## Friday, February 11, 2011

### More on Final Sales and GDP: Sumner is Right.

Suppose money expenditure targeting is implemented.   There is one product produced by one firm.  The good is apples.   In period one, the productive capacity of the orchard is 100 apples.     In period 2, the productive capacity is 103 apples.   The price per apple is \$2.    The amount of expenditures needed to purchase the apples is \$200 in the first period and \$206 in the second period.

With a target for final sales of domestic product, the target is for the households buying apples to spend \$200 on apples in the first period and \$206 on apples in the second period.

With a target for GDP (nominal), the target is for the orchard to produce \$200 worth of apples in the first period and \$206 worth of apples in the second period.

Suppose that everything works perfectly.   The households spend \$200 on apples in the first period and buy 100 apples at \$2 each.  The orchard produces 100 apples and sells them for \$2 each.   Final sales is \$200 and GDP is also \$200.   Then in the second period the households spend \$206 on apples, purchasing 103 apples at \$2 each.   The orchard produces  103 apples and sells them for \$2.    Final sales  and GDP are both \$206.      There is no difference in the two approaches.

Now, suppose that in the first period, there in an increase in money demand and the monetary authority fails to increase in the quantity of money.   The households seek to build up their money balances by purchasing fewer apples.   The households spend only \$196 on apples and purchase 98 apples.     The orchard, having produced 100 apples, now has 2 apples in inventory.  Assume they carry these forward to period 2.

Final Sales would have been \$196 and so it is \$4 below target.   The failure to expand the quantity of money to meet the demand for money shows up in the monetary authority’s failure to meet its target.   On the other hand, GDP would be \$200.   The total amount spent by the households on apples, \$196 plus the 2 apples added to the orchard’s inventory which valued at \$2 results in \$4 worth of inventory investment.   While the monetary authority failed to increase the quantity of money to match the increase in the demand to hold money, its performance was “perfect,”  because the orchard kept the two apples in inventory.

Now, let’s consider the next period.   With the final sales rule, household spending is still targeted to be \$206.    The orchard is able to produce 103 apples, but there are two apples in inventory.  If the price of apples remains at \$2, then sales will be 103.    There is no need to produce 103 apples , and so, presumably production goes from 100 in period 1 to 101 in period 2.     The result of the excess demand for money in period 1 is a “growth recession”  in period 2.

With GDP targeting, production of goods and services needs to be \$206 in period 2.   Given the 2 apples in inventory, households must buy 105 apples in period 2, spending \$210. With the two apples being taken from inventory, this would be negative inventory investment and so the \$210 in final sales minus the \$4 decrease in inventory would result in \$206 GDP.    The orchard keeps production at capacity.     In fact, in this scenario, production remained at capacity during both periods.

GDP targeting keeps real GDP at capacity both periods.   Final Sales targeting resulting in a mild recession in period 2.

What possible advantage does Final Sales targeting have?

Most obviously, there is the cost of holding the inventories.    In the scenario above, the shortfall of final sales in the first period was given, however, with final sales targeting, someone is at least trying to avoid it.

With index futures targeting, speculators would be seeking  profit  if there was a deviation of final sales from target.   Those speculators who had correctly determined that spending on output would be less than capacity would have profited.   Those who had expected that final sales would be above capacity would have suffered losses.

With GDP targeting, there is no reason to avoid shortfalls of final sales as long as producers will hold inventories.    With index futures targeting, those speculators who went  short, and created a signal for a more expansionary policy, tending to bring final sales up to productive capacity, would not profit.   Those who had gone long, tending to keep final sales below capacity, would not suffer losses.

Of course, the since the target is for GDP, they would have no motivation to keep final sales at capacity.   Still, this perhaps avoidable cost of holding inventories is born by producers.   This is an external cost generated by GDP targeting relative to final sales targeting.

Further, in the second period, GDP targeting requires that  final sales be somehow stimulated.   In this simple scenario, the households must expand expenditures extra fast.  Rather than the usual increase of 3 percent each period, they must go from 98 to 210.   This would be a 7 percent increase in household expenditures.

Still further, this would be dissaving.   In this very simple example, households who are earning \$206 must be motivated to consume \$210 worth of apples.

However, while  instability in spending growth appears disruptive, that  is mostly an illusion.   In an unanchored monetary order, some might extrapolate growth rates into the future.   If someone expected that final sales would grow another 7 percent and be \$225 in period 3, then this would be disruptive.  However, the benefit of growth path targeting is that in period 3, GDP (or Final Sales) would be \$212.18 and everyone would know that.    There is no need to extrapolate past growth rates into the future.

