standard errors estimate
ln(Real Exchange Rate)t = α + β*t + γ*ln(Real Commodity Price)t + εt
where εt follows an AR(1)
3.
ln(Real Exchange Rate)t = α + γ*ln(Real Commodity Price)t + γ1*∆ln(Real Commodity Price)t+1 +
γ0*∆ln(Real Commodity Price)t + γ-1*∆ln(Real Commodity Price)t-1 + εt, where ∆ is the first difference
operator. Here real exchange rates and real commodity prices are assumed to be non-stationary and cointegrated, so DOLS produces super-consistent estimators (Stock and Watson 1993).
3.3. Parameter Stability
As we mentioned earlier, all three countries adopted inflation targeting in the early 1990s.
Together with our findings in Section 3.1 that the estimates for the Canadian dollar appear
qualitatively different when we look at a shorter sample beginning in 1985, testing for the
possibility of structure breaks seems warranted. While there are various parameter stability tests
available, the applicability of some of these tests is constrained by our small sample sizes.23
Here we perform the classic Chow test on pre-selected potential breakpoints, and the Hansen
(1992) test for structural break of unknown timing. Table III presents the results of these two
structural break tests on the commodity price elasticity estimates for the three U.S.-dollar
23
See Hansen (2001) for a lucid summary of recent developments in the econometrics of structural change.
11
exchange rates. 24 As we are interested in possible instability in the commodity price elasticities
but not so much in shifts in underlying trend, we use detrended variables for this analysis.
The Chow test, designed to test the null hypothesis of constant parameters against an
alternative of a one-time shift at some known time, suffers several well-known criticisms.25 In
particular, because the pre-selected candidate breakpoint is often endogenous, the Chow test is
likely to falsely indicate a break when none in fact exists. In our analysis, for example, we
choose as candidate break-dates the year each of these countries adopted formal inflation targets
(1990 for New Zealand, 1991 for Canada, and 1993 for Australia). It is easy to make a case that
these regime shifts were endogenous. Nevertheless, the Chow test results do no show clear
indication of parameter shifts pre- and post-inflation targeting, despite a likely bias towards
doing so.26 The Hansen procedure, adopted from his 1992 paper, is approximately the Lagrange
multiplier test of the null of constant parameters against the alternative of structural breaks of
unknown timing and/or random walk parameters.27 The critical value for the stability of
individual parameter is drawn from Hansen (1992). As is apparent from Table IV, the Chow
test, which requires an a priori determination of the timing for the structural change, and the
Hansen test, which tests for parameter instability over the full sample period, do not always
produce consistent conclusions, such as in the case of the linearly detrended New Zealand data.
We note that the Hansen test relies on asymptotic properties our small data samples may not
adequately satisfy. Nevertheless, the conclusion we draw from these tests is that while there
24
It is evident from the figures 1-6 that although commodity prices and exchange rates have been remarkably
correlated over the sample, the relationship notably breaks down over the past two years, especially for the U.S.
dollar cross rates. Thus, any out-of-sample test, particularly one that focuses on the last few years, is likely to lead
to fairly negative results. We acknowledge this, but given the striking correlation over the longer sample – far more
striking than for typical empirical exchange rate equations – we will focus here mainly on in-sample parameter
stability tests. The reader should interpret our results accordingly.
25
See Hansen (1992).
26
For Australian dollar against the non-dollar basket, there is similarly no evidence of parameter instability based
on both the Chow break point test and the Hansen test. However, both tests reject parameter stability for the
Australian-UK exchange rate, showing small and insignificant coefficient estimate before the break date and 0.65
(S.E. 0.25) after. Estimates for Canada remain negative and insignificant for the other two currencies. For New
Zealand, neither the Chow nor the Hansen test indicates parameter instability when the exchange rate is measured
against the other anchor currencies.
27
This particular version of the Hansen test does require stationary regressors, or else a different distributional
theory applies. So, these results are valid only under the assumption that our series are trend-stationary.
12
may have been some parameter shifts over time, the basic sign and magnitude of the coefficients
are notably stable for this kind of data.28
Table IVa: Parameter Stability Tests using Detrended Variables: Australia
Dependent Variable: Log of Real Exchange Rate, vs. U.S. Dollar
Detrended ln(Real Exchange Rate)t = α + dt + (β + γ*dt)* Detrended ln(Real Commodity Price)t + εt,
where dt = 1 if t ≥ Breakpoint; dt = 0 otherwise
Australia
Detrending Filter:
Linear
0.81*
Linear + Break
Dummy
0.74 *
Ln(Real Commodity Prices): β
0.58 *
HP + Break
Dummy
0.60 *
(0.12)
(0.17)
(0.12)
(0.15)
Dummy* Ln(Real Commodity
Prices): γ
Breakpoint tested
Hansen test 2
2
Adj. R
1
NA
HP
0.18
-0.05
(0.26)
(0.26)
1993Q1
NA
0.37
1993Q1
0.49 *
0.53
0.52
N Obs.
