Stationary Sunspot Equilibria Research Articles

Nominal exchange rate determination and dynamics in an OLG framework

The empirical evidence on nominal exchange rate dynamics shows a long-run relationship of this variable with the fundamentals of the economy, although such relationship disappears at shorter horizons. This apparently contrasting behaviour of the nominal exchange rate can be explained in an overlapping generations model where the currencies are not perfect substitutes. In this framework, we show that the nominal exchange rate is pinned down by the fundamentals at the monetary steady state. We study the local dynamics and show that when the monetary steady state is locally indeterminate, then fluctuations of the nominal exchange rate around its long-run value can emerge. In particular, we prove the existence of stationary sunspot equilibria, where random fluctuations of the nominal exchange rate arise as a result of self-fulfilling beliefs.

Bubbles, growth and sunspots with credit market frictions

This paper explores the role of bubbles in an overlapping-generations economy where some agents are more productive than the others. Due to missing credit markets, productive and unproductive agents cannot trade their financial assets to achieve mutual benefit, making the economy to perform below its potential. Introducing bubbles on the one hand crowds out some productive resources as it does in the current literature. It on the other hand may divert resources away from unproductive agents to productive ones. We find that bubbles are growth enhancing when the unproductive agents’ productivity level lies within an interval. Furthermore, in sharp contrast to the existing literature, the equilibrium bubble size is stable. This finding enables us to construct a two-state stationary sunspot equilibrium in which one state is associated with small bubbles and low growth whereas the other one has large bubbles and high growth.

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International transmission of bubble crashes in a two-country overlapping generations model

We study the international transmission of bubble crashes by analyzing stationary sunspot equilibria in a two-country overlapping generations exchange economy with stochastic bubbles. We consider two cases of sunspot shocks. In the first case, we assume that only the foreign country receives a sunspot shock, while in the second, we assume that both countries independently receive sunspot shocks. In the first case, a bubble crash in the foreign country is always accompanied by a bubble crash in the home country. In the second case, a bubble crash in the foreign country can have a positive or negative effect on the home bubble. We also show that there exists a unique locally isolated stationary sunspot equilibrium, and that it is locally unstable.

Habit Persistence, Currency Competition and Sunspot Equilibria

This paper cites the concept of consumption habit persistence and sunspot equilibria with uncertainty for analyzing the issue of currency competition to discuss the necessity of Gresham's Law and provide a complement of explanation to the euro exchange rate movements. We study the economy in one-good, two-currency Brock model with perfect currency substitution in discrete time. With habit persistence, we show that the optimal holding of currency asset is affected by the elasticity of intertemporal substitution. Besides, the higher-growth-rate currency does not always dominate the other currency in the long run. The Gresham-law result obtained in the deterministic model could not be true in a stationary sunspot equilibrium with a first-order Markov extrinsic uncertainty process. The existence of sunspot equilibria expresses another situation of currency competition depending on the possibility of people's expectations and supports complementally the investor-emotion view of the empirical studies in the currency-asset holding and the euro exchange rate movements.

Alternative government financing and aggregate fluctuations driven by self-fulfilling expectations

Using Woodford's finance-constrained model [Woodford, M., 1986. Stationary sunspot equilibria in a finance constrained economy. Journal of Economic Theory 40, 128–137] with external effects in production as in Barinci and Cheron [2001. Sunspots and business cycle in a finance constrained economy. Journal of Economic Theory 97, 30–49], this paper investigates the effects of alternative government financing methods on the range of values of increasing returns leading to an indeterminate steady state. It will be shown that indeterminacy may easily arise at a wide range of values of increasing returns if constant government expenditure is financed through labor income taxes, and with difficulty if constant government expenditure is financed by taxes on capital. In addition, we explore how the consequences of endogenous income taxes are changed if tax rates on labor and capital income are kept constant and government expenditure is endogenously adjusted to satisfy the budget constraint.

