## Archive for the 'Irving Fisher' Category

### Who Sets the Real Rate of Interest?

Understanding economics requires, among other things, understanding the distinction between real and nominal variables. Confusion between real and nominal variables is pervasive, constantly presenting barriers to clear thinking, and snares and delusions for the mentally lazy. In this post, I want to talk about the distinction between the real rate of interest and the nominal rate of interest. That distinction has been recognized for at least a couple of centuries, Henry Thornton having mentioned it early in the nineteenth century. But the importance of the distinction wasn’t really fully understood until Irving Fisher made the distinction between the real and nominal rates of interest a key element of his theory of interest and his theory of money, expressing the relationship in algebraic form — what we now call the Fisher equation. Notation varies, but the Fisher equation can be written more or less as follows:

i = r + dP/dt,

where i is the nominal rate, r is the real rate, and dP/dt is the rate of inflation. It is important to bear in mind that the Fisher equation can be understood in two very different ways. It can either represent an ex ante relationship, with dP/dt referring to expected inflation, or it can represent an ex post relationship, with dP/dt referring to actual inflation.

What I want to discuss in this post is the tacit assumption that usually underlies our understanding, and our application, of the ex ante version of the Fisher equation. There are three distinct variables in the Fisher equation: the real and the nominal rates of interest and the rate of inflation. If we think of the Fisher equation as an ex post relationship, it holds identically, because the unobservable ex post real rate is defined as the difference between the nominal rate and the inflation rate. The ex post, or the realized, real rate has no independent existence; it is merely a semantic convention. But if we consider the more interesting interpretation of the Fisher equation as an ex ante relationship, the real interest rate, though still unobservable, is not just a semantic convention. It becomes the theoretically fundamental interest rate of capital theory — the market rate of intertemporal exchange, reflecting, as Fisher masterfully explained in his canonical renderings of the theory of capital and interest, the “fundamental” forces of time preference and the productivity of capital. Because it is determined by economic “fundamentals,” economists of a certain mindset naturally assume that the real interest rate is independent of monetary forces, except insofar as monetary factors are incorporated in inflation expectations. But if money is neutral, at least in the long run, then the real rate has to be independent of monetary factors, at least in the long run. So in most expositions of the Fisher equation, it is tacitly assumed that the real rate can be treated as a parameter determined, outside the model, by the “fundamentals.” With r determined exogenously, fluctuations in i are correlated with, and reflect, changes in expected inflation.

Now there’s an obvious problem with the Fisher equation, which is that in many, if not most, monetary models, going back to Thornton and Wicksell in the nineteenth century, and to Hawtrey and Keynes in the twentieth, and in today’s modern New Keynesian models, it is precisely by way of changes in its lending rate to the banking system that the central bank controls the rate of inflation. And in this framework, the nominal interest rate is negatively correlated with inflation, not positively correlated, as implied by the usual understanding of the Fisher equation. Raising the nominal interest rate reduces inflation, and reducing the nominal interest rate raises inflation. The conventional resolution of this anomaly is that the change in the nominal interest rate is just temporary, so that, after the economy adjusts to the policy of the central bank, the nominal interest rate also adjusts to a level consistent with the exogenous real rate and to the rate of inflation implied by the policy of the central bank. The Fisher equation is thus an equilibrium relationship, while central-bank policy operates by creating a short-term disequilibrium. But the short-term disequilibrium imposed by the central bank cannot be sustained, because the economy inevitably begins an adjustment process that restores the equilibrium real interest rate, a rate determined by fundamental forces that eventually override any nominal interest rate set by the central bank if that rate is inconsistent with the equilibrium real interest rate and the expected rate of inflation.

It was just this analogy between the powerlessness of the central bank to hold the nominal interest rate below the sum of the exogenously determined equilibrium real rate and the expected rate of inflation that led Milton Friedman to the idea of a “natural rate of unemployment” when he argued that monetary policy could not keep the unemployment rate below the “natural rate ground out by the Walrasian system of general equilibrium equations.” Having been used by Wicksell as a synonym for the Fisherian equilibrium real rate, the term “natural rate” was undoubtedly adopted by Friedman, because monetarily induced deviations between the actual rate of unemployment and the natural rate of unemployment set in motion an adjustment process that restores unemployment to its “natural” level, just as any deviation between the nominal interest rate and the sum of the equilibrium real rate and expected inflation triggers an adjustment process that restores equality between the nominal rate and the sum of the equilibrium real rate and expected inflation.

