The Inconsistency of Common Scale Estimators When Output Prices Are Unobserved and Engogenous

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 the scale estimates will tend to be downward biased in the production function case, under a wide range of assumptions about the pattern of technology, demand and factor price shocks. The result also holds for scale estimates obtained from cost functions. The empirical part of the paper presents various estimates of scale economies for a sample of Norwegian manufacturing plants. The findings provide some support for the hypothesis that the firms face an imperfectly competitive environment. The estimates suggests that there are significant markups and scale economies to the variable factors of production in our sample. However, the estimates of markups and scale economies presented in this paper are substantially lower than the results obtained by Hall (1988, 1990) and others using industry level data.