Futures beacon:
Can commodity futures and interest rate expectations
help predict the value of the Canadian dollar?*
By Robert Lafrance and Loyal Chow
International Department
Bank of Canada
This version: 270508
Presented at the 2008 CEA Meetings, University of British Columbia, Vancouver, June 7.
The views expressed in this paper are those of the authors.
No responsibility for them should be attributed to the Bank of Canada.
.
ABSTRACT
While Canada has a free floating exchange rate regime and official intervention was abandoned in 1998,
monetary policy decisions take into account current and anticipated movements in the exchange rate to the
extent that they are deemed to affect aggregate demand and ultimately inflation. One instrument in
interpreting exchange rates movements is a reduced-form equation that links the Canada-US exchange rate
to lagged movements in commodity price and interest rate differentials. The exchange rate, however, as an
asset price also reflects expectations about future economic developments at home and abroad. Our paper
investigates the potential empirical contribution of relevant futures prices and market-based interest rate
expectations to explain and predict the short-run evolution of the bilateral exchange rate in order to
improve our interpretative framework of exchange rate movements.
*We have benefited from comments by our colleagues for which we are grateful.
e-mail contact: rlafrance@bankofcanada.ca
1
1. INTRODUCTION
This paper examines the value of using market expectations of fundamentals to explain the evolution of the
exchange rate, more specifically, the Canadian dollar. Our motivation is pragmatic. The Bank of Canada is
dedicated to maintaining an environment of low, stable, and predictable inflation. To this end, it has
adopted an inflation-targeting (IT) framework, and commensurably, a flexible exchange rate regime
(Macklem 2006). Given Canada’s openness to international trade and financial transactions, movements in
foreign prices and exchange rates can play an important part in shaping domestic inflation.1 Thus a better
understanding of what drives the exchange rate and how it is likely to evolve in the short to medium run is
crucial for the conduct of monetary policy.
Our paper follows a long tradition, going back over twenty years, in trying to encapsulate the forces
impinging on the Canadian dollar in a few key variables, notably commodity prices and the perceived
stance of Canadian monetary policy relative to that of Canada’s major trading partner, the United States
(Amano and van Norden 1993; Helliwell et al. 2005; Bailliu et al. 2007; Issa, Lafrance, and Murray 2008).2
The survival of this approach, in the face of the conventional wisdom post-Meese and Rogoff (1983) that
all empirical exchange rate models are no longer valid from the time they are published, is a testament to its
viability.
The Bank’s approach has also survived doubts raised about Canada’s membership in the commodity
currency club. For instance, Laidler and Aba (2001) note that the importance of commodity prices for the
exchange rate declined between the 1970s and the 1990s. Reinhart and Rogoff (2002) find limited
correspondence between commodity price and exchange rate movements for Canada. Chen and Rogoff
(2003) argue that the long-run relationship between commodity prices and the Canadian dollar may be due
to deterministic rather than stochastic trends and that there is relatively weak comovement in the short run.
Cashin, Cepésdes, and Sahay (2003) in testing for cointegration between commodity export prices and the
real exchange rate for 58 countries fail to find it for Canada (as well as New Zealand and Norway among
the industrialized countries). In contrast, our findings and those of our other Bank of Canada researchers
support the view that the evolution of the Canadian dollar in real terms has been greatly influence by the
cycles in real commodity prices.3
Recent research has suggested that exchange rates may be reflecting expectations about developments in
commodity prices. Chen, Rogoff, and Rossi (2008) argue, on the basis of Granger-causality tests that allow
for parameter instability, that the relationship between the exchange and commodity prices should be
1
At least in theory, in practice, it has been difficult to identify large exchange rate pass-through effects.
The seeds of this approach, inspired by the exchange rate literature that followed the oil price shocks of the 1970s,
were sown in Lafrance and Longworth (1987).
3
Lalonde et al (2008) provide an analysis in a multilateral setting, while Maier and DePratto (2008) underline the
growing importance of commodity prices, and notably energy prices, in influencing the Canadian dollar.
2
2
inverted: the former explaining or predicting the latter, in contrast to the Bank of Canada’s traditional view.
