
 Start

4251
 Prefix

For example, central
banks and private sector forecasters view the price of oil as one of the key variables in generating
macroeconomic projections and in assessing macroeconomic risks. Of particular interest is the
question of the extent to which the price of oil is helpful in predicting recessions. For example,
 Exact

Hamilton (2009),
 Suffix

building on the analysis in Edelstein and Kilian (2009), provides evidence that
the recession of late 2008 was amplified and preceded by an economic slowdown in the
automobile industry and a deterioration in consumer sentiment.
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 Start

4309
 Prefix

For example, central
banks and private sector forecasters view the price of oil as one of the key variables in generating
macroeconomic projections and in assessing macroeconomic risks. Of particular interest is the
question of the extent to which the price of oil is helpful in predicting recessions. For example,
Hamilton (2009), building on the analysis in Edelstein and
 Exact

Kilian (2009),
 Suffix

provides evidence that
the recession of late 2008 was amplified and preceded by an economic slowdown in the
automobile industry and a deterioration in consumer sentiment. Thus, more accurate forecasts of
the price of oil have the potential of improving forecast accuracy for a wide range of
macroeconomic outcomes and of improving macroeconomic policy responses.
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6256
 Prefix

Section 4 studies the extent to which the nominal price of oil and the real price of oil are
predictable based on macroeconomic aggregates. We document strong evidence of predictability
1 See, e.g.,
 Exact

Kahn (1986),
 Suffix

Davis and Kilian (2010).
2 See, e.g., Goldberg (1998), Allcott and Wozny (2010), Busse, Knittel and Zettelmeyer (2010), Kellogg (2010).
in population. Predictability in population, however, need not translate into outofsample
forecastability.
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6279
 Prefix

Section 4 studies the extent to which the nominal price of oil and the real price of oil are
predictable based on macroeconomic aggregates. We document strong evidence of predictability
1 See, e.g., Kahn (1986), Davis and
 Exact

Kilian (2010).
 Suffix

2 See, e.g., Goldberg (1998), Allcott and Wozny (2010), Busse, Knittel and Zettelmeyer (2010), Kellogg (2010).
in population. Predictability in population, however, need not translate into outofsample
forecastability.
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6307
 Prefix

Section 4 studies the extent to which the nominal price of oil and the real price of oil are
predictable based on macroeconomic aggregates. We document strong evidence of predictability
1 See, e.g., Kahn (1986), Davis and Kilian (2010). 2 See, e.g.,
 Exact

Goldberg (1998),
 Suffix

Allcott and Wozny (2010), Busse, Knittel and Zettelmeyer (2010), Kellogg (2010).
in population. Predictability in population, however, need not translate into outofsample
forecastability. The latter question is the main focus of sections 5 through 8.
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6389
 Prefix

We document strong evidence of predictability
1 See, e.g., Kahn (1986), Davis and Kilian (2010). 2 See, e.g., Goldberg (1998), Allcott and Wozny (2010), Busse, Knittel and Zettelmeyer (2010),
 Exact

Kellogg (2010).
 Suffix

in population. Predictability in population, however, need not translate into outofsample
forecastability. The latter question is the main focus of sections 5 through 8.
In sections 5, 6 and 7, we compare a wide range of outofsample forecasting methods for
the nominal price of oil.
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 Prefix

There is no evidence of significant
forecast accuracy gains at shorter horizons, and at the long horizons of interest to policymakers,
oil futures prices are clearly inferior to the nochange forecast.
Similarly, forecasting models based on the dollar exchange rates of major commodity
exporters, models based on the
 Exact

Hotelling (1931), and
 Suffix

a variety of simple time series regression
models are not successful at significantly lowering the MSPE at short horizons. There is
evidence, however, that recent percent changes in the nominal price of industrial raw materials
other than oil can be used to substantially and significantly reduce the MSPE of the nochange
forecast of the nominal price of oil at horizons of 1 and 3 months.
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12309
 Prefix

The net oil price increase is a censored predictor that assigns zero weight
to net oil price decreases. There is little evidence that this type of asymmetry is reflected in the
responses of U.S. real GDP to innovations in the real price of oil, as documented in Kilian and
Vigfusson (2010a,b), but
 Exact

Hamilton (2010)
 Suffix

suggests that the net oil price increase specification is
best thought of as a parsimonious forecasting device. We provide a comprehensive analysis of
this conjecture.
Point forecasts of the price of oil are important, but they fail to convey the large
uncertainty associated with oil price forecasts.
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 Prefix

The WTI data until 1973 tend to exhibit a pattern
resembling a stepfunction. The price remains constant for extended periods, followed by
discrete adjustments. The U.S. wholesale price of oil for 19481972 used in
 Exact

Hamilton (1983)
 Suffix

is
numerically identical with this WTI series. As discussed in Hamilton (1983, 1985) the discrete
pattern of crude oil price changes during this period is explained by the specific regulatory
structure of the oil industry during 194872.
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13795
 Prefix

The price remains constant for extended periods, followed by
discrete adjustments. The U.S. wholesale price of oil for 19481972 used in Hamilton (1983) is
numerically identical with this WTI series. As discussed in
 Exact

Hamilton (1983, 1985)
 Suffix

the discrete
pattern of crude oil price changes during this period is explained by the specific regulatory
structure of the oil industry during 194872. Each month the Texas Railroad Commission and
other U.
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14514
 Prefix

As a result,
much of the cyclically endogenous component of oil demand was reflected in shifts in quantities
rather than prices. The commission was generally unable or unwilling to accommodate sudden
disruptions in oil production, preferring instead to exploit these events to implement sometimes
dramatic price increases
 Exact

(Hamilton 1983,
 Suffix

p. 230).
Whereas the WTI price is a good proxy for the U.S. price for oil during 194872, when
the U.S. was largely selfsufficient in oil, it becomes less representative after 1973, when the
share of U.
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21073
 Prefix

First, there is little evidence to support the notion that OPEC has been successfully acting as a
cartel in the 1970s and early 1980s, and the role of OPEC has diminished further since 1986 (see,
e.g.,
 Exact

Skeet 1988; Smith 2005;
 Suffix

Almoguera, Douglas and Herrera 2010). Second, even if we were
to accept the notion that an OPEC cartel sets the nominal price of oil, economic theory predicts
that this cartel price will endogenously respond to U.
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21636
 Prefix

This
theoretical prediction is consistent with anecdotal evidence of OPEC oil producers raising the
price of oil (or equivalently lowering oil production) in response to unanticipated U.S. inflation,
low U.S. interest rates and the depreciation of the dollar. Moreover, as observed by Barsky and
 Exact

Kilian (2002),
 Suffix

economic theory predicts that the strength of the oil cartel itself (measured by the
extent to which individual cartel members choose to deviate from cartel guidelines) will be
positively related to the state of the global business cycle (see Green and Porter 1984).
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23191
 Prefix

