Diffusion of Satellite-supported Telematics in European Passenger Cars ISF 2005, San Antonio,12th – 15th June Birgit LoeckerMichael A. Hauser ARC Seibersdorf research GmbHVienna University of Economics and Business Administration Mail:

2 Agenda Motivation and Scope of the Study Data Modelling: Durables Models: Bass and Gompertz Models: Specification Results of the Bass Model Estimation Results of the Gompertz Estimation Comparison of Bass & Gompertz Results Summary Discussion

3 Motivation Capacity problems on European road transport (EU15) infrastructure and potentials for improvement by: Rapid development of modern information and communication technologies & combined use with satellite navigation systems; Telematic systems and services offer market opportunities to the industrial actors; Higher transport safety; Better transport information, management & control.

4 Scope of the Study Modelling and forecasting the diffusion of satellite- supported telematic systems implemented in new luxury and middle class passenger cars by 5 European (EU 15) car manufacturers; Application of different types of diffusion models for consumer durables, comparison of the models:  Bass model;  Gompertz model.

5 Data (1) Cumulative sales data of satellite-supported telematic devices of 5 European car makers (anonymous) since market introduction; Market share of 20.7 % in the overall market (2002,EU15); Evidence of three groups of car makers with different diffusion behaviour:  Pioneers M4 and M5;  Follower M3;  Laggards M1 and M2.

6 Data (2)  Market potential: 2002 total stock of new registered cars;  Individual market shares of each car maker in this stock (average from 1995 – 2002);  Portion of luxury and middle class cars of each car maker is chosen;  Growth of the market potential of 2 % p.a., (transformation of the data to 2002 levels by adequate discounting).

7 Modelling: Durables Notation s t …… sales (units) in period t (observed) S t …… cumulative sales (units) up to period t, S t = ∑ t j=0 s j n t ……adopters in period t, new purchasers (unobserved) N t ……cumulative adopters, N t = ∑ t j=0 n j r t ……replacement demand, recurrent purchasers (units) N*…… potential adopters, potential stock of cars to be equipped (units) Replacement Demand (cp. Islam/Mead(2002) EJOR) Passenger cars and telematic systems are durable goods with the same scrappage incidence r t = d N t-1, t=1,2,…; Assumption: constant scrappage rate implying av. life time of 10; Current sales are composed of the demand of new adopters and replacement demand s t = n t + r t ; Adopter series (N 0 = 0): n t = s t - r t and N t = N t-1 + n t, t=1,2,…

8 Models: Bass and Gompertz Bass Model & Estimation Pooled estimation in discrete time and fixed effect form: n it = N it - N i(t-1) = [ p + q (N t-1 / N*) ] (N i *– N i(t-1) ) + ε t  i ….number of the car maker, i=1,..,5  imitators use information from the whole market (innovative) [n it /N i *]= p [(N i *–N i(t-1) )/N i *] + q [(N (t-1) /N*) (N i *– N i(t-1) )/N i *] + ξ it Gompertz Model & Estimation Linearisation of data by using a different time axis: F(t) = exp(-exp(-[a+b t c ])) a,b,c > 0 generalised Gompertz function Pooled estimation in levels partially linearised and with fixed effects: -ln(-ln (N it / N i *)) = a +b t c + ε t for i=1,…,5, Iterative procedure for (c) by minimising sum of squared residuals;

9 Models: Specification The model estimation addresses the problem of:  Small sample size  pooled estimation (Islam et al.(2002) IJF)  Individual potentials are taken into account by modelling relative values for the Bass model and the rate of market penetration for the Gompertz function. Identification of different groups of car makers:  Estimation of all car makers in one pool;  Different diffusion behaviour of three groups (Chow test): Pioneers (M4 and M5), Follower (M3), Laggards (M1 and M2).

