1. Introduction
The combined profit split method requires an allocation key, and the choice of key determines the reliability of the entire exercise. We propose relative payroll as the allocation key for splitting the combined operating profits of controlled enterprises within a multinational group. The method rests on a single economic assumption, made explicit below, and the resulting allocation formula follows in a single line of algebra. The exposition addresses a small number of controlled entities; each located in a separate tax jurisdiction.
2. Assumptions
Three assumptions, stated explicitly:
(I) Proportionality. Each controlled entity’s operating profit is proportional to its payroll, with a common factor of proportionality across entities:
(1)\quad P(j) = \beta\,W(j), \qquad j = 1,\dots,n
where P(j) denotes the operating profit of controlled entity j, W(j) denotes its payroll expense, \beta (beta) is the common profit-to-payroll coefficient, and n is a small number of controlled entities, such as 2, 3, or 4. Equation (1) is the firm-level analog of Weintraub’s (1959) aggregate relation R=kW, in which business receipts are proportional to payroll with a stable coefficient. The economic content is that payroll reflects the functions performed: employees perform the functions, deploy the assets, and manage the risks that the functional analysis under Treas. Reg. §1.482-1(d)(3) and Chapter I of the OECD Guidelines enumerate.
(II) Additivity. The combined operating profit of the group is the sum of controlled entity profits, and the combined payroll is the sum of entity payrolls:
(2)\quad P = \sum_{j=1}^{n} P(j),
\qquad
W = \sum_{j=1}^{n} W(j)(III) Measurability. Payroll is recorded at current market prices (wages and salaries) in each entity’s books. Unlike fixed assets (Compustat mnemonic PPENT), payroll is not subject to vintage mixing, divergent depreciation conventions, or impairment policies that undermine cross-entity comparability of asset-based allocation keys.
3. Derivation
Summing equation (1) over the n entities and applying (2):
(3)\quad P
=
\sum_{j=1}^{n} \beta W(j)
=
\beta \sum_{j=1}^{n} W(j)
=
\beta WSo the common coefficient is identified from group totals:
(4)\quad \beta = \frac{P}{W}Substituting (4) back into (1) yields the adjusted (allocated) operating profit of entity j:
(5) \quad \hat{P}(j)
=
\beta W(j)
=
\left(\frac{W(j)}{W}\right)P
=
s(j)\,Pwhere s(j) =\frac {W(j)}{W} is entity j’s payroll share. Each controlled entity receives the share of the combined operating profit equal to its share of the combined payroll. Since the shares sum to one, \sum s(j) = 1, the allocation is exhaustive by construction:
(6) \quad \sum_{j=1}^{n} \hat{P}(j) = PNo residual remains, and no plug is required. The parameter \beta cancels out of the allocation formula (5); only the observable payroll shares s(j) matter. The method, therefore, requires no estimation to implement, only an objective and verifiable entity-level payroll, and the combined operating profit to be split.
4. The Testable Restriction
The proportional form (1) is the affine relation P(j) = \alpha + \beta\, W(j) with the restriction \alpha = 0. With a panel of comparable companies, this restriction can be tested directly from the intercept estimate: the closure \alpha = 0 is retained when zero lies within the 68% confidence interval \hat{\alpha} \pm \mathrm{SE}(\hat{\alpha}). The proportionality assumption underlying the payroll split is thus not an article of faith but an empirical proposition subject to the reliability discipline of Treas. Reg. §1.482-1(c).
5. Regulatory Support
The OECD Transfer Pricing Guidelines (2022) recognize employee compensation as an acceptable profit-splitting factor. Paragraph 2.172 states that profit-splitting factors appropriate in the circumstances of a given case include employee compensation for individuals involved in the key functions that generate value in the transaction, and that headcount or time spent by a group of similarly skilled employees may be used where there is a strong and relatively consistent correlation with the creation of value represented by the relevant profits. Paragraph 2.181 adds that employee remuneration may be relevant in situations where functions related to staff skills and experience are the primary factor in generating the relevant profits. Paragraph 2.166 requires that splitting factors be based on objective data, be verifiable, and be independent of transfer pricing policy formulation — conditions that entity payroll, recorded at current transaction prices in statutory accounts, satisfies directly. Paragraphs 2.176–2.177 endorse internal data, including employee costs extracted from the taxpayer’s cost accounting, for the construction of cost-based splitting factors.
Under U.S. regulations, the profit split method of Treas. Reg. §1.482-6 requires that relative contributions be measured in a manner that reliably reflects the functions performed, assets employed, and risks assumed; the best method rule of §1.482-1(c) provides the criterion for
arguing payroll’s measurement advantages over asset-based keys. A century of U.S. subnational practice with formulary apportionment (the three-factor Massachusetts formula of property, payroll, and sales) attests that payroll is a canonical, administrable factor for dividing the income of a unitary business.
6. Why Payroll Rather Than Assets
Paragraph 2.171 of the OECD Guidelines permits asset-based splitting factors when they capture relative contributions and can be measured reliably. The reliability condition is where asset keys fail. Book values of property, plant, and equipment mix acquisition vintages; depreciation schedules and impairment policies differ across jurisdictions; and self-developed intangibles are absent from the balance sheet altogether — a concern that paragraph 2.104 of the Guidelines explicitly acknowledges for book-value comparisons. The OECD’s suggested remedy, market valuation of assets, is costly, uncertain, and itself a source of dispute. Payroll requires none of this repair: it is a current-period flow, measured at transaction prices, consistently defined across entities, and audited in every jurisdiction.
References
Gollin, D. (2002), “Getting Income Shares Right,” Journal of Political Economy, 110(2), 458–474. — Measurement of labor’s share across countries; relevant when controlled entities span jurisdictions with different self-employment and compensation structures.
Kaldor, N. (1961), “Capital Accumulation and Economic Growth,” in F. Lutz and D. Hague (eds.), The Theory of Capital, Macmillan, London. — The stylized fact of wage-share stability, supporting a stable profit-to-payroll coefficient δ across comparable entities.
McLure, C. (1980), “The State Corporate Income Tax: Lambs in Wolves’ Clothing,” in H. Aaron and M. Boskin (eds.), The Economics of Taxation, Brookings Institution, Washington, D.C. — Analysis of the three-factor (property, payroll, sales) formula — a century of U.S. subnational practice using payroll as an allocation key.
Musgrave, P. (1972), “International Tax Base Division and the Multinational Corporation,” Public Finance, 27(4), 394–413. — Classic statement of factor-based division of multinational profits; payroll is among the canonical apportionment factors.
OECD (2022), Transfer Pricing Guidelines for Multinational Enterprises and Tax Administrations, OECD Publishing, Paris. Chapter II, Part III, Section C.5, ¶¶2.166–2.183; in particular ¶2.172 and ¶2.181 on employee compensation as a profit splitting factor, and ¶¶2.176–2.177 on internal cost-accounting data. — Recognizes employee compensation and remuneration among acceptable profit splitting factors where staff functions are the primary generator of the relevant profits.
Treas. Reg. §1.482-6; §1.482-1(c). — The U.S. profit split method and the best method (reliability) rule under which the choice of allocation key must be defended.
Weintraub, S. (1959), A General Theory of the Price Level, Output, Income Distribution, and Economic Growth, Chilton, Philadelphia. — Source of Z = kW: aggregate business proceeds proportional to the wage bill with a stable coefficient k — the macroeconomic foundation of the payroll split