Usage-Based Pricing of the Internet

Transcription

1 Usage-Based Pricing of the Internet Aviv Nevo Northwestern University John L. Turner and Jonathan Williams University of Georgia November 212

2 Pricing of the Internet For the most part, internet service providers (ISPs) have sold unlimited access to the internet for a monthly fee. Usage has grown 5% per year the past several years, driven largely by increasing use of online video (e.g. Netflix). Increasing last mile bandwidth is not costless, many internet service providers have implemented usage-based service plans. e.g. AT&T, Comcast, TWC. Bell Canada attempted to introduce usage-based billing in 211, abandoned plans in face of large opposition.

3 Usage-Based Service The most common usage-based plan is a three-part tariff (Lambrecht et al. 27): an access price, an allowance of (zero marginal price) usage, and a marginal price for usage in excess of the allowance.

4 A Gigabyte of Content To fix ideas, here are example of what a Gb of content includes: 1,,, or 1,73,741,824 (2 3 ) bytes, depending on who is defining it. Around 7, plain s....or 57 digital photos....or 277 digital songs....or 34 hours of online gaming....or.4 standard definition movies....or.2 high definition movies.

5 Usage-Based Service Usage-based service is itself controversial. The Federal Communications Commission (FCC) favors the practice. Usage-based pricing would help drive efficiency in the networks, Julian Genachowski, FCC Chairman (Chicago Tribune, May 22, 212) Many organizations are devoted to preventing it. It s like locking the doors to the library, Nicholas Longo, Geekdom director (NY Times, June 26, 212). Stop the Cap ( Openmedia.ca (Canadian, openmedia.ca/meter). Little, however, is known about the efficiency properties of usage-based service.

6 Literature Large empirical literature on cell phone usage under three-part tariffs. Estimating discount factors (Yao, Mela, Chiang and Chen 211). Welfare effects of capping overage charges (Jiang 211). Estimates of cross-price elasticities between voice and short message services (Kim, Telang, Vogt and Krishnan 21). Bill Shock and consumer notification of excess usage (Grubb and Osborne 212). Demand for Internet Usage Paris Metro Pricing may alleviate congestion problems (Odlyzko 1999). Time-use-based and experimental estimates of demand (Goolsbee and Klenow 26) and (Varian 21), respectively. Importance of uncertainty on demand for broadband (Lambrecht, Seim and Skiera 27).

7 Our Project Proprietary data on residential internet service from multiple North American ISPs during Some, but not all, come from consumers on usage-based plans. Internet Protocol Data Records (IPDR) record 15-6 minute intervals of up/down usage, packets lost, packets delayed, etc., for individual consumers. Subscribers link to CMTS interfaces are known. SamKnows modems measure network performance. The data permit us to use intertemporal decisions to estimate consumer preferences for features of broadband service. This will permit detailed study of the relationship between pricing, consumption of content, network congestion and connection speed, as well as counterfactual analysis of potential policy changes.

8 This Paper: Research Questions Application-specific Contributions Demand for broadband when congestion is not present. How are consumers heterogeneous (preference for speed, price elasticity, etc.)? Marginal and average value of a Gb of content. Welfare consequences of usage-based billing. What must costs of capacity be to justify the losses in subscriber welfare? Methodological Contributions Demonstrate usefulness of high-frequency consumption data for estimating demand. Estimate demand without variation in pricing schedule by exploiting variation in shadow price over billing cycle. Gowrisankaran and Rysman (211) and Hendel and Nevo (26). First to adapt/apply flexible nonparametric techniques of Ackerberg (29), Fox and Kim (211), and Fox et. al (211) to estimate demand.

9 This Paper: Data Proprietary data on residential internet service from one North American ISP during months of hourly IPDR usage data. aggregated to daily consumption, 8% usage on peak 6-11pm. Representative market with more than 3, subscribers. information linking subscribers to CMTS interfaces. pristine network, delayed and dropped packets never greater than.1% (not noticeable to human eye). no features of plan changes, so almost no plan switching. speed (Mb/s), overage price, and usage allowance is non-decreasing across plans with higher access fees.

10 This Paper: Data Aggregate descriptive statistics across tiers. Average usage is 21.7GB. Median usage is 8.5GB. Very skewed distribution makes convenient parametric assumptions on types difficult. Average usage on unlimited plans is more than twice. On average, 7% of users exceed usage allowance. Average user that exceeds allowance does so by 26.9 GB. Median user that exceeds allowance does so by 14.2 GB. Price per GB. Median price paid per GB is 5.73 (25% is 1.79 and 75% is 19.73). Lower bound on willingness to pay.

11 Utility Quasi-linear preferences u h (c t, y t ; k) = 1 β h [(γ h ln (s k ) + υ t ) c t 1 2 c2 t ] + y t, over Gb of internet content (c t ) and numeraire consumption (y t ) at a daily frequency. Quadratic preferences allow for satiation. Preferences differ by subscriber type, h. speed (s k, varies by plan k) preference (γ h ). marginal utility of numeraire (βh ). daily (t) uncertainty in preferences for content (υ t G(υ)).

