Posts Tagged 'Earl Thompson'

OK, Tell Me — Please Tell Me — Why Bitcoins Aren’t a Bubble

It’s customary at the Passover seder for the youngest person in attendance to ask four questions about why the first night of Passover is different from all other nights. For some reason, at my seder a different question was raised as well: what are bitcoins all about? I guess everybody wants to know about bitcoins now. Well, how embarrassing is that? Not only do I not understand why bitcoins have spectacularly increased in value since their inception (though the current price of a bitcoin is less than half of what it was last December), I don’t even understand why the market price of a bitcoin is now, or ever has been, greater than zero.

Here’s a chart showing how the value of a bitcoin has soared over the past two years:


Why am I so perplexed about bitcoins?

The problem I have is that bitcoins can’t be used for anything except as a means of payment for something else. Bitcoins provide no real service distinct from being a means of payment. Think about it; if a bitcoin can’t be used for anything except to be given to someone else in exchange, that means that someday, someone is going to be stuck holding a bitcoin with no one left to give it to in exchange. When that happens, that stinky bitcoin won’t be worth a plum (or plugged) nickel, or a red cent. It will be as worthless as a three-dollar bill.

Now I grant you that that final moment of clarity might not happen for a long time – maybe not even for a very long time. But if anything is certain, it is certain that, sooner or later, such a moment must certainly come. But if it is certain that ultimately no one will accept a bitcoin in exchange, then it follows that no one forseeing that inevitable outcome would accept a bitcoin in exchange prior to that moment unless he or she is confident that there is some sucker out there who will accept in the interim. But since when does a theory of asset valuation premised on the existence of an unlimited supply of suckers count as an acceptable theory? Under the normal rationality assumptions that economists like to use, it is not possible to rationalize a positive price for a bitcoin at any point in its history.

So if, as the above chart so dramatically shows, bitcoins are in fact trading at a positive price, how does one avoid concluding that bitcoins are a massive bubble, a Ponzi scheme that must inevitably collapse, as soon as people realize where things are headed? To see just how massive a bubble bitcoins are, compare the above chart to this one constructed by Earl Thompson from actual prices in tulip contracts during the Dutch tulip mania of 1636-37. Compared to bitcoins, the tulips were barely more than a blip.


Now one could respond that if bitcoins are a bubble, then so is fiat currency. That is a pretty good response, and the positive value that we typically observe for most fiat currencies is far from unproblematic. But, as I have pointed out before on this blog (here and here), it is possible to account for the positive value of fiat currency by reference to its acceptability in discharging tax liabilities to the government. The acceptability of fiat currency in payment of taxes is a real service provided by fiat currency that is conceptually distinct from, though certainly facilitated by, its acceptability as payment in ordinary transactions. So, as long as one expects the government issuing fiat currency to remain in power and to be able to punish tax evasion, there is a rational basis for the positive value of a fiat currency. The backward induction argument that establishes the worthlessness of bitcoins does not apply to fiat currency.

Another possible explanation for the positive value of bitcoins is that they are very useful to those wanting to engage in illegal transactions on line, because, unlike other forms of electronic payment, payment via bitcoin is hard to trace. That is certainly a good reason for people to want to use bitcoins in certain kinds of transactions. However, the difficulty of tracing transactions via bitcoin is not an explanation of why bitcoins have a positive value in the first place, only an argument why, if they do have a positive value, the demand for them might be greater than it would have been if it were not for that advantage. Without an independent explanation for the positive value of a bitcoin, you can’t bootstrap a positive value for bitcoins by way of the difficulty of tracing bitcoin transactions.

So there you have it. As far as I can tell, the value of a bitcoin should be zero. But it’s obviously not zero,and though falling, the value of bitcoins is showing little sign of moving rapidly toward its apparent zero equilibrium value. There seem to be only a couple of ways of explaining this anomalous state of affairs. Either I have overlooked some material fact about bitcoins that might impart a positive value to them, or there is a problem with the theory of valuation that I am using. So I ask, in all sincerity, for enlightenment. Help me understand why bitcoins are not a bubble.

