Still More on Final Sales and GDP (nominal).

Is it better to target nominal GDP (which is just GDP) or Final Sales of Domestic Product?

Return to the scenario from the last post, where in period one, orchards produce 100 apples and they produce 103 in period two.   The price is $2.   The target for money expenditures is $200 in period one and $206 in period 2.   Either Final Sales or GDP is used to measure money expenditures on current output.

Suppose there is an excess supply of money.     The monetary authority expands the quantity of money and there has been no increase in the demand to hold money.    Households spend their excess money balances on apples.   They purchase 102 apples, spending $204.     Suppose the orchards were holding inventories of at least 2 apples, and so they sell those 2 apples out of inventory.

If Final Sales is used to measurer spending on output, then the monetary authority misses the target.   Final Sales will be $204, $4 above target.    If, on the other hand, GDP is used to measure spending, then the unplanned inventory disinvestment of $4 is taken from the household spending on apples of $204 so that GDP would be $200.  It remains on target.

With Final Sales targeting the excess supply of money created by  the monetary authority is signaled by its failure to hit the target.   With index futures targeting,  those speculators who had gone long on the contract would profit under Final Sales targeting, being rewarded for their signal that an excess supply of money had developed.   Those who had gone short, wrongly signaling that there would be an excess demand for money, would lose.   With GDP targeting, the target is hit, and there would be no profits or losses.

Now consider period 2.   The orchard can produce 103 apples.   Assuming the price of apples is $2, then that is $206.   Further, assume the orchard wants to replenish its inventory, adding 2 apples.      With final sales targeting, spending by the households on apples must be $206.    While the orchard can produce 103 apples, it will only choose to sell 101 to rebuild its inventory.     Either the orchard will sell those apples and not replenish of its inventory, or there will be a shortage of apples, or the assumption that the price remains $2 cannot be maintained.   The most realistic scenario is that the price of apples will rise.   There will be inflation, even if Final Sales remain on target.

With GDP targeting, the inventory investment of $4 plus spending by households on apples must add up to $206.    This requires that the households spend $202 on apples.   That happens to be exactly equal to what they spent in period 1, but that is just an artifact of the particular example.    Assuming the baseline is that they would have spent an amount equal to their income, $206, the monetary authority needs to follow some “contractionary” policy to motivate them to spend $4 less than they otherwise would.   This, of course, is exactly equal to the planned inventory investment.

Like in the deflationary scenario, total spending on output (including inventory investment) remains equal to the productive capacity of the economy in both periods with GDP targeting.    With Final Sales, targeting, an excess supply of money that results in unplanned inventory disinvestment in the first period results in an excess demand for goods when the inventories are replenished.     In other words, there will be some inflation between the first and second period.   

While it isn’t exactly clear what would be the cost of having low inventories between the first and second periods,  presumably there is some cost and the initial excess supply of money imposed those costs on firms as an externality.    The monetary authority really should try to avoid excess supplies of money.   With index futures convertibility, those speculators who recognize this problem should be rewarded at the expense of those who were completely wrong and expected an excess demand for money.

On the other hand, the GDP target does a much better job in avoiding readjustment costs in the second period.   Just as inventories provide a buffer  to balacne production and consumption in particular markets, allowing the economy as a whole to use them is a benefit of GDP targeting relative to Final Sales targeting.

A hybrid approach in which unplanned inventory investment (such as in the first period) doesn’t count towards the target for money expenditures (representing a failure to maintain monetary equilibrium) but planned inventory investment does count, like the planned replenishing of inventories in the second period, would appear to be superior to both GDP and Final Sales targeting.    However, in this inflationary scenario, it still seems that GDP targeting is better than Final Sales targeting.    Production remains at capacity with GDP targeting and there is no inflationary adjustment in the second period.  

Oddly enough, if the assumption is a “bolt out of the blue” increase in the quantity of money,  it would seem that excess supply of money in the first period is being offset by an excess demand for money in the second period.    Assuming a credit money system, the “bolt from the blue” would be excessively low interest rates in the first period, with excessively high interest rates in the second period.     Could this generate some Austrian-style malinvestment?    While more study is appropriate, the balance of the evidence still looks like GDP targeting is the least bad option for now.

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.

More on Inventories

For several years I have advocated the use of Final Sales of Domestic Product to measure money expenditures. This is as opposed to GDP. (Scott Sumner is always calling it NGDP, which is a bit redundant. RGDP is GDP corrected for changes in the price level.) The difference between the two measures is changes in inventories. Perhaps remembering early explanations of Keynesian economics, where unplanned inventory investment plays a key role in keeping expenditure equal to output, it was just those changes in inventories that I thought should not be included in a proper measure of monetary expenditure. Counting goods produced and not sold as having been purchased by the producer hardly counts.

