An Empirical Analysis of Competitive Nonlinear Pricing

In this paper I estimate a model of competitive nonlinear pricing with multidimensional adverse selection. I model competition using a Stackelberg duopoly and solve the multidimensional screening problem by aggregating the multidimensional type into a single dimensional type. I study identification and estimation of the utility and cost parameters and the joint density of consumer types. The truncated marginal densities of the aggregated types can be nonparametrically identified but not the joint density. I use the classic Cramér-von Mises and Vuong’s test to select one parametric family of copula to estimate the joint density from the unspecified marginals. Using a unique data for advertisements collected from two Yellow Pages Directories in Central Pennsylvania I find that: (a) Joe copula characterizes the joint density of adverse selection; (b) there is a substantial heterogeneity among advertisers; (c) the estimated density rationalizes why there is more competition at the lower end of the ads than at the upper end; (d) consumers treat the ads as substitutes; and (e) a counterfactual exercise suggests that there is a substantial (3.8% of the sales) loss of welfare due to asymmetric information.