Oil-Price Density Forecasts of GDP

Transcription

1 Oil-Price Density Forecasts of GDP Francesco Ravazzolo a,b Philip Rothman c a Norges Bank b Handelshøyskolen BI c East Carolina University August 16, 2012 Presentation at Handelshøyskolen BI CAMP Workshop on Forecasting and Analysing Oil Prices Ravazzolo & Rothman Oil-Price Density Forecasts of GDP 1 / 17

2 Introduction: What We Do Pseudo out-of-sample (OOS) density forecasting study of predictability from crude oil prices to US GDP growth rates. Main findings: 1 Statistically significant predictability from oil prices to GDP via density forecasts. 2 Importance of use of real-time vs. ex-post revised data depends upon forecast horizon and OOS period considered. 3 Economically significant differences between benchmark without oil prices and models with oil via risk measures. Ravazzolo & Rothman Oil-Price Density Forecasts of GDP 2 / 17

3 Why Do This? Oil and the Macroeconomy Hamilton (JPE, 1983) showed that jumps in crude oil prices preceded all post-wwii US recessions but one: 1 Oil prices Granger-causal for GDP growth , , and Analysis suggested these oil price increases were exogenous wrt business cycle movements. 3 Large literature followed over past roughly 30 years, focusing on both in-sample (IS) and OOS analysis 4 Some questions in the subsequent IS literature: Has the relationship dissipated over time? Is the relationship linear or nonlinear? Was the effect Hamilton uncovered due to monetary policy? Should oil-price movements be treated as exogenous? Due to oil supply shocks or shifts in demand? What s learned through decomposing demand shocks? See, e.g., Kilian (JEL, 2008) for a thorough discussion. Ravazzolo & Rothman Oil-Price Density Forecasts of GDP 3 / 17

4 Why Do This? Oil and the Macroeconomy A recent part of literature has focused on the OOS predictability of oil prices for GDP via point forecasts. For example: 1 Bachmeier et al. (EI, 2008) do not find evidence of such predictability. 2 Alquist et al. (HEF, 2012) report similar results in linear VARs, but find oil-to-gdp predictability when they consider nonlinear specifications; further supported by extensive analysis in Kilian and Vigfusson (2012). 3 Ravazzolo and Rothman (JMCB, forthcoming) find OOS predictability at the longer forecast horizon considered, using both real-time and ex-post revised data. Ravazzolo & Rothman Oil-Price Density Forecasts of GDP 4 / 17

5 In-Sample Predictability Evidence As per Inoue and Kilian (ER, 2004), using the same models it would be surprising to find strong OOS predictability from crude oil prices to US GDP absent IS predictability: 1 We present evidence of IS predictability from crude oil prices to US GDP using sequence of expanding windows of post-opec I data. 2 The first and last IS periods are 1975Q1-1989Q4 and 1975Q1-2012Q1. 3 Oil price measure: Nonlinear transformations of imported RAC composite index. Ravazzolo & Rothman Oil-Price Density Forecasts of GDP 5 / 17

6 In-Sample Predictability Evidence Relative BIC (model without oil vs. model with oil ) 12 NOPI NET NET GAP Q1 1995Q1 2000Q1 2005Q1 2010Q1 Real-time first-release data; recursive estimation windows, 1975Q1-1989Q4, 1975Q1-1990Q1,..., 1975Q1-2012:Q1. Ravazzolo & Rothman Oil-Price Density Forecasts of GDP 6 / 17

7 Forecasting Models Linear AR(4) benchmark: y t = α + 4 β i y t i + σɛ t, (1) i=1 where y t = GDP growth rate and ɛ t N(0, 1). It s standard in the literature to set p of the AR(p) model to 4. In Bayesian strategy we use, ɛ t N(0, 1) assumption, along with others, implies that predictive densities are Student t distributed. Ravazzolo & Rothman Oil-Price Density Forecasts of GDP 7 / 17

8 Forecasting Models Linear alternative extends the AR(4) with an oil price measure: y t = α + 4 β i y t i + i=1 4 γ i oil t i + σɛ t, (2) i=1 where oil t = NOPI, NET, NET, and GAP as defined in Hamilton (JME, 1996) and Kilian and Vigfusson (2012). Ravazzolo & Rothman Oil-Price Density Forecasts of GDP 8 / 17