While I still think that intuition is correct, it is based upon identifying inventories with stocks of unsold final goods. Cars are sitting on the lot or cans of beans are sitting on the shelf in the grocery store. What of other types of inventories? I am especially concerned with partially finished goods.

Perhaps keeping the focus on the future--the target should be for Final Sales for Domestic Product in a year, makes it so that every part of inventory changes can be ignored. However, more study is needed and I am more and more thinking that the best measure doesn't yet exist.

Bob Murphy asked me to explain the Fed's new accounting rules about remitting earnings to the Treasury. I did an internet search and it appears that the conspiracy theorists see something nefarious. I was doubtful.

The general explanation of the policy is a bit difficult to decipher.

Effective January 1, 2011, as a result of the accounting policy change, on a daily basis each Federal Reserve Bank will adjust the balance in its surplus account to equate surplus with capital paid-in and, in addition, will adjust its liability for the distribution of residual earnings to the U.S. Treasury. Previously these adjustments were made only at year-end.

It helps to understand that "surplus" is basically required retained earnings.   Member banks in the Federal Reserve system must purchase stock (at $100 per share) equal in value to 3 percent of their net worths.   A member bank with a net worth, or capital, of $100 million must buy $3 million worth of stock in its Federal Reserve bank.   The Federal Reserve banks must keep a "surplus" or retained earnings equal to the amount of stock that the member banks had to purchase.

The member banks of the Richmond Fed have purchased $5,439 million worth of stock, so the Richmond Fed must keep retained earnings of $5,439 million.

That is simple enough and doesn't really seem to have much to do with hiding losses.

However, if you go to the link where this new policy is described (H4.1) and scroll down to table 10,  you can see that several Federal Reserve banks have negative balances in their amount due to the Treasury.    Under liabilities, the line for Interest on Federal Reserve notes due to the U.S. Treasury is negative for several Federal Reserve Banks.   It is -$31 million for the Richmond Fed.

There is a note at the end of the table:

15. Represents the estimated weekly remittances to U.S Treasury as interest on Federal Reserve notes or, in those cases where the Reserve Bank's net earnings are not sufficient to equate surplus to capital paid-in, the deferred asset for interest on Federal Reserve notes. The amount of any deferred asset, which is presented as a negative amount in this line, represents the amount of the Federal Reserve Bank's earnings that must be retained before remittances to the U.S. Treasury resume. The amounts on this line are calculated in accordance with Board of Governors policy, which requires the Federal Reserve Banks to remit residual earnings to the U.S. Treasury as interest on Federal Reserve notes after providing for the costs of operations, payment of dividends, and the amount necessary to equate surplus with capital paid-in.

While this seems a bit odd to me, it amounts to how short the Federal Reserve bank is to meeting the requirement that it have a surplus equal to its capital paid in.  While the Richmond Fed shows that it has the required retained earnings, a surplus of about $5,439 million, it really doesn't.   It only really has $5,408 million.   It is short the $31 million.      Before it can start sending any money to the Treasury, it must make that up by additional retained earnings.

If a Federal Reserve bank took a loss, then this item would be negative.   However, it will turn negative if the Federal Reserve bank didn't have enough earnings to cover the 6 percent required dividend on the stock held by member banks.   And it could turn negative if the Federal Reserve bank failed to  increase its retained earnings enough to match an increase in the amount of stock purchased by member banks.   This would happen if the member banks are increasing their net worth, perhaps due to growth in the overall size of their balance sheets.     

Currently, the total amount due to the Treasury  for all Federal Reserve banks is $613 million, and so the Treasury should expect a substantial weekly payment from the Fed.    If that total number starts turning negative, then it is time to question the payment of dividends to the member banks.    If it becomes progressively more negative, losses will start to look like the problem.   And if it starts to approach the surplus and paid in capital of the Federal Reserve banks, the insolvency of the Federal Reserve approaches.

However, describing Federal Reserve insolvency as being how much the Federal Reserve banks must retain before they can resume payments to the U.S. Treasury would be a bit of a euphemism, to say the least.

Is Final Sales of Domestic Product Flawed?

Years ago, I began to favor a  target for money expenditures on currently produced output.    In abstract, I usually thought of it as "nominal income targeting."    For some time, I have thought that the best measure is Final Sales of Domestic Product.   As I noted in a recent post, that statistic grew at a more than 7 percent annual rate in the fourth quarter of 2010.   Since it's current value is well below any sensible target, I counted that as a very good sign that perhaps a decent recovery will soon begin.    The positive news on the unemployment rate--down to 9 percent--is another positive sign.

