Interest Rates and Investment

Scott Sumner recently responded to a question from a commenter.  Dustin asked:

"An elementary question on the topic of interest rates that I’ve been unable to resolve via google:   Regarding Fed actions, I understand that reduced interest rates are thought to be expansionary because the resulting decrease in cost of capital induces greater investment. But I also understand that reduced interest rates are thought to be contractionary because the resulting decrease in opportunity cost of holding money increases demand for money.

One? Neither? Both? Little of each? Depends?"

Sumner claimed that it was difficult to answer.   He doubted whether most macroeconomists could give a sensible answer.   He made a remarkable claim:

"It’s not at all clear that lower interest rates boost investment (never reason from a price change.)  And even if they did boost investment it is not at all clear that they would boost GDP."

(On the other hand, he immediately followed that with the statement that open market purchases reduce short term nominal interest rates and boost nominal GDP.)

David Glasner found Sumner's response puzzling and accused Sumner of confusing a change in demand with a change in quantity demanded. 

The solution to that puzzle is simple.   Sumner has recently been drawing supply and demand diagrams for base money with 1/P on the vertical axis. Patinkin did the same ages ago.  A change in the interest rate shifts that demand curve. A change in the price level is a movement along the curve.

And so, if  we consider an exogenous decrease in the interest rate, the demand for money curve shifts to the right.  The new equilibrium price level is lower.   Given real output, that implies lower nominal GDP.

Most economists who teach introductory macro (as opposed to Macroeconomists, I suppose,) would deal with the question easily.   I would use it as an opportunity to discuss the difference between a change in demand and a change in quantity demanded using a Keynesian money market diagram–with the interest rate on the vertical axis.  In other words, I would answer the question much like Glasner.

If the quantity of money is given, and starting at equilibrium, a lower interest rate leads to a shortage of money. Those short on money sell securities, forcing the interest rate back up. The lower interest rate that might raise investment and nominal GDP is impossible. Unless of course, the quantity of money increased.

Now, consider a more classical framework. An increase in the supply of saving results in a lower interest rate.  At the old interest rate, desired saving is greater than desired investment.   The lower interest rate causes the quantity of saving supplied to decrease and the quantity of investment demanded to increase, making them again equal.  There is no direct impact on nominal GDP.   Nominal and real consumption decrease and nominal and real investment increase.  

However, this lower interest rate that coordinates saving and investment also raises the demand to hold money.   Sumner's (and Patinkin's) curve shifts right.  If the price level doesn't fall immediately, due to sticky prices (including wages,) the economy goes into recession. That could very well reduce investment (and saving, for that matter.) It also reduces the demand for money. (Sumner’s and Patinkin's curve shifts back left due to lower real income.)
 
In the long run, the price level falls. Real output recovers, and in the end, the interest rate is lower, real saving and real investment are both higher, but nominal GDP is lower.   Real and nominal consumption are both lower, but nominal investment is ambiguous.

Rather than thinking about a coordinating change in interest rates, we could think of interest rates being lowered through a price ceiling. The quantity of saving supplied decreases and quantity of investment demanded increases. The short side prevails. People are saving less and consuming more. Investment falls to match the quantity of saving supplied. No change in nominal GDP.   Real and nominal consumption are higher.   Real and nominal investment are lower.

The demand for money increases as before   The Sumner/Patinkin demand curve shifts right.  Some of the frustrated savers just accumulate money balances since they no longer find it attractive to fund investment by purchasing new debt and equity.    The economy goes into recession. This reduces real output and desired saving and investment. But, in the long run, the price level falls.

Given the price ceiling on “the” interest rate, we end up with more real consumption and less real investment than the start.   Nominal GDP is lower.   Nominal investment is lower, but nominal consumption is ambiguous.

But, of course, Sumner's real point is that an expansionary monetary policy involves an increase in the quantity of money.   It is not simply a lower interest rate generated by households saving more or tighter regulations on usury.

Is a lower interest rate expansionary?   As Yeager always would say, it depends on what caused it. 

How Important Is Shadow Banking?

During the great Williamson internet debate on purportedly deflationary quantitative easing, Nick Rowe mentioned in passing that he didn't understand Izabella Kaminska.   Scott Sumner wrote a post about how macroeconomists have views so different that they are in effect speaking different languages.   He linked to Nick's remark, using Kaminska as an example of someone doing macro that he doesn't understand.  

How was Kaminska relevant?   She has also argued that quantitative easing is deflationary, though not for the same reasons as Williamson.   It rather has to do with the Fed purchasing safe collateral, which interferes with the operation of the shadow banking system.   

Market Monetarists frame quantitative easing as a means of increasing the growth path of nominal GDP.     I think it is fair to say that all Market Monetarists believe that the level of nominal GDP could reach any target without there being a shadow banking system.   And further, that the real economy could survive without a shadow bank system.

On the other hand, I suspect there is more controversy as to whether the shadow banking system adds any value.   I, at least, suspect that it is at best a work around various undesirable banking regulations.   An appropriate deregulation of banking would result in the end of shadow banking and an enhancement of social welfare.  At worst, shadow banking is a net loss to the economy.

Of course, there are many people whose private interests are closely tied to shadow banking.   Kaminska covers them, and I think she may be too influenced by their special pleading.

Still, I think there is a fundamental intellectual error, very common among noneconomists.    It is the distinction between the nominal and the real.    A high level of nominal GDP (or price level) may imply a large nominal credit sector, but is  quite consistent with a small real credit sector.    Failure to make this distinction is sometimes called the money illusion.  That is the significance of Scott Sumner's claim that Zimbabwe proves that it is always possible for a central bank to generate inflation.   More to the point, it is always possible for a central bank to generate a higher level of nominal GDP.   Having a shadow banking system operating as it did in 2006 might be necessary for a full recovery of the real incomes of shadow bankers, but it is not necessary to return nominal GDP to the growth path of the Great Moderation.

Suppose all payments were made with sacks of gold coins.   The nominal interest rate on the coins is zero (and there are heavy storage costs.)   The government has a national debt and funds part of it with treasury bills.    Financial firms and other large businesses begin to hold treasury bills rather than sacks of gold.   The bills coming due every week or so provide extra cash receipts to cover needed expenditures.  

From the point of view of the firms holding the bills, they are saving a bit on their storage costs.   They earn interest on the T-bills rather than nothing on the sacks of gold.   Assuming the government has a modest national debt and is fiscally responsible, there is little credit risk.   And since the bills are claims to gold, the real risk is approximately the same as holding the sacks of gold.

From the point of view of society, the reduction in the demand for gold results in a slightly higher price level and some transitional inflation.   Some resources that would have been used to mine gold instead produce other consumer and capital goods.   And some of the gold that made up the coins now provides services in circuitry, dentistry, and as lovely jewelry.  

The government  will also benefit by funding the national debt at a slightly lower interest rate.   This will allow for slightly more government services or, better yet, lower taxes.   Since all plausible taxes distort, this further enhances welfare.

Private and social benefits.     Of course, those who are unable to economize on their cash balances suffer a capital loss due to the transitory inflation.   It isn't all benefit and no cost.

The benefits of using Treasury bills as a substitute for money is greatly enhanced by the development of a secondary market.   Rather than only purchasing new issues and waiting until the bills mature, cash balances can be used to purchase the T-bills and when cash is needed, the T-bills can be sold.   Of course, each firm using this technique bears transactions costs--they hire traders who are soon picking maturities and even buying and selling to try to profit from slight moves in the prices of the T-bills.   There is a bid-ask spread, which represents the transactions costs for those making the market.    These costs are traded off against the cost of storing the gold coins and the opportunity cost of the interest foregone.

But the private benefits and the social benefits are at least loosely aligned.

Suppose that a sudden massive loss in trust in the market makers causes the use of Treasury bills as money substitute to be much less attractive.    The traders on the secondary market would face disaster.     Instead of constant transactions as payments are received and then used to purchase T-bills and then sales of T-bills to fund purchases, there would be little activity.   The market makers would obviously suffer.  Some of those who had been managing their employers cash balances could even be laid off!