Local determinacy with non-separable utility

This paper introduces general formulations for both technology (with input substitution) and non-separable utility (compatible with balanced growth and stationary worked hours) into a benchmark RBC model. It is shown that intertemporal substitution and input substitutability lead to local determinacy and rule out stationary sunspot equilibria when labor demand is downward-sloping, in contrast with recent results obtained under the assumption of separable utility. The main intuition behind this result is shown to work as follows: in contrast with separable preferences, increasing the elasticity of intertemporal substitution in consumption necessarily implies decreasing the elasticity of constant-consumption labor supply, when utility is non-separable and concave, which affects unfavorably the occurrence of local indeterminacy.

Comments on “Global sunspots in OLG models”

This comment discusses the paper “Global Sunspot Equilibria in OLG Models” by Gianluca Gazzola and Alfredo Medio with an emphasis on the importance of the role of dynamic noise in economic dynamics. After summarizing the main findings of the paper, the implications of dynamic noise for nonlinear time series analysis are discussed, and an empirical measure is suggested for establishing whether observed noisy time series data might have been generated by a stationary sunspot equilibrium of a given deterministic attractor. The discussion is illustrated with the analyses of some time series generated by the model studied by the authors.

On competitive cycles and sunspots in productive economies with a positive money stock

This paper shows that stationary sunspot equilibria may occur in productive, overlapping-generations economies when the stock of outside money is positive. More precisely, a destabilizing real-balance effect makes sunspots compatible with positive money, substitutable inputs and inelastic labor. Key to the results is the presence of capital externalities associated with learning-by-doing creation of knowledge.

Stable sunspot solutions in models with predetermined variables

We consider a linear stochastic univariate rational expectations model, with a predetermined variable, and provide alternative representations of stationary sunspot equilibria (SSEs). For a strict subset of the parameter space there exist SSEs that are locally stable under least-squares learning provided agents use a common factor representation for their estimated law of motion. These results indicate that for some parameter regions SSEs are more likely to arise under private agent learning than previously recognized.

Extraneous shocks and international linkage of business cycles in a two-country monetary model

This paper analyzes how extraneous shocks can be the source of world business cycles. Using a two-country monetary model with the cash-in-advance constraint, we find that there exist stationary sunspot equilibria when either the relative risk aversion of the utility function or external effects in production are large. In both cases, stationary sunspot equilibria are a more likely outcome for the world aggregate output than for country-specific output. Therefore, even if the fundamental value shows small cross-country output correlations, extraneous shocks can cause large synchronization of business cycles under rational expectations.

Existence of adaptively stable sunspot equilibria near an indeterminate steady state

We examine the nonlinear model x t = E t F( x t+1 ). Markov stationary sunspot equilibria (SSEs) exist near an indeterminate steady state, x ̂ =F( x ̂ ) , provided |F′( x ̂ )|>1 . Despite the importance of indeterminacy in macroeconomics, earlier results have not provided conditions for the existence of adaptively stable SSEs near an indeterminate steady state. We show that there exist Markov SSEs near x̂ that are E-stable, and therefore locally stable under adaptive learning, if F′( x ̂ )<−1 .

On the plausibility of sunspot equilibria

This paper presents a one-sector business cycle model with variable capacity utilization and externalities that stem from aggregate economic activity. It uses a new formulation of the endogenous capital utilization rate in which utilization costs appear in the form of variable maintenance expenses. Indeterminacy arises at approximate constant returns to scale. This result challenges the viewpoint that indeterminacy is empirically implausible. Sunspot driven model fluctuations duplicate a number of stylized facts of the business cycle. Plausible parameter space contains regions in which stationary sunspot equilibria are stable under learning.

