Empirical Models of Inventory Investment and Price Determination by Durable Commodity Intermediaries

本研究建立了耐久商品中介机构库存投资与价格决定的动态规划模型，并进行了实证检验。这些公司从生产商那里购买大量耐用商品，如钢铁、木材或煤炭，然后以加价将库存出售给客户。调查人员已经与一家这样的中介机构--一家美国钢铁供应商--建立了工作关系，自1997年6月以来，该公司向他们提供了2000多种产品的详细每日采购、销售和库存数据，并持续每月更新。这项研究的一个主要组成部分是面向微观的，重点是开发计算和计量经济学方法，以确定公司的行为是否可以从动态规划问题的解准确地近似为最优交易策略。由于这些数据提供了每个中介客户的身份以及他们购买的价格和数量，调查人员可以研究最优价格歧视的动态模型是否可以解释向不同客户收取的价格的显著差异。该项目开发了新的计量经济学程序，以纠正中介机构获得新库存时对价格进行内生抽样所产生的动态选择性偏差问题。这项研究还通过聚合微观层面的模型来得出宏观层面的影响，以开发市场层面的(非均衡)价格决定模型。研究人员分析了宏观冲击和利率周期性波动对这些市场行为的影响，以提供对库存在商业周期中作为传播或稳定机制的作用的新见解。最后，通过将离散近似方法(如均匀离散化、基于求积的方法、随机和低偏差多重网格方法)与基于值函数和决策规则的多项式和神经网络逼近的连续逼近方法进行比较，本研究计划扩展了连续动态规划问题(如库存问题)的数值方法的技术水平。研究人员还评估了欧拉方程方法(例如，参数期望)，以及人工智能/学习文献中的方法，如“Q-学习”和神经动态编程。

This research develops and empirically tests dynamic programming models of inventory investment and price determination by durable commodity intermediaries. These firms acquire bulk quantities of durable commodities such as steel, lumber, or coal from producers and subsequently sell their inventories to customers at a markup. The investigators have established a working relationship with one such intermediary, a U.S. steel supplier, which has provided them with detailed daily data on purchases, sales, and inventory holdings for over 2,000 products since June, 1997 with monthly updates on an on-going basis. A major component of the research is micro-oriented, focusing on developing computational and econometric methods to determine whether the firm's behavior can be accurately approximated as an optimal trading strategy from the solution to a dynamic programming problem. Since the data provide identities of each of the intermediary's customers and the prices and quantities they purchased, the investigators can study whether dynamic models of optimal price discrimination can explain significant variations in prices charged to different customers. The project develops new econometric procedures for correcting the problem of dynamic selectivity bias resulting from endogenous sampling of the prices at which the intermediary acquires new inventories. The research also draws macro-level implications by aggregating the micro-level models to develop a market-level (disequilibrium) model of price determination. The investigators analyze the impact of macro shocks and cyclical fluctuations in interest rates on the behavior of these markets to provide new insights into the role of inventories as propagating or stabilizing mechanisms in business cycles. Finally, this research program extends the state of the art on numerical methods for continuous dynamic programming problems such as the inventory problem by comparing discrete approximation methods such as uniform discretization, quadrature-based methods, and random and low-discrepancy multi-grid methods to continuous approximation methods based on polynomial and neural network approximations to the value function and decision rule. The investigators also evaluate Euler equation methods (e.g. parameterized expectations), and methods from the AI/learning literature such as "Q-learning" and neuro-dynamic programming.