Endogenous participation risk in speculative markets

This paper analyses the dynamic implications of an asset-pricing model with incomplete participation due to entry costs. It is shown that heterogeneity in entry costs can lead to the existence of multiple stochastic sunspot equilibria, whereby the number of agents in the market and asset prices fluctuate endogeneously over time in the absence of fundamental uncertainty. Such asset-price fluctuations occur despite the uniqueness of the deterministic equilibrium, and thus bear no link to the usual notion of steady-state indeterminacy. In addition to excess volatility, the equilibria exhibit predictable and conditionally heteroskedastic returns.     

Survival and the art of profit maximization

We study the relationship between rationality and economic survival in a simple dynamic model, where agents from different populations interact repeatedly through random matching. An explicit criterion (“bankruptcy”) determines whether agents survive each interaction; all agents are presumed to be aware of this criterion. Survival in each interaction depends on two factors: the strategies agents adopt when they interact, and the wealth levels they bring to the game. The model is completely symmetric with the only difference between the agents of different populations being their objectives. We consider the case where there are two populations of agents in which all agents from one group have as their objective, maximizing the expected profits from each interaction, while all agents from the other attempt simply to maximize the probability of surviving (i.e., not going bankrupt in) the interaction. We show that under the equilibrium dynamics, the proportions of each group in the total population must be bounded away from zero, but the balance is in favor of the survival-probability maximizers in that their numbers as a fraction of total population must always exceed 1/2, and can be arbitrarily close to unity. On the other hand, the fraction of total wealth controlled by the expected profit maximizers must also be at least 1/2, and can asymptotically tend to unity.     

Further Evidence on PPP Adjustment Speeds: the Case of Effective Real Exchange Rates and the EMS*

Two different approaches intend to resolve the ‘puzzling’ slow convergence to purchasing power parity (PPP) reported in the literature [see Rogoff (1996) , Journal of Economic Literature, Vol. 34.] On the one hand, there are models that consider a non‐linear adjustment of real exchange rate to PPP induced by transaction costs. Such costs imply the presence of a certain transaction band where adjustment is too costly to be undertaken. On the other hand, there are models that relax the ‘classical’ PPP assumption of constant equilibrium real exchange rates. A prominent theory put together by Balassa (1964, Journal of Political Economy, Vol. 72) and Samuelson (1964 Review of Economics and Statistics, Vol. 46) , the BS effect, suggests that a non‐constant real exchange rate equilibrium is induced by different productivity growth rates between countries. This paper reconciles those two approaches by considering an exponential smooth transition‐in‐deviation non‐linear adjustment mechanism towards non‐constant equilibrium real exchange rates within the EMS (European Monetary System) and effective rates. The equilibrium is proxied, in a theoretically appealing manner, using deterministic trends and the relative price of non‐tradables to proxy for BS effects. The empirical results provide further support for the hypothesis that real exchange rates are well described by symmetric, nonlinear processes. Furthermore, the half‐life of shocks in such models is found to be dramatically shorter than that obtained in linear models.     

An equivalence theorem for a differential information economy

In a pure exchange economy with differential information and a finite set of traders, physical commodities and states of nature, we characterize the Walrasian expectations or Radner equilibria by using the veto power of the grand coalition. We prove that an allocation x is a Radner equilibrium allocation if and only if it is “privately non-dominated” by the grand coalition in every economy obtained by perturbing the original initial endowments in the direction of x. The first and second welfare theorems become particular cases of our main result. Since the deterministic Arrow–Debreu–McKenzie model is a special case of the differential information economy model we also provide a new characterization of the Walrasian equilibria.     

The impact of transportation cost uncertainty on urban structure

Under an uncertain transportation cost, residential choice is made before the actual state of the world reveals itself. Formally, this resembles the theory of saving under uncertainty. Exploring this resemblance, we investigate the effect on urban structure of introducing uncertainty in transportation cost. Our main conclusion is that risk does not necessarily have the same effect on the city that an increase in transportation cost does in the deterministic case. If the utility function obeys the ‘principle of decreasing risk aversion to concentration’, introducing risk causes the urban area to contract (as in the case of an increasing transportation cost), but the equilibrium utility level may either increase or decrease. If, on the other hand, utility does not satisfy the above principle, introducing risk causes the utility level to decline (as if the case of an increasing transportation cost), but the urban area may either expand or contract.     

