Paul A. Samuelson, 1915-2009

"Gentlemen, did we pass?"

That's what Joseph Schumpeter is reported to have asked the other members of Paul Samuelson's dissertation committee at the end of his doctoral defense. Many a true word is spoken in jest.

Over the next few days there will be a lot of testimonials to Samuelson's brilliance and professional accomplishments, but the two passages I found most poignant in the New York Times obituary concern his character. First, his unwillingness to accept a political appointment:

Though Professor Samuelson was President Kennedy’s first choice to become chairman of the Council of Economic Advisers, he refused, on principle, to take any government office because, he said, he did not want to put himself in a position in which he could not say and write what he believed.

And second, his opinion of himself and his profession:

Despite his celebrated accomplishments, Mr. Samuelson preached and practiced humility. The M.I.T. economics department became famous for collegiality, in no small part because no one else could play prima donna if Mr. Samuelson refused the role, and, of course, he did. Economists, he told his students, as Churchill said of political colleagues, “have much to be humble about.”

Indeed.

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Update (12/14): William Barnett's version of the Schumpeter anecdote differs slightly from that of Wolfgang Stolper (as reported by Arnold Heertje), and neither is confirmed. Apocryphal or not, the plausibility of the story itself says a lot about Samuelson.

On the Choice of Maturities for New Treasury Issues

Every week the Treasury issues new securities with maturities ranging from a few days to several years. In the first ten days of December, for instance, bills and bonds with aggregate face value in excess of 220 billion dollars were auctioned; these had maturities ranging from four days to thirty years and annualized interest rates ranging from practically zero to 4.4%. About two-thirds of the total was short term borrowing due for repayment within the next six months, and the remainder was raised by issuing three and ten year notes, and thirty year bonds. Since there is no prospect of a budget surplus at any time over the next few years, incoming tax revenues will be fully absorbed by projected spending and the short-term debt will have to be rolled over on an ongoing basis (or converted at some point to long-term debt).

Clearly, the Treasury has a fair amount of discretion regarding the manner in which the deficit is financed. How ought this discretion to be exercised? And how is it exercised in practice? Theories of corporate maturity choice (such as Diamond, 1991) are not terribly useful in answering these questions because the goals and constraints are so different. The Treasury does not have to worry about liquidation by its creditors, for example, and corporations are not generally concerned with the effects of their actions on the term structure of interest rates or the value of the currency.

The issue is really quite important. A couple of weeks ago, Paul Krugman suggested that the Treasury should shift towards shorter-term maturities to finance the deficit if long term interest rates were to start rising. Two days later New York Times reported that the Treasury was in fact doing just the opposite, "exchanging short-term borrowings for long-term bonds." Without a theory (either positive or normative) of maturity choices for new issues, such proposals and actions are hard to evaluate. Furthermore, the costs of making poor judgments can be very high, both in terms of the interest burden on taxpayers, and the effects on private sector choices of changes in the yield curve.

If the future path of interest rates could be anticipated with perfect precision, then the yield curve at any point in time would be fully determined by no-arbitrage conditions. In this case the cost of borrowing would be essentially independent of maturity choice. But there is always uncertainty about future rates, so rates on short term debt, which is a preferred habitat of lenders, typically tend to be lower than long term rates.  In this case the cost of debt service will be smaller if the deficit is financed with short rather than long term obligations.

Aside from the cost of financing the deficit, maturity choices by the Treasury affect the shape of the yield curve and the extent to which private sector institutions engage in maturity transformation. This has implications for the stability of the system and its vulnerability to liquidity crises, as Bill Dudley has recently observed. In light of these considerations, I find it a bit surprising that while the size of the deficit is a topic of endless controversy, there is such little debate about the manner in which the deficit is financed.

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Update (12/17): In an interesting post, Andy Harless discusses related issues.

On the Consequences of Nominal Wage Flexibility

With the unemployment rate hovering above 10% and likely to stay in this range for some time, there has been a lot of discussion about what (if anything) the government should do to stimulate job creation. Following a link on Greg Mankiw's blog, I came across Gary Becker's view of the matter:

Keynes and many earlier economists emphasized that unemployment rises during recessions because nominal wage rates tend to be inflexible in the downward direction. The natural way that markets usually eliminate insufficient demand for a good or service, such as labor, is for the price of this good or service to fall. A fall in price stimulates demand and reduces supply until they are brought back to rough equality. Downward inflexible wages prevents that from happening quickly when there is insufficient demand for workers.

