Moment-Based Impulse and Its Measure with an Application to Oil Price Uncertainty

Abstract In this paper, we introduce a new concept: moment-based impulse. The standard definition of an impulse, a sudden mean shift, has been a ubiquitous fixture across the literature to date. Consider a one-time external intervention to a system that alters the distribution of its structural errors. If the intervention leads only to a location shift, it corresponds to the traditional mean shift impulse or a first-moment-based impulse. However, if the change affects the scale of the error distribution while keeping the mean unchanged, it constitutes an uncertainty shock that is, a second-moment-based impulse. We derive closed-form representations of response functions called the “variance impulse response function” and the “covariance impulse response function,” in order to capture the full impact of uncertainty shocks. We apply our framework to analyze the impact of oil price uncertainty shocks on the GDP growth rate, using the US data. When a positive uncertainty shock in oil prices occurs, the price of oil tends to increase significantly, whereas the growth rate of GDP is affected adversely and persistently. Such an uncertainty shock in oil prices can have an effect similar to an unexpected increase (a mean shift shock) in oil prices, but in a much worse manner. This is because the negative impact on output induced by uncertainty shocks is much more persistent than that from mean shift shocks.