Wednesday, October 8, 2014

Salter and Hogan on NGDP Level Targeting

Alex Salter and Thomas Hogan have a working paper that points to problems with a central-bank directed policy of targeting the level of nominal GDP.   The argument is that while such a policy may helpfully stabilize aggregate demand, it will create undesirable consequences for aggregate supply.

I certainly appreciate the work that Salter is doing on Nominal GDP level targeting   I don't find their argument persuasive   Or at least, I think there is a problem with the example they use to argue that divergent expectations between the central bank and market participants will cause problems.

They consider a situation where some shock has pushed nominal GDP below target.   A central bank targeting nominal GDP will seek to return nominal GDP to its previous growth path.   They assume that the central bank considers the shock "nominal" and so increases the quantity of money to offset the decrease in velocity   Market participants, however, believe that the shock was structural.   Real wealth has been destroyed.   And so the market participants do not believe that the central banks commitment to returning nominal GDP to target is credible.

However, a belief that a shock is "real" and has destroyed wealth doesn't prevent the central bank from returning nominal GDP to target.   It simply means that that the price level will shift to a higher growth path.   The inflation rate would pick up for a time, and then return to its previous rate, but now on a higher growth path.   This "structural" problem would also be reflected in a lower growth path for real output.

The central bank, believing that the shock was solely nominal, would expect instead that real output would recover to its previous growth path, and the price level would also return to its previous growth path.

The divergence in expectations in this situation would be that the market participants, believing the problem to be structural, will expect the recovery of nominal GDP to be a shift to a higher growth path of prices while real output remains on a lower growth path.   The central bank, on the other hand, expects that real output and the price to will return to their initial growth paths once the monetary disequilibrium is relieved.

What is most puzzling about this example is that if the central bank agreed with the market participants and thought the problem was structural, it would still expand the quantity of money enough to offset any change in velocity and return nominal GDP to the target growth path.   Then the central bank, like the market participants, would expect this to involve a shift to a higher growth path for the price level and a lower growth path for real output.

That there is some structural problem that persistently reduces productive capacity does not make returning nominal GDP to target unfeasible.  Further, it is difficult to see how this leads to an excess supply of money.

Salter and Hogan describe how the supposed structural problems have result in a leftward shift in the long run and short run aggregate supply curve.  Then they oddly describe this in micro terms as a inward shift in the production possibilities for various goods and services.  (I would think production possibilities is a macro concept.)   The relevant micro concept is that the supply curves for various goods and services are believed to have shifted to the left.   Firms believing that would tend to raise their prices along with reducing their production.   While this response is undesirable if they are making a mistake, it is consistent with a return of nominal GDP target.   As explained above, this micro response is consistent with the price level shifting to a higher growth path and real output shifting to a lower growth path.

Salter and Hogan are concerned by the excess supply of money generated by the central bank as it pushes the price level higher and point to the stagflation of the seventies and a variety of empirical studies that suggest that increased inflation is disruptive.   In my view, the seventies are not very instructive, since that was a period where nominal GDP was not on a stable growth path but rather had an accelerating growth rate.  

Of course, a study of a nominal GDP level path would most certainly show that higher inflation was associated with lower real growth in the short run.   That is how it works.   When supply side factors lead to slower growth in productivity, inflation will be higher.   As for any long run relationship between inflation and real output growth, this involves setting the growth rate implied by the rule.   Is a 5 percent growth path for nominal GDP better?   That would imply 2 percent inflation if potential output is on a 3% trend.   Or would 4 percent, 3 percent, or 2 percent be better.

There is no doubt that a nominal GDP level target will do worse than an inflation target in stabilizing short term inflation expectations.   However, I believe that expectations that nominal GDP will be at a particular level in future periods provides a better macroeconomic anchor than knowing that the price level next period will be at the same level.  

I do think that divergent expectations between firms setting prices and making production and employment decisions and the central bank could lead to problems.   I believe that nominal GDP targeting avoids problems due to difference in views about whether shocks are nominal or structural--at least to the degree that this simply involves differences expectations regarding the growth path of the price level or real output.   Instead, I would be more worried that entrepreneurs are naive Keynesians and believe something like the paradox of thrift.