HT: Dana Dachman

Big Ideas in Macroeconomics: A Review

Steve Williamson recently plugged a new book by Kartik Athreya (Big Ideas in Macroeconomics), an economist at the Federal Reserve Bank of Richmond, which tries to explain in relatively non-technical terms what modern macroeconomics is all about. I will acknowledge that my graduate training in macroeconomics predated the rise of modern macro, and I am not fluent in the language of modern macro, though I am trying to fill in the gaps. And this book is a good place to start. I found Athreya’s book a good overview of the field, explaining the fundamental ideas and how they fit together.

Big Ideas in Macroeconomics is a moderately big book, 415 pages, covering a very wide range of topics. It is noteworthy, I think, that despite its size, there is so little overlap between the topics covered in this book, and those covered in more traditional, perhaps old-fashioned, books on macroeconomics. The index contains not a single entry on the price level, inflation, deflation, money, interest, total output, employment or unemployment. Which is not to say that none of those concepts are ever mentioned or discussed, just that they are not treated, as they are in traditional macroeconomics books, as the principal objects of macroeconomic inquiry. The conduct of monetary or fiscal policy to achieve some explicit macroeconomic objective is never discussed. In contrast, there are repeated references to Walrasian equilibrium, the Arrow-Debreu-McKenzie model, the Radner model, Nash-equilibria, Pareto optimality, the first and second Welfare theorems. It’s a new world.

The first two chapters present a fairly detailed description of the idea of Walrasian general equilibrium and its modern incarnation in the canonical Arrow-Debreu-McKenzie (ADM) model.The ADM model describes an economy of utility-maximizing households and profit-maximizing firms engaged in the production and consumption of commodities through time and space. There are markets for commodities dated by time period, specified by location and classified by foreseeable contingent states of the world, so that the same physical commodity corresponds to many separate commodities, each corresponding to different time periods and locations and to contingent states of the world. Prices for such physically identical commodities are not necessarily uniform across times, locations or contingent states.The demand for road salt to de-ice roads depends on whether conditions, which depend on time and location and on states of the world. For each different possible weather contingency, there would be a distinct market for road salt for each location and time period.

The ADM model is solved once for all time periods and all states of the world. Under appropriate conditions, there is one (and possibly more than one) intertemporal equilibrium, all trades being executed in advance, with all deliveries subsequently being carried out, as time an contingencies unfold, in accordance with the terms of the original contracts.

Given the existence of an equilibrium, i.e., a set of prices subject to which all agents are individually optimizing, and all markets are clearing, there are two classical welfare theorems stating that any such equilibrium involves a Pareto-optimal allocation and any Pareto-optimal allocation could be supported by an equilibrium set of prices corresponding to a suitably chosen set of initial endowments. For these optimality results to obtain, it is necessary that markets be complete in the sense that there is a market for each commodity in each time period and contingent state of the world. Without a complete set of markets in this sense, the Pareto-optimality of the Walrasian equilibrium cannot be proved.

Readers may wonder about the process by which an equilibrium price vector would actually be found through some trading process. Athreya invokes the fiction of a Walrasian clearinghouse in which all agents (truthfully) register their notional demands and supplies at alternative price vectors. Based on these responses the clearinghouse is able to determine, by a process of trial and error, the equilibrium price vector. Since the Walrasian clearinghouse presumes that no trading occurs except at an equilibrium price vector, there can be no assurance that an equilibrium price vector would ever be arrived at under an actual trading process in which trading occurs at disequilibrium prices. Moreover, as Clower and Leijonhufvud showed over 40 years ago (“Say’s Principle: What it Means and What it Doesn’t Mean”), trading at disequilibrium prices may cause cumulative contractions of aggregate demand because the total volume of trade at a disequilibrium price will always be less than the volume of trade at an equilibrium price, the volume of trade being constrained by the lesser of quantity supplied and quantity demanded.

