Empirical evidence shows that large firms are generally more efficient than small and medium-sized firms. Empirical tests have evaluated cost efficiency while assuming homogeneity among firms and mainly examined the size-efficiency relationship in a hypothetical average firm. However, in practice, firms have different resources for multiple reasons and are therefore heterogeneous. This paper uses the concept of profit efficiency to study size-efficiency relationships in individual firms while assuming heterogeneity among firms. For this purpose and in contrast to the traditional approach, we estimate a stochastic frontier model with random coefficients using Bayesian techniques to assess the differences in profit efficiency between small and large firms in the manufacturing industry in Spain. The results show that the relationship between efficiency and size heavily depends on the internal properties and characteristics of the firm and environment in which it operates and that there is heterogeneity among firms; ignoring such heterogeneity can lead to an overestimation of inefficiency of 4.92 percentage points. We also discuss the implications of these results.

经验证据表明，大企业通常比中小型企业更有效率。实证检验评估了成本效率，同时假设了企业之间的同质性，并且主要检验了假设的平均企业中的规模效率关系。但是，实际上，由于多种原因，企业拥有不同的资源，因此是异质的。本文使用利润效率的概念来研究单个公司的规模效率关系，同时假设公司之间存在异质性。为此，与传统方法相反，我们使用贝叶斯技术估计带有随机系数的随机前沿模型，以评估西班牙制造业中小公司与大公司之间的利润效率差异。结果表明，效率与规模之间的关系在很大程度上取决于企业的内部特性和特征以及企业所处的环境，企业之间存在异质性。忽略这种异质性可能导致效率低估了4.92个百分点。我们还将讨论这些结果的含义。