Full Length Research Paper
Growth of mobile phone subscribers in India
Debabrata Das
Indus Business Academy, Plot No. 44, Knowledge Park-III, Greater Noida-201308, Uttar Pradesh, India. Email: debabrata69@hotmail.com: Tel. +91-120-3921000
Accepted 13 August, 2012
The aim of this paper is to forecast the growth of mobile phone subscribers in India. Based on the data of mobile phone subscribers from the year 1996-97 to 2007-08, a short term forecast is made up to the year 2015-16. Under assumed saturation level, the logistic and Gompertz distribution function are used for forecasting the growth of mobile phone subscribers in India. It is observed that, the coefficient of determination is high and mean square error is low in case of logistic distribution. This distribution forecasts the growth of mobile phone subscriber to 98 per 100 people in India by the year 2015-16. This study will be useful for planners, policy makers and researchers in the area of the telecommunications sector for realistic view of the subject and for planning appropriate strategy accordingly.
Keywords: Mobile phone subscribers, Logistic model, Gompertz model, Saturation level, Forecasting.
INTRODUCTION
Today is the era of wireless communication which gives rise to mobile phones. Mobile phones are the latest invention and common way to communicate now-a-days. It is a long range, portable and wireless electronic device of communication. A few years back, when mobile phones were not so common, the device was expensive and communication costs were pretty high to the user. But in last a few years as the use of mobiles increased, their cost decreased considerably and this factor helped a lot to make them available for common man. Mobile phones are now inexpensive, easy to use, and comfortable and equipped with almost every latest feature we desire. The growth of mobile phone subscribers and its usage is expanding rapidly throughout the world. The ability of mobile phone to keep in touch with family, business associates, etc., provides the user with a sense of safety and security. Today's technologically advanced mobile phones are capable of not only receiving and making phone calls, but also storing data, taking pictures and can even provide access to email and internet, to name just a few of the available options. The latest developments in mobile communication include, tablet PCs, which are hand-held devices that help you in both communications as well as using these devices as mobile offices. Mobile phones also proved to be a big help in emergencies. These devices have proved to be lifesavers as helping people in emergencies; when someone gets stuck in the middle of the road and find no one for help then he or she can call for
help by using these mobile devices. There is also this obvious convenience of quick access to help in emergencies big and small. The mobile phones are both economical and essential for travelers trying to stay connected. Nowadays it has become a necessity for many people. However, in recent time some of the reports have been published, which have highlighted the potential impact of electromagnetic fields generated by cellular phones on the human brain. Accumulating evidence indicate that microwave radiation from mobile phones may cause serious diseases and disturbances in the human physiology. This includes an increased cancer risk and genetic damage, disturbed brain function and other effects. Besides, the mobiles have been helpful in making the markets efficient. They have proved to be a boon for small producers, in effective price discovery mechanisms. In the olden times, when mobile phones were available at premium, and was out of reach of common man; small time businessmen like fishermen, farmers etc., used to take their produce to the nearest wholesale market and sell them at prices prevalent in the market place. In case of many suppliers reaching the same wholesale market, it would make the farmers and fishermen to sell their produce at throw-away prices; sometimes even below their cost. However, in another nearby wholesale market, which would only be a couple of hundred kilometers away, there could a short supply and the prices could be soaring. With the advent of mobile phones, and its cheap availability;
Table 1. Mobile Phone Subscribers and Population in India
Year Total Population*
Total Subscribers Density of Mobile Subscriber# 1996-97 949878000 339031 0.04 1997-98 965607000 882316 0.09 1998-99 981324000 1199578 0.12 1999-00 996944000 1884311 0.19 2000-01 1028610000 3577095 0.35 2001-02 1045547000 6431520 0.62 2002-03 1062388000 12687637 1.19 2003-04 1079117000 33311561 3.09 2004-05 1095722000 56888928 5.19 2005-06 1112186000 101809676 9.15 2006-07 1128521000 165093655 14.63 2007-08 1144734000 261081713 22.81
Source: Telecom Regulatory Authority of India
* Estimated by Registrar General of India based on 1991 and 2001 census. # Mobile phone subscriber per 100 persons
such anomalies have been removed, and it has enabled the producers to communicate with other producers as well as traders in different markets; ascertain the prices prevalent in different markets; and divert their vehicles/boats in the direction of the market where supply is less and they are able to fetch better prices.
