Competitive Nonlinear Pricing in Duopoly Equilibrium: The Early U.S.

Cellular Telephone Industry

Eugenio J. Miravete

University of Pennsylvania & CEPR

Lars-Hendrik Röller

WZB, Humboldt University & CEPR

(Chief Competition Economist, European Commission)

This version: February 24, 2005

Introduction

Road Map

• Motivation

• Literature Review

• The Data

• Model Description

• Econometric Implementation

• Policy Evaluations

• Things that still need to be done.

Motivation

• Nonlinear pricing under competition:– Abundant evidence that firms engage in price discrimination

practices even when they operate in competitive environments.

– Business practices have not been matched by theoretical models until very recently.

Identification Issues

• What are the basic estimation problems of the NEIO?– Marginal cost data is very rarely available.– Price-cost margins have to be estimated together with

demand and cost parameters.– They change with consumption level in nonlinear tariffs.

– Difficulties concerning the identification of the actual competition regime.

Our Approach

• How do we incorporate the features of second degree price discrimination into the estimation of a structural equilibrium model of nonlinear pricing competition?

– Nonparametric identification: Provided a given specification of demand, there is a one-to-one mapping between the distribution of types and the optimal nonlinear tariff.

– Then we can make use of the information contained in the SHAPESHAPE of the tariffs offered by competing firms.

– We assume Nash equilibrium in nonlinear tariffs.

Our Approach

Modeling Choices

• Several approaches are possible to deal with nonlinear pricing competition:

Single-Dimensional

Types

Multidimensional Types

Exclusive Agency Stole (1995)

Rochet and Stole (2002)

Random Participation

Serious Identification Issues

Common Agency

Rey (2000)

Better for models of vertical product differentiation

Martimort-Rochet-Stole

Horizontal Product Diff.

Suits best the available information (spec. test).

Literature Review

• Second degree price discrimination (reduced form):– Shepard, JPE´91: Full service vs. self-service gasoline.– Borenstein, RAND´91: Leaded vs. unleaded gasoline.– Cohen, 2000: Packaging size of paper towels.

• Non-uniform markup changes (reduced form):– Borenstein, RAND´89: Airline pricing.– Busse and Rysman, 2001: Advertisements in yellow pages.– Busse, JEMS´00: Similarity of cellular phone tariffs.

Literature Review

• Second degree price discrimination (equilibrium models):– Clerides, IJIO´02: Inter-temporal pricing of books.– Leslie, 2000: Pricing of a Broadway theater.– Cohen, 2001: Packaging size of paper towels.– McManus, 2001: Pricing of specialty coffee (size), U.Va.– Ivaldi and Martimort, Rev. Ec. et Stat´94: Power in France.– Basaluzzo and Miravete, 2004.

• Linear Pricing (conjectural variations approach):– Parker and Röller, RAND´97.

Goals

• Provide with an operationally feasible method of estimation for competitive markets where price discrimination is common.

• Minimize the data requirements.

• Evaluate how non-uniform markups change with competition. Who benefits the most?– Incumbent vs. entrants.– Large vs. small customers.

• Policy analysis: – Mergers, pricing restrictions, and other counterfactual

evaluations.

The Data

Some Facts: World

• Cellular phones are quintessential part of IT revolution of the 1990s.

• Currently, there are 1.3 billion subscribers worldwide.

• The number of wireless phones will surpass the number of fixed-line subscribes in 2002.

• It currently accounts for more than 30% of the $1 trillion total worldwide telecommunications revenues.

Some Facts

Some Facts

Some Facts: U.S.

• United States, 2001:– Market penetration of 45% with 136 million subscribers.– Sales: $60 billion.– Employment: 200,000 direct jobs.

• United States, 1988:– 1.6 million subscribers.– Sales: $2 billion.– Employment: 9,000 direct jobs.– Average monthly bill: $98.02.

Market Definition

• Technological constraint: Scarce radio spectrum.

• Solution:– Service areas divided in small cells served by its own low-

powered transmitter. It allows this frequency to carry a different call in a non-adjacent cell.

– A mobile telephone switching office maintains a continuous transmission when customers move to a cell that uses a different frequency.

• FCC design of the early US cellular market:– Define 305 non-overlapping markets SMSAs.– Assign 50 MHz in the 800 MHz band for cellular services.– Wireline license: fixed line carriers in that area (Block B).– Non-wireline license: any other US citizen or company (Block A).

