There is probably no issue in macroeconomics that is more misunderstood than the zero interest rate environment. Let's go over some of the misconceptions:
1. Most people correctly understand that the zero bound is bad news for monetary stimulus, but they don't know why. They think it's because monetary stimulus works through lowering interest rates, and nominal rates cannot be cut significantly below zero. In fact, monetary stimulus is easy to do at the zero bound, just peg NGDP futures contracts at a price 5% above current NGDP and your policy will be expected to succeed. In all likelihood no QE will be needed.
2. So why do I say zero rates are "bad news" for monetary stimulus? Because they represent a market prediction of slow NGDP growth. Thus for policymakers to succeed in creating fast NGDP growth, they must do more than the market expects. But the market forecast is probably the best forecast of what policymakers are likely to do. Markets understand the mindset of policymakers, and have a pretty good grasp of how they are likely to react to a given situation. When rates are zero, we should all rationally expect failure.
3. Many people don't realize that zero interest rates are also bad news for proponents of fiscal stimulus, as near-zero rates represent a rational bond market forecast that whatever fiscal stimulus is done will be inadequate. A good example occurred in November 2008, when Obama's fiscal stimulus failed to boost the economy, or the markets. You might be thinking, "wait a minute, I thought Obama's stimulus didn't take effect until well into 2009." If you were thinking that, you haven't kept up with the latest New Keynesian models. A change in fiscal policy occurs when there is a change in the expected future path of fiscal stimulus over time. Thus an expected future tax cut is expansionary right now. So the collapse of nominal interest rates in late 2008 and early 2009 was a prediction that the expected Obama fiscal stimulus would be inadequate. My hunch is that this is why Paul Krugman insisted the ($800 billion) stimulus proposed by Obama was too small---he read the market tea leaves. If it had been $1300 billion he still would have said it was too small.
4. This leads to the next point. Many people believe that monetary and fiscal policies are there to "fix problems." No, they are there to prevent problems. Aggregate demand problems occur precisely because markets expect policymakers to fail to generate adequate growth in aggregate demand (historically about 5%/year, although perhaps 4% today.) If there's a problem to be fixed, it means you've already failed to do your job. Lags are not the issue, if markets had expected adequate stimulus, even after a modest lag, they probably would not have crashed in late 2008 and early 2009. Instead of lags, the real problem is that the markets correctly saw that adequate stimulus will not be forthcoming, even after a lag. You need a rules-based regime in place to prevent problems, don't expect to grab a monetary or fiscal stimulus tool as if you are pulling a hammer out of the tool shed---it will be too late.
5. Many people are dismissive of monetary stimulus at the zero bound on the grounds that it relies on the "expectations fairy." As noted above, you still have the option of pegging NGDP futures prices. But these critics also fail to perceive that fiscal stimulus is equally dependent on the expectations fairy. Japan has run big fiscal deficits for 20 years, and had falling NGDP---one of the worst growth rates of aggregate demand in all of modern world history. How can that be? Very simple, expectations of deflationary BOJ monetary policies prevented the fiscal stimulus from boosting current AD. Just because the Japanese government gives out a tax rebate, the public isn't going to run out and buy new houses if the BOJ's deflationary monetary policy is expected to drive house prices relentlessly lower. To work, fiscal policy must be accompanied by an expansionary expected future monetary policy. But if you have that, why bother with fiscal?
The big mistake in all this is thinking of low interest rates as a sort of "easy money tool." In contrast, recall that Milton Friedman said low rates are a sign that money has been tight. If you reverse the standard view of cause and effect you won't always be correct, but you'll be right far more often than if you think low rates are easy money. Suddenly it will make sense that Brazil has high inflation "despite" high interest rates. Or that the US had deflation and falling RGDP in the early 1930s "despite" low and falling interest rates. Most of the public and even most economists look through the wrong end of the telescope.
Start thinking of expected NGDP growth as the monetary policy, and nominal interest rates as the effect of that policy. Then you can avoid the following trap: Many people think that if the Fed and BOJ have already cut rates to zero and done QE, just imagine how much more they'd have to do to get fast NGDP growth. In fact, those countries that do "enough," like Australia, do not have zero rates and lots of QE, precisely because their policies did not fail. They appear to do very little.
PS. I've retired from teaching at Bentley University and will devote myself full time to promoting the sort of ideas expressed in this post. Through a very generous donation from Kenneth Duda, I'll be directing a program on monetary policy at the Mercatus Center. I have a much longer post at TheMoneyIllusion that provides additional details.