An Argument Against NGDP-Level Targets
As an aside, basically, what he means by "monotone" is this: because of the recession, inflation is now below the long-run trend. In the long-run, by definition, we know that inflation will return to its long-run trend. But there are a variety of possible transition paths: one is that inflation could slowly rise until it converges to the long run trend, and another is that inflation could actually rise to above trend, and then fall until it converges to the trend. The former is monotone, while the latter is not.
Andolfatto's argument is that the optimal policy is almost certainly to slowly increase inflation until it converges to trend. By contrast, advocates of NGDP-level targets are arguing that the optimal policy is non-monotone--we should have above trend inflation until real GDP returns to trend, then slowly decrease inflation until price levels converge to trend. One important thing to note is that achieving an NGDP-level target requires that both the levels of real GDP and prices need to return to their pre-crisis trends.
This feature of NGDP-level targets should raise eyebrows. Here's why: aggregate economic wellbeing does depend on inflation in the sense that high and variable inflation imposes costs on society. But wellbeing does not depend on aggregate price level. The aggregate price level is just a matter of how we choose to measure prices, so we shouldn't care anymore about the price level as we do about whether we express distances in yards or in feet, so long as we preserve the relative prices, which is the inflation rate. Therefore, we ought to favor reducing volatility in inflation more than about preserving the pre-crisis price level trend. Here is an example of what happened after the great depression:
The point is this. The Fed had a choice in 1933. It could respond to the massive inflation volatility of the 1929-1932 years by either 1) creating an equal amount of volatility again in 1933 to restore the price-level trend or 2) minimize volatility by targeting an inflation rate. The former would have looked a lot like the gold standard years, discussed here. The latter would look a lot more like what the Fed is doing now, but with a modestly higher inflation target.
Conclusion:
This discussion has actually said nothing about whether the optimal policy is monotonic or not. It may very well be the case that above-trend inflation is optimal in the short run. But what it does say is that we should be targeting inflation not price levels. Hence gold standards and NGDP-level targets are clearly sub-optimal. An NGDP-growth target, on the other hand, would suggest above-trend inflation in the short run, but without the need to restore the pre-crisis price level, so that it is clearly preferable to the NGDP-level target because it involves far less volatility in inflation (and thus is far less costly).
I will just add that I see the NGDP-growth target as a largely rhetorical device. Since NGDP is a completely arbitrary measure, it is almost certainly not going to be optimal to target it. However, in a world in which policies are constrained by public opinion, an NGDP-growth target could allow the Fed to enact policies that would normally be prohibited by public opinion (such as a higher inflation target), thus making it potentially constrained-optimal.