Specification and estimation of primal production models

While estimating production technology in a primal framework production function, input and output distance functions and input requirement functions are widely used in the empirical literature. This paper shows that these popular primal based models are algebraically equivalent in the sense that they can be derived from the same underlying transformation (production possibility) function. By assuming that producers maximize profit, we show that in all cases, except one, the use of ordinary least squares (OLS) gives inconsistent estimates irrespective of whether the production, input distance and input requirement functions are used. Based on several specifications of the production and input distance function models, we conclude that one can estimate the input elasticities and returns to scale consistently using instruments on only one regressor. No instruments are needed if either it is assumed that producers know the technology entirely (including the so-called error term) or a system approach is used. We used Norwegian timber harvesting data to illustrate workings of various model specifications.     

Oligopoly and stability

In this paper, the so called Theocharis–Cournot problem is reconsidered. It concerns the relation between oligopoly and perfect competition, in particular the destabilization of Cournot equilibrium when the number of competitors increases. Using a CES production function where one input, capital, is fixed during periods of investment, a mixed short/long run market dynamics is set up. In the short run, with capital fixed, there is a capacity limit for production possibilities, whereas, at moments of capital renewal there are constant returns to scale. In this setting the local stability of Cournot equilibrium is reconsidered. It is demonstrated that if no more than two firms reinvest in the same time period, and the wage rate is not too high, then the Cournot equilibrium is stable.     

About negative efficiencies in Cross Evaluation BCC input oriented models

It will be shown in this paper that the input oriented DEA BCC model can generate negative efficiencies that are usually hidden in the model. The impact of these negative efficiencies becomes obvious when using input oriented Cross Evaluation models. With the help of an example with one input and one output, the conditions for the possible occurrence of negative efficiencies will be shown. Furthermore, we will show that a small intuitive change in the BCC multipliers model, previously presented in other papers, corrects this situation. We show why this change is used and compared it with an alternative formulation, which avoid negative efficiencies, namely the Non-Decreasing Returns to Scale (NDRS) model. We also show that the formulation studied in this paper is less restrictive than the NDRS model. The study of this variation in the DEA BCC model will be complemented with the formulation of the dual envelope model. This model changes the original frontier. Using the concept of non-observed DMUs, those variations can be graphically analyzed. We have also carried out some algebraic studies concerning benchmarks, multipliers and returns to scale.     

Technical efficiency and economies of scale: A non-parametric analysis of REIT operating efficiency

This study measures technical efficiency and economies of scale for real estate investment trusts (REITs) by employing data envelopment analysis (DEA), a linear-programming technique. Using data from the National Association of Real Estate Investment Trusts (NAREITs) for the years 1992–1996, we find that REITs are technically inefficient, and the inefficiencies are a result of both poor input utilization and failure to operate at constant returns to scale. With respect to scale inefficiency, most REITs are operating at increasing returns to scale, suggesting that REITs could improve performance through expansion. Moreover, we employ regression analysis to determine what characteristics influence the efficiency measures obtained. The results show that internal REIT management is positively related to all measures of efficiency. Increasing leverage is negatively related to REIT input utilization. Finally, increasing REIT diversification across property types enhances scale efficiency (SE) but reduces input usage efficiency.     

规模收益状况的动态因素分析

基于DEA理论的"交形式"生产可能集,从投入增大和缩小两种角度,对多投入多产出生产系统的各种规模收益状态进行分析,研究部分投入要素变化对部分产出要素的作用效果,即对规模收益状况给予"动态"因素分析,得到判定部分投入与部分产出之间规模收益各种状态的充要条件,从而为研究规模收益各状态的产生原因提供理论依据.     

