Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems
为差异化产品市场中的广义矩估计量提供了渐近分布理论，考虑了三种误差来源，并分析了BLP随机系数logit模型和纯特征模型所需的不同增长率，蒙特卡洛模拟验证了理论结果。
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 <link rid="b3">Berry, Levinsohn and Pakes (1995)</link> random coefficient logit model and the pure characteristics model analysed in <link rid="b5">Berry and Pakes (2002)</link>. 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. Copyright 2004 The Review of Economic Studies Ltd.