Guy Arie

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Bundling SoftwareAn MPEC Approach to BLP

• Guy Arie
• Oleg Baranov
• Benn Eifert
• Hector Perez-Saiz
• Ben SkrainKa

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Extension of BLP to multi-product markets

• Observation a large share of word processors and
  spreadsheets are sold as part of a suite (or
  bundle).
• Interpretation 1 word processors and
  spreadsheets are complementary products (in the
  usual sense).
• Interpretation 2 people have positively
  correlated preferences for a variety of software
  applications.

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The Problem

• Goal to estimate consumer preferences over
  observed and unobserved characteristics of
  products in a market.
• Application Gandal, Markovich and Riordan
  (2006), office software. Extend BLP (1995) to
  markets with bundling and product
  complementarities.
• Idea think of the product space as containing
  every possible combination of word processors
  and/or spreadsheets. Generates accounting
  problem.
• Data US market shares for Microsoft, Lotus and
  Novell spreadsheets, word processors and suites,
  1992-1998.

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The office software space in the 1990s
-three companies (Microsoft, Lotus/IBM,
Novell/Corel) -two types of individual products
(spreadsheets, word processors) plus
suites -fifteen possible combinations a consumer
could buy -significant changes in prices and
product availability over the 1990s
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Structure of the model, I
Heterogeneous consumers with preferences over
product attributes
Products and their characteristics
Probabilistic demands for individual consumers
Multidimensional quadrature formulas
Market share functions for all possible
product combinations
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Structure of the model, II
Market share functions for all possible product
combinations
Aggregate market shares for individual products
and bundles
Constraint predicted shares observed shares
Residuals (unobserved product quality)
Instruments
GMM objective function
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Our Approach

• Main obstacles
• numerical instability, convergence problems, slow
  in MATLAB.
• usual methods require inner loop, outer loop
• Solutions
• Substitute multidimensional quadrature for Monte
  Carlo
• MPEC/AMPL/KNITRO takes five seconds.
• Impose constraints instead of using nested loops.
• Multi-starts to deal with tons of local minima
  (still a problem...)

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The basics

• Consumer is utility for each product j as a
  function of product characteristics and
  individual preferences

• Aggregate market shares computed by integrating
  over distribution of preferences

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The basics

• For a given set of structural parameters,
  compute ?jt by implicit relation

• Using instruments Zjt , form GMM objective
  function

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Gaussian quadrature interlude
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Integration Technique
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Integration technique
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Quadrature faster and more accuratebut still
problem of many local minima
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Results plausible at best objective function
value?
Results from solution with lowest objective
function value
15
but some parameter estimates are unstable even
among good solutions
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Price coefficients are stable among good
solutions
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Trends in unobserved product quality
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Summary

• Solution much improved over MATLAB method in
  working paper.
• Numerical stability is still a significant
  problem.
• Model is probably not well-identified need more
  diagnostics.
• One thing is for sure Microsoft fixed effect is
  huge!

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Reaching out to a new demographic?