CURRENT FINANCIAL MELTDOWN: PIGOU JEVONS “SUNSPOT EQUILIBRIA” AND EXTRINSIC RANDOM VARIABLES AND UNCERTAINTY

August 1, 2010 at 4:07 pm | Posted in Books, Economics, Financial, Philosophy, Research | Leave a comment

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Sunspots (economics)

Sunspot Equilibria

“The current financial meltdown is largely

financial and partly sunspot driven.“

In a sunspot equilibrium (SE), the allocation of resources depends on some purely extrinsic random variable – a random variable that has no effect on the fundamentals. The SE concept provides a basis for rational-expectations (RE) models of excess market volatility. The best way to analyze bank runs and related financial fragilities is as a sunspot equilibrium outcome. The current financial meltdown is largely financial and partly sunspot driven.

In economics, the term sunspots (or sometimes “a sunspot”) usually refers to an extrinsic random variable, that is, a random variable that does not directly affect economic fundamentals (such as endowments, preferences, or technology). Sunspots can also refer to the related concept of extrinsic uncertainty, that is, economic uncertainty that does not come from variation in economic fundamentals. David Cass and Karl Shell also coined the term sunspots as a suggestive and less technical way of saying “extrinsic random variable”. [1]

Use

The idea that arbitrary changes in expectations might influence the economy, even if they bear no relation to fundamentals, is controversial but has been widespread in many areas of economics. For example, in the words of Arthur C. Pigou,

The varying expectations of business men… and nothing else, constitute the immediate cause and direct causes or antecedents of industrial fluctuations.[2]

‘Sunspots’ have been included in economic models as a way of capturing these ‘extrinsic’ fluctuations, in fields like asset pricing, financial crises,[3],[4] business cycles, economic growth,[5] and monetary policy.[6] Experimental economics researchers have demonstrated how sunspots could affect economic activity.[7]

The name is a whimsical reference to 19th-century economist William Stanley Jevons, who attempted to correlate business cycle patterns with sunspot counts (on the actual sun) on the grounds that they might cause variations in weather and thus agricultural output.[8] Subsequent studies have found no evidence for the hypothesis that the sun influences the business cycle.

Sunspot equilibrium

In economics, a sunspot equilibrium is an economic equilibrium where the market outcome or allocation of resources varies in a way unrelated to economic fundamentals. In other words, the outcome depends on an “extrinsic” random variable, meaning a random influence that matters only because people think it matters. The sunspot equilibrium concept was defined by David Cass and Karl Shell.

Origin of terminology

While Cass and Shell’s 1983 paper [1] defined the term sunspot in the context of general equilibrium, their use of the term sunspot (a term originally used in astronomy) alludes to the earlier econometric work of William Stanley Jevons, who explored the correlation between the degree of sunspot activity and the price of corn [9]. In Jevons’ work, uncertainty about sunspots could be considered intrinsic, for example, if sunspots have some demonstrable effect on agricultural productivity, or some other relevant variable. In modern economics, the term does not indicate any relationship with solar phenomena, and is instead used to describe random variables that have no impact on the preferences, allocations, or production technology of a general equilibrium model. The modern theory suggests that such a nonfundamental variable might have an effect on equilibrium outcomes if it influences expectations[1].

Cass and Shell refer to Keynes‘ “animal spirits”, and to the notion of self-fulfilling prophecy to illuminate their use of the term “extrinsic uncertainty”. Formally however they define it as any variable that does not directly affect the fundamentals of the economy.

Occurrence of equilibria

Much work on sunspot equilibria aims to prove the possible existence of equilibria differing from a given model’s competitive equilibria, which can result from various types of extrinsic uncertainty. [1] The sunspot equilibrium framework supplies a basis for rational expectations modeling of excess volatility (volatility resulting from sources other than randomness in the economic fundamentals). Proper sunspot equilibria can exist in a number of economic situations, including asymmetric information, externalities in consumption or production, imperfect competition, incomplete markets, and restrictions on market participation.

References

1. a b c d Cass, David; Shell, Karl (1983). “Do Sunspots Matter?”. Journalof Political Economy 91 (21): 193–228.

2. Pigou, Arthur C., (1927). Industrial fluctuations. Macmillan, London. Cited in Hans O. Melberg (1998), ‘Psychology and economic fluctuations – Pigou, Mill, and Keynes.’

3. Obstfeld, Maurice, (1996). “Models of currency crises with self-fulfilling features”, European Economic Review 40, pp. 1037-47.

4. Diamond, Douglas, and Philip Dybvig, (1983). “Bank runs, deposit insurance, and liquidity”, Journal of Political Economy 91, pp. 401-19.

