Generalized Impulse and Its Measure

Given the importance of uncertainty shocks to economic agents such as consumers, producers, investors, or policymakers, it seems surprising that little attention has been paid to developing models analyzing the effect of uncertainty (second-moment) shocks. In contrast, there have been a vast amount of literature dealing with the impact of level (first-moment) shocks. In this paper, we attempt to fill this gap by proposing a new concept: ‘generalized impulse.’ This concept is defined as a one-off external intervention given to a system which results in a change in the distribution of the internal structural errors of the system. Such an intervention can be given to the system in order to achieve some policy objectives, or it can be given exogenously by an external force outside the system. Uncertainty shocks are generated as a special case of such a generalized impulse. We also propose new impulse response functions called ‘variance impulse response function’ and ‘covariance impulse response function,’ which can enable researchers to measure the impact of uncertainty shocks. We then apply our new methods to analyze the impact of uncertainty shocks in oil prices on the GDP growth rate, using data from the United States. When the level of uncertainty in oil prices unexpectedly increases, the price of oil tends to increase significantly and persistently, whereas the growth rate of GDP is adversely affected. Such a negative impact on GDP is present even after five years. Hence, our results indicate that an unexpected increase in uncertainty in oil prices can have an effect similar to an unexpected increase in oil prices themselves, but in a much worse manner. This is because the negative impact on output induced by uncertainty shocks can be much more persistent than the impact from level shocks.