Small Trends and Big Cycles in Crude Oil Prices.

AuthorMu, Xiaoyi

    The continued surge in oil prices since 2001 has renewed the interests in the questions of whether global oil production has peaked or will soon peak, whether the price increase reflects a long-run upward trend arising from "scarcity rent" or simply a cyclical movement, and whether the price of oil is predictable at all (see, for example, Geman [2005], Hamilton [2009], Alquist and Kilian [2010], and Alquist, Kilian and Vigfusson [2012]). In this paper, we employ an unobserved components (UC) model to disentangle the long-run trend from shorter-term cyclical patterns in the price of internationally traded crude oil using data from 1861 to 2010. Our objective is twofold. First, we are interested in testing both the shape of the long-run trend and the patterns of cycles. Second, we will examine the forecastability of oil price at longer horizons, which should matter more to investment decisions as well as policy-making.

    A long-standing debate in the natural resource economics literature is whether the price of an exhaustible resource product rises in the long run. The Hotelling (1931) model suggests that the price (net of marginal cost) of an exhaustible resource will rise at the rate of interest rate in a competitive market equilibrium. Modifications of the basic Hotelling model yield a decreasing, flat or U-shaped long-run price path (see Nordhaus [1973], Fisher [1979], Pindyck [1978] and Slade [1982] among others). In particular, Pindyck (1978) and Slade (1982) demonstrate that the price of a non-renewable resource product could initially decline as reserves accumulate or as technological advancement lowers the marginal extraction cost, but over time, as the depletion effect dominates the effect of technological change, the price could increase, resulting in a U-shaped long-run price path. Krautkraemer (1998) surveys the empirical literature and finds that, while there is little empirical support for the original Hotelling prediction, the conclusion regarding the long-run price trend varies considerably with the sample period and the commodities chosen (see also Slade and Thille [2009] and Livernois [2009]). (1) In this paper, we re-examine the long-run time series properties of oil prices with extended data and establish some stylized facts, which can shed light on new theories about the price of oil over the long run.

    We first demonstrate that the real price of crude oil is stationary around a U-shaped long-run trend with a significant structural break in 1973/1974, corroborating some of the earlier findings. We then estimate an unobserved components model to determine the trend and cycle patterns. Two types of cycles stand out, with the short cycle having a period of six years and the long cycle having an average length of 29 years. The amplitude of the long cycle can be as much as 90 percent above or 45 percent below the long-run trend. Compared to the cyclical movements, however, the quadratic trend is small. To our knowledge, no previous studies have quantified the relative importance of long-run trend and cycles of crude oil prices in a unified framework while accounting for the presence of structural breaks.

    The major contribution of our work lies in the out-of-sample forecastability of oil price at long horizons. An important literature has developed recently that empirically examines the forecastability of oil prices. At short horizons up to one year, Alquist and Kilian (2010) have shown that a "no change" random walk model tends to predict the monthly price of oil more accurately than the futures prices, reduced-form time series models, and an interest rate based Hotelling model, while Alquist, Kilian and Vigfusson (hereafter AKV, 2012) and Baumeister and Kilian (2012) show that models incorporating lagged values of global real activity and oil inventories can have significant forecasting power. As for long-horizon forecasts, AKV(2012) finds that, while oil futures prices fail to improve forecast accuracy relative to the no-change forecasts, forecasts obtained by adjusting current oil price for expected inflation outperform the no-change forecasts for the nominal price of oil at the horizon of five years. In this study, our out-of-sample forecasting analysis suggests that, while the no-change forecasts tend to be the most accurate at the one-year horizon among the models considered, the trend-cycle models significantly improve the forecast accuracy at horizons of five and ten years. The results hold for both real and nominal oil prices and provide robust evidence that the oil price is predictable at long horizons.

    The rest of the paper is set up as follows. Section 2 briefly reviews the empirical literature on the long-run behaviour of oil prices. Section 3 describes the data and modelling approach. In-sample model estimation is presented in Section 4 and out-of-sample forecast accuracy evaluation results in Section 5. Section 6 concludes.


