The OECD *Transfer Pricing Guidelines* (2017, ¶ 6.192) makes a perfunctory reference to multi-year data analysis covering intangibles. The guidance about using multi-year analysis of profit indicators is described on ¶ 3.75 to ¶ 3.79 (“examining multiple year data is often useful in a comparability analysis, but it is not a systematic requirement.”). One expects more competence in economics and statistical principles from the OECD Guidelines, instead of the misleading quote. Unsystematic requirement is nonsense.

Multi-year analysis (audit year plus two or more data years) of profit indicators was introduced in the US 1994 transfer pricing regulations to control the effects of short-term *inventory cycles*. See Treas. Reg. § 1.482-1(f)(2)(iii) (Multiple year data). However, the usual three-year analysis of profit indicators may be inadequate (not sufficiently reliable) for several reasons.

First, analysis of profit indicators should consider the effects of *investment cycles*, lasting from eight to 12 years (depending on the major product life cycles of the taxpayer and its comparables). See Treas. Reg. § 1.482-1(f)(2)(iii)(B) (“Circumstances that may warrant consideration of data from multiple years include … the effect of business cycles in the controlled taxpayer’s industry, or the effects of life cycles of the product or intangible property being examined.”). Business cycles are surveyed by Nicholas Rau, *Trade Cycles* (Theory and Evidence), Macmillan, 1974 and by Günter Gabisch and Hans-Walter Lorenz, *Business Cycle Theory* (A Survey of Methods and Concepts), Springer-Verlag, 1989.

Second, the statistical law of large numbers indicates that parameter stability (including multivariate regression coefficients, or the mean and standard deviation of the selected univariate profit indicator, and the ratio of the mean to standard deviation as a reliability measure) requires larger samples. In statistics, random samples containing more than 30 observations are considered large, as verified by the usual truncation of William Gosset’s *t*-distribution. See Ronald Fisher and Frank Yates, *Statistical Tables* (6^{th} edition), Longman, 1974, Table III, p. 46.

Here, I show repeated measures of operating profit margins after depreciation and amortization (OMAD) using three-year, five-year, seven-year, ten-year of data analyses, and all data available for a group of benchmark companies. For illustration, I use four “downstream” (refining and marketing) US petroleum refiners classified in SIC code 2911. For industry information, see Mark Kaiser, Arno de Klerk, James Gary, and Glenn Handwerk, *Petroleum Refining* (Technology, Economics and Markets) (6^{th} edition), Taylor & Francis, 2020.

The benchmark petroleum refiners are Delek Holdings Inc. (GVKEY 166563), HollyFrontier Corp. (5667), Marathon Petroleum Corp. (186989), and Valero Energy Corp. (15247).

I use simple regression analysis positing that company-level operating profit after depreciation (OIADP) is proportional to Net Sales (subject to random errors):

OIADP = α + β Net Sales + random error,

where alpha is the intercept and beta (OMAD) is the slope coefficient (β ± standard error).

The annual OIADP and Net Sales company-level data are obtained from RoyaltyStat/Compustat, and the regression algorithms are built-in functions in RoyaltyStat.

Data Range Years Count Slope StdError *t*-Stat R^{2}

2020-2018 3 12 0.0398 0.0067 5.9159 0.4419

2020-2016 5 20 0.0398 0.0047 8.4253 0.5024

2020-2014 7 28 0.0438 0.0033 13.1705 0.5822

2020-2011 10 40 0.0379 0.0032 11.6866 0.5889

All available data 132 0.0418 0.0041 10.2176 0.7134

I have not reported the intercept of the regression equation for easier interpretation. The standard errors of the regression slope coefficients (OMAD) are corrected for serial correlation and heterogenous variances among the residuals using the Newey-West algorithm. See Carter Hill, William Griffiths and Guay Lim, *Principles of Econometrics* (4^{th} edition), John Wiley & Sons, 2011, p. 357 (Newey-West standard errors).

The most stable OMAD (highest *t*-Statistics, which is the ratio of the slope coefficient divided by its standard error) is obtained with seven years of individual data points, totaling 28 observations. Multi-year analysis of sizable data samples is vital to estimate reliable profit indicators. This illustration shows that *always using quartiles of three-year grouped data* is contrived, rudimentary data analysis, because reliable profit indicators can be ascertained with confidence by considering regression analysis and applying more than three years of company-level annual data.

The most reliable method to estimate OMAD is using indirect least squares (ILS) (see reference link at end of this paragraph). Quartiles of the ratio OIADP/Net Sales = OMAD (aka OPM) is the mode (most frequent) profit indicator in transfer pricing. However, the statistical relationship between OIADP and Net Sales lacks theoretical consistency, and should be replaced by the operating profit markup relationship between Net Sales and Total Cost. See https://blog.royaltystat.com/transfer-pricing-methods-based-on-operating-profits

**Ednaldo Silva**(Ph.D.) is founder and managing director of RoyaltyStat. He helped draft the US transfer pricing regulations and developed the comparable profits method called TNNM by the OECD. He can be contacted at: esilva@royaltystat.com

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