Some models and measures for evaluating performances with DEA: past accomplishments and future prospects

This paper covers some of the past accomplishments of DEA (Data Envelopment Analysis) and some of its future prospects. It starts with the “engineering-science” definitions of efficiency and uses the duality theory of linear programming to show how, in DEA, they can be related to the Pareto–Koopmans definitions used in “welfare economics” as well as in the economic theory of production. Some of the models that have now been developed for implementing these concepts are then described and properties of these models and the associated measures of efficiency are examined for weaknesses and strengths along with measures of distance that may be used to determine their optimal values. Relations between the models are also demonstrated en route to delineating paths for future developments. These include extensions to different objectives such as “satisfactory” versus “full” (or “strong”) efficiency. They also include extensions from “efficiency” to “effectiveness” evaluations of performances as well as extensions to evaluate social-economic performances of countries and other entities where “inputs” and “outputs” give way to other categories in which increases and decreases are located in the numerator or denominator of the ratio (=engineering-science) definition of efficiency in a manner analogous to the way output (in the numerator) and input (in the denominator) are usually positioned in the fractional programming form of DEA. Beginnings in each of these extensions are noted and the role of applications in bringing further possibilities to the fore is highlighted.

Natural and double implementation of public ownership solutions in differentiable production economies

This paper examines the implementation of two public ownership solutions in convex production economies with differentiable production functions. The two public ownership solutions we focus on are the proportional and equal benefit solutions. Two “natural” mechanisms which doubly implement the proportional and equal benefit solutions respectively in Nash and strong Nash equilibria are proposed without assuming free disposal. Received: 7 May 1996 / Accepted: 1 December 1998     

On the smoothness of optimal paths II: some local turnpike results

We study the local turnpike property for two classes of infinite-horizon discrete-time deterministic maximization problems which have common applications, e.g., optimal growth theory. We follow a functional-analytic approach and rely on an implicit function theorem for the space of the sequences which converge to zero. We shall assume the existence of an optimal path which is not necessarily a steady-state. Relying on material developped in Blot and Crettez (Decis Econo Finance 27:1–34, 2004), “On the smoothness of optimal paths” Decis Econ Finance, 21:1–34, 2004), we provide conditions under which a variation in the initial conditions (i.e., capital stock and discount rate) yields an optimal solution which converges toward a reference solution when time becomes infinite. We also provide new results on bounded solutions of difference equations. We gratefully thank the editor, Silvano Holzer, and two anonymous referees for remarks and advices on a previous version of this paper.     

A unified approach to optimal process control

Summary In this paper a unified approach to optimal process control is developed, which leads to relatively simple and rather general objective functions for optimization. These two features “simplicity” and “generality” are the basis for the development of powerful algorithms and nomograms to determine approximately optimal solutions. Research supported by the Deutsche Forschungsgemeinschaft.     

Nash implementation through elementary mechanisms in economic environments

This paper identifies a class of mechanisms, called elementary mechanisms, which are (in a precisely defined sense) the “simplest” mechanisms that can implement efficient outcomes in economic environments. The class of social choice correspondences that can be implemented by elementary mechanisms is completely characterized in a variety of different economic contexts.     

Bargaining solutions with non-standard objectives

I examine the pure-strategy solutions of the sealed-bid bargaining game with incomplete information, when the buyer's and seller's objectives are other than the standard objective, namely maximization of expected profit. The motivation for this exploration lies in three problems of the standard formulation: the necessity of assuming common priors, the existence of uncountably many Nash equilibria, with no means for the players to coordinate on any one of them, and the uncertain relationship between these equilibria and observed behavior in bargaining experiments. Specifically, I consider two alternative objectives: minimization of maximum regret, and maximization of maximum profit. The solution concept here is not Nash equilibrium, but rather -individually rational strategy bundle. For that reason, I shall, where appropriate, use the word “solution” in place of “equilibrium.” Yet we find that the notion of Nash Equilibrium reappears, in a sense to be explained. In the minimax-regret case I find (in contrast to the case of expected profit) a unique solution; this solution reduces, for priors with coincident support, to the linear equilibrium of Chatterjee-Samuelson. In the maximum-profit case there are many solutions; they turn out to be slight generalizations of the one-step equilibria of Leininger-Linhart-Radner.     

Does sentiment explain consumption?

