In
economics
Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services.
Economics focuses on the behaviour and intera ...
, the term sunspots (or sometimes "a sunspot") refers to an ''extrinsic''
random variable
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the po ...
, that is, a random variable that does not affect economic fundamentals (such as
endowments,
preferences
In psychology, economics and philosophy, preference is a technical term usually used in relation to choosing between alternatives. For example, someone prefers A over B if they would rather choose A than B. Preferences are central to decision theo ...
, or
technology
Technology is the application of knowledge to reach practical goals in a specifiable and reproducible way. The word ''technology'' may also mean the product of such an endeavor. The use of technology is widely prevalent in medicine, science, ...
). ''Sunspots'' can also refer to the related concept of extrinsic
uncertainty
Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable or ...
, that is, economic uncertainty that does not come from variation in economic fundamentals.
David Cass
David Cass (January 19, 1937 – April 15, 2008) 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 ...
and
Karl Shell
Karl Shell (born May 10, 1938) is an American theoretical economist, specializing in macroeconomics and monetary economics.
Shell received an A.B. in mathematics from Princeton University in 1960. He earned his Ph.D. in economics in 1965 at St ...
coined the term ''sunspots'' as a suggestive and less technical way of saying "extrinsic random variable".
[
]
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
Arthur Cecil Pigou (; 18 November 1877 – 7 March 1959) was an English economist. As a teacher and builder of the School of Economics at the University of Cambridge, he trained and influenced many Cambridge economists who went on to take chair ...
,
:The varying expectations of business men... and nothing else, constitute the immediate cause and direct causes or antecedents of industrial fluctuations.
'Sunspots' have been included in
economic models
In economics, a model is a theoretical construct representing economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified, often mathematical, framework desig ...
as a way of capturing these 'extrinsic' fluctuations, in fields like
asset pricing
In financial economics, asset pricing refers to a formal treatment and development of two main Price, pricing principles, outlined below, together with the resultant models.
There have been many models developed for different situations, but cor ...
,
financial crises
A financial crisis is any of a broad variety of situations in which some financial assets suddenly lose a large part of their nominal value. In the 19th and early 20th centuries, many financial crises were associated with banking panics, and man ...
,
business cycle
Business cycles are intervals of Economic expansion, expansion followed by recession in economic activity. These changes have implications for the welfare of the broad population as well as for private institutions. Typically business cycles are ...
s,
economic growth
Economic growth can be defined as the increase or improvement in the inflation-adjusted market value of the goods and services produced by an economy in a financial year. Statisticians conventionally measure such growth as the percent rate of ...
, and
monetary policy
Monetary policy is the policy adopted by the monetary authority of a nation to control either the interest rate payable for very short-term borrowing (borrowing by banks from each other to meet their short-term needs) or the money supply, often a ...
.
Experimental economics
Experimental economics is the application of experimental methods to study economic questions. Data collected in experiments are used to estimate effect size, test the validity of economic theories, and illuminate market mechanisms. Economic expe ...
researchers have demonstrated how sunspots could affect economic activity.
The name is a whimsical reference to 19th-century economist
William Stanley Jevons
William Stanley Jevons (; 1 September 183513 August 1882) was an English economist and logician.
Irving Fisher described Jevons's book ''A General Mathematical Theory of Political Economy'' (1862) as the start of the mathematical method in ec ...
, who attempted to correlate business cycle patterns with
sunspot
Sunspots are phenomena on the Sun's photosphere that appear as temporary spots that are darker than the surrounding areas. They are regions of reduced surface temperature caused by concentrations of magnetic flux that inhibit convection. Sun ...
counts (on the actual
sun
The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
) on the grounds that they might cause variations in weather and thus agricultural output. 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.
Sunspot equilibrium
In economics, a sunspot equilibrium is an
economic equilibrium
In economics, economic equilibrium is a situation in which economic forces such as supply and demand are balanced and in the absence of external influences the ( equilibrium) values of economic variables will not change. For example, in the st ...
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
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the po ...
, meaning a random influence that matters only because people think it matters. The sunspot equilibrium concept was defined by
David Cass
David Cass (January 19, 1937 – April 15, 2008) 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 ...
and
Karl Shell
Karl Shell (born May 10, 1938) is an American theoretical economist, specializing in macroeconomics and monetary economics.
