Sunspots (economics)

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In economics, the term sunspots (or sometimes "a sunspot") refers to an extrinsic random variable, that is, a random variable that does not 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 coined the term sunspots as a suggestive and less technical way of saying "extrinsic random variable". [1]

Contents

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. On the other hand, sunny weather has a small but significant positive impact on stock returns, probably due to its impact on traders' moods. [9]

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. [10] 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]

The possibility of sunspot equilibria is associated with the existence of multiple equilibria in general equilibrium models. The initial formation by Cass and Shell [1] was constructed in the context of a two period model in which a group of people trade financial contacts in period 1 that depends on the realization of a random variable in period 2. They showed that, if some people are unable to participate in the financial market in period 1, the resulting equilibrium in period 2 can depend on the realization of a random variable that is completely unrelated to economic fundamentals. They call the random variable a sunspot and the resulting allocation is a 'sunspot equilibrium’.

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.

Sunspots and the Indeterminacy School in Macroeconomics

The Cass Shell example relies on the fact that general equilibrium models often possess multiple equilibria. Cass and Shell construct an example with three equilibria in period 2 and they showed that, if a subset of people cannot trade financial securities in period 1, there exist additional equilibria which are constructed as randomizations across the multiple equilibria of the original model. If, in contrast, everyone is present in period 1, these randomizations are not possible as a consequence of the first welfare theorem of economics (Fundamental theorems of welfare economics). Although the model was simple, the assumption of limited participation extends to all dynamic models based on the overlapping generations model. [11] [12]

Sunspot equilibria are important because they introduce the possibility that extraneous uncertainty may cause business cycles. The first paper to exploit this idea is due to Azariadis who introduced the term "self-fulfilling prophecy," a term he borrowed from Robert K. Merton, [13] to refer to a complete dynamic model in which economic fluctuations arise simply because people believe that they will occur. The idea was extended by Roger Farmer and Michael Woodford to a class of autoregressive models [14] [15] and forms the basis for the Indeterminacy School in Macroeconomics. [16] [17] [18]

Sunspot equilibria are closely connected to the possibility of indeterminacy in dynamic economic models. In a general equilibrium model with a finite number of commodities, there is always a finite odd number of equilibria, each of which is isolated from every other equilibrium. In models with an infinite number of commodities, and this includes most dynamic models, an equilibrium can be characterized by a bounded sequence of price vectors. [19] When the set of traders changes over time, as it must in any model with birth and death, there are typically open sets of indeterminate equilibria where, arbitrarily close to one equilibrium, there is another one. Although the initial work in the area was in the context of the overlapping generations model, Jess Benhabib and Farmer [20] and Farmer and Guo [21] showed that representative agent models with increasing returns to scale in production also lead to business cycle models driven by self-fulfilling prophecies. [20] [22]

See also

Related Research Articles

In economics, general equilibrium theory attempts to explain the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that the interaction of demand and supply will result in an overall general equilibrium. General equilibrium theory contrasts to the theory of partial equilibrium, which analyzes a specific part of an economy while its other factors are held constant. In general equilibrium, constant influences are considered to be noneconomic, therefore, resulting beyond the natural scope of economic analysis. The noneconomic influences is possible to be non-constant when the economic variables change, and the prediction accuracy may depend on the independence of the economic factors.

<span class="mw-page-title-main">IS–LM model</span> Macroeconomic model relating interest rates and asset market

IS–LM model, or Hicks–Hansen model, is a two-dimensional macroeconomic tool that shows the relationship between interest rates and assets market. The intersection of the "investment–saving" (IS) and "liquidity preference–money supply" (LM) curves models "general equilibrium" where supposed simultaneous equilibria occur in both the goods and the asset markets. Yet two equivalent interpretations are possible: first, the IS–LM model explains changes in national income when the price level is fixed in the short-run; second, the IS–LM model shows why an aggregate demand curve can shift. Hence, this tool is sometimes used not only to analyse economic fluctuations but also to suggest potential levels for appropriate stabilisation policies.

<span class="mw-page-title-main">Macroeconomic model</span> Model used in Macroeconomics

A macroeconomic model is an analytical tool designed to describe the operation of the problems of economy of a country or a region. These models are usually designed to examine the comparative statics and dynamics of aggregate quantities such as the total amount of goods and services produced, total income earned, the level of employment of productive resources, and the level of prices.

<span class="mw-page-title-main">Overlapping generations model</span>

The overlapping generations (OLG) model is one of the dominating frameworks of analysis in the study of macroeconomic dynamics and economic growth. In contrast, to the Ramsey–Cass–Koopmans neoclassical growth model in which individuals are infinitely-lived, in the OLG model individuals live a finite length of time, long enough to overlap with at least one period of another agent's life.

Constantine Christos "Costas" Azariadis is a macroeconomist born in Athens, Greece. He has worked on numerous topics, such as labor markets, business cycles, and economic growth and development. Azariadis originated and developed implicit contract theory.

Karl Shell is an American theoretical economist, specializing in macroeconomics and monetary economics.

