More Criticisms of Index Futures Convertibility

Lawrence White and Roger Garrison criticized a version of index futures convertibility. (Can Monetary Stabilization Policy Be Improved by CPI Futures Targeting? Roger W. Garrison, Lawrence H. White; Journal of Money, Credit & Banking, Vol. 29, 1997) Sumner had proposed that the Fed buy and sell CPI index futures during the month proceeding the date the futures contract matures. For example, during May, the Fed would buy and sell CPI index futures contracts for June.

Like Woodford and Bernanke, White and Garrison claim that if Sumner's system works, then there will be no incentive for anyone to trade the contracts. If the CPI remains on target, the contracts mature without any payments being made.

In truth, the actual trades of the contracts depend on the dispersion of market expectations about the value of the targeted macroeconomic variable. Those who expect the variable to be above target buy and those who expect it to be below target sell.

Consider three traders, Smith, Jones, and Davis. All expect that the CPI will be 1% above target. Because they ignore the operation of the system, they all buy futures from the Fed, leaving the Fed short three contracts. The Fed contracts the quantity of money. Suppose that all three traders revise their expectations and now expect the CPI to be on target. They all sell contracts to close out their positions. (They have no reason to take a risky position on the contract with no expected profit.) Now, the Fed has no position the contract and is hedged. However, the traders incurred transactions costs and received no benefit. Why would they do that?

Now, suppose that the expectations are heterogeneous. Smith expects that the CPI will be 5% above target, and Jones expects it will be 1% above target. Davis expects that it will be 1% below target. Smith and Jones buy and Davis sells. The Fed is short one contract. The Fed contracts the quantity of money. Suppose everyone expects the CPI to be 1% lower than before. Jones expects the CPI to be 4% above target. He stays long. Jones expects the CPI to be on target and sells a contract to close his position. Davis now expects the CPI to be 2% below target, and remains short. The Fed is hedged.

If Jones expects the operation of the system, (a heroic assumption,) then he bears transactions costs for no benefit. However, even if Smith expects this, he will still buy a contract. He is buying a contract to make money from Davis, not from the Fed.

However, suppose Davis understands the system too. Won't he sell a contract as well? Won't Smith buy a contract and Davis sell, leaving the Fed hedged? Jones expects the CPI to be 1% above target, but he fails to purchase a contract, because if he does, the quantity of money will fall until it closes his position.

But let's add a fourth trader, Brown, who initially expects the CPI to be on target, and didn't trade at all. When the Fed contracts, he began to expect the CPI be below target, and he sells a contract. Davis and Brown are now short, Smith and Davis are long, and all of them expect to make money on the contract.

Of course, if everyone expects this outcome, then why don't they all trade immediately? As explained in the previous post, if everyone knows that everyone knows, then what is the problem? The Fed just undertakes the appropriate monetary policy. If the rule prohibits the Fed from taking any action unless it first has short or long on the contract, the chairman of the Fed can just call a public spirited individual and ask him to take the needed position. And then the Fed sets monetary policy at the level that everyone knows is appropriate. In the real world, no one has all of this knowledge.

The example, however, is instructive because it illustrates White and Garrison's other criticism of Sumner's proposal. Why don't the speculators all wait until the very last minute to trade? White and Garrison emphasized how such last minutes trades would leave little or no time for the Fed to engineer a change in the quantity of money much less impact the price level. Keep in mind that they were criticizing Sumner's proposal to have the Fed trade the June CPI contract through the end of May. Trades on May 31 would be very late for even heroic Fed actions to have much impact on the June CPI.

Superficially, the late trade problem isn't too hard to correct. If all of the trades come in late in the day on May 31, and Fed policy that night cannot impact the June price level, then stop trading the June contract on May 15. Perhaps trading for the June contract can be from May 1 to May 15. Or, perhaps it can be from April 15 to May 15. And, perhaps, the June contract can be traded in April. (A proposal to trade first quarter 2012 NGDP index futures contracts in the first quarter of 2011 makes the "too late" complaint a bit less pressing.)

Sumner (and I) have often argued that ordinary open market operations should be made in parallel with trades of the index futures contracts. If the trades of the futures contracts are bunched up at the end of the trading period, it would be possible that the Fed could not complete the matching open market operations before trade in the future contract closes. However, that isn't really a problem. The futures trading desk reports to the open market trading desk its position on the contract, and then the open market operations trading desk completes the trades as promptly as possible. If there is a backlog of needed security trades when the futures trading closes, then the trades of the securities can be completed as time permits.

For passive and automatic versions of the system, where the Fed makes open market operations with securities in response to its net position on the futures contract, the compression of all trades to the end of the period makes little difference. Trading closes on the futures contract, and the Fed is left with a short or long position. The Fed sells or purchases securities in an equal amount after trading on the futures contract is complete.

The implications for the constrained discretion version of the system, (which I favor,) are more troubling. The Fed is supposed to adjust monetary policy subject to the constraint that it remains hedged on the futures contract. If all the trading come at the end of the period, the constraint would not be binding during most of the period because no one is trading. Then, with the end of the period rush, simultaneous changes in monetary policy could be insufficient to generate sufficient trades to leave the Fed fully hedged before it ceases its trades of the futures contract.

With the constrained discretion version of the system, the Fed can continue to adjust monetary policy after it stops trading the futures contracts. It will, of course, be trading the next period's future contract, but if trading in that contract will also be concentrated at the end of the next period, the Fed would be free to respond to its short or long position from the last period.
I believe that some of the intuition behind White and Garrison's argument is that speculators would be motivated to game the system by sticking the Fed with an unfavorable position on the contract at the last minute. If the Fed is able to respond by adjusting monetary policy after trading ceases, the joke might be on those speculators. They have left themselves open to exploitation by the Fed! Of course, such a possibility is not a benefit of the system. For the Fed to engineer a recession because it was left with a short position on the contract would be very undesirable. However, this reasoning does provide a reason for speculators to give the Fed plenty of time to hedge, and to understand that they are speculating against the rest of the market rather than the Fed.

Finally, when considering the possibility of an end of the period rush, what happens if congestion prevents some trades from being completed? How much should be invested to make sure everyone can record desired trades at the last instant before close of business (right before midnight?) on the last day the Fed is trading the contract? People did have all month (or quarter) to trade.

Another modification that would help the Fed (and others) hedge would be to end trading with a close out period. For example, during the last month of the quarter, if the Fed is short, it will not sell any more contracts, but it will buy to close out its position. Similarly, if the Fed is long, it won't buy any more contracts, but it will sell to close out its position.

Sumner has proposed shortening the contracts to a single day. For example, on December 24, 2010, a contract for December 24, 2011 should be traded. The target value would be based upon a weighted average of the targets for third quarter and fourth quarter 2011 NGDP. The settlement value would be a similarly weighted average of the actual values of third and fourth quarter 2011 NGDP.

In my view, this modification creates an additional incentive to trade on the last day of the quarter. For example, suppose it is October 2010. A speculator determines that 4th quarter NGDP in 2011 will be above target, but that third quarter NGDP will remain on target. The greatest difference between the weighted average and the target will be on December 31, 2011. Without the daily contracts and the weighting, the payoff will be the same regardless of when the contract is traded during the quarter.

Perhaps the answer is to charge lower (like zero) "brokerage" fees at the beginning of the quarter and higher ones at the end. Keeping zero brokerage fees for those closing their positions, or even those helping the Fed to close its position might help solve the problem of last minute trading.

White and Garrison claim that index futures convertibility can't avoid the time inconsistency because the Fed can print currency to cover any losses. There is some truth to their argument, however, no monetary system is free from the threat of blatant repudiation. With index futures convertibility, an independent monetary authority will book growing accounting losses as it fails to meet its nominal target. And since each failure will involve substantial rewards to more and more "speculators," these losses can hardly be kept secret. Any repudiation of the nominal target will be at least as spectacular as a gold devaluation.

Index Futures and the Circularity Problem

In some of the comments on my post about Sumner and DeLong on index futures convertibility, there was reference to the circularity problem.

The circularity problem is that if the Fed trades based on the price of a futures contract, then the price of the futures contract will depend on expectations of the Fed's trades. That certainly looks like a circularity. The chairman of the Federal Reserve, Ben Bernanke, made this point years ago. (Bernanke & Michael Woodford, 1997. "Inflation Forecasts and Monetary Policy," NBER Working Papers 6157, National Bureau of Economic Research.)

As others have pointed out, this is an application of Goodhart's law. If the Fed starts targeting something, then the price begins to reflect what the market expects the Fed to do.

With index futures convertibility, where the money issuer (or issuers) buys and sells the contract, there is not a circularity problem exactly, but it is related. Under certain circumstances, people with relevant information don't trade the futures contract.

Suppose the Fed cannot change base money except to reverse a long or short position. Perhaps we can call this a passive or automatic version of index futures convertibility.

If everyone (perhaps including the Fed) knows that base money needs to increase some amount, say exactly $100 billion, or else NGDP will be exactly 1% below target, then no one will trade. If anyone did sell the future, then the Fed could, and must, buy $100 billion worth of bonds, raising base money $100 billion. Then those who sold the futures contract would buy (because now they expect NGDP to be on target) and the Fed would be hedged. No profits were made by the "speculator." Now that base money is exactly where it should be, no one has a position on the contract.

