How can we estimate the separate economic effects of shocks to oil supply and demand? I’ve just finished a research paper with Notre Dame Professor Christiane Baumeister that develops a new approach to this question.

The basic reason the question is hard to answer is that we would need to know the value of two key parameters: the response to price of the quantity supplied (summarized by the supply elasticity) and the response to price of the quantity demanded (summarized by the demand elasticity). If we only observe one number from the data (the correlation between price and quantity), we can’t estimate both parameters, and can’t say how much of observed movements come from supply shocks and how much from demand.

One way to resolve this problem is to find another observed variable that affects supply but not demand. A generalization of this idea is the basic principle behind what is referred to as structural vector autoregressions, in which we might also exploit information about the timing of different responses. The simplest version of this would be an assumption that it takes longer than one month for supply to respond to changes in price. If the very short-run supply elasticity is zero, and if supply shocks are uncorrelated with demand shocks, then the correlation between the error we’d make in forecasting quantity and price one month ahead could be interpreted as resulting from the very short-run response of demand to price. Putting this together with the observed dynamic correlations between the variables (for example, the correlation between this month’s quantity and last month’s price) would allow us to identify the effects of the different shocks over time.

In a previous paper that will be published in the September issue of Econometrica, Christiane and I proposed that Bayesian methods could allow us to generalize the traditional approach to structural vector autoregressions. We noted that what is usually treated as an identifying assumption (for example, the restriction that there is zero response of supply to the unexpected component of this month’s change in price) could more generally be represented as a Bayesian prior belief– we may believe it’s unlikely there is a big immediate response of supply to price but should not rule the possibility out altogether. Our paper showed how one can perform Bayesian inference in general vector dynamic systems where there may be good prior information about some of the relations but much weaker information about others.

In our research paper Christiane and I apply this method to study the role of shocks to oil supply and demand. We begin by reproducing an influential investigation of this question by University of Michigan Professor Lutz Kilian that was published in American Economic Review in 2009. Kilian studied a 3-variable system based on oil production, price and a measure of global economic activity. He assumed that supply does not respond contemporaneously to price or economic activity and that economic activity does not respond contemporaneously to oil production, assumptions that are referred to as the Cholesky approach to identification.

We first reproduced Kilian’s results using his dataset and his methodology. The panels below summarize the effects of three different kind of shocks (represented by different rows) on each of the three variables (represented by different columns). The horizontal axis in each panel is the number of months since the shock first hits at date 0. The red lines are the estimates that Kilian came up with based on his Cholesky identification.