On the whole, Jan Hatzius and Sven Jari Stehn have done a good job.
They propose a target for nominal GDP that starts growing at 4.5% in 2007. This is less than the trend growth rate of the Great Moderation, which they estimate as 5.3 percent. Nominal GDP is 10 percent below that target. This is very similar to my methodology for generating the 3 percent target growth paths. It starts at the trend of the Great Moderation when nominal GDP was on that trend, and then goes forward at a new target rate. Presumably, they use the slower rate because estimates of potential output growth are below the 3 percent trend of the Great Moderation. If the estimate is 2.5 percent going forward, then 4.5 percent nominal GDP growth implies 2 percent inflation. If and when potential growth recovers, the result would be a slight disinflation.
They use their model to simulate the effects of the policy. Their model is a standard new Keynesian model, based upon the assumption that the Fed shifts the Federal Funds rate depending on current inflation and unemployment, which impacts real expenditures, real output, and the output gap. The output gap determines unemployment, and unemployment, along with expected and past inflation determines current inflation.
They account for quantitative easing by making it equivalent to a change in the Federal Funds rate. According to their estimate, $1 trillion of asset purchases is equivalent to a 100 basis point decrease in the Federal Funds rate. The current base is about $2.6 trillion. Increasing it to $3.6 trillion would be equivalent to reducing the federal funds rate 1 percent. (I am not sure how "global" this relationship is supposed to be. The target for the Federal Funds rate is .25 percent, and while I am sure that a base money of zero isn't really the same thing as a Federal Funds rate of 2.85 percent, perhaps the "extra" $1.8 trillion is supposed to make the current Federal Funds rate equivalent to -1.55 percent.)
Their "rule" tying the target for the Federal Funds rate to nominal GDP is .6 of the gap between nominal GDP and target. (I find this a bit puzzling. Their "Taylor" rule implies a Federal Funds rate of 4% if inflation is on target and the unemployment rate is at the natural rate. It looks to me like they have the Federal Fund rate set at zero when nominal GDP is on target. Maybe it is supposed to be i* = 4 + .6 (y - y*).)
They propose increasing the Fed's balance sheet to $5 trillion over the next year. That would be an increase of about $3.4 trillion. The level of base money would be approximately 1/3 of nominal GDP. But they also propose that the Fed sell off all of those assets by 2013 and return base money to its current (high) level. At that point, the Fed would need to start raising the Federal Fund rate.
From a Market Monetarist point of view, the key problem with the argument is that they claim that the effect of the policy will operate through its effect on real long term interest rates. The asset purchases lower the term premium, while getting back to target implies a lower Federal Funds rate in the future and higher expected inflation compared to a policy based upon their version of the Taylor rule.
The "IS" relationship does take expected real growth into account, with the current output gap depending on future output gaps. (If it is expected that next year's shortfall of real output from potential will be smaller, then this will raise real expenditure this year, and so real GDP, bringing real GDP closer to potential.)
xt = 1/3xt+1 + 2/3 xt-1 - .09(it-1 - inflation t+3 + qt-1) + ft
The "f" represents private sector balance sheet impacts and fiscal policy. (I suppose the "f" stands for "fiscal," but maybe "financial.") The q represents their adjustment for quantitative easing, -1% for every trillion.)
I suppose the simplest way to account for the Market Monetarist view that this policy can result in higher real interest rates would be for the new regime to have a higher coefficient on next period's output gap. An alternative approach would be to include nominal GDP expectations as an additional term. Or, of course, there is always Sumner's radical approach of replacing future inflation with future nominal GDP growth.
I hope someone will put this in front of Bernanke, (and Obama and his Republican opponents.)