Here are two pictures. The first shows harvest cropland, failed cropland (with the infamous dust bowl years on 1934-1936 being the only clear discernible events), and acres in set-aside and conservation programs. Since 1986, the set-aside and conservation acres are comprised entirely of land in the Conservation Reserve Program.
It's also interesting to note that while production has increase steadily with yields, there is no discernible trend in crop acreage: it's been about 300-350 million acres for a hundred years. That's about the size of nine or ten average-sized states (the area of North Carolina is 34.5 million acres).So what drives variations in conservation acreage? That would be prices. Acres in conservation increase when prices fall, and vice versa. Which brings me to the second graph: it shows conservation acreage plotted with an index of key commodity prices (corn, soybeans and wheat, which comprise most U.S. cropland), adjusted for inflation and lagged one year. I lagged the price index one year because it takes a year for policy to respond to prices.

It could be that harvested cropland would have responded to price fluctuations even without changes in conservation policy. But I think that's a tough argument to make.
Anyhow, I wish both popular and scholarly reporting on agricultural policy and commodity prices would keep in mind the central importance of conservation policy.
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