Estimating Individual Cross-Section Coefficients from the Random Coefficient Regression Model

Marketing researchers frequently encounter cross-sectional, time-series data when developing sales response models. One approach to analyzing such data is to estimate a separate OLS equation for each cross-section. Alternatively, one could pool the data from all cross-sections to estimate a single set of response coefficients for all cross-sections. However, when data are pooled, the responsiveness of individual cross-sections cannot be evaluated. In this note, we introduce a version of the random coefficient model that can be used to estimate separate sets of response coefficients for each cross-section, thereby circumventing the assumption that coefficients are homogeneous in all cross-sections. We demonstrate this approach with an empirical model that relates brand level sales to price and advertising.