So, suppose there is some structural change so that real wealth has been reduced.   Being poorer, people spend less.   That implies that nominal GDP will remain below target.   While the central bank  create more money and lower interest rates, if no one wants to borrow, then they are just pushing on a string.

Now, in reality, a decrease in wealth does reduce consumption and increase saving.    Those who are poorer seek to rebuild their lost wealth.   However, the increase in saving supply results in a lower natural interest rate.   Assuming market rates adjust, investment expands enough so that total spending is not depressed    Thinking of a misallocation of resources--capital specific to housing construction lost, for example, then this added investment can be used to rebuild the other types of capital goods that had been crowded out by the excessive investment in sawmills or cement plants.

What would be ideal is for the reallocation of resources to occur with prices and output based upon on target nominal GDP.    That productive capacity might be permanently reduced doesn't make this impossible at all.   For example, capacity constraints for capital goods more in demand may result in higher spending on them generating only modest increases in production and substantially higher prices.   Meanwhile, the reduction in prices for houses and housing construction equipment and perhaps other consumer goods might be much smaller along with larger decreases in output.   The price level rises and real output falls.    Hopefully, this upward shift in the growth path for the price level and reduction in real output will be partially relieved and reversed as resources shift and bottlenecks ease.

But suppose entrepreneurs are naive Keynesians.   They don't believe that nominal GDP will return to target.   They base their investment decisions on the assumption that spending on output will remain on its current growth path.   With those expectations, they invest less.   Must the central bank create an excess supply of money to force nominal GDP back to target?  

Perhaps.   Of course, these perverse expectations imply a lower demand for investment and so a lower natural interest rate.   A lower market interest rate implies a higher demand for money.   Is the quantity of money necessary to return nominal income to target simply accommodating this unusually high demand for money?  

Perhaps this is what Salter and Hogan have in mind.   My thought is that such entrepreneurial error is possible.   It seems to me that what is an excess supply of money and a market rate below the natural interest rate is ambiguous in this situation.     However, I would also see this as less a persistent problem and more an issue of learning the new regime.   And so, any such problems would become less severe as time passed.  

Sunday, October 5, 2014

Sumner on Currency, Lotteries and Free Banking

Scott Sumner argued against the notion that because the federal government can print money, it doesn't need to worry about the cost of providing services.   He argued that while the issue of currency allows the government to collect a small revenue--perhaps 1% of GDP--through seignorge, government spending is much greater than that, so on the margin, changes in government spending require taxes.

In response to a comment, Sumner then amended his argument to recognize that seignorage revenue is not free.   However, he argued that if we compare a scenario with no currency to one with currency, those bearing the cost of holding currency receive benefits greater than that cost.

As an analogy, he describes the introduction of a government lottery.   Those participating in the lottery get to enjoy legal gambling, and the government collects the revenue.   He notes that since private competitive lotteries are clearly possible, a more appropriate baseline shows that funds from a government monopoly lottery are not "free" but rather they come at the expense of those purchasing lottery tickets.

Sumner then considers privatized hand-to-hand currency and repeats his longstanding proposal to have the government contract out the provision of hand-to-hand currency.   He holds that competitive issue would be wasteful, pointing to the practice of banks of giving away toasters to those making deposits as a work-around interest rate ceilings.

First, the seignorage income of the government from the monopoly issue of currency is imposed on those using currency.   With a zero inflation rate and growing currency demand, those wishing to increase real currency balances must increase their nominal currency balances.  They do that by having nominal expenditures less than nominal receipts.   Real consumption plus real saving in forms other than the accumulation of money balances must be less than real income.

With inflation, say at the 2% rate Sumner favors, it is necessary to accumulate nominal balances to maintain real balances.   Again, nominal expenditures must exceed nominal receipts.   And so, real consumption plus real saving must be less than real income.   The inflation tax on real money balances is paid by those seeking to maintain their real money balances.

