The 171 reference contexts in paper Ron Alquist, Lutz Kilian, Robert J. Vigfusson (2011) “Forecasting the Price of Oil” / RePEc:bca:bocawp:11-15

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    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,
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    Hamilton (2009),
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    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
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    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
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    Edelstein and Kilian (2009),
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    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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    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.,
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    Kahn (1986), Davis and Kilian (2010).
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    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 out-of-sample forecastability.
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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., Kahn (1986), Davis and Kilian (2010). 2 See, e.g.,
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    Goldberg (1998), Allcott and Wozny (2010), Busse, Knittel and Zettelmeyer (2010), Kellogg (2010).
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    in population. Predictability in population, however, need not translate into out-of-sample 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 out-of-sample 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 no-change forecast. Similarly, forecasting models based on the dollar exchange rates of major commodity exporters, models based on the
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    Hotelling (1931), and
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    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 no-change 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 no-change forecast benchmark. We also contrast this survey forecast with the price of the corresponding futures contracts. Following
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    Anderson, Kellogg and Sallee (2010),
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    we document that, after controlling for inflation, long-term household gasoline price expectations are well approximated by a random walk. This finding has immediate implications for modeling purchases of energy-intensive 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
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    Kilian and Vigfusson (2010a,b),
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    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
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    Hamilton (2010)
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    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 WTI data until 1973 tend to exhibit a pattern resembling a step-function. The price remains constant for extended periods, followed by discrete adjustments. The U.S. wholesale price of oil for 1948-1972 used in
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    Hamilton (1983)
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    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 1948-72.
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    The price remains constant for extended periods, followed by discrete adjustments. The U.S. wholesale price of oil for 1948-1972 used in Hamilton (1983) is numerically identical with this WTI series. As discussed in
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    Hamilton (1983, 1985)
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    the discrete pattern of crude oil price changes during this period is explained by the specific regulatory structure of the oil industry during 1948-72. Each month the Texas Railroad Commission and other U.
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    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
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    (Hamilton 1983,
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    p. 230). Whereas the WTI price is a good proxy for the U.S. price for oil during 1948-72, when the U.S. was largely self-sufficient 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,
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    Dvir and Rogoff (2010)
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    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 post-1973 real oil price data is not a valid option.
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    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
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    Gillman and Nakov 2009).
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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 trade-offs 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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    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 trade-offs between alternative oil price definitions from an economic point of view see
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    Kilian and Vigfusson (2010b).
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    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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    an episode as an oil price shock involving a doubling of the 4 For further discussion of the trade-offs 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
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    Cooley and LeRoy (1985).
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    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.,
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    Skeet 1988; Smith 2005; Almoguera, Douglas and Herrera 2010).
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    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
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    Barsky and Kilian (2002),
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    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
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    Green and Porter 1984).
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    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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    There is evidence from in-sample 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
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    Hamilton (1996, 2003).
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    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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    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.
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    Hamilton (2010),
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    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
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    Hamilton (2003)
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    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 2003-08 was driven in large part by a surge in the demand for oil.
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    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,
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    Hamilton (2009)
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    concedes that the net oil price increase of 2003-08 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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    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 2003-08 was driven in large part by a surge in the demand for oil.
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    Kilian (2009a,b;
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    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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    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
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    Hamilton (2003)
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    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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    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.,
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    Kilian and Vigfusson 2010a; Herrera, Lagalo and Wada 2010).
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    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
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    Baumeister and Peersman (2010).
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    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 out-of-sample forecastability (see
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    Inoue and Kilian 2004a).
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    Within the linear VAR framework the absence of predictability from one variable to another in population may be tested using Granger non-causality tests. 4.1. Nominal Oil Price Predictability 4.1.1.
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    The Pre-1973 Evidence Granger causality from macroeconomic aggregates to the price of oil has received attention in part because Granger non-causality 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
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    Hamilton (1983),
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    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 1948-1972. 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
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    Kilian (2008b;
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    2009a,b; 2010). Even if we accept Hamilton’s interpretation of the pre-1973 period, the institutional conditions that Hamilton (1983) appeals to ceased to exist in the early 1970s, and Hamilton’s results for the 1948-1972 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 pre-1973 period, the institutional conditions that
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    Hamilton (1983)
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    appeals to ceased to exist in the early 1970s, and Hamilton’s results for the 1948-1972 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 post-1973 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 post-1973 period. 4.1.2. The Post-1973 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
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    Kilian 2008a).
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    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 post-1973 data (see, e.g.,
    Exact
    Cooley and LeRoy 1985).
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    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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    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 post-1973 data (see, e.g., Cooley and LeRoy 1985). A recent study by
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    Kilian and Vega (2010)
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    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
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    Hamilton (1994,
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    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 1973.1-2009.12 or 1975.1-2009.12.8 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
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    Barsky and Kilian (2002),
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    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 dollar-denominated nominal price of oil to respond to changes in nominal U.
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    There are several reasons to expect the dollar-denominated 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,
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    Gillman and Nakov (2009)
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    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).
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    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 post-1973 period as rooted in persistent changes in the growth rate of money. 10 Thus, an alternative approach of tes
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    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 post-1973 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)
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    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
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    Barsky and Kilian 2002).
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    Table 1a nevertheless shows that there is considerable lagged feedback 8 In the former case, the pre-1974.1 observations are only used as pre-sample 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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    lagged feedback 8 In the former case, the pre-1974.1 observations are only used as pre-sample 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
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    Barsky and Kilian (2002).
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    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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    8 In the former case, the pre-1974.1 observations are only used as pre-sample 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
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    Barsky and Kilian (2002) and Gillman and Nakov (2009)
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    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).
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    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 1975.2-2009.12 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 Post-1973 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 pre-1973 period. As shown in
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    Hamilton (1983)
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    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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    Reconciling the Pre- and Post-1973 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 pre-1973 period. As shown in Hamilton (1983) using quarterly data and in
    Exact
    Gillman and Nakov (2009)
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    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
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    Kilian, Rebucci and Spatafora 2009).
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    caution. This problem with the pre-1973 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 discrete-continuous choice process with data from the post-Texas 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.,
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    Balke, Brown and Yücel 2002).
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    The p-value 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 post-war period are not informative about the strength of these relationships
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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 p-value for the null hypothesis that there is no break in 1973.Q4 in the coefficients of this predictive regression is 0.001 (see
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    Kilian and Vigfusson 2010b).
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    12 For that reason, regression estimates of the relationship between the real price of oil and domestic macroeconomic aggregates obtained from the entire post-war period are not informative about the strength of these relationships in post-1973 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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    Prefix
    Thus, regressions on long time spans of real exchange rate data produce average estimates that by construction are not informative about the speed of adjustment in the Bretton Woods system. 14 For a review of this literature see
    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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  49. Start
    44356
    Prefix
    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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  50. Start
    46985
    Prefix
    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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  51. Start
    47770
    Prefix
    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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  52. Start
    49836
    Prefix
    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.
    (check this in PDF content)

