I gasped out loud last week at the low values for short term elasticity in the IMF World Economic Outlook:
This was picked up by Kevin Drum, and that set off a small blogospheric storm in a teacup with posts by Ryan Avent, Megan McArdle, Kevin Drum again, Jim Manzi, Kevin Drum a third time, Marginal Revolution, Modeled Behavior, and probably others I missed. Much of this discussion was about the implications for carbon taxes, which are not my concern here. But a secondary theme was skepticism that the IMF's estimates are correct. In particular, it was widely noted that there are much higher estimates in the economic literature. I was familiar with this (which was why I titled the original post "Wow..."), and I was also aware of the trend to lower elasticity estimates over time but had never seen an estimate as low as the IMF's latest one.
In this post, I wanted to present an admittedly crude exercise, partly for my own education, but which I think illustrates that the IMF's short term estimates for elasticity are not crazy on their own terms (ie as describing behavior between 1990 and 2009). What I did was take annual data for oil prices (the inflation adjusted ones from the BP spreadsheet), world GDP from the IMF, and total oil production also from BP. The year-over-prior-year changes look as follows:
We focus on year-over-prior-year to get at the "short term" here.
If we start by looking at the univariate correlations, this is what we get if we plot the oil production changes (y) against GDP changes (x):
Clearly there is some real correlation here, though with an R2 of 32%, it's far from a cast iron relationship.
The 0.7097 coefficient in the trendline relates the average percentage change in oil production to the average percentage change in real GDP. And it is not a million miles from the IMF's 0.685 (derived using a more sophisticated statistical model). Note that there's also a non-trivial constant term here (the intercept is at -1.2%) which I interpret as due to the slow steady improvements in oil efficiency that have been going on since the 1970s oil shocks.
Now, if we just directly correlate oil production change with price changes, we get this:
Wait - oil usage increases when price increases? Well, yes, at least during the last twenty years, when the economy grows, it tends to cause oil price increases as well as growth in oil production (witness the last year or two). So this univariate correlation is not telling us about the independent effects of price on consumption. To try and get at what we really want, let us use the linear relationship between oil production change and gdp change from the graph up above (that y = 0.7097x - 0.0123 business), and subtract that out, and then see if price explains the residuals (ie that portion of oil usage changes that are not explained by GDP changes). That gives us:
Well, it just barely slopes downwards, and the coefficient -0.0012 is a bit outside of the IMF's range of -0.009 to -0.028. However, I think the overwhelming impression here is this: once you adjust for GDP changes, oil production/usage changes are almost completely uncorrelated with price changes, at least at this annual time scale. There's really no relationship there over the interval of interest.
And that's why the IMF is coming up with tiny values for price elasticity.