The Periodicity of Competitor Pricing

Pricing series reflect multiple decisions (e.g., regular pricing and discounting) often made by multiple decision makers. For example, temporary price reductions (high frequency price changes) can be used to price discriminate in the short run, while regular price adjustments (low frequency price changes) reflect more strategic or long-term goals. It is therefore not implausible that the “reaction” of one brand’s price to another depends on the frequency of the data analysed. Time disaggregation does not remedy this problem, because frequency aggregation exists even when data are analyzed at the lowest possible level of time aggregation. This paper proposes an approach to decompose pricing interactions across pricing frequencies to shed some light on the nature of pricing interactions across price cycles (i.e., planning horizons). We use a spectral decomposition of weekly sku-level price data in 37 grocery categories. We find that cross-brand correlation in prices occurs at multiple planning horizons, and the planning horizon of the predominant interaction does not typically coincide with the sampling rate of the data. Using spectral analysis to identify planning horizons inherent in the data, we calibrate a structural model of competitive price responses at these different frequencies. Different conclusions about the nature of price competition emerge. Calibrated on short-term price variation, the model indicates that pricing among brands is cooperative, whereas the long-term price variation suggests independent, or Nash competitive behavior. We interpret this finding, and we conclude that periodicity matters in the inference of competitive response.