<span class="mw-page-title-main">David Cass</span> American economist

David Cass was a professor of economics at the University of Pennsylvania, mostly known for his contributions to general equilibrium theory. His most famous work was on the Ramsey–Cass–Koopmans model of economic growth.

Dynamic stochastic general equilibrium modeling is a macroeconomic method which is often employed by monetary and fiscal authorities for policy analysis, explaining historical time-series data, as well as future forecasting purposes. DSGE econometric modelling applies general equilibrium theory and microeconomic principles in a tractable manner to postulate economic phenomena, such as economic growth and business cycles, as well as policy effects and market shocks.

In economics and game theory, global games are games of incomplete information where players receive possibly-correlated signals of the underlying state of the world. Global games were originally defined by Carlsson and van Damme (1993).

Michael Dean Woodford is an American macroeconomist and monetary theorist who currently teaches at Columbia University.

<span class="mw-page-title-main">New classical macroeconomics</span> School of thought in macroeconomics

New classical macroeconomics, sometimes simply called new classical economics, is a school of thought in macroeconomics that builds its analysis entirely on a neoclassical framework. Specifically, it emphasizes the importance of rigorous foundations based on microeconomics, especially rational expectations.

The Cass criterion, also known as the Malinvaud–Cass criterion, is a central result in theory of overlapping generations models in economics. It is named after David Cass.

In game theory a Poisson game is a game with a random number of players, where the distribution of the number of players follows a Poisson random process. An extension of games of imperfect information, Poisson games have mostly seen application to models of voting.

Christian Hellwig is a German economic theorist and macroeconomist who did research in the field of global games. He is the editor of the Journal of Economic Theory.

In economics, coordination failure is a concept that can explain recessions through the failure of firms and other price setters to coordinate. In an economic system with multiple equilibria, coordination failure occurs when a group of firms could achieve a more desirable equilibrium but fail to because they do not coordinate their decision making. Coordination failure can result in a self-fulfilling prophecy. For example, if one firm decides a recession is imminent and fires its workers, other firms might lose demand from the lay-offs and respond by firing their own workers leading to a recession at a new equilibrium. Coordination failure can also be associated with sunspot equilibria and animal spirits.

<span class="mw-page-title-main">Real business-cycle theory</span> Macroeconomic model

Real business-cycle theory is a class of new classical macroeconomics models in which business-cycle fluctuations are accounted for by real shocks. Unlike other leading theories of the business cycle, RBC theory sees business cycle fluctuations as the efficient response to exogenous changes in the real economic environment. That is, the level of national output necessarily maximizes expected utility, and governments should therefore concentrate on long-run structural policy changes and not intervene through discretionary fiscal or monetary policy designed to actively smooth out economic short-term fluctuations.

Self-fulfilling crisis refers to a situation that a financial crisis is not directly caused by the unhealthy economic fundamental conditions or improper government policies, but a consequence of pessimistic expectations of investors. In other words, investors' fear of the crisis makes the crisis inevitable, which justified their initial expectations.

Jess Benhabib is a professor at New York University, and known for his contributions to growth theory and sunspot equilibria.

Roger Edward Alfred Farmer is a British/American economist. He is currently a Professor at the University of Warwick and is a Distinguished Emeritus Professor and former Chair of the Economics department at the University of California, Los Angeles. He has also held positions at the University of Pennsylvania, the European University Institute and the University of Toronto. He is a Fellow of the Econometric Society, Research Associate of the National Bureau of Economic Research, and Research Fellow of the Centre for Economic Policy Research, and the former Research Director of the National Institute of Economic and Social Research (NIESR). In 2013, he was the Senior Houblon-Norman Fellow at the Bank of England. He is internationally recognized for his work on self-fulfilling prophecies. Farmer has published several scholarly articles in leading academic journals. He is also a co-founder of the Indeterminacy School in Macroeconomics. His body of work has advanced the view that beliefs are a new fundamental in economics that have the same methodological status as preferences, technology, and endowments. In his 1993 book, Macroeconomics of Self-fulfilling Prophecies, he argues that beliefs should be modeled with the introduction of a Belief Function, which explains how people form ideas about the future based on things they have seen in the past. In his 2010 book, Expectations, Employment and Prices, he suggests an alternative paradigm to New Keynesian economics which reintroduces a central idea from John Maynard Keynes' The General Theory of Employment, Interest and Money; that high involuntary unemployment can persist as a permanent equilibrium outcome. He provided an accessible introduction to these ideas in his 2010 book How the Economy Works, and more recently, in his 2016 book Prosperity for All, both of which were written for a general audience. The Farmer Monetary Model has different and high policy implications and relevance. Farmer's policy proposal to achieve full employment by controlling and stabilizing asset prices shows promise as a way to help prevent stock market crashes and deep recessions. His son is the economist Leland Edward Farmer, who joined the faculty at the University of Virginia in July 2017.

Stephanie Schmitt-Grohé is a German economist who currently works as a professor of economics at Columbia University. Schmitt-Grohé's research has been focused on macroeconomics as well as fiscal and monetary policy in open and closed economies. In 2004 she was awarded the Bernacer prize, for her research of monetary stabilization policies.

