Expenditure elasticities of the demand for leisure services

Abstract

Although some research has already focused on the analysis of expenditure elasticities of leisure demand, some shortcomings with regard to the content and the underlying theoretical model as well as the applied methods exist. This article aims at avoiding these problems to provide consistent derivatives of leisure service expenditure elasticities. Therefore, a regular demand system is derived from microeconomic duality theory. To implement leisure specific demand factors (i.e. demand- and supply-based sports and recreational opportunities as well as sports and recreational preferences) while still being consistent with neoclassical demand theory, the basic model is extended by applying the demographic translation framework. Data of the continuous household budget survey (n = 7724) from Germany is used for the estimation of the derived demand system. It is shown how sensitive the results are depending on the applied (censored) regression model: 16 out of 18 analysed services are indicated as luxury goods based on the findings of the Tobit model type I but as necessities based on the findings of the Tobit model type II. Possible implications are presented and discussed.

Keywords:

• consumer expenditure
• Tobit
• censored sample
• duality theory
• services

JEL Classification::

• C24
• D12
• L83

Notes

¹ Since it is likely that consumers show different consumption patterns for different subcategories, (management) implications derived from the analysis of highly aggregated data might be biased (Robinson, 1950).

² While other single-equation models (e.g. the double hurdle model) do not appear to be more appropriate from the theoretical point of view, it has to be discussed whether a multivariate Tobit model might be necessary. Such models are required if the qualitative and/or the quantitative decisions of a certain leisure service depend on the corresponding decisions concerning other leisure services. From a statistical point of view, this is the case if the error terms of two leisure services in the same stage are correlated. While this does not seem unrealistic (e.g. a general preference factor for or against sport might exist that is not part of the set of available independent variables), the development of adequate multivariate models is not satisfying: an approach developed by Heien and Wessells (1990) is not consistent while the model developed by Shonkwiler and Yen (1999) generates inefficient estimates (Tauchmann, 2005). However, since Halvorsen and Nesbakken (2004) find that stochastic interdependencies (e.g. a Seemingly Unrelated Regression (SUR) in the second stage of the Tobit model type II) do not yield appreciable different estimates, our analysis is focused on the single-equation approaches by Tobin and Heckman. To compare the results, we also present the subsample OLS estimation without correction of the sample selection.