0.37
0.36
70
Sample Period
1984Q1 - 2001Q2
Note: * indicates significance at the 5% level. Newey-West heteroskedasticity and autocorrelation consistent
(HAC) standard errors in parentheses.
1. The breakpoint is the starting year for the use of formal inflation targets in the country.
2. The 5% asymptotic critical value for the Hansen individual parameter test is 0.47 (see Hansen 1992, Table 1).
28
Given this conclusion, it is natural to examine the out-of-sample performance of this apparent correlation,
especially for Australia and New Zealand. Comparing the root mean square errors (RMSEs) of various commodity
price-augmented exchange rate specifications against the RW, we do not observe significant out-of-sample gain.
This is likely due to the divergent of exchange rate and commodity price series in the past 2 years, as evident in
Figures 1-6.
13
Table IVb: Parameter Stability Tests using Detrended Variables: Canada
Dependent Variable: Log of Real Exchange Rate, vs. U.S. Dollar
Detrended ln(Real Exchange Rate)t = α + dt + (β + γ*dt)* Detrended ln(Real Commodity Price)t + εt,
where dt = 1 if t ≥ Breakpoint; dt = 0 otherwise
Canada
Detrending Filter:
Ln(Real Commodity Prices): β
Linear
HP
HP + Break Dummy
0.21
Linear + Break
Dummy
0.38 *
0.09
0.13
(0.15)
(0.16)
(0.07)
(0.09)
Dummy* Ln(Real Commodity
-0.60 *
-0.09
Prices): γ
(0.29)
(0.13)
Breakpoint tested 1
Hansen test
NA
1991Q1
NA
0.49 *
2
Adj. R
1991Q1
0.38
0.05
0.14
0.03
N Obs.
0.02
114
Sample Period
1973Q1 - 2001Q2
Table IVc: Parameter Stability Tests using Detrended Variables: New Zealand
New Zealand
Detrending Filter:
Ln(Real Commodity Prices): β
Linear
HP
HP + Break Dummy
1.10
Linear + Break
Dummy
2.13 *
0.72
1.23 *
(0.32)
(0.38)
(0.20)
(0.45)
Dummy* Ln(Real Commodity
-1.14 *
-0.66
Prices): γ
(0.50)
(0.50)
Breakpoint tested 1
NA
Hansen test
0.39
2
Adj. R
1990Q1
NA
1990Q1
0.47
0.27
0.37
N Obs.
0.25
0.26
62
Sample Period
1986Q1 - 2001Q2
Note: * indicates significance at the 5% level. Newey-West heteroskedasticity and autocorrelation consistent
(HAC) standard errors in parentheses.
1. The breakpoint is the starting year for the use of formal inflation targets in the country.
2. The 5% asymptotic critical value for the Hansen individual parameter test is 0.47 (see Hansen 1992, Table 1).
14
4. Endogeneity and Instrumental Variables
Although we have treated the commodity export prices as exogenous in the analysis
above, we consider here two possible channels of endogeneity that could bias our estimates.
First of all, as alluded to earlier, certain omitted variables related to cycles and shocks in the
United States, or even the global economy, might affect both the exchange rate and the
commodity markets independently. For example, a boom in the U.S. economy is likely to affect
all dollar cross rates as well as the world price of the commodities Australia exports.29 However,
it seems unlikely that the Australian cross rates against the British pound or a broad set of
currencies would be similarly affected in response to events in the U.S. economy, generating the
similar coefficient estimates we observe. A broad boom affecting all industrial countries (except
Australia) would also drive up commodity prices, of course, and might exert an independent
effect on the exchange rate. We note, however, that most models would predict that the
independent effect would tend to depreciate rather than appreciate the Australian currency, so
the fact that our coefficient estimates are consistently positive tends to mitigate against this
source of bias.30
Another source of endogeneity can operate through the significant market power these
countries exert in certain commodity markets. As mentioned above, New Zealand controls a
near majority of the global sheep market. As such, the world sheep price may be set or
significantly influenced by New Zealand’s exchange rate value. To address this potential form of
endogeneity, we use the world price index of all non-energy commodities, each weighted by
their global export earning shares, as an instrument for the country-specific, production-weighted
commodity price index.31
Table V compares the results of single-variable GMM-IV regressions with their OLS
counterparts. We employ a GMM procedure to optimally weight the orthogonality conditions
29
See Borensztein and Reinhart (1994)
Although the Canadian dollar regressions occasionally show negative significant estimates, in the most cases the
coefficient is insignificantly different from zero. We don’t observe any consistent pattern in the Canadian analysis.
