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Analysis of demand equations using mixtures of Tobit models

Research project The aim of the project is to develop statistical methods useful for inference on systems of demand equations. Such a system describes how household expenditure (or demand) is distributed over goods and services and how the distribution varies with household income as well as household demographics.

Understanding and measuring consumer behavior is essential for planning and policy making. Estimates of demand functions are necessary inputs to these kinds of analyses, as they provide the link between theoretical models of consumer behavior and their real behavior. This project especially focuses on methods to estimate demand equations using data from Statistic Sweden’s annual survey about household expenditures.

Head of project

Maria Karlsson
Associate professor
E-mail
Email

Project overview

Project period:

2013-01-01 2015-12-31

Funding

The Swedish Foundation for Humanities and Social Sciences, 2013-2015: SEK 2,800,000

Participating departments and units at Umeå University

Umeå School of Business, Economics and Statistics

Research subject

Statistics

Project description

The aim of the proposal is to develop statistical methods useful for inference on systems of demand equations. Such a system describes how household expenditure (or demand) is distributed over goods and services and how the distribution varies with household income as well as household demographics.

Understanding and measuring consumer behavior is essential for planning and policy making. Estimates of demand functions are necessary inputs to these kinds of analyses, as they provide the link between theoretical models of consumer behavior and their real behavior.

This project especially focuses on methods to estimate demand equations using data from Statistic Sweden’s annual survey about household expenditures, i.e., the Household Budget Survey (HBS). Estimation of demand equations for individual households are complicated by observations of households with zero expenditure on one or several goods and/or services. This problem is called censoring and biases standard regression estimation methods. Moreover, a system of demand equations should be estimated instead of one equation at a time since demand of a good/service is affected by the demand of other goods/service via the budget restriction.

We suggest the use of a finite mixture of multivariate Tobit models which addresses both censoring and the budget restriction. This approach will also be less sensitive to assumptions about error term distribution then earlier suggested models and methods.

Besides new theoretical results on the proposed methods, the ambition is to provide practical recommendations for the benefit of empirical scientists using household data to estimate demand equations. The intention is also to implement the proposed methods in free statistical software to facilitate the usage of them by researchers and policy makers.