Representing preferences with nontransitive indifference by a single real-valued function

Let be an interval order on a topological space (X, τ), and let x _˜^* y if and only if [y z x z], and x _˜^** y if and only if [z x z y]. Then _˜^* and _˜^** are complete preorders. In the particular case when is a semiorder, let x _˜⁰ y if and only if x _˜^* y and x _˜^** y. Then _˜⁰ is a complete preorder, too. We present sufficient conditions for the existence of continuous utility functions representing _˜^*, _˜^** and _˜⁰, by using the notion of strong separability of a preference relation, which was introduced by Chateauneuf (Journal of Mathematical Economics, 1987, 16, 139–146). Finally, we discuss the existence of a pair of continuous functions u, υ representing a strongly separable interval order on a measurable topological space (X, τ, μ, ).     

Distribution of correlation coefficient under mixture normal model

The present paper obtains the nonnull distribution of the product moment correlation coefficient r when sample is drawn from a mixture of two bivariate Gaussian distributions. The moments of 1−r ² have been used to derive the nonnull density of r. Received September 2000     

Continua of stochastic dominance relations for bounded probability distributions

Let P={F,G,…} be the set of probability distribution functions on [0,b]. For each αε[1, ∞), F_αG means that ∫^x_o(x−y^α−1dF(y)∫^x_o(x−y)^α−1dG(y) for all xε[0, b], and F>_αG means that F_αG and F≠G. Each _α is reflexive and transitive and each>_α is asymmetric and transitive. Both _α and>_α increase as α increases but their limits are not complete. A class U_α of utility functions is defined to give F>_αG iff ∫udF>∫udG for all uεU_α. These classes decrease as α increases, and their limit is empty. Similar decreasing classes are defined for each _α, and their limit is essentially the constant functions on (0, b].     

Continua of stochastic dominance relations for unbounded probability distributions

Let P = {F,G,…} be the set of all probability distribution functions with support (0, ∞). An unrestricted stochastic dominance relation>_∞ is defined on P for each real ∞ 1, where F >_∞ G means that ^x_y = 0 (x - y)^{∞ - 1} dG(y) ^x_{n = 0}(x − y)^∞−1 dG(y) for all ∞ 0, with < for some x. These relations are partial orders that increase as ∞ increases with limit relation>_∞. A class U_∞ of utility functions u on (0, ∞) is defined in such a way that F >_∞ G iff udF > udG for all u ε U_∞. The U_∞ decrease as ∞ increases and have a non-empty intersection U_∞. Each u ε U_∞ is an increasing function that has derivatives of all orders that alternate in sign. Criteria which tell when F eventually dominates G in the sense of F >_∞ G are noted. Comparisons with bounded stochastic dominance results are made in several places.     

Accessibility of optima in pure exchange economies

Assuming differentiable monotonicity and differentiable convexity of utility functions, we show that if y and z are allocations of a pure exchange economy with z optimal and preferred to y by every agent, then there is a trade curve of finite length from y to z. We make no assumption on utility functions designed to ‘keep away from the boundary’. The conclusion need not hold if z is not optimal, unless a special boundary condition is assumed and (l, m) ≠ (2, 2).     

An alternative approach to housing market segmentation using hedonic price data

Much empirical research has been devoted to housing market segmentation and the implications for the application of the Hedonic Price Model. Market segmentation is demonstrated empirically in (J. Urban Econ., 3:2, 146–166 (1976); J. Urban Econ., 7:1, 102–108 (1980); Rev. Econ. Statist., 66:3, 404–406 (1974)). There appears to be theoretical evidence (J. Pol. Econ., 82:1, 34–55 (1974)) that such empirical efforts may have been less than adequate. Unfortunately, the empirical applications of Rosen's model (J. Environ. Econ. Manag., 5, 81–102 (1978); J. Urban Econ., 5, 3, 357–369 (1978)) do not seem to effectively account for the complexity of the factors which cause multiple equilibria (market segmentation). This paper demonstrates empirically that market segments can be defined along more dimensions than hitherto have been included in any analysis.     

