Archive for the 'zero lower bound' Category

Is John Cochrane Really an (Irving) Fisherian?

I’m pretty late getting to this Wall Street Journal op-ed by John Cochrane (here’s an ungated version), and Noah Smith has already given it an admirable working over, but, even after Noah Smith, there’s an assertion or two by Cochrane that could use a bit of elucidation. Like this one:

Keynesians told us that once interest rates got stuck at or near zero, economies would fall into a deflationary spiral. Deflation would lower demand, causing more deflation, and so on.

Noah seems to think this is a good point, but I guess that I am less easily impressed than Noah. Feeling no need to provide citations for the views he attributes to Keynesians, Cochrane does not bother either to tell us which Keynesian has asserted that the zero lower bound creates the danger of a deflationary spiral, though in a previous blog post, Cochrane does provide a number of statements by Paul Krugman (who I guess qualifies as the default representative of all Keynesians) about the danger of a deflationary spiral. Interestingly all but one of these quotations were from 2009 when, in the wake of the fall 2008 financial crisis, a nasty little relapse in early 2009 having driven the stock market to a 12-year low, the Fed finally launched its first round of quantitative easing, the threat of a deflationary spiral did not seem at all remote.

Now an internet search shows that Krugman does have a model showing that a downward deflationary spiral is possible at the zero lower bound. I would just note, for the record, that Earl Thompson, in an unpublished 1976 paper, derived a similar result from an aggregate model based on a neo-classical aggregate production function with the Keynesian expenditure functions (through application of Walras’s Law) excluded. So what’s Keynes got to do with it?

But even more remarkable is that the most famous model of a deflationary downward spiral was constructed not by a Keynesian, but by the grandfather of modern Monetarism, Irving Fisher, in his famous 1933 paper on debt deflation, “The Debt-Deflation Theory of Great Depressions.” So the suggestion that there is something uniquely Keynesian about a downward deflationary spiral at the zero lower bound is simply not credible.

Cochrane also believes that because inflation has stabilized at very low levels, slow growth cannot be blamed on insufficient aggregate demand.

Zero interest rates and low inflation turn out to be quite a stable state, even in Japan. Yes, Japan is growing more slowly than one might wish, but with 3.5% unemployment and no deflationary spiral, it’s hard to blame slow growth on lack of “demand.”

Except that, since 2009 when the threat of a downward deflationary spiral seemed more visibly on the horizon than it does now, Krugman has consistently argued that, at the zero lower bound, chronic stagnation and underemployment are perfectly capable of coexisting with a positive rate of inflation. So it’s not clear why Cochrane thinks the coincidence of low inflation and sluggish economic growth for five years since the end of the 2008-09 downturn somehow refutes Krugman’s diagnosis of what has been ailing the economy in recent years.

And, again, what’s even more interesting is that the proposition that there can be insufficient aggregate demand, even with positive inflation, follows directly from the Fisher equation, of which Cochrane claims to be a fervent devotee. After all, if the real rate of interest is negative, then the Fisher equation tells us that the equilibrium expected rate of inflation cannot be less than the absolute value of the real rate of interest. So if, at the zero lower bound, the real rate of interest is minus 1%, then the equilibrium expected rate of inflation is 1%, and if the actual rate of inflation equals the equilibrium expected rate, then the economy, even if it is operating at less than full employment and less than its potential output, may be in a state of macroeconomic equilibrium. And it may not be possible to escape from that low-level equilibrium and increase output and employment without a burst of unexpected inflation, providing a self-sustaining stimulus to economic growth, thereby moving the economy to a higher-level equilibrium with a higher real rate of interest than the rate corresponding to lower-level equilibrium. If I am not mistaken, Roger Farmer has been making an argument along these lines.

Given the close correspondence between the Keynesian and Fisherian analyses of what happens in the neighborhood of the zero lower bound, I am really curious to know what part of the Fisherian analysis Cochrane finds difficult to comprehend.

Forget the Monetary Base and Just Pay Attention to the Price Level

Kudos to David Beckworth for eliciting a welcome concession or clarification from Paul Krugman that monetary policy is not necessarily ineffectual at the zero lower bound. The clarification is welcome because Krugman and Simon Wren Lewis seemed to be making a big deal about insisting that monetary policy at the zero lower bound is useless if it affects only the current, but not the future, money supply, and touting the discovery as if it were a point that was not already well understood.

Now it’s true that Krugman is entitled to take credit for having come up with an elegant way of showing the difference between a permanent and a temporary increase in the monetary base, but it’s a point that, WADR, was understood even before Krugman. See, for example, the discussion in chapter 5 of Jack Hirshleifer’s textbook on capital theory (published in 1970), Investment, Interest and Capital, showing that the Fisher equation follows straightforwardly in an intertemporal equilibrium model, so that the nominal interest rate can be decomposed into a real component and an expected-inflation component. If holding money is costless, then the nominal rate of interest cannot be negative, and expected deflation cannot exceed the equilibrium real rate of interest. This implies that, at the zero lower bound, the current price level cannot be raised without raising the future price level proportionately. That is all Krugman was saying in asserting that monetary policy is ineffective at the zero lower bound, even though he couched the analysis in terms of the current and future money supplies rather than in terms of the current and future price levels. But the entire argument is implicit in the Fisher equation. And contrary to Krugman, the IS-LM model (with which I am certainly willing to coexist) offers no unique insight into this proposition; it would be remarkable if it did, because the IS-LM model in essence is a static model that has to be re-engineered to be used in an intertemporal setting.

