The size of the critical mass as a function of the strength of network externalities: a mobile telephone estimation

Abstract

The amount of financial incentives required to stimulate network growth depends on the size of the critical mass which, in its turn, depends on the intensity with which network externalities play their role in the diffusion process. The measurement of the strength of network effects and all that can enforce or depress them is fundamental for forecasting the diffusion of new goods. Looking at the mobile telephone network for the OECD countries surveyed between 1989 and 2006, we propose a new methodology which allows us to estimate the size of the critical mass through the estimation of the parameters which determines the concavity degree of the inverse demand curve for mobiles. We found that socio-demographic variables, as well as variables which proxy the efficiency of fixed-line operators or the availability and cost of alternative services, affect the strength of network effects and, therefore, the critical mass size.

Keywords:

• network externalities
• critical mass
• mobile telecommunication

JEL Classification :

• D12
• L96

Acknowledgements

The author thank Cristiano Antonelli (the editor) and the anonymous EINT reviewers for comments and guidance. Of course, the author retains the responsibility for errors.

Notes

A network is a market in which the benefit each consumer obtains from a good is an increasing function of the number of consumers who own the same or similar goods.

In the mobile telephone market, the number of firms in the market has been decided by the number of licenses offered by governments. In most countries, cellular phones were first available to end consumers in the 1980s with first-generation (1G) cellular networks, based on analogue signal transmission, which offered lower service quality and incompatible systems. The second generation (2G–GSM) network, based on digital technology, appeared in 1992 offering greater network capacity and the SMS functionality, which enabled users to send short text messages to each other. Once introduced, 2G mobile telecommunications in the USA and Europe was always in strong demand. In the 1990s, the rapid and sustained growth rate was accompanied by profound changes in the telecommunication markets. The third generation (3G) networks, first introduced in 2001 in Japan, allowed data transmission; this is the technology in usage nowadays.

The literature on network externalities also mentions indirect network externalities, characterizing the PC and the credit card network (Economides 1996).

The well-known theoretical literature on network externalities (Farrel and Soloner 1985; Katz and Shapiro 1985; Church and Gandal 1993; Shapiro and Varian 1999) showed that, in the presence of network effects, the inverse demand function do not slope downward everywhere but it has an increasing part appearing as an inverted U function of the installed base of subscribers.

4G means the fourth generation of cellular wireless standards. It is basically the extension of the 3G technology with more bandwidth and service offers in the 3G. It refers to all-IP (Internet protocol) packet-switched networks, mobile ultra-broadband (gigabit speed) access and multi-carrier transmission. A 4G system is expected to provide a comprehensive and secure all-IP-based solution where facilities such as IP telephony, ultra-broadband Internet access, gaming services and streamed multimedia may be provided to users. In 2006, it was still a prototype.

In our opinion, they lack the right specification of the hedonic price model, which is appropriate for market with direct network externalities and not with indirect ones, as the spreadsheets network.

The black line in Figure 1 shows, for every year from 1989 to 2006, the mean of the mobile cellular telephone subscribers over population across the 30 OECD countries (Australia, Austria, Belgium, Canada, Czech Republic, Denmark, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Japan, Korea, Luxemburg, Mexico, The Netherlands, New Zealand, Norway, Poland, Portugal, Slovak Republic, Spain, Sweden, Switzerland, Turkey, UK and USA). The grey line shows the same mean for the real 3-min cellular calls price, which, in its turn for every year and country, is the mean between the real 3-min cellular calls price peak and off-peak rate.

We provide the justification of the functional form capturing the network externalities we chose. Even a quadratic specification such as (as proposed by Grajek and Kretschmer 2010), with a and b determining the extent of network externalities, would have met the constraints on h(base^e). Therefore, we make the exercise of estimating two diffusion equation of mobile as function of two different network effects h(base^e) functions:

and

where base _i, t is the Mobile cellular telephone subscribers (post-paid + pre-paid), for country i at time t, k is the stand-alone value of the network good, the matrix X _i, t contains control variables, both for country i at time t and are the general stochastic terms. We perform the estimation twice, using first the data on mobile cellular subscribers of 140 countries of the world from 1989 to 2006 (world panel), and later restricting the analysis at the 30 OECD countries (OECD panel) during the same period of time. Equations (a) and (b) show dynamic panel data which we estimate by the usual Arellano–Bond GMM estimator (the description of this estimator can be found elsewhere in this article). We do not show the estimated coefficients but we just comment them. Looking at the Equation (a), the estimated coefficient of the variable base _{i, t} is positive and that of is negative, both highly significant either in the world or in the OECD panel. But, in order to be h′>0, it must be which is not possible for the values of the installed base in both panels. Indeed, looking at Equation (b), the coefficients of base _{i, t} and ln(base _{i, t} ) are positive and significant and both the conditions h′>0 and h″<0 hold. This is the reason why we have chosen the log specification of the network externalities function for mobiles.

We check the robustness of the network externalities function specification by using another functional form in the estimating demand, which also respects the constraints on h(base^e).

The data come from the ITU database.

Given the compatibility of network in the same country and among countries, we can consider the price of 3-min calls from a mobile cellular telephone to a mobile cellular subscriber of the same network as a good proxy of the price of calls from a mobile cellular telephone to a mobile cellular subscriber of a different network (even to a fixed telephone network).

We perform the Maddala and Wu (1999) panel unit root test for variables base and price. Maddala and Wu (1999) combines the p-values from N independent unit root tests. Based on the p-values of individual unit root tests, this test assumes that all series are non-stationary under the null hypothesis against the alternative that at least one series in the panel is stationary. Test for panel unit root using an augmented Dickey–Fuller test (1 lag): variable base

At 10% we reject the null of non-stationary of the base. Test for panel unit root using an augmented Dickey–Fuller test (1 lag): variable price At 1% we reject the null of non-stationary of the price.

Revenue from mobile communication is the revenue from the provision of all types of mobile communications services such as mobile cellular, private trunked radio and radio paging. We derived the number of telephone calls by dividing this Revenue from mobile communication for the prices of 3-min calls. Then this is just a proxy of the quantity of calls.

Below the result of the Wooldridge (2002) test for serial correlation in the idiosyncratic errors of a linear panel-data model relative to Equation (a). The null hypothesis of the test is of no first-order autocorrelation.

We reject the null of no autocorrelation.

In Equation (a), the variable ln(quantity) is taken at time t−1 for endogeneity problems. In Equations from (b) to (g) ln(quantity) _{i, t} is treated as an endogenous variable.

The OECD countries with a per capita GDP lower than the general mean are: Australia, Belgium, Canada, Czech Republic, France, Greece, Hungary, Ireland, Italy, Korea, Mexico, The Netherlands, New Zealand, Poland, Portugal, Slovak Republic, Spain, UK; the remaining countries have a per capita GDP greater than the general per capita GDP mean.

In the light of testing the robustness of the model, we do two more thinks. First, in order to consider the possible reverse causality between the subscriber's base and the price of calls, we run an estimation (Arellano–Bond estimator) treating the variable base _{i, t} as endogenous; we do not show the result but the sign and the magnitude of the coefficients do not change. Secondly, we used as an independent variable the base of subscribers of mobile and its logarithm because we thought it would be the most appropriate to grasp the dimensional effect (which is the network effect). Following Grajek and Kretschmer (2010), we run an Arellano–Bond one-step robust estimation using the ratio (base/pop) _{i, t} and ln(base/pop) _{i, t−1} as regressors: even in this case, the estimation result does not change, (base/pop) _{i, t} is negative and ln(base/pop) _{i, t−1} is positive, both highly significant; certainly the coefficients are different in their magnitudes.

Missing observations are randomly distributed along the panel, that is, there are no countries and years totally omitted.

Note that the number of observations decreases to 216 because of lots of missing values in the series of the total capacity of local public-switching exchanges.

The total number of all types of public telephones, including coin- and card-operated and public telephones in call offices. Publicly available phones installed in private places are also included, as should mobile public telephones. All public telephones regardless of capability (e.g. local calls or national only) are counted. If the national definition of ‘payphone’ differs from that above (e.g. by excluding pay phones in private places), then countries indicate their own definition (ITU).