Proactive data envelopment analysis: Effective production and capacity expansion in stochastic environments

Demand fluctuations that cause variations in output levels will affect a firm’s technical inefficiency. To assess this demand effect, a demand-truncated production function is developed and an “effectiveness” measure is proposed. Often a firm can adjust some input resources influencing the output level in an attempt to match demand. We propose a short-run capacity planning method, termed proactive data envelopment analysis, which quantifies the effectiveness of a firm’s production system under demand uncertainty. Using a stochastic programming DEA approach, we improve upon short-run capacity expansion planning models by accounting for the decreasing marginal benefit of inputs and estimating the expected value of effectiveness, given demand. The law of diminishing marginal returns is an important property of production function; however, constant marginal productivity is usually assumed for capacity expansion problems resulting in biased capacity estimates. Applying the proposed model in an empirical study of convenience stores in Japan demonstrates the actionable advice the model provides about the levels of variable inputs in uncertain demand environments. We conclude that the method is most suitable for characterizing production systems with perishable goods or service systems that cannot store inventories.     

Finding strong defining hyperplanes of PPS using multiplier form

The production possibility set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs. In this paper, we deal with the problem of finding the strong defining hyperplanes of the PPS. These hyperplanes are equations that form efficient surfaces. It is well known that the optimal solutions of the envelopment formulation for extreme efficient units are often highly degenerate and, therefore, may have alternate optima for the multiplier form. Every optimal solution of the multiplier form yields a hyperplane which is supporting at the PPS. We will show that the hyperplane which corresponds to an extreme optimal solution of the multiplier form (in evaluating an efficient DMU), and whose components corresponding to inputs and outputs are non zero is a strong defining hyperplane of the PPS. This will be discussed in details in this paper. These hyperplanes are useful in sensitivity and stability analysis, the status of returns to scale of a DMU, incorporating performance into the efficient frontier analysis, and so on. Using numerical examples, we will demonstrate how to use the results.     

Optimal maintenance of a production-inventory system with idle periods

In this paper we consider a production-inventory system in which an input generating installation supplies a buffer with a raw material and a production unit pulls the raw material from the buffer with constant rate. The installation deteriorates in time and the problem of its optimal preventive maintenance is considered. It is assumed that the installation after the completion of its maintenance remains idle until the buffer is evacuated. Under a suitable cost structure it is shown that the average-cost optimal policy for fixed buffer content is of control-limit type, i.e. it prescribes a preventive maintenance of the installation if and only if its degree of deterioration is greater than or equal to a critical level. Using the usual regenerative argument, the average cost of a control-limit policy is computed exactly and then, the optimal control-limit policy is determined. Furthermore, the stationary probabilities of the system under the optimal policy are computed.     

An integrated product returns model with logistics and marketing coordination

We develop an integrated approach for analyzing logistics and marketing decisions within the context of designing an optimal returns system for a retailer servicing two distinct market segments. At the operational level, we show that the optimal refund price is not unique. Moreover, it is such that if both market segments return a purchased product, then neither segment will receive a full money-back refund; and it is such that if one or both segments do not return a purchased product, then a refund premium over the purchase price is possible, but the refund premium will not be enough to offset a customer's total net cost of purchase and return. We also show that any improvement to the returns system that results in increased logistical efficiency or marketing effectiveness will be accompanied by an increase in the selling price of the product. At the strategic level, we show that if the retailer does not coordinate its logistics and marketing efforts to improve the overall returns system, then it will tend to over-invest in one of the functions and under-invest in the other. Finally, we illustrate how our model can be generalized to the case in which a customer's ex post valuation of the product falls along a continuum.     

基于Translog生产函数的中国汽车工业规模经济与替代弹性及价格弹性研究

使用迭代似无关回归(ISUR)方法估计了以生产工人、非生产工人和资本为投入要素的中国汽车工业Translog生产函数及中国汽车工业规模报酬的阶数,利用获得的估计计算了投入要素之间的替代弹性并通过替代弹性计算了要素需求的价格弹性。在此基础上,对中国汽车工业规模经济的状况、投入要素之间的替代或互补关系和要素价格变化对要素需求的影响进行了分析.结果显示:在所研究的期间内,中国汽车工业处于规模报酬不变阶段;生产工人和资本之间以及非生产工人和资本之间是替代关系,而生产工人和非生产工人之间是互补关系;对中国汽车工业而言,三个要素需求缺乏弹性。     

