Forecasting the real price of oil in a changing world: a forecast combination approach : [Version November 13, 2013]

The U.S. Energy Information Administration (EIA) regularly publishes monthly and quarterly forecasts of the price of crude oil for horizons up to two years, which are widely used by practitioners. Traditionally, such out-of-sample forecasts have been largely judgmental, making them difficult to replicate and justify. An alternative is the use of real-time econometric oil price forecasting models. We investigate the merits of constructing combinations of six such models. Forecast combinations have received little attention in the oil price forecasting literature to date. We demonstrate that over the last 20 years suitably constructed real-time forecast combinations would have been systematically more accurate than the no-change forecast at horizons up to 6 quarters or 18 months. MSPE reduction may be as high as 12% and directional accuracy as high as 72%. The gains in accuracy are robust over time. In contrast, the EIA oil price forecasts not only tend to be less accurate than no-change forecasts, but are much less accurate than our preferred forecast combination. Moreover, including EIA forecasts in the forecast combination systematically lowers the accuracy of the combination forecast. We conclude that suitably constructed forecast combinations should replace traditional judgmental forecasts of the price of oil

Do oil price increases cause higher food prices?

U.S. retail food price increases in recent years may seem large in nominal terms, but after adjusting for inflation have been quite modest even after the change in U.S. biofuel policies in 2006. In contrast, increases in the real prices of corn, soybeans, wheat and rice received by U.S. farmers have been more substantial and can be linked in part to increases in the real price of oil. That link, however, appears largely driven by common macroeconomic determinants of the prices of oil and agricultural commodities rather than the pass-through from higher oil prices. We show that there is no evidence that corn ethanol mandates have created a tight link between oil and agricultural markets. Rather increases in food commodity prices not associated with changes in global real activity appear to reflect a wide range of idiosyncratic shocks ranging from changes in biofuel policies to poor harvests. Increases in agricultural commodity prices in turn contribute little to U.S. retail food price increases, because of the small cost share of agricultural products in food prices. There is no evidence that oil price shocks have caused more than a negligible increase in retail food prices in recent years. Nor is there evidence for the prevailing wisdom that oil-price driven increases in the cost of food processing, packaging, transportation and distribution are responsible for higher retail food prices. Finally, there is no evidence that oil-market specific events or for that matter U.S. biofuel policies help explain the evolution of the real price of rice, which is perhaps the single most important food commodity for many developing countries

Real-Time Analysis of Oil Price Risks Using Forecast Scenarios

Recently, there has been increased interest in real-time forecasts of the real price of crude oil. Standard oil price forecasts based on reduced-form regressions or based on oil futures prices do not allow consumers of forecasts to explore how much the forecast would change relative to the baseline forecast under alternative scenarios about future oil demand and oil supply conditions. Such scenario analysis is of central importance for end-users of oil price forecasts interested in evaluating the risks underlying these forecasts. We show how policy-relevant forecast scenarios can be constructed from recently proposed structural vector autoregressive models of the global oil market and how changes in the probability weights attached to these scenarios affect the upside and downside risks embodied in the baseline real-time oil price forecast. Such risk analysis helps forecast users understand what assumptions are driving the forecast. An application to real-time data for December 2010 illustrates the use of these tools in conjunction with reduced-form vector autoregressive forecasts of the real price of oil, the superior realtime forecast accuracy of which has recently been established.Econometric and statistical methods; International topics

Bagging Time Series Models

A common problem in out-of-sample prediction is that there are potentially many relevant predictors that individually have only weak explanatory power. We propose bootstrap aggregation of pre-test predictors (or bagging for short) as a means of constructing forecasts from multiple regression models with local-to-zero regression parameters and errors subject to possible serial correlation or conditional heteroskedasticity. Bagging is designed for situations in which the number of predictors (M) is moderately large relative to the sample size (T). We show how to implement bagging in the dynamic multiple regression model and provide asymptotic justification for the bagging predictor. A simulation study shows that bagging tends to produce large reductions in the out-of-sample prediction mean squared error and provides a useful alternative to forecasting from factor models when M is large, but much smaller than T. We also find that bagging indicators of real economic activity greatly redcues the prediction mean squared error of forecasts of U.S. CPI inflation at horizons of one month and one yearforecasting; bootstrap; model selection; pre-testing; forecast aggregation; factor models; inflation.