This paper examines whether “consumer sentiment,” an often neglected variable, explains consumption expenditures for Australia. Since household consumption accounts for more than 60 percent of U.S. GDP and a similar proportion in other developed economies, fluctuations in consumption may result in significant changes in the state of the economy. Therefore, we develop a theoretical model that suggests why consumer sentiment may influence consumption expenditures. Furthermore, using a carefully specified consumption function as the “test-bed,” we consider empirically whether there is an independent impact of sentiment on consumption. Our results suggest that consumer sentiment does influence variations in consumption expenditure.     

The PC as electronic nag

While often well-meant and sometimes unintended, nagging is an irritation we can easily do without. Whether personal or electronic, low-tech or high, it matters not. With PC proliferation, problem potential increases—even at home. Resisting the urge to telecommute unless anticipated gains can be “proved” in advance, and self-discipline if and when the PC becomes a “family member,” are urged.     

On the active approach of stochastic linear programming

Summary The problem of statistical distribution of the optimal objective function under the so-called active approach of stochastic linear programming is investigated here from two interrelated aspects. First, the active approach is viewed as a method of decomposition. Second, some results on the asymptotic form of distribution of extreme values are utilized to derive the asymptotic form of the distribution of the maximand under the active approach. Research done under the partial support of the U.S. National Science Foundation Grant No. 420-04-62 at the Department of Economics, Iowa State University. Some of the work related to this paper may be found in the following references:Sengupta, J. K., G. Tintner, andC. Millham: “On Some Theorems of Stochastic Linear Programming”. Management Science, Vol. 10, October 1963, pp. 143–159.Sengupta, J. K.: “The stability of truncated solutions of stochastic linear programming”. Econometrica, Vol. 34, January 1966. pp. 77–104.Sengupta, J. K.: “On the stability of solution under recursive programming”. Metrika 1966.Sengupta, J. K. andT. Kumar: “An application of sensitivity analysis to a linear programming problem”. Unternehmensforschung, Vol. 9, 1965.     

A family of measures of uncertainty involving utilities: Definition,properties, applications and statistical inferences

Consider an experiment involving the observation of a discrete random variable, or quantitative classification process. When, in addition to the probability of each value or class we know its “utility” (or, more precisely, we can quantify the “nature” of each value or class), the “uncertainty corresponding to the utilities” may be evaluated. In this paper, we are first going to introduce a family of Measures of Uncertainty involving Utilities and several properties of this family are studied. Then, some immediate applications are discussed: the definition of criteria for Comparing Experiments in Statistical Decision problems, and the quantification of the Inequality with respect to an economical attribute or the Industrial Concentration. Finally, we will analyze the asymptotic behaviour of the measures in simple random sampling, and some related problems. This work was partially supported by the Comisión Asesora de Investigación Científica Técnica (CAICYT) under the contract PB85-0401.     

Redistribution and individual characteristics

I study a model where personal income is a function of two different groups of individual characteristics, called “talent” and “effort” respectively. The distinction between these two groups is that society has taken the prior decision that the influence of traits from the first group needs to be moderated by any fair redistribution mechanism while differences in income due to traits from the second group must be preserved. I present two solutions that satisfy several intuitive properties of fairness and I use these properties to characterize both of them. Received: 29 October 1995 / Accepted: 6 January 1997     

Implementation by demand mechanisms

This paper introduces a class of implementation mechanisms for exchange economies, calleddemand mechanisms. Each agent “demands” a consumption bundle, and equilibria are situations where each agent receives the bundle he asked for. A simple necessary and sufficient condition for implementation by a demand mechanism is derived.     

Determining of threat perceptions affecting direction of the US defense expenditures by using ordinal regression models

The article examines whether the US threat perceptions defined in terms of federal government national defense outlays in billions of constant (FY 2000) dollars change along with periodical changes in international politics between 1945 and 2007. Three different models affecting direction of the US defense expenditures are developed. The first model are estimated by using five link functions even though results of only two of them, complementary log–log and cauchit, are presented. As complementary log–log produced the best results, others models are predicted by using only this function. The parameter estimates of complementary log–log function for the first model indicate that four of these variables (Ford, Carter, Reagan and Bush Sr.) out of eleven are significant in the category of presidents. “Truman Docrtrine/Cominform”, “Korean War”, “Vietnam War”, and “Invasion of Iraq” also seem to be the important independent variables on empirical grounds for the first model. While “Party”, “Invasion of Iraq”, “Vietnam War”, “Korean War”, and “Cuban Missile Crisis” constitute the important independent variables on empirical grounds for the second model, “Korean War”, “Vietnam War”, “Invasion of Iraq”, “Truman Docrtrine/Cominform”, “The Cold War and New World Order”, and “Cuban Missile Crisis” are important independent variables on empirical grounds for the third model. Estimations based on these three models therefore suggest that aforementioned independent variables do indeed have effect on the US defense expenditures.     

