Recoverability revisited

This study considers the uniqueness problem of the preference relation corresponding to a demand function, which is called the “recoverability problem”. We show that if a demand function has sufficiently wide range and is income-Lipschitzian, then there exists a unique corresponding upper semi-continuous preference relation. Moreover, we explicitly construct a utility function that represents this preference relation. Compared with related research, a feature of our result is that it ensures not only the uniqueness, but also the existence of the corresponding upper semi-continuous preference relation. Further, we introduce two axioms related to demand functions, and show that these axioms are equivalent to the continuity of our preference relation in the interior of the consumption set. In addition to these results, we present three examples that explain why our requirements (including the upper semi-continuity of preference relations and the wide range requirement and income-Lipschitzian property of demand functions) are necessary, and a further two examples in which there is no continuous preference relation corresponding to the given demand function.     

On continuous utility functions derived from demand functions

In the theory of revealed preference and in the approach to integrability theory of Hurwicz and Uzawa certain conditions are proposed implying the existence of a utility function generating the given demand function. This article presents a hypothesis which, under supposition of some well-known axioms of those models, is necessary and sufficient for the existence of a continuous utility function. This hypothesis implies the existence of a utility function u with the property that all of the boundary points of the set $\text{{x|u(x)≧α}}$ for every $\text{α?}\text{R}$ are lower boundary points, being fundamental for the continuity of the utility function.     

A simple proof of the existence of an equilibrium when the weak axiom holds

An elementary proof of the existence of a competitive equilibrium is given for economies where the weak axiom holds. It is shown by an induction argument on the number of goods that the problem is reduced to the question of the existence of an equilibrium in a two-good economy.     

Does risk sharing increase with risk aversion and risk when commitment is limited?

I consider a risk-sharing game with limited commitment, and study how the discount factor above which perfect risk sharing is self-enforcing in the long run depends on agents׳ risk aversion and the riskiness of their endowment. When agents face no aggregate risk, a mean-preserving spread may destroy the sustainability of perfect risk sharing if each agent׳s endowment may take more than three values. With aggregate risk the same can happen with only two possible endowment realizations. With respect to risk aversion the intuitive comparative statics result holds without aggregate risk, but it holds only under strong assumptions in the presence of aggregate risk. In simple settings with two endowment values I also show that the threshold discount factor co-moves with popular measures of risk sharing.     

When worlds collide: Different comparative static predictions of continuous and discrete agent models with land

This paper presents a difference in the comparative statics of general equilibrium models with land when there are finitely many agents, and when there is a continuum of agents. Restricting attention to quasi-linear and Cobb–Douglas utility, it is shown that with finitely many agents, an increase in the (marginal) commuting cost increases land rent per unit (that is, land rent averaged over the consumer's equilibrium parcel) paid by the consumer located at each fixed distance from the central business district. In contrast, with a continuum of agents, average land rent goes up for consumers at each fixed distance close to the central business district, is constant at some intermediate distance, and decreases for locations farther away. Therefore, there is a qualitative difference between the two types of models, and this difference is potentially testable.     

Selective hedging with market views and risk limits: the case of Hydro-Quebec

This study presents how Hydro-Quebec manages its short-term financial risks. The quantitative hedging model is articulated over forward and volatility premia and constrained by a yearly risk limit provided by the firm's Finance Committee. The hedging solutions provide the optimal linear hedging parameters and option strike levels. The second part of the paper is devoted to a theoretical analysis of the sensitivity of the optimal solutions to changes in the premia, by means of the general implicit function theorem.     

How risky is a random process?

The riskiness of random processes is compared by (a) employing a decision theoretic equivalence between processes and lotteries on path-spaces to identify the riskiness of the former with that of the latter, and (b) using the theory of comparative riskiness of lotteries over vector spaces to compare the riskiness of lotteries on a given path-space. We derive the equivalence used in step (a) and contribute a new criterion to the theory applied in step (b). The validity of the new criterion, which applies second order stochastic dominance to utility distributions, is established by showing its equivalence to the benchmark decision theoretic criterion when comparing the riskiness of lotteries over any vector space. We demonstrate the theory’s tractability via diverse economic applications.     

Price-induced technical progress in 80 years of US agriculture

This paper presents a theory of technical progress that interprets the price-induced conjecture of Hicks. It provides also an exhaustive set of comparative statics conditions that constitute the scaffolding for an empirical test of the theory. A crucial assumption is that entrepreneurs make decisions about techniques on the basis of expected information about prices and quantities. Another assumption is that these decisions are made in order to fulfill a profitability objective. The novelty of our approach is that expected relative prices enter the production function as shifter of the technology frontier. The consequence of this assumption is an expansion of the traditional Shephard lemma that is useful for identifying the portion of input quantities that has been determined by the conjecture of price-induced technical progress (PITP). The theory is applied to a sample of 80 years of US agriculture. Three versions of the general model are presented. The first version deals only with expected relative prices. The empirical results do not reject the PITP hypothesis. The second and third versions introduce lagged expected relative prices, lagged R&D expenditures and lagged extension expenditures as explanatory variables of the portion of the input quantities that may be attributable to technical progress. I acknowledge invaluable discussions on this subject held over several years with Michael R. Caputo. I also acknowledge the use of the theory and its justifications that were presented in previous papers by Paris and Caputo (2001) and by Caputo and Paris (2005). All the errors are mine. I dedicate this paper to my wife, Carlene, who died of a rare cancer on May 5, 2001.     

