Scale efficiency and homotheticity: equivalence of primal and dual measures

We address the issue of equivalence of primal and dual measures of scale efficiency in general production theory framework. We find that particular types of homotheticity of technologies, which we refer to here as scale homotheticity, provide necessary and sufficient condition for such equivalence. We also identify the case when the scale homotheticity is equivalent to the homothetic structures from Shephard (Theory of cost and production functions, Princeton studies in mathematical economics. Princeton University Press, Princeton, 1970).     

Micro versus macro cointegration in heterogeneous panels

We consider the issue of cross-sectional aggregation in nonstationary and heterogeneous panels where each unit cointegrates. We derive asymptotic properties of the aggregate estimate, and necessary and sufficient conditions for cointegration to hold in the aggregate relationship. We then analyze the case when cointegration does not carry through the aggregation process, and we investigate whether the violation of the formal conditions for perfect aggregation can still lead to an aggregate equation that is observationally equivalent to a cointegrated relationship. We derive a measure of the degree of noncointegration of the aggregate relationship and we explore its asymptotic properties. We propose a valid bootstrap approximation of the test. A Monte Carlo exercise evaluates size and power properties of the bootstrap test.     

When is an aggregate of a time series efficiently forecast by its past?

The paper gives necessary and sufficient conditions for a linear combination of the elements of a vector time series to be efficiently forecast by its own past values, where by past we mean both the infinite and also the finite past. We observe that the problem is equivalent to testing a single element of a vector for exogeneity, this observation also suggesting a method for empirically testing the derived conditions.     

Queues with service speed adaptations

In this paper, we consider various queueing models in which the server can work at two different service speeds. The speed of the server depends on either the number of customers or the workload. Our main interest is in the model in which service speed adaptations can take place only at the arrival instants of an external Poisson observer. Using insightful probabilistic arguments, we give the structure of the steady‐state queue length and workload distributions in the various models. In addition, in case the service speed can only be adapted right after departure instants based on the number of customers, we provide explicit and intuitively appealing expressions for the steady‐state distribution of the number of customers present.     

A Path Construction for the Virtual Waiting Time of an M/G/1 Queue

Consider the M/G/1 queue, the finite dam M/G/1 with capacity T, and the impatient customer M/G/1 model, where customers become lost customers if their waiting time exceeds τ. In this note we prove that for all three models and each xe(0, r) the distribution of the number of downcrossings of the virtual waiting time process with level x during a busy cycle is identical. This implies the weaker statement that on [0, T) the distribution functions of the steady state distributions of the amount of unprocessed work (virtual waiting time) are proportional. A number of applications is given.     

Stochastic stability on general state spaces

This paper studies stochastic stability methods applied to processes on general state spaces. This includes settings in which agents repeatedly interact and choose from an uncountable set of strategies. Dynamics exist for which the stochastically stable states differ from those of any reasonable finite discretization. When there are a finite number of rest points of the unperturbed dynamic, sufficient conditions for analogues of results from the finite state space literature are derived and studied. Illustrative examples are given.     

The no-arbitrage condition and financial markets with heterogeneous information

This paper examines the role of the no-arbitrage condition in financial markets with heterogeneous expectations. We consider a single-period, state-contingent claims model, withM risky securities andS states. There exist two types of heterogeneously informed investors, where the information heterogeneity is defined with respect to either the security payoff matrix, the state probability vector, or state partitions. When the information heterogeneity is defined with respect to either the security payoff matrix or state partitions, the no-arbitrage condition imposes a constraint on the dispersion of information between informed and uninformed investors. Further, the no-arbitrage condition is useful in ascertaining the patterns of heterogeneity among investors that are consistent with equilibrium. However, when the information heterogeneity is defined with respect to state probabilities, the role of the no-arbitrage condition is severely restricted. Finally, the no-arbitrage condition may have important implications for the (necessary and sufficient) conditions for the existence of an equilibrium price vector in financial markets with heterogeneous expectations.     

Strategic Ramsey equilibrium dynamics

We study strategic Ramsey equilibria. First, we give necessary and sufficient conditions for a stationary equilibrium point to exist where only the most patient household owns capital. We develop the dynamics of strategic Ramsey equilibrium trajectories when the turnpike property holds and there is a stationary equilibrium with only the most patient household owning capital. We conclude by showing there is a class of economies for which the turnpike property obtains.     

电信业网间价格歧视的经济学分析——以“集团用户”为例

本文的研究发现,由于网络规模效应的存在,各运营商推行的“集团用户”、“亲情号码”业务使得集团内“大网”对于“小网”客户的吸附作用较为明显,集团内部初始市场份额对运营商有着较为重要的影响,这导致了移动运营商之间的竞争更加激烈;同时指出“集团用户”推出的主要目的是移动运营商争取对方客户,但无形中减少了客户对固定电话的使用,固话成了移动网络竞争的牺牲品,导致移动对固话的替代作用更加明显,以上两方面加剧了中国电信业市场结构的失衡.     

On a class of discrete distributions arising from the birth-death-with-immigration process

This paper considers a class of distributions which may be regarded as the convolution of a negative binomial and a stopped-sum generalized hypergeometric factorial-moment random variables. Some properties are derived and it is shown that this class of distributions is a subset of distributions for the birth-and-death process with immigration (also reversible counter system). Formulations by mixing, limiting distributions and maximum likelihood equations are also discussed.     