Oil and the Macroeconomy Since the 1970s

Increases in oil prices have been held responsible for recessions, periods of excessive inflation, reduced productivity and lower economic growth. In this paper, we review the arguments supporting such views. First, we highlight some of the conceptual difficulties in assigning a central role to oil price shocks in explaining macroeconomic fluctuations, and we trace how the arguments of proponents of the oil view have evolved in response to these difficulties. Second, we challenge the notion that at least the major oil price movements can be viewed as exogenous with respect to the US macroeconomy. We examine critically the evidence that has led many economists to ascribe a central role to exogenous political events in modeling the oil market, and we provide arguments in favor of 'reverse causality' from macroeconomic variables to oil prices. Third, although none of the more recent oil price shocks has been associated with stagflation in the US economy, a major reason for the continued popularity of the oil shock hypothesis has been the perception that only oil price shocks are able to explain the US stagflation of the 1970s. We show that this is not the case.

Quantifying the half-life of deviations from PPP: The role of economic priors

The half-life of deviations from purchasing power parity (PPP) plays a central role in the ongoing debate about the ability of macroeconomic models to account for the time series behavior of the real exchange rate. The main contribution of this paper is a general framework in which alternative priors for the half-life of deviations from PPP can be examined. We show how to incorporate formally the prior views of economists about the half-life. In our empirical analysis we provide two examples of such priors. One example is a consensus prior consistent with widely held views among economists with a professional interest in the PPP debate. The other example is a relatively diffuse prior designed to capture a large degree of uncertainty about the half-life. Our methodology allows us to make explicit probability statements about the half-life and to assess the likelihood that the half-life exceeds a given number of years, without taking a stand on whether or not the data have a unit root. We find only very limited support for the common view in the PPP literature that the half-life is between three and five years.Econometric models ; Purchasing power parity ; Time-series analysis

Real-Time Forecasts of the Real Price of Oil

We construct a monthly real-time data set consisting of vintages for 1991.1-2010.12 that is suitable for generating forecasts of the real price of oil from a variety of models. We document that revisions of the data typically represent news, and we introduce backcasting and nowcasting techniques to fill gaps in the real-time data. We show that real-time forecasts of the real price of oil can be more accurate than the no-change forecast at horizons up to one year. In some cases real-time MSPE reductions may be as high as 25 percent one month ahead and 24 percent three months ahead. This result is in striking contrast to related results in the literature for asset prices. In particular, recursive vector autoregressive (VAR) forecasts based on global oil market variables tend to have lower MSPE at short horizons than forecasts based on oil futures prices, forecasts based on AR and ARMA models, and the no-change forecast. In addition, these VAR models have consistently higher directional accuracy. We demonstrate how with additional identifying assumptions such VAR models may be used not only to understand historical fluctuations in the real price of oil, but to construct conditional forecasts that reflect hypothetical scenarios about future demand and supply conditions in the market for crude oil. These tools are designed to allow forecasters to interpret their oil price forecast in light of economic models and to evaluate its sensitivity to alternative assumptions.Econometric and statistical methods; International topics

Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form

Conditional heteroskedasticity is an important feature of many macroeconomic and financial time series. Standard residual-based bootstrap procedures for dynamic regression models treat the regression error as i.i.d. These procedures are invalid in the presence of conditional heteroskedasticity. We establish the asymptotic validity of three easy-toimplement alternative bootstrap proposals for stationary autoregressive processes with m.d.s. errors subject to possible conditional heteroskedasticity of unknown form. These proposals are the fixed-design wild bootstrap, the recursive-design wild bootstrap and the pairwise bootstrap. In a simulation study all three procedures tend to be more accurate in small samples than the conventional large-sample approximation based on robust standard errors. In contrast, standard residual-based bootstrap methods for models with i.i.d. errors may be very inaccurate if the i.i.d. assumption is violated. We conclude that in many empirical applications the proposed robust bootstrap procedures should routinely replace conventional bootstrap procedures based on the i.i.d. error assumption. -- Bedingte Heteroskedastizität ist eine wichtige Eigenschaft von vielen Daten über Finanzmärkte und die Makroökonomie. Standard bootstrap Verfahren für dynamische Regressionsmodelle behandeln die Residuen der Regression als i. i. d. Bei bedingter Heteroskedastizität sind diese Prozeduren nicht angemessen. Wir zeigen die asymptotische Gültigkeit von 3 alternativen bootstrap Methoden für stationäre autoregressive Prozesse mit m. d. s. Fehler, die eine bedingte Heteroskedastizität unbekannter Form aufweisen. Es geht dabei um ein fixed-design wild bootstrap, den recursive-design wild bootstrap und den paarweisen bootstrap. In einer Simulationsstudie erscheinen alle 3 Prozeduren in kleinen Stichproben angewandt genauer als die konventionellen Approximationen, die auf robusten Standardfehlern basieren. Diese letztgenannten Methoden können dagegen sehr ungenau sein, wenn die i. i. d. Annahme nicht gilt. Wir schließen daraus, dass bei vielen empirischen Anwendungen die robusten bootstrap Verfahren, die hier vorgestellt werden und leicht zu implementieren sind, die üblichen bootstrap Verfahren ersetzen sollten.wild bootstrap,pairwise bootstrap,robust inference

Bootstrapping Autoregressive Processes with Possible Unit Roots

An important question in applied work is how to bootstrap autoregressive processes involving highly persistent time series of unknown order of integration. In this paper, we show that in many cases of interest in applied work the standard bootstrap algorithm for unrestricted autoregressions remains valid for processes with exact unit roots; no pre-tests are required, at least asymptotically, and applied researchers may proceed as in the stationary case. Specifically, we prove the first-order asymptotic validity of bootstrapping any linear combination of the slope parameters in autoregressive models with drift. We also establish the bootstrap validity for the marginal distribution of slope parameters and for most linear combinations of slope parameters in higher-order autoregressions without drift. The latter result is in sharp contrast to the well-known bootstrap invalidity result for the random walk without drift. A simulation study examines the finite-sample accuracy of the bootstrap approximation both for integrated and for near-integrated processes. We find that in many, but not all circumstances, the bootstrap distribution closely approximates the exact finite- sample distribution.

The central bank as a risk manager: quantifying and forecasting inflation risks

In deciding the monetary policy stance, central bankers need to evaluate carefully the risks the current economic situation poses to price stability. We propose to regard the central banker as a risk manager who aims to contain inflation within pre-specified bounds. We develop formal tools of risk management that may be used to quantify and forecast the risks of failing to attain that objective. We illustrate the use of these risk measures in practice. First, we show how to construct genuine real time forecasts of year-on-year risks that may be used in policy-making. We demonstrate the usefulness of these risk forecasts in understanding the Fed's decision to tighten monetary policy in 1984, 1988, and 1994. Second, we forecast the risks of worldwide deflation for horizons of up to two years. Although recently fears of worldwide deflation have increased, we find that, as of September 2002, with the exception of Japan there is no evidence of substantial deflation risks. We also put the estimates of deflation risk for the United States, Germany and Japan into historical perspective. We find that only for Japan there is evidence of deflation risks that are unusually high by historical standards. JEL Classification: E31, E37, E52, E58, C22deflation, forecast, inflation, monetary policy, risk