# Knockout!

In martial arts, a good rule of thumb is to spend as little time on the floor as you can. For monetary policy, this is also true. "The floor" -- the zero lower bound on the short-term nominal interest rate -- is a place where you're defenseless, where conventional monetary policy is widely understood to be ineffective. A knockout in martial arts often involves staying "down" on the floor for a certain amount of time; a monetary policy knockout, you might say, is the same -- the extended liquidity trap scenario we've seen in Japan and risk seeing in the United States is such a situation.

*(I note here that monetary policy itself actually not ineffective, but the solution is to raise the rate of inflation, by which you can depress real interest rates without having to push against a nominal interest rate which cannot go lower.)*

I've been thinking over my views about raising the expected rate of inflation, something which has won support from Paul Krugman and Matt O'Brien. I've never been too enthusiastic about the idea, because beyond the fact that I think NGDP should grow along a stable path, I'm a hard-line, low-and-stable inflation hawk. I see huge costs to inflation, particularly when it is unstable.

In this post, I want to recognize what I see as the strongest argument for [indeed] raising the Fed's inflation target, which currently stands at 2.0 percent in annual growth of the price index attached to personal consumption expenditures: there is a trade off between the nominal interest rate and the probability of zero lower bound events. Given the fact that the Fed targets inflation in the longer-run and stabilizes real variables in the short run by changing the federal funds rate, there is a rate of inflation so low that it jeopardizes the goal of real stabilization. In short, bring the long-term nominal interest rate low enough, and you'll run out of room to cut it and end up on the floor. Knockout.

With the 2 percent target for PCE index inflation, given the average level of business cycle volatility we have seen in the last decade, we give ourselves nearly a 50-50 chance of a zero lower bound event occurring at least once every decade.I made this graph by calculating the standard deviation and mean of the federal funds rate recommended by the Mankiw rule -- a regression equation fit from the unemployment rate and core PCE inflation -- and then found the fraction of the resultant probability distribution to the right of zero.

I've used the Mankiw rule, rather than the actual federal funds rate, because we're trying to find out how often, given consistent economic volatility and a consistent monetary policy reaction function, we are supposed to go below zero but are constrained by the bound.

There are several reasons behind the recent jump. First, the level of business cycle volatility has increased markedly, even before the 2008 recession, towards the end of the so-called "Great Moderation." And second, we've been bringing down inflation expectations slowly, ever since the 1980 recession and the rise of Paul Volcker, which means that recommended nominal interest rates have fallen too. Put those two together, and you get a massive increase in the frequency of zero lower bound events.

Although I don't believe the business cycle exhibits normally-distributed properties, I assumed a normal distribution because it is a reasonable estimate of the lowest likelihood of extreme events. If you think, as I do, that there are "fat tails" -- likelihoods in excess of a normal distribution to extreme events -- then it follows logically that the probability here estimated of zero lower bound events is the minimum probability.

What all this suggests is that 2 percent inflation is not the ideal position in the tradeoff between the expected rate of inflation and the decadal probability of zero lower bound events. Given an estimate of the average cost of such a ZLB event and the marginal cost function of inflation, there should be an optimal rate of expected inflation. Since I don't have such numbers, nor do I know if they exist, we can look at this graph of inflation expectations vs. the decadal probability of ZLB events -- and it's pretty suggestive of the fact that moving a little bit higher in terms of inflation will be more than worth it in terms of the reduction in ZLB event probability and frequency.

**Addendum (8/3/12): **I just found this insightful 2011 paper by Gorodnichenko et al. which investigates the same question considered in this blog post. Using a different method, they find generally lower probabilities of ZLB events and conclude that the optimal rate of inflation for an inflation-targeting central bank is 1.3 percent year-over-year; for a price-level-targeting central bank, 0.3 percent year-over-year. In my graph above of probability of ZLB events, I calibrated my model with the most recent data point for the variance of the Mankiw indicator. That is my high-end estimate -- basically if the economy was to remain as unstable as it has been from 2008 onwards forever. That lines up with their high-end estimate on page 22 of the paper; they conclude that under such circumstances, the optimal rate of inflation rises to 2.5 percent year-over-year.