India is one of the fastest growing mobile markets in the world. In terms of mobile phone subscribers it holds the second position, just after China. However, the density of mobile phone subscribers in India is still low i.e. 23 percent until year 2007-08 (Cellular Operator Association of India, 2007). As there is a huge potential for growth of mobile phone subscriber in India, the objective of this paper is to forecast the growth of mobile phone subscribers, up to year 2015-16. Using an exogenously defined saturation level and annual mobile phone subscriber’s data from the year 1996-97 to 2007-08, the logistic and Gompertz aggregate diffusion models are used to forecast the growth of mobile phone subscribers. On the basis of curve fitting, the coefficient of determination (R2) and the mean square error (MSE) are calculated for the most accurate model to be selected. Developing models, based on these distributions is to explain the growth of mobile subscribers, especially in evolutionary markets, is critical for policy formulation, capacity planning and introduction of new services. These models will help the mobile service providers to formulate appropriate strategies and policies to tap the future market in India.
This paper proceeds as follows. Section 2 discusses the mobile market in India; review of literature is presented in Section 3; Section 4 models the mobile market in India; evaluation of the models is presented in Section 5; and conclusion of the paper is summarized in Section 6.
Mobile market in India
In 1995, the first mobile telephone service started operating in metro cities of India, after the telecom sector was opened up by the Government for private investment, as a part of Liberalization-Privatization-Globalization policy. A year later, the services spread towards rest of the geographical areas of India. During the initial five to six years, the average growth of mobile phone subscribers was very tardy; probably due to the high price of mobile phone equipment and air time charges of the service providers. After the New Telecom Policy in 1999, the mobile phone industry introduced several consumer friendly initiatives. Since then the mobile subscriber additions started picking up and crossed the fixed-line connections in September 2004. Till January 2009, India had 267.54 million mobile phone subscribers (Cellular Operator Association of India, 2007). In India, the mobile phone service operators use the GSM (global system for mobile communications) and CDMA (code-division multiple access) technologies. About 75 per cent of the mobile phone users under GSM technology with 900 MHz band but, recently, the providers operate in the 1800 MHz band, as well (TRAI Annual Report, 2006-07). At present, the dominant players in India are Airtel, Reliance Infocomm, Vodafone, Idea cellular, AirCell, Tata Telecom and BSNL (Bharat Sanchar Nigam Limited) / MTNL (Mahanagar Telephone Nigam Limited). There are also many smaller players, operating in only a few states.
The growth of mobile phone subscribers in India has increased tremendously over the last few years (Table 1). From year 1996-97 to 2007-08, the number of mobile phone subscribers increased from 0.34 million to 26.11
Figure 1. Mobile phone subscribers
million i.e. more than 77 fold increase; while in the same duration population rose to about 1.21 fold i.e. from 949.78 million to 1.15 billion. Similar growth rate can also be observed in the analysis of density of mobile phone subscribers. In 1996-97, the density of mobile phone subscribers was about 0.04 per cent, but after twelve years, it increased to 22.81 per cent.
The data reveals the real potential for growth of the Indian mobile phone market. Thus, the rapid increase in mobile phone subscribers during the last decade may be primarily due to the increase of the average household income and mobile phone production. Besides, there has been a significant decrease in price of mobile phones along with corresponding tariffs. All these factors have contributed to the increase of the mobile phone subscribers. However, equally important reasons are to be found in the decrease of growth rate in land line phone. Service quality, convenience, flexibility and availability favor adoption of mobile phones than land line phones. Latest research suggested that the growth of mobile phones in India would be among the fastest anywhere for years (Cellular Operator Association of India, 2007).
Figure 1 shows the graph of mobile phone subscribers per 100 persons with respect to the year from 1996-97 to 2007-08. It is observed that the actual growth of the curve is initially slow up to 2005-06 and then it increases rapidly. Therefore, these data seem to fit well in S shaped curve of Gompertz and the logistic model for forecasting the mobile phone subscribers. Finally, using this trend the forecasting model will be developed for India.
