The 103 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,
    Exact
    Hamilton (2009),
    Suffix
    building on the analysis in Edelstein and Kilian (2009), provides evidence that the recession of late 2008 was amplified and preceded by an economic slowdown in the automobile industry and a deterioration in consumer sentiment.
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  2. Start
    4309
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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 Edelstein and
    Exact
    Kilian (2009),
    Suffix
    provides evidence that the recession of late 2008 was amplified and preceded by an economic slowdown in the automobile industry and a deterioration in consumer sentiment. Thus, more accurate forecasts of the price of oil have the potential of improving forecast accuracy for a wide range of macroeconomic outcomes and of improving macroeconomic policy responses.
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  3. Start
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    Section 4 studies the extent to which the nominal price of oil and the real price of oil are predictable based on macroeconomic aggregates. We document strong evidence of predictability 1 See, e.g.,
    Exact
    Kahn (1986),
    Suffix
    Davis and Kilian (2010). 2 See, e.g., Goldberg (1998), Allcott and Wozny (2010), Busse, Knittel and Zettelmeyer (2010), Kellogg (2010). in population. Predictability in population, however, need not translate into out-of-sample forecastability.
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  4. Start
    6279
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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
    Exact
    Kilian (2010).
    Suffix
    2 See, e.g., Goldberg (1998), Allcott and Wozny (2010), Busse, Knittel and Zettelmeyer (2010), Kellogg (2010). in population. Predictability in population, however, need not translate into out-of-sample forecastability.
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  5. Start
    6307
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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.,
    Exact
    Goldberg (1998),
    Suffix
    Allcott and Wozny (2010), Busse, Knittel and Zettelmeyer (2010), Kellogg (2010). in population. Predictability in population, however, need not translate into out-of-sample forecastability. The latter question is the main focus of sections 5 through 8.
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    We document strong evidence of predictability 1 See, e.g., Kahn (1986), Davis and Kilian (2010). 2 See, e.g., Goldberg (1998), Allcott and Wozny (2010), Busse, Knittel and Zettelmeyer (2010),
    Exact
    Kellogg (2010).
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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
    Exact
    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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    The net oil price increase is a censored predictor that assigns zero weight to net oil price decreases. There is little evidence that this type of asymmetry is reflected in the responses of U.S. real GDP to innovations in the real price of oil, as documented in Kilian and Vigfusson (2010a,b), but
    Exact
    Hamilton (2010)
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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
    Exact
    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
    Exact
    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
    Exact
    (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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    First, there is little evidence to support the notion that OPEC has been successfully acting as a cartel in the 1970s and early 1980s, and the role of OPEC has diminished further since 1986 (see, e.g.,
    Exact
    Skeet 1988; Smith 2005;
    Suffix
    Almoguera, Douglas and Herrera 2010). Second, even if we were to accept the notion that an OPEC cartel sets the nominal price of oil, economic theory predicts that this cartel price will endogenously respond to U.
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    This theoretical prediction is consistent with anecdotal evidence of OPEC oil producers raising the price of oil (or equivalently lowering oil production) in response to unanticipated U.S. inflation, low U.S. interest rates and the depreciation of the dollar. Moreover, as observed by Barsky and
    Exact
    Kilian (2002),
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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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    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
    Exact
    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.
    Exact
    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
    Exact
    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;
    Suffix
    2010), on the other hand, provides evidence based on structural VAR models that in fact most net oil price increases have contained a large demand component driven by global macroeconomic conditions, even 6 Interestingly, the behavioral rationale for the net oil price increase measure applies equally to the nominal price of oil and t
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    evidence based on structural VAR models that in fact most net oil price increases have contained a large demand component driven by global macroeconomic conditions, even 6 Interestingly, the behavioral rationale for the net oil price increase measure applies equally to the nominal price of oil and the real price of oil. Although
    Exact
    Hamilton (2003)
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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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    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 Inoue and
    Exact
    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
    Exact
    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
    Exact
    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
    Exact
    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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    Table 1a investigates the evidence of Granger causality from selected nominal U.S. macroeconomic variables to the nominal price of oil. All results are based on pairwise vector autoregressions. The lag order is fixed at 12. Similar results would have been obtained 7
    Exact
    Hamilton (1994,
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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 Barsky and
    Exact
    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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    Given the general instability in the link from changes in monetary aggregates to inflation, one would not necessarily expect changes in monetary aggregates to have much predictive power for the price of oil, except perhaps in the 1970s (see Barsky and
    Exact
    Kilian 2002).