EXPECTATIONS COORDINATION ON A SUNSPOT EQUILIBRIUM: AN EDUCTIVE APPROACH

We analyze expectations coordination on a stationary sunspot equilibrium (SSE) using an eductive approach in which agents forecast the forecasts of others. This approach is grounded in some common-knowledge assumptions. We show that two institutional contexts may be envisaged; we also distinguish between stationary and nonstationary beliefs. We show that the conditions for eductive stability depend mainly on whether stationarity of beliefs is imposed. We also prove the existence of eductively stable SSEs by means of the Poincaré–Hopf theorem and show that eductively stable SSEs exist in a neighborhood of some indeterminate steady states.

Stable Sunspot Equilibria in Models with Predetermined Variables

We consider a linear stochastic univariate rational expectations model, with a predetermined variable, and provide alternative representations of SSEs (stationary sunspot equilibria). For a strict subset of the parameter space there exist SSEs that are locally stable under least squares learning provided agents use a common factor representation for their estimated law of motion. These results indicate that for some parameter regions SSEs are more likely to arise under private agent learning than previously recognized.

Local Sunspot Equilibria Reconsidered

This paper re-examines the conditions for the existence of local stationary sunspot equilibria (SSE) in the standard OLG model from a broader perspective than before. We say that local SSE exist around a steady state of a given OLG economy if, in any arbitrarily small neighborhood of the steady state, we can find a SSE of a nearby economy. We show that when the domain where nearby economies may lie is defined by agents' endowments and probabilities, the indeterminacy of the steady state remains both necessary and sufficient for the existence of local SSE. On the other hand, when the domain of economies is defined by by agents' preferences and probabilities, local SSE may exist even around determinate steady states. We also show that if a slightly weaker notion of distance is used to identify nearby' economies. SSE in the vicinity of a steady state equilibrium generically exist.

Apprentissage et équilibres à taches solaires. Un point de vue divinatoire

Dans un modèle simple à générations imbriquées, on étudie la coordination des anticipations sur un équilibre à taches solaires stationnaire (ESS) au moyen d'une approche « divinatoire » selon laquelle chaque agent s'efforce de deviner les anticipations des autres en tirant les conséquences d'hypothèses de connaissance commune de la rationalité des agents et de l'économie. On présente une caractérisation de la stabilité locale d'un ESS en termes d'élasticité de l'offre de travail et deux résultats d'existence d'ESS localement stables reposant respectivement sur le théorème de Poincaré-Hopf et sur un argument de bifurcation locale.

Endogenous real exchange rate fluctuations in an optimizing open economy model

This paper constructs a simple intertemporal model of a small open economy inhabited by forward looking agents, in which endogenous fluctuations in the real exchange rate can arise in equilibrium, i.e. fluctuations that are not linked to movements in economic fundamentals. The key condition for the main results is the assumption that the Marshall–Lerner condition does not hold (i.e. that the country's exports and imports are inelastic to its real exchange rate). It is shown that, given that the Marshall–Lerner condition fails, there exist periodic equilibria and/or stationary sunspot equilibria in the neighborhood of the stationary state.

Sunspot equilibria and periodic cycles under idiosyncratic uncertainty

This paper investigates how some intrinsic uncertainty affects the existence of sunspot equilibria and deterministic cycles in an overlapping generations model. In the model, there exists an intrinsic idiosyncratic uncertainty under which each individual has a small probability of losing consumption goods. Due to the law of large numbers, this uncertainty causes no fundamental macroeconomic fluctuation. However, since it may change the dynamic stability, the model may have both stationary sunspot equilibria and deterministic cycles even if the degree of relative risk aversion is small. In particular, these equilibria can exist even if the probability of loss is negligible.

Sunspot fluctuations in dynamics with predetermined variables

In this paper, I study the existence of Sunspot Equilibria in a general framework whose dynamics allow for the presence of predetermined variables in the system. The main motivation for this research comes from the fact that previous studies did not allow for such predetermined variables which, nevertheless, appear quite naturally in economic models. I show, for a non-negligible subset of dynamics with predetermined variables verifying usual assumptions, the existence of Stationary Sunspot Equilibria fluctuating between an arbitrary finite number of states arbitrarily close to a steady state.