  53. Start
    50027
    Prefix
    This series has recently been introduced by Baumeister and Peersman (2010) in the context of modeling the demand for oil. Although there are serious methodological concerns regarding the construction of any such index, as discussed in
    Exact
    Beyer, Doornik and Hendry (2001),
    Suffix
    one would expect this series to be a better proxy for global fluctuations in the demand for crude oil than U.S. real GDP. Indeed, Table 2 shows strong evidence of Granger causality from world industrial production to the real WTI price in the full sample period for the LT model.
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  54. Start
    50659
    Prefix
    For the four shorter series there are three additional rejections for the LT model; the other p-value is not much higher than 0.1. The reduction in p-values 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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  55. Start
    51351
    Prefix
    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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  56. Start
    52424
    Prefix
    Even OECD+6 industrial production, however, is an imperfect proxy for business-cycle 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 broad-based 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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  57. Start
    53090
    Prefix
    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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  58. Start
    53577
    Prefix
    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 2000.11-2008.12 after weighting each country’s forecast revision by its PPP-GDP share.
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  59. Start
    53947
    Prefix
    by evidence in Kilian and Hicks (2010) based on distributed lag models that revisions to professional real GDP growth forecasts have significant predictive power for the real price of oil during 2000.11-2008.12 after weighting each country’s forecast revision by its PPP-GDP share. Predictability in population, of course, does not necessarily imply out-of-sample 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 outof-sample. 5. Short-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
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  60. Start
    54505
    Prefix
    -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 freight-rate 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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  61. Start
    55659
    Prefix
    For this paper, this series has been extended based on the Baltic Exchange Dry Index, which is available from Bloomberg. The latter index, which is commonly discussed in the financial press, is essentially identical to the nominal index in
    Exact
    Kilian (2009a),
    Suffix
    but only available since 1985. futures contract of maturity h as the h-period 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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  62. Start
    56452
    Prefix
    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 output-gap 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). Futures-based forecasts of the price of oil also play a role in policy discussions at the Federal Reserve Board.
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  63. Start
    57303
    Prefix
    Such attitudes have persisted notwithstanding recent empirical evidence to the contrary and notwithstanding the development of theoretical models aimed at explaining the lack of predictive ability of oil futures prices and spreads (see, e.g.,
    Exact
    Knetsch 2007; Alquist and Kilian 2010).
    Suffix
    Interestingly, the conventional wisdom in macroeconomics and finance is at odds with long-held 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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  64. Start
    57511
    Prefix
    evidence to the contrary and notwithstanding the development of theoretical models aimed at explaining the lack of predictive ability of oil futures prices and spreads (see, e.g., Knetsch 2007; Alquist and Kilian 2010). Interestingly, the conventional wisdom in macroeconomics and finance is at odds with long-held 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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  65. Start
    57757
    Prefix
    For example, Peck (1985) emphasized that “expectations are reflected nearly equally in current and in futures prices. In this sense cash prices will be nearly as good predictions of subsequent cash prices as futures prices”, echoing in turn the discussion in
    Exact
    Working (1942)
    Suffix
    who was critical of the “general opinion among economists that prices of commodity futures are ... the market expression of consciously formed opinions on probable prices in the future” whereas “spot prices are not generally supposed to reflect anticipation of the future in the same degree as futures prices”.
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  66. Start
    59211
    Prefix
    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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  67. Start
    61264
    Prefix
    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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  68. Start
    61481
    Prefix
    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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  69. Start
    63765
    Prefix
    The forecast evaluation period is 1991.1-2009.12 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).
    (check this in PDF content)

