The inconsistency of common scale estimators when output prices are unobserved and endogenous
证明，当企业面临不完全竞争且价格不同时，用行业统一价格平减销售额作为产出代理变量会导致规模估计向下偏误，该结论在多种技术、需求和要素价格冲击假设下均成立。
This paper explores the inconsistency of common scale estimators when output is proxied by deflated sales, based on a common output deflator across firms. The problems arise when firms operate in an imperfectly competitive environment and prices differ between firms. In particular, we show that this problem reveals itself as a downward bias in the scale estimates obtained from production function regressions, under a variety of assumptions about the pattern of technology, demand and factor price shocks. The result also holds for scale estimates obtained from cost functions. The analysis is carried one step further by adding a model of product demand. Within this augmented model we examine the probability limit of the scale estimate obtained from an ordinary production function regression. This analysis reveals that the OLS estimate will be biased towards unity - or possibly a value below unity. We have included an empirical section which illustrates the issues. The empirical analysis presents a tentative approach to avoid the problems discussed in the theoretical part of this paper.