In the circularity argument, the price of the future actually would fall (supposedly) but the Fed would buy T-bills, expand base money, and get it back to target. But because the market expects this, the price would never actually fall. The price of the future would stay on target without the Fed buying or selling them, because everyone expects the Fed to do ordinary open market operations to get it back to target.

But if we don't treat "the market" as a representative agent, but rather as bulls and bears, then this problem doesn't arise. Or at least not always. Those who think that base money needs to increase by more than $100 billion sell the futures contract, and those who think it should rise by less than $100 billion buy the futures contract. The Fed is hedged when base money increases by $100 billion and NGDP is expected to be on target.

More importantly, from the perspective of traders, base money is always at the level where the market expects NGDP to be on target, and when a speculator expects something different, he or she trades. Even if everyone know this same thing, unless everyone knows that everyone knows, they still trade.

Of course, if keeping expected NGDP on target means that NGDP always will be on target, (so the system works perfectly) then no one will trade. If the Fed is on automatic, or passive, then the system would fail.

So, what a puzzle. Everyone knows that base money needs to increase by $100 billion, and if it increases by $100 billion, then NGDP will certainly be exactly on target. No one trades because if they do, there will be no profit. The Fed cannot increase base money unless "speculators" trade. There are no profits from trading. NGDP comes in below target, and this is known in advance, with certainty!

Now, if the Fed is allowed to adjust base money subject to the constraint that it remains hedged, these "everyone knows" scenarios, including the "with certainty" variant aren't a problem. The Fed increases base money by $100 billion. We might call these variants "constrained discretion" index futures convertibility.

The problem still exists if the Fed thinks that base money needs to increase $90 billion, and everyone else (the market) knows the needed increase is $100 billion, and further, everyone else knows that everyone else knows. Then they don't trade, because if they do, and the Fed is corrected, then there are no profits. So, the Fed is allowed to operate without the constraint binding because "the market" knows too much. Surely that is a bit odd. That modeling with representative agents makes this unusual situation into the norm is a failure of representative agent modeling.

I would also note that if we don't assume that all speculators are always self-interested, then in the everyone knows scenarios, it just takes one public spirited citizen to trade (bearing solely transactions costs) to solve the problem.

This would be important if the Fed knows exactly what it is doing, but chooses to keep NGDP away from target. Perhaps it expands base money in a way that will leave expected NGDP above target to help fund the national debt. Just one fiscal conservative who is willing to bear the transactions costs of a trade, and the Fed is forced to keep to the target.

Sumner has proposed trading contracts for very short periods of time, say a day, with value of NGDP for a day calculated as a weighted average of the past and future value. He has sometimes proposed keeping the trades secret, a bit like sealed bids (and offers, of course.) To some degree, these modification are efforts to avoid the circularity problem. Another reason for the modifications is to limit last minute trading by speculators so that they will avoid "showing their hand" to the Fed.

While further research on all of these problems is worthwhile, I think many of these problems involve unrealistic assumptions that "the market" is a single individual, and that the scenarios described in my post, where we imagine "Taylor" and "Krugman" taking different positions on the contract because they have quite different views, is the world in which we live.

Sumner and DeLong on Index Futures Convertibility

Scott Sumner provided a good explanation of the benefits of money expenditure targeting on National Review Online. He even gave a brief plug for index futures convertibility

In an ideal world, we’d remove all discretion from central bankers. The Fed would simply define the dollar as a given fraction of 12- or 24-month forward nominal GDP, and make dollars convertible into futures contracts at the target price. If the public expected NGDP to veer off target, purchases and sales of these contracts would automatically adjust the money supply and interest rates in such a way as to move expected NGDP back on target. It would be something like the classical gold standard, but with the dollar defined in terms of a specific NGDP futures contract, instead of a given weight of gold. The public, not policymakers in Washington, would determine the level of the money supply and interest rates most consistent with a stable economy.

I am very comfortable with describing the gold standard in terms of defining the dollar as a weight of gold. This is equivalent to fixing the dollar price of gold. Similarly, the BFH payments system defines the dollar in terms of a broad bundle of goods and services. This is equivalent to fixing the dollar price of the bundle, which is the sum of the dollar prices of the items in the bundle. Such a system is, in effect, a rule for stabilizing some measure of the price level.

Yet, somehow, defining the dollar as a fraction of 12 or 24 month forward nominal GDP leaves me puzzled. I do favor a rule keeping money expenditures (which can be measured by nominal GDP) on a stable growth path. I am persuaded that stabilizing its expected future value is both desirable and the best that can be done in an imperfect world. Sumner is trying to make the system appealing to those sympathetic to a gold standard. But to me, Sumner is proposing to define the dollar as a unit of fiat currency combined with a rule for stabilizing expected nominal GDP. Translating that back into a definition of the dollar in terms of a fraction of forward nominal GDP doesn't help me understand. (The privatized versions of the system I favor amount to the dollar being a debt claim that is settled according to a rule that keeps expected money expenditures on a target growth path. So, maybe I need to think harder about definitions of the dollar as a fraction of future money expenditures.)

More troubling is Sumner's claim that with dollars convertible into futures contracts, purchases and sales of the contracts automatically cause changes in the quantity of money and interest rates that move the expected value of NGDP to target. The problem with his brief explanation is that it creates the impression that money is created or destroyed when the Fed buys or sells futures contracts. While it might be possible to create a new type of security with a nominal interest rate that varies with deviations of NGDP from target, it would not be a futures contract. Index futures convertibility requires that the central bank use more conventional tools of monetary policy depending on its trades of the index futures contract. (Sumner understands all of this. We have been going back and forth on these issues for nearly twenty years.)

Brad DeLong commented on Sumner's article and explained how he thinks the system would operate.

As I understand Scott's proposal, it is this: Nominal GDP in the fourth quarter of 2007 was $14.291 trillion. A 5% growth rate from that base would give us a value of $17.455 trillion for the fourth quarter of 2011.

So far, DeLong's interpretation isn't bad. I think Sumner would be satisfied with using the quarter before the recession began as a base, and creating targets based upon a 5 percent growth rate from there. My approach has been to find the trend for the Great Moderation and then extend it into the future. The target I propose for fourth quarter 2011 is $17.896 trillion for Final Sales of Domestic Product. Not too different from DeLong. (I think the reason for the difference is that NGDP growth had been slow for the year before the recession began.)

DeLong continues:

Add on another 3% for the average short-term nominal interest rate we would like to see, and we have $18.153 trillion. Therefore the Federal Reserve would, today, announce that it stands ready to buy and sell dollar deposits to qualified customers at a price of $1 = 1/18,155,000,000,000 of 2011Q4 GDP.

Here DeLong begins to go wrong. He adds in 3 percent because he believes that is a proper target for the long run average nominal interest rate. His figure assumes a 3 percent average nominal interest rate between 2007 and 2011. Whether or not that would be desirable, it plays no role in determining what the Fed should be doing during either the 4th quarter of 2011 or the 4th quarter of 2010. He has effectively put NGDP on an 8 percent growth path. Neither $18.155 trillion nor its reciprocal should play any role in the system.

Why does DeLong make this error? It is because he understands the proposal as automatically changing the quantity of money when futures are purchased and sold. In DeLong's view, when the Fed buys these contracts, it is providing money now, in the fourth quarter of 2010 and will receives the money back in the fourth quarter of 2011. The Fed is making a type of loan when it buys contracts. It makes sense that the Fed would charge interest on these loans. If the Fed charges 3 percent interest on the loans per year, then it provides dollar deposits (makes a loan of a dollar now) in return for (1+.03) times 1/$17.455 trillion of 4th quarter NGDP to be paid in one year. That is 1/(17.455 trillion/ 1.03) or 1/16.947 trillion of 4th quarter 2011 NGDP. When the Fed sells the contracts, it is borrowing (accepting a deposit) of a dollar in exchange for paying 1/16.947 trillion of 4th quarter 2011 NGDP in one year. It pays 3 percent interest on these deposits, again, adjusted for any deviation of NGDP from target.

DeLong's error was to calculate the interest payment for 4 years compounded, and then multiplying when he should have divided. If the contract was defined based on the borrowers paying the Fed a dollar when the loan comes due, like a T-bill, then multiplication would have been appropriate. The appropriate adjustment, however, is 1.03 times $17.455 trillion, which is $17.979 trillion, not $18,155 trillion. More importantly, because the adjustment for the deviation of NGDP from target would not be known up front, this would be inappropriate. Division is really the only sensible approach.

DeLong continues, explaining how the system operates:

If investors thought that nominal GDP in the fourth quarter of 2011 was likely to be lower than $18.15 trillion, they would take the Fed up on its offer: demand the cash
now, pay off the contract in a year by then paying 1/18,155,000,000,000 of
2011Q4 GDP, and (hopefully, if they were right) make money--thus the money stock
would increase.

