Evaluating wireless carrier consolidation using semiparametric demand estimation

The maximum score approach has previously been used in industrial organization and marketing by Briesch et al. (2002).

The FCC uses data on the number of telephone numbers assigned to carriers to approximate market shares, rather than using data on actual customers. The FCC writes in response to a Department of Justice request to access its data on market shares, “The Commission has recognized that disaggregated, carrier-specific forecast and utilization data should be treated as confidential and should be exempt from public disclosure under 5 U.S.C. Section 552(b)(4).”

Some carriers have decided to take advantage of the network aspect of their products by offering free in-network calling. If two Verizon or two Cingular customers talk, the length of the call is not deducted from either customer’s bucket of included minutes from their subscription plans. Merging carriers create larger networks so that customers can better exploit free in-network calling. Unfortunately, major carriers either include unlimited in-network calling as part of all plans, or offer it as an add-on option. There is no variation within a carrier in whether in-network calling is included in a subscription plan, so we cannot estimate its value without using across-carrier variation in market share ranks.

We did not collect data on overage charges. An overage charge is the per-minute cost for calls that exceed the calling minutes for plan j. While we have no data on the usage of plan minutes, our measure does not account for the entirety of a plan’s price. Our assumption (relaxed a little in Section 5.4) is that a consumer uses all the minutes in his or her plan, and no more, so there are no overage charges.

The nests do not represent a dynamic choice problem. Rather, each nest represents the set of products that have the same fixed effect for consumer i, ν _ihm .

Consumer-specific fixed effects at the carrier level capture carrier-specific features such as the coverage near a consumer’s house. In a model without fixed effects, the market and subscription plan specific errors ξ _jm would account for omitted variables such as coverage quality.

Manski initially studied the properties of this estimator both for the two choice case and the three or more choices case. Much of the attention in the subsequent maximum score literature focuses on the two choice case, because the two choice case allows for relatively weak median independence assumptions about the relationship between errors and observables (Manski 1985; Horowitz 1992). Also, others have extended estimators for the two-choice case to more general ordered choice problems (Han 1987; Abrevaya 2000).

We can weaken the assumption of i.i.d. errors across choices in the same nest to be an exchangeable joint density. See Fox (2007).

For example, if we have added a penalty term \(\left(x_{j}^{'}\beta-p_{j}>x_{k}^{'}\beta-p_{k}\right)^{2}\) in the degree of an inequality violation and minimized the resulting penalties, then there is no guarantee that the true parameter in the data generating process would be in the identified set.

See Fox (2008) for another case where an objective function like (6) has both Manski (1975) and Han (1987) asymptotics. Note that Han (1987) motivates his estimator with ordered choice problems. His estimator involves combining different observations in a double summation. We study an unordered choice problem. Under a much stronger version of Assumption 1, we could use Han’s estimator to interact observations across markets if all markets had exactly the same set of plans. While most of the plans on offer are the same across markets, there is some small degree of variation in the offered plans, so we do not pursue this further.

Fox (2007) discusses this point in more detail for the maximum score estimator with individual data.

Bajari et al. (2007) prove the nonparametric identification of the distribution of random coefficients in the random coefficients logit model, with market share levels. Our results rely on continuous product characteristic variation across markets, the type of variation that we do not have in the mobile phone market. Therefore, we are skeptical about identifying the distribution of random coefficients with this type of data.

A referee points out that for some set-identified estimators, the 95% confidence sets and set estimates will be the same with probability 1. Maximum score is not such an estimator. If the dependent variable (market share ranks) vary a lot conditional on covariates, the estimates using some subsamples will not be the same as with the full sample.

Note that we are discussing variation in the dependent variable. If the independent variables vary a lot across markets, then the identified set will be smaller than a case with no or a small amount of characteristic variation. If at least one independent variable per product has continuous support, then Manski (1985) and others show that the model is point identified and that the maximum score estimator is consistent. The typical large support assumption for the continuous characteristic can be relaxed while still maintaining point identification, as Horowitz (1998) discusses.

Some companies collect phone bills from consumers. Bill harvest data are not entirely appropriate, as at any given point in time the stock of mobile phone users has plans purchased from the menus of plans available in many different time periods. The time of plan purchase may not be observable.

If a researcher has another dataset with continuously measured shares s _jm , it is easy to convert those shares into ranks.

We have used the Amazon site extensively and wish to explain a little of how the site worked in late 2005, when the data were collected. When you go to the site to shop for mobile phone plans, you are prompted to enter your zip code. Amazon uses the zip code to look up your geographic market. We collect market share rank data by choosing a zip code corresponding to each city. There are various pages. The page that presents the plans rank ordered by sales is reached by using the toolbar to search “Wireless Plans” for a blank string. All plans will appear, and you can sort them by sales rank. The resulting plans are presented in a matrix, with the top three plans in the first row, plans three to six in the second row, etc. A plan’s rank comes from its position in the matrix, not from a text label, as Amazon includes for books. You can verify the ordering of plans in the matrix by consulting another page, which lists the top five plans in numeric order, with the rankings listed explicitly. We clicked on each plan and manually copied its characteristics.

Amazon sells prepaid service, where a customer does not pay a set monthly fee. We do not consider the data on prepaid service, because plan characteristics such as price and anytime minutes are not comparable to the monthly values for subscription plans. A customer that uses all of his or her monthly minutes will find it cheaper to subscribe to a monthly plan.

While not in the table and our estimation sample, Nextel offers four plans that do not include free long distance. Nextel uses a proprietary phone technology that prohibits its customers from operating on networks owned by almost all other carriers. Consequently, Nextel does not levy charges to travelers, in part because its phones are incapable of operating off its network. We do not consider Nextel. Also, Cingular dropped its regional plans from Amazon just before data collection began.

The software toolkit Santiago and Fox (2007) implements subsampling and is available on the internet.

A referee reports out that the natural generalization of a confidence set for a point estimate to set estimation is a confidence collection (a set of sets). It is hard to visually describe a set of sets. Given that the natural measure is the (hard to compute) set of sets, the marginal benefit of reporting the set estimates in addition to the confidence sets may be small. We report both in Table 2 only to drive home their similarity.

A similar argument can be used to show that the confidence sets will be the same as the set estimates for other subsample sizes.

We did not collect data on the overage charge, the per-minute fee for making calls that exceed the monthly bucket of minutes. Therefore, we consider only one aspect of the price.

We cannot compute the presumably huge standard errors for an estimate using data on only market.