A Micro-Modeling Approach to Determine the Advertising-Sales Relationship, Management Science
The purpose of this paper is to derive a model of advertising effects on the firm's sales. A micromodel is postulated and aggregated across individuals and over time to produce a macromodel of the aggregate sales-advertising relationship for a single product. The micromodel postulated is very simple. It incorporates two factors: reach of the ads and rate of decay of their effectiveness over time. This approach to modeling advertising effects is shown to be fruitful in several respects: (1) the coefficients of the aggregate equation are easily interpretable -- in terms of the reach and decay parameters; (2) the model derived is nonlinear yet estimable; (3) a special case of the model is very similar to lag models that have been in use; (4) the model can be used whatever the unit of time is; (5) the carryover effect of advertising (as commonly defined) is not constant, but depends upon the previous spending levels; and (6) the model helps illustrate that the duration of advertising may be greatly overstated if aggregate lagged dependent variable models are simplistically interpreted.
Blattberg, Robert. 1981. A Micro-Modeling Approach to Determine the Advertising-Sales Relationship. Management Science. 27(9): 988-1005.