Deterministic multi-player Dynkin games

A multi-player Dynkin game is a sequential game in which at every stage one of the players is chosen, and that player can decide whether to continue the game or to stop it, in which case all players receive some terminal payoff.We study a variant of this model, where the order by which players are chosen is deterministic, and the probability that the game terminates once the chosen player decides to stop may be strictly less than 1.We prove that a subgame-perfect ε-equilibrium in Markovian strategies exists. If the game is not degenerate this ε-equilibrium is actually in pure strategies.     

Trend stationarity in the I(2) cointegration model

A vector autoregressive model for I(2) processes which allows for trend-stationary components and restricts the deterministic part of the process to be at most linear is defined. A two-step statistical analysis of the model is derived. The joint test of I(1) and I(2) cointegrating ranks is shown to be asymptotically similar with respect to the drift terms and the asymptotic distribution is tabulated. The cointegrating parameters are shown to be mixed Gaussian and an application for UK monetary data illustrates the proposed analysis.     

Testing the Null of Cointegration with Structural Breaks*

We propose a Lagrange Multiplier‐type statistic to test the null hypothesis of cointegration allowing for the possibility of a structural break, in both the deterministic and the cointegration vectors. Our proposal focuses on the presence of endogenous regressors. The test complements the usual non‐cointegration tests so as to obtain stronger evidence of cointegration. We consider the cases of known and unknown dates of the break. In the latter case, we show that minimizing the Sum of Squared Residuals results in a super‐consistent estimator of the break fraction. Finally, the behaviour of the tests is studied through Monte Carlo experiments.     

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.     

Coordinating under incomplete information

We show that, in a minimum effort game with incomplete information where player types are independently drawn, there is a largest and smallest Bayesian equilibrium, leading to the set of equilibrium payoffs (as evaluated at the interim stage) having a lattice structure. Furthermore, the range of equilibrium payoffs converges to those of the deterministic complete information version of the game, in the limit as the incomplete information vanishes. This entails that such incomplete information alone cannot explain the equilibrium selection suggested by experimental evidence. We thank Atila Abdulkadiroglu, Hans Carlsson, Ani Guerdjikova and an anonymous referee for helpful comments. Part of this work was done while Asheim was visiting Cornell University, which hospitality is gratefully acknowledged.     

Existence of equilibrium actions and of equilibrium : A note on the ‘new’ existence theorems

A lemma by Ky Fan, which asserts the existence of a maximal element relative to some ordering (an equilibrium action) in a compact choice set, is extended to a larger class of orderings. This extension allows one to generalize slightly several existence theorems and seems to be useful for the applications. Kakutani's fixed-point theorem and the existence of an equilibrium in a generalized game are used to exemplify this. In the last case the method of proof may be of some independent interest involving, as it does, the reduction of an n-person game to a corresponding 1-person game.     

Location decisions and welfare under spatial price discrimination

The welfare effects of regulation are of crucial importance to policy makers. To this end, we present a model of n firms with differentiated costs competing in a linear market within the framework of spatial price discrimination. We prove that the Nash equilibrium locations of firms are always socially optimal irrespective of the number of competitors, the distribution of consumers, firms' cost heterogeneity, the level of privatization, and the number and/or the varieties of the produced goods. We also provide an algorithm on how to find the unique Nash equilibrium in the case of uniformly distributed consumers.     

Pareto optimality in continuous-time OLG economies

The aim of this paper is the achievement of a complete characterization of the Pareto optimality of competitive equilibria for deterministic, pure exchange, continuous-time economies with a countable number of overlapping generations, where each consumer’s life-span consists in a bounded interval of time. For such an environment, we obtain separate sufficient and necessary conditions for Pareto optimality in the form of the Cass’ criterion, that is, in terms of the equilibrium prices. However, these conditions are not equivalent in general. Therefore, in order to get that equivalence we are compelled to impose certain restrictions, either on consumers’ lifetimes, assuming that all of them have the same longevity, or on the dynamic behaviour of relative intertemporal equilibrium prices. In both cases, we are able to derive a single condition that is sufficient and necessary for efficiency, thus achieving full characterizations.     

