Unique and multiple equilibria in a macroeconomic model with environmental quality: An analysis of local stability

This paper develops and analyzes an economic growth model which incorporates environmental quality into the production and utility functions. We solve our model for the balanced growth path and find that a unique low growth equilibrium is attained when environmental quality is given less weight in the utility function. Multiple equilibria exist if environment quality is given greater weight in the utility function. We also perform local stability analysis of our model. We conclude that an economy in which the environmental quality is given relatively less importance by the agents will be caught in low growth, high consumption poverty traps as is the case for many developing countries while other economies can potentially reach a relatively low consumption, high growth steady state if they place greater weight on environmental quality. Finally we look at how the gap between low and high growth equilibria shrinks when individuals place greater weight on environmental quality and how governmental policies can promote growth when societies give less weight to the environment.     

Growth and multiple equilibria: A unique local dynamics

The paper investigates the local dynamics of a simple growth model with a public health factor. A notable feature of the model is that it employs a non-separable utility function between consumption and the level of public health infrastructure (publicly provided health environment). In addition to the effects on utility, an increase in the public health level contributes to labor productivity growth. From a three-dimensional dynamic system that includes physical capital, public health infrastructure and consumption, our model is found to have multiple equilibria (dual steady states) if the deep parameters of the utility function satisfy certain conditions. Then, numerical computations demonstrate that each equilibrium exhibits local saddle-path stability. This result deserves careful attention, as it indicates that the economy experiences a relatively undiversified growth pattern when converging on high- and low-growth equilibria. Our striking result has important implications in the study of growth and development.     

Walrasian versus quasi-competitive equilibrium and the core of a production economy

Summary. This paper presents very general conditions guaranteeing that a quasi-competitive equilibrium is a Walrasian equilibrium. We also develop a generalization (and a simplified proof) of Nikaidos and McKenzies extensions of the classic Debreu-Scarf theorem on core convergence, and apply the first result to obtain an equivalence between the set of Edgeworth equilibria and the set of Walrasian equilibria in a production economy.Received: 6 September 2002, Revised: 14 November 2003, JEL Classification Numbers: C71, D50, D51.     

Creditworthiness and thresholds in a credit market model with multiple equilibria

Summary. The paper studies creditworthiness in a model with endogenous credit cost and debt constraints. Such a model can give rise to multiple candidates for steady state equilibria. We use new analytical techniques such as dynamic programming (DP) with flexible grid size to find solutions and to locate thresholds that separate different domains of attraction. More specifically, we (1) compute present value borrowing constraints and thus creditworthiness, (2) locate thresholds where the dynamics separate to different domains of attraction, (3) show jumps in the decision variable, (4) distinguish between optimal and non-optimal steady states, (5) demonstrate how creditworthiness and thresholds change with change of the credit cost function of the debtor and (6) explore the impact of debt ceilings and consumption paths on creditworthiness.JEL Classification Numbers: C61, C63, D91, D92, E51, G12, G32.An earlier version of this paper has been prepared for the 1998 North American Winter Meeting of the Econometric Society, January 1998, Chicago. We want to thank Jess Benhabib, Buz Brock, Gustav Feichtinger, Franz Wirl, Michael Woodford, Wolf-Jürgen Beyn and Thorsten Pampel for helpful discussions and comments on various versions of the paper. We also want to thank participants in a workshop at the University of Technology, Vienna, the Macroeconomic Workshop at Columbia University, and the SCE conference, at Yale University, June 2001. We are also grateful for comments from a referee of the journal.     

The strong sequential core in a dynamic exchange economy

Summary. Dynamic exchange economies with uncertainty are considered where the information is released over infinite time. The strong sequential core of such an economy consists of those consumption streams that can be improved upon by no coalition at no moment of time. Non-emptiness of the strong sequential core is established given a high enough discount factor. Moreover, sufficient conditions are given under which the strong sequential core contains only time and history independent consumption streams.Received: 22 August 2002, Revised: 22 May 2003, JEL Classification Numbers: C71, C73, D51, D52.Correspondence to: P. Jean-Jacques HeringsJean-Jacques Herings would like to thank the Netherlands Organization for Scientific Research for financial support.     