31
We want to reiterate the point that despite having significant market power in a few commodities, these three
countries are relatively small in the overall global commodity market. In 1999, for example, Australia represents
less than 5 percent of the total world commodity exports, Canada about 9 percent, and New Zealand 1 percent. (For
non-energy commodities only: the shares are 6.7%, 10%, and 1.6% respectively.)
30
15
and automatically correct the standard errors for serial correlation. As we have nine domesticanchor currencies combinations, we report three representative results in Table V. (We note that
while the unreported results for Australia and New Zealand are similar to the ones in the table,
the other Canadian results are all insignificantly different from zero, unlike one reported here
under the IV specification.) As evident from the table, the world commodity price series works
well as an instrument for the country specific commodity prices, and the IV estimations
corroborate the least-squares findings. Namely, for Australia and New Zealand, world
commodity price movements are associated with large and significant real exchange rate
responses, while the effects are much smaller and mostly insignificant for Canada.
Table V: Representative Univariate Regressions with Instrumental Variables
Dependent Variable: Log Real Exchange Rate
ln(Real Exchange Rate)t = α + β*t + γ*ln(Real Commodity Price)t + εt
Australian vs. U.S. Dollar
Ln(Real Comm
0.81 *
GMM IV1:
World
Commodity Price2
0.90 *
Price)
(0.12)
(0.17)
OLS
OLS: Adj. R2
IV: 1st Stage R2
N Obs.
Sample Period
0.57
Canadian Dollar vs. NonDollar Basket
OLS
GMM IV:
World
Commodity Price
-0.31
-0.69 *
New Zealand Dollar vs.
British Pound
OLS
GMM IV:
World
Commodity Price
1.25 *
1.97 *
(0.21)
(0.24)
(0.23)
0.46
0.55
0.91
0.89
70
1984Q1 – 2001Q2
(0.40)
0.79
85
1980Q1 – 2001Q1
62
3
1986Q1 – 2001Q2
Note: * indicates significance at the 5% level. Newey-West heteroskedasticity and autocorrelation consistent
(HAC) standard errors in parentheses.
1.
Instrumental variable estimations are performed under 2SLS with GMM standard errors, using Bartlett kernel
and variable Newey-West bandwidth.
2.
The world commodity price index of all commodities is used as an instrument for the country-specific
commodity price in the IV specifications. The world price index is the “non-fuel primary commodity price
index” from the IMF. It consists of the US dollar prices of about 40 globally traded commodities, each
weighted by their 1987-98 average world export earnings.
3.
The Canadian sample here is limited to 1980Q1 to 2001Q1, the period over which world commodity price data
is available.
16
5. Solving the Puzzle?
Dornbusch’s (1976) overshooting monetary model seemed to broadly fit the facts for the
1970s and the early 1980s. However, as inflation gradually stabilized in major OECD countries
over the ensuing period, it became clear that monetary instability alone could not possibly
explain the persistent volatility in the exchange rates that remains even to this date. The failing
of the monetary models is further resonated in the related purchasing power parity (PPP) puzzle.
Solving the purchasing power parity (PPP) puzzle entails reconciling the extremely slow rate at
which deviations from PPP seem to die out (half life of 3-4 years), with the enormous observed
short-term volatility in the real exchange rates.32 Conventional shocks to the real economy, such
as taste or technology shocks, while capable of generating the observed slow adjustment, are
simply not volatile enough to account for the short-term variation in the exchange rates.
Monetary or financial shocks, on the other hand, may help explain this short-term volatility, but
the long half-lives of the shocks are simply incompatible with long-run monetary neutrality.
After all, nominal rigidities, through which monetary shocks can temporarily impact the real
economy, are believed to fully adjust within a much shorter time span (1-2 years). Therefore, a
potential solution to this puzzle, it seems, lies in finding a real shock that is sufficiently volatile.
The success of our univariate regressions suggests that commodity prices may be this
missing shock. In this section, we explore whether the Dornbusch-type monetary models would
work better in these rare country cases where certain real shocks are observable and can be
substantially controlled for.33 We approach this first by including commodity prices into the
standard monetary-type regressions. We then look at whether their inclusion can sufficiently
remove the persistence in the data in order for monetary factors to play a role. Finally, we look
at the interaction of these variables in a VAR setup.