Über eine Variante der empirischen Verteilungsfunktion

Summary If ₁, ₂,..., _n and ₁, ₂,..., _–1 are two ordered samples from a population with continuous distribution functionF(x), then the points ( _r ,r/n),r=1, 2,..., n–1 provide a better approximation ofF(x) than the points ( _r ,r/n),r=1, 2,..., n, in the following sense:A maximal upper deviation and a maximal lower deviation of more theny have — contrary to the points ( _r ,r/n) — equal probability for anyy0, if we deal with the points ( _r ,r/n). This probability is at least for ally in the interval , 1 less than the probability for a maximal upper deviation of more thany in the case of the points ( _r ,r/n). This is shown by a comparison of the Smirnow-Birnbaum-Tingey — formula with an analogous formula for the maximal one-sided deviations of the points( _r ,r/n).     

Problems with detecting assumed mediation using the hierarchical multiple regression strategy

In human resource management (HRM) and allied fields (e.g., organizational behavior, management, and industrial and organizational psychology), tests of mediation are frequently conducted using the hierarchical multiple regression (HMR) strategy of Baron and Kenny [Baron, R. M., & Kenny, D. A. (1986). The moderator–mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, 1173–1182]. Although previous research has identified a number of serious problems with this approach, the present study adds to the literature by identifying yet additional problems with its use in inferring the existence of mediation. Using a statistical simulation, we found that certain patterns of correlation coefficients guarantee inferences about mediation, whereas other patterns preclude such inferences. On the basis of various analyses including logistic regression and inspection of three-dimensional plots, we identified patterns of correlation coefficients needed to satisfy Baron and Kenny's [Baron, R. M., & Kenny, D. A. (1986). The moderator–mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, 1173–1182] conditions for inferring mediation. The same patterns have no necessary relation to actual causal connections among variables in mediation models. Moreover, as a consequence of the failure of the HMR strategy to detect mediating effects, many instances of actual mediation in HRM and allied fields may have gone undetected. In view of the foregoing, we conclude that the HMR strategy should no longer be used in testing for mediation.     

Continuous semiorder representations

Given X,, where X is a topologically connected space and is an asymmetric binary relation, necessary and sufficient conditions are presented for the existence of a continuous representation of the form, u, δ; that is, for x,yX, xy if and only if u(x)>u(y)+δ where u:X→ is continuous and δ is a strictly positive real number. The results are related to existing results for numerical representations of interval orders and semiorders.     

On the upper and lower semicontinuity of the Aumann integral

Let (T,τ,μ) be a finite measure space, X be a Banach space, P be a metric space and let L₁(μ,X) denote the space of equivalence classes of X-valued Bochner integrable functions on (T,τ,μ). We show that if φ:T×P→2^X is a set-valued function such that for each fixed pεP, φ(·,p) has a measurable graph and for each fixed tεT, φ(t,·) is either upper or lower semicontinuous then the Aumann integral of φ, i.e.,∫_Tφ(t,p)dμ(t)= {∫_Tx(t)dμ(t):xεS_φ(p)}, where S_φ(p)= {yεL₁(μ,X):y(t)εφ(t,p)μ−a.e.}, is either upper or lower semicontinuous in the variable p as well. Our results generalize those of Aumann (1965, 1976) who has considered the above problem for X=Rⁿ, and they have useful applications in general equilibrium and game theory.     

Are regulations the answer for emerging stock markets? Evidence from the Czech Republic and Poland

