Sunspots and Hopf bifurcations in continuous time endogenous growth models

First we treat a three-dimensional continuous time abstract stationary model that includes one predetermined variable and two non-predetermined variables. We construct stationary sunspot equilibria in this model under the following two alternative conditions: (i) a steady state has two stable roots and one unstable root; and (ii) A closed orbit has a two-dimensional manifold on which it is asymptotically stable. Next, we apply these results to the models due to Lucas and Romer that undergo Hopf bifurcations for some parameter values. We construct sunspot equilibria in these models.     

Mixed strategy equilibria in repeated games with one-period memory

Infinitely repeated games is the pre-dominant paradigm within which economists study long-term strategic interaction. The standard framework allows players to condition their strategies on all past actions; that is, assumes that they have unbounded memory. That is clearly a convenient simplification that is at odds with reality. In this paper we restrict attention to one-period memory and characterize all totally mixed equilibria. In particular, we focus on strongly mixed equilibria. We provide conditions that are necessary and sufficient for a game to have such an equilibrium. We further demonstrate the exact set of payoffs that can be generated by such equilibria.     

Some stability results for Markovian economic semigroups

The present paper studies existence, uniqueness and stability of stationary equilibrium distributions in a class of stochastic dynamic models common to economic analysis. We provide applications to a heterogeneous agent model and two nonlinear multisector time series models with unbounded state space.     

Interest rate rules and global determinacy: An alternative to the Taylor principle

A well‐known determinacy condition on interest rate rules is the “Taylor principle,” which states that nominal interest rates should respond more than 100 percent to inflation. Unfortunately, notably because interest rates must be positive, the Taylor principle cannot be satisfied for all interest rates, and as a consequence global determinacy may not prevail even though there exists a locally determinate equilibrium. We propose here a simple alternative to the Taylor principle, which takes the form of a new condition on interest rate rules that ensures global determinacy. An important feature of the policy package is that it does not rely at all on any of the fiscal policies associated with the “fiscal theory of the price level,” which has so far been the main alternative for determinacy.     

Unique Equilibrium in a Dynamic Model of Speculative Attacks

A main challenge of understanding currency crises is explaining their puzzling timing. Most “second generation” currency crisis models are static models with multiple equilibria, and exogenous shifts between equilibria are interpreted as shifts of sentiments on financial markets leading to crises. This article develops a dynamic, continuous time model with a payoff structure similar to second generation models. We derive endogenous conditions under which shifts in sentiment occur over time, characterise them in terms the strategic risk associated with speculation, and provide comparative statics. Moreover, we show that the findings correspond almost exactly to the implications of global game currency crisis models, which are often used for equilibrium selection in the static context.     

The macroeconomics of self-fulfilling prophecies Roger E. A. Farmer MIT Press, 1993, 259 pp.

In The Macroeconomics of Self-Fulfilling Prophecies, Roger Farmer argues that dynamic general equilibrium models represent a useful means for organizing and representing one's understanding of macroeconomic behavior. Reasonably small departures from the standard assumptions of Arrow-Debreu economies can lead to equilibria with non-trivial roles for macroeconomic policy. Farmer demonstrates through theory and example the potential for multiple equilibria, which he suggests can be treated by better specification of agents' beliefs. The existence of multiple equilibria creates the possibility of bounded fluctuations due to animal spirits or "self-fulfilling prophecies." The author is indebted to Robert Holland and Chris Waller for comments on a previous draft.     

Free entry equilibria with positive profits: A unified approach to quantity and price competition games

Free entry equilibria are usually characterized by the zero profit condition. We plead instead for a strict application of the Nash equilibrium concept to a symmetric simultaneous game played by actual and potential entrants, producing under decreasing average cost. Equilibrium is then typically indeterminate, with a number of active firms varying between an upper bound imposed by profitability and a lower bound required by sustainability. We use a canonical model with strategies represented by prices, although covering standard regimes of quantity and price competition, to show that in equilibrium the critical (profit maximizing) price must lie between the break-even and the limit prices.     