In the view of modern macroeconomics, then, Walrasian general equilibrium, as characterized by the ADM model, is the basic and overarching paradigm of macroeconomic analysis. To be sure, modern macroeconomics tries to go beyond the highly restrictive assumptions of the ADM model, but it is not clear whether the concessions made by modern macroeconomics to the real world go very far in enhancing the realism of the basic model.

Chapter 3, contains some interesting reflections on the importance of efficiency (Pareto-optimality) as a policy objective and on the trade-offs between efficiency and equity and between ex-ante and ex-post efficiency. But these topics are on the periphery of macroeconomics, so I will offer no comment here.

In chapter 4, Athreya turns to some common criticisms of modern macroeconomics: that it is too highly aggregated, too wedded to the rationality assumption, too focused on equilibrium steady states, and too highly mathematical. Athreya correctly points out that older macroeconomic models were also highly aggregated, so that if aggregation is a problem it is not unique to modern macroeconomics. That’s a fair point, but skirts some thorny issues. As Athreya acknowledges in chapter 5, an important issue separating certain older macroeconomic traditions (both Keynesian and Austrian among others) is the idea that macroeconomic dysfunction is a manifestation of coordination failure. It is a property – a remarkable property – of Walrasian general equilibrium that it achieves perfect (i.e., Pareto-optimal) coordination of disparate, self-interested, competitive individual agents, fully reconciling their plans in a way that might have been achieved by an omniscient and benevolent central planner. Walrasian general equilibrium fully solves the coordination problem. Insofar as important results of modern macroeconomics depend on the assumption that a real-life economy can be realistically characterized as a Walrasian equilibrium, modern macroeconomics is assuming that coordination failures are irrelevant to macroeconomics. It is only after coordination failures have been excluded from the purview of macroeconomics that it became legitimate (for the sake of mathematical tractability) to deploy representative-agent models in macroeconomics, a coordination failure being tantamount, in the context of a representative agent model, to a form of irrationality on the part of the representative agent. Athreya characterizes choices about the level of aggregation as a trade-off between realism and tractability, but it seems to me that, rather than making a trade-off between realism and tractability, modern macroeconomics has simply made an a priori decision that coordination problems are not a relevant macroeconomic concern.

A similar argument applies to Athreya’s defense of rational expectations and the use of equilibrium in modern macroeconomic models. I would not deny that there are good reasons to adopt rational expectations and full equilibrium in some modeling situations, depending on the problem that theorist is trying to address. The question is whether it can be appropriate to deviate from the assumption of a full rational-expectations equilibrium for the purposes of modeling fluctuations over the course of a business cycle, especially a deep cyclical downturn. In particular, the idea of a Hicksian temporary equilibrium in which agents hold divergent expectations about future prices, but markets clear period by period given those divergent expectations, seems to offer (as in, e.g., Thompson’s “Reformulation of Macroeconomic Theory“) more realism and richer empirical content than modern macromodels of rational expectations.

Athreya offers the following explanation and defense of rational expectations:

[Rational expectations] purports to explain the expectations people actually have about the relevant items in their own futures. It does so by asking that their expectations lead to economy-wide outcomes that do not contradict their views. By imposing the requirement that expectations not be systematically contradicted by outcomes, economists keep an unobservable object from becoming a source of “free parameters” through which we can cheaply claim to have “explained” some phenomenon. In other words, in rational-expectations models, expectations are part of what is solved for, and so they are not left to the discretion of the modeler to impose willy-nilly. In so doing, the assumption of rational expectations protects the public from economists.

