Forecasting the Critical Mass of Wireless Communications

Forecasting the Critical Mass of Wireless Communications Sanna Sundqvist, Lauri Frank, Kaisu Puumalainen and Joni Kämäräinen, Lappeenranta University of Technology Abstract The aim of this paper is to determine and forecast the timing and level of critical mass in the development of market penetration for wireless communications. We assume that critical mass is fulfilled at the point when the acceleration of the diffusion process is at its maximum. In practice, this point is determined by calculating the second derivative with respect to time of the diffusion path. Thus, the diffusion has first to be modelled in order to have a function to differentiate. The diffusion of wireless communications in 30 countries is modelled employing the Bass diffusion model. These functions’ second derivatives’ maximums yield the timing of critical mass, and the respective penetration levels. The penetration levels and points of time of critical masses are regressed with explanatory variables, reflecting characteristics of the countries. A regression model for critical mass timings and levels by country characteristics is used for calculating values for 72 additional countries. The findings suggest that critical mass is achieved faster and on lower penetration levels in later adopting countries. Introduction Positive network effects are a significant feature of the market penetration and the diffusion process of many modern technologies (Witt, 1997). Economides (1991) defines that network effects occur when “The buyer of the last unit of a good has a higher benefit than the buyer of the first because the sale of the earlier units has created some benefits in a related dimension”. As Rogers (1983, p. 293) observes “we must understand the nature of networks if we are to comprehend the diffusion of innovations fully”. The existence of network effects makes the forecasting of the success of telecommunication services less easy and reliable when the traditional forecasting methods are applied (Schoder, 2000). It has also been pointed out that network effects can significantly influence the adoption and hence the diffusion of goods and services (Church and Gandal, 1993; Katz and Shapiro, 1985; Witt, 1997). Thus models, which aim to explain the diffusion of telecommunication services, must be able to capture the network effects. In this study, we aim to explain the cross-country differences in critical mass points by the countries’ characteristics. First, we look closer at the concept of network effects in the context of innovation diffusion models. Next, we conduct an empirical study, in which we evaluate the critical mass points of countries, and further explain the differences by country characteristics. Finally, we provide our conclusions and some further research suggestions. Country and Cultural Characteristics Geographic, socio-economic, demographic, and cultural differences of countries, which are uncontrollable by the firm, are likely to influence the way in which a product or service diffuses over time. The present study assesses the effects of economic (GNP and inflation rate), political (country’s risk index), socio-cultural (cosmopolitanism, social heterogeneity and human development), technological (technological achievement), adoption timing (lead- ANZMAC 2002 Conference Proceedings 551 lag effect) and cultural (Hofstede’s indices, 1991) variables on the level and timing of critical mass. The wealth of a country, which is often operationalized as GNP per capita, has a positive effect on the diffusion process in reducing the time before a country adopts as well as in speeding up the diffusion within the country. High inflation rate and the country’s risk index are proposed to hinder diffusion as they increase uncertainty. Socio-cultural and technological variables are believed to facilitate diffusion, as they reflect wealth and the amount of communication. A consistent finding in cross-country diffusion studies is that there exists a cross-national learning effect (Dekimpe, Parker and Sarvary, 2000; Kumar, Ganesh and Echambadi, 1998; Mahajan and Muller, 1994; Takada and Jain, 1991). Countries, which introduce an innovation later, seem to have faster domestic diffusion patterns. Hofstede’s (1991) indices (power distance, which focuses on authority orientation; collectivism versus individualism, which focuses on self-orientation; femininity versus masculinity, which focuses on achievement orientation; and uncertainty avoidance, which focuses on risk orientation) are applied in diffusion research (c.f. Parker and Sarvary, 1994; Steenkamp, ter Hofstede and Wedel, 1999). Steenkamp, ter Hofstede and Wedel (1999) propose that the degree of individualism of a national culture has a positive effect