There is evidence
from insample fitting exercises, however, of a predictive relationship between suitable nonlinear
transformations of the nominal price of oil and U.S. real output, in particular. The most
successful of these transformations is the net oil price increase measure of
 Exact

Hamilton (1996, 2003).
 Suffix

Let ts denote the nominal price of oil in logs and the difference operator. Then the net
oil price increase is defined as:
,*
max 0,,
net
sssttt
where
*
st is the highest oil price in the preceding 12 months or, alternatively, the preceding 36
months.
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24693
 Prefix

Nevertheless,
Hamilton’s nominal net oil price increase variable has become one of the leading specifications
in the literature on predictive relationships between the price of oil and the U.S. economy.
 Exact

Hamilton (2010),
 Suffix

for example, interprets this specification as capturing nonlinear changes in
consumer sentiment in response to nominal oil price increases.6
As with other oil price specifications there is reason to expect lagged feedback from
global macroeconomic aggregates to the net oil price increase.
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25008
 Prefix

Hamilton (2010), for example, interprets this specification as capturing nonlinear changes in
consumer sentiment in response to nominal oil price increases.6
As with other oil price specifications there is reason to expect lagged feedback from
global macroeconomic aggregates to the net oil price increase. Whereas
 Exact

Hamilton (2003)
 Suffix

made
the case that net oil price increases in the 1970s, 1980s and 1990s were capturing exogenous
events in the Middle East, Hamilton (2009) concedes that the net oil price increase of 200308
was driven in large part by a surge in the demand for oil.
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25149
 Prefix

capturing nonlinear changes in
consumer sentiment in response to nominal oil price increases.6
As with other oil price specifications there is reason to expect lagged feedback from
global macroeconomic aggregates to the net oil price increase. Whereas Hamilton (2003) made
the case that net oil price increases in the 1970s, 1980s and 1990s were capturing exogenous
events in the Middle East,
 Exact

Hamilton (2009)
 Suffix

concedes that the net oil price increase of 200308
was driven in large part by a surge in the demand for oil. Kilian (2009a,b; 2010), on the other
hand, provides evidence based on structural VAR models that in fact most net oil price increases
have contained a large demand component driven by global macroeconomic conditions, even
6
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25276
 Prefix

Whereas Hamilton (2003) made
the case that net oil price increases in the 1970s, 1980s and 1990s were capturing exogenous
events in the Middle East, Hamilton (2009) concedes that the net oil price increase of 200308
was driven in large part by a surge in the demand for oil.
 Exact

Kilian (2009a,b;
 Suffix

2010), on the other
hand, provides evidence based on structural VAR models that in fact most net oil price increases
have contained a large demand component driven by global macroeconomic conditions, even
6 Interestingly, the behavioral rationale for the net oil price increase measure applies equally to the nominal price of
oil and t
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25719
 Prefix

evidence based on structural VAR models that in fact most net oil price increases
have contained a large demand component driven by global macroeconomic conditions, even
6 Interestingly, the behavioral rationale for the net oil price increase measure applies equally to the nominal price of
oil and the real price of oil. Although
 Exact

Hamilton (2003)
 Suffix

applied this transformation to the nominal price of oil,
several other studies have recently explored models that apply the same transformation to the real price of oil (see,
e.g., Kilian and Vigfusson 2010a; Herrera, Lagalo and Wada 2010).
prior to 2003.
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26723
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Granger Causality Tests
Much of the existing work on predicting the price of oil has focused on testing for the existence
of a predictive relationship from macroeconomic aggregates to the price of oil. The existence of
predictability in population is a necessary precondition for outofsample forecastability (see
Inoue and
 Exact

Kilian 2004a).
 Suffix

Within the linear VAR framework the absence of predictability from
one variable to another in population may be tested using Granger noncausality tests.
4.1. Nominal Oil Price Predictability
4.1.1.
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The Pre1973 Evidence
Granger causality from macroeconomic aggregates to the price of oil has received attention in
part because Granger noncausality is one of the testable implications of strict exogeneity. The
notion that the percent change in the nominal price of oil may be considered exogenous with
respect to the U.S. economy was bolstered by evidence in
 Exact

Hamilton (1983),
 Suffix

who observed that
there is no apparent Granger causality from U.S. domestic macroeconomic aggregates to the
percent change in the nominal price of oil during 19481972. Of course, the absence of Granger
causality is merely a necessary condition for strict exogeneity.
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features of the oil market
during this period, discussed in section 2, and on historical evidence that unexpected supply
disruptions under this institutional regime appear to be associated with exogenous political
events in the Middle East, allowing us to treat the resulting price spikes as exogenous with
respect to the U.S. economy. For a more nuanced view of these historical episodes see
 Exact

Kilian (2008b;
 Suffix

2009a,b; 2010). Even if we accept Hamilton’s interpretation of the pre1973 period, the
institutional conditions that Hamilton (1983) appeals to ceased to exist in the early 1970s, and
Hamilton’s results for the 19481972 period are mainly of historical interest.
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28410
 Prefix

under this institutional regime appear to be associated with exogenous political
events in the Middle East, allowing us to treat the resulting price spikes as exogenous with
respect to the U.S. economy. For a more nuanced view of these historical episodes see Kilian (2008b; 2009a,b; 2010). Even if we accept Hamilton’s interpretation of the pre1973 period, the
institutional conditions that
 Exact

Hamilton (1983)
 Suffix

appeals to ceased to exist in the early 1970s, and
Hamilton’s results for the 19481972 period are mainly of historical interest. The real question
for our purposes is to what extent there is evidence that oil prices can be predicted from
macroeconomic aggregates in the post1973 period.
4.1.2.
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The real question
for our purposes is to what extent there is evidence that oil prices can be predicted from
macroeconomic aggregates in the post1973 period.
4.1.2. The Post1973 Evidence
There is widespread agreement among oil economists that, starting in 1973, nominal oil prices
must be considered endogenous with respect to U.S. macroeconomic variables (see
 Exact

Kilian 2008a).
 Suffix

Whether this endogeneity makes the nominal price of oil predictable on the basis of
lagged U.S. macroeconomic aggregates depends on whether the price of oil behaves like a
typical asset price or not.
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 Prefix

Table 1a investigates the evidence of Granger causality from selected nominal
U.S. macroeconomic variables to the nominal price of oil. All results are based on pairwise
vector autoregressions. The lag order is fixed at 12. Similar results would have been obtained
7
 Exact

Hamilton (1994,
 Suffix

p. 306) illustrates this point in the context of a model of stock prices and expected dividends.
with 24 lags. We consider four alternative nominal oil price series. The evaluation period is
alternatively 1973.12009.12 or 1975.12009.12.8 It is not clear a priori which oil price series is
best suited for finding predictability.
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 Prefix

On the one hand, one would expect the evidence of
predictability to be stronger for oil price series that are unregulated (such as the refiners’
acquisition cost for imported crude oil) than for partially regulated domestic price series. On the
other hand, to the extent that the 1973/74 oil price shock episode was driven by monetary factors,
as proposed by Barsky and
 Exact

