Modeling Consumer Demand Systems for a Variety of Goods

• Activity Number: 467
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Ignacio Vidal*+ and Walter Gómez and Felipe Vásquez
• Companies: Universidad de Talca and Universidad de La Frontera and Universidad de Concepción
• Keywords: Demand system models ; Kuhn-Tucker approach ; discrete-continuous distribution ; quadratic utility function

Abstract

The main objective of this work is to answer the following question, how is the distribution of the consumers expenditure on a set of consumption goods? Since many of goods are not consumed, the sample contains a significant proportion of observations in which expenditure on one or more goods is zero. There are several works that approach this problem by using a continuous joint distribution which assigns a positive probability for zero expenditures. Some of this works have deduced a complicated likelihood function requiring multi-dimensional integration by numerical methods. Besides, the complexity increases with the number of alternatives. Other works obtain a closed form for the likelihood by assuming the standard extreme value distribution for the errors. This assumption together with advances in computing power have permitted to make inferences with a larger numbers of choice alternatives. However, the use of the extreme value distribution only is justified by its mathematical tractability. In this work, we give a method to obtain a closed form for the expression of the consumer demand model for any number of goods and assuming a more reasonable distribution for the errors.