Linear valuation without OLS: the Theil-Sen estimation approach
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OLS-based archival accounting research encounters two well-known problems. First, outliers tend to influence results excessively. Second, heteroscedastic error terms raise the specter of inefficient estimation and the need to scale variables. This paper applies a robust estimation approach due to Theil (Nederlandse Akademie Wetenchappen Ser A 53:386–392, 1950) and Sen (J Am Stat Assoc 63(324):1379–1389, 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, Fundamentals of modern statistical methods: substantially improving power and accuracy, 2nd edn. Springer, New York 2010), one naturally hypothesizes that TS should be more efficient than OLS under non-ideal conditions. This research compares the relative efficiency of OLS versus 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.
KeywordsLinear valuation Estimation methods Theil-Sen estimator OLS
JEL ClassificationM40 M41 G17
We thank Sudipta Basu, Ilia Dichev, Stan Markov, Stephen Penman, Kam-Ming Wan, and Rand Wilcox for helpful comments. Kim gratefully acknowledges financial support from the Samsung Scholarship.
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