From coordination devices to coordination failures: on the changing epistemology of sunspots since the 1970s

Abstract

The widespread adoption of the rational expectations hypothesis in macroeconomic literature from the 1970s onwards has often overlooked the issue of coordinating individual decisions, particularly regarding expectations. How is common knowledge, essential for rational expectations equilibrium, established? When common knowledge supports multiple equilibria, how do expectations converge to a specific one? These pivotal questions have always been at the core of sunspot literature, which emerged at the turn of the 1980s, albeit sometimes implicitly. While unspots were initially regarded by pioneers David Cass and Karl Shell as essential coordination devices, their epistemological status evolved with the introduction of competing models in ndogenous fluctuations (chaos, bifurcations, deterministic cycles) and the transition from the overlapping generations to the infinitely lived agent framework. Ultimately identified as anticipation shocks, sunspots were portrayed as instability triggers and markers of coordination failures. However, recent advancements in sunspot theory, especially in the areas of financial crises and experimental economics, have started to rehabilitate the original interpretation of sunspots as coordination mechanisms. This article maps out the historical development, shedding light on the evolving concepts surrounding sunspots.

Keywords:

• Sunspots
• Common knowledge
• Coordination device
• Coordination failures
• Learning
• Indeterminacy

Acknowledgment

I would like to thank two anonymous referees, Beatrice Cherrier, and the organizers and participants of the 2022 Nice conference on Economics and Coordination for their helpful comments and suggestions. They significantly contributed to enrich this article. I also wish to pay tribute to the memory of my former professor Alain Goergen (†), the first to steer me towards exploring sunspots.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The expression “psychology of the market” was recurrent in the work of Cass and Shell (1983, 193), “self-perpetuating beliefs” and “fears” may be found in Azariadis (1981, 380) or Azariadis and Guesnerie (1986) (725). “Animal spirits,” directly borrowed from Keynes, appeared in Azariadis’s (1981) seminal paper and was favored by the second generation of sunspot theorists (see, for instance, Farmer 1993), in conjunction with “self-fulfilling prophecies.”

2 They considered that the rational expectations hypothesis was the most ‘reasonable’ assumption to study stationary processes: “we can think of no objection to this assumption which is not better phrased as an objection to our hypothesis that the stochastic component of demand has a regular, stationary structure,” they claimed (Lucas and Prescott 1971, footnote 9, 664). See also Lucas (1978, 1429).

3 “I had close colleagues, Thomas Sargent and Christopher Sims … I was a great admirer of their work, and found interaction with them stimulating. But I gave up my faith in strict rational expectations models more definitively than they did, or sooner. My tendency towards skepticism began to divide us a bit … Maybe I overreacted against these models, but the good result was that I began to get much more interested in other social sciences,” Shiller remembers in his Nobel Prize autobiography.

4 Shiller thought that even if such expectation formation and sharing process converged toward expectations that were rational in a sense that they were consistent with the true model of the economy, there was no reason for this set of expectations to be stable.

5 Cass and Shell had learned to operate this model at Stanford, in particular under the influence of another graduate student (and Cass’s future colleague at the Cowles Foundation), Menahem Yaari.

6 The paper was presented at the Minneapolis Fed conference organized by John Kareken and Neil Wallace in 1978. By contrast, the optimal growth model, which was the focus of Cass and Shell’s Ph.D. dissertation, guaranteed that the first welfare theorem would apply in the absence of any distortion.

7 The wording “sunspot” they took from Jevons and Granger, though the way the term was used in this work was not consistent with the definition offered by Cass and Shell (see Cherrier Saidi 2018).

8 Cass and Shell did not conclude however that the existence of extrinsic uncertainty necessarily implied coordination issues. The work of a series of younger scholars in the 1980s (James Peck, Stephen Spears, Mike Woodford) indeed confirmed Cass and Shell’s 1983 intuition that sunspot “matters” only when at least one hypothesis underlying the first welfare theorem was not satisfied.

9 Chaotic complex systems have been extensively studied in disciplines like mathematics and physics. However, their recognition in economic literature came somewhat later. For an overview of the early economic contributions on this topic, see Boldrin and Woodford (1990). Unlike cyclical patterns, chaotic solutions lack a fixed period: the economy consistently gravitates towards certain (strange) attractors but never replicates the exact same state, lending a semblance of consistency to the dynamics.