Social Distance,Respondent Cooperation and Item Nonresponse in Sex Survey

This paper examines the ways in which the number of item nonresponses is determined by social distance and/or interview rapport, with a focus on responses of “refusal” and “don’t know”, implying the respondent’s lack of willingness and ability to provide substantive responses to sensitive questions. The data analyzed were from 39 self- administered questions concerning sexual attitudes and behaviors in the 2002 Taiwan Social Change Survey for module “Family and Changing Gender Role”. Poisson Regression in 2-level Hierarchical Linear Model was employed to enhance the accuracy of the analysis of the accumulation of “don’t know” and “refusal” responses. The results showed that respondent cooperation significantly decreased the number of both “don’t know” and “refusal” replies. The decrease was not conditioned by any kind of social distance. Age and education distances have respectively negative and positive effect on the number of “don’t know” and “refusal” answers. The married–married interview produced more “don’t know” and “refusal” than other paired interview types. The larger the ethnicity distance is, the more “refusal” appears. The substantial findings imply that the effects of social-distance and rapport (respondent cooperation) on the number of item nonresponses deserve more attention in research on survey methodology. The divergent findings on gender-distance effect and marital-status effect, however, call for replication studies in the future.     

The Qualitative and Quantitative Models for Performance Measurement Systems: The Agile Service Development

A decision model for selection using analytic hierarchy process (AHP), however, they did not consider interdependence property but consider independence property among alternatives or criteria. It could become inadequate in measurement of actual performance of the decision process. In order to reduce the decision gap, this paper considers when independence among different elements of a system assumption is violated and takes into account the degree of the interdependence among them. The fuzzy analytic network process (FANP) approach with agile theory is developed to apply in analyzing the new service development in the wholesale center. The FANP could not only offer a hierarchy framework more efficiency and accuracy but also improve human judgment on the importance of requirements involving imprecise and vague. The technique has proved useful for comparing the importance among the determinants of agile for new service development in decision maker’s mind, including agile cost, time, robustness and scope. The empirical result points out that “Diverse designs” of new service development is the best choice for the wholesale center, following as “Service extended” and “Technological core”.     

Verbesserung des nicht-randomisierten exakten Testes von R.A. Fisher

Summary The so-called Exact Test of R. A. Fisher for comparing two probabilitiesp ₁ andp ₂ in a Fourfold-Table with small cell frequencies is known as a UMPU-Test. But in practice the test is used in a nonrandomized, often tabulated version. Given a certain level of significanceα it is shown: the critical region of this nonrandomized test, referred to as “Fisher 1”, can be enlarged considerably. For instance for all sample-size-sums up to 20 andα=0.01 the total number of points in the critical regions of “Fisher 1” is 552 whereas the analogous number of the new version “Fisher 2” is 788. The size of tables for “Fisher 2” can be reduced considerably because the main parts of the critical regions can be described by the aid of some Chi-square-test versions. In particular Yates’ continuity-correction turns out to be always conservative in the above mentioned region relative to “Fisher 2” whereas this is not strictly true relative to “Fisher 1”.      

Selezione degli investimenti e costo del denaro

Alcuni Autori ritengono che non abbia senso il costo del denaro, in uno schema lineare in cui si può ripartire il proprio denaro in tutte e sole le operazioni che determinano il tasso di sconto. La conclusione di tali Autori appare azzardata: infatti il loro risultato discende da una ipotesi estranea al modello lineare. In questo lavoro io interpreto lo stesso modello, mostro che in esso ha senso il costo del denaro e propongo delle impostazioni alternative.