Liquidity traps with global Taylor Rules

An important theme in the writings of Jess Benhabib is the global stability of equilibrium in monetary economies. A key result emerging from his research is that Taylor-type interest rate feedback rules that are bounded below by zero can lead to unintended liquidity traps. The present paper shows that even if the interest rate rule is not bounded below by zero, that is, even if the government could credibly commit to a globally active Taylor rule, self-fulfilling liquidity traps cannot be ruled out. This result is shown to obtain in models with flexible and sticky prices and under continuous and discrete time.     

Testing the Taylor Model Predictability for Exchange Rates in Latin America

Exchange rates forecasting performance is tested by a model which incorporates endogenous monetary policy through a Taylor rule reaction function. Other usual monetary and equilibrium empirical exchange rate models are also evaluated for comparison purposes. Predictability is tested by comparing the models to a benchmark random walk specification. We contribute to the recent literature in many ways. First, we include models of forward-looking endogenous monetary policy to the exchange rate forecasting exercise, the Taylor model. Second, our data, set across countries, is uniform in terms of economies adopting both inflation targeting and a flexible exchange rate. Third, our study sheds light on exchange rate determinants for emerging economies: Brazil, Chile, Colombia, Peru and Mexico. Our results show strong predictability evidence for the Taylor model and indicate that assuming models of endogenous monetary policy and the present value of expected fundamentals is a rewarding strategy to model exchange rate determination.     

Perfect foresight dynamics in binary supermodular games

The present paper considers equilibrium selection in binary supermodular games based on perfect foresight dynamics. We provide complete characterizations of absorbing and globally accessible equilibria and apply them to two subclasses of games. First, for unanimity games, it is shown that our selection criterion is not in agreement with that in terms of Nash products, and an example is presented in which two strict Nash equilibria are simultaneously globally accessible when the friction is sufficiently small. Second, a class of games with invariant diagonal are proposed and shown to generically admit an absorbing and globally accessible equilibrium for small frictions.     

International environmental agreements under different evolutionary imitation mechanisms

This paper explores how the formation and stability of international environmental agreements vary with two often adopted mechanisms: imitating-the-best-average and imitating-the-best-total rules. We first show that the possible long-run equilibria of two dynamics are the same. They are countries' full participation, no-participation, and the two equilibria combined. However, the occurring conditions of these equilibria under two dynamics may differ. Then, we prove that countries' full participation is more likely to be long-run equilibrium in international environmental agreements when imitating-the-best-average rule is adopted. Moreover, all findings of this study hold whatever the function forms of countries' abnoatement benefits and costs are, and are unaffected by the positive affine transformation of countries' total payoffs.     

Measures of economies with an arbitrarily large number of equilibria

Balasko (1978) shows that in a compact subset of the space of economies, not too many economies can have too many equilibria. We extend Balasko’s result to the whole set of economies for a suitable measure. We show that the measure of economies with a large number of equilibria approaches zero as this number tends to infinity. An analogous result in the infinite‐dimensional setting is also established.     

开放经济条件下中国泰勒规则及其拓展形式的实证研究

文章从标准泰勒规则的内涵和适用条件出发,应用中国1995年第1季度到2010年第1季度的数估计了标准的线性泰勒规则,逐步从利率平滑、前瞻性变量、汇率因素和资产价格等方面放宽适用条件,根据开放经济条件下的货币政策数据对泰勒规则的拓展模型进行实证检验并验证泰勒规则在我国的适应性。     

On payoff heterogeneity in games with strategic complementarities

Recent papers involving binary choices have argued that increasingheterogeneity decreases positive feedback. We show that no suchresult holds in models where all agents make interior choices.The results in the binary choice case arise for two reasons.First, if we increase heterogeneity without limit but imposea bounded choice set, then almost all players eventually becomecompletely unresponsive, preferring some corner so stronglythat they do not react to any feasible change in the behaviorof others. Second, discrete choice permits the constructionof strong, but fragile, positive feedbacks through compositioneffects.     

