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Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems

机译:估计差异产品需求系统参数的极限定理

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We provide an asymptotic distribution theory for a class of generalized method of moments estimators that arise in the study of differentiated product markets when the number of observations is associated with the number of products within a given market.We allow for three sources of error:sampling error in estimating market shares,simulation error in approximating the shares predicted by the model,and the underlying model error.It is shown that the estimators are CAN provided the size of the consumer sample and the number of simulation draws grow at a large enough rate relative to the number of products.We consider the implications of the results for the Berry,Levinsohn and Pakes (1995) random coefficient logit model and the pure characteristics model analysed in Berry and Pakes (2002).The required rates differ for these two frequently used demand models.A small Monte Carlo study shows that the differences in asymptotic properties of the two models are reflected,in quite a striking way,in the models' small sample properties.Moreover the limit distributions provide a good approximation to the actual Monte Carlo distribution of the parameter estimates.The results have important implications for the computational burden of the two models.
机译:当观察数与给定市场内产品的数量相关时,我们为差异化产品市场研究中出现的一类广义矩估计器的渐近分布理论提供渐近分布理论。我们考虑了三种误差来源:抽样估计市场份额的误差,近似模型所预测的份额的模拟误差以及潜在的模型误差。这表明,只要消费者样本的大小和估计的抽取数量以足够大的速度增长,估计量就可以我们考虑了结果对Berry,Levinsohn和Pakes(1995)随机系数logit模型以及Berry和Pakes(2002)中分析的纯特征模型的影响。这两种情况的要求比率经常不同一项小的蒙特卡洛研究表明,两个模型的渐近性质的差异得到了明显的体现。 y,在模型的小样本属性中。此外,极限分布为参数估计的实际蒙特卡洛分布提供了很好的近似值。结果对这两个模型的计算负担具有重要意义。

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