  70. Start
    63988
    Prefix
    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 no-change forecast.
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  71. Start
    64607
    Prefix
    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 outof-sample 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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  72. Start
    66542
    Prefix
    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 no-change 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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  73. Start
    67517
    Prefix
    While economists have used survey data extensively in measuring the risk premium embedded in foreign exchange futures, this approach has not been applied to oil futures, with the exception of recent work by
    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 no-change forecast for inflation expectations and for recent percent changes in other nominal prices. 5.2.1.
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  74. Start
    67599
    Prefix
    While economists have used survey data extensively in measuring the risk premium embedded in foreign exchange futures, this approach has not been applied to oil futures, with the exception of recent work by Wu and McCallum (2005). Yet another approach is to exploit the implication of the
    Exact
    Hotelling (1931)
    Suffix
    model that the price of oil should grow at the rate of interest. Finally, we also consider forecasting models that adjust the no-change forecast for inflation expectations and for recent percent changes in other nominal prices. 5.2.1.
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  75. Start
    68076
    Prefix
    Parsimonious Econometric Forecasts One example of parsimonious econometric forecasting models is the random walk model without drift introduced earlier. An alternative is the double-differenced forecasting model proposed in
    Exact
    Hendry (2006).
    Suffix
    Hendry observed that when time series are subject to infrequent trend changes, the no-change 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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  76. Start
    75749
    Prefix
    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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  77. Start
    82023
    Prefix
    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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  78. Start
    83840
    Prefix
    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. 108-120) proposes a rule for constructing samplesize dependent critical values. For example, for the F-statistic, 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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  79. Start
    86235
    Prefix
    Long-Horizon Forecasts of the Nominal Price of Oil For oil industry managers facing investment decisions or for policymakers pondering the medium-term 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 6-year oil futures contract in assessing effective long-term supply prices.
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  80. Start
    86344
    Prefix
    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 6-year oil futures contract in assessing effective long-term 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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  81. Start
    86498
    Prefix
    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 6-year oil futures contract in assessing effective long-term 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 end-of-month observations for oil futures prices.
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  82. Start
    93033
    Prefix
    Although there can be substantial discrepancies between the evolution of the price of crude oil and the price of gasoline in the short run, long-horizon forecasts of the price of gasoline will track long-horizon 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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  83. Start
    93372
    Prefix
    A variety of modeling strategies has been explored, often with widely different results. Candidates include ARIMA models, no-change 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 out-of-sample 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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  84. Start
    93936
    Prefix
    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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  85. Start
    96585
    Prefix
    The evidence in Figure 6 supports the view that the no-change 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 out-of-sample 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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  86. Start
    102608
    Prefix
    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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  87. Start
    104745
    Prefix
    The local-to-zero asymptotic approximation of predictive models suggests that using the no-change forecast may lower the asymptotic MSPE even relative to the correctly specified non-random 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 p0,...,12 .
    (check this in PDF content)

