Tuesday, September 10, 2013

Taylor and Hall on Nominal GDP Targeting

John Taylor quotes Robert Hall approvingly about nominal GDP targeting.    Hall said

“A policy of stabilizing nominal GDP growth would require contractionary policies to lower inflation when productivity growth is unusually high. Such a policy might easily trigger a spell at the zero lower bound.”

What is Hall's framing?

One possibility is that "tight money" means lower inflation.   If productivity increases, then the central bank must lower its target for the inflation rate.   A lower target inflation rate will lower the nominal interest rate consistent with any given real interest rate.    A lower nominal interest rate is one more likely to be equal to zero. 

One problem with that framing is that it has the central bank targeting inflation.   With nominal GDP targeting, it is targeting nominal GDP.   More rapid productivity growth will result in lower inflation.   Given monetary policy, inflation depends on productivity growth.    It remains true that given the real interest rate, lower anticipated inflation results in lower nominal interest rates, but there is no contractionary monetary policy.

Another possible framing is that inflation is given, though not targeted, and the increase in productivity results in more real output growth.   The higher real output growth with given inflation results in above target nominal GDP growth.   The central bank must then tighten monetary policy to return nominal GDP to target.    If output is assumed to remain high, this requires disinflation.  Given the equilibrium real interest, the lower inflation would reduce the nominal interest rate.   If the nominal interest rate is already low, the result could be a nominal interest rate that hits zero.

One problem with this framing is that it seems inconsistent with basic microeconomics.   An increase in productivity reduces marginal costs for at least some firms.   With imperfect competition, each firm will maximize profit by expanding output and lowering its price to sell the output.   While the reason the lower price results in a larger quantity demand is due to a lower relative price, and this would not be true if all firms had the same improvement in productivity, the lower price level and increase in aggregate real output is roughly consistent with nominal GDP remaining on target.   

For a single firm to respond to a decrease in marginal cost by producing more at the same price, it would need to anticipate a rightward shift in its demand curve.    No single firm can expect that to occur as a consequence of its own improved productivity and reduced marginal cost.  

No, what would have to happen is that all firms would know that productivity has improved in aggregate, and that an inflation targeting central bank is going to cause aggregate spending to rise with the increase in real output.   And so, they can all expect a rightward shift in their demand curves.  

But with a nominal GDP targeting central bank, there is no  reason for there to be any such expectation.  And so, each firm can simply behave as if the improved productivity impacted them alone.

What does this imply for nominal interest rates?

If the improvement in productivity and disinflation was unanticipated, then there would be no impact on nominal interest rates for existing debt contracts.  The nominal interest rates are already determined.   The lower inflation rate causes an increase in realized real interest rates.   Creditors share in the unanticipated increase in real output and real income.   Does that mean that debtors are worse off?   Not at all.   The debtors make exactly the same nominal payment to creditors as before, and have the exact same nominal income, that is, profits or wages, remaining as before.   The disinflation means that their real incomes rise due to the unanticipated increase in productivity.

A policy of preventing (or reversing) the disinflation so that creditors share nothing of the increase in productivity would likely just blow up profit.   With wages being sticky, workers would receive no gain.  

What about nominal interest rates on contracts made once the increase in productivity materializes?  If the increase in productivity were permanent, then the price level is now on a permanently lower growth path.   However, its rate of change is the same.   Nominal interest rates are not impacted at all.

If the increase in productivity were temporary, then during the next period, the disinflation will be reversed.   The anticipated inflation as the price level returns to its previous growth path would tend to raise nominal interest rates.

Suppose that the improvement in productivity were anticipated.   With nominal GDP targeting, the result will be disinflation.   The effect on real interest rates would be anticipated.   If the equilibrium real interest rate is unchanged, then the anticipated disinflation would lower nominal interest rates.   If nominal interest rates were sufficiently low already, this could push the nominal interest rate to zero.

Let's explore a bit more the process by which nominal interest rates would fall.   Lenders would find it more attractive to lend at any given nominal interest rate because they will receive more real purchasing power in the future.   However, consider the lender's alternatives.   The lender might go into business or buy an equity claim to a business.     Assuming constant output, the lower product prices in the future imply lower nominal profits and so a lower value of equity claims.   A loan at a given nominal interest rate would avoid that and so there is a motivation to lend more rather than hold equity claims in business.

But output is not constant.   Output rises in inverse proportion to any disinflation leaving nominal profits and so the value of equity claims to those profits unchanged.    Because of the disinflation, the real purchasing power of those nominal profits will be higher.     And so, the notion that lending at a given nominal interest rate will be more attractive due to the disinflation is false.      

Of course, lenders are also sacrificing consumption today and making loans in order to fund consumption in the future.    With the anticipated deflation, any given nominal interest rate implies that more future consumption is provided for any sacrifice of current consumption.   It would seem that saving becomes more attractive, forcing down the nominal interest rate and returning the real interest rate to its previous equilibrium. 

