Tuesday, September 29, 2009

Hamilton 3:

Hamilton's second post on the Cato Unbound debate continues to show skepticism regarding index futures convertibility. He states that a divergence between the future expected value of nominal GDP and the fixed target price would result in speculators taking an infinite position on the contract. Then he again expresses concern that changes in the quantity of money will only impact the economy with long and variable lags. He worries that with the lagged effects of a change in the quantity of money being larger, output will be distrupted by the changes in nominal expenditure.

The reason why infinite positions on the futures contract are unlikely is that the market process runs from a divergence between market expectations of the value of future nominal GDP and the target, trading in index futures contracts with the monetary authority at a price reflecting the target, open market operations in bonds by the monetary authority, changes in the quantity of base money, changes in the quantity of money, changes in the future value of nominal GDP, and finally, changes in market expectations of future nominal GDP. An infinite position on the contract would result in an infinite change in the quantity of base money, and a level of base money equal to zero or infinity, a quantity of money equal to zero or infinity, a value of nominal GDP equal to zero or infinity, and supposedly an expectation that nominal GDP will remain above target even though the quantity of money is zero or else below target despite an infinite quantity of money.

This shows that equilibrium in this futures market does require that speculators have at least some slight clue regarding monetary economics. What actually happens to nominal expenditure only plays a role in equilibrating this futures market if the speculators understand that changes in the quantity of money will impact future nominal GDP. For the proposal to be beneficial, speculators must have more than just a clue, and should rather invest in the futures contract based upon their understanding of exactly how today's monetary and financial conditions will impact nominal expenditures in the future.

It should be noted that if speculators are mistaken so that, for example, an infinite level of base money really does result in nominal GDP rising above target (even a little) then the speculators would suffer infinite losses. My view is that even with long and variable lags, an infinite quantity of base money would result in worse than Zimbabwean hyperinflation--infinite inflation. Given the nature of their error and the consequences, infinite losses would be just about what these remarkably ignorant and pigheaded speculators would deserve.

Hamilton also argues that because of the long and variable lags,that most of the impact of an increase in the quantity of money will only impact expenditure in later periods, and so the efforts, perhaps largely futile, to raise nominal expenditure next quarter will result in disruptions to real output in later quarters.

I think the concept of nominal expenditure targeting has yet to sink in with Hamilton and some of his criticisms would apply to price level or inflation targeting. Second, he doesn't seem to recognize that index futures targeting is targeting the future value of nominal expenditures. Some of his criticisms would apply to a scheme that tried to stablize the price level in real time, or absurdly, a feedback rule that effectively tries to stabilize the past value of the price level. (OK, no one thinks that is possible, but a feedback rule is changing the policy instrument in ways that would have been desirable if the changes had occured before the value of the macroeconomic value was realized.)

During the eighties and nineties, I studied and published some papers on the Greenfield-Yeager payments system. They (and I) called it the Black-Fama-Hall payments system. It is a privatized monetary system that would create market forces that stablize the price level in real time though indirect convertibility. The sorts of concerns raised by Hamilton would apply to the Greenfield-Yeager system. With sticky prices, shocks to the price level would plausibly lead to very destructive changes in the quantity of money, nominal expenditures, and real output.

Those of us working in this area, such as Kevin Dowd and including Yeager, moved towards index futures convertibility. More modest changes in the quantity of money and nominal expenditures are needed to budge sticky prices if it is future prices rather than current prices that are targetted. Once the concept of index futures convertibility is adopted, stabilization of any measured macroeconomic magnitude is possible, and for a variety of reasons, I came to view a 3% growth path of nominal expenditure--total final sales--as the least bad option.

While I remain sympathetic to free banking, in the context of the status quo, I think that the Federal Reserve should seek to adjust the quantity of money today to keep expected future nominal expenditure on a stable growth path. While nothing is perfect, stable expected growth of nominal expenditure provides the least bad environment for microeconomic coordination.

Since many of the reasons I came to support targetting expected future nominal expenditure were to specifically avoid the sorts of problems Hamilton describes, problems that would apply to an effort to target the price level in real time, I am left with the impression that he just doesn't get it.

For example, I can imagine index future targeting of a growth path of the CPI involving large flucuations in the quantity of money and nominal expenditure. Unfortunately, fluctuations in real output and employment might be destructive side effects. I am doubtful that the sort of explosive cycles that Hamilton hints at are possible--since they require substantial myopia. However, sticky price problems are irrelevant to nominal expenditure targeting. While there may be large changes in the quantity of money and short term interest rates, there can never be a need to generate large fluctuations in nominal expenditure. Nominal expenditure is what is being stabilized. To the degree that it is fluctuations in nominal expenditure in the face of sticky prices that are causing fluctuations in real output, targetting nominal expenditure avoids that difficulty.

Selgin on Sumner's Penalty Rate on Excess Reserves

The discussion on Cato Unbound continues.

Selgin endorsed Hummel's criticism of Sumner's proposal to impose a penalty on excess reserves.

I think that the interest rate that the Fed pays on reserve balances should be less than zero--right now.

Consider the following:

  • Private issue of currency.
  • No reserve requirements.
  • Frozen monetary base.

But, the base is a money market mutual fund. The shares are kept at one dollar and invested in Treasury bills. The interest return on the portfolio it transferred to the banks holding the reserves, but the banks pay a 25 basis point management free.

The cost of holding reserves is the management fee. The benefit is reduced transactions costs of more active asset and liability management to continue to meet net clearing obligations. Presumably, the equilibrium demand for reserves is larger than would be the case with zero interest reserves. Less asset and liability management is necessary for the banks. Generally, the cost of financial intermediation is a bit less, the margin between the interest rates banks charge and pay is smaller, and the total size of bank balance sheets are larger.

However, the demand for reserves should still be positively related to the variance of net clearings, the amount of gross clearings, and so nominal income. The market process by which free banking stabilizes nominal income should still apply.

Further, changes in the interest rate will not change the opportunity cost of holding reserves. It will change the interest rate earned on clearing balances in proportion to changes in other interest rates.

If T-bill rates fall, then the interest rate that banks earn on their reserve balances fall too. If T-bill rates fall to something very near zero, the interest rates that banks earn on reserve balances will fall to something a bit less than zero.

It is a feature, not a bug. If interest rates on Treasury bills fall to zero, and there remains an excess demand at zero, and reserve balances have a zero interest rate, it is certainly possible, if not likely, that banks would seek to increase reserve holdings, and disrupt the market process that stabilizes nominal income. If, on the other hand, the interest rate on reserves moves with other interest rates, this will not be a problem.

Some scenarios where a free banking system would need to use the option clause would be unnecessary with interest bearing clearing balances--and those are scenarios where it is the ability of interest rates to fall, even less than zero, that avoids the disruption of using the option clause.

Empirics and Leads and Lags

On his blog, Macro and other Market Musings, economist David Beckworth reports on some empirical work he has done regarding money, velocity, and monthly nominal GDP figures. He shows very rapid impacts of money changes on expected inflation and real macroeconomic variables. Very interesting.

Monday, September 28, 2009

Hummel on Sumner's excess reserve "tax."

Sumner asked those commenting on his essay on Cato Unbound to discuss his proposal for imposing penalties on banks for holding on excess reserves. Hummel responded negatively to negative interest rates.

Hummel has claimed that when the Fed pays interest on reserve balances it mixes up fiscal and monetary policy. I find this claim puzzling. The relationship between the Fed and banks holding reserve balances is exactly analogous to the relationship between banks and their depositors holding transactions accounts. Banks pay interest on transactions accounts. Why shouldn't the Fed pay interest on reserve balances?

