Linear valuation without OLS: the Theil-Sen estimation approach

James Arvid Ohlson, Seil Kim

Research output: Journal article publicationJournal articleAcademic researchpeer-review

62 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)395-435
Number of pages41
JournalReview of Accounting Studies
Issue number1
Publication statusPublished - 1 Jan 2015


  • Estimation methods
  • Linear valuation
  • OLS
  • Theil-Sen estimator

ASJC Scopus subject areas

  • Accounting
  • Business, Management and Accounting(all)


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