Do We Exploit all Information for Counterfactual Analysis? Benefits of Factor Models and Idiosyncratic Correction
Do We Exploit all Information for Counterfactual Analysis? Benefits of Factor Models and Idiosyncratic Correction
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DOI：
10.1080/01621459.2021.2004895
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发表时间：
2020-11
影响因子：
3.7
通讯作者：
Jianqing Fan;Ricardo P. Masini;M. C. Medeiros
中科院分区：
文献类型：
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作者：
Jianqing Fan;Ricardo P. Masini;M. C. Medeiros
摘要最优定价，即确定使给定产品的利润或收入最大化的价格水平，是零售业的一项重要任务。要选择这样一个数量，首先需要从产品需求中估计价格弹性。回归方法通常无法恢复这种弹性，由于混杂效应和价格的内生性。因此，通常需要随机化实验。然而，弹性可以是高度异质性的，这取决于例如商店的位置。由于随机化经常发生在市政一级，标准的差异中的差异方法也可能失败。可能的解决方案是基于方法来测量处理对单个（或仅仅几个）处理单元的影响，该方法基于从人工控制构建的反事实。例如，对于处理组中的每个城市，可以从未处理的位置构建反事实。在这篇文章中，我们应用一种新的高维统计方法来衡量价格变化对巴西一家大型零售商日常销售额的影响。所提出的方法结合了主成分（因子）和稀疏回归，从而产生了一种称为因子调整正则化方法的方法。这些数据包括400多个城市的五种不同产品的每日销售和价格。所考虑的产品属于甜食和糖果类别，并在2016年和2017年进行了实验。我们的研究结果证实了假设的高度异质性产生非常不同的定价策略，在不同的城市。本文的补充材料可在网上查阅。
Abstract Optimal pricing, that is determining the price level that maximizes profit or revenue of a given product, is a vital task for the retail industry. To select such a quantity, one needs first to estimate the price elasticity from the product demand. Regression methods usually fail to recover such elasticities due to confounding effects and price endogeneity. Therefore, randomized experiments are typically required. However, elasticities can be highly heterogeneous depending on the location of stores, for example. As the randomization frequently occurs at the municipal level, standard difference-in-differences methods may also fail. Possible solutions are based on methodologies to measure the effects of treatments on a single (or just a few) treated unit(s) based on counterfactuals constructed from artificial controls. For example, for each city in the treatment group, a counterfactual may be constructed from the untreated locations. In this article, we apply a novel high-dimensional statistical method to measure the effects of price changes on daily sales from a major retailer in Brazil. The proposed methodology combines principal components (factors) and sparse regressions, resulting in a method called Factor-Adjusted Regularized Method for Treatment evaluation (FarmTreat). The data consist of daily sales and prices of five different products over more than 400 municipalities. The products considered belong to the sweet and candies category and experiments have been conducted over the years of 2016 and 2017. Our results confirm the hypothesis of a high degree of heterogeneity yielding very different pricing strategies over distinct municipalities. Supplementary materials for this article are available online.