If the clearing operations of the Federal Reserve were privatized, along the lines of the clearinghouse associations of the past, why wouldn't banks organize and join clearinghouse associations that paid interest on their clearing balances? Of course, that would require that the clearinghouses hold some kind of earning assets, and since financial intermediation isn't costless, the interest paid would need to be somewhat less than the interest earned on those portfolios, even if banks were charged specific processing fees for clearing electronic payments, checks, and any other monetary liabilities (yes, banknotes.)

Sadly, for the banks, if the earnings on the asset portfolio were low enough, the interest payments on clearing balances could turn negative. If we imagine a situation where a private clearinghouse can simply store gold or treasury currency, then, of course, sensible banks would choose a clearinghouse that would store these if it were cheaper than managing a portfolio of very low yielding earning assets. And then, the "negative' interest rate on balances would be storage costs for the gold or treasury currency.

To the degree the Fed proxies the behavior of a private clearinghouse, it should usually pay interest on reserve balances less that it earns on its earning assets, making proper adjustments for risk. Further, there should a lower limit approximately equal to the cost of storing currency. Assuming that the Fed will be bailed out by the Feds if necessary, then the risk of reserve balances is the same as government debt. And reserve balances are more liquid than the shortest T-bills. And so, a simple rule would be to set interest rates on reserve balances perhaps 25 or 50 basis points below the interest rate on four-week T-bills.

Under current conditions, the Fed is offering a financial instrument that is perfectly liquid and riskless. Why shouldn't banks pay for the privilege of holding such an appealing asset? The purpose of saving, or even holding wealth, is to fund real investment. Production processes involving capital goods are not perfectly liquid or riskless. Letting someone fund these projects without risk and with additional liquidity means that someone is taking extra risk. The margin between the interest rate paid by any financial intermediary and what it earns on its asset portfolio should reflect the difference in risk and liquidity. With the yield on the lower risk, highly liquid assets in the Federal Reserves portfolio approaching zero, negative interest on reserve balances is entirely appropriate.

Hummel is concerned that charging interest on excess reserves would tax the clearing balances banks hold for M2 and M3 liabilities. I think this is confused. What would really happen is that the sweep programs would be closed down and the banks would begin to honestly report the quantity of transactions accounts. This would increase their required reserves and so reduce their excess reserves. Sadly, it appears that no one knows what proportion of transactions accounts are falsely reported as some variant of savings account, and so the size of this effect is difficult to determine.

As Hummel notes, there would be a strong motivation to make what are truly savings accounts (beyond the transactions accounts that are falsely reported as savings accounts using sweep software) into transactions accounts. Since this would transfer what is a very near money into the medium of exchange, the economic effect is probably minimal. One can imagine the letter. Great news. You now have unlimited checking privileges on the funds in your savings account. A debit card will soon arrive in the mail. On the other hand, the motivation of banks to fund their asset portfolio with transactions accounts as opposed to certificates of deposit or other debt instruments would involve an expansion in the quantity of money.

Sumner, however, has focused more on banks expanding their asset portfolios. To the degree that banks are capital constrained, and because government bonds have a zero risk weight under current capital regulations, banks will naturally buy government bonds. The usual money multiplier process would directly expand the value of transactions accounts in the banking system, increasing the quantity of the various measures of the money supply, while increasing required reserves and so reducing excess reserves and so the interest banks must pay on excess reserves.

Conventional money multiplier analysis suggests that an expansion in transactions accounts will result in currency withdrawals from the banking system. This follows from the assumption that there is "currency/deposit ratio." However, under the unusual circumstances of an increase in the demand to hold money, it isn't at all obvious that the usual relationships would apply. That is, the currency deposit ratio could fall. However, a currency drain from the banking system would reduce total reserves, and so reduce excess reserves.

Hummel worries that taxing excess reserves would be a subsidy for money market mutual funds. I disagree. The banks are not required to hold excess reserves, and the money market mutual funds are not eligible to hold reserves balances. If banks are accumulating excess reserves because they find it a good investment, the Fed is subsidizing the banks by reducing risk and providing liquidity. Charging for that service would put banks on a level playing field relative to other financial intermediaries.

Hummel mentions that banks would never borrow from the Fed's discount window if they had to pay interest to the Fed and also pay interest on the reserves they hold. However, banks could still borrow to meet reserve requirements. Sumner advocates charging interest on excess reserves only. Of course, the Fed is lending huge amounts of money to banks at this time. However, it is a mistake to assume that the Fed is lending money to the same banks that are holding excess reserves. Currently, the banks pay a quarter percent more than they earn.

Suppose a large money center bank had been funding a huge portfolio of mortgage backed securities using off balance sheet commercial paper, overnight borrowing from other banks, and large, brokered, certificiates of deposit. There is a loss in confidence in this bank, and all of those sources of funds dry up. The Fed lends money to the bank. The bank obtains reserves immediately, but pays them out as it pays off the commercial paper coming due, pays off overnight loans from other banks, and pays off the large brokered certificates of deposit. It is other banks, ending up with those additional reserves that would have excess reserves and who would have to pay for holding them. The Fed would be bearing the risk of funding the portfolio of toxic assets, while the banks who have those toxic assets transformed into something risk free and perfectly liquid would pay the Fed for this service. If the banks would instead prefer to hold some other kind of asset, perhaps less risky and more liquid than toxic assets, but more risky and less liquid than reserve balances at the Fed, they should be able to do so, and perhaps earn interest rather than pay.

Sumner has suggested that the Fed also assess banks on their holdings of vault cash. My view is that the Fed should instead keep the charge for holding reserves less than the cost of holding vault cash. Setting up a more careful scheme for reporting vault cash and then imposing charges seems excessive. If temporary, setting up this system is more trouble that it is worth. If permanent, trying to have some kind of Fed police stamp out currency warehouses would be futile.

While I don't think Hummel's notion that T-bills will replace base money makes much sense, he may have gotten an inkling of an equilibrium where all of the highly liquid, low risk assets have slightly negative yields. FDIC insured transactions accounts are perfectly liquid and riskless. Savings accounts are little different. FDIC insured certificates of deposit are highly liquid and riskless. T-bills are highly liquid and riskless. Reserve balances at the Fed are perfectly liquid and riskless. If there is an excess demand for these assets at a zero yield, why shouldn't the yields on all of them be negative? That the Fed provides riskless, perfectly liquid currency with a zero yield may make it impossible for nominal interest rates to be negative enough for the markets for these other financial assets to clear, but there is no reason to try to keep their rates positive, zero, or anything less negative that the storage cost of currency.

Hummel correctly points out that the Fed can always clear these markets by just increasing the quantity of money enough. So, suppose the Fed is purchasing zero interest T-bills to expand the quantity of money. The Fed is supposed to provide this intermediation for free? And if the Fed is instead purchasing longer term government bonds, or even private securities, then Fed is bearing the risk. Why should it provide this subsidy?

The greater the subsidy the Fed provides to those holding highly liquid and low risk financial assets, the greater the amount of quantitative easing that the Fed must undertake, and the greater the risk that the Fed must bear. In the final analysis, depending on a larger increase in the Fed's balance sheet while keeping interest rates above zero means that the taxpayer is responsible for more risk, and is providing a subsidy to those who want to hold low risk, highly liquid assets. If those holding those sorts of assets pay for the privilege, then less of a subsidy is provided, less quantitive easing is required and less risk is imposed on the taxpayer.

Hamilton on Sumner 2

When I read Sumner's article, I thought his citation of Hume was a nice touch. Sumner's point was that monetary disequilibrium can be caused by an increase in the demand to hold money as well as a decrease in the quantity of money. Locking up coin in a strong box is the same as having the coin disappear. How clever.