  88. Start
    104871
    Prefix
    of predictive models suggests that using the no-change forecast may lower the asymptotic MSPE even relative to the correctly specified non-random 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 p0,...,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 no-change forecast.
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  89. Start
    104916
    Prefix
    no-change forecast may lower the asymptotic MSPE even relative to the correctly specified non-random 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 p0,...,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 no-change forecast.
    (check this in PDF content)

  90. Start
    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 no-change 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 p-values 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 no-change forecast at short horizons.
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  91. Start
    105359
    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 no-change 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 p-values 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 no-change forecast at short horizons.
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  92. Start
    107927
    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 no-change 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 reduced-form representation of the VAR model in Kilian and Murphy (2010).
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  93. Start
    108202
    Prefix
    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 reduced-form representation of the VAR model in
    Exact
    Kilian and Murphy (2010).
    Suffix
    The sample period is 1973.2-2009.8. 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 above-ground crude oil inventories.
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  94. Start
    108565
    Prefix
    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 above-ground 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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  95. Start
    108712
    Prefix
    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 above-ground 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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  96. Start
    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 four-variable model used in
    Exact
    Kilian and Murphy (2010).
    Suffix
    Table 13 shows that this unrestricted VAR forecast has lower recursive MSPE than the no-change 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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  97. Start
    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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  98. Start
    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 out-of-sample 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 out-of-sample predictability does not matter asymptotically under fixed parameter asymptotics, but fixed parameter asymptotics typically provide a poor approximation to the finite-sample accuracy of f
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  99. Start
    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 local-to-zero 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 out-of-sample 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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  100. Start
    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 out-of-sampl
    (check this in PDF content)

  101. Start
    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 out-of-sample forecasts and also proposes alternative asymptotic approximations based on many predictors.
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  102. 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 out-of-sample forecasts and also proposes alternative asymptotic approximations based on many predictors.
    (check this in PDF content)

  103. 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 out-of-sample 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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  104. Start
    118617
    Prefix
    How imposing these real-time data constraints alters the relative accuracy of no-change 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 real-time 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 real-time forecast accuracy.
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  105. Start
    119283
    Prefix
    At longer horizons the MSPE reductions diminish even for the best VAR models. Beyond one year, the no-change 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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  106. Start
    121326
    Prefix
    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 real-time data (see
    Exact
    Baumeister and Kilian 2011).
    Suffix
    Unlike for the real refiners’ acquisition cost, the differences between real-time forecasts of the real WTI price and forecasts based on ex-post 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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  107. Start
    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 data-based 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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  108. Start
    122788
    Prefix
    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 single-equation 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 data-based procedure in Giannone et al. (2010).
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  109. Start
    123109
    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 data-based 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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  110. Start
    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 real-time 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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  111. Start
    124661
    Prefix
    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 forward-looking 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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  112. Start
    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 no-change 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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  113. Start
    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 reduced-form 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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  114. Start
    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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  115. Start
    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 forward-looking behavio
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  116. Start
    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 best-case 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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  117. Start
    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 mid-1979 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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  118. Start
    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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  119. Start
    136887
    Prefix
    We determined the lag order of this benchmark model based on a forecast accuracy comparison involving all combinations of horizons 1,..., 8hand lag orders 1,..., 24 .pThe 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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  120. Start
    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 time-varying 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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  121. Start
    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 out-of-sample forecasts of cumulative real GDP growth. 11.2.
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  122. Start
    141891
    Prefix
    Of particular concern is the possibility that nonlinear dynamic regression models may generate more accurate out-of-sample 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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  123. Start
    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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  124. Start
    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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  125. Start
    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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  126. Start
    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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  127. Start
    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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  128. Start
    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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  129. Start
    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 out-of-sample forecasting.
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  130. Start
    145333
    Prefix
    We consider both one-quarter-ahead 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 single-equation 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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  131. Start
    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.
    (check this in PDF content)

  132. Start
    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 reduced-form 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
    (check this in PDF content)

  133. Start
    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 reduced-form 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.
    (check this in PDF content)

