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.     

Efficiency of temporary equilibria

A temporary equilibrium model of a production economy with various capital markets in which producers maximize the expected utility of cash flows in various periods is considered. Without restricting the price expectation of producers, it is shown that, if contracts to buy or sell goods at future periods can be trated in a market and if the producer's utility functions are increasing in the cash flow of the first period, then the temporary equilibrium allocations are technically efficient. Also, production is technically efficient even in the presence of some quantity constraints on sales of futures contracts which are sufficient for existence of an equilibrium.     

A note on computing equilibria in economies with activity analysis models of production

Equilibria in economies without production can be approximated by computing fixed points of continuous functions. With production present, the functions are usually replaced by set-valued mappings and fixed-point algorithms converge slowly. Here we propose continuous functions whose fixed points are equilibria in economies whose production is modelled by a finite list of activities. The penalty is that a least-distance program must be solved at each iteraction. The approach generalizes to allow ad valorem taxes on production. Finally, analogous arguments apply to the computation of an invariant optimal vector of capital stocks.     

A note on the existence of CAPM equilibria with homogeneous cumulative prospect theory preferences

This note identifies and fixes a minor gap in Proposition 1 in Barberis and Huang (Am Econ Rev 98(5):2066–2100, 2008). Assuming homogeneous cumulative prospect theory decision makers, we show that CAPM is a necessary (though not sufficient) condition that must hold in equilibrium. We support our results with numerical examples where security prices become negative.     

A note on the symmetry of all Nash equilibria in games with increasing best replies

It is well known that a symmetric game has only symmetric (pure strategy) Nash equilibria if its best-reply correspondences admit only increasing selections and its strategy sets are totally ordered. Several nonexamples of the literature show that this result is generally false when the totality condition of the relation that orders the strategy sets is simply dropped. Making use of the structure of interaction functions, this note provides sufficient conditions for the symmetry of all (pure strategy) Nash equilibria in symmetric games where best-reply correspondences admit only increasing selections, but strategy sets are not necessarily totally ordered.     

Stochastic equilibria of an asset pricing model with heterogeneous beliefs and random dividends

We investigate dynamical properties of a heterogeneous agent model with random dividends and further study the relationship between dynamical properties of the random model and those of the corresponding deterministic skeleton, which is obtained by setting the random dividends as their constant mean value. Based on our recent mathematical results, we prove the existence and stability of random fixed points as the perturbation intensity of random dividends is sufficiently small. Furthermore, we prove that the random fixed points converge almost surely to the corresponding fixed points of the deterministic skeleton as the perturbation intensity tends to zero. Moreover, simulations suggest similar behaviors in the case of more complicated attractors. Therefore, the corresponding deterministic skeleton is a good approximation of the random model with sufficiently small random perturbations of dividends. Given that dividends in real markets are generally very low, it is reasonable and significant to some extent to study the effects of heterogeneous agents’ behaviors on price fluctuations by the corresponding deterministic skeleton of the random model.     

Causality reconsidered: A note

This note extends the recent work of Steinnes by formulating and testing a similar but more complete dynamic reduced form model of intraurban location decisions. The formulation of the model corrects a specification error by Steinnes, and a dummy variable technique is applied to yield consistent estimates. The results include relations between the employment sectors as well as between population and employment and, when they differ from those previously published, they are more plausible. The basic conclusion of the note is that “jobs follow people.”     

Stochastic Index Numbers: A Review

The stochastic approach is a new way of viewing index numbers in which uncertainty and statistical ideas play a central role. Rather than just providing a single number for the rate of inflation, the stochastic approach provides the whole probability distribution of inflation. This paper reviews the key elements of the approach and then discusses its early history, including some previously overlooked links with Fisher's work contained in his book The Making of Index Numbers. We then consider some more recent developments, including Diewert's well-known critique of the stochastic approach, and provide responses to his criticisms. We also provide a review of Theil's work on the stochastic approach, and present and extend Diewert's work on this topic within the context of the Country Product Dummy method which measures price levels internationally. The paper also contains some recent material on the value of information from the perspective of the stochastic approach, as well as illustrative applications.     

A tractable analysis of contagious equilibria

This paper studies contagious equilibrium in infinitely repeated matching games. The innovation is to identify a key statistic of contagious punishment that, used together with a recursive formulation, generates tractable closed-form expressions for continuation payoffs, off equilibrium. This allows a transparent characterization of the dynamic incentives created by contagious punishment schemes.     

Formation of expectations: A model in temporary general equilibrium theory

The paper studies, in a temporary general equilibrium framework, the way expectations of agents can be formed along time through some learning mechanism. One is then faced with a set of coupled equations from which the time evolution of both the state of the economy and the individual expectations have to be derived. Three main results are proven, for an open dense set of economies. First, there actually exists a recurrence which allows to determine, locally around some stationary temporary equilibrium, the time dependant dynamics for the states and the time dependant expectations. Next, sufficient first-order conditions are given for the dynamics and expectations to converge to some limits when time goes to infinity. Last, additional sufficient first-order conditions guarantee that the chosen stationary temporary equilibrium has definite stability properties for the time dependant dynamics.     

Existence of proportional distribution schemes: A note

It is shown that existence of a proportional distribution scheme as discussed by Sobel (1981) is an easy consequence of uniqueness.     

The Components of Output Growth: A Stochastic Frontier Analysis

This paper uses Bayesian stochastic frontier methods to decompose output change into technical, efficiency and input changes. In the context of macroeconomic growth exercises, which typically involve small and noisy data sets, we argue that stochastic frontier methods are useful since they incorporate measurement error and assume a (flexible) parametric form for the production relationship. These properties enable us to calculate measures of uncertainty associated with the decomposition and minimize the risk of overfitting the noise in the data. Tools for Bayesian inference in such models are developed. An empirical investigation using data from 17 OECD countries for 10 years illustrates the practicality and usefulness of our approach.     

Prediction from binary choice models: A note

The results of Westin (1974) can be obtained, to a satisfactory approximation, without recourse to numerical integration. We also show how to attach a standard error to his point estimates.     

Monopolies and mergers commission reports: A note

It is shown that the UK Monopolies and Mergers Commission has typically neither produced, nor correctly processed, the information necessary for making rational decisions. The case for an explicit quantitative approach using the expected value criterion is outlined.     

A note on redistribution

A consequence of income redistribution may well be to make everyone (including lower-income groups to which redistribution takes place) worse off after a period of years. Possibly income redistribution might gain consent because of risk aversion. The paper also draws attention to the tendency for people to be more concerned about poverty close at hand rather than far away.     

国际货币政策协调的随机模型分析

本文采用一个简单的新开放宏观经济随机模型。在名义粘性工资的假定下，应用对数线性模型，通过求工资设定问题、预期的产出、预期的贸易条件、预期的效用等变量的解析解，分析得出了任何偏离均衡状态的国内货币政策都会给本国居民带来期望效用的损失；采用统一的国际货币时，只要采用谨慎的货币政策将优于多种货币共存的情形。