on the innovativeness of its consumers. Also, uncertainty avoidance is believed to have a negative, and masculinity to have a positive effect on innovativeness. Consumers in more individualistic and more masculine countries tended to be more innovative in Steenkamp, ter Hofstede and Wedel (1999) study. Furthermore, innovativeness was found to be weaker in cultures that emphasize uncertainty avoidance. Apart from Steenkamp, ter Hofstede and Wedel (1999), Ganesh, Kumar and Subramaniam (1997) have also included Hofstede’s indices in cross-cultural diffusion or adoption research. Ganesh, Kumar and Subramaniam (1997) measured cultural similarity as a negative index of the sum of the absolute differences in each of Hofstede’s dimensions between the lead and lag countries, and found that the more culturally similar markets, the greater the learning effect and the faster the diffusion. Figure 1 summarizes the hypotheses proposed above. COUNTRY CHARACTERISTICS Earliness of Adoption: Lead-lag effect Economic: GNP & Inflation Rate Political: Risk index Sociocultural: Cosmopolitanism & HDI, Number of ethnic groups Technological: TAI CULTURAL CHARACTERISTICS Uncertainty Avoidance Power Distance Masculinity Individualism CRITICAL MASS Time Level Figure 1. Hypothesized Relationships Network Effects and Critical Mass in the Diffusion of an Innovation Network effects create a so-called critical mass point in the innovation’s diffusion process. The rate of adoption of interactive innovations does not take off in the familiar S shape curve until a critical mass of adopters has been reached (Mahler and Rogers, 1999). In the early ANZMAC 2002 Conference Proceedings 552 phase of the diffusion the network does not seem attractive to potential adopters, because there are only few users. Thus, the network effect is not strong enough, i.e. the network does not create enough utility for a potential adopter to join the network. If critical mass is not fulfilled, the diffusion will fail. However, when critical mass is reached, the interactive innovation is thereafter perceived as valuable by potential adopters (Mahler and Rogers, 1999). At that point, the network has enough users to be attractive to the rest of the users – and the diffusion is a success. By Mahler and Rogers (1999), a telecommunications service provider introducing new interactive services often faces formidable problems in getting the innovation to critical mass, but thereafter can almost halt further promotional activities as the diffusion process becomes self-sustaining. Thus, it is very valuable to identify the critical mass in order to have an innovation with network effects diffused successfully. A comparison of innovations with and without network effects shows, how the latter is seen to diffuse more slowly until a critical mass of adopters is reached (see figure 2). Figure 2. Diffusion without (Solid) and with (Dotted) Network Effects (Schoder, 2000). Critical mass also may be defined as the minimal number of adopters of an interactive innovation for the further rate of adoption to be self-sustaining (Mahler and Rogers, 1999). It can also be interpreted as the turning point between positive and negative returns to adoption (Markus, 1990b). The critical mass point in the diffusion process is generally expected to occur approximately between 10 and 20% adoption (Rogers, 1983; Valente, 1995). Weiber (1995) explained the left-skewed diffusion curve and the critical mass at the early stages of diffusion by market-related factors. He argued that these factors first hamper the rate of diffusion and later, after reaching critical mass, accelerate the diffusion process. As mentioned above, it has been proposed that critical mass does not only speed up the rate of adoption but also may cause the collapse of an innovation (e.g. Markus, 1990a). Formally, the point of time of critical mass achievement may be extracted from the diffusion curve as follows. Griliches (1957) suggests three phases from the sigmoid aggregate diffusion curve: 1) origin, 2) diffusion and 3) saturation. These phases can be identified, for example, using the sigmoid shaped curve’s second time derivatives’ extreme points as cut points for the phases. Figure 3 shows the derivation of stages for the lifecycle of an innovation: In the beginning, the innovation diffuses slowly. At this point, the innovation is new and in its first stage. As Figure 3 shows, the first stage is cut by the maximum of the second derivative with respect to time (the acceleration), which is the moment when the increase of the innovation’s adopters is at its maximum. Thus, it may also be considered as the point of critical mass fulfillment. ANZMAC 2002 Conference Proceedings 553 Figure 3. Deriving the Critical Mass Point from the S-Curves Second Derivative. Empirical