This would make sense if future real income and so real consumption out of that real income were unchanged.   For example, if the disinflation just reduced nominal income while leaving real income the same.

But the increase in productivity raises real income in the future and also the real consumption can be funded out of that future real income.    If the real interest rate remained the same, then this effect would cause households to shift some of that added future consumption to the present, and so reduce saving.    The real interest rate must rise to bring today's saving and investment into balance and so current consumption and investment to a level consistent with today's potential output.

If the real interest rate must rise in exact proportion to the increase in the growth rate of real output, then the inversely proportional disinflation will generate exactly the needed increase in the real interest rate at an unchanged nominal interest rate.   While models that generate exactly that result might not be entirely realistic, they are certainly more realistic than just ignoring the effect of the increase in future real income.

How does the expected disinflation impact borrowers?   Supposedly there is a reduction in the willingness to borrow.     Again, this makes perfect sense if output is assumed constant.   For example, firms borrowing to fund production processes would find it more difficult to repay loans at any given nominal interest rate if they sold a given amount of output at a lower price.    But with productivity rising, they are selling more output at a lower prices, and with nominal GDP targeting, they are earning the exact same revenue.   Their ability to pay any given nominal interest claim is not reduced.   And further, their remaining nominal profit generates a larger real income because of the disinflation.  

The same occurs for household borrowing to fund consumption.    If future real income is assumed to be constant, then disinflation implies lower nominal income.   Nominal interest claims become more difficult to pay.   But with nominal GDP targeting, nominal income does not decrease, and the increase in productivity generates an increase in real income.   The nominal interest payments of the indebted households will be the same as will their nominal incomes.   Their nominal incomes net of interest payments are the same, and because of the disinflation, their real consumption increases.    As above, rather than this expected disinflation creating a deterrent to borrowing at any given nominal interest rate, it rather generates the needed increase in real interest rates to limit efforts to bring the added future real income into the present.

As long as the target growth rate for nominal GDP is greater than any difference between the natural interest rate and the growth rate of the productive capacity of the economy, there is no problem with the zero nominal bound.    For example, if the growth rate of potential output is 3% and the natural interest rate is 2%, and the target for nominal GDP is a 3% growth path, then the price level will be stable and the nominal interest rate will be 2%.

On the other hand, if the target for nominal GDP is a 3% growth path, and the productive capacity of the economy is growing 5%, and the natural interest rate is 1%, then the deflation rate is 2% and the nominal interest rate would need to be -1%.

Is it impossible that a shift in potential output growth from 3% to 5% would be associated with a reduction of the natural interest rate from 2% to 1%, rather than an increase?   I don't think it is impossible and so I favor monetary institutions that are not subject to the zero nominal bound.  But I also don't believe that nominal GDP level targeting should be dismissed when the more likely scenario is that anticipations of slower growth in potential output lead to a decrease in the natural interest rate so that inflation targeting would be more likely to result in problems with the zero nominal bound.

HT Scott Sumner.


  1. "On the other hand, if the target for nominal GDP is a 3% growth path, and the productive capacity of the economy is growing 5%, and the natural interest rate is 1%, then the deflation rate is 2% and the nominal interest rate would need to be -1%."

    If something like this did happen, what would be the consequence?

    1. I think hitting the nominal GDP target would require heroic open market operations, including the purchase of long and risky assets. The central bank bears more risk, and the nominal market interest rate on long and risky assets is driven down until the real interest rate on them equals their natural interest rate.

      I don't think there is any simple market process by which the natural interest rate rises and the rate of growth in potential output falls.

      And certainly not one that is attractive. Any monetary regime that requires a slower growth path of potential output would be undesirable.

  2. "No, what would have to happen is that all firms would know that productivity has improved in aggregate, and that an inflation targeting central bank is going to cause aggregate spending to rise with the increase in real output. And so, they can all expect a rightward shift in their demand curves."--Woolsey.

    In theory, I suppose this is right.

    And among economists, the proper response to empirical data is, "Sure, this may be true in fact. But is it true in theory?"

    Seriously, in the real world, do firms price their goods after pondering industry productivity in the aggregate and also central bank policies?

    And so many goods (and services) are differentiated today. Who sells commodities? Many goods and services are marketed heavily, and for better or worse, better marketing can mean better sales...at any price point.

    I like this very thoughtful post, and largely concur that central banks should steer wide and clear of ZLB, just as they might double-digit inflation.

    1. Benjamin:

      It isn't just industry-wide but rather economy wide productivity that counts. I don't think firms would need to understand this exactly, but rather the overall-state of productivity growth would impact the demand for their products and so the best pricing strategy.

      My assumption is of imperfect competition. The best price to set does depend on marketing etc., but also overall macro conditions. More aggregate demand makes a higher price than otherwise more desirable.

      What you point out is that having each firm figure out the aggregate productivity of the economy is difficult. This whole issue disappears if you assume a single product and a representative agent.

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