Nonparametric Analysis in Accounting Research

Advancements in statistical packages and computing power have made various forms of nonparametric estimation accessible to empirical researchers. However, these methods have been underutilized in accounting research, and many accounting researchers may have limited exposure on how to apply these tools. This study explores two nonparametric estimation techniques: kernel density estimation and locally weighted regression. We focus on the practical implementation of these methods, including settings in which they may be useful, key inputs over which researchers have discretion, and sample code to program them. We contribute to the tax, audit, and methodological literatures by providing two illustrative examples of how nonparametric techniques may be used in accounting. First, we analyze time-trends of effective tax rates (ETRs) in the financial service industry using kernel density estimates. Our results document that the distribution of ETRs among financial services firms has become less focused around the mean over time, with more probability mass occurring for below-average ETRs. Second, we study the relation between audit fees and size using nonparametric regression and document that omitting small firms due to sample attrition may introduce nonlinearity to the relation. This result is not readily apparent without visualizing the data and is difficult to discern using OLS regressions. Additionally, we demonstrate the flexibility of nonparametric analysis across broad areas of accounting research and discuss how these techniques may be used to complement ordinary least squares regression and guide research design choices.