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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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    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 Barsky and
    Exact
    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 Barsky and
    Exact
    Kilian (2002) and
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    Gillman and Nakov (2009) view the shifts in U.S. inflation in the early 1970s as caused by persistent changes in the growth rate of the money supply, but there are important differences in emphasis. Whereas Barsky and Kilian stress the real effects of unanticipated monetary expansions on real domestic output, on the demand for oil and hence on the real price of oil, Gillman and Nakov stress tha
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    Whereas Barsky and Kilian stress the real effects of unanticipated monetary expansions on real domestic output, on the demand for oil and hence on the real price of oil, Gillman and Nakov stress that the relative price of oil must not decline in response to a monetary expansion, necessitating a higher nominal price of oil, consistent with anecdotal evidence on OPEC price decisions (see, e.g.,
    Exact
    Kilian 2008b).
    Suffix
    These two explanations are complementary. from narrow measures of money such as M1 for the refiners’ acquisition cost and the WTI price of oil based on the 1975.2-2009.12 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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    Thus, regressions on long time spans of real exchange rate data produce average estimates that by construction are not informative about the speed of adjustment in the Bretton Woods system. 14 For a review of this literature see Barsky and
    Exact
    Kilian (2002).
    Suffix
    difficult to pin down, especially at longer horizons, and that the relevant horizon for resource extraction is not clear. We therefore focus on the predictive power of fluctuations in real aggregate output.
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    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;
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    Kilian and Murphy 2010). In particular, the demand for oil depends not merely on U.S. demand, but on global demand. The bivariate model for the real price of oil and U.S. real GDP by construction omits fluctuations in real GDP in the rest of the world.
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    This series has recently been introduced by Baumeister and Peersman (2010) in the context of modeling the demand for oil. Although there are serious methodological concerns regarding the construction of any such index, as discussed in
    Exact
    Beyer, Doornik and Hendry (2001),
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    one would expect this series to be a better proxy for global fluctuations in the demand for crude oil than U.S. real GDP. Indeed, Table 2 shows strong evidence of Granger causality from world industrial production to the real WTI price in the full sample period for the LT model.
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    For the four shorter series there are three additional rejections for the LT model; the other 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),
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    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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    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).
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    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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    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 Inoue and
    Exact
    Kilian 2004a).
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    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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    -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).
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    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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    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),
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    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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    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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    Such attitudes have persisted notwithstanding recent empirical evidence to the contrary and notwithstanding the development of theoretical models aimed at explaining the lack of predictive ability of oil futures prices and spreads (see, e.g.,
    Exact
    Knetsch 2007;
    Suffix
    Alquist and Kilian 2010). Interestingly, the conventional wisdom in macroeconomics and finance is at odds with 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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    Such attitudes have persisted notwithstanding recent empirical evidence to the contrary and notwithstanding the development of theoretical models aimed at explaining the lack of predictive ability of oil futures prices and spreads (see, e.g., Knetsch 2007; Alquist and
    Exact
    Kilian 2010).
    Suffix
    Interestingly, the conventional wisdom in macroeconomics and finance is at odds with 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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    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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    For example, Peck (1985) emphasized that “expectations are reflected nearly equally in current and in futures prices. In this sense cash prices will be nearly as good predictions of subsequent cash prices as futures prices”, echoing in turn the discussion in
    Exact
    Working (1942)
    Suffix
    who was critical of the “general opinion among economists that prices of commodity futures are ... the market expression of consciously formed opinions on probable prices in the future” whereas “spot prices are not generally supposed to reflect anticipation of the future in the same degree as futures prices”.
