
 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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4295
 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
 Exact

Edelstein and 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
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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), Davis and 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), Allcott and Wozny (2010), Busse, Knittel and Zettelmeyer (2010), 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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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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We evaluate this survey forecast of
the nominal retail price of gasoline against the nochange forecast benchmark. We also contrast
this survey forecast with the price of the corresponding futures contracts. Following
 Exact

Anderson, Kellogg and Sallee (2010),
 Suffix

we document that, after controlling for inflation, longterm household
gasoline price expectations are well approximated by a random walk. This finding has immediate
implications for modeling purchases of energyintensive consumer durables.
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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
 Exact

Kilian and Vigfusson (2010a,b),
 Suffix

but Hamilton (2010) 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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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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13716
 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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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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Shifting the starting date of
the OPEC period to 1974.1, in contrast, implies a considerable increase in volatility after 1985.
Extending the ending date of the OPEC period to include the price collapse in 1986 induced by
3 In related work,
 Exact

Dvir and Rogoff (2010)
 Suffix

present formal evidence of a structural break in the process driving the
annual real price of oil in 1973. Given this evidence of instability, combining pre and post1973 real oil price data
is not a valid option.
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19882
 Prefix

If the U.S. money supply
unexpectedly doubles, for example, then, according to standard macroeconomic models, so will
all nominal prices denominated in dollars (including the nominal price of oil), leaving the
relative price or real price of crude oil unaffected (see
 Exact

Gillman and Nakov 2009).
 Suffix

Clearly, one
would not want to interpret such an episode as an oil price shock involving a doubling of the
4 For further discussion of the tradeoffs between alternative oil price definitions from an economic point of view
see Kilian and Vigfusson (2010b).
5 For a review of the relationship between the concepts of (strict) exogeneity
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20194
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Clearly, one
would not want to interpret such an episode as an oil price shock involving a doubling of the
4 For further discussion of the tradeoffs between alternative oil price definitions from an economic point of view
see
 Exact

Kilian and Vigfusson (2010b).
 Suffix

5 For a review of the relationship between the concepts of (strict) exogeneity and predictability in linear models see
Cooley and LeRoy (1985).
nominal price of oil. Indeed, economic models of the impact of the price of oil on the U.
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 Prefix

an episode as an oil price shock involving a doubling of the
4 For further discussion of the tradeoffs between alternative oil price definitions from an economic point of view
see Kilian and Vigfusson (2010b). 5 For a review of the relationship between the concepts of (strict) exogeneity and predictability in linear models see
 Exact

Cooley and LeRoy (1985).
 Suffix

nominal price of oil. Indeed, economic models of the impact of the price of oil on the U.S.
economy correctly predict that such a nominal oil price shock should have no effect on the U.S.
economy because theoretical models inevitably are specified in terms of the real price of oil,
which has not changed in this example.
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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; Almoguera, Douglas and Herrera 2010).
 Suffix

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.S. macroeconomic conditions.
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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
 Exact

Barsky and 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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Moreover, as observed by Barsky and Kilian (2002), 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
 Exact

Green and Porter 1984).
 Suffix

Thus,
both nominal and real oil prices must be considered endogenous with respect to the global
economy, unless proven otherwise.
A third and distinct argument has been that consumers of refined oil products choose to
respond to changes in the nominal price of oil rather than the real price of oil, perhaps because
the nominal price of oil is more visible.
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 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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 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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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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 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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 Prefix

Although Hamilton (2003) 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.,
 Exact

Kilian and Vigfusson 2010a; Herrera, Lagalo and Wada 2010).
 Suffix

prior to 2003. This finding is also consistent with the empirical results in Baumeister and
Peersman (2010).
For now we set aside all nonlinear transformations of the price of oil and focus on linear
forecasting models for the nominal price of oil and for the real price of oil.
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Although Hamilton (2003) 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. This finding is also consistent with the empirical results in
 Exact

Baumeister and Peersman (2010).
 Suffix

For now we set aside all nonlinear transformations of the price of oil and focus on linear
forecasting models for the nominal price of oil and for the real price of oil. Nonlinear joint
forecasting models for U.
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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
 Exact

Inoue and 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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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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This line of reasoning is familiar from the analysis of stock and bond prices as well
as exchange rates.
7
In the latter case, the endogeneity of the nominal price of oil with respect to
the U.S. economy implies that lagged changes in U.S. macroeconomic aggregates have
predictive power for the nominal price of oil in the post1973 data (see, e.g.,
 Exact

Cooley and LeRoy 1985).
 Suffix

A recent study by Kilian and Vega (2010) helps resolve the question of which
interpretation is more appropriate. Kilian and Vega find no evidence of systematic feedback from
news about a wide range of U.
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29784
 Prefix

