Friday, April 29, 2011

IMF Short Term Elasticities Are Not Crazy

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 McArdleKevin Drum again, Jim ManziKevin 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.


Mr. Sunshine said...

Interesting. So the skill as production has flatlined is to balance the maximum oil price against potential economic collapse for as long as possible, with the support of digital money printing central banks, while simultaneously converting the depreciating paper oil revenue value into real wealth assets.

Burk Braun said...

A longer-term trend is that energy use rose even faster than economic activity, so this low elasticity may still be significant in showing a flattening of this otherwise exponential curve. We may be at a responsiveness plateau or hill-top, as it were. In short, there may be reason to think the basic tenets of economics have not been repealed. It is just going to take a little more pain to induce actual reductions in use.

bmerson said...

How are the results affected if you use change in per capita consumption instead of change in overall production? It seems to me that population growth would tend to offset the negative elasticity when viewed in the aggregate. By using per capita usage instead, wouldn't you get a better idea of the actual impact of price?

Nick G said...

But why do we care about short term price elasticity? Isn't long-term price elasticity far more important?

And why do we care about price elasticity as shown during periods of low prices? Consumer responses will be very different to a 50% price increase from a base of $100, as compared to an increase from a base of $10.

When oil prices rise from $10 to $15, or even $40 to $60, it's not a big deal. On the other hand, oil prices above $100 will price oil of out of the market, in the long-term: plug-in hybrids (like the plug-in Prius and the Volt) and EVs will be far cheaper to operate, and mostly eliminate oil consumption.

Som said...

Everything you've said is correct. But it doesn't establish that the IMF estimate is correct, (I notice you did not claim that it was, but that seems to be what you are implying.)

Any factor that shifts oil demand will generate a positive correlation between the price and the quantity. This will obscure the negative relation between price and demand. So netting out GDP is not enough. For example, technological change, changes in the sectoral composition of GDP, and lifestyle changes not stemming from price changes will also shift the demand curve. So I believe the elasticity, especially for price increases is higher than it seems.

By the way, if you didn't use real, rather than nominal, oil price changes, then you'll be introducing measurement error in the price. That will bias any estimated relationship towards zero, as you can see by experimenting with a scatterplot.

The fact is, it's not easy to pin down the response of demand to price, since there are a lot of confounding factors that are hard to take into account.

With regard to the broader point in your original post, I think you are quite correct in pointing out that the IMF's growth forecasts are over-optimistic. I don't believe the elasticity is large enough to change your conclusion. Very well called.

Stuart Staniford said...


I did use real prices.

The above procedure is pretty much equivalent to standard econometric techniques for estimating elasticities - eg sere here for a tutorial. The only difference is I'm doing my regressions in two steps, rather than jointly fitting, but given that one variable (income) is much more powerful than the other, I wouldn't expect it to make much difference. I expect that's why I get pretty much the same values as the IMF for this data.

Stuart Staniford said...

Nick G:

I think short term elasticity is important because I don't think you get to long term elasticity smoothly - it happens because people experience enough pain to undergo a permanent change of attitude. And that process has political and economic implications.

Nick G said...


I'm not sure what you mean. I assume the IMF values are based on actual observation of behavior over time, not political assumptions. Long-term means long-term: behavior over longer time periods. Using short-term elasticities for price changes that persist over long periods is a mis-use of the numbers, I should think.

I don't think we need to think in terms of pain, just changes in expectations. No one is going to invest in fuel efficiency (e.g., by paying a little more for a hybrid) if they think the price increase is temporary.

Behavioral change isn't necessarily caused by overwhelming pain, it's due to prevailing perceptions and culture. If SUVs are fashionable (and gas prices are expected to be moderate), that's what people will buy.

On the other hand, affluent and rich people are more careful about their purchases (and more price sensitive) than people with moderate or low incomes - they have the time and education to make good purchasing decisions. For instance, the average Prius buyer is rather older and more affluent than the average car buyer.

Again, these things are non-linear: we persist with one set of plans and expectations despite changes in our environment, but they can all change fairly quickly with the right conditions.