5. Matsuyama, Kiminori (1991). “Increasing returns, industrialization, and indeterminacy of equilibrium”, Quarterly Journal of Economics 106, pp. 617-50.

6. Benhabib, Jess; Stephanie Schmitt-Grohe; and Martin Uribe (2001). “The perils of Taylor rules”, Journal of Economic Theory 96, pp. 40-69.

7. Duffy, John and Eric O’N. Fisher (2005). “Sunspots in the laboratory”, American Economic Review 95, 510-529.

8. Jevons, William Stanley (Nov. 14, 1878). “Commercial crises and sun-spots”, Nature xix, pp. 33-37.

9. Jevons, WS (1875). Influence of the Sun-Spot Period on the Price of Corn.

Karl Shell on sunspot equilibrium

“The current financial meltdown is largely financial and partly sunspot driven.“

In a sunspot equilibrium (SE), the allocation of resources depends on some purely extrinsic random variable – a random variable that has no effect on the fundamentals. The SE concept provides a basis for rational-expectations (RE) models of excess market volatility. The best way to analyze bank runs and related financial fragilities is as a sunspot equilibrium outcome. The current financial meltdown is largely financial and partly sunspot driven.

Sunspots can improve resource allocation in non-convex economies.

Any one of the following departures from the basic Walrasian model allows there to be proper SE:

· The “double infinity” of consumers and dated commodities (as naturally arises in OG models). See Shell JPE (1971), Shell (1977) and Cass and Shell (1989).

· Restrictions on market participation (as naturally arise in OG models). See Shell (1977) and Cass and Shell (1983).

· Incomplete markets (as naturally arise in OG models and elsewhere). See Shell (1977) and the work of David Cass and others.

· Asymmetric information. See Peck and Shell (1985, 1991) and Aumann, Peck and Shell (1988).

· Imperfect competition (as modeled, e.g. by market games). See Peck and Shell (1985, 1991).

· Consumption or production externalities, as introduced by Steve Spear and successfully explored in applied work on economic fluctuations by Jess Benhabib, Roger Farmer, Stephanie Schmitt-Grohé, Yi Wen and others.

· Nonconvexities in consumption or production. See Shell and Wright (1993) Goenka and Shell (1997), and Garratt, Keister, Qin, and Shell (JET, 2002).

· Monetary indeterminacy. See Bhattacharya, Guzman and Shell (1998) for a very simple model that elucidates “the fundamental source of sunspot equilibria”.

· Search. See, e.g. Rocheteau, Rupert, Shell, and Wright (2008)

· “Monnaie et allocation intertemporelle” [title and abstract in French, text in English] mimeo., Séminaire Roy-Malinvaud, Centre National de la Recherche Scientifique, Paris, November 21, 1977. Translation to be published in Macroeconomic Dynamics as a Vintage Unpublished Paper.

· “Les tâches solaires ont-elles de l’importance?” (with David Cass), Cahiers du séminaire d’économétrie, 24, 1982, 93-127. This is slightly more general than the JPE version.

· “Do Sunspots Matter?” (with David Cass), Journal of Political Economy, Vol. 91(2), April 1983, 193-227. Reprinted in General Equilibrium Theory (G. Debreu, ed.), The International Library of Critical Writings in Economics 67, London: Edgar Elgar Publishing, 1996, Vol. I, Chapter 17, 295-329.

· “Market Uncertainty: Sunspot Equilibria in Imperfectly Competitive Economies” (with James Peck), Working Paper 85-21, Center for Analytic Research in Economics and the Social Sciences, University of Pennsylvania, Philadelphia, July 1985. This is more complete than the RES version.

· “Sunspot Equilibrium” in The New Palgrave: A Dictionary of Economics (J. Eatwell, M. Milgate, and P. Newman, eds.), Vol. 4, New York: Macmillan, 1987, 549-551. Reprinted in The New Palgrave: General Equilibrium (J. Eatwell, M. Milgate, and P. Newman, eds.), New York: Macmillan, 1989, 274-280.

· “Asymmetric Information and Sunspot Equilibria: A Family of Simple Examples” (with Robert J. Aumann and James Peck), Working Paper 88-34, Center for Analytic Economics, Cornell University, Ithaca, October 1988.

· “Sunspot Equilibrium in an Overlapping-Generations Economy with an Idealized Contingent-Commodities Market” (with David Cass), Part 1, Chapter 1 in Economic Complexity: Chaos, Sunspots, Bubbles, and Nonlinearity (W. Barnett, J. Geweke, and K. Shell, eds.), New York: Cambridge University Press, 1989, 3-20.