This defense of rational expectations plainly belies betrays the methodological arrogance of modern macroeconomics. I am all in favor of solving a model for equilibrium expectations, but solving for equilibrium expectations is certainly not the same as insisting that the only interesting or relevant result of a model is the one generated by the assumption of full equilibrium under rational expectations. (Again see Thompson’s “Reformulation of Macroeconomic Theory” as well as the classic paper by Foley and Sidrauski, and this post by Rajiv Sethi on his blog.) It may be relevant and useful to look at a model and examine its properties in a state in which agents hold inconsistent expectations about future prices; the temporary equilibrium existing at a point in time does not correspond to a steady state. Why is such an equilibrium uninteresting and uninformative about what happens in a business cycle? But evidently modern macroeconomists such as Athreya consider it their duty to ban such models from polite discourse — certainly from the leading economics journals — lest the public be tainted by economists who might otherwise dare to abuse their models by making illicit assumptions about expectations formation and equilibrium concepts.

Chapter 5 is the most important chapter of the book. It is in this chapter that Athreya examines in more detail the kinds of adjustments that modern macroeconomists make in the Walrasian/ADM paradigm to accommodate the incompleteness of markets and the imperfections of expectation formation that limit the empirical relevance of the full ADM model as a macroeconomic paradigm. To do so, Athreya starts by explaining how the Radner model in which a less than the full complement of Arrow-Debreu contingent-laims markets is available. In the Radner model, unlike the ADM model, trading takes place through time for those markets that actually exist, so that the full Walrasian equilibrium exists only if agents are able to form correct expectations about future prices. And even if the full Walrasian equilibrium exists, in the absence of a complete set of Arrow-Debreu markets, the classical welfare theorems may not obtain.

To Athreya, these limitations on the Radner version of the Walrasian model seem manageable. After all, if no one really knows how to improve on the equilibrium of the Radner model, the potential existence of Pareto improvements to the Radner equilibrium is not necessarily that big a deal. Athreya expands on the discussion of the Radner model by introducing the neoclassical growth model in both its deterministic and stochastic versions, all the elements of the dynamic stochastic general equilibrium (DSGE) model that characterizes modern macroeconomics now being in place. Athreya closes out the chapter with additional discussions of the role of further modifications to the basic Walrasian paradigm, particularly search models and overlapping-generations models.

I found the discussion in chapter 5 highly informative and useful, but it doesn’t seem to me that Athreya faces up to the limitations of the Radner model or to the implied disconnect between the Walraisan paradigm and macroeconomic analysis. A full Walrasian equilibrium exists in the Radner model only if all agents correctly anticipate future prices. If they don’t correctly anticipate future prices, then we are in the world of Hicksian temporary equilibrium. But in that world, the kind of coordination failures that Athreya so casually dismisses seem all too likely to occur. In a world of temporary equilibrium, there is no guarantee that intertemporal budget constraints will be effective, because those budget constraint reflect expected, not actual, future prices, and, in temporary equilibrium, expected prices are not the same for all transactors. Budget constraints are not binding in a world in which trading takes place through time based on possibly incorrect expectations of future prices. Not only does this mean that all the standard equilibrium and optimality conditions of Walrasian theory are violated, but that defaults on IOUs and, thus, financial-market breakdowns, are entirely possible.

In a key passage in chapter 5, Athreya dismisses coordination-failure explanations, invidiously characterized as Keynesian, for inefficient declines in output and employment. While acknowledging that such fluctuations could, in theory, be caused by “self-fulfilling pessimism or fear,” Athreya invokes the benchmark Radner trading arrangement of the ADM model. “In the Radner economy, Athreya writes, “households and firms have correct expectations for the spot market prices one period hence.” The justification for that expectational assumption, which seems indistinguishable from the assumption of a full, rational-expectations equilibrium, is left unstated. Athreya continues:

Granting that they indeed have such expectations, we can now ask about the extent to which, in a modern economy, we can have outcomes that are extremely sensitive to them. In particular, is it the case that under fairly plausible conditions, “optimism” and “pessimism” can be self-fulfilling in ways that make everyone (or nearly everyone) better off in the former than the latter?

