(Dt. Sunday, September 21, 2008)

Update 3.2: A Mathematician's Apology

I request the Professors' indulgence for receiving another e-mail from me, hardly two weeks after I sent a hurried "Update 3: Fire-sales, Bazookas and Hospitals" on Monday, September 8. My excuse is that the ill-advised, bazooka-wielding bailout of Fannie Mae and Freddie Mac on Sunday, September 7, had so compelled me to send out an unplanned update urgently the next day, that I feel the need to elaborate further to complete my update properly. So, I request the reader to please treat this message as the second part of the same update sent on September 8, i.e., Update 3.2. This article is divided into four sections -- I. Introduction, II. Risk Management, III. Game Theory, IV. Econometrics. At the end of this update is a Corrigendum to one of my previous updates, "Update 2: A Marginalistic Interpretation of the GARCH Model", which I had sent out on Sunday, May 4, 2008. I need to remove one sentence from that previous update -- it does not seem that an assumption that markets are efficient necessarily implies that changes in asset prices are solely caused by new information (i.e., asset prices are random walks).

I. Introduction

Most professional economists around the world would agree, I suppose, that the American economy is currently going through its worst financial crisis since the Great Depression of the late 1920s and the early 30s. There is plenty of debates and discussions about this crisis going on all the time, across all sections of society, all over the world. However, no one seems to be able to explain convincingly where the root cause of the problem is, nor when this crisis would end. Even after this crisis comes to a conclusion, it is seriously doubtful that anyone could truly understand exactly where things went wrong. Being a mathematician, I figure that I owe an apology -- one plausible root of this crisis could be the fundamental failure of 20th century mathematics to come to grips with some subtle issues concerning the modern economy. Yes, a major cause of this financial crisis, according to me, is the failure of the mathematical theories of economics, for example, asset pricing, equilibrium theory, game theory and econometrics, to adequately capture the nuances in the economic reality of the day. I can assure the reader that it is no pleasure to have to apologize for it. I can only ask that the blame for the failure of mathematical theories be amortized against any credit the reader is willing to give me for this update and for earlier articles on my research proposal.

According to the conventional wisdom, financial crises, as they come, are initiated by speculative bubbles. Historically exacerbated levels of human vices, like greed, profligacy, fear, panic and paranoia are, in general, naturally suited environments for speculative bubbles to thrive. In a financial crisis, the initial spark of a speculative bubble, provided by human fallibility, is further amplified by the incompetence of the institutions of the state at the macroeconomic level. These amplification factors include mismanagement of the monetary supply, failure to provide liquidity at the right instances and at the right amounts, political expediency, and lack of transparency in decision making. Lastly, hovering above these short-term contributions, is the Marxian critique that in the long-term, capitalist systems are inherently unstable, because of the over-accumulation of surplus value, a distinctly Marxian notion. Economists like Milton Friedman/Anna Schwartz, John Kenneth Galbraith, Charles Kindleberger and Karl Marx have done a much better job of recording the characteristics of a financial crisis from these human and social perspectives than I, as a mathematician, could ever hope to do. Perhaps posterity would yet decide that these causes, just stated, would provide the best possible explanation for this current financial crisis as well.

The perspective of Galbraith can be seen as providing an Economist's Apology for financial crises -- that it is beyond the economist's professional ability to anticipate human fallibility, and that the economist's proper role is to accurately record the crisis after its occurrence. If my responsibility stopped with writing the mathematician's equivalent of the Economist's Apology then it would undoubtedly be a great honor to attempt to emulate such stalwart economists as mentioned above. However, I emphasize once again that my task is far from a happy experience. Whereas the challenge of writing prose as clear and elegant as Galbraith's would indeed be an honor, there is no similar honor nor any pleasure in seeing celebrated mathematical theories fail so decisively. My task is further complicated by the fact that to provide a reasonable estimate of the measure of the blame that should be accorded a mathematician, one has to first make sense of this human, all-too-human drama that has been unfolding on the markets this year.

On the Right, politicians have been promising this week, an 'expeditious and comprehensive' program to prevent 'systemic risk'. It is no matter that an expeditious program is simply not possible, because there is no one in the whole world who understands the full extent of the current financial crisis. Moreover, it hardly seems to matter that there does not exist any clear description of 'systemic risk' to date. 'Systemic risk' was the reason put forward for the 30-billion-dollar rescue of Bear Stearns in March 2008. The same 'systemic risk' is the reason being put forward now in September 2008 for establishing a half-a-trillion-dollar mortgage bail-out program modeled after the Resolution Trust Corporation of the 1990s. It appears to me that 'systemic risk', if it exists at all, is the one-size-fits-all ghostly garb of witchcraft. In fact, the concept of risk, as understood currently, does not adequately address the uncertainties faced by the economies around the world today, as I will try to explain in the next section. As a result, any comprehensive solution to the current crisis is, to my knowledge, necessarily years ahead in the future. In addition, Right-leaning economists have been suggesting that the finance industry is too bloated and needs to shrink. If so, where are the corporate profits going to come from, given the current state of manufacturing, food, energy, automobiles, wholesale and technology industries? Also, does this mean that these economists agree that globalization is the only adequate source of economic growth in the next decade? Worst of all, the starkly Right-wing interpretation of the concept of the 'prime borrower', which is the predominant interpretation among the economists and the media-pundits today, has greatly obstructed the democratization of finance across America. Please recall that I had severely criticized the method, currently employed by the finance industry, for measuring the credit-worthiness of a homeowner in my "Update 2: A Marginalistic Interpretation of the GARCH model" (dt. Sunday, May 4, 2008).

