Stochastic processes of temporary equilibria

It is the aim of the paper to study within the framework of an ‘overlapping generation model’ the evolution of temporary equilibria. At date t, there are ‘newborn’ agents and ‘old’ agents who were born in previous periods; the old agents hold cash balances (fiat money) that they carried over from the previous period. At the beginning of period t, all agents receive a random endowment of consumption goods. Then the agents exchange these endowments and money on spot markets at date t (trading in future markets is not considered). Once a temporary equilibrium is reached, the economy move to the next date. Agents who were born at date t then become old and meet agents born at period t+1.It is shown that the evolution of temporary equilibria in this model leads to analyse the ergodic properties of a certain class of Markov processes with stationary transition probability.     

General consumption constraints and regular economies

In the spirit of Smale’s work, we consider pure exchange economies with general consumption sets. In this paper, the consumption set of each household is described in terms of a function called possibility function. The main innovation comes from the dependency of each possibility function with respect to the individual endowments. We prove that, generically in the space of endowments and possibility functions, economies are regular. A regular economy has a finite number of equilibria, which locally depend on endowments and possibility functions in a continuous manner.     

Market selection with an endogenous state

This paper explores market selection in general equilibrium when the state of the economy is endogenous. Analysis of consumer survival in this case requires solution of the model’s dynamics, for which evolutionary game theory can be useful; for instance, if the state and beliefs are Markovian and utility logarithmic, then the dynamics of consumption shares are described by the replicator dynamics. This is illustrated in a simple exchange economy, and in a standard monetary economy with multiple long-run equilibria where a plausible form of inflation targeting serves to destabilize a liquidity trap in favor of the target equilibrium.     

Stationary Markov equilibria on a non-compact self-justified set

The existence of stationary processes of temporary equilibria is examined in an OLG model, where there are finitely many commodities and consumers in each period, and endowments profiles and expectations profiles are subject to stochastic shocks. A state space is taken as the set of all payoff-relevant variables, and dynamics of the economy is captured as a stochastic process in the state space. In our model, however, the state space does not necessarily admit a compact-truncation consistent with the intertemporal restrictions because distributions over expectations profiles may have non-compact supports. As shown in Duffie et al. [Duffie, D., Geanakoplos, J., Mas-Colell, A., McLennan, A., 1994. Stationary Markov equilibria. Econometrica 62, 745–781), such a compact-truncation, called a self-justified set, is essential for the existence of stationary Markov equilibria. We extend their existence theorem so as to be applicable to our model.     

Arbitrage and equilibrium in unbounded exchange economies with satiation

In his seminal paper on arbitrage and competitive equilibrium in unbounded exchange economies, Werner (1987) proved the existence of a competitive equilibrium, under a price no-arbitrage condition, without assuming either local or global nonsatiation. Werner’s existence result contrasts sharply with classical existence results for bounded exchange economies which require, at minimum, global nonsatiation at rational allocations. Why do unbounded exchange economies admit existence without local or global nonsatiation? This question is the focus of our paper. First, we show that in unbounded exchange economies, even if some agents’ preferences are satiated, the absence of arbitrage is sufficient for the existence of competitive equilibria, as long as each agent who is satiated has a nonempty set of useful net trades– that is, as long as agents’ preferences satisfy weak nonsatiation. Second, we provide a new approach to proving existence in unbounded exchange economies. The key step in our new approach is to transform the original economy to an economy satisfying global nonsatiation such that all equilibria of the transformed economy are equilibria of the original economy. What our approach makes clear is that it is precisely the condition of weak nonsatiation – a condition considerably weaker than local or global nonsatiation – that makes possible this transformation.     

Asset bubbles and borrowing constraints

In this paper, we study the existence of asset bubbles in an overlapping generations economy à la Tirole [Tirole, J., 1985. Asset bubbles and overlapping generations. Econometrica 53, 1499–1528] with borrowing constraints. Deriving a condition for the existence of equilibrium paths with bubbles, we demonstrate that (i) a monetary steady state (a steady state with bubbles) is constrained dynamically inefficient, whereas capital in the monetary steady state is underaccumulating relative to the quasi-golden rule, (ii) there exists a government intervention which corrects the constrained dynamic inefficiency, and (iii) for some parameter values, such a government intervention reduces the utilities of agents with high productivity, while it increases per capita consumption.     

Intertemporal coordination in two-period markets

This paper studies the stability of the intertemporal coordination dynamics when the common knowledge of individual expectations of future prices is perturbed in a neighborhood of a perfect foresight equilibrium. The main forces that affect stability are: (i) the effect of a change in asset demand on second period spot market prices, and (ii) the effect on asset demand of a small change in second period prices. In an intertemporal market game whose interior Markov perfect equilibria correspond to perfect foresight equilibria, it is shown that though M-rationalizability implies the stability of the intertemporal dynamics, the converse is not always true.     