Athreya argues that this is possible only if the aggregate production function of the economy is characterized by increasing returns to scale, so that productivity increases as output rises.

[W]hat I have in mind is that the structure of the economy must be such that when, for example, all households suddenly defer consumption spending (and save instead), interest rates do not adjust rapidly to forestall such a fall in spending by encouraging firms to invest.

Notice that Athreya makes no distinction between a reduction in consumption in which people shift into long-term real or financial assets and one in which people shift into holding cash. The two cases are hardly identical, but Athreya has nothing to say about the demand for money and its role in macroeconomics.

If they did, under what I will later describe as a “standard” production side for the economy, wages would, barring any countervailing forces, promptly rise (as the capital stock rises and makes workers more productive). In turn, output would not fall in response to pessimism.

What Athreya is saying is that if we assume that there is a reduction in the time preference of households, causing them to defer present consumption in order to increase their future consumption, the shift in time preference should be reflected in a rise in asset prices, causing an increase in the production of durable assets, and leading to an increase in wages insofar as the increase in the stock of fixed capital implies an increase in the marginal product of labor. Thus, if all the consequences of increased thrift are foreseen at the moment that current demand for output falls, there would be a smooth transition from the previous steady state corresponding to a high rate of time preference to the new steady state corresponding to a low rate of time preference.

Fine. If you assume that the economy always remains in full equilibrium, even in the transition from one steady state to another, because everyone has rational expectations, you will avoid a lot of unpleasantness. But what if entrepreneurial expectations do not change instantaneously, and the reduction in current demand for output corresponding to reduced spending on consumption causes entrepreneurs to reduce, not increase, their demand for capital equipment? If, after the shift in time preference, total spending actually falls, there may be a chain of disappointments in expectations, and a series of defaults on IOUs, culminating in a financial crisis. Pessimism may indeed be self-fulfilling. But Athreya has a just-so story to tell, and he seems satisfied that there is no other story to be told. Others may not be so easily satisfied, especially when his just-so story depends on a) the rational expectations assumption that many smart people have a hard time accepting as even remotely plausible, and b) the assumption that no trading takes place at disequilibrium prices. Athreya continues:

Thus, at least within the context of models in which households and firms are not routinely incorrect about the future, multiple self-fulfilling outcomes require particular features of the production side of the economy to prevail.

Actually what Athreya should have said is: “within the context of models in which households and firms always predict future prices correctly.”

In chapter 6, Athreya discusses how modern macroeconomics can and has contributed to the understanding of the financial crisis of 2007-08 and the subsequent downturn and anemic recovery. There is a lot of very useful information and discussion of various issues, especially in connection with banking and financial markets. But further comment at this point would be largely repetitive.

Anyway, despite my obvious and strong disagreements with much of what I read, I learned a lot from Athreya’s well-written and stimulating book, and I actually enjoyed reading it.

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.

Armen Alchian, The Economists’ Economist

The first time that I ever heard of Armen Alchian was when I took introductory economics at UCLA as a freshman, and his book (co-authored with his colleague William R. Allen who was probably responsible for the macro and international chapters) University Economics (the greatest economics textbook ever written) was the required text. I had only just started to get interested in economics, and was still more interested in political philosophy than in economics, but I found myself captivated by what I was reading in Alchian’s textbook, even though I didn’t find the professor teaching the course very exciting. And after 10 weeks (the University of California had switched to a quarter system) of introductory micro, I changed my major to economics. So there is no doubt that I became an economist because the textbook that I was taught from was written by Alchian.

