On the generalized principal-agent problem: Decomposition and existence results

This paper addresses the class of generalized agency problems: situations in which adverse selection and moral hazard are jointly present. We present a decomposition of the principal's optimization problem under the first-order approach that sheds light on the interactions between the two types of private information, and also significantly improves tractability. We use the decomposition to (1) provide examples of closed form solutions of the optimal contract, and (2) analyze the existence of optimal contracts. We also show that the first-order approach is valid in generalized agency problems if the production technology satisfies the linear distribution function condition (LDFC) in actions and types. For more general production technologies the Mirrlees-Rogerson sufficient conditions need to be extended to include restrictions on the form of the optimal contract. Received: 11 August 1997 / 26 September 1999     

Stock Prices and the Real Economy: Power Law versus Exponential Distributions

This paper explores the relationship between the stock prices and the real economy. The standard approach – the so called consumption-based asset pricing model – attempts to explain it based on the assumption of the representative agent. In this paper, we argue that the representative agent assumption is fundamentally flawed. Drawing on the recent advancement of “econophysics” on financial markets See Mantegna and Stanley (An Introduction to econophysics: correlations and complexity in finance, 2000) for the introduction to econophysics, we argue that in contrast to the neoclassical view, there is in fact a wedge between financial markets, the stock prices in particular, and the real economy.     

Contracting with Private Knowledge of Production Capacity

We analyze the design of procurement contracts when the supplier is privately informed about both his innate production capacity (K) and his innate unit cost of production. We identify conditions under which the supplier will strategically employ an inefficient production technology to expand output above K. We also show that when the buyer employs the simple fixed‐price cost‐reimbursement (FPCR) contracts in the setting examined by Rogerson (2003), the supplier has no incentive to exaggerate K. Furthermore, the buyer can secure with FPCR contracts at least 75% of the surplus she secures with fully optimal contracts.     

Information Matrices for Non Full Rank Subsystems

Consider the standard linear model Y=X θ + ε. If the parameter of interest is a full rank subsystem K′θ of mean parameters, the associated information matrix can be defined via an extremal representation. For rank deficient subsystems, Pukelsheim (1993) introduced the notion of generalized information matrices that inherit many properties of the information matrices. However, this notion is not a direct extension of the full rank case in the sense that the definition of the generalized information matrix applied to full rank subsystems does not lead to the usual information matrix. In this paper, we propose a definition of the information matrix via an extremal representation that encompasses the full rank and the non-full rank cases. We also study its properties and show its links with the generalized information matrices.     

Non-self-averaging of a two-person game with only positive spillover: a new formulation of Avatamsaka’s dilemma

In this game [Aruka in Avatamsaka game structure and experiment on the web. In: Aruka Y (ed) Evolutionary controversies in economics. Springer, Tokyo, pp 115–132, 2001], selfishness may not be determined even if an agent selfishly adopts the strategy of defection. Individual selfishness can only be realized if the other agent cooperates, therefore gain from defection can never be assured by defection alone. The sanction by defection as a reaction of the rival agent cannot necessarily reduce the selfishness of the rival. In this game, explicit direct reciprocity cannot be guaranteed. Now we introduce different spillovers or payoff matrices, so that each agent may then be faced with a different payoff matrix. A ball in the urn is interpreted as the number of cooperators, and the urn as a payoff matrix. We apply Ewens’ sampling formula to our urn process in this game theoretic environment. In this case, there is a similar result as in the classic case, because there is “self-averaging” for the variances of the number who cooperate. Applying Pitman’s sampling formula to the urn process, the invariance of the random partition vectors under the properties of exchangeability and size-biased permutation does not hold in general. Pitman’s sampling formula depends on the two-parameter Poisson–Dirichlet distribution whose special case is just Ewens’ formula. In the Ewens setting, only one probability α of a new entry matters. On the other hand, there is an additional probability θ of an unknown entry, as will be argued in the Pitman formula. More concretely, we will investigate the effects of different payoff sizes from playing a series of different games for newly emerging agents. As Aoki and Yoshikawa (Non-self-averaging in macroeconomic models: a criticism of modern micro-founded macroeconomics, Economics Discussion Papers 2007-49. . November 26, 2007) and Aoki (J Econ Interact Coord 3:1–3, 2008) dealt with a product innovation and a process innovation, they criticized Lucas’ representative method and the idea that players face micro shocks drawn from the same unchanged probability distribution. In the light of Aoki and Yoshikawa (Non-self-averaging in macroeconomic models: a criticism of modern micro-founded macroeconomics, Economics Discussion Papers 2007-49. . November 26, 2007), we show the same argument in our Avatamsaka game with different payoffs. In this setting, innovations occurring in urns may be regarded as increases of the number of cooperators in urns whose payoffs are different.     