5.1. The Augmented Monetary Model
We do not propose any particular structural identification framework here, but aim to
explore how the inclusion of commodity prices affects the role certain macroeconomic variables
32
See Rogoff (1996) for a full account of the PPP puzzle.
17
play in real exchange rate estimations.34 Specifically, we consider the following regression,
focusing on real output differentials and real interest differentials between home and the anchor
country,35
ln(Real Exchange Rate)t = α + β*t + γ1*ln(Real Commodity Price)t + γ2* (Real Interest
Differential)t + γ3*(Real Output Differential)t + εt
Again, we face possible endogeneity problem in the above contemporaneous
specification. To address it, we use the world price index of all commodities to instrument for
country-specific commodity prices, as explained earlier in Section 4. For the other
contemporaneous regressors, we resort to notably cruder options – the one period lagged output
and interest rate – as instruments.36 The regression results for the three national currencies
against the British pound are reported in tables VIa-c below. We first note that even with the
inclusion of these macro variables, the exchange rate-commodity price connection remains a
strong “Down Under” phenomenon. However, even for these countries, commodity prices
appear no Deus ex Machina. While it shows some promise in the Australian regressions by
bringing out the output differentials, no significant results are found when the cross-currency is
the U.S. dollar (Table VId), as in the case for New Zealand. These estimates seem only to
corroborate further the “fickleness” of the monetary-type models documented extensively in the
literature, and do not provide much evidence in favor of an augmented-Dornbusch type model.
33
While there have been previous efforts to incorporate terms of trade shocks into empirical exchange rate
estimations of major currencies, sluggish nominal price adjustments and minimal pass-throughs typically make
proper identification close to impossible.
34
See, for example, Obstfeld and Rogoff (1996) ch. 9, for structural models supporting such monetary-type
regression specifications and their variants.
35
Real interest rate is measured by three-month Treasury bill rates adjusted by annualized quarter-by-quarter CPI
inflation.
36
Lag real interest rate is an especially weak instrument, and mechanically does not always work well in all
combinations of country vs. anchor currency regressions. Here we present a few examples where they do provide
sensible results, despite the notably larger standard errors. We do not pretend the IV specification provides the
correct identification, and therefore present the VAR analysis in the next section to better capture the dynamic
interactions among these variables.
18
Table VIa : Specifications with Macro Variables: Australian Dollar vs. British Pound
Dependent Variable: Log Real Exchange Rate, vs. British Pound
ln(Real Exchange Rate)t = α + β*t + γ1*ln(Real Commodity Price)t + γ2* (Real Interest Differential)t +
γ3*(Real Output Differential)t + εt
Australia
Australian Dollar
vs. British Pound
(1) OLS:
Basic Monetary
(2) OLS:
4 Variable Baseline
(3) GMM IV 1:
Lagged Macro Vars
(4) GMM IV:
World Comm. Price &
Lagged Macro Vars
Ln(Real
0.65 *
1.05 *
Commodity Prices)
(0.17)
(0.26)
Real Interest
0.79 *
0.45
-1.32
0.16
Differential
(0.26)
(0.28)
(1.87)
(1.06)
Real Output
0.11
3.25 *
-1.05
5.51 *
Differential
(1.08)
(1.26)
(1.35)
(1.84)
0.50
0.62
2
Adj. R
N Obs.
69
Sample Period
1984Q1 – 2001Q1
Table VIb: Specifications with Macro Variables: Canadian Dollar vs. British Pound
Canada
Canadian Dollar
vs. British Pound
(1) OLS:
Basic Monetary
(2) OLS:
4 Variable Baseline
(3) GMM IV 1:
Lagged Macro Vars
(4) GMM IV:
World Comm. Price &
Lagged Macro Vars
Ln(Real
-0.41
-0.49
Commodity Prices)
(0.32)
(0.34)
Real Interest
-0.04
0.23
1.58
-0.92
Differential
(0.31)
(0.34)
(2.92)
(1.63)
Real Output
-0.17
-0.42
0.58
0.43
Differential
(1.45)
(1.27)
(2.02)
(1.17)
0.31
0.36
2
Adj. R
N Obs.
85
Sample Period
1980Q1 – 2001Q1
Note: * indicates significance at the 5% level. Newey-West heteroskedasticity and autocorrelation consistent
(HAC) standard errors in parentheses.
Instrumental variable estimations are performed under 2SLS with GMM standard errors, using Bartlett kernel and
variable Newey-West bandwidth.
