Planning capital-labor substitution and intertemporal equilibrium with a non-linear multi-sector growth model

A non-linear multi-sector model, postulating sectoral production functions and price-responsive demand functions linked around an input-output matrix in a general equilibrium framework, is used to simulate capital-labor substitution on a growth path characterized by intertemporal equilibrium. It demonstrates how the ‘temporary equilibrium’ or ‘sequential temporary equilibrium’ form of models that allow substitution can be extended into an intertemporally indecomposable equilibrium model without abandoning interaction between prices and quantities in the determination of technology and demand. The model is applied to the analysis of the impact of changes in real-wage growth on the characteristics of the equilibrium growth path of the Turkish economy with special attention given to the employment problem.     

A Takayama–Judge activity model applied to the analysis of allocation and trade in Sweden

The purpose of this article is to formulate a numerical general equilibrium model of the Swedish economy, and to use the model for a quantitative evaluation of the pattern of comparative advantages. The model is essentially a Leontief type of input-output model, extended with linear demand functions for final commodities, foreign trade activities and capacity and resource constraints. Due to the linearity the model can easily be reformulated and solved as a quadratic programming model. The evaluation of the pattern of comparative advantages of the Swedish economy is carried out as an analysis of the choice between inport and domestic production in a temporary equilibrium framework with exogenously given world market prices, exports and domestic production capacities.     

No-arbitrage Equilibria with Differential Information: An Existence Proof

On the example of a pure exchange financial economy with two periods incomplete nominal-asset markets and differential information of the adverse selection’s type, Cornet-De Boisdeffre (J Math Econ 38:393-410, 2002) introduced refined concepts of no-arbitrage prices and equilibria, which extended to the asymmetric information setting the classical concepts of the symmetric information literature. We now assess existence issues and extend a standard property of symmetric information models. Namely, we prove that a no-arbitrage equilibrium always exists, as long as financial markets preclude arbitrage, under the same standard conditions, whether agents have symmetric or asymmetric information.     

Computable general equilibrium with financial markets

Summary. There are a wide variety of theoretical general equilibrium models with incomplete security markets. In this paper we give a general recipe for using homotopy algorithm to compute equilibria in these models. In many models, taxes, transaction-costs or other market frictions introduce the additional difficulty that equilibrium prices or choices (but not equilibrium allocations) may be undetermined. In order to demonstrate how these difficulties can be dealt with, we develop a globally convergent algorithm to compute equilibria in a model with cash-in-advance constraints, several goods and incomplete financial markets. Furthermore we describe how to implement the algorithm using a publicly available suite of subroutines for homotopy-pathfollowing. Received: October 1, 1999; revised version: December 16, 2000     

Disaggregation of excess demand and comparative statics with incomplete markets and nominal assets

Summary. We prove that locally, Walras' law and homogeneity characterize the structure of market excess demand functions when financial markets are incomplete and assets' returns are nominal. The method of proof is substantially different from all existing arguments as the properties of individual demand are also different. We show that this result has important implications and is part of a more general result that excess demand is an essentially arbitrary function not just of prices, but also of the exogenous parameters of the economy as asset returns, preferences, and endowments. Thus locally the equilibrium manifold, relating equilibrium prices to these parameters has also no structure. Received: September 17, 1996; revised version: November 7, 1997     

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     

General equilibrium with endogenous securities and moral hazard

Summary. This paper studies a class of general equilibrium economies in which the individuals endowments depend on privately observed effort choices and the financial markets are endogenous. The environment is modeled as a two-stage game. Individuals first make strategic financial-innovation decisions. They then act in a Radner-type economy with the previously designed securities. Consumption goods, portfolios, and effort levels are chosen competitively (i.e., taking prices as given). An equilibrium concept is adapted for these moral hazard economies and its existence is proven. It is shown through an example how incentive motives might lead to the endogenous emergence of financial incompleteness.Received: 18 March 2002, Revised: 16 February 2004, JEL Classification Numbers: D52, D82, G10, G22.This paper is based on an essay from my Ph.D. dissertation at the University of Chicago. I am thankful for comments from Fernando Alvarez, Rodrigo Cerda, Pierre-André Chiappori, Rubens P. Cysne, Carlos E. da Costa, Milton Harris, Lars Stole, Juan P. Torres-Martínez, Paulo K. Monteiro, Philip Reny, Iván Werning, an anonymous referee, and seminar participants at the 6th SAET Conference and the 22th SBE Meeting. Financial support from CNPq is gratefully acknowledged.     