供应链委托代理问题的一阶有效性研究

供应链的最优契约设计经常可以归结为一个委托代理问题．该问题所涉及的模型是一个特殊形式的二层优化问题。目前对该问题的研究非常困难。在经济学领域，解决委托代理模型常用的方法是一阶条件方法，但该方法通常是无效的。文章的主要创新点在于给出了两类满足单调似然率（MLRP）和凸性条件（CDFC）概率分布函数，这两类函数是满足一阶条件的。文章的研究拓广了一阶条件方法有效性的应用范围。     

An approach to fuzzy hypothesis testing

In this paper an approach is presented how to test fuzzily formulated hypotheses with crisp data. The quantitiesα andβ, the probabilities of the errors of type I and of type II, are suitably generalized and the concept of a best test is introduced. Within the framework of a one-parameter exponential distribution family the search for a best test is considerably reduced. Furthermore, it is shown under very weak conditions thatα andβ can simultaneously be diminished by increasing the sample size even in the case of testingH ₀ against the omnibus alternativeH ₁: notH ₀, a result completely different from the case of crisp setsH ₀ andH ₁: notH ₀.     

A note on connections among criteria for asymmetrical factorials

Various optimal criteria have been proposed to rank asymmetrical fractional factorial designs. Among them, the generalized minimum aberration and the minimum moment aberration criteria are the most popular ones and have received much attention. Recently, Liu et al. (Stat Sin 16:1285–1297, 2006) proposed the minimum χ ² criterion in terms of level-combinations. In this paper, the equivalency of the generalized minimum aberration and the minimum χ ² criteria is reported, which not only provides another justification for each other but also develops some theoretical results for designs with generalized minimum aberration and some lower bounds for the generalized wordlength pattern. Besides, an analytic relationship between generalized minimum aberration and minimum moment aberration is obtained for asymmetrical fractional factorial designs.     

Determinants of Economic Interaction: Behavior or Structure

Experimental economics originated as examination of the behavior of aggregate phenomena, especially markets, populated by human participants motivated by their desire to attain their goals. The past two decades have brought two newer trends. One is a gradual but steady shift in the focus of the questions sought to be addressed through human experiments towards examination of micro level phenomena – individual preferences and behavior. The second is the expansion in the role of computer simulations to examine questions about aggregate level phenomena. This shift to individual behavior has accentuated the ever-present dilemma of social sciences in trying to be a science on one hand, and to understand our own self-conscious selves – human beings – on the other. To address this dilemma, it would be useful to recognize three streams of experimental economics: (1) macro stream to examine the properties of social structures, (2) micro stream to examine the behavior of individuals, and (3) agent stream to explore the links between the micro and macro phenomena using computer simulations. At least the structural stream can be firmly rooted in the tradition of sciences (bypassing the free-will dilemma of social sciences), while the agent stream can span the gap between the behavioral and structural streams.The author is thankful to Dorota Dobija and Juergen Huber for their helpful comments. Science does not know its debt to imagination. – Ralph Waldo Emerson Vivisection is a social evil because if it advances human knowledge, it does so at the expense of human character. – George Bernard Shaw The theoretical broadening which comes from having many humanities subjects on the campus is offset by the general dopiness of the people who study these things. – Richard P. Feynman Economics has an amazing capacity to summarize staggeringly complex phenomena by the application of only a handful of principles. – Charles R. Plott Being outside and above individual and local contingencies, collective consciousness sees things only in their permanent and fundamental aspects, which it crystallizes in ideas that can be communicated. – Emile Durkheim     

Mixture sets on finite domains

Mixture sets were introduced by Herstein and Milnor (Econometrica 21:291–297, 1953) to prove a generalised expected utility theorem. Mixture sets provide an axiomatisation of convexity suitable for discrete, as well as continuous, environments (Mongin in Decis Econ Finance 24:59–69, 2001). However, the nature of mixture sets over finite domains has been little studied. In this paper, we provide a complete characterisation. More recently, another abstract convex structure for finite domains, the antimatroid, has appeared in the literature on decision theory and social choice. The relationship between mixture sets and antimatroids has not previously been explored. We show here that neither concept is a special case of the other.     

