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

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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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Notes

  1. 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).

  2. 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.

  3. 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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Acknowledgments

The authors thank the review work of Robert Kunst as editor of Empirical Economics and the comments of two anonymous referees. The authors also wish to thank the Office for National Statistics in the UK for providing Living Costs and Food Survey data and the helpdesk from the University of Manchester for its assistance. In addition, we thank Drs. Alastair Bailey, Philip Dawson and Harry Kaiser for their comments on the first draft of this article. We thank the audience at the Agricultural and Applied Economics Association (AAEA) annual meeting, Washington DC, August 4–6, 2013, for providing constructive comments which enhanced the quality of the article. Also we thank Dr. John Robinson, Professor and Extension Economist, and Dr. David Bessler, Professor, both of the Department of Agricultural Economics at Texas A&M University for providing valuable comments. Any errors and shortcomings are our own. The views expressed in this article are those of the authors and do not necessarily represent those of their institutions.

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  1. Andres Silva

    Present address: Department of Economic and Management Sciences, Universidad Central de Chile, Lord Cochrane 417, Torre A, third floor, Santiago, Chile

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  1. UR 1303 Food and Social Science Research Unit (ALISS), The French National Institute for Agricultural Research (INRA), 65, Boulevard de Brandebourg, Ivry sur Seine, 94205, France

    Andres Silva

  2. Department of Agricultural Economics, Texas A&M University, College Station, TX, 77843-2124, USA

    Senarath Dharmasena

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  1. Andres Silva
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Table 10 Autocorrelations, Partial Autocorrelations and Portmanteau (Q) statistics
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Silva, A., Dharmasena, S. Considering seasonal unit root in a demand system: an empirical approach. Empir Econ 51, 1443–1463 (2016). https://doi.org/10.1007/s00181-015-1052-6

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