Pseudo conditional maximum likelihood estimation of the dynamic logit model for binary panel data

We show how the dynamic logit model for binary panel data may be approximated by a quadratic exponential model. Under the approximating model, simple sufficient statistics exist for the subject-specific parameters introduced to capture the unobserved heterogeneity between subjects. The latter must be distinguished from the state dependence which is accounted for by including the lagged response variable among the regressors. By conditioning on the sufficient statistics, we derive a pseudo conditional likelihood estimator of the structural parameters of the dynamic logit model, which is simple to compute. Asymptotic properties of this estimator are studied in detail. Simulation results show that the estimator is competitive in terms of efficiency with estimators recently proposed in the econometric literature.     

Stable cost sharing in production allocation games

Suppose that a group of agents have demands for some good. Every agent owns a technology which allows them to produce the good, with these technologies varying in their effectiveness. If all technologies exhibit increasing returns to scale (IRS) then it is always efficient to centralize production of the good, whereas efficiency in the case of decreasing returns to scale (DRS) typically requires to spread production. We search for stable cost allocations while differentiating allocations with homogeneous prices, in which all units produced are traded at the same price, from allocations with heterogeneous prices. For the respective cases of IRS or DRS, it is shown that there always exist stable cost sharing rules with homogeneous prices. Finally, in the general framework (under which there may exist no stable allocation at all) we provide a sufficient condition for the existence of stable allocations with homogeneous prices. This condition is shown to be both necessary and sufficient in problems with unitary demands.     

Investments in education and welfare in a two-sector,random matching economy

We consider a random matching model where heterogeneous agents choose optimally to invest time and real resources in education. Generically, there is a steady state equilibrium where some agents, but not all of them, invest. Regular steady state equilibria are constrained inefficient in a strong sense. The Hosios (1990) condition is neither necessary nor sufficient for constrained efficiency. We also provide restrictions on the fundamentals sufficient to guarantee that equilibria are characterized by overeducation (or undereducation), present some results on their comparative statics properties, and discuss the nature of welfare improving policies.     

Processi stocastici semi-markoviani non-omogenei conservativi

In questo lavoro si introduce il concetto di non-omogeneità nei processi stocastici semi-markoviani conservativi. Si dimostra un teorema di esistenza per la soluzione dell’equazione integrale associata al processo. Si studia infine in un caso particolare il comportamento asintotico di tale soluzione.

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Aim of this paper is to state an existence theorem for the integral equation imbedded with a non-homogenous semi-markov process. If some stochasticity conditions are satisfied, the solution is sole. Finally we study the asymptotic behaviour of this solution in a particular case, that is for a class of birth-and-death linear non-homogenous process.

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Lavoro svolto nell’ambito del GNIM-CNR, Sezione problemi non numerici.     

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.     

Financial risk taking in the presence of correlated non-financial background risk

This paper characterizes the stochastic deterioration resulting from taking a zero-mean financial risk in the presence of correlated non-financial background risk. We show in particular that it has an equivalent stochastic order as well as a necessary and sufficient “integral condition” that implies and is implied by a particular sense in which the stochastic deterioration can be decomposed into a “correlation increase” and a “marginal risk increase”. We further characterize a measure of aversion to the stochastic deterioration. These characterizations provide for a more general framework for formulating concepts of increases in risk and correlation and for better understanding risk management decisions governed by individuals’ attitudes to them.     

The geometry of arbitrage and the existence of competitive equilibrium

We present the basic geometry of arbitrage, and use this basic geometry to shed new light on the relationships between various no-arbitrage conditions found in the literature. For example, under very mild conditions, we show that the no-arbitrage conditions of Hart [Journal of Economic Theory 9 (1974) 293] and Werner [Econometrica 55 (1987) 1403] are equivalent and imply the compactness of the set of utility possibilities. Moreover, we show that if agents’ sets of useless net trades are linearly independent, then the Hart–Werner conditions are equivalent to the stronger condition of no-unbounded-arbitrage due to Page [Journal of Economic theory 41 (1987) 392]—and, in turn, all are equivalent to compactness of the set of rational allocations. We also consider the problem of existence of equilibrium. We show, for example, that under a uniformity condition on preferences weaker than Werner’s uniformity condition, the Hart–Werner no-arbitrage conditions are sufficient for existence. With an additional condition of weak no-half-lines—a condition weaker than Werner’s no-half-lines condition—we show that the Hart–Werner conditions are both necessary and sufficient for existence.     

Delay,multiplicity, and non-existence of equilibrium in unanimity bargaining games

We consider a class of perfect information bargaining games with unanimity acceptance rule. The proposer and the order of responding players are determined by the state that evolves stochastically over time. The probability distribution of the state in the next period is determined jointly by the current state and the identity of the player who rejected the current proposal. This protocol encompasses a vast number of special cases studied in the literature. We show that subgame perfect equilibria in pure stationary strategies need not exist. When such equilibria do exist, they may exhibit delay. Limit equilibria as the players become infinitely patient need not be unique.     

A Simple Proof of the Equivalence of the Limiting Distributions of the Continuous-Time and the Embedded Process of the Queue Size in the M/G/1 Queue*

This paper presents an extremely simple proof of the known remarkable fact that for the M/G/1 queue the continuous-time process describing the number of customers in the system has the same limiting distribution as the embedded process describing the number of customers in the system just after service completion epochs.     

Prediction market prices under risk aversion and heterogeneous beliefs

In this paper, we examine the properties of prediction market prices when risk averse traders have heterogeneous beliefs in state probabilities. We show that the equilibrium state prices equal the mean beliefs of traders about that state if and only if the traders’ common utility function is logarithmic. We also provide a necessary and sufficient condition ensuring that the state prices are systematically below or above the mean beliefs of traders, thus providing a rational explanation to the favorite-longshot bias in prediction markets.