  134. Start
    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 out-of-sample.
    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 out-of-sample MSPE, but no systematic evidence has been presented to make this case for this model.
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  135. Start
    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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  136. Start
    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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  137. Start
    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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  138. Start
    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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  139. Start
    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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  140. Start
    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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  141. Start
    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 one-year net increase model motivated by Hamilton (1996) is more accurate than the AR(4) benchmark at the one-quarter 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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  142. Start
    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 one-year net increase model motivated by
    Exact
    Hamilton (1996)
    Suffix
    is more accurate than the AR(4) benchmark at the one-quarter 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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  143. Start
    158303
    Prefix
    The first two columns of Table 20 focus on the evaluation period 1990.Q1-2010.Q2. Column (1) shows that, for eight of ten model specifications, the one-quarter 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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  144. Start
    158583
    Prefix
    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 in-sample diagnostics is less accurate than the AR benchmark model. Much more favorable results are obtained at the one-year 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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  145. Start
    159923
    Prefix
    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 one-step-ahead real GDP growth forecasts from single-equation 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 pre-1973 data.
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  146. Start
    159959
    Prefix
    This remains an open question at this point.32 32 Some preliminary evidence on this question has been provided by Ravazzolo and Rothman (2010) and by
    Exact
    Carlton (2010).
    Suffix
    It is not straightforward to compare their results to those in Tables 19 and 20, however. Not only is their analysis based on one-step-ahead real GDP growth forecasts from single-equation 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 pre-1973 data. 11.3.
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  147. Start
    160595
    Prefix
    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 one-quarter 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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  148. Start
    160671
    Prefix
    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 one-quarter 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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  149. Start
    161413
    Prefix
    The p-value 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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  150. Start
    164113
    Prefix
    The upper panel of Figure 15 shows the 1-month implied volatility time series for 2001.1-2009.12, 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 1-month-ahead conditional variance obtained from recursively estimated Gaussian GARCH(1,1) models. 33 The initial estimation period is 1974.12000.12.
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  151. Start
    165593
    Prefix
    Given that oil is only one of many assets handled by portfolio managers, however, it is not clear that the GARCHin-Mean model for single-asset 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 1-month 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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  152. Start
    168014
    Prefix
    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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  153. Start
    168582
    Prefix
    An analogous argument holds for consumers considering the purchase of energy-intensive 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 short-term no
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  154. Start
    169401
    Prefix
    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 short-horizon volatility as a proxy for longer-horizon 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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  155. Start
    170086
    Prefix
    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 5-year-ahead 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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  156. Start
    170261
    Prefix
    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 5-year-ahead 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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  157. Start
    171271
    Prefix
    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 oil-futures options price data that would allow the construction of implied volatility measures.
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  158. Start
    171573
    Prefix
    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 oil-futures options price data that would allow the construction of implied volatility measures.
    Exact
    Kellogg (2010)
    Suffix
    therefore converts the one-month volatility to 18-month 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 large-scale use of alternative technologies with adverse consequences for the long-run price of crude oil.36 Thus, the oil
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  159. Start
    172725
    Prefix
    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 energy-efficient 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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  160. Start
    173762
    Prefix
    One requirement is that the measure of risk must be related to the probability distribution ()Fof 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).
    Suffix
    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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  161. Start
    174571
    Prefix
    functions ()lthat 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 thRdenotes the real price of oil in dollars hperiods from date ,t 01ais the weight attached to downside ris
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  162. Start
    174707
    Prefix
    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 thRdenotes the real price of oil in dollars hperiods from date ,t 01ais the weight attached to downside risks, and 0 and 0 measure the user’s degree of risk aversion.
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  163. Start
    176748
    Prefix
    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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  164. Start
    176829
    Prefix
    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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  165. Start
    176958
    Prefix
    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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  166. Start
    177074
    Prefix
    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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  167. Start
    178100
    Prefix
    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).
    Suffix
    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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  168. Start
    183807
    Prefix
    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 energy-intensive durables (see
    Exact
    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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  169. Start
    184663
    Prefix
    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,
    Exact
    Zagaglia (2010)
    Suffix
    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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  170. Start
    185941
    Prefix
    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 real-time 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 cross-section of data on energy prices, quantities, and other oil-market 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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  171. Start
    193523
    Prefix
    For example, we found no evidence that the nominal PPI three-year net increase model is more accurate than linear models for real GDP growth at the one-quarter 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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