A solution to a big commodity price puzzle (super wonkish)

A long standing puzzle in the economics of commodity prices concerns the large amount of autocorrelation observed in most price series.  While most commodity prices appear to revert to historical means eventually, it typically takes a long time, so much so that, at least statistically, it's hard to reject the hypothesis that price shocks are permanent and historical reversions have simply been due to chance.

This "puzzle" was so articulated in a series of very influential papers by Angus Deaton and Guy Laroque.  They reasoned that commodity prices should be autocorrelated to some extent due to the buffering effects of storage.  In plentiful times some production is saved; in bad years, inventories are drawn down to supplement production.  Consumption is therefore smoother than production and prices are less volatile that they would be without storage, but are autocorrelated even though production shocks can appear random (like from the weather).   The puzzle came about from the formal modeling of this process and some sophisticated techniques they used to fit that model to observed commodity prices.  That model indicated a certain amount of autocorrelation but nowhere near as much as we observe in reality.

So, all this might sound very technical, and it is, but it is pretty fundamental for understanding why we occasionally have huge commodity price spikes like the one in 2008, which can cause starvation, malnutrition, and civil conflict in developing countries.  When staple food gets too expensive the world turns very ugly.

A new paper by Carlo Cafiero, Eugenio and Juan Bobenrieth, and Brian Wright (one of my professors at Berkeley) in the Journal of Econometrics (sorry, only a gated version)  have a pretty clear solution to this puzzle.  It turns out that Deaton and Laroque's puzzling findings stemmed mainly from imperfect calibration of their model that came from using approximation methods that were too coarse.  I'd guess computers simply weren't fast enough back then to make super fine approximations.  Cafiero et al. simply improved the resolution of the approximation, obtained better estimates of the few key parameters, and can now model commodity prices that look very much like the real world.

The crux, it seems, is that demand for commodities is extremely inelastic.  Thus, when inventories get very low, prices spike very high.  This creates a strong incentive to keep a lot of inventories in speculation for the day when prices do spike.  So we rarely get stock outs but when we do, or get close, prices can go very high.  That's pretty much what happened in 2008.  It may have been precipitated somewhat by the ethanol boom that increased grain demand more than expected.  In the initial years after the boom, inventories were probably too low for the new demand regime, which made the market particularly susceptible to inventory draw downs and a huge price spike.

To my mind, this is one of the best examples of a dynamic rational expectations economic model that actually works.

Update: Below is a picture of the solution and how a poor approximation missed what was critical.  The essential problem involves finding a function that relates price (p) to the available supply (z).  Available supply includes inventories carried over from the last period plus current production, which can vary randomly.  The 'kink' in the line is where storage reaches zero and the market consumes everything that's available.  So the upper part of the price function is just the consumption demand curve.  When prices are below that line, the amount stored is the horizontal difference between the price function and the dashed line that follows from the straight line above the kink.  So, this is the essential picture that tells when its optimal to sell high and buy low when it comes to commodities.  The kink is critical--that's where prices can really start to spike more in relation to small shocks.  The red line is Deaton and Laroque's approximation, which doesn't quite fit to correct (more finely callibrated) line.  It's especially far off near the kink, which is key. The incorrectly smooth price function suggested prices less autocorrelated that we observe.  But it was all just approximation error, not necessarily a fundamental flaw in the theory.


  1. there's an easier explanation:

    How Goldman Sachs Starved Millions and Got Away With It


  2. rjs: Yes, for many it seems much easier for them psychologically to simply follow prior beliefs and salacious conspiracy theories. But reality is sometimes a little more more complex.

  3. What about a situation where inventory is non-zero, and in fact increasing, but the price increases are dramatic? I am thinking of oil in 2008, where we saw a combination of increasing stock (http://tonto.eia.doe.gov/dnav/pet/pet_stoc_wstk_dcu_nus_w.htm) but $145 price. I remember OPEC announcing supply increases as well. Is this just a case of perceived increased world demand outstripping growing inventory and supply? Or is there something else in a rational expectations framework that would explain the large rise and mass collapse of oil prices in 2008? I’m thinking weak dollar on the way up, and financial system chaos on the way down.