However, there would also be adverse macroeconomic consequences.   The demand for gold coins would expand.  If wages, and perhaps other prices, were sticky, then the increase in the demand for gold coins would result in lower output and employment.   And while a sufficiently lower price level would result in an adequate real quantity of gold coins, the increase in the real burden of private debt would be disruptive.   This would include a higher real government debt.  Not only must the government fund a higher real debt, it must do so without being able to sell T-bills as a substitute for money.  This would require a reduction in the provision of government services or higher distortionary taxes.

The private disaster faced by those trading the T-bills would be matched by a social disaster.   What can be done to recover confidence in the traders, allow them regain their livelihoods, and at the same time, allow aggregate demand and real output to recover?   The recovery of prices would alleviate the pressure on private debtors as well as reverse the increase in real government debt.

Leaving aside the gold, the trading off of interest and transactions costs was worked out by Tobin years ago.   Something that all monetary economists learn early on.

Now, suppose that rather than sacks of gold coins, government-issued paper currency is used as money.   Because a variety of denominations can be issued, including very large denominations, storage costs are insignificant.  Instead, it is simply a matter of trading off transactions costs and interest.   Otherwise, the logic of holding T-bills rather than paper currency is little different from sacks of gold coins from the private perspective.  

But the social point of view is much different.   The paper money is cheap to print and has no other use than money.   The ability to reduce balances of paper currency by trading T-bills provides no social benefit.   If the quantity of paper currency is assumed to track that of the gold coins, then there would be real capital losses due to inflation for those who cannot economize on their holdings of paper currency.  

But that is not necessary.   Instead, the quantity of currency can be reduced to maintain its purchasing power.   In other words, as the demand to hold paper currency falls, the central bank/treasury can reduce the quantity of paper currency   To do so, the central bank would make open market sales.   Alternatively, the treasury funds more of the national debt with T- bills and less with paper currency.

Once these adjustments are made, then there are no social benefits at all.   The firms using T-bills as a money substitute have employees to manage their trades.   There are firms making markets in the T-bills.   While all of these transactions costs are offset by private benefits--reduction in interest forgone, there are no social benefits at all.   All those financial traders are being pulled away from the production of useful goods and services.   There are no savings on the national debt.   Rather than funding it at zero interest with currency, it is necessary to pay interest on the T-bills.   This implies fewer government services or somewhat higher distortionary taxation.

Now, let us suppose that there is a loss of confidence in the market makers and there is much less willingness to use T-bills as a money substitute.   The demand for paper currency rises.   If the quantity remained fixed, or grew too little, the various social calamities described above would still occur.  However, it is possible to increase to the quantity of paper money as much as needed.   The central bank purchases T-bills.   The T-bills no longer held as money substitutes are now being held by the central bank.   Those who would have held the T-bills are instead holding paper currency.   

Unfortunately for those who traded the T-bills, they still suffer a private calamity.    And all of those now holding currency can look back at the interest they had earned when they could trust the T-bill traders.   A journalist who had been covering them might be quite focused on their private disaster.   Open market purchases?  What good will that do them?    The T-bills that they would have been trading over and over would just sit idle at the central bank (or be destroyed by the treasury.)

But there is more liquidity than before.   And if the quantity of money rises to meet the demand, there is no need for a reduction in spending on output or prices. Further, social costs are reduced.  The government is funding more of the national debt with zero-interest currency.   There is no need to mine the paper money out of the ground or pull it out of alternative uses like jewelry.   And, all of those T-bill traders can find some more productive work.

Of course, in the real world, bank deposits play the role of paper currency for most purposes.   And a loss in confidence in those trading T-bills was not a major factor in 2008.   The demand for T-bills has expanded greatly.   It was rather the more exotic money market instruments cooked up in an effort to enhance the yield earned by those managing cash balances that flopped.    But there is no gold standard.    It is not at all clear that shifting business from the conventional banking system to the shadow banking system provides any social benefit.    On the contrary, it is quite possible that shifting back the other way was on net beneficial.   But just not to those in the shadow banking industry.
    

Private Money and "Quantitative Easing."

Suppose an single bank in a competitive banking system wanted to expand its lending, perhaps by holding a larger portfolio of bonds.    It would need to obtain funding.   In perfect competition, it would pay the going interest rate on deposits.   It would expand its balance sheet until the marginal cost of providing intermediation services equals to interest margin.

However, I never think in terms of perfect competition.   With imperfect competition, an individual bank expanding its balance sheet would both charge less on loans and pay more on deposits.   The interest rate margin is driven down as the marginal cost of providing intermediation services rises.   When marginal revenue equals marginal cost, profits are maximized.

To me, Williamson's account of quantitative easing is similar.   A central bank wanting to expand its portfolio of long term bonds, perhaps because it wants to drive down the yield on them, must provide a higher yield on its liabilities.   Of course, a single bank is mostly seeking to gain market share at the expense of other banks offering very similar liabilities.   A central bank in a closed economy is competing with other sorts of assets, and so the liquidity premium on its liabilities are central.

What about deflation?

Consider Hayek's model of  banks issuing private currency.    Unlike a conventional banking system where each bank accepts the other banks' monetary liabilities for deposit at par and settle net clearing balances, Hayek's system had each bank's monetary liabilities float.   He also emphasized a scenario where all the banks seek to stabilize the purchasing power of their monetary liabilities.   In other words, the price level in terms of each bank's money would be  stable.    Perhaps because the private and competitive issue of deposits is conventional, Hayek at least seemed to emphasize the issue of banknotes--hand-to-hand currency.   Still, given this picture of the monetary order, any bank could expand it lending--undertake quantitative easing--by paying a higher nominal interest rate on deposits, just as would occur in a more conventional banking system.

Interestingly, Benjamin Klein described the same institutional order as Hayek, but he emphasized the return each bank would provide on hand-to-hand currency by generating inflation or deflation.   From that perspective, a bank wanting to expand its asset portfolio would need to provide a increased yield on its currency.     A bank would need to lower the inflation rate.   In other words, a bank wanting to expand its asset portfolio would generate a higher deflation rate for the currency it issues.

How could a bank actually implement the policy?   Obviously, it would announce and advertise its new policy, generate added demand for its liabilities, and purchase the assets it wants.    Of course, it would need to adjust its policy to generate the promised rate of deflation.   

Consider a bank paying an increased nominal interest rate on deposits.   We could imagine the bank just adding funds to deposit accounts.   It would hope that its customers would notice this occurrence, and come to expect a higher nominal interest rate.   But what bank would do that?   They tell their customers that they are paying a higher interest rate and would advertise what they are doing.

Consider then a central bank.   If it wanted to expand the size of its balance sheet, and it didn't want to pay a higher nominal interest rate on its reserve deposits, it could instead promise a lower inflation rate.    And how would it do that?   Step one would be to promise lower inflation or deflation.

Now, imagine a single bank in a competitive banking system that simply purchases the assets it wants and does nothing to provide funding.   The result would be adverse net clearings.   It would be compelled to take action to pay off its claims at the clearinghouse.   With a Hayek/Klein regime, the result would not be an automatic appreciation of the currency.   On the contrary, the result would be a depreciation of the currency on the interbank exchange.  

And suppose a central bank creates money and buys assets, keeps the interest rate on reserve balances unchanged or even lowers it.  What happens?    Inflation, not deflation.

Finally, suppose a central bank wants to expand its balance sheet, and it promises lower inflation (even to the point of deflation) to raise money demand, and expands its balance sheet beyond that greater demand to hold money and generates inflation.   Suppose it breaks its word?   This, of course, is exactly the problem that concerned Klein.    Why not undertake an inflationary expropriation?

Larry White insists that this is why banks need to issue redeemable banknotes and deposits.   Inflationary default is prohibited by contract.   And for a central bank, James Buchanan always insisted that this is why constitutional restrictions of the issue of money are necessary.

Does Quantitative Easing Cause Deflation?

Steven Williamson developed a model that seems to imply that quantitative easing results in deflation.    Nick Rowe was very critical.  

