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Applying Regression Analysis to the CUP Method

Posted by Ednaldo Silva

The comparable uncontrolled price (CUP) method is described in the United States Title 26 (Internal Revenue), Treas. Reg. §1.482-3(b). A few transfer pricing analysts claim the existence of CUP transactions to determine taxable income in connection with the transfer of tangible property; however, determining the existence of CUP transactions requires empirical verification that is best measured by regression analysis.

CUP Rules Aren’t Will-o’-the-Wisp (Ignis fatuss)

The CUP method is used to evaluate if the amount charged in a controlled transaction involving the transfer of tangible property is arm’s length by reference to the amount charged in a comparable uncontrolled transaction. This can be tested using the law of one-price regression:

     (1)     Y(i, t) = β X(i, t) + V(i, t)

     (2)     V(i, t) ≈ Normal(0, σ2)

Equation (1) must be subject to a reliable statistical test that the estimated slope coefficient β ≈ 1.0 (assuming that the intercept ≈ 0). In addition, the random error V(i, t) must be examined to determine if they are well-behaved. The usual assumptions are that the residual errors are indepedent of the other (no serial correlation); they have zero mean and constant variance (σ2), and they follow a normal distribution. See Draper & Smith (1981), Chapter 3 (Examination of Residuals). 

The variables Y(i, t) and X(i, t) denote the controlled and uncontrolled unit prices of the tangible property transferred between affiliates, and V(i, t) denotes the random error with mean zero and constant variance. The double subscripts i = 1 to N denotes the product number measured by SKU; and t = 1 to T denotes the time (e.g., day) of the paired or matching controlled and uncontrolled transactions.

Ex post knowledge if the results derived from the application of the CUP method are the most reliable measure of the arm’s length unit prices must be determined using the factors described under the best method rule of Treas. Reg. §1.482-1(c). The application of these factors under the CUP method is discussed in Treas. Reg. §1.482-3(b)(2)(ii) and (iii), as follows:

Treas. Reg. §1.482-3(b)(2)(ii) (Comparability) has two sub-sections (which we paraphrase in extenso).

     (A) The comparability between controlled and uncontrolled transactions is determined by applying the provisions of §1.482-1(d). Although all the factors described in §1.482-1(d)(3) must be considered, similarity of products will have the greatest effect on comparability under the CUP method.

In addition, comparability under the CUP method depends on close similarity respecting contractual terms or economic conditions, or adjustments to account for any differences.

The results derived from applying the CUP method can be the most direct and reliable measure of an arm’s length price for the controlled transaction if an uncontrolled transaction has no differences with the controlled transaction that would affect the price, or if there are only minor differences that have a definite and reasonably ascertainable effect on price and for which appropriate adjustments are made.

If such adjustments cannot be made, or if there are more than minor differences between the controlled and uncontrolled transactions, the CUP method may be used, but the reliability of the results as a measure of the arm’s length price will be reduced. Further, if there are material product differences for which reliable adjustments cannot be made, the CUP method cannot provide a reliable measure of an arm’s length result.

     (B) Adjustments for differences between controlled and uncontrolled transactions. If there are differences between the controlled and uncontrolled transactions that would affect price, adjustments must be made to the price of the uncontrolled transaction according to the comparability provisions of §1.482-1(d)(2). Specific examples of the adjustment factors that may be relevant to the CUP method include the (1) Quality of the product; (2) Contractual terms (e.g., scope and terms of warranties provided, sales or purchase volume, credit terms, transport terms); (3) Level of the market (i.e., wholesale, retail, etc.); (4) Geographic market in which the transaction takes place; (5) Date of the transaction; (6) Intangible property associated with the sale; (7) Foreign currency risks; and (8) Alternatives realistically available to the buyer and seller.

In addition, Treas. Reg. §1.482-3(b)(2)(iii) (Data and assumptions) imposes conditions about data quality. The reliability of the results derived from the CUP method is affected by the completeness and accuracy of the data used and the reliability of the assumptions made to apply the method. See §1.482-1(c) (Best method rule).

Special CUP Rule for Quoted Prices

The CUP method includes a special rule under Treas. Reg. §1.482-2(b)(5) (Indirect evidence of comparable uncontrolled transactions), which contains two conditional sub-sections:

     (i)  A CUP may be derived from data from public exchanges or quotation media, but only if the following requirements are met:

     (A) The data is widely and routinely used in the ordinary course of business in the industry to negotiate prices for uncontrolled sales;

     (B) The data derived from public exchanges or quotation media is used to set prices in the controlled transaction in the same way it is used by uncontrolled taxpayers in the industry; and

     (C) The amount charged in the controlled transaction is adjusted to reflect differences in product quality and quantity, contractual terms, transportation costs, market conditions, risks borne, and other factors that affect the price that would be agreed to by uncontrolled taxpayers.

     (ii) Limitation. Use of data from public exchanges or quotation media may not be appropriate under extraordinary market conditions.

Gather Stores of Knowledge

Like Cavafy's Ithaca, the existence of CUP transactions is not an elusive goal. This means that we must prove the existence of claimed CUP transactions establishing the law of one-price by using regression analysis to compare transactions between affiliates and matching transactions with uncontrolled parties. Without the rigor offered by regression analysis, we may not reach CUP island.


Norman Draper & Harry Smith, Applied Regression Analysis (2nd edition), John Wiley & Sons, 1981.

Ednaldo Silva, “Applying Regression Analysis to the Cup Method,” Tax Management Transfer Pricing Report, Vol. 10, No. 15, November 28, 2001. This article uses unidentifiable data from an actual transfer pricing case docketed in the US Tax Court (but settled in pretrial negotiations) in which we served as expert witness and utilized the CUP method to demonstrate that the IRS audit claim was unwarranted.

Download the article.

Treas. Reg. §1.482-3 (Methods to determine taxable income in connection with a transfer of tangible property):

Published on Oct 7, 2019 11:42:15 AM

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: CUP Method