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Article Excerpt
I. INTRODUCTION
Oil prices are monitored by consumers, firms, financial market traders, and government officials and are the subject of much media coverage. This in large part reflects the view that higher oil prices tend to be followed by inflation and recessions. (1) Early work by Hamilton (1983) as well as recent papers by Hamilton (2003) and Lee and Ni (2002) have provided convincing evidence of a relationship between oil prices and future economic activity. (2) Much of the literature has focused on whether oil prices improve the fit of a benchmark model via examination of impulse response functions as done by Lee and Ni (2002) or hypothesis testing as done by Hamilton (2003). Guo and Kliesen (2005) discussed a number of theoretical explanations for the oil price-macroeconomy relationship. The textbook explanation is that higher oil prices represent an increase in production costs, causing a fall in output and higher inflation. Another strand of literature has argued that large oil price movements cause uncertainty about future oil prices or costly reallocation of labor, (3) causing large oil price movements to have asymmetric effects on the economy, even to the point that both positive and negative oil price movements hurt output. Along these lines, Hamilton (1996) motivated the construction of a "net oil price increase" (NOPI) variable by arguing that it is the behavior of oil prices relative to recent experience that matters. This implies that the only time oil shocks have an impact on gross domestic product (GDP) is when the price of oil is above the high of the previous year.
For many purposes, though, the relevant question is whether the information in oil prices can be used to improve forecasts of macroeconomic variables. Examples include Federal Reserve policymaking (using the price of oil as an "indicator variable"), private sector planning, and portfolio management. For these applications, it should be of interest to evaluate the historical out-of-sample forecast performance of models that include oil prices. Moreover, impulse response functions and hypothesis tests are not able to provide information about how much out-of-sample forecasts can be improved. (4)
This paper evaluates forecasts of different measures of output, inflation, and monetary policy, all of which are important macroeconomic variables that can plausibly be expected to respond to oil shocks, based on both economic theory and media reports. We apply standard out-of-sample predictive ability tests to data covering the period January 1986 to December 2004. This time period has seen substantial variation in the price of oil, from a low of $11 per barrel in late 1998 to a high of $53 per barrel in October 2004, and includes two Gulf Wars, as well as multiple boom-and-bust cycles. If oil prices have value as an indicator variable, it should clearly be present in our sample, as oil price fluctuations of this magnitude will explain a large proportion of the variance of the macroeconomic variables.
Our results suggest that there are few cases where models with oil prices are even able to improve upon the forecasts of simple autoregressive (AR) models. This finding is robust to changes in specification that allow for nonlinearities, the use of rolling estimation windows to account for possible parameter instability, the use of industry-level data, and changes in the forecast horizon. To ensure that our results are not due to low power of the predictive ability tests that we employ, we show that the potential forecasting gains from including oil prices are in most cases close to 0. We conclude that oil prices provide little information about the future direction of the economy.
The rest of the paper proceeds as follows. The next section describes our methodology, Section III describes the data, Section IV presents and discusses the results of tests for predictive ability of oil prices for the macroeconomic variables, and Section V concludes the paper.
II. METHODOLOGY
Denote by [x.sub.t] the value of a macroeconomic variable that we want to forecast and by [DELTA][o.sub.t] the percentage change in the nominal price of crude oil over period t. The null hypothesis to be tested is that [DELTA]o does not help to predict x, so that the mean-squared prediction error (MSE) for the model [x.sub.t] = g([x.sub.t-1], [x.sub.t-2] ..., [x.sub.t-p], [DELTA][o.sub.t-1], [DELTA][o.sub.t-2],..., [DELTA][o.sub.t-q]) is not less than the MSE for the model [x.sub.t] = f([x.sub.t-1], [x.sub.t-2], ..., [x.sub.t-p]). Let [u.sub.1t] = [x.sub.t] - f([x.sub.t-1], [x.sub.t-2], ..., [x.sub.t-p]) be the time t forecast error for the smaller model and [u.sub.2t] = [x.sub.t] - g([x.sub.t-1], [x.sub.t-2], ..., [x.sub.t-p], [DELTA][o.sub.t-1], [DELTA][o.sub.t-2], ..., [DELTA][o.sub.t-q]) be the time t forecast error for the model that includes [DELTA]o. The null hypothesis can then be stated as
[H.sub.0] : E([u.sup.2.sub.1t]) = E([u.sup.2.sub.2t]).
The alternative hypothesis is [H.sub.a] : E([u.sup.2t.sub.1t]) > E([u.sup.2.sub.2t]).
There are a total of T observations in the data set, P out-of-sample predictions are made, and the estimation sample is R = T - p. (5) Let [[??].sub.1t] and [[??].sub.2t] denote some consistent estimators for [u.sub.1t] and [U.sub.2t]. Then, we expect that
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] under [H.sub.0]
and
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [H.sub.a]
Several tests for equal predictive ability of nested models have been proposed, including Clark and McCracken (2001), McCracken (2007), and Clark and West (2007); see Corradi and Swanson (2006) and West (2006) for reviews of the literature and references on predictive ability testing. The first test we use is the Chao, Corradi, and Swanson (2001) (hereafter CCS) test. If both f(x) and g(x) are linear functions so that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], then [H.sub.0] being true implies that the expected value of the statistic
(1) [m.sub.p] = (1 / [square root of P]) [T.summation over (t = R+1)] [[??].sub.1t][W.sub.t-1]
is (asymptotically), where [W.sub.t-1] = ([DELTA][o.sub.t-1], [DELTA][o.sub.t-2], ..., [DELTA][o.sub.t-1])'. (6)
A wealth of evidence has accumulated that, at least for output, it is important to relax assumptions about g(x) being a linear function. Two commonly used transformations of the oil price series are the NOPI introduced by Hamilton (1996) and the volatility of oil prices. The motivation for NOPI is that it is the price of oil relative to recent experience that matters most to consumers and producers. The motivation for volatility is that uncertainty about oil prices can cause consumers to postpone major purchases and firms to postpone investment. (7) Our second test is therefore that neither the NOPI variable nor the oil price volatility has marginal predictive content for any of the macroeconomic variables. NOPI is constructed as in Bernanke, Gertler, and Watson (1997) to be equal to the maximum of and the percentage change over the highest price observed in the previous 12 mo. The availability of daily market prices for crude oil and the fact that oil prices exhibit substantial day-to-day fluctuations make the realized volatility of oil prices a natural measure of volatility (see, e.g. Andersen et al. 2003). (8) Because neither of these transformations require estimation, the CCS test statistic given by Equation (1) can be used directly, where [W.sub.t-1] a represents either lags of NOPI or realized volatility as opposed to lagged oil price changes.
The above CCS test relies on the assumption of a linear forecasting model under both [H.sub.0] and [H.sub.a]. To remedy this, we consider the integrated conditional moment test of...
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