While the proper number is 1/16.947 trillion, everything is correct except that what is really happening is that the Fed is lending money at an interest rate of 3 percent adjusted by the deviation of NGDP from target. If NGDP was expected to be 1 percent below target, the amount repaid would be 99 percent of 1.03, which is a nominal interest rate of about 2 percent.

While I agree that more will be borrowed from the Fed at a lower interest rate than at a higher interest rate, unless that natural interest rate was 1 percent, (the 3 percent target for the nominal interest rate DeLong built into his system less the 2 percent trend inflation implied by a 5 percent growth path) this is not necessarily expansionary.

If investors thought that nominal GDP in the fourth quarter of 2011 was likely to be greater than $18.155 trillion, they would take the Fed up on its offer: give cash to the
Fed now, collect the contract in a year by receiving 1/18,155,000,000,000 of
2011Q4 GDP, and (hopefully, if they were right) make money--thus the money stock
would fall.

Here people are making a sort of term deposit at the Fed. The Fed pays 3 percent on these deposits Again, leaving aside that the numbers are just a bit off, if NGDP comes in above target, then it pays more than 3 percent. Higher interest rates will attract more of these deposits, and so the amount of reserves and currency available now will be lower than otherwise. Of course, if the natural interest rate is above one percent, this approach will not keep NGDP on target.

The actual characteristics of such a system would be for the expected deviation of NGDP from target to generate an effective interest rate charged on loans or paid on deposits that cause an expected interest rate to equal to the natural interest rate. The scheme automatically limits the size of any deviations of NGDP from target. If the natural interest rate is 1 percent, then it should keep NGDP on target.

DeLong continues:

If nominal GDP were expected to fall, the Federal Reserve would be shoveling money out the door at negative expected nominal interest rates. If his scheme were applied today it would be quantitative easing on a pan-galactic scale, as everybody would run to the Fed with bonds to use as collateral for their promises to pay the expected futures contract in a year in exchange for the cash now.

The Federal Reserve would then become truly the lender of not just last but first resort. Why would anybody borrow on the private market even at 0% per year when they could borrow from the Fed at -3%/year? Savers would simply hold cash rather than try to match the terms that the Fed was offering borrowers. Borrowing firms
would borrow from the Fed exclusively. The Fed would thus create a wedge between
the minimum nominal interest rate that savers would accept (zero, determined by
the alternative of stuffing cash in your mattress) and the nominal interest rate
open to borrowers.

If NGDP was expected to be below target by more than 3 percent, then the Fed would lend at negative nominal interest rates. DeLong's error here was embedding the 3 percent interest rate target into the NGDP target and then to forget what he had done. If negative nominal interest rates at the Fed are necessary to stop a downward deviation of NGDP from target, then the scenario of all lenders holding currency, and all borrowers borrowing from the Fed seems plausible--at least for credit transactions with a duration of one year or less. I think the most problematic part of the negative nominal interest rate scenario is that people could borrow from the Fed and just hold currency and make a profit.

DeLong continues:

I see how this would solve a monetarist downturn--a shortage of liquid cash money projected to lead to nominal GDP below its target. Once arbitrage had kicked in there would be no shortage of cash money.

I see how this would solve a Keynesian downturn--a shortage of savings vehicles that means that balancing savings and investment at full employment requires a nominal interest rate of -3%, which the zero-bound keeps you from getting to. The Fed would lend to all comers at a nominal interest rate of -3%.

I cannot quite see how this would solve a Minskyite downturn--a flight to quality because of a collapse in the market's risk tolerance and a shortage of safe assets.

The only problem created by a Minskyite downturn (with the DeLong rule,) involves the collateral that the Fed requires for loans from the Fed. Generally, the borrowers that the now risk adverse lenders reject can go to the Fed. DeLong's scenario where the Fed crowds out all private sector credit would imply this. The only thing different from the Keynesian scenario is that if the Fed is liberal regarding the collateral it accepts, nominal interest rates don't need to be negative.

Anyway, index futures convertibility does not involve the Fed making loans or accepting deposits at a 3 percent interest rate adjusted for deviations of NGDP from target.

In the fourth quarter of 2010, The Fed buys and sells a one dollar index future on fourth quarter 2011 NGDP (or Final Sales of Domestic Product) for one dollar. When the figures for fourth quarter 2011 NGDP come in, the contracts are settled. For every percentage point that NGDP exceeds its target, sellers pay buyers a penny per contract. For every percentage point that NGDP falls short of its target, buyers pay sellers a penny per contract. (Make the contracts $100, then the payoff is a dollar per percentage point, and cents for fractions of a percent. Index futures contracts of $10,000 or $100,000 are more common.)

These payoffs create incentives to buy or sell the contacts during the fourth quarter of 2010. Those expecting NGDP to be above target in the fourth quarter of 2011 have an incentive to buy the contracts. Those expecting NGDP to be below target in the fourth quarter of 2011, have an incentive to sell the contracts. Because the Fed buys and sells them for $1, then the price remains at $1, at least during the fourth quarter of 2010.

Suppose Tayor, thinking that Fed policy is too inflationary, believes that NGDP will be above target in the fourth quarter of 2011. Taylor is a "bull." He goes long on the contract. He buys the contract.

Krugman, on the other hand, thinks that monetary policy is ineffective or, maybe just too tight, and expects that NGDP will be below target in the fourth quarter of 2011. He sells the contracts. Krugman is a "bear," and goes short.

If Taylor and Krugman trade the exact same amount, then the Fed is fully hedged. The Fed's net position on the contract is zero, Taylor is long, and Krugman is short. If Taylor is correct, and the Fed's policy created massive inflation, with NGDP for the fourth quarter 2011 coming in at 5 percent above target, then he will earn 5 cents on each contract he bought. Where does that money come from? From Krugman, who must pay 5 cents on every contract he sold.

But suppose Krugman was right. If the liquidity trap keeps NGDP below target no matter what the Fed's does, and it comes in 10 percent too low, then Krugman will make 10 cents on each contract he sold. Where does the money come from? The money comes from Taylor, who must pay 10 cents on each contract he bought.

Finally, if NGDP comes in exactly on target, then the contracts expire without any payments being made. Tayor and Krugman neither collect nor pay anything.

Now, suppose that the bulls, like Taylor, purchase more contracts than the bears, like Krugman, sell. At the current price, the desired long position by the market exceeds the desired short position. The market expectation is that NGDP will be above target. In an ordinary index futures market, the price of the contract would rise until the bears balance the bulls. The price rises until the desired long and short positions match.

However, with the Fed buying or selling at a price of $1, no such price change would occur, even for a second. Instead, the Fed would sell to the bulls, taking a short position to balance the long position of the market. If Taylor, and the other bulls are correct, and NGDP comes in above target, then the Fed, like Krugman and the other bears, must pay. On the other hand, if NGDP comes in below target, then the Fed collects from Taylor and the other bulls, along with Krugman and the other bears.

The opposite scenario is possible too. Suppose the market expects NGDP to be below target. This means that bears, like Krugman, sell more than bulls, like Taylor, buy. Rather than the price of the contract falling to reflect the market expectation of below target NGDP in the fourth quarter of 2011, balancing the desired short and long positions, the Fed buys contracts from the bears at a price of one dollar, taking a long position to match their short position. If Krugman and the other bears are correct, then they will make money on the contracts. The Fed, like Taylor and the other bulls, must pay. On the other hand, if Taylor and the other bulls are correct, then they and the Fed make money at the expense of Krugman and the other bears.

Again, if the NGDP is on target, then the contracts expire without any payments being made. Regardless of whether the Fed had to take a short position or a long position to keep the price of the contracts at $1, it pays or receives nothing.

Superficially, the Fed creates or destroys money when the contracts are settled to the degree it makes or loses money. When does this happen? When the contracts are settled.

If NGDP is on target, no one makes or loses money, including the Fed. If the Fed is hedged, and the market expectation is that NGDP will be on target, then money may be transferred between longs and shorts if NGDP actually deviates from target, but the Fed neither makes nor loses money.

Only if the Fed is compelled to take a position on the contract and that position loses money, does the Fed pay out and so, create money. And, similarly, if the Fed must take a position on the contract and it makes money, the Fed collects the funds and destroys money. However, any such changes in the quantity of money are undesirable, and the Fed should sterilize such changes. If the Fed makes money, it should buy ordinary securities--maybe T-bills--with its profits. Similarly, if it loses money, it should sell off ordinary securities, such as T-bills to fund its payoffs.

What about during the fourth quarter of 2010, when the contracts are being traded? Isn't money being created and destroyed? No. When Krugman and other bears sell the contracts, they receive no money now. What they have done is received a promise to receive money in a year if NGDP comes in below target in exchange for a promise to pay money in a year if NGDP comes in above target. Similarly, when Taylor and the other bulls buy contracts, they don't pay anything for the contracts now. They are being promised money in one year if NGDP comes in above target in exchange for a promise to pay money in one year if NGDP comes in below target.

What about margin requirements? Don't index futures contracts require margin accounts?

Yes, they do. Margin requirements are performance bonds. The purpose is to make sure that those losing money on the futures contracts make the promised payments. While it is true that those buying futures must put up a margin payment, and so, superficially are making a kind of down payment, they are really posting a performance bond. They are promising to pay the difference between the future price they contracted and the spot price when the contract expires.

