Sales, Consumer Inventory and Non-Linear Prices

可储存商品的显著特点是，它们可以被购买用于库存。消费者可以在销售期间囤积。许多产品，如食品杂货和中间产品都是可以储存的。该项目的目标是开发一个可处理库存、多品牌采购和不同数量(大小)采购的易处理的需求估计模型。第一步，根据购买的大小(数量)最大化所观察到的品牌选择的可能性，以便恢复那些不直接影响动态行为的参数。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，将选择集限制为每个时期实际购买的相同大小(数量)的可用期权。在第二步中，使用第一阶段的估计，我们计算每种尺寸(数量)的“包含值”，即购买每种集装箱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，我们将动态估计的标准嵌套算法应用于简化的动态问题，通过最大化所观察到的尺寸(数量)序列的可能性来估计其余的参数。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两个阶段的计算负担。动态规划问题只在第三阶段得到解决，该模型能够将个体选择分解成两个可以单独识别的不同部分。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动态(存储)行为的关键参数。简化的问题将每一种购买规模视为单一选择，其预期效用(吸引力)由包含值(在第一阶段估计)决定。我们关心可储存商品的销售和需求的原因有几个。首先，当一种商品可以储存时，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。我们研究应该如何对待市场需求，以及如何区分短期和长期价格反应。对于任何依赖于需求估计的研究来说，这种区别都很重要，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。基于不考虑需求动态的估计得出的结论可能具有误导性。其次，关于可储存产品的丰富扫描数据为研究家庭行为是否符合具有动态前瞻性行为的模型提供了一个有趣的机会。第三，了解需求使我们能够研究卖家间歇性价格歧视的动机。这些估计将有助于确定在模拟卖家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.