In my four years as an undergraduate at UCLA, I took three classes from Axel Leijonhufvud, two from Ben Klein, two from Bill Allen, and one each from Robert Rooney, Nicos Devletoglou, James Buchanan, Jack Hirshleifer, George Murphy, and Jean Balbach. But Alchian, who in those days was not teaching undergrads, was a looming presence. It became obvious that Alchian was the central figure in the department, the leader and the role model that everyone else looked up to. I would see him occasionally on campus, but was too shy or too much in awe of him to introduce myself to him. One incident that I particularly recall is when, in my junior year, F. A. Hayek visited UCLA in the fall and winter quarters (in the department of philosophy!) teaching an undergraduate course in the philosophy of the social sciences and a graduate seminar on the first draft of Law, Legislation and Liberty. I took Hayek’s course on the philosophy of the social sciences, and audited his graduate seminar, and I occasionally used to visit his office to ask him some questions. I once asked his advice about which graduate programs he would suggest that I apply to. He mentioned two schools, Chicago, of course, and Princeton where his friends Fritz Machlup and Jacob Viner were still teaching, before asking, “but why would you think of going to graduate school anywhere else than UCLA? You will get the best training in economics in the world from Alchian, Hirshleifer and Leijonhufvud.” And so it was, I applied to, and was accepted at, Chicago, but stayed at UCLA.

As a first year graduate student, I took the (three-quarter) microeconomics sequence from Jack Hirshleifer (who in the scholarly hierarachy at UCLA ranked only slightly below Alchian) and the two-quarter macroeconomics sequence from Leijonhufvud. Hirshleifer taught a great course. He was totally prepared, very organized and his lectures were always clear and easy to follow. To do well, you had to sit back listen, review the lecture notes, read through the reading assignments, and do the homework problems. For me at least, with the benefit of four years of UCLA undergraduate training, it was a breeze.

Great as Hirshleifer was as a teacher, I still felt that I was missing out by not having been taught by Alchian. Perhaps Alchian felt that the students who took the microeconomics sequence from Hirshleifer should get some training from him as well, so the next year he taught a graduate seminar in topics in price theory, to give us an opportunity to learn from him how to do economics. You could also see how Alchian operated if you went to a workshop or lecture by a visiting scholar, when Alchian would start to ask questions. He would smile, put his head on his forehead, and say something like, “I just don’t understand that,” and force whoever it was to try to explain the logic by which he had arrived at some conclusion. And Alchian would just keep smiling, explain what the problem was with the answer he got, and ask more questions. Alchian didn’t shout or rant or rave, but if Alchian was questioning you, you were not in a very comfortable position.

So I was more than a bit apprehensive going into Alchian’s seminar. There were all kinds of stories told by graduate students about how tough Alchian could be on his students if they weren’t able to respond adequately when subjected to his questioning in the Socratic style. But the seminar could not have been more enjoyable. There was give and take, but I don’t remember seeing any blood spilled. Perhaps by the time I got to his seminar, Alchian, then about 57, had mellowed a bit, or, maybe, because we had all gone through the graduate microeconomics sequence, he felt that we didn’t require such an intense learning environment. At any rate, the seminar, which met twice a week for an hour and a quarter for 10 weeks, usually involved Alchian picking a story from the newspaper and asking us how to analyze the economics underlying the story. Armed with nothing but a chalkboard and piece of chalk, Alchian would lead us relatively painlessly from confusion to clarity, from obscurity to enlightenment. The key concepts with which to approach any problem were to understand the choices available to those involved, to define the relevant costs, and to understand the constraints under which choices are made, the constraints being determined largely by the delimitation of the property rights under which the resources can be used or exchanged, or, to be more precise, the property rights to use those resources can be exchanged.

