Krugman worries about deflation.
He performs a simple calculation
Now here’s the thing: the slump of the early 1980s produced the Great Disinflation, which brought the core inflation rate down from about 10 to about 4.
This time, however, we entered the slump with a core inflation rate of about 2.5 percent. If we experienced a disinflation comparable to that of the 1980s, that would mean ending up with deflation at a rate of -3.5 percent.
First: the argument is based on the assumption that the change in the inflation rate doesn’t depend on the current inflation rate. If I redid the calculation looking at the change in the log of the inflation rate in the Volker disinflation I sure wouldn’t get to a prediction of a negative inflation rate. That would be a silly calculation, since negative inflation is clearly possible. My point is just that an assumption about functional forms is critical and Krugman’s calculation is extrapolating linearly far out of sample.
Second: It is possible that a factor in the Volker disinflation was the huge appreciation of the dollar. This made imports cheaper and a decline in the price charged by competitors might have more of an effect than a decline in demand for other reasons (I mean who knows what kind of demand curves price setters imagine).