Large Market Asymptotics for Differentiated Product Demand Estimators With Economic Models of Supply
研究了在少数大市场中，随着产品数量增加，常用需求模型的工具变量估计是否一致，发现伯川德-纳什均衡下产品特征作为价格工具会失效，但合理建模仍可得到一致估计。
IO economists often estimate demand for differentiated products using data sets with a small number of large markets. By modeling demand as depending on a small number of product characteristics, one might hope to obtain increasingly precise estimates of demand parameters as the number of products in a single market grows large. In this paper, I address the question of consistency and asymptotic distributions of IV estimates of demand in a small number of markets as the number of products increases in some commonly used demand models under conditions on economic primitives. I show that, under the common assumption of a Bertrand-Nash equilibrium in prices, product characteristics lose their identifying power as price instruments in the limit in many of these models, giving inconsistent estimates in these cases. I find that consistent estimates can still be obtained for many of the cases I consider, but care must be taken in modeling demand and choosing instruments. For cases where consistent estimates can be obtained, I provide sufficient conditions for consistency and asymptotic normality of estimates of parameters and counterfactual outcomes. A monte carlo study confirms that the asymptotic results provide an accurate description