Of course, those selling futures also must meet margin requirements. Clearly, the sellers are not receiving money now for some kind of future delivery. And they aren't selling at a negative price. Just like they buyers, they are posting a bond to cover any loss from the difference between the agreed price and spot price when the contract expires.

With index futures convertibility, both bulls, like Taylor, and bears, like Krugman, must keep "funds" in a margin account. The amount per contract depends on the size of the likely deviations of NGDP from target. Perhaps 10 cents per contract would be appropriate.

It would be possible to require "cash" margin requirements. Those trading the contracts would write checks (or wire funds) to the Fed, and then the Fed would decrease the reserve balances of the traders' banks. While the traditional monetary base would shrink by the volume of futures trading, there would be a new type of Fed liability, which would be a margin deposit at the Fed. Other things being equal, any trading of the security would be contractionary. (Sumner sometimes assumes this institutional framework and insists that the Fed pay interest on these margin accounts at a bonus rate. This would be even more contractionary.)

Ignoring what kind of margin requirements might apply to the Fed itself, consider a situtation where NGDP is expected to be below target and bears sell contracts. The bears must all post margin requirements equal to, say, 10 percent of their short positions, and so base money contracts by that amount. The Fed, and whatever bulls are in the market, take the matching long positions. The bulls also post margin equal to 10% of their positions, further adding to contractionary pressure. The effect of the margin requirements is perverse.

If, instead, the market expects NGDP to be above target, then the bulls buy contracts. They must post margin requirements equal to some fraction of their positions, which reduces base money. The contractionary consequence is desirable. The Fed must take the offseting short position, but if there are any bears who also take a short position on the contract, their margin payments reinforce the contractionary impact of those of the bulls!

Existing commodity exchanges use continuous settlement. As the price of a future contract changes, funds are transfered between the margin accounts of the shorts and the longs. For example, if the price of a contract rises by a $1, a dollar is moved from the margin account for each short contract to the margin account of each long contract. If the price of a contract falls by a dollar, the change is reversed. Funds are moved from the longs to the shorts. When the contract expires, there is no need to make significant shifts in funds for settlement because the funds were already shifted as the market price of the futures contract changed.

With index futures convertibility, during the fourth quarter of 2010, when the Fed is buying and selling futures contracts for fourth quarter of 2011 at a price of a dollar, the price of the contract does not change, and no funds are shifted between the margin accounts of longs and shorts.

Once the Fed stops trading that particular futures contract, then it would certainly be possible for those with short or long position to continue to trade at whatever market price they find agreeable. Following the conventions of existing commodity exchanges, funds could be transfered between margin accounts based upon changes in the market price of the futures contract.

To the degree that the Fed was hedged, having no short or long position on the contract, these changes would shift funds between longs and shorts in the private sector and have no contractionary or expansionary impact. However, if the Fed was left with a position on the contract, then continuous settlement would involve the creation or destruction of money depending on if the Fed suffered losses or made profits.

For example, if the market expected NGDP to be below target, and the Fed took a long position on the contract, when the Fed ceased targeting the price, and the price began to fall, then the Fed, like any other long, would begin to lose money. While the transfers between the shorts and any private sector longs would simply transfer funds, any payment by the Fed to cover its own losses would be an increase in the quantity of this special type of base money. If, as is customary, those making money can remove excess funds from margin accounts, then this would be expansionary. The Fed would, presumably, wire funds to their banks, and credit their banks' reserve balances.

Further, if the bears were wrong, and further information shows that NGDP will turn out to be above target, then the price of the contract would rise. As the Fed made money, it would decrease the margin accounts of those bears. If they had to make margin calls (replenish their margin accounts,) then there would be a further contractionary impact. On the other hand, if they refuse to make the margin calls, their positions could be closed out by selling to any private sector bulls, which simply transfers funds. If the Fed were permitted to close out its position by selling at a price greater than one, it would be taking profits. While the margin accounts of shorts would be somewhat depleted, when there accounts are closed and any remainer is returned to the shorts, the effect would be expansionary.

Worse, consider the situation where the market expects NGDP to be above target and buys, with the Fed being forced to take the matching short position. Once the Fed stops trading the contract at a price of $1, continued trading on the market could cause the price to rise. Using continuous settlement, the margin accounts of the bulls are increased. The bulls begin to make money at the expense of the Fed. If they are permitted to take profts from those margin accounts, then the Fed would wire funds to their banks, crediting the banks' reserve balances. The Fed would be creating a perverse expansion in the quantity of money. Similarly, if the market turned out to be wrong and the market price of the contract fell below $1, then continuous settlement would have the Fed decreasing the margin accounts of the longs, creating an additional contractionary effect.

The most sensible approach is for the Fed to sterilize the impact of the creation of any special margin accounts by offsetting open market purchases. Similarly, any changes in such margin accounts due to continuous settlement should be offset by additional open market operations as needed.

In my view, a better approach is to require those trading the futures to meet margin requirements with securities, such as T-bills. While changes in the demand for securities to meet margin requirements might have some kind of contractionary or expansionary effect on the economy, it is likely to be minimal and does not play any significant role in the process that tends to keep expected money expenditures on target.

As explained above, index futures convertibility requires that the Fed use some conventional tool of monetary policy to impact future money expenditures and bring the expected value of money expenditures back to target. The Fed could change reserve requirements, change the level of the interest rate it pays on reserves balances, change the primary credit rate it charges banks for loans at the discount window, undertake open market operations with T-bills, with longer term to maturity government bonds, or even with some other kind of security.

In my view, the Fed's goal should be to remain fully hedged. The market expection should be that NGDP remain on target. The long positions of the bulls should be exactly offset by the short positions of the bears.

If the market expectation is that NGDP will be above target, then the purchases of the bulls will be greater than the sales of the bears. The Fed will be left with a short position on the contract. To avoid the risk of loss, the Fed needs to undertake a contractionary policy--raise reserve requirements, raise interest rates paid on reserve balances, raise the primary credit rate to charge more for loans at the discount window, or make open market sales of T-bills, longer term government bonds, or whatever other assets it owns. Those bulls who expected only a slight increase in NGDP will start to find the risk of loss too great, and sell. Those who already thought that Fed policy was too contractionary sell more. Some who held no position on the contract perhaps will notice the Fed's contractionary policy and sell. When the Fed is hedged, and its position is zero, then the policy is right.

If the market expectation is that NGDP will be below target, then the sales of the bears will be greater than the purchases of the bulls. The Fed will be left with a long position on the contract. To avoid the risk of loss, the Fed needs to undertake an expansionary policy--lower reserve requirements, lower interest rates paid on reserve balances (perhaps to something less than zero,) lower the primary credit rate and charge less for loans at the discount window, or make open market purchases of T-bills, longer term government bonds, or some other type of security. This expansionary policy will result in those bears who were expecting that NGDP will be only slightly below target to close out their short positions by purchasing futures contracts. Those bulls who already expected NGDP to be above target will perhaps purchase more. And others, who weren't in the market, may buy as well. Once the market expectation of NGDP in the fourth quarter on 2011 is on target, then the Fed is fully hedged. The Fed's policy is right.

The Fed policy is right, or rather, the market expectation is that NGDP will be on target in the fourth quarter of 2011. Some of Sumner's versions of the system leave the Fed much less discretion and could be implemented by computer. For example, the Fed could be required to make parallel open market operations with the trades in the futures contract. If Taylor expects NGDP to be above target and buys a future contract at a price of $1, then the Fed not only sells the future, it also sells T-bills worth a dollar. Base money contracts by dollar for every futures contract purchased by bulls. If Krugman expects NGDP to be below target and sells a futures contract, then the Fed buys the futures contract and at the same time buys a dollar's worth of T-bills. Base money increases by a dollar.

If the market expectation is that NGDP will be on target, then the purchases of bulls like Taylor and sales by bears like Krugman offset, and while the Fed might purchase and sell equal amounts of T-bills, leaving the monetary base unchanged, the simplest approach is for the Fed to net out the required T-bill transactions, trade no T-bills, and leave base money unchanged.

The Fed then would change base money through conventional open market operations according to the size of its net position on the futures contract. Sumner argues that the equilibrium quantity of base money will keep the market expectation of NGDP on target.

It is a type of arbitrage argument. Suppose the current value of base money is expected to result in NGDP being above target in the fourth quarter of 2011. Base money is "too high." The market expects to profit by purchasing futures contracts from the Fed. The Fed sells the contracts at a price of $1, and it also sells a dollar's worth of T-bills, shrinking base money. If this new, lower level of base money is still too high so that NGDP is expected to be above target, then there must be expectations of profits from buying index futures from the Fed. The Fed sells still more futures contracts and more sells T-bills, with base money again decreasing by the value of the T-bills sold. In equilibrium, there can be no more expected profits from buying the futures, and so NGDP must be on target, and so, base money must have decreased enough for NGDP to be on target.

