In 1994, Robert Hall and Greg Mankiw wrote a paper on "Nominal Income Targeting."
They advocate what Svensson would call a "target rule" for nominal GDP and propose that the Fed look at the consensus private forecast for nominal GDP either four quarters or eight quarters in the future and adjust current monetary conditions to keep the forecast on target. They do not favor an "instrument rule," that would specify a formula relating a policy interest rate or base money to nominal GDP.
They consider a rule for the growth rate of nominal GDP, a growth path of nominal GDP, and a "hybrid rule," that adjusts the target growth rate of nominal GDP according to deviations of real GDP from potential. They run simulations using a simple phillips curve model. They use errors from the actual consensus forecast to estimate the errors that would be generated by the alternative policy. They use the inflation shocks actually observed and assumed those same shocks would apply to the new regime. They simulate the period of the seventies and the eighties. The trend growth rate of nominal GDP is 2.5%.
They find that the growth path policy performs better than the growth rate rule both in avoiding variation in the price level and real output. However, real output is less stable that the actual performance. Since the period is the seventies and the eighties, this is very troubling. The hybrid policy--for example, raising the growth rate of nominal GDP when real GDP is below potential, did better with output stability.
They note that some of the errors in the consensus forecast involved errors in forecasting monetary policy. For example, the consensus forecast didn't predict the Volcker disinflation. If there had never been the Great Inflation of the seventies, there would have never been a Volcker disinflation. They also ran the simulation on the assumption that the forecasts were perfect, and the variance of real output relative to potential was better than actual performance.
Still, part of the reason for the output variance was the response to "supply shocks." The way they describe it, an inflation shock must be reversed within one year. Their simulation shows a deep recession in the early eighties. To the degree that this reflects the Volcker disinflation, it is an illusion. However, their model would generate a deep recession to reverse the inflation caused by the increase in oil prices during the Iranian revolution.
Their model is:
The change in the log of the price level is the trend inflation rate plus a term that shows the persistence of inflation plus a term that shows how the output gap impacts inflation plus the inflation shock term.
So, a supply shock this period just causes inflation this period. This forces nominal GDP above target, and then next period, this extra high inflation will continue to force prices up (the second term,) and based upon the consensus forecast, monetary policy must contract enough to force real GDP below potential enough to force prices down. Given their trend of 2.5 percent nominal GDP, deflation must be generated. Of course, the reduction of real GDP reduces nominal GDP directly and so the recession and deflation must combine to get nominal GDP back to target.
I see two problems with this model. First, there is no recognition that supply shocks combine a decrease in potential output with an increase in the price level. For example, if there is a bad harvest for corn, the supply of corn falls. The price of corn rises and the quantity of corn falls. The decrease in the quantity of corn is simultaneously a decrease in actual and potential output.
This just doesn't show up in the model at all. The increase in the price of corn would show up as inflation in the current period. That the production of corn falls, and that this is a decrease in both real output and potential output is left out. Assuming that the supply shock persists, both potential output and real output remain low and the price level remains high.
In the Hall and Mankiw model, potential output is basically the trend of real GDP. (.98 times its own lagged output plus .02 times current real GDP.) And so, the gap between real output and potential output is basically the deviation of real GDP from trend. That adverse supply shocks also reduce potential output is necessarily ignored, (well 98% ignored,) and overstates the actual deviation of real GDP from potential.
The second problem is the persistence of inflation. If the central bank will accommodate inflation, then it is certainly possible that higher inflation this period will cause people to expect more inflation and raise prices. However, with nominal GDP level targeting, particularly with a 2.5 percent growth path, there should be no persistence to inflation. In their model, inflation this period is partly reversed next period. More generally, if nominal GDP is above target and generates inflation, it will be reversed. A temporary adverse supply shock will be reversed. And a persistent adverse aggregate supply shock will raise the price level and leave it at the new, higher level.
A proper model of nominal GDP targeting will have the expected price level be equal to the target for nominal GDP divided by the expected level of potential output. Any deviation for the price level from that expected level should be expected to be reversed rather than continue to grow. Further shocks to that price level should have a negative covariance with shocks to both output and potential output.
However, Hall and Mankiw claim that only 2% of the volatility they find was due to these price shocks. Apparently, 98 percent was due to forecast errors. With nominal GDP targeting, that would imply a failure to hit the target.
Bernanke and Woodford in 1997 criticized using the consensus forecast for targeting. Under some circumstances such efforts to free ride on the consensus forecast results in indeterminacy. (However, using its own forecast but also considering outside forecasts is feasible.)
Bennett McCallum, also in 1997, proposed an "instrument rule" with feedback between the quantity of base money and nominal GDP. He ran simulations using both levels and growth rates of nominal GDP. His simulation found explosive results when an interest rate instrument was used to target the level of nominal GDP. This was less of a problem with base money targeting, though too large of a change in base money to a deviation of nominal GDP from its target growth path was explosive as well.
Targeting the growth rate of nominal GDP did not have explosive results whether interest rates or base money is used. Perhaps it is this potential for explosive results that has lead McCallum to favor targeting the growth rate rather than the growth path. McCallum also looked at a weighted average of the growth path and growth rate. It avoided explosive results too.
In my view, high frequency oscillations are very unrealistic. Perhaps it is because people don't respond mechanically to controls. Explosive oscillations require that past changes, especially for prices, be projected into the future, when in reality they will be reversed.
Still, even if large fluctuations in short interest rates or base money end up having little effect on nominal expenditure, much less prices or production, there would be little benefit in generating such changes. Targeting the forecast, as suggested by Hall and Mankiw, and allowing market participants to develop expectations that support the regime seems like a better approach that a mechanical feedback rule.