19
Table VIc: Specifications with Macro Variables: New Zealand Dollar vs. British Pound
Dependent Variable: Log Real Exchange Rate, vs. British Pound
ln(Real Exchange Rate)t = α + β*t + γ1*ln(Real Commodity Price)t + γ2* (Real Interest Differential)t +
γ3*(Real Output Differential)t + εt
New Zealand
New Zealand
Dollar vs. British
Pound
(1) OLS:
Basic Monetary
(2) OLS:
4 Variable Baseline
(3) GMM IV 1:
Lagged Macro Vars
(4) GMM IV:
World Comm. Price &
Lagged Macro Vars
Ln(Real
1.29 *
1.82 *
Commodity Prices)
(0.24)
(0.50)
Real Interest
0.61 *
0.21
-4.89
-0.22
Differential
(0.28)
(0.16)
(7.98)
(1.23)
Real Output
-0.14
-0.52
-2.77
-1.20
Differential
(0.60)
(0.41)
(5.14)
(0.96)
0.23
0.58
2
Adj. R
N Obs.
60
Sample Period
1986Q1 – 2001Q1
Table VId : Specifications with Macro Variables: Australian Dollar vs. U.S. Dollar
Australia
Australian Dollar
vs. U.S. Dollar
(1) OLS:
Basic Monetary
(2) OLS:
4 Variable Baseline
(3) GMM IV 1:
Lagged Macro Vars
(4) GMM IV:
World Comm. Price &
Lagged Macro Vars
Ln(Real
0.72 *
0.66 *
Commodity Prices)
(0.09)
(0.22)
Real Interest
1.98 *
1.37 *
8.10 *
5.96
Differential
(0.34)
(0.28)
(4.05)
(3.59)
Real Output
1.41
-0.36
0.85
-0.52
Differential
(2.42)
(1.49)
(4.39)
(2.51)
0.26
0.65
Adj. R2
N Obs.
69
Sample Period
1984Q1 – 2001Q1
Note: * indicates significance at the 5% level. Newey-West heteroskedasticity and autocorrelation consistent
(HAC) standard errors in parentheses.
Instrumental variable estimations are performed under 2SLS with GMM standard errors, using Bartlett kernel and
variable Newey-West bandwidth.
20
5.2. “The Nagging Persistence”
Although commodity prices appear quite important in the exchange rate equations for
these commodity economies, the above results suggest little evidence that their introduction can
otherwise resuscitate the monetary approach to the exchange rate, at least from an empirical
perspective. This section looks further at why the monetary fundamentals in the Dornbusch
model may indeed be powerless in explaining the remaining variation in our augmented
exchange rate equations.
In the analysis below, we assume that real exchange rate shocks follow an AR(1) process
and focus on the magnitude of this serial correlation.37 While we recognize that our small
sample sizes may preclude very precise estimates of the autocorrelation coefficients, the analysis
nevertheless provides meaningful insight to the nature of the “puzzle” at hand. The AR(1)
columns in Table VII below demonstrate the persistence side of the PPP puzzle for the three
commodity currencies. We note that the estimated serial correlation of the residuals appear
broadly similar to what we see in the PPP literature, indicating half-lives much longer than what
monetary factors can explain.38
Having established the PPP puzzle in our specific currencies, we then control for the
effects of commodity prices, and further instrument them with the world commodity price index
to address potential endogeneity. The next two columns in Table VII report the results. As
evident from the AR(1) root estimates, after controlling for one major source of real shocks –
commodity price shocks- the residuals still exhibit a generally similar degree of persistence as
before! These implied half-lives are far longer than one can justify if the main source of the
remaining shocks is monetary. Therefore, it is no surprise that the performance of our
commodity price augmented Dornbusch-type equations is mixed at best. Furthermore, while we
have peeled off one layer of the empirical exchange rate mystery by providing one explanation
for the exchange rate movements in these commodity currencies, we find ourselves staring at the
same PPP puzzle yet again.
37
See Froot and Rogoff (1995) and Rogoff (1996) for discussions of previous literature using this specification and
other variants.
21
Table VII: Persistence in the Real Exchange Rates
Dependent Variable: Log of Real Exchange Rate, vs. U.S. Dollar
Australia
AR(1) +
AR(1)
1
Comm
Price 2
Canada
AR(1)
+ IV
3
AR(1) +
AR(1)
Comm
Price
New Zealand
AR(1) +
IV
AR(1) +
AR(1)
Comm
Price
AR(1) +
IV
Ln(Real
0.54 *
0.97 *
0.04
-0.27
0.51 *
0.72 *
Comm Prices)
(0.14)
(0.35)
(0.08)
(0.16)
(0.21)
(0.35)
0.94 *
0.88 *
0.84 *
0.97 *
0.96 *
0.97 *
0.92 *
0.95 *
0.95 *
(0.04)
(0.05)
(0.08)
(0.03)
(0.03)
(0.03)
(0.04)
(0.05)
(0.06)
2.03
2.15
2.06
1.98
2.01
1.67
2.03
1.99
1.92
0.84
0.86
0.95
0.95
0.90
0.90
AR(1) root
DurbinWatson stat
Adj. R2
1st Stage R2
Sample Period
0.94
0.89
0.92
70
86
62
1984Q1 - 2001Q2
1980Q1 - 2001Q2
1986Q1 - 2001Q2
Note: * indicates significance at the 5% level.