Kilian (2002),
 Suffix

one would expect stronger evidence in favor of such
feedback from the WTI price series that includes this episode.
There are several reasons to expect the dollardenominated nominal price of oil to
respond to changes in nominal U.
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33348
 Prefix

Given the general instability in the link from changes in
monetary aggregates to inflation, one would not necessarily expect changes in monetary
aggregates to have much predictive power for the price of oil, except perhaps in the 1970s (see
Barsky and
 Exact

Kilian 2002).
 Suffix

Table 1a nevertheless shows that there is considerable lagged feedback
8 In the former case, the pre1974.1 observations are only used as presample observations.
9 It can be shown that similar results hold for the CPI excluding energy, albeit not for the CPI excluding food and
energy.
10 For an earlier exposition of the role of mone
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 Prefix

feedback
8 In the former case, the pre1974.1 observations are only used as presample observations.
9 It can be shown that similar results hold for the CPI excluding energy, albeit not for the CPI excluding food and
energy.
10 For an earlier exposition of the role of monetary factors in determining the price of oil see Barsky and
 Exact

Kilian (2002).
 Suffix

Both Barsky and Kilian (2002) and Gillman and Nakov (2009) view the shifts in U.S. inflation in the early
1970s as caused by persistent changes in the growth rate of the money supply, but there are important differences in
emphasis.
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33848
 Prefix

8 In the former case, the pre1974.1 observations are only used as presample observations.
9 It can be shown that similar results hold for the CPI excluding energy, albeit not for the CPI excluding food and
energy.
10 For an earlier exposition of the role of monetary factors in determining the price of oil see Barsky and Kilian (2002). Both Barsky and
 Exact

Kilian (2002) and
 Suffix

Gillman and Nakov (2009) view the shifts in U.S. inflation in the early
1970s as caused by persistent changes in the growth rate of the money supply, but there are important differences in
emphasis. Whereas Barsky and Kilian stress the real effects of unanticipated monetary expansions on real domestic
output, on the demand for oil and hence on the real price of oil, Gillman and Nakov stress tha
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34461
 Prefix

Whereas Barsky and Kilian stress the real effects of unanticipated monetary expansions on real domestic
output, on the demand for oil and hence on the real price of oil, Gillman and Nakov stress that the relative price of
oil must not decline in response to a monetary expansion, necessitating a higher nominal price of oil, consistent with
anecdotal evidence on OPEC price decisions (see, e.g.,
 Exact

Kilian 2008b).
 Suffix

These two explanations are complementary.
from narrow measures of money such as M1 for the refiners’ acquisition cost and the WTI price
of oil based on the 1975.22009.12 evaluation period. The much weaker evidence for the full
WTI series may reflect the stronger effect of regulatory policies on the WTI price during the
early 1970s.
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Reconciling the Pre and Post1973 Evidence on Predictability
Tables 1a and 1b suggest that indicators of U.S. inflation have significant predictive power for
the nominal price of oil. This result is in striking contrast to the pre1973 period. As shown in
 Exact

Hamilton (1983)
 Suffix

using quarterly data and in Gillman and Nakov (2009) using monthly data,
there is no significant Granger causality from U.S. inflation to the percent change in the nominal
price of oil in the 1950s and 1960s.
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 Prefix

Thus, regressions on long time spans of real exchange rate data produce average estimates that
by construction are not informative about the speed of adjustment in the Bretton Woods system.
14 For a review of this literature see Barsky and
 Exact

Kilian (2002).
 Suffix

difficult to pin down, especially at longer horizons, and that the relevant horizon for resource
extraction is not clear. We therefore focus on the predictive power of fluctuations in real
aggregate output.
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46985
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This possibility is more
than a theoretical curiosity in our context. Recent models of the determination of the real price
of oil after 1973 have stressed that this price is determined in global markets (see, e.g.,
 Exact

Kilian 2009a;
 Suffix

Kilian and Murphy 2010). In particular, the demand for oil depends not merely on U.S.
demand, but on global demand. The bivariate model for the real price of oil and U.S. real GDP
by construction omits fluctuations in real GDP in the rest of the world.
 (check this in PDF content)

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50027
 Prefix

This series has
recently been introduced by Baumeister and Peersman (2010) in the context of modeling the
demand for oil. Although there are serious methodological concerns regarding the construction
of any such index, as discussed in
 Exact

Beyer, Doornik and Hendry (2001),
 Suffix

one would expect this
series to be a better proxy for global fluctuations in the demand for crude oil than U.S. real GDP.
Indeed, Table 2 shows strong evidence of Granger causality from world industrial production to
the real WTI price in the full sample period for the LT model.
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For the four shorter series there
are three additional rejections for the LT model; the other pvalue is not much higher than 0.1.
The reduction in pvalues compared with U.S. real GDP is dramatic. The fact that there is
evidence of predictability only for the linearly detrended series makes sense. As discussed in
 Exact

Kilian (2009b),
 Suffix

the demand for industrial commodities such as crude oil is subject to long
swings. Detrending methods such as HP filtering (and even more so first differencing) eliminate
much of this low frequency covariation in the data, removing the feature of the data we are
interested in testing.
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52424
 Prefix

Even OECD+6 industrial production, however, is an
imperfect proxy for businesscycle driven fluctuations in the global demand for industrial
commodities such as crude oil.
One alternative is the index of global real activity recently proposed in
 Exact

Kilian (2009a).
 Suffix

This index does not rely on any country weights and has truly global coverage. It has been
constructed with the explicit purpose of measuring fluctuations in the broadbased demand for
industrial commodities associated with the global business cycle.
16
As expected, the last row of
Table 3 indicates even stronger evidence of Granger causality from this index to the real price of
oil, regardle
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53957
 Prefix

by evidence in Kilian and Hicks (2010) based on distributed
lag models that revisions to professional real GDP growth forecasts have significant predictive
power for the real price of oil during 2000.112008.12 after weighting each country’s forecast
revision by its PPPGDP share. Predictability in population, of course, does not necessarily
imply outofsample forecastability (see Inoue and
 Exact

Kilian 2004a).
 Suffix

The next two sections
therefore examine alternative approaches to forecasting the nominal and the real price of oil outofsample.
5. ShortHorizon Forecasts of the Nominal Price of Oil
The most common approach to forecasting the nominal price of oil is to treat the price of the oil
16 This index is constructed from ocean shipping
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Horizon Forecasts of the Nominal Price of Oil
The most common approach to forecasting the nominal price of oil is to treat the price of the oil
16 This index is constructed from ocean shipping freight rates. The idea of using fluctuations in shipping freight rates
as indicators of shifts in the global real activity dates back to
 Exact

Isserlis (1938) and Tinbergen (1959).
 Suffix

The panel of
monthly freightrate data underlying the global real activity index was collected manually from Drewry’s Shipping
Monthly using various issues since 1970. The data set is restricted to dry cargo rates.
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 Prefix