Ultimately, the lesson that I learned from Alchian is that, at its best, economic theory is a tool for solving actual real problems, and the nature of the problem ought to dictate the way in which the theory (verbal, numerical, graphical, higher mathematical) is deployed, not the other way around. The goal is not to reach any particular conclusion, but to apply the tools in the best and most authentic way that they can be applied. Alchian did not wear his politics on his sleeve, though it wasn’t too hard to figure out that he was politically conservative with libertarian tendencies. But you never got the feeling that his politics dictated his economic analysis. In many respects, Alchian’s closest disciple was Earl Thompson, who studied under Alchian as an undergraduate, and then, after playing minor-league baseball for a couple of years, going to Harvard for graduate school, eventually coming back to UCLA as an assistant professor where he remained for his entire career. Earl, discarding his youthful libertarianism early on, developed many completely original, often eccentric, theories about the optimality of all kinds of government interventions – even protectionism – opposed by most economists, but Alchian took them all in stride. Mere policy disagreements never affected their close personal bond, and Alchian wrote the forward to Earl’s book with Charles Hickson, Ideology and the Evolution of Vital Economics Institutions. If Alchian was friendly with and an admirer of Milton Friedman, he just as friendly with, and just as admiring of, Paul Samuelson and Kenneth Arrow, with whom he collaborated on several projects in the 1950s when they consulted for the Rand Corporation. Alchian cared less about the policy conclusion than he did about the quality of the underlying economic analysis.

As I have pointed out on several prior occasions, it is simply scandalous that Alchian was not awarded the Noble Prize. His published output was not as voluminous as that of some other luminaries, but there is a remarkably high proportion of classics among his publications. So many important ideas came from him, especially thinking about economic competition as an evolutionary process, the distinction between the functional relationship between cost and volume of output and cost and rate of output, the effect of incomplete information on economic action, the economics of property rights, the effects of inflation on economic activity. (Two volumes of his Collected Works, a must for anyone really serious about economics, contain a number of previously unpublished or hard to find papers, and are available here.) Perhaps in the future I will discuss some of my favorites among his articles.

Although Alchian did not win the Nobel Prize, in 1990 the Nobel Prize was awarded to Harry Markowitz, Merton Miller, and William F. Sharpe for their work on financial economics. Sharp, went to UCLA, writing his Ph.D. dissertation on securities prices under Alchian, and worked at the Rand Corporation in the 1950s and 1960s with Markowitz.  Here’s what Sharpe wrote about Alchian:

Armen Alchian, a professor of economics, was my role model at UCLA. He taught his students to question everything; to always begin an analysis with first principles; to concentrate on essential elements and abstract from secondary ones; and to play devil’s advocate with one’s own ideas. In his classes we were able to watch a first-rate mind work on a host of fascinating problems. I have attempted to emulate his approach to research ever since.

And if you go to the Amazon page for University Economics and look at the comments you will see a comment from none other than Harry Markowitz:

I am about to order this book. I have just read its quite favorable reviews, and I am not a bit surprised at their being impressed by Armen Alchian’s writings. I was a colleague of Armen’s, at the Rand Corporation “think tank,” during the 1950s, and hold no economist in higher regard. When I sat down at my keyboard just now it was to find out what happened to Armen’s works. One Google response was someone saying that Armen should get a Nobel Prize. I concur. My own Nobel Prize in Economics was awarded in 1990 along with the prize for Wm. Sharpe. I see in Wikipedia that Armen “influenced” Bill, and that Armen is still alive and is 96 years old. I’ll see if I can contact him, but first I’ll buy this book.

I will always remember Alchian’s air of amused, philosophical detachment, occasionally bemused (though, perhaps only apparently so, as he tried to guide his students and colleagues with question to figure out a point that he already grasped), always curious, always eager for the intellectual challenge of discovery and problem solving. Has there ever been a greater teacher of economics than Alchian? Perhaps, but I don’t know who. I close with one more quotation, this one from Axel Leijonhufvud written about Alchian 25 years ago.  It still rings true.