1.
ln(Real Exchange Rate)t = α + β*t + εt, where εt follows an AR(1)
2.
ln(Real Exchange Rate)t = α + β*t + γ*ln(Real Commodity Price)t + εt, where εt follows an AR(1)
3. ln(Real Exchange Rate)t = α + β*t + γ*ln(Real Commodity Price)t + εt, where εt follows an AR(1) and
ln(World Commodity Price Index) is used as an IV
5.3. Vector Autoregressions
Despite the failure of the single equation specifications, we look at the dynamic
interactions of these variables in a VAR set up. As demonstrated in the Appendix, the effects of
commodity price shocks on the exchange rate can be extremely long lasting, if not quite
permanent. In the canonical Dornbusch (1976) sticky-price model where the exchange rate does
not enter the deflator for real balances, a permanent shock to the steady state terms of trade leads
to an immediate and permanent adjustment of the exchange rate. VARs provide a natural
38
See Froot and Rogoff (1995) for a comprehensive survey of the estimated half-lives for PPP deviations.
22
framework to capture richer dynamics in a multivariable setting.39 As can be seen below, the
results, via both impulse responses and variance decompositions, provide further support for the
relevance of commodity prices in understanding real exchange rate behavior in these economies.
In a 4-variable VAR setup, we examine the dynamic interactions among the Australian-US dollar
real exchange rate, the world price index of Australia’s major commodities, and the real output
and interest differentials between Australian and the United States. Each of these variables
enters the VAR with one lag, which is optimally selected based on the Schwarz information
criterion.
To orthogonalize the shocks in the VAR, a simple Cholesky decomposition is used.
Consistent with our view that world commodity prices are exogenous to events in the home
small open economy, log of real commodity price is ordered first, followed by real output
differential, real interest differential, and the log of real exchange rate.40 The impulse responses
in Figure 7 clearly show the long-lasting effect real commodity price shocks have on the real
exchange rates.41 A one standard deviation shock takes, for example, over 80 quarters (20 years)
to fully die out. Interest differentials, on the other hand, do not have much impact on the real
exchange rate. The same impression is conveyed by the forecast error variance decomposition,
shown in Table VII below. Here we observe the short- and long-term relative relevance of
individual shocks in affecting the volatility of the real exchange rate. Again, commodity prices
clearly play a consequential role.
The VAR results are broadly supportive of our empirical estimating equation, in which
we implicitly assume that the impact of commodity price shocks is the dominant effect.
However, they also suggest that further research, allowing for richer intrinsic and extrinsic
dynamics, is warranted.
39
In this section, the VARs are set up under the assumption that all series are stationary. No detrending is done on
the data, allowing the VAR to more closely mimic the true data-generating process.
40
The results are not sensitive to the order of real interest differentials and real output differentials.
41
Impulse responses for other variables as well as other country-currency pairs are available upon request.
23
Table VII. Variance Decompositions from 4-Variable VAR
Ordered as ln(Com. P), dY, dR, ln(Q)
1.
Forecast
Forecast
Horizon
Standard
(Quarters)
Error
1
0.034
9.0
0.1
3.6
87.3
4
0.066
18.6
6.6
2.6
72.2
8
0.093
29.1
17.9
1.7
51.3
12
0.112
35.8
20.9
1.5
41.9
16
0.128
39.8
19.6
1.5
39.2
20 1
0.141
41.6
18.3
1.5
38.5
Variance Decomposition for Log Real Exchange Rate
(Percentage Points)
log (Real
Real Output
Real Interest
log (Real
Commodity Price)
Differential
Differential
Exchange Rate)
The evolution of the distribution of variances begins to stabilize roughly at period 20 (5 years).
6. Conclusion
The world real prices of commodity exports do appear to have a strong and relatively
stable influence on the real exchange rates of New Zealand and Australia. For Canada, the
relationship is somewhat less robust, especially to detrending. Thus, despite the fact that these
countries had open capital markets and floating exchange rates over the sample period, one can
identify an important real explanatory variable. Moreover, the quantitative size of the coefficient
is broadly consistent with the predictions of standard theoretical models of optimal monetary
policy. Though perhaps relatively modest, this is a significant result in a literature largely
populated by negative findings.