As one might expect given his diagnosis of the problem, Becker goes on to "fully endorse" a cut in the minimum wage, but does not see this as being politically feasible at present.

I found this post striking for three reasons. First, it expresses a view that is actually quite widely held among economists today, namely that if nominal wages were flexible in the downward direction, involuntary unemployment could not persist for very long. This view is held even by many who would strenuously object on fairness grounds to a cut in the minimum wage. Second, Becker attributes to Keynes an opinion that is precisely the opposite of that expressed in the General Theory.  And third, there has been very little serious analysis of the consequences of nominal wage flexibility in an economy with involuntary unemployment. A notable exception is a 1975 paper by James Tobin that has been largely (and unjustly) forgotten. For reasons discussed below, Tobin's analysis does not support Becker's position.

Keynes did indeed assume for the most part that nominal wages were inflexible, but also maintained that wage flexibility would make matters worse rather than better: "it would be much better that wages should be rigidly fixed and deemed incapable of of material changes, than that depressions should be accompanied by a gradual downward tendency of money wages" (p. 265). This is the starting point for Tobin's analysis:

Keynes tried to make a double argument about wage reduction and employment. One was that wage rates were very slow to decline in the face of excess supply. The other was that, even if they declined faster, employment would not - in depression circumstances - increase. As to the second point, he was well aware of the dynamic argument that declining money wage rates are unfavorable to aggregate demand. But perhaps he did not insist upon it strongly enough, for the subsequent theoretical argument focused on the statics of alternative stable wage levels.

To drive this point home, Tobin builds a simple model with three dynamic equations: output adjusts in response to excess demand in the goods market, inflation (relative to expectations) adjusts in response to deviations of output from its full employment level, and expectations of inflation adjust adaptively in response to the difference between actual and expected inflation. So prices (and nominal wages) are fully flexible and there is no limit to how low these can fall if output remains persistently below its full employment level.

An equilibrium of this model is characterized by full employment, steady inflation, and correct expectations. But Tobin is less interested in the equilibrium behavior of the economy than in the dynamic adjustment process from an initial state of disequilibrium. He establishes that even if the equilibrium is locally stable, it need not be globally stable: if, for whatever reason, output drops far enough below its full employment level, then (as in Axel Leijonhufvud's corridor hypothesis) cumulative declines in employment and prices can result.  Instead of improving matters, the downward flexibility of money wages can prolong and deepen an economic contraction.

Tobin's analysis here is methodologically old-fashioned in the sense that no attempt is made to provide microfoundations for the postulated adjustment processes.  But the logic is compelling, and I am certain that with sufficient ingenuity, the argument could be expressed in more modern terms. In any case, it is no less convincing than the partial equilibrium Walrasian analysis of the labor market that has led some to prescribe lower nominal wages as a solution to our current woes.

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Update (12/9): Thanks to Mark Thoma for reposting this, to Paul Krugman for his comments and references, and The Economist for linking. I should note that aside from Keynes and Tobin, Fisher (1933) and DeLong and Summers (1986) have also explored mechanisms that can cause price flexibility to be destabilizing.

On Animal Spirits and Knee-Jerk Reactions

A couple of weeks ago Robert Shiller published a piece in the New York Times in which he explored the role of mass psychology in generating business cycles, and argued that "the economic recovery that appears under way may be based on little more than self-fulfilling prophecy." This led Mark Thoma to respond as follows:

I find that I have a knee-jerk, negative reaction to explanations based upon mass psychology, sentiment, story-telling, and the like. I have to consciously force myself not to dismiss them. I'm not sure why that is, though it probably has something to do with a feeling that such explanations aren't scientific, and hence have no place in serious academic investigations. That is, prior to the crisis I thought that the real economy drove sentiment, and not the other way around. Sentiment could definitely provide a feedback loop that strengthens negative or positive economic shocks, but psychology was not the prime mover. Thus, sentiment changes that did not have evidence to support them would quickly die out before having much, if any effect.

But this crisis has caused me to reevaluate. I still find the Shiller-type animal spirits, psychology based explanations hard to swallow, but when the foundation supporting your beliefs is called into question (in this case modern macroeconomic models), it's important to open your mind and at least give alternative explanations a chance. That's particularly true when the person pushing the stories has a pretty darn good record of using them to warn of bubbles, as Shiller does. So I'm trying.

