Demand in a Portfolio-Choice Environment: The Evolution of Telecommunications

This appendix provides an alternative estimation and robustness analysis to what is presented in the main section. We can confirm that the estimation results are in substantial agreement with virtually all our principal results. The primary change here is that we estimate consumers’ portfolio choices via a bivariate probit model. Unlike the mixed logit estimation which presumes that households make a single choice among all possible portfolios, the bivariate probit estimation assumes that households make two choices: (1) whether to subscribe to landline telephone service or not; and (2) whether to subscribe to a mobile network or not.

The Bivariate Probit (BVP) model consists of two simultaneous binomial probits that derive from latent utilities for each service:

where we expect that β p j j < 0 and that β p j k > 0 for j ≠ k when the two services are price substitutes. The utility of the bundle is the simple sum of standalone utilities of the individual services in (A-1). In particular, the error term associated with the bundle is the sum of the errors of the two standalone utilities. The no landline and no cellphone options are normalized to have zero utility.

Let the errors be jointly normally distributed ϵ h L , ϵ h C ∼ N ( 0,0,1,1 , ρ ) where ρ ∈ (−1, 1) is the correlation coefficient. When the errors are uncorrelated (ρ = 0) the system reduces to two independent probits. Using symmetry of bivariate normal distribution, the choice probability for both services is given by:

where Φ₂ is the c.d.f. of the bivariate standard normal N(0, 0, 1, 1, ρ). Expressions for the probability that each of the other portfolios will be selected, π h 0 , π h L and π h C , can be derived in a similar way.

We first estimate two univariate probit models – one each for subscriptions to a landline and cellphone – as if the two decisions were unrelated. Against this benchmark we compare a bivariate probit model that allows for correlation between the two alternatives. In both versions, we control for the potential endogeneity of prices that arises either from the omission of relevant exogenous variables (e.g. unobserved landline and cellular service characteristics) or from the causal feedback of demand on prices. Failure to account for endogeneity would otherwise bias the price coefficients.

We approach endogeneity in a similar fashion to the control function we used for the mixed logit case. We perform a two-stage conditional maximum likelihood (2SCML) estimation as defined by Rivers and Vuong (1988). This estimator can be computed in two steps using standard probit and regression routines. The 2SCML estimator has good small sample and large sample properties relative to other limited information estimators. The procedure also lends itself to simple tests of exogeneity that are easy to compute and that compare favorably with alternative tests.

To perform the first stage, we regress fixed and mobile prices on the exogenous variables and a set of instruments:

where X _h contain the same exogenous variables as given in (3) and Z _h is a vector of instrumental variables that vary by time and place. The pair of error terms, v h L and v h C , obey a bivariate normal distribution N(0, 0, 1, 1, ρ) where ρ is the correlation between the two error terms.^[42]

In the second stage, we compute the residuals v ̂ h L and v ̂ h C from the first-stage equations (A-3), and enter them into the following regressions for latent utilities:

where the error terms are again distributed bivariate standard normal. As with our mixed logit estimations, we utilize Telecommunications Wages and Percent Democrat PUC as instruments.^[43]

The results for the two stages of the preferred BVP model are presented in Tables A-1 and A-2. The parameter estimates provide evidence regarding price and non-price determinants of households’ portfolio choices.

Table A-1 contains the first-stage results of the 2SCML estimation. The two instruments that are included are statistically significant, and F-tests of joint significance confirm their relevance. Telecommunications Wages is positively correlated with both landline and cellphone service prices and highly statistically significant. Percent Democrat PUC is negatively and significantly associated with both prices.

Table A-2 reports the second-stage results of the 2SCML estimation. The second stage represents households’ binary decisions to adopt landline and cellphone services. We first present the results for Model I which consists of two independent probits. In contrast, Model II is a bivariate probit model that allows for correlation between the two error terms. Both Models I and II incorporate the endogeneity corrections from the first-stage regressions. Model III has the same specification as Model II except that the endogeneity correction is excluded in order to isolate its effect on price coefficients.

The estimation results of Models I and II are similar in sign, magnitude, and statistical significance. The Model II estimation, however, shows a negative and statistically-significant correlation of the two errors, ρ ̂ = − 0.49 . The null hypothesis that households make two independent binomial choices for each of the two technologies is strongly rejected.^[44] Clearly, unobserved factors other than price cause household choices to substitute between the two services. In other words, idiosyncratic tastes that cause a household to favor a landline will also tend to cause it to disfavor a cellphone, and vice versa.

Estimation results for Models II and III are in rough agreement regarding signs of their coefficients.^[45] However, the first-stage landline and cellphone price residuals enter significantly in Model II confirming the presence of price endogeneity. A comparison of the two sets of price coefficients shows how failure to account for endogeneity tends to bias price coefficients toward zero. In addition, the predictions of portfolio choices under Model II reveal a good fit of that specification: 68 and 97 percent of households’ landline and cellphone subscriptions, respectively, are correctly predicted. Based on these results, we choose to concentrate our discussion on the BVP specification of Model II.

Consistent with the mixed logit estimations presented in the body of the paper, the 2SCML estimation of the BVP model confirm the importance of mobility characteristics, pricing, family income, household demographics, wireless network coverage and quality and network externalities as important determinants of households’ portfolio choice decisions regarding landline and mobile telephone services.

A review of the coefficients on the various proxies for household mobility confirms that more “nodal” households are more likely to favor a landline over a cellphone, while “on the go” households prefer a cellphone over a landline. This correspondence between portfolio choice and household mobility is evident from coefficient estimates in three types of proxies. First, household member age tends to lower cellphone adoption and raise landline adoption. We find a monotonic relationship between the age of the household members and their subscription portfolios. Second, household member employment tends to raise cellphone subscription rates and corresponds to a lower landline rates. In addition, households with part-time working members are more likely to subscribe to both services. Third, health-limited adult households, who are likely to be more “nodal”, rely less heavily on cellphones. Finally, home ownership matters: households that own their home are more likely to subscribe to both landline services than households that rent. Apparently, the locational stability that comes with home ownership is more compatible with both subscriptions, while renting is more compatible with cellphone service.^[46]

Table A-2 similarly reveals that the prices of both landline and cell service are significant drivers of households’ portfolio choices. Landline and cellphone prices are consistently negative and statistically significant determinants of households’ decisions to adopt landline and cellphone service, respectively. Model II also corroborates the results of the mixed logit estimation that cellphone and landline subscriptions are substitutes, with positive cross-price effects, though the effect of landline prices on the decision to adopt cellphone service is statistically insignificant.

As with the mixed logit estimations, family income has significant positive impacts on subscriptions to both services. Given how the NHIS collected the data, income effects must be expressed relative to the Federal Poverty Guidelines (FPG). In comparison to the baseline poverty threshold (Income1), families with higher income levels are more likely to subscribe to both services. The marginal effect from the lowest to the highest income category increases the likelihood of landline subscription by roughly 6 percent and cellphone subscription by roughly 25 percent – indicating a stronger income effect for cellphone than landline.

Finally, the BVP estimations confirm the relevance of network quality and network effects in households’ portfolio choice decisions. As a robustness check, we substituted the CTIA direct measure of Cellsites over time. The results indicate that the improving mobile network quality increases households’ adoption of cellphone service and decreases adoption of landline service, consistent with the mixed logit estimations. The results also indicate that the higher levels of mobile subscriptions in the county of the focal household are associated with higher levels of both landline and cellphone subscriptions.