Competing with Menus Competing with Menus of Tariff Optionsof Tariff Options

Eugenio J. MiraveteEugenio J. MiraveteUniversity of Texas at Austin & CEPRUniversity of Texas at Austin & CEPR

IESE Business School, 06 / 14 / 2007

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Motivation: Economic Theory

Firms rarely offer the fully nonlinear tariff predicted by theoretical models.

Offering a menu of few two-part tariffs may respond to commercialization costs exclusively…

… or alternatively to the existence of discrete types.

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More interestingly, the number of options offered may also respond to strategic considerations:

Attempt to segment the market.

Attempt to differentiate products/services that are otherwise homogeneous.

To take advantage of any bounded rationality limitation of consumers.

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Competing views:

Symmetric equilibrium – minimal product differentiation. Armstrong and Vickers (2001). Rochet and Stole (2002).

Asymmetric equilibrium – differentiation through pricing. Yang and Ye (2006).

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What is the question of economic interest?

Are the pricing policies of competing firms strategic substitutes or strategic complements?

Of course we need to control for observed heterogeneity (and ideally by unobserved heterogeneity as well).

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Motivation: Econometrics

Ideally we want to estimate a SUR count data model…

… not such model exists, or at least not one with the following properties: Accommodate both over and underdispersion of

counts. Allow for positive and negative correlations of the

errors. Dispersion and correlation determined by different

parameters.

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This paper develops such flexible econometric model.

Ingredients: Efron’s (1986) Double Poisson distribution. Sklar’s (1959) copula result. Gaussian copula specification.

Advantages: Straightforward generalizations to n-dimensions. Very fast computation.

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Data

50 U.S. local cellular monopolist (1984-1988). Temporary monopoly of the wireline carrier.

Exogenous entry of the second firm.

No need to model entry or entry deterrence strategies.

Largest SMSA markets.

All tariff plans offered by the incumbent:

Focus on the lower envelope of the peak tariff.

Include the first and last quarter in the sample.

Complemented with data from: Census, FBI, and U.S. HCN.

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Model

Double Poisson:

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Straightforward estimation:

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Continuation of count variables:

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Gaussian copula:

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More to Come…

A more formal paper on this double Poisson –

Gaussian copula method.

An alternative Gamma – Sarmanov copula.

Some other application.