Archive for the 'Fisher equation' Category

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

Published February 20, 2013 Alchian , Austrian Business-Cycle Theory , Fisher equation , Hayek , Irving Fisher , Keynes , Piero Sraffa , Uncategorized 13 Comments
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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

Published September 11, 2012 David Laidler , expectations , Fisher equation , Friedman , Monetarism , monetary policy , monetary theory 24 Comments

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

Published August 14, 2012 expectations , monetary theory , Fisher equation , gold standard , Earl Thompson 5 Comments

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

Published July 6, 2012 expectations , Fisher equation , Friedman , inflation , monetary policy 22 Comments

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

Published May 14, 2012 Eurozone crisis , expectations , Fisher equation , inflation , Little Depression , monetary policy , monetary theory 16 Comments

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?

Published December 28, 2011 expectations , Fisher equation , monetary policy , monetary theory 9 Comments

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.

Some Unpleasant Fisherian Arithmetic

Published November 14, 2011 expectations , Fisher equation , monetary policy , monetary theory 27 Comments

I have been arguing for the past four months on this blog and before that in my paper “The Fisher Effect Under Deflationary Expectations” (available here), that the Fisher equation which relates the nominal rate of interest to the real (inflation-adjusted) interest rate and to expected inflation conveys critical information about the future course of asset prices and the economy when the expected rate of deflation comes close to or exceeds the real rate of interest. When that happens, the expected return to holding cash is greater than the expected rate of return on real capital, inducing those holding real capital to try to liquidate their holdings in exchange for cash. The result is a crash in asset prices, such as we had in 2008 and early 2009, when expected inflation was either negative or very close to zero, and the expected return on real capital was negative. Ever since, expected inflation has been low, usually less than 2%, and the expected return on real capital has been in the neighborhood of zero or even negative. With the expected return on real capital so low, people (i.e., households and businesses) are reluctant to spend to acquire assets (either consumer durables or new plant and equipment), preferring to stay liquid while trying to reduce, or at least not add to, their indebtedness.

According to this way of thinking about the economy, a recovery can occur either because holding cash becomes less attractive or because holding real assets more attractive. Holding cash becomes less attractive if expected inflation rises; holding assets becomes more attractive if the expected cash flows associated with those real assets increase (either because expected demand is rising or because the productivity of capital is rising).

The attached chart plots expected inflation since January 2010 as measured by the breakeven 5-year TIPS spread on constant maturity Treasuries, and it plots the expected real return over a 5-year time horizon since January 2010 as reflected in the yield on constant maturity 5-year TIPS bonds.

In the late winter and early spring of 2010, real yields were rising even as inflation expectations were stable; stock prices were also rising and there were some encouraging signs of economic expansion. But in the late spring and summer of 2010, inflation expectations began to fall from 2% to less about 1.2% even as real yields started to drop.  With stock prices falling and amid fears of deflation and a renewed recession, the Fed felt compelled to adopt QE2, leading to an almost immediate increase in inflation expectations. At first, the increase in inflation expectations allowed real yields to drop, suggesting that expected yields on real assets had dropped further than implied by the narrowing TIPS spreads in the spring and summer. By late fall and winter, real yields reversed course and were rising along with inflation expectations, producing a substantial increase in stock prices. Rising optimism was reflected in a sharp increase in real yields to their highest levels in nearly a year in February of 2011. But the increase in real yields was quickly reversed by a combination of adverse supply side shocks that drove inflation expectations to their highest levels since the summer before the 2008 crash. However, after the termination of QE2, inflation expectations started sliding back towards the low levels of the summer before QE2 was adopted. The fall in inflation expectations was accompanied by an ominous fall in real yields and in stock prices.

Although suggestions that weakness in the economy might cause the Fed to resume some form of monetary easing seem to have caused some recovery in inflation expectations, real yields continue to fall. With real yield on capital well into negative territory (the real yield on a constant maturity 5-year TIPS bond is now around -1%, an astonishing circumstance. With real yields that low, 2% expected inflation would almost certainly not be enough to trigger a significant increase in spending. To generate a rebound in spending sufficient to spark a recovery, 3 to 4% inflation (the average rate of inflation in the recovery following the 1981-82 recovery in the golden age of Reagan) is probably the absolute minimum required.

