Lera Sandro Claudio, Sornette Didier
ETH Zurich, Singapore-ETH Centre, Singapore, Singapore.
ETH Zurich, Department of Management, Technology, and Economics, Zurich, Switzerland.
PLoS One. 2017 Aug 25;12(8):e0183627. doi: 10.1371/journal.pone.0183627. eCollection 2017.
The distribution of firm sizes is known to be heavy tailed. In order to account for this stylized fact, previous economic models have focused mainly on growth through investments in a company's own operations (internal growth). Thereby, the impact of mergers and acquisitions (M&A) on the firm size (external growth) is often not taken into consideration, notwithstanding its potential large impact. In this article, we make a first step into accounting for M&A. Specifically, we describe the effect of mergers and acquisitions on the firm size distribution in terms of an integro-differential equation. This equation is subsequently solved both analytically and numerically for various initial conditions, which allows us to account for different observations of previous empirical studies. In particular, it rationalises shortcomings of past work by quantifying that mergers and acquisitions develop a significant influence on the firm size distribution only over time scales much longer than a few decades. This explains why M&A has apparently little impact on the firm size distributions in existing data sets. Our approach is very flexible and can be extended to account for other sources of external growth, thus contributing towards a holistic understanding of the distribution of firm sizes.
企业规模分布已知是重尾的。为了解释这一典型事实，以往的经济模型主要关注通过对公司自身运营的投资实现增长（内部增长）。因此，尽管并购（M&A）对企业规模（外部增长）可能有巨大影响，但其影响往往未被考虑在内。在本文中，我们首次尝试考虑并购因素。具体而言，我们用一个积分 - 微分方程来描述并购对企业规模分布的影响。随后，针对各种初始条件，我们对该方程进行了解析求解和数值求解，这使我们能够解释以往实证研究中的不同观察结果。特别是，通过量化并购仅在比几十年长得多的时间尺度上才会对企业规模分布产生显著影响，从而解释了过去研究的不足之处。这也解释了为什么在现有数据集中，并购对企业规模分布的影响显然很小。我们的方法非常灵活，可以扩展以考虑其他外部增长来源，从而有助于全面理解企业规模分布。