This line of reasoning is familiar from the analysis of stock and bond prices as well
as exchange rates.
7
In the latter case, the endogeneity of the nominal price of oil with respect to
the U.S. economy implies that lagged changes in U.S. macroeconomic aggregates have
predictive power for the nominal price of oil in the post1973 data (see, e.g., Cooley and LeRoy 1985). A recent study by
 Exact

Kilian and Vega (2010)
 Suffix

helps resolve the question of which
interpretation is more appropriate. Kilian and Vega find no evidence of systematic feedback from
news about a wide range of U.S. macroeconomic aggregates to the nominal price of oil within a
month.
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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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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
 Exact

Barsky and 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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There are several reasons to expect the dollardenominated nominal price of oil to
respond to changes in nominal U.S. macroeconomic aggregates. One channel of transmission is
purely monetary and operates through U.S. inflation. For example,
 Exact

Gillman and Nakov (2009)
 Suffix

stress that changes in the nominal price of oil must occur in equilibrium just to offset persistent
shifts in U.S. inflation, given that the price of oil is denominated in dollars. Indeed, the Granger
causality tests in Table 1a indicate highly significant lagged feedback from U.
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Indeed, the Granger
causality tests in Table 1a indicate highly significant lagged feedback from U.S. headline CPI
inflation to the percent change in the nominal WTI price of oil for the full sample, consistent
with the findings in
 Exact

Gillman and Nakov (2009).
 Suffix

The evidence for the other oil price series is
somewhat weaker with the exception of the refiners’ acquisition cost for imported crude oil, but
that result may simply reflect a loss of power when the sample size is shortened.9
Gillman and Nakov view changes in inflation in the post1973 period as rooted in
persistent changes in the growth rate of money.
10
Thus, an alternative approach of tes
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32984
 Prefix

oil price series is
somewhat weaker with the exception of the refiners’ acquisition cost for imported crude oil, but
that result may simply reflect a loss of power when the sample size is shortened.9
Gillman and Nakov view changes in inflation in the post1973 period as rooted in
persistent changes in the growth rate of money.
10
Thus, an alternative approach of testing the
hypothesis of
 Exact

Gillman and Nakov (2009)
 Suffix

is to focus on Granger causality from monetary
aggregates to the nominal price of oil. 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 Kilian 2002).
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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
 Exact

Barsky and 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

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 monetary factors in determining the price of oil see
 Exact

Barsky and 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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 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
 Exact

Barsky and Kilian (2002) and Gillman and Nakov (2009)
 Suffix

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 that the relative price of
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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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38649
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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
Hamilton (1983) using quarterly data and in
 Exact

Gillman and Nakov (2009)
 Suffix

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. This difference in results is suggestive of a structural break
in late 1973 in the predictive relationship between the price of oil and the U.
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In other words, autoregressive or moving average time series
processes are inappropriate for these data and tests based on such models have to be viewed with
11 Although the U.K. has been exporting crude oil starting in the late 1970s, its share of petroleum exports is too low
to consider the U.K. a commodity exporter (see
 Exact

Kilian, Rebucci and Spatafora 2009).
 Suffix

caution.
This problem with the pre1973 data may be ameliorated by deflating the nominal price
of oil, which renders the oil price data continuous and more amenable to VAR analysis (see
Figure 2). Additional problems arise, however, when combining oil price data generated by a
discretecontinuous choice process with data from the postTexas Railroad Commission era that
are fully continuous.
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This instability manifests itself in a structural
break in the predictive regressions commonly used to test for lagged potentially nonlinear
feedback from the real of price of oil to real GDP growth (see, e.g.,
 Exact

Balke, Brown and Yücel 2002).
 Suffix

The pvalue for the null hypothesis that there is no break in 1973.Q4 in the coefficients of
this predictive regression is 0.001 (see Kilian and Vigfusson 2010b).
12
For that reason, regression
estimates of the relationship between the real price of oil and domestic macroeconomic
aggregates obtained from the entire postwar period are not informative about the strength of
these relationships
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41757
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This instability manifests itself in a structural
break in the predictive regressions commonly used to test for lagged potentially nonlinear
feedback from the real of price of oil to real GDP growth (see, e.g., Balke, Brown and Yücel 2002). The pvalue for the null hypothesis that there is no break in 1973.Q4 in the coefficients of
this predictive regression is 0.001 (see
 Exact

Kilian and Vigfusson 2010b).
 Suffix

12
For that reason, regression
estimates of the relationship between the real price of oil and domestic macroeconomic
aggregates obtained from the entire postwar period are not informative about the strength of
these relationships in post1973 data.
13
In the analysis of the real price of oil below we therefore
restrict the evaluation period to start no earlier than 1973.1.
4.2.
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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
 Exact

