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Development of estimation method for an index of complementarity/substitutability without price variables

无价格变量的互补性/替代性指数估计方法的开发

基本信息

批准号：
18530171
负责人：
TORII Akio
金额：
$ 1.84万
依托单位：
Yokohama National University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2006
资助国家：
日本
起止时间：
2006 至 2007
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18530171/
关键词：
complementarity substitutability discrete choice model ロジット分析交差弾力性

项目摘要

An index of complementarity/substitutability is introduced which is calculable even when explicit price variables are not observable. The index Prob(Y=1 | X=1)-Prob(Y=1 | X=0) is proved to have the appropriate properties for an index using a probabilistic utility model. Also methods to estimate the index empirically are shown and their statistical properties of estimators are examined by Monte-Carlo simulation methods. The summary of results are: the index shows expected appropriate properties as an index of complemantarity/substitutability, that is, the index shows monotonistic association with the degree of complementarity/substitutability; under certain construction, the index shows the same value with its cross-elasticity normalized by their own price elasticity; simultaneous logit regression can be employed for estimation of the index proposed in Schmidt and Strauss(1975), on the other hand simple multinominal logit regression provides almost the same estimates of the index; although estimates have a significant bias from the true values expected by theory, the bias does not deteriorate tests of complementarity/substitutability; robust estimators are provided even without price variables.As a case study, the index is applied to analyze viewers' choice behavior with respect to terrestrial TV broadcasting services in Japan. The public broadcasting channel seems to provide programs that are substitutes to those provided by private channels supported by advertising, while those private channels seem to provide complements each other.

引入了一个互补性/可替代性指标，即使在显性价格变量不可观测的情况下，该指标也可计算。利用概率实用新型证明了索引Prob(Y=1 | X=1)-Prob（Y=1 | X=0）具有索引的适当性质。此外，还给出了对指标进行经验估计的方法，并用蒙特卡罗模拟方法检验了估计器的统计性质。结果总结为：指标作为互补性/可替代性指标表现出预期的适宜性质，即指标与互补性/可替代性程度呈现单调关联；在一定的结构下，指数的交叉弹性被各自的价格弹性归一化后显示出相同的值；同时对数回归可以用于Schmidt和Strauss（1975）提出的指标的估计，另一方面，简单多项式对数回归提供了几乎相同的指标估计；虽然估计值与理论所期望的真实值有很大偏差，但这种偏差并不影响互补性/可替代性测试；即使没有价格变量，也提供了鲁棒估计。作为一个案例研究，该指数被用于分析观众对地面电视广播服务的选择行为。公共广播频道提供的节目似乎是广告支持的私人频道提供的节目的替代品，而私人频道提供的节目似乎是相互补充的。