Does the emergence of a stock market require a well-developed legal and/or regulatory system? Although historical work by Neal and Davis [Neal, L., & Davis, L. (2005). The evolution of the rules and regulations of the first emerging markets: The London, New York, and Paris stock exchanges, 1792–1914. Quarterly Review of Economics and Finance, 45, 296–311] and Stringham [Stringham, E. (2003). The extralegal development of securities trading in seventeenth century Amsterdam. Quarterly Review of Economics and Finance, 43, 321–344] suggests that securities markets have successfully developed with little government oversight, numerous authors [including Black, B. (2001). The legal and institutional preconditions for strong securities markets. University of California Law Angeles Law Review, 48, 781–855; Coffee, J. (1999). Privatization and corporate governance: The lessons from securities market failure. Journal of Corporation Law, 25, 1–39; Frye, T. (2000). Brokers and bureaucrats: Building market institutions in Russia. Ann Arbor: University of Michigan Press; Glaeser, E., Johnson, S., & Shleifer, A. (2001). Coase versus the Coasians. Quarterly Journal of Economics, 116, 853–899; Mlčoch, L. (2000). Restructuring of property rights: An institutional view. In L. Mlčoch et al. (Eds.), Economic and Social Changes in Czech Society After 1989. Prague: The Karolinum Press; Pistor, K. (2001). Law as a determinant for equity market development – the experience of transition economies. In Peter Murrell (Ed.), The Value of Law in Transition Economies (pp. 249–287). Ann Arbor: Michigan University Press; Stiglitz, J. (1999). Whither reform. Ten years of the transition. Keynote Address, Annual Bank Conference on Development Economics, Washington, DC, April 28–30, 1999; Zhang, X. (2006). Financial market governance in developing countries: Getting the political underpinnings right. Journal of Developing Societies, 2, 169–196] argue that the Czech Republic and other Eastern European governments need more regulation for their newly created stock markets. They maintain that the Warsaw Stock Exchange, which is seen as more regulated, has outperformed the Prague Stock Exchange which is seen as largely unregulated. Thus increased regulations are a key to increased performance. This article, however, maintains that the evidence from the Czech experience has been misinterpreted. This article provides an in depth case study of the Czech stock market and finds that (a) Czech capital markets have been hindered by government intervention from their beginning, (b) that the evidence on Poland's superior performance is not as strong as suggested, and (c) that Czech regulators seem to be unqualified, lack the proper incentives, and are unlikely to benefit the market. Under these circumstances it appears that Neal and Davis (2005:311) are correct that increased government involvement is unlikely to improve the situation.     

Restricted houseswapping games

Restricted houseswapping games (RHGs) are a generalization of ‘one-sided matching games’, in which we specify a class II* of ‘allowable’ simple trading cycles. The cores of such games may be empty. Given II*, all possible closed RHGs have non-empty cores of II* is ‘strongly balanced’. Examples include the one-sided matching markets (^{Shapley and Scarf. Journal of Mathematical Economics 1974. 1. 23–37}. ^{Tijs et al., OR Spektrum 1984, 6, 119–123}; ^{Quinzii, International Journal of Game Theory 1984, 13, 41–60}) and the two-sided matching markets (^{Gale and Shapley. American Mathematical Monthly 1962. 69, 9–16}; ^{Shapley and Shubik, International Journal of Game Theory 1972, 1, 111–130}: and ^{Demange and Gale Econometrica 1985, 53, 873–888}).We then consider the subclass of RHGs in which there is no transferable resource. In this case, a weaker condition on II*, called ‘weak balancedness’, is sufficient to guarantee core non-emptiness. In addition, if II* is not weakly balanced, then there exists a preference profile such that the strict core of the resultant game is empty.Several other examples are given of II* that are (a) strongly balanced: (b) weakly balanced but not strongly balanced: and (c) not even weakly balanced.Finally, we discuss the issues of equilibrium definition, existence, and core-equilibrium allocation equivalence in RHGs.     

A view on Bhattacharyya bounds for inverse Gaussian distributions

Shanbhag (J Appl Probab 9:580–587, 1972; Theory Probab Appl 24:430–433, 1979) showed that the diagonality of the Bhattacharyya matrix characterizes the set of Normal, Poisson, Binomial, negative Binomial, Gamma or Meixner hypergeometric distributions. In this note, using Shanbhag (J Appl Probab 9:580–587, 1972; Theory Probab Appl 24:430–433, 1979) and Pommeret (J Multivar Anal 63:105–118, 1997) techniques, we evaluated the general form of the 5 × 5 Bhattacharyya matrix in the natural exponential family satisfying f(x|q)=\fracexp{xg(q)}b(g(q))y(x){f(x|\theta)=\frac{\exp\{xg(\theta)\}}{\beta(g(\theta))}\psi(x)} with cubic variance function (NEF-CVF) of θ. We see that the matrix is not diagonal like distribution with quadratic variance function and has off-diagonal elements. In addition, we calculate the 5 × 5 Bhattacharyya matrix for inverse Gaussian distribution and evaluated different Bhattacharyya bounds for the variance of estimator of the failure rate, coefficient of variation, mode and moment generating function due to inverse Gaussian distribution.     