Cyclical equilibria in multi-sector productive economies: The role of substitution and factor intensity

The paper examines the existence of cyclical perfect foresight equilibria in a two-sector overlapping generations economy with production in which both goods enter consumption. Conditions for the existence of two types of cyclical equilibra are obtained in terms of elasticities of substitution in production and consumption, factor shares in production, and expenditure shares in consumption. The role of substitution possibilities and factor intensities is highlighted. It is shown that factor intensity assumptions are not enough to rule out cyclical equilibria and that limit cycles may exist for substantial amounts of substitution possibilities in production; what matters is the relative sizes of the consumption and production elasticities. The results are illustrated using CES functions. A dynamical simulation of an economy which exhibits a Hopf cycle is presented.     

On the Edgeworth conjecture for production economies with public goods: A contract-based approach

The paper applies and elaborates a contractual approach to study economies with a production of public goods. The barter contractual approach was developed in  and  for exchange economies; it is now modified and extended to the production economy. This includes hereby the introduction of a production contract and the adoption of known earlier notions: a web of contracts, coalitional domination for webs, a partial breaking of contracts, and so on. Thus specific notions of properly contractual and fuzzy contractual allocations for an economy with public goods are introduced and their equivalence with Lindahl equilibria is stated. These theorems can be interpreted as a new way of perfect competition presentation.     

The role of liquid government bonds in the great transformation of American monetary policy

A fundamental shift in monetary policy occurred around 1980: the Fed went from a “passive” policy to an “active” policy. We study a model in which government bonds provide transactions services. We present two calibrations of our model, using pre- and post-1980 data. We show that estimates of pre- and post-1980 policy rules all lie within our determinacy regions. But, the pre-1980 policy was a very bad monetary policy, even if it avoided sunspot equilibria. Model simulations suggest that household welfare would have increased by 3.3 percent of permanent consumption in this period under an active policy.     

Indeterminacy and nonlinear dynamics in an OLG growth model with endogenous labour supply and inherited tastes

This study analyses the dynamics of a two-dimensional overlapping generations economy with endogenous labour supply à la Reichlin (J Econ Theory 40(1):89–102, 1986) and aspirations. We show that the degree of nonlinearity of consumption externality in individual utility is responsible for the existence of either one steady state or two steady states. In addition, some interesting global dynamic properties, such as cyclical behaviour and/or global indeterminacy, emerge depending on the relative importance of aspirations in utility.     

Active intermediation in a monetary overlapping generations economy

This paper establishes that the profit-seeking activities of private intermediaries can ensure Pareto efficiency in the standard pure-exchange monetary overlapping generations economy without the need for government monetary or fiscal policy intervention. Moreover, these profit-seeking activities are shown to rule out all aperiodic and k-periodic cycles for k greater than 2. Contrary to much recent work on intermediation, the profit opportunities that arise for intermediaries in this context are not due to assumed frictions or asymmetric information. Rather, they are due to the dynamic open-ended structure of the economy, which permits debt roll-over.     

Population monotonic and strategy-proof mechanisms respecting welfare lower bounds

The significance of population monotonicity and welfare bounds is well-recognized in the fair division literature. We consider the welfare bounds that are central to the fair allocation literature, namely, the identical-preferences lower-bound, individual rationality, the stand-alone lower-bound,   and k$k$-fairness. We characterize population monotonic and incentive compatible mechanisms which allocate an object efficiently and respect a welfare lower bound chosen in the fair allocation problem of allocating a collectively owned indivisible good or bad when monetary transfers are possible and preferences are private information.     

Equilibria without the survival assumption

It is well known that an equilibrium in the Arrow–Debreu model may fail to exist if a very restrictive condition called the survival assumption is not satisfied. We study two approaches that allow for the relaxation of this condition. Danilov and Sotskov [Danilov, V.I., Sotskov, A.I., 1990. A generalized economic equilibrium. Journal of Mathematical Economics 19, 341–356], and Florig [Florig, M., 2001. Hierarchic competitive equilibria. Journal of Mathematical Economics 35, 515–546] developed a concept of a generalized equilibrium based on a notion of hierarchic prices. Marakulin [Marakulin, V., 1988. An equilibrium with nonstandard prices and its properties in mathematical models of economy. Discussion Paper No. 18. Institute of Mathematics, Siberian Branch of the USSR Academy of Sciences, Novosibirsk, 51 pp. (in Russian); Marakulin, V., 1990. Equilibrium with nonstandard prices in exchange economies. In: Quandt, R., Triska, D. (Eds.), Optimal Decisions in Market and Planned Economies. Westview Press, London, pp. 268–282] proposed a concept of an equilibrium with non-standard prices. In this paper, we establish the equivalence between non-standard and hierarchic equilibria. Furthermore, we show that for any specified system of dividends the set of such equilibria is generically finite. As a consequence, we have generic finiteness of Mas-Colell’s equilibria with slack, uniform dividend equilibria, and other special cases of our concept.     

