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Incorporating Prior Information into A GMM Objective For Mixed Logit Demand Systems
Author(s) -
Romeo Charles J.
Publication year - 2016
Publication title -
the journal of industrial economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.93
H-Index - 77
eISSN - 1467-6451
pISSN - 0022-1821
DOI - 10.1111/joie.12100
Subject(s) - profit maximization , estimator , economics , econometrics , logit , maximization , profit (economics) , inequality , nested logit , product (mathematics) , constraint (computer aided design) , demand curve , mathematical economics , microeconomics , mathematics , statistics , mathematical analysis , geometry
Random parameters demand system estimates can generate upward sloping demands and imply margins outside of the theoretical bounds for profit maximization. If such violations are numerous enough, they can confound merger simulation exercises. Using Lerner indices for multiproduct firms playing static Bertrand games, we find that up to 35 per cent of implied margins for beer are outside the bounds. We characterize downward sloping demand and the theoretical bounds for profit maximization as prior information and extend the GMM objective function, incorporating inequality moments for product‐level own‐elasticities and brand level or product level Lerner indices. Very few violations remain when an inequality constrained estimator is used.