A note on strategies for bandit problems with infinitely many arms

A bandit problem consisting of a sequence of n choices (n) from a number of infinitely many Bernoulli arms is considered. The parameters of Bernoulli arms are independent and identically distributed random variables from a common distribution F on the interval [0,1] and F is continuous with F(0)=0 and F(1)=1. The goal is to investigate the asymptotic expected failure rates of k-failure strategies, and obtain a lower bound for the expected failure proportion over all strategies presented in Berry et al. (1997). We show that the asymptotic expected failure rates of k-failure strategies when 0<b1 and a lower bound can be evaluated if the limit of the ratio F(1)–F(t) versus (1–t)^b exists as t1^– for some b>0.     

Discrete choice modeling with nonstationary panels applied to exchange rate regime choice

This paper develops a regression limit theory for discrete choice nonstationary panels with large cross section (N) and time series (T) dimensions. Some results emerging from this theory are directly applicable in the wider context of M-estimation. This includes an extension of work by Wooldridge [Wooldridge, J.M., 1994. Estimation and Inference for Dependent Processes. In: Engle, R.F., McFadden, D.L. (Eds.). Handbook of Econometrics, vol. 4, North-Holland, Amsterdam] on the limit theory of local extremum estimators to multi-indexed processes in nonlinear nonstationary panel data models.It is shown that the maximum likelihood (ML) estimator is consistent without an incidental parameters problem and has a limit theory with a fast rate of convergence N^1/2T^3/4 (in the stationary case, the rate is N^1/2T^1/2) for the regression coefficients and thresholds, and a normal limit distribution. In contrast, the limit distribution is known to be mixed normal in time series modeling, as shown in [Park, J.Y., Phillips, P.C.B., 2000, Nonstationary binary choice. Econometrica, 68, 1249–1280] (hereafter PP), and [Phillips, P.C.B., Jin, S., Hu, L., 2007. Nonstationary discrete choice: A corrigendum and addendum. Journal of Econometrics 141(2), 1115–1130] (hereafter, PJH).The approach is applied to exchange rate regime choice by monetary authorities, and we provide an analysis of the empirical phenomenon known as “fear of floating”.     

A fuzzy-QFD approach to supplier selection

This article suggests a new method that transfers the house of quality (HOQ) approach typical of quality function deployment (QFD) problems to the supplier selection process. To test its efficacy, the method is applied to a supplier selection process for a medium-to-large industry that manufactures complete clutch couplings.The study starts by identifying the features that the purchased product should have (internal variables “WHAT”) in order to satisfy the company's needs, then it seeks to establish the relevant supplier assessment criteria (external variables “HOW”) in order to come up with a final ranking based on the fuzzy suitability index (FSI). The whole procedure was implemented using fuzzy numbers; the application of a fuzzy algorithm allowed the company to define by means of linguistic variables the relative importance of the “WHAT”, the “HOW”–“WHAT” correlation scores, the resulting weights of the “HOW” and the impact of each potential supplier.Special attention is paid to the various subjective assessments in the HOQ process, and symmetrical triangular fuzzy numbers are suggested to capture the vagueness in people's verbal assessments.     

Controlling for Burnout in Estimating Mortgage Prepayment Models

Burnout is a consequence of unobservable predictive variables. This paper describes a methodology for estimating mortgage prepayment models which corrects for burnout. The paper generalizes the approach of Deng, Quigley, and Van Order (Econometrica, 68, 275–307, 1998) and Stanton (Rev. Finan. Stud.8, 677–708, 1995) in modeling the impact of unobservable variables as a probability distribution. The estimator is applied to a sample of loan histories and the results compared to a conventional logit analysis of the data. Predictions and simulations from both models are compared to illustrate the properties of the new estimator.     

Die messende Prüfung bei Abweichung von der Normalverteilungsannahme

Summary For sampling inspection by variables in the one-sided case (item bad if variablex>a) under the usual assumption of normality with known variance ₂ the operating characteristic is given by , wherep denotes the fraction defective. If instead of a normal distribution ((·–a–)/) there is a distributionF((·–a–)/) whereF is sufficiently regular and normed like , one has the approximative operating characteristic . It is shown that for arbitrarily fixed parametersn andc the function takes the valueL _n,c ⁽⁾ (p) at the pointp _F (p)=1–F(–^–1(p)). Sufficient conditions for a simple behavior of the differencep _F (p)–p are given. In the cases of rectangular and symmetrically truncated normal distribution these conditions are shown to be fulfilled.     