12 Utility Maximization Conditional on choosing plan k, subscriber maximizes T δ t 1 E [u h (c t, y t ; k)] t=1 discount factor is δ, expectation is over future values of υt, days in billing cycle is T. Subject to an income constraint F k + p k (C T C k )1 [ C T > C k ] + YT I total consumption by end of period, day T, is C T = t j=1 c t, Y T = t j=1 y t,. fixed fee, F k, overage price, p k, usage allowance, C k, characterize plan k pricing schedule assume income, I, is high enough to afford satiation level of content model loss in utility from numeraire through β h

13 Dynamic Program Finite-horizon dynamic program (T = 3) Solution, conditional on choosing plan k, is characterized by policy functions c hkt (C t 1, υ t ) Integrated policy functions E [c hkt (C t 1, υ t )] = υ c hkt (C t 1, υ)dg h (υ) gives model s prediction of conditional moments of usage. Conditional mean and variance of policy functions are basis for method-of-moments approach

14 Identification Observe consumer sorting over billing cycle high Ct 1 states, high demand types, equate marginal utility to overage price (static). low Ct 1 states, low demand types, equate marginal utility to (static w/ zero probability of overage). intermediate C t 1 states, mixing of types, equate marginal utility to shadow price (some probability of overage). exploits richness of high-frequency data. observing marginal utility over range of prices identifies utility function Plan selection identifying variation, selection into plans that couldn t otherwise be rationalized choosing high usage allowance and speed and not using the allowance, high marginal utility of speed identifies marginal utility of income (β h ) and speed (γ h )

15 Method of Simulated Moments Straightforward method-of-moments estimator. Ackerberg (29), Fox and Kim (211), and Fox et. al (211). 1. limits (still a lot) computational time. 2. no parametric assumptions on distribution of types. 3. naturally deals with selection into plans. Two stages 1. flexibly recover conditional moments. estimated moments are a mixture of type-specific (h) moments, E [chkt(c t 1, υ t)] and Var [chkt(c t 1, υ t)]. 2. identify distribution of consumer types to best match empirical moments (joint distribution of {γ h,β h,g(υ)}).

16 First Stage Estimate conditional mean and variance of usage over state space, (C t 1,t). what are subscribers doing at each state? Estimate a surface over the (C t 1,t) plane. recovered surface is a mixture of policy functions from unobserved types (h) at each state. Nearest-Neighbor approach Fixed number of observations nearest to the point on the surface being estimated are used. Small state space (C t 1,t), allows for flexible nonparametric approach. Naturally bandwidth-adaptive, accounts for rapid change in density across state space. Point-wise standard errors are computed via block-resampling (subscriber-specific dependence).

17 Most Popular Tier, Density

18 Most Popular Tier, Conditional Mean Most Popular Plan Nearest Neighbor Mean GB Cumulative Consumption (GB) Days into Billing Cycle

19 Most Popular Tier, Conditional Variance Most Popular Plan Nearest Neighbor Std. Dev GB Cumulative Consumption (GB) Days into Billing Cycle

20 Second Stage Proceed in two steps, following Ackerberg (29), Fox and Kim (211), and Fox et. al (211). 1. Solve dynamic program for a wide range of types, {γ h,β h,g(υ)}. solve program for 2, types (12 points of support for each dimension of heterogeneity) for each of K plans. identify types optimal plan using V hk (C = ), or outside option with value of. store moments of policy functions and implied invariant distribution of Markov process under optimal plan. 2. Estimate joint distribution of types (weights on each type) to match empirical moments. match mass and behavior (mean and variance in usage) of subscribers at each state.

21 Estimating Type Distribution Weights on each type, θ h, are chosen to satisfy θ = argmin θ such that each θ h and K g(θ) g(θ) k=1 H θ h = 1. h=1 The difference between moments predicted by model and empirical moments is g k (θ). Convex optimization problem, convergence takes less than 1 minute.

22 Most Popular Tier, Model Fit 1 Model Fit for Last Day of Bill Cycle, Most Popular Plan.9.8 CDF of Cumulative Consumption Model Data Cumulative Consumption

23 Marginal Distribution of Preference Parameters, Mu.7 Figure 6a: Marginal Distribution of µ.6.5 Frequency µ

24 Marginal Distribution of Preference Parameters, Sigma.7 Figure 6b: Marginal Distribution of σ.6.5 Frequency σ

25 Marginal Distribution of Preference Parameters, Gamma.7 Figure 6c: Marginal Distribution of γ.6.5 Frequency γ

26 Marginal Distribution of Preference Parameters, Beta.15 Figure 6d: Marginal Distribution of β.1 Frequency β

27 Preliminary Counterfactuals How effective is usage-based pricing in driving efficiency in broadband networks? Some Preliminary Estimates Average value on GB consumed is just over $8. Marginal value of first units in excess of $35. Eliminating overage charges from existing menu of plans. Average usage and subscriber surplus increase by 45% and 4%, respectively. Only 11% of subscribers surplus increases by eliminating overage fees. Eliminating overage charges from existing menu of plans and allowing ISP to re-optimize access fees. Average usage and subscriber surplus increase by 38% and 2%, respectively. Only 8% of subscribers surplus increases by eliminating overage fees.

28 Comments, Criticism, and/or Questions?

29 Intuition for Identification - An Example Let C k = 15 and suppose the consumer enters period 29 (of 3) with C 28 = 14. Let υ be distributed Uniform on [,1] and that she has an average draw, υ 29 = 5. Notwithstanding the cap, optimal consumption c 29 = 5. However, this is not optimal because the shadow price of consumption exceeds. Further, let β h = 1 and p k = 1, so that the shadow price exactly equals the probability the consumer will exceeds the cap by the end of period 3.

30 An Example, Continued C k = 15, C 28 = 14, β h = 1, p k = 1. υ Uniform on [,1], υ 29 = 5.

31 Low Demand: Policy Functions (µ=.75,σ=.55,γ=.11,β=.35) GB/day t fraction of Ck.5

32 High Demand: Policy Functions (µ=.75,σ=.55,γ=.11,β=.35) GB/day t fraction of Ck.5

33 Two Types on Tier 3, Mixing Probabilities Invariant Distribution w/ 2 Types Choosing Plan Density t fraction of Ck

34 Policy Function Mixture Mixture of Policy Functions GB/day fraction of Ck t