This captures my sentiments almost exactly. I'm trying. I too have the greatest respect for Shiller and consider his 1981 paper on stock price (relative to dividend) volatility to be an absolute classic. But I can't help thinking that too much is being asked of behavioral economics at this time, much more than it has the capacity to deliver. In an earlier post on Elinor Ostrom I expressed this view as follows:

Behavioral economics... has been very successful in identifying the value of commitment devices in household savings decisions, and accounting for certain anomalies in asset price behavior. But regularities identified in controlled laboratory experiments with standard subject pools have limited application to environments in which the distribution of behavioral propensities is both endogenous and psychologically rare. This is the case in financial markets, which are subject to selection at a number of levels. Those who enter the profession are unlikely to be psychologically typical, and market conditions determine which behavioral propensities survive and thrive at any point in historical time.

If one is to look beyond economics for metaphors and models, why stop at psychology? For financial market behavior, a more appropriate discipline might be evolutionary ecology. This is not a new idea. Consider, for instance, this recent article in Nature. Or take a look at the chapter on "The Ecology of Markets" in Victor Niederhoffer's extraordinary memoir. Or study Hyman Minsky's financial instability hypothesis (discussed at some length in an earlier post), which depends explicitly on the assumption that aggressive financial practices are rapidly replicated during periods of stable growth, eventually becoming so widespread that systemic stability is put at risk. To my mind this reflects an ecological rather than psychological understanding of financial market behavior.

The Economics of Hyman Minsky

There has been a resurgence of interest in the economic writings of Hyman Minsky over the past few years, and for good reason. I find this immensely gratifying. I first came across his work as a graduate student, and remember being struck by the manner in which he was able to weave together sweeping macroeconomic hypotheses with rich institutional and historical detail. In a 2002 review of a collected volume in his honor, I summarized the broad outlines of his argument as follows:

Minsky's theoretical framework combines a cash-flow approach to investment with a theory of financial instability. Investment is motivated by the expectation that it will yield a stream of cash flows sufficient to cover contractual debt obligations as they come due, while allowing for adequate margins of safety. During stable expansions, profits accrue disproportionately to firms with the most aggressive financial practices, resulting in an erosion of margins of safety. This raises the probability that a major default will trigger a widespread crisis. When a crisis does eventually occur, its most devastating impact is on the highly indebted firms that prospered during the expansion. Balance sheets are purged of debt, margins of safety rise, and the stage is set for the process to begin anew. From this perspective, expectations of financial tranquility are self-falsifying. Stability, as Minsky liked to put it, is itself destabilizing. The real effects of a crisis depend on the size of government and the role of the central bank. Large countercyclical budget deficits can sustain profit flows even when investment collapses, preventing a crisis from resulting in a debt-deflation. Similarly, lender-of-last-resort interventions can keep a crisis from spreading beyond its point of origin.

Ten years earlier I had grappled with the question of whether or not Minsky's financial instability hypothesis requires substantial departures from economic rationality at the level of individuals and firms. I tried to argue in a 1992 paper that it did not, because even sophisticated models of learning at the individual level need not result in convergence to rational expectations equilibrium paths. The formal analysis in that paper is largely forgettable, but it does have the merit of containing the following reasonably faithful overview of Minsky's conceptual framework:

An essential feature of Minsky's financial instability hypothesis is that a long period of sustained stability gives rise to changes in financial practices which are not conducive to the persistence of stable growth:

"The natural starting place for analyzing the relation between debt and income is to take an economy with a cyclical past that is now doing well. The inherited debt reflects the history of the economy, which includes a period in the not too distant past in which the economy did not do well. Acceptable liability structures are based upon some margin of safety, so that expected cash flows, even in periods when the economy is not doing well, will cover contractual debt payments. As the period over which the economy does well lengthens, two things become evident in board rooms. Existing debts are easily validated and units that were heavily in debt prospered; it paid to lever. After the event it becomes apparent that the margins of safety built into debt structures were too great. As a result, over a period in which the economy does well, views about acceptable debt structure change. In the deal making that goes on between banks, investment bankers, and businessmen, the acceptable amount of debt to use in financing various types of activity and positions increases. This increase in the weight of debt financing raises the market price for capital assets and increases investment. As this continues, the economy is transformed into a boom economy." (Minsky, 1982, pp. 65 f.)

