Substitution between fixed-line and mobile access: the role of complementarities

Abstract

We study substitution from fixed-line to mobile voice access, and the role of various complementarities that may slow down this process. We use survey data of 160,363 households from 27 EU countries during 2005–2011. We estimate a discrete choice model where households may choose one or both voice technologies, possibly in combination with internet access. We obtain the following main findings. First, there is significant fixed-to-mobile substitution, especially in recent years: without mobile telephony, fixed-line penetration would have been 14.1 % higher at the end of 2011. But there is substantial heterogeneity across households and EU regions, with a stronger substitution in Central and Eastern European countries. Second, the decline in fixed telephony has been slowed down because of a significant complementarity between the fixed-line and mobile connections offered by the fixed-line incumbent operator. This gives the incumbent a possibility to protect its position in the fixed-line market, raising market share by 2.7 %, and to leverage it into the mobile market, raising market share by 5.4 % points. Third, the decline in fixed telephony has also been slowed down because of the complementarity with broadband internet: the introduction of DSL avoided an additional decline in fixed-line penetration of 8.7 % points at the end of 2011. The emergence of fixed broadband has thus been the main source through which incumbents maintain their strong position in the fixed-line network.

Appendices

Appendix 1

In this Appendix we describe the model with unobserved heterogeneity for fixed and mobile alternatives. The utilities for the four bundles $r\in \{0,F,M,F$+$M\}$ are given by:

$$\begin{aligned} u_{i0}= & {} \epsilon _{i0} \\ u_{iF}= & {} \theta _{iF}+x_{i}\beta _{F}+\alpha p_{iF}+\epsilon _{iF} \\ u_{iM}= & {} \theta _{iM}+x_{i}\beta _{M}+\alpha p_{iM}+\epsilon _{iM} \\ u_{iF+M}= & {} (\theta _{iF}+\theta _{iM})+x_{i}(\beta _{F}+\beta _{M}+\gamma )+\alpha (p_{iF}+p_{iM})+\epsilon _{iF+M} \end{aligned}$$

Unobserved preferences for fixed-line and mobile access $j=F,M$ are denoted by the random coefficients vector $\theta _{i}=(\theta _{iF},\theta _{iM})$, which is assumed to follow a bivariate normal distribution with the following mean and covariance matrix:

$$\begin{aligned} \left( \begin{array}{c} \theta _{iF} \\ \theta _{iM} \end{array} \right) \sim \left( \begin{array}{c} \theta _{F} \\ \theta _{M} \end{array} \right) , \quad \left( \begin{array}{cc} \sigma _{F}^{2} &{} \sigma _{FM} \\ \sigma _{FM} &{} \sigma _{M}^{2} \end{array}\right) . \end{aligned}$$

Because the sum of two normal variables is also a normal variable, the vector $\theta _{i}=(\theta _{iF},\theta _{iM},\theta _{iF}+\theta _{iM})$ has a trivariate normal distribution with mean $\theta$ and covariance matrix $\Sigma$:

$$\begin{aligned} \left( \begin{array}{c} \theta _{iF} \\ \theta _{iM} \\ \theta _{iF}+\theta _{iM} \end{array}\right) \sim \left( \begin{array}{c} \theta _{F} \\ \theta _{M} \\ \theta _{F}+\theta _{M} \end{array} \right) , \quad \left( \begin{array}{ccc} \sigma _{F}^{2} &{} \sigma _{FM} &{} \sigma _{F}^{2}+\sigma _{FM} \\ \sigma _{FM} &{} \sigma _{M}^{2} &{} \sigma _{M}^{2}+\sigma _{FM} \\ \sigma _{F}^{2}+\sigma _{FM} &{} \sigma _{M}^{2}+\sigma _{FM} &{} \sigma _{F}^{2}+\sigma _{M}^{2}+2\sigma _{FM} \end{array}\right) . \end{aligned}$$

Hence, we have a special case of a general mixed logit with trivariate normal distribution, where we impose restrictions on the mean and covariance elements relating to the third option. We can use the Cholesky decomposition $\Sigma =RR^{\prime }$, where R is a lower triangular matrix,

$$\begin{aligned} R=\left( \begin{array}{ccc} r_{1} &{} \quad 0 &{} \quad 0 \\ r_{3} &{} \quad r_{2} &{} \quad 0 \\ r_{1}+r_{3} &{} \quad r_{2} &{} \quad 0 \end{array} \right) , \end{aligned}$$

Table 12 Choice model for voice services: comparison logit and random coefficients logit

to write the random coefficients vector as $\theta _{i}=\theta +Rv_{i}$ where $v_{i}=(v_{iF},v_{iM},v_{iF}+v_{iM})$ and $v_{iF}$ and $v_{iM}$ are standard normal random variables. After substitution, the above utilities can then be written as

$$\begin{aligned} u_{i0}= & {} \epsilon _{i0} \\ u_{iF}= & {} \theta _{F}+r_{1}v_{iF}+x_{i}\beta _{F}+\alpha p_{iF}+\epsilon _{iF} \\ u_{iM}= & {} \theta _{M}+r_{2}v_{iM}+r_{3}v_{iF}+x_{i}\beta _{M}+\alpha p_{iM}+\epsilon _{iM} \\ u_{iF+M}= & {} (\theta _{F}+\theta _{M})+(r_{1}+r_{3})v_{iF}+r_{2}v_{iM}+x_{i}(\beta _{F}+\beta _{M}+\gamma )\\&+ \, \alpha (p_{iF}+p_{iM})+\epsilon _{iF+M}. \end{aligned}$$

We estimate the parameters $r_{1}$, $r_{2}$ and $r_{3}$, from which we can compute the variances $\sigma _{F}^{2}$, $\sigma _{M}^{2}$ and covariance $\sigma _{FM}$. In practice, we can use a more general Cholesky matrix for three variables

$$\begin{aligned} R=\left( \begin{array}{ccc} r_{1} &{} \quad 0 &{} \quad 0 \\ r_{3} &{} \quad r_{2} &{} \quad 0 \\ r_{6} &{} \quad r_{5} &{} \quad r_{4} \end{array} \right) , \end{aligned}$$

and impose restrictions relating to the third option, namely that $r_{4}=0$, $r_{5}=r_{2}$ and $r_{6}=r_{1}+r_{3}$.

Table 12 shows the parameter estimates for several specifications. We compare a logit and random coefficients in a model without accounting for household characteristics (two left columns) and in a model with accounting for household characteristics (two right columns). To reduce the computational burden, the latter model only includes a selected set of interactions between household characteristics and $\gamma$.

The Table shows that without accounting for the household characteristics, the random coefficients are highly significant, in particular also the standard deviation $\sigma _{FM}$, which is equal to 0.462 with a small standard error of 0.07). The price coefficient increases (in absolute value) in the random coefficients model, from $-$0.042 to $-$0.058. In contrast, in the model that accounts for observed household characteristics, the random coefficients become much smaller and are statistically insignificant. In particular, the standard deviation $\sigma _{FM}$ is now 0.106 with a standard error of 0.103. Furthermore, the price coefficient and other parameters remain very similar when the random coefficients are added. These findings indicate that there is only limited unobserved heterogeneity once the observed household characteristics are added. We therefore focus on the computationally simpler conditional logit model (with also household characteristics interacted with $\gamma$) in the main text.

Appendix 2

See Table 13.

Table 13 Choice models for voice and internet services: household characteristics effect