Inference on an extended Roy model,with an application to schooling decisions in France

This paper considers the identification and estimation of an extension of Roy’s model (1951) of sectoral choice, which includes a non-pecuniary component in the selection equation and allows for uncertainty on potential earnings. We focus on the identification of the non-pecuniary component, which is key to disentangling the relative importance of monetary incentives versus preferences in the context of sorting across sectors. By making the most of the structure of the selection equation, we show that this component is point identified from the knowledge of the covariate effects on earnings, as soon as one covariate is continuous. Notably, and in contrast to most results on the identification of Roy models, this implies that identification can be achieved without any exclusion restriction nor large support condition on the covariates. As a by-product, bounds are obtained on the distribution of the ex ante   monetary returns. We propose a three-stage semiparametric estimation procedure for this model, which yields root-n$n$ consistent and asymptotically normal estimators. Finally, we apply our results to the educational context, by providing new evidence from French data that non-pecuniary factors are a key determinant of higher education attendance decisions.     

On existence in equilibrium models with endogenous default

The equilibrium concept defined by Dubey et al. ,  and  generates equilibria such that asset buyers could raise expected returns by paying more for the assets that they purchase. A simple example shows that, in fact, all equilibria may be return-dominated in that sense. Universal existence in the DGS model thus depends critically on the assumption that lenders are unable to exploit an obvious profit opportunity.     

Exchangeability and non-self-averaging

To pass from a deterministic dynamics of aggregate quantities to a probabilistic dynamics of a system of microvariables that describe the individual strategies of a population of economic agents, the route is that of Boltzmann??s kinetic theory at the half of XIX century (more suitable than that of Gibbs?? statistical mechanics), that is the introduction of n ??elements?? (molecules, agents,??), submitted to some microdynamics, wherefrom to derive the macroscopic behavior. The macrovariate is interpreted as a (time) mean of the average (on all elements) of the individual study-property at time t. The micro-derivation looks unproblematic if means and averages tend to constant values in the limit n ?? ??. If this property, defined ??self-averaging?? in some recent papers by Aoki, holds, it would separate a deterministic result from fluctuations; consequently well defined macroeconomic deterministic relations prevail. However it is easy to show that in most cases in economy this property does not hold, due to long-range correlation existing among economic agents. If individual agents are not independent but exchangeable, also in the limit n ?? ?? the coefficient of variation of the macrovariable is finite, which tends to a random limit rather than a constant. Finally the term ??indistinguishable agent?? is criticized, and the alternative ??exchangeable agent?? is discussed.     

Intertemporal coordination in two-period markets

This paper studies the stability of the intertemporal coordination dynamics when the common knowledge of individual expectations of future prices is perturbed in a neighborhood of a perfect foresight equilibrium. The main forces that affect stability are: (i) the effect of a change in asset demand on second period spot market prices, and (ii) the effect on asset demand of a small change in second period prices. In an intertemporal market game whose interior Markov perfect equilibria correspond to perfect foresight equilibria, it is shown that though M-rationalizability implies the stability of the intertemporal dynamics, the converse is not always true.     

Voluntary contributions to multiple public goods in a production economy with widespread externalities

In a production economy, multiple public goods are produced by firms in competitive markets, and provided by the government together with contributions from consumers. There are widespread externalities: all consumers’ consumption and contributions and all firms’ production enter into utility functions. Public goods can be imperfect substitutes or complements, and they can be local public goods or club goods. Zero bounds that require consumers to make nonnegative contributions complicate the differentiable approach. Applying the transversality theorem for smooth economies in a regular parameterization, we obtain the existence of equilibrium in such an economy, and generically equilibria are regular and locally unique.     

Strictly monotonic preferences on continuum of goods commodity spaces

We consider a set K of differentiated commodities. A preference relation on the set of consumption plans is strictly monotonic whenever to consume more of at least one commodity is more preferred. It is an easy task to find examples of strictly monotonic preference relations when K   is finite or countable. However, it is not easy for spaces like ?^∞([0,1])${?}^{\infty }([0\text{,}1])$, the space of bounded functions on the unit interval.