Because orthodox monetarists spent so much effort trying to argue that velocity is sufficiently stable so that a money supply rule--slow steady growth of some measure of the quantity of money--would result in stable growth of nominal income, monetary disequilibrium theorists constantly must point out that monetary disequilibrium doesn't solely come from changes in the quantity of money. The problem is an imbalance between the quantity of money and the demand to hold it.

Like many monetary disequilibrium theorists, Sumner likes the supply and demand approach to the problem rather than the equation of exchange. That is because he focuses on the medium of account function of money, and has spent much time thinking about the gold standard in that way, where the nonmonetary uses of gold must be analyzed using supply and demand.

But Sumner brought up the equation of exchange, and Hamilton responded with a discussion of the ambiguous nature of the concept of "velocity." What exact version of the equation of exchange does Sumner have in mind?

I think the real answer is no version. Monetary disequilibrium theorists all understand that income velocity is the reciprocal of the Cambridge k. So, "velocity" is most definitely the ratio of nominal income to the quantity of money, just as k is the ratio of money to nominal income. And that is related to a notion of treating the demand for money in proportion to nominal income. As shown by Sumner's quote of Hume about how locking coins in a strongbox has the same effect as a decrease in the quantity of coin, it is clear that there is no assumption that money demand, k, or V are constant.

The current crisis exists because the demand for money rose, and the quantity of money didn't increase enough to match the increase in demand. That velocity fell and the quantity of money didn't rise enough to offset the drop in velocity is just another way of saying the same thing.

Hamilton then raises concerns regarding "long and variable lags." On this view, a change in the quantity of money will only impact nominal income after many months, and maybe it could be as much as a year or two. This is the orthodox monetarist view, and it leads them to look at the huge increase in base money over the last year and to worry that within the next few months, quarters or years, massive inflation will occur. Those of us who claim that the drop in nominal GDP proves that however large was the increase in the monetary base by historical standards, it was evidently too small, supposedly fail to recognize the lag issue. Nominal income today depends on the quantity of money created in the past, and changes in the quantity of money today will have no impact on nominal income today, but will only add to the tremendous inflationary pressures that will be generated in the future, which will be coming any time now.

Hamilton then shows a chart of M1 and M1 velocity since 1980, and it looks to me like changes in M1 are matched by opposite changes in velocity. Certainly, this seems plausible enough. My view is that if new money is created, and it is placed in someone's hands, then the immediate effect is that the individual holds more money. If the demand to hold money was unchanged, then it takes some time for that person to choose how to spend the excess money balances. But that is the relevant issue--how long does it take people to decide how to spend excess money balances.

If we imagine an exogenous change in the quantity of money, with a given demand for money, and we consider how fast that excess money will be spent, I think that little will be spent in the first few minutes or even hours. And, it is possible that not all will be spent in the first month. But to imagine that the issue is a single individual gradually spending money ignores a key part of the process. Excess money balances are spent, and then those receiving them have excess balances, and they must decide how to spend it. At each step of the process, there is increased demand for assets, goods or services, and so only gradually does the growing demand for the goods and services raise nominal expenditure. That the full impact of a given change in the quantity of money might only gradually be felt is entirely reasonable. But that isn't the same thing as saying that a change in the quantity of money, no matter how large, will not have any effect on nominal expenditures for several months, quarters or years.

Further, suppose that there was an increase in the demand for money, and people are gradually figuring out what expenditures to cut in order to build up money balances. It might take some time for any individual to determine how to cut spending to build up money balances. And as one person cuts spending, those who would have received the money have reduced money balances, and they in turn must cut spending. It could be a long, drawn out process.

Now, suppose that an increase in the quantity of money occurs simultaneously with the increase in the demand for money. To what degree does the gradual, drawn out process get short circuited? Someone who was working out ways to cut spending to build money balances now has more money balances. There is no need to figure out how to spend excess balances. They just have less need to cut expenditures. Similarly, some of those who would have ended up with less money as those short on money cut spending, will receive extra money from those spending excess money balanceces. Such persons have no need to adjust their actual money holdings to desired money holdings at all.

So what about Hamilton's charts of M1 and M1 velocity? Suppose that Sumner's proposal of index futures targeting was implemented and it worked better than his wildest dreams. Nominal expenditures remained exactly on a 5% (or 3%, 0r 2%) growth path. If the demand for money changes, then the quantity of money would change with it. In other words, the quantity of money would exactly change to offset any change in velocity, generating the exact pattern shown by Hamilton.

Of course, the Federal Reserve has not used index futures convertibility. However, the Fed has targeted interest rates, making the quantity of money endogenous. The traditional rationale for this policy is that the open market trading desk will cause changes in the monetary base and the broader money aggregates to accommodate changes in the demand for them. This is fully consistent with Wicksellian monetary economics, and as long as the target for the interest rate is just right, changes in bank lending will generate bank monetary liabilities that do exactly match the demand to hold them. The result should be changes in the quantity of money that exactly offset changes in velocity. Of course, when the central bank fails to make the appropriate changes in interest rates--to match changes in the natural interest rate--changes in the quantity of money will passively accommodate changes in nominal expenditure. That the "Great Moderation" shows a period where changes in the quantity of money largely offset changes in velocity should be what is expected. If the Fed had failed to make the proper adjustments in interest rates, it wouldn't have been quite so moderate.

None of this proves that changes in the quantity of money don't just result in people passively increasing their money balances and leaving excess balances unspent. If we imagine that increases in money demand occur on one isolated island, and the expansions in the quantity of money occur on another isolated island, then it could well be that lagged effects of the added money demand will hit at a time when the increased quantity of money is having little effect. Without trade between the islands, as the excess money gradually spreads to more and more people, it will never be to any of those being hit with reduced sales and so reduced money balances.

Sumner tends to focus more on rational expectations. Everyone knows that the increase in money balances will raise nominal expenditure eventually, and expectations of higher prices and output in the future raise spending today. My view is that to the degree people understand that Paulson and Bush's threats of another Great Depression are false, and that nominal expenditure will not fall in half and remain depressed for a decade, then they will not be so motivated to cut spending and accumulate money balances at this time. I admit, however, that I also insist on a market process that generates increased nominal expenditure even with pigheaded market participants who listen to the likes of Paulson and Bush.

Hamilton then argues that using monetary policy to target nominal expenditure is problematic because monetary policy will impact commodity prices faster than wages or the prices of services. I was entirely puzzled as to why Hamilton would think that the goal of the policy is to raise wages or the prices of services. The goal is to avoid a drop in nominal expenditure and the associated drop in output and employment. If that cannot be avoided, then the goal is to return nominal expenditure back to its previous growth path in order to generate a recovery of output and employment. Ideally, price and wage changes should be avoided, and if that has failed, and falling nominal expenditure has already lead to a deflation of commodity prices, then reflating them is appropriate.

Hamilton's comment sometimes gives the impression that he is commenting on a proposal to stabilize the price level, or even to cause inflation. No, the proposal is to stabilize nominal expenditure. How this impacts various measures of the price level or real output will depend on the particular measures and more importantly, on the market forces determining production and pricing at a given growth path of nominal expenditure.

Hamilton on Sumner 1

Last but not least, economist James Hamilton commented on Sumner. His responses are the most challenging to both Sumner and my perspectives.

When I read Sumner's original article and his claim that the subprime mortgage crisis was "a fluke," I thought, what is up with that, Scott? Hamilton apparently interpreted it to mean that Sumner was claiming that the subprime mortgage crisis was unimportant. Hamilton, then, provided some great anecdotal information about how bad one of the pools of mortgages behind some of the mortgage backed securities really were. Perhaps he thought Sumner's claim of "fluke" meant that Sumner was one of those who thinks that subprime mortgage crisis was just an irrational panic and that the solution would be for investors to go back to buying the commercial paper issued by the investment banks so they can continue funding mortgage backed securities, raising housing demand and prices, and the entire shadow banking house of cards could be reconstructed.