As Nick and others have pointed out, Williamson showed the weakness of his framing.   Some real world market phenomenon cannot be usefully described by carefully modeling a long run equilibrium.

Williamson's model has an element of truth.   Suppose a central bank wanted to have a large balance sheet.   And further, it wanted to keep nominal interest rates low.   How could it manage that?    All it would need to do is generate expectations of deflation.   This would raise the real interest rate that could be earned on its liabilities for any given nominal interest rate.  That would increase the demand to hold its liabilities.   And so, the central bank could issue more liabilities and hold a larger portfolio of assets.     Why would it want to do that?   Perhaps it wants to funnel more credit into the housing market than private investors consider wise.

None of this is news to Market Monetarists.   But it has a bit of a  "through the looking glass" aspect, because Market Monetarists are always making these arguments in reverse.   Sumner is constantly arguing that low expected inflation results in a high demand for base money, and it is either explicitly or implicitly considered a bad thing.   In Boom and Bust Banking,  Jeff Hummel's contribution is a long attack on what appears to be an effort by the Fed to expand its balance sheet so that it can allocate credit.     The key complaint is the payment of interest on reserves.

So, Market Monetarists would say that trying to generate a large balance sheet for the central bank should be avoided.   Paying interest on reserve balances tends to raise the demand for central bank reserves, which we recognize means that a higher quantity of base money would be needed for macroeconomic equilibrium.   The inference that Market Monetarists would draw is that the interest rate on reserves should be low, zero, or negative.     We don't see such a low interest rate as valuable in and of itself, and so do not favor generating deflation to make the low interest rate consistent with long run equilibrium.  Quite the contrary, we sometimes predict and perhaps just hope that a recovery of spending on output would allow credit markets to clear at higher real and nominal interest rates, including any interest rate paid on reserves.   If anything, the thrust of Market Monetarist arguments is that one reason to target a more rapid trend growth rate of nominal GDP is to generate slightly higher nominal interest rates and a smaller equilibrium balance sheet for the central bank.  

Why have Market Monetarists supported quantitative easing?    The reason is to raise spending on output--nominal GDP.    If the current growth path of nominal GDP is counted as an equilibrium, then the point is to generate a disequilibrium--an excess supply of base money-- that will be cleared up through an increase in the demand for nominal base money balances by an increase in spending on output--a higher growth path of prices, a higher growth path of real output, or some of both.  

Nick Rowe finally emphasized this point, after it was pointed to by Robert Murphy.  Williamson has the central bank seeking to have a large balance sheet in real terms, which must be done by making base money more attractive to hold.   Paying higher nominal interest rates on reserves, or given whatever interest rate is paid, generating expectations of lower inflation, increase the real demand to hold base money balances.   To the degree that quantitative easing is supposed to generate a higher growth path of for the price level, the goal is not to raise the central bank's balance sheet in real terms.   The higher nominal quantity of base money is supposed to be held in the long run because the higher growth path of prices reduces real balances back to equilibrium.

However, pretty much all the Market Monetarists have been more and more inclined to see the current level of base money as more than adequate.   (And how is that different than excessive?)   The problem is the target.   Creating large amounts of base money that will be soon removed has little effect on spending on output.     If the Fed wants more spending on output, it needs to target a higher growth path for nominal GDP.    Lower unemployment on the condition that inflation doesn't rise above 2.5% in the medium run just doesn't make it.

Oddly enough, the target is implicit in Williamson's framing too.   If the "target" were for the central bank to have a large "real" balance sheet and keep nominal interest rates low, then it must generate expectations of deflation.      The problem would be with this odd target.

And, of course, there is Williamson's odd notion that this would somehow actually result in goods and services being exchanged at progressively lower prices.

Efficiency Wage? It Doesn't Make Sense

Miles Kimball wrote an oddly titled post claiming that Janet Yellen is not a "dove" because she knows that the U.S. economy needs some inflation.    The actual post argues that the U.S. economy needs some unemployment.   Yellen supposedly knows the economy needs some unemployment because her husband, George Akerlof, played a key role in developing "efficiency wage" models of unemployment.

Kimball explains the intuition behind the theory well enough.   In a perfectly competitive labor market, with all workers identical and all firms identical, each worker earns the same wage which is equal to the marginal value product of labor.   The market clears, and there is no surplus or shortage of labor.   Any worker who quits one job can immediately find another job.

The "efficiency wage" argument is that a firm will be motivated to pay its workers more than this equilibrium wage.   This will provide each worker an incentive to work for them rather than some other employer.   Such workers, then, will be motivated to work harder for fear of being fired.

With all firms and workers identical, they all think the same way.   The result is a wage above the competitive equilibrium, so that there is a surplus of labor.   The fear of becoming one of the surplus workers motivates each worker to obey orders, work hard, and avoid being fired.

The dual labor market hypotheses is that there are two technologies for producing goods.  One is the low supervision technology.   Some firms use that technology and pay their workers a high wage.   The other technology is the high supervision technology.   The firms using that technology pay their workers a low wage.    The low supervision technology is only possible because employees fear being fired for not working hard.  If they are fired, then they might end up with a job using the high supervision technique and earn lower wages.

If all the firms are identical, however, this dual labor market can hardly be stable.   All the firms will want to use the more profitable technology.   This "problem" is solved by just having the unemployed workers do nothing.   I don't really see that as a solution if the high supervision technology is still profitable.   That is, the wage the unemployed workers will accept is less than the marginal value product of labor using the high supervision technology.

Anyway, the solution to this problem is pretty simple.   The same firm can use both technologies.   They use the high supervision/low wage technology for some workers and the low supervision/high wage technology for other workers.    Workers who do a poor job under low supervision lose their high wages and are shifted to high supervision/low wage jobs.   Even if all firms are identical, they can all use this approach.

While this "solution" seems disconnected from reality, where workers are much more likely to be fired than receive pay cuts, the actual labor market institutions that allow this to occur are common.   Workers initially are paid a low wage.   They begin working in a high supervision/low pay job.   After a time, they are shifted to the low supervision/high wage job.    If they fail to perform, then they are fired.   They can get a new job, but it will be with a different firm, and they will start in a job with the high supervision/low wage technology at the other firm.   This provides the motivation to work hard without excessive supervision.

Now, let's suppose that new employees are not all that productive and need extra supervision.   They are paid lower wages.    Then, after a time, they learn the ropes and are more productive for a variety of reasons, one of which is that they need less supervision.   Suppose the employer increases pay after a probationary period.   Workers seek to prove that they are good workers when their pay is low, so that they will pass the probationary test.   Workers who have passed the test and earn higher wages are motivated to do a good job because if they are fired, they will have to start again, proving themselves through probationary work at some other firm.   Workers are paid more or less what they are worth now, and the "problem" that would be solved by "efficiency wages" never exists.

Of course, in a world where the demand for labor is growing faster than the supply of labor, the typical worker earns higher wages.   With all workers identical, they all get the same wage increase.   But in the real world, not all workers are identical.   And so, employers really need to provide different raises to different workers.   This also tends to solve the "problem" that efficiency wages supposedly solves.

Bryan Caplan wrote that the survey data from Bewley suggests that employers do not pay workers more so that they can threaten to fire them if they shirk.   Employers instead describe that as bad management.

In my view, unemployment of labor is a disequilibrium phenomenon.   If all employers and employees were the same, and they always produced the same amounts of the same things, then I think it likely that the unemployment rate would be zero.   That is, unless there is some market intervention, like a minimum wage or universal unionism, that pushed wages above the market clearing level.

That said, a monetary regime that tries to drive the unemployment rate down to zero in a real world dynamic economy, is likely to result in a hyperinflationary disaster.   If the reason Yellen will avoid such errors is because of wrongheaded efficiency wage theories of unemployment--well, better to do the right thing for the wrong reason than to do the wrong thing.

Monopsonistic Competition

Don Boudreaux has been arguing that monopsony cannot be an important factor in unskilled labor markets because if it were, there would be profit opportunities from starting a new business that employs unskilled labor.   If there is no monopsony in those markets, then a minimum wage would tend to reduce the employment of unskilled labor.   Since destroying the jobs of unskilled workers is a bad thing, Boudreaux considers this a good argument against the minimum wage.

