What I found most puzzling was his adoption of McKinnon's call for the Fed and other major central banks to jointly raise their target interest rates. While it would be interesting to see the Fed commit to make open market purchases until the federal funds rate rises from .25 to 2 percent, (as opposed to the conventional approach of making open market sales until that happens,) I generally think making any commitment to the future path of interest rates is a mistake. The sole commitment should be to a series of levels for nominal GDP. Interest rates now and in the future should just be wherever they must be to hit the target for nominal GDP.
However, I have continued working with the Goldman-Sachs toy model. I sent out an email to various market monetarists asking about the instabilities I found (and the Svensson paper that pointed out the problem years ago. Thank you Peter for pointing this out in a comment on the earlier post. I just found your blog, NGDP.info.) Josh Hendrickson and David Beckworth both replied, pointing out that McCallum had made a reply, also years ago. (Thanks guys.) Hendrickson's was especially helpful with a suggestion about "the intuition." Models where the flow of nominal expenditure on output don't appear are unlikely to show much benefit from nominal GDP targeting. The instability comes because the interest rate set today effects the output gap next period, and the output gap next period effects the inflation rate one period later.
Anyway, I modified the "IS curve" by replacing the GDP gap with a nominal GDP gap (between nominal GDP and the target, rather than between real GDP and potential) and then added an equation relating the GDP gap to that nominal GDP gap. It twisted the phillips curve out of recognition, with the expected future price level being the target for nominal GDP divided by potential output and the expected inflation rate being the difference between that price level and last period's price level. The current Nominal GDP gap also impacts the current inflation rate. (Thanks Marcus Nunes for the data showing that inflation responds with output and not solely after output.) Rather than the interest rate being based upon the size of the nominal GDP gap, it is set to close the expected nominal GDP gap in the next period.
What does this have to do with Clark Johnson?
Just this morning I set the coefficients in the quasi-IS function so that the current nominal GDP gap solely depends on the expected future one and not at all on the past one. To close the gap next quarter, the Fed needs to set the interest rate at...
And while next quarter there is a 35% inflation rate, the output gap closes and the unemployment rate falls to the natural rate. (After that the inflation rate slows to 3% and then gradually slows from there. This is a return to the nominal GDP trend of the Great Moderation, rather than the modified growth path used in the Goldman-Sach's simulation.)
So, 2%? My "model" says that is way too low. (The "target" interest rate rapidly falls to something closer to 6%.)
The more last period's nominal GDP gap impacts this period's nominal GDP gap, the lower the "target" interest rate. For example, a 40-60 past future weighting requires a negative nominal interest rate to close the gap and so, massive quantitative easing with the Goldman Sachs assumption that $1 trillion equals -1%. Also, if the weighting is the opposite, like in the Goldman-Sachs toy model, stability problems still appear.