IDENTIFYING MARKET TAKEOFF IN HIGH TECH INDUSTRIES
Dr. Yi-Nung Peng, Yuan Ze University, Taiwan
pengyn@saturn.yzu.edu.tw
Dr. Susan Sandrson, Rensselaer Polytechnic Institute, USA
sandes@rpi.edu
ABSTRACT
This research we collect US data from both the personal computer (PC) and portable digital
music player (commonly referred as MP3 players) industries and used derivative
approximation by finite differences method to identify market takeoff. In addition, we
examined the relationship between market takeoff and product innovations in the PC and
MP3 markets. The derivative approximation by finite differences method eatables
researchers to identify the market takeoff at a timely fashion which is an important advantage
over the traditional statistical methods which can only perform the task in a retrofitting
manner.
Keywords: Market takeoff, Method, PC industry, MP3 industry
INTRODUCTION
Although entry timing often depends on a firm’s resources and capabilities (Kerin,
Varadarajan, 1992;Lambkin, 1988;Lieberman and Montgomery, 1988;Lieberman and
Montgomery, 1998), firms are often confused about which stage of the product life cycle an
industry is in and whether it is too early or too late to enter.
The transition between the early commercialization and growth stages has been defined as
market takeoff (Golder and Tellis, 1997). On the other hand, Agarwal and Bayus (2002)
described market takeoff as “the first large increase in sales,” or “the hockey-stick pattern of
sales growth also seems to be popular among industry pundits.” They used discriminant
analysis to determine the timing of takeoff. Similar statistical methods have also been used
by other scholars in distinguishing different stages of innovations (Agarwal and Gort,
1996;Gort and Klepper, 1982).
Recognition of market takeoff (the period in which the entire product category has reached
the growth stage) is important given the perceived advantage of entering a market just before
or at the growth stage (Lilien and Yoon, 1990;Shankar, Carpenter, 1999). The stream of
literature describing the dual market development of the early stage innovations (Moore,
2002;Muller and Yogev, 2006) also pointed out the importance of market take off from the
aspect of characteristics of customers.
Factors such as economic, and cultural factors (Tellis, Stremersh, 2003), firm promotional
activities and timing (Delre, Jager, 2007), social network characteristics (Delre, Jager,
2010;Hohnisch, Pittnauer, 2008) and price drop (Hohnisch, Pittnauer, 2008) can impact the
timing of takeoff.
Product innovation may also trigger the market takeoff. A product innovation can provide
relative advantages that can increase the adoption rate (Rogers, 2003;Tornatzky and Klein,
1982).
Because this period of takeoff is so significant, it would be helpful for firms to understand the
factors that trigger market takeoff. A better understanding of what triggers takeoff and how
to recognize it would aid managers in becoming more proactive and effective in their product
development efforts and in understanding how timing of product introduction may affect
their success (Foster, Golder, 2004;Tellis, 2008).
Employing statistical methods to identiy market takeoff is rigorous but it relies on 20/20
hindsight. One needs to have many data points to determine the market takeoff time. An
industry participant during the early stage of an innovation might face difficulties in
identifying market takeoff using their method.
Addressing this issue, Golder and Tellis (1997) provided an alternative method to identify
market takeoff. They developed a threshold for takeoff defining takeoff as the first year in
which an individual category’s growth rate, relative to base sales, crosses this threshold.
According to the authors, this method identifies 90% of the takeoffs correctly. Further, visual
verification helps to ensure the correct identification of takeoff. Their method used a
minimum of 50,000 unit sales as a threshold because they found that a relatively large
percentage increase could occur without signaling real takeoff. Their method has the
advantage in identifying takeoffs in real-time even during the early stages of an innovation.
However, is there other method we can use to identify market takeoff in a proactive manner?
The market takeoff, it is a “sudden” increase in sales. It is essentially a “big acceleration”
in market sales. The industry sales of the PC innovation was increasing every year. Can we
identify the “big acceleration” in the PC industry mathematically instead of statistically?
We are proposing to use the derivative approximation of finite differences (Eberly, 2001) as
an alternative method for the takeoff identification. To achieve this goal, we collected the US
PC and MP3 player industry data to examine the possibility of using derivative
approximation of finite differences as a market takeoff identification method.
DATA
US Personal Computer Data
In searching for a consistent source for market information for US Personal Computer (PC)
industry, I utilized the annual publication of Datamation, the “Datamation 50 and the
Datamation 100.” Datamation magazine was the key professional magazine for “data
processing” industry during the time frame of the study. It was widely subscribed by
information technology professionals. I used the following sections of Datamation to
construct the quantitative aspect of the industry.
1. The Datamation 50 (1979) conducted by Datamation magazine, is an annual
systematic revenue summary of the top 50 Data Processing firms including computer
hardware, software, peripherals, and etc.
2. Datamation 100 (1980-1989).
The Datamation 100 is similar to Datamation 50 but includes top 100 firms. (timeframe)
Datamation data helped in estimating annual sales for the PC industry which were hard to get
from other sources. It was used by Chandler (2001) for his history of the electronics industry
(citation). I obtained market share data of the companies through various secondary sources
which will be discussed in detail in following sections.
In calculating firm market share I used the following:
Company Sales
Company Market Share= Industry Sales
I used this relationship to calculate “annual industry sales” by multiplying “annual company
sales” (from Datamation) and “company market share (from other sources and books
mentioned above). This is a reasonable method for estimating industry sales as it is difficult
to get access to this data for the early stage of the industry in any other way. Datamation’s
data helped to determine the progression of personal computer industry sales over time.
US Portable Digital Music Players Data
Due to the lack of well-organized texts, I performed two broad-term keyword searches on
ABInform Database to promote an understanding of technology advances and market size
data. The two keywords were 1) MP3, and 2) digital music. The market sales data is thus
assembled. The publications on which I performed keyword search can be categorized as 4
types:
1. Business Magazines: 1) Business Week, and 2) Fortune
2. Newspapers: 1) New York Times, and 2) Wall Street Journal
3. Two Popular Technology Magazines: 1) PC Magazine and 2) PC world
4. One Popular Music Magazine: Rolling Stone Magazine
ANALYSIS
Before we presenting our analysis details, we must clarify what is the “big acceleration” in
sales means. An analogy to concepts in physics is helpful. The annual sales number is
actually the “speed of sales” because the annual sales of an innovation represents its sales per
year (sales/year). Therefore, it is the “speed of sales” if we think of the annual industry sales
as the displacement of an object. Following this analogy, the annual increase in sales is the
“acceleration of sales”. This analogy helps in the identification of the “big acceleration” of
sales. Following this line of thinking, the “big acceleration” of sales is actually “the
maximum change” on the acceleration of sales.
However, mathematically how can we identify “the maximum acceleration of sales”? The
concept of derivative approximation of finite differences (Eberly, 2001) is helpful.
The detail analysis and rationales are presented as follow:
Derivative Approximation of Finite Differences