Literature review
The S shaped or sigmoid curves have often been used in the fields of demography, biology and economics. In case of demography and biology, these curves describe the evolution of populations, but later on, the processes of
dissemination and self organization associated with the spread of new technologies and products, technological change and in general, economic growth is described. First use of these models to analyze the economic growth is attributed to the French sociologist Tarde (1903) more specifically, in relation to innovation. Tarde’s idea followed by other scholars like Mansfield (1961) sought to explain the observed patterns of diffusion in terms of the expected profitability of the innovation, and the dissemination of information about its technical and economic characteristics. Artle and Averous (1973) were analyzing the telephone system offered a “network consumption externality” explanation wherein the value of the network for a subscriber increases with the number of adopters of the system. Similarly, Rogers (1983) employed a communications-based model for explaining diffusion patterns.
There are a number of different functional forms that can describe S-shaped curves, for example, Brass, logistic, Gompertz, etc. (Kim and Kim, 2004, Michalakelis et al., 2008). These curves are to forecast how and when a given new product (innovation) based on a number of parameter such as rate of penetration, market potential and industry-specific constant will reach its saturation limit. The two frequently used diffusion model of S-curve representing different growth patterns are the logistic and the Gompertz functions (Botelho and Pinto, 2000, Barros and Cdima, 2001, Sridhar, 2006). Both the Gompertz and the logistic functions were developed in reaction to the Malthus’ natural growth function, in which the population grows exponentially, which seems to be unrealistic because environment imposes limitations to every growth pattern. Gompertz’ original work was presented at the Royal Society of London in 1825 and is described in the literature of Smith and Keyfitz (1977). However, the logistic model was applied for the first time by Verhulst, who published his research in 1838 in the journal “Correspondence Mathematique et Physique”. Almost a century later, in
1920, Pearl and Reed rediscovered the logistic model in course of their study of the evolution of fly population (Jarnc, et al. 2005). Originally these models were developed to describe the self-limiting growth of population. Although the path of these growth functions can be represented in general S-shape fashion, different types of entities can grow different patterns. Hence, the exact form of the curves, including the slope and the asymptote, may be different for each particular growth pattern. For example, the slope may be very steep during early phases, including rapid growth, or it may be gradual, suggesting a slow and hesitant start; but all of them will level into saturation limit. Main advantage of these models is to reach the saturation level in long term forecast, as most of the systems, whether natural or artificial, attain saturation level after a certain period. The properties of the S-curve growth model is such that if the growth is quite rapid at an early phase and relatively slow when approaching the saturation level, then the Gompertz function is the best method because it attains its maximum rate of growth at an earlier phase than that of logistic model. If, on the other hand, the diffusion process is such that growth is initially slow and relatively rapid during the maturing phases, then the logistic model is a superior forecasting method because, it grows more rapidly towards the maximum level than the Gompertz model.
The major problem that has to be solved first in these models is the saturation level. A few studies have estimated the saturation level from the S-curve growth function, but most of the studies provide the saturation level externally by applying rule of thumb, e.g. 60 mobile phone subscribers per 100 persons (Gruber and Verboven, 1999), 70 mobile phone subscribers per 100 persons (Barros and Cadima, 2001), 100 mobile phone subscribers per 100 persons (Kim and Kim, 2004, Ozan et al., 2007).
Modeling the mobile market in India
Consistent with these theories and research findings, it is hypothesized that the cumulative number of mobile phone subscribers in India grows over time according to a sigmoid or S-shaped curve. Based on past research and current market scenario, this paper assumes the saturation limit will be attained, when the density of mobile phone subscriber is 100 per cent in India. Another problem is to find out the starting year of diffusion of mobile phone service. The first mobile telephone service was launched in India in the year 1995-96. Using saturation level and time period, the model is developed based on logistic and Gompertz distributions to forecast the mobile phone subscribers.
Let
M
t be the mobile phone subscribers per 100 persons at time (year)t
andS
be the saturation level. Thelogistic distribution has been developed as follows: The change in mobile phone subscribers with respect to time i.e.
dt
dM
tis proportional to the product of the level of mobile phone subscribers at time
t
i.e.M
t and thefraction of market untapped i.e.
S
M
S
t . The corresponding differential equation isS
M
S
bM
dt
dM
t t(
t)
[1]where
b
0
is the proportionality constant i.e. the penetration rate.Integrating equation [1] over the interval 0 to
t
, we get that the logistic function isbt t
ae
S
M
1
[2]The parameters
a
andb
model the location and shape of the curve, respectively. Fort
0
,a
S
M
1
0 is thestarting level of the mobile phone subscribers and for
t
= very large,M
S
is the saturation limit. The logistic curve reaches its maximum penetration rate at half of the saturation level i.e.M
t
S
/
2
, called the point of inflection of the curve and occurs atb
a
t
ln
. The logistic curve is symmetric about the point of inflection.Similarly, the Gompertz distribution has been developed as follows: The change in mobile phone subscribers with respect to time i.e.
dt
dM
tis proportional to the product of present level of mobile phone subscribers at time
t
i.e.t
M
and the logarithm of mobile phone subscriber densitylevel i.e.
t
M
S
ln
. The corresponding differential equation is
t t tM
S
bM
dt
dM
ln
[3]where
b
0
is the proportionality constant i.e. the penetration rate.Integrating equation [3] over the interval 0 to
t
, we get that the Gompertz function isbt
ae t
Se
M
[4]Table 2. Estimated results of Logistic and Gompertz models
Model Parameter Maximum Growth Rate b ln a R2 MSE Mobile Subscriber Year Logistic -0.61 8.56 0.99 0.18 50 2009-10
-(41.87) (79.12)
Gompertz -0.15 2.37 0.95 3.78 37 2011-12 -(14.41) (31.15)
Note: Figures in the parenthesis are value of t-statistics
Figure 2. Forecasting mobile phone subscribers in India
the curve, respectively. The Gompertz curve reaches its maximum penetration rate at
M
t
S
/
e
, which is the point of inflection of the curve that occurs atb
a
t
ln
. Fort
0
,a
Se
M
0
is the starting level of mobile phonesubscribers and for
t
= very large,M
S
, is the saturation limit. Unlike logistic curve, it is not symmetrical about its point of inflection.Finally, using saturation level
S
and time variablet
, the parametersa
andb
are estimated by ordinary least square procedure after transforming the logistic {equation [2]} and Gompertz {equation [4]} functions into logarithmic form,bt
a
M
S
t
1
ln
ln
[5]bt
a
M
S
t
ln
ln
ln
[6]where
t
is taken as 0 for 1995-96, 1 for 1996-97, 2 for 1997-98, and 12 for 2007-08. The ordinary least square estimation is carried out using Microsoft Excel software.Based on the coefficient of determination (R2) value and the mean square error (MSE), the model is selected and used for forecasting the mobile phone subscribers up to the year 2015-16, where MSE is the average of square of the difference between actual and forecasted values.
Evaluation of the models
The estimated results of mobile phone subscribers’ growth, using the logistic and the Gompertz diffusion model are reported in Table 2. Though these distributions have different functional forms, they have several features in common. All of them are monotonically increasing and have horizontal asymptotes with one of them representing saturation level. According to the R2 value, both of these models fit the data very well. Similarly, the estimated parameters of these distributions have the expected sign and all are highly significant i.e. significance under 99 per cent confidence level as observed from t-statistics. However, between these two models, the logistic provides the highest R2and the lowest MSE values, as compared to the Gompertz model.