So, if the ability of the central bank to use its power over the nominal rate to control the real rate of interest is as limited as the conventional interpretation of the Fisher equation suggests, here’s my question: When critics of monetary stimulus accuse the Fed of rigging interest rates, using the Fed’s power to keep interest rates “artificially low,” taking bread out of the mouths of widows, orphans and millionaires, what exactly are they talking about? The Fed has no legal power to set interest rates; it can only announce what interest rate it will lend at, and it can buy and sell assets in the market. It has an advantage because it can create the money with which to buy assets. But if you believe that the Fed cannot reduce the rate of unemployment below the “natural rate of unemployment” by printing money, why would you believe that the Fed can reduce the real rate of interest below the “natural rate of interest” by printing money? Martin Feldstein and the Wall Street Journal believe that the Fed is unable to do one, but perfectly able to do the other. Sorry, but I just don’t get it.

Look at the accompanying chart. It tracks the three variables in the Fisher equation (the nominal interest rate, the real interest rate, and expected inflation) from October 1, 2007 to July 2, 2013. To measure the nominal interest rate, I use the yield on 10-year Treasury bonds; to measure the real interest rate, I use the yield on 10-year TIPS; to measure expected inflation, I use the 10-year breakeven TIPS spread. The yield on the 10-year TIPS is an imperfect measure of the real rate, and the 10-year TIPS spread is an imperfect measure of inflation expectations, especially during financial crises, when the rates on TIPS are distorted by illiquidity in the TIPS market. Those aren’t the only problems with identifying the TIPS yield with the real rate and the TIPS spread with inflation expectations, but those variables usually do provide a decent approximation of what is happening to real rates and to inflation expectations over time.

Before getting to the main point, I want to make a couple of preliminary observations about the behavior of the real rate over time. First, notice that the real rate declined steadily, with a few small blips, from October 2007 to March 2008, when the Fed was reducing the Fed Funds target rate from 4.75 to 3% as the economy was sliding into a recession that officially began in December 2007. The Fed reduced the Fed Funds target to 2% at the end of April, but real interest rates had already started climbing in early March, so the failure of the FOMC to reduce the Fed Funds target again till October 2008, three weeks after the onset of the financial crisis, clearly meant that there was at least a passive tightening of monetary policy throughout the second and third quarters, helping create the conditions that precipitated the crisis in September. The rapid reduction in the Fed Funds target from 2% in October to 0.25% in December 2008 brought real interest rates down, but, despite the low Fed Funds rate, a lack of liquidity caused a severe tightening of monetary conditions in early 2009, forcing real interest rates to rise sharply until the Fed announced its first QE program in March 2009.

I won’t go into more detail about ups and downs in the real rate since March 2009. Let’s just focus on the overall trend. From that time forward, what we see is a steady decline in real interest rates from over 2% at the start of the initial QE program till real rates bottomed out in early 2012 at just over -1%. So, over a period of three years, there was a steady 3% decline in real interest rates. This was no temporary phenomenon; it was a sustained trend. I have yet to hear anyone explain how the Fed could have single-handedly produced a steady downward trend in real interest rates by way of monetary expansion over a period of three years. To claim that decline in real interest rates was caused by monetary expansion on the part of the Fed flatly contradicts everything that we think we know about the determination of real interest rates. Maybe what we think we know is all wrong. But if it is, people who blame the Fed for a three-year decline in real interest rates that few reputable economists – and certainly no economists that Fed critics pay any attention to — ever thought was achievable by monetary policy ought to provide an explanation for how the Fed suddenly got new and unimagined powers to determine real interest rates. Until they come forward with such an explanation, Fed critics have a major credibility problem.

So please – pleaseWall Street Journal editorial page, Martin Feldstein, John Taylor, et al., enlighten us. We’re waiting.