  4. Tatonnement:

    Rising inventories coupled with rising prices could be indicative of a bubble, someone trying to corner the market (e.g., Hunt brothers attempt for Silver in the late 70s and recent cocoa activity by Anthony Ward (aka Choc Finger)).

    But it could also be a rational speculative action due to an outward anticipated *shift* in demand or anticipated inward shift in supply.

    While it is usually pretty easy to spot an attempt at cornering the market, it can be very hard to separate a bubble from a speculative buildup in inventories for fundamental reasons.

    In 2008, for most commodities, there was no real build up of inventories and so most of us economists *did not* view the situation as a bubble. Paul Krugman, Jim Hamilton and a few others wrote about that.

  5. I should have stated my question more clearly, I was trying to drill down on how you could tell the story of 2008 oil in terms of supply and/or demand shifts given what you said about demand for commodities being ‘extremely inelastic’ in explaining the model. I remember Krugman writing about oil in 2008, and accepted his view that more or less steady inventories and other factors indicated that the price changes were a result of increased world demand and not a bubble. So my question is, given that oil peaked in 2008 and bottomed out again by the end of the year, what explains those big price moves in terms of rational expectations? I was trying to hint at the argument that a weakening dollar helped propel oil upward in the first half of 2008, while the financial crisis helped it crash in the second half. But given that it didn’t take very long for the BRICs to get back on track in terms of growth, why aren’t we back at $145 oil if that was a rational price? In light of the fact that there was a massive run up in inventories (land and especially tanker) in 2009, it seems like, if anything, oil prices during that time period were inflated. Leaving that aside, let’s say you index world oil consumption to 2007 levels, even after the big drops in U.S. demand in 2008 and world demand in 2009, you are still 1.34% above 2007 level consumption (data from here http://www.eia.doe.gov/steo/ ‘world liquid fuels consumption’ series). I guess if people were projecting steady supply and increased world demand to rationally arrive at $145, its unclear why we aren’t back to that price now. I know that you could argue that there is still a lot of uncertainty revolving around world recovery (and the U.S. in particular as a key consumer), but given the asymmetric nature of the bet involved, why isn’t the price difference being arbitraged away? If you believe the fundamentally driven price should be $145, and its trading at $78 today that is an 86% return versus a 40% potential loss (assuming it returns to old lows). Given not just the probability of either state of the world occurring, but also the skew in P&L potential, wouldn’t you have to put on that trade? It seems like the only reason not to do so would be if you don’t believe $145 is a fundamentally supported price. Current news doesn’t seem to indicate a lot of support amongst futures traders for a return to $145 either http://online.wsj.com/article/BT-CO-20100730-715102.html.

  6. Tantonnement:

    I think the main reason prices fell was an unexpected precipitous fall in demand following from Lehman Bros. collapse and the ensuing recession. I think oil prices would be very high right now if it weren't for the worldwide economic collapse.

    Yes, consumption worldwide may be higher today than it was in 2007. But that's the wrong comparison. You need to think about what markets thought consumption would be today in comparison to what it actually is. There's a huge trend in there and we're far below that trend, unexpectedly, due to the Great Recession.

    There's lots of uncertainty and I believe we sometimes have bubbles that appear fundamentally irrational. But at least right now, I think commodity prices are one area where markets appear to behave pretty well--i.e. textbook neoclassical economics with modern stochastic dynamics playing a key role. (Granted, this may be a rare example.)

    Someone might convince me otherwise someday, but right now I don't see compelling evidence that bubble-like speculation had much to do with the 2008 run up in commodity prices.

  7. Thank you for taking the time to respond by the way. I wasn't trying to argue that current consumption was the right benchmark, and I agree that we are below trend after the collapse in aggregate demand. Obviously, expectations for the future carry more weight than the present moment since markets are forward looking. But my question remains, if you are not convinced that 2008 was a bubble, and if you think we will get back to those fundamental prices (assuming you believe that eventually the recovery will take hold either worldwide or at least some kind of new era BRIC decoupling from the U.S. scenario) then why isn’t money being mobilized currently to take those prices back to fundamental levels? Oil has been in the same range for roughly the last year. If forward looking market participants are rationally interpreting world recovery, shouldn’t we see rising oil prices? I think many people would argue that things look a lot better now than they did in August of last year. My example about the asymmetry of the payoff to making this bet (even if you assume there is a 50-50 chance of double dip versus recovery) should be bringing money in off the sidelines. Unless, in retrospect, the market believes a price of $145 was irrational. Or are you arguing that we are so far off trend, and will never return to trend, that the global fundamentals that supported $145 have entirely changed?