This is motivated by theory that sees the exchange rate, as the relative price of two monies or assets, as a
forward-looking variable.4 Engel and West (2005) interpret this basic postulate, and the oft-observed
statistical property of exchange rates as random walks (or very close approximations to random walks), as a
strong basis for arguing that an exchange rate represents long-term views of market participants on the
prospects of economic fundamentals that drive exchange rates.5 While accepting that exchange rates reflect
market perceptions about future fundamentals, we take the view that these perceptions are held for
relatively short horizons as new information and trades are constantly being evaluated by market
participants. Our maintained hypothesis is quite modest. We assume that changes in the Canada-U.S. real
exchange rate can be explained by its tendency to gravitate towards a long-run relationship with real
commodity prices, which are determined in world markets and are thus strictly exogenous,
contemporaneous changes in commodity futures, and expected changes in Canada-US short-term interest
rates. In this paper, we are looking at the merits of integrating available market information on commodity
futures and interest rate expectations to improve the current version of the Bank’s exchange rate equation
as described in Issa, Lafrance, and Murray (2008) or ILM. Our research question is: can commodity futures
and interest rate expectations help predict the value of the Canadian dollar?
Our findings show promise. Adding market expectations of commodity prices and interest rate changes
reduce the unexplained variance of the Canadian dollar in real terms beyond the ability of the Bank’s
traditional equation to do so.6 Meese-Rogoff tests indicate that the exchange rate equation is superior to a
random walk alternative in out-of-sample ex post forecasts. And dynamic simulations track the data more
closely in recent years by including commodity price futures as well as expectations of relative change in
short-term interest rates. Less positive are the findings that the exchange rate equation, with or without
additional expectation terms, is not particularly robust to historical sample variations. Section 2 outlines
our hypothesis, which is tested in section 3 and checked for robustness. The results and their implications
are summarized in the conclusion.
2. HYPOTHESIS
Ceteris paribus, for a commodity exporter, an increase in commodity prices determined on world markets
leads to an improvement in the current account, higher domestic income as wage rates are bid up to induce
labour to shift into the resource sector, and excess demand and inflation pressures as demand increases.
4
Certain studies have purported to find a reverse link as US dollar movements can affect specific commodities and
their future prices, notably in the case of coffee and cocoa (Jumah and Kunst 1999), and oil and related products
(Sadorsky 2000). Chen, Rogoff, and Rossi (2008) show that exchange rates predict world commodity prices, both inand out-of-sample, after taking account of parameter instability. An important consideration is that most commodities
are quoted in US dollar terms. Thus, a depreciation of the US dollar, ceteris paribus, reduces commodities in other local
currencies, boosting demand (and thus their prices in US dollars).
5
Nason and Rogers (2007) also show why exchange rates mimic a random walk by using the present value model of
exchange rate as an interpretative framework.
6
As commodity futures are determined in world markets (Chicago, New York and London), the presumption that they
can be considered as exogenous in our setting seems reasonable.
3
There is a presumption that this leads to an increase in the price of non-tradables, or a real exchange rate
appreciation, to restore internal balance. Depending on the perceived persistence of the shock, anticipated
wealth effects will further stimulate domestic demand and imports, offsetting part of the initial
appreciation. This mainstream view follows from numerous papers that explored these phenomena in the
wake of the oil shocks of the 1970s. A representative sample includes Bruno (1982), Buiter and Purvis
(1982), Corden (1984), and Neary (1988).
Amano and van Norden (1995), or AvN, base their pioneering empirical study of the Canadian dollar on
Neary’s analysis.7 Neary considers the case of a small open economy that produces a variety of traded and
non-traded goods under competitive conditions and examines the required adjustment in the real exchange
rate to re-equilibrate the current account following a terms-of-trade shock. His insight is that the effect is a
priori undetermined as it depends on its net effect on the excess demand for non-traded goods, and thus on
the nexus of demand and supply elasticities. Amano and van Norden find that the Canada’s terms-of-trade
need to be decomposed to get a stable relationship with the real exchange rate. Their analysis points to the
need to treat energy related resources differently from other commodities, such as forestry products,
minerals, and agricultural goods. Subsequent work has followed in this vein.
