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November 28, 2009

Economist's View - 3 new articles

"Catastrophe Theory and the Business Cycle"

As a follow up to the recent post on non-linear dynamics that continued the discussion on what's wrong with modern macroeconomics, here is a paper written many years ago by Hal Varian that extends the Goodwin-Kaldor model of business cycles. It is old-fashioned macro, but the interesting part is the wealth effect causing the difference between recessions and depressions. In particular, the results of the paper imply that shocks to wealth that change savings propensities -- as we are seeing now -- can cause recoveries that "may take a very long time, and differ quite substantially from the recovery pattern of a [typical] recession."

Here are a few selections from the paper:

Catastrophe Theory and the Business Cycle, by Hal Varian: In this paper we examine a variation on Kaldor's (1940) model of the business cycle using some of the methods of catastrophe theory. (Thom (1975), Zeeman (1977)). The development proceeds in several stages. Section I provides a brief outline of catastrophe theory, while Section II applies some of these techniques to a simple macroeconomic model. This model yields, as a special case, Kaldor's business cycles. ... In Section III, we describe a generalization of Kaldor's model that allows not only for cyclical recessions, but also allows for long term depressions. Section IV presents a brief review and summary.

This paper is frankly speculative. It presents, in my opinion, some interesting models concerning important macroeconomic phenomena. However, the hypotheses of the models are neither derived from microeconomic models of maximizing behavior, nor are they subjected to serious empirical testing. The hypotheses are not without economic plausibility, but they are far from being established truths. Hence, this paper can only be said to present some interesting stories of macroeconomic instability. Whether these stories have any empirical basis is an important, and much more difficult, question. ...

Applied catastrophe theory is not without its detractors (Sussman and Zahler (1978)). Some of the applied work in catastrophe theory has been criticized for being ad hoc, unscientific, and oversimplified. As with any new approach to established subjects, catastrophe theory has been to some extent oversold. In some cases, applications of the techniques may have been overly hasty. Nevertheless, the basic approach of the subject seems, to this author at least, potentially fruitful. Catastrophe theory may provide some descriptive models and some hypotheses which, when coupled with serious empirical work, may help to explain real phenomena. ...

[I]t makes sense to model the system as if the state variables adjust immediately to some "short run" equilibrium, and then the parameters adjust in some "long run" manner. In the parlance of catastrophe theory, the state variables are referred to as "fast" variables, and the "parameters" are referred to as "slow" variables. This distinction is, of course, common in economic modeling. For example, when we model short run macroeconomic processes we take certain variables, such as the capital stock, as fixed at some predetermined level. Then when we wish to examine long run macroeconomic growth processes, we imagine that economy instantaneously adjusts to a short run equilibrium, and focus exclusively on the long run adjustment process.

Catastrophe theory is concerned with the interactions between the short run equilibria and the long term dynamic process. To be more explicit, catastrophe theory studies the movements of short run equilibria as the long run variables evolve. A particularly interesting kind of movement is when a short run equilibrium jumps from one region of the state space to another. Such jumps are known as catastrophes. Under certain assumptions catastrophes can be classified into a small number of distinct qualitative types. ... In the economic model that follows we will only utilize the two simplest catastrophes, the fold and the cusp. In these low dimensional cases, there are no restrictions on the nature of dynamical systems involved. ...

[One result from the macroeconomic model] is the case considered by Kaldor (1940) and, more rigorously, by Chang and Smyth (1972). It has been shown by Chang and Smyth that when the speed of adjustment parameter is large enough, and certain technical conditions are met, there must exist a limit cycle in the phase space. In the appendix I prove a slightly simplified and modified version of this result.

This "business cycle" proposition is clearly the result intuited by Kaldor thirty years ago. However, the existence of a regular, periodic business cycle causes certain theoretical and empirical difficulties. Recent theoretical work involving rational expectations (Lucas (1975)) and empirical work on business cycles (McCullough (1975), (1977), Savin (1977)) have argued that (1) regular cycles seem to be incompatible with rational economic behavior, and (2) there is little statistically significant evidence for a business cycle anyway.

However, there does seem to be some evidence for a kind of "cyclic behavior" in the economy. It is commonplace to hear descriptions of how exogenous shocks may send the economy spiraling into a recession, from which it sooner or later recovers. Leijonhufvud (1973) has suggested that economies operate as if there is a kind of "corridor of stability": that is, there is a local stability of equilibrium, but a global instability. Small shocks are dampened out, but large shocks may be amplified. ...

Such a story seems to me to be a reasonable description of the functioning of the commonly described "inventory recession." [L]et us, for the sake of argument, accept such a story as providing a possible explanation of the "cyclic" behavior of an economy. Then there is yet another puzzle. Each recession in this model will behave rather similarly: First some kind of shock, then a rapid fall, followed by a slow change in some stock variables with, eventually, a rapid recovery. Although this story seems to be descriptive of some recessions, it does not describe all types of fluctuations of income. Sometimes the economy experiences depressions. That is, sometimes the return from a crash is very gradual and drawn out. ...

Here is the interesting feature of the model. Suppose as before, that there is some kind of perturbation in one of the stock variables. For definiteness let us suppose [there is] some kind of shock (a stock market crash?).... If the shock is relatively small, we have much the same story as with the inventory recession... If on the other hand the shock is relatively large, wealth may decrease so much as to significantly affect the propensity to save. In this case,... national income will remain at a relatively low level rather than experience a jump return. Eventually the gradual increase in wealth due to the increased savings will move the system slowly back towards the long run equilibrium. ...

According to this story the major difference between a recession and a depression is in the effect on consumption. If a shock affects wealth so much as to change savings propensities, recovery may take a very long time, and differ quite substantially from the recovery pattern of a recession. This explanation does not seem to be in contradiction with observed behavior, but as I have mentioned earlier, it rests on unproven (but not implausible) assumptions about savings and investment behavior.

