Simultaneous optimal estimation in linear mixed models

Simultaneous optimal estimation in linear mixed models is considered. A necessary and sufficient condition is presented for the least squares estimator of the fixed effects and the analysis of variance estimator of the variance components to be of uniformly minimum variance simultaneously in a general variance components model. That is, the matrix obtained by orthogonally projecting the covariance matrix onto the orthogonal complement space of the column space of the design matrix is symmetric, each eigenvalue of the matrix is a linear combinations of the variance components and the number of all distinct eigenvalues of the matrix is equal to the the number of the variance components. Under this condition, uniformly optimal unbiased tests and uniformly most accurate unbiased confidence intervals are constructed for the parameters of interest. A necessary and sufficient condition is also given for the equivalence of several common estimators of variance components. Two examples of their application are given.     

Some further remarks on a superiority problem in misspecified restricted singular linear models

Razzaghi (1987) examined the difference of covariance matrices of competing estimators in misspecified restricted linear models. Further, Gross, Trenkler and Liski (1998) extended Razzaghi's result by asserting his sufficient condition for nonnegative definiteness of the covariance matrix difference to be also necessary. In this paper, when the covariance matrix of the disturbance vector is nonnegative definite, the necessary and sufficient conditions for nonnegative definiteness of the covariance matrix difference are derived. So above results are strengthened. Received: February 1999     

Bayesian Nash equilibrium and variational inequalities

This paper provides a sufficient condition for the existence and uniqueness of a Bayesian Nash equilibrium by regarding it as a solution of a variational inequality. The payoff gradient of a game is defined as a vector whose component is a partial derivative of each player’s payoff function with respect to the player’s own action. If the Jacobian matrix of the payoff gradient is negative definite for each state, then a Bayesian Nash equilibrium is unique. This result unifies and generalizes the uniqueness of an equilibrium in a complete information game by Rosen (1965) and that in a team by Radner (1962). In a Bayesian game played on a network, the Jacobian matrix of the payoff gradient coincides with the weighted adjacency matrix of the underlying graph.     

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.     

A Triangularization Algorithm without Ringshift Permutation

Triangularization methods which have provided a tool for studying the production structure of an economy are considered. The previous triangularization methods are founded on a permutation theorem which defines a necessary condition to the triangularization problem: to permute the industries in an input–output matrix so as to maximize the sum of the below-diagonal elements. This paper shows that a sufficient condition can also be defined in a branch and bound state. Consequently, a powerful triangularization algorithm can be formulated.     

A necessary and sufficient condition for an NTU fuzzy game to have a non-empty fuzzy core

In 2004, Predtetchinski and Herings [A. Predtetchinski, P.J.J. Herings, “A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game”, Journal of Economic Theory 116 (2004) 84–92] provided a necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game. In this paper, we extend this theorem to its counterpart in fuzzy games and give a necessary and sufficient condition for a non-transferable utility fuzzy game to have a non-empty fuzzy core. As a consequence, we derive a necessary and sufficient condition for non-emptiness of the fuzzy core of a TU fuzzy game.     

Non-normal bivariate densities with normal marginals and linear regression functions *

Summary It is well known that for a bivariate density in order to be bivariate normal, the possession of univariate normal marginal densities alone is not sufficient. In this paper it will be shown by means of some counterexamples that the additional requirement of linearity of the regression functions does not supply a sufficient condition either.     

Several efficient two-step estimators for the dynamic simultaneous equations model with autoregressive disturbances

Several asymptotically efficient methods are suggested on both the full and the limited information approach to estimate the simultaneous equations model in which the lagged endogenous variables and the autoregressive disturbances coexist. They are two-step procedures and do not involve iterations. A method is suggested also for the case where any portion of the autoregressive parameter matrix is specified to be zero. Since the consistency and efficiency depend upon the asymptotic, local identifiability, the necessary and sufficient condition is derived for it. It does not depend on the exclusion of the lagged endogenous variables.     

一类与工程设计相关的Jacobi矩阵逆特征值问题

Jacobi矩阵逆特征值问题,在振动工程、结构设计、工程设计应用和系数参数识别等领域有重要应用,文章考虑了由混合型特征对构造一个Jacobi矩阵的问题,给出了问题有唯一解的充分必要条件。     

DISTRIBUTIONAL INVARIANCE AND THE DESIGN OF SAMS

The decomposition of a matrix multiplier derived from a social accounting matrix (SAM) by Pyatt and Round [(1979). Accounting and Fixed Price Multipliers in a Social Accounting Matrix Framework. Economic Journal, 89, 850–873] has prompted a number of subsequent applications. In one of the earliest examples Stone [(1985). The Disaggregation of the Household Sector in the National Accounts, Chapter 8. In: G. Pyatt and J.I. Round (eds.) Social Accounting Matrices: A Basis for Planning. Washington, DC, The World Bank, 145–185] made the intriguing observation that the higher order (circular) effects of an exogenous change in final demand on the distribution of income and the structure of production were more or less independent of the sectoral composition of the initial injection. Our initial objective in this article is to explore this phenomenon of distributional invariance and to derive sufficient conditions for it. We then argue that these conditions have important implications for the design of SAMs, for the taxonomies they adopt and for levels of disaggregation, all of which strongly condition the quality of results that can be generated via subsequent modelling.     