More recently, Issa, Lafrance, and Murray (2008), or ILM, fine-tune the AvN analysis by showing that a
structural break occurred in the effect of energy prices on the Canadian dollar in the early nineties. They
argue that market distortions created by supply management policies, notably the National Energy Policy in
1980 might explain why higher energy prices were not translated into a Canadian dollar appreciation prior
to early 1990s. With the end of the National Energy Policy in 1985, the implementation of the Canada-US
Free Trade Agreement in 1989 (with Mexico joining in 1993), the loosening of Canadian ownership
restrictions in the oil and gas sector in 1992, and other measures designed to support the development of the
Alberta oil sands in 1993, the way was paved for Canada to become a “petro-currency”. This has been
reflected in an estimated positive relationship between the Canadian dollar and energy as well as nonenergy prices since 1993Q3.
7
In parallel fashion, researchers in Australia were linking their exchange rate to commodity prices (Blunndell-Wignall
and Gregory 1989; Gruen and Wilkinson 1994; Freebairn 2002). Gruen and Kortian (1996) show that the Australian
dollar is predictable over the medium term (4 to 8 quarters ahead) and that a lack of depth in the exchange market for
the Australian dollar leads to excess returns that are not exploited. Kears (2007) argues that commodity futures have
predictive power in Australia’s case but uncertainty about monetary policy actions limits the predictive content of
exchange rate futures, even though the Australian dollar is a commodity currency.
4
Table 1 – The AvN/ILM real exchange rate equation
(1)
(2)
qt = pt − pt* − et
qt = β ′xt
∆qt = α (qt −1 − β ′xt −1 ) + χ ′zt + v,
(3)
Where:
q: real exchange rate; e: nominal exchange rate
p: Canadian aggregate prices (CPI); p*: US aggregate prices (CPI)
xt: a vector of long-run fundamentals and a constant term; zt: a vector of short-run determinants
vt: stochastic error term
The real exchange rate is defined in bilateral terms (equation 1), which is deemed to be sufficient given the
dominance of the US economy in Canada’s international trade and financial transactions.8 The real
exchange rate is posited to have a long-run relationship (equation 2) with commodity prices (distinguishing
between energy and non-energy commodities). This has been repeatedly established in previous work. As
shown in Amano and van Norden and Issa, Murray, and Lafrance, the time series of the real exchange rate
and real commodity prices split into energy and non-energy components are integrated of order one and
cointegrated.9 Commodity prices are also assumed to be exogenous to the real exchange rate as they
represent a broad range of commodities whose prices are mainly determined in world markets.
The estimated equation is given by (3). The short-run dynamics are kept to a minimum. In the ILM
equation, only the interest rate differential is considered.10 While the ILM equation gives a fair account of
the dollar’s evolution (see Chart 4b), its specification does not embody the expectations of economic agents
regarding the evolution of key macroeconomic variables as presumed in economic theory. The nature of
these variables depends on the approach that one favours to explain exchange rates, such as cross-country
differences in money demand and supply, portfolio balance choices and wealth allocation considerations,
terms-of-trade effects, differences in consumer preferences, cross-country productivity differentials,
consumption smoothing and long-run external indebtedness sustainability constraints, or combinations of
the above.
Engel and West (2005) are strong proponents of the forward-looking view. They show that, under certain
assumptions, exchange rates may reflect expectations of future economic fundamentals while exhibiting
random walk behavior. In their model, future fundamentals matter much more than current fundamentals
when the discount factor is close to one. For large values of the discount factor, the log of the exchange rate
8
The specification ignores the structural break introduced by ILM as the market expectations data that we use are only
available as time series from 1996 onward.
9
As this paper, while using higher frequency data (weekly or monthly averages), covers a short period (post 1996) and
cointegration relationships are best established over a long time span, we will take these results as given. The evidence
in favour of cointegration is less clear in Issa, Lafrance, and Murray, however.
10
To avoid apprehended simultaneity problems, the differential is lagged one period in the estimation. Note that
changes in spot commodity prices (not reported here) were found to be not significant when estimated.
5
is approximately a random walk, irrespective of the underlying model. Engel, Mark, and West (2007) build
on this foundation to argue that exchange rate models have empirical validity. They show that exchange
rates incorporate news about future fundamentals as the models imply and that the out-of-sample
forecasting power of models can be enhanced by using panel estimation and long-run horizon forecasts.
Our perspective is different. Market participants in exchange markets are likely to have limited confidence
in their long-run expectations and are more prone to re-assess their positions on the basis of near-term
developments. Thus, our focus is on exploiting market data on expectations of commodity price and
relative interest rate developments to improve our understanding of the evolution of the Canadian dollar.
