McCallum on Growth vs. Level Targeting

Bennett McCallum has a short paper on growth vs. level targeting.   He again argues for targeting the growth rate of nominal GDP rather than the level.   To some degree he is criticizing Woodford's proposal to return nominal GDP back to something like the growth path of the Great Moderation.   However, his argument is more general.

It is great to see more new work from McCallum on nominal GDP level targeting.

He emphasizes discretionary and time invariant approaches to policy rules.    He also mentions a purported rule he calls strategically incoherent.   I am not sure I fully understand, but it looks to me that this is exactly the approach that Market Monetarists favor.   Right now, we have to decide where the initial growth path for nominal GDP will commence, and then we stick with it.   This is supposedly incoherent because why don't we start it all up again every period?    Next year, why don't we imagine we have no rule, and we will again choose a new starting point for the growth path.

Suppose we are considering the institution of  very strict gold standard.   In the future, the price of gold will be fixed.   The price next period will equal the price this period which equals the price last period.   Now, at what price do we set this fixed price of gold?   Is it strategically incoherent to use anything other than last period's market price of gold?   I don't think so.   The relative price of gold can easily be impacted by using it as medium of account.   We are instituting a regime.   The logic for choosing a rule initially is not the same as the logic for sticking to the rule.

Anyway, he refers to the literature that suggests that period by period optimization is a bad idea.   And then describes Woodford's approach of time invariant policy as imagining that the policy we follow now was introduced far in the past.  

He then notes that nominal GDP growth rate targeting has results more similar to this time invariant approach while level targeting would close output gaps more quickly,  which is also what would happen with the period by period optimization approach.

What would be so bad about a rule that closes output gaps more rapidly?   McCallum just states that lots of studies suggest that immediately closing output gap is rarely optimal on average.

But why?  The only other thing that could be a cost in this model is deviations of inflation from target.   In other words, if we get the output gap back to zero this period, then this will have a cost of causing inflation to deviate "too much" from target.

Could it really be so simple as the assumption that changes in the inflation rate are bad?

With nominal GDP level targeting, a positive aggregate demand shock will cause higher inflation this period and then lower inflation next period.    With a negative aggregate demand shock, there is lower inflation this period and then higher inflation next period.    What is happening is changes in the price level, or more generally, its growth path, are being reversed.

If it is deviations of inflation from target that is considered bad, then nominal GDP level targeting  would be inferior to nominal GDP growth rate targeting.  On the other hand, if it is changes in the expected value of the price level that cause a problem, then a deviation of inflation from target in the opposite direction is not to add insult to injury, but rather a corrective.

Ignore supply shocks and assume the trend inflation rate is zero.   A price level target for the GDP deflator is 100.   An inflation target is for its rate of change to be zero.    In a perfect world, it stays at 100.   Sadly, there is 1% inflation.   It is now 101.   If the "loss" is inflation, then there is a loss, and if the GDP deflator stays at 101 forever, there is no further loss.

But suppose the "loss" is the deviation of the price level from 100.   If  it stays at 101 forever, then there is an ever continuing loss that is only kept from being infinite by discounting.

If the loss is inflation, then a 1 percent deflation returning the price level to 100 just adds an additional loss to the first one.   A unavoidable 1% inflation plus an additional easily avoidable 1% deflation.   If the loss is the deviation of the price level from target, then the 1 percent deflation returning the price level to 100 limits the duration of the loss to one period.

Of course, this is the simple version of the model.   The studies McCallum refers to presumably use calculations of utility loss from inflation rather than a simple "loss" function.

But to what degree are these utility calculations based on the assumption of Calvo pricing?  That seems to me to put too much weight on an obviously unrealistic model whose only virtue is that it can be used to make calculations of utility in rational expectations models.

If instead, some prices are flexible and others are sticky, reversing the changes in the flexible ones so that the sticky ones don't have to change is desirable.   This reasoning also applies when the sticky prices are those of labor--wages.   And that seems much more plausible.   Rather than keep the price level change and then make wages adjust, it makes much more sense to reverse the price level change so that labor markets clear at the sticky wage levels.

What about supply shocks?   While nominal GDP level targeting is the same as price level targeting when there are no aggregate supply shocks, one of the chief virtues of nominal GDP level targeting is that it does much better than price level targeting when there is a supply shock.

The model McCallum uses has an inflation shock.   It is just a random term at the end of the quasi-Phillips curve.   It seems to me that any such shock would push nominal GDP above target.   A growth rate target would just leave nominal GDP on a new, higher growth path.   In my view, that would be best.   (At least if these price level shocks are really just random and not regime dependent.)   Pushing the price level back down the next period would be pointless.   Nominal GDP level targeting would require a return of nominal GDP to target, and would likely push output below capacity.

However, what these random shocks in the model represent are real microeconomic events that impact both prices and capacity.   Negative covariance is very likely, and so just when the price level is shocked up, real output and capacity are both pushed down.   Any deviation of nominal GDP from target is likely to be small.     Further, to the degree they are temporary, when they end, nominal GDP will return to target with no change in "monetary policy" at all.   It isn't always necessary to cause an output gap to get some disinflation.   When peace breaks out in the Persian Gulf, lower oil prices bring disinflation without a need to cause a recession and output gap.

So, there may be a case for nominal GDP growth targeting as opposed to level targeting, but McCallum didn't make it here.