10 Grandmont (1985) delved into the periodic solutions inherent to the OLG model. Azariadis and Guesnerie (1986) posited that the second-order cycles observed in Grandmont’s findings could be interpreted as a specialized version of the stochastic sunspot equilibria previously highlighted by Azariadis in 1981. Within this framework, a second-order cycle represents a sunspot equilibrium where agents deterministically alternate states from one period to the next. Building upon this, it’s feasible to conceive stationary equilibria wherein agents have a probability less than one to shift to an alternate state, leaving a residual probability to persist in their current state. These transition probabilities are theoretically influenced by an external random event, such as the sporadic emergence of sunspots.

11 The 1989 volume gathers the proceedings from a conference hosted by the University of Texas at Austin in May 1987. Organized by William Barnett, John Geweke, and Karl Shell, the event was themed “Economic Complexity: Chaos, Sunspots, Bubbles, and Nonlinearity.” Contributions, spanning topics from deterministic chaos and bifurcations to speculative bubble phenomena, underscored a strong connection to sunspots. The term “endogenous fluctuations” as subsequently introduced by Guesnerie and Woodford (1993) effectively encapsulated and synthesized the array of preceding approaches.

12 One of his most cited papers from his early years (Andrada 2016, 215), published in 1978, was an attempt to be more specific on this out-of-equilibrium “unspecified process” in a general equilibrium asset pricing model, discussing the relation between rational expectations and Eugene Fama’s efficient market hypothesis.

13 Muth (1961, 316) rephrased the hypothesis as follows: “expectations of [agents] (or, more generally, the subjective probability distribution of outcomes) tend to be distributed, for the same information set, about the prediction of the theory (or the ‘objective’ probability distributions of outcomes).” The objective probability distributions are usually endogenous: they hinge on economic agents’ beliefs about these distributions. Thus, aligning objective distributions with subjective distributions isn’t straightforward (DeGroot 1974, Aumann 1976).

14 This gathering highlighted influential pieces by the likes of Margaret Bray, Lawrence Blume, and David Easley. A concise overview of this period can be found in Blume, Bray, and Easley (1982). Notably, the works of Taylor (1975) and Friedman (1979) stand apart as they pivot around the macroeconomic concern of monetary policy effectiveness. For those seeking a deeper dive, Sargent (1993) chronicled the early contributions.

15 Evans’s doctoral dissertation Three Essays on the Variance of Inflation, Expectations and Macroeconomic Stability was defended under Richard Sutch and James Pierce.

16 For a comprehensive definition of expectational stability and an in-depth exploration of the nuances between weak and strong stabilities, we recommend consulting Evans and Honkapohja (2001).

17 Howitt and McAffee (1992) later provided an example of a sunspot equilibrium immune to Evans’s (1989) argument and is strongly stable under Bayesian learning.

18 Bray (1982) defines her model based on five hypotheses, four of which specify the contours of the common knowledge shared by the various agents composing her economy. The common knowledge property is then used to solve the model.

19 In an interview Béatrice Cherrier and I conducted in 2013 (pers. comm. Oct. 29, 2013), Woodford made an explicit reference to Shiller’s (1978) article as a content he studied during the course Shiller taught when he was visiting MIT in 1981-1982.

20 In a dynamic framework, indeterminacy usually refers to a continuum of (deterministic) equilibrium trajectories converging asymptotically to the same long-term steady state (which is said to be indeterminate). They all satisfy the necessary first-order conditions for utility maximization. They are all compatible with the rational expectations hypothesis. In a specific state of nature, defined for instance by the capital stock level, agents can choose any of the available trajectories. They also have the flexibility to switch between these paths from one period to the next. As a result, alongside the original set of deterministic paths, there emerges a large array of stochastic trajectories driven by the agents’ shifting trajectories and expectations.

21 The method used by Farmer and Woodford (1984) or Peck (1988) consisted in starting from the two deterministic steady states (pre-existing any form of extrinsic uncertainty). While it is straightforward to construct trivial stationary sunspot equilibria by performing a mere randomization between the two steady states, Peck, Farmer and Woodford managed to obtain non-trivial stochastic equilibria from convex combinations of the two deterministic equilibria.

