Sunday, October 30, 2011

Targeting the Growth Path vs. the Growth Rate.

Scott Sumner has commented on Bennett McCallum's article on nominal GDP targeting. Summer comments on McCallum's support for growth rate targeting. While he defends his support for growth path targeting, he also says:
Perhaps I’ve been overly influenced by the 2008 period, when the advantages of level targeting seem relatively large. I would also point to Michael Woodford’s work on liquidity traps. Woodford argues that level targeting is especially important when a central bank hits the zero bound (as he is even more skeptical about QE than I am.) McCallum may be right that when the central bank is doing its job, growth rate targeting is as good as or even better than level targeting. By “doing its job,” I mean targeting the forecast.
In my view, growth rate targeting works great, as long as it works perfectly, and is expected to work perfectly. If the growth rate remains constant always, then nominal GDP remains on a constant growth path.

In my view, changes in the growth rate of nominal GDP that return it to the target growth path are coordinating. Any notion that it is the changes in the growth rate of nominal GDP that cause problems are mistaken.

This is easiest to see when the growth path of nominal GDP has a growth rate equal to the growth rate of potential output, so that the trend price level remains stable. If an excess supply or demand for money causes nominal GDP to shift to a higher or lower growth path, reversing the deviation is less disruptive than accommodating the new growth path and continuing at the old growth rate.

Consider the following numerical example of an economy in equilibrium:

Y* is the target growth path of nominal GDP, Y is nominal GDP, P is the price level, y is real income, yp is potential output, gY is the growth rate of nominal income, inf is the inflation rate, gy is the growth rate of real income, and gyp is the growth rate of potential output.

The economy is in equilibrium with nominal GDP on target and growing at the 3 percent target growth rate. Real output equals potential output and they are growing together at a 3 percent annual rate. The price level is 100 and the inflation rate is zero.

Now, suppose an excess supply of money causes nominal expenditure to grow more rapidly in period 2 at a 4% rate. Further suppose that the short run aggregate supply curve implies that firms respond to the more rapid growth in sales with a split of 40% in prices and 60% in output.

The calculations for period two are simple enough.

Inflation is .4% and real growth is 3.6%. There is a boom in the economy, with the price level rising to 100.4 and real income rising to $10,360 billion, approximately $60 billion beyond potential.

Suppose growth rate targeting is used. Does period 3 then allow a return to equilibrium as follows?

3 10,712 100.4 10,712 10,712 3% 0% 3% 3%

No, it doesn't. Because potential output is $10,609. It rose 3% rather than 3.6% with real income.

Assuming growth rate targeting, the least disruptive possibility would be slower growth in real output during the next period so that it returns to potential. Unfortunately, that implies another period of inflation.

The growth rate of real income is 2.4% so that it returns to potential output and the inflation rate is the difference between that growth rate and the growth rate of nominal GDP, .6%.

Only then can there be a return to equilibrium.

4. 11,033 101 10,927 10,927 3% 0% 3% 3%

With growth path targeting, there is also an adjustment in period 3.

The growth rate of real income again slows as before so that it returns to potential output. However, there is a .4% deflation rate. (The assumption here is that the short run aggregate supply curve implies a similar split for output and prices when growth slows.)

So, is an additional .6 percent inflation more or less disruptive than a .4% deflation? Real output growth is going to slow, one way or another.

If prices were perfectly and instantly flexible, it would make no difference. But suppose prices are sticky?

If the most flexible prices adjust first to more rapid growth in nominal GDP, reversing the inflation of those prices won't be very disruptive. Growth path targeting has exactly that consequence. It is growth rate targeting that would require that the most sticky prices adjust as well.

Suppose that product prices are flexible, and it is wage rates that are sticky. The more rapid growth in nominal expenditure in period two raises product prices, reduces the growth rate of real wages, lowers real unit labor costs, and makes increased production profitable. With growth path targeting, the price level falls back to its initial level, nominal wages continue to grow at trend and real wages grow more rapidly. Unit costs return to equilibrium and so does production and prices. With growth rate targeting, on the other hand, sticky nominal wages must grow more rapidly and rise to a higher growth path, so that real wages and real unit costs return to equilibrium.

Further, considering the reverse shock, where nominal GDP grows more slowly or even shrinks, the most flexible prices may fall or grow more slowly at first. Nominal GDP level targeting reverses the decrease in spending, raising sales, production, and causes the most flexible prices to rise back to their initial growth path. Growth rate targeting requires that the more sticky prices, perhaps including wages, move to a lower growth path in order to return to equilibrium.

What possible benefit would growth rate targeting have? As discussed in an earlier post, it involves a scenario with a supply shocks when the particular goods being shocked have other than unit elastic demand.

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