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, 1992-1998.

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

Heterogeneous consumers with preferences over product

attributes

Probabilistic demands for individual consumersProbabilistic demands

for individual consumers

Multidimensional quadrature formulas

Multidimensional quadrature formulas

Products and their characteristics

Products and their characteristics

“Market share” functions for all possible product combinations

“Market share” functions for all possible product combinations

Structure of the model, II

“Market share functions” for all possible product combinations “Market share functions” for all possible product combinations

Constraint: predicted shares = observed shares

Constraint: predicted shares = observed shares

Residuals (“unobserved product quality”)

Residuals (“unobserved product quality”)

InstrumentsInstruments

Aggregate market shares for individual products and bundles

Aggregate market shares for individual products and bundles

GMM objective functionGMM 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

exp( )ˆ , 1,...,

exp( )jt jt

jtkt ktk

ps d j k J

p

i

jt jt ii

kt kt iμ

X β Z μμ

X β Z μ

1,..., , 1,...,ijt jt jt ijtu p j J t T jt jt iX β Z μ

• 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:

ˆˆ ( , ) 1,..., 1,...,jt jt jts s j J t T θ

• Using instruments Zjt , form GMM objective function:

ˆ ˆ ˆ ˆ ˆˆ ˆarg min ( ) ( )jt jtE E jt jtθ

θ Z θ Ω Z θ

Gaussian quadrature interlude…

Integration Technique

Integration technique…

Quadrature faster and more accurate…but still problem of many local minima

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-20

0

0.5

1

1.5

2

2.5

3

3.5

4distribution of 50 best objective function values from 5000 starts

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-19

0

5

10

15

20

25distribution of 100 best objective function values

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

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.60

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5Histogram for rho coeffic ient (1% of All Solutions )

rho coeffic ient

Fre

qu

en

cy

Price coefficients are stable among “good” solutions

-0.1 -0.09 -0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.010

1

2

3

4

5

6

7

8

9Histogram for Price coeffic ient (1% of All Solutions )

Price coeffic ient

Fre

qu

en

cy

Trends in unobserved product quality

92 93 94 95 96 97 98-4

-3

-2

-1

0

1

2

3

4

5

6Unobserved means

Years

Va

lue

IBM SS

COREL WP

IBM S

COREL S

MS WP

MS SS

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?