Soon after last quarter's statistics came out, I received an email from Scott Sumner in which he pointed to a possible flaw in the statistic.   He said that he had been told that  Final Sales of Domestic Product includes sales of goods that were imported during the previous quarter.    Spending on those goods is not spending on domestic product in the current period.   It is spending on foreign products in the current period.    It is just that they didn't enter the country in the current period.    As best I can tell, this is correct.  

As usual, my review of the procedures used to measure income and output left me troubled regarding the degree of extrapolation and "judgement" that is involved.   In particular, the BEA has a good explanation of the calculation of inventory investment.    As far as I can see, there is no effort to determine what part of inventory changes represent changes in inventories of foreign goods, or goods in process or finished goods produced partially with foreign goods and services.  

Reviewing the calculation of inventory investment, however, suggests that such calculations could be made much as many of the calculations are made--by extrapolation.    In other words, while such an adjustment could be made, it would be unclear how objective such calculations would be.    My own view has always been that planned inventory investment should be included in a proper measure of money expenditures on domestic product, but that unplanned inventory investment should not.    While polling firms about their plans to accumulate inventory and comparing that to actual inventory accumulation might seem a bit subjective, I can only recommend reading what they in fact do.   It will shatter any illusions you might have regarding the objectivity of these measures.

Perhaps quasi-monetarists can add to our wish list of macroeconomic statistics, (with monthly measurements of GDP on the top of the list) more information about inventory changes, such as planned versus unplanned and inventories of domestic versus imported products.

While those of us who favor targeting money expenditures have a special interest in this issue, others are more concerned about whether the strong growth in Final Sales of Domestic Product in the Fourth Quarter of 2010 was not quite the good news it seemed.    The speculation is that the much of the increased spending on goods and services was for goods that were imported in the third quarter of 2010.    Now (more than 1/3 of the way into the first quarter of 2011) firms will be busily importing goods to replenish those inventories, and a recovery in U.S. output and employment will not occur.

Final Sales to Domestic Purchasers increased at a 5.2 percent annual rate in the fourth quarter.   This is how much U.S. residents spent on consumer goods and services, capital goods, and government goods and services.  It does not include expansions of inventories.  It increased by $200 billion.  This is the most rapid growth since the beginning of the recession.

Final Sales to Domestic Purchasers doesn't include exports.   Exports increased at a 16 percent annual rate, which is $75 billion.    So, when the additional exports are added to the additional purchases by U.S. residents, the total would be $275 billion.  

Of course, some of those consumer goods and services, capital goods, and perhaps even government goods and services were imports.   Imports increased at a 3 percent annual rate, or $17 billion.    The increase in  Final Sales of Domestic Product is found by subtracting those imports from the $275 billion, which was $258 billion.   That is an increase at a 7 percent annual rate.   However, these are good imported in the fourth quarter, which is not exactly the same thing as imported goods and services sold in the fourth quarter, much less those and goods and services sold in the fourth quarter that had used imported goods and services in the production process.    

What about inventories?   They increased $5.2 billion in the fourth quarter of 2010, after increasing $139 billion in the third quarter of 2010.    Interestingly, by the fourth quarter of 2010, inventories were still $400 billion below the level before the beginning of the Great Recession.    They fell approximately $673 billion before starting to recover in the first quarter of 2010.   While this would be very puzzling if inventories are visualized solely as finished goods, they also include stockpiled inputs and goods in process.    Meeting a lower level of sales by using up already purchased inputs and completing partially finished goods will result in falling inventories even if any excess inventory of finished goods has been sold off long ago.

There is not enough data to determine whether the increase in inventories in the fourth quarter of 2010 masks a large depletion of inventories of imported goods.   Perhaps imports will grow rapidly in the first quarter of 2011 as those hypothetically depleted inventories are replenished.  

I would point out however, that a decrease in the dollar exchange rate or more rapid inflation in those parts of the developing world that try to maintain a fixed dollar exchange rate should result in more rapid growth of U.S. exports and slower growth in U.S. imports.   Only time will tell.

Still, the goal should be for growth in money expenditures on currently produced U.S. output to remain on a predictable path.    I favor adjusting the growth path from that of the Great Moderation, but with the current level being so low compared to the Great Moderation (12.5 percent too low,) some reflation is desirable. Until some new measure of money expenditures is developed, perhaps including planned inventory investment and excluding inventories of imported goods and the value added by imported goods and services to  inventories, I am still calling for $16.4 trillion of Final Sales of Domestic Product in the fourth quarter of 2011.  Yes, 9 percent more than in the fourth quarter of 2010.