PS Of course, there is a perfectly obvious explanation for the three-year long decline in real interest rates, but not one very attractive to critics of QE. Either the equilibrium real interest rate has been falling since 2009, or the equilibrium real interest rate fell before 2009, but nominal rates adjusted slowly to the reduced real rate. The real interest rate might have adjusted more rapidly to the reduced equilibrium rate, but that would have required expected inflation to have risen. What that means is that sometimes it is the real interest rate, not, as is usually assumed, the nominal rate, that adjusts to the expected rate of inflation. My next post will discuss that alternative understanding of the implicit dynamics of the Fisher equation.

### That Oh So Elusive Natural Rate of Interest

Last week, I did a short post linking to the new draft of my paper with Paul Zimmerman about the Sraffa-Hayek exchange on the natural rate of interest. In the paper, we attempt to assess Sraffa’s criticism in his 1932 review of Prices and Production of Hayek’s use of the idea of a natural rate of interest as well as Hayek’s response, or, perhaps, his lack of response, to Sraffa’s criticism. The issues raised by Sraffa are devilishly tricky, especially because he introduced the unfamiliar terminology of own-rates of interest, later adopted Keynes in chapter 17 of the General Theory in order to express his criticism. The consensus about this debate is that Sraffa got the best of Hayek in this exchange – the natural rate of interest was just one of the issues Sraffa raised, and, in the process, he took Hayek down a peg or two after the startling success that Hayek enjoyed upon his arrival in England, and publication of Prices and Production. In a comment to my post, Greg Ransom questions this conventional version of the exchange, but that’s my story and I’m sticking to it.

What Paul and I do in the paper is to try to understand Sraffa’s criticism of Hayek. It seems to us that the stridency of Sraffa’s attack on Hayek suggests that Sraffa was arguing that Hayek’s conception of a natural rate of interest was somehow incoherent in a barter economy in which there is growth and investment and, thus, changes in relative prices over time, implying that commodity own rates of interest would have differ. If, in a barter economy with growth and savings and investment, there are many own-rates, Sraffa seemed to be saying, it is impossible to identify any one of them as the natural rate of interest. In a later account of the exchange between Sraffa and Hayek, Ludwig Lachmann, a pupil of Hayek, pointed out that, even if there are many own rates in a barter economy, the own rates must, in an intertemporal equilibrium, stand in a unique relationship to each other: the expected net return from holding any asset cannot differ from the expected net return on holding any other asset. That is a condition of equilibrium. If so, it is possible, at least conceptually, to infer a unique real interest rate. That unique real interest rate could be identified with Hayek’s natural rate of interest.

In fact, as we point out in our paper, Irving Fisher in his classic Appreciation and Interest (1896) had demonstrated precisely this point, theoretically extracting the real rate from the different nominal rates of interest corresponding to loans contracted in terms of different assets with different expected rates of price appreciation. Thus, Sraffa did not demonstrate that there was no natural rate of interest. There is a unique real rate of interest in intertemporal equilibrium which corresponds to the Hayekian natural rate. However, what Sraffa could have demonstrated — though had he done so, he would still have been 35 years behind Irving Fisher – is that the unique real rate is consistent with an infinite number of nominal rates provided that those nominal rates reflected corresponding anticipated rate of price appreciation. But, instead, Sraffa argued that there is no unique real rate in intertemporal equilibrium. That was a mistake.

Another interesting (at least to us) point in our paper is that Keynes who, as editor of the Economic Journal, asked Sraffa to review Prices and Production, borrowed Sraffa’s own-rate terminology in chapter 17 of the General Theory, but, instead of following Sraffa’s analysis and arguing that there is no natural rate of interest, Keynes proceeded to derive, using (without acknowledgment) a generalized version of Fisher’s argument of 1896, a unique relationship between commodity own rates, adjusted for expected price changes, and net service yields, such that the expected net returns on all assets would be equalized. From this, Keynes did not conclude, as had Sraffa, that there is no natural rate of interest. Rather, he made a very different argument: that the natural rate of interest is a useless concept, because there are many natural rates each corresponding to a different the level of income and employment, a consideration that Hayek, and presumably Fisher, had avoided by assuming full intertemporal equilibrium. But Keynes never disputed that for any given level of income and employment, there would be a unique real rate to which all commodity own rates had to correspond. Thus, Keynes turned Sraffa’s analysis on its head. And the final point of interest is that even though Keynes, in chapter 17, presented essentially the same analysis of own rates, though in more general terms, that Fisher had presented 40 years earlier, Keynes in chapter 13 explicitly rejected Fisher’s distinction between the real and nominal rates of interest. Go figure.

