Regression Analysis in Accounting Disclosure Studies

A problem that sometimes occurs in undertaking empirical research in accounting and finance is that the theoretically correct form of the relation between the dependent and independent variables is not known, although often thought or assumed to be monotonic. In addition, transformations of disclosure measures and independent variables are proxies for underlying constructs and hence, while theory may specify a functional form for the underlying theoretical construct, it is unlikely to hold for empirical proxies. In order to cope with this problem a number of accounting disclosure studies have transformed variables so that the statistical analysis is more meaningful. One approach that has been advocated in such circumstances is to rank the data and then apply regression techniques, a method that has been used recently in a number of accounting disclosure studies. This paper reviews a number of transformations including the Rank Regression procedure. Because of the inherent properties of ranks and their use in regression analysis, an extension is proposed that provides an alternative mapping that replaces the data with their normal scores. The normal scores approach retains the advantages of using ranks but has other beneficial characteristics, particularly in hypothesis testing. Regressions based on untransformed data, on the log odds ratio of the dependent variable, on ranks and regression using normal scores, are applied to data on the disclosure of information in the annual reports of companies in Japan and Saudi Arabia. It is found that regression using normal scores has some advantages over ranks that, in part, depend on the structure of the data. However, the case studies demonstrate that no one procedure is best but that multiple approaches are helpful to ensure the results are robust across methods.