Edgeworth and Walras equilibria of an arbitrage-free exchange economy

Summary. In this paper, we first give a direct proof of the existence of Edgeworth equilibria for exchange economies with consumption sets which are (possibly) unbounded below. The key assumption is that the individually rational utility set is compact. It is worth noticing that the statement of this result and its proof do not depend on the dimension or the particular structure of the commodity space. In a second part of the paper, we give conditions under which Edgeworth allocations can be decentralized by continuous prices in a finite dimensional and in an infinite dimensional setting. We then show how these results apply to some finance models.Received: 15 April 2002, Revised: 25 February 2003, JEL Classification Numbers: C62, D58, G12. Correspondence to: Monique FlorenzanoThis paper was presented at seminars of the Economic Departments of Brown University, The Johns Hopkins University, The University of Alabama, Purdue University and at the Centro de Modelamiento Matematico de la Universidad de Chile at Santiago. The paper has benefitted of the comments of these diverse audiences. Part of this work was done while the authors were visiting respectively Brown University and the Centro de Modelamiento Matematico. We thank them for their hospitality.     

Sensitivity analysis for applied general equilibrium models in the presence of multiple Walrasian equilibria

Summary. Pagan and Shannon's (1985) widely used approach employs local linearizations of a system of non-linear equations to obtain asymptotic distributions for the endogenous parameters (such as prices) from distributions over the exogenous parameters (such as estimates of taste, technology, or policy variables, for example). However, this approach ignores both the possibility of multiple equilibria as well as the problem (related to that of multiplicity) that critical points might be contained in the confidence interval of an exogenous parameter. We generalize Pagan and Shannon's approach to account for multiple equilibria by assuming that the choice of equilibrium is described by a random selection. We develop an asymptotic theory regarding equilibrium prices, which establishes that their probability density function is multimodal and that it converges to a weighted sum of normal density functions. An important insight is that if a model allows multiple equilibria, say , but multiplicity is ignored, then the computed solution for the i-th equilibrium generally no longer coincides with the expected value of that i-th equilibrium. The error can be large and correspond to several standard deviations of the mean's estimate. Received: December 7, 1999; revised version: December 4, 2000     

Run equilibria in the Green–Lin model of financial intermediation

We study the Green–Lin model of financial intermediation [E.J. Green, P. Lin, Implementing efficient allocations in a model of financial intermediation, J. Econ. Theory 109 (2003) 1–23] under a more general specification of the distribution of types across agents. We derive the efficient allocation in closed form. We show that, in some cases, the intermediary cannot uniquely implement the efficient allocation using a direct revelation mechanism. In these cases, the mechanism also admits an equilibrium in which some (but not all) agents “run” on the intermediary and withdraw their funds regardless of their true liquidity needs. In other words, self-fulfilling runs can arise in a generalized Green–Lin model and these runs are necessarily partial, with only some agents participating.     

The relative interior of the base polyhedron and the core

Summary. This note provides two necessary and sufficient conditions for the relative interior of the core (and the base polyhedron) to be non-empty: (i) the second largest excess of the prenucleolus is negative; (ii) the grand coalition's payoff is greater than the minimum no-blocking payoff. Such conditions imply an intuitive method in proving core existence, they also imply results on the sensitivity of the base polyhedron and the core. Received: June 25, 1999; revised version: May 8, 2000     

Stochastic convergence of per capita carbon dioxide emissions and multiple structural breaks in OECD countries

This research applies an innovative panel data stationarity testing procedure developed by Carrion-i-Silvestre et al. [Carrion-i-Silvestre, J.L., Barrio-Castro, T.D. and Lopez-Bazo, E., 2005. Breaking the panels: An application to the GDP per capita, Econometrics Journal 8, 159–175.], which has the advantage of recognizing multiple structural breaks and the presence of cross-section dependence in order to re-investigate the hypothesis that per capita carbon dioxide (CO₂) emissions stochastically converge for 21 OECD countries from 1950 to 2002. Remarkably, the evidence clearly indicates that the panel dataset of relative per capita CO₂ emissions is stationary after the structural breaks and cross-sectional dependence are introduced into the model. These findings offer strong policy implications for governments, regardless of whether they are in “convergent group” or “divergent group” countries. We also find that the structural breaks in the 1960s and over the 1970–1982 period are associated with time periods of fossil fuel becoming the main source of productivity, higher oil prices, and the development of nuclear power.     

A persistence-weighted measure of core inflation in the Euro area

We propose a new core inflation measure for the Euro area which places the emphasis on the more lasting, i.e. persistent, price developments at a disaggregated level. The importance of each component of the HICP is reweighted according to its relative persistence, as measured by the sum of the autoregressive coefficients or by an indicator of mean reversion. Unlike headline inflation, our baseline core inflation measure is highly correlated with ECB monetary policy decisions, which could mean that they contain ex ante (pre monetary policy) information on inflationary pressure.     