S(t) is the unit sales of an innovation; where t represents time;
The maximum change in the acceleration of sales is the maximum of S(t) ; that is the
maximum rate of change in the speed of sales. To calculate the S(t) , we must fist
understand the calculation of S(t) under the notion of derivative approximation of finite
differences, the derivate of S(t) can be calculated by forward, backward, and centered
difference approximations. Similarly, S(t) also can be found. 




To approximate the derivatives of a univariate function f k  by finite difference, given a
small value of h, where h>0, the f k and f k can be calculated as follow:
Forward difference approximation
f k  
f k  h   f k 
h


Where h 1

f k   f k  1  f k 
(1)
 f k   f k  1  f k 
1
f k   f k  2  f k 1  f k 1  f k   f k  2  2 f k 1  f k


(2)
Backward difference approximation

f k  
f k   f k  h
h
Where h 1


f k   f k   f k 1
 f k   f k   f k 1
1
f k   f k  f k 1  f k 1  f k  2  f k   2 f k 1  f k  2

(3)
(4)
Centered difference approximation

f k  
f k  h   f k  h
2h
Where h 1


f k  
f k  

f k  

f k  1  f k 1
2
f k  1  f k 1
2

 f k  2  f k  2   f k  f k  2 2
2
f k  2  2 f k   f k  2
4
To identify the market takeoff of the PC innovation we apply the equations 1 to 6.
Where S(t) is the unit sales of an innovation; t represents year; h=1 (year)


(5)
(6)
Forward difference approximation
S t   S t  1  St 
S t   S t  2  2S t  1  St 