The expectation for the orchard with GDP targeting would be that if spending on apples is “too low” in one period, then that shortfall will be made up in the next period.   The firm would be more motivated to smooth production and hold inventories.

With Final Sales targeting, spending would grow more rapidly between the first and second period as well.    The increase from the actual, below target,  \$196 to \$206 would be approximately 5 percent.   If that is forecast into the future, that would also be disruptive, but everyone should know that final sales will be \$212.18 in period 3.

Also, if final sales had been kept equal to productive capacity in the first period, there would have to have been some way to motivate people to spend more.   While it is true that an increase in the quantity of money would have accommodated the increase in the demand for money and allowed the \$200 income to be spent on \$200 worth of apples, real monetary institutions will generally have some people spending less to accumulate money and other people spending more.    With GDP targeting, that extra spending (the dissaving by some people) is being postponed to the second period.

Return to the perfect scenario.    The demand for money rose, which involved some people saving.   The quantity of money rose to match it, and some people dissaved.    Spending remained \$200 in period 1, just equal  to the productive capacity of the economy.   Then, in period 2, spending is \$206, perhaps with everyone spending their \$206 income on apples.

With GDP targeting, the demand for money rises, and some people save.    Spending on apples falls, and the orchards accumulate inventory.   Then, in period 2, everyone spends their period 2 income of \$206 on apples, and those people who would have dissaved in period 1 must be motivated to dissave now, in period 2, and purchase the \$4 worth of apples they would have purchased in period 1 if there had been no error.

While the example had the same error and the same response in period 1, \$4 fewer sales of apples in period one and \$4 worth of added inventory, the amount of inventory would probably not be the same.   With final sales targeting, there would be less motivation to accumulate inventory, and so, production might well drop in period 1.   And so, rather than simply a recession in period 2, there would be a recession in period 1 as well.

So far, the analysis has taken the price of apples as constant at \$2.     To the degree that the orchard lowers the price of apples in period one, then both GDP and Final Sales decrease.     The difference between the two targets depends on the real inventories carried forward.   Lower prices of apples or apples that are not sold and thrown out  have the same impact.     With index futures targeting, they create the same profits and losses for speculators.

On the other hand, final sales targeting should be expected to result in lower prices when there is an error in both the current and the future period.   This is the other aspect of the lack of a catch up.    Since there is less motivation to hold inventories to the next period, there is more motivation to lower prices now to sell them.   Similarly, to the degree they are held over, then prices will be somewhat lower in period two as the carry over inventory is sold.

The lower prices in the two periods would simply mean that the impact of the volume of production would be somewhat less than it otherwise would be under final sales targeting.     And, of course, since carrying inventory is costly, it is likely that there would be some decrease in output in the first period with GDP targeting.

To sum up, with final sales targeting, a deflationary error would be expected to cause a larger drop in output but a smaller decrease in real consumption in the current period, less inventory accumulation in the current period, and then less production and less real consumption in the second period as well.    However, the size and amount of these deflationary errors should be less.     In the example, the only problem with a “deflationary” error with GDP targeting, was that there are costs to holding inventory.     In reality, of course, deflationary errors would be costly with GDP targeting, and the monetary authority would not meet its target.   With index futures convertibility, those deviations would create profit for those predicting them.   The profits would just be less if it weren’t for the inventory effect.

A measure of expenditures that included planned inventory investment but not unplanned inventory investment would provide the best of all worlds.   Suppose that in period 1, the apple growers planned to produce and sell 100 apples.   They planned no change in inventories.   When sales fell to 98, the 2 apples were unplanned inventory investment.    However, in period 2, their plan is to get rid of those 2 extra apples, and so this is planned inventory disinvestment.   That would be added to consumption in period 2 and consumption would need to be \$210 in period 2 for consumption plus planned investment (negative in this situation) adds up to the target of \$206.     The target was \$200 in period one, and the actual value was \$196.    That is the consumption of \$196 plus the planned inventory investment of zero.    The target is missed.    Then, in period two, the target is \$206, but consumption must be \$210 so that when added to the planned inventory investment (disinvestnment) of -\$4, it adds up to target.

Dreaming about new macroeconomic measures is nice.   But until such a measure is created, I have to conclude the GDP (nominal ) is the least bad option.    Since index futures targeting is unlikely to be implemented soon, and so any target for the Fed will be more like a suggestion, the Fed can still be criticized for a slowdown in final sales and unplanned inventory investment.

In conclusion, Sumner is right.