Bayesian estimation of the random coefficients logit from aggregate count data

The random coefficients logit model is a workhorse in marketing and empirical industrial organizations research. When only aggregate data are available, it is customary to calibrate the model based on market shares as data input, even if the data are available in the form of aggregate counts. Howeve...

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Bibliographic Details
Published in:Quantitative marketing and economics 2014-03, Vol.12 (1), p.43-84
Main Authors: Zenetti, German, Otter, Thomas
Format: Article
Language:English
Subjects:
Business and Management
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Insurance
Management
Market shares
Marketing
Purchase options
Statistics for Business
Time series
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Summary:The random coefficients logit model is a workhorse in marketing and empirical industrial organizations research. When only aggregate data are available, it is customary to calibrate the model based on market shares as data input, even if the data are available in the form of aggregate counts. However, market shares are functionally related to model primitives in the random coefficients model whereas finite aggregate counts are only probabilistic functions of these model primitives. A recent paper by Park and Gupta ( Journal of Marketing Research, 46 (4), 531–543 2009 ) stresses this distinction but is hamstrung by numerical problems when demonstrating its potential practical importance. We develop Bayesian inference for the likelihood function proposed by Park and Gupta ( Journal of Marketing Research, 46 (4), 531–543 2009 ), sidestepping the numerical problem encountered by these authors. We show how taking account of the amount of information about shares by modeling counts directly results in improved inference.
ISSN:1570-7156
1573-711X
DOI:10.1007/s11129-013-9140-4