Barsky and 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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Unless the real price of oil is forward
looking and already embodies all information about future U.S. real GDP, a reasonable
conjecture therefore is that lagged U.S. real GDP should help predict the real price of oil. Recent
research by
 Exact

Kilian and Murphy (2010)
 Suffix

has shown that the real price of oil indeed contains an
asset price component, but that this component most of the time explains only a small fraction of
the historical variation in the real price of oil.
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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; Kilian and Murphy 2010).
 Suffix

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.
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Only when real GDP fluctuations are highly correlated across countries
would we expect U.S. real GDP to be a good proxy for world real GDP.
15
In addition, as the
U.S. share in world GDP evolves, by construction so do the predictive correlations underlying
Table 2. In this regard,
 Exact

Kilian and Hicks (2010)
 Suffix

have documented dramatic changes in the PPPadjusted share in GDP of the major industrialized economies and of the main emerging
economies in recent years that cast further doubt on the U.S. real GDP results in Table 2.
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An alternative quarterly predictor that partially addresses these last two concerns is
quarterly world industrial production from the U.N. Monthly Bulletin of Statistics. This series has
recently been introduced by
 Exact

Baumeister and Peersman (2010)
 Suffix

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 Beyer, Doornik and Hendry (2001), one would expect this
series to be a better proxy for global fluctuations in the demand for crude oil than U.
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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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This is a broad measure of monthly real economic activity in the United States obtained from
applying principal component analysis to a wide range of monthly indicators of real activity
expressed in growth rates (see
 Exact

Stock and Watson 1999).
 Suffix

As in the case of quarterly U.S. real
GDP, there is no evidence of Granger causality. If we rely on U.S. industrial production as the
predictor, there is weak evidence of feedback to the domestic price of oil for the LT model.
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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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It also highlights a fourth issue. There is
evidence that allowing for two years worth of lags rather than one year often strengthens the
significance of the rejections. This finding mirrors the point made in
 Exact

Hamilton and Herrera (2004)
 Suffix

that it is essential to allow for a rich lag structure in studying the dynamic relationship
between the economy and the price of oil.
Although none of the proxies for global fluctuations in demand is without limitations, we
conclude that there is a robust pattern of Granger causality, as we correct for problems of model
misspecification and of data mismeasurement that undermine the power of th
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Although none of the proxies for global fluctuations in demand is without limitations, we
conclude that there is a robust pattern of Granger causality, as we correct for problems of model
misspecification and of data mismeasurement that undermine the power of the test. This
conclusion is further strengthened by evidence in
 Exact

Kilian and Hicks (2010)
 Suffix

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.
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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
 Exact

Inoue and 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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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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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; Alquist and 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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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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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
 Exact

Alquist and 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
 Exact

Alquist and 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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predictor, 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
 Exact

Alquist and 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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The
forecast evaluation period is 1991.12009.12 with suitable adjustments, as the forecast horizon is
varied. The assessment of which forecasting model is most accurate may depend on the loss
function of the forecaster (see
 Exact

Elliott and Timmermann 2008).
 Suffix

We report results for the MSPE
and the relative frequency with which a forecasting model correctly predicts the sign of the
change in the spot price based on the success ratio statistic of Pesaran and Timmermann (2009).
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The assessment of which forecasting model is most accurate may depend on the loss
function of the forecaster (see Elliott and Timmermann 2008). We report results for the MSPE
and the relative frequency with which a forecasting model correctly predicts the sign of the
change in the spot price based on the success ratio statistic of
 Exact

Pesaran and Timmermann (2009).
 Suffix

We formally test the null hypothesis that a given candidate forecasting model is as accurate as
the random walk without drift against the alternative that the candidate model is more accurate
than the nochange forecast.
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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.,
 Exact

Inoue and Kilian 2004a,b; Clark and McCracken 2010).
 Suffix

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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We conclude that there is no compelling evidence that, over this sample period, monthly
oil futures prices were more accurate predictors of the nominal price of oil than simple nochange forecasts. 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
 Exact

Alquist and 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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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
 Exact

Wu and McCallum (2005).
 Suffix

Yet another approach is to exploit the implication of the Hotelling (1931) 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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67599
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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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68076
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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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Note that the daily data are sparse in that there are many days for which no price quotes
exist. We eliminate these dates from the sample and stack the remaining observations similar to
the approach taken in
 Exact

Kilian and Vega (2010)
 Suffix

in the context of modeling the impact of U.S.
macroeconomic news on the nominal price of oil. Table 9 summarizes our findings. The MSPE
ratios in Table 9 indicate somewhat larger gains in forecasting accuracy from using oil futures
prices than in Tables 4 through 8.
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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
 Exact

Alquist and 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; Davis and Kilian 2010; Allcott and Wozny 2010).
 Suffix

