2.1. Empirical evidence using DK's corrected methodology

The adoption of communication technologies (mobile telephony included) has followed the functional form of a sigmoid process that grows at a diminishing rate. Such a process can be analyzed using a technology diffusion model with a logistic form. These models are based on the functional form proposed by ^{Griliches (1957)} to study the diffusion of hybrid corn:

where Yit is the number of users, Yit* is the potential number of users, a is the initial condition and β is the growth rate of the diffusion model. ^{Gruber and Verboven (2001)} use a similar model and apply it to the mobile telephony sector, where the saturation level is measured as a proportion of the population of a given country at a certain time. ^{Gruber and Verboven (2001)} carry out their market penetration analysis of mobile telephone markets using a dataset of 140 countries; they control for variables such as per capita product, per capita fixed-telephone lines, waiting list, time of entry of competitors into the industry, and technological changes. They conclude that the two main variables affecting the growth of the diffusion process are: (i) the time between the granting of the first license and any subsequent license for mobile telephone operators, and; (ii) the time required by network operators to switch from analog to digital technology. Similarly, DK use an unbalanced panel of 84 countries to assess the impact of regulatory changes and regime switching (i.e., from RPP to CPP) on the diffusion process.

As mentioned previously, DK estimate the impact of different regulatory systems on mobile telephone penetration with a panel data set. In order to model MTU, DK use a logistic function to determine the diffusion of mobile phones as a function of regulatory variables and time.

A functional form of the saturation level must be imposed to estimate the model. DK take saturation as a proportion of the population:

where ⋋i> is the saturation parameter. To estimate the parameter ⋋i DK use the following expression:

The latter expression proves misleading and the expression that should be used in this case (i.e., considering that the population growth rate is different than zero) is:

Nonetheless, this expression differs from the result presented in DK. To overcome the limitations of using the expression proposed by DK, we propose a different approach. We define zit as the proportion of users in the population and, after some algebraic manipulation, we obtain:³

The equilibrium assumption can be understood as the convergence in growth rates, and eq. (5) is therefore valid. To prove the hypothesis of the quadratic relationship between MTR and MTU, we use the following specification:

which can be estimated by standard linear methods. With the quadratic relationship parameterized, computing the optimal MTR is straightforward:

with the second order condition β2<0 .

As stated earlier, the model is estimated using panel dataset of 34 countries (all OECD members) spanning the period 2000-2018. The data includes MTU, population (^{World Bank, 2019}), and MTR in US dollars, as reported by the ^{OECD (2019a)}.

We first obtain estimates of λ via equation (5) through a linear regression with no constant. A histogram of these estimates for each OECD country is shown in figure 2. We then compare three different regression estimates of eq. (6): OLS, Fixed Effects and Random Effects (robust Jackknife-estimated covariance matrices are always used). The results are shown in table 1.

Source: Authors' own graph based on ^{OECD (2019a)} data.

Figure 2 Histogram of estimated saturation rates for OECD countries 

Based on the third model, i.e., the random-effects model (see table 1, third column), we infer that OLS is not a consistent estimator.⁴ Moreover, the Hausman test provides evidence of a non-systematic difference in coefficients (p = 0.25). In sum, the random-effects model appears to be consistent and efficient. The estimates associated with MTR are statistically significant and yield the expected concave quadratic form. Based on the random-effects model estimates, we compute the optimal MTR, which is equal to US$ 0.16 in real (2012) prices.

These estimates, along with the population predictions for OECD countries, allow us to measure the potential benefits that each country would obtain if the optimal termination rate (US $0.16) prevailed rather than the actual one (i.e., the last one available in the sample). We present this counterfactual exercise by calculating the potential increase in MTU (as a proportion of the actual MTU). A word of caution is required: in figure 3, we show the gap between the optimal termination rate and the actual. It is clear that this gap has been decreasing over time in all countries.

Source: Authors' own graph based on ^{OECD (2019a}, ^2019b) data.

Figure 3 Trend towards optimal termination rate 

Hence, the benefits of using the optimal rate diminish over time too. That said, we next present a counterfactual exercise (using the population predictions for some OECD countries) that compares the difference (or gap) between the total number of users (MTU) yielded by the optimal MTR and that yielded by the observed MTR. The results for selected countries are shown in table 2.⁵

2.2. Penetration rate estimates under exogenous/endogenous regimes and degree of competition

We consider a range of variables that might influence penetration rates in OECD countries, including: (i) the telecommunications payment regime (CPP or RPP and “Bill and Keep”); (ii) the degree of competition in the telecommunications market; (iii) the existence of prepaid cards in the market; (iv) the number of fixed-telephone lines; (v) the number of inhabitants; (vi) the population density; (vii) the GDP per capita, and; (viii) the ratio of individuals using the internet. The variables are those used in DK's work, except the last one. We test the same group of variables in our empirical analysis for comparison purposes. That said, we must take into account that DK's data sample was constructed prior to the emergence of massive internet use. The proportion of Internet users in a given country allow us to study the relationship, if any, between Internet use and the mobile telephone sector.

As mentioned previously, there are 32 countries in our sample that use CPP and two that use RPP during the sample period (2000-2018).⁶ As stated, the mobile penetration rate in OECD countries exhibits an upward though gradually declining trend; this would suggest that a logistic curve might be appropriate for modeling the dynamics of the MTU.

Following DK, the prices and costs of the cellphone companies are not considered in our study; and the population density variable will only be used to find out if it has any statistical significance on the penetration rate. We expect it to have a positive effect on penetration rates, as DK suggest: the higher the concentration of inhabitants in an area, the lower the costs should be for companies to provide mobile telephony services; in other words, the same infrastructure would cover a larger number of inhabitants in a more densely-populated country than it would in a less densely populated one. It is worth noting that Korea, the Netherlands, and Japan have the highest population densities, whilst Australia, Iceland, and Canada have the lowest.