I don't favor a minimum wage and I think Boudreaux's argument has an element of truth.  However, when reading it, I began to think about monopolistic competition.   In long run equilibrium, there is no profit and no incentive for further entry.   Price is equal to average cost.   But price still exceeds marginal cost.   The downward sloping demand curve for each firm results in a marginal revenue less than price.   The profit maximum, which happens to be a break even point, is where marginal revenue equals marginal cost.   Price and average cost are both greater than marginal cost.    With a U-shaped long run cost curve, that makes output less than the level that would minimize long run average costs.   Each firm has "excess capacity."

Can the same kind of reasoning apply to monopsony?   The firms face an upward sloping supply of labor function.   If they pay all of their workers more, then more workers will be willing to work for the firm.   This makes the marginal cost of labor greater than the wage.   The increase in wages that must be paid to the additional worker is an added cost, but the added wages paid to all of those workers who would have being willing to work at the existing wage is an added cost as well.  

The firm maximizes profit where the marginal revenue product of labor is equal to the marginal cost of labor.   The marginal cost of labor is greater than the wage.   The marginal revenue product of labor is also greater than the wage.     This implies that hiring another worker at the existing wage would add to profit.    But paying more to all the workers so that another worker will come will reduce profit.

This might suggest that entering the industry would be profitable.   However, profits depend on revenue and total cost, or equivalently, price and average cost.   Does the fact that the wage is less than the marginal cost of labor and the marginal revenue product of labor, have the implication that average cost is less than price?    The wage is something that impacts average cost.

Still, consider the following simple scenario.   Workers walk to their jobs.   The firms are distributed across the landscape.     At a low wage, only the workers closest to a firm will choose to work there.   At a higher wage, workers a bit further off will work at the firm.   Each firm faces an upward sloping supply curve for labor due to geography.   This results in monopsony.

Suppose all the firms are profitable.   Entry occurs.   The firms are bit more crowded across the landscape.   The typical worker is closer to a firm.    Still, each firm faces an upward sloping supply curve, and maximizes profit where the marginal revenue product of labor equals the marginal cost of labor.   However, entry continues until the price is equal to average cost and there are no more profits.  

As with the simple monopolistic competition model, there are "too many" firms.  Here, each firm is paying too little rather than charging too much.   The offsetting benefit of monopolistic competition, the added variety of products,  is here represented by having more households having more convenient places of employment--closer to home.   The same would be possible with monopolistic competition, more firms would make it possible for more households to have shops closer to home.

A minimum wage, then, would result in fewer firms, each operating at a larger, more efficient scale, hiring more workers and paying them more.   Shifting to this new equilibrium would involve transitional losses for all firms and failure for some.   The stronger firms survive, face less competition, and are able to expand to a more efficient scale.   Some of the workers have to travel further to work because there are fewer places of employment.

Anyway, it seems possible.

As I have explained before, there is a range of minimum wages that would expand employment in a monopsonistic  firm.   A minimum wage at the going monopsony wage leaves  a shortage.   Actual employment is supply constrained.   As the minimum wage rises, quantity of labor supplied rises, and firms hire the extra workers.   At some point a maximum employment is reached and there is no shortage of labor.   The minimum wage equals the marginal revenue product of labor.   Increasing the minimum wage above that level results in the firm reducing its desired hires.   Now employment is demand constrained.   At some point employment matches what would have been provided by the monopsonist, though at a lower wage.  Of course, there is a much larger range, going to infinitely high, that would reduce employment from what the wage-setting, profit maximizing monopsonist would choose.  

Having the political system set a different minimum wage for each firm is unrealistic.   Setting a single minimum wage for all firms will almost certainly result in a minimum wage that raises employment in some monopsonistic firms and lowers it in others.   And, of course, those firms where monopsony is irrelevant, or even appears irrelevant to the employers, would have a straightforward negative employment effect due to the minimum wage.

Interestingly, a monopsonistic labor market is in shortage.   The marginal revenue product of labor is greater than the wage.   This creates a motivation for firms to keep their employees happy.   When employees leave, employers are anxious to replace them.   

Further, if the supply of labor increases, there is an immediate incentive to take on more workers.   They will add to profit!

Of course,  the firms will have an incentive to lower wages in response to an increase in the supply of labor.   Now there is an interesting empirical test.   Do firms that receive a resume respond with a new compensation schedule of lower pay for everyone?

If the demand for labor is rising faster than the supply, the equilibrium monoponistic wage will be rising too.   And so, a more rapid increase in the supply of labor would just result in slower wage increases.   Which is, of course, exactly what would be observed in a competitive labor market. 

That is the first test I would use when considering a minimum wage.   Is the market in question in shortage?   Are all those workers who want to work employed?   Do those workers not employed say that the problem is excessively low wages and they would rather stay home?    If a labor market is demand constrained, with unemployed workers desiring a job at the going wage, monopsony is not likely to be a problem.    

Romer's Lecture on Monetary Policy

Christina Romer has an interesting lecture on monetary policy.

On the bright side she again advocates nominal GDP level targeting, both as a solution for the current crisis and a long term regime.

She also explains how the shift in monetary policy in the Great Depression spurred the recovery of 1933.    In fact, it seemed she just covered ground that Scott Sumner covered years ago.

Less happily, she advocates greater bank regulation.   On the other hand, increased capital requirements are one of the least bad approaches--at least if banks can "use" their capital cushions when losses develop.

Worse, she wants central banks to try to pop asset bubbles.     My view is that the monetary authority should focus entirely on expected nominal GDP.    Allowing/causing expected nominal GDP to fall in order to cause asset prices to fall towards what the monetary authority thinks is the proper mistake is malpractice.

HT Marcus Nunes.

Government Default and Financial Crisis

There have been claims that a world financial crisis is possible if  the U.S. government has any delay paying interest or principle on bonds.   While I have my doubts about that, there is no reason to expect a world financial crisis if the government fails to pay for goods it already has received much less fail to spend money on what Congress has appropriated.     The claim that failure to increase the debt limit creates a threat of world financial crisis is again, dishonest.   What is really happening is that the Obama administration is threatening to cause a world financial crisis by failing to pay interest and principle on the national debt and instead spend that money on other things. 

Now, suppose the Obama Administration carries out this threat.   The debt limit is reached and the treasury just spends appropriated funds as it receives requests for funds.  When they run out of cash,  they just stop making payments.   And if some interest and principle claim show up during that period, then they are not paid.

Some claim that the interest rates the government would have to pay would rise.   This seems plausible enough.   But the next step in the argument is wrong.   The notion that higher interest rates would slow the economy and lead to recession is false.

By purchasing government bonds that the government is selling, the Federal Reserve can keep interest rates on both government bonds and the economy low.   As the government sells new bonds as old bonds are repaid (in an apparent hit or miss fashion,) the yield on the bonds can stay low.   The interest rate on these bonds will only need to rise to head off inflation.   And while that is a very possible scenario, the problem will not be anything like what happens when the Fed increases interest rates by restricting growth in the quantity of money.

Further, it is a mistake to assume that other borrowers would have to pay higher interest rates.   Usually, U.S. government bonds are assumed to be risk free.   Other sorts of bonds have higher interest rates because of default risk.   If the "risk free" interest rate on government bonds should rise, then all of the other interest rates will rise with them, with the "spreads" representing different levels of risk assumed to be constant.   But when the government bonds have higher interest rates because of higher default risk, then this is no longer the correct analysis.   What happens instead is that some of those who were holding government bonds as a "perfectly" safe asset will respond to the greater risk on them by selling them and purchasing other securities that were slightly more risky.   The interest rates on those securities will fall, making it easier, not harder, or the firms issuing those securities to borrow.

Of course, there is another effect.   Those holding short and safe assets like government bonds, would likely respond to the risk of delayed payment by holding money instead.   If the quantity of money fails to expand enough, the resulting liquidity squeeze will tend to raise all interest rates.    But then, that is why the Federal Reserve would need to expand the quantity of money in such a situation.   It can and should supply the extra money that people would want to hold, and so avoid a liquidity crunch.







