Marketing Spending Models - Innovation and Marketing in the Pharmaceutical Industry - page 564

other direction. Interestingly, authors note that the across-market interaction leads
to more homogenous price-cost margins across the international markets.
The relevance of launch investment . Another stream of work contributes to our
understanding of the temporal variation of marketing expenditures across the life of
a new drug. In an early paper, Lilien et al. ( 1981 , p. 503) derive from their diffusion
model a policy that the market share of the new product should be driven to some
competitive level and then maintained at that level. In order to achieve that target,
detailing expenditures should be high in the introductory phase until the target share
is achieved.
Recently, Osinga et al. ( 2010 ) introduced a dynamic brand sales model that is to
capture transient and persistent effects of marketing efforts. Let y t measure brand
sales in period t , x t measure marketing expenditures, and β 0 t denote a stochastic
trend in sales:

y =+ + bb e

0

x (19.4)

t t 1 tt t

The authors assume that the stochastic trend β 0 t follows a random walk with drift
β 2 t -1 x t , which leads to the following transition equation

bb b = + x + h (19.5)

0 t 0 t − 1 2 t − 1 t 0 t

where ε and η are uncorrelated and normally distributed error terms. The parameter
β 1 t measures the transient marketing effect and β 2 t -1 captures the persistent market-
ing effect. Osinga et al. ( 2010 ) assume a double-log sales response function and
estimate the model by means of Kalman filtering for 88 prescription drugs from 39
categories. Their findings show that both persistent and transient marketing effects
are strongest at the beginning of the life cycle. They become smaller or even disap-
pear in later periods. From these findings, the authors conclude that it pays off to
invest in marketing early in the life cycle, which is consistent with the expenditure
patterns in their data.
Another noteworthy brand sales model suggested by Narayanan et al. ( 2005 )
incorporates the changing role of communication over the life cycle of a new prod-
uct category. Their model distinguishes between an early phase of a product's life
cycle, where detailing helps physicians to reduce uncertainty about the true quality
of the product by updating their prior beliefs via a Bayesian learning process, and a
subsequent phase, where detailing has a reminder effect and directly influences
goodwill accumulation. Based on the estimates for the magnitudes of the two types
of effects, the authors can show via simulation analysis that detailing expenditures
should follow a temporal pattern with an emphasis put on expenditures during the
early phase.
To summarize, the observation of high marketing investments around product
launch seems to be well justified. Various approaches of modeling drug sales
response suggest such temporal differences in marketing expenditures.