Here is how Hirshleifer concludes his discussion:

The simple two-period model of choice between dated consumptive goods and dated real liquidities has been shown to be sufficiently comprehensive as to display both the quantity theorists’ and the Keynesian theorists’ predicted results consequent upon “changes in the money supply.” The seeming contradiction is resolved by noting that one result or the other follows, or possibly some mixture of the two, depending upon the precise meaning of the phrase “changes in the quantity of money.” More exactly, the result follows from the assumption made about changes in the time-distributed endowments of money and consumption goods.  pp. 150-51

Another passage from Hirshleifer is also worth quoting:

Imagine a financial “panic.” Current money is very scarce relative to future money – and so monetary interest rates are very high. The monetary authorities might then provide an increment [to the money stock] while announcing that an equal aggregate amount of money would be retired at some date thereafter. Such a change making current money relatively more plentiful (or less scarce) than before in comparison with future money, would clearly tend to reduce the monetary rate of interest. (p. 149)

In this passage Hirshleifer accurately describes the objective of Fed policy since the crisis: provide as much liquidity as needed to prevent a panic, but without even trying to generate a substantial increase in aggregate demand by increasing inflation or expected inflation. The refusal to increase aggregate demand was implicit in the Fed’s refusal to increase its inflation target.

However, I do want to make explicit a point of disagreement between me and Hirshleifer, Krugman and Beckworth. The point is more conceptual than analytical, by which I mean that although the analysis of monetary policy can formally be carried out either in terms of current and future money supplies, as Hirshleifer, Krugman and Beckworth do, or in terms of price levels, as I prefer to do so in terms of price levels. For one thing, reasoning in terms of price levels immediately puts you in the framework of the Fisher equation, while thinking in terms of current and future money supplies puts you in the framework of the quantity theory, which I always prefer to avoid.

The problem with the quantity theory framework is that it assumes that quantity of money is a policy variable over which a monetary authority can exercise effective control, a mistake — imprinted in our economic intuition by two or three centuries of quantity-theorizing, regrettably reinforced in the second-half of the twentieth century by the preposterous theoretical detour of monomaniacal Friedmanian Monetarism, as if there were no such thing as an identification problem. Thus, to analyze monetary policy by doing thought experiments that change the quantity of money is likely to mislead or confuse.

I can’t think of an effective monetary policy that was ever implemented by targeting a monetary aggregate. The optimal time path of a monetary aggregate can never be specified in advance, so that trying to target any monetary aggregate will inevitably fail, thereby undermining the credibility of the monetary authority. Effective monetary policies have instead tried to target some nominal price while allowing monetary aggregates to adjust automatically given that price. Sometimes the price being targeted has been the conversion price of money into a real asset, as was the case under the gold standard, or an exchange rate between one currency and another, as the Swiss National Bank is now doing with the franc/euro exchange rate. Monetary policies aimed at stabilizing a single price are easy to implement and can therefore be highly credible, but they are vulnerable to sudden changes with highly deflationary or inflationary implications. Nineteenth century bimetallism was an attempt to avoid or at least mitigate such risks. We now prefer inflation targeting, but we have learned (or at least we should have) from the Fed’s focus on inflation in 2008 that inflation targeting can also lead to disastrous consequences.

I emphasize the distinction between targeting monetary aggregates and targeting the price level, because David Beckworth in his post is so focused on showing 1) that the expansion of the Fed’s balance sheet under QE has been temoprary and 2) that to have been effective in raising aggregate demand at the zero lower bound, the increase in the monetary base needed to be permanent. And I say: both of the facts cited by David are implied by the fact that the Fed did not raise its inflation target or, preferably, replace its inflation target with a sufficiently high price-level target. With a higher inflation target or a suitable price-level target, the monetary base would have taken care of itself.

PS If your name is Scott Sumner, you have my permission to insert “NGDP” wherever “price level” appears in this post.

Just How Infamous Was that Infamous Open Letter to Bernanke?

There’s been a lot of comment recently about the infamous 2010 open letter to Ben Bernanke penned by an assorted group of economists, journalists, and financiers warning that the Fed’s quantitative easing policy would cause inflation and currency debasement.

Critics of that letter (e.g., Paul Krugman and Brad Delong) have been having fun with the signatories, ridiculing them for what now seems like a chicken-little forecast of disaster. Those signatories who have responded to inquiries about how they now feel about that letter, notably Cliff Asness and Nial Ferguson, have made two arguments: 1) the letter was just a warning that QE was creating a risk of inflation, and 2) despite the historically low levels of inflation since the letter was written, the risk that inflation could increase as a result of QE still exists.