Notice that the Fed is left exposed with a short position. To the degree transactions cost, risk aversion, or anthing else leaves NGDP above target, the Fed will take a loss on this short position. Those trading with the Fed will earn enough profit to cover any costs. Unfortunately, if some unancipated shock causes NGDP to rise above target, then the Fed could be subject to heavy losses. In fact, it is the chance of just such an event that motivates those buying the futures to maintain the long position.

Of course, this scenario requires that base money was initially too high. How did it get so high? Consider the opposite scenario, where base money is too low. NGDP is expected to be below target. With a 5 percent target growth path for NGDP, all hand-to-hand currency being base money, and banks being required to keep base money reserves, the quantity of base money should generally be increasing.

Suppose base money is "too low," so NGDP is expected to be below target. There are profits to be made by selling the index futures contract, and the Fed must buy at at price of $1. The Fed makes open market purchases of T-bills in parallel with its purchases of the futures contract. This causes base money to rise. But if base money is still "too low" so that NGDP is still expected to remain below target, there are still profits from selling futures contracts--shorting NGDP, or at least the index futures contract on NGDP. In equilibrium, there can be no profits from selling the index futures contract, so NGDP must be expected to be on target. That means that the level of base money must be at the correct level.

Notice that this leaves the Fed exposed to a long position on the futures contract. If transactions costs or risk aversion leaves the expected NGDP below target, then the Fed will take a loss. This will compensate those short positions resulting in the increase in base money for any costs. Of course, if some unexpected shock causes NGDP to fall substantially below target, the Fed would be subject to heavy losses.

If the institution of parallel open market operations were taken literally, then the entire quantity of base money would need to be matched by purchases of futures by the Fed. The private sector would have to take a short position on the futures contract of hundreds of billions of dollars each and every quarter, growing by the year. To avoid that consequence, the obvious solution is for the rule to apply solely to changes in base money, and so, the Fed's security portfolio and the quantity of base money would initially be the level from the previous quarter (or whatever period,) and then change according to the Fed's net position on the futures contract for the current quarter. A rather simple modification would allow the Fed to use conventional open market operations to increase base money according to trend (say, 5 percent) at the beginng of each period, and then make changes from that level based upon changes in its net position on the futures contract.

Sumner has gone so far as to suggest that the Fed set base money however it thinks best at the beginning of each period, and then make adjustments to its target according the net position on the futures contract. In effect, the Fed sets base money and then allows the market to fine tune. As explained above, those who believe that the quantity of base money determined by the Fed is too high (Taylor) would buy contracts and those thinking the quantity of base money is too low (Krugman) would sell contracts. If "the market" agrees with the Fed, purchases and sales match, and the Fed leaves base money unchanged at what it thought was the appropriate level.

If instead, the bulls purchase more than the bears sell, "the market" expects NGDP to be above target, and the Fed sells futures contracts and T-bills, decreasing base money relative to its tentative target. While a requirement that the Fed always trade T-bills in parallel to its trades of the futures contract would suggest that if the decrease in base money results in bulls selling futures to close out their long positions, or bears selling even more, the matching purchases of futures contracts by the Fed, which hedges and closes out its short position, should be matched by purchases of T-bills which would again raise base money. A more sensible approach would be for the Fed to do nothing as its short position shrinks. Only if the selling goes so far that the Fed has a net long position should the Fed begin buying T-bills and raise base money.

Suppose "the market" finds the Fed's tentative level of base money too low. The bears sell more than the bulls buy, and the Fed purchases futures contracts and T-bills, increases base money relative to its tentative target. As the Fed purchases T-bills and expands base money, some bears may purchase futures to close their short positions, and bulls may expand their long positions. As the Fed sells futures, it hedges and closes its long position. The Fed should not sell T-bills and contract base money as sales shrink its long position. Only if the purchases by "the market" go so far as to cause the Fed's long position to disappear and turn into a short position, should be the Fed begin to sell securities and shrink base money.

Such a rule may be workable--the Fed must buy T-bills in parallel with its purchases of futures contracts if it is hedged or already has a long position, while selling T-bills in parallel with its sales of futures contracts if it is hedged or already has a short position. However, I still think the better approach is to allow the Fed discretion to adjust monetary policy as it chooses subject to the constraint--always stay hedged. While the Fed would have some discretion, this rule would require that "the market" expects money expenditures to remain on target.

P.S. And the proper target is an adjusted 3 percent growth path for Final Sales of Domestic Product starting at the end of the Great Moderation.

Scarcity and Unemployment

A key principle of macroeconomics is scarcity. There are not enough resources, including labor, to produce all goods and services in quantities sufficient for everyone to achieve their goals. While it is possible to over produce one or a few goods, perhaps even to the point where those particular goods are no longer scarce, what that overproduction means is that resources are devoted to expanding production to a point where those goods are worth less than their opportunity cost. The opportunity cost is the value of the other goods that could have been produced instead. Overproduction of some goods means underproduction of other goods. In a world of scarcity, a general glut of goods must be due to a coordination failure.

Arnold Kling fails to grasp this important principle of macroeconomics. He argues that a general glut of goods is not necessarily due to an excess demand for money. He instead sticks with his "recalculation" story. That story combines a common place and correct idea with a novel and absurd idea.

The common place idea is structural unemployment. Some parts of the economy shrink and others grow. People lose jobs in the shrinking sectors of the economy and obtain new jobs in the growing sectors of the economy. Because of a mismatch of skills, this process can be painful and gradual. Those who lose their jobs in shrinking sectors may remain unemployed for a substantial period of time before they are employed in the growing sectors of the economy.

A situation of structural unemployment involves matching shortages and surpluses in product markets. For example, if the demand for new homes falls 50 percent and new homes make up 10 percent of the economy, then the demand for other products in the economy should grow more than otherwise. To offset those shrinking sectors, the real volume of demand for the other products of the economy should grow approximately 5 percent. With growing productive capacity due to a growing labor force, saving, investment and capital accumulation, and improved technology, the real volume of demand in the rest of the economy should be growing a bit more than 8 percent.

If, on the other hand, the demand for other goods and services grows less than 8%, which would include zero or else the demand for other products shrink as well, then the problem isn't "structural." That is, the problem isn't simply difficulties in shifting labor from where it is needed less to where it is needed more.

Kling's innovation is to claim that some industries are shrinking because people don't want the products any more, and nothing is growing because people don't know what they want instead. It is necessary to recalculate and discover what people want to buy. Certainly, this view has a certain appeal. If those spending less on houses had wanted to spend on something else instead, the demands for those goods would have risen.

The problem with this argument is that it ignores scarcity. There are not enough resources (including labor) to produce all good in quantities sufficient for everyone to achieve their goals. There are any number of goods, currently being produced, that could be produced in larger quantities and help people achieve their goals. Resources would be needed to produce those goods and services.

To say that houses are over produced is to mean that the value of the additional homes is less than their opportunity costs. The opportunity cost is the value of the other goods that could have been produced with the resources. The reason to reduce the production of houses is to free up labor and other resources to expand the production of those other goods that are the opportunity cost of producing the houses.

But clearly, individuals who don't want to buy houses can instead just hold money. And that is the problem. When people choose to hold more money than the existing quantity, then total spending in the economy falls. It is still true that scarcity exists and that the reason to reduce the production of homes is that the resources could be used to produce other more valuable goods, but nominal expenditures on those other goods doesn't increase.

What happens? It depends on monetary institutions.

Suppose the monetary institution is a 100 percent reserve gold standard, and people decide that they don't want to purchase new houses, and instead want to hold more gold rather than spend on some other good or service. People are laid off from the housing industry. There is no increase in demand for any other good, other than gold mining. So, it is necessary for the unemployed workers to just wait until someone comes up with a new product that tickles the fancy of the former home buyers. Right?

WRONG!

What happens is that the surplus of labor and other resources results in lower resource prices, including wages. This reduces the costs of producing various products, and so, firms expand output of those goods and lower their prices enough so that people will purchase the additional output.

While the lower prices appear to make it possible for people to be able to buy more products, the lower wages and other resource prices means that money incomes are lower as well. However, the real value of the gold has increased. Everyone who holds money earns a real capital gain. Now, if the former home buyers still have no desire to buy anything, they just have higher real money balances. But other people, who also hold money, earn a real capital gain. And some of them could use more consumer goods and services. And they buy more of them.

The real volume of expenditures on various goods (and perhaps, to some degree housing) rises enough to match the productive capacity of the economy. By far, the most likely scenario is that the real demand for houses is lower and the demand for other goods rise. There is still a need to redeploy resources from the housing industry to other industries. However, there is no need to wait for somone to find some product that appeals to those who don't want to buy houses and instead want to hold money. The level of prices (and wages) fall enough that the real quantity of money rises enough that some of those holding money expand their expenditures on goods and services. Other people holding money who do want more of the existing goods buy them.

Suppose instead the nominal quantity of money is increased to match the additional demand for money. Those who don't want to buy houses and just don't want to buy anything else, hold more money. The quantity of money is increased enough to offset the increase in the demand for money and keep money expenditures growing with the productive capacity of the economy.

How is the quantity of money increased? Suppose it increases by helicopter drop. New money is printed and dropped out of helicopters. People pick up the money. Those people who have nothing they want to spend money on, presumably just hold the additional money. (I suppose they rake up whatever appears in their yard because some good may appear at some unknown future time that they will want.) However, all of those people who are currently holding money, not because they don't want additional goods and services, but instead only because they prefer holding the money, spend at least some of the additional money on whatever it is that they want.

