审计质量与审计任期的倒U形关系——估计方法与统计意义

The Invert U-shaped Relation between Audit Quality and Auditor Tenure:Estimation Method and Statistic Implication

经历了几个重大的财务丑闻之后,审计师及会计师事务所的任期对审计质量的影响开始受到学术界的关注。理论上,两者存在倒U形关系。对于想要设置强制轮换限制的监管者而言,他们有必要知道关于这个倒U形关系的详细信息,例如这个倒U形关系的转折点发生在哪一年。以往文献用二次函数模型捕捉这一倒U形关系,并利用二次函数模型参数的普通最小二乘法(OLS)估计值计算出一个代表性的转折点。但是以往文献没有讨论这一代表性转折点的统计意义,从而限制了这个代表性转折点的数值在评估强制轮换限制时的用处。本文证明这个转折点收敛或近似地收敛于样本中所有个体(如客户一审计师/客户一会计师事务所)的转折点的中位数。此外,本文还提出一种基于生存分析的方法,可以用来估计所有样本转折点的整体分布曲线。我们使用蒙特卡罗模拟展示这两种估计方法的效果,如准确性、稳健性和信息的有用性等。

After several major financial scandals, the tenure of auditor/audit firm came into the focus of academic researches. Theoretically,there is an inverted U-shaped relationship between the auditing tenure and the auditing quality. For the regulators who are to set mandatory rotation limit need detailed information about the turning points of the inverted U-shaped,such as the turning point’s location. The extant literatures used a model of quadric function to capture this inverted U-shaped relationship,and used the OLS estimates of the quadric model’s parameters to calculate a representative turning point. But no literature discussed the statistical implication of this representative turning point, which restricted its application to the assessment of the mandatory rotation limits. This paper proves that this representative turning point converges exactly or approximately to the median of the turning points of all the individuals in sample, such as client-auditors/client-audit-firms. In addition,an estimating method based on survival analysis is put up in this paper to estimate the entire distribution of the entire turning points set in the form of their cumulative probability curve.Monte Carlo simulations are used to demonstrate the performance of these two estimating methods, such as errors, robustness, and information usefulness.