Key points are not available for this paper at this time.
Markus Christen, Sachin Gupta, John C. Porter, Richard Staelin, Dick R. Wittink, Using Market-Level Data to Understand Promotion Effects in a Nonlinear Model, Journal of Marketing Research, Vol. 34, No. 3 (Aug., 1997), pp. 322-334
Christen et al. (Fri,) studied this question.