As for the remaining controls, we employ GDP per capita variable in real terms (2012 dollars) as a proxy for each country's income per capita. The number of subscribers to mobile telephony services per country will be useful in order to estimate the saturation rate in each one. Moreover, the relationship between the Internet use and the saturation rate is expected to be positive. It should be taken into account, however, that use of social media applications on cellphones was not as widespread at the beginning of the sample as it currently is.⁷

Diffusion process with exogenous regulation: We first assume that the adoption of the billing regime is settled independently (exogenous regulation), i.e., the authorities of each country make their decisions without considering the behavior of the telecommunications market.

Remember that the regression to be estimated is given by Zit=ai+bi+eit where a _i is the individual effect per country and b _i the country-specific control variables. In table 3, the results are shown for the regression where we assume exogenous regulation. It is important to emphasize that we decided to employ a General-to-Specific (G2S) modelling strategy. The latter removes the 'most statistically insignificant' estimated coefficient (provided its p-value is greater than 10%) and re-estimates the model. It proceeds as aforementioned until the surviving estimated parameters are all statistically significant.

There are four different estimators: regression I includes all of the OECD-member countries during the period of study; regression II excludes countries that have adopted an RPP payment regime; regression III considers only those that use RPP (Canada and the United States). Finally, regression IV also considers only those countries that use RPP, but is estimated using a different methodology (pooled OLS; see below).

Regression I: the effect of being under a CPP regime on the MTUs is negative, that is … results in a decline of 1.1% in the rate of users. The effect of internet use is a 7.7% increase in the saturation rate. Pre-paid cards and fixed lines have a negative impact on the MTUs. Note that the trend effect is a slight increase (0.16%). Unexpectedly, the GDP per capita has a negative impact on the MTU. This counterintuitive result may be due to possible collinearities with population, as argued by DK.

Regression II: since most OECD countries are under a CPP regime, results obtained in regressions I and II are similar, as can be seen in the second column of table 3. Nonetheless, note that the effect of a population increase on the penetration rate in CPP countries is greater than with the full sample. The later result suggests that there is greater sensitivity to the growth rate of population in the market under CPP. Moreover, the positive effect of internet use prevails, but at a lower rate than in regression I.

Regression III and IV: when only RPP countries are included (i.e., Canada and the United States), the estimates are not statistically significant, and the null hypothesis of a common intercept is rejected. This result suggests that, given the similarities in the Canadian and US telecommunication markets, the fixed-effects method is an adequate approach. We also estimate the regression using pooled OLS to compare the latter approach with the principal alternatives (fixed effects and random effects models). When we calculate the Hausman test for regressions I and II, the null hypothesis is rejected at the 1% level, so we infer that the fixed-effects method is a more appropriate methodology. As for regression III, we reject the null hypothesis of the Welch test (as the groups have a common intercept). We then calculate a joint-significance test for the means of the different groups test. On the basis of that test, we reject the null hypothesis--that pooled OLS is the adequate model, in favor of the fixed effects model.

Diffusion process with endogenous regulation: In a second stage, we allow the payment regime to be endogenous. The regime adopted and the number of competitors in the market are endogenously defined. We therefore estimate the regression via instrumental variables. To do so, a number of variables related to political and institutional characteristics are considered as instruments (see table C in the appendix for a description of these).⁸ Since the variables are binary, a logistic regression is used to obtain estimates of the type of regime and existence of competition (first step). The results are shown in table 4.

Regarding the two regressions (i.e., regime and competition) presented in table 4, we can state the following:

We now proceed to measure the impact, if any, on the penetration rates in the OECD countries. Table 5 summarizes the results of the regressions obtained by considering endogenous regulation. The selection of variables is also made following the G2 S modelling strategy, as in the exogenous regulation section. We present results of the same four regressions specified in the previous section.

The output of regression I shows that there was no significant difference in the impact of the variables on the saturation rate growth in CPP countries compared to RPP countries. Nonetheless, once endogeneity was taken into account, the impact of competition on the saturation growth rate was positive (5.2%) under both regimes. This is consistent with economic theory; it provides an insight on the benefits of competition in the mobile telecommunication sector, at least for OECD countries. Furthermore, the relation between internet users and saturation rates remains positive, but the effect is greater in this case (8.5%). Note also that prepaid cards, fixed lines and population density have negative effects, whilst population effect is positive. GDP per capita has a counterintuitive negative effect, which we conjecture may be due to collinearities with population, as in DK. Note also that the overall effect on MTU is positive (0.17), and should be interpreted as a pervasive and persisting force (in all countries) that drives people to use mobile phones.

Regression II (CPP countries) shows estimated coefficients similar to those of regression I, although there are some interesting differences. This is particularly noticeable with the effect of internet use (2.9%): the effect is almost three times smaller than in the full sample case. Note however that fixed lines and population have a stronger negative effect. Unfortunately, the negative effect of GDP per capita remains.

As for RPP countries (regressions III and IV), the results show a very strong positive impact of competition, whilst the trend has a negative impact on the penetration rate (this may be due to the fact that the United States and Canada have already a rather high MTU and the secular force that drives it has been slowly dying out). It is also worth noting that in regression III, the Welch test is rejected only at the 5% level. The latter result may reflect similarities in the mobile sector between RPP countries in the OECD. We therefore estimate the regression using pooled OLS (regression IV). In this case, the regulatory regime is statistically significant. The joint significance test is high and the corresponding p-value rather small, which suggests that fixed effects should be preferred. That said, the sample size of RPP regressions is very small and inference could be misleading and should therefore be drawn with caution.