For this paper, this series has been extended based on
the Baltic Exchange Dry Index, which is available from Bloomberg. The latter index, which is commonly discussed
in the financial press, is essentially identical to the nominal index in
 Exact

Kilian (2009a),
 Suffix

but only available since 1985.
futures contract of maturity h as the hperiod forecast of the price of oil.
17
In particular, many
central banks and the International Monetary Fund (IMF) use the price of NYMEX oil futures as
a proxy for the market’s expectation of the spot price of crude oil.
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Forecasts of the spot price of
oil are used as inputs in the macroeconomic forecasting exercises that these institutions produce.
For example, the European Central Bank (ECB) employs oil futures prices in constructing the
inflation and outputgap forecasts that guide monetary policy (see
 Exact

Svensson 2005).
 Suffix

Likewise the
IMF relies on futures prices as a predictor of future spot prices (see, e.g., International Monetary
Fund 2005, p. 67; 2007, p. 42). Futuresbased forecasts of the price of oil also play a role in
policy discussions at the Federal Reserve Board.
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57303
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Such
attitudes have persisted notwithstanding recent empirical evidence to the contrary and
notwithstanding the development of theoretical models aimed at explaining the lack of predictive
ability of oil futures prices and spreads (see, e.g.,
 Exact

Knetsch 2007;
 Suffix

Alquist and Kilian 2010).
Interestingly, the conventional wisdom in macroeconomics and finance is at odds with
longheld views about storable commodities in agricultural economics. For example, Peck
(1985) emphasized that “expectations are reflected nearly equally in current and in futures prices.
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57329
 Prefix

Such
attitudes have persisted notwithstanding recent empirical evidence to the contrary and
notwithstanding the development of theoretical models aimed at explaining the lack of predictive
ability of oil futures prices and spreads (see, e.g., Knetsch 2007; Alquist and
 Exact

Kilian 2010).
 Suffix

Interestingly, the conventional wisdom in macroeconomics and finance is at odds with
longheld views about storable commodities in agricultural economics. For example, Peck
(1985) emphasized that “expectations are reflected nearly equally in current and in futures prices.
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57511
 Prefix

evidence to the contrary and
notwithstanding the development of theoretical models aimed at explaining the lack of predictive
ability of oil futures prices and spreads (see, e.g., Knetsch 2007; Alquist and Kilian 2010). Interestingly, the conventional wisdom in macroeconomics and finance is at odds with
longheld views about storable commodities in agricultural economics. For example,
 Exact

Peck (1985)
 Suffix

emphasized that “expectations are reflected nearly equally in current and in futures prices.
In this sense cash prices will be nearly as good predictions of subsequent cash prices as futures
prices”, echoing in turn the discussion in Working (1942) who was critical of the “general
opinion among economists that prices of commodity futures are ... the market expression of
consciously formed opin
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 Prefix

For example, Peck (1985) emphasized that “expectations are reflected nearly equally in current and in futures prices.
In this sense cash prices will be nearly as good predictions of subsequent cash prices as futures
prices”, echoing in turn the discussion in
 Exact

Working (1942)
 Suffix

who was critical of the “general
opinion among economists that prices of commodity futures are ... the market expression of
consciously formed opinions on probable prices in the future” whereas “spot prices are not
generally supposed to reflect anticipation of the future in the same degree as futures prices”.
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The NYMEX light sweet crude contract is the most liquid and
largest volume market for crude oil trading.
more strongly influenced by these anticipations than are spot prices”. The next section
investigates the empirical merits of these competing views in the context of oil markets.
5.1. Forecasting Methods Based on Monthly Oil Futures Prices
Alquist and
 Exact

Kilian (2010)
 Suffix

recently provided a comprehensive evaluation of the forecast accuracy
of models based on monthly oil futures prices using data ending in 2007.2. Below we update
their analysis until 2009.12 and expand the range of alternative forecasting models under
consideration.18 In this subsection, attention is limited to forecast horizons of up to one year.
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The simplest model is:
()

ˆ1/ln()h
SthttttSFS, 1, 3, 6, 9, 1 2h (3)
To allow for the possibility that the spread may be a biased predictor, it is common to relax the
18 Because the Datastream data for the daily WTI spot price of oil used in Alquist and
 Exact

Kilian (2010)
 Suffix

were
discontinued, we rely instead on data from the Energy Information Administration. As a result the estimation
window for the forecast comparison is somewhat shorter in some cases than in Alquist and Kilian (2010).
assumption of a zero intercept:
()ˆ1/ˆln()htttthtSSFS, 1, 3, 6, 9, 12h (4)
Alternatively, one can relax the proportionality restriction:
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61493
 Prefix

, it is common to relax the
18 Because the Datastream data for the daily WTI spot price of oil used in Alquist and Kilian (2010) were
discontinued, we rely instead on data from the Energy Information Administration. As a result the estimation
window for the forecast comparison is somewhat shorter in some cases than in Alquist and
 Exact

Kilian (2010).
 Suffix

assumption of a zero intercept:
()ˆ1/ˆln()htttthtSSFS, 1, 3, 6, 9, 12h (4)
Alternatively, one can relax the proportionality restriction:
()

ˆ1/ˆln()h
SthttttSFS, 1, 3, 6, 9, 12h (5)
Finally, we can relax both the unbiasedness and proportionality restrictions:
()ˆ1/ˆˆln()htttthtSSFS, 1, 3, 6, 9, 12h.
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It should be noted that commonly used tests of equal
predictive accuracy for nested models (including the tests we rely on in this chapter) by
construction are tests of the null of no predictability in population rather than tests of equal outofsample MSPEs (see, e.g., Inoue and
 Exact

Kilian 2004a,b;
 Suffix

Clark and McCracken 2010). This means
that these tests will reject the null of equal predictive accuracy more often than they should under
the null, suggesting caution in interpreting test results that are only marginally statistically
significant.
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Put differently, a forecaster using the most recent spot price would have done
just as well in forecasting the nominal price of oil. This finding is broadly consistent with the
empirical results in Alquist and
 Exact

Kilian (2010). To
 Suffix

the extent that some earlier studies have
reported evidence more favorable to oil futures prices, the difference in results can be traced to
the use of shorter samples.
19
5.2. Other Forecasting Methods
The preceding subsection demonstrated that simple nochange forecasts of the price of oil tend to
be as accurate in the MSPE sense as forecasts based on oil futures prices, but this does
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 Prefix

While economists have used survey data
extensively in measuring the risk premium embedded in foreign exchange futures, this approach
has not been applied to oil futures, with the exception of recent work by Wu and McCallum
(2005). Yet another approach is to exploit the implication of the
 Exact

Hotelling (1931)
 Suffix

model that the
price of oil should grow at the rate of interest. Finally, we also consider forecasting models that
adjust the nochange forecast for inflation expectations and for recent percent changes in other
nominal prices.
5.2.1.
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Parsimonious Econometric Forecasts
One example of parsimonious econometric forecasting models is the random walk model without
drift introduced earlier. An alternative is the doubledifferenced forecasting model proposed in
 Exact

