1. The Planning Structure A common transfer pricing plan assigns a fixed role to each member of a multinational group. A contract manufacturer, a limited risk distributor, or a retailer is labeled a “routine” entity and is promised a low…
1. The issue: a ratio is a restricted model Financial ratios are the lingua franca of transfer pricing and credit analysis. Profit indicators such as and coverage indicators such as , leverage covenants expressed as net debt/EBITDA, and distress scores…
1. The IQR does not shrink with sample size (n) For a normal population (Abramowitz and Stegun 1964, ch. 26; Hoaglin, Mosteller and Tukey 1983), and . Therefore: The half-width is the classical “probable error” (der wahrscheinliche Fehler), which the…
1. The dispute A recurring objection from some practitioners holds that a corporate transfer pricing audit must proceed transaction-by-transaction: one adjustment for tangible goