A general revealed preference theorem for stochastic demand behavior

Summary. We present a general revealed preference theorem concerning stochastic choice behavior by consumers. We show that, when the consumer spends her entire wealth, the Weak Axiom of Stochastic Revealed Preference due to Bandyopadhyay, Dasgupta, and Pattanaik (1999) is equivalent to a restriction on stochastic demand behavior that we call stochastic substitutability. We also show that the relationship between the Weak Axiom of Revealed Preference and Samuelson's inequality in the deterministic theory, and the main result of Bandyopadhyay, Dasgupta, and Pattanaik (1999) are both special cases of our result.Received: 10 September 2001, Revised: 4 April 2003, JEL Classification Numbers: D11. Correspondence to: Prasanta K. PattanaikOur greatest debt is to the referee of this paper, who made numerous helpful suggestions. We thank Robin Cubitt, Kunal Sengupta and seminar audiences at Jawaharlal Nehru University, Indian Statistical Institute, University of East Anglia, Universidad Carlos III, University of Essex and University of Montreal for their helpful comments. Prasanta K. Pattanaik acknowledges his intellectual debt to Salvador Barbera, Tapas Majumdar and Amartya Sen.     

A trigonometric flexible consumer demand system

Abstract.  This paper proposes the first ever empirical specification of a trigonometric demand system. The new model is potentially useful because of some attractive features. It is flexible, amenable to exact aggregation over consumers, possessed of trigonometric Engel curves, which can oscillate, and able to have an unusually large regular region. With comparisons between the new model and two other popular models, an illustration is given for Japanese demand for non‐durables and services. The new model shows relatively gentle Engel curves with an inflection point on each of them, which seem reasonable, given that aggregate expenditure is used in parameter estimation. JEL classification: C51, D12     

A general theory of demand for information about product quality

The purpose of this paper is to construct a general theory—analogous to the neoclassical theory of consumer demand—of demand for information about product quality. The model proposed here introduces uncertain product quality by assuming that commodities possess attributes which consumers desire and that an uncertain commodity possesses are unknown quantity of some attribute. It is assumed that information about the quality of uncertain products is available. The consumer's utility function of information is derived and his information demand function is obtained.Partial analogues of the neoclassical theorems are proved for information demand. Roughly, we find that the Slutsky matrix is symmetric and that a submatrix is negative definite. The negative definite submatrix contains those terms which measure the effect of (income compensated) changes in information prices on information demand.The analysis employed to obtain these results parallels—with some important modifications—the neoclassical analysis of commodity demand. The method used to obtain expressions for the Slutsky substitution terms is an extension of the approach introduced by McKenzie [10] and later used by Hurwicz and Uzawa [6]. This approach uses an “income compensation” function to arrive at an “income compensated” demand function.     

A system of demand equations for Austria

This paper presents results of parameter estimations of a small system of demand equations for Austria. The functional form of the equations follows the log-linear specification well known as the “Rotterdam”-System. Using annual data from 1954 to 1977 we estimate the absolute price version for a rather aggregated system consisting of four sectors of consumption expenditures. Aitken estimation with and without linear restrictions is the adopted estimation method. Tests for the validity of the general linear restrictions axe performed employing the usual criteria. Relations among the test statistics are discussed. Taking into accountBeaton's [1972] argument of the appropriate use of likelihood ratio tests we present results also after iterating on the restricted error-covariance matrix. The question of negative semidefiniteness of the matrix of price coefficients is examined by inspection of its characteristic roots and the calculation of their approximated asymptotic covariance matrix. Finally, our results are confronted with such of other comparable studies.     

A money demand system for German M3

A small macroeconomic model is constructed starting from a German money demand relation for M3 based on quarterly, seasonally unadjusted data for the period from 1976 to 1996. In contrast to previous studies we build a vector error correction model for M3, GNP, an inflation rate and an interest rate spread variable to represent opportunity costs of holding money. Furthermore, import price inflation is added as an exogenous variable. The model is used to analyze the relation between money growth and inflation by means of an impulse response analysis.We thank Gerd Hansen for soliciting two anonymous referee reports on an earlier version of this article and thereby helping in the editorial process for this volume. We are grateful to him, Timo Teräsvirta, Kirstin Hubrich and the two referees for comments that helped us to improve our paper. Financial support was provided by the DFG, Sonderforschungsbereich 373.     

Global stability condition on the plane: A general law of demand

It is well known that global stability of competitive equilibrium obtains only under quite stringent restrictions. This paper identifies a set of restrictions which may be interpreted as a very weak form of the so-called Law of Demand and shows how this may imply global stability for motion on the plane. It is also of some interest that this condition is satisfied by a perturbed version of the celebrated Scarf example which does not satisfy existing conditions for global stability.     

Unilateral effects of mergers with general linear demand

We derive the formula for the unilateral price effects of mergers of two products with linear demand in the general asymmetric situation. The formula uses the same information required to calculate upward pricing pressure in the 2010 Horizontal Merger Guidelines.     

A cointegrated VECM demand system for meat in Italy

This article applies cointegration techniques to estimate a monthly demand system for meat in Italy. In contrast to existing studies where Engle and Granger's two step procedure and Triangular Vector Error Correction Model (TVECM) representations are usually exploited, it applies a cointegrated Vector Error Correction Model (VECM) where also prices and expenditure enter endogenously the system and the cointegration rank is not assumed to be known a priori but subject to inference. It highlights some of the advantages of using the VECM compared to the TVECM, including the possibility of testing the cointegration rank of the system and the (weak and strong) exogeneity of prices and expenditure within a well-specified statistical model. This may lead to remarkable improvements in the efficiency of parameters system estimates.     

Regional consumption of antibiotics: A demand system approach

Through this paper, we have attempted to model the demand for different classes of antibiotics used for respiratory infections in outpatient care in Switzerland using a spatial version of the linear approximate Almost Ideal Demand System (AIDS) model. This model takes spatial dependency into account by means of spatial lags of antibiotic budget shares. We control for the health status of patients and the potential harmful effects of antibiotic use in terms of bacterial resistance. Elasticities to socioeconomic determinants of consumption and own- and cross-price elasticities between different groups of antibiotic have also been computed in this paper. Significant cross-price elasticities are found between newer or more expensive generations and older or less expensive generations of antibiotics.     

A money demand system for euro area M3

In order to assess the importance of monetary and financial developments for key macroeconomic variables in the euro area a money demand system for M3 is estimated adopting a structural cointegrating VAR approach. While maintaining a good statistical representation of the data, long-run relationships are based on economic theory. By using generalized response profiles the dynamics of the money demand system is investigated without any further identifying assumptions. Error bounds of the profiles are derived using bootstrap simulations.     

Alcohol content and demand for alcoholic beverages: A system approach

This paper examines how alcohol content affects the consumption of alcoholic beverages in Finland. Three different quality hypotheses are studied and compared: Fisher and Shell, Theil, and an additive one. The comparison of the hypotheses is based on quality elasticities implied by the hypotheses. The results show that, under all hypotheses, alcohol content positively affects the demand for alcoholic beverages, and this effect depends negatively on income. The results of the comparison of the hypotheses show that the additive fits the data best. However, the other hypotheses are almost as good: Fisher and Shell's hypothesis better than Theil's.I would like to thank K. Koskela, A. Nyberg, M. Salo, M. Stenius, and I. Suoniemi for their useful comments and suggestions. The author bears sole responsibility for any remaining errors.     

A simple and efficient estimation method for a non-linear demand system

A least-squares-type estimation method appears to be about as efficient as maximum likelihood with a known contemporaneous covariance matrix.     

Testing for negativity in a demand system: A Bayesian approach

The paper introduces Bayesian inference into a demand model. This allows us to test for the negativity condition of the substitution matrix which is difficult to handle directly in the traditional approach. To illustrate the Bayesian inference procedures, we estimate the Rotterdam model and test the demand properties using Japanese data. The empirical results show the importance of specifically considering negativity in demand analysis. First version received: September 1997/final version received: February 1998     

Verifying a demand system by simulation

An intriguingly small value of the asymptotic standard error of the estimate of the income flexibility inspired us to simulate the demand system. The procedure used should have more general applicability.     

An even simpler differential demand system

Keller (1984) proposed three simple variants of the well-known Rotterdam demand model. This paper proposes an even simpler differential demand system which has some attractive properties and is easy to estimate. The new model is estimated with Dutch and British data.     

Conditional and unconditional food demand elasticities in a dynamic multistage demand system

This paper estimates conditional and unconditional demand elasticities in a three stage analysis of consumer demand for food and non-food items in Greece. A dynamic version of the AIDS model is specified and estimated, and full system misspecification tests applied. Correction formulas for price and expenditure elasticities are used to calculate unconditional elasticities from conditional demand sub-systems. All food items rank as price inelastic. Deviations between the calculated conditional and unconditional price and expenditure elasticities are found to be significant, demonstrating the importance of correcting conditional elasticities before they can be used for policy purposes or welfare analyses.     

A linear demand system within a seemingly unrelated time series equations framework

A seemingly unrelated time series equations framework for the linear almost ideal (AID) demand system is considered. The framework is applied to a consumer demand system covering nine non-durable commodities. Within a specification where the static linear AID system is augmented by latent variables representing stochastic trends and seasonality, demand homogeneity is tested; both in each equation and in the system as a whole. Income and own-price elasticities are calculated under homogeneity restrictions. Although the homogeneous model is formally rejected by statistical tests, it performs well with respect to interpretability, parameter stability and forecasting.     

A system of equations model of UK tourism demand in neighbouring countries

This paper uses a system of equations model to examine tourism demand during periods of destination country transition and integration into the wider international community. The Almost Ideal Demand System model is applied to the UK demand for tourism in the neighbouring destinations, France, Spain and Portugal. Spain and Portugal are interesting cases as, during the period under consideration, they experienced a process of transition from economies with characteristics typical of developing countries, only entering the World Bank's industrialized countries classification in the 1980s. The paper examines the evolution of tourism demand during these countries' transition from ‘developing’ to ‘developed’ status. Consideration of France as a neighbouring destination also allows the behaviour of tourism demand to be compared between relatively rich and poor countries. The results show the extent to which the cross-country behaviour of demand becomes more or less similar over time with respect to changes in expenditure and effective prices. The expenditure elasticities are greater for Spain than France during the initial period, indicating that tourism can assist countries to ‘catch-up’ with their richer neighbours. However, this outcome is not always the case and may not persist, as Portugal had a low initial expenditure elasticity and Spain's relatively high expenditure elasticity decreased over time. Destinations' sensitivity to changes in their own and competitors' prices can also change over time, as indicated by the increases in the own- and cross-price elasticities for Spain, compared with the decreases for France and Portugal. The cross-price elasticity estimates indicate substitutability between the immediate neighbours, Portugal and Spain, and France and Spain.