One might hope that, by being able to control for a major source of real shocks, standard
exchange rate equations - adjusted for commodity price shocks - might perform better for "the
commodity currencies" than they have been found to perform for the major currencies.
Unfortunately, our results do not offer very strong encouragement for this point of view. The
performance of our commodity price augmented Dornbusch-type equations is mixed at best,
corroborating the well-known unreliability of such models. In addition, the substantial
persistence that remains in the commodity price-adjusted exchange rates left us facing the same
24
PPP puzzle again, where neither standard monetary nor real shocks seems suitable for explaining
the remaining variations that is both so volatile and persistent.
Nevertheless, one may view the glass as half full rather than half empty; at least
something works! Moreover, the findings here may be of more general interest. Although
Australia, Canada and New Zealand are fairly unique among OECD countries, commodity price
shocks (both export and import) have long been recognized as of great importance to many
developing countries. Thus exchange rate equations for many such currencies may hold more
promise than for cross exchange rates among the major currencies.
25
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small open economies, IMF Working Paper WP/00/141.
27
Appendix: A Structural Interpretation of the Coefficients
Given the remarkable consistency in the estimated sign and size of the elasticity of the
real exchange rate with respect to real commodity prices, it is worth briefly considering the
predictions of a simple theoretical model. Consider the following extension of the version of the
Belassa-Samuelson model exposited in Obstfeld and Rogoff (1996, ch. 4). Suppose Home
agents consume three goods, nontraded goods, exports and imports, but only produce the first
two. Assume that labor is perfectly mobile across industries, and that physical capital can be
freely imported from abroad at real interest rate r, measured in importables. The production
function for the exportables is
yX = AXf(kX),
where y and k are output and capital per unit labor, and
yN = ANf(kN),
is the analogous function for nontraded goods production. Let px be the world price of
exportables, which is given exogenously to the small country, and let pN be the home price of
nontradables, both measured in terms of importables. Then, assuming that labor mobility leads
to a common wage across the two home industries, and following steps analogous to pages 205206 in Obstfeld and Rogoff, one can derive the approximate relation:
µ  $
$
p$ N =  LN  (A
+ p$ X ) − A
N
 µ LX  X
where a “hat” above a variable represents logarithmic derivatives, and 6LN and 6LX are the
labor’s income share in the nontraded and export goods sectors, respectively. Thus, the effects
of a rise in the relative price of exportables is the same as a rise in traded goods productivity in
the standard Belassa-Samuelson model. If 6LN = 6LX, a rise in the price of exportables leads to a
proportional rise in the price of nontraded goods. The impact on the real exchange rate depends,
of course, on the utility function. Assume a simple logarithmic (unit-elastic) utility function:
U = CN) CI* CX(1-)-*)
28
and normalizing the price of importables to one, the consumption-based consumer price index is
then given by
pN)pX(1-)-*)
Therefore, as p$ N moves proportionately in response to p$ X , the effect of an export price shock
on the utility-based real CPI is then given by
p$ X
(1-*)
Assuming that importables account for 25% of consumption, then the elasticity of the CPI with
respect to a unit change in the price of exportables would then be 0.75, which is broadly
consistent with our estimated coefficients. (If 6LN > 6LX – it is standard to assume that nontraded
goods production is labor intensive -- one gets a larger effect).
What if the price of nontraded goods is sticky? Than a simple model of optimal
monetary policy would predict that the exchange rate should be adjusted one for one with
changes in the world price of exportables, in order to accommodate the requisite rise in the
relative price of nontradable goods. (This assumes that export prices are flexible with complete
pass-through, as otherwise a larger change in the exchange rate would be needed.) Of course, if
the central bank is mechanically trying to stabilize CPI inflation, and if its rule does not allow
any offset for export price shocks, then the authorities would not allow the nominal exchange
rate to move by the amount required to mimic the flexible-price equilibrium, but instead only by
a smaller amount.
We have only offered one model, but many others can give parallel results. For example,
the classic model of Dornbusch (1976) would also prescribe a one-for-one movement of the
exchange rate in response to terms of trade shocks, in order to mimic the real allocation of the
flexible price equilibrium. Whereas we have no illusions that the simple model presented here
fully describes the data, it still provides a useful benchmark for assessing the estimated
coefficients.