Evidently, people benefit from holding currency more than this cost.  But the tax on currency balances results in an excess burden like any other tax.   The conventional wisdom is that the proper baseline for comparison is a deflation rate equal to the real rate of interest so that there is no opportunity cost to holding currency.   Little seignorage revenue is possible with a deflation rate equal to the real interest rate.   If the real interest rate is equal to the growth rate of real output and the demand for currency is proportional to real income, then there is exactly no seignorage revenue--a constant nominal quantity of money is optimal.

Just about all of this analysis is worthless when considering free banking.   Banknotes are debt instruments.    While the nominal interest rate may be zero, a bank that issues them is still borrowing and must stand ready to pay them all back.   There is nothing like seignorage revenue for any bank.

Of course, borrowing at a zero-nominal interest rate is lucrative under normal circumstances.   Banks can fund a portion of their asset portfolios with no interest cost.  The immediate effect then is to enhance the profitability of banks.

However, if banks make more than normal profits, then there will be entry into the industry.  Considering banks as financial intermediaries, the resulting increase supply of banking services will reduce the equilibrium margin between the interest rates banks charge and pay.  Entry continues until profitability returns to normal.   The impact then will be an increase in the interest rates banks pay on deposits and a decrease in the interest rates banks charge on loans.

And so, if the government monopolizes the issue of currency so that it can collect seignorage, then this comes at the expense the customers of banks--you and I.   We earn lower interest on bank deposits and pay higher interest on bank loans.  

Hand-to-hand paper currency was initially issued by private, competing banks.  The government step-by-step monopolized the issue through legal restrictions.    Since this paper currency was initially redeemable in terms of gold, it was either a liability of a private central bank or a type of government debt    By creating a monopoly, the tendency of competition to dissipate the rents made possible from borrowing at a zero nominal interest rate could be shared by the private owners of the central bank and the government   As time passed, those benefits have gone more and more to governments.   With the end of the gold standard, it became possible to think of this monopoly government currency as if it is paper gold--a pure outside money with the amount issued creating a revenue.

But the private alternative remains a competitive banking system.   My own view is that it is entirely possible to pay interest on hand-to-hand currency.   When depositors withdraw currency, they can continue to earn interest until the currency is returned to their bank.   One hundred years ago, the record keeping would have been very burdensome, but it is very feasible today.

Further, to the degree it is desirable to tie price level performance to optimal holdings of  hand-to-hand currency, how much more likely would this occur when it doesn't involve government giving up a source of "free" revenue and instead involves shifts in how the benefits are distributed among the customers of banks?

Friday, October 3, 2014

Happy 90th to Leland Yeager

October 4, 2014  will be Leland B. Yeager's 90th birthday.  He has made many contributions to economics and political economy.

Like the other charter members of the Virginia School of Political Economy, he is a mainstream libertarian.   However, he has been a consistent supporter of a rule-utilitarian approach to moral and political philosophy.   He has always worked to weave together the best insights from the neoclassical and Austrian  traditions.     But perhaps more importantly,  his contributions to Chicago-school monetarism  provided tremendous insight into the essential role of money in the economy--what he described as monetary disequilibrium.   Finally, when monetary innovation made the definition of quantity of money problematic and measured velocity lost its remarkable stability, Yeager did not follow the rather convenient shift in Chicago-school monetarism, towards rational expectations and market clearing.  Rather he turned towards free banking and privatized money.

Yeager took the view that the most important and interesting macroeconomic problems involve the process by which a market economy adjusts to imbalances between the quantity of money and the demand to hold money.  In particular, inflation is the equilibrium result of  a quantity of money greater than demand and recession is part of the adjustment process of a quantity of money less than the demand.   While for many years Yeager favored a money supply rule, suggesting he judged that shifts in the demand for money were unlikely to be a serious problem,  he always considered possible a recession due to an increase in the demand to hold money.  

In an early paper, "A  Cash Balances Approach to Depression" (1956,) he discussed a possible scenario where an increase in the demand for short and safe government bonds might spillover to an increased demand for money, leading to a recession.    That a recession might occur despite an increase in the quantity of money and in combination with exceptionally low interest rates would be no surprise to those who grasp Yeager's view of monetary disequilibrium.