22 As Cass and Shell published their article in the Economic Complexity volume in 1989 (see footnote 11), the notion of sunspots as coordinating device they had promoted was already largely eclipsed, with the ideas of indeterminacy and the instability it induces gaining prominence.

23 On the issue of tractability, Farmer stated in his 1993 textbook: “Overlapping generations models have been used widely as a research tool in monetary theory, and their theoretical properties have been explored in theory journals. As vehicles for developing quantitative empirical predictions, OG models have been less successful, mainly for reason of tractability” (p. 115).

24 True to the spirit of RBC pioneers, Benhabib and Farmer’s (1994) model exhibits real indeterminacy: no monetary mechanism is at work in this approach, unlike the original OLG framework. The early framework considered by Benhabib and Farmer included monetary settings but was quickly abandoned for tractability reasons. It was eventually published years after but remained confidential. Subsequent models reintroduced monetary features.

25 Both terms already appeared in Azariadis’s (1981) seminal article. Animal spirits has been widely used in the literature. Self-fulfilling prophecies is enshrined in Farmer’s (1993) textbook, The Macroeconomics of Self-fulfilling Prophecies. From a purely theoretical point of view, this latter term adds a touch of confusion to the debate on coordination (and common knowledge) for non-sunspot rational expectations equilibria may nonetheless be considered as self-fulfilling.

26 In the presence of non-convexities, optimal trajectories may be subject to jumps (in consumption or worked hours), or even chattering. The most commonly proposed stabilisation policies (e.g. Guo and Lansing 1998, Guo and Harrison 2001) smoothed economic fluctuations, which may reveal suboptimal. Stabilization was thus achieved at the cost of efficiency.

27 On the sidelines of the discussions that could animate the NBER, Basu and Fernald (1995, 32) claimed that “a number of recent influential papers have modeled business cycles as products of sunspots or indeterminacy, which can even result in monetary non-neutrality. A high degree of returns to scale is critical for the success of most of these models—their ability to explain business cycle fluctuations is not just reduced but eliminated if returns to scale are below a (high) minimum.” The whole strategy of the new generation has been to reduce this threshold to almost zero.

28 Benjamin Bental, Dan Peled, and Zvi Eckstein completed their dissertations at the University of Minnesota around the onset of the 1980s. Bental and Peled studied under the guidance of Neil Wallace, while Eckstein was mentored by Anne Krueger. Later, Peled secured a position at the Technion-Israel Institute of Technology alongside Bental and also collaborated with the Carnegie-Mellon University in the mid-1980s. Here, he engaged in discussions with Spear and Srivastava and partnered on projects with Martin Eichembaum. Meanwhile, Zvi Eckstein, during his tenure at Tel-Aviv University, spent the academic year of 1986–87 at Carnegie and moved to the University of Pittsburgh the subsequent year.

29 Throughout the 1980s and 1990s, the influence of experimental economics expanded beyond just Carnegie. Alvin Roth and John Kagel joined the ranks at the University of Pittsburgh, where they collaborated with Jack Ochs. For a detailed exploration of these historical developments, refer to Maas and Svorencik’s (2015) work.

30 The existence of this history might be seen as the initial step in establishing common knowledge, or as part of the preliminary learning needed to converge to a sunspot equilibrium.

31 In their 2005 study, Duffy and Fisher examined scenarios where participants converged towards a low equilibrium even when the public signal indicated a high state, and vice versa. Here, sunspots primarily served as tools for coordination. However, the actual selection was influenced by participants’ interpretation of these signals, which was further shaped by the surrounding social and cultural contexts.

32 In Marimon, Spear, and Sunder (1994), sunspots were represented by blinking squares that varied in color, either yellow or red. In contrast, Duffy and Fisher 2005 opted to provide context by defining them as public announcements.

33 Unlike much of the experimental economics literature, Beugnot et al. (2012) view sunspots as potential catalysts for coordination failures.

34 The discourse about market psychology and the ensuing instability, while not central, is indeed present in Cass and Shell’s work, becoming explicit with their 1983 paper. A key stance that Cass, Shell, and their heirs maintained against the indeterminacy literature is the view that sunspot equilibria are more than just a mere randomization over certainty equilibria. This point is emphasized repeatedly, as seen in works like Shell (2008) or Ennis and Kreister (2003 7).