Simulated Maximum Likelihood Estimator for the Random Coefficient Logit Model Using Aggregate Data
Simulated Maximum Likelihood Estimator for the Random Coefficient Logit Model Using Aggregate Data
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DOI：
10.1509/jmkr.46.4.531
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发表时间：
2009-08
影响因子：
6.1
通讯作者：
Sungho Park;Sachin Gupta
中科院分区：
文献类型：
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作者：
Sungho Park;Sachin Gupta
本文提出了一种考虑异质性和内禀性的随机系数Logit模型的模拟极大似然估计方法。该方法允许在观察到的市场份额的随机性的两个来源：未观察到的产品特性和抽样误差。由于后者，该方法是合适的，当样本大小的股票是有限的。相反，Berry、Levinsohn和Pakes常用的方法假设观察到的份额没有抽样误差。该方法可以看作是Villas-Boas和Winer方法的推广，与Petrin和Train的“控制函数”方法密切相关。作者表明，所提出的方法提供了无偏和有效的估计需求参数。他们还获得了作为副产品的内隐检验统计数据，包括内隐偏差的方向。该模型可以扩展到将马尔可夫机制切换动态参数，并开放给其他扩展的基础上最大似然。所提出的方法的好处是通过假设正常的未观察到的需求属性，一个假设，施加约束的类型的定价行为，容纳。然而，作者在模拟中发现，需求估计是相当强大的违反这些假设。
The authors propose a simulated maximum likelihood estimation method for the random coefficient logit model using aggregate data, accounting for heterogeneity and endogeneity. The method allows for two sources of randomness in observed market shares: unobserved product characteristics and sampling error. Because of the latter, the method is suitable when sample sizes underlying the shares are finite. In contrast, Berry, Levinsohn and Pakes's commonly used approach assumes that observed shares have no sampling error. The method can be viewed as a generalization of Villas-Boas and Winer's approach and is closely related to Petrin and Train's “control function” approach. The authors show that the proposed method provides unbiased and efficient estimates of demand parameters. They also obtain endogeneity test statistics as a by-product, including the direction of endogeneity bias. The model can be extended to incorporate Markov regime-switching dynamics in parameters and is open to other extensions based on maximum likelihood. The benefits of the proposed approach are achieved by assuming normality of the unobserved demand attributes, an assumption that imposes constraints on the types of pricing behaviors that are accommodated. However, the authors find in simulations that demand estimates are fairly robust to violations of these assumptions.