Bayesian–Walrasian equilibria: beyond the rational expectations equilibrium

In general rational expectations equilibrium (REE), as introduced in Radner (Econometrica 47:655–678, 1978) in an Arrow–Debreu–McKenzie setting with uncertainty, does not exist. Moreover, it fails to be fully Pareto optimal and incentive compatible and is also not implementable as a perfect Bayesian equilibrium of an extensive form game (Glycopantis et al. in Econ Theory 26:765–791, 2005). The lack of all the above properties is mainly due to the fact that the agents are supposed to predict the equilibrium market clearing price (as agent’s expected maximized utility is conditioned on the information that equilibrium prices reveal), which leads inevitably to the presumption that agents know all the primitives in the economy, i.e., random initial endowments, random utility functions and private information sets. To get around this problematic equilibrium notion, we introduce a new concept called Bayesian–Walrasian equilibrium (BWE) which has Bayesian features. In particular, agents try to predict the market-clearing prices using Bayesian updating and evaluate their consumption in terms of Bayesian price estimates, which are different for each individual. In this framework agents maximize expected utility conditioned on their own private information about the state of nature, subject to a Bayesian estimated budget constraint. Market clearing is not an intrinsic part of the definition of BWE. However, both in the case of perfect foresight and in the case of symmetric information BWE leads to a statewise market clearing; it then becomes an ex post Walrasian equilibrium allocation. This new BWE exists under standard assumptions, in contrast to the REE. In particular, we show that our new BWE exists in the well-known example in Kreps (J Econ Theory 14:32–43, 1977), where REE fails to exist. This work was done in the Spring of 2005, when EJB was a visiting professor at the University of Illinois.     

Arrow's equivalency theorem in a model with neoclassical firms

Summary. In this paper we consider a two-period general equilibrium model with uncertainty and real assets as financial instruments. The novelty of the analysis is that real assets are the stocks of neoclassical firms, so that both returns and yields depend on anticipated spot goods prices (and, of course, the yield matrix may change rank with prices). Assuming that financial markets are potentially complete, we establish generic existence of financial equilibrium and prove that there exists a dense set of economies such that financial equilibria are efficient.Received: 19 April 2001, Revised: 23 April 2003, JEL Classification Numbers: C60, D51, G10, D60.I am extremely grateful to Dave Cass for drawing my attention to this problem and inspiring me to work on it as well as for many stimulating discussions. I also benefited from discussions with H. Polemarchakis, M. Stinchcombe, and A. Villanacci. I am thankful to the anonymous referee of the first versions of the paper for thoughtful comments and suggestions, and to participants of a recruiting seminar at the University of Texas at Austin (January 2001), the Conference on Economic Design SED 2000, Istanbul, Turkey (June 2000), and Inter-University Student Conference, New York University, New York (May 2000).     

Diffusion of innovations in globally stable Walrasian equilibrium

When all products in the economy are weak gross substitutes, preferences are homothetic, and firms face menu costs then all prices in an industry move together at the same rate. In the closed-loop Nash noncooperative equilibrium, all firms invest in productivity and reduce real prices. As a result, in the case of quadratic menu costs, the outputs of industries and the economy go up along S-shaped time paths characteristic of diffusion of innovations.     

Walrasian bargaining

Given any two-person economy, consider an alternating-offer bargaining game with complete information where the proposers offer prices, and the responders either choose the amount of trade at the offered prices or reject the offer. We provide conditions under which the outcomes of all subgame-perfect equilibria converge to the Walrasian equilibrium (the price and the allocation) as the discount rates approach 1. Therefore, price-taking behavior can be achieved with only two agents.     

Growth in economies with non convexities: sunspots and lottery equilibria

Summary. We investigate the relation between lotteries and sunspot allocations in a dynamic economy where the utility functions are not concave. In an intertemporal competitive economy, the household consumption set is identified with the set of lotteries, while in the intertemporal sunspot economy it is the set of measurable allocations in the given probability space of sunspots. Sunspot intertemporal equilibria whenever they exist are efficient, independently of the sunspot space specification. If feasibility is, at each point in time, a restriction over the average value of the lotteries, competitive equilibrium prices are linear in basic commodities and intertemporal sunspot and competitive equilibria are equivalent. Two models have this feature: Large economies and economies with semi-linear technologies. We provide examples showing that in general, intertemporal competitive equilibrium prices are non-linear in basic commodities and, hence, intertemporal sunspot equilibria do not exist. The competitive static equilibrium allocations are stationary, intertemporal equilibrium allocations, but the static sunspot equilibria need not to be stationary, intertemporal sunspot equilibria. We construct examples of non-convex economies with indeterminate and Pareto ranked static sunspot equilibrium allocations associated to distinct specifications of the sunspot probability space.Received: 25 August 2003, Revised: 16 March 2004, JEL Classification Numbers: D84, D90.Correspondence to: Paolo SiconolfiWe thank Herakles Polemarchakis for helpful conversations on the topic. The research of Aldo Rustichini was supported by the NSF grant NSF/SES-0136556.     

On Shapley–Shubik equilibria with financial markets

In this paper, we extend the Shapley–Shubik model to a two period financial economy, and essentially address the question of the existence of an equilibrium. More precisely, we show the existence of nice equilibria, i.e. situations in which prices for both assets and commodities are strictly positive. Even if the general lines of the proof are largely influenced by the paper of Dubey and Shubik (J Econ Theory 17:1–20, 1978), most of the arguments are new because of the financial nature of the economy. It forces us to deal with a generalized Nash equilibrium, and to proscribe the use of arguments which only work with a single cash-in-advance constraint.      