On the existence and computation of an equilibrium in an economy with constant returns to scale production

In this paper we consider the problem of finding an equilibrium in an economy with non-linear constant returns to scale production activities. To find an equilibrium we propose an adjustment process in which the prices of the commodities and the activity levels of production adjust simultaneously. The process starts at a price vector at which each production activity has non-positive profit. We show that the process follows a path which connects the starting point with an equilibrium of the economy. From this it follows that the existence of a price vector at which each production activity has non-positive profit implies the existence of an equilibrium. The equilibrium can be computed by using a simplicial algorithm or by solving a sequence of Linear Variational Inequality Problems.This research is part of the VF-program Competition and Cooperation. The authors are very grateful to Dolf Talman and two unknown referees for their valuable comments and suggestions.     

A full-scale investigation of the directional returns to scale in data envelopment analysis

Returns to scale is considered as one of the important concepts in data envelopment analysis (DEA) which can be useful for deciding to increase or decrease the size of a particular decision making unit. Traditional returns to scale on the efficient surface of the production possibility set with variable returns to scale (VRS) technology is introduced as a ratio of proportional changes of output components to proportional changes of input components. However, a problem which may arise in the real world is the impossibility or undesirability of proportional change in the input or output components. One of the attempts which is made to solve the aforementioned problem is the work of Yang et al., 2014. They have introduced the “directional returns to scale” in the DEA framework and have proposed some procedures to estimate and measure it. In this paper, the introduced directional returns to scale is investigated from a new perspective based on the defining hyperplanes of the production possibility set with VRS technology. We propose some algebraic equations and linear programming models which in addition to measuring the directional returns to scale, they enable us to analyse it. Moreover, we introduce the concepts of the best input and output direction vectors for expansion of input components or compression of output components, respectively, and propose two linear programming models in order to obtain these directions. The presented equations and models are demonstrated using a case study and numerical examples.     

Optimal input substitution of a firm facing an environmental constraint

In this paper we consider the dynamic behavior of a firm subject to environmental regulation. As a social planner the government wants to reduce the level of pollution. To reach that aim it can, among others, set an upper limit on polluting emissions of the firm. The paper determines how this policy instrument influences the firm's decisions concerning investments, abatement efforts, and the choice whether to leave some capacity unused or not. The abatement process is modeled as input substitution rather than end-of-pipe. Using standard control theory in determining the firm's optimal dynamic investment decisions it turns out that it is always optimal to approach a long run optimal level of capital. In some cases, this equilibrium is reached within finite time, but usually it will be approached asymptotically. Different scenarios are considered, ranging from attractive clean input to unattractive clean input, and from a mild emission limit to a very tight one. It is shown that for large capital stocks and/or when marginal cash flow per unit of emissions is larger for the dirty input than for the clean input, it can be optimal to actually leave some production capacity unused. Also, since the convex installation costs suggest to spread investments over time, it can happen that investment in productive capital is positive although capacity remains unused.     

Production planning for hybrid remanufacturing and manufacturing system with component recovery

In this paper, we address component recovery under the condition of limited resources from the OEM's (Original Equipment Manufacturer's) standpoint. We develop a linear programming model for a hybrid remanufacturing and manufacturing system for production planning problems with deterministic returns. In this paper, a data set from an OEM that both remanufactures and manufactures the products is used to demonstrate the performance of the proposed model. Subsequently, an analysis of the impact of the remanufactured product’s price and the quantity of returns on revenue and total cost will be discussed. We have found that uncertain factors of manufacturing influence the profit and uncertain factors of remanufacturing influence the production planning, such as the rate of the yield on component remanufacturing and the quantity of returns.     

