Competing with Menus of
Tariff Options
Eugenio J. Miravete
University of Texas at Austin & CEPR
IESE Business School, 06 / 14 / 2007
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:
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 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.
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