Hendry (2006).
 Suffix

Hendry observed that when time series are subject to infrequent trend changes,
the nochange forecast may be improved upon by extrapolating today’s oil price at the most
recent growth rate:
ˆ1
h
SsthtttS 1, 3, 6, 9, 1 2h (7)
where ts denotes the percent growth rate between 1t and .t In other words, we apply the nochange forecast to the growth rate rather than the
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This result is
consistent with common views among oil experts. For example, Peter Davies, chief economist of
British Petroleum, has noted that “we cannot forecast oil prices with any degree of accuracy over
any period whether short or long” (see
 Exact

Davies 2007).
 Suffix

5.2.4. Predictors Based on Other Nominal Prices
The evidence on Granger causality in section 4.1.2 suggests that some asset prices may have
predictive power in real time for the nominal price of oil.
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As is well known, for sufficiently large
sample sizes, any null hypothesis is bound to be rejected at conventional significance levels,
making it inappropriate to apply the same significance level as in Tables 4 through 8. In
recognition of this problem,
 Exact

Leamer (1978,
 Suffix

p. 108120) proposes a rule for constructing samplesize dependent critical values. For example, for the Fstatistic, the appropriate level of statistical
significance is (1/ )1(1)(1),1,.tfcdfttt For 216,t as in Table 4, this rule of thumb
implies a threshold for rejecting the null hypothesis of0.0209.
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LongHorizon Forecasts of the Nominal Price of Oil
For oil industry managers facing investment decisions or for policymakers pondering the
mediumterm economic outlook a horizon of one year is too short. Crude oil futures may have
maturities as long as seven years. Notwithstanding the low liquidity of oil futures markets at such
long horizons, documented in Alquist and
 Exact

Kilian (2010),
 Suffix

it is precisely these long horizons that
many policymakers focus on. For example, Greenspan (2004a) explicitly referred to the 6year
oil futures contract in assessing effective longterm supply prices.
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Notwithstanding the low liquidity of oil futures markets at such
long horizons, documented in Alquist and Kilian (2010), it is precisely these long horizons that
many policymakers focus on. For example,
 Exact

Greenspan (2004a)
 Suffix

explicitly referred to the 6year
oil futures contract in assessing effective longterm supply prices. For similar statements also see
Greenspan (2004b), Gramlich (2004) and Bernanke (2004). In this section we focus on
forecasting the nominal price of oil at horizons up to seven years.
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Notwithstanding the low liquidity of oil futures markets at such
long horizons, documented in Alquist and Kilian (2010), it is precisely these long horizons that
many policymakers focus on. For example, Greenspan (2004a) explicitly referred to the 6year
oil futures contract in assessing effective longterm supply prices. For similar statements also see
 Exact

Greenspan (2004b), Gramlich (2004) and Bernanke (2004).
 Suffix

In this section we focus on
forecasting the nominal price of oil at horizons up to seven years.
It can be shown that the daily data are too sparse at horizons beyond one year to allow the
construction of time series of endofmonth observations for oil futures prices.
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Although there can be
substantial discrepancies between the evolution of the price of crude oil and the price of gasoline
in the short run, longhorizon forecasts of the price of gasoline will track longhorizon forecasts
of the price of crude oil (see
 Exact

Kilian 2010).
 Suffix

In modeling automobile purchases researchers often
need to take a stand on consumers’ expectations of gasoline prices. A variety of modeling
strategies has been explored, often with widely different results.
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A variety of modeling
strategies has been explored, often with widely different results. Candidates include ARIMA
models, nochange forecasts, oil futures prices and gasoline futures prices (see, e.g.,
 Exact

Kahn 1986;
 Suffix

Davis and Kilian 2010; Allcott and Wozny 2010). The issue is not only one of finding a
forecasting method that achieves the smallest possible outofsample forecast error, but of
understanding how consumers form their price expectations.
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A variety of modeling
strategies has been explored, often with widely different results. Candidates include ARIMA
models, nochange forecasts, oil futures prices and gasoline futures prices (see, e.g., Kahn 1986; Davis and
 Exact

Kilian 2010;
 Suffix

Allcott and Wozny 2010). The issue is not only one of finding a
forecasting method that achieves the smallest possible outofsample forecast error, but of
understanding how consumers form their price expectations.
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The evidence in Figure 6 supports the view that the nochange forecast for the real price
of gasoline is a better proxy than alternative forecasting models for modeling durables purchases.
That evidence also is of interest more generally, given the finding in Edelstein and
 Exact

Kilian (2009)
 Suffix

that fluctuations in retail energy prices are dominated by fluctuations in gasoline prices. Finally,
the absence of money illusion in households’ gasoline price forecasts is of independent interest.
An outofsample forecast accuracy comparison between the survey forecast and the no
change forecast of the nominal price of gasoline shows that survey data are quite accurate with
an MSPE ratio
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At short horizons, inflation is expected to be at best moderate and
it may seem that there is every reason to expect the high forecast accuracy of the random walk
model without drift relative to less parsimonious regression models to carry over to the real price
of oil (see
 Exact

Kilian 2010).
 Suffix

25 On the other hand, in forecasting the real price of oil we may rely on
additional economic structure and on additional predictors that could potentially improve
forecast accuracy. Section 8 explores a number of such models.
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The
localtozero asymptotic approximation of predictive models suggests that using the nochange forecast may lower
the asymptotic MSPE even relative to the correctly specified nonrandom walk model, provided the local drift
parameter governing the predictive relationship is close enough to zero (see, e.g., Inoue and
 Exact

Kilian (2004b),
 Suffix

Clark
and McCracken 2010).
26 The refiners’ acquisition cost was extrapolated back to 1973.2 as in Barsky and Kilian (2002).
selection (see Inoue and Kilian 2006; Marcellino, Stock and Watson 2006).
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 Prefix

models suggests that using the nochange forecast may lower
the asymptotic MSPE even relative to the correctly specified nonrandom walk model, provided the local drift
parameter governing the predictive relationship is close enough to zero (see, e.g., Inoue and Kilian (2004b), Clark
and McCracken 2010).
26 The refiners’ acquisition cost was extrapolated back to 1973.2 as in Barsky and
 Exact

Kilian (2002).
 Suffix

selection (see Inoue and Kilian 2006; Marcellino, Stock and Watson 2006). We search over
p0,...,12 . The forecast accuracy results are robust to allowing for a larger upper bound.
There are no theoretical results in the forecasting literature on how to assess the null of
equal predictive accuracy when comparing iterated AR or ARMA forecasts to the nochange
forecast.
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104926
 Prefix

forecast may lower
the asymptotic MSPE even relative to the correctly specified nonrandom walk model, provided the local drift
parameter governing the predictive relationship is close enough to zero (see, e.g., Inoue and Kilian (2004b), Clark
and McCracken 2010).
26 The refiners’ acquisition cost was extrapolated back to 1973.2 as in Barsky and Kilian (2002). selection (see Inoue and
 Exact