The GMLE based Buckley–James estimator with modified case–cohort data

We consider the estimation problem under the linear regression model with the modified case–cohort design. The extensions of the Buckley–James estimator (BJE) under the case–cohort designs have been studied under an additional assumption that the censoring variable and the covariate are independent. If this assumption is violated, as is the case in a typical real data set in the literature, our simulation results suggest that those extensions are not consistent and we propose a new extension. Our estimator is based on the generalized maximum likelihood estimator (GMLE) of the underlying distributions. We propose a self-consistent algorithm, which is quite different from the one for multivariate interval-censored data. We also show that under certain regularity conditions, the GMLE and the BJE are consistent and asymptotically normally distributed. Some simulation results are presented. The BJE is also applied to the real data set in the literature.     

On bootstrapping periodic random arrays with increasing period

The aim of the paper is to determine when the periodic block bootstrap, procedure introduced by Chan et al. (Technometrics 46(2):215–224, 2004), can be applied to arrays of random variables. Formal consistency is obtained under α-mixing or m-dependence conditions together with the assumption that the length of the period tends to infinity. On the other hand, if the period is constant, inconsistency is shown. The performance of periodic block bootstrap is also compared in simulations with moving block bootstrap. It is suggested that for the case of long-period data the first method is more effective and much more stable with respect to the length of the block size.     

Bayesian U-type design for nonparametric response surface prediction

This paper deals with Bayesian design over U-type designs of n runs and s factors with q levels for nonparametric response surface prediction. The criterion is developed in terms of the asymptotic approach of Mitchell et al. (Ann Statist 22: 634–651, 1994) for a specific covariance kernel. An optimal design is given in approximate design theory over the all level combinations. A connection with orthogonality and aberration is established. A lower bound for the criterion is provided, and numerical results show that this lower bound is tight.     

Inference on Reliability in Two-parameter Exponential Stress–strength Model

The problem of hypothesis testing and interval estimation of the reliability parameter in a stress–strength model involving two-parameter exponential distributions is considered. Test and interval estimation procedures based on the generalized variable approach are given. Statistical properties of the generalized variable approach and an asymptotic method are evaluated by Monte Carlo simulation. Simulation studies show that the proposed generalized variable approach is satisfactory for practical applications while the asymptotic approach is not satisfactory even for large samples. The results are illustrated using simulated data.     

On sequential comparisons of means of first-order autoregressive models

The problem of estimating a linear combination,μ, of means ofp-independent, first-order autoregressive models is considered. Sequential procedures are derived (i) to estimateμ pointwise using the linear combination of sample means, subject to a loss function (squared error plus cost per observation), and (ii) to arrive at a fixed-width confidence interval forμ. It is observed that in the case of point estimation we do not require a sampling scheme, where as in the case of interval estimation we do require a sampling scheme and a scheme similar to the one given in Mukhopadhyay and Liberman (1989) is proposed. All the first order efficiency properties of the sequential procedures involved here are derived. This paper is an extension of results of Sriram (1987) involving one time series to multiple time series. Research supported by AFOSR Grant number 89-0225.     

Elasticities of Substitution and Complementarity: A Synthesis

We derive the relationships between the net and gross elasticities of substitution and complementarity (i.e., the elasticities that refer either to the conditional or unconditional, direct or inverse demand system) in the general case of non-homothetic, variable-returns-to-scale technologies. We also show that the so-called Hicks Elasticity of Complementarity (Hicks, Oxford economic Papers 22, 289–296 (1970)) is dual to a full-fledged elasticity of gross input substitution that we call the Hotelling/Lau Elasticity of Substitution (Lau, Production Economics: A Dual Approach to Theory and Applications. Amsterdam: North-Holand (1978)). The former is, in fact, the proper elasticity of substitution in the case of the inverse, unconditional input demand. Our results should clarify some issues about the input substitutability classification.     