· “On the Nonequivalence of the Arrow-Securities Game and the Contingent-Commodities Game” (with James Peck), Part 1, Chapter 4 in Economic Complexity: Chaos, Sunspots, Bubbles, and Nonlinearity (W. Barnett, J. Geweke, and K. Shell, eds.), New York: Cambridge University Press, 1989, 61-85.

· “Market Uncertainty: Correlated and Sunspot Equilibria in Imperfectly Competitive Economies” (with James Peck), The Review of Economic Studies, Vol. 58(5), October 1991, 1011-1029.

· “Sunspot Equilibrium” (with Bruce D. Smith), in the New Palgrave Dictionary of Money and Finance (J. Eatwell, M. Milgate, and P. Newman, eds.), Vol. 3, London: Macmillan, 1992, 601-605.

· “Indivisibilities, Lotteries, and Sunspot Equilibria” (with Randall D. Wright), Economic Theory, Vol. 3(1), January 1993, 1-17.

· “Sunspot Equilibrium” Jacob Marschak Colloquium at UCLA, November 13, 1992, abstract in Mathematical Social Sciences, Vol. 26, July 1993, 101.

· “Further Evidence of the Necessity of Sunspots” (with Rod J. Garratt), Working Paper in Economics 6-93, Department of Economics, University of California, Santa Barbara, April 1993.

· “Market Participation and Sunspot Equilibria” (with Yves Balasko and David Cass), The Review of Economic Studies, Vol. 62(3), No. 212, July 1995, 491-512. Reprinted in Equilibrium (D. Walker, ed.), Critical Ideas in Economics Volume 3, London: Edward Elgar, 2000, 591-615.

· “When Sunspots Don’t Matter” (with Aditya Goenka), Economic Theory, Vol. 9(1), January 1997, 169-178.

· “Robustness of Sunspot Equilibria” (with Aditya Goenka), Economic Theory, Vol. 10(1), July 1997, 79-98.

· “Price Level Volatility: A Simple Model of Money Taxes and Sunspots” (with Joydeep Bhattacharya and Mark Guzman), Journal of Economic Theory, Vol. 81(2), August 1998, 401-430. (doi:10.1006/jeth.1997.2362)

· “Introduction to Sunspots and Lotteries” (with Edward C. Prescott), Journal of Economic Theory, Vol. 107(1), November 2002, 1-10. (doi:10.1006/jeth.2002.2946)

· “Equilibrium Prices when the Sunspot Variable is Continuous” (with Rod Garratt, Todd Keister, and Cheng-Zon Qin), Journal of Economic Theory, Vol. 107(1), November 2002, 11-38. (doi:10.1006/jeth.1999.2634)

· “Equilibrium Bank Runs” (with James Peck), Journal of Political Economy, Vol. 111(1), February 2003, 103-123.

· “Comparing Sunspot Equilibrium and Lottery Equilibrium Allocations: The Finite Case” (with Rod Garratt and Todd Keister), International Economic Review, Vol. 45(2), May 2004, 351-386. (doi: 10.1111/j.1468-2354.2004.00129.x)

· “General Equilibrium with Nonconvexities and Money” (with Guillaume Rocheteau, Peter Rupert, and Randall Wright), Journal of Economic Theory, Vol. 142(1), September 2008, 294-317.

· “Sunspot Equilibrium”, The New Palgrave: A Dictionary of Economics, 2nd Edition (L. Blume and S. Durlauf, eds.), New York: Palgrave Macmillan, 2008. The New Palgrave Dictionary of Economics Online. 03 June 2009, http://www.dictionaryofeconomics.com/article?id=pde2008_S000325 doi:10.1057/9780230226203.1648.

· “Could Making Banks Hold Only Liquid Assets Induce Bank Runs?” (with James Peck), Journal of Monetary Economics, forthcoming (Vol. 7:4, May 2010). Proofs and computations are available in the Web Supplement.

“The current financial meltdown is largely financial and partly sunspot driven.“

In a sunspot equilibrium (SE), the allocation of resources depends on some purely extrinsic random variable – a random variable that has no effect on the fundamentals. The SE concept provides a basis for rational-expectations (RE) models of excess market volatility. The best way to analyze bank runs and related financial fragilities is as a sunspot equilibrium outcome. The current financial meltdown is largely financial and partly sunspot driven.

In economics, the term sunspots (or sometimes “a sunspot”) usually refers to an extrinsic random variable, that is, a random variable that does not directly affect economic fundamentals (such as endowments, preferences, or technology). Sunspots can also refer to the related concept of extrinsic uncertainty, that is, economic uncertainty that does not come from variation in economic fundamentals. David Cass and Karl Shell also coined the term sunspots as a suggestive and less technical way of saying “extrinsic random variable”.

For more:

http://www.karlshell.com/sum1.html

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