In particular, there is an increase in the degree to which investment is debt financed, and in the ratio of "speculative" to "hedge" financing. Speculative financing differs from hedge financing in that the expected cash receipts fall short of the debt-repayment commitments in some periods, particularly in periods which are in the immediate future with respect to the date at which the investment is undertaken. Hence there arises a need to roll-over debt during initial periods after the investment. Since the present value of all expected future cash flows exceeds the present value of debt repayments by an amount which includes acceptable margins of safety, firms do not generally foresee problems with regard to raising funds for purposes of rolling-over debt during the initial periods. Nevertheless, the possibility of present value reversals in the face of sharp rises in interest rates cannot be ruled out entirely, and this is what makes speculative financing riskier from the point of view of economy-wide-stability. On the other hand, if firms were able to borrow an amount which was strictly constrained by their expected receipts in every period, the potential for expansion would be severely curtailed and several reasonable profit opportunities would have to be foregone. The degree to which bankers are willing to engage in speculative finance clearly depends on their state of confidence with regard to general economic conditions in the future, as well as the merits of the specific projects at hand. The willingness to refinance positions as debt repayments become due is likewise influenced by their expectations, as well as the liquidity constraints they face.

Hence hedge financing is conducive to stability while speculative financing is conducive to faster expansion. A sustained period of stability gives rise to optimistic expectations and a rise in speculative financing. As long as the investments undertaken during this period are effective in raising productivity and engender a steady expansion of output, the optimism can be sustained. However, if a large number of investments which are prompted by the availability of speculative finance are found to be inept, so that immediate cash flows are significantly lower than expected, then the need for short-term refinancing becomes acute while at the same time banks are less willing to roll over existing debt. A sharp rise in short-term interest rates occurs which can lead to present value reversals, a rush towards liquidity, a plunge in the prices of illiquid assets, both real and financial, and a corresponding drop in new investments. Such an event, depending on its severity, is generally described as a credit crunch, a state of financial distress, or a financial crisis.

The severity of the recession that follows on the heels of a financial crisis depends on the size of the government relative to the private sector and the degree to which the drop in investment is compensated for by a rise in the government deficit. A sufficient rise in the deficit can help maintain the gross profits of business and hence validate the existing liability structure. This is achieved, however, at the cost of sustaining an inefficient industrial structure and inevitably leads to accelerating inflation. In the case of small government or a government that is determined to maintain a balanced budget, the financial crisis is likely to be much more severe, and the collapse of gross profits, by further curtailing investment, may be expected to give rise to a protracted depression. Lender-of-last-resort action by the monetary authorities can help offset the liquidity squeeze, preventing an extreme escalation of short-term interest rates and allowing the refinancing of positions which have been created through speculative financing. The fall in asset prices which is engendered by the rush towards liquid assets can thereby be contained, so that the financial crisis is less acute. There is a serious long-run cost to indiscriminate lender-of-last-resort action, however, in that the expectation of such action on the part of banks and firms, once it has become established, leads to the general (and correct) perception that the risks associated with speculative financing are not too severe. Imprudent financing may thereby be encouraged.

To summarize, there are inherent tendencies in advanced capitalist economies with sophisticated financial structures which give rise to instability in financial markets. The severity of the financial crises that occur, and the subsequent losses in output and employment depend on the size and actions of the government. Instability is generated endogenously, in the sense that a period of sustained stability encourages an increase in speculative financing which renders the financial structure fragile. Instability on the other hand encourages financial prudence, and thereby creates the conditions for a period of sustained growth. It is within the context of such dynamic interactions that Minsky is able to speak of the "destabilizing effects of stability."

