Some observers have questioned whether the news on fundamentals affecting supply and demand in commodities markets has been sufficient to justify the sharp price increases in recent months. Some of these commentators have cited the actions of the Federal Reserve in reducing interest rates as an important consideration boosting commodity prices. To be sure, commodity prices did rise as interest rates fell. However, for many commodities, inventories have fallen to all-time lows, a development that casts doubt on the premise that speculative demand boosted by low interest rates has pushed prices above levels that would be consistent with the fundamentals of supply and demand. As interest rates in the United States fell relative to those abroad, the dollar declined, which could have boosted the prices of commodities commonly priced in dollars by reducing their cost in terms of other currencies, hence raising the amount demanded by people using those currencies. But the prices of commodities have risen substantially in terms of all currencies, not just the dollar. In sum, lower interest rates and the reduced foreign exchange value of the dollar may have played a role in the rise in the prices of oil and other commodities, but it probably has been a small one.
By my calculation, at least one third of the rise in the price of oil can be attributed directly to the decline of the dollar. This can be seen by looking at the rise in the price of oil in Euros versus the rise in the price in US Dollars. The rise in Euros has been less than the rise in dollars ergo, some of the Dollar based rise can be directly attributed to the decline of the currency. You can make your own decision about whether that effect is a "small one".
But this exercise only captures part of the reason commodity prices have risen. Jeffrey Frankel responds to Kohn in this article from Vox. The explanation is backed up by data and quite persuasive although anyone not really interested in economics might find it a bit complex.
I think Kohn and Frankel are both missing part of the equation though (not that I have the economic bona fides of either) when they don't look at the effect US monetary policy has had on other economies with currencies linked to the dollar. Kohn rightly points out that "emerging market economies have increased demand for many of these commodities and world supply has not kept pace with this growing demand". Many economists and other commentators have pointed to increased demand from China to explain the rise in demand and prices of commodities. But how much of that excess demand was driven by an aggressively expansive US monetary policy? The Chinese currency is linked to the US dollar and therefore US monetary policy has a direct impact on the Chinese economy. How much did the US policy of negative real interest rates affect the growth rate of the Chinese economy (and any other country with a currency linked to the dollar) over this decade? My guess is quite a lot.