RoyaltyStat Blog

“We shall renounce . . . the subterfuges.”

We suggested on prior blogs that operating assets (measured by property, plant & equipment) are endogenous and that structural equation estimates of return on assets produce biased coefficients. Here, we provide another alternative from biased estimates of return on assets than using exotic algorithms like two-stage least squares.

Economic models must have mathematical beauty; they must be parsimonious!

Paraphrasing Paul Dirac (1955), Physical laws should have mathematical beauty, quoted in Abraham País, Maurice Jacob, David Olive, Michael Atiyah, Paul Dirac (The Man and his Work), Cambridge University Press, 1998, p. 46.

Después de tanto soportar la pena de sentir tu olvido … y si pretendes remover las ruinas que tú mismo hiciste

Cenizas in the poignant voice of Toña La Negra. Classic bolero lyrics by Wello Rivas (1913-1990).

In applying the comparable profits method (CPM) in the U.S. or the “transactional” net margin method (TNMM) in other OECD countries, many transfer pricing analysts assume that the depreciation rate of property, plant, and equipment is the same among the individual comparables and the tested party.

L’un fece il mundo e l’altro l’ha distrutto.

The “return on assets” is an unsatisfactory profit level indicator (PLI) for the “transactional” net margin and comparable profits methods in transfer pricing because (among other major defects) self-developed intangibles are excluded from the assets base denominator. Assets are also composed of heterogeneous balance sheet accounts with different depreciation rates.

Operating assets are “solid, massy, hard” and cannot be moved from one company to another within the same industry (horizontal market consolidation) or across companies in different industries (vertical market consolidation), without a time-consuming assets purchase agreement. Moreover, if the intra-company assets transfers are large, anti-trust regulatory impediments may occur.

The idea that “return on assets” is a superior PLI because of its fluent or gravitation properties is not consistent with reality. This dubious return on assets sobriquet is posited as a matter of faith because to our knowledge economics is devoid of rigorous demonstrations of the conditions required for such gravitation to occur in actual industries dominated by oligopoly groups.

Like other expressions, economic categories reflect reality, and the term royalty isn't an exception.

Michiel de Vaa’s Etymological Dictionary of Latin and the Other Italic Languages (Brill, 2008) has no entry for royalty or its lemma. See his near-neighbor entry (Vaa, pp. 517-518): rego ("to direct, guide, govern"), but the listed cognates don't refer to payments or other economics allusions.

The Oxford English Dictionary, an erudite arbiter of the English language, includes several meanings for royalty (noun (plural royalties)), and attributes its origin from Old French roialté, from roial (regal): 

“The sense ‘royal right (especially over minerals)’ (late 15th century) developed into the sense ‘payment made by a mineral producer to the site owner’ (mid-19th century), which was then transferred to payments for the use of patents, trademarks, and copyrighted materials.”

See the Oxford English Dictionary. Cite: “royalty, n.”

We take another look that computing profit indicators using restricted data samples can lead to unreliable measures of arm’s length taxable income to benchmark controlled inter-group transactions. To produce reliable measures, we must change the pervasive transfer pricing practice of considering three-years of data, and consider as many individual company financial data as available.

Consider two aspects of statistical reliability principles. First, reliability can be measured by the ratio of the selected parameter estimate divided by its standard error.  We want this reliability ratio to be as high as possible. Second, reliability depends on sample size such that larger samples produce more reliable estimates.

Transfer pricing rules recognize that statistical estimates of the selected profit indicator must consider multiple-year analysis to achieve a reliable measure of arm’s length taxable income. See OECD (2017), ¶¶ 3.75-3.79 and US Treas. Reg. § 1.482-1(f)(2)(iii).