We prefer to use market-based data rather than survey data because markets synthesize a broad set of
opinions, and market data are more timely and easier to track. For the purposes of this analysis, we have
constructed future price proxies for energy and non-energy commodity prices as traded on the NYMEX in
New York or the London Metal Exchange. These futures cover only a sub-sample of the commodities
tracked by the Bank of Canada’s two commodity price indices. We assume that they are representative.11
We constructed futures indices for energy and non-energy commodities by weighting the available futures
on the same basis as in the Bank’s indices, and renormalized to one. Data definitions and sources are
reported in the Appendix.
3. EMPIRICS
Our preliminary findings fall under four sub-headings. First, commodity price futures play a role in
predicting exchange rate movements, but it is a small one. At the monthly (and weekly) frequencies that we
examine, most of the variation in the real exchange rate remains unexplained, and the marginal effect of
commodities futures has an elasticity of less than 0.1. Second, the exchange rate equation is not particularly
robust to sample changes. Expanding rolling regressions (as well as fixed-window rolling regressions
which are not reported here) indicate that parameter stability and significance is somewhat fragile to the
sample used for the estimation. While this instability may reflect the difficulty in pinning down an error
correction formulation with short sample periods, it might also warn us that our specification is too
parsimonious to capture the dynamics of the exchange market since the mid-1990s. Third, on a more
positive note, the exchange rate equation passes the simple Meese-Rogoff out-of-sample predictability test,
showing that the fundamentals add, in principle, some forecasting value. Fourth, the fairly wide confidence
intervals of the adjustment parameter of the error correction process suggests that the underlying assumed
cointegration between real commodity prices and the real exchange rate requires additional validation. The
estimates at various frequencies also confirm that the adjustment process is a relatively slow one, though
time aggregation bias may be playing a role at lower frequencies.
11
The correlations of changes between our constructed one month futures indices and the Bank of Canada’s
commodity price indices are 0.81 (for non-energy commodities) to 0.83 (for energy commodities).
6
Are commodity price futures useful in predicting the real exchange rate in sample?
The results reported in Table 2 suggest that futures prices of energy and non-energy commodities and
interest rate expectations can provide some additional predictive power for the real exchange rate, at least
within sample (equation 2). Expected relative interest rate changes play a role (equation 3), and combined
with commodity price futures, they contribute to raising the adjusted R2 from 2 to 20 per cent (equation
4).12
Table 2 - Estimated coefficients (standard errors) *
Variables
1. Original
exchange rate
equation
2. With commodity
futures
3. With interest rate
expectations
4. With both
Long run
Adjustment
-0.136 (0.047)
-0.168 (0.046)
-0.041 (0.033)
-0.056 (0.031)
Constant
-0.329 (0.082)
-0.350 (0.058)
-0.470 (0.076)
-0.526 (0.068)
Non-energy prices
0.752 (0.343)
0.384 (0.168)
0.371 (0.147)
0.869 (0.502)
Energy prices
0.207 (0.070)
0.222 (0.087)
0.261 (0.081)
0.231 (0.119)
Short run
Interest rate differential
0.004 (0.002)
0.004 (0.002)
(t-1)
0.071 (0.031)
0.125 (0.059)
∆ Non-energy futures
0.060 (0.017)
0.101 (0.025)
∆ Energy futures
Expected change in the
0.035 (0.012)
0.044 (0.0135)
interest rate differential
Statistics
Adjusted R2
0.036**
0.116
0.063
0.202
D.W.
1.52
1.44
1.44
1.33
Sample
96:07-08:01
96:07-08:01
02:05-08:01
02:05 – 08:01
* Based on monthly data and one-month futures or forwards. Bold denotes coefficients not significant at the 5% level.
** Adjusted R2 over the 2002:05-2008:01 sample is 0.016.
Is the exchange rate equation robust?