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. An obvious concern is that actual
consumer expectations may differ from the predictions generated by the forecasting methods
considered so far.
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An obvious concern is that actual
consumer expectations may differ from the predictions generated by the forecasting methods
considered so far. Unfortunately, time series data on consumer expectations of gasoline prices
are rare, which has prevented a systematic investigation of this important question.
Recently,
 Exact

Anderson, Kellogg and Sallee (2010)
 Suffix

obtained a previously unused data set
from the Michigan Survey of Consumers on U.S. households’ expectations of gasoline prices.
The survey asks consumers about how many cents per gallon they think gasoline prices will
increase or decrease during the next five years compared to now.
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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
 Exact

Edelstein and 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.,
 Exact

Inoue and Kilian (2004b), Clark and McCracken 2010).
 Suffix

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). We search over
p0,...,12 .
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104871
 Prefix

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 Kilian (2004b), Clark and McCracken 2010). 26 The refiners’ acquisition cost was extrapolated back to 1973.2 as in
 Exact

Barsky and 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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104916
 Prefix

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 Kilian (2002). selection (see
 Exact

Inoue and Kilian 2006; Marcellino, Stock and Watson 2006).
 Suffix

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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105322
 Prefix

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. In particular, the standard tests discussed in
 Exact

Clark and McCracken (2001, 2005)
 Suffix

or
Clark and West (2007) are only designed for direct forecasts. Below we assess the significance
of the MSPE reductions based on bootstrap pvalues for the MSPE ratio constructed under the
null of a random walk model without drift.
27
The upper panel of Table 12 suggests that AR and
ARMA models in log levels have lower recursive MSPE than the nochange forecast at short
horizons.
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105359
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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. In particular, the standard tests discussed in Clark and McCracken (2001, 2005) or
 Exact

Clark and West (2007)
 Suffix

are only designed for direct forecasts. Below we assess the significance
of the MSPE reductions based on bootstrap pvalues for the MSPE ratio constructed under the
null of a random walk model without drift.
27
The upper panel of Table 12 suggests that AR and
ARMA models in log levels have lower recursive MSPE than the nochange forecast at short
horizons.
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 Prefix

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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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
 Exact

Kilian and Murphy (2010).
 Suffix

The sample period is 1973.22009.8. The variables in
this model include the percent change in global crude oil production, the global real activity
measure we already discussed in section 4, the log of the real price of oil, and a proxy for the
change in global aboveground crude oil inventories.
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The variables in
this model include the percent change in global crude oil production, the global real activity
measure we already discussed in section 4, the log of the real price of oil, and a proxy for the
change in global aboveground crude oil inventories. For further discussion of the data see
 Exact

Kilian and Murphy (2010).
 Suffix

The VAR model may be consistently estimated without taking a stand on
whether the real price of oil is I(0) or I(1) (see Sims, Stock and Watson 1990). We focus on
recursive rather than rolling regression forecasts throughout this section.
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108712
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in global crude oil production, the global real activity
measure we already discussed in section 4, the log of the real price of oil, and a proxy for the
change in global aboveground crude oil inventories. For further discussion of the data see Kilian and Murphy (2010). The VAR model may be consistently estimated without taking a stand on
whether the real price of oil is I(0) or I(1) (see
 Exact

Sims, Stock and Watson 1990).
 Suffix

We focus on
recursive rather than rolling regression forecasts throughout this section. This approach makes
sense in the absence of structural change, given the greater efficiency of recursive regressions
and the small sample size.
28
A natural starting point for the forecast accuracy comparison is the unrestricted VAR
model.
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109565
 Prefix

For that reason unrestricted VAR models are rarely
used in applied forecasting. They nevertheless provide a useful point of departure. The upper
panel of Table 13 shows results for unrestricted VAR models with 12 lags. Column (1)
corresponds to the fourvariable model used in
 Exact

Kilian and Murphy (2010).
 Suffix

Table 13 shows that
this unrestricted VAR forecast has lower recursive MSPE than the nochange forecast at all
horizons but one and nontrivial directional accuracy.
29
Despite the lack of parsimony, the
reductions in the MSPE are somewhat larger than for the AR and ARMA models in Table 12.
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110555
 Prefix

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
 Exact

Inoue and 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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113654
 Prefix

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
 Exact

Inoue and 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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115350
 Prefix

Which model is the population model, of course, is irrelevant for the question of which
model generates more accurate forecasts in finite samples, so we have to interpret this rejection
with some caution. This type of insight recently has prompted the development of alternative
tests of equal predictive accuracy based on localtozero asymptotic approximations to the
predictive regression.
 Exact

Clark and McCracken (2010)
 Suffix

for the first time proposed a correctly
specified test of the null of equal outofsample MSPEs. Their analysis is limited to direct
forecasts from much simpler forecasting models, however, and cannot be applied in Table 13.30
This caveat suggests that we discount only marginally statistically significant rejections of the no
predictability null hypothesis in Table 13 and focus on the highly
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116183
 Prefix