Market Definition: SMSA

• It includes a central city or urbanized area of at least 50,000 people.

• It also includes the county containing the central city and other contiguous counties with strong economic and social ties to the central city.

• US Census (1990):– 76% of the population.– 16% of the land.

Market Definition: SMSA-1980

Sources: Tariff Plans

• Cellular Price and Marketing Letter, Information Enterprises:– Pricing plans information reported by firms between August of 1984

and August of 1988.– Price plans are typically two-part tariffs with quantity discounts.– The number of plans varies from 1 to 9.– Plans normally include a peak-load component and airtime allowance.

• Our focus: Retail market and peak period.

Concavity of Tariffs

Sources: Market Size

• Cellular Business, various issues, 1984-1988:– Cell sites.– Start-up date.

• Remarks:– Output level is not directly observable.– Each cell site represents between 1,100 to 1,300 subscribers.– In a sample of 22 observations in 8 markets between 1985 and 1987, the

correlation between number of cells and subscribers was about 0.92.– Market shares of competing firms are not known (except for the above

mentioned markets).

Sources: Factor Prices

Sources: Demand

Cellular Phones and Security

The Model

Demand

• Duopoly. Horizontally differentiated products:

• Monopoly:

Distribution of Types

• Burr type XII distribution:

• Market specific markups:

Cost

• Cost function:

• Marginal cost specification:

Monopoly Solution

• The monopolist solves the following mechanism:

• Optimal tariff:

• Optimal purchase:

Monopoly: Stochastic Structure

• First stage quadratic approximation:– Measurement errors: Optional two-part tariffs vs. fully nonlinear tariff.

• Interpretation of first stage coefficients:

How does the model work?

How does the model work?

AIRTIME 5000

How does the model work?

How does the model work?

How does the model work?

Approximation Error

Approximation Error

Approximation Error

Identification of Structural Param.

• Highest consumer type:

• Distribution parameter:

• Marginal cost:

Participation Constraint

• Marginal consumer type:

• Determinants of participation:

Duopoly: Quadratic Tariffs

• Basic assumption:

• Redefinition of types:

Duopoly: Distribution of Types

• Joint Distribution of types (Sarmanov):

• Marginal Distribution of Types (Burr type XII):

Duopoly: Solution• Duopolist 1 solves the following mechanism:

• Optimal tariff payment and purchase:

Duopoly: Stochastic Structure

• First stage regressions:– Measurement errors: Optional two-part tariffs vs. fully nonlinear tariff.

• Interpretation of first stage regression estimates:

Identification of Structural Param.

• Highest consumer type:

• Marginal consumer type:

Identification of Structural Param.

• Distribution parameters (implements Nash perfection):

• Marginal cost:

Estimation

Further Identification Restrictions

• Reduced form parameters:

• Structural parameters of interest:

• Still need to fix:

Estimation of Demand Parameters

• Makes use of a smaller sample (of the largest markets) for which the number of subscribers of both firms is available for a couple of years.

• It is assumed that consumers do not differ in their substitution pattern conditional on their observed characteristics.

• System estimation from the necessary conditions of consumption:

Alternative Demand Estimates

11.021

2 bb

Structural Estimates

Tariff Change After Competition

• Tariffs are uniformly lower for all levels of airtime usage.

• The reduction in the rate per minute is more important for intensive consumers.

• Markups tend to be higher in the duopoly phase:– Efficiency gains of competition vs. identification issues.

• Most of the gain is due to the increase in variety.

• There is very important unobserved heterogeneity:– Very important differences of pricing across cities.

Tariff Change After Competition

Estimates & Market Characteristics

Total Welfare Effects

Elasticities

Passing Gains of Competition

Welfare & Market Characteristics

Policy Evaluations

Performance of Pricing Strategies

• Alternative Pricing Strategies:– Two-Part Tariffs.– Linear Pricing.– Flat Tariff.

Performance of Pricing Strategies

• Alternative Pricing Strategies:– Two-Part Tariffs: Achieve most of the potential profits of screening.– Linear Pricing: Really bad.– Flat Tariff: Excludes “too many” low valuation customers.

Things to do…

Performance of Pricing Strategies

• The paper could still be improved in several ways:– Addressing a model of exclusive agency.– Dealing with a real common agency problem.– Estimation of demand using micro data.– Explaining the number of tariff options offered by firms.– Fitting the lower envelope of the predicted menu of two-part

tariffs:– Taking the actual number of plans as given.– Predicting the number of plans to be offered.