For the most part, critics of the open letter have focused on the absence of inflation since the Fed adopted QE, the critics characterizing the absence of inflation despite QE as an easily predictable outcome, a straightforward implication of basic macroeconomics, which it was ignorant or foolish of the signatories to have ignored. In particular, the signatories should have known that, once interest rates fall to the zero lower bound, the demand for money becoming highly elastic so that the public willingly holds any amount of money that is created, monetary policy is rendered ineffective. Just as a semantic point, I would observe that the term “liquidity trap” used to describe such a situation is actually a slight misnomer inasmuch as the term was coined to describe a situation posited by Keynes in which the demand for money becomes elastic above the zero lower bound. So the assertion that monetary policy is ineffective at the zero lower bound is actually a weaker claim than the one Keynes made about the liquidity trap. As I have suggested previously, the current zero-lower-bound argument is better described as a Hawtreyan credit deadlock than a Keynesian liquidity trap.

Sorry, but I couldn’t resist the parenthetical history-of-thought digression; let’s get back to that infamous open letter.

Those now heaping scorn on signatories to the open letter are claiming that it was obvious that quantitative easing would not increase inflation. I must confess that I did not think that that was the case; I believed that quantitative easing by the Fed could indeed produce inflation. And that’s why I was in favor of quantitative easing. I was hoping for a repeat of what I have called the short but sweat recovery of 1933, when, in the depths of the Great Depression, almost immediately following the worst financial crisis in American history capped by a one-week bank holiday announced by FDR upon being inaugurated President in March 1933, the US economy, propelled by a 14% rise in wholesale prices in the aftermath of FDR’s suspension of the gold standard and 40% devaluation of the dollar, began the fastest expansion it ever had, industrial production leaping by 70% from April to July, and the Dow Jones average more than doubling. Unfortunately, FDR spoiled it all by getting Congress to pass the monumentally stupid National Industrial Recovery Act, thereby strangling the recovery with mandatory wage increases, cost increases, and regulatory ceilings on output as a way to raise prices. Talk about snatching defeat from the jaws of victory!

Inflation having worked splendidly as a recovery strategy during the Great Depression, I have believed all along that we could quickly recover from the Little Depression if only we would give inflation a chance. In the Great Depression, too, there were those that argued either that monetary policy is ineffective – “you can’t push on a string” — or that it would be calamitous — causing inflation and currency debasement – or, even both. But the undeniable fact is that inflation worked; countries that left the gold standard recovered, because once currencies were detached from gold, prices could rise sufficiently to make production profitable again, thereby stimulating multiplier effects (aka supply-side increases in resource utilization) that fueled further economic expansion. And oh yes, don’t forget providing badly needed relief to debtors, relief that actually served the interests of creditors as well.

So my problem with the open letter to Bernanke is not that the letter failed to recognize the existence of a Keynesian liquidity trap or a Hawtreyan credit deadlock, but that the open letter viewed inflation as the problem when, in my estimation at any rate, inflation is the solution.

Now, it is certainly possible that, as critics of the open letter maintain, monetary policy at the zero lower bound is ineffective. However, there is evidence that QE announcements, at least initially, did raise inflation expectations as reflected in TIPS spreads. And we also know (see my paper) that for a considerable period of time (from 2008 through at least 2012) stock prices were positively correlated with inflation expectations, a correlation that one would not expect to observe under normal circumstances.

So why did the huge increase in the monetary base during the Little Depression not cause significant inflation even though monetary policy during the Great Depression clearly did raise the price level in the US and in the other countries that left the gold standard? Well, perhaps the success of monetary policy in ending the Great Depression could not be repeated under modern conditions when all currencies are already fiat currencies. It may be that, starting from an interwar gold standard inherently biased toward deflation, abandoning the gold standard created, more or less automatically, inflationary expectations that allowed prices to rise rapidly toward levels consistent with a restoration of macroeconomic equilibrium. However, in the current fiat money system in which inflation expectations have become anchored to an inflation target of 2 percent or less, no amount of money creation can budge inflation off its expected path, especially at the zero lower bound, and especially when the Fed is paying higher interest on reserves than yielded by short-term Treasuries.

Under our current inflation-targeting monetary regime, the expectation of low inflation seems to have become self-fulfilling. Without an explicit increase in the inflation target or the price-level target (or the NGDP target), the Fed cannot deliver the inflation that could provide a significant economic stimulus. So the problem, it seems to me, is not that we are stuck in a liquidity trap; the problem is that we are stuck in an inflation-targeting monetary regime.

 

The Irrelevance of QE as Explained by Three Bank of England Economists

An article by Michael McLeay, Amara Radia and Ryland Thomas (“Money Creation in the Modern Economy”) published in the Bank of England Quarterly Bulletin has gotten a lot of attention recently. JKH, who liked it a lot, highlighting it on his blog, and prompting critical responses from, among others, Nick Rowe and Scott Sumner.

Let’s look at the overview of the article provided by the authors.