The estimates are not robust to variations in the sample.13 We conducted numerous expanding and fixedwindows rolling regressions with the specifications reported in Table 2, with both one month and three
month futures, with weekly and monthly data, and for different sample periods. The results all suggested
that some of the parameters were not significant in certain periods. Chart 2a shows typical results with
equation 2. The blue lines indicate how the coefficients evolve when the sample is expanded from January
2005. The red lines show the associated p-values and the yellow shaded zone represents the 10 per cent
level for the latter. While it is difficult to establish the long-run relationship over most of the sample, as the
adjustment parameter has large standard errors, energy prices seem to be strongly linked to the evolution of
the real exchange rate, with commodity futures playing an increasingly important role. Chart 2b, which
shows regressions with an expanding window starting with the most recent data, provides corroborating
evidence. A charitable interpretation of the results is that the exchange market was in transition as market
12
This is comparable to the adjusted R2 of the ILM equation (0.204) which was estimated with quarterly data over the
1973-2005 period in Isssa, Lafrance, and Murray (2008).
13
These results are consistent with those of Issa, Lafrance, and Murray (2008) and Maier and DePratto (2008).
7
participants focused more and more on the importance of energy prices for the Canadian economy and
trade balance in the latter part of the sample. It remains that our results can only be characterized as
tentative and further work will have to see if the exchange rate equation stands the test of time.
Is the long-run relationship robust?
We also examined whether the long-run relationship between both commodity price indices and the real
exchange rate are sensitive to the sampling frequency. In Table 3 we report comparisons of estimates of
equation 2 using weekly, monthly, and quarterly data over a common sample period. While the differences
are not statistically meaningful, the results suggest that lower frequency data infer slower estimated
adjustment to equilibrium. With samples over a relatively short time span, however, the underlying
cointegration relationship is more an act of faith than something that can be established statistically as the
standard errors of the adjustment coefficient are quite large.
Table 3 - Equation 2 estimated at different frequencies: Selected coefficients
Variables
Weekly
960531 – 080125
-0.016 (0.009)
43
Adjustment (s.e.)
Estimated half-life
(in weeks)
0.760 (0.303)
Non-energy commodity prices
0.194 (0.069)
Energy prices
0.06
Adjusted R2
598
Degrees of freedom
Coefficients which are not significant at the 5% level are denoted in bold.
Monthly
96:07 – 08:01
-0.056 (0.031)
53
Quarterly
96:04 – 07:04
-0.116 (0.093)
77
0.752 (0.343)
0.207 (0.070)
0.16
131
0.905 (0.529)
0.255 (0.131)
0.23
37
Can we beat a random walk?
In short, yes. This is not unexpected, since both AvN in its time and ILM more recently could do so. Chart
3 shows the Theil U-statistics for forecasts from one to twelve months ahead, using the Meese-Rogoff
methodology.14 This test allows the model the advantage of “knowing” the future values of the explanatory
variables. Sequential expanding rolling regressions are then run and the model’s predictive ability at
different forecast horizons is compared to that of a no change, or random walk, benchmark. The
researcher’s model does better than a random walk when the calculated Theil statistic is less than one. This
is the case for equations 2 and 4 in Table 2 at all horizons up to twelve months. Having said that, the use of
futures in this context seems a bit of a stretch. In future work, we will explore our ability to predict
exchange rate movements ex ante by using historical commodity price Bank of Canada staff forecasts.
14
Inoue and Kilian (2004) question the wisdom of relying on out-of-sample predictability tests. Based on the higher
power of in-sample tests of predictability, they argue that results of in-sample tests are more credible than those of outof-sample tests.
8
Can we improve our forecasts?
This remains to be seen for true ex ante forecasts over the horizon that is relevant for monetary policy (up
to three years). The key challenge lies in developing good forecasting models for commodity prices. What
we can say at this time is that dynamic simulations of the AvN/ILM equation augmented by commodity
price futures and market expectations of relative interest rate changes can track the historical data relatively
well, particularly in recent years (Chart 4a). Further work will be required, however, to establish this more
convincingly over the long run.
4. CONCLUSION.
The findings in this paper suggest that using commodity price futures and market expectations of
anticipated interest rate changes can help explain more recent movements of the Canadian dollar. Further
work will be required to see if this approach can yield interesting results to improve our ability to forecast
these movements ex ante over short horizons. Our other main result, that the reduced-form exchange rate
equation that we considered in its limited variants is not robust to the historical samples considered, is not
as comforting. This evidence might be pointing to changes over time in the relative importance of
fundamentals, notably the growing importance of net energy exports as other researchers have emphasized
(Bayoumi and Muhleisen 2006). Alternatively, it might be pointing to a shift in perception by market
participants of the growing importance of the Canadian dollar as a petro-currency. In either case, the results
are indicative of the challenges that one faces when trying to explain exchange rate movements and the
modesty that one is compelled to adopt in presenting new results. Yet, as the commodity based approach to
explaining the Canadian dollar at the Bank of Canada enters its third decade, there is a certain sense of
comfort in the ability of a simple equation to stand, albeit with qualifications, the test of time.