(7)
Backward difference approximation
S t   S t   St 1
S t   S t   2S t 1  St  2
(8)
Centered difference approximation
S t  1  S t 1
2
S t  2  2S t   S t  2
S t  
4
S t  
(9)
For the purposes of this analysis, market takeoff is defined as the year the maximum increase
in sales rate. This point can be estimated from the discrete sales data using the centered
difference approximation
S t 1  St 1
2
S t  2  2S t   St  2
St  
4
St  


where S(t) is the unit sales in year t.
Takeoff Identification for PC and MP3 Markets
To identify the time of takeoff, given the method’s different approaches, we must discuss the
advantages of approaches. By plotting the industry sales and maximum peak of three
approximation
approaches
for
the
PC
(
Figure 1) and MP3 innovations (Figure 2), we can see that the market takeoff of the PC
innovation is identified to be in 1980, 1981, and 1982 respectively by the forward, centered
and backward approximations. The year of takeoff for MP3 players were in 2003, 2003 and
2005 respectively.
The Determination of the Proposed Approach—Backward Difference Approximation
However, which of the 3 approximation approaches is correct? We believe that the backward
difference approximation because its first order and second order derivatives are generated by
the comparison of current and the previous periods. Therefore, the output is more concurrent
which is the major purpose of this study—proactive takeoff identification.
8000
8000
7000
7000
6000
6000
5000
5000
4000
4000
Forward Centered Backward
Diff.
Diff.
Diff.
Max Peak Max Peak Max Peak
3000
3000
2000
2000
1000
1000
0
Chang or Rate of Change
Sales in thousand Units
Figure 1: PC Industry Unit Sales Evolution and Takeoff Identification.
0
75
76
77
78
79
80
81
82
83
84
85
-1000
-1000
Year
S(t) Unit Sales
S"(t) Centered Diff.
S"(t) Backward Diff.
S"(t) Forward Diff.
Figure 2: US MP3 Player Sales Evolution and Takeoff Identification.
24000
Forward
Diff.
Max Peak
Backward
Diff.
Max
Peak
17000
15000
13000
Sales in thousand Units
19000
14000
11000
Centered
Diff.
Max Peak
9000
7000
9000
5000
3000
4000
1000
-10001998 1999 2000 2001 2002 2003 2004 2005 2006 2007-1000
Year
S(t) Unit Sales
S"(t) Centered Diff.
S"(t) Backward Diff.
S"(t) Forward Diff.
Chang or Rate of Change
29000
8000
8000
7000
7000
6000
6000
5000
5000
4000
Backward
Diff.
First Peak
3000
4000
Backward
Diff.
Max Peak
3000
2000
2000
1000
1000
0
Chang or Rate of Change
Sales in thousand Units
Figure 3: Multiple Takeoffs of the U.S. PC Industry under the Backward Difference
Approximation.
0
75
76
77
78
79
80
81
82
83
84
-1000
85
-1000
Year
S(t) Unit Sales
S"(t) Backward Diff.
Figure 4: Multiple Takeoffs of the U.S. MP3 Players Industry under the Backward
Difference Approximation.
29000
24000
17000
15000
Sales in thousand Units
13000
19000
11000
9000
14000
7000
9000
Backward
Diff.
First Peak
5000
3000
4000
1000
-10001998 1999 2000 2001 2002 2003 2004 2005 2006 2007-1000
Year
S(t) Unit Sales
S"(t) Backward Diff.
Chang or Rate of Change
Backward
Diff.
Max
Peak
Multiple Takeoffs
Peng (2006) pointed out that , theoretically speaking, there maybe multiple take offs in the
product life cycle of an innovation. Such pheromone has been confirmed by Muller and
Yogve (2006) using the market takeoff identification tool developed by Golder and Tellis
(1997). Muller and Yogve (2006) observed three takeoffs in various consumer electronic
industries such as PC, printers, and remote controls. The multiple-takeoff characteristic of
innovations impacts our analysis profoundly.
Our identification of the peak of the rate of change on the acceleration of sales is only try to
identify the “the maximum rate of change” on the acceleration of sales. The “the of change”
on the acceleration of sales is naturally time-based. Therefore, the “the maximum change”
on the acceleration of sales is contingent upon the period of time which one studies.
Given this notion, to really identify the time of market takeoff, we must examine the first
peak of the curve of the rate of acceleration of sales. Figure 3 and Figure 4 show the first
peak and the maximum peak of the curve under the backward difference approximation
approach. We can see that the first takeoff for the PC and the MP3 player innovations are
actually in 1979 and 2002 respectively.
CONCLUSTION AND DISCUSSION
Market takeoff is an important phenomenon in the course of an innovation’s development.
Scholars in the field of technology and innovation management had developed statistical
tools (Agarwal and Bayus, 2002) and graphical tool (Golder and Tellis, 1997) to facilitate the
identification of market takeoffs.
The statistical method, though rigorous, can only identify the takeoffs in the retrospect.
Researchers need to collect a more complete sales data for the takeoff identifications. That is