  

The Fed and Default

The Administration claims that they are too incompetent to prioritize interest and principle on the national debt.   While that is likely a lie, and they are simply threatening to default on U.S. government bonds to coerce fiscal conservatives to let them continue to borrow and spend, there is an alternative.   If the Federal Reserve buys the maturing debt, then those holding the debt are paid off.   The Fed is then left holding debt whose payment is delayed until the Treasury obtains enough cash to pay it off using its "system," presumably first come first serve.

Default on the National Debt.

I think the U.S. government should pay the principle and interest on the national debt.    Failure to do so would be default on the national debt.

The United States has a statutory debt limit.   The U.S. Treasury can only borrow up to a certain limit.   Once that is reached, it cannot borrow more.

If the limit is reached, the current government expenditures will be limited to current government revenues.   That is, the budget must balance.  

Robert Murphy reproduced CBO estimates for 2014, here.

Since the amount of money appropriated by Congress exceeds current revenues by nearly $600 billion, the government would have to spend less than what has been appropriated--about 16 percent less.

President Obama and his supporters in Congress are using the term "default" to mean failure to obtain enough money to spend everything appropriated by Congress.   That is a dishonest.

If the debt limit is reached, then as government bonds come due and the principle paid off, the national debt will fall below the limit.   The government can sell new bonds to raise the funds needed to pay off the next set of bonds that come due.  

However, the interest that is paid on these bonds is a current expenditure of the government.  The net interest is about $250 billion per year, which is approximately 8% of the approximately $3 trillion of government revenues.   The government collects way more current revenue than is needed to cover interest payments. 

So, the government can pay interest and principle on the national debt with no problem.   The cuts in all other government spending would be slightly deeper, a bit more than 18 percent, rather than 16 percent.

Certainly such deep cuts in government spending are no joke.   It is approximately 4% of the total economy.   Of course, that does leave 96 percent of the economy.    And what is sacrificed is the value of the government goods and services that aren't provided.   Normally, I would anticipate that the production of private goods would only gradually expand as resources are freed, and further, if the reduction in government spending is temporary, that increase in private production would never occur.   However, what if the government reduces transfer payments?     Also, I believe the current production of private goods is well below capacity, so there is room for a rapid increase in the production of private goods and services.

What does President Obama and his apologists say to arguments that default isn't necessary?   Mostly, they just repeat their dishonest talking point.   Failure to spend whatever Congress appropriated is defined as "default."

But there have been some arguments.   Supposedly the Treasury is not up to the job of making sure that interest and principle are paid on the national debt.   It is just too complicated.    If that is really true, the Secretary of the Treasury should be fired and President Obama should resign in shame for incompetence.    Just because the Treasury has considered its job to be coming up with the money to cover all appropriated expenditures in the past, does not mean that they shouldn't be prepared to face a hard budget constraint--limit spending to what is available rather than assume an unlimited ability to borrow.

And, of course, the Obama Administration has opposed legislation officially making debt and interest payments a priority.     I heard an administration apologist on the radio already making the argument that interest and principle shouldn't be a priority.    Which is more important, paying the Chinese (interest and principle on the bonds,) or Grandma (social security.)   Cutting social security checks and failing to pay interest and principle on bonds when due is a choice to default.    Of course, Social Security payments are running about $700 billion, so $3 trillion in revenue would be enough to cover those payments as well.  

The bottom line is that if the government fails to pay principle and interest on the national debt, it will be because President Obama decided that is what he wants to do.   It is a policy determination that other sorts of government spending, say on Obamacare or food stamps, is more important.

Some claim that it would still be a default if the government didn't pay all of its bills.    Well, to the degree that the government has already committed to a vendor to purchase a good or service, and especially if it has already received delivery, it does owe the money.   Once a payroll is due, the work has already been done.   That is a debt of sorts.   Of course, when you are running out of money, you need to stop ordering new products.   And it is also when you start implementing furloughs and layoffs.   You stop making commitments to spend money you won't have.

However, appropriations by Congress aren't the same thing as goods and services already purchased and outstanding bills.      I heard on the radio someone argue that if you pay the mortgage and don't pay your utilities, your credit rating will still suffer.

Admittedly, it would be difficult to do without electricity.   But consider the following scenario.    The family made a budget for the year.   They plan to spend all of their income, and use their home equity line of credit to go into debt.    They are careful planners and decide up front to start going to a healthier restaurant once a week rather than the fast food restaurant they had been patronizing.   And they finally get cable TV, with all the bells and whistles.

In the middle of the year, the line of credit is cut off.     They stop going out to eat at the health food restaurant and return to fast food.   Is that a default?    No, not in anyway.   But President Obama is defining government default to be any cut in planned spending.   Suppose they cancel their cable subscription.   Is that a default?   No.   

But suppose they just don't pay the last cable bill because they need to money to make their mortgage payment, including the payment on the home equity line.    Is that a default?   Yes.   And it would hurt their credit rating.

Now, what does the bank collecting their mortgage think about that?   While it would be better for the family to have paid their last cable bill and then cut off the service, maybe skipping the fast food restaurant meal and staying home for dinner, the banker would actually like that they treat the mortgage as a priority.

In my view, failure to raise the money appropriated by Congress that has not actually been spent is not a problem at all.   It is like economizing by purchasing less expensive food at the grocery story and spending less on recreation.    It would be a clear positive from the point of view of bond holders.   This is especially relative to the status quo where President Obama is threating not to pay them even when there is 10 times more money than what is needed to pay them because he wants to spend on his favorite new programs.

Now, if the Treasury were to stiff vendors who had already delivered goods of some types, say jet aircraft and used the savings to maintain spending on other goods where no commitment had been made, that would be bad.   It is like continuing to eat at the health food restaurant while failing to pay the cable bill received for last month's services.   A sign of irresponsibility.     

However, it is still true that if the Treasury won't pay for the jet aircraft already produced and delivered, and the reason is that they needed that money to pay interest and principle on the national debt, that would help reassure those holding the debt.     They have made the debt a priority.

Hummel on Money and Interest

Jeffrey Hummel has a good article about the relationship between money and interest rates.   I think that there is a bit too much emphasis on the thought experiment of a permanent change in the growth rate of the quantity of money.   I have become more and more focused on a situation where the quantity of money is endogenous because the monetary regime targets something else.   Sometimes I focus on the growth path of nominal GDP.  That is because I am very interested in the characteristics of such a regime.   I also think about a target for the inflation rate, because that appears to be a key characteristic of really existing monetary regimes.  

Given these other targets, what happens when there is a temporary increase (or decrease) in the quantity of money?   No longer are we working out the equilibration process of a permanent change in the growth path of the quantity of money.   What happens when the quantity of money rises, and those holding the money expect the increase to be reversed because it is inconsistent with the nominal anchor?

Hummel's argument is very consistent with the Market Monetarist notion that permanent changes in the quantity of money impact spending on output.    Much of the argument that changes in money growth do not impact interest rates very much depends on a prompt impact on spending on output and the consequent change in inflation and real output growth.    It is much less consistent with a simplistic New Keynesian approach where monetary policy is a lower interest rate, which results in higher real consumption and real output, and so an output gap that leads to higher inflation.

It is wrongheaded to combine these two views and say that an expansionary monetary policy will not lower interest rates, and because interest rates don't fall, real expenditure and real output won't rise and so inflation won't rise, and therefore the sum of real output and inflation, nominal GDP growth, will not rise.   There is a contradiction there.   It is the more rapid growth in real output and inflation that eventually reverses any decrease in interest rates, and in the extreme, leave interest rates unchanged despite more rapid money growth.

But if the nominal anchor is such that an increase in the quantity of money must be temporary, and so there will be little or no increase in spending on output and so little or no inflation or additional real growth, then what does the unusually high quantity of money imply for interest rates?

Wallace Neutrality

Miles Kimball has another post on Wallace Neutrality, which is the theoretical argument proving that quantitative easing is not effective.    Kimball explains that the math shows that open market operations can have no effect, given Wallace's assumptions.   The assumptions, however, are highly unrealistic.