Neither Sumner nor I dispute that financial institutions will lose money if they make loans secured by overvalued assets to people who cannot afford to make the payments. I think Hamilton is exactly right that these loans could only be paid if there had been continued rapid appreciation in home prices. I would summarize the problem as lending into a speculative bubble.

Hamilton writes less about the macroeconomic implications of the losses. He mentions that financial institutions had "leveraged" exposure to these losses. Again, that financial intermediaries are highly leveraged is normal, so that the risk of bankruptcy is relatively high. Personally, I think the concept of leverage is confusing, especially for financial intermediaries, and prefer the standard money and banking concept of capital ratios. To me, 5 to 1 leverage sounds alarming, but I think a 20% capital ratio would be great. Keep in mind that a 10% capital ratio, or 10 to 1 leverage is counted as well capitalized. The very alarming 20 to 1 or even 35 to 1 leverage ratios, represent 5% and 3% capital ratios. None of these capital ratios will be sufficient to protect those lending to a financial institution that concentrates its lending into a speculative bubble.

Finally, the key. Hamilton asserts:

fear of their failure crippled lending, sending economic activity into a
nosedive in the fall of 2008.
And that is where Sumner and other monetary disequilibrium theorists disagree. Certainly, we don't want to deny that crippled lending would negatively impact the productive capacity of the economy. While lending into a speculative bubble was hardly helping the effective allocation of resources, credit markets that move funds from less valued to more valued uses are better than universal self-financing.

The economy did go into a tailspin during the fall of 2008. By tailspin, I mean falling nominal expenditure. If prices and wages were perfectly flexible, real expenditure could have been maintained, but they aren't, so the falling nominal expenditure resulted in demand constrained sales in almost every sector of the economy. Real output dropped rapidly, employment began to drop more rapidly, and the unemployment rate began to skyrocket.

Monetary disequilibrium theorists, like Sumner, insist that this can only occur if there is either a decrease the the quantity of money or else an increase in the demand for money. Fear of failure of financial institutions with low capital ratios holding claims to pools of mortgages made to people who cannot afford the payments and secured by overvalued real estate could plausibly lead to a decrease in the quantity of money or an increase in the demand for money. But to get lower nominal expenditure, the crisis must have such an impact.

And, of course, Sumner's key argument is that the Federal Reserve can control the quantity of money, if it chooses, and that it could have increased the quantity of money enough to meet any increase in the demand for money, leaving nominal expenditure unchanged.

How is it possible for nominal expenditure to be maintained despite crippled lending? First, nearly all expenditure is funded from current income. People earn income and purchase consumer goods. Similarly, firms earn revenue and purchase capital goods with funds accounted for as depreciation or retained earnings. Credit transactions (and new issues of equity) involve shifting funds between and among households and firms. If credit markets are crippled, then those who would have borrowed spend less, but those who would have lent have those funds to spend. The source of the problem, then, is that those who have those funds available to spend, don't, and instead increase their money holdings. Or, the banking system would have lent the money into existence, and doesn't, so the money doesn't exist.

If the nominal quantity of money rose enough to match any increase in the demand for money at the target value of nominal expenditure, and credit markets were crippled, then any resulting change in the composition of expenditure would be reflected in rising demand, prices, profits, production and employment in some sectors, and falling demand, falling profits or rising losses, falling production and employment in other sectors. Because of bottlenecks in expanding sectors, production rises more slowly there than it falls elsewhere. Because of sticky prices in shrinking sectors, those prices don't fall as much as prices rise in growing sectors. The result would be reduced production (from its long run growth path) and higher prices, stagflation. Assuming there really was a speculative bubble in housing, it is not at all clear that productivity would be hampered by the crippled credit markets compared to what went on before, but compared to healthy credit markets, some productive investments would be forgone, and resources would be used for less productive investments or else consumption. Obviously, crippled credit markets are a bad thing.

What Sumner and other monetary disequilibrium theorists find troubling is that there is some kind of easy shift among many economists from, lending is crippled, to aggregate expenditure falls, and so there is a demand constrained contraction in output. No, not necessarily. With the proper monetary institutions, demand constrained contractions in output could be prevented, though that doesn't prevent sectoral shifts or reduced productivity from depressing productive capacity.

Sunday, September 27, 2009

Jeffrey Hummel on Sumner 1

Jeffrey Hummel commented on Sumner's article on Cato Unbound. Like Selgin, his comment was supportive. That is natural because Hummel is also a monetary disequilibrium theorist and a free banker.

Hummel is best known (to me, anyway) as a historian of of the Civil War and slavery. His Emancipating Slaves, Enslaving Free Men: A History of the Civil War, is a libertarian classic. Recently, however, I have found his posts on the Liberty and Power blog about the Fed's balance sheet very helpful. I would see something in the news, try to decipher the New York Fed or Board of Governors reports, develop some limited clue, and then, there is a great post by Hummel clarifying it all.

Hummel's discussion of orthodox monetarism and conventional Keynesian economics was an excellent summary of the monetary disequilibrium view. Keynesians try to hide the monetary disequilibrium in some back closet, while orthodox monetarists struggled mightily to show that the demand for money remains on a constant growth path, so that it is fluctuations in some measure of the quantity of money that causes the fluctuations in nominal expenditures.

Like Sumner, Hummel criticizes the Fed's policy of paying interest on reserve balances. However, I don't really agree that this policy turns monetary policy into fiscal policy. My view is that the Fed should pay interest on reserves--just lower than the opportunity cost of those funds--say 25 or 50 basis points below 4 week T-bills. Reducing the rents collected by the government from money creation is a good idea. And under current conditions, the result would involve charging banks for keeping their funds in a perfectly liquid and riskless form. I find Sumner's particular schemes for penalty rates on excess reserves a bit irritating, especially when combined with paying bonus interest on required reserves. Probably it is because I oppose the existence of reserve requirements, and can see draconian penalties on excess reserves (Sumner sometimes chooses 4% for some reason,) as requiring just one new regulation after the other to control what is in the final analysis the inevitable result of making all money redeemable in zero-interest currency. If it is profitable to operate money warehouses, having Federal Reserve police try to close them down is futile.

Hummel, like Sumner, points to the danger of interest rate targeting. Pointing to historically low interest rates and claiming that means that there is plenty of money is usually a symptom of what Yeager called, "Money and Credit Confused." However, perhaps because of an emphasis on pure credit monies and cashless payments system, I am more open to a "Wicksellian" approach to understanding monetary disequilibrium. The problem is a divergence between the market interest rate, that central bank policy impacts, and the unobservable natural interest rate, the real interest rate that coordinates saving and investment with real income equal to productive capacity. While controlling the quantity of money allows market interest rates to adjust with market forces of supply and demand, keeping the quantity of money equal to the unobservable demand for money that would exist if real income equaled productive capacity and the interest rate is at the level that coordinates saving and investment is no less challenging.

Hummel challenges Sumner to look towards monetary deregulation to avoid monetary disequilibrium. I don't think Hummel quite grasps the degree to which Sumner's index futures targeting (or as I prefer to call it, index futures convertibility,) puts the banking system in the (invisible) hands of market forces. However, my main comment here is to say, yes, Scott, think about free banking a bit more.

Selgin on Sumner 1

George Selgin's response to Sumner's essay on Cato Unbound was very supportive. It should be no surprise.

