Panel regression (cross sectional-time series) in same store sales analysis

Abstract

Most retail analytic frameworks are either ordinary or auto regression. That is, each row is a cross section or time period, but if a framework included both, better estimates and insights should result. These improved estimates come from the additional informational content supplied by both cross sections and time periods. Cross section means analysis by-customer, by-store or by-geography: time series data on each cross section could be used as independent variables (eg that which is designed to explain the movement in a dependent variable, that is, the dependent variable depends on the independent variables). The power of panel regression is in using both cross section and time series observations accounting for both cross sectional and time series effects. The following shows a common problem in retail: same store sales solved by taking into account differences in stores and differences in time series on sales, promotions, media, etc. Panel regression specifically analyses cross sectional time series data and incorporates these effects into the model. It also increases the sample size, which may be a trivial benefit while panel models (especially fixed effects) can control for unobserved heterogeneity which may be crucial. The business problem herein addressed is same store sales (SSS): this is an important business creator for retail companies in particular, and the source and focus of a large amount of analysis. Typical examples of SSS analyses include demand (by store) and marcomm (marketing communication)/media (by time period). There is a need to incorporate information from both a cross section and a time series point of view as SSS is about measuring change in a store over time. To incorporate both by-store and over-time effects something other tan ordinary regression (time series or not) needs to be incorporated. That is, if the approach is by-store (each row is a store) then the effect of bytime is lost. If the approach is time series (each row is a time period) then the store data are aggregated and the by-store effect is lost. Another common issue with SSS is a hidden/ unobserved variable that affects SSS: that is, there may be another variable (competitive moves, socio demographics, etc.) that the retailer cannot account for. Ordinary Least Squares (OLS) will be biased if used, which panel regression can account for and partial out its effects. The goal of the retailer is therefore to measure the effect of different types of media by store over time which can result in a plan to optimally spend where it has the most effect.