RoyaltyStat Blog

Using a distributed lag model to determine arm’s length profits in transfer pricing

Posted by Ednaldo Silva

Most empirical research in transfer pricing lack valid economic principles, relying instead on ad hoc specification. This faulty practice is somewhat permitted by misconceived transfer pricing regulations based on the OECD model.

Following the issuance of US transfer pricing regulations on the comparable profits method (which we were a major developer), the OECD ordained a special profit model under the transactional net margin method (TNMM) in which “net [operating] profits” (hereafter profits) are only proportional to revenue. Today, the quartiles of simple profit margins derived from accepted comparable companies is the dominant profit indicator used by tax administrators and controlled taxpayers under the TNMM.

Under certain facts, however, the OECD special profit model, though simple, is not the most reliable method for determining arm’s length profits to benchmark transactions between related parties. In many circumstances, a distributed lag (or another specified regression) model can produce better or more reliable results.

We suggest that selected comparable company data, and not a simple OECD formula, can provide a defensible (or scientifically acceptable) basis to determine the most reliable arm’s length profits. RoyaltyStat®’s premier databases of royalty rates and company financials are programmed to provide online such defensible results by allowing the subscriber or client to select the best fit among various statistical (including regression) models.

Contemporaneous profits, sales

In what follows, we abstract from the random disturbance and consider the causal part of the OECD special profit model.

Let P = Profits and S = Sales of a selected enterprise which is comparable to the tested party regarding the functions performed, assets employed, and risks assumed with respect to identified controlled transactions, such as manufacturing, distribution, or retail of inventory goods.

The OECD prescribed model can be posited as a simple linear regression:

     (1)  P(t) = β S(t),

where the audit year profits are proportional to only the same year sales, considering the audit and two or more prior years of data.

The OECD prescription forces a zero intercept (α = 0) à priori, which is misconceived because the actual intercept may be nonzero and thus the determination of arm’s length profits can be distorted using model (1) because of a missing intercept alone.

Prior years’ revenue/sales

In fact, audit year profits may depend on the corresponding yearand previous year revenues. Thus, a more general formula than (1) can allow for the audit and past year revenues to affect target profits.

In symbols, a series of previous year revenues, combined with the audit year revenue, may generate uncontrolled profits to provide more reliable taxable income benchmarks for a controlled tested party under transfer pricing compliance obligations:

     (2)  P(t) = α + β S(t) + β1 R(t – 1) + β2 S(t – 2) + β3 S(t – 3) + …

Two key differences separate model (2) from (1). First, we let the data determine the intercept value. Second, we recognize that a series of prior year revenues, instead of a single year revenue, may determine audit year profits. Hence, model (2) is more general than (1).

Regression estimation of the parameters (α, β, β1, β2, etc.) in (2) is awkward, but from experience we know that these partial coefficients decline exponentially, which means that distant beta coefficients exert less weight than more recent coefficients on the dependent variable, P(t). Thus, we can assume:

     (3)  βk = β λk,

where 0 < λ < 1, the index k = 1, 2, 3, …, and obtain β1 = β λ, β2 = β λ2, β3 = β λ3, etc.

Distributed lag model for transfer pricing

Eq. (3) is called a Koyck transformation, which is a well-known distributed lag model of consumption and investment, including of activities generating intangibles such as advertising and research and development. See L. Koyck, Distributed Lags and Investment Analysis, North-Holland, 1954, pp. 11, 16, 18, 20, 22, 39.

This Koyck device (3) is used to transform an infinite geometric lag model (2) into a finite model with a lagged dependent variable (see model (4)).

While this makes for parsimonious parameter estimation, the transformed model is likely to have serial correlation among the regression residuals; thus, OLS (ordinary least squares) estimates may not be adequate. Instead of OLS, we can apply Cochrane-Orcutt or Prais-Winsten estimation. Many flowers may bloom, and certain economists like to apply more complex and subjective instrumental variables (IV) estimates. See Jan Kmenta, Elements of Econometrics (2nd edition), Macmillan, 1986, Chapter 11-4 (Distributed lag models).

Using (3), model (2) becomes:

      (4)  P(t) = µ + λ P(t − 1) + β S(t),

where µ = α (1 – λ) is the transformed intercept.

Reliable data to find comparables

Model (4) provides more information than the OECD special model (1). First, the intercept of (4) is not forced to zero. Second, model (4) is dynamic, measured by the lagged dependent variable, and we can test the stability of P(t) over the selected period. Third, the profit margin is not a simple ratio of profits to revenue because, if we divide (4) by R(t), we obtain:

     (5)  M(t) = P(t) / S(t ) = β + µ / S(t ) + λ [P(t − 1) / S(t )],

including an interesting testable hypothesis that the profit margin, M(t), is inversely proportional to S(t ), company size measured by sales revenue, and directly proportional to the profit margin of the previous year.

In addition to be the premier database of royalty rates extracted from license agreements, including over 20,100 (live count) license agreements with disclosed royalty rates, RoyaltyStat contains another premier database with over 36,000 listed company financials. This company financials database has been programmed with the Cochrane-Orcutt and Prais-Winsten algorithms for interactive or online estimation of the parameters of distributed lag model (4).

Again, see Kmenta, pp. 313-317 (Cochrane-Orcutt estimation) and pp. 318-320 (Prais-Winsten estimation).

More reliable models

Like Lévi-Strauss in Tristes Tropiques (1955), we consider it harmful for granfino regulators to overreach beyond their competence to force a special profit model à priori, thereby creating a nursery school of rote transfer pricing analysis in which controlled taxable income is assessed as if science (economics and statistics knowledge) doesn’t have a place in tax compliance.

Simple prescription and arbitrary procedures are unlikely to produce reliable arm’s length results, and the analyst must have the competence and discretion to make such determination, subject to a Daubert challenge. Under certain circumstances, quartiles of simple profit margins calculated from selected comparables are unlikely to pass any significance test of reliability. Economics and statistics competence require more expertise than blind knowledge of quartiles, and routine (though arbitrary) asset-based adjustments to the reported profits of the accepted comparables.

Using an acceptable principle of model reliability, which is also embedded in the OECD transfer pricing guidelines, and in its progenitor US transfer pricing regulations (for which we assume major responsibility), is an important escape from unreliable controlled taxable income assessment.

The distributed lag model (4) presented here is an important step to confront routine “best practices” (an oxymoron) with accepted scientific procedures in which model selection is determined by knowledge-based falsifiable propositions instead of being predetermined by regulatory grace.

Forcing model (1), like the OECD and US transfer pricing rules prescribe, without appeal to empirical significance testing, is more likely to produce distorted measures of arm’s length profits. Again, we appeal to knowledge-based data analysis against the prevailing mechanical application of misconceived or simplistic transfer pricing rules. Analysis of the selected comparable company data dictates the best fit model to be adopted, including model (1), (4), or a more reliable regression model specification.

Published on Feb 11, 2018 6:24:46 PM

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:

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Topics: Net Profit Indicator