Like Sumner, Selgin is a monetary disequilibrium theorist, with some unique twists. Selgin edited The Fluttering Veil, Essays and Monetary Disequilibrium which is a collection of essays by Leland Yeager. When I bought it, some years ago, I looked through to make sure I had read all the essays included and then it sat on my shelf. With the start of the crisis, I began a review and began to see how much of my analysis of the crisis is right there in chapter one, "A Cash Balance Approach to Depression," an article written in 1956, the year I was born.

However, it is Selgin's own Theory of Free Banking that is must reading. His argument that the demand for reserves in a free banking system generates a market process that stabilizes nominal expenditure is an important contribution to both the monetary disequilibrium and free banking traditions.

Selgin comes out of the "Austrian" tradition, and this shows in his comment. He gently criticized Sumner for failing to consider how an expansive monetary policy in the early part of the decade helped cause the housing boom, the end of which initiated the crisis. My understanding of Sumner's view is that monetary policy was too expansive during the middle of the decade, as shown by excessive growth in nominal GDP. Sumner, however, puts little weight on this as being a cause of the financial crises. Lending against overpriced homes to people who can't afford to make payments is likely to cause problems, even if there were no monetary policy mistakes. Further, monetary policy mistakes provide no excuse for lending against overpriced real estate to people who cannot afford to make the payments. That isn't to suggest that policy mistakes that create excess nominal expenditure growth are harmless. (Sumner and I pretty much agree on the above, I think. I am more likely to see what happened in the housing market as a speculative bubble than Sumner.)

Selgin's view that a higher trend rate of nominal expenditure growth is will lead to malinvestments is suggested as well. Selgin favors very slow growth in nominal expenditures, and so a deflationary trend for the price level. Sumner's view is that while the trend growth rate of nominal expenditure does have negative interactions with the tax system, he tends to be dismissive of arguments about malinvestment. My view is similar to Sumner's, though I prefer a 3% growth path for spending as opposed to the 5% growth path that he has been advocating.

I take concerns about malinvestment seriously, but see them as being associated with shifts in policy regimes as well as possible consequence of policy mistakes where the monetary authority and entrepreneurs make the same errors. Regardless, Selgin, Sumner, and I all agree that productivity changes (often called "supply-side shocks") should result changes in the price level, and so deviations from the trend inflation rate. Roughly, the growth path of nominal incomes remain unchanged. (It was Selgin's arguments that long ago convinced me that generating fluctuations in nominal expenditure to stabilize the price level in the face of supply shocks is a mistake, and that stable nominal expenditure is the better alternative. )

Selgin agrees with Sumner that engineering a disinflation during the fall of 2008 would have been very poor timing, when the banking system was already stressed because of the subprime mortgage crisis. For that reason, I had adopted Sumner's call for a return to a 5% growth path of nominal expenditure. However, as Selgin suggests in his comment, I am now inclined to accept fait accompli, and favor reflation back to what would have been a 3% growth path and carrying on from there with price level stability.

Klingonomics 4


I think I have it.

Suppose that real income does not impact the demand to hold money. That will lead to Kling's result--nominal income adjusts with real income. The quantity of money and the demand to hold money only impact the price level.

To see this, start with the standard approach. The demand for money depends on the price level, real income, the interest rate on other assets, the interest rate on money, and other unspecified things--
+ + - +
Md = Md(P, y, Rb, Rd, X)

(I haven't figured out superscripts on my blog editor yet.)

If the demand for money is a demand for real money balances--a command over goods and services--then this can be written--

Md = P md(y, Rb, Rd, X)

The nominal demand for money is proportional to the price level and the real demand for money.

If the demand for money is also proportional to real income, then:

Md = Pyk(Rb, Rd, X)

Where "k" is the "Cambridge k," introduced by Alfred Marshall. Marshall actually defines it in terms of nominal income, Y, where Y = Py.

Md = kY

This approach is only sensible if money is a normal good. The demand for money (or really the demand for the flow of services from the real quantity of money) is positively related to income. And further, that money is exactly on the cusp between necessity and luxury, so that the demand for money (services) is unit income elastic.

If that it not true, then you are left with Md = Py k(y, Rb, Rd, X), which is not a simplification. At some point, I saw empirical evidence that the income elasticity of money demand was .9. Of course, that all depends on exactly how money is measured, but that was enough for me. Why should it be exactly one? And so, sometimes I use "k" and "V" to communicate to other economists, but I understand that they must be used with care.

But, let us stick with tradition.

Md = Pyk(Rb, Rd, X).

Marshall mentions that k probably depends on interest rates, as shown here, but says that the effect is small and he will ignore it. I have often thought that it is no coincidence that in my integral calculus class we used "k" to refer to the constant found when finding the anti-derivative. Anyway, I think interest rates should appear as an opportunity cost of holding money, (Rb - Rd), which is negatively related to real money demand.

In equilibrium, Ms = Md. Leaving off the subscript for the quantity of money--

M = Pyk.

Rearranging terms,

M(1/k) = Py

And so, we see that if V is defined as 1/k, and k is derived from money demand, then we have the equation of exchange.

MV = Py

It is an equilibrium condition following from Ms = Md.

Since V depends on the interest rate on assets other than money, the interest rate on money, and any number of other unspecified things, it is hardly a constant. To my way of thinking, monetary disequilibrium generally has financial effects that impact the opportunity cost of holding money, and so "correct" monetary disequilibrium almost immediately, while interfering with the ability of interest rates to coordinate saving and investment--the Wicksell approach.

But back to Kling.

Suppose that y doesn't impact money demand.

Md = P md(Rb-Rd, X)

In equilibrium, Ms = Md

So, P = M/md

Nominal income still equals the price level multiplied by real income, Y = Py.

So, Y = (M/md) y

Changes in real income lead to proportional changes in nominal income. Changes in the quantity of money lead to changes in the price level.

With V = Y/M, as an identity rather than an equilibrium condition, then,

V = y/md.

Velocity is proportional to real income, given the demand for real money balances.

And, of course, V = Py/M. So, if P is given because of price stickiness, and real income is given by productive capacity, them V must be inversely proportional to the quantity of money? Right? Wrong!

The fundamental problem with Kling's view is that in reality the demand for money does depend on real income. (It isn't just on the cusp between being a normal and an inferior good with an income elasticity of zero.)

More importantly, in disequilibrium, shortages or surpluses of money will still disrupt production if the price level is sticky. I have no simple algebra to describe that process. The process is that if there is a shortage of money at the current price level, each individual can obtain more money by spending less. Nominal expenditure falls. Firms sell less. The usual way to respond to lower sales is to reduce production and prices. Prices are assumed to be sticky (and let us say, stuck for now.) And so, output falls.

With the standard, more realistic approach, the reduced output and income results in lower money demand, and so the demand for money drops, resolving the disequilibrium. Ceteris paribus, productive capacity has not changed, and so there are at least notional surpluses of goods and resources, and continued downward pressure on prices. As prices make the needed adjustment, real output and real income recover.

With Kling's version, however, reduced output and income has no impact on money demand. Until prices drop enough to bring the real supply of money to the demand for money, the contraction continues. Of course, this shows why the assumption in so absurd. Nothing prevents real income from falling to zero. So people will continue to demand the same amount of services from holding money, while entirely giving up the services provided by food, clothing, and shelter. Not likely. Of course, while absurd globally, that doesn't mean that the demand for money couldn't possibly be independent of income, or even that money cannot be inferior, over some ranges.

So let me grant that Kling is right. If the demand to hold money is independent of real income, and real income has fallen due to a drop in productive capacity, and nominal income has fallen in proportion to real income at the existing price level, increasing the money supply, causing monetary disequilibrium, and so causing the price level and nominal income to rise to its previous level would be undesirable.