Kimball points out that the Wallace result  requires assumptions of  perfect knowledge of the fundamental values of whatever the Fed is purchasing as well as an ability to borrow unlimited funds at the zero-risk interest rate and no concerns regarding risk by the arbitrageurs.   None of that is even close to reality.   Following the convention in financial economics, failure to meet these requirements are "frictions."  To me, frictions sound like small things that slightly gum things up.   However, might it be that assumptions behind an absence of these "frictions" are so far removed from reality that it tells us approximately nothing about the real world?

What I found more interesting was the "intuitive" explanations that depended on the Fed eventually reversing its open market operations.   For example, if there is perfect knowledge of the future equilibrium price of gold, and the Fed creates large amounts of money and buys gold now, this will not impact the price of gold at all.   That is because the Fed will sell all of that gold and reabsorb all of the money in the future, and the price will be back where it was supposed to be.   What happens in the meantime?   "Arbitrage."   Kimball didn't explain the process, but I guess someone will borrow gold and sell it short to the central bank.   That no one is really in a position to sell gold short in unlimited quantities is just a "friction" in the world of Wallace neutrality.

But one hardly needs "Wallace Neutrality" to understand that temporary changes in the quantity of money have little effect on anything.   Krugman's unpublished paper on the issue is probably the best known argument, though we Market Monetarists know that Sumner explained it before Krugman.    It has nothing to do with open market operations.    If the quantity of money doubles this year, with the new money appearing out of thin air, then we would expect that the price level would roughly double.   But suppose all of that money will be sucked away one year later.   Then that would cause the price level to fall back to its initial level.   This is a temporary increase in the quantity of money.   Who would buy a house at twice its current value when it is expected to fall in half in a year or less?   What is going to happen then?   People will largely hold the excess money balances during the period when they are extra high.   The demand for money temporarily rises and velocity temporarily falls enough to offset the temporary increase in the quantity of money.

What is the likely result?  At first pass, the price level will rise immediately when the quantity of money increases, but only enough so that as it returns to its initial level, the rate of deflation will equal the real interest rate.   If the price level rises more, then the deflation will make holding money more attractive than holding other assets.   This motivates the increase in the demand to hold money and the reduction in velocity sufficient to prevent any further temporary increase in the price level.

However, why doesn't Wallace neutrality apply when short and safe interest rates are above the zero nominal bound?   Of course, in new Keynesian models, there is no process by which open market operations cause changes in the policy interest rate.   The policy interest rate is taken as exogenous.   The interest rate is adjusted, and consumption is shifted between now and the future.   The future level of consumption is fixed at the full employment level, and so a lower interest rate increases current consumption and a higher interest rate lowers current consumption.   The Wallace Neutrality result doesn't come into play because there are no open market operations going on at all.   New Keynesian economics is reasoning from a price change.    As Sumner constantly points out, that is not sound economics.

Still, whether Wallace neutrality only works when at least one interest rate hits zero, or supposedly keeps the central bank from ever impacting any interest rate (see Kling here,) it still remains true that quantitative easing, in even massive quantities, will have very little impact if the central bank promises to reverse it.   Suppose the central bank undertook massive quantitative easing but committed to keeping spending on output on its existing growth path.    Would quantitative easing have any effect?   And what would be the point of quantitative easing if not to increase spending on output?

Now, suppose that the central bank would be happy for spending on output to rise, but only if there is no inflation.    In other words, the central bank wants to reduce the output gap with no increase in inflation.   That would have an impact only to the degree this was believed possible.   But those who expect that closing the output gap will resulted in higher inflation (rather than reduced disinflation,) then they would expect that increase in the quantity of money would be temporary.   And so they would be willing to accumulate more money, implying reduced velocity and so little impact on current expenditures.

It is considerations like these that make Market Monetarists insist that if spending on output should increase, then the central bank needs to target an increase in spending on output.   Quantitative easing until labor markets improve unless inflation gets too high is just not very effective.  

Now, if spending on output is targeted, then the proper amount of quantitative easing is whatever it takes.   But the "whatever it takes" is pointless when a central bank creates expectations that it will prevent any increase in spending on output.   Unfortunately, committing to prevent inflation has that effect.

The Money Multiplier

Arnold Kling has a post about whether the money multiplier exists.   Scott Sumner commented.      Sumner points that that the money multiplier exists, because it is simply the ratio of some measure of the quantity of money and the monetary base.     Sumner then presents some simple algebra, so that the money multiplier equals (1+c)/(c+r), where c is the ratio of currency to deposits and r is the ratio of reserves to deposits.   He states that these ratios depend on utility maximization.   

Sumner's claim is true enough, though I think most economists studying banking would use something like maximizing expected profit to relate the demand for reserves by banks to the deposits they supply.    Further, I don't think a the ratio of reserves to deposits is the best framing for the banks' relationship, though of course a ratio  exists between the profit maximizing quantity of deposits and the profit maximizing demand for reserves.   Neither do I think that most people optimize a ratio between currency and checkable deposits.   I know I don't.   I do think that both the demand for currency and deposits are positively related to spending on output.

The paper Kling cites appears to focus more on reserve requirements and emphasizes that a substantial portion of M2 has no reserve requirement.   Their approach assumes that the central bank offsets currency drains, making the quantity of currency endogenous, and instead controls the quantity of reserves.   The reserve requirement then creates a fixed ratio between reserves and bank deposits.    To read Kling's discussion, the purpose of controlling deposits would be to control bank lending.   And so, showing that there is no close relationship between bank lending and reserves proves that there is no money multiplier.   A dollar of additional reserves does not create a more than proportional increase in bank loans.

Kling goes on to argue that the Fed supposedly is impacting the economy by purchasing bonds, which lowers long term interest rates.   He argues that since the Fed's purchases or sales of bonds are so small compared to the world supply and demand for bonds, it can have no more than a minimal impact on world long term interest rates, and so has no impact on anything.    While I think there is an element of truth in Kling's argument, a central bank in a small economy with completely open capital markets would impact spending on output and inflation through changes in the exchange rate.    If the central bank is pegging the exchange rate, then sure enough, it has no effect on much of anything else.

Of course, neither traditional monetarists nor market monetarists were much interested in what, if any, effect  central banks might have on long term interest rates or the quantity of bank loans.   While Sumner has long given up on worrying about any measure of the quantity of money broader than the base, most market monetarists focus on the quantity of the medium of exchange relative to the demand to hold it.   The medium of exchange is made up of a variety of financial instruments, and the day in which most of them were issued by commercial banks is long past.  

Kling expressed surprise that retail mutual money market funds are included in M2.   He says that he thought that M2 was M2.   What would that be?   Currency, checkable deposits, and savings accounts?   I am not really sure.    My concern with M2 was primarily the inclusion of small certificates of deposits.   What sense does that make?    In world where other nominal magnitudes are growing, can a $100,000 limit make any sense?    I had no trouble with the addition of retail money market funds.   As they came into existence, adding them to the measure of the quantity of money made perfect sense.   But how can a $50,000 cut off make sense?   Why not all of them?

Fortunately, MZM has existed for years, and it supposedly included all financial instruments with a zero term to maturity.   No certificates of deposit and all money market mutual funds.   Unfortunately, my personal experience always left me a bit troubled.   My savings account balance is subject to restrictions on withdrawals.   More important, I don't count it as part of my ready money balances.    Further, when I did have a money market mutual fund account, the restrictions on using it were more burdensome than a saving account.   Of course, I am just a small retail customer.

Years ago, Eurodollar accounts and repurchase agreements were included in M3, but both overnight and term instruments were included.   And then, M3 was no longer measured.   Overnight repurchase agreements, which have served as a monetary instrument for years, was never included in M2, but was not added to MZM.    As the shadow banking system developed, repurchase agreements became a progressively larger portion of the quantity of money.   Of course, those held by money market mutual funds were included in MZM indirectly, but any directly held by corporate treasurers or financial institutions were an unmeasured portion of the quantity of money, a portion whose quantity collapsed in 2008.   The Divisia measures of the quantity of money did capture that effect.    The M3 and M4 Divisia measures collapsed during that period.

