Small bank managers are prudent: A Benford’s Law approach to analyzing loan loss allowances

Abstract

Using an analysis of the two leading digits based on Benford’s Law, we analyze rounding patterns in loan loss allowances (LLAs) for a bank sample based on good and bad times, net income, profitability, bank size, regulatory level, and whether the banks are private or public. We find clear evidence of upward rounding during good times. Banks that are smaller, private, and subject to more lenient regulatory and supervisory levels also tend to round LLAs upward more than their larger, public, and more heavily regulated counterparts. The results are consistent with previous studies supporting non-opportunistic incentives (including signaling, reducing pro-cyclicality, and pursuing prudence and efficiency) under which bank managers increase the LLA. In addition to shedding more light on the ongoing debate about the management of provisioning for loan losses, we present an argument for why the rounding mechanism in LLAs is a rational consequence of U.S. commercial banks being subjected to opposing regulatory forces coming from bank regulators and securities regulators.