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Empirical Economics

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22-01-2016

Considering seasonal unit root in a demand system: an empirical approach

Authors: Andres Silva, Senarath Dharmasena

Published in: Empirical Economics | Issue 4/2016

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Abstract

Practitioners commonly treat time series and structural approaches as mutually exclusive methodologies to model empirical data. Our objective is to show that time series and structural approaches are not irreconcilable. Specifically, we show that time series properties can be informative for modeling habits in a structural demand system model. Using non-alcoholic beverage expenditure data from the UK, we empirically show that unit roots results can help to model habits in a structural demand system. Habits are a relevant determinant to understanding food expenditure and to quantifying the impact of interventions from the private (e.g., advertising campaigns) and public (e.g., food taxes) sectors. We find that the seasonal-habit QUAIDS outperforms the static and myopic-habit specifications. We also show that taking seasonal habits into account helps to control for autocorrelation in error terms. Therefore, time series properties such as unit roots can help to understand the underlying patterns in the residuals beyond correcting for autocorrelation.

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In formal way, Dynan (2000) defined habits as the utility depending on the current expenditure, as well as on a “stock” formed by lagged expenditure. In other words, the utility derived from current consumption is conditioned by lagged consumption patterns. Habit formation implies the non-separability of intertemporal consumption, which has been tested numerous times, such as by Ferson and Constantinides (1991), Naik and Moore (1996) and Zhen et al. (2010).

The adding-up restrictions are given by: \(\mathop \sum \nolimits _{i=1}^m \alpha _i =1,\mathop \sum \nolimits _{i=1}^m \beta _i =0,\mathop \sum \nolimits _{i=1}^m \gamma _{ij} =0\), where j = 1,2,...6. The homogeneity restrictions are given by: \(\mathop \sum \nolimits _{j=1}^m \gamma _{ij} =0\), i = 1,2,...6. The Slutsky symmetry conditions are satisfied via the restrictions: \(\gamma _{ij} =\gamma _{ji} \), i,j = 1,2,...6.

The Living Costs and Food Survey was initially collected as the British Family Expenditure Survey, which has been used in seminal articles in applied microeconomics. Some examples of well-known works: Banks et al. (1997), Blundell et al. (1993), Atkinson and Stern (1980), Pollak and Wales (1978). Consequently, we are working with a dataset with an established reputation.

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Title: Considering seasonal unit root in a demand system: an empirical approach
Authors: Andres Silva
Senarath Dharmasena
Publication date: 22-01-2016
Publisher: Springer Berlin Heidelberg
Published in: Empirical Economics / Issue 4/2016
Print ISSN: 0377-7332
Electronic ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-015-1052-6

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