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An interesting economic problem consist in the search of the optimal allocation of one’s monetary resources in different financial transactions. We often consider as “optimal” the allocation which makes the sum of the actual values of investiments the highest possible, within the limits of all feasible operations. These values are reckoned according to the discount rates established by the financial market. This type of abstraction can be acceptable when we can split our capital into a number of operations that are on the whole negligible, if compared with the movement of the market. In case of a considerable turn over that may therefore affect the cost of money, it follows that we can’t determine an appropriate discount rate before establishing the distribution policy; on the other hand we cannot determine the distribution policy before defining the discount rate. As a border-line case we have that of an “enclosed” economy, where funds can be rationed into all and only those operations which determine the cost of capital. That is the case of “pure capital rationing”. To solve the problem of reckoning the cost of capital under pure capital rationing, some Authors have formulated the two dual linear programs (1) and (2) and have deduced that f is the vector of market prices if and only if the optimal dual solution is equal to f. As that happens if and only if f=0, Burton and Damon [2] consider their “main result a rigorous proof that there does not exist a meaningful solution for the pure capital rationing problem” and conclude “that if there exist a solution to the problem it is not to be found by the traditional linear programming formulations”. On the contrary I demonstrate that f=0 is the only possible capital cost because of the hypotesis =f, which is not related to the linear pattern and is not acceptable from an economic-financial point of view. Then I demonstrate that the market prices are all and only those based on which the actual values of the operations considered are 0. Nor was it right to expect more sophisticated conclusions of such an elementary scheme. Finally I express an alternative linear formulation, where the dual optimal solutions are exactly the market prices.

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Lavoro effettuato nell’ambito del G.N.A.F.A. del C.N.R.     

“Your Job No Longer Exists!”: From Experiences of Alienation to Expectations of Resilience—A Phenomenological Study

We have entered the age of the contingent or temporary worker, the consultant and the subcontractor. Workers are expected to be pliable and tractable; to “fit in.” Being made redundant is also an area where modern workers are expected to be flexible and resilient. However, when these so-called “flexible” workers are told their job no longer exists, the accompanying sense of rejection and alienation can be excruciating. Stories of being made redundant were collected during an exploratory, qualitative study, using Heideggerian phenomenology as the methodological vehicle to capture the lived experiences of those affected. Focused, in-depth interviews were conducted with the ten respondents; nine men and one woman. The stories shared suggest that being made redundant is an alienating experience with respondents sharing feelings of powerlessness, shock, betrayal, shame and social isolation. Unfortunately, those having experienced redundancy were also not as resilient as is routinely assumed. They did not “bounce back” unchanged, but reported significant negative outcomes including fear for the future, underemployment, family disruptions and an erosion of trust. Recommendations are made orienting organisations towards a more human process of redundancy.     

Causality in qualitative and quantitative research

We are flooded with a wave of writings on causality in the social sciences during the last decades. The same holds for the relationship between quantitative and qualitative research in the social sciences. An enormous amount of texts appears on (causality in) qualitative research, mostly in a controversy with quantitative research. These writings induced us to develop the thesis of “unity in diversity”, i.e., that there is no difference “in principle” between causality in qualitative and quantitative research, because both are supported by what I will call an “experimental logic”. In developing this thesis a plea is being made for going back to the sources. A historical overview of theories of causality is presented, which develops into two prominent views: INUS-causation and causal realism. A historical framework is also outlined for the opposition between quantitative and qualitative research, in which French positivism and British empiricism are opposed to German neo-kantianism and neo-hegelianism. After having developed the thesis of “unity in diversity” for this historical framework, the same is being done for the recent literature: “mixed methods research”, the book DSI of KKV, the reactions of David Collier and “QCA” of Charles Ragin. At the end the question of small-n research and the case n = 1 is examined.     

Median unbiased estimates for M.L.R.-families

Summary Lehmann [p. 83] has shown that some families of probability measures with monotone likelihood ratios (m.l.r.) admit median unbiased estimates which are optimum in the sense that among all median unbiased estimates they minimize the expected loss for any loss function which assumes its minimal value zero for the “true” parameter value and is nondecreasing as the parameter moves away from the true value in either direction. This very strong optimum property was proved under the assumption that all probability measures of the m.l.r.-family have continuous distribution functions, that they are mutually absolutely continuous and that each element of the support is the median of somep-measure of the family. This result does therefore not cover important cases such as the binomial families or thePoisson family. The purpose of the present paper is to show the existence ofrandomized median unbiased estimates with the same optimum property for m.l.r.-families which are closed and connected with respect to the strong topology. Such families are always dominated. We do, however, neither assume that thep-measures are mutually absolutely continuous nor that the distribution functions are continuous. We remark that the use of randomized estimates is indispensable here because nonrandomized median unbiased estimates do not always exist in the general case.