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1. Introduction

This paper is intended as a review of existing models of Television Adstock transformations that enable the inclusion of dynamic and nonlinear effects of Television advertising within linear sales response models.

Television advertising is one of the largest investments for consumer marketing and companies invest a lot of effort in measuring the impact and ROI of TV advertising. This is typically done using either individual response (e.g. Discrete Choice models) aggregate response (e.g. Marketing-mix models). For the purposes of this paper, we will restrict our inquiry to aggregate response models. These models are linear in parameters but can account for non-linearity through variable transformations.

It is well known that TV advertising has both dynamic and diminishing returns effects on sales. Television advertising has an effect extending several periods after the original exposure, which is generally referred to as advertising carry-over or ‘Adstock’ (Broadbent, 1979).

The underlying theory of Adstock is that exposure to Television Advertising builds awareness in consumer markets, resulting in sales. Each new exposure to advertising increases awareness to a new level and this awareness will be higher if there have been recent exposures and lower if there have not been. This is the decay effect of Adstock and this decay eventually reduces awareness to its base level, unless or until this decay is reduced by new exposures.

1.1. Decay Effect

This decay effect can be mathematically modelled and is usually expressed in terms of the ‘half-life’ of the advertising. A ‘two-week half-life’ means that it takes two weeks for the awareness of an advertising to decay to half its present level. Every Ad copy is assumed to have a unique half-life. Some academic studies have suggested half-life range around 7- 12 weeks (Leone 1995), while industry practitioners typically report half- lives between 2-5 weeks, with the average for Fast Moving Consumer Goods (FMCG) Brands at 2.5 weeks.

Adstock half-life can be estimated through a distributed lag model response with lags of the TV Gross Ratings Point (GRP) variable, using Least Squares, or from the lag parameter in the Adstock formulation (geometric lag), or indirectly using a ‘t-ratio’ method by recursively testing different values for the decay parameter through an iterative process with sales panel data or awareness/image tracking data against the corresponding advertising schedules (Fry, Broadbent, Dixon 1999).

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