Response of double-auction markets to instantaneous Selling�CBuying signals with stochastic Bid�CAsk spread

Statistical properties of order-driven double-auction markets with Bid–Ask spread are investigated through the dynamical quantities such as response function. We first attempt to utilize the so-called Madhavan–Richardson–Roomans model (MRR for short) to simulate the stochastic process of the price-change in empirical data sets (say, EUR/JPY or USD/JPY exchange rates) in which the Bid–Ask spread fluctuates in time. We find that the MRR theory apparently fails to simulate so much as the qualitative behaviour (‘non-monotonic’ behaviour) of the response function R(l) (l denotes the difference of times at which the response function is evaluated) calculated from the data. Especially, we confirm that the stochastic nature of the Bid–Ask spread causes apparent deviations from a linear relationship between the R(l) and the auto-correlation function C(l), namely, R(l) μ -C(l){R(l) \propto -C(l)}. To make the microscopic model of double-auction markets having stochastic Bid–Ask spread, we use the minority game with a finite market history length and find numerically that appropriate extension of the game shows quite similar behaviour of the response function to the empirical evidence. We also reveal that the minority game modeling with the adaptive (‘annealed’) look-up table reproduces the non-linear relationship R(l) μ -f(C(l)){R(l) \propto -f(C(l))} (f(x) stands for a non-linear function leading to ‘λ-shapes’) more effectively than the fixed (‘quenched’) look-up table does.     

A conditional distribution approach to uniform sampling on spheres and balls in Lp spaces

Liang and Ng (Metrika 68:83–98, 2008) proposed a componentwise conditional distribution method for L _p -uniform sampling on L _p -norm n-spheres. On the basis of properties of a special family of L _p -norm spherical distributions we suggest a wide class of algorithms for sampling uniformly distributed points on n-spheres and n-balls in L _p spaces, generalizing the approach of Harman and Lacko (J Multivar Anal 101:2297–2304, 2010), and including the method of Liang and Ng as a special case. We also present results of a numerical study proving that the choice of the best algorithm from the class significantly depends on the value of p.     

Stochastic FDH/DEA estimators for frontier analysis

In this paper we extend the work of Simar (J Product Ananl 28:183–201, 2007) introducing noise in nonparametric frontier models. We develop an approach that synthesizes the best features of the two main methods in the estimation of production efficiency. Specifically, our approach first allows for statistical noise, similar to Stochastic frontier analysis (even in a more flexible way), and second, it allows modelling multiple-inputs-multiple-outputs technologies without imposing parametric assumptions on production relationship, similar to what is done in non-parametric methods, like Data Envelopment Analysis (DEA), Free Disposal Hull (FDH), etc.... The methodology is based on the theory of local maximum likelihood estimation and extends recent works of Kumbhakar et al. (J Econom 137(1):1–27, 2007) and Park et al. (J Econom 146:185–198, 2008). Our method is suitable for modelling and estimation of the marginal effects onto inefficiency level jointly with estimation of marginal effects of input. The approach is robust to heteroskedastic cases and to various (unknown) distributions of statistical noise and inefficiency, despite assuming simple anchorage models. The method also improves DEA/FDH estimators, by allowing them to be quite robust to statistical noise and especially to outliers, which were the main problems of the original DEA/FDH estimators. The procedure shows great performance for various simulated cases and is also illustrated for some real data sets. Even in the single-output case, our simulated examples show that our stochastic DEA/FDH improves the Kumbhakar et al. (J Econom 137(1):1–27, 2007) method, by making the resulting frontier smoother, monotonic and, if we wish, concave.     

Optimal extended complete block designs for dependent observations

Optimal designs under general dependence structures are usually difficult to specify theoretically or find algorithmically. However, they can sometimes be found for a specific dependence structure and a particular parameter value. In this paper, a class of generalized binary block designs with t treatments and b blocks of size k>t is considered. Each block consists of h consecutive complete blocks and, at the end, an incomplete block of size k−ht (if k > ht). For a suitable number of blocks, a universally optimal design is found for a first-order stationary autoregressive process with positive correlations. Optimal generalized binary designs and balanced block designs are also considered. Some constructions for a universally optimal design are described. A negative dependence parameter, and some other dependence structures, are also considered.