Bundling Software: An MPEC Approach to BLP GUY ARIE OLEG BARANOV BENN EIFERT HECTOR PEREZ-SAIZ BEN SKRAINKA
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.
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.
The office software space in the 1990 s -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 1990 s
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
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
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. . . )
The basics • Consumer i’s utility for each product j as a function of product characteristics and individual preferences: • Aggregate market shares computed by integrating over distribution of preferences:
The basics • For a given set of structural parameters, compute ξjt by implicit relation: • Using instruments Zjt , form GMM objective function:
Gaussian quadrature interlude…
Integration Technique
Integration technique…
Quadrature faster and more accurate… but still problem of many local minima
Results plausible at best objective function value? Factor Coefficient $ Equivalent Price -0. 034 - Bundle 1. 89 $90. 01 Microsoft 5. 00 $238. 10 Lotus -1. 84 -$87. 62 Quality (7 to 10) -0. 317 -$15. 09 Rho -0. 05 - Sigma. WP 4. 72 - *Results from solution with lowest objective function value
…but some parameter estimates are unstable even among “good” solutions
Price coefficients are stable among “good” solutions
Trends in unobserved product quality
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!
Reaching out to a new demographic?
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