Shell received an A.B. in mathematics from Princeton University in 1960. He earned his Ph.D. in economics in 1965 at St ...
.
Origin of terminology
While Cass and Shell's 1983 paper
defined the term sunspot in the context of
general equilibrium
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 ov ...
, their use of the term sunspot (a term originally used in
astronomy
Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
) alludes to the earlier
econometric
Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics," '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. 8 ...
work of
William Stanley Jevons
William Stanley Jevons (; 1 September 183513 August 1882) was an English economist and logician.
Irving Fisher described Jevons's book ''A General Mathematical Theory of Political Economy'' (1862) as the start of the mathematical method in ec ...
, who explored the correlation between the degree of sunspot activity and the price of corn. 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
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 ov ...
model. The modern theory suggests that such a nonfundamental variable might have an effect on equilibrium outcomes if it influences
expectations.
The possibility of sunspot equilibria is associated with the existence of multiple equilibria in general equilibrium models. The initial formation by Cass and Shell
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.
The sunspot equilibrium framework supplies a basis for
rational expectations
In economics, "rational expectations" are model-consistent expectations, in that agents inside the model
A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16 ...
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
In contract theory and economics, information asymmetry deals with the study of decisions in transactions where one party has more or better information than the other.
Information asymmetry creates an imbalance of power in transactions, which can ...
,
externalities
In economics, an externality or external cost is an indirect cost or benefit to an uninvolved third party that arises as an effect of another party's (or parties') activity. Externalities can be considered as unpriced goods involved in either co ...
in
consumption
Consumption may refer to:
*Resource consumption
*Tuberculosis, an infectious disease, historically
* Consumption (ecology), receipt of energy by consuming other organisms
* Consumption (economics), the purchasing of newly produced goods for curren ...
or
production
Production may refer to:
Economics and business
* Production (economics)
* Production, the act of manufacturing goods
* Production, in the outline of industrial organization, the act of making products (goods and services)
* Production as a stati ...
,
imperfect competition In economics, imperfect competition refers to a situation where the characteristics of an economic market do not fulfil all the necessary conditions of a perfectly competitive market. Imperfect competition will cause market inefficiency when it hap ...
, 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
There are two fundamental theorems of welfare economics. The first states that in economic equilibrium, a set of complete markets, with complete information, and in perfect competition, will be Pareto optimal (in the sense that no further exchange ...
). Although the model was simple, the assumption of limited participation extends to all dynamic models based on the
overlapping generations model
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 ...
.
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
Robert King Merton (born Meyer Robert Schkolnick; July 4, 1910 – February 23, 2003) was an American sociologist who is considered a founding father of modern sociology, and a major contributor to the subfield of criminology. He served as th ...
, 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
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 Ange ...
and
Michael Woodford to a class of autoregressive models and forms the basis for the Indeterminacy School in Macroeconomics.
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. 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
Jess Benhabib (born 9 June 1948) is a professor at New York University, and known for his contributions to growth theory and sunspot equilibria.
Benhabib earned his Ph.D. from Columbia University in 1976. He started his teaching career as an ass ...
and Farmer
and Farmer and Guo showed that representative agent models with increasing returns to scale in production also lead to business cycle models driven by self-fulfilling prophecies.
See also
*
Irrational exuberance
"Irrational exuberance" is the phrase used by the then-Federal Reserve Board chairman, Alan Greenspan, in a speech given at the American Enterprise Institute during the dot-com bubble of the 1990s. The phrase was interpreted as a warning that the ...
*
Stock market bubble
A stock market bubble is a type of economic bubble taking place in stock markets when market participants drive stock prices above their value in relation to some system of stock valuation.
Behavioral finance theory attributes stock market bub ...
*
Tulip mania
Tulip mania ( nl, tulpenmanie) was a period during the Dutch Golden Age when contract prices for some bulbs of the recently introduced and fashionable tulip reached extraordinarily high levels. The major acceleration started in 1634 and then ...
References
{{Reflist, 30em
Economic methodology
Randomness