# What might a NGDP inflation target look like in a policy rule?

A nominal GDP target makes sense. If inflation runs below target for a while, it makes sense for inflation to run over target in the future in order to achieve the desired long run growth to inflation.

So how might a policy rule to determine the Fed rate be modified for a NGDP target?

A policy rule has this essential structure…

Policy rule rate = short term real rate + inflation target + 1.5*(core inflation – inflation target)

So if core inflation runs over target, the policy rule rate rises to move inflation back down to target. As well, if core inflation runs below target, the policy rule rate drops to move inflation back up to target.

However, in nominal GDP targeting, the idea is to move inflation beyond the desired long run inflation target in order to compensate for the time being off target. So for example, if core inflation runs below target, the inflation target in the policy rule would be raised to guide inflation to a higher level above the target.

Thus the inflation target in the policy rule would have to be adjusted to allow core inflation to average to its long run target. The adjusted inflation target could look like this…

Adjusted inflation target = long-run inflation target + (long-run inflation target – average core inflation over previous time period)

Let’s put this equation to a graph. I plot core inflation (blue) over time going through periods over a 2% target, followed by periods under the target. The orange line gives the adjusted inflation target through time averaging all the previous core inflation from time 0. So as core inflation is averaged over longer and longer time periods, the adjusted inflation target for NGDP targeting stabilizes near 2%. The grey line is the adjusted inflation target if core inflation is averaged after it ran below target. That line too will stabilize near 2% through time.

Whether the adjusted inflation target is measured from time 0 or time 4, it will stabilize near the constant inflation target currently used in policy rules. So is there really a need for adjusting the inflation target?

Let’s apply this equation to core inflation data since 1967. In the following graph, the line represents the inflation target that you would use now depending on how far back you averaged core inflation. For example, if you averaged core inflation back to 1987, you would need an adjusted inflation target of 1.3% in your current policy rule, instead of the constant 2.0% being used. If you averaged core inflation back to the end of 2008, you would use an adjusted inflation target of 2.3%, which is already close to the 2.0% inflation target being used. If you averaged back to the 1960’s, you would use an adjusted target of -0.2%. So there is a big difference depending on how far back you average core inflation. Your adjusted inflation target for the policy rule may be above or below your desired long-run target.

The graph above assumes a long-run inflation target of 2.0% for NGDP targeting. What if you desired a LR inflation target of 3.0%? Even though you have raised your inflation target by 1%, the adjusted inflation target for the policy rule rises by 2.0%. The 1987 target rose from 1.3% to 3.3%. The end of 2008 target rose from 2.3% to 4.3%.

Now what if your long-run inflation target were 4% as Paul Krugman has suggested, and then used the adjusted inflation target for NGDP targeting? The adjusted inflation target rises by 4%. For example, the end of 2008 adjusted target rose to 6.3% from 2.3%. Let’s put some numbers into the policy rule for NGDP targeting assuming a short term real rate of 0% and a current core inflation of 1.7%. Let’s average core inflation back to the end of 2008. What Fed rate would the policy rule prescribe for us?

Policy rule rate (2% LR inflation target, 2.3% adjusted target) = 0% + 2.3% + 1.5*(1.7% – 2.3%) = 1.4%

Policy rule rate (3% LR inflation target, 4.3% adjusted target) = 0% + 4.3% + 1.5*(1.7% – 4.3%) = 0.4%

Policy rule rate (4% LR inflation target, 6.3% adjusted target) = 0% + 6.3% + 1.5*(1.7% – 6.3%) = -0.6%

So if you want a LR inflation target at or above 3.5% for your NGDP targeting, you would keep the Fed rate at its zero lower bound because the policy rule is giving a Fed rate below 0%. However, if you wanted a LR inflation target below 3.5% for your NGDP targeting, you would want the Fed rate above the ZLB. (assuming a short term real rate of 0%).

So NGDP targeting could be a good idea for balancing inflation to its LR target over time, but the method seems open to a lot of discretion. How far back do we average core inflation? What should the LR inflation target be? And in that range of discretion, the policy rule would give a wide range of options. Is it any wonder that discretionary monetary policy is dominant now?