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 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
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:
uijt   p jt  Xjt β  Zjt μ i   jt   ijt
j  1,..., J , t  1,..., T
• Aggregate market shares computed by integrating over
distribution of preferences:
exp( p jt  Xjt β  Zjt μi   jt )
sˆ jt  
dμi
exp( pkt  Xkt β  Zkt μi  kt )
μ k
i
j, k  1,..., J
The basics
• For a given set of structural parameters, compute ξjt by
implicit relation:
sˆ jt (θ, ˆjt )  s jt
j  1,..., J t  1,..., T
• Using instruments Zjt , form GMM objective function:

θˆ  arg min Eˆ Z jtˆjt (θˆ )  Ω Eˆ Z jtˆjt (θˆ ) 
θ
Gaussian quadrature interlude…
Integration Technique
Integration technique…
Quadrature faster and more accurate…
but still problem of many local minima
distribution of 100 best objective function values
distribution of 50 best objective function values from 5000 starts
25
4
3.5
20
3
2.5
15
2
10
1.5
1
5
0.5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-19
x 10
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-20
x 10
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
Histogram for rho coefficient (1% of All Solutions )
5
4.5
4
Frequency
3.5
3
2.5
2
1.5
1
0.5
0
-0.8
-0.6
-0.4
-0.2
0
rho coefficient
0.2
0.4
0.6
Price coefficients are stable among “good” solutions
Histogram for Price coefficient (1% of All Solutions )
9
8
7
Frequency
6
5
4
3
2
1
0
-0.1
-0.09
-0.08
-0.07
-0.06 -0.05 -0.04
Price coefficient
-0.03
-0.02
-0.01
Trends in unobserved product quality
Unobserved means
6
5
4
3
IBM SS
COREL WP
IBM S
COREL S
MS WP
MS SS
Value
2
1
0
-1
-2
-3
-4
92
93
94
95
Years
96
97
98
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?