Aggregation Bias in Estimating Log‐Log Demand Function
Aggregation Bias in Estimating Log‐Log Demand Function
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DOI：
10.1111/poms.13488
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发表时间：
2021-05
影响因子：
5
通讯作者：
Zizhuo Wang;Chaolin Yang;Hongsong Yuan;Yaowu Zhang
中科院分区：
文献类型：
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作者：
Zizhuo Wang;Chaolin Yang;Hongsong Yuan;Yaowu Zhang
在这项研究中，我们考虑了利用历史销售数据估计需求函数的问题。特别是，我们研究了使用聚合数据可能会导致此类估计中的偏差。我们考虑一个对数-对数需求模型，以及如何计算聚合数据中的价格的两种方法，简单平均价格或加权平均价格。我们研究了两种情况下是否都存在估计偏差，以及估计偏差的方向。我们发现，总体上，各个时期的“平均价格”和“价格离散度”之间的相关性对偏差的方向有影响。然后，我们提出了减少聚集偏差的方法。我们证明了当价格过程满足一定的温和条件时，我们的去偏过程可以渐近恢复真实参数。我们还得到了无偏参数的统计性质。我们在合成数据和真实数据上进行了数值实验，以证明我们方法的有效性。数值结果表明，无论是在合成环境中还是在实际环境中，我们所提出的偏差抑制方法都具有有效降低偏差的潜力。
In this study, we consider the problem of estimating demand functions using historical sales data. In particular, we study how using aggregate data may result in bias in such estimations. We consider a log‐log demand model, and two ways of how the price in the aggregate data is calculated, simple average price or weighted average price. We study whether there exists estimation bias in each of the two cases as well as the direction of the bias. We show that in general, the correlation between “average price” and “price dispersion” in each time period has an effect on the direction of the bias. We then propose ways to reduce the aggregation bias. We prove that when the price processes satisfy certain mild conditions, our debiasing procedure can recover the true parameters asymptotically. We also obtain statistical properties of the debiased parameters. We perform numerical experiments on both synthetic and real data to demonstrate the effectiveness of our approach. The numerical results show that our proposed bias mitigation approach has the potential of effectively reducing the bias in both synthetic and practical settings.