Yeager always argued that economists understood the importance of aggregate demand and sticky prices and wages long before Keynes.   The review of earlier textbook economics in "The Keynesian Diversion" (1973)  is instructive, but I greatly appreciated his discussion there of what I like to describe as the "Yeager Effect."    Because the demand to hold money is positively related to real income, any reduction in real income results in a reduced demand to hold cash balances.   Starting from a condition of monetary equilibrium, as long as the quantity of money doesn't decrease as well, the result will be excess money balances and so increased spending on output.   In one sense, this just shows how adverse productivity shocks are inflationary.  However, it is more important when considering supposed "demand shocks" that are not associated with changes in the quantity of money or the demand to hold it.  

Consider the paradox of thrift.   Does an increase in saving result in reduced real output and income?   Unless that increased saving involves either directly or indirectly an increase in the demand to hold money, then any reduction in real output and real income will result in reduced money demand and increased expenditures on output.    For another example, suppose that one firm reduces its investment expenditure because it is building capacity to sell to some other firm, and weak animal spirits cause it to fear that the other firm will not undertake the investment expenditures necessary for the planned sales to materialize.   Supposedly, the reduced expenditure then leads to reduced output.   However, unless these firms are holding money rather than spending on capital goods, the reduced real output and income would lead to a reduced demand to hold money, and increased expenditure on output.    Coordination failure accounts of demand constrained production, absent an imbalance between the quantity of money and the demand to hold it, are self-contradictory.

The "Yeager Effect" is dependent on the monetary regime.  The assumption is that real output and real income shift, the demand to hold money changes the same, but the quantity of money remains unchanged.    Yeager was certainly aware that a banking system might respond to depressed economic conditions by reducing the quantity of money rather than holding it steady.    This points to an additional major emphasis of his work--the distinction between money and credit.   For Yeager, money is the medium of exchange.   The quantity is the amount that exists and the demand is the amount that people would like to hold.   Credit, on the other hand, involves borrowing and lending.   Banks can lend money into existence, expanding the quantity of money even if there is no one who wants to hold the additional balances.   And those wishing to hold additional money balances have no directly reason to show up at a bank seeking to borrow.   The interest rate that clears credit markets does not necessarily keep the quantity of money equal to the demand to hold it.    It is the price level for goods and services, along with the prices of resources, including nominal wages, that must adjust to keep the real quantity  of money equal to the demand to hold it.

As financial innovation made measurement of the quantity of money problematic, Yeager became more interested in free banking and privatized monetary alternatives.   Along with Robert Greenfield, he introduced the Black-Fama-Hall Payments System in "A Laissez-Faire Approach to Monetary Stability" in 1983.    The emphasis was on a medium of account separate from the medium of exchange.   They suggest that the medium of account sould be  a broad bundle of goods and services.    This would be roughly similar to a gold standard, but with a bundle of goods defining the dollar rather than a specific quantity of gold.   With the relative price of this bundle of goods stable, there would be no need for shifts in the price level to clear markets.   There could be no significant inflation and no need for a painful recession to generate necessary deflation.

The competing media of exchange were to take the form of checkable mutual fund shares.   The prices and yields on each, as well as the quantities, would adjust to keep the quantity supplied and demanded equal for each monetary instrument.   Monetary disequilibrium would be avoided without the need for adjustments in prices of goods and services or wages and other nominal incomes.   Interestingly, there would be no zero nominal bound on interest rates with such a monetary order.   The nominal yields on these mutual-fund like monetary instruments could be less than zero, along with the yields on any other financial instruments.   Of course, that would only be true if such negative nominal yields were necessary to equate quantity demanded and quantity supplied for the monetary and other financial instruments.

As Yeager and others explored this alternative regime, it became clear that the market processes that would apply are similar to a conventional monetary order than appeared at first glance.  In particular, indirect convertibility received more emphasis.   Checks made out in dollar amounts, and especially inter-bank clearings, would need to be settled.  Indirect convertibility is the notion that a dollar claim would be settled with some financial asset, or perhaps even gold, that has a current market value equal to the sum of the market prices of the items in the bundle of goods defining the dollar.    The process that would reverse any deviation of the price level from the equilibrium implied by the definition of the dollar would involve shortages of money if the price level were too high and surpluses of money if it is too low.    And while individual issuers of mutual funds competing for market share would make appropriate changes in prices and yields as well s quantities to reflect the demands for those using the monies, the entire monetary system would be constrained through at least incipient pressure on the price level, particularly the prices of the items defining the dollar.