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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116351
 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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 Start

116451
 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 Calhoun (2010) who shows that
standard tests of equal predictive accuracy for nested models such as
 Exact

Clark and McCracken (2001)
 Suffix

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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 Start

116481
 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 Calhoun (2010) who shows that
standard tests of equal predictive accuracy for nested models such as Clark and McCracken (2001) or
 Exact

Clark and West (2007)
 Suffix

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. None of the remedies
is directly applicable in the context of Table 12, however.
8.1.2.
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118617
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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
 Exact

Baumeister and 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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119283
 Prefix

At longer horizons the MSPE reductions diminish even for the best
VAR models. Beyond one year, the nochange forecast usually has lower MSPE than the VAR
model. Baumeister and Kilian also show that VAR forecasting models based on
 Exact

Kilian and Murphy (2010)
 Suffix

exhibit significantly improved directional accuracy. The improved directional
accuracy persists even at horizons at which the MSPE gains have vanished. The success ratios
range from 0.51 to 0.60, depending on the model specification and horizon.
8.2.
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121326
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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
 Exact

Baumeister and 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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122107
 Prefix

In the
VAR model at hand a natural starting point would be to shrink all lagged parameters toward zero
under the maintained assumption of stationarity. This leaves open the question of how to
determine the weights of the prior relative to the information in the likelihood.
 Exact

Giannone, Lenza and Primiceri (2010)
 Suffix

recently proposed a simple and theoretically founded databased method for
the selection of priors in recursively estimated Bayesian VARs (BVARs). Their
recommendation is to select priors using the marginal data density (i.e., the likelihood function
integrated over the model parameters), which only depends on the hyperparameters that
characterize the relative weight of the prior and the info
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122788
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They provide
empirical examples in which the forecasting accuracy of that model in recursive settings is not
only superior to unrestricted VAR models, but is comparable to that of singleequation dynamic
factor models (see
 Exact

Stock and Watson 1999).
 Suffix

Table 16 compares the forecasting accuracy of this approach with that of the unrestricted
VAR models considered in Tables 13 and 15. In all cases, we shrink the model parameters
toward a white noise prior mean with the desired degree of shrinkage being determined by the
databased procedure in Giannone et al. (2010).
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 Prefix

Table 16 compares the forecasting accuracy of this approach with that of the unrestricted
VAR models considered in Tables 13 and 15. In all cases, we shrink the model parameters
toward a white noise prior mean with the desired degree of shrinkage being determined by the
databased procedure in
 Exact

Giannone et al. (2010).
 Suffix

For models with 12 lags, there is no strong
evidence that shrinkage estimation reduces the MSPE. Although there are some cases in which
imposing Bayesian priors reduces the MSPE slightly, in other cases it increases the MSPE
slightly.
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123989
 Prefix

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
 Exact

Baumeister and 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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124661
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Structural VAR Forecasts of the Real Price of Oil
Recent research has shown that historical fluctuations in the real price of oil can be decomposed
into the effects of distinct oil demand and oil supply shocks associated with unpredictable shifts
in global oil production, real activity and a forwardlooking or speculative element in the real
price of oil (see, e.g.,
 Exact

Kilian and Murphy 2010).
 Suffix

Changes in the composition of these shocks help
explain why conventional regressions of macroeconomic aggregates on the price of oil tend to be
unstable. They also are potentially important in interpreting oil price forecasts.
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125045
 Prefix

They also are potentially important in interpreting oil price forecasts.
In section 8 we showed that recursive forecasts of the real price of oil based on the type
of oil market VAR model proposed in
 Exact

Kilian and Murphy (2010)
 Suffix

for the purpose of structural
analysis are not necessarily inferior to simple nochange forecasts. The case for the use of VAR
models, however, does not rest on their predictive accuracy alone. Policymakers expect oil price
forecasts to be interpretable in light of an economic model.
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125865
 Prefix

Questions of interest include, for example, what effects an unexpected slowing of Asian growth
would have on the forecast of the real price of oil; or what the effect would be of an unexpected
decline in global oil production associated with peak oil. Answering questions of this type is
impossible using reducedform time series models. It requires a fully structural VAR model (see
 Exact

Waggoner and Zha 1999).
 Suffix

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 Kilian (2011).
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126022
 Prefix

It requires a fully structural VAR model (see
Waggoner and Zha 1999). In this section we illustrate how to generate such projections from the structural moving
average representation of the VAR model of
 Exact

Kilian and Murphy (2010)
 Suffix

estimated on data
extending to 2009.8. The discussion closely follows Baumeister and Kilian (2011). 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 bu
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126117
 Prefix