Intertemporal price–quality discrimination and the Coase conjecture

We examine time-consistent intertemporal price–quality discrimination by a durable goods monopolist, when there are a continuum of buyer demand-intensities with respect to product quality, and it is profitable for the monopolist to trade with the marginal buyer-type (i.e., the “gap” case). We show that along every subgame perfect equilibrium path, with probability 1, prices and qualities decline over time, and the market is completely and monotonically depleted according to buyer-type in a finite number of offers. But, unlike the fixed quality literature, the monopolist may randomize over price–quality offers along the equilibrium path. We also show that the Coase conjecture continues to be valid here, but in a form that is significantly different from the usual formulation. In the limit, as the time between offers evaporates, the monopolist makes a continuum of offers and perfectly screens the market. However, he effectively cannot price-discriminate, because the equilibrium profits converge to the complete “pooling” profits that would be made if the entire market had the marginal buyer-type’s valuation.     

The generalized Stackelberg equilibrium of the all-pay auction with complete information

We characterize the equilibrium of the all-pay auction with general convex cost of effort and sequential effort choices. We consider a set of n players who are arbitrarily partitioned into a group of players who choose their efforts ‘early’ and a group of players who choose ‘late’. Only the player with the lowest cost of effort has a positive payoff in any equilibrium. This payoff depends on his own timing vis-a-vis the timing of others. We also show that the choice of timing can be endogenized, in which case the strongest player typically chooses ‘late’, whereas all other players are indifferent with respect to their choice of timing. In the most prominent equilibrium the player with the lowest cost of effort wins the auction at zero aggregate cost. We thank Dan Kovenock and Luis C. Corchón for discussion and helpful comments. The usual caveat applies. Wolfgang Leininger likes to express his gratitude to Wissenschaftszentrum Berlin (WZB) for its generous hospitality and financial support.     

Asymmetric‐information allocation to avoid coordination failure

In the context of team production, this paper studies the optimal (deterministic and stochastic) information allocation that implements desired effort levels as the unique Bayesian equilibrium. We show that under certain conditions, it is optimal to asymmetrically inform agents even though they may be ex ante symmetric. The main intuition is that informing the agents asymmetrically can be effective in avoiding “bad” equilibria, that is, equilibria with coordination failure.     

Bartlett correction in the stable second‐order autoregressive model with intercept and trend

This paper derives the Bartlett factors that can be used to obtain higher‐order improvements for testing hypotheses about the autoregressive (AR) parameters in the stable AR(2) model with possible intercept and linear trend. The factors are obtained for testing hypotheses about individual parameters (φ₁ and φ₂) as well as their sum. Moreover, the effect of deterministic terms on the correction factors is found explicitly. All corrections are non‐decreasing in the AR parameters. Furthermore, the Bartlett corrections for φ₁ and φ₂ tend to infinity as φ₂ approaches 1, whereas the correction for φ₁ + φ₂ tends to infinity as φ₁ + φ₂ is close to 1. The effectiveness of these Bartlett corrections in finite samples is evaluated by simulations.     

Stochastic Jacobian and Riccati ODE in affine term structure models

In affine term structure models (ATSM) the stochastic Jacobian under the forward measure plays a crucial role for pricing, as discussed in Elliott and van der Hoek (Finance Stoch 5:511–525, 2001). Their approach leads to a deterministic integro-differential equation which, apparently, has the advantage of by-passing the solution to the Riccati ODE obtained by the standard Feynman-Kac argument. In the generic multi-dimensional case, we find a procedure to reduce such integro-differential equation to a non linear matrix ODE. We prove that its solution does necessarily require the solution of the vector Riccati ODE. This result is obtained proving an extension of the celebrated Radon Lemma, which allows us to highlight a deep relation between the geometry of the Riccati flow and the stochastic calculus of variations for an ATSM. We are grateful to two anonymous referees for their careful reading of the paper.     

On the relationship between product substitutability and tacit collusion

This paper examines the effect of increased product substitutability on quantity‐setting firms’ ability to sustain tacit collusion in a market. It uses a general demand function and the trigger strategy of Friedman (Friedman JW. 1971. A non‐cooperative equilibrium for supergames. Review of Economic Studies 38: 1–12) to show that while increased product substitutability hinders sustainability of tacit collusion in the case of linear and concave demand functions, it may either hinder or facilitate firms’ ability to sustain tacit collusion in the case of convex demand functions. Thus, this paper adds to the growing view that one must use a case‐by‐case analysis in judging whether firms in more homogenous product markets find it easier or harder to tacitly collude. Copyright © 1999 John Wiley & Sons, Ltd.