10 Results of the Bass Model Estimation (1) Laggards (M1, M2) [n it /N i *]=0.0008[(N i *–N i(t-1) )/N i *] [(N (t-1) /N*)(N i *–N i(t-1) )/N i *] + ξ it p-values for the innovator and imitator parameters are and respectively; r 2 is 0.834, and DW statistic is 1.51; 18 obs. Follower (M3) [n it /N i *]=0.0025[(N i *–N i(t-1) )/N i *] [(N (t-1) /N*)(N i *–N i(t-1) )/N i *] + ξ it p-values for the innovator and imitator parameters are and respectively; r 2 is 0.922, DW = 1.41; 9 obs. Pioneers (M4, M5) [n it /N i *]= [(N i *–N i(t-1) )/N i *] [(N (t-1) /N*)(N i *–N i(t-1) )/N i *]+ ξ it p-values for the innovator and imitator parameters are and respectively; r 2 is 0.872, DW =1.21; 18 obs.

11 Results of the Bass Model Estimation (2) Long run level of cumulative adopters is normalised by the indiv. market potential of each car maker to 1; Different shapes due to pioneer, follower and laggard behaviour; Half of the long run level is obtained for the pioneer group in 2020, for the follower in 2028 and in 2052 for the laggards. Path of total adopters normalised: Pioneers, Follower, Laggards

12 Results of the Bass Model Estimation (3) Pioneers show an overshooting behaviour: from 2022 onwards, annual sales are above the long run level, reaching their peak in 2027 with 112% of the long run level, and decreasing slowly afterwards. Reason for the overshooting behaviour seems to origin in the slope of new adopters and the development of the replacement demand. Total Sales (s t ) of Pioneers Sales to New Adopters (n t ) Replacement Demand (r t )

13 Results of the Bass Model Estimation (4) Total Sales (s t ) of Laggards Sales to New Adopters (n t ) Replacement Demand (r t ) Total Sales (s t ) of Follower Sales to New Adopters (n t ) Replacement Demand (r t )

14 Results of the Gompertz Estimation (1) Laggards (M1, M2) -ln(-ln (N it / N i *)) = t ξ it p-values for the parameters are and respectively, r 2 is 0.985, DW = 1.33, 18 observations. Follower (M3) -ln(-ln (N it / N i *)) = t ξ it p-values for the parameters are and respectively, r 2 is 0.989, DW = 1.68, 9 observations. Pioneers (M4, M5) -ln(-ln (N it / N i *)) = t ξ it p-values for the parameters are and respectively, r 2 is 0.985, DW = 1.03, 18 observations.

15 Results of the Gompertz Estimation (2) Long run level of cum. adopters is normalised by the individual market potential of each car maker to 1; Different shapes due to pioneer, follower and laggard behaviour; Half of the long run level is obtained for the pioneer group in 2019, for the follower in 2025 and in 2061 for the laggards. Path of total adopters normalised: Pioneers, Follower, Laggards

16 Results of the Gompertz Estimation (3) Contrary to Bass model, no overshooting is observed in the total sales with respect to the long run level. The number of new adopters obtains its peak in 2015 – 6 years before the pioneers in the Bass model (shape is clearly skewed to the right); Market saturation by years after the Bass model result. Total Sales (s t ) of Pioneers Sales to New Adopters (n t ) Replacement Demand (r t )

17 Results of the Gompertz Estimation (4) Total Sales (s t ) of Laggards Sales to New Adopters (n t ) Replacement Demand (r t ) Total Sales (s t ) of Follower Sales to New Adopters (n t ) Replacement Demand (r t )

18 Comparison of Bass & Gompertz Results Pioneers (M4, M5) Cumulative adopters: Half of the potentials are reached at the same (approx.) time in both models; Then the Bass model shows a faster increase in cumulative adopters than the Gompertz model, Total Sales: Increases are higher in the Gompertz than in the Bass model and within 4 years total sales of the Bass model catch up with that of the Gompertz model which takes 9 years for the same increase ; Follower (M3) and Laggards (M1 and M2) Differences are even more pronounced.

19 Summary Discussion Modelling of the diffusion of satellite-supported telematic systems implemented in European passenger cars outlines future market development in the long run; Several comprehensive (ceteris paribus) sensitivity analyses with respect to:  Overall saturation level,  Possible compounding to take into account a growing saturation level (0 – 2 % p.a.),  Scrappage rate (av. life time 10 to 15 years),  Share of newly sold cars equipped with telematic systems of a single car maker. Results for both models are robust for all but the market share choices; In case of overshooting behaviour, the Bass model is more realistic; in the absence of overshooting behaviour, the Gompertz function seems to model the diffusion more adequately.