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

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.