In Figure 1, the original growth of mobile phone subscribers is initially slow, and then it follows a, relatively, rapid growth, hence following the logistic curve as observed in Figure 2, where it becomes clear that in the near future the growth rate will be higher. On the other
Table 3. Projected Population and Mobile Phone Subscribers
Year
Total Population #
Mobile Phone Subscribers
Pessimistic Moderate Optimistic 2007-08* 1144734000 261081713 261081713 261081713
2010-11 1192506000 578506894 789554615 957525379
2015-16 1268961000 1199812500 1239791953 1256889133 Note: * Actual Data
Note: # Population is estimated by Registrar General of India
hand, the slow growth of mobile phone subscribers in initial phase is due to the expensive and communication. Alternatively, the growth of mobile phone subscribers is quite rapid in early phase, as predicted by the Gompertz curve, which is not in accordance with actual growth of mobile phone subscribers.
Therefore, it is inferred that the logistic model provides better fitting for mobile phone subscribers in India than the Gompertz. Finally, using saturation levels S = 100 and the selected parameters
a
andb
(Table 2) in logistic equations [2], we get the forecasting models of mobile phone subscribers per 100 persons as given below.t t
e
M
0.6209
.
5209
1
100
[7]Using t = 15, 20 and 25, the equation [7] forecasts the growth of total number of mobile phone subscribers in different scenarios such as pessimistic, moderate and optimistic in India for the years 2010-11 and 2015-16 are reported in Table 3.
The total number of mobile phone subscribers in India will rise from 261.08 million in 2007-08 to 1.24 billion in 2015-16, which is equivalent to the projected population at that time in moderate forecasting scenario. In the year 2010-11, the mobile phone subscribers is significantly difference in all the scenarios, however the difference is minimize in the year 2015-16. On the other hand, following the analysis of the growth of mobile phone subscribers per 100 people, it is also observed that the density of mobile phone subscribers will increase to 98 per cent by year 2015-16. Additionally, the mobile phone subscription is likely to attain the maximum growth rate in 2009-10, when the density of mobile phone subscription is expected to be around 50 per cent
(
M
t
S
/
2
100
/
2
)
. As discussed earlier, the logistic and Gompertz models assume different distribution functions for the threshold values of mobile phone subscribers. While the logistic function is based on a symmetric frequency distribution, the Gompertz function is derived from a skewed frequency distribution. The distinction has important implications for capacity planners. The results show that the rate of growth in case of mobile phone subscribers is closer to symmetric, as implied by logistic model, rather than attaining its maximum growth at an earlier phase as the Gompertz model suggests. Thisforecasting of future growth of mobile phone subscribers will help in estimating the untapped market of mobile phone subscribers in India.
CONCLUSION
Technological advances in recent years made available mobile telecommunication services at an unprecedented scale. The introduction of the digital technology as well as a more liberal stance on spectrum licensing has lead to a fast diffusion of mobile telephones. A simple examination of trends over the past twelve years clearly shows the rapid increase in mobile phone subscribers in India. This trend employs the logistic and the Gompertz diffusion models to forecast the growth in density of the mobile phone subscribers up to year 2015-16. Using annual data for mobile phone subscribers from year 1996-97 to 2007-08, the parameters of the two models were estimated by the means of ordinary least squares. These parameters are statistically significant and fit well under the assumed saturation levels. The R2values and mean square errors of these models suggest that the Logistic distribution is a better fit, for forecasting mobile phone subscribers. This indicates high expensive and communication costs of mobile phone user restrict the growth at initial phase of the introduction of new technology. In year 2015-16, the total number of mobile phone subscribers in India is likely to be around 1.24 million. This study is very useful for planners, policy makers and researchers in the area of telecommunication sector for a realistic view of the subject and the accordingly up taking of appropriate strategic moves. It is evident that, in these models, the mobile phone subscribers depend only on time. It can be also tested by taking other independent factors like income, mobile phone cost, call rate, etc. Extending the models with more independent factors may result in better forecasting of mobile phone subscriber growth. Despite this huge growth, the Indian market still has lot of potential. Majority of Indian population lives in the rural areas; which remains predominantly untapped. There is still lot of scope. The mobile operators is dominated by the private players, who do not find much incentive in getting into the rural regions, because, these are geographically scattered and the buying potential and average revenue per user (ARPU) is also seeming low. Hence, government should
intervene and provide incentives to encourage these private operators to move into these rural regions and increase the penetration of mobiles phones, so that the entire Indian economy is benefitted.
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