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
 Exact

Baumeister and 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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128133
 Prefix

The first scenario involves a successful stimulus to U.S. oil production, as
had been considered by the Obama administration prior to the 2010 oil spill in the Gulf of
Mexico. Here we consider the likely effects of a 20% increase in U.S. crude oil output in 2009.9,
after the estimation sample of
 Exact

Kilian and Murphy (2010)
 Suffix

ends. This is not to say that such a
dramatic and sudden increase would be feasible, but that it would be a bestcase scenario. Such a
U.S. oil supply stimulus would translate to a 1.5% increase in world oil production, which is well
within the variation of historical data.
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130066
 Prefix

Alternatively, one could express these
results relative to the unconditional VAR forecast.
Finally, we consider the possibility of a speculative frenzy such as occurred starting in
mid1979 after the Iranian Revolution (see
 Exact

Kilian and Murphy 2010).
 Suffix

This scenario involves
feeding into the model future structural shocks corresponding to the sequence of speculative
demand shocks that occurred between 1979.1 and 1980.2 and were a major contributor to the
1979/80 oil price shock episode.
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135875
 Prefix

The baseline results are for the U.S. refiners’ acquisition cost for imported
crude oil. Toward the end of the section we discuss how these results are affected by other oil
price choices. Our discussion draws on results in
 Exact

Kilian and Vigfusson (2010c).
 Suffix

11.1. Linear Autoregressive Models
A natural starting point is a linear VAR(p) model for the real price of oil and for U.S. real GDP
expressed in quarterly percent changes. The general structure of the model is 1()tttxBLxe,
where [,] ,tttxry tr denotes the log of real price of oil, ty the log of real GDP, is the
difference operator, tethe regression error, and
21
( )12 3.
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136887
 Prefix

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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141297
 Prefix

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
 Exact

Edelstein and 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
 Prefix

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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141891
 Prefix

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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142882
 Prefix

Hamilton’s line of reasoning has prompted many researchers to construct asymmetric
responses to positive and negative oil price innovations from censored oil price VAR models.
Censored oil price VAR models refer to linear VAR models for
,,3
[,],
netyr
possibly
sytt
31 In related work,
 Exact

Ramey and Vine (2010)
 Suffix

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.
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143161
 Prefix

3
[,],
netyr
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
 Exact

Edelstein and 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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143213
 Prefix

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 Kilian (2009) and that postulated in
 Exact

Ramey and Vine (2010)
 Suffix

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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143307
 Prefix

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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143491
 Prefix

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 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. Recently,
 Exact

Kilian and Vigfusson (2010a)
 Suffix

have shown that impulse
response estimates from VAR models involving censored oil price variables are inconsistent
even when equation (18) is correctly specified. Specifically, that paper demonstrated, first, that
asymmetric models of the transmission of oil price shocks cannot be represented as censored oil
price VAR models and are fundamentally misspecified whether the data generating proces
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144281
 Prefix

Second, standard approaches to the construction of structural impulse
responses in this literature are invalid, even when applied to correctly specified models. Instead,
Kilian and Vigfusson proposed a modification of the procedure discussed in
 Exact

Koop, Pesaran and Potter (1996).
 Suffix

Third, standard tests for asymmetry based on the slope coefficients of singleequation predictive models are neither necessary nor sufficient for judging the degree of
asymmetry in the structural response functions, which is the question of ultimate interest to users
of these models.
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144803
 Prefix

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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145333
 Prefix

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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145916
 Prefix

whether the predictive model should be specified as
44
,,3
11
netyr
titiitit
ii
yysu
, (18)
as in Hamilton (2003), or rather as:
444
,,3
111
netyr
titiitiitit
iii
yyssu
(19)
as in
 Exact

Balke, Brown and Yücel (2002)
 Suffix

or Herrera, Lagalo and Wada (2010), for example. The
latter specification encompasses the linear reducedform model as a special case. Kilian and
Vigfusson prove that dropping the lagged percent changes from model (19) will cause an
inconsistency of the OLS estimates, except in the theoretically implausible case that there is no
lagged feedback from percent changes in the price of oil to real
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145949
 Prefix

be specified as
44
,,3
11
netyr
titiitit
ii
yysu
, (18)
as in Hamilton (2003), or rather as:
444
,,3
111
netyr
titiitiitit
iii
yyssu
(19)
as in Balke, Brown and Yücel (2002) or
 Exact

Herrera, Lagalo and Wada (2010),
 Suffix

for example. The
latter specification encompasses the linear reducedform model as a special case. Kilian and
Vigfusson prove that dropping the lagged percent changes from model (19) will cause an
inconsistency of the OLS estimates, except in the theoretically implausible case that there is no
lagged feedback from percent changes in the price of oil to real GDP.
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146862
 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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148426
 Prefix