While mutual-fund type monetary instruments have some potential advantages, the growing emphasis on indirect convertibility made it clear that the BFH system was consistent with more conventional checkable deposit accounts.   The yields and quantities of those could adjust just as well as those on mutual fund shares.    And while Yeager and Greenfield had mentioned the possibility of some subsidiary role for privately-issued hand-to-hand currency from the start, the growing emphasis on indirect convertibility suggested that the quantities of banknotes could be limited to the demand to hold them even if the nominal yield on such currency were always zero.  Of course, if banks found it unprofitable to issue such currency, then there would be none and all payments would be made by some type of checkable account--deposit or mutual fund.

In working out some of the practical issues in choosing an appropriate bundle of goods to define a dollar, Yeager proposed that monetary instruments be redeemed partially on demand, and then a remainder be settled up subsequent to the measure of the price of the bundle.   This pointed to redeemability with futures contracts on a price index, an approach that was pursued by Kevin Dowd and which also pointed to Scott Sumner's parallel work on index futures targeting.   Yeager, working again with Greenfield, also explored a "real GDP dollar." which directly points towards a stable value for nominal GDP.

Finally, Yeager not only traced concern with monetary disequilibrium and aggregate demand to pre-Keynesian economics, he also maintained a common sense view that economics is about explaining the real world.   He was critical of what he called "hyperclassical" doctrines that in the name of rigor or methodological presuppositions ignore the reality of nominal stickiness and instead seek to explain business cycles as optimal responses to real factors.    While better explanations of wage or price stickiness should be welcomed, the absence of such explanation is no excuse to imagine that prices adjust continuously to clear all markets.  

I have learned a tremendous amount from Leland Yeager and I hope to learn more.   I would encourage other economists to do the same.  Happy 90th Birthday!

Thursday, September 18, 2014

Woodford on Nominal GPD Level Targeting

Woodford was interviewed by the Minneapolis Fed and has some positive things to say about Nominal GDP level targeting.

Sunday, September 14, 2014

Caton on Nominal GDP Level Targeting

James Caton defends nominal income targeting.   He is mostly concerned with "Austrian" critics and emphasizes the injection effects associated with a central bank targeting nominal income.

He argues that the ability of banks to adjust the quantity of money through credit creation remains operable with a central bank that targets nominal GDP.   He grants that central banks do cause injection effects when they change the quantity of base money.   However, he argues that a failure to adjust the quantity of base money when the demand for it changes leads to liquidity effects on interest rates that push the market rate away from the natural interest rate.   He emphasizes how an increase in the demand to hold base money not accommodated by an increase in the quantity of base money will tend to force the market rate above the natural rate, leading to distortions in inter-temporal coordination.   He notes that with a gold standard, the quantity of gold used as base money would tend to increase in response to an increase in demand, but argues that this adjustment is relatively slow.   For a single country in a  gold standard world, it is largely through gold imports.   For the world as a whole or for a country with a gold mining industry, there is an increase in mining.   According to Caton, either of these avenues for the expansion of base money involve injection effects.

Caton argues that there is a tradeoff--a slower adjustment in the quantity of base money and so less monetary disequilibrium along the injection effects implied by the gold standard, or else a more rapid adjustment in the quantity of base money and so less monetary disequilibrium but the injection effects associated with the creation of money by the central bank.

Caton points out that Hayek considered the stabilization of MV as a monetary policy ideal.   This would mean that the quantity of money should adjust to offset any shift in velocity.   However, Hayek insisted that the new money injected must enter at exactly the points where money is removed from circulation by the added demand to hold money.   If that doesn't occur, money is not neutral and there are injection effects.   Hayek was skeptical that money could be created in that fashion.

