An Empirical Model of Nonlinear Pricing Competition

这项研究提出了一个框架来估计非线性定价竞争的均衡模型，使用的数据很容易为电力、电信和其他公用事业等许多行业提供。计量经济学方法背后的基本思想是，利用实际提供给消费者的关税形式所包含的信息，得出有关消费者使用强度分布的信息。关税的形状确定了卖家对不同数量或质量水平收取的最优加价，以诱导顾客群体根据他们的类型进行自我选择，即他们的偏好强度，或他们不同的需求弹性。因此，该模型克服了个人消费数据的缺失，而个人消费数据不太可能用于大型客户市场。我考虑了一个最优非线性定价模型，包括其垄断和双寡头两种版本。对需求和消费者类型分布的特定假设允许为这些不同的市场配置获得灵活的封闭形式的模型解。这种方法适用于产品水平差异化和允许消费者口味相关的情况。该模型的预测是一个二次关税函数，它取决于可观察到的市场和企业的具体特征。费率解的曲率与消费者不可观察个体特征分布的风险率有关，并驱动每个购买水平的最优定价规则。然后，将模型预测的二次电价拟合到每个市场和时间中每个企业的实际非线性电价，从而可以估计模型的结构参数，即市场特定需求效应、企业特定成本效应和消费者特定的未观察异质性。尽管价格歧视行为很普遍，但理论上直到最近才得到解决。经验使得确定不同类型消费者的最佳加价的决定因素成为可能。这种结构性办法的主要优点是可以进行若干次政策评价。例如，我们可以考虑使用非线性定价而不是线性定价策略在福利和利润方面的收益。也许最有趣的政策评估，考虑到数据的结构，可能是研究当企业从事非线性定价时横向合并的福利效应。在竞争和垄断环境中明确处理二级价格歧视，不仅可以研究效率收益或损失如何在不同类型的消费者中扩散，还可以研究横向合并的批准决定是否会受到企业对其产品定价方式的限制。

This research suggest a framework to estimate equilibrium models of nonlinear pricing competition using data that is readily available for many industries such as power, telecommunications, and other utilities. The basic idea behind the econometric approach is to make use of the information contained in the shape of tariffs actually offered to consumers to derive information about the distribution of consumers' usage intensity. The shape of the tariffs identifies the optimal markup that a seller charges for different quantity or quality levels to induce a population of customers to self-select according to their type, i.e., the intensity of their preferences, or their different elasticity of demand. The model thus overcomes the absence of individual consumption data, unlikely to be available for large customer markets. I consider a model of optimal nonlinear pricing, both in its monopoly and duopoly versions. Specific assumptions on demand and the distribution of consumer types allow obtaining a flexible closed form solution of the model for these different market configurations. This approach applies to cases where products are horizontally differentiated and where consumer tastes are allowed to be correlated. The prediction of the model is a quadratic tariff function that depends on observable market and firm specific characteristics. The curvature of the tariff solution is related to the hazard rate of the distribution of unobservable individual characteristics of consumers, and drives the optimal pricing rule for each purchase level. The quadratic tariff predicted by the model is then fitted to the actual nonlinear tariff of each firm in each market and time, thus allowing to estimate the structural parameters of the model, i.e., market specific demand effects, firm specific cost effects, and consumer specific unobserved heterogeneity.While price discrimination practices are common, they have been theoretically addressed only recently. The empirical makes possible to identify the determinants of the optimal markups for different types of consumers. The major advantage of this structural approach is the possibility of conducting several policy evaluations. For instance, we could account for the gains in welfare and profits of using nonlinear pricing instead of linear pricing strategies. Perhaps the most interesting policy evaluation, given the structure of the data, could be to study the welfare effects of horizontal mergers when firms engage in nonlinear pricing. Dealing explicitly with second-degree price discrimination in a competitive as well as monopolistic environment makes possible to study not only how are efficiency gains or losses spread over different consumer types, but also whether approval decisions on horizontal mergers could be subject to restrictions on the way firms price their products.