On the Left, economists have been demonizing Wall Street executives -- that the high bonuses that these executives take home during the good years is somehow an indication of fraud. If so, would they admit that the famed innovations in the finance industry during the last two decades have no economic value? Please recall that I had stated clearly in my 'Update 1' (dt. Tuesday, April 8, 2008) that "... modern economic theories could not guide us in figuring out how to safeguard the enormous transitory wealth created during the tech boom of the 90s". The tech bust of the early 2000s, I suppose, would make many people agree with that quoted statement. In the next two sections, I will try to explain why modern economic theories are not properly equipped to capture the economic value of financial innovations as well. I had stated further in my Update 1, that "... to face the emerging challenges of globalization in the 21st century, America needs to have a clear sense of the sources of its own wealth. Rising home-ownership speaks directly to core American values which include working hard to gain wealth." It is important for the Left to realize that they need to put aside, even if only temporarily, the Utopian notion of the 21st century's innovation economy, and actually focus on finding solutions to this financial crisis. The solutions need to be something other than just telling themselves, 'let's nationalize our way out of this annoying distraction that people call a financial crisis', or 'Alan Greenspan is responsible for this financial crisis because he kept interest rates too low for too long'. Blaming Alan Greenspan, the former Chairman of the Federal Reserve Bank of the United States, who retired 31 months ago, is not going to solve any problem. Moreover, Greenspan has done yeoman service to the world by having the American economy cash in on the 'empire-premium', as I will explain in Section III.

Thus, I embark with what I hope is ample warning that a mathematician's willingness to apologize for the current financial crisis, should be strongly tempered with a bird's eye-view of the layers and layers of human follies that are unfolding, in real time, on the American economy these days. I might also draw attention to the fact that this game of smoke and mirrors that is being played out in the financial markets and in the political arena is especially murky this year given that this is a year of Presidential election. Then again, I would like to point out that Friedman/Schwartz, Galbraith and Kindleberger published their respective studies on financial crises several decades after the Great Depression, which was the single most important event during the periods covered in their studies. Whereas, in my case, I am writing this apology right in the middle of the current financial crisis, an individual situation which is quite incongruous for a mathematician to be in, because a mathematician's insights arrive at their own time. On the other hand, perhaps my situation is not so inappropriate for me, because a mathematician, by training, should see his/her own faults quickly, for how else would (s)he know for certain, the difference between a proof and a fallacy, except by purely intellectual reasoning? In that case, I should also state that the clarity of a mathematician's viewpoint should not be held as evidence that (s)he is anywhere nearly as close as the other idiots are, to blame for this financial crisis.

II. Risk Management

If one asked a natural scientist about the concept of risk, one would, no doubt, be provided with an explanation based on probability and statistics. In contrast, it appears that some schools of economic thought have pursued their own non-quantitative, intuitive understanding of the concept of risk. I became aware of this only recently. A day after I sent out my "Update 2: A Marginalistic Interpretation of the GARCH model" on May 4, 2008, I received a message from Professor Edmund Phelps referring me to his Op-Ed article in the March 14 edition of Wall Street Journal entitled, "Our Uncertain Economy". Upon reading it, I came to understand that 'Hayekian uncertainty' and 'Knightian uncertainty' are terms that appeal to well-established traditions in economics and that economists have an intuitive recognition of the phenomena referred to by these terms. I am yet to gain a thorough understanding of Professor Phelps' Op-Ed article. However, I would like to explain here how my view on economic uncertainty, as developed in my research proposal, "A New Perspective on the Role of Markets in an Economy", which I had sent out in the second week of March, 2008 is different from the what Professor Phelps discusses in his Op-Ed article.

My view on economic uncertainty is simply an extension of that of the natural scientist. Basically, if any phenomena we come across in the real world could be repeated under independent and identical conditions, then the probability theorists and the statisticians would have a lot more to say about the real world than they do now. This is because, in trying to apply probability theory to their data, statisticians assume that a random variable has been sampled repeatedly under identical and independent conditions. Further, most of the results in probability theory, like limit theorems and stochastic models, deal with collections of identically and independently distributed random variables. However, the world is constantly changing. Except for obviously independent events like coin tosses, it is not clear that experiments, particularly those measuring instantaneous, microscopic events, could be repeated under identical and independent conditions. There is a fundamental doubt whether the statistical measurements that one makes do, in fact, constitute a single random variable, or they are each simply disparate, unrelated phenomenon. Hence, my view on uncertainty tries to avoid making such unreliable measurements. Instead, if one allowed the duration of interaction between the buyer and the seller in a market to take non-instantaneous values, then one could possibly build more robust theories about the functioning of markets. This is the basis of my research proposal and the subsequent updates on it that I have been sending out.

