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 new 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.

We then formulated the same approach as a special case of Bayesian inference, in which we have dogmatic prior beliefs about the contemporaneous response of supply to price and economic activity but very uninformative prior information about the contemporaneous response of demand to price and economic activity. We conducted this Bayesian inference as a special case of the algorithms developed in our Econometrica paper. Incidentally, anybody can download the MATLAB code to do this kind of exercise themselves from my webpage. The Bayesian posterior median and 95% posterior credibility sets are indicated in blue. Not surprisingly, these are exactly the same answer as Kilian obtained using the traditional method.

Is there any benefit to reframing the traditional approach as a special case of Bayesian inference? One of the natural byproducts of our algorithm is the Bayesian posterior inference (that is, what we believe now that we have seen the data) about magnitudes such as the short-run demand elasticity of oil. It turns out that if we had the Bayesian prior beliefs that are implicit in Kilian’s approach, now that we have seen the data, we would still insist that the short-run supply response is zero (because our Bayesian prior beliefs about this parameter were dogmatic), but we would now also be very confident that the short-run demand elasticity is greater than two in absolute value and readily believe that it might be minus or plus infinity. In other words, we do not regard it as the least implausible to conclude that within a month of a 1% increase in oil price, in response consumers might increase their consumption of oil by a million percent or more. Quoting from our paper:

The claim that we know for certain that supply has no response to price at all within a month, and yet have no reason to doubt that the response of demand could easily be plus or minus infinity is hardly the place we would have started if we had catalogued from first principles what we expected to find and how surprised we would be at various outcomes. The only reason that thousands of previous researchers have done exactly this kind of thing is that the traditional approach required us to choose some parameters whose values we pretend to know for certain while acting as if we know nothing at all about plausible values for others. Scholars have unfortunately been trained to believe that such a dichotomization is the only way that one could approach these matters scientifically.

Misgivings about the traditional method are one reason that many researchers have looked for other approaches to identification, such as relying on sign restrictions– surely we can at least rule out that consumers increase the quantity they buy when the price goes up. In a subsequent paper with University of Virginia Professor Daniel Murphy, Kilian used sign restrictions to achieve partial identification and replaced the assumption that there is no contemporaneous response of supply with a hard upper bound on the size of the contemporaneous response. My paper with Christiane shows that the Kilian-Murphy results can also be obtained as a special case of Bayesian inference. We note among other concerns that their specification still allows for an implausibly large contemporaneous response of demand, ignores a good deal of other informative prior information, and yet is still dogmatic about other magnitudes that we really do not know for certain.

The main point of our paper is that if researchers had thought about what they were doing as a Bayesian exercise from the very beginning, there is a much richer set of prior information that could be drawn on while simultaneously relaxing many of the dogmatic restrictions. We illustrate how this can be done for the question of the role of oil supply and demand shocks in particular. Among other contributions, as in a later paper by Kilian and Murphy (2014) we bring inventories into the analysis (as a key reason why quantity and price need not move together), allow for measurement error in the variables (a ubiquitous problem in macroeconomics that is usually entirely ignored in most research), allow the possibility that the relations have changed over time (with the Bayesian approach offering a middle ground between assuming on the one hand that all the data are equally useful or throwing out earlier data altogether on the other), and make use of detailed evidence from other datasets about the price and income elasticities of supply and demand.

The figure below presents a few of the results we come up with. These are dynamic responses (like those in the first figure above) of global industrial production (the first column) and the real oil price (the second column) to each of the four shocks we study (shocks to supply, economic activity, oil consumption demand, and inventory demand). All four shocks would raise the price of oil, as seen in the second column. But whereas an oil price increase that results from a supply reduction leads to a decline in economic activity, the same is not true of an oil price increase that results from an increase in demand.

Another thing we do in the paper is look at the contribution of different shocks to historical movements in each of the variables. The red lines in each of the 4 panels below plot the actual percent change in the crude oil price each month over 1975-2014. The blue lines give the Bayesian posterior estimate of how big the percent change that month would have been if there had been only one shock. For example, the first panel isolates the contribution of supply shocks. Ninety-five percent posterior credibility regions for the estimates are indicated by light blue shaded regions.





Again quoting from the paper:

Supply shocks were the biggest factor in the oil price spike in 1990, whereas demand was more important in the price run-up in the first half of 2008. All four structural shocks contributed to the oil price drop in 2008:H2 and rebound in 2009, but apart from this episode, economic activity shocks and speculative demand shocks were usually not a big factor in oil price movements. Interestingly, demand is judged to be a little more important than supply in the price collapse of 2014:H2.

We have drawn on a lot of prior information in producing the above graphs, though none of that information was used dogmatically as has been the case in previous studies. Another advantage of our approach is that we can examine what happens if we had considerably less confidence in any elements of the maintained prior beliefs. The last section of our paper explores the sensitivity of our main conclusions to such changes. We find that although our posterior credibility sets for most objects of interest would be wider when we have less faith in any specified components of the Bayesian prior, most of our broad conclusions would still emerge. For example, we did not find any specification for which there is more than a 2.5% posterior probability that supply shocks accounted for more than 2/3 of the cumulative oil price decline in the second half of 2014.

Our paper concludes: