Archive for the 'Fisher equation' Category

The Internal Contradiction of Quantitative Easing

Last week I was struggling to cut and paste my 11-part series on Hawtrey’s Good and Bad Trade into the paper on that topic that I am scheduled to present next week at the Southern Economic Association meetings in Tampa Florida, completing the task just before coming down with a cold which has kept me from doing anything useful since last Thursday. But I was at least sufficiently aware of my surroundings to notice another flurry of interest in quantitative easing, presumably coinciding with Janet Yellen’s testimony at the hearings conducted by the Senate Banking Committee about her nomination to succeed Ben Bernanke as Chairman of Federal Reserve Board.

In my cursory reading of the latest discussions, I didn’t find see a lot that has not already been said, so I will take that as an opportunity to restate some points that I have previously made on this blog. But before I do that, I can’t help observing (not for the first time either) that the two main arguments made by critics of QE do not exactly coexist harmoniously with each other. First, QE is ineffective; second it is dangerous. To be sure, the tension between these two claims about QE does not prove that both can’t be true, and certainly doesn’t prove that both are wrong. But the tension might at least have given a moment’s pause to those crying that Quantitative Easing, having failed for five years to accomplish anything besides enriching Wall Street and taking bread from the mouths of struggling retirees, is going to cause the sky to fall any minute.

Nor, come to think of it, does the faux populism of the attack on a rising stock market and of the crocodile tears for helpless retirees living off the interest on their CDs coexist harmoniously with the support by many of the same characters opposing QE (e.g., Freedomworks, CATO, the Heritage Foundation, and the Wall Street Journal editorial page) for privatizing social security via private investment accounts to be invested in the stock market, the argument being that the rate of return on investing in stocks has historically been greater than the rate of return on payments into the social security system. I am also waiting for an explanation of why abused pensioners unhappy with the returns on their CDs can’t cash in the CDs and buy dividend-paying-stocks? In which charter of the inalienable rights of Americans, I wonder, does one find it written that a perfectly secure real rate of interest of not less than 2% on any debt instrument issued by the US government shall always be guaranteed?

Now there is no denying that what is characterized as a massive program of asset purchases by the Federal Reserve System has failed to stimulate a recovery comparable in strength to almost every recovery since World War II. However, not even the opponents of QE are suggesting that the recovery has been weak as a direct result of QE — that would be a bridge too far even for the hard money caucus — only that whatever benefits may have been generated by QE are too paltry to justify its supposedly bad side-effects (present or future inflation, reduced real wages, asset bubbles, harm to savers, enabling of deficit-spending, among others). But to draw any conclusion about the effects of QE, you need some kind of a baseline of comparison. QE opponents therefore like to use previous US recoveries, without the benefit of QE, as their baseline.

But that is not the only baseline available for purposes of comparison. There is also the Eurozone, which has avoided QE and until recently kept interest rates higher than in the US, though to be sure not as high as US opponents of QE (and defenders of the natural rights of savers) would have liked. Compared to the Eurozone, where nominal GDP has barely risen since 2010, and real GDP and employment have shrunk, QE, which has been associated with nearly 4% annual growth in US nominal GDP and slightly more than 2% annual growth in US real GDP, has clearly outperformed the eurozone.

Now maybe you don’t like the Eurozone, as it includes all those dysfunctional debt-ridden southern European countries, as a baseline for comparison. OK, then let’s just do a straight, head-to-head matchup between the inflation-addicted US and solid, budget-balancing, inflation-hating Germany. Well that comparison shows (see the chart below) that since 2011 US real GDP has increased by about 5% while German real GDP has increased by less than 2%.


So it does seem possible that, after all, QE and low interest rates may well have made things measurably better than they would have otherwise been. But don’t expect to opponents of QE to acknowledge that possibility.

Of course that still leaves the question on the table, why has this recovery been so weak? Well, Paul Krugman, channeling Larry Summers, offered a demographic hypothesis in his column Monday: that with declining population growth, there have been diminishing investment opportunities, which, together with an aging population, trying to save enough to support themselves in their old age, causes the supply of savings to outstrip the available investment opportunities, driving the real interest rate down to zero. As real interest rates fall, the ability of the economy to tolerate deflation — or even very low inflation — declines. That is a straightforward, and inescapable, implication of the Fisher equation (see my paper “The Fisher Effect Under Deflationary Expectations”).

So, if Summers and Krugman are right – and the trend of real interest rates for the past three decades is not inconsistent with their position – then we need to rethink revise upwards our estimates of what rate of inflation is too low. I will note parenthetically, that Samuel Brittan, who has been for decades just about the most sensible economic journalist in the world, needs to figure out that too little inflation may indeed be a bad thing.

But this brings me back to the puzzling question that causes so many people to assume that monetary policy is useless. Why have trillions of dollars of asset purchases not generated the inflation that other monetary expansions have generated? And if all those assets now on the Fed balance sheet haven’t generated inflation, what reason is there to think that the Fed could increase the rate of inflation if that is what is necessary to avoid chronic (secular) stagnation?

The answer, it seems to me is the following. If everyone believes that the Fed is committed to its inflation target — and not even the supposedly dovish Janet Yellen, bless her heart, has given the slightest indication that she favors raising the Fed’s inflation target, a target that, recent experience shows, the Fed is far more willing to undershoot than to overshoot – then Fed purchases of assets with currency are not going to stimulate additional private spending. Private spending, at or near the zero lower bound, are determined largely by expectations of future income and prices. The quantity of money in private hands, being almost costless to hold, is no longer a hot potato. So if there is no desire to reduce excess cash holdings, the only mechanism by which monetary policy can affect private spending is through expectations. But the Fed, having succeeded in anchoring inflation expectations at 2%, has succeeded in unilaterally disarming itself. So economic expansion is constrained by the combination of a zero real interest rate and expected inflation held at or below 2% by a political consensus that the Fed, even if it were inclined to, is effectively powerless to challenge.

Scott Sumner calls this monetary offset. I don’t think that we disagree much on the economic analysis, but it seems to me that he overestimates the amount of discretion that the Fed can actually exercise over monetary policy. Except at the margins, the Fed is completely boxed in by a political consensus it dares not question. FDR came into office in 1933, and was able to effect a revolution in monetary policy within his first month in office, thereby saving the country and Western Civilization. Perhaps Obama had an opportunity to do something similar early in his first term, but not any more. We are stuck at 2%, but it is no solution.

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.

On a Difficult Passage in the General Theory

Keynes’s General Theory is not, in my estimation, an easy read. The terminology is often unfamiliar, and, so even after learning one of his definitions, I have trouble remembering what the term means the next time it’s used.. And his prose style, though powerful and very impressive, is not always clear, so you can spend a long time reading and rereading a sentence or a paragraph before you can figure out exactly what he is trying to say. I am not trying to be critical, just to point out that the General Theory is a very challenging book to read, which is one, but not the only, reason why it is subject to a lot of conflicting interpretations. And, as Harry Johnson once pointed out, there is an optimum level of difficulty for a book with revolutionary aspirations. If it’s too simple, it won’t be taken seriously. And if it’s too hard, no one will understand it. Optimally, a revolutionary book should be hard enough so that younger readers will be able to figure it out, and too difficult for the older guys to understand or to make the investment in effort to understand.

In this post, which is, in a certain sense, a follow-up to an earlier post about what, or who, determines the real rate of interest, I want to consider an especially perplexing passage in the General Theory about the Fisher equation. It is perplexing taken in isolation, and it is even more perplexing when compared to other passages in both the General Theory itself and in Keynes’s other writings. Here’s the passage that I am interested in.

The expectation of a fall in the value of money stimulates investment, and hence employment generally, because it raises the schedule of the marginal efficiency of capital, i.e., the investment demand-schedule; and the expectation of a rise in the value of money is depressing, because it lowers the schedule of the marginal efficiency of capital. This is the truth which lies behind Professor Irving Fisher’s theory of what he originally called “Appreciation and Interest” – the distinction between the money rate of interest and the real rate of interest where the latter is equal to the former after correction for changes in the value of money. It is difficult to make sense of this theory as stated, because it is not clear whether the change in the value of money is or is not assumed to be foreseen. There is no escape from the dilemma that, if it is not foreseen, there will be no effect on current affairs; whilst, if it is foreseen, the prices of exiting goods will be forthwith so adjusted that the advantages of holding money and of holding goods are again equalized, and it will be too late for holders of money to gain or to suffer a change in the rate of interest which will offset the prospective change during the period of the loan in the value of the money lent. For the dilemma is not successfully escaped by Professor Pigou’s expedient of supposing that the prospective change in the value of money is foreseen by one set of people but not foreseen by another. (p. 142)

The statement is problematic on just about every level, and one hardly knows where to begin in discussing it. But just for starters, it is amazing that Keynes seems (or, for rhetorical purposes, pretends) to be in doubt whether Fisher is talking about anticipated or unanticipated inflation, because Fisher himself explicitly distinguished between anticipated and unanticipated inflation, and Keynes could hardly have been unaware that Fisher was explicitly speaking about anticipated inflation. So the implication that the Fisher equation involves some confusion on Fisher’s part between anticipated and unanticipated inflation was both unwarranted and unseemly.

What’s even more puzzling is that in his Tract on Monetary Reform, Keynes expounded the covered interest arbitrage principle that the nominal-interest-rate-differential between two currencies corresponds to the difference between the spot and forward rates, which is simply an extension of Fisher’s uncovered interest arbitrage condition (alluded to by Keynes in referring to “Appreciation and Interest”). So when Keynes found Fisher’s distinction between the nominal and real rates of interest to be incoherent, did he really mean to exempt his own covered interest arbitrage condition from the charge?

But it gets worse, because if we flip some pages from chapter 11, where the above quotation is found, to chapter 17, we see on page 224, the following passage in which Keynes extends the idea of a commodity or “own rate of interest” to different currencies.

It may be added that, just as there are differing commodity-rates of interest at any time, so also exchange dealers are familiar with the fact that the rate of interest is not even the same in terms of two different moneys, e.g. sterling and dollars. For here also the difference between the “spot” and “future” contracts for a foreign money in terms of sterling are not, as a rule, the same for different foreign moneys. . . .

If no change is expected in the relative value of two alternative standards, then the marginal efficiency of a capital-asset will be the same in whichever of the two standards it is measured, since the numerator and denominator of the fraction which leads up to the marginal efficiency will be changed in the same proportion. If, however, one of the alternative standards is expected to change in value in terms of the other, the marginal efficiencies of capital-assets will be changed by the same percentage, according to which standard they are measured in. To illustrate this let us take the simplest case where wheat, one of the alternative standards, is expected to appreciate at a steady rate of a percent per annum in terms of money; the marginal efficiency of an asset, which is x percent in terms of money, will then be x – a percent in terms of wheat. Since the marginal efficiencies of all capital assets will be altered by the same amount, it follows that their order of magnitude will be the same irrespective of the standard which is selected.

So Keynes in chapter 17 explicitly allows for the nominal rate of interest to be adjusted to reflect changes in the expected value of the asset (whether a money or a commodity) in terms of which the interest rate is being calculated. Mr. Keynes, please meet Mr. Keynes.

I think that one source of Keynes’s confusion in attacking the Fisher equation was his attempt to force the analysis of a change in inflation expectations, clearly a disequilibrium, into an equilibrium framework. In other words, Keynes is trying to analyze what happens when there has been a change in inflation expectations as if the change had been foreseen. But any change in inflation expectations, by definition, cannot have been foreseen, because to say that an expectation has changed means that the expectation is different from what it was before. Perhaps that is why Keynes tied himself into knots trying to figure out whether Fisher was talking about a change in the value of money that was foreseen or not foreseen. In any equilibrium, the change in the value of money is foreseen, but in the transition from one equilibrium to another, the change is not foreseen. When an unforeseen change occurs in expected inflation, leading to a once-and-for-all change in the value of money relative to other assets, the new equilibrium will be reestablished given the new value of money relative to other assets.

But I think that something else is also going on here, which is that Keynes was implicitly assuming that a change in inflation expectations would alter the real rate of interest. This is a point that Keynes makes in the paragraph following the one I quoted above.

The mistake lies in supposing that it is the rate of interest on which prospective changes in the value of money will directly react, instead of the marginal efficiency of a given stock of capital. The prices of existing assets will always adjust themselves to changes in expectation concerning the prospective value of money. The significance of such changes in expectation lies in their effect on the readiness to produce new assets through their reaction on the marginal efficiency of capital. The stimulating effect of the expectation of higher prices is due, not to its raising the rate of interest (that would be a paradoxical way of stimulating output – insofar as the rate of interest rises, the stimulating effect is to that extent offset) but to its raising the marginal efficiency of a given stock of capital. If the rate of interest were to rise pari passu with the marginal efficiency of capital, there would be no stimulating effect from the expectation of rising prices. For the stimulating effect depends on the marginal efficiency of capital rising relativevly to the rate of interest. Indeed Professor Fisher’s theory could best be rewritten in terms of a “real rate of interest” defined as being the rate of interest which would have to rule, consequently on change in the state of expectation as to the future value of money, in order that this change should have no effect on current output. (pp. 142-43)

Keynes’s mistake lies in supposing that an increase in inflation expectations could not have a stimulating effect except as it raises the marginal efficiency of capital relative to the rate of interest. However, the increase in the value of real assets relative to money will increase the incentive to produce new assets. It is the rise in the value of existing assets relative to money that raises the marginal efficiency of those assets, creating an incentive to produce new assets even if the nominal interest rate were to rise by as much as the rise in expected inflation.

Keynes comes back to this point at the end of chapter 17, making it more forcefully than he did the first time.

In my Treatise on Money I defined what purported to be a unique rate of interest, which I called the natural rate of interest – namely, the rate of interest which, in the terminology of my Treatise, preserved equality between the rate of saving (as there defined) and the rate of investment. I believed this to be a development and clarification of of Wicksell’s “natural rate of interest,” which was, according to him, the rate which would preserve the stability of some, not quite clearly specified, price-level.

I had, however, overlooked the fact that in any given society there is, on this definition, a different natural rate for each hypothetical level of employment. And, similarly, for every rate of interest there is a level of employment for which that rate is the “natural” rate, in the sense that the system will be in equilibrium with that rate of interest and that level of employment. Thus, it was a mistake to speak of the natural rate of interest or to suggest that the above definition would yield a unique value for the rate of interest irrespective of the level of employment. . . .

If there is any such rate of interest, which is unique and significant, it must be the rate which we might term the neutral rate of interest, namely, the natural rate in the above sense which is consistent with full employment, given the other parameters of the system; though this rate might be better described, perhaps, as the optimum rate. (pp. 242-43)

So what Keynes is saying, I think, is this. Consider an economy with a given fixed marginal efficiency of capital (MEC) schedule. There is some interest rate that will induce sufficient investment expenditure to generate enough spending to generate full employment. That interest rate Keynes calls the “neutral” rate of interest. If the nominal rate of interest is more than the neutral rate, the amount of investment will be less than the amount necessary to generate full employment. In such a situation an expectation that the price level will rise will shift up the MEC schedule by the amount of the expected increase in inflation, thereby generating additional investment spending. However, because the MEC schedule is downward-sloping, the upward shift in the MEC schedule that induces increased investment spending will correspond to an increase in the rate of interest that is less than the increase in expected inflation, the upward shift in the MEC schedule being partially offset by the downward movement along the MEC schedule. In other words, the increase in expected inflation raises the nominal rate of interest by less than increase in expected inflation by inducing additional investment that is undertaken only because the real rate of interest has fallen.

However, for an economy already operating at full employment, an increase in expected inflation would not increase employment, so whether there was any effect on the real rate of interest would depend on the extent to which there was a shift from holding money to holding real capital assets in order to avoid the inflation tax.

Before closing, I will just make two side comments. First, my interpretation of Keynes’s take on the Fisher equation is similar to that of Allin Cottrell in his 1994 paper “Keynes and the Keynesians on the Fisher Effect.” Second, I would point out that the Keynesian analysis violates the standard neoclassical assumption that, in a two-factor production function, the factors are complementary, which implies that an increase in employment raises the MEC schedule. The IS curve is not downward-sloping, but upward sloping. This is point, as I have explained previously (here and here), was made a long time ago by Earl Thompson, and it has been made recently by Nick Rowe and Miles Kimball.

I hope in a future post to work out in more detail the relationship between the Keynesian and the Fisherian analyses of real and nominal interest rates.

What Gives? Has the Market Stopped Loving Inflation?

One of my few, and not very compelling, claims to fame is a (still unpublished) paper (“The Fisher Effect Under Deflationary Expectations“) that I wrote in late 2010 in which I used the Fisher Equation relating the real and nominal rates of interest via the expected rate of inflation to explain what happens in a financial panic. I pointed out that the usual understanding that the nominal rate of interest and the expected rate of inflation move in the same direction, and possibly even by the same amount, cannot be valid when the expected rate of inflation is negative and the real rate is less than expected deflation. In those perilous conditions, the normal equilibrating process, by which the nominal rate adjusts to reflect changes in inflation expectations, becomes inoperative, because the nominal rate gets stuck at zero. In that unstable environment, the only avenue for adjustment is in the market for assets. In particular, when the expected yield from holding money (the expected rate of deflation) approaches or exceeds the expected yield on real capital, asset prices crash as asset owners all try to sell at the same time, the crash continuing until the expected yield on holding assets is no longer less than the expected yield from holding money. Of course, even that adjustment mechanism will restore an equilibrium only if the economy does not collapse entirely before a new equilibrium of asset prices and expected yields can be attained, a contingency not necessarily as unlikely as one might hope.

I therefore hypothesized that while there is not much reason, in a well-behaved economy, for asset prices to be very sensitive to changes in expected inflation, when expected inflation approaches, or exceeds, the expected return on capital assets (the real rate of interest), changes in expected inflation are likely to have large effects on asset values. This possibility that the relationship between expected inflation and asset prices could differ depending on the prevalent macroeconomic environment suggested an empirical study of the relationship between expected inflation (as approximated by the TIPS spread on 10-year Treasuries) and the S&P 500 stock index. My results were fairly remarkable, showing that, since early 2008 (just after the start of the downturn in late 2007), there was a consistently strong positive correlation between expected inflation and the S&P 500. However, from 2003 to 2008, no statistically significant correlation between expected inflation and asset prices showed up in the data.

Ever since then, I have used this study (and subsequent informal follow-ups that have consistently generated similar results) as the basis for my oft-repeated claim that the stock market loves inflation. But now, guess what? The correlation between inflation expectations and the S&P 500 has recently vanished. The first of the two attached charts plots both expected inflation, as measured by the 10-year TIPS spread, and the S&P 500 (normalized to 1 on March 2, 2009). It is obvious that two series are highly correlated. However, you can see that over the last few months it looks as if the correlation has been reversed, with inflation expectations falling even as the S&P 500 has been regularly reaching new all-time highs.


Here is a second chart that provides a closer look at the behavior of the S&P 500 and the TIPS spread since the beginning of March.


So what’s going on? I wish I knew. But here is one possibility. Maybe the economy is finally emerging from its malaise, and, after four years of an almost imperceptible recovery, perhaps the overall economic outlook has improved enough so that, even if we haven’t yet returned to normalcy, we are at least within shouting distance of it. If so, maybe asset prices are no longer as sensitive to inflation expectations as they were from 2008 to 2012. But then the natural question becomes: what caused the economy to reach a kind of tipping point into normalcy in March? I just don’t know.

And if we really are back to normal, then why is the real rate implied by the TIPS negative? True, the TIPS yield is not really the real rate in the Fisher equation, but a negative yield on a 10-year TIPS does not strike me as characteristic of a normal state of affairs. Nevertheless, the real yield on the 10-year TIPS has risen by about 50 basis points since March and by 75 basis points since December, so something noteworthy seems to have happened. And a fairly sharp rise in real rates suggests that recent increases in stock prices have been associated with expectations of increasing real cash flows and a strengthening economy. Increasing optimism about real economic growth, given that there has been no real change in monetary policy since last September when QE3 was announced, may themselves have contributed to declining inflation expectations.

What does this mean for policy? The empirical correlation between inflation expectations and asset prices is subject to an identification problem. Just because recent developments may have caused the observed correlation between inflation expectations and stock prices to disappear, one can’t conclude that, in the “true” structural model, the effect of a monetary policy that raised inflation expectations would not be to raise asset prices. The current semi-normal is not necessarily a true normal.

So my cautionary message is: Don’t use the recent disappearance of the correlation between inflation expectations and asset prices to conclude that it’s safe to abandon QE.

My Paper (co-authored with Paul Zimmerman) on Hayek and Sraffa

I have just uploaded to the SSRN website a new draft of the paper (co-authored with Paul Zimmerman) on Hayek and Sraffa and the natural rate of interest, presented last June at the History of Economics Society conference at Brock University. The paper evolved from an early post on this blog in September 2011. I also wrote about the Hayek-Sraffa controversy in a post in June 2012 just after the HES conference.

One interesting wrinkle that occurred to me just as I was making revisions in the paper this week is that Keynes’s treatment of own rates in chapter 17 of the General Theory, which was in an important sense inspired by Sraffa, but, in my view, came to a very different conclusion from Sraffa’s, was actually nothing more than a generalization of Irving Fisher’s analysis of the real and nominal rates of interest, first presented in Fisher’s 1896 book Appreciation and Interest. In his Tract on Monetary Reform, Keynes extended Fisher’s analysis into his theory of covered interest rate arbitrage. What is really surprising is that, despite his reliance on Fisher’s analysis in the Tract and also in the Treatise on Money, Keynes sharply criticized Fisher’s analysis of the nominal and real rates of interest in chapter 13 of the General Theory. (I discussed that difficult passage in the General Theory in this post).  That is certainly surprising. But what is astonishing to me is that, after trashing Fisher in chapter 13 of the GT, Keynes goes back to Fisher in chapter 17, giving a generalized restatement of Fisher’s analysis in his discussion of own rates. Am I the first person to have noticed Keynes’s schizophrenic treatment of Fisher in the General Theory?

PS: My revered teacher, the great Armen Alchian passed away yesterday at the age of 98. There have been many tributes to him, such as this one by David Henderson, also a student of Alchian’s, in the Wall Street Journal. I have written about Alchian in the past (here, here, here, here, and here), and I hope to write about Alchian again in the near future. There was none like him; he will be missed terribly.

The Wisdom of David Laidler

Michael Woodford’s paper for the Jackson Hole Symposium on Monetary Policy wasn’t the only important paper on monetary economics to be posted on the internet last month. David Laidler, perhaps the world’s greatest expert on the history of monetary theory and macroeconomics since the time of Adam Smith, has written an important paper with the somewhat cryptic title, “Two Crises, Two Ideas, and One Question.” Most people will figure out pretty quickly which two crises Laidler is referring to, but you will have to read the paper in order to figure out which two ideas and which question, Laidler has on his mind. Actually, you won’t have to read the paper if you keep reading this post, because I am about to tell you. The two ideas are what Laidler calls the “Fisher relation” between real and nominal interest rates, and the idea of a lender of last resort. The question is whether a market economy is inherently stable or unstable.

How does one weave these threads into a coherent narrative? Well, to really understand that you really will just have to read Laidler’s paper, but this snippet from the introduction will give you some sense of what he is up to.

These two particular ideas are especially interesting, because in the 1960s and ’70s, between our two crises, they feature prominently in the Monetarist reassessment of the Great Depression, which helped to establish the dominance in macroeconomic thought of the view that, far from being a manifestation of deep flaws in the very structure of the market economy, as it had at first been taken to be, this crisis was the consequence of serious policy errors visited upon an otherwise robustly self-stabilizing system. The crisis that began in 2007 has re-opened this question.

The Monetarist counterargument to the Keynesian view that the market economy is inherently subject to wide fluctuations and has no strong tendency toward full employment was that the Great Depression was caused primarily by a policy shock, the failure of the Fed to fulfill its duty to act as a lender of last resort during the US financial crisis of 1930-31. Originally, the Fisher relation did not figure prominently in this argument, but it eventually came to dominate Monetarism and the post-Monetarist/New Keynesian orthodoxy in which the job of monetary policy was viewed as setting a nominal interest rate (via a Taylor rule) that would be consistent with expectations of an almost negligible rate of inflation of about 2%.

This comfortable state of affairs – Monetarism without money is how Laidler describes it — in which an inherently stable economy would glide along its long-run growth path with low inflation, only rarely interrupted by short, shallow recessions, was unpleasantly overturned by the housing bubble and the subsequent financial crisis, producing the steepest downturn since 1937-38. That downturn has posed a challenge to Monetarist orthodoxy inasmuch as the sudden collapse, more or less out of nowhere in 2008, seemed to suggest that the market economy is indeed subject to a profound instability, as the Keynesians of old used to maintain. In the Great Depression, Monetarists could argue, it was all, or almost all, the fault of the Federal Reserve for not taking prompt action to save failing banks and for not expanding the money supply sufficiently to avoid deflation. But in 2008, the Fed provided massive support to banks, and even to non-banks like AIG, to prevent a financial meltdown, and then embarked on an aggressive program of open-market purchases that prevented an incipient deflation from taking hold.

As a result, self-identifying Monetarists have split into two camps. I will call one camp the Market Monetarists, with whom I identify even though I am much less of a fan of Milton Friedman, the father of Monetarism, than most Market Monetarists, and, borrowing terminology adopted in the last twenty years or so by political conservatives in the US to distinguish between old-fashioned conservatives and neoconservatives, I will call the old-style Monetarists, paleo-Monetarists. The paelo-Monetarists are those like Alan Meltzer, the late Anna Schwartz, Thomas Humphrey, and John Taylor (a late-comer to Monetarism who has learned quite well how to talk to the Monetarist talk). For the paleo-Monetarists, in the absence of deflation, the extension of Fed support to non-banking institutions and the massive expansion of the Fed’s balance sheet cannot be justified. But this poses a dilemma for them. If there is no deflation, why is an inherently stable economy not recovering? It seems to me that it is this conundrum which has led paleo-Monetarists into taking the dubious position that the extreme weakness of the economic recovery is a consequence of fiscal and monetary-policy uncertainty, the passage of interventionist legislation like the Affordable Health Care Act and the Dodd-Frank Bill, and the imposition of various other forms of interventionist regulations by the Obama administration.

Market Monetarists, on the other hand, have all along looked to monetary policy as the ultimate cause of both the downturn in 2008 and the lack of a recovery subsequently. So, on this interpretation, what separates paleo-Monetarists from Market Monetarists is whether you need outright deflation in order to precipitate a serious malfunction in a market economy, or whether something less drastic can suffice. Paleo-Monetarists agree that Japan in the 1990s and even early in the 2000s was suffering from a deflationary monetary policy, a policy requiring extraordinary measures to counteract. But the annual rate of deflation in Japan was never more than about 1% a year, a far cry from the 10% annual rate of deflation in the US between late 1929 and early 1933. Paleo-Monetarists must therefore explain why there is a radical difference between 1% inflation and 1% deflation. Market Monetarists also have a problem in explaining why a positive rate of inflation, albeit less than the 2% rate that is generally preferred, is not adequate to sustain a real recovery from starting more than four years after the original downturn. Or, if you prefer, the question could be restated as why a 3 to 4% rate of increase in NGDP is not adequate to sustain a real recovery, especially given the assumption, shared by paleo-Monetarists and Market Monetarists, that a market economy is generally stable and tends to move toward a full-employment equilibrium.

Here is where I think Laidler’s focus on the Fisher relation is critically important, though Laidler doesn’t explicitly address the argument that I am about to make. This argument, which I originally made in my paper “The Fisher Effect under Deflationary Expectations,” and have repeated in several subsequent blog posts (e.g., here) is that there is no specific rate of deflation that necessarily results in a contracting economy. There is plenty of historical experience, as George Selgin and others have demonstrated, that deflation is consistent with strong economic growth and full employment. In a certain sense, deflation can be a healthy manifestation of growth, allowing that growth, i.e., increasing productivity of some or all factors of production, to be translated into falling output prices. However, deflation is only healthy in an economy that is growing because of productivity gains. If productivity is flagging, there is no space for healthy (productivity-driven) deflation.

The Fisher relation between the nominal interest rate, the real interest rate and the expected rate of deflation basically tells us how much room there is for healthy deflation. If we take the real interest rate as given, that rate constitutes the upper bound on healthy deflation. Why, because deflation greater than real rate of interest implies a nominal rate of interest less than zero. But the nominal rate of interest has a lower bound at zero. So what happens if the expected rate of deflation is greater than the real rate of interest? Fisher doesn’t tell us, because in equilibrium it isn’t possible for the rate of deflation to exceed the real rate of interest. But that doesn’t mean that there can’t be a disequilibrium in which the expected rate of deflation is greater than the real rate of interest. We (or I) can’t exactly model that disequilibrium process, but whatever it is, it’s ugly. Really ugly. Most investment stops, the rate of return on cash (i.e., expected rate of deflation) being greater than the rate of return on real capital. Because the expected yield on holding cash exceeds the expected yield on holding real capital, holders of real capital try to sell their assets for cash. The only problem is that no one wants to buy real capital with cash. The result is a collapse of asset values. At some point, asset values having fallen, and the stock of real capital having worn out without being replaced, a new equilibrium may be reached at which the real rate will again exceed the expected rate of deflation. But that is an optimistic scenario, because the adjustment process of falling asset values and a declining stock of real capital may itself feed pessimistic expectations about the future value of real capital so that there literally might not be a floor to the downward spiral, at least not unless there is some exogenous force that can reverse the downward spiral, e.g., by changing price-level expectations.  Given the riskiness of allowing the rate of deflation to come too close to the real interest rate, it seems prudent to keep deflation below the real rate of interest by a couple of points, so that the nominal interest rate doesn’t fall below 2%.

But notice that this cumulative downward process doesn’t really require actual deflation. The same process could take place even if the expected rate of inflation were positive in an economy with a negative real interest rate. Real interest rates have been steadily falling for over a year, and are now negative even at maturities up to 10 years. What that suggests is that ceiling on tolerable deflation is negative. Negative deflation is the same as inflation, which means that there is a lower bound to tolerable inflation.  When the economy is operating in an environment of very low or negative real rates of interest, the economy can’t recover unless the rate of inflation is above the lower bound of tolerable inflation. We are not in the critical situation that we were in four years ago, when the expected yield on cash was greater than the expected yield on real capital, but it is a close call. Why are businesses, despite high earnings, holding so much cash rather than using it to purchase real capital assets? My interpretation is that with real interest rates negative, businesses do not see a sufficient number of profitable investment projects to invest in. Raising the expected price level would increase the number of investment projects that appear profitable, thereby inducing additional investment spending, finally inducing businesses to draw down, rather than add to, their cash holdings.

So it seems to me that paleo-Monetarists have been misled by a false criterion, one not implied by the Fisher relation that has become central to Monetarist and Post-Monetarist policy orthodoxy. The mere fact that we have not had deflation since 2009 does not mean that monetary policy has not been contractionary, or, at any rate, insufficiently expansionary. So someone committed to the proposition that a market economy is inherently stable is not obliged, as the paleo-Monetarists seem to think, to take the position that monetary policy could not have been responsible for the failure of the feeble recovery since 2009 to bring us back to full employment. Whether it even makes sense to think about an economy as being inherently stable or unstable is a whole other question that I will leave for another day.

HT:  Lars Christensen

Thompson’s Reformulation of Macroeconomic Theory, Part III: Solving the FF-LM Model

In my two previous installments on Earl Thompson’s reformulation of macroeconomic theory (here and here), I have described the paradigm shift from the Keynesian model to Thompson’s reformulation — the explicit modeling of the second factor of production needed to account for a declining marginal product of labor, and the substitution of a factor-market equilibrium condition for equality between savings and investment to solve the model. I have also explained how the Hicksian concept of temporary equilibrium could be used to reconcile market clearing with involuntary Keynesian unemployment by way of incorrect expectations of future wages by workers occasioned by incorrect expectations of the current (unobservable) price level.

In this installment I provide details of how Thompson solved his macroeconomic model in terms of equilibrium in two factor markets instead of equality between savings and investment. The model consists of four markets: a market for output (C – a capital/consumption good), labor (L), capital services (K), and money (M). Each market has its own price: the price of output is P; the price of labor services is W; the price of capital services is R; the price of money, which serves as numeraire, is unity. Walras’s Law allows exclusion of one of these markets, and in the neoclassical spirit of the model, the excluded market is the one for output, i.e., the market characterized by the Keynesian expenditure functions. The model is solved by setting three excess demand functions equal to zero: the excess demand for capital services, XK, the excess demand for labor services, XL, and the excess demand for money, XM. The excess demands all depend on W, P, and R, so the solution determines an equilibrium wage rate, an equilibrium rental rate for capital services, and an equilibrium price level for output.

In contrast, the standard Keynesian model includes a bond market instead of a market for capital services. The excluded market is the bond market, with equilibrium determined by setting the excess demands for labor services, for output, and for money equal to zero. The market for output is analyzed in terms of the Keynesian expenditure functions for household consumption and business investment, reflected in the savings-equals-investment equilibrium condition.

Thompson’s model is solved by applying the simple logic of the neoclassical theory of production, without reliance on the Keynesian speculations about household and business spending functions. Given perfect competition, and an aggregate production function, F(K, L), with the standard positive first derivatives and negative second derivatives, the excess demand for capital services can be represented by the condition that the rental rate for capital equal the value of the marginal product of capital (MPK) given the fixed endowment of capital, K*, inherited from the last period, i.e.,

R = P times MPK.

The excess demand for labor can similarly be represented by the condition that the reservation wage at which workers are willing to accept employment equals the value of the marginal product of labor given the inherited stock of capital K*. As I explained in the previous installment, this condition allows for the possibility of Keynesian involuntary unemployment when wage expectations by workers are overly optimistic.

The market rate of interest, r, satisfies the following version of the Fisher equation:

r = R/P + (Pe – P)/P), where Pe is the expected price level in the next period.

Because K* is assumed to be fully employed with a positive marginal product, a given value of P determines a unique corresponding equilibrium value of L, the supply of labor services being upward-sloping, but relatively elastic with respect to the nominal wage for given wage expectations by workers. That value of L in turn determines an equilibrium value of R for the given value of P. If we assume that inflation expectations are constant (i.e., that Pe varies in proportion to P), then a given value of P must correspond to a unique value of r. Because simultaneous equilibrium in the markets for capital services and labor services can be represented by unique combinations of P and r, a factor-market equilibrium condition can be represented by a locus of points labeled the FF curve in Figure 1 below.

The FF curve must be upward-sloping, because a linear homogenous production function of two scarce factors (i.e., doubling inputs always doubles output) displaying diminishing marginal products in both factors implies that the factors are complementary (i.e., adding more of one factor increases the marginal productivity of the other factor). Because an increase in P increases employment, the marginal product of capital increases, owing to complementarity between the factors, implying that R must increase by more than P. An increase in the price level, P, is therefore associated with an increase in the market interest rate r.

Beyond the positive slope of the FF curve, Thompson makes a further argument about the position of the FF curve, trying to establish that the FF curve must intersect the horizontal (P) axis at a positive price level as the nominal interest rate goes to 0. The point of establishing that the FF curve intersects the horizontal axis at a positive value of r is to set up a further argument about the stability of the model’s equilibrium. I find that argument problematic. But discussion of stability issues are better left for a future post.

Corresponding to the FF curve, it is straightforward to derive another curve, closely analogous to the Keynesian LM curve, with which to complete a graphical solution of the model. The two LM curves are not the same, Thompson’s LM curve being constructed in terms of the nominal interest rate and the price level rather than in terms of nominal interest rate and nominal income, as is the Keynesian LM curve. The switch in axes allows Thompson to construct two versions of his LM curve. In the conventional case, a fixed nominal quantity of non-interest-bearing money being determined exogenously by the monetary authority, increasing price levels imply a corresponding increase in the nominal demand for money. Thus, with a fixed nominal quantity of money, as the price level rises the nominal interest rate must rise to reduce the quantity of money demanded to match the nominal quantity exogenously determined. This version of the LM curve is shown in Figure 2.

A second version of the LM curve can be constructed corresponding to Thompson’s characterization of the classical model of a competitively supplied interest-bearing money supply convertible into commodities at a fixed exchange rate (i.e., a gold standard except that with only one output money is convertible into output in general not one of many commodities). The quantity of money competitively supplied by the banking system would equal the quantity of money demanded at the price level determined by convertibility between money and output. Because money in the classical model pays competitive interest, changes in the nominal rate of interest do not affect the quantity of money demanded. Thus, the LM curve in the classical case is a vertical line corresponding to the price level determined by the convertibility of money into output. The classical LM curve is shown in Figure 3.

The full solution of the model (in the conventional case) is represented graphically by the intersection of the FF curve with the LM curve in Figure 4.

Note that by applying Walras’s Law, one could draw a CC curve representing equilibrium in the market for commodities (an analogue to the Keynesian IS curve) in the space between the FF and the LM curves and intersecting the two curves precisely at their point of intersection. Thus, Thompson’s reformulation supports Nick Rowe’s conjecture that the IS curve, contrary to the usual derivation, is really upward-sloping.

Williamson v. Sumner

Stephen Williamson weighed in on nominal GDP targeting in a blog post on Monday. Scott Sumner and Marcus Nunes have already responded, and Williamson has already responded to Scott, so I will just offer a few semi-random comments about Williamson’s post, the responses and counter-response.

Let’s start with Williamson’s first post. He interprets Fed policy, since the Volcker era, as an implementation of the Taylor rule:

The Taylor rule takes as given the operating procedure of the Fed, under which the FOMC determines a target for the overnight federal funds rate, and the job of the New York Fed people who manage the System Open Market Account (SOMA) is to hit that target. The Taylor rule, if the FOMC follows it, simply dictates how the fed funds rate target should be set every six weeks, given new information.

So, from the mid-1980s until 2008, everything seemed to be going swimmingly. Just as the inflation targeters envisioned, inflation was not only low, but we had a Great Moderation in the United States. Ben Bernanke, who had long been a supporter of inflation targeting, became Fed Chair in 2006, and I think it was widely anticipated that he would push for inflation targeting with the US Congress.

Thus, under the Taylor rule, as implemented, ever more systematically, by the FOMC, the federal funds rate (FFR) was set with a view to achieving an implicit inflation target, presumably in the neighborhood of 2%. However, as a result of the Little Depression beginning in 2008, Scott Sumner et al. have proposed targeting NGDP instead of inflation. Williamson has problems with NGDP targeting that I will come back to, but he makes a positive case for inflation targeting in terms of Friedman’s optimal-supply-of-money rule, under which the nominal rate of interest is held at zero via a rate of inflation that is the negative of the real interest rate (i.e., deflation whenever the real rate of interest is positive). Back to Williamson:

The Friedman rule . . . dictates that monetary policy be conducted so that the nominal interest rate is always zero. Of course we know that no central bank does that, and we have good reasons to think that there are other frictions in the economy which imply that we should depart from the Friedman rule. However, the lesson from the Friedman rule argument is that the nominal interest rate reflects a distortion and that, once we take account of other frictions, we should arrive at an optimal policy rule that will imply that the nominal interest rate should be smooth. One of the frictions some macroeconomists like to think about is price stickiness. In New Keynesian models, price stickiness leads to relative price distortions that monetary policy can correct.

If monetary policy is about managing price distortions, what does that have to do with targeting some nominal quantity? Any model I know about, if subjected to a NGDP targeting rule, would yield a suboptimal allocation of resources.

I really don’t understand this. Williamson is apparently defending current Fed practice (i.e., targeting a rate of inflation) by presenting it as a practical implementation of Friedman’s proposal to set the nominal interest rate at zero. But setting the nominal interest rate at zero is analogous to inflation targeting only if the real rate of interest doesn’t change. Friedman’s rule implies that the rate of deflation changes by as much as the real rate of interest changes. Or does Williamson believe that the real rate of interest never changes? Those of us now calling for monetary stimulus believe that we are stuck in a trap of widespread entrepreneurial pessimism, reflected in very low nominal and negative real interest rates. To get out of such a self-reinforcing network of pessimistic expectations, the economy needs a jolt of inflationary shock therapy like the one administered by FDR in 1933 when he devalued the dollar by 40%.

As I said a moment ago, even apart from Friedman’s optimality argument for a zero nominal interest rate, Williamson thinks that NGDP targeting is a bad idea, but the reasons that he offers for thinking it a bad idea strike me as a bit odd. Consider this one. The Fed would never adopt NGDP targeting, because it would be inconsistent with the Fed’s own past practice. I kid you not; that’s just what he said:

It will be a cold day in hell when the Fed adopts NGDP targeting. Just as the Fed likes the Taylor rule, as it confirms the Fed’s belief in the wisdom of its own actions, the Fed will not buy into a policy rule that makes its previous actions look stupid.

So is Williamson saying that the Fed will not adopt any policy that is inconsistent with its actions in, say, the Great Depression? That will surely do a lot to enhance the Fed’s institutional credibility, about which Williamson is so solicitous.

Then Williamson makes another curious argument based on a comparison of Hodrick-Prescott-filtered NGDP and RGDP data from 1947 to 2011. Williamson plotted the two series on the accompanying graph. Observing that while NGDP was less variable than RDGP in the 1970s, the two series tracked each other closely in the Great-Moderation period (1983-2007), Williamson suggests that, inasmuch as the 1970s are now considered to have been a period of bad monetary policy, low variability of NGDP does not seem to matter that much.

Marcus Nunes, I think properly, concludes that Williamson’s graph is wrong, because Williamson ignores the fact that there was a rising trend of NGDP growth during the 1970s, while during the Great Moderation, NGDP growth was stationary. Marcus corrects Williamson’s error with two graphs of his own (which I attach), showing that the shift to NGDP targeting was associated with diminished volatility in RGDP during the Great Moderation.

Furthermore, Scott Sumner questions whether the application of the Hodrick-Prescott filter to the entire 1947-2011 period was appropriate, given the collapse of NGDP after 2008, thereby distorting estimates of the trend.

There may be further issues associated with the appropriateness of the Hodrick-Prescott filter, issues which I am certainly not competent to assess, but I will just quote from Andrew Harvey’s article on filters for Business Cycles and Depressions: An Encyclopedia, to which I referred recently in my post about Anna Schwartz. Here is what Harvey said about the HP filter.

Thus for quarterly data, applying the [Hodrick-Prescott] filter to a random walk is likely to create a spurious cycle with a period of about seven or eight years which could easily be identified as a business cycle . . . Of course, the application of the Hodrick-Prescott filter yields quite sensible results in some cases, but everything depends on the properties of the series in question.

Williamson then wonders, if stabilizing NGDP is such a good idea, why not stabilize raw NGDP rather than seasonally adjusted NGDP, as just about all advocates of NGDP targeting implicitly or explicitly recommend? In a comment on Williamson’s blog, Nick Rowe raised the following point:

The seasonality question is interesting. We could push it further. Should we want the same level of NGDP on weekends as during the week? What about nighttime?

But then I think the same question could be asked for inflation targeting, or price level path targeting, because there is a seasonal pattern to CPI too. And (my guess is) the CPI is higher on weekends. Not sure if the CPI is lower or higher at night.

In a subsequent comment, Nick made the following, quite telling, observation:

Actually, thinking about seasonality is a regular repeated shock reminds me of something Lucas once said about rational expectations equilibria. I don’t remember his precise words, but it was something to the effect that we should be very wary of assuming the economy will hit the RE equilibrium after a shock that is genuinely new, but if the shock is regular and repeated agents will have figured out the RE equilibrium. Seasonality, and day of the week effects, will be presumably like that.

So, I think the point about eliminating seasonal fluctuations has been pretty much laid to rest. But perhaps Williamson will try to resurrect it (see below).

In his reply to Scott, Williamson reiterates his long-held position that the Fed is powerless to affect the economy except by altering the interest rate, now 0.25%, paid to banks on their reserves held at the Fed. Since the Fed could do no more than cut the rate to zero, and a negative interest rate would be deemed an illegal tax, Williamson sees no scope for monetary policy to be effective. Lars Chritensen, however, points out that the Fed could aim at a lower foreign exchange value of the dollar and conduct its monetary policy via unsterilized sales of dollars in the foreign-exchange markets in support of an explicit price level or NGDP target.

Williamson defends his comments about stabilizing seasonal fluctuations as follows:

My point in looking at seasonally adjusted nominal GDP was to point out that fluctuations in nominal GDP can’t be intrinsically bad. I think we all recognize that seasonal variation in NGDP is something that policy need not be doing anything to eliminate. So how do we know that we want to eliminate this variation at business cycle frequencies? In contrast to what Sumner states, it is widely recognized that some of the business cycle variability in RGDP we observe is in fact not suboptimal. Most of what we spend our time discussing (or fighting about) is the nature and quantitative significance of the suboptimalities. Sumner seems to think (like old-fashioned quantity theorists), that there is a sufficient statistic for subomptimality – in this case NGDP. I don’t see it.

So, apparently, Williamson does accept the comment from Nick Rowe (quoted above) on his first post. He now suggests that Scott Sumner and other NGDP targeters are too quick to assume that observed business-cycle fluctuations are non-optimal, because some business-cycle fluctuations may actually be no less optimal than the sort of responses to seasonal fluctuations that are general conceded to be unproblematic. The difference, of course, is that seasonal fluctuations are generally predictable and predicted, which is not the case for business-cycle fluctuations. Why, then, is there any theoretical presumption that unpredictable business-cycle fluctuations that falsify widely held expectations result in optimal responses? The rational for counter-cyclical policy is to minimize incorrect expectations that lead to inefficient search (unemployment) and speculative withholding of resources from their most valuable uses. The first-best policy for doing this, as I explained in the last chapter of my book Free Banking and Monetary Reform, would be to stabilize a comprehensive index of wage rates.  Practical considerations may dictate choosing a less esoteric policy target than stabilizing a wage index, say, stablizing the growth path of NGDP.

I think I’ve said more than enough for one post, so I’ll pass on Williamson’s further comments of the Friedman rule and why he chooses to call himself a Monetarist.

PS Yesterday was the first anniversary of this blog. Happy birthday and many happy returns to all my readers.

Inflation Expectations Are Falling; Run for Cover

The S&P 500 fell today by more than 1 percent, continuing the downward trend began last month when the euro crisis, thought by some commentators to have been surmounted last November thanks to the consummate statesmanship of Mrs. Merkel, resurfaced once again, even more acute than in previous episodes. The S&P 500, having reached a post-crisis high of 1419.04 on April 2, a 10% increase since the end of 2011, closed today at 1338.35, almost 8% below its April 2nd peak.

What accounts for the drop in the stock market since April 2? Well, as I have explained previously on this blog (here, here, here) and in my paper “The Fisher Effect under Deflationary Expectations,” when expected yield on holding cash is greater or even close to the expected yield on real capital, there is insufficient incentive for business to invest in real capital and for households to purchase consumer durables. Real interest rates have been consistently negative since early 2008, except in periods of acute financial distress (e.g., October 2008 to March 2009) when real interest rates, reflecting not the yield on capital, but a dearth of liquidity, were abnormally high. Thus, unless expected inflation is high enough to discourage hoarding, holding money becomes more attractive than investing in real capital. That is why ever since 2008, movements in stock prices have been positively correlated with expected inflation, a correlation neither implied by conventional models of stock-market valuation nor evident in the data under normal conditions.

As the euro crisis has worsened, the dollar has been appreciating relative to the euro, dampening expectations for US inflation, which have anyway been receding after last year’s temporary supply-driven uptick, and after the ambiguous signals about monetary policy emanating from Chairman Bernanke and the FOMC. The correspondence between inflation expectations, as reflected in the breakeven spread between the 10-year fixed maturity Treasury note and 10-year fixed maturity TIPS, and the S&P 500 is strikingly evident in the chart below showing the relative movements in inflation expectations and the S&P 500 (both normalized to 1.0 at the start of 2012.

With the euro crisis showing no signs of movement toward a satisfactory resolution, with news from China also indicating a deteriorating economy and possible deflation, the Fed’s current ineffectual monetary policy will not prevent a further slowing of inflation and a further perpetuation of our national agony. If inflation and expected inflation keep falling, the hopeful signs of recovery that we saw during the winter and early spring will, once again, turn out to have been nothing more than a mirage

Which Fed Policy Is Boosting Stocks?

In yesterday’s (December 27, 2011) Wall Street Journal, Cynthia Lin (“Fed Policy Delivers a Tonic for Stocks”) informs us that the Fed’s Operation Twist program “has been a boon for investors during the year’s final quarter.”

The program, which has its final sale of short-dated debt for the year on Wednesday, pushed up a volatile U.S. stock market over the past few months and helped lower mortgage rates, breathing some life into the otherwise struggling U.S. housing sector, they said. Last week, Freddie Mac showed a variety of loan rates notching or matching record lows; the 30-year fixed rate fell to 3.91%, a record low.

In Operation Twist, the Fed sells short-dated paper and buys longer-dated securities. The program’s aim is to push down longer-term yields making Treasurys less attractive and giving investors more reason to buy riskier bonds and stocks. While share prices have risen considerably since then, Treasury yields have barely budged from their historic lows. Fear about the euro zone has caused an overwhelming number of investors to seek safety in Treasury debt. . . .

The Fed’s stimulus plan is the central bank’s third definitive attempt to aid the U.S.’s patchy economy since 2008. As expectations grew that the Fed would act in the weeks leading up to the bank’s actual announcement, which came Sept. 21, 10-year yields dropped nearly 0.30 percentage point. Since the Fed’s official statement, yields have risen modestly, to 2.026% on Friday, from 1.95% on Sept. 20. Fed Chairman Ben Bernanke said in October that rejiggering the bank’s balance sheet with Operation Twist would bring longer-term rates down 0.20 percentage points.

Sounds as if we should credit Chairman Bernanke with yet another brilliant monetary policy move. There have been so many that it’s getting hard to keep track of all his many successes. Just one little problem. On September 1, around the time that expectations that the Fed would embark on Operation Twist were starting to become widespread, the yield on the 10-year Treasury stood at 2.15% and the S&P 500 closed at 1204.42. Three weeks later on September 22, the 10-year Treasury stood at 1.72%, but the S&P 500, dropped to 1129.56. Well, since then the S&P 500 has bounced back, rising about 10% to 1265.43 at yesterday’s close. But, guess what? So did the yield on the 10-year Treasury, rising to 2.02%. So, the S&P 500 may have been risen since Operation Twist began, but it would be hard to argue that the reason that stocks rose was that the yield on longer-term Treasuries was falling. On the contrary, it seems that stocks rise when yields on long-term Treasuries rise and fall when yields on long-term Treasuries fall.

Regular readers of this blog already know that I have a different explanation for movements in the stock market. As I argued in my paper “The Fisher Effect Under Deflationary Expectations,” movements in asset prices since the spring of 2008 have been dominated by movements (up or down) in inflation expectations. That is very unusual. Aside from tax effects, there is little reason to expect stocks to be affected by inflation expectations, but when expected deflation exceeds the expected yield on real capital, asset holders want to sell their assets to hold cash instead, thereby causing asset prices to crash until some sort of equilibrium between the expected yields on cash and on real assets is restored. Ever since the end of the end of the financial crisis in early 2009, there has been an unstable equilibrium between very low expected inflation and low expected yields on real assets. In this environment small changes in expected inflation cause substantial movements into and out of assets, which is why movements in the S&P 500 have been dominated by changes in expected inflation.  And this unhealthy dependence will not be broken until either expected inflation or the expected yield on real assets increases substantially.

The close relationship between changes in expected inflation (as measured by the breakeven TIPS spread for 10-year Treasuries) and changes in the S&P 500 from September 1 through December 27 is shown in the chart below.

In my paper on the Fisher effect, I estimated a simple regression equation in which the dependent variable was the daily percentage change in the S&P 500 and the independent variables were the daily change in the TIPS yield (an imperfect estimate of the expected yield on real capital), the daily change in the TIPS spread and the percentage change in the dollar/euro exchange rate (higher values signifying a lower exchange value of the dollar, thus providing an additional measure of inflation expectations or possibly a measure of the real exchange rate). Before the spring of 2008, this equation showed almost no explanatory power, from 2008 till the end of 2010, the equation showed remarkable explanatory power in accounting for movements in the S&P 500. My regression results for the various subperiods between January 2003 till the end of 2010 are presented in the paper.

I estimated the same regression for the period from September 1, 2011 to December 27, 2011. The results were startlingly good. With a sample of 79 observations, the adjusted R-squared was .636. The coefficients on both the TIPS and the TIPS spread variables were positive and statistically significant at over a 99.9% level. An increase of .1 in the real interest rate was associated with a 1.2% increase in the S&P and an increase of .1 in expected inflation was associated with a 1.7% increase in the S&P 500. A 1% increase the number of euros per dollar (i.e., a fall in the value of the dollar in terms of euros) was associated with a 0.57% increase in the S&P 500. I also introduced a variable defined as the daily change in the ratio of the yield on a 10-year Treasury to the yield on a 2-year Treasury, calculating this ratio for each day in my sample. Adding the variable to the regression slightly improved the fit of the regression, the adjusted R-squared rising from .636 to .641. However, the coefficient on the variable was positive and not statistically significant. If the supposed rationale of Operation Twist had been responsible for the increase in the S&P 500, the coefficient on this variable would have been negative, not positive. So, contrary to the story in yesterday’s Journal, Operation Twist has almost certainly not been responsible for the rise in stock prices since it was implemented.

Why has the stock market been rising? I’m not sure, but most likely market pessimism about the sway of the inflation hawks on the FOMC was a bit overdone during the summer when the inflation expectations and the S&P 500 both were dropping rapidly. The mere fact that Chairman Bernanke was able to implement Operation Twist may have convinced the market that the three horseman of the apocalypse on the FOMC (Plosser, Kocherlakota, and Fisher) had not gained an absolute veto over monetary policy, so that the doomsday scenario the market may have been anticipating was less likely to be realized than had been feared. I suppose that we should be thankful even for small favors.

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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