Given a sufficient increase in the quantity of money, the demand for the scarce goods that those picking up the money want will increase enough so that total spending matches productive capacity. Perhaps some of those picking up money buy houses, but the likely result is that there will still be less spending on houses and more on other things. There remains a need to redeploy resources away from houses and towards other goods.

In the real world, the closest thing to a helicopter drop of money is a tax cut financed by money creation. The government cuts taxes and instead borrows money by selling bonds. The central bank buys the bonds with new money created out of thin air. Again, those people who used to buy houses and were holding more money because they could think of nothing else to do with it, presumably just hold on to the additional money they receive. However, other people, who are holding money despite valuing the additional goods they might buy, spend the additional money on whatever goods they want the most. Perhaps some of them spend more on houses. Given sufficiently large tax cuts funded by money creation, total spending will rise enough to match the productive capacity of the economy. The most likely scenario will be that fewer houses are demanded and more other goods are demanded. There remains a need to redeploy resources, including labor, from the production of houses to other goods.

Suppose that instead of these schemes of creating "outside" money and giving it away, instead, money is "inside" and lent into existence. Those who used to buy houses and instead hold money because they have nothing else they want to buy are clearly saving. By holding money, they are choosing to lend additional funds to the banking system. The demand to hold inside money represents increased lending to the issuing banks--either private banks or the central bank. The money issuer (or issuers) then expand the quantity of money enough to match that increase in demand to hold money. With inside money, new money is issued by lending. This could be in the form of loans, but it can also occur through the purchase of already existing bonds.

As the money issuers expands loans (or purchases bonds,) they lower interest rates. The lower interest rates provides an incentive to reduce saving and so, increase consumption, or else expand investment. Further, the reduced interest rates that the money issuer or issuers can earn also reduces the interest rates they can pay on the money. This reduces the benefit from holding money, and so results in some of those holding money spending it on consumer goods or capital goods.

Superficially, the increase in the quantity of inside money requires an increase in debt. And it certainly requires that the money issuers hold more debt. However, it is entirely possible for the money issuers to expand their market share in the credit market, so that while the quantity of money expands, total lending actually shrinks. How can spending on goods and services expand, even if total lending shrinks? All that is necessary is that some of those who would have lent by holding existing bonds instead sell them and spend on consumer good or capital goods.

Interestingly, because money issuers pay lower interest rates than they charge, it is possible that the decrease in interest rates could go so far as to make the interest rates "paid" on money negative. This is interesting, because those who spend less on housing and then just hold money because they have nothing better to do with it, may have to pay.

The changes in interest rates motivate people who have use for additional goods ands services to purchase them. To some degree, this will be people borrowing money that they must pay back later, but it also could involve people spending more out of current income on consumer good and services or capital goods. And it can involve people selling off previously accumulated assets to fund purchases of consumer goods and services or capital goods. (And, yes, the zero nominal bound on interest rates can cause problems with a pure inside monetary system.)

The resolution of monetary disequilibrium, either through a lower price level and increased real balances, or an increase in the nominal quantity of money, results in increased real expenditures on scarce goods and services. Resources are shifted from the production of goods that people don't want to the production of goods that people do want. As long as there are scarce goods, as long as there are some people who want to purchase consumer good and services or capital goods, the correction of monetary disequilibrium will result in increased production of those goods. There is no need for the particular individuals who chose to reduce spending and accumulated money balances to choose to spend on anything in particular. The process that corrects monetary disequilibrium, whether a lower price level, helicopter drops, or reduced interest rates, results in increased expenditures on goods and services by other people.

The notion that it is necessary to wait until some new good is found that will appeal to those demanding fewer existing goods, and that production should or must be reduced until such products are found is an error. It is an error that ignores the fundamental reality of scarcity.

Saving and the Purpose of Production

If the purpose of production is consumption, where does that leave saving? To a remarkable degree, saving simply shifts consumption between households so that each household can shift its consumption over time. To focus on this aspect of saving, I will ignore investment. (I will get to that later.) To the degree that saving simply shifts consumption between households, it remains completely consistent with the principle that the purpose of production is consumption.

Saving is disposable income less consumption. Disposable income is income less tax payments. Saving is that part of income not paid in taxes or spent on consumer goods and services. Saving implies an increase in net worth by a household. By convention, saving occurs when consumption is less than disposable income. Negative saving, called dissaving, occurs when consumption is greater than disposable income. Dissaving implies a decrease in net worth.

Income, tax payments, and consumption are all flows that occur over a period of time, and so is saving or dissaving. Net worth--assets minus liabilities--is a stock. What is a household's net worth at a point in time?

For example, Smith earns $50,000 per year, pays $5,000 in taxes, and spends $44,000 on consumer goods and services during the year. Smith's disposable income is $45,000 per year. Since he only consumes $44,000, he saves $1,000 per year. Saving requires that he either accumulate assets or repay debts, so that his net worth rises by $1,000 over the period.

Jones, on the other hand, also earns $50,000 per year. He pays $5,ooo in taxes, and spends $46,000 on consumer goods and services. Jones' disposable income is $45,ooo per year. Since he consumes $46,000, he dissaves $1,000 per year. Jones' net worth decreases by $1000 over the year. His assets decrease or his liabilities increase.

How is it possible to dissave? How can Jones pay $5,000 in taxes and spend $46,000 on consumer goods and services, when he only earns $50,000? One way to dissave is to borrow. Jones can borrow $1,000 and so consume at a rate grater than his disposable income. This increases his liabilities and reduces his net worth over the year.

Suppose Jones borrows from Smith, which is equivalent to Smith lending to Jones. Suppose the interest rate is 5% per year, payable as a coupon, but the principal is due many years in the future. The loan is liability to Jones and an asset to Smith. Jones' has a lower net worth. Smith has a higher net worth.

The loan has allowed Jones to spend more on consumer good and services. Does that mean that total spending on consumer goods and services has risen? No, because Smith is consuming less than he would have if he hadn't lent to Jones. If there was no saving or dissaving, total consumption would have been the sum of their disposable incomes, $45,000 plus $45,000 or $90,000. Because of the saving and dissaving, because of the lending and borrowing, consumption is $44,000 for Smith plus $46,000 for Jones. Consumption remains $90,000 per year.

The following year, Smith has a slightly higher income. He earns $50,050. That is, his initial annual income plus 5 percent of the $1000 he lent to Jones. Suppose his taxes remain $5,000, so that his disposable income is $45,050. And suppose he now spends all of that on consumer goods and services, so that he saves nothing.

Meanwhile, Jones is in debt. He owes Smith $1,000. The total stock of debt is $1000. Using the language of financial investment, some say he is "leveraged." He still earns $50,000 per year and pays $5,000 in taxes. He spends all of his remaining $45,000 in disposable income, but he buys $44,950 in consumer goods and services, and pays $50 to Smith in interest.

Does the fact that Jones is in debt (leveraged and maybe "overly" so,) result in less consumption? He consumes less. He consumes $50 less. However, in total, consumption doesn't change. If there had never been any saving or dissaving, no lending or borrowing, then both households would have continued to consume an amount equal to their disposable incomes, which would total to $90,000. Because Jones is in debt, he consumes $50 per year less, but Smith, with his higher disposable income, consumes $50 more. Total consumption remains $90,000.

There is no saving and no dissaving. However, there is debt and interest payments on that debt, providing income to the creditors. Total consumption remains unchanged. The "leverage" of Jones does not reduced total consumption.

While borrowing is one way to dissave, there is a second method. It is possible to dissave by selling off assets that have been accumulated in the past, and so the flow of consumer expenditure is greater than the flow of disposable income during a particular period. Oddly enough, a second way to save is to pay down existing debts.

Suppose Jones tires of paying $50 per year to Smith. Or, perhaps, Smith wants his $1000 back. Jones repays his debts. Smith collects on the loans he has made. (Jones is deleveraging.)

When this occurs, Smith earns $50,050, and pays $5,000 in taxes. His disposable income is $45,050. However, he spends $46,050 on consumer goods and services. How does he do that? He collects on the $1,000 loan he had made to Jones. Because Smith's consumption of $46,050 is greater than his disposable income of $45,050, he is dissaving. Notice, however, he does so without borrowing or going into debt. Smith's net worth still falls, because when he collects the money he lent to Jones and spends it on consumer goods and services, his assets decrease.

Meanwhile, Jones has a disposable income of $45,000. He makes his regular interest payment to Smith of $50, but also repays the full amount of the loan of $1,000. He spends $43,950 on consumer goods and services. The difference between his disposable income and his total expenditures, both interest and spending on consumer goods and services is $1,000. Jones saves $1,000.

Jones has delevered. What happened to consumption? Jones spent less on consumer goods and services, but total consumption remained unchanged. Smith spent $46,050 and Jones spent $43,950, for a total of $90,000.

