Other factors matter too of course. One way to control for other factors is to employ measures of convenience yield and risk in the equation that determines inventory holdings. My recent papers on the subject use those variables, along with inventories, to determine commodity prices:
High interest rates reduce the price of storable commodities through four channels: ¤ by increasing the incentive for extraction today rather than tomorrow (think of the rates at which oil is pumped, gold mined, forests logged, or livestock herds culled) ¤ by decreasing firms' desire to carry inventories (think of oil inventories held in tanks) ¤ by encouraging speculators to shift out of commodity contracts, and into treasury bills ¤ by appreciating the domestic currency and so reducing the price of internationally traded commodities in domestic terms (even if the price hasn't fallen in terms of foreign currency).
All four mechanisms work to reduce the real market price of commodities, as happened when real interest rates where high in the early 1980s. A decrease in real interest rates has the opposite effect, lowering the cost of carrying inventories, and raising commodity prices, as happened in 2007-08 and 2010-11.
The theoretical model can be summarized as follows. A monetary contraction temporarily raises the real interest rate (whether via a rise in the nominal interest rate, a fall in expected inflation, or both). Real commodity prices fall. How far? Until commodities are widely considered "undervalued" -- so undervalued that there is an expectation of future appreciation (together with other advantages of holding inventories, namely the "convenience yield") that is sufficient to offset the higher interest rate (and other costs of carrying inventories: storage costs plus any risk premium). Only then are firms willing to hold the inventories despite the high carrying cost. In the long run, the general price level adjusts to the change in the money supply. As a result, the real money supply, real interest rate, and real commodity price eventually return to where they were. The theory is the same as Rudiger Dornbusch's famous theory of exchange rate overshooting, with the price of commodities substituted for the price of foreign exchange. See: "Expectations and Commodity Price Dynamics: The Overshooting Model," American Journal of Agricultural Economics 68, no. 2, May 1986, 344-348. Reprinted in Frankel, Financial Markets and Monetary Policy, MIT Press, 1995. The deep reason for the overshooting phenomenon is that agricultural and mineral prices adjust rapidly, while most other prices adjust slowly. See: "Commodity Prices and Money: Lessons from International Finance," American J. of Agricultural Economics 66, no. 5, Dec. 1984, 560-66. Of course many other things beyond real interest rates and growth influence commodity prices. One can try to control for some variables, such as global economic activity and uncertainty, as in the 2010 and 2013 papers.
Another way of isolating the monetary effects on commodity prices is to look at jumps in financial market prices that occur in immediate response to government announcements that change perceptions of monetary policy, as was true of Fed money supply announcements in the early 1980s. Money announcements that caused interest rates to jump up would on average cause commodity prices to fall, and vice versa. The experiment was interesting, because news regarding supply disruptions and so forth was unlikely to have come out during the short time intervals in question.
Simple graphs of real commodity price index versus short-term real interest rate. (Earlierversions here.)
Real commodity prices (in $) have been negatively correlated with the real 3-month T-bill rate.
(Update thanks to Marco Martinez.)
The relationship is statistically significant. Regression results for 1950-2012 are available in Frankel (2013), as are tests with alternative indices from CRB, Dow Jones, Reuters & Goldman Sachs, thanks to R.A. Marco Martinez del Angel. All these results are still significant in regression results updated to 2018, Frankel & Martinez (pdf).
Commodity price spikes in the 1970s, 2008 & 2011 can be explained by real interest rates that are zero or even negative.
Updates Update: April 2008 The dominant macroeconomic explanation for the 2001-07 run-up in commodity prices had been strong real growth in the world economy. But after August 2007 growth slowed worldwide, yet commodity prices accelerated (see graph)-- undercutting that theory. That episode supported the importance of declining real interest rates, as argued here. King Abdullah of Saudi Arabia, for one, apparently believed that the rate of return on oil reserves was higher if he didn't pump than if he did. On April 12, 2008, he said "Let them remain in the ground for our children and grandchildren..." Update: 2009 Prices of oil and most other minerals peaked in mid-2008. Over the subsequent year they came down sharply. The obvious explanation was the financial crisis and the onset of global recession. If my point about the positive effect of low real interest rates is correct, it was during this period overwhelmed by the negative effect of the weak economy. (The equation has both macroeconomic factors in it.) Update: 2011 The big new upsurge in commodity prices over the last two years again fits the story, as US interest rates fell virtually to zero. Update: Jan. 2014 If US interest rates rise in future years, as widely expected, that should put downward pressure on real commodity prices.