Unnoticed predecessors of the early Negishi theorems

From the studies of the history of economic thought, we can learn that many theorems of the modern general equilibrium theory were well anticipated in the classical economics and the economics of the marginal revolution. For example, first, what Johann Heinrich von Thünen (1783–1850) did, in his strange theory of natural wage, can be interpreted as an early, pioneering attempt to use the so-called Negishi method (1960), which is now intensively used for the proof of the existence theorem and the numerical calculation of a general equilibrium. Second, as is well known, no exchanged transactions are permitted out of equilibria in the famous Walrasian tatonnement adjustment process towards market equilibria. Against this, the importance of transactions carried out at disequilibria is emphasized in the studies of the so-called Hahn–Negishi non-tatonnement process (1962). As a matter of fact, in the classical economics, this is exactly what William Thomas Thornton (1813–1380) insisted against the authority of John Stuart Mill (1800–1873). Finally, subjectively perceived (often kinked) demand curves are considered in my proof of the existence of a general equilibrium in the case of monopolistic competition (1961). To my surprise, however, I found later that such demand curves were already hidden in Adam Smith's (1723–1790) consideration of markets and the division of labor, and that the increase of demand never fails to lower the price of goods.     

Expectation-driven fluctuations and welfare loss under free trade in two-country models

This paper investigates the interlinkage in the business cycles based on expectation-driven fluctuations of large-country economies in a free-trade equilibrium. We consider a two-country, two-good, two-factor general equilibrium model with sector-specific externalities. We show that some country's expectation-driven fluctuations can spread throughout the world once trade opens even if the other country has determinacy under autarky. We thus prove that under free trade, globalization and market integration can have destabilizing effects on a country's competitive equilibrium. Finally, we characterize a configuration in which opening to international trade improves the stationary welfare at the world level but deteriorates the stationary welfare of the country that imports investment goods and exports consumption goods. We conclude that in opposition to the standard belief, international trade might not be beneficial to all trading partners in the long run.     

A dynamic common property resource problem with amenity value and extraction costs

An analytically tractable differential game is presented that describes the exploitation of a common-property resource by finitely many competing players. The resource stock has an amenity value and there are positive extraction costs. We derive both the cooperative solution and Markov-perfect Nash equilibria of the non-cooperative game. After a comparative analysis of the equilibrium strategies and payoffs with respect to all model parameters, we study the effect of a unilateral extraction restriction and discuss the design of a revenue-neutral tax/transfer scheme that supports the cooperative solution.     

Existence of Bertrand equilibrium revisited

In this paper we reconsider existence of Bertrand equilibrium in a symmetric‐cost, homogenous‐product oligopoly. We prove the following main results. (a) If the cost function is strictly superadditive on [0, ∞) then there exists a pure strategy Bertrand equilibrium. Such Bertrand equilibria are necessarily non‐unique. (b) If the cost function is strictly subadditive on [0, ∞) then there exists no Bertrand equilibrium, either in pure strategies or in mixed strategies.     

Size of nested cities

Models of cities based on conventional spatial market theory are unable to replicate a realistic size distribution. The stochastic process approach to size distribution, which assumes proportionate growth, does not provide an economic foundation for spatial trades. There is an apparent irreconcilability. We propose that since there is a continuum of equilibria in models of spatial markets with endogenous location, proportionate growth can work as equilibrium selection. We present computations for an urban configuration that has not been presented in the literature before. A small city locates inside a larger city's agricultural supply zone. This generates a larger variation in city size that may include a realistic size distribution.     

Nash equilibria of games when players’ preferences are quasi‐transitive

Much of game theory is founded on the assumption that individual players are endowed with preferences that can be represented by a real‐valued utility function. However, in reality human preferences are often not transitive. This is especially true for the indifference relation, which can lead an individual to make a series of choices which in their totality would be viewed by the same individual as erroneous. There is a substantial literature that raises intricate questions about individual liberty and the role of government intervention in such contexts. The aim of this paper is not to go into these ethical matters but to provide a formal structure for such analysis by characterizing games where individual preferences are quasi‐transitive. The paper identifies a set of axioms which are sufficient for the existence of Nash equilibria in such “games.”