Caton has been carefully reading Hayek recently, and I have enjoyed reading his posts on the matter.   My view is that Hayek was correct that realistically money can never be neutral because new money will enter the economy in a different place than it leaves the stream of expenditure when the demand to hold money rises and so velocity falls.    However, I find it puzzling that Hayek or anyone else, would see this as a problem or else consider neutral money as particularly desirable.

When velocity, and so, the demand for money, changes, there is no reason to expect that there should be no change in the flow of expenditure or the allocation of resources.   For example, consider a situation where people choose to save by reducing spending on particular consumer goods and accumulate larger balances of base money.  This is an increase in the demand to hold base money and a reduction in base money velocity.   Perhaps Caton can correct me if I am wrong, but I have always understood Hayek as claiming that monetary neutrality would require that a central bank someone inject new base money into the economy such that it was spent on the very consumer goods that were not purchased.    But why is that the relevant standard of comparison?   If saving had occurred instead by the purchase of newly-issued corporate bonds, the sellers of the consumer goods would have had less money and those issuers of the corporate bonds would have more.   Presumably, the corporations would use those monies to fund some capital expenditure.    Why wouldn't the standard be that the central bank issue the new money by the purchase of those bonds?     Issuing the money so that it ended up in the hands of the sellers of consumer goods means that there is no change in patterns of expenditures in the economy, but if there is a decision to save whether by accumulating money or purchasing corporate bonds, there should be an adjustment.

I presume that since Caton agrees with the free bankers that when privately-issued monetary liabilities are accumulated, the shift of the funds to the bank's loan customers is not distortionary, he would accept the reasoning above.   But suppose rather than a corporate bond, the saver would have purchased a government bond.    If the saver instead accumulates base money, then why isn't a standard open market purchase of the government bond the non-distortionary standard?

Of course, when velocity falls due to an increase in the demand for money, those accumulating money balances are not obviously accumulating money rather than some other financial asset.   They are simply choosing to accumulate some kind of money.   They are choosing to reduce their expenditure on something (or perhaps sell some other asset) and instead hold additional money balances.   By this very decision, they are choosing to shift the expenditure from what they choose to whatever the issuer of money chooses.   Why is this distortionary.

Of course, because money serves as the medium of exchange, it can be issued and spent and those receiving it will accept it even if they do not desire to hold larger money balances.     This possibility of an excess supply of money and the injection effects due to the excess money entering the flow of expenditure at some point or other should never be confused with a scenario where the quantity of money, whether issued by private banks or a central bank, simply accommodates changes in the demand for money.   The difference isn't that there is no injection effect.   There is a change in the flow of expenditure and there ought to be.   However, there is no sense in which that change is someone more distortionary or less sustainable than any other change in the pattern of demands.

The Fed's New 4% NGDP Target

Lars Christensen appeared to congratulate the Fed on the 4% nominal GDP level target it has been following since 2009.    I have noted this apparent new path before, particularly during the debate about the fiscal cliff.   Some Keynesians argued that the tightening of fiscal policy must have prevented what would have been an expansion in nominal GDP due to various types of private spending recovering.   I noted that the data looked like the economy was on a stable growth path.   Still, I have continued to argue for a Reagan/Volcker nominal recovery before setting on a new 3%  growth path for nominal GDP.

Sumner responded by saying that in 2009 he would have been unhappy that the Fed had shifted to a lower growth path for nominal GDP, as well as a lower growth rate.    And further, he worries that the Fed is still not really targeting the level of nominal GDP.   If there is some shock, then nominal GDP with shift to a new growth path--one consistent with inflation remaining at 2%.    This would probably be close to nominal GDP growth at 4%, but the level could be anywhere.

Christensen's more recent post on the issue suggests that it is time to forget the old growth path and instead propose that the Fed formally commit to remaining on the growth path for nominal GDP that has been blazed since 2009.   In other words, he is rejecting any partial, much less total, return to the growth path of the Great Moderation.

If we believe the more recent estimates of real output being 2 percent below potential, then staying on the new growth path would require an approximate 2 percent deflation of output prices and matching decrease in wages an nominal incomes.   Presumably, something like zero inflation for a year and holding the line on pay increases to something like 1% should allow the needed adjustment in prices and wages to the new growth path to occur more gradually--over a single year.

