Bullard at least attempts to use received macroeconomic theory to make his arguments, which is more than I can say for Krugman (see this). Krugman, apparently under some pressure from his readers, comes up with some arguments for why deflation is bad. These are essentially: (i) at the zero lower bound on the nominal interest rate, deflation makes the real interest rate "too high," and people will not want to borrow and spend; (ii) unanticipated deflation redistributes income from borrowers to lenders; and (iii) nominal wage rigidity implies that, with deflation, the real wage rises, and unemployment grows.
On (i): I think what Krugman is trying to say is that, given the high anticipated rate of return on cash when there is an anticipated deflation, people would rather hold money as an asset than alternative assets - loans for example. The problem is that this cannot continue indefinitely. In real terms, the quantity of cash ultimately gets very large, and people will eventually want to spend it. A long-run deflation cannot be supported without the money stock declining on trend - and we know that is not happening.
On (ii): This is certainly true. But why is a reduction of the inflation rate from, say, 2% per annum to -0.5% per annum a big deal? The large disinflation we had in the 1980s certainly does not seem to have been a disaster.
On (iii): Anyone who thinks that wage rigidity (or price rigidity) is important to any current macroeconomic phenomena in the United States should provide some serious evidence. The serious evidence cannot be: "I see a large quantity of unemployed people, and in Econ 101 I was taught that people are only unemployed due to nominal wage rigidity."
Now, Krugman's bottom line seems to be this:
And when that happens, the economy may stay depressed because people expect deflation, and deflation may continue because the economy remains depressed. That’s the deflationary trap we keep worrying about.As I mentioned above, Bullard at least tries to use received theory to think about this. Some serious macroeconomic researchers have written down models with multiple equilibria, and there is the possibility that, in these models, we can converge to a deflationary steady state. These results were vetted by serious editors and serious referees, and published in serious economics journals. Bullard thinks the results have something to do with our current predicament, and draws some policy conclusions. I think he is blowing hot air.
Krugman is also blowing hot air, but in a different way. Whatever deflationary "trap" he is thinking about makes no economic sense to me - I can't see how to write down the model that produces this.
It is certainly clear that the inflation rate is low, by any measure. The most broad measure, the implicit GDP price deflator, grew 0.8% between 2009Q2 and 2010Q2. But of course what matters for economic policy, particularly for the FOMC meeting next week, is future inflation. What can we say about that? One measure of anticipated future inflation is the difference in yields between nominal Treasury bonds and TIPS (inflation-indexed Treasury bonds) of the same maturity. The first chart shows the difference in yields between nominal 10-year Treasuries and 10-year tips. This yield differential is not literally the anticipated inflation rate over a 10-year horizon. We have to worry about effects due to inflation risk premia, and the fact that the zero lower bound on inflation-contingent TIPS coupon payments biases the measure up. However, this is the best we can do in terms of a market measure of anticipated inflation, and we can at least attach some significance to movements in the measure. Note that the yield margin has dropped recently below 2%, though the drop has not been large. Further, the most recent observation (Friday, August 6) was 1.92, which is up from the last observation in the chart, which is the average for July. I don't see anything here that tells me financial markets are expecting a prolonged deflation - and these are people that have to put their money where their mouth is.
What does standard macroeconomics tell us about inflation forecasting? New Keynesians, and Krugmaniacs, typically think in Phillips-curve terms. There is a very large output gap, so we should expect inflation to be very low. There is strong empirical evidence, however, (here) that Phillips-curve constructs are useless for forecasting inflation, and the recent data is entirely consistent with that evidence.
How would a New Monetarist think about the causes of inflation? The price level is the inverse of the price of outside money in terms of goods and services. The component of outside money that is actually exchanged for goods and services is currency. Thus, what determines the price level is the demand and supply of currency. Of course this may not be very helpful if I want to forecast inflation. As is well-known, a large fraction of the stock of US currency (half?) is held outside of the United States. Also, inside and outside the US, currency is widely used as a medium of exchange in various illegal transactions. Thus, we know at the outset that some important factors that determine the demand for currency are going to be difficult or impossible to measure. However, let's take a stab at this anyway.
The first chart shows the stock of currency (the currency component of M1) relative to nominal GDP for the period 1947Q1 to 2010Q2. Now, if anyone thinks that currency is somehow going away (based on their own use of the stuff), this chart should disabuse them of that notion. Currency is still important, not only because it is financing essentially all of the central bank's portfolio in normal times, but because there is a lot of it in circulation. The quantity of currency bottomed out in about 1980 at 4% of GDP, but it currently sits at about 6%. That is, the quantity of US currency in circulation in the world at any point in time is 6% of annual US GDP.
Now, what if I conduct a standard Old Monetarist exercise, which is to plot the log of the ratio of currency to nominal GDP against the nominal interest rate (the 3-month T-bill rate)? This is in the next chart. Observations from 2000Q1 to 2010Q2 are shown in red, tracking from right to left (with a loop). This doesn't look bad, in terms of "money demand" observations, and the recent data does not look anomalous, i.e. there does not appear to have been a large increase in the demand for currency associated with the financial crisis, which would have tended to drive down the price level.
Next, what has been happening to the nominal stock of currency recently? For this, see the next chart. The currency stock has been growing at a reasonable pace - indeed a pace that is entirely consistent with the inflation we have been seeing, given the short-run fluctuations in currency demand that we are typically prone to. Further, since 2008Q1, the currency stock has been growing at an average annual rate of about 6.4%. There is nothing here that would make us anticipate deflation.