Market potential dynamics and diffusion of innovation: modelling synergy between two driving forces

Market potential dynamics and diffusion of innovation: modelling synergy between two driving forces Renato Guseo 1 Mariangela Guidolin 1 1 Department of Statistical Sciences University of Padova, Italy Milan, September 14-16, 2009/ S.Co. 2009, Politecnico di Milano R. Guseo, M. Guidolin Slowdown and Market Dynamics 1/ 22

Outline 1 Introduction to Innovation Diffusion Approaches 2 Dynamic Market Potential and Diffusion (Guseo and Guidolin, 2009) 3 4 Co Evolutionary Model Statistical Aspects: Slowdown and likelihood ratio order R. Guseo, M. Guidolin Slowdown and Market Dynamics 2/ 22

Slowdown Rationale 1 Slowdown in new products The presence of a slowdown in new products life cycle has recently received notable attention. R. Guseo, M. Guidolin Slowdown and Market Dynamics 3/ 22

Slowdown Rationale 2 Dual Market Hypotheses Recent literature on innovation diffusion has followed the idea that the market for new products needs to be divided into two segments that give rise to a mixture: "visionaries and pragmatists", Moore (1991); "early market and main market", Karmeshu and Goswami (2001), Vakratsas and Kolsarici (2008); "influentials and imitators", Van den Bulte and Joshi (2007). This classification has been theorized as a possible explanation of the slowdown pattern also known as chasm, saddle or dip. After a rapid takeoff, product s sales reach an initial peak followed by a decline and eventually by a resumption that may exceed the initial peak. R. Guseo, M. Guidolin Slowdown and Market Dynamics 4/ 22

Slowdown Rationale 3 Dual Effect Hypothesis A new model proposed by Guseo and Guidolin (2009) shows that a slowdown may emerge as consequence of the existence of a dual-effect in market evolution. Diffusion is modelled through two distinct co evolving processes: communication and adoption. A multiplicative framework: not a mixture. Communication dynamics are seen as determinants of the market potential, whose structure is not fixed. The dual-effect modelling allows for a dynamic ranking between the two co evolving processes, communication and adoption, with different managerial implications. R. Guseo, M. Guidolin Slowdown and Market Dynamics 5/ 22

A Dynamic Market Potential 1 Communication and Adoption Effects Guseo and Guidolin (2009): a mean field approximation of a Cellular Automaton y y(t) (t) = m(t) r s m(t) + y(t) p s + q s m(t) 1 y(t) x(t)+y(t) m (t) m(t) m(t), (1) y (t), y(t): instantaneous/cumulative adoptions at time t; p s and q s : usual Bass like parameters depicting innovation and imitation effects; r s : decay parameter for not retained adoptions; m(t) 0: a non negative function for dynamic potential;, self reinforcing term; x(t): exogenous interventions function (marketing mix strategies, policies, incentives). y(t) m (t) m(t) R. Guseo, M. Guidolin Slowdown and Market Dynamics 6/ 22

A Dynamic Market Potential 2 Basic Solution Equation (1) defines a non autonomous Riccati equation. Its closed form solution is R t0 1 e Ds x(τ)dτ y(t) = m(t) 1 1 R, e Ds t0 x(τ)dτ sr 2 sr 1 Ds = q (q s p s r s) 2 + 4q sp s > 0, where sr i = ( (q s p s r s) ± D s)/( 2q s), i = 1, 2, with sr 2 > sr 1. Function m(t) may be modelled in different ways. (2) R. Guseo, M. Guidolin Slowdown and Market Dynamics 7/ 22

A Dynamic Market Potential 3 Potential Specification In Guseo and Guidolin (2009) communication dynamics are represented by a Network Automata whose mean field approximation is an autonomous Riccati equation, ν (t) = (q c + w c)ν 2 (t) + (q c p c e c)ν(t) + p c, q c > p c > 0, (3) p c : external component of the communication process; q c and w c : positive and negative word of mouth parameters; e c : loss of information due to ageing. We assume m(t) = K ν(t) as the actual market potential. If communication effects are persistent, e c = 0, and there is no negative word of mouth, w c = 0, then we obtain m(t) = K vut 1 e (pc +qc )t. (4) 1 + qc e (pc +qc )t p c R. Guseo, M. Guidolin Slowdown and Market Dynamics 8/ 22

Pharmaceutical Drugs Diffusion in Italian Areas 1 Weekly data of the diffusion of new pharmaceutical drugs in Italy are provided by IMS Health. Period: April/August 2005 July 2007. Pharmaceutical products: an ideal candidate for modelling the co-evolution of communication and adoption. The first usually precedes and pulls the second. This common order may be contradicted in some cases. Often the pharmaceutical market is created from patients need for treatment resulting in an accumulation of demand, prior to product launch. We may expect that a new drug, treating a severe pathology, will be characterized by a diffusion process where the accumulated demand of patients determines an early dominance of adoptions. R. Guseo, M. Guidolin Slowdown and Market Dynamics 9/ 22

Pharmaceutical Drugs Diffusion in Italian Areas 2 KEP (Ketoprofen): launched in Italy in April 2005. Commonly employed for treating pain and inflammations. LYR (Pregabalin): initially approved for treating epilepsy, neuropathic pain and post-herpetic neuralgia pain. Effective in patients who have previously failed to respond to other active principles (e.g. Gabapentin). Model without exit rates (w c = e c = r s = 0) and exogenous interventions (x(t) = 1), w(t) = K vut 1 e (pc +qc )t 1 1 + qc e (pc +qc )t p c e (ps+qs)t 1 + qs e p (ps+qs)t + ε(t). (5) s R. Guseo, M. Guidolin Slowdown and Market Dynamics 10/ 22