The amount that Smith saved and Jones dissaved was quite modest. Suppose that the saving and dissaving was $10,000. Smith would initially consume only $35,000 and Jones would consume $55,000. If the interest rate remained 5 percent, then during the period when Jones was a debtor and Smith a creditor, Smith would be consuming $45,500 per year, while Jones would only be purchasing consumer goods and services worth $44,500. And finally, when Jones "delevers," Smith consumes $55,500, dissaving $10,000, while Jones must reduce his purchases of consumer goods and services to $34,500, saving because he spends much less than his disposable income. Total consumption remains $90,000.

Now, suppose that instead of simply saving and dissaving one year, Smith and Jones repeat year after year. Smith saves $10,000 each year and Jones dissaves $10,000 each year. After 5 years, Jones owes Smith $50,000. Jones' debts are equal to his total $50,000 per year income! Jones pays $2,500 in interest to Smith, and so his consumption expenditure is his $45,000 in disposable income less his $2,500 interest payment, plus the new $10,000 loan from Smith for a total of $52,500. Smith earns the $2500 in interest and so has $47,500 to spend. But he saves and lends $10,00 more to Jones, so his consumption is $37,500. Total consumption remains $90,000.

Now, suppose that they carry on for an additional 5 years. Now, Jones owes Smith $100,000--twice his income. Comparing to the initial total income of the two of $100,000, then total household debt is equal to total household income. Clearly, there is too much leverage! There must have been a massive consumption binge, right? Well, maybe for Jones, but not in aggregate.

Suppose Smith and Jones are going to continue on and bring total household debt to something greater than household income. Jones continues to earn $50,000 and has a disposable income of $45,000. His interest payments are now $5,000 and he borrows an additional $10,000. His spending on consumer goods and services is now $50,000. That is, $45,000 less $5,000 in interest payments, plus a new loan of $10,000. Smith is now earning $55,000, with a disposable income of $50,000. He lends $10,000 to Jones, and spends $40,000 on consumer goods and services. Total spending on consumer goods and services remains $90,000 as it has all along. The huge build of of household consumer debt has occurred without there being any increase in total consumption. Smith has consumed less, and Jones has consumed more.

Now, instead suppose Jones begins to worry about his ability to honor his debts, and so stops additional borrowing. Or, perhaps, Smith begins to worry about collecting the money he is owed, and stops additional lending. Total household debt will remain $100,000.

Smith now earns $55,000, including the interest he collects from Jones. He pays $5,000 in taxes. His disposable income is $50,000, and that is what he spends on consumer goods and services. Smith saves nothing. Jones, on the other hand, earns $50,000. He pays $5000 in taxes. He pays $5000 in interest to Smith. That leaves him $40,000 to spend on consumer goods and services. He no longer dissaves. Total spending on consumer goods and services remains $90,000. The highly leveraged nature of the economy in no way reduces the ability of households in aggregate to spend on consumer goods and services.

Now, let's go with deleveraging. Clearly, there is no way for Jones to repay the entire $100,000 he owes to Smith all in one year. His disposable income, even before the $5000 in interest he owes, is too low. And, of course, while it would be possible for Smith to consume $150,000 in one year, that is a very substantial increase.

However, Jones can pay it off gradually. Suppose he pays $10,000 per year. At first, Smith earns the $55,000, including the interest from Jones, and pays his $5,000 in taxes. His disposable income is $50,000. But he collects an additional $10,000 from Jones, and so spends $60,000 on consumer goods and services. Because he consumes more than his disposable income, he dissaves at a rate of $10,000 per year.

Jones, meanwhile, earns $50,000. He pays $5,000 in taxes, and $5,000 in interest. He pays back Smith $10,000 per year. Jones saves at a rate of $10,000 per year. He purchases $30,000 worth of consumer goods and services.

Total spending on consumer goods and services is $90,000. As Jones gradually repays his debts, Smith earns less and less interest income, and so his spending on consumer goods falls. On the other hand, Jones has more income after paying interest to Smith, and expands his consumption.

After 10 years are up, Jones has repaid his debts. Neither Smith nor Jones save or dissave. Smith's disposable income is $45,000 as is Jones'. They each spend $45,000 on consumer goods and services. Total spending on consumer goods and services is $90,000.

Both Smith and Jones were contributing resources to production all along. Firms were using those resources to produce consumer goods and services. Smith and Jones paid taxes, and that funded government spending. Some resources were used by the government, either directly or used by firms to produce goods and services for sale to the government. While both Smith and Jones mostly contributed resources to production in order to purchase consumer goods and services, during some periods, Smith produced more than he consumed, but in other periods he consumed more than he produced. Jones was the same. He consumed more than he produced sometimes, and produced more than he consumed other times. In aggregate, total consumption matched total production. Because saving and dissaving matched, in aggregate, production was continually directed towards consumption.

The life-cycle approach to saving and dissaving suggests that young people dissave. They borrow and go into debt. To the degree they borrow to purchase durable consumer goods, like cars or even houses, the impact on their net worth is ambiguous since they are accumulating real assets. As people move into middle age, they make payments on their installment debt, and so, save. In their later middle years, they have paid down their debts and accumulate financial assets--they save and lend. Finally, when people reach their senior years, they retire and dissave. They spend the funds they accumulated in their later middle years.

The permanent income hypothesis suggests that households save and dissave to smooth consumption as income fluctuates. If income is more than normal, households save by accumulating assets or paying down debts. if income is less than normal, then households dissave by selling off accumulated assets or paying down debts.

These approaches to saving, income, and consumption are very consistent with the principle that the purpose of production is consumption. Consider instead a "class" approach. Wealthy households earn interest income, and limit their consumption to that income. Dissaving, described as "dipping into capital" or some such, is considered a sin against one's progeny. Successful households save, adding to their net worth, seeking to join the ranks of the wealthy. The working people are the debtors, making these interest payments to the wealthy. Ignoring investment, the situation appears rather bleak, as those saving to accumulate wealth can only do so to the degree others go into debt.

Even here, production is directed towards consumption. The rich hold wealth in order to consume. Those who owe them money must reduce their consumption by their interest payments. Those who save and accumulate wealth to lend reduce their consumption out of current income. The savers lend to poor borrowers who consume an amount greater than their incomes.

Production is directed to consumption as long as saving matches dissaving. How can a market economic system, without any conscious direction, coordinate the decisions of the millions of households so that saving and dissaving match? As usual, the answer is prices. In particular, interest rates.

Suppose that at the current level of "the" interest rate, desired dissaving is greater than desired saving. Clearly, this is a problem. The households are providing resources to firms to produce goods and services. This generates an equal income, which households can spend on consumer goods and services. If desired dissaving is greater than desired saving, then households in aggregate are trying to purchase more consumer goods and services than can be produced with the resources they are willing to provide.

The solution is a higher interest rate. Households who would dissave by borrowing in order consume beyond their income will have to sacrifice more consumption in the future when they repay the loans. They receive a signal and incentive to keep their current levels of consumption closer to their current incomes. Households that are saving by paying down the debts they have incurred have an incentive to speed those repayments, particularly if the interest rates on their debts float. The longer they wait, the more future consumption they must sacrifice. Households saving by accumulating assets are rewarded by the additional future interest income, obtaining even more consumer goods and services in the future. And finally, households dissaving by selling off the assets they have accumulated are motivated by the higher interest to slow the pace of sales and current consumption. All of these incentives to reduce current consumption result in expanded saving and reduced dissaving until they are again in balance.

However, there are income effects that have perverse effects for consumption. Households that hold assets and earn more interest income can afford to consume more. That is offset by the households that are currently indebted whose interest payments make up that interest income. They have less income after interest to fund consumption. Generally, the income effects between borrower and lender (like any buyer and seller) offset, leaving a substitution effect--less current consumption and added future consumption. So the result then is more saving and less dissaving.

While it is natural to focus on the impact of higher interest rates on desired saving and dissaving at a given level of income, it is certainly possible, and even likely, that higher interest rates will elicit more work effort--a higher supply of labor and increased current income. The notion that people will work more hours or obtain an additional job so that they can save the added labor income to earn higher interest rates seems implausible. Similarly, the notion that net creditor households will respond to higher interest income by taking an additional job to maintain consumption with reduced dissaving is very unrealistic.

However, households that are borrowing less and so reducing consumption may well seek added opportunities to work and obtain the desired consumer goods by other means. And, most importantly, those households that are already in debt and whose interest payments are increased, will face a very strong incentive to work additional hours, even to the point of taking another job, to try to maintain consumption.

What about the other type of imbalance? Suppose desired saving is greater than desired dissaving. While trying to consume more goods and services than can be produced with the resources households provide to firms is infeasible, there is nothing impossible about households purchasing fewer consumer goods and services than the resources they provide to firms can produce. Saving certainly is possible. If firms cannot sell the goods, they won't produce them. If firms don't produce the goods, they won't hire labor and other resources to produce them. And so, the result of interest rates being too high, and leaving desired saving greater than desired dissaving will be that households won't be able to sell labor and other resources. Households will earn less income than desired.