Expectations play a central role in the precipitation of the crisis, as well as in the creation of the conditions which characterize financial fragility. The basic assumption made by Minsky with regard to the formation of expectations is reflected in the following passages:

"Financing is often based on an assumption 'that the existing state of affairs will continue indefinitely' (GT, p. 152), but of course this assumption proves false. During a boom the existing state is the boom with its accompanying capital gains and asset revaluations. During both a debt-deflation and a stagnant recession the same conventional assumption of the present always ruling is made; the guiding wisdom is that debts are to be avoided, for debts lead to disaster." (Minsky, 1975, p. 128)

"A recovery starts with strong memories of the penalty extracted because of exposed liability positions during the debt-deflation and with liability structures that have been purged of debt. However, success breeds daring, and over time the memory of the past disaster is eroded. Stability -- even of an expansion -- is destabilizing in that more adventuresome financing of investment pays off to the leaders, and others follow." (Minsky, 1975, p. 126)

Although fully conscious of operating in a cyclical economy, the individuals described above are prone to making decisions, particularly with regard to liability structures, on the basis of assumptions that are periodically discovered to be false. This exposes Minsky's analysis to the charge that his explanation of financial instability depends on an assumption of irrationality on the part of financiers and entrepreneurs, in the sense that they persist in holding expectations that are systematically wrong.

But is it really true that Minsky's theory depends on an assumption of significant and persistent departures from economic rationality on the part of firms? I tried to argue that this was not necessarily the case:

From a theoretical point of view, it is desirable to determine what manner of departures from rationality, if any, are required for Minsky's central propositions to hold. Bernanke (1983, p. 258) has stated for instance that Minsky and Kindleberger "have in several place argued for the inherent instability of the financial system, but in doing so have had to depart from the assumption of rational behavior." Bernanke does not elaborate on the precise nature of the departures which are a necessary component of the FIH, and his conclusion is somewhat perplexing in the light of Minsky's repeated assertions to the effect that "capitalism abhors unexploited profit opportunities" (1986, p. 219). In fact profit maximizing banks and firms are central actors in the scenario that is depicted, to the extent that financial innovation itself is explained on the basis of self-interested behavior, often in response to policy initiatives. It is possible that Bernanke is referring to irrationality with regard to expectation formation, and if this is the case, then his sentiments are shared by Flemming who believes that "the argument depends on agents failing to distinguish a run of good luck from a favorable structural shift in their environment." It is indeed true that Minsky refers occasionally to "conventional" assumptions which prove to be false, and to psychological phenomena such as "success breeds daring" (1975, p. 128). It is far from clear, however, that such features of the theory are in any way essential to the argument. The possibility that an optimizing approach to expectation formation may not be inconsistent with the theory arises because Minsky is dealing explicitly with what has come to be called a self-referential system (Marcet and Sargent, 1989), in which the actual law of motion describing the evolution of economic magnitudes is not independent of the perceived law of motion which guides the actions of agents. In such environments, the convergence to rational expectations trajectories even of extremely sophisticated learning procedures cannot be taken for granted. It is true that the FIH does not appear to be compatible with the RE hypothesis, in that firms persist in adopting liability structures which give rise to outcomes which violate the assumptions on the basis of which the liability structures were chosen. This occurs both in the case of excessive caution following a period of instability, and excessive boldness following a long expansion. Nevertheless, simply because a Minsky economy is not characterized by a movement along a rational expectations equilibrium trajectory, this does not force one to conclude that the agents described therein are in any meaningful sense irrational; the question must be raised within an explicit model of learning.

In retrospect, my attempt to answer this question fell woefully short. But the question itself seems worth addressing, as part of an attempt to explore the logical consistency of the financial instability hypothesis and clarify the assumptions on which it is based.

Cormac McCarthy's Typewriter

The Santa Fe Institute is a fascinating place, built on an unusual vision of how academic research should be conducted. It has a small core of resident faculty, and a large group of rotating short-term visitors. Interaction continually crosses disciplinary boundaries, with a healthy mix of natural and social scientists (and some non-academics) at each seminar. Offices are shared and doors usually left open. Lunch at noon and tea at three are communal events: there are a few large tables around which everyone gathers. And there is a broad range in ages: undergraduate researchers mingle with post-docs, professors, and the occasional Nobel Laureate. 

A few years ago I had the good fortune to share an office for a few weeks with Cormac McCarthy. I'm not sure which book he was working on at the time (I think it may have been The Road), but I noticed right away that there was no computer at his desk. This is what he was using:

That's right, a manual typewriter. One that he bought for $50 in 1963 and has now put up for auction: 

Lately this dependable machine has been showing irrevocable signs of age. So after his friend and colleague John Miller offered to buy him another, Mr. McCarthy agreed to auction off his Olivetti Lettera 32 and donate the proceeds to the Santa Fe Institute, a nonprofit interdisciplinary scientific research organization with which both men are affiliated.