Kilian 2006;
 Suffix

Marcellino, Stock and Watson 2006). We search over
p0,...,12 . The forecast accuracy results are robust to allowing for a larger upper bound.
There are no theoretical results in the forecasting literature on how to assess the null of
equal predictive accuracy when comparing iterated AR or ARMA forecasts to the nochange
forecast.
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27 Because there is no reason to expect the limiting distribution of the DM test statistic to be pivotal in this context,
we bootstrap the average loss differential instead.
macroeconomic predictors can be used to improve further on the nochange forecast. Recently, a
number of structural vector autoregressive models of the global market for crude oil have been
proposed (see, e.g.,
 Exact

Kilian 2009).
 Suffix

These models produce empirically plausible estimates of the
impact of demand and supply shocks in the oil market. A natural conjecture is that such models
may also have value for forecasting. Here we focus on the reducedform representation of the
VAR model in Kilian and Murphy (2010).
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It has been shown that the
presence of structural breaks at unknown points in the future invalidates the use of forecasting model rankings
obtained in forecast accuracy comparisons whether one uses rolling or recursive regression forecasts (see Inoue and
 Exact

Kilian 2006).
 Suffix

29 It also outperforms the random walk model with drift in both of these dimensions, whether the drift is estimated
recursively or as the average growth rate over the most recent h months. These results are not shown to conserve
space.
statistically significant reductions in the MSPE.
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The reason for this counterintuitive result is that, as discussed earlier, standard tests of
equal predictive accuracy do not test the null of equal outofsample MSPEs, but actually test the
null of no predictability in population – much like the Granger causality tests we applied earlier –
as pointed out by Inoue and
 Exact

Kilian (2004a).
 Suffix

This point is readily apparent from the underlying
proofs of asymptotic validity as well as the way in which critical values are simulated.
The distinction between population predictability and outofsample predictability does
not matter asymptotically under fixed parameter asymptotics, but fixed parameter asymptotics
typically provide a poor approximation to the finitesample accuracy of f
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The tests for directional accuracy are not affected, of course.
30 The size problem of conventional tests of equal predictive accuracy gets worse, when the number of extra
predictors under the alternative grows large relative to the sample size. This point has also been discussed in a much
simpler context by
 Exact

Anatolyev (2007)
 Suffix

who shows that modifying conventional test statistics for equal predictive
accuracy may remove these size distortions. Related results can be found in Calhoun (2010) who shows that
standard tests of equal predictive accuracy for nested models such as Clark and McCracken (2001) or Clark and
West (2007) will choose the larger model too often when the smaller model is more accurate in outofsampl
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 Prefix

This point has also been discussed in a much
simpler context by Anatolyev (2007) who shows that modifying conventional test statistics for equal predictive
accuracy may remove these size distortions. Related results can be found in
 Exact

Calhoun (2010)
 Suffix

who shows that
standard tests of equal predictive accuracy for nested models such as Clark and McCracken (2001) or Clark and
West (2007) will choose the larger model too often when the smaller model is more accurate in outofsample
forecasts and also proposes alternative asymptotic approximations based on many predictors.
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How imposing these realtime data constraints alters the
relative accuracy of nochange benchmark model compared with VAR models is not clear a
priori because both the benchmark model and the alternative model are affected.
The first study to investigate this question is Baumeister and
 Exact

Kilian (2011)
 Suffix

who recently
developed a realtime data set for the variables in question. They find (based on a data set
extending until 2010.6) that VAR forecasting models of the type considered in this section can
generate substantial improvements in realtime forecast accuracy.
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Clearly, the real price of WTI crude oil is more difficult to forecast in the short run than the real
U.S. refiners’ acquisition cost for imported crude oil.
Broadly similar results would be obtained with realtime data (see Baumeister and
 Exact

Kilian 2011).
 Suffix

Unlike for the real refiners’ acquisition cost, the differences between realtime forecasts
of the real WTI price and forecasts based on expost revised data tend to be small.
8.3. Restricted VAR Models
Although the results for the unrestricted VAR models in Tables 13 and 15 are encouraging, there
is reason to believe that alternative estimation methods may reduce the MSPE of the VAR
forec
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For example, model (1) with 12 lags yields MSPE reductions of 20% at horizon
1, 12% at horizon 3, and 3% at horizon 6 with no further gains at longer horizons. Model (1)
with 24 lags yields gains of 20%, 12% and 1%, respectively. Again, it can be shown that similar
gains in accuracy are feasible even using realtime data (see Baumeister and
 Exact

Kilian 2011).
 Suffix

In addition, such VAR models can also be useful for studying how baseline forecasts of
the real price of oil must be adjusted under hypothetical forecasting scenarios, as illustrated in
the next section.
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In this section we illustrate how to generate such projections from the structural moving
average representation of the VAR model of Kilian and Murphy (2010) estimated on data
extending to 2009.8. The discussion closely follows Baumeister and
 Exact

Kilian (2011).
 Suffix

This model
allows the identification of three structural shocks: (1) a shock to the flow of the production of
crude oil (“flow supply shock), (2) a shock to the flow demand for crude oil and other industrial
commodities (“flow demand shock”) that reflects unexpected fluctuations in the global business
cycle, and (3) a shock to the demand for oil inventories arising from forwardlooking behavio
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We determined the lag order of this benchmark model based on a forecast accuracy
comparison involving all combinations of horizons 1,..., 8hand lag orders 1,..., 24 .pThe
AR(4) model for real GDP growth proved to have the lowest MSPE or about the same MSPE as
the most accurate model at all horizons. The same AR(4) benchmark model has also been used
by
 Exact

Hamilton (2003) and
 Suffix

others, facilitating comparisons with existing results in the literature.
We compare the benchmark model with two alternative models. One model is the
unrestricted VAR(p) model obtained with
1112
2122
()()
().
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141311
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This suggests that we replace the percent change in the real price of oil in the linear VAR
model by the percent change in the real price of oil weighted by the timevarying share of oil in
domestic expenditures, building on the analysis in Edelstein and
 Exact

Kilian (2009). Hamilton (2009)
 Suffix

reported some success in employing a similar strategy.31 Another source of time variation may
be changes in the composition of the underlying oil demand and oil supply shocks, as discussed
in Kilian (2009).
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141534
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Hamilton (2009) reported some success in employing a similar strategy.31 Another source of time variation may
be changes in the composition of the underlying oil demand and oil supply shocks, as discussed
in
 Exact

Kilian (2009).
 Suffix

Finally, yet another potential explanation investigated below is that the linear
forecasting model may be inherently misspecified. Of particular concern is the possibility that
nonlinear dynamic regression models may generate more accurate outofsample forecasts of
cumulative real GDP growth.
11.2.
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Of particular concern is the possibility that
nonlinear dynamic regression models may generate more accurate outofsample forecasts of
cumulative real GDP growth.
11.2. Nonlinear Dynamic Models
In this regard,
 Exact