In the modern economy, most money takes the form of bank deposits. But how those bank deposits are created is often misunderstood: the principal way is through commercial banks making loans. Whenever a bank makes a loan, it simultaneously creates a matching deposit in the borrower’s bank account, thereby creating new money.

The reality of how money is created today differs from the description found in some economics textbooks:

• Rather than banks receiving deposits when households save and then lending them out, bank lending creates deposits.

• In normal times, the central bank does not fix the amount of money in circulation, nor is central bank money ‘multiplied up’ into more loans and deposits.

I start with a small point. What the authors mean by a “modern economy” is unclear, but presumably when they speak about the money created in a modern economy they are referring to the fact that the money held by the non-bank public has increasingly been held in the form of deposits rather than currency or coins (either tokens or precious metals). Thus, Scott Sumner’s complaint that the authors’ usage of “modern” flies in the face of the huge increase in the ratio of base money to broad money is off-target. The relevant ratio is that between currency and the stock of some measure of broad money held by the public, which is not the same as the ratio of base money to the stock of broad money.

I agree that the reality of how money is created differs from the textbook money-multiplier description. See my book on free banking and various posts I have written about the money multiplier and endogenous money. There is no meaningful distinction between “normal times” and “exceptional circumstances” for purposes of understanding how money is created.

Although commercial banks create money through lending, they cannot do so freely without limit. Banks are limited in how much they can lend if they are to remain profitable in a competitive banking system. Prudential regulation also acts as a constraint on banks’ activities in order to maintain the resilience of the financial system. And the households and companies who receive the money created by new lending may take actions that affect the stock of money — they could quickly ‘destroy’ money by using it to repay their existing debt, for instance.

I agree that commercial banks cannot create money without limit. They are constrained by the willingness of the public to hold their liabilities. Not all monies are the same, despite being convertible into each other at par. The ability of a bank to lend is constrained by the willingness of the public to hold the deposits of that bank rather than currency or the deposits of another bank.

Monetary policy acts as the ultimate limit on money creation. The Bank of England aims to make sure the amount of money creation in the economy is consistent with low and stable inflation. In normal times, the Bank of England implements monetary policy by setting the interest rate on central bank reserves. This then influences a range of interest rates in the economy, including those on bank loans.

Monetary policy is certainly a constraint on money creation, but I don’t understand why it is somehow more important (the constraint of last resort?) than the demand of the public to hold money. Monetary policy, in the framework suggested by this article, affects the costs borne by banks in creating deposits. Adopting Marshallian terminology, we could speak of the two blades of a scissors. Which bade is the ultimate blade? I don’t think there is an ultimate blade. In this context, the term “normal times” refers to periods in which interest rates are above the effective zero lower bound (see the following paragraph). But the underlying confusion here is that the authors seem to think that the amount of money created by the banking system actually matters. In fact, it doesn’t matter, because (at least in the theoretical framework being described) the banks create no more and no less money that the amount that the public willingly holds. Thus the amount of bank money created has zero macroeconomic significance.

In exceptional circumstances, when interest rates are at their effective lower bound, money creation and spending in the economy may still be too low to be consistent with the central bank’s monetary policy objectives. One possible response is to undertake a series of asset purchases, or ‘quantitative easing’ (QE). QE is intended to boost the amount of money in the economy directly by purchasing assets, mainly from non-bank financial companies.

Again the underlying problem with this argument is the presumption that the amount of money created by banks – money convertible into the base money created by the central bank – is a magnitude with macroeconomic significance. In the framework being described, there is no macroeconomic significance to that magnitude, because the value of bank money is determined by its convertibility into central bank money and the banking system creates exactly as much money as is willingly held. If the central bank wants to affect the price level, it has to do so by creating an excess demand or excess supply of the money that it — the central bank — creates, not the money created by the banking system.

QE initially increases the amount of bank deposits those companies hold (in place of the assets they sell). Those companies will then wish to rebalance their portfolios of assets by buying higher-yielding assets, raising the price of those assets and stimulating spending in the economy.

If the amount of bank deposits in the economy is the amount that the public wants to hold, QE cannot affect anything by increasing the amount of bank deposits; any unwanted bank deposits are returned to the banking system. It is only an excess of central-bank money that can possibly affect spending.

As a by-product of QE, new central bank reserves are created. But these are not an important part of the transmission mechanism. This article explains how, just as in normal times, these reserves cannot be multiplied into more loans and deposits and how these reserves do not represent ‘free money’ for banks.

The problem with the creation of new central-bank reserves by QE at the zero lower bound is that, central-bank reserves earn a higher return than alternative assets that might be held by banks, so any and all reserves created by the central bank are held willingly by the banking system. The demand of the banking for central bank reserves is unbounded at the zero-lower bound when the central bank pays a higher rate of interest than the yield on the next best alternative asset the bank could hold. If the central bank wants to increase spending, it can only do so by creating reserves that are not willingly held. Thus, in the theortetical framework described by the authors, QE cannot possibly have any effect on any macroeconomic variable. Now that’s a problem.

Stephen Williamson Gets Stuck at the Zero Lower Bound

Stephen Williamson started quite a ruckus on the econblogosphere with his recent posts arguing that, contrary to the express intentions of the FOMC, Quantitative Easing has actually caused inflation to go down. Whether Williamson’s discovery will have any practical effect remains to be seen, but in the meantime, there has been a lot head-scratching by Williamson’s readers trying to figure out how he reached such a counterintuitive conclusion. I apologize for getting to this discussion so late, but I have been trying off and on, amid a number of distractions, including travel to Switzerland where I am now visiting, to think my way through this discussion for the past several days. Let’s see if I have come up with anything enlightening to contribute.

The key ideas that Williamson relies on to derive his result are the standard ones of a real and a nominal interest rate that are related to each other by way of the expected rate of inflation (though Williamson does not distinguish between expected and annual inflation, that distinction perhaps not existing in his rational-expectations universe). The nominal rate must equal the real rate plus the expected rate of inflation. One way to think of the real rate is as the expected net pecuniary return (adjusted for inflation) from holding a real asset expressed as a percentage of the asset’s value, exclusive of any non-pecuniary benefits that it might provide (e.g., the aesthetic services provided by an art object to its owner). Insofar as an asset provides such services, the anticipated real return of the asset would be correspondingly reduced, and its current value enhanced compared to assets providing no non-pecuniary services. The value of assets providing additional non-pecuniary services includes a premium reflecting those services. The non-pecuniary benefit on which Williamson is focused is liquidity — the ease of buying or selling the asset at a price near its actual value — and the value enhancement accruing to assets providing such liquidity services is the liquidity premium.

Suppose that there are just two kinds of assets: real assets that generate (or are expected to do so) real pecuniary returns and money. Money provides liquidity services more effectively than any other asset. Now in any equilibrium in which both money and non-money assets are held, the expected net return from holding each asset must equal the expected net return from holding the other. If money, at the margin, is providing net liquidity services provided by no other asset, the expected pecuniary yield from holding money must be correspondingly less than the expected yield on the alternative real asset. Otherwise people would just hold money rather than the real asset (equivalently, the value of real assets would have to fall before people would be willing to hold those assets).

Here’s how I understand what Williamson is trying to do. I am not confident in my understanding, because Williamson’s first post was very difficult to follow. He started off with a series of propositions derived from Milton Friedman’s argument about the optimality of deflation at the real rate of interest, which implies a zero nominal interest rate, making it costless to hold money. Liquidity would be free, and the liquidity premium would be zero.

From this Friedmanian analysis of the optimality of expected deflation at a rate equal to the real rate of interest, Williamson transitions to a very different argument in which the zero lower bound does not eliminate the liquidity premium. Williamson posits a liquidity premium on bonds, the motivation for which being that bonds are useful by being readily acceptable as collateral. Williamson posits this liquidity premium as a fact, but without providing evidence, just an argument that the financial crisis destroyed or rendered unusable lots of assets that previously were, or could have been, used as collateral, thereby making Treasury bonds of short duration highly liquid and imparting to them a liquidity premium. If both bonds and money are held, and both offer the same zero nominal pecuniary return, then an equal liquidity premium must accrue to both bonds and money.

But something weird seems to have happened. We are supposed to be at the zero lower bound, and bonds and money are earning a liquidity premium, which means that the real pecuniary yield on bonds and money is negative, which contradicts Friedman’s proposition that a zero nominal interest rate implies that holding money is costless and that there is no liquidity premium. As best as I can figure this out, Williamson seems to be assuming that the real yield on real (illiquid) capital is positive, so that the zero lower bound is really an illusion, a mirage created by the atypical demand for government bonds for use as collateral.

As I suggested before, this is an empirical claim, and it should be possible to provide empirical support for the proposition that there is an unusual liquidity premium attaching to government debt of short duration in virtue of its superior acceptability as collateral. One test of the proposition would be to compare the yields on government debt of short duration versus non-government debt of short duration. A quick check here indicates that the yields on 90-day commercial paper issued by non-financial firms are very close to zero, suggesting to me that government debt of short duration is not providing any liquidity premium. If so, then the expected short-term yield on real capital may not be significantly greater than the yield on government debt, so that we really are at the zero lower bound rather than at a pseudo-zero lower bound as Williamson seems to be suggesting.

Given his assumption that there is a significant liquidity premium attaching to money and short-term government debt, I understand Williamson to be making the following argument about Quantitative Easing. There is a shortage of government debt in the sense that the public would like to hold more government debt than is being supplied. Since the federal budget deficit is rapidly shrinking, leaving the demand for short-term government debt unsatisfied, quantitative easing at least provides the public with the opportunity to exchange their relatively illiquid long-term government debt for highly liquid bank reserves created by the Fed. By so doing, the Fed is reducing the liquidity premium. But at the pseudo-zero-lower bound, a reduction in the liquidity premium implies a reduced rate of inflation, because it is the expected rate of inflation that reduces the expected return on holding money to offset the liquidity yield provided by money.

Williamson argues that by reducing the liquidity premium on holding money, QE has been the cause of the steadily declining rate of inflation over the past three years. This is a very tricky claim, because, even if we accept Williamson’s premises, he is leaving something important out of the analysis. Williamson’s argument is really about the effect of QE on expected inflation in equilibrium. But he pays no attention to the immediate effect of a change in the liquidity premium. If people reduce their valuation of money, because it is providing a reduced level of liquidity services, that change must be reflected in an immediate reduction in the demand to hold money, which would imply an immediate shift out of money into other assets. In other words, the value of money must fall. Conceptually, this would be an instantaneous, once and for all change, but if Williamson’s analysis is correct, the immediate once and for all changes should have been reflected in increased measured rates of inflation even though inflation expectations were falling. So it seems to me that the empirical fact of observed declines in the rate of inflation that motivates Williamson’s analysis turns out to be inconsistent with the implications of his analysis.

Keynes on the Fisher Equation and Real Interest Rates

Almost two months ago, I wrote a post (“Who Sets the Real Rate of Interest?”) about the Fisher equation, questioning the idea that the Fed can, at will, reduce the real rate of interest by printing money, an idea espoused by a lot of people who also deny that the Fed has the power to reduce the rate of unemployment by printing money. A few weeks later, I wrote another post (“On a Difficult Passage in the General Theory“) in which I pointed out the inconsistency between Keynes’s attack on the Fisher equation in chapter 11 of the General Theory and his analysis in chapter 17 of the liquidity premium and the conditions for asset-market equilibrium, an analysis that led Keynes to write down what is actually a generalized version of the Fisher equation. In both of those posts I promised a future post about how to understand the dynamic implications of the Fisher equation and the relationship between Fisher equation and the Keynesian analysis. This post is an attempt to make good on those promises.

As I observed in my earlier post, the Fisher equation is best understood as a property of equilibrium. If the Fisher equation does not hold, then it is reasonable to attribute the failure to some sort of disequilibrium. The most obvious, but not the only, source of disequilibrium is incorrectly expected inflation. Other sources of disequilibrium could be a general economic disorder, the entire economic system being (seriously) out of equilibrium, implying that the real rate of interest is somehow different from the “equilibrium” rate, or, as Milton Friedman might put it, that the real rate is different from the rate that would be ground out by the system of Walrasian (or Casselian or Paretian or Fisherian) equations.

Still a third possibility is that there is more than one equilibrium (i.e., more than one solution to whichever system of equations we are trying to solve). If so, as an economy moves from one equilibrium path to another through time, the nominal (and hence the real) rate of that economy could be changing independently of changes in expected inflation, thereby nullifying the empirical relationship implied (under the assumption of a unique equilibrium) by the Fisher equation.

Now in the canonical Fisherian theory of interest, there is, at any moment of time, a unique equilibrium rate of interest (actually a unique structure of equilibrium rates for all possible combinations of time periods), increasing thrift tending to reduce rates and increasing productivity of capital tending to raise them. While uniqueness of the interest rate cannot easily be derived outside a one-commodity model, the assumption did not seem all that implausible in the context of the canonical Fisherian model with a given technology and given endowments of present and future resources. In the real world, however, the future is unknown, so the future exists now only in our imagination, which means that, fundamentally, the determination of real interest rates cannot be independent of our expectations of the future. There is no unique set of expectations that is consistent with “fundamentals.” Fundamentals and expectations interact to create the future; expectations can be self-fulfilling. One of the reasons why expectations can be self-fulfilling is that often it is the case that individual expectations can only be realized if they are congruent with the expectations of others; expectations are subject to network effects. That was the valid insight in Keynes’s “beauty contest” theory of the stock market in chapter 12 of the GT.

There simply is no reason why there would be only one possible equilibrium time path. Actually, the idea that there is just one possible equilibrium time path seems incredible to me. It seems infinitely more likely that there are many potential equilibrium time paths, each path conditional on a corresponding set of individual expectations. To be sure, not all expectations can be realized. Expectations that can’t be realized produce bubbles. But just because expectations are not realized doesn’t mean that the observed price paths were bubbles; as long as it was possible, under conditions that could possibly have obtained, that the expectations could have been realized, the observed price paths were not bubbles.

Keynes was not the first economist to attribute economic fluctuations to shifts in expectations; J. S. Mill, Stanley Jevons, and A. C. Pigou, among others, emphasized recurrent waves of optimism and pessimism as the key source of cyclical fluctuations. The concept of the marginal efficiency of capital was used by Keynes to show the dependence of the desired capital stock, and hence the amount of investment, on the state of entrepreneurial expectations, but Keynes, just before criticizing the Fisher equation, explicitly identified the MEC with the Fisherian concept of “the rate of return over cost.” At a formal level, at any rate, Keynes was not attacking the Fisherian theory of interest.