These other monetary instruments have become more and more entwined with checkable deposits.   The development of sweep accounts has allowed liquid funds to be held, or at least reported as being held, in a money market account, a money market mutual fund or as a repurchase agreement, while always being available to cover checks, or electronic payments.     The existence of sweep accounts is at least partly motivated on the prohibition of interest payments on demand deposits, or in other words, for the transactions accounts held by business customers.   They can earn interest by having excess funds swept into interest bearing accounts.   

However, there is another impact of sweep accounts.   Banks sweep funds out of transactions accounts before they report the quantity to the Fed, and it is that reported quantity that determines the amount of required reserves.   By convincing customers to use sweep accounts, banks can reduce their required reserves to something below what they find it profitable to hold.    Since vault cash counts as reserves, and at least some banks need vault cash to meet the needs of their retail customers, the banks' desired reserve ratio remains positive.   And there is little reason to believe that the banks required reserves were much different.  

Of course, with the payment of interest on reserves, and the very low interest rates on other money market instruments, there is little reason to use sweep accounts to reduce required reserves.   The level of reserves banks find it profitable to hold is much larger than the requirements.   The reserve requirements are ineffective under current conditions.  

Given what amount to scams aimed at getting around unnecessary and undesirable regulation, is there any surprise that reserves have no fixed relationship to incomplete measures of the quantity of money?  

Free banking theorists, like George Selgin, have developed the theory of the precautionary demand for reserves.   It doesn't have a fixed relationship to the quantity of deposits.   Selgin argues that it depends on spending on output.   The argument runs through the volume of gross payments and so the variance of net clearing balances.   In particular, if the demand to hold bank deposits rise, the demand for reserves falls, leading to a lower equilibrium reserve ratio.  Selgin emphasizes the argument that the reduced reserve ratio causes an increase in the quantity of deposits, accommodating the increased demand to hold deposits.

One key element of the status quo that is very different from the regimes Selgin describes is that banks cannot issue hand-to-hand currency.    Holding reserves in the form of vault cash is necessary to meet customers' routine demands for hand-to-hand currency.

Further, consider the role of inter-day overdrafts.     Do banks have to hold sufficient reserve balances to cover all claims, or can they maintain negative balances at the central bank/clearinghouse as long as they are covered later?    That rule will influence the demand for reserves.  

More importantly, if there is a central bank that is targeting the interbank clearing rate, then the incentive to hold reserve balances is greatly reduced.    One reason to hold reserve balances is that if there is a shortage of reserves in the system, excess reserves can be lent at higher interest.  And, of course, banks with a need for reserves in such a scenario avoid high borrowing costs.   They have the reserves they need.

My answer to these issues is not to develop some regulatory scheme that keeps the true measure of the quantity of money proportional to base money.   The tie between base money and the broader monetary aggregates is redeemability.    Those other instruments are redeemable for base money.   While there is no guarantee for any kind of proportional relationship between the aggregates, control over the base is sufficient to prevent an excess supply of the other aggregates.    And what about excess demand?   In the end, base money is part of the quantity of money, and by expanding it enough, decreases in the quantity of other monetary instruments can be offset.

Like Sumner, I think the answer is to a money multiplier that can shift is to adjust the quantity of base money according to the demand to hold it.  Unfortunately, that begs the question of what is the nominal anchor.   If the quantity of base money adjusts to the demand to hold it, it cannot serve as nominal anchor.   In my view, a growth path for spending on output, in particular, nominal GDP, is the least bad approach.

Hall on Interest on Reserves

I was reading Robert Hall's 2013 paper, "The Routes into and out of the Zero Lower Bound."   I found it quite interesting.  I have already commented on his criticism of nominal GDP level targeting here.

Today at lunch, I was struck by the following passage:

With respect to the interest paid on reserves, there seems to be a general failure to appreciate that paying an above-market rate on reserves changes the sign of the effect of a portfolio expansion. Under the traditional policy of paying well below market rates on reserves, banks treated excess reserves as hot potatoes. Every economic principles book describes how, when banks collectively hold excess reserves, the banks expand the economy by lending them out. The process stops only when the demand for deposits rises to the point
that the excess reserves become required reserves and banks are in equilibrium. That process remains at the heart of our explanation of the primary channel of expansionary monetary policy. 

So far so good.

With an interest rate on reserves above the market rate, the process operates in the opposite direction: Banks prefer to hold reserves over other assets, risk adjusted. They protect their reserve holdings rather than trying to foist them on other banks. An expansion of reserves contracts the economy.

I don't really understand this.   An expansion of reserves will contract the economy?    I think the higher interest rate on reserves contracts the economy by raising the demand for base money.   Expanding the quantity of reserves helps satisfy the additional demand.

What could Hall have in mind?

Is this only true when the Fed purchases T-bills?    If T-bills provide more monetary services than reserves for some purposes, then having the Fed buy them could contract the quantity of money services.   And if T-bills have yields below those of reserves, maybe they do provide more monetary services than reserves.   That is at least one reason why they might have such low yields.

But suppose the Fed purchases securities with yields greater than those on reserves?   For example, long term government bonds or mortgage backed securities.   How could that be contractionary?

Anyway, if it is really true that an expansion of reserves contracts the economy when interest rates on reserves are above market rates, then quantitative easing is counter-productive.

Regardless of whether expanding reserves is contractionary, I am all for Hall's solution:

The Fed could halt this drag on the economy by cutting the rate paid on reserves to zero or perhaps -25 basis points.

And I agree with this response to the supposed reason the Fed pays interest on reserves at this time:

The only excuse for not cutting the reserve rate is the belief that short rates would fall and money-market funds would go out of business. This amounts to an accusation that the funds are not smart enough to figure out how to charge their customers for their services. Traditionally, funds imposed charges ranging from 4 to 50 basis points, in the form of deductions from interest paid. A money-market fund using a  floating net asset value can simply impose a modest fee, as do conventional stock and bond funds. The SEC may accelerate this move by requiring all money funds to use floating NAVs.

Sumner on Summers

A real sarcastic gem from Scott Sumner:

"At the opposite extreme is someone like Larry Summers, who worries that low interest rates and a bloated balance sheet might lead to bubbles, and misallocation of investment.  In that case fiscal policy could be “effective.”  That sort of central banker would essentially be holding the economy hostage, much as the GOP radicals in the house are accused of doing.  A central banker with that objective function would intentionally hold NGDP below the optimal path, unless and until the Federal government would assure him or her that the extra NGDP growth would be in the public sector, where (unlike the private sector) the expenditures would not be wasted on foolish projects driven by a bubble mentality.  The Federal government spends money very wisely, especially when under pressure to quickly ramp up investment during temporary slumps in the economy."

So true. 

McCallum on Growth vs. Level Targeting

Bennett McCallum has a short paper on growth vs. level targeting.   He again argues for targeting the growth rate of nominal GDP rather than the level.   To some degree he is criticizing Woodford's proposal to return nominal GDP back to something like the growth path of the Great Moderation.   However, his argument is more general.

It is great to see more new work from McCallum on nominal GDP level targeting.

He emphasizes discretionary and time invariant approaches to policy rules.    He also mentions a purported rule he calls strategically incoherent.   I am not sure I fully understand, but it looks to me that this is exactly the approach that Market Monetarists favor.   Right now, we have to decide where the initial growth path for nominal GDP will commence, and then we stick with it.   This is supposedly incoherent because why don't we start it all up again every period?    Next year, why don't we imagine we have no rule, and we will again choose a new starting point for the growth path.

Suppose we are considering the institution of  very strict gold standard.   In the future, the price of gold will be fixed.   The price next period will equal the price this period which equals the price last period.   Now, at what price do we set this fixed price of gold?   Is it strategically incoherent to use anything other than last period's market price of gold?   I don't think so.   The relative price of gold can easily be impacted by using it as medium of account.   We are instituting a regime.   The logic for choosing a rule initially is not the same as the logic for sticking to the rule.

