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ESTIMATION OF HETEROGENEOUS PREFERENCES, WITH AN APPLICATION TO DEMAND FOR INTERNET SERVICES ESTIMATION OF HETEROGENEOUS PREFERENCES, WITH AN
APPLICATION TO DEMAND FOR INTERNET SERVICES
Walter Beckert*
AbstractThis paper presents a structural econometric framework for
discrete and continuous consumer choices in which unobserved intraper-
sonal and interpersonal preference heterogeneity is modeled explicitly. It
outlines a simulation-assisted estimation methodology applicable in this
framework. This methodology is illustrated in an application to analyze
data from the U.C. Berkeley Internet Demand Experiment.
I.
Introduction
Situations in which consumers rst make a discrete
choice, such as a particular tariff, and then a continuous
choice over service demanded are now very common for
telephone, utilities, pay television, and many other services.
Discrete-continuous consumer choice data are commonly
available to service providers and, less often, to academics.
This paper provides a structural-utility-based econometric
model for the analysis of discrete and continuous consumer
choices, which explicitly incorporates unobserved intra- and
interpersonal preference heterogeneity. It demonstrates how
this model can be estimated using a simulation-assisted
estimation methodology. This econometric approach to de-
mand estimation in the presence of unobserved preference
heterogeneity is illustrated in a small-scale application to
analyze demand for Internet access, using data from the
U.C. Berkeley Internet Demand Experiment (INDEX).
An econometric methodology for modeling and estimat-
ing unobserved preference heterogeneity is of interest for a
number of reason. Preference heterogeneity plays a central
role in the management of capacity-constrained resources,
such as network services. When consumers use services
provided under capacity constraints, a consumers service
consumption and induced capacity utilization may impose a
negative consumption externality on all contemporaneous
users, degrading the effective quality of service. To manage
such resources efciently and effectively, it is therefore of
interest to assess the entire distribution of service valuations
and utilization among competing users. Internet access via
local area networks (LANs) and via wireless networks are
prime examples.
Quality of service can be assured through efcient capac-
ity allocation. Nonlinear prices, at least in theory, enhance
the efciency of capacity allocations. The theoretical moti-
vation for the welfare-enhancing effects of optimal nonlin-
ear prices, and a primitive in their construction, is prefer-
ence heterogeneity (Wilson, 1993). Therefore, modeling
and measuring unobserved preference heterogeneity is nec-
essary to implement optimal nonlinear prices.
Offering different qualities of service at different prices is
akin to differentiated products and services. Estimating
unobserved preference heterogeneity allows one to assess
users valuations of a given set of differentiated products
and services, and to determine an optimal degree of product
and service differentiation.
Finally, modeling unobserved preference heterogeneity
reconciles the potential discordance between typical micro-
econometric choice rationality assumptions and revealed-
preference violations of demand data. With precise
measurements, such failures cannot be attributed to
measurement error. Microeconometric demand analysis typ-
ically stipulates some notion of choice rationality, such as
utility maximization. An econometric methodology ac-
knowledging unobserved preference heterogeneity permits
enough exibility to reconcile the patterns in demand data
with the maintained hypothesis of choice rationality.
The econometric methodology advanced in this paper
builds on a random utility model for jointly endogenous
discrete and continuous choices. Discrete-continuous con-
sumer choice data available to service providers and aca-
demics are typically in the form of a nonequispaced, unbal-
anced panel. The econometric methodology in this paper
exploits such data in order to empirically identify intraper-
sonal and interpersonal preference heterogeneity. Related
work by Dubin and McFadden (1984) and Dubin (1985),
using cross-section data on pairs of discrete electrical ap-
pliance and continuous consumption choices, calibrates in-
terpersonal preference heterogeneity only, whereas Rust
(1987, 1994) examines the dynamics of jointly endogenous
sequential discrete equipment investment choices, suppress-
ing jointly endogenous equipment utilization choices.
The paper proceeds as follows. The main part outlines an
econometric methodology for the analysis of discrete-
continuous choice data in the presence of unobserved pref-
erence heterogeneity. Section II describes the econometric
model, and section III provides a suitable estimation meth-
odology. Section IV presents a small-scale illustrative ap-
plication of this methodology to data from INDEX. Section
V concludes.
II.
The Econometric Model
A. Inter- and Intrapersonal Preference Heterogeneity
Consider a generic quality-differentiated service. Users
are presented with a menu of prices per unit time connected
to the service provider, during which they are set up to
Received for publication February 14, 2002. Revision accepted for
publication September 28, 2004.
* Birkbeck College, University of London.
I thank Chunrong Ai, Richard Blundell, David Brillinger, Daniel Mc-
Fadden, Paul Ruud, David Sappington, Ron Smith, Kenneth Train, Pravin
Varaiya, Hal Varian, the INDEX team, various seminar participants, the
editor, and two referees for helpful comments and suggestions. All errors
are mine. This work was funded in part by the National Science Founda-
tion, grant ANI-9714559, and in part by the Cal@Silicon-Valley Fellow-
ship of U.C. Berkeley.
The Review of Economics and Statistics, August 2005, 87(3): 495502
©
2005 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology utilize the service; and of prices per unit volume for service
usage. These prices differ by quality of service, which can
be thought of broadly as maximum volume per time unit. As
an example, in calling-party-pays mobile telephony, users
have a choice between pay-as-you-go service and monthly
and annual service contracts providing various blocks of
free minutes and/or text messages per month, possibly
limited to the carrier, and beyond that incremental per-
minute prices. Similar price structures are currently avail-
able for broadband Internet access. In landline telephony, a
monthly connection charge combines with a per-minute
calling rate, typically differentiated by the extent of low-
priced or free calling periods.
In usage data for such a service one observes the users
discrete service quality choice b
B, where B denotes the
set of available service qualities; and one observes the time
T the user is connected to the chosen quality level, as well
as service usage in terms of volume v. Generally, the users
specic higher-level applications which the service feeds
into are not observed. Applications typically differ in terms
of their service quality requirements,
1
and such differences
induce heterogeneity in choicesnot only interpersonal
preference heterogeneity between users, but also intraper-
sonal between a users choices over time, as the users
higher-level applications may change.
A typical feature of such services is that the quality of
service is chosen on the basis of anticipated usage, whereas
the outcome of usage, in terms of its utility for higher-level
applications, is ex ante uncertain; the resolution of this
uncertainty, in the process of usage, may induce a discrep-
ancy between anticipated and actual usage. This suggests a
distinction between preferences giving rise to initial discrete
service quality choices, referred to as ex ante service valu-
ations, and preferences giving rise to subsequent usage
choices, referred to as online service valuations. A way to
succinctly parameterize it is that the (marginal) utility of
service usage, v, is ex ante unknown, but becomes revealed
in the usage process. This implies that actual service usage,
in addition to being subject to service quality-specic prices
per unit time and volume, may be subject to intrapersonal
preference shifts, in response to the actual experience of
consuming the service.
This distinction between ex ante and online valuations
rationalizes a number of empirical regularities in choice
data. During some of the time a user is connected, it may be
that no usage occurs, but by staying connected the user
retains the convenience or option to use the chosen service
quality without reconnecting. This time, in excess of the
time actually used, will be referred to as the convenience
time t, where t
T. In service plans other than pay-as-you-
go, it typically carries a pecuniary cost for the user. Users
may be willing to pay for it, because, beyond its option
value, it may be valuable in that it can be used to react to an
ex ante uncertain utility of the service usage. The distinction
between ex ante and online valuations thus rationalizes
demand for convenie