So what I want to suggest is that, in attacking the Fisher equation, Keynes was really questioning the idea that a change in inflation expectations operates strictly on the nominal rate of interest without affecting the real rate. In a world in which there is a unique equilibrium real rate, and in which the world is moving along a time-path in the neighborhood of that equilibrium, a change in inflation expectations may operate strictly on the nominal rate and leave the real rate unchanged. In chapter 11, Keynes tried to argue the opposite: that the entire adjustment to a change in expected inflation is concentrated on real rate with the nominal rate unchanged. This idea seems completely unfounded. However, if the equilibrium real rate is not unique, why assume, as the standard renditions of the Fisher equation usually do, that a change in expected inflation affects only the nominal rate? Indeed, even if there is a unique real rate – remember that “unique real rate” in this context refers to a unique yield curve – the assumption that the real rate is invariant with respect to expected inflation may not be true in an appropriate comparative-statics exercise, such as the 1950s-1960s literature on inflation and growth, which recognized the possibility that inflation could induce a shift from holding cash to holding real assets, thereby increasing the rate of capital accumulation and growth, and, consequently, reducing the equilibrium real rate. That literature was flawed, or at least incomplete, in its analysis of inflation, but it was motivated by a valid insight.

In chapter 17, after deriving his generalized version of the Fisher equation, Keynes came back to this point when explaining why he had now abandoned the Wicksellian natural-rate analysis of the Treatise on Money. The natural-rate analysis, Keynes pointed out, presumes the existence of a unique natural rate of interest, but having come to believe that there could be an equilibrium associated with any level of employment, Keynes now concluded that there is actually a natural rate of interest corresponding to each level of employment. What Keynes failed to do in this discussion was to specify the relationship between natural rates of interest and levels of employment, leaving a major gap in his theoretical structure. Had he specified the relationship, we would have an explicit Keynesian IS curve, which might well differ from the downward-sloping Hicksian IS curve. As Earl Thompson, and perhaps others, pointed out about 40 years ago, the Hicksian IS curve is inconsistent with the standard neoclassical theory of production, which Keynes seems (provisionally at least) to have accepted when arguing that, with a given technology and capital stock, increased employment is possible only at a reduced real wage.

But if the Keynesian IS curve is upward-sloping, then Keynes’s criticism of the Fisher equation in chapter 11 is even harder to make sense of than it seems at first sight, because an increase in expected inflation would tend to raise, not (as Keynes implicitly assumed) reduce, the real rate of interest. In other words, for an economy operating at less than full employment, with all expectations except the rate of expected inflation held constant, an increase in the expected rate of inflation, by raising the marginal efficiency of capital, and thereby increasing the expected return on investment, ought to be associated with increased nominal and real rates of interest. If we further assume that entrepreneurial expectations are positively related to the state of the economy, then the positive correlation between inflation expectations and real interest rates would be enhanced. On this interpretation, Keynes’s criticism of the Fisher equation in chapter 11 seems indefensible.

That is one way of looking at the relationship between inflation expectations and the real rate of interest. But there is also another way.

The Fisher equation tells us that, in equilibrium, the nominal rate equals the sum of the prospective real rate and the expected rate of inflation. Usually that’s not a problem, because the prospective real rate tends to be positive, and inflation (at least since about 1938) is almost always positive. That’s the normal case. But there’s also an abnormal (even pathological) case, where the sum of expected inflation and the prospective real rate of interest is less than zero. We know right away that such a situation is abnormal, because it is incompatible with equilibrium. Who would lend money at a negative rate when it’s possible to hold the money and get a zero return? The nominal rate of interest can’t be negative. So if the sum of the prospective real rate (the expected yield on real capital) and the expected inflation rate (the negative of the expected yield on money with a zero nominal interest rate) is negative, then the return to holding money exceeds the yield on real capital, and the Fisher equation breaks down.

In other words, if r + dP/dt < 0, where r is the real rate of interest and dP/dt is the expected rate of inflation, then r < –dP/dt. But since i, the nominal rate of interest, cannot be less than zero, the Fisher equation does not hold, and must be replaced by the Fisher inequality

i > r + dP/dt.

If the Fisher equation can’t be satisfied, all hell breaks loose. Asset prices start crashing as asset owners try to unload their real assets for cash. (Note that I have not specified the time period over which the sum of expected inflation and the prospective yield on real capital are negative. Presumably the duration of that period is not indefinitely long. If it were, the system might implode.)

That’s what was happening in the autumn of 2008, when short-term inflation expectations turned negative in a contracting economy in which the short-term prospects for investment were really lousy and getting worse. The prices of real assets had to fall enough to raise the prospective yield on real assets above the expected yield from holding cash. However, falling asset prices don’t necessary restore equilibrium, because, once a panic starts it can become contagious, with falling asset prices reinforcing the expectation that asset prices will fall, depressing the prospective yield on real capital, so that, rather than bottoming out, the downward spiral feeds on itself.