Hamilton (2003)
 Suffix

suggested that the predictive relationship between oil prices and
U.S. real GDP is nonlinear in that (1) oil price increases matter only to the extent that they
exceed the maximum oil price in recent years and that (2) oil price decreases do not matter at all.
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possibly
sytt
31 In related work, Ramey and Vine (2010) propose an alternative adjustment to the price of gasoline that reflects the
time cost of queuing in gasoline markets during the 1970s. That adjustment as well serves to remove a nonlinearity
in the transmission process. Both the nonlinearity postulated in Edelstein and
 Exact

Kilian (2009) and
 Suffix

that postulated in
Ramey and Vine (2010) is incompatible with the specific nonlinearity embodied in the models of Mork (1989) and
Hamilton (1996, 2003). In fact, the aforementioned papers rely on linear regressions after adjusting the energy price
data.
augmented by other variables.
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That adjustment as well serves to remove a nonlinearity
in the transmission process. Both the nonlinearity postulated in Edelstein and Kilian (2009) and that postulated in
Ramey and Vine (2010) is incompatible with the specific nonlinearity embodied in the models of
 Exact

Mork (1989) and Hamilton (1996, 2003).
 Suffix

In fact, the aforementioned papers rely on linear regressions after adjusting the energy price
data.
augmented by other variables. Recently, Kilian and Vigfusson (2010a) have shown that impulse
response estimates from VAR models involving censored oil price variables are inconsistent
even when equation (18) is correctly specified.
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Kilian and Vigfusson proposed a direct test of the latter hypothesis and showed
empirically that there is no statistically significant evidence of asymmetry in the response
functions for U.S. real GDP.
 Exact

Hamilton (2010)
 Suffix

agrees with Kilian and Vigfusson on the lack of validity of impulse
response analysis from censored oil price VAR models, but suggests that nonlinear predictive
models such as model (18) may still be useful for outofsample forecasting.
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We consider both onequarterahead forecasts of real GDP growth and
forecasts of the cumulative real GDP growth rate several quarters ahead. The latter forecasts
require a generalization of the singleequation forecasting approach proposed by
 Exact

Hamilton (2010).
 Suffix

In implementing this approach, there are several potentially important modeling choices
to be made.
First, even granting the presence of asymmetries in the predictive model, one question is
whether the predictive model should be specified as
44
,,3
11
netyr
titiitit
ii
yysu
, (18)
as in
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145737
 Prefix

First, even granting the presence of asymmetries in the predictive model, one question is
whether the predictive model should be specified as
44
,,3
11
netyr
titiitit
ii
yysu
, (18)
as in
 Exact

Hamilton (2003),
 Suffix

or rather as:
444
,,3
111
netyr
titiitiitit
iii
yyssu
(19)
as in Balke, Brown and Yücel (2002) or Herrera, Lagalo and Wada (2010), for example.
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 Prefix

This motivation
for the use of model (18) is new in that heretofore the focus in the literature – including
Hamilton’s own work – has been on establishing nonlinear predictability in population rather
than outofsample.
 Exact

Hamilton (2010)
 Suffix

is, of course, correct that there is a tradeoff between
estimation variance and bias. Indeed, in many other contexts parsimony has been shown to help
reduce the outofsample MSPE, but no systematic evidence has been presented to make this
case for this model.
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147627
 Prefix

A second point of contention is whether nonlinear forecasting models should be specified
in terms of the nominal price of oil or the real price of oil. For linear models, a strong economic
case can be made for using the real price of oil. For nonlinear models, the situation is less clear,
as noted by
 Exact

Hamilton (2010).
 Suffix

Because the argument for using net oil price increases is
behavioral, one specification appears as reasonable as the other. Below we therefore will
consider models specified in real as well as in nominal oil prices.
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In Table 19, we investigate whether there are MSPE reductions associated with the use of
censored oil price variables at horizons 1,..., 8 ,h drawing on the analysis in Kilian and
Vigfusson (2010b, c). For completeness, we also include results for the percent increase
specification proposed in
 Exact

Mork (1989),
 Suffix

the forecasting performance of which has not been
investigated to date. We consider nonlinear models based on the real price of oil as in Kilian and
Vigfusson and nonlinear models based on the nominal price of oil as in Hamilton (2003).
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148790
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For completeness, we also include results for the percent increase
specification proposed in Mork (1989), the forecasting performance of which has not been
investigated to date. We consider nonlinear models based on the real price of oil as in Kilian and
Vigfusson and nonlinear models based on the nominal price of oil as in
 Exact

Hamilton (2003).
 Suffix

The
unrestricted multivariate nonlinear forecasting model takes the form
44
111,12,1,
11
44 4
221,22,2,
11 1
titiitit
ii
titiitiitit
ii i
rBrBye
yBrByr e
(20)
where ,,3,,1,,,netyrnetyrttttrrrr(0)tttrrIr as in Mork (1989), and I(•) denotes the
ind
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149141
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The
unrestricted multivariate nonlinear forecasting model takes the form
44
111,12,1,
11
44 4
221,22,2,
11 1
titiitit
ii
titiitiitit
ii i
rBrBye
yBrByr e
(20)
where ,,3,,1,,,netyrnetyrttttrrrr(0)tttrrIr as in
 Exact

Mork (1989), and
 Suffix

I(•) denotes the
indicator function. Analogous nonlinear forecasting models may be constructed based on the
nominal price of oil, denoted in logs as :ts
44
111,12,1,
11
44 4
221,22,2,
11 1
titiitit
ii
titiitii tit
ii i
sBsBye
yBsBys e
(20)
where
,,3,,1
,,.
netyrnetyr
ssttttss
In addition, we consider
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150038
 Prefix

ii i
rBre
yBrByr e
(21)
and
4
111,1,
1
44 4
221,22,2,
11 1
titit
i
titiitiitit
ii i
sBse
yBsBys e
(21)
Alternatively, we may restrict the feedback from lagged percent changes in the price of oil, as
suggested by
 Exact

Hamilton (2003).
 Suffix

After imposing21,0,iBi the baseline nonlinear forecasting
model reduces to:
44
111,12,1,
11
44
222,2,
11
titiitit
ii
titiitit
ii
rBrBye
yByre
(22)
and
44
111,12,1,
11
44
222,2,
11
titiitit
ii
titiitit
ii
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152570
 Prefix

accounting for 11 percentage points by itself) and the omission of lagged percent
changes in the nominal price of oil (accounting for 4 percentage points by itself) are mainly
responsible for the additional gain in accuracy; the imposition of exogeneity plays no role.
Accuracy gains at slightly shorter or longer horizons are closer to 10%.
Second, neither the percent increase model based on
 Exact