My aim in the previous two paragraphs was to make the reader understand that risk is an extremely subtle concept. The usual understanding that the risk involved in an asset is indicated by the volatility of the asset's price, and that volatility is measured by the variance and other higher order moments of a probability distribution is indeed quite simplistic. On the other hand, it is precisely this quantitative formulation of risk that has made it so applicable in many different contexts. The concept of risk that entrepreneurs encounter in their business ventures has a strongly psychological, non-quantitative component which shares some basic features with the kinds of uncertainty that Professor Phelps refers to in his Op-Ed article. Whereas the concept of risk that the Wall Street establishments deal with in their financial calculations needs precise calibrations, even if it is, at times, divorced from reality. Thus these finance firms work within the probabilistic framework. This leads us to the question as to what exactly is the economic value of the activities of the Wall Street investment banks during the last three decades, activities that particularly involved heavy use of derivative instruments? In my opinion, the great achievement of the financial innovation that these Wall Street firms undertook over the period of the last three decades is risk management. This credit due for this achievement is all the greater when one keeps in mind that the variety of assets that needed to be valued in daily economic activities had undergone an explosion after the underlying foundations of the economies of the first-world nations shifted from manufacturing to services to information technology during the course of the twentieth century. In addition, the nature of the most valuable assets became more and more intangible, subtle and ephemeral.

To appreciate this point properly, let us go back in history and consider the basis of economic wealth. In the agricultural economy, the wealth of an individual was reflected by the ownership of arable land. Mercantilism was the economic theory that existed in 18th century Britain, just before the time of Adam Smith. In the Mercantilist's view, the wealth of a nation was measured by its reserves of gold. This attitude would have suited the agricultural economy whose activities were mainly concentrated on producing edible goods. However, the only prescription that Mercantilism came up with for producing wealth for a European nation was gun-boat diplomacy -- to enforce payments in gold for the trade with its colonies. It was Adam Smith's great vision that manufactured goods and non-perishable agricultural goods, like spices and cotton, also accounted for economic wealth, and that the free trade of these goods maximized a nation's wealth. Adam Smith's worldview laid the foundation for the industrial economy. Over time, the factors of industrial production, which were classified as land, labor and capital came to be considered as the basis of economic wealth. Capital constituted of buildings and machinery, and more liquid assets like cash, bank deposits, bonds, promissory notes and company shares. Money-lending did exist, but was invariably looked upon as greed. Even at this early stage in economic theory, the relative importance of land, labor and capital was a greatly controversial topic, involving the lifetime efforts of famous economists like Thomas Malthus and David Ricardo.

In the later half of the 19th century, Karl Marx attempted to develop a complete sociological theory based on the notion of intrinsic economic value. In this theory, the value of a good was proportional to the effort it took to produce this good, and thus labor could be made to play the predominant role in the measurement of economic wealth, by simply having capital and land administered by the state. Marxist theory had the great advantage that inequality of wealth could be avoided altogether. Moreover, Marx had deep insights about the nature of knowledge, social justice and history. However, there were some severe drawbacks in his theory from an economic perspective. Already in Adam Smith's Wealth of Nations, published in 1776, the famous example of improving the output in a pin-factory, even while keeping the factors of production constant, by employing division of labor was analyzed thoroughly. Thus efficient utilization of the factors of production and technological improvements proved to be two issues that had continued to be important considerations for producing economic wealth since Adam Smith, even though it was not always clear how to measure them. The emphasis on efficiency provided a role for the entrepreneur who supervised the distribution of resources, with the goal of optimizing production, keeping his own self-interest in mind.

Now, labor was compensated regularly by wages and salaries, whereas the capitalist-entrepreneur had to wait for the duration of the production cycle, which could be as long as a year, in the case of internationally traded goods or cash crops. Moreover, Marxist theory of intrinsic value worked well for goods which are basic necessities, but not so well for luxury goods. For one thing, the inherent unpredictability of human gratification meant that scarcity and abundance could not be ignored in valuing a good. Thus marginal utility came to play an important role in ascertaining economic value, as demonstrated by the oft-quoted diamond-water paradox. This meant that there was great uncertainty about the compensation that should accrue to the capitalist-entrepreneur at the end of the production cycle, even if one ignored the fact that the capitalist-entrepreneur waits for his/her compensation unlike the laborer. The cause of the uncertainty was that the market would determine the value of the produced good according to the supply and the demand prevailing at that later time, not according to an intrinsic value of the good. Thus it came to be regarded, through the theory of marginal utility, that the risk that the capitalist-entrepreneur was assuming in his/her business venture accounted for the compensation that was due for his/her capital.



[The rest of this article would be made available next week, upon request]



PS: In the interest of full disclosure, perhaps I should state here that I hold a software job in the mid-West with an annual salary of $40,000. In defending the role of Wall Street in this article, I do not obtain any monetary benefit whatsoever.