9 Forecasting Models Equations (1) and (2) are estimated with a recursive estimation scheme: 1975Q1-1989Q4, 1975Q1-1990Q1,... Last observation for which we have data is 2012Q1. Initial observation determined by availability of RAC data. Compute 1-step-ahead and 5-step-ahead direct forecasts with real-time and ex-post revised data. For real-time, h = 1 is a nowcast and h = 5 is a 1-year-ahead forecast. Ravazzolo & Rothman Oil-Price Density Forecasts of GDP 9 / 17

10 Ex-Post Revised vs. Real-Time U.S. Real GDP Growth Rates: What Happened Post-Lehman Collapse? Different Stories from Different Data Ravazzolo & Rothman Oil-Price Density Forecasts of GDP 10 / 17

11 Forecast Evaluation Density forecasts evaluated via continuous ranked probability score (CRPS): CRPS(t + h, l) = (F (z) I {y t+h z}) 2 dz = E f Y t+h,l y t+h 1 /2E f Y t+h,l Y t+h where F is the cumulative distribution function that corresponds to the predictive density f of model l estimated at time t, I ( ) takes a value 1 if y t+h z and equals 0 otherwise, E f is the expectations operator, and Y t+h,l and are independent random variables with common sampling density equal to the posterior predictive density of model l for y t+h estimated at time t. Y t+h (3) Ravazzolo & Rothman Oil-Price Density Forecasts of GDP 11 / 17

12 Forecast Evaluation Groen, Paap, and Ravazzolo (JBES, forthcoming) provide a useful explanation of the CRPS: 1 It provides a measure of the distance between the predictive CDF as implied by a model and the CDF of realizations h periods ahead. 2 Accordingly, a relatively low CRPS value reflects a relatively good density forecast. 3 To assess the density forecasting performance of model l over a certain OOS sample, one can compute the historical average of (3) across forecasts. Refer to that average as avcrps l. 4 We use the Groen et al. procedure to implement a Diebold-Mariano (JBES, 1995)-type test, with a Harvey, et al. (IJF, 1997) correction, based on the difference between avcrsp l measures between the no-oil-price AR(4) benchmark and the oil-price alternatives. Ravazzolo & Rothman Oil-Price Density Forecasts of GDP 12 / 17

13 Forecast Evaluation We also examine the Risk of a Negative Gap (NGR) and Risk of a Positive Gap (PGR) measures introduced by Kilian and Manganelli (JMCB, 2008): x NGR γ = (x y t ) γ df yt ( y t ), γ 0 PGR δ = x ( y t x) δ df yt ( y t ), δ 0, where the parameters γ and δ are measures of risk aversion. These are probability-weighted average of the losses incurred when realizations of y t fall outside the bounds [x, x]. Ravazzolo & Rothman Oil-Price Density Forecasts of GDP 13 / 17

14 Table: Density Forecasting Results:1990Q1-2012Q1 Ex-Post Revised Real-Time Release I NOPI NET NET GAP NOPI NET NET GAP h = 1 MSPE Ratio avcrps Ratio CRPS Test h = 4 MSPE Ratio avcrps Ratio CRPS Test Ratio relative to benchmark: alternative-measure / benchmark-measure Ravazzolo & Rothman Oil-Price Density Forecasts of GDP 14 / 17

15 In-Sample Predictability Evidence Cumulative Sums of Relative CRPS, Real-Time First Release, h = NOPI NET NET GAP Q1 1995Q1 2000Q1 2005Q1 2010Q1 cusum t = t N+1 CRPS(t,l) CRPS(t,m),t=N+1,...,T,l=benchmark,m=alternative. Ravazzolo & Rothman Oil-Price Density Forecasts of GDP 15 / 17

16 In-Sample Predictability Evidence Risk of Negative Gap: Benchmark vs. Alternative with NET Oil-Price Measure Ravazzolo & Rothman Oil-Price Density Forecasts of GDP 16 / 17

17 More Work to Do Have produced statistically and economically significant density forecast improvement by incorporating nonlinear oil-price measures in forecasting model. We obtained first set of results this past week. Some stuff on our To Do List : 1 Examine more systematically results, e.g., sub-samples of the OOS period. 2 Explore robustness of density forecast improvement wrt: Including some other variables in benchmark model, e.g., Kilian s (AER, 2009) real global activity measure. Following work Francesco and Todd Clark have done, consider allowing for stochastic volatility in the benchmark and alternative models. Ravazzolo & Rothman Oil-Price Density Forecasts of GDP 17 / 17