Research The empirical study consisted of data from 112 countries with a population of more than 1 million. The cellular data was obtained from the International Telecommunications Union (ITU) database. The effect of political environment was measured using a composite country risk index obtained from PRS Group. Following Antonelli (1993), Dekimpe, Parker and Sarvary (2000), and Helsen, Jedidi and DeSarbo (1993), GDP per capita corrected with purchasing power parity was used as a measure of the country´s wealth (from the ITU database). The technological environment was described by the Technology Achievement Index (TAI) from United Nations Development Report. Indicators for the socio-cultural environment included cultural homogeneity (number of ethnic groups, Dekimpe, Parker and Sarvary, 2000), cosmopolitanism (outgoing international telephone call minutes per capita 1991), and standard of living (Human Development Index 1990). The earliness of adoption was measured by the starting year of the diffusion data. At the first stage of analysis the second derivative of the Bass diffusion model was calculated. The timing of the critical mass point was identified based on the maximum point of second derivative (see Equation 1). (( ) t = ln 2 + 3 p q (1) ) −( p + q) Critical time was further inserted into the Bass equation in order to calculate the level of penetration at the critical mass point. However, the Bass model (1969) gave plausible estimates for only 30 countries. At the second stage of the analysis we studied factors that affect both the timing and the level of critical mass. The proposed hypotheses were tested by stepwise regression. The results did not support our hypotheses as only adoption timing, i.e. the lead-lag effect turned out to be significant predictor of critical mass. Additionally, cosmopolitanism predicted the level of critical mass (see Table 1). Table 1. Regression Results – Timing and Level of Critical Mass as Dependent. Dependent Timing of CMP R2 .88 F (df) 135 (1, 18) Sig. .000 Amount of CMP .58 11.9 (2, 17) .001 ANZMAC 2002 Conference Proceedings Independent Constant Adoption timing Constant Cosmopolitanism Adoption timing B 1554 -.777 20.6 .001 -.01 Sig. .000 .000 .043 .014 .044 554 At the third stage of the analysis we validated the results by using 15 percent of the countries, were the Bass model performed well, as a hold-out sample. The coefficients of determination did not differ across modeling and hold-out samples. The fourth and final stage of the analysis was forecasting the critical mass also for those countries where the Bass model did not work (n = 72), thus the total n = 102. The forecasts for critical mass timing varied from 0.4 to 15.2 years (mean 6.9 years, sd 3.5). For the critical mass level, only 96 forecasts were gained because cosmopolitanism was not available for all countries. The results for critical mass level predictions varied from 0.01 to 0.34 with a mean of 0.13 (sd 0.074). The predictions for the critical mass timings and levels by geographic regions are depicted in the figure below. ,4 ,3 REGION eeurope ,2 asia predicted y cr se-asia south america ,1 africa north america weurope 0,0 0 2 4 6 8 10 12 14 16 predicted t cr Figure 4. Critical Mass Point Predictions (t cr – Timing, y cr – Level). Figure 4 reveals that there is almost a smooth connection between the critical masses timings and levels: The earlier the critical mass is fulfilled, the smaller it is. However, for the later occurring critical masses the levels are somewhat dispersed. If also the observation from the regression equation of critical mass timing being negatively related with the adoption timing is noted, the conclusion is as follows: The later a country adopts, the faster it achieves critical mass, which is smaller. This might be due to a cross-national learning or network effect: Users of earlier countries might increase the actual critical mass for later adopting countries. Conclusions and Further Research This paper studied the critical mass timing and level of the diffusion of wireless communications. The differences in countries’ critical mass timings and levels were explained with countries’ characteristics. However, only adoption time and cosmopolitanism were significant. Using the created model, critical mass timings and levels were predicted for countries, where they were not calculable. As a result, it seems that a country’s critical mass timing and level are negatively related with its adoption year. The relationship between the adoption timing and critical mass also needs to be confirmed from other innovations’ diffusion processes. Also, further research could try to investigate strategies aimed to hasten the achievement of critical mass. 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