References

  1. 1 2 3 4 5 Cass, David; Shell, Karl (1983). "Do Sunspots Matter?". Journal of Political Economy. 91 (21): 193–228. doi:10.1086/261139. S2CID   1981980.
  2. ↑ Pigou, Arthur C. (1927). Industrial fluctuations. London: Macmillan. ISBN   9780816104222. OCLC   1827301. Cited in Melberg, Hans O. (1998). "Psychology and economic fluctuations - Pigou, Mill, and Keynes". Archived from the original on October 27, 2009.
  3. ↑ Obstfeld, Maurice (1996). "Models of currency crises with self-fulfilling features" (PDF). European Economic Review . 40 (3–5): 1037–47. doi:10.1016/0014-2921(95)00111-5. S2CID   14506793.
  4. ↑ Diamond, Douglas; Dybvig, Philip (1983). "Bank runs, deposit insurance, and liquidity" (PDF). Journal of Political Economy . 91 (3): 401–19. doi:10.1086/261155. S2CID   14214187.
  5. ↑ Matsuyama, Kiminori (1991). "Increasing returns, industrialization, and indeterminacy of equilibrium" (PDF). Quarterly Journal of Economics . 106 (2): 617–50. doi:10.2307/2937949. JSTOR   2937949.
  6. ↑ Benhabib, Jess; Schmitt-Grohe, Stephanie; Uribe, Martin (2001). "The perils of Taylor rules". Journal of Economic Theory . 96 (1–2): 40–69. doi:10.1006/jeth.1999.2585.
  7. ↑ Duffy, John; Fisher, Eric O'N. (2005). "Sunspots in the laboratory". American Economic Review . 95 (3): 510–529. doi:10.1257/0002828054201350.
  8. ↑ Jevons, William Stanley (Nov. 14, 1878). “Commercial crises and sun-spots”, Nature xix, pp. 33-37.
  9. ↑ Hirshleifer, David; Shumway, Tyler (2003). "Good day sunshine: stock returns and the weather". Journal of Finance . 58 (3): 1009–1032. doi:10.1111/1540-6261.00556.
  10. ↑ Jevons, WS (1875). "Influence of the Sun-Spot Period on the Price of Corn".{{cite journal}}: Cite journal requires |journal= (help)
  11. ↑ Samuel, Paul (1958). "An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money". The Journal of Political Economy. 66 (6): 467–482. doi:10.1086/258100. S2CID   153586213.
  12. ↑ Maurice, Allais (1947). Économie & intérêt: présentation nouvelle des problèmes fondamentaux relatifs au rôle économique du taux de l'intérêt et de leurs solutions. Imprimerie Nationale.
  13. ↑ Merton, Robert K. (1948). "The Self-Fulfilling Prophecy". The Antioch Review. 8 (2): 193–210. doi:10.2307/4609267. JSTOR   4609267.
  14. ↑ Farmer, Roger E. A.; Woodford, Michael (1984). "Self-fulfilling prophecies and the business cycle". University of Pennsylvania CARESS Working Paper 84-12.
  15. ↑ Farmer, Roger E. A.; Woodford, Michael (1997). "Self-fulfilling prophecies and the business cycle". Macroeconomic Dynamics. 1 (4): 740–769. doi:10.1017/S1365100597005051. S2CID   16915270.
  16. ↑ Cherrier, Beatrice; Saïdi, Aurélien (2018). "The Indeterminate Fate of Sunspots in Economics". History of Political Economy. 50 (3): 425–481. doi:10.1215/00182702-7023434.
  17. ↑ Farmer, Roger E. A. (2020). "The Indeterminacy School of Macroeconomics". Oxford Research Encyclopaedia of Economics and Finance. doi:10.1093/acrefore/9780190625979.013.511. ISBN   978-0-19-062597-9.
  18. ↑ Farmer, Roger E. A. (2014). "The Evolution of Endogenous Business Cycles" (PDF). Macroeconomic Dynamics. 20 (2): 544–557. doi:10.1017/S1365100514000248. S2CID   17748854.
  19. ↑ Kehoe, Timothy J.; Levine, David K. (1985). "Comparative Statics and Perfect Foresight in Infinite Horizon Economies". Econometrica. 53 (2): 433–453. doi:10.2307/1911244. hdl: 1721.1/63398 . JSTOR   1911244.
  20. 1 2 Benhabib, Jess; Farmer, Roger E. A. (1994). "Indeterminacy and increasing returns" (PDF). Journal of Economic Theory. 63: 19–41. doi:10.1006/jeth.1994.1031.
  21. ↑ Farmer, Roger E. A.; Jang-Ting, Guo (1994). "Real business cycles and the animal spirits hypothesis" (PDF). Journal of Economic Theory. 63 (1): 42–72. doi:10.1006/jeth.1994.1032.
  22. ↑ Farmer, Roger E. A. (1999). Macroeconomics of Self-fulfilling Prophecies. MIT Press; second edition. ISBN   978-0262062039.
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