[Alchian's] unique brand of price theory is what gave UCLA Economics its own intellectual profile and achieved for us international recognition as an independent school of some importance—as a group of scholars who did not always take their leads from MIT, Chicago or wherever. When I came here (in 1964) the Department had Armen’s intellectual stamp on it (and he remained the obvious leader until just a couple of years ago ….). Even people outside Armen’s fields, like myself, learned to do Armen’s brand of economic analysis and a strong esprit de corps among both faculty and graduate students sprang from the consciousness that this ‘New Institutional Economics’ was one of the waves of the future and that we, at UCLA, were surfing it way ahead of the rest. But Armen’s true importance to the UCLA school did not stem just from the new ideas he taught or the outwardly recognized “brandname” that he created for us. For many of his young colleagues he embodied qualities of mind and character that seemed the more important to seek to emulate the more closely you got to know him.

What Kind of Equilibrium Is This?

In my previous post, I suggested that Stephen Williamson’s views about the incapacity of monetary policy to reduce unemployment, and his fears that monetary expansion would simply lead to higher inflation and a repeat of the bad old days the 1970s when inflation and unemployment spun out of control, follow from a theoretical presumption that the US economy is now operating (as it almost always does) in the neighborhood of equilibrium. This does not seem right to me, but it is the sort of deep theoretical assumption (e.g., like the rationality of economic agents) that is not subject to direct empirical testing. It is part of what the philosopher Imre Lakatos called the hard core of a (in this case Williamson’s) scientific research program. Whatever happens, Williamson will process the observed facts in terms of a theoretical paradigm in which prices adjust and markets clear. No other way of viewing reality makes sense, because Williamson cannot make any sense of it in terms of the theoretical paradigm or world view to which he is committed. I actually have some sympathy with that way of looking at the world, but not because I think it’s really true; it’s just the best paradigm we have at the moment. But I don’t want to follow that line of thought too far now, but who knows, maybe another time.

A good illustration of how Williamson understands his paradigm was provided by blogger J. P. Koning in his comment on my previous post copying the following quotation from a post written by Williamson a couple of years on his blog.

In other cases, as in the link you mention, there are people concerned about disequilibrium phenomena. These approaches are or were popular in Europe – I looked up Benassy and he is still hard at work. However, most of the mainstream – and here I’m including New Keynesians – sticks to equilibrium economics. New Keynesian models may have some stuck prices and wages, but those models don’t have to depart much from standard competitive equilibrium (or, if you like, competitive equilibrium with monopolistic competition). In those models, you have to determine what a firm with a stuck price produces, and that is where the big leap is. However, in terms of determining everything mathematically, it’s not a big deal. Equilibrium economics is hard enough as it is, without having to deal with the lack of discipline associated with “disequilibrium.” In equilibrium economics, particularly monetary equilibrium economics, we have all the equilibria (and more) we can handle, thanks.

I actually agree that departing from the assumption of equilibrium can involve a lack of discipline. Market clearing is a very powerful analytical tool, and to give it up without replacing it with an equally powerful analytical tool leaves us theoretically impoverished. But Williamson seems to suggest (or at least leaves ambiguous) that there is only one kind of equilibrium that can be handled theoretically, namely a fully optimal general equilibrium with perfect foresight (i.e., rational expectations) or at least with a learning process leading toward rational expectations. But there are other equilibrium concepts that preserve market clearing, but without imposing, what seems to me, the unreasonable condition of rational expectations and (near) optimality.

In particular, there is the Hicksian concept of a temporary equilibrium (inspired by Hayek’s discussion of intertemporal equilibrium) which allows for inconsistent expectations by economic agents, but assumes market clearing based on supply and demand schedules reflecting those inconsistent expectations. Nearly 40 years ago, Earl Thompson was able to deploy that equilibrium concept to derive a sub-optimal temporary equilibrium with Keynesian unemployment and a role for countercyclical monetary policy in minimizing inefficient unemployment. I have summarized and discussed Thompson’s model previously in some previous posts (here, here, here, and here), and I hope to do a few more in the future. The model is hardly the last word, but it might at least serve as a starting point for thinking seriously about the possibility that not every state of the economy is an optimal equilibrium state, but without abandoning market clearing as an analytical tool.

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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