However, I don't believe that this situation applies in the real world. Further, my view of current conditions is that the real demand for money rose, nominal expenditure fell. Because prices are sticky, real expenditure fell. Real output fell with real expenditure and it is currently well below the admittedly depressed level of productive capacity. Increasing the quantity of money and nominal expenditure will return real output to productive capacity. And further, as a policy rule, stable growth of nominal expenditure, and particularly, expected stable growth of nominal expenditure, is not a bad macroeconomic environment for adjustment to shifts in productive capacity.

Saturday, September 26, 2009

Cowen on Sumner

In his blog, Marginal Revolution*, Tyler Cowen discusses Sumner's view of the crisis.

He argues:
1. Scott's recommendation of higher price inflation, or higher nominal gdp
growth, would have eased the crisis, in my very rough guesstimate by one-third
and in absolute terms that is a lot. It's the best free lunch I've seen in

Good. One small quibble. Sumner doesn't really think that higher price inflation is the goal. Increased production is the goal, which results from more rapid nominal GDP growth. The increase in price inflation is a side effect that he believes likely due to his emphasis on sticky wages.

Anyway, that leaves 2/3 of the drop in real output to be due to some kind of "real" problem. What are the real problems?

Cowen continues:

Yet, in my view, easier money would not have eliminated most of the crisis, given the partial or total insolvency of many financial institutions, the negative AD shock from the collapse of the housing bubble, and the need to halt and reverse the ongoing accumulation of debt, among other

I believe that there is a need to reallocate resources, and can accept that the partial or total insolvency of many financial institutions can impact the productive capacity of the economy. Bankruptcy involves real costs. If operations stop during liquidation, that obviously reduces productive capacity. And even if operations continue, it is difficult to believe that the process doesn't impact the effective allocation of resources.

However, I totally reject the view that there is such a thing as an AD shock independent of monetary disequilibrium.

Cowen continues:

2. Scott's account does not deny (but does not emphasize) that the initial
downturn was accompanied by a fall in monetary velocity. This opens up
room for real shocks, resource reallocations and recalculations,
and animal spirits to be driving the broader story.

Obviously, there is some difference in perspective here. Apparently, Sumner has not emphasized enough that it was an increase in money demand/drop in velocity that was the problem.

The monetary disequilibrium approach is that imbalances between the quantity of money and the demand to hold money cause changes in nominal expenditure. Imbalances can be generated by changes in the quantity of money, changes in the demand for money, or both simultaneously. Because prices are not perfectly flexible, changes in nominal expenditure disrupt production.

Apparently, Cowen and many others are inclined to read into what monetary disequilibrium theorist actually say an assumption that it is changes in the quantity of money that are causing all the disturbances. In other words, some kind of assumption that monetary disequilibrium theorists assume that demand to hold money balances always remains on a constant growth path.

In other words, that all of the orthodox monetarist arguments that a money supply rule will stabilize nominal expenditures, the price level, and the growth rate of real output are correct.


In particular, a decrease in housing wealth can plausibly result in a decrease in consumption and an increase in saving. From a Keynesian perspective, where the implied increase in the demand to hold money is hidden in a back closet somewhere, the result of the reduced consumption is a decrease in aggregate demand. (Hummel's response to Sumner on Cato Unbound is exactly correct in summarizing the monetary disequilibrium perspective.)

If the quantity of money adjusts to meet the increase in the demand for money, then aggregate demand, real or nominal, will not decrease. It is possible that some households will increase saving and reduce consumption because of their loss in housing wealth. Other households will increase consumption and decrease saving, perhaps even dissaving. If, on net, households save more, then firms increase investment.

The changes in the composition of demand may temporarily depress the productive capacity of the economy, but if there is no monetary disequilibrium, there will be sectors of the economy with growing demand, rising prices, rising profits, rising production, and employment. The reason why total output falls would be bottlenecks that slow the expansion of those sectors with growing demand. The shrinking sectors shrink quickly, the growing sectors expand slowly, so productive capacity is temporarily depressed.

Obviously, there must be some mechanism for added saving by some households to generate offsetting reduced saving (or dissaving) by other households or else increased investment by firms. The usual process involves lower interest rates. If this requires real interest rates to become negative, the problem is the "liquidity trap." And, of course, Sumner, like every monetary disequilibrium theorist, is perfectly aware of that issue and tries to deal with it.

A second issue Cowen discusses is the need to reduce debt. However, net debt is zero. The only way that a reduction in gross debt reduces nominal expenditures is if it results in a decrease in the quantity of money or an increase in the demand for money. Generally, a superficial analysis of excessive debt and aggregate demand just leaves the monetary disequilibrium in some back closet. For example, if bank loans are repaid, and the banks respond by shrinking their issue of monetary liabilities, this results in monetary disequilibrium. However, bank loans are only a small fraction of the total credit market, and it is entirely possible for total debt to decrease while the share of credit funded by bank-issued monetary liabilities expands. The quantity of money can remain constant or grow.

The alternative avenue for monetary disequilibrium is an increase in money demand. Those who repay debts are saving more. Those who receive the debt repayments can save less or dissave. If we just imagine that those receiving debt repayments accumulate money balances, then this is an increase in the demand to hold money and debt repayments will cause monetary disequilibrium. Similarly, if firms are "overleveraged" and repay debt, those households receiving repayments can save less or dissave. Or, perhaps they could save by purchasing equity stakes in firms. Firms could deleverage by funding their activities by less debt and more equity. Again, if the assumption is instead that those receiving the debt repayments just accumulate money balances, then the result is monetary disequilibrium.

Sumner's argument, typical of monetary disequilibrium theorists, is that if the quantity of money rises to meet any increase in the quantity of money demanded, even if the increase in money demand is indirectly caused by added saving aimed at offsetting the effects of reduced asset prices or else aimed at paying down excessive debts, the result will be stable nominal income growth, along with successful efforts to save and reduce debt. It is entirely possible that this will be associated with changes in the composition of demand and the needed allocation of resources. The best environment for such adjustments is stable growth of nominal expenditure.

*Thanks Tyler, for giving my new blog a plug!

Friday, September 25, 2009

Rowe on Kling's Mackerel Velocity

Nick Rowe responded to Arnold Kling regarding "mackerel velocity" on his blog, Worthwhile Canadian Initiative:

Kling asks why are mackerels different from money? Why should the M in MV=PY stand for money, and not mackerels?
Why can't an excess demand for mackerel cause a recession? Why can't an excess supply of other goods be matched by an excess demand for mackerel?
(snipped material, but it is all worth reading, follow the link.)
The textbooks mention three properties of money:
1. Money is a store of value. So are mackerel (if frozen or canned). Forget that.
2. Money is a medium of account (we measure prices in money). Mackerel aren't. But so what? Prices are sticky in terms of money. But the price of mackerel is also sticky in terms of money. So prices are sticky in terms of mackerel as well, by transitivity. So no difference there between money and mackerel.
3. Money is a medium of exchange. Aha! Because (outside of US prisons) mackerel is not a medium of exchange. An excess demand for mackerel might cause a general glut and recession in US prisons, but only an excess demand for what the rest of us
law-abiding folk use as money can cause a general glut and recession elsewhere.

I don't agree with Rowe about the medium of account. If mackerel were the medium of account, then clearing the mackerel market would require that everyone in the economy adjust their prices. With the price of a mackerel being one, and all the other prices changing, then the price level and nominal income (which is measured in mackerels) would change depending on the supply and demand conditions in the mackerel market.

As I have said before, I don't really think barter is relevant. Kling is claiming that the ratio of the quantity of mackerel to nominal GDP is irrelevant. I agree. And that money is no different than mackerel. The ratio of the quantity of money to nominal GDP is irrelevant too. And, in a way, I agree. But the demand to hold money and the quantity of money is essential.