Update:  Daniel Kuehn just posted an interesting comment on this post in his blog, correctly noting the conceptual similarity (if not identity) between the Fisher effect under deflationary expectations and the Keynesian liquidity trap.  I think that insight points to a solution of Keynes’s puzzling criticism of the Fisher effect in the General Theory even though he had previously endorsed Fisher’s reasoning in the Treatise on Money.

Scott Sumner Bans Inflation

Published November 6, 2011 Fisher equation , monetary theory 11 Comments

Scott Sumner, the world’s greatest economics blogger, has had it with inflation. He hates inflation so much he wants to stop people from even talking about it or even mentioning it. He has banned use of the i-word on his blog, and if Scott has his way, the i-word will be banned from polite discourse from here to eternity.

Why is Scott so upset about inflation? It has nothing to do with the economic effects of inflation. It is all about people’s inability to think clearly about it.

Some days I want to just shoot myself, like when I read the one millionth comment that easy money will hurt consumers by raising prices.  Yes, there are some types of inflation that hurt consumers.  And yes, there are some types of inflation created by Fed policy.  But in a Venn diagram those two types of inflation have no overlap.

So Scott thinks that if only we could get people to stop talking about inflation, they would start thinking more clearly. Well, maybe yes, maybe no.

At any rate, if we are no longer allowed to speak about inflation, that is going to make my life a lot more complicated, because I have been trying to explain to people almost since I started this blog started four months ago why the stock market loves inflation and have repeated myself again and again and again and again. In a comment on my last iteration of that refrain, Marcus Nunes anticipated Scott with this comment.

That´s why I think mentioning the I word is bad. Even among “like thinkers” it gives many the “goosebumps”. What the stock market loves is to envision (even if temporarily) the possibility that NGDP will climb towards trend.

And when Scott announced the ban on the i-word on his blog, Marcus posted this comment on Scott’s blog:

Scott: David Glasner won´t be allowed to place comments here. Early this month I did a post on the I word.
http://thefaintofheart.wordpress.com/2011/10/07/two-words-you-should-never-use-inflation-stimulus/

In DG´s latest post Yes, Virginia, the stock market loves inflation I commented:

That´s why I think mentioning the I word is bad. Even among “like thinkers” it gives many the “goosebumps”. What the stock market loves is to envision (even if temporarily) the possibility that NGDP will climb towards trend.

He answered:

Marcus, I think inflation is important because it focuses on the choice between holding assets and holding money.!

Scott replied

We’ll see how David reacts to this post.

Well after that invitation, of course I had to respond. And I did as follows:

Scott, Even before I started blogging, I couldn’t keep up with you and now that I am blogging I have been falling farther and farther behind. So I just saw your kind invitation to weigh in on your “modest proposal.” I actually am not opposed to your proposal, and I greatly sympathize with and share your frustration with the confusion that attributes a fall in real income to an increase in prices as if it were the increase in prices that caused the fall in income rather than the other way around. On the other hand, on my blog I will continue to talk about inflation and every so often, despite annoying you and Marcus, I will continue to point out that since 2008 the stock market has been in love with inflation, even though it normally is indifferent or hostile to inflation.

I also don’t think that you have properly characterized the Fisher equation in terms of the real interest rate and expected NGDP growth. As a rough approximation the real interest rate (r) equals the rate of growth in real GDP; and the nominal interest rate (i) equals the rate of growth in nominal GDP. So stating the Fisher equation in terms of GDP should give you i = r + p (where p is the rate of inflation or the ratio of nominal to real GDP).

Finally, I am wondering whether you also want to ban use of the world “deflation” from polite discourse. I think it would be a shame if you did, because you and I both think that it was an increase in the value of gold (AKA deflation) that caused the decline in NGDP in the Great Depression, not a decline in NGDP that caused the increase in the value of gold.

So what is the upshot of all this? I guess I am just too conservative to give up using a word that I have grown up using since I started studying economics. It would also help if I could make sense of the Fisher equation — think of it as Newton’s law of monetary motion — without the rate of inflation. So I am waiting for Scott to explain that one to me. And I think that we need to have some notion of the purchasing power of money in order to explain the preferences of individuals for holding money versus other assets. If so, the concepts of a price level and a rate of inflation seem to be necessary as well.

Having said all that, I would add that Scott is a very persistent and persuasive guy, so I am definitely keeping all my options open.

Update:  Thanks to the ever-vigilant Scott Sumner for flagging my mistaken version of the Fisher equation.  It’s i = r + p, not r = i + p, as I originally had it.  I just corrected the equation in the body of the post as well and reduced the font to its normal size.

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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