Knightian uncertainty and poverty trap in a model of economic growth

This paper explores how Knightian uncertainty affects dynamic properties in an economic growth model. The decision-making theory employed in the analysis is the theory of expected utility under a non-additive probability measure, i.e., the Choquet expected utility model of preference. We apply this decision-making theory to an overlapping generations model where producers face “uncertainty” in their technologies. When the producer is averse to uncertainty, the firm's profit function may not be differentiable. Therefore, the firm's decision to invest and hire labor becomes rigid for a certain measurable range of real interest rates. In dynamic equilibrium, the existence of firm-level rigidity causes discontinuity in the wage function; this makes multiple equilibria the more likely outcomes under the log utility and Cobb–Douglas production functions. In this paper, we show that even if aversion to uncertainty is small, the “poverty trap” can arise for a wide range of parameter values.     

The number of pure Nash equilibria in a random game with nondecreasing best responses

We randomly draw a game from a distribution on the set of two-player games with a given size. We compute the distribution and the expectation of the number of pure-strategy Nash equilibria of the game conditional on the game having nondecreasing best-response functions. The conditional expected number of pure-strategy Nash equilibria becomes much larger than the unconditional expected number as the size of the game grows.     

A differentiable homotopy to compute Nash equilibria of n-person games

Summary. The literature on the computation of Nash equilibria in n-person games is dominated by simplicial methods. This paper is the first to introduce a globally convergent algorithm that fully exploits the differentiability present in the problem. It presents an everywhere differentiable homotopy to do the computations. The homotopy path can therefore be followed by several numerical techniques. Moreover, instead of computing some Nash equilibrium, the algorithm is constructed in such a way that it computes the Nash equilibrium selected by the tracing procedure of Harsanyi and Selten. As a by-product of our proofs it follows that for a generic game the tracing procedure defines a unique feasible path. The numerical performance of the algorithm is illustrated by means of several examples. Received: December 21, 1999; revised version: December 27, 2000     

区域经济增长的动态趋同性--基于"长三角"地区的实证分析

本文采用Bernand和 Durlarf的时间序列技术方法从另一个角度考察了长三角地区经济增长的收敛性,并利用VAR模型的脉冲响应函数方法动态模拟了区域内部之间的溢出效应和累积效应.实证研究表明,长三角地区经济增长具有明显的"俱乐部"收敛特征,同时区域内三大地区在系统内相互作用产生了动态联动效应.该地区为其它区域经济发展战略乃至全国区域协调发展战略提供了启示.     

Karl Polanyi on economy and society: a critical analysis of core concepts

The Review of Social Economy was founded to highlight the irreducible social aspects of economic activity. Yet, the nature of the ‘social’ and the ‘economic’ are both unresolved, and they are much more problematic than often assumed. This article probes Karl Polanyi’s depiction of the relationship between the ‘social’ and the ‘economic’ and subsequent discourse on ‘embeddedness’. In his Great Transformation (1944) Polanyi associated the ‘economic’ with motives of material gain, while ‘social’ referred to norms of reciprocity and redistribution: his distinction between the ‘social’ and the ‘economic’ then focused primarily on different kinds of motivation. But in a 1957 essay he brought in different kinds of institutions that engender different types of motivation. Polanyi (1944) argued that after 1800 Britain was transformed into a market-oriented ‘economic’ system, based on motives of greed and material gain. He also proposed that an effective market system had to be ‘self-adjusting’ and free of political interference, despite his important additional claim that the state was involved in its creation. Some of Polanyi’s core concepts and arguments are contradictory and problematic, and need to be reconsidered, especially if his enduring insights are to be salvaged.     

A graphic representation of the Nash and Lindahl equilibria in an economy with a public good

In an economy with a public good the noncooperative Nash equilibrium and the cooperative Lindahl equilibrium are represented graphically. The Nash equilibrium is shown to be non-optimal, while the Lindahl equilibrium is shown to be optimal. Simple stability analyses are undertaken. Finally, the two equilibria are compared. It appears that more public good will be allocated in the Lindahl than in the Nash equilibrium, and that in a sufficiently large economy a transition from a Nash to a Lindahl equilibrium will be advantageous for everyone.     

A reassessment of total factor productivity convergence: Evidence from cross-country analysis

This study revisits total factor productivity (TFP) convergence by employing the latest Lagrange multiplier and residual augmented least squares Lagrange multiplier unit root tests and Phillips and Sul panel club convergence technique. The study uses annual data for 44 developing and 29 developed countries covering the time-period 1970–2014. Our findings from these unit root tests support evidence of TFP convergence. Region-based results (Africa, Asia, and Latin America and the Caribbean) also confirm TFP convergence. Further, results derived from the Phillips and Sul test support evidence of TFP convergence, although the speed of convergence varies by region. The highest speed is noted in the Asia region, whereas, the lowest of speed productivity convergence is observed in the Africa region.