Daily retail demand forecasting using machine learning with emphasis on calendric special days

Demand forecasting is an important task for retailers as it is required for various operational decisions. One key challenge is to forecast demand on special days that are subject to vastly different demand patterns than on regular days. We present the case of a bakery chain with an emphasis on special calendar days, for which we address the problem of forecasting the daily demand for different product categories at the store level. Such forecasts are an input for production and ordering decisions. We treat the forecasting problem as a supervised machine learning task and provide an evaluation of different methods, including artificial neural networks and gradient-boosted decision trees. In particular, we outline and discuss the possibility of formulating a classification instead of a regression problem. An empirical comparison with established approaches reveals the superiority of machine learning methods, while classification-based approaches outperform regression-based approaches. We also found that machine learning methods not only provide more accurate forecasts but are also more suitable for applications in a large-scale demand forecasting scenario that often occurs in the retail industry.     

Measuring Productivity from Vertically Integrated Sectors

There are many ways to measure productivity. The choice will depend on the suitability of each index to the main purpose the researcher has in mind. Whenever we are interested in 'competitiveness', the proper measure will be the inverse of the total labour embodied in one unit of final product; or, what amounts to the same, the labour employed in the vertically integrated sector corresponding to each final good. A weighted mean of these yields an index of aggregate productivity suitable for measuring social welfare. Another index of aggregate productivity (this one related to the profit rate and potential growth) coincides with the inverse of the maximum eigenvalue of the 'socio-technical matrix'. These indices are computed for the Spanish economy and compared with more conventional ones.     

Asymptotic properties of random extremes under general normalization from nonidentical distributions

In this paper we study the weak convergence of the generally normalized extremes (extremes under nonlinear monotone normalization) of random number of independent (nonidentically distributed) random variables. When the random sample size is assumed to converge in probability and the interrelation between the basic variables and their random size is not restricted, the limit forms as well as the sufficient conditions of convergence are derived. Moreover, when the random sample size is assumed to converge weakly and independent of the basic variables, the necessary and sufficient conditions for the convergence are derived.Acknowledgment. The authors are grateful to a referee for several helpful comments and for pointing out the extensive paper by Galambos (1992) leading to improvement of the representation of the paper.Received January 2002     

Modelling short- and long-term effects in the aggregate demand for soft drinks

A dynamic regression model for non-durable commodity demand is specified based on the additive unobserved components seasonal model with causal variables. The seasonal component which includes retailer stock effects is modelled as a seasonal ARMA process with fixed temperature effects. The non-seasonal component incorporates both short-run consumer responses and long-run adaptation to steady-state growth paths. Aggregation effects on per capita demand caused by the increase of new consumers as real income grows are investigated and the resulting growth trends accounted for. It is shown that neglecting these trends in the long-run adaptation process is likely to produce biased predictions and misleading estimates of crucial response parameters.     

An unobserved component model for multi-rate forecasting of telephone call demand: the design of a forecasting support system

An Unobserved Components (UC) Model based on an enhanced version of the Dynamic Harmonic Regression model, including new multi-rate and modulated cycle procedures, is used to develop a customised package for forecasting and signal extraction applied to hourly telephone call numbers made to Barclaycard plc. service centres, with a forecasting horizon of up to several weeks in advance. The paper outlines both the methodological and algorithmic aspects of the modelling, forecasting and signal extraction procedures, including the design and implementation of forecasting support software with a specially designed Graphical User Interface within the ^® computing environment. The forecasting performance is evaluated comprehensively in comparison with the well-known seasonal ARIMA approach.     

Measuring performance in the presence of stochastic demand for hospital services: an analysis of Belgian general care hospitals

Since demand for hospital services is subject to substantial variability, the relationship between uncertain demand, excess capacity, hospital costs and performance should be investigated thoroughly. In this paper a waiting time indicator to proxy hospital standby capacity is incorporated into a multi-product translog cost function for Belgian general care hospitals. The indicator is derived from queuing theory and improves on the conventionally used (inverse of the) occupancy rate. The multi-product stochastic frontier specification allows calculation of cost elasticities and marginal cost of seven hospital departments, as well as the degree of economies of scale and scope and enables identification of differences in efficiency.

Measuring Scale Efficiency from a Translog Production Function

In parametric analysis based on a frontier production function, usually the scale elasticity rather than scale efficiency level is reported. In this paper we show how one can use an estimated translog production function to obtain output- and input-oriented measures of scale efficiency at an observed input bundle. We also show how the estimated model can be used to determine the optimal quantity of labor input for an exogenously fixed quantity of capital.     

Financial reforms and money demand: Evidence from 20 developing countries

The effects of financial reforms on money demand (M1) are analysed with estimates for two sets of sub-samples and two break dates for twenty developing Asian and African countries. In all cases, the magnitude of income elasticity does not change significantly when compared with sub-samples and whole sample periods. Using CUSUM and CUSUMSQ tests, we find that the demand for money functions in our selected countries are temporally stable and therefore the respective monetary authorities may target money supply as the conduct of monetary policy.     

Measuring TQEM returns from the application of quality frameworks

This study addresses one of the major perceived barriers to total quality environmental management (TQEM): cost measurement. Operations managers have difficulty assessing the impact of TQEM programs because of the lack of appropriate measures. In order for TQEM to be given serious consideration, a cost framework is required for evaluating TQEM by appropriately including all the environmental costs and savings for each investment option. At present, frameworks such as life‐cycle assessment (LCA) and environmental cost accounting (ECA) exist, but they have both been recognized as too difficult to implement at the plant level among operations managers. This study focuses on identifying and formulating a set of easy‐to‐use quantitative cost measures. The structure of these measures is taken from the operations management (OM) literature itself, and specifically the total quality management (TQM) and cost of quality (COQ) frameworks developed by Joseph Juran. However, an empirical examination of this remains untested. The findings of this study provide an important foundation for theory development and set the stage for further research in this burgeoning field of TQEM. Copyright © 2005 John Wiley & Sons, Ltd and ERP Environment.