An Empirical Model of Nonlinear Pricing Competition

这项研究建议了一个框架，利用电力、电信和其他公用事业等许多行业随时可用的数据来估计非线性定价竞争的均衡模型。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中包含的信息，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为不同数量或质量水平收取的最优加价，以诱导一群客户根据他们的类型，即他们的偏好强度，或他们不同的需求弹性进行自我选择。因此，该模型克服了缺乏个人消费数据的问题，这些数据不太可能适用于大型客户市场。我考虑了一个最优非线性定价模型，无论是垄断版本还是双寡头版本。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该模型的灵活封闭形式解。这种方法适用于产品水平差异化和允许消费者品味相关的情况。该模型的预测是一个依赖于可观察市场和企业特性的二次关税函数。价格解的曲率与消费者不可见的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与每个企业在每个市场和时间的实际非线性电价进行拟合，从而可以估计模型的结构参数，即市场特定的需求效应、企业特定的成本效应和消费者特定的未观察到的异质性。虽然价格歧视做法很常见，但最近才从理论上解决了这些问题。这一经验使得确定不同类型消费者的最优加价的决定因素成为可能。这种结构性办法的主要优点是有可能进行几次政策评估。例如，我们可以解释使用非线性定价策略而不是线性定价策略在福利和利润方面的收益。考虑到数据的结构，也许最有趣的政策评估可能是研究当公司进行非线性定价时，横向兼并的福利效应。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身上分配，而且可以研究横向合并的批准决定是否会受到公司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.