Pharmaceutical Drugs Diffusion in Italian Areas 3 Figure: KEP-NordEst : two synergistic components. Communication (k 1 ) is a precursor of adoption (k 2 ); R 2 = 0.999702. R. Guseo, M. Guidolin Slowdown and Market Dynamics 11/ 22

Pharmaceutical Drugs Diffusion in Italian Areas 4 Figure: LYR-Italy : two synergistic components. Adoption (k 2 ) is a precursor of communication (k 1 ); R 2 = 0.99991. R. Guseo, M. Guidolin Slowdown and Market Dynamics 12/ 22

Pharmaceutical Drugs Diffusion in Italian Areas 5 Figure: Rate data, co evolutionary model, ARMAX sharpening. R. Guseo, M. Guidolin Slowdown and Market Dynamics 13/ 22

Model Components 1 w(t) = K vut 1 e (pc +qc )t 1 1 + qc e (pc +qc )t p c e (ps+qs)t 1 + qs e p (ps+qs)t + ε(t) = K K (t) + ε(t). (6) s where K (t) = F(t) G(t) is a probability distribution function whose density k(t) = K (t)/ t is k(t) = 1 2 F(t) 1/2 G(t)f (t)+f(t) 1/2 g(t) = k 1 (t)+k 2 (t), t > 0, where f (t) = F(t)/ t and g(t) = G(t)/ t. R. Guseo, M. Guidolin Slowdown and Market Dynamics 14/ 22

Model Components 2 Normalized non negative functions k 1 (t) and k 2 (t) define densities k i (t) = k i (t)/k i with K i = 0 k i(t)dt, i = 1, 2. Random v. X and Y may be associated to k 1 (t) and k 2 (t). Definition. We say that Y is larger than X in likelihood ratio order, X lr Y, if X and Y have densities such that, for all s t, k 1 (t) k 2 (s) k 1 (s) k 2 (t). (7) Inequality based on k i (t), i = 1, 2 densities does not depend on the quantities K 1 or K 2 or their ratio. We can compare directly k i (t), i = 1, 2. Equation (7) states that k 2 (t)/ k 1 (t) or k 2 (t)/k 1 (t) is increasing avoiding the special cases with vanishing denominators. R. Guseo, M. Guidolin Slowdown and Market Dynamics 15/ 22

Likelihood Ratio Order 1 Figure: Likelihood Ratio Order between k 2 (t) and k 1 (t) for pharmaceutical drugs FOL-NordEst, FOL-Centro, LIB-NordEst and KEP-NordEst in Italy. The increasing ratio denotes a (first order) stochastic dominance of k 2 (t) component or, equivalently, a driving role of communication, k 1 (t). R. Guseo, M. Guidolin Slowdown and Market Dynamics 16/ 22

Likelihood Ratio Order 2 Figure: Likelihood Ratio Order between k 2 (t) and k 1 (t) for pharmaceutical drugs REX-Italy and LYR-Italy in Italy. The decreasing ratio denotes a (first order) stochastic dominance of k 1 (t) component or, equivalently, a driving role of adoption, k 2 (t). R. Guseo, M. Guidolin Slowdown and Market Dynamics 17/ 22

Pharmaceutical Drugs Diffusion in Italian Areas 6 As a direct control, we can compute the likelihood ratios k 2 (t)/ k 1 (t) or k 2 (t)/k 1 (t). For KEP we obtain an increasing function. The effect associated to k 1 (t), i.e. the communication effect, has an earlier dominance in the evolution of this drug. Vice versa, the opposite diffusion structure of LYR, with an earlier driving role pertaining to adoption forces, is denoted by a decreasing ratio. R. Guseo, M. Guidolin Slowdown and Market Dynamics 18/ 22

Pharmaceutical Drugs Diffusion in Italian Areas 7 Observing Figure 2, for KEP the likelihood order confirms a predictable behaviour, according to which communication has a driving role, preceding and pulling adoptions. Instead, in the case of LYR, depicted in Figure 4, we observe an explicit inversion, so that the adoption component dominates the first part of diffusion. We believe that this difference in behaviour may be related to the nature of the drugs considered. R. Guseo, M. Guidolin Slowdown and Market Dynamics 19/ 22

Pharmaceutical Drugs Diffusion in Italian Areas 8 The use of antiepileptic drugs for neuropathic pain management begun with, Carbamazepine and Gabapentin. These drugs had not always the expected results. Physicians and patients were waiting for new generation of neurostabilizers drugs. When LYR was put into commerce there probably was an accumulation of demand for it: consistently, adoption dynamics have a driving role in the first part of its diffusion. Moreover, LYR exhibits a saturating life cycle probably due to its special formulation, which is based on a cumulative concentration with a natural delayed response, and to the cost of a prolonged therapy. This may explain the reduction of adoptions (and a return to Gabapentin). R. Guseo, M. Guidolin Slowdown and Market Dynamics 20/ 22

Pharmaceutical Drugs Diffusion in Italian Areas 9 On the other side, KEP does not treat specific pathologies but is assumed for minor ailments. KEP does not seem to have the characteristics of a really innovative product, we argue that the pattern first communication, then adoption is explained by the simple need of promoting the new product, when put in commerce. In these cases communication, both institutional and informal, has exerted its natural effect of stimulating adoptions through the generation of the market potential. R. Guseo, M. Guidolin Slowdown and Market Dynamics 21/ 22

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