Non-computability of competitive equilibrium

Summary. We provide a “computable counterexample” to the Arrow-Debreu competitive equilibrium existence theorem [2]. In particular, we find an exchange economy in which all components are (Turing) computable, but in which no competitive equilibrium is computable. This result can be interpreted as an impossibility result in both computability-bounded rationality (cf. Binmore [5], Richter and Wong [35]) and computational economics (cf. Scarf [39]). To prove the theorem, we establish a “computable counterexample” to Brouwer's Fixed Point Theorem (similar to Orevkov [32]) and a computable analogue of a characterization of excess demand functions (cf. Mas-Colell [26], Geanakoplos [16], Wong [50]). Received: September 9, 1997; revised version: December 17, 1997     

Asset price volatility in a nonconvex general equilibrium model

Summary. Asset prices and returns are known to vary significantly more than␣output or aggregate consumption growth, and an order of magnitude in excess of what is justified by innovations to fundamentals. We study excess price volatility in a lifecycle economy with two assets (claims on capital and␣a public debt bubble), heterogeneous agents, and increasing returns to financial intermediation. We show that a relatively modest nonconvexity generates a set valued equilibrium correspondence in asset prices, with two␣stable branches. Price volatility is the outcome of an equilibrium selection mechanism, which mixes adaptive learning with “noise”, and alternates stochastically between the two stable branches of the price correspondence. Received: March 19, 1998; revised version: June 2, 1998     

中国金融状况指数对货币政策传导作用研究

文章利用VECM模型构建了我国的金融状况指数,并对我国通货膨胀进行预测检验,发现包含资产价格信息的金融状况指数能够在当前金融市场频繁波动、资产价格急剧变化的市场条件下,对通货膨胀做出及时、有效的预测.这表明资产对经济的作用日益增强,中央银行在实施货币政策时,必须考虑到资产价格对货币政策的传导影响.然而,当利用金融状况指数对货币政策的资产传递渠道进行分析时,却发现货币政策传导过程中资产价格对产出的影响不大.因此,在实施货币政策时,可以关注资产价格变化时通货膨胀的影响,但由于资产价格在传导过程反应不足,目前还暂不能将资产价格作为货币政策的实际操作指标.     

Cournot-Nash and Lindahl equilibria in pure public “bad” economies

Summary. Using a general equilibrium framework, this paper analyzes the equilibrium provision of a pure public bad commodity (for example pollution). Considering a finite economy with one desired private good and one pure public “bad” we explicitly introduce the concept of Lindahl equilibrium and the Lindahl prices into a pure public bad economy. Then, the Lindahl provision is analyzed and compared with the Cournot-Nash provision. The main results for economies with heterogeneous agents state that the asymptotic Lindahl allocation of the pure public bad is the null allocation. In contrast, the asymptotic Cournot-Nash provision of the public bad might approach infinity. Other results were obtained in concert with the broad analysis of the large finite economies with pure public bad commodities. Received: July 26, 2001; revised version: March 12, 2002 RID="*" ID="*" We are indebt to Nicholas Yannelis and anonymous referee for their valuable comments and suggestions. Correspondence to: B. Shitovitz     

The financial accelerator and the real economy: A small macroeconometric model for Norway with financial frictions

This paper studies the salient features of a core macro econometric model that allows for self-reinforcing co-movements between credit, asset prices and real economic activity. In contrast to the economic literature that cultivates highly stylized model representations aimed at illustrating the workings and the implications of such a feature, the model of this paper integrates two mutually reinforcing financial accelerator mechanisms within the framework of a fully-fledged core macroeconomic model. The impulse responses of such a model is in line with the ones typical of SVAR/DSGE models, though the amplitude of shocks is in most cases stronger than the ones pertaining to these kinds of models. This is due to the workings of the financial accelerators that contribute to magnify the effects of shocks to the economy. A forecast comparison undertaken between our model and an alternative macro econometric model without a financial block, suggests that financial feedback mechanisms may be forecast improving.     

Value Cores for Finite Agents*

The standard definition of the competitive equilibrium, at given prices, presents the difficulty that finite agents (i.e. agents with finite budget and production sets), and a fortiori coalitions of such agents, need not be price takers and will upset the equilibrium. Since 1963 an extensive literature has sprung up, which has dealt with the problem, essentially by considering infinite numbers of infinitesimal agents. The present article outlines two alternative approaches to deal with this problem, both of which, realistically, admit (a finite number of) finite agents and redefine the core in terms of the value structure of the economy, viz. prices in the presence of controls, and cost and revenue functions in their absence. It is shown that the notion of value core, here introduced, coincides with that of competitive equilibrium, which is formulated as a characteristic-function game.     

Multiplicity of Cournot Equilibria and Involuntary Unemployment

In an overlapping generations model with Cournot competition on the goods market it is shown that a continuum of stationary states and perfect foresight trajectories exists with unemployment at arbitrary low wages. Decisive for this is the influence that different forecast functions have on the objective demand curve, even though they are consistent with perfect foresight. With an example it is shown that simple adaptive and constant memory forecast rules generate such unemployment equilibria. The corresponding temporary equilibrium dynamics may display stable unemployment and unstable full employment equilibria.Journal of Economic LiteratureClassification Numbers: D43, D51, E24