John Butler has a great piece  in yesterday's City A.M. making the case against central bank interest rate interference. He uses the devastating insights  of Ludwig von Mises  and Friedrich Hayek  to show why central planning cannot work rationally for basic epistemic reasons. His example is of the Soviet shoe industry, constantly providing surfeits of boots in summer and sandals during winter.
Absent a pricing mechanism to match supply and demand, there was invariably either a glut or a shortage. And even when there was a glut, there were plenty of summer shoes, but a shortage of winter boots. By contrast, the largely capitalist West, responding to real price signals in real markets, did a pretty good job at producing, in sufficient quantities, a range of shoes that customers wanted, that fit, that they could afford.
Butler argues that in the significantly more important financial markets, which coordinate plans about saving and investment, together determining the future's capital structure, the same rules apply. We need real prices to convey information and organise society into a rational economic order. He claims the monetary policies of many countries—cutting headline interest rates and buying hundreds of millions of bonds—distort market interest rates (the most important prices in the economy) and thereby drive capital to be used in suboptimal ways.
I think there's a problem with his approach. Going with the title of this post—isn't it possible that the free market interest rate  is below zero? German bund yields have fallen below zero  several times during the Euro crisis, despite no central bank engaging in any major programme to buy them up. In times with few good investment opportunities, lots of funds (saving rates have boomed during the bust), and lots of worrying risky areas, it makes sense that some safe assets would see crashing rates. Bond yields can fall below zero even in a zero inflation or deflationary environment, but that's not true for many of the myriad interest rates in a modern economy. There is a zero lower bound on most rates, that is, no one would accept a nominal rate less than zero, as they could usually change the money into cash and put it under their mattress. But quantitative easing raises inflation expectations (and inflation), allowing real rates to go below zero, potentially clearing some otherwise stuck markets.
Now this isn't necessarily telling on Butler's argument. It might be that sometimes rates need to fall below zero, potentially justifying inflation above zero, but the QE needed to achieve this inflation distorts markets in general more than it benefits in these cases. Other things being equal, the extra demand from bond purchases means higher prices and lower yields on those bonds, and this would be expected to hit all substitute assets. This seems to hold even if the other effects of extra QE (higher inflation and demand growth (NGDP growth) expectations) work in the other direction, or even exactly balance out the demand effect of QE. Compared to the hypothetical situation where the central bank boosts growth expectations without buying up bonds, assets will be more expensive, or yield less.
Funds will look cheaper to firms than they "actually are" in the sense of their social cost as approximated by the information that would have been contained in the relevant market interest rates. Firms will tie up slightly more productive capital in improving capacity when society as a whole would seem to prefer slightly more devoted to consumption. This mispricing of loanable funds seems like it would have distortionary effects, with the size of the efficiency loss depending on the responsiveness of the supply of deposits and the demand for investment to their prices.
Before this starts to sounds one-sided against QE, there is one (big) consideration to take into account—the extra inflation and demand growth expectations that asset purchases create don't just help some interest rates adjust, but also create the space for a vast number of relative price moves. Labour markets tend not to clear after demand shocks because wages take a long time to adjust downwards . The price of avoiding any interference could be deep, ongoing recessions. So a prudent central banker may need to risk some misallocation of resources into investment if they wish to avoid the probably worse cost of punishing unemployment and slashed living standards.