Sales, Consumer Inventory and Non-Linear Prices

可储存商品的显著特点是可以购买库存。 消费者可以在销售期间囤积。许多产品，如杂货和中间产品都是可储存的。本项目的目标是开发一个易于处理的需求估计模型，以处理库存，以及多个品牌的购买，以及不同数量（大小）的购买。我们提出了一个三步估计过程。第一步，包括最大限度地提高观察到的品牌选择的可能性的大小（数量）购买，以恢复这些参数，不直接影响动态行为的条件。如图所示，我们不需要解决动态规划问题来恢复它们。我们估计了一个离散选择模型，将选择集限制在每个时期实际购买的相同大小（数量）的可用期权上。在第二步中，使用第一阶段的估计，我们计算每个尺寸（数量）的“包含值”，即购买每个容器尺寸对消费者的预期效用。包含值将有关大小的所有相关信息聚合到标量中。最后，我们应用标准的嵌套算法动态估计简化的动态问题，估计其余的参数，通过最大化的可能性所观察到的序列的大小（数量）购买。该框架的优点是将评估分为三个步骤。 前两个阶段的估计有助于大大减少后者的计算负担。动态规划问题只在第三阶段解决。直观地说，该模型可以将个人选择分解为两个不同的组成部分，可以分别识别。首先，在任何特定的时间点，当消费者购买给定尺寸的产品时，我们可以估计她对不同品牌的偏好。其次，我们可以通过查看问题的简化版本来估计决定消费者的动态（存储）行为的关键参数。简化的问题将每种购买规模视为一个单一的选择，其预期效用（吸引力）由包含值（在第一阶段估计）决定。第一，当一种商品是可储存的时，对价格变化的短期反应和长期反应是有区别的。这种区别对需求估计有影响。我们研究如何对待市场需求，以及如何区分短期和长期的价格反应。 这一区别对于任何依赖于需求估计的研究都很重要，无论是合并分析、计算新商品的福利收益还是建筑价格指数。基于忽视需求动态的估计得出的结论可能会产生误导。其次，关于可储存产品的丰富扫描数据提供了一个有趣的机会，可以研究家庭行为是否符合动态前瞻性行为的模型。第三，了解需求使我们能够研究卖方的跨期价格歧视的动机。这些估计将有助于确定在模拟卖方行为时要考虑的关键因素。

The distinctive feature of storable goods is that they can be purchased for inventory. Consumers can stockpile during sales. Numerous products like groceries, and intermediate goods are storable. The goal of this project is to develop a tractable model for demand estimation that handles inventories, as well as multiple brand purchases, and purchases of different quantities (sizes).We propose a three-step estimation procedure. The first step, consist of maximizing the likelihood of the observed brand choice conditional on the size (quantity) bought in order to recover those parameters that do not directly affect the dynamic behavior. As shown, we do not need to solve the dynamic programming problem to recover them. We estimate a discrete choice model, restricting the choice set to available options of the same size (quantity) actually bought in each period. In the second step, using the estimates from the first stage, we compute the "inclusive values" for each size (quantity), namely, the expected utility to the consumer from purchasing each container size. The inclusive values aggregate all the relevant information about a size into a scalar. Finally, we apply the standard nested algorithm for dynamic estimation to the simplified dynamic problem to estimate the rest of the parameters by maximizing the likelihood of the observed sequence of sizes (quantities) purchased. The advantage of the framework is that breaks the estimation into three steps. Estimates from the first two stages help substantially reduce the computational burden of the latter. The dynamic programming problem is solved only in the third stage.Intuitively, the model enables the decomposition of the individual choices into two different components that can be separately identified. First, at any specific point in time, when the consumer purchases a product of a given size, we can estimate her preferences for the different brands. Second, we can estimate the key parameters that determine the dynamic (storing) behavior of the consumer by looking at a simplified version of the problem. The simplified problem treats each size of purchase as a single choice whose expected utility (appeal) is determined by the inclusive values (estimated in the first stage).There are several reasons why we care about sales and demand for storable goods. First, when a good is storable, there is a distinction between the short run and long run reaction to price changes. This distinction has implications for demand estimation. We study how market demand should be treated and how short run and long run price responses can be distinguished. The distinction is important for any study that relies on demand estimation, be it merger analysis, computation of welfare gains from new goods, or building price indices. Conclusions based on estimates that disregard demand dynamics are likely to be misleading. Second, the rich scanner data on storable products presents an interesting opportunity to study whether household behavior fits a model with dynamic forward-looking behavior. Third, understanding demand allows us to study sellers' incentives to intertemporally price discriminate. The estimates will help identify the key factors to be considered in modeling sellers' behavior.