Linear Valuation without OLS: The Theil-Sen Estimation Approach

Abstract

OLS-based archival accounting research encounters two well-known problems. First, outliers tend to influence results excessively. Second, heteroscedastic error terms raise the spectre of inefficient estimation and the need to scale variables. This paper applies a robust estimation approach due to Theil (1950) and Sen (1968) (TS henceforth). The TS method is easily understood and it circumvents the two problems in an elegant, direct way. Because TS and OLS are roughly equally efficient under OLS-ideal conditions (Wilcox 2010), one naturally hypothesizes that TS should be more efficient than OLS under non-ideal conditions. This research compares the relative efficiency of OLS vs. TS in cross-sectional valuation settings. There are two dependent variables, market value and subsequent year earnings; basic accounting variables appear on the equations’ right-hand side. Two criteria are used to compare the estimation methods’ performance: (i) the inter-temporal stability of estimated coefficients and (ii) the goodness-of-fit as measured by the fitted values’ ability to explain actual values. TS dominates OLS on both criteria, and often materially so. Differences in inter-temporal stability of estimated coefficients are particularly apparent, partially due to OLS estimates occasionally resulting in “incorrect” signs. Conclusions remain even if winsorization and the scaling of variables modify OLS.