How much do crop yields respond to commodity prices?

There's an old paper by Houck and Gallagher that examines how corn yields respond to price changes.  They found corn yields went up 21 to 76 percent with a 100 percent increase in price, presumably a response to increase fertilizer use.  In econ speak this is called an "elasticity" between 0.26 and 0.76.  The total supply response would be this elasticity plus the land area response.

The middle estimates in that old paper are being used by some to justify relatively benign effects from ethanol policy on food commodity prices.

Some recent updates to that old work are finding numbers at the lower end of that range, but also find large acreage response elasticities.  Those arguing for a big yield response acknowledge that the land response is small, around 0.1.  But there are lots of folks saying that the overall, yield plus land area, supply response to price is between 0.5 and 1.

These results contrast sharply with my own work with Wolfram Schlenker.  After accounting for endogeneity bias (which makes elasticities too small) we find the yield-plus-land elasticity to be around 0.1. It's also hard to reconcile a large supply response to some basic facts about commodity prices and production. 

Consider:

(i) It's a truly global agricultural commodity market; 

(ii) global production of agricultural commodities is very smooth (weather shocks mostly average out);

(iii) consumption is smoother than production due to storage ;

(iv) prices vary a LOT and are highly autocorrelated (a price shock sticks around for a long time), which is due mainly to (iii);

(v)  prices change sharply, and persistently, in response small, transitory production shocks (e.g., bad weather or USDA forecast updates). 

These facts tell me that both supply and demand must be very inelastic.  If supply response were as elastic as 0.5, we just wouldn't get big, persistent price shocks in response to small weather surprises.  This is because production shocks could be so easily smoothed with inventories and greater or lesser production in future time periods.  Indeed, commodity price behavior by itself implies a total economic response (that's the supply elasticity plus demand elasticity) on the order of 0.2 or possibly much less (this can be traced to the famous work by Deaton and Laroque, or to more recent work by Cafiero et. al, that I've mentioned before on this blog).

Also, if you just look at yields, you will find they look like random noise (weather) around a linear trend.  There's no autocorrelation there while there's a ton of autocorrelation in prices.  I certainly can't "see" a big price response (although there may be a small one).

So, I'm super skeptical.  I need to do more crunching to figure out how these folks are getting such crazy numbers.  But there's something fishy here.  These elasticities just don't add up to the stylized facts we all know well. 

Cynical me is thinking about those economists who believe that all elasticities lie between 0.5 and 2, and so hunt around for a specification that gives them the answer they expect.  Also, the real number is probably so small that it can't be estimated with statistical significance, which makes it difficult to publish.  So, all we see in print are the big "statistically significant" numbers from badly specified models.

Update :  There is also the problem with finding the mechanism for a large yield response to price.  We have experimental data on yields in relation to fertilizer applications and yield simulation models put together by crop scientists.  Both show a highly non-linear link between fertilizer and yield.  That is, yields go up sharply with higher application rates up to a threshold, above which fertilizer has little or no marginal influence.  The steepness of the yield/fertilizer link below the threshold suggests farmers will generally apply at near-threshold levels over a broad range of output prices (the threshold depends a bit on the weather, and weather effects output price, so statistics here can be tricky).  Anyway, the point is that if farmers apply fertilizer at near yield-maximizing rates even when prices are pretty low, so it's hard to see how prices could cause a very large yield effect via fertilizer inputs, even though a modest effect is plausible.