Discrete Choice Demand Model

The plain multinomial logit imposes independence of irrelevant alternatives (IIA), which forces substitution to be proportional to market shares regardless of how similar products are — the 'red bus / blue bus' problem. That yields unrealistic cross-price elasticities: raising a luxury car's price would shift demand to economy cars in proportion to their shares. The BLP random-coefficients model relaxes IIA by letting tastes for characteristics vary across consumers, so similar products are closer substitutes, producing realistic elasticities needed for merger and welfare analysis.

BLP adds random coefficients (consumer heterogeneity in tastes and price sensitivity) and an explicit unobserved-quality term ξ that makes price endogenous, estimated from aggregate market shares via a share-inversion contraction and GMM with instruments. The payoff is flexible substitution and a correction for price endogeneity. The cost is computation: the market-share equation is an integral with no closed form (requiring simulation), the inversion needs an iterative contraction, and the GMM objective can have local optima, so careful instruments, integration, and optimization are essential.

Valid instruments must be correlated with price but uncorrelated with the unobserved product quality ξ. Common choices are cost shifters (input prices, exchange rates) and 'BLP instruments' or differentiation instruments — functions of the characteristics of rival products in the same market, which shift markups through competition without entering the product's own demand shock. More recent work derives approximations to the optimal instruments to improve efficiency. Weak or invalid instruments are the main threat to credible price-sensitivity and markup estimates.