Linear valuation without OLS: the Theil-Sen estimation
James A. Ohlson
Published online: 26 June 2014
Ó Springer Science+Business Media New York 2014
Abstract 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 vari-
ables. 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 efﬁ-
cient than OLS under non-ideal conditions. This research compares the relative efﬁ-
ciency 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.
J. A. Ohlson (&)
Hong Kong Polytechnic University, Kowloon, Hong Kong
J. A. Ohlson
Cheung Kong Graduate School of Business, Beijing, China
New York University, New York, NY, USA
Rev Account Stud (2015) 20:395–435