Mixed Demand Systems Research Articles

Appendices B and C: Incorporating Prior Information into a GMM Objective for Mixed Logit Demand Systems

Discusses formulation of the outside share and instrumental variable choice specific to an illustration using beer data.

Effective global regularity and empirical modelling of direct, inverse, and mixed demand systems

Abstract This paper utilizes the notion of ‘effective global regularity’ and the intuition stemming from Cooper and McLaren (1996)'s General Exponential Form to develop a family of ‘composite’ (product and ratio) direct, inverse and mixed demand systems. Apart from having larger regularity regions, the resulting specifications are also of potentially arbitrary rank, which can better approximate non‐linear Engel curves. We also make extensive use of duality theory and a numerical inversion estimation method to rectify the endogeneity problem encountered in the estimation of the mixed demand systems. We illustrate the techniques by estimating different types of demand systems for Japanese quarterly meat and fish consumption.

Samuelson's Full Duality and the Use of Directed Acyclical Graphs

To date, mixed demand systems have been all but ignored in empirical work. A possible reason for the scarcity of such applications is that one needs to know a priori which prices and quantities are endogenous in the mixed demand system. By using a directed acyclical graph (DAG), causal relationships among price and quantity variables are identified giving rise to a causally identified mixed demand system. A statistical comparison is made of the traditional Rotterdam model, a synthetic demand system, which subsumes the traditional Rotterdam model, and a Rotterdam mixed demand system identified through the use of a DAG. In this analysis, the respective demand systems consist of five products: steak, ground beef, beef roasts, pork, and chicken.

Deriving a Flexible Mixed Demand System: The Normalized Quadratic Model

AbstractThis article deals with the specification of a locally flexible and theory‐consistent system of mixed demand functions, a framework that allows for a rich set of possibilities about what is assumed as exogenous in a demand model. A coherent mixed demand system is derived by using the restricted expenditure function typically studied in the related area of rationed demands. The method is implemented by a new normalized quadratic (NQ) parameterization of the restricted expenditure function. The resulting NQ mixed demand system is illustrated with an application to a nine‐good model of the Italian demand for vegetables.

The Use of Conditional Cost Functions to Generate Estimable Mixed Demand Systems

Mixed demand systems have been virtually ignored in empirical work solely because derivation of these systems requires closed forms for both direct and indirect utility functions. This article proposes the alternative of using a conditional cost function to generate empirical mixed demand models. This approach allows the estimation of mixed demand systems, which are explicit in an unobservable variable (utility), but may lack a closed form representation in terms of observable variables such as prices, quantities and expenditure. Results indicate that this approach is operationally feasible, which opens up a wider range of mixed demand specifications in static analyses.

Incorporating Generalized Marginal Budget Shares in a Mixed Demand System

This article extends a Rotterdam type of mixed demand system by replacing its constant marginal budget shares with the ones derived from originally defined and specified mixed Engel curves that take a generalized functional form using the Box‐Cox transformation. An empirical illustration is given for Japanese demand for fresh and processed fruits and vegetables. The results show that the Rotterdam parameterization of marginal budget shares, which corresponds to those in linear mixed Engel curves, is preferred by the data, and that improper assumptions of the form of mixed Engel curves underlying a mixed demand system can bias its elasticities.

Consistency in Mixed Demand Systems: Contingent Valuation and Travel Cost Data

In contrast to previous literature, we propose a consistency test that does not impose any particular common functional form for the preference structure underlying the travel cost (TC) and contingent valuation (CV) models. We derive testable consistency conditions between TC and CV data in the context of mixed demand systems when valuing changes in environmental quality. These conditions are a subset of the rationality conditions. The proposed consistency tests are implemented combining TC and CV data. The empirical results show that it is possible to combine stated TC and CV, but not revealed TC and CV data.

A Mixed Demand System of Fresh and Processed Food

A Mixed Demand System of Fresh and Processed Food

Specification Tests for Mixed Demand Systems with an Emphasis on Combining Contingent Valuation and Revealed Data

In a world characterized by r unrationed goods (i.e., market goods) and ( n − r) rationed goods, such as most environmental goods, necessary and sufficient conditions for the existence of an underlying rational preference structure are derived based on a system of mixed demand functions with complete information. With incomplete information, the case of a partial demand system is addressed, and a test for separability is proposed. The implications for testing rationality in a world characterized by combined (RP and SP) individual data are examined for data consistency. Testable conditions are derived.

Flexible Specification of Mixed Demand Systems

AbstractCommon flexible functional forms are not very useful for modeling mixed demand systems because derivation of mixed demands requires closed forms for both direct and indirect utility functions. In this paper we study the alternative of using a direct approximation to mixed demands. We develop a new approach to Slutsky relations for mixed demand functions allowing formulation of a Rotterdam mixed demand model. The resulting mixed demand system is illustrated with an application to meat demand in Canada.