Equality of opportunity and the alignment of incentives

Under what conditions are the incentives of the members of society more aligned? We address this question in a setup in which individuals choose a policy without knowing who will benefit and who will be hurt by each policy. Our central result identifies a sufficient condition for a measure of disagreement in society, which has been linked to the equilibrium level of rent-seeking, to weakly decrease. This sufficient condition captures increasing equality of opportunity in a specific sense.     

Exogeneity in Vector Error Correction Models with Purely Exogenous Long-Run Paths

Existing exogeneity conditions of literature are only sufficient and imply 'overly strong' constraints on long-run parameters. This paper presents some new results on exogeneity in vector error correction models. A key concept of the analysis is the 'purely exogenous long-run path', i.e. a cointegrating vector only including 'exogenous' variables. Extending earlier results of Johansen, S. (1992). 'Cointegration in partial systems and the efficiency of single-equation analysis', Journal of Econometrics , Vol. 52, pp. 389–402 and of Toda and Phillips (1991) . Vector Autoregressions and Causality , Cowles Foundation Discussion Paper, No. 977 among others, we propose a framework based on two canonical representations of the long-run matrix, which can constitute a suitable basis to formulate a necessary and sufficient condition for non-causality as well as a condition for strong exogeneity. An interesting property is that the statistics involved in the sequential procedures for testing these conditions are distributed as χ ² variables and can, therefore, easily be calculated with the usual statistical computer packages, which makes our approach fully operational, empirically. Finally, the power and size distortions of the sequential test procedures are analysed using Monte Carlo experiments.     

The Ignored Performance Measure

This paper studies a setting in which a risk-averse agent must be motivated to work on two tasks: evaluating a potential project and, if the project is adopted, implementing it. Although a performance measure that is informative of an agent's action is typically valuable because it can be used to improve the risk sharing of the contract, this is not necessarily the case in this two-task setting. I provide a sufficient condition under which a performance measure that is informative of the agent's implementation effort is worthless for contracting despite the agent being risk averse. This shows that information content is a necessary but not a sufficient condition for a performance measure to be valuable.     

A theorem on the additivity of the quasi-concave closure of an additive convex function

In this paper a necessary and sufficient condition for the additivity of the quasi-concave closure of an additive convex function is given.     

Necessary and sufficient conditions for consistency of generalizedM-estimates

GeneralizedM-estimates (minimum contrast estimates) and their asymptotically equivalent approximate versions are considered. A relatively simple condition is found which is equivalent with consistency of all approximateM-estimates under wide assumptions about the model. This condition is applied in several directions. (i) A more easily verifiable condition equivalent with consistency of all approximateM-estimates is derived and illustrated on models with stationary and ergodic observations. (ii) A condition sufficient for inconsistency of all approximateM-estimates is obtained and illustrated on models with i.i.d. observations. (iii) A simple necessary and sufficient condition for consistency of all approximateM-estimates in linear regression with i.i.d. errors is found. This condition is weaker than sufficient conditions for consistency ofM-estimators known from the literature. A linear regression example is presented where theM-estimate is consistent and an approximateM-estimate is incosistent.Supported by CSAS grant N. 17503.     

Multilateral negotiations and formation of coalitions

This paper analyses properties of games modeling multilateral negotiations leading to the formation of coalitions in an environment with widespread externalities. The payoff generated by each coalition is determined by an exogenous partition function (the parameter space). We show that in almost all games, except in a set of measure zero of the parameter space, the Markov perfect equilibrium value of coalitions and the state transition probability that describe the path of coalition formation is locally unique and stable. Therefore, comparative statics analysis are well-defined and can be performed using standard calculus tools. Global uniqueness does not hold in general, but the number of equilibria is finite and odd. In addition, a sufficient condition for global uniqueness is derived, and using this sufficient condition we show that there is a globally unique equilibrium in three-player superadditive games.     

Existence of optimal strategies in linear multisector models with several consumption goods

In this paper, we give a sufficient and almost necessary condition for the existence of optimal strategies in linear multisector models when time is continuous.     

一类积分微分不等式的振动性

研究了一类二阶积分微分不等式的振动性问题。首先利用Lebesgue控制收敛定理研究了其正解的存在性;接着得到了其不存在正解的条件;最后通过讨论给出了其解振动的充要条件。     

Combining Significance of Correlated Statistics with Application to Panel Data*

The inverse normal method, which is used to combine P‐values from a series of statistical tests, requires independence of single test statistics in order to obtain asymptotic normality of the joint test statistic. The paper discusses the modification by Hartung (1999, Biometrical Journal, Vol. 41, pp. 849–855) , which is designed to allow for a certain correlation matrix of the transformed P‐values. First, the modified inverse normal method is shown here to be valid with more general correlation matrices. Secondly, a necessary and sufficient condition for (asymptotic) normality is provided, using the copula approach. Thirdly, applications to panels of cross‐correlated time series, stationary as well as integrated, are considered. The behaviour of the modified inverse normal method is quantified by means of Monte Carlo experiments.     

On the Relationship Between Validity and Power

This article examines the relationship between predictive validity and statistical power. It is shown that higher validity may be associated with scales exhibiting lower power, whereas higher power may be warranted for scales possessing lower validity. High validity is in general neither a necessary nor sufficient condition for high power with scales contemplated for use as dependent variables in social science research. Conversely, high power is neither necessary nor sufficient for high validity. A numerical example illustrates this interrelation.