Thus, for an economy at the zero lower bound, with the expected yield from holding money greater than the prospective yield on real capital, a crash in asset prices may not stabilize itself. If so, something else has to happen to stop the crash: the expected yield from holding money must be forced below the prospective yield on real capital. With the prospective yield on real capital already negative, forcing down the expected yield on money below the prospective yield on capital requires raising expected inflation above the absolute value of the prospective yield on real capital. Thus, if the prospective yield on real capital is -5%, then, to stop the crash, expected inflation would have to be raised to over 5%.

But there is a further practical problem. At the zero lower bound, not only is the prospective real rate not observable, it can’t even be inferred from the Fisher equation, the Fisher equation having become an inequality. All that can be said is that r < –dP/dt.

So, at the zero lower bound, achieving a recovery requires raising expected inflation. But how does raising expected inflation affect the nominal rate of interest? If r + dP/dt < 0, then increasing expected inflation will not increase the nominal rate of interest unless dP/dt increases enough to make r + dP/dt greater than zero. That’s what Keynes seemed to be saying in chapter 11, raising expected inflation won’t affect the nominal rate of interest, just the real rate. So Keynes’s criticism of the Fisher equation seems valid only in the pathological case when the Fisher equation is replaced by the Fisher inequality.

In my paper “The Fisher Effect Under Deflationary Expectations,” I found that a strongly positive correlation between inflation expectations (approximated by the breakeven TIPS spread on 10-year Treasuries) and asset prices (approximated by S&P 500) over the time period from spring 2008 through the end of 2010, while finding no such correlation over the period from 2003 to 2008. (Extending the data set through 2012 showed the relationship persisted through 2012 but may have broken down in 2013.) This empirical finding seems consistent with the notion that there has been something pathological about the period since 2008. Perhaps one way to think about the nature of the pathology is that the Fisher equation has been replaced by the Fisher inequality, a world in which changes in inflation expectations are reflected in changes in real interest rates instead of changes in nominal rates, the most peculiar kind of world described by Keynes in chapter 11 of the General Theory.

They Come not to Praise Market Monetarism, but to Bury It

For some reason – maybe he is still annoyed with Scott Sumner – Paul Krugman decided to channel a post by Mike Konczal purporting to show that Market Monetarism has been refuted by the preliminary first quarter GDP numbers showing NGDP increasing at a 3.7% rate and real GDP increasing at a 2.5% rate in Q1. To Konczal and Krugman (hereinafter K&K) this shows that fiscal policy, not monetary policy, is what matters most for macroeconomic performance. Why is that? Because the Fed, since embarking on its latest splurge of bond purchasing last September, has failed to stimulate economic activity in the face of the increasingly contractionary stance of fiscal policy since them (the fiscal 2013 budget deficit recently being projected to be $775 billion, a mere 4.8% of GDP).

So can we get this straight? GDP is now rising at about the same rate it has been rising since the start of the “recovery” from the 2007-09 downturn. Since September monetary policy has become easier and fiscal policy tighter. And that proves what? Sorry, I still don’t get it. But then again, I was always a little slow on the uptake.

Marcus Nunes, the Economist, Scott Sumner, and David Beckworth all weigh in on the not very devastating K&K onslaught. (Also see this post by Evan Soltas written before the fact.) But let me try to cool things down a bit.

If we posit that we are still in something akin to a zero-lower-bound situation, there are perfectly respectable theoretical grounds on which to recommend both fiscal and monetary stimulus. It is true that monetary policy, in principle, could stimulate a recovery even without fiscal stimulus — and even in the face of fiscal contraction — but for monetary policy to be able to be that effective, it would have to operate through the expectations channel, raising price-level expectations sufficiently to induce private spending. However, for good or ill, monetary policy is not aiming at more than a marginal change in inflation expectations. In that kind of policy environment, the potential effect of monetary policy is sharply constrained. Hence, the monetary theoretical case for fiscal stimulus. This is classic Hawtreyan credit deadlock (see here and here).

If monetary policy can’t do all the work by itself, then the question is whether fiscal policy can help. In principle it could if the Fed is willing to monetize the added debt generated by the fiscal stimulus. But there’s the rub. If the Fed has to monetize the added debt created by the fiscal stimulus — which, for argument’s sake, let us assume is more stimulative than equivalent monetary expansion without the fiscal stimulus — what are we supposed to assume will happen to inflation and inflation expectations?

Here is the internal contradiction – the Sumner critique, if you will – implicit in the Keynesian fiscal-policy prescription. Can fiscal policy work without increasing the rate of inflation or inflation expectations? If monetary policy alone cannot work, because it cannot break through the inflation targeting regime that traps us at the 2 percent inflation ceiling, how is fiscal policy supposed to work its way around the 2% inflation ceiling, except by absolving monetary policy of the obligation to keep inflation at or below the ceiling? But if we can allow the ceiling to be pierced by fiscal policy, why can’t we allow it to be pierced by monetary policy?

Perhaps K&K can explain that one to us.


About Me

David Glasner
Washington, DC

I am an economist at the Federal Trade Commission. Nothing that you read on this blog necessarily reflects the views of the FTC or the individual commissioners. Although I work at the FTC as an antitrust economist, most of my research and writing has been on monetary economics and policy and the history of monetary theory. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.

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