9
Appendix
Chart 1: Data
Monthly
Real US dollar per Canadian dollar
Nom inal US dollar per Canadian dollar
.0
1.1
-.1
1.0
-.2
0.9
-.3
0.8
-.4
0.7
-.5
1996
1998
2000
2002
2004
0.6
1996
2006
1998
Non-energy com m odity price index
2000
2002
2004
2006
Energy com m odity price index
.3
1.6
.2
1.2
.1
.0
0.8
-.1
0.4
-.2
0.0
-.3
-.4
1996
1998
2000
2002
2004
-0.4
1996
2006
Non-energy com m odity futures (1-m onth)
1998
2000
2002
2004
2006
Energy com m odity futures (1-m onth)
.4
1.6
1.2
.2
0.8
.0
0.4
-.2
-.4
1996
0.0
1998
2000
2002
2004
-0.4
1996
2006
Canada-US interes t rate differential
3
1.00
2
0.75
1
0.50
0
0.25
-1
0.00
-2
-0.25
-3
1996
1998
2000
2002
2004
2006
Expected change in interes t differential
(1-m onth)
-0.50
1998
2000
2002
2004
2006
2002
10
2003
2004
2005
2006
2007
Chart 2a: Coefficient Estimates Using an Expanding Rolling Window
Equation 2
Adjustment
Interest rate dif ferential
-.020
1.0
.0050
-.025
1.0
.0045
0.8
0.8
-.030
.0040
-.035
0.6
0.6
-.040
.0035
0.4
-.045
0.4
.0030
-.050
0.2
-.060
05M01
05M07
06M01
Beta (lef t axis)
06M07
07M01
07M07
0.2
.0025
-.055
0.0
08M01
.0020
05M01
P-Value (right axis)
06M07
07M01
07M07
0.0
08M01
P-Value (right axis)
Energy commodity price index
1.0
1.0
06M01
Beta (lef t axis)
Non-energy commodity price index
1.2
05M07
.40
1.0
.35
0.8
0.8
0.8
.30
0.6
0.6
0.6
.25
0.4
0.4
0.4
.20
0.2
0.2
0.0
05M01
05M07
06M01
Beta (lef t axis)
06M07
07M01
07M07
0.2
.15
0.0
08M01
.10
05M01
P-Value (right axis)
06M07
07M01
07M07
0.0
08M01
P-Value (right axis)
Energy commodity f utures (1-month)
1.0
.07
06M01
Beta (lef t axis)
Non-energy commodity f utures (1-month)
.08
05M07
.065
1.0
.060
0.8
.06
0.8
.055
0.6
0.6
.05
.050
0.4
0.4
.04
.045
0.2
.03
.02
05M01
05M07
06M01
Beta (lef t axis)
06M07
07M01
07M07
0.2
.040
0.0
08M01
.035
05M01
P-Value (right axis)
05M07
06M01
Beta (lef t axis)
11
06M07
07M01
07M07
P-Value (right axis)
0.0
08M01
Chart 2b: Coefficient Estimates Using an Expanding Backward Rolling Window
Equation 2
Adjustment
Interest rate dif f erential
-.04
1.0
.009
1.0
.008
-.06
0.8
0.8
.007
-.08
.006
0.6
-.10
0.6
.005
-.12
0.4
0.4
.004
-.14
.003
0.2
0.2
-.16
-.18
1996
.002
0.0
1997
1998
1999
Beta (lef t axis)
2000
2001
2002
.001
1996
2003
0.0
1997
P-Value (right axis)
1998
1999
Beta (lef t axis)
Non-energy commodity price index
2000
2001
2002
2003
P-Value (right axis)
Energy commodity price index
.8
1.0
.36
1.0
.34
.7
0.8
.6
0.6
0.8
.32
.30
0.6
.28
.26
.5
0.4
0.4
.24
.4
.22
0.2
0.2
.20
.3
1996
0.0
1997
1998
1999
Beta (lef t axis)
2000
2001
2002
.18
1996
2003
0.0
1997
P-Value (right axis)
1998
1999
Beta (lef t axis)
Non-energy commodity f utures (1-month)
2000
2001
2002
2003
P-Value (right axis)
Energy commodity price f utures (1-month)
.11
1.0
.10
0.8
.09
0.6
.14
1.0
.13
0.8
.12
.11
0.6
.10
.09
.08
0.4
0.4
.08
.07
.07
0.2
0.2
.06
.06
1996
0.0
1997
1998
1999
Beta (lef t axis)
2000
2001
2002
.05
1996
2003
P-Value (right axis)
0.0
1997
1998
1999
Beta (lef t axis)
12
2000
2001
2002
P-Value (right axis)
2003
Chart 3: Theil’s U-statistic
Model-based forecasts versus random walk
1.0
Equation 1
Equation 2
Equation 4
0.9
0.8
0.7
0.6
0.5
1
2
3
4
5
6
7
8
9
10
11
12
Forecast horizon (months)
*Equations 1 and 2 are estimated from 1996:7-2004:1.