“He found another one just like this,” a portable Olivetti that looks practically brand new, Mr. McCarthy said from his home in New Mexico. “I think he paid $11, and the shipping was about $19.95.”

In an accompanying letter of authentication, Cormac writes:

"I have typed on this typewriter every book I have written including three not published. Including all drafts and correspondence I would put this at about five million words over a period of 50 years."

I hope that the auction brings in a substantial sum, and that the collector with the winning bid draws some satisfaction from the fact that the proceeds will be funding basic research at the Institute.

Maturity Transformation and Liquidity Crises

William Dudley's keynote address at a recent CEPS symposium on the financial system is worth reading in full. What I found especially interesting were the following remarks on structural sources of instability:

The risks of liquidity crises are also exacerbated by some structural sources of instability in the financial system. Some of these sources are endemic to the nature of the financial intermediation process and banking. Others are more specific to the idiosyncratic features of our particular system. Both types deserve attention because they tend to amplify the pressures that lead to liquidity runs.

Turning first to the more inherent sources of instability, there are at least two that are worthy of mention. The first instability stems from the fact that most financial firms engage in maturity transformation — the maturity of their assets is longer than the maturity of their liabilities. The need for maturity transformation arises from the fact that the preferred habitat of borrowers tends toward longer-term maturities used to finance long-lived assets such as a house or a manufacturing plant, compared with the preferred habitat of investors, who generally have a preference to be able to access their funds quickly. Financial intermediaries act to span these preferences, earning profits by engaging in maturity transformation — borrowing shorter-term in order to finance longer-term lending.

If a firm engages in maturity transformation so that its assets mature more slowly than its liabilities, it does not have the option of simply allowing its assets to mature when funding dries up. If the liabilities cannot be rolled over, liquidity buffers will soon be weakened. Maturity transformation means that if funding is not forthcoming, the firm will have to sell assets. Although this is easy if the assets are high-quality and liquid, it is hard if the assets are lower quality. In that case, the forced asset sales are likely to lead to losses, which deplete capital and raise concerns about insolvency.

The second inherent source of instability stems from the fact that firms are typically worth much more as going concerns than in liquidation. This loss of value in liquidation helps to explain why liquidity crises can happen so suddenly. Initially, no one is worried about liquidation. The firm is well understood to be solvent... But once counterparties start to worry about liquidation, the probability distribution can shift very quickly toward the insolvency line... because the liquidation value is lower than the firm’s value as a going concern...

These sources of instability create the risk of a cascade... Once the firm’s viability is in question and it is does not have access to an insured deposit funding base, the next stop is often a full-scale liquidity crisis that often cannot be stopped without massive government intervention.

As Dudley notes, maturity transformation is "endemic to the nature of the financial intermediation process and banking." But non-financial firms (and the United States Treasury) can also engage in maturity transformation by borrowing short relative to their expected revenue streams. This is what Hyman Minsky called speculative (as opposed to hedge) financing. One of Minsky's key insights was that over a period of stable growth with relatively tranquil financial markets, there is a progressive shift away from hedge and towards speculative financing:

The natural starting place for analyzing the relation between debt and income is to take an economy with a cyclical past that is now doing well. The inherited debt reflects the history of the economy, which includes a period in the not too distant past in which the economy did not do well. Acceptable liability structures are based upon some margin of safety, so that expected cash flows, even in periods when the economy is not doing well, will cover contractual debt payments. As the period over which the economy does well lengthens, two things become evident in board rooms. Existing debts are easily validated and units that were heavily in debt prospered; it paid to lever. After the event it becomes apparent that the margins of safety built into debt structures were too great. As a result, over a period in which the economy does well, views about acceptable debt structure change. In the deal making that goes on between banks, investment bankers, and businessmen, the acceptable amount of debt to use in financing various types of activity and positions increases. (Minsky 1982, p.65)

Short-term financing of long-lived capital assets is lucrative as long as debts can be rolled over easily at relatively stable interest rates. But this induces more firms to engage in speculative rather than hedge financing, making the demand for refinancing increasingly inelastic. The eventual result is a crisis of liquidity and a shift back towards hedge financing.

Many economists (myself included) have tried to construct formal models of the process described by Minsky, but with limited success to date. This may be a good time to give it another shot.