  8. Well, I do think the $145 oil was rational at the time and was probably driven by fundamentals. But that doesn't mean prices would have stayed that high indefinitely in the absence of a recession. Indeed, quite the opposite. That's what the theory of competitive storage tells us: that we should expect to sometimes get large and rapid run ups in price, but we eventually get mean reversion. Speculation about these possible run ups is what makes it profitable to keep inventories in the first place. Now the higher the price, the more tempting it is to dump those inventories, and the lower those inventories can get. In equilibrium prices can stay high for awhile but before too long either new supply comes along or demand attenuates, and prices fall.

    Actually, one important way that oil differs from the textbook case is the fact that demand response is very different in the short run as compared to the long run. In the short run people are stuck with their SUVs; in the long run they can buy Priuses. So pries can be rationally be super high but won't necessarily stay super high that long.

    My totally off-the-cuff guess is that oil would be above $100 bbl today if it weren't for the recession. But it probably wouldn't be as high as it was in 2008. And that reasoning is pretty consistent with theoretical simulations as I see them.

  9. Many private sector commodity players are very familiar with the types of price fly-ups you describe - industries like oil & gas, electric power, metals, and commodity chemicals jump to mind. But I think they'd say the fundamental cause is the inability to expand physical supply beyond total capacity in the short term, period. So if demand grows quickly (demand curve shifts to the right), all of a sudden there is not enough physical supply to go around at the marginal cost of production, and buyers are scrambling to buy at prices that end up closer to their own value-in-use.

    There could also be sudden reductions in available supply which have a similar effect (think hurricanes shutting down oil wells in the Gulf of Mexico, or refineries closing for maintenance, or an outbreak of a pest like wheat rust during a growing season).

    There's a certain lag to bringing on new capacity (at least a growing season in agriculture, and probably longer in general to build a new power plant or producing oil well). I wonder how long this lag is compared to the delay in mean reversion that economists observe.

    All of this may not be inconsistent with the Cafiero/Bobenrieth/Wright model and your inelastic demand explanation, but I don't yet see how they link up.

  10. R,

    Those are nice points. Actually, I think what you're describing is very much in the same spirit as the textbook models. The key is that "response to price" on both supply and demand sides is just very inelastic. In some instances there might be a response, but it takes time.

    One thing to keep clearly separate in our minds: *shifts* in demand and *demand response*. A shift in demand changes the whole schedule of what people will buy at a each price; demand response simply measures how much quantity consumed changes as prices change, holding all else the same.

    So, what you're describing is a situation where demand for energy *shifts* randomly in response to something like the weather. But because both supply and demand are very inelastic (the slopes of the curves are very steep), we can get these big price spikes. Speculative stores attenuate huge price volatility by keeping a lot of inventories and occasionally profiting from the spikes.

    Energy can get really interesting because often regulation constrains *retail* prices but does not constrain wholesale prices. This can get very ugly because it essentially makes wholesale demand vertical. It also makes the wholesale market susceptible to manipulation. That's exactly what happened in California about decade or so ago during the ENRON saga.

  11. Agreed, except that to be provocative I'd generalize to a broader set of drivers of demand shifts (not just sudden and random, e.g. weather-driven). Couldn't the demand shift just be driven by rapid economic growth? Imagine how much demand might have grown in 3 months during 2007 or 2008... and then imagine that capacity didn't expand at all during that time, and you've tipped over into the world where the demand and supply curves no longer meet (since the marginal value-in-use is higher than the marginal cost at the world's max production capacity).

    Metals might be an easier example to demonstrate this since demand is not as driven by micro events like weather. Iron ore spiked as much as any other commodity during the 2008 run-up (and by the way, I don't think it's index-traded so it's also a case against the "evil financial speculators" argument).

  12. Yes, unexpectedly large demand growth can drive prices. And it can take awhile for inventories to adjust to a higher growth rate. I think that was a key problem with ethanol.

    Technically, so called nonstationarity is another thing we in academia have a hard time dealing with in these models. Thus far I think it's been ignored in this context.


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