1.4 Review and summary

We have shown how nonlinearities in investment behavior can give rise to cyclic or cycle like behavior in a simple dynamic macroeconomic model.

This behavior shares some features with empirically observed behavior. If savings behavior also exhibits nonlinearities of a plausible sort, the model can allow for both rapid recoveries which characterize recessions, as well as extended recoveries typical of a depression.


"Independent Does Not Mean Unaccountable"

As you might guess given my recent posts defending Fed independence, I agree with this:

The right reform for the Fed, by Ben Bernanke, Commentary, Washington Post: For many Americans, the financial crisis, and the recession it spawned, have been devastating... Understandably, many people are calling for change. ... As a nation, our challenge is to design a system of financial oversight that will ... provide a robust framework for preventing future crises...
I am concerned ... that ... some leading proposals in the Senate would strip the Fed of all its bank regulatory powers. And a House committee recently voted to repeal a 1978 provision that was intended to protect monetary policy from short-term political influence. These measures ... would seriously impair the prospects for economic and financial stability in the United States. The Fed played a major part in arresting the crisis, and we should be seeking to preserve, not degrade, the institution's ability to foster financial stability and to promote economic recovery without inflation. ...
The proposed measures are at least in part the product of public anger over ... the rescues of some individual financial firms. The government's actions... -- as distasteful and unfair as some undoubtedly were -- were unfortunately necessary to prevent a global economic catastrophe that could have rivaled the Great Depression in length and severity...
Moreover, looking to the future, we strongly support measures -- including the development of a special bankruptcy regime for financial firms whose disorderly failure would threaten the integrity of the financial system -- to ensure that ad hoc interventions of the type we were forced to use last fall never happen again. Adopting such a resolution regime, together with tougher oversight of large, complex financial firms, would make clear that no institution is "too big to fail" -- while ensuring that the costs of failure are borne by owners, managers, creditors and the financial services industry, not by taxpayers.
The Federal Reserve ... did not do all that it could have to constrain excessive risk-taking in the financial sector in the period leading up to the crisis. We have extensively reviewed our performance and moved aggressively to fix the problems. ... There is a strong case for a continued role for the Federal Reserve in bank supervision. Because of our role in making monetary policy, the Fed brings unparalleled economic and financial expertise to its oversight of banks...
This expertise is essential for supervising highly complex financial firms and for analyzing the interactions among key firms and markets. Our supervision is also informed by the grass-roots perspective derived from the Fed's unique regional structure and our experience in supervising community banks. At the same time, our ability to make effective monetary policy and to promote financial stability depends vitally on the information, expertise and authorities we gain as bank supervisors, as demonstrated in episodes such as the 1987 stock market crash and the financial disruptions of Sept. 11, 2001, as well as by the crisis of the past two years.
Of course, the ... ability to take such actions without engendering sharp increases in inflation depends heavily on our credibility and independence from short-term political pressures. Many studies have shown that countries whose central banks make monetary policy independently of such political influence have better economic performance...
Independent does not mean unaccountable. In its making of monetary policy, the Fed is highly transparent, providing detailed minutes of policy meetings and regular testimony before Congress, among other information. Our financial statements are public and audited by an outside accounting firm; we publish our balance sheet weekly; and we provide monthly reports with extensive information on all the temporary lending facilities... Congress, through the Government Accountability Office, can and does audit all parts of our operations except for the monetary policy deliberations and actions covered by the 1978 exemption. The general repeal of that exemption would serve only to increase the perceived influence of Congress on monetary policy decisions, which would undermine the confidence the public and the markets have in the Fed to act in the long-term economic interest of the nation. ...
Now more than ever, America needs a strong, nonpolitical and independent central bank with the tools to promote financial stability and to help steer our economy to recovery without inflation.

While I agree on the independence and regulation statements, one thing I do wonder about is why there is such widespread acceptance of the idea that we have to live with institutions that are so big that their failure is a threat to the financial system and the economy. The notion seems to be that large, dangerous firms are inevitable, so we need special procedures in place that we hope will allow them to fail without the problems spreading and creating a devastating domino effect. The concern seems to be mainly about having the procedures and authority to allow orderly dissolution of large, dangerous firms rather than preventing these firms from getting too large and too interconnected to begin with.

We need procedures for orderly dissolution in any case -- we didn't think firms were systemically important before the crash, so we need to be ready (e.g., recall the many, many statements that the crisis would be "contained"). But what is the minimum efficient scale (MES) for financial firms? That is, what is the smallest size at which economies of scale and economies of scope are fully realized?

There has been some discussion of this (e.g. Economics of Contempt versus The Baseline Scenario), but it doesn't seem to me that this question is very close to being settled. I want to know how the MES relates to the minimum size where a bank becomes systemically important. If the MES is smaller than the size where banks become systemically dangerous, break them up - their size adds nothing but risk. But if the MES is greater than the minimum dangerous size, then we have a tradeoff to make -- safety for efficiency -- and we may or may not want to force firms to reduce their size and connectedness. It depends upon the tradeoff.

But until we know what these tradeoffs are -- and I don't think we have a good sense of this -- it's very difficult to determine if the costs of breaking up banks and reducing their connectedness are greater than the benefits. I suspect that if the MES is greater than the minimum safe size, then the extra safety from reducing bank size and connectedness would be worth the loss of efficiency, and I'd like to push that position much more than I have to date. But without knowing the MES, the minimum threatening size, the minimum threatening degree of connectedness, and the costs and benefits of reducing size and connectedness, it's hard to do so with confidence.


links for 2009-11-27

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