Below we therefore consider specifications with and without imposing
exogeneity.
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
 Exact

Kilian and Vigfusson (2010b,
 Suffix

c). 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 Hamilton (2003).
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148556
 Prefix

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
 Prefix

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
 Prefix

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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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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additional question would be how the results of the forecast accuracy comparison for
U.S. real GDP growth would have changed, had we only used data sets actually available as of
the time the forecast is generated. This remains an open question at this point.32
32 Some preliminary evidence on this question has been provided by
 Exact

Ravazzolo and Rothman (2010) and
 Suffix

by Carlton
(2010). 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.
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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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Nonparametric Approaches
Our approach in this section has been parametric. Alternatively, one could have used
nonparametric econometric models to investigate the forecasting ability of the price of oil for
real GDP. In related work,
 Exact

Bachmeier, Li and Liu (2008)
 Suffix

used the integrated conditional
moment test of Corradi and Swanson (2002, 2007) to investigate whether oil prices help forecast
real GDP growth onequarter ahead. The advantage of this approach is that – while imposing
linearity under the null – it allows for general nonlinear models under the alternative; the
disadvantage is that the test is less powerful than the parametric approach if the p
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Alternatively, one could have used
nonparametric econometric models to investigate the forecasting ability of the price of oil for
real GDP. In related work, Bachmeier, Li and Liu (2008) used the integrated conditional
moment test of
 Exact

Corradi and Swanson (2002, 2007) to
 Suffix

investigate whether oil prices help forecast
real GDP growth onequarter ahead. The advantage of this approach is that – while imposing
linearity under the null – it allows for general nonlinear models under the alternative; the
disadvantage is that the test is less powerful than the parametric approach if the parametric
structure is known.
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The pvalue for percent
changes in the WTI price of crude oil is 0.77. Similar results are obtained for real net increases
and for percent changes in the real WTI price. These findings are broadly consistent with ours.
 Exact

Bachmeier et al. (2008)
 Suffix

also report qualitatively similar results using a number of fully
nonparametric approaches. An obvious caveat is that their analysis is based on data since 1949,
which is not appropriate for the reasons discussed earlier, and ends before the 2008/09 recession.
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The upper panel of Figure 15 shows the 1month implied volatility time series
for 2001.12009.12, computed from daily CRB data, following the same procedure as for the
spot and futures prices in section 5. Alternatively, we may use daily percent changes in the
nominal WTI price of oil to construct measures of realized volatility, as shown in the second
panel of Figure 15 (see, e.g.,
 Exact

Bachmeier, Li and Liu 2008).
 Suffix

Finally, yet another measure of
volatility can be constructed from parametric GARCH or stochastic volatility models. The
bottom panel of Figure 15 shows the 1monthahead conditional variance obtained from
recursively estimated Gaussian GARCH(1,1) models.
33
The initial estimation period is 1974.12000.12.
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Given that oil is only one of many assets handled by portfolio managers, however, it is not clear that the GARCHinMean model for singleasset markets is appropriate in this context, while more general multivariate GARCH
models are all but impossible to estimate reliably on the small samples available for our purposes (see, e.g.,
 Exact

Bollerslev, Chou and Kroner 1992).
 Suffix

34 We deliberately focus on oil price volatility at the 1month horizon. Although from an economic point of view
volatility forecasting at longer horizons would be of great interest, the sparsity of options price data makes it
difficult to extend the implied volatility approach to longer horizons.
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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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Measuring the volatility of the real
price of oil at such long forecast horizons is inherently difficult given how short the available
time series are, and indeed researchers in practice have typically asserted rather than measured
these shifts in real price volatility or they have treated shorthorizon volatility as a proxy for
longerhorizon volatility (see, e.g.,
 Exact

Elder and Serletis 2010).
 Suffix

35 This approach is unlikely to work.
Standard monthly or quarterly GARCH model cannot be used to quantify changes in the longerrun expected volatility of the real price of oil because GARCH forecasts of the conditional
variance quickly revert to their time invariant unconditional expectation, as the forecasting
horizon increases.
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If volatility at the economically relevant horizon is constant by construction, it
cannot explain variation in real activity over time, suggesting that survey data may be better
suited for characterizing changes in forecast uncertainty over time. Some progress in this
direction may be expected from ongoing work conducted by
 Exact

Anderson, Kellogg and Sallee (2010)
 Suffix

based on the distribution of Michigan consumer expectations of 5yearahead gasoline
prices. For further discussion of this point also see Kilian and Vigfusson (2010b).
12.3. Quantifying Oil Price Risks
Although oil price volatility shifts play an important role in discussions of the impact of oil price
shocks, it is important to keep in mind that volatility measures are not in general usefu
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Some progress in this
direction may be expected from ongoing work conducted by Anderson, Kellogg and Sallee (2010) based on the distribution of Michigan consumer expectations of 5yearahead gasoline
prices. For further discussion of this point also see
 Exact