Why not just shift the growth path up by 2 percent?   Of course, if you believe that the estimates of potential output are too high--perhaps real output is at potential now--then the upward shift in the growth of nominal GDP would at best just general a jump in the price level and at worse create an unsustainable boom in  real output.

Of course, the Fed's actual policy is that just such a jump in nominal GDP would be desirable, if it could occur with inflation remaining on target--in the medium run, anyway.   The Fed won't commit to shifting nominal GDP up to the higher path.   Nor will they commit to keeping it on the current path.  They instead will keep monetary policy accommodative--interest rates "relatively" low--until the output gap closes consistent with inflation remaining pretty much on target.    And so, an upward shift in nominal GDP is still a possibility.

I think the new 4 percent growth rate is desirable, but I continue to favor an upward shift in the growth path of nominal GDP.   Is it really 2 percent?   How much faith do I have in the potential output numbers?  Still, the more time that passes, the more I will have to adopt Christensen's view--have the Fed make a commitment to the new path for nominal GDP.    If the Fed continues with flexible inflation targeting and we have another recession, it could be worse.   And are we sure the Fed has learned its lesson regarding adverse supply shocks?    There are advantages to shifting to a new regime--even if some deflation is needed to get real output back to potential.

Sunday, August 31, 2014

The Equation of Exchange

I would write the equation of exchange as MV = Py.

The second term, Py is equal to nominal GDP.    Assuming y is measured by real GDP, and that is calculated as Y/P, where Y is nominal GDP and P as measured by a price index, then y = Y/P  implies that Y = Py.

So, the equation of exchange implies that Y = MV.  

If M is the quantity of money and V is the number of times money is spent on final goods and services per period, then MV is spending on output per period.    More money, or a change in how fast (veloclity?) it is spent on current output, might cause changes in nominal GDP.

On the other hand, if V is defined so that V = Py/M, then V is whatever it takes to make MV = Py hold.   If M rises, then V falls.   If P rises, V rises, and so on.

I think that one way to understand what those economists who use the equation of exchange as a theory have in mind simply requires that M be given two different subscripts.   Ms for the quantity of money supplied and Md for quantity of money demanded.

The equation of exchange is Ms V = Py.

And V is defined such that V = Py/Md

By substitution,   Ms *Py/Md = Py.

This implies that Ms/Md = 1

Or Ms = Md.

The equation of exchange is an economy theory based upon the quantity of money supplied being equal to the quantity of money demanded.

Now, if you define the quantity of money demanded as the amount of money people are actually holding and the quantity of money supplied as the amount of money that actually exists, and then add that someone is always holding whatever money that exists, then Md = Ms always.

I think that is what it means to treat velocity as being defined as V = Py/M.

Of course, what is usually done instead is to understand the demand for money to be the amount of money that people would like to hold.   And further, that it is possible for people to actually be holding more or less money than they would like.

As an analogy, suppose quantity demanded is identified as the amount bought and quantity supplied as the amount sold.   Since the amount sold is always equal to the amount bought by definition, quantity supplied and demanded are always equal.    It is nonsensical, then, to claim that price depends on supply and demand, and in particular, the price adjusts so that quantity supplied and quantity demanded are equal.  Since the amount bought and sold are always equal, it is not intelligible.

But, of course, quantity supplied is how much sellers would like to sell and quantity demanded is how much buyers would like to buy.   Quantity supplied and demanded are not always equal.   It is possible that the amount sold is less than the amount sellers would like to sell.   Or that the amount bought is more than the amount buyers would like to buy.

Similarly, the amount of money people would like to hold may be more or less than the amount that they actually hold.

And that implies that velocity can differ from what people would like it to be.    Does that sound odd and awkward?   It does to me.   And that is why I usually prefer to think about monetary economics in terms of the quantity of money and the demand to hold it, rather in terms of the equation of exchange.   But still, I balk at claims that the equation of exchange is nothing but an identity.     Because if it is, so is the notion that prices and real income adjust to bring the quantity of money demanded into equilibrium with the quantity of money supplied.   And so is the notion that relative price adjusts to bring quantity supplied into equilibrium with quantity demanded.