If mackerel were the medium of account, then the ratio of mackerel to nominal GDP wouldn't be that important, but the supply and demand for mackerel would determine the equilibrium price level and so the equilibrium level of nominal income.

Rowe argues that even if a barter economy quoted prices in mackerel, it would suffer no general glut or recession in response to an excess demand for mackerel. Those who cannot buy mackerel at its current "price" would instead buy something else.

I don't really understand how prices in terms of mackerel, and so, the price level and nominal income in mackerel, all get to equilibrium in barter. But I agree that it isn't through a general glut.

On the other hand, I know a good bit about how a monetary economy using something other than money, say mackerel, as a medium of account would work. And basically, monetary disequilibrium would be generated to clear the mackerel market, an excess demand for mackerel would involve a general glut, and in equilibrium, the price level and nominal income would depend on the supply and demand for mackerel.

Sumner on Cato Unbound

On Cato Unbound, Scott Sumner presented his argument that the "Great Recession" was caused by tight money. In his view, a serious error of omission by the Federal Reserve is responsible for the sharp drop in nominal expenditure, real output, and employment that occurred in the fourth quarter of 2008 and the first quarter of 2009, as well as the continuing low levels of output and employment and high level of unemployment in September of 2009. He briefly described how the use of index futures contracts on nominal income could end the recession and avoid similar difficulties in the future.

For those following Sumner's blog, The Money Illusion, there was nothing new. Sumner is a monetary disequilibrium theorist. While his approach has some unique twists, he accepts the key view that changes in nominal expenditure are necessarily the result of changes in the quantity of money or the demand to hold money. Further, that fluctuations in nominal expenditure have a disruptive impact on production and employment. And still further, that if the nominal quantity of money changes to accommodate changes in the demand to hold money, these disruptive changes in nominal expenditures can be avoided.

All monetary disequilibrium theorists have noted that both the monetary base and the broader measures of money, M1, M2, and MZM have expanded during a period of rapid decreases in nominal expenditures. The demand to hold money must have increased significantly. Velocity must have fallen. From a policy perspective, it is apparent that however large by historical standards, the increase in the monetary base was too small to keep nominal income from falling, much less continuing to grow at its previous trajectory.

One of Sumner's interesting contributions to the debate has been his theory that the demand for money began to rapidly increase in the fall of 2008, because market participants became convinced that the Federal Reserve would not increase the quantity of money enough to accommodate increases in money demand. It seems a bit odd. Expectations that the Fed will not increase in the quantity of money in response to an increase in the demand for money cause an increase in the demand to hold money. Of course, this expectation didn't hit as a bolt from the blue. The idea is that money demand increased slightly, perhaps because of the subprime mortgage crisis. The Fed failed to increase base money enough to accommodate that initial increase in demand, depressing the growth rate of nominal expenditures. Market participants saw that the Federal Reserve was willing to allow nominal expenditure to slow and even drop. The consequent fear of recession and deflation caused a large increase in the demand for money. In Sumner's view, if the Fed had responded strongly to the initial increase in the demand for money, then the secondary increase in the demand to hold money would have never happened. Given that previous failure, even larger increases in base money are necessary to reverse the resulting steep drop in nominal expenditure.

In my view, the collapse of the shadow banking system was directly tied to the collapse of the housing bubble. Those who had funds "deposited" in the shadow banking system fled to T-bills and FDIC insured deposits provided by the conventional banking system. At least some of those FDIC insured deposits are money, and so the demand for money rose. However, a few weeks later, the stock market crashed, and those selling stocks fled into "cash." While that again included FDIC insured deposits and T-bills, it was at this point that T-bill yields began approaching zero. As the zero nominal bound is approached, excess demands for T-bills began to be shunted over into an excess demand for money. The increase in the demand for money that was the reflection of the stock market crash is plausibly related to the the market response to the Fed's failure to effectively respond to the collapse of the shadow banking system.

Sumner also mentioned his view, shared by nearly all monetary disequilibrium theorists, that the Fed's decision to pay interest on reserves was a disaster. Paying interest on money increases the demand for money. If the demand for money is rising faster than the quantity of money, paying interest to further increase money demand is a mistake.

Sumner suggested that instead of paying interest on the reserve balances banks hold at the Fed, the banks should pay the Fed for keeping excess reserves. In my view, the near zero yields on T-bills (and actual zero and even negative yields on some T-bills on some days,) resulted in a shifting of the excess demand for T-bills to money. Paying higher interest on reserve balances at the Fed, so that reserves were not only more liquid, but had a better yield than T-bills, greatly exacerbated this problem. Requiring that banks pay for the privilege of holding a perfectly liquid, riskless asset, seems entirely sensible to me.

Sumner proposed that the Fed explicitly commit to a growth path for nominal GDP. He favors a 5% growth path. Partly, this is the growth path of nominal expenditure that is consistent with a 3% trend growth in real output and the 2% inflation target that has been popular with central bankers over the last decade. But Sumner's key argument is that keeping nominal GDP on a stable growth path is desirable, and the trend growth rate of nominal GDP has been close to 5% for the past decade.

In my view, a 3% growth path for nominal expenditure is best. However, engineering a disinflation during the subprime mortgage crisis would have been a mistake. During the fall of 2008, like Sumner, I was very supportive of retuning nominal GDP to its previous growth path. At this time, a year later, I would be happy with a commitment to reflate nominal expenditure next year to a level consistent with a new, 3% growth path.

Finally, Sumner briefly described index futures convertibility. The Fed commits to buying and selling index futures contracts on nominal GDP one year in the future. As investors initiate transactions based upon their expectation about the future value of nominal GDP, the Fed trades them and then makes parallel open market operations in government bonds. These open market operations in bonds impact base money in the usual way, and this impacts future values of nominal GDP, and the expectations of investors. In equilibrium, the quantity of base money is equal to the level that investors expect will leave nominal GDP on target.

When I read Sumner's post, I thought he did a good job explaining his views. And then came the responses--first by Hamilton, then Selgin, and finally, Hummel. More later....

Arnold Kling Replies

Arnold Kling replies to my post on Klingonomics:
Woolsey is trying to take the Recalculation story and rework it into the MV= PY framework. While the economy is Recalculating, potential GDP goes down. Accordingly, if the monetary authority maintains a high MV, we will get inflation and not more real output.

Equation of Exchange? Me? Well, yes...my post was full of P's, y's, V's and M's. I need to watch that.

My perspective is that nominal expenditure depends on the quantity of money and the demand to hold money. At first pass, a shift of demand between sectors of the economy impacts neither the quantity of money nor the demand to hold money, and so leaves nominal expenditure unchanged. There is a change in the composition of demand, rather than in aggregate demand. And so, reduced productive capacity results in lower output and higher prices. The lower real income reduces the real demand for money, but the higher price level reduces the real quantity of money leaving nominal expenditures the same.

Kling continues:
I think that is a pretty fair description of what happened in the 1970's. But right now, I am saying that the Fed cannot raise MV. It raises M and V goes down. If the Fed really worked at it for a long period of time, I am sure that they could bring back inflation, like in the 1970's. However, I do not think that they can cure the Recalculation problem by raising nominal expenditure. If anything, I think more inflation would make the Recalculation problem even harder for the economy to solve.

Looking at nominal expenditure in the seventies, I don't see stable nominal expenditure growth combined with lower real output growth and higher inflation. Rather, I see out of control aggregate expenditures.

This chart shows the compounded annual growth rate of total final sales between first quarter 1970 and first quarter 1980. It was well above my preferred target of 3% each and every quarter. It soon skyrockets beyond Sumner's preferred 5% growth rate, heading for double digits by the end of the decade. Note the 23% annual growth rate near the end of the decade. While there may have been a slow down in productivity growth during the period, the high and increasing growth rates of nominal expenditures should have been expected to cause high and rising inflation.