Time substitution with application to data envelopment analysis

In this paper we analyze resource allocation distinguishing between the decision of when to begin allocation and over how many periods to apply the resources. We present analytical results for specific production technologies under different returns to scale assumptions, under capacity constraints and for production with technical change. Using a dynamic activity analysis framework we show how to compute in general optimal solutions for resource intensity use.     

Calculating scale elasticity in DEA models

In the data envelopment analysis (DEA) efficiency literature, qualitative characterizations of returns to scale (increasing, constant, or decreasing) are most common. In economics it is standard to use the scale elasticity as a quantification of scale properties for a production function representing efficient operations. Our contributions are to review DEA practices, apply the concept of scale elasticity from economic multi-output production theory to DEA piecewise linear frontier production functions, and develop formulas for scale elasticity for radial projections of inefficient observations in the relative interior of fully dimensional facets. The formulas are applied to both constructed and real data and show the differences between scale elasticities for the two valid projections (input and output orientations). Instead of getting qualitative measures of returns to scale only as was done earlier in the DEA literature, we now get a quantitative range of scale elasticity values providing more information to policy-makers.     

Autonomous and induced production learning under price and quality competition

Recent empirical studies indicate that improvements in product conformance quality exhibit learning-by-doing patterns. We address quality improvement in a competitive duopoly market for partially substitutable products characterized by levels of quality that are not necessarily identical. The products’ quality is described with a hazard rate that can be improved both by accumulating production experience (autonomous learning) and quality improvement efforts (induced learning). Given that defective items are fully reimbursable and the demands exhibit increasing returns to scale, we derive Nash equilibrium pricing and induced learning effort dynamic policies. We show that when the effectiveness of autonomous learning prevails over the effectiveness of efforts in induced learning, equilibrium prices gradually grow over time; the trend is quite the opposite when autonomous learning is less effective than induced learning.     

Financial market equilibria with heterogeneous agents: CAPM and market segmentation

We consider a single-period financial market model with normally distributed returns and heterogeneous agents. Specifically, some investors are classical expected utility maximizers whereas some others follow cumulative prospect theory. Using well-known functional forms for the preferences, we analytically prove that a Security Market Line Theorem holds. This implies that capital asset pricing model is a necessary (though not sufficient) requirement in equilibria with positive prices. We prove that equilibria may not exist and we give explicit sufficient conditions for an equilibrium to exist. To circumvent the complexity arising from the interaction of heterogeneous agents, we propose a segmented-market equilibrium model where segmentation is endogenously determined.     

A bi-objective generalized data envelopment analysis model and point-to-set mapping projection

This work introduces a bi-objective generalized data envelopment analysis (Bi-GDEA) model and defines its efficiency. We show the equivalence between the Bi-GDEA efficiency and the non-dominated solutions of the multi-objective programming problem defined on the production possibility set (PPS) and discuss the returns to scale under the Bi-GDEA model. The most essential contribution is that we further define a point-to-set mapping and the mapping projection of a decision making unit (DMU) on the frontier of the PPS under the Bi-GDEA model. We give an effective approach for the construction of the point-to-set-mapping projection which distinguishes our model from other non-radial models for simultaneously considering input and output. The Bi-GDEA model represents decision makers’ specific preference on input and output and the point-to-set mapping projection provides decision makers with more possibility to determine different input and output alternatives when considering efficiency improvement. Numerical examples are employed for the illustration of the procedure of point-to-set mapping.     

上证指数收益率分布的拟合

本文旨在讨论上证指数收益率序列的分布特征 ,通过对上证指数 1 997年 5月 2 3日至 2 0 0 1年 7月1 3日 ,总计 1 0 0 0多个交易日的统计分析 ,发现上证指数收益率的分布具有“尖峰、厚尾”的特性 .我们试图用文献 [1 ]给出 Lévy flight来拟合其分布 ,但结果并不理想 .为此我们提出了一种类似 Weibull分布的函数来拟合上证指数收益率分布 ,模拟结果较好 .同时 ,我们按通常的方法对尾部作了截尾处理 ,以更接近实际数据在尾部表现出来的“厚尾”现象