why the graphical tool developed by Golder and Tellis (1997) is being used by practitioners
in the real world setting (Foster, Golder, 2004). However, we still rely on human visual
confirmation for the correct identification of market takeoffs and the method still can missidentify the market takeoffs (Golder and Tellis, 1997).
Therefore, we proposed to use the derivative approximation of finite differences method as a
new market takeoff identification method. This method can identify the takeoff earlier than
the traditional statistical methods given its only demand sales data of the next period. Given
its numeric nature, we can identify market takeoffs objectively.
We identify 1979 as the year of market takeoff for the PC innovation. Although differ from
the conclusion from Agarwal and Bayus (2002). However 1979 is one year after the
introduction of the complete package of the Apple II (Peng, 2006) in the PC innovation. And
2002 is one year after the introduction of the iPod. This shows that takeoff may be closed
related to the product innovation which is consist with existing diffusion literature. We still
need to examine more innovations and compare the conclusions draw from the new method
with existing methods to better evaluate the validity of identifying marketing using the
derivative approximation of finite differences method.
.
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
Kerin, R.A., Varadarajan, R.P., and Peterson, R.A. (1992), First-Mover Advantage: A
Synthesis, Conceptual Framework, and Research Propositions., Journal of Marketing.
56 33-52.
Lambkin, M. (1988), Order off Entry and Performance in New Markets, Strategic
Management Journal. 9 127-140.
Lieberman, M.B. and Montgomery, D.B. (1988), First-Mover Advantages, Strategic
Management Journal. 9 41-58.
Lieberman, M.B. and Montgomery, D.B. (1998), First-Mover (Dis)Advantages:
Retrospective And Link With the Resource-Based View, Strategic Management
Journal. 19 1111-1125.
Golder, P.N. and Tellis, G.J. (1997), Will It Ever Fly? Modeling the Takeoff of Really
New Consumer Durables, Marketing Science. 16(3) 256-270.
Agarwal, R. and Bayus, B.L. (2002), The Market Evolution and Sales Take off of
Product Innovations, Management Science. 48(8) 1024-1041.
Agarwal, R. and Gort, M. (1996), The evolution of markets, and entry, exit and
survival of firms, The Reviews of Economic Statistics. 78(3) 489-498.
Gort, M. and Klepper, S. (1982), Time paths in the diffusion of product innovations,
The Economic Journal. 92(3) 630-653.
Lilien, G.L. and Yoon, E. (1990), The Timing of Competitive Market Entry: An
Exploratory Study of New Industrial Products, Management Science. 36(5) 568-585.
Shankar, V., Carpenter, G.S., and Krishnamurthi, L. (1999), The Advantages of Entry
in the Growth Stage of the Product Life Cycle: An Empirical Analysis, Journal of
Marketing Research. 36 269-276.
Moore, G.A., Crossing the chasm : marketing and selling high-tech products to
mainstream customers2002, New York: Harper Business Essentials.
Muller, E. and Yogev, G. (2006), When does the majority become a majority?
Empirical analysis of the time at which main market adopters purchase the bulk of our
sales, Technological Forecasting and Social Change. 73(9) 1107-1120.
Tellis, G.J., Stremersh, S., and Yin, E. (2003), The International Takeoff of New
Products: The Role of Economics, Culture, and Country innovativness, Marketing
Science. 22(2) 188-208.
Delre, S.A., et al. (2007), Targeting and timing promotional activities: An agent-based
model for the takeoff of new products, Journal of Business Research. 60(8) 826-835.
Delre, S.A., et al. (2010), Will It Spread or Not? The Effects of Social Influences and
Network Topology on Innovation Diffusion, Journal of Product Innovation
Management. 27(2) 267-282.
Hohnisch, M., Pittnauer, S., and Stauffer, D. (2008), A percolation-based model
explaining delayed takeoff in new-product diffusion, Industrial and Corporate
Change. 17(5) 1001-1017.
Rogers, E.M., Diffusion of Innovations2003, New York: Free Press.
Tornatzky, L.G. and Klein, K.J. (1982), Innovation Characteristics and Innovation
Adoption-Implementation: A Meta-Analysis of Findings, IEEE Transactions on
Engineering Management. 29(1) 28-45.
Foster, J.A., Golder, P.N., and Tellis, G.J. (2004), Predicting sales takeoff for
Whirlpool's new Personal Valet, Marketing Science. 23(2) 182-185.
Tellis, G.J. (2008), Important research questions in technology and innovation,
Industrial Marketing Management. 37(6) 629-632.
21.
22.
Eberly, D., Derivative Approximation by Finite Differences, in Geometric Tools2001,
Geometric Tools, LLC.
Peng, Y.-N., The Influence of Major Product Innovations in Early Stage High
Technology Markets in Management2006, Rensselaer Polytechnic Institute: Troy.