Increasing human and social capital by applying job embeddedness theory

Most modern lives are complicated. When employees feel that their organization values the complexity of their entire lives and tries to do something about making it a little easier for them to balance all the conflicting demands, the employees tend to be more productive and stay with those organizations longer. Job embeddedness captures some of this complexity by measuring both the on-the-job and off-the-job components that most contribute to a person's staying. Research evidence as well as ample anecdotal evidence (discussed here and other places) supports the value of using the job embeddedness framework for developing a world-class retention strategy based on corporate strengths and employee preferences.To execute effectively their corporate strategy, different organizations require different knowledge, skills and abilities from their people. And because of occupational, geographic, demographic or other differences, these people will have needs that are different from other organizations. For that reason, the retention program of the week from international consultants won’t always work. Instead, organizations need to carefully assess the needs/desires of their unique employee base. Then, these organizations need to determine which of these needs/desires they can address in a cost effective fashion (confer more benefits than the cost of the program). Many times this requires an investment that will pay off over a longer term – not just a quarter or even year. Put differently, executives will need to carefully understand the fully loaded costs of turnover (loss of tacit knowledge, reduced customer service, slowed production, lost contracts, lack of internal candidates to lead the organization in the future, etc., in addition to the obvious costs like recruiting, selecting and training new people). Then, these executives need to recognize the expected benefits of various retention practices. Only then can leaders make informed decisions about strategic investments in human and social capital.

Selected bibliography

A number of articles have influenced our thinking about the importance of connecting employee retention strategies to business strategies:

• R. W. Beatty, M. A. Huselid, and C. E. Schneier. “New HR Metrics: Scoring on the Business Scorecard,” Organizational Dynamics, 2003, 32 (2), 107–121.

• Bradach. “Organizational Alignment: The 7-S Model,” Harvard Business Review, 1998.

• J. Pfeffer. “Producing Sustainable Competitive Advantage Through the Effective Management of People,” Academy of Management Executive, 1995 (9), 1–13.

• C. J. Collins, and K. D. Clark. “Strategic Human Resources Practices and Top Management Team Social Networks: An Examination of the Role of HR Practices in Creating Organizational Competitive Advantage,” Academy of Management Journal, 2003, 46, 740–752.

The theoretical development and empirical support for the Unfolding Model of turnover are captured in the following articles:

• T. Lee, and T. Mitchell. “An Alternative Approach: The Unfolding Model of Voluntary Employee Turnover,” Academy of Management Review, 1994, 19, 57–89.

• B. Holtom, T. Mitchell, T. Lee, and E.Inderrieden. “Shocks as Causes of Turnover: What They Are and How Organizations Can Manage Them,” Human Resource Management, 2005, 44(3), 337–352.

The development of job embeddedness theory is captured in the following articles:

• T. Mitchell, B. Holtom, T. Lee, C. Sablynski, and M. Erez. “Why People Stay: Using Job Embeddedness to Predict Voluntary Turnover,” Academy of Management Journal, 2001, 44, 1102–1121.

• T. Mitchell, B. Holtom, and T. Lee. “How To Keep Your Best employees: The Development Of An Effective Retention Policy,” Academy of Management Executive, 2001, 15(4), 96–108.

• B. Holtom, and E. Inderrieden. “Integrating the Unfolding Model and Job Embeddedness To Better Understand Voluntary Turnover,” Journal of Managerial Issues, in press.

• D.G. Allen. “Do Organizational Socialization Tactics Influence Newcomer Embeddedness and Turnover?” Journal of Management, 2006, 32, 237–257.

Executive SummaryEmployee turnover is costly to organizations. Some of the costs are obvious (e.g., recruiting, selecting, and training expenses) and others are not so obvious (e.g., diminished customer service ability, lack of continuity on key projects, and loss of future leadership talent). Understanding the value inherent in attracting and keeping excellent employees is the first step toward investing systematically to build the human and social capital in an organization. The second step is to identify retention practices that align with the organization's strategy and culture. Through extensive research, we have developed a framework for creating this alignment. We call this theory job embeddedness. Across multiple industries, we have found that job embeddedness is a stronger predictor of important organizational outcomes, such as employee attendance, retention and performance than the best, well-known and accepted psychological explanations (e.g., job satisfaction and organizational commitment). The third step is to implement the ideas. Throughout this article we discuss examples from the Fortune 100 Best Companies to Work For and many others to demonstrate how job embeddedness theory can be used to build human and social capital by increasing employee retention.