Anyway, he refers to the literature that suggests that period by period optimization is a bad idea.   And then describes Woodford's approach of time invariant policy as imagining that the policy we follow now was introduced far in the past.  

He then notes that nominal GDP growth rate targeting has results more similar to this time invariant approach while level targeting would close output gaps more quickly,  which is also what would happen with the period by period optimization approach.

What would be so bad about a rule that closes output gaps more rapidly?   McCallum just states that lots of studies suggest that immediately closing output gap is rarely optimal on average.

But why?  The only other thing that could be a cost in this model is deviations of inflation from target.   In other words, if we get the output gap back to zero this period, then this will have a cost of causing inflation to deviate "too much" from target.

Could it really be so simple as the assumption that changes in the inflation rate are bad?

With nominal GDP level targeting, a positive aggregate demand shock will cause higher inflation this period and then lower inflation next period.    With a negative aggregate demand shock, there is lower inflation this period and then higher inflation next period.    What is happening is changes in the price level, or more generally, its growth path, are being reversed.

If it is deviations of inflation from target that is considered bad, then nominal GDP level targeting  would be inferior to nominal GDP growth rate targeting.  On the other hand, if it is changes in the expected value of the price level that cause a problem, then a deviation of inflation from target in the opposite direction is not to add insult to injury, but rather a corrective.

Ignore supply shocks and assume the trend inflation rate is zero.   A price level target for the GDP deflator is 100.   An inflation target is for its rate of change to be zero.    In a perfect world, it stays at 100.   Sadly, there is 1% inflation.   It is now 101.   If the "loss" is inflation, then there is a loss, and if the GDP deflator stays at 101 forever, there is no further loss.

But suppose the "loss" is the deviation of the price level from 100.   If  it stays at 101 forever, then there is an ever continuing loss that is only kept from being infinite by discounting.

If the loss is inflation, then a 1 percent deflation returning the price level to 100 just adds an additional loss to the first one.   A unavoidable 1% inflation plus an additional easily avoidable 1% deflation.   If the loss is the deviation of the price level from target, then the 1 percent deflation returning the price level to 100 limits the duration of the loss to one period.

Of course, this is the simple version of the model.   The studies McCallum refers to presumably use calculations of utility loss from inflation rather than a simple "loss" function.

But to what degree are these utility calculations based on the assumption of Calvo pricing?  That seems to me to put too much weight on an obviously unrealistic model whose only virtue is that it can be used to make calculations of utility in rational expectations models.

If instead, some prices are flexible and others are sticky, reversing the changes in the flexible ones so that the sticky ones don't have to change is desirable.   This reasoning also applies when the sticky prices are those of labor--wages.   And that seems much more plausible.   Rather than keep the price level change and then make wages adjust, it makes much more sense to reverse the price level change so that labor markets clear at the sticky wage levels.

What about supply shocks?   While nominal GDP level targeting is the same as price level targeting when there are no aggregate supply shocks, one of the chief virtues of nominal GDP level targeting is that it does much better than price level targeting when there is a supply shock.

The model McCallum uses has an inflation shock.   It is just a random term at the end of the quasi-Phillips curve.   It seems to me that any such shock would push nominal GDP above target.   A growth rate target would just leave nominal GDP on a new, higher growth path.   In my view, that would be best.   (At least if these price level shocks are really just random and not regime dependent.)   Pushing the price level back down the next period would be pointless.   Nominal GDP level targeting would require a return of nominal GDP to target, and would likely push output below capacity.

However, what these random shocks in the model represent are real microeconomic events that impact both prices and capacity.   Negative covariance is very likely, and so just when the price level is shocked up, real output and capacity are both pushed down.   Any deviation of nominal GDP from target is likely to be small.     Further, to the degree they are temporary, when they end, nominal GDP will return to target with no change in "monetary policy" at all.   It isn't always necessary to cause an output gap to get some disinflation.   When peace breaks out in the Persian Gulf, lower oil prices bring disinflation without a need to cause a recession and output gap.

So, there may be a case for nominal GDP growth targeting as opposed to level targeting, but McCallum didn't make it here.  

AEI on Market Monetarism

The American Enterprise Institute's website has had some excellent posts on monetary policy.   James Pethokoukis has been writing on monetary policy from a Market Monetarist perspective for some time.   He has a series of short posts that allowed several market monetarists to answer some questions about quantitative easing.    The last one is about the charge that quantitative easing is like central planning.   Check the links back to the previous four.

HT David Beckworth

QE Continues

Ryan Avant at the Economist has a good discussion of why quantitative easing has an impact.    It is all about expectations.    It isn't about how many and what type of securities the Fed purchases--how big its balance sheet will be.   It is rather hints about the outcomes for the economy that the Fed wants to acheive.   Market Monetarists, and Avant should be counted as one, want clear communication--a target for the growth path of nominal GDP.    Where does the Fed want spending on output to be, which is, necessarily, how much money income does the Fed want people to earn?   (Unfortunately, Avant, as does Sumner too often, plays to those tied to the status quo, talking about a commitment to full employment and higher inflation, with a mere passing reference to nominal income.)  

Nick Rowe has another in his series of posts about why interest rates are not fundamental to monetary policy.     Rowe has been arguing that New Keynesian models assume full employment in the long run, without there being any mechanism to get there.   In their models, the central bank sets an interest rate, which determines spending now relative to later.   In the model, real spending later is equal to potential output--the full employment level of output.    A lower interest rate now then results in more spending now.   However, if spending later is not tied down, then a lower interest rate now could just mean less spending later.    That a lower interest rate now means more spending now is based upon an assumption rather than any implication of the model. 

While all of this makes sense to me, it seemed to me that it was just about imperfections in New Keynesian modeling strategy.    In the real world, central banks create and destroy money.   Why can't the implications of the quantity of money the central bank creates be included as an assumption in the model, even if that part of the economy is not part of the model?   Sure, calling it "general equilibrium," is a misnomer, but can't partial analysis provide insight?

In this post, Rowe connects his critique to Leijonhufvud's theory of the corridor.   In Rowe's view, as long as most people believe that the economy will bounce back soon, then an interest rate policy will work well enough.   But if people do not believe that the economy will bounce back soon, then a policy based on interest rates can fail.   Leijonhufvud's theory was that the macroeconomy is reasonably stable within a corridor of small fluctuations, tending to revert to full employment.   On the other hand, if the economy is somehow pushed well outside the corridor, it won't return.

Rowe's argument suggests that the problem Leijonhufvud described as the corridor is with the traditional focus of central banks--interest rates.   The New Keynesian insistence that adjustmetns in short term interest rates, and promises about where their time path in the future, are all that is necessary to provide for macroeconomic stability, is mistaken.   It follows from this flaw in their model.   Instead, Rowe suggests that central banks need to emphasize the quantity of money.   It is the quantity of money, and not interest rates, that determines the nominal economy in a monetary economy.    When people sell goods for money and buy goods with money, the quantity of money matters.   

I think Rowe is correct, however, I would go one step further.     It is the nominal anchor that ties down the nominal economy.   A monetary regime that fixes the nominal quantity of money has a nominal anchor, but a poor one.   Of course, Rowe doesn't advocate a fixed quantity of money.  My point is that to provide for macroeconomic stability, a monetary regime must tie down the level of some nominal magnitude.  The price level or spending on output are much better than the quantity of money.

Do these nominal magnitudes require some commitment about the quantity of money?   Not really.   Changes in the quantity of money that are expected to be temporary have little effect on other nominal magnitudes.   Changes in the quantity of money that are perceived as inconsistent with the central bank's goals for other nominal magnitudes will be seen as temporary and so have little effect.  

And this brings us back to Avant's point.   How many bonds or what type of bonds the central bank purchases is not important.   The quantity of money is not important.  What is important is the nominal magnitude the central bank is aiming to achieve.

Taylor and Hall on Nominal GDP Targeting

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

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

What is Hall's framing?

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

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

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

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

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

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

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

What does this imply for nominal interest rates?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

HT Scott Sumner.