    The long-run trend of the crude oil price has been empirically studied by a number of authors in the literature. Using data from 1870 to 1978, Slade (1982) finds statistically significant evidence for a U-shaped curve, represented by a quadratic time trend in the prices of crude oil and ten other commodities out of the 12 price series she tested. In an influential paper, Pindyck (1999) shows that the prices of energy products (oil, gas and coal) are mean-reverting to a quadratic trend line but the rate of reversion is slow, and for practical applications, the random walk assumption is not bad at all. Armed with advancements in time series techniques, a series of papers have tested whether the trend in natural resource commodity prices is deterministic or stochastic. Extending Slade's (1982) data to 1990, Berk and Roberts (1996) find the prices of oil and other commodities are non-stationary based on the Lagrange-Multiplier test and Dickey-Fuller test. Using the same data but with different unit root test techniques, Ahrens and Sharma (1997) conclude that among the 11 commodity price series, the price of oil along with five others is stationary around a deterministic trend. Still with the same data, Lee, List and Strazicich (hereinafter LLS, 2006) employ a Lagrange multiplier test allowing up to two endogenously determined structural breaks and reject the unit root hypothesis for all of the 11 commodities.

    Note that all the studies reviewed above focus solely on the trend component of oil prices and ignore the potential cyclical behaviour of oil prices. Dvir and Rogoff (2010) examine changes in persistence and volatility of crude oil prices across three periods from 1861 to 2009 and document striking similarities between the periods of 1861-1878 and 1973-2009. Cashin and McDermott (2002) look at the long-run behaviour of a real commodity price index that consists of non-food agricultural products and industrial metals and document a small downward trend along with the large variability in real commodity prices for the period 1862-1999. Erten and Ocampo (2012) and Zellou and Cuddington (2012) are the two studies that have explicitly modelled the long-run trend and cyclical behaviour of crude oil prices. Erten and Ocampo (2012) use an asymmetric band-pass filter to decompose crude oil prices from 1875 to 2010 into a trend component and super-cycles, defined as periods lasting from 20 to 70 years. They find an upward trend in oil price before the 1920s, a modest downward trend between the 1920s and the 1960s and an upward trend afterwards, and show that the super-cycles in the price of crude oil were rather modest in the early twentieth century and became more pronounced after the 1970s. Applying a similar band-pass filter method to the annual crude oil price data over the period 1861-2010, Zellou and Cuddington (2012) find that there is strong evidence for super-cycles in oil price during the post-WWI period but weak evidence in the pre-WWI period and that the upward long-term trend for the post-WWI period is quite small relative to the super-cycles.

    While our conclusions about the trend and cycle behaviour of crude oil price are somewhat similar to those in Erten and Ocampo (2012) and Zellou and Cuddington (2012), this study differs from theirs in several important aspects. First, we take the UC model approach to model the trend and cycles in oil prices. The UC model is more general than the band-pass filters typically used to extract the trend and cycles in oil prices in the sense that the band-pass filters have the length of cycles predefined and can be obtained as special cases of the UC model (Harvey and Trimbur, 2003). Particularly, the model-based approach automatically adapts to the endpoints of a sample and allows us to extract trend and cycles by filters that are optimal and mutually consistent even at the beginning and end of the series. Second, and perhaps more importantly, we focus more on the ability of the trend and cycle models to improve out-of-sample forecast accuracy at long horizons, which has not been done in the two cited super-cycles papers. Last, we allow for structural breaks when modelling the long-run trend and cyclical movements of real oil prices.


    Our oil price data are from the BP Statistical Review of the World Energy (2009 and 2010) and are the annual averages of oil prices in the US for 1861-1944, Arabian Light crude oil for 1945-1983 and Brent crude oil for 1984-2010. (2) The switch in the type of crude oils reflects the evolution of the oil market. A more detailed description of the data is provided in the appendix. The real price expressed in 2009 dollar values is used in our analysis.

    Figure 1 plots the logged real oil price (p), along with its linear and quadratic trend lines, over the full sample period. (3) Even a cursory look reveals several important features. First, there is a quite dramatic change in the trend...

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