Kilian and Vigfusson (2010b).
 Suffix

12.3. Quantifying Oil Price Risks
Although oil price volatility shifts play an important role in discussions of the impact of oil price
shocks, it is important to keep in mind that volatility measures are not in general useful measures
of the price risks faced by either producers or consumers of crude oil (or of refined products).
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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)
 Suffix

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.
 Exact

Kellogg (2010)
 Suffix

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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In fact, it can be shown
that risk measures are not only quantitatively different from volatility measures, but in practice
may move in the opposite direction.
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
 Exact

Edelstein and Kilian 2009).
 Suffix

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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One requirement is that the measure of risk
must be related to the probability distribution ()Fof the random variable of interest; the other
requirement is that it must be linked to the preferences of the user, typically parameterized by a
loss function (see
 Exact

Machina and Rothschild 1987).
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Except in special cases these requirements rule
out commonly used measures of risk based on the predictive distribution alone such as the
sample moments, sample quantiles or the value at risk. In deriving appropriate risk measures that
characterize the predictive distribution for the real price of oil, it is useful to start with the loss
function.
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functions ()lthat encompasses the two empirical
examples above is:
36 A similar irreversible shift in OECD demand occurred after the oil price shocks of the 1970s when fuel oil was
increasingly replaced by natural gas. The fuel oil market never recovered, even as the price of this fuel fell
dramatically in the 1980s and 1990s (see
 Exact

Dargay and Gately 2010).
 Suffix

37 The threshold of $120 in this example follows from adjusting the cost estimates for shale oil production in Farrell
and Brandt (2006) for the cumulative inflation rate since 2000.
lRifR RR
aRR ifRR
()
()0
(1) ()
thth
thth
aR RifRR
thth
where thRdenotes the real price of oil in dollars hperiods from date ,t 01ais the weight
attached to downside ris
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The fuel oil market never recovered, even as the price of this fuel fell
dramatically in the 1980s and 1990s (see Dargay and Gately 2010). 37 The threshold of $120 in this example follows from adjusting the cost estimates for shale oil production in
 Exact

Farrell and Brandt (2006)
 Suffix

for the cumulative inflation rate since 2000.
lRifR RR
aRR ifRR
()
()0
(1) ()
thth
thth
aR RifRR
thth
where thRdenotes the real price of oil in dollars hperiods from date ,t 01ais the weight
attached to downside risks, and 0 and 0 measure the user’s degree of risk aversion.
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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
 Exact

Fishburn (1977), Holthausen (1981),
 Suffix

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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Even that target variance, however, is distinct
38 Measures of risk of this type were first introduced by Fishburn (1977), Holthausen (1981), Artzner, Delbaen, Eber
and Heath (1999), and
 Exact

Basak and Shapiro (2001)
 Suffix

in the context of portfolio risk management and have become a
standard tool in recent years (see, e.g., Engle and Brownlees 2010). For a general exposition of risk measures and
risk management in a different context see Kilian and Manganelli (2007, 2008).
from conventionally used measures of oil price volatility, defined as the variance about the
sample mean of the predictive distribution.
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Even that target variance, however, is distinct
38 Measures of risk of this type were first introduced by Fishburn (1977), Holthausen (1981), 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.,
 Exact

Engle and Brownlees 2010).
 Suffix

For a general exposition of risk measures and
risk management in a different context see Kilian and Manganelli (2007, 2008).
from conventionally used measures of oil price volatility, defined as the variance about the
sample mean of the predictive distribution.
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38 Measures of risk of this type were first introduced by Fishburn (1977), Holthausen (1981), 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). For a general exposition of risk measures and
risk management in a different context see
 Exact

Kilian and Manganelli (2007, 2008).
 Suffix

from conventionally used measures of oil price volatility, defined as the variance about the
sample mean of the predictive distribution. The latter measure under no circumstances can be
interpreted as a risk measure because it depends entirely on the predictive distribution of the
price of oil and not at all on the user’s preferences.
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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.,
 Exact

Gonçalves and 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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Models that incorporate information about
such spreads or about the underlying determinants of demand have the potential of improving
forecasts of the price of a given grade of crude oil.
A second issue of interest is the role played by heterogenous oil price and gasoline price
expectations in modeling the demand for energyintensive durables (see
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Anderson, Kellogg and Sallee 2010).
 Suffix

There is strong evidence that not all households share the same expectations,
casting doubt on standard rational expectations models with homogeneous agents. This also calls
into question the use of a single price forecast in modeling purchasing decisions in the aggregate.
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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
 Exact

Zagaglia (2010)
 Suffix

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
 Exact

Hamilton (2003, 2010)
 Suffix

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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