Equity premium prediction using the price of crude oil: Uncovering the nonlinear predictive impact

Highly cited studies, such as Mork (1989), Hamilton (1996), Hamilton (2003) and Kilian and Vigfusson (2013) establish a nonlinear connection between movements in the real (nominal) price of crude oil and the real gross domestic product (GDP) growth rate. Based on the observation that crude oil price increases have a different impact on the real GDP growth rate than crude oil price decreases, the authors introduce various nonlinear transformations of the price of crude oil to account for the nonlinear predictive impact. Using predictive regressions à la Goyal and Welch (2008), a growing number of studies in recent years have conditioned on these nonlinear crude oil price measures to predict equity premium out-of-sample. By applying the dynamic rotation rule suggested in Zhu and Timmermann (2021), we demonstrate that the form of nonlinearity that helps improve relative out-of-sample point prediction accuracy the most does not have to do with crude oil price increases (decreases) relative to recent prices as perceived by the current literature, but with connecting the relative out-of-sample point prediction performance between the benchmark and the crude oil price-based model with movements in economic variables measuring equity market volatility, economic activity, uncertainty and financial conditions. The statistical evidence of out-of-sample equity premium predictability also translates to economic gains.