Mork (1989)
 Suffix

nor the oneyear net
increase model motivated by Hamilton (1996) is more accurate than the AR(4) benchmark at the
onequarter horizon. This is true regardless of whether the price of oil is specified in nominal or
real terms and regardless of what additional restrictions we impose.
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152631
 Prefix

of lagged percent
changes in the nominal price of oil (accounting for 4 percentage points by itself) are mainly
responsible for the additional gain in accuracy; the imposition of exogeneity plays no role.
Accuracy gains at slightly shorter or longer horizons are closer to 10%.
Second, neither the percent increase model based on Mork (1989) nor the oneyear net
increase model motivated by
 Exact

Hamilton (1996)
 Suffix

is more accurate than the AR(4) benchmark at the
onequarter horizon. This is true regardless of whether the price of oil is specified in nominal or
real terms and regardless of what additional restrictions we impose.
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The first two columns of Table 20 focus on the evaluation period 1990.Q12010.Q2. Column (1)
shows that, for eight of ten model specifications, the onequarter ahead nonlinear forecasting
model proposed by
 Exact

Hamilton (2010)
 Suffix

fails to outperform the AR(4) benchmark model for real
GDP. Only for the real refiners’ acquisition cost for imported crude oil and for the nominal WTI
specification are there any gains in forecast accuracy.
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158583
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Only for the real refiners’ acquisition cost for imported crude oil and for the nominal WTI
specification are there any gains in forecast accuracy. In particular, the nominal PPI specification
favored by
 Exact

Hamilton (2010)
 Suffix

on the basis of insample diagnostics is less accurate than the AR
benchmark model. Much more favorable results are obtained at the oneyear horizon in column
(2) of Table 20. All but one nonlinear forecasting model yields reductions in the MSPE, although
the extent of these reductions greatly differs across models and can range from negligible to
substantial.
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159959
 Prefix

This remains an open question at this point.32
32 Some preliminary evidence on this question has been provided by Ravazzolo and Rothman (2010) and by
 Exact

Carlton (2010).
 Suffix

It is not straightforward to compare their results to those in Tables 19 and 20, however. Not only is their
analysis based on onestepahead real GDP growth forecasts from singleequation predictive models evaluated at the
relevant forecasting horizon (rather than iterated forecasts from multivariate models), but it is based on a sample
period that includes pre1973 data.
11.3.
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Real Oil Price Volatility
Interest in the volatility of oil prices also has been prompted by research aimed at establishing a
direct link from oil price volatility to business cycle fluctuations in the real economy. For
example,
 Exact

Bernanke (1983) and Pindyck (1991)
 Suffix

showed that the uncertainty of the price of oil
(measured by the volatility of the price of oil) matters for investment decisions if firms
contemplate an irreversible investment, the cash flow of which depends on the price of oil.
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An
analogous argument holds for consumers considering the purchase of energyintensive durables
such as cars. Real options theory implies that, all else equal, an increase in expected volatility
will cause marginal investment decisions to be postponed, causing a reduction in investment
expenditures.
 Exact

Kellogg (2010)
 Suffix

provides evidence that such mechanisms are at work in the Texas
oil industry, for example.
Unlike in empirical finance, the relevant volatility measure in these models is the
volatility of the real price of oil at horizons relevant to purchase and investment decisions, which
is typically measured in years or even decades rather than days or months, making standard
measures of shortterm no
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That might be the case at a threshold of $120 a barrel, for example, at
35 In rare cases, the relevant forecast horizon may be short enough for empirical analysis. For example,
 Exact

Kellogg (2010)
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makes the case that for the purpose of drilling oil wells in Texas, as opposed to Saudi Arabia, a forecast
horizon of only 18 months is adequate. Even at that horizon, however, there are no oilfutures options price data that
would allow the construction of implied volatility measures.
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For example, Kellogg (2010) makes the case that for the purpose of drilling oil wells in Texas, as opposed to Saudi Arabia, a forecast
horizon of only 18 months is adequate. Even at that horizon, however, there are no oilfutures options price data that
would allow the construction of implied volatility measures.
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Kellogg (2010)
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therefore converts the onemonth
volatility to 18month volatilities based on the term structure of oil futures. That approach relies on the assumption
that oil futures prices are reliable predictors of future oil prices.
which price major oil producers risk inducing the largescale use of alternative technologies with
adverse consequences for the longrun price of crude oil.36 Thus, the oil
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Likewise, a consumer of retail motor gasoline (and hence indirectly of crude oil) is likely
to be concerned with the price of gasoline exceeding what he can afford to spend each month
(see Edelstein and
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Kilian 2009).
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The threshold at which consumers might trade in their SUV for
a more energyefficient car is near $3 a gallon perhaps. The threshold at which commuters may
decide to relocate closer to their place of work might be at a price near $5 a gallon.
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In particular, if and only if the loss function is quadratic
and symmetric about zero, the variance of the price of oil about zero provides an adequate
summary statistic for the risk in oil price forecasts. Even that target variance, however, is distinct
38 Measures of risk of this type were first introduced by
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Fishburn (1977), Holthausen (1981),
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Artzner, Delbaen, Eber
and Heath (1999), and Basak and Shapiro (2001) in the context of portfolio risk management and have become a
standard tool in recent years (see, e.g., Engle and Brownlees 2010).
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For example, when fitting a random walk model of the
form 11tttss, the forecast errors at horizon 1 may be resampled using standard bootstrap
methods for homoskedastic or conditionally heteroskedastic data (see, e.g., Gonçalves and
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Kilian 2004).
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At longer horizons, one option is to fit the forecasting model on nonoverlapping
observations and proceed as for h = 1. This approach is simple, but may involve a considerable
reduction in estimation precision.
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Both of these effects may undermine the predictive power
of the price of oil for macroeconomic aggregates as well as the explanatory power of theoretical
models based on oil price forecasts.
Third, we have deliberately refrained from exploring the use of factor models for
forecasting the price of oil. In related work,
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Zagaglia (2010)
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reports some success in using a
factor model in forecasting the nominal price of oil at short horizons, although his evaluation
period is limited to early 2003 to early 2008, given the data limitations, and it is unclear how
sensitive the results would be to extending the evaluation period.
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Short
of developing a comprehensive worldwide data set of real aggregates at monthly frequency, it is
not clear whether there are enough predictors available for reliable realtime estimation of the
factors. For example, drawing excessively on U.S. real aggregates as in
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Zagaglia (2010)
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is
unlikely to be useful for forecasting the global price of oil for the reasons discussed in section 4.
Using a crosssection of data on energy prices, quantities, and other oilmarket related indicators
may be more promising, but almost half of the series used by Zagaglia are specific to the United
States and unlikely to be representative of global markets.
14.
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For example, we
found no evidence that the nominal PPI threeyear net increase model is more accurate than
linear models for real GDP growth at the onequarter horizon. A multivariate generalization of
the model proposed by
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Hamilton (2003, 2010)
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tended to provide MSPE gains of up to 12%
relative to the AR(4) benchmark model at longer horizons. Even more accurate results were
obtained with some alternative oil price series. All these forecasting successes, however, were
driven entirely by the 2008/09 recession.
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