In this scenario, the problem is that interest rates are too high too coordinate the decisions of households and the solution is a lower interest rate, signaling households to expand consumption expenditure. While this may include some households borrowing more, going further into debt, and consuming beyond their incomes, it can also involve other households paying down their debts more slowly. They are reducing their "leverage," but less rapidly. Of course, they could go so far as to stop, and leave their total indebtedness the same. Perhaps more importantly, it signals still other households to reduce their saving. They increase consumption but they obtain to money to pay for that consumption from current income. And finally, it signals those households that are dissaving by collecting on old loans to do so at a more rapid rate. These increases in consumption result in less saving and more dissaving, bring the two into balance. The demand for consumer goods expands, and so, firms demand more resources--labor, land, and capital, to produce them. At the new, lower, level of interest rates, households' decisions to provide resources to earn incomes, and then to consume, to save or dissave, are coordinated. Their plans are consistent.

Again, there are complications due to income effects. The lower interest rates reduce the interest incomes of creditor households. The lower incomes likely result in lower consumption. However, debtor households have more income remaining after their interest payments, and so can expand consumption.

Further, the changes in intereset rates may impact work effort. While the notion that households that are saving will work less (and so, enjoy more leisure) because of the lower benefit of saving is implausible. However, less work effort by households who can borrow to obtain consumer goods is plausible. More importantly, the income effect on indebted households whose interest payments are reduced may result in less work effort. On the other hand, that retirees living on interest income might go back to work to maintain consumption is plausible, which would result in greater resource supplies and an increased ability to produce consumer goods.

If there is a situation where households are saving and not borrowing, and consumer expenditures are low, such that households have difficulty in finding employment of resources, like labor, it is quite posssible that the problem is that interest rates are too high and consumption is too low. While it is certainly possible that people could be choosing to save more and dissave less because there is "too much" debt, meaning either debtors are worried about honoring their debts or creditors are worried about collecting, that doesn't mean that consumption in aggregate must fall. Nor does it mean that consumption in aggregate should fall. It simply means that perhaps some households should consume less, and other households consume more.

In conclusion, it is a mistake to ignore the important role of increased consumer expenditure in bringing a depressed economy to recovery. Complaints about excessive consumption and debt in the past "causing" the problem are wrongheaded. Perhaps the market clearing interest rate is lower now than it would have been if no one had borrowed in the past and current levels of consumer debt where lower. But that is hardly an argument for keeping interest rates above market clearing levels. It is the lower market interest rates that keep saving and dissaving in balance, and allow those households that are in debt to earn incomes and pay down their debts. While some households may choose to borrow more, other households can simply save less out of current income. And further, those households that had saved funds in the past, and accumulated wealth, can now use that wealth to fund consumption. Those households can act in a way consistent with the principle that the purpose of production is consumption, if not now, then in the future. And the future is now.

Finally, how does this tie into monetary disequilibrium? It is simple. In the absence of monetary disequilibrium, for a household to save, it must lend (or purchase some other asset.) For a household to dissave, it must somehow obtain the money. It must borrow (or sell some other type of asset.) If saving and dissaving are the same as lending and borrowing, then the interest rate that clears credit markets keeps saving and dissaving equal. (Similarly, the prices of other assets balances the purchases of savers and the sales of dissavers.) However, if households can save by accumulating money balances, or household can dissave by spending down previously accumulated money balances, then market interest rates that clear the market for loans do not necessality keep saving and dissaving in balance.

Further, if banks (and especially a central bank) can fund loans with newly created money, and people will accept that money in exchange for consumer goods even if they do not intend to hold that money but rather spend it, then again, it is possible that the interest rate that keeps the supply and demand for credit in balance will not balance saving and dissaving.

If the quantity of money is equal to the demand to hold money, then the interest rate that clears credit markets keeps desired saving and dissaving in balance. If not, the economy is out of equilibrium. While it is possible to simply say--keep the quantity of money in balance with the demand to hold money, fixing that problem will at some times result in lower interest rates and increased consumer expenditures. Increased consumer expenditures is sometimes what is needed to generate economic recovery. And that should be no surprise. Because the purpose of production is consumption. Or, at least, it should be.

A Principle of Macroeconomics: Consumption is the Purpose of Production

I have always said that the most important principle of macroeconomics is scarcity. There are not enough resources (land, labor, and capital) to produce enough goods and services (consumer goods and services, capital goods, and government goods and services,) to achieve everyone's goals.

Scarcity is important because it implies that "overproduction" is not a plausible explanation for recession, and that overproduction of some goods should always be understood as implying the under production of other, more valuable goods. While there may be a "general glut" of goods, the problem is some kind of coordination failure rather than too much production of everything. Increasing the productive capacity of the economy--the supplies of resources like land, labor, and capital and the enhancement of resource productivity--is a "good" thing, and the key issue is the allocation of resources to produce the most valuable goods and services.

However, a more fundamental principle of macroeconomics is that the purpose of production is consumption. This principle is worth emphasizing because some criticisms of Keynesian economics by free market economists go too far in dismissing the importance of consumer expenditure for the economy. Production by firms in consumer goods industries is driven by expectations of consumer expenditures in the near future. And the production of many intermediate goods--materials and partially finished goods--while directly driven by expectations of purchases by other firms in the near future, are indirectly driven by expected future consumer expenditures. Since firms will not produce what they do not expect sell, expected consumer expenditures are important in determining both output and employment.

It is not only productive capacity, or "supply" that drives production, employment, and income, it is also expenditure on that productive capacity, or "demand." Both supply and demand are important.

Consider, then, the principle that the purpose of production is consumption. It is not a fact about the world, but rather a judgement about what economic activity should be about. For Robinson Crusoe, alone on this island, the reason he catches fish in the lagoon is to eat the fish. He produces in order to consume. In a social order, including a market order, people produce goods and services for other people to consume, and they consume goods and services that other people produce. If Robinson Crusoe isn't alone, but rather there is a group of people on the desert island, working as a team, it still is clear. They divide up various tasks necessary for survival (produce) in order to obtain the goods and services (food, and shelter) they want (consume.)

However, in a market system, people directly provide resources for sale to others, who use those resources to produce goods and services, in order to sell products to others. They sell these resources and products for money, and then use that money to purchase goods and services. What appears so obvious with Robinson Crusoe alone on his island, or even an isolated team working together, can become muddied in a market economic system. But still, the purpose of production is consumption.

Adam Smith's metaphor of the invisible hand suggests even if the people in a market economic order fail to see that the purpose of their production is consumption, prices should create signals and incentives that coordinate their activities so that their production is directed towards consumption. For example, someone may think that they work to accumulate wealth, but some prices will adjust to a level where their efforts to accumulate wealth become consistent with the purpose of production--the consumption of goods and services.

For the most part, there is no problem at all. People provide resources to others, selling those resources to earn incomes like rents, wages, and interest. Firms use those resources to produce consumer goods and services, capital goods, or government goods and services, to sell them, and receive a revenue that covers their expenses and generates a profit. The profit is income to the owners of the firms, and so the value of the output produced generates a matching income to those providing resources, including the owners of the firms.

For the most part, the reason households want to earn income is consumption, buying consumer goods and services. So while people directly provide resources to firms is to earn income, and the reason firms use the resources to produce goods and services is to pay for the resources and earn profit, people do this mostly to spend the income they earn on consumer goods and services. The provision of resources and the production of goods and services is mostly being directed towards consumption. For the most part, the market economic system creates a flow of employment of resources, production of goods and services, and expenditures on those goods and services consistent with the basic principle that the purpose of production is consumption.

Usually, I think about the economy without government, but explaining how production gets directed towards the provision of government goods and services rather than consumer goods and services is simple. For the most part, governments fund their purchases of resources (like labor) and government goods and services by taxation. Those earning incomes pay taxes to the government. This reduces their disposable income (after tax income) and so their ability to purchase consumer goods and services. The government hires workers and purchases various goods and services. Sadly, this reduces the capacity of the private sector to produce goods and services, which matches the reduction in the ability of households to buy consumer goods and services. (What about budget deficits and budget surpluses? That must wait a bit. )

What about saving? Saving is disposable income less consumption. It is that part of income not paid in taxes or spent on consumer goods and services. If the purpose of production is consumption, does that make saving "bad?"

And what about investment? Firms purchase capital goods--machines buildings and equipment. And, the resources provided by households to firms--the land, labor, and capital--are partly used to produce capital goods. Is the production of capital goods inconsistent with the principle that the purpose of production is consumption? Is investment "bad?"

Saving and investment are consistent with the principle that the purpose of production is consumption to the degree that households save in order to fund future consumption and firms invest in order to produce consumer goods in the future. The key question then, is how (or if) the market process generates prices that create the signals and incentives that cause households to save in order to consume in the future and firms to invest in order to produce consumer goods in the future.

If those prices are not at the right level to provide the correct signals and incentives, it is possible that consumption is too low. If consumption is expected to remain too low in the near future, then the production of consumer goods will likely be too low as well. In that situation, recovery requires expectations of increased consumer expenditure and an increase in the production of consumer goods.

Free market economists who denigrate the need to expand consumption expenditure and insist that somehow, all problems will be solved by an increase in the productive capacity of the economy--greater supplies of land, labor, and capital--are failing to take into account this key principle of macroeconomics--the purpose of production is consumption.