29
Data Appendix:
Exchange Rates:
-
End of period quarterly nominal exchange rates are taken from IMF’s International Financial
Statistics (IFS) and Global Financial Database for 1973Q1 to 2001Q2. Real exchange rates
are nominal rates adjusted by the CPI ratios. To construct the real rates against the nondollar basket, we use the broad (real) index published by the Federal Reserve to adjust the
country real rates against the U.S. dollar. The broad index measures the foreign exchange
value of the U.S. dollar against the currencies of a large group of U.S. trading partner.
CPI and Real Output:
-
Quarterly consumer prices and GDP volume (1995 = 100) are taken from the IFS. Inflation
rates are calculated as annualized quarterly changes of the CPI.
Short Term Interest Rates:
-
We use three-month Treasury bill rates as a measure of short-term interest rate. The sources
are IFS and Global Financial Database. The real rates are the nominal rates adjusted for
expected inflation, which we proxy with lagged inflation rate, calculated as the annualized
quarterly change of the CPI from the previous quarter.
Commodity Prices:
-
The country specific commodity export price index is constructed by geometrically
weighting the world market prices in U.S. dollar of each country’s major non-energy
commodity exports. The weights, taken from Djoudad, Murray, Chan, and Daw (2000),
represent the average production value of the commodity over the 1982-90 period and are
listed in Table A. The following commodities from the original Djoudad et al indices are
excluded, as we were unable to update the price series. Their original weights in the relevant
countries are in the parentheses: barley (2.4% in Australia, 1.8% in Canada), sulphur (1.4%
in Canada), cod (0.01% in Canada), lobster (0.5% in Canada), and salmon (0.6% in Canada).
-
The world price index of all non-energy commodities is the “non-fuel primary commodity
price index” of the IMF. It comprises the U.S. dollar prices of about 40 globally traded
commodities, each weighted by their 1987-98 average world export earnings.
30
-
The world market price of individual commodities is taken from various sources (see Table
A). They are quarterly average spot or cash prices in U.S. dollars. The commodities in
general are traded in different markets, including NYMEX, IPE, CBT, CME, KCB, ASX and
SFE, and the prices are considered "world prices".
A. Composition of Non-Energy Commodity Price Index
World Market Price in U.S. Dollar
Australia
Canada
New Zealand
1983Q1 – 2001Q2
1972Q1 - 2001Q2
1986Q1 - 2001Q2
Product
Wt.
Source
Aluminum
9.1%
IMF
Beef
9.2%
Copper
Product
Wt.
Source
Aluminum
4.8%
BOC
IMF
Beef
9.8%
3.2%
BOC
Canola
Cotton
3.4%
IMF
Gold
19.9%
Iron Ore
Wt.
Source
Aluminum
8.3%
ANZ
GFD
Apples
3.1%
ANZ
2.1%
BOC
Beef
9.4%
ANZ
Copper
4.7%
BOC
Butter
6.5%
ANZ
IMF
Corn
1.3%
BOC
Casein
6.7%
ANZ
10.9%
IMF
Gold
4.5%
GFD
Cheese
8.3%
ANZ
Lead
1.3%
IMF
Hogs
5.1%
GFD
Fish
6.7%
ANZ
Nickel
2.6%
BOC
Lumber
14.4%
IMF
Kiwi
3.7%
ANZ
Rice
0.8%
IMF
Newsprint
13.4%
IMF
Lamb
12.5%
ANZ
Sugar
5.9%
GFD
Nickel
3.9%
BOC
Logs
3.5%
ANZ
Wheat
13.5%
BOC
Potash
2.1%
IMF
Pulp
3.1%
ANZ
Wool
18.3%
ANZ +
Pulp
19.7%
IMF
Sawn
4.6%
ANZ
IMF
Zinc
1.8%
BOC
Product
Timber
Silver
0.9%
GFD
Skim MP
3.7%
ANZ
Wheat
8.9%
BOC
Skins
1.6%
ANZ
Zinc
4.4%
BOC
Wholemeal
10.6%
ANZ
7.7%
ANZ
MP
Wool
Note: BOC (Bank of Canada); ANZ (Australia-New Zealand Bank); GFD (Global Financial Database)
31
Impulse Responses of Australian - US Real Exchange Rate
Response of log(Real Exchange Rate)
to log(Real Comm. Price)
Response of log(Real Exchange Rate)
to Real Output Differential
.05
.05
.04
.04
.03
.03
.02
.02
.01
.01
.00
.00
-.01
-.01
-.02
-.02
25
50
75
100
25
Response of log(Real Exchange Rate)
to Real Interest Differential
50
75
100
Response of log(Real Exchange Rate)
to log(Real Exchange Rate)
.05
.05
.04
.04
.03
.03
.02
.02
.01
.01
.00
.00
-.01
-.01
-.02
-.02
25
50
75
100
25
50
75
100