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    The NYMEX light sweet crude contract is the most liquid and largest volume market for crude oil trading. more strongly influenced by these anticipations than are spot prices”. The next section investigates the empirical merits of these competing views in the context of oil markets. 5.1. Forecasting Methods Based on Monthly Oil Futures Prices Alquist and
    Exact
    Kilian (2010)
    Suffix
    recently provided a comprehensive evaluation of the forecast accuracy of models based on monthly oil futures prices using data ending in 2007.2. Below we update their analysis until 2009.12 and expand the range of alternative forecasting models under consideration.18 In this subsection, attention is limited to forecast horizons of up to one year.
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    The simplest model is:  () | ˆ1/ln()h SthttttSFS, 1, 3, 6, 9, 1 2h (3) To allow for the possibility that the spread may be a biased predictor, it is common to relax the 18 Because the Datastream data for the daily WTI spot price of oil used in Alquist and
    Exact
    Kilian (2010)
    Suffix
    were discontinued, we rely instead on data from the Energy Information Administration. As a result the estimation window for the forecast comparison is somewhat shorter in some cases than in Alquist and Kilian (2010). assumption of a zero intercept: ()|ˆ1/ˆln()htttthtSSFS, 1, 3, 6, 9, 12h (4) Alternatively, one can relax the proportionality restriction: 
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  47. Start
    61493
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    , it is common to relax the 18 Because the Datastream data for the daily WTI spot price of oil used in Alquist and Kilian (2010) were discontinued, we rely instead on data from the Energy Information Administration. As a result the estimation window for the forecast comparison is somewhat shorter in some cases than in Alquist and
    Exact
    Kilian (2010).
    Suffix
    assumption of a zero intercept: ()|ˆ1/ˆln()htttthtSSFS, 1, 3, 6, 9, 12h (4) Alternatively, one can relax the proportionality restriction:  () | ˆ1/ˆln()h SthttttSFS, 1, 3, 6, 9, 12h (5) Finally, we can relax both the unbiasedness and proportionality restrictions: ()|ˆ1/ˆˆln()htttthtSSFS, 1, 3, 6, 9, 12h.
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    64617
    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., Inoue and
    Exact
    Kilian 2004a,b;
    Suffix
    Clark and McCracken 2010). This means that these tests will reject the null of equal predictive accuracy more often than they should under the null, suggesting caution in interpreting test results that are only marginally statistically significant.
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  49. Start
    66554
    Prefix
    Put differently, a forecaster using the most recent spot price would have done just as well in forecasting the nominal price of oil. This finding is broadly consistent with the empirical results in Alquist and
    Exact
    Kilian (2010). To
    Suffix
    the extent that some earlier studies have reported evidence more favorable to oil futures prices, the difference in results can be traced to the use of shorter samples. 19 5.2. Other Forecasting Methods The preceding subsection demonstrated that simple 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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  50. 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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  51. 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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  52. 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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  53. 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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  54. Start
    86247
    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 Alquist and
    Exact
    Kilian (2010),
    Suffix
    it is precisely these long horizons that many policymakers focus on. For example, Greenspan (2004a) explicitly referred to the 6-year oil futures contract in assessing effective long-term supply prices.
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  55. 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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  56. 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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  57. 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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  58. 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;
    Suffix
    Davis and Kilian 2010; Allcott and Wozny 2010). The issue is not only one of finding a forecasting method that achieves the smallest possible out-of-sample forecast error, but of understanding how consumers form their price expectations.
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  59. Start
    93393
    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., Kahn 1986; Davis and
    Exact
    Kilian 2010;
    Suffix
    Allcott and Wozny 2010). The issue is not only one of finding a forecasting method that achieves the smallest possible out-of-sample forecast error, but of understanding how consumers form their price expectations.