Equation 5 is estimated from 2002:5-2006:1.
Chart 4a: Dynamic Simulation versus Actual
US dollar per Canadian dollar
1.1
1.0
0.9
0.8
Equation 1
Equation 4
Actual
0.7
0.6
2002
2003
2004
2005
13
2006
2007
Chart 4b: Dynamic Simulation Versus Actual
Monthly, Estimated from 1995:3-2008:1
US dollar per Canadian dollar
1.1
1.0
0.9
0.8
0.7
Actual
Equation 1
0.6
1996
1998
2000
14
2002
2004
2006
References
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Blunndell-Wignall, A., and R. G. Gregory. 1989. “Exchange Rate Policy in Advanced Commodity
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Sources and definitions of variables
All data comes from Bloomberg, unless otherwise indicated. *Denotes data retrieved from Global Insight.
rfx:
Real U.S. per Canadian dollar exchange rate.
Average of the daily noon spot rate recorded by the Bank of Canada, multiplied by the ratio of
Canada to U.S. consumer price index (CPI). CPI indices are indexed to 2002=100 and are
obtained from Statistics Canada (v41690973) and the Bureau of Labor Statistics.
com:
Real commodity price index excluding energy.
Average of the daily non-energy commodity price index calculated by the Bank of Canada
(Statistics Canada series v36383). Deflated by the U.S. CPI index.
ene:
Real energy price index.
Average of the daily energy commodity price index calculated by the Bank of Canada
(Statistics Canada series v36384). Deflated by the U.S. CPI index.
int:
Canada-U.S. nominal interest rate differential.
Average of the daily Canadian three-month prime corporate paper rate (Statistics Canada
series v39074) and U.S. 90-day AA non-financial commercial paper closing rate from the
Federal Reserve Board.
int_1m:
Expected change in the Canada-U.S. interest rate differential. Measured by the difference in
the fixed rate of the 1-month overnight index swap and the current overnight rate for Canada,
and the 1-month overnight index swap and the current effective fed funds rate for the United
States. Data available beginning from May 2002.
com_1m:
Real non-energy commodity price index, constructed using 1-month ahead futures prices.
Deflated by the U.S. CPI index.
ene_1m:
Real energy commodity price index, constructed using 1-month ahead futures prices. Deflated
by the U.S. CPI index.
com_3m:
Real non-energy commodity price index, constructed using 3-month ahead futures prices.
Deflated by the U.S. CPI index.
ene_3m:
Real energy commodity price index, constructed using 3-month ahead futures prices. Deflated
by the U.S. CPI index.
Components of commodity price indices constructed using futures prices
Energy
Light, sweet crude oil futures: traded on the New York Mercantile Exchange (NYMEX), trading symbol CL
Henry Hub natural gas futures: traded on the NYMEX, trading symbol NG
Non-Energy
Wheat futures: traded on the Chicago Board of Trade (CBOT), trading symbol W
Live cattle futures: traded on the Chicago Mercantile Exchange (CME), trading symbol LC
Random length lumber futures: traded on the CME, trading symbol LC
Aluminum futures: traded on the London Metals Exchange (LME), trading symbol AL*
Copper futures: traded on the LME*
Gold futures: traded on the NYMEX, trading symbol GC
Nickel: traded on the LME*
Zinc: traded on the LME *
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