Diffusion of
Satellite-supported Telematics
in European Passenger Cars
ISF 2005, San Antonio,12th – 15th June
Birgit Loecker
ARC Seibersdorf research GmbH
Michael A. Hauser
Vienna University of Economics
and Business Administration
Mail: birgit.loecker@arcs.ac.at
Mail: michael.hauser@wu-wien.ac.at
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
2
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
4,000
actors;
3,500
3,000
Higher transport
2,500
safety;
2,000
1,500
Better transport
1,000
500
information,
0
management &
1970
1980
1990
2000
control.
Passenger Transport in
Passenger-kilometres (billion)

Cars
Buses & Coaches
Railw ay
3
Scope of the Study

Modelling and forecasting the diffusion of satellitesupported 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.
4
Data (1)

Cumulative sales data of satellite-supported telematic devices of 5
European car makers (anonymous) since market introduction;
700,000
Cumulative Sales (units)
600,000
M1
500,000
M2
400,000
M3
300,000
M4
200,000
M5
100,000
0
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003


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.
5
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).
Car Makers
M1
Market shares (%)
20.6 %
Portion of luxury &
middle class cars of the
80%
stock (%)
Market Potential (abs.)
5,086,400
M2
15.9 %
M3
3%
M4
21.8 %
M5
38.6 %
Sum
100 %
30 %
80 %
60 %
100 %
-
3,927,000
748,000
5,385,600 9,537,000 24,684,000
6
Modelling: Durables
Notation
st …… sales (units) in period t (observed)
St …… cumulative sales (units) up to period t, St = ∑tj=0 sj
nt …… adopters in period t, new purchasers (unobserved)
Nt ……cumulative adopters, Nt = ∑tj=0 nj
rt …… 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 rt = d Nt-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 st = nt + rt;
Adopter series (N0= 0): nt = st - rt and Nt = Nt-1 + nt , t=1,2,…
7
Models: Bass and Gompertz
Bass Model & Estimation

Pooled estimation in discrete time and fixed effect form:
nit = Nit - Ni(t-1) = [ p + q (Nt-1 / N*) ] (Ni*– Ni(t-1)) + εt

i ….number of the car maker, i=1,..,5

imitators use information from the whole market (innovative)
[nit /Ni*]= p [(Ni*–Ni(t-1))/Ni*] + q [(N(t-1) /N*) (Ni*– Ni(t-1))/Ni*] + ξit
Gompertz Model & Estimation



Linearisation of data by using a different time axis:
F(t) = exp(-exp(-[a+b tc])) a,b,c > 0 generalised Gompertz function
Pooled estimation in levels partially linearised and with fixed effects:
-ln(-ln (Nit / Ni*)) = a +b tc + εt for i=1,…,5,
Iterative procedure for (c) by minimising sum of squared residuals;
8
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).
9
Results of the Bass Model Estimation (1)
Laggards (M1, M2)

[nit/Ni*]=0.0008[(Ni*–Ni(t-1))/Ni*]+0.0274[(N(t-1)/N*)(Ni*–Ni(t-1))/Ni*] + ξit

p-values for the innovator and imitator parameters are 0.0003 and
0.0261 respectively; r2 is 0.834, and DW statistic is 1.51; 18 obs.
Follower (M3)

[nit/Ni*]=0.0025[(Ni*–Ni(t-1))/Ni*]+0.1088[(N(t-1)/N*)(Ni*–Ni(t-1))/Ni*] + ξit

p-values for the innovator and imitator parameters are 0.0133 and
0.0738 respectively; r2 is 0.922, DW = 1.41; 9 obs.
Pioneers (M4, M5)

[nit/Ni*]= 0.0014[(Ni*–Ni(t-1))/Ni*]+0.2822[(N(t-1)/N*)(Ni*–Ni(t-1))/Ni*]+ ξit

p-values for the innovator and imitator parameters are 0.0153 and
0.0000 respectively; r2 is 0.872, DW =1.21; 18 obs.
10
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.
1.0
0.8
0.6
0.4
0.2
0.0
2000
2020
2040
2060
2080
Path of FC_FSST_P
total adopters normalised:
FC_FSST_MA
Pioneers,
Follower, Laggards
FC_FSST_F
FC_05
11
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.
1.2
1.0
0.8
0.6
0.4
0.2

Reason
for
the
overshooting
behaviour
seems to origin in the
slope of new adopters and
the development of the
replacement demand.
0.0
2000
2020
2040
2060
Total Sales (sFC_ASR__BM
FC_ASN__BM
t) of Pioneers
Sales to New Adopters (nt)
Replacement Demand (rt)
2080
FC_AS__B
12
Results of the Bass Model Estimation (4)
1.2
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0
2000
2020
FC_ASN__MA
2040
2060
FC_ASR__MA
Total Sales (st) of Follower
Sales to New Adopters (nt)
Replacement Demand (rt)
2080
FC_AS__MA
2000
2020
FC_ASN__AU
2040
2060
FC_ASR__AU
2080
FC_AS__AU
Total Sales (st) of Laggards
Sales to New Adopters (nt)
Replacement Demand (rt)
13
Results of the Gompertz Estimation (1)
Laggards (M1, M2)

-ln(-ln (Nit / Ni*)) = - 2.282 + 0.231 t0.58 + ξit

p-values for the parameters are 0.0000 and 0.0000 respectively,
r2 is 0.985, DW = 1.33, 18 observations.
Follower (M3)

-ln(-ln (Nit / Ni*)) = - 2.108 + 0.204 t0.73 + ξit

p-values for the parameters are 0.0000 and 0.0000 respectively,
r2 is 0.989, DW = 1.68, 9 observations.
Pioneers (M4, M5)

-ln(-ln (Nit / Ni*)) = - 2.070 + 0.130 t0.92 + ξit

p-values for the parameters are 0.0000 and 0.0000 respectively,
r2 is 0.985, DW = 1.03, 18 observations.
14
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.
1.0
0.8
0.6
0.4
0.2
0.0
2000
2020
2040
2060
2080
FC_F SST_MA
Path ofFC_FSST_P
total adopters normalised:
FC_FSST_F
FC_05
Pioneers,
Follower, Laggards
15
Results of the Gompertz Estimation (3)
1.0



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 2080
- 30 years after the Bass
model result.
0.8
0.6
0.4
0.2
0.0
2000
2020
2040
2060
FC_ASN__BM
Total Sales (sFC_ASR__BM
t) of Pioneers
Sales to New Adopters (nt)
Replacement Demand (rt)
2080
FC_AS__B
16
Results of the Gompertz Estimation (4)
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0
2000
2020
FC_ASN__MA
2040
2060
FC_ASR__MA
Total Sales (st) of Follower
Sales to New Adopters (nt)
Replacement Demand (rt)
2080
FC_AS__MA
2000
2020
FC_ASN__AU
2040
2060
FC_ASR__AU
2080
FC_AS__AU
Total Sales (st) of Laggards
Sales to New Adopters (nt)
Replacement Demand (rt)
17
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 ;
Bass
Gompertz
Cum. Adopters (N):
50 %
Cum. Adopters (N):
80 %
Sales (s):
50 %
Sales (s):
80 %
Max. of new
adopters (n)
2020
2019
2027
2031
2014
2010
2018
2019
2021
2015
Follower (M3) and Laggards (M1 and M2)
 Differences are even more pronounced.
18
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
19
seems to model the diffusion more adequately.