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  60. Start
    96599
    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 Edelstein and
    Exact
    Kilian (2009)
    Suffix
    that fluctuations in retail energy prices are dominated by fluctuations in gasoline prices. Finally, the absence of money illusion in households’ gasoline price forecasts is of independent interest. An 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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  61. 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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  62. Start
    104755
    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., Inoue and
    Exact
    Kilian (2004b),
    Suffix
    Clark and McCracken 2010). 26 The refiners’ acquisition cost was extrapolated back to 1973.2 as in Barsky and Kilian (2002). selection (see Inoue and Kilian 2006; Marcellino, Stock and Watson 2006).
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  63. Start
    104882
    Prefix
    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 Barsky and
    Exact
    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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  64. Start
    104926
    Prefix
    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 Inoue and
    Exact
    Kilian 2006;
    Suffix
    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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  65. 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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  66. Start
    110566
    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 Inoue and
    Exact
    Kilian 2006).
    Suffix
    29 It also outperforms the random walk model with drift in both of these dimensions, whether the drift is estimated recursively or as the average growth rate over the most recent h months. These results are not shown to conserve space. statistically significant reductions in the MSPE.
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  67. Start
    113664
    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 Inoue and
    Exact
    Kilian (2004a).
    Suffix
    This point is readily apparent from the underlying proofs of asymptotic validity as well as the way in which critical values are simulated. The distinction between population predictability and 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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  68. 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
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  69. 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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  70. Start
    118632
    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 Baumeister and
    Exact
    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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  71. Start
    121341
    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 Baumeister and
    Exact
    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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  72. Start
    124004
    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 Baumeister and
    Exact
    Kilian 2011).
    Suffix
    In addition, such VAR models can also be useful for studying how baseline forecasts of the real price of oil must be adjusted under hypothetical forecasting scenarios, as illustrated in the next section.
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  73. Start
    126132
    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 Baumeister and
    Exact
    Kilian (2011).
    Suffix
    This model allows the identification of three structural shocks: (1) a shock to the flow of the production of crude oil (“flow supply shock), (2) a shock to the flow demand for crude oil and other industrial commodities (“flow demand shock”) that reflects unexpected fluctuations in the global business cycle, and (3) a shock to the demand for oil inventories arising from forward-looking behavio
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  74. 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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  75. Start
    141311
    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 Edelstein and
    Exact
    Kilian (2009). Hamilton (2009)
    Suffix
    reported some success in employing a similar strategy.31 Another source of time variation may be changes in the composition of the underlying oil demand and oil supply shocks, as discussed in Kilian (2009).
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  76. 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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  77. 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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  78. Start
    143175
    Prefix
      possibly sytt 31 In related work, Ramey and Vine (2010) propose an alternative adjustment to the price of gasoline that reflects the time cost of queuing in gasoline markets during the 1970s. That adjustment as well serves to remove a nonlinearity in the transmission process. Both the nonlinearity postulated in Edelstein and
    Exact
    Kilian (2009) and
    Suffix
    that postulated in Ramey and Vine (2010) is incompatible with the specific nonlinearity embodied in the models of Mork (1989) and Hamilton (1996, 2003). In fact, the aforementioned papers rely on linear regressions after adjusting the energy price data. augmented by other variables.
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  79. 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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  80. 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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  81. 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
    (check this in PDF content)

  82. 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.
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  83. 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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  84. 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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  85. 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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  86. 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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  87. 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
    (check this in PDF content)

  88. 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
    (check this in PDF content)

  89. 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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  90. 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.
    (check this in PDF content)

  91. 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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  92. 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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  93. 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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  94. 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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  95. 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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  96. 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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  97. 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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  98. Start
    172739
    Prefix
    Likewise, a consumer of retail motor gasoline (and hence indirectly of crude oil) is likely to be concerned with the price of gasoline exceeding what he can afford to spend each month (see Edelstein and
    Exact
    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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  99. 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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  100. Start
    178114
    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., Gonçalves and
    Exact
    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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  101. 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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  102. 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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  103. 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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