Kling's argument that "right now" the Fed cannot increase nominal expenditure, because any increase in M leads to a fall in V is the same thing as arguing that the demand for money--the amount of money households and firms want to hold--will passively increase to match increases in the quantity of money.

To some degree, this is consistent with the long and variable lags that was a tenant of orthodox monetarism. The quantity of money increases. If the demand for money is unchanged, there is an excess supply of money. Excess money balances will be spent. However, it is impractical make large changes in spending instantly. And so, spending increases over time, gradually reducing actual money balances to their desired levels.

Kling, on the other hand, appears to be making a stronger claim. And so his view comes close to the "liquidity trap." The liquidity trap usually involves a claim that increases in the quantity of money fail to lower interest rates, and without a decrease in interest rates, nominal expenditure won't increase. However, the implication is that V falls to match the increase in M. The traditional graphic representation of the liquidity trap shows a horizontal liquidity preference or demand for money curve, so that the quantity of money demanded passively adjusts to changes in the quantity of money.

While I don't believe that changes in the quantity of money impact nominal expenditures in a few seconds, minutes, or hours, neither do I think that there is no effect for months. Habits of thought derived from thinking about how a given change in the nominal quantity of money will impact the price level over time cannot be directly applied to an alternative policy framework where the quantity of money adjusts whatever amount needed to target the expected value of nominal expenditure several quarters in the future.

As for the liquidity trap, it is almost certainly an artifact of "conventional" monetary policy, particularly targeting interest rates, but also from limiting open market operations to Treasury bills. A commitment to adjust the quantity of money however much is needed to target nominal income implies a willingness to purchase longer term government bonds or even foreign bonds or private securities, if purchase of the entire outstanding stock of T-bills fails to do the job.

Finally, to the degree a "Recalculation" is a reallocation of resources, stable growth of nominal expenditure provides an excellent environment for readjustments. Prices and profits rise in the sectors that need to expand, clearly signalling that production should rise. Prices and profits fall in the shrinking sectors, signaling that they should shrink.

Wednesday, September 23, 2009

Klingonomics 3

Kling is skeptical about the ability of monetary policy to expand nominal expenditures. It is difficult to see how it is much different from the old "pushing on a string" canard.

He argues that if nominal income wants to be 5% lower, then increases in the quantity of money will make no difference. Presumably, Kling means that if the total amount that all the households and firms together want to spend on goods and services is 5% less, then no increase in the quantity of money will cause households and firms to, in effect, change their minds, and not reduce their spending after all. (Of course, some households or firms might reduce spending and others increase spending.) If it is too late to preempt the reduction in spending, so that nominal income has already fallen by 5%, then no increase in the quantity of money can reverse that decrease, and return nominal expenditure to its previous level.

From the equation of exchange, MV = Py, the 5% drop in nominal income is a drop in Py. It must be matched by a drop in MV. And so this desire by nominal income to drop means a drop in either M or V. If M is given, then it is a drop in V, the income velocity of money. But this is just the reciprocal of k, the ratio of real money balances to real income. And so, the desire to reduce nominal expenditure is the same thing as a desire to increase money holdings relative to real income.

Certainly, it is possible that households and firms will prefer to hold more money, which would raise the amount they prefer to hold relative to their real incomes. That raises k and reduces V. The reason an expansion of the quantity of money should solve this problem is that it allows the household's and firms to expand their money holdings as desired without reducing their spending.

Kling's argument that increases in the quantity of money will not prevent or reverse a decrease in spending implies that each increase in the quantity of money generates a further decrease in velocity. In other words, an increase in the quantity of money causes households and firms to being willing to hold larger money balances relative to their incomes. The demand to hold money will passively adjust to meet whatever quantity is created.

This is the liquidity trap. The amount of money people choose to hold passively adjusts to accommodate the amount created. While taking the liquidity trap seriously is a characteristic of Keynesians of one stripe or another, monetarists have a similar concept with their long and variable lags. For the monetarist, the quantity of money is expanded, and only gradually do those holding what are now excess balances begin to spend. How long does it take? Sometimes more quarters, othertimes fewer months. How long will bear speculators keep interest rates high? Few Keynesians claim that it is forever.

Perhaps one might argue that in September of 2008, it was already too late to prevent the rapid drop in nominal expenditure in the fourth quarter of that year. Maybe it was even too late to reverse that drop by the first quarter of 2009. Perhaps it was too late to prevent the equally large drop in nominal expenditure in that same quarter. Now it is September 2009. Nominal expenditure is about 6% below the growth path for the last decade or so. Could prompt action a year ago have impacted nominal income today?

I doubt that nominal expenditure on final goods and services is much impacted by an increase in the quantity of money after a few minutes or even hours. But no effect for a year? I doubt it.

If people were convinced that nominal expenditure would have returned to its previous growth path by now, (a year after the crisis,) how far would the panicky reductions in consumption and investment spending have gone during the fourth quarter 2008 and the first quarter 2009?

Klingonomics 2

Kling's argument that the current recession involves a need to reallocate resources, is plausible. It seems likely that resources need to be moved away from producing single family homes, building SUV's and other low mileage vehicles, and perhaps less financial engineering on Wall Street. The resources need to be redeployed to more valuable uses. Because this adjustment takes time, the productive capacity of the economy will be temporarily depressed.

What is remarkable, however, is Kling's view that the decrease in productive capacity somehow generates a matching decrease in nominal expenditure. He argues that "recalculation" generates a reduction in "y," that is real income. Given "P," the price level, that implies a decrease in "Y," nominal income and nominal expenditure. And given "M," the quantity of money, this necessarily implies a decrease in "V," the income velocity of money. From the equation of exchange MV = Py, V = Py/M.

However, the income velocity of money is equal to the reciprocal of the ratio of real money balances to real income, or k. This decrease in "V" is simultaneously an increase in k. Somehow, the readjustment in the allocation of resources that is temporarily causing depressed productive capacity must be causing people to be willing to hold increased real money balances, despite being made poorer by that lower real income. Not only is this implausible on its face, it would be remarkable that they would be willing to expand money holdings the exact amount necessary to cause nominal expenditure and income to drop with the productive capacity of the economy.

The usual market-clearing, real business cycle approach would be to argue that P instantly and smoothly adjusts so that real expenditure (MV/P) is equal to the productive capacity of the economy. From deep within this perspective, the current value of P is always at the level such that the real volume of expenditures matches the productive capacity of the economy. If observed real output has fallen, then it must be that productive capacity has fallen. From that perspective, real income (y) is always equal to productive capacity, and MV simply determines the value of P needed to make real expenditure equal to that capacity.

If, on the other hand, prices are sticky, then real expenditures are not necessarily equal to productive capacity. If one simply asserts that nominal expenditures drop so that at current prices, real expenditures are equal to capacity, then it is evident that velocity, and more fundamentally, the demand to hold money must be adjusting. Why would people adjust the amount of money they choose to hold so that nominal expenditures exactly track the adjustment in resource allocation from relatively less valued to relatively more valued goods?

The most likely answer is that there is no such reason. Kling is simply mistaken. There is no particular reason to believe that the current level of nominal or real expenditure is equal to the productive capacity of the economy. A great recalculation may have depressed the productive capacity of the economy, but a drop in nominal expenditure may have caused real expenditure and real income to fall well below that productive capacity. The great recalculation may have increased structural unemployment, and so the natural rate of unemployment, but the drop in nominal expenditure, may have caused the unemployment rate to rise above the natural unemployment rate.