GUY ARIE OLEG BARANOV BENN EIFERT HECTOR PEREZ-SAIZ BEN SKRAINKA Bundling Software: An MPEC Approach to BLP.

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Presentation transcript:

GUY ARIE OLEG BARANOV BENN EIFERT HECTOR PEREZ-SAIZ BEN SKRAINKA Bundling Software: An MPEC Approach to BLP

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,

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

Structure of the model, I Heterogeneous consumers with preferences over product attributes Probabilistic demands for individual consumers Probabilistic demands for individual consumers Multidimensional quadrature formulas Products and their characteristics “Market share” functions for all possible product combinations

Structure of the model, II “Market share functions” for all possible product combinations Constraint: predicted shares = observed shares Residuals (“unobserved product quality”) Residuals (“unobserved product quality”) Instruments Aggregate market shares for individual products and bundles 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 ξ jt by implicit relation: Using instruments Z jt, 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? FactorCoefficient$ Equivalent Price Bundle1.89$90.01 Microsoft5.00$ Lotus-1.84-$87.62 Quality (7 to 10) $15.09 Rho Sigma.WP4.72- *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?