Heteroscedastic Exponomial Choice
46 Pages Posted: 26 Aug 2018
Date Written: August 15, 2018
We develop analytical properties of the Heteroscedastic Exponomial Choice (HEC) model to lay the groundwork for its use in theoretical and empirical research that build demand models on a discrete choice foundation. The HEC model generalizes the Exponomial Choice model by including choice-specific variances for the random components of utility (the error terms) – a generalization that is intractable for multinomial logit. Under HEC, the choice probabilities, the elasticity of demand and the expected consumer surplus all have simple, closed-form expressions. The HEC loglikelihood function is a concave function of the utility parameters for a given set of error term distributions. HEC can easily accommodate an outside option with a deterministic utility (no random error term), thus permitting choices with zero probability. Finally, HEC can also be used to disentangle price endogeneity in empirical research. To that end, we analyze equilibrium prices for an oligopoly and show that the unique Nash equilibrium is equivalent to a Stackelberg equilibrium that can be efficiently computed via a sequence of well-behaved single-variable equations. In addition, we present a variety of analytical results that shed light on the impact of error heteroscedasticity on equilibrium prices. We find that the individual and collective incentives differ in equilibrium: Firms individually want lower error variability for their own product, but collectively prefer higher error variability for all products – including their own – because higher error variability softens the price competition.
Keywords: discrete choice, price competition
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