Amirteimoori Alireza, Sahoo Biresh K, Mehdizadeh Saber
Faculty of Engineering & Natural Sciences, Istinye University, Istanbul, Turkey.
Xavier Institute of Management, XIM University, Bhubaneswar, 7571013 India.
Financ Innov. 2023;9(1):31. doi: 10.1186/s40854-022-00447-1. Epub 2023 Jan 16.
In the nonparametric data envelopment analysis literature, scale elasticity is evaluated in two alternative ways: using either the technical efficiency model or the cost efficiency model. This evaluation becomes problematic in several situations, for example (a) when input proportions change in the long run, (b) when inputs are heterogeneous, and (c) when firms face price uncertainty in making their production decisions. To address these situations, a scale elasticity evaluation was performed using a value-based cost efficiency model. However, this alternative value-based scale elasticity evaluation is sensitive to the uncertainty and variability underlying input and output data. Therefore, in this study, we introduce a stochastic cost-efficiency model based on chance-constrained programming to develop a value-based measure of the scale elasticity of firms facing data uncertainty. An illustrative empirical application to the Indian banking industry comprising 71 banks for eight years (1998-2005) was made to compare inferences about their efficiency and scale properties. The key findings are as follows: First, both the deterministic model and our proposed stochastic model yield distinctly different results concerning the efficiency and scale elasticity scores at various tolerance levels of chance constraints. However, both models yield the same results at a tolerance level of 0.5, implying that the deterministic model is a special case of the stochastic model in that it reveals the same efficiency and returns to scale characterizations of banks. Second, the stochastic model generates higher efficiency scores for inefficient banks than its deterministic counterpart. Third, public banks exhibit higher efficiency than private and foreign banks. Finally, public and old private banks mostly exhibit either decreasing or constant returns to scale, whereas foreign and new private banks experience either increasing or decreasing returns to scale. Although the application of our proposed stochastic model is illustrative, it can be potentially applied to all firms in the information and distribution-intensive industry with high fixed costs, which have ample potential for reaping scale and scope benefits.
在非参数数据包络分析文献中，规模弹性通过两种替代方法进行评估：使用技术效率模型或成本效率模型。这种评估在几种情况下会出现问题，例如：（a）长期内投入比例发生变化时；（b）投入要素具有异质性时；（c）企业在做出生产决策时面临价格不确定性时。为解决这些情况，使用基于价值的成本效率模型进行了规模弹性评估。然而，这种基于价值的替代规模弹性评估对投入和产出数据背后的不确定性和可变性很敏感。因此，在本研究中，我们引入了一种基于机会约束规划的随机成本效率模型，以开发一种基于价值的方法来衡量面临数据不确定性的企业的规模弹性。对印度银行业的71家银行在八年（1998 - 2005年）期间进行了实证说明性应用，以比较关于它们的效率和规模属性的推断。主要发现如下：第一，在机会约束的不同容忍水平下，确定性模型和我们提出的随机模型在效率和规模弹性得分方面产生了明显不同的结果。然而，在容忍水平为0.5时，两个模型产生了相同的结果，这意味着确定性模型是随机模型的一个特殊情况，因为它揭示了银行相同的效率和规模收益特征。第二，对于效率低下的银行，随机模型产生的效率得分高于其确定性对应模型。第三，国有银行表现出比私有银行和外国银行更高的效率。最后，国有银行和老牌私有银行大多表现出规模收益递减或不变，而外国银行和新的私有银行则经历规模收益递增或递减。尽管我们提出的随机模型的应用是说明性的，但它有可能应用于所有具有高固定成本、有充分潜力获取规模和范围效益的信息和分销密集型行业的企业。