Bob Murphy wrote a nice paper on the Sraffa-Hayek debate, which I have referred to before on this blog. However, I disagree with him that Sraffa’s criticism of Hayek was correct. In a post earlier this week, he infers, from our statement that, as long as price expectations are correct, any nominal rate is consistent with the unique real natural rate, that we must agree with him that Sraffa was right and Hayek was wrong about the natural rate. I think that Bob is in error on the pure theory here. There is a unique real natural rate in intertemporal equilibrium, and, in principle, the monetary authority could set a money rate equal to that real rate, provided that that nominal rate was consistent with the price expectations held by the public. However, intertemporal equilibrium could be achieved by any nominal interest rate selected by the monetary authority, again provided that the nominal rate chosen was consistent with the price expectations held by the public. In practice, either formulation is very damaging to Hayek’s policy criterion of setting the nominal interest rate equal to the real natural rate. But contrary to Sraffa’s charge, the policy criterion is not incoherent. It is just unworkable, as Hayek formulated it, and, on Hayek’s own theory, the criterion is unnecessary to avoid distorting malinvestments.

### 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.

### Falling Real Interest Rates, Winner-Take-All Markets, and Lance Armstrong

In my previous post, I suggested that real interest rates are largely determined by expectations, entrepreneurial expectations of profit and household expectations of future income. Increased entrepreneurial optimism implies that entrepreneurs are revising upwards the anticipated net cash flows from the current stock of capital assets, in other words an increasing demand for capital assets. Because the stock of capital assets doesn’t change much in the short run, an increased demand for those assets tends, in the short run, to raise real interest rates as people switch from fixed income assets (bonds) into the real assets associated with increased expected net cash flows. Increased optimism by households about their future income prospects implies that their demand for long-lived assets, real or financial, tends to decline as household devote an increased share of current income to present consumption and less to saving for future consumption, because an increase in future income reduces the amount of current savings needed to achieve a given level of future consumption. The more optimistic I am about my future income, the less I will save in the present. If I win the lottery, I will start spending even before I collect my winnings. The reduced household demand for long-lived assets with which to provide for future consumption reduces the value of such assets, implying, for given expectations of their future yields, an increased real interest rate.

This is the appropriate neoclassical (Fisherian) framework within which to think about the determination of real interest rates. The Fisherian theory may not be right, but I don’t think that we have another theory of comparable analytical power and elegance. Other theories are just ad hoc, and lack the aesthetic appeal of the Fisherian theory. Alas, the world is a messy place, and we have no guarantee that the elegant theory will always win out. Truth and beauty need not the same. (Sigh!)

Commenting on my previous post, Joshua Wojnilower characterized my explanation as “a combination of a Keynesian-demand side story in the first paragraph and an Austrian/Lachmann subjective expectations view in the second section.” I agree that Keynes emphasized the importance of changes in the state of entrepreneurial expectations in causing shifts in the marginal efficiency of capital, and that Austrian theory is notable for its single-minded emphasis on the subjectivity of expectations. But these ideas are encompassed by the Fisherian neoclassical paradigm, entrepreneurial expectations about profits determining the relevant slope of the production possibility curve embodying opportunities for the current and future production of consumption goods on the one hand, and household expectations about future income determining the slope of household indifference curves reflecting their willingness to exchange current for future consumption. So it’s all in Fisher.

Thus, as I observed, falling real interest rates could be explained, under the Fisherian theory, by deteriorating entrepreneurial expectations, or by worsening household expectations about future income (employment). In my previous post, I suggested that, at least since the 2007-09 downturn, entrepreneurial profit expectations have been declining along with the income (employment) expectations of households. However, I am reluctant to suggest that this trend of expectational pessimism started before the 2007-09 downturn. One commenter, Diego Espinosa, offered some good reasons to think that since 2009 entrepreneurial expectations have been improving, so that falling real interest rates must be attributed to monetary policy. Although I find it implausible that entrepreneurial expectations have recovered (at least fully) since the 2007-09 downturn, I take Diego’s points seriously, and I am going to try to think through his arguments carefully, and perhaps respond further in a future post.

I also suggested in my previous post that there might be other reasons why real interest rates have been falling, which brings me to the point of this post. By way of disclaimer, I would say that what follows is purely speculative, and I raise it only because the idea seems interesting and worth thinking about, not because I am convinced that it is empirically significant in causing real interest rates to decline over the past two or three decades.

Almost ten months ago, I discussed the basic idea in a post in which I speculated about why there is no evidence of a strong correlation between reductions in marginal income tax rates and economic growth, notwithstanding the seemingly powerful theoretical argument for such a correlation. Relying on Jack Hirshleifer’s important distinction between the social and private value of information, I argued that insofar as reduced marginal tax rates contributed to an expansion of the financial sector of the economy, reduced marginal tax rates may have retarded, rather than spurred, growth.  The problem with the financial sector is that the resources employed in that sector, especially resources devoted to trading, are socially wasted, the profits accruing to trading reflecting not net additions to output, but losses incurred by other traders. In their quest for such gains, trading establishments incur huge expenses with a view to obtaining information advantages by which profits can be extracted as a result of trading with the informationally disadvantaged.

But financial trading is not the only socially wasteful activity that attracted vast amounts of resources from other (socially productive) activities, i.e., making and delivering real goods and services valued by consumers. There’s a whole set of markets that fall under the heading of winner-take-all markets. There are some who attribute increasing income inequality to the recent proliferation of winner-take-all markets. What distinguishes these markets is that, as the name implies, rewards in these markets are very much skewed to the most successful participants. Participants compete for a reward, and rewards are distributed very unevenly, small differences in performance implying very large differences in reward. Because the payoff at the margin to an incremental improvement in performance is so large, the incentives to devote resources to improve performance are inefficiently exaggerated. Because of the gap between the large private return and the near-zero social return from improved performance, far too much effort and resources is wasted on achieving minor gains in performance. Lance Armstrong is but one of the unpleasant outcomes of a winner-take-all market.

It is also worth noting that competition in winner-take-all markets is far from benign. Sports leagues, which are classic examples of winner-take-all markets, operate on the premise that competition must be controlled, not just to prevent match-ups from being too lopsided, but to keep unrestricted competition from driving up costs to uneconomic levels. At one time, major league baseball had a reserve clause. The reserve clause exists no longer, but salary caps and other methods of controlling competition were needed to replace it. The main, albeit covert, function of the NCAA is to suppress competition for college athletes that would render college football and college basketball unprofitable if it were uncontrolled, with player salaries determined by supply and demand.

So if the share of economic activity taking place in winner-take-all markets has increased, the waste of resources associated with such markets has likely been increasing as well. Because of the distortion in the pricing of resources employed in winner-take-all markets, those resources typically receiving more than their net social product, employers in non-winner-take-all markets must pay an inefficient premium to employ those overpaid resources. These considerations suggest that the return on investment in non-winner-take-all markets may also be depressed because of such pricing distortions. But I am not sure that this static distortion has a straightforward implication about the trend of real interest rates over time.

A more straightforward connection between falling real interest rates and the increase in share of resources employed in winner-take-all markets might be that winner-take-all markets (e.g., most of the financial sector) are somehow diverting those most likely to innovate and generate new productive ideas into socially wasteful activities. That hypothesis certainly seems to accord with the oft-heard observation that, until recently at any rate, a disproportionate share of the best and brightest graduates of elite institutions of higher learning have been finding employment on Wall Street and in hedge funds. If so, the rate of technological advance in the productive sector of the economy would have been less rapid than the rate of advance in the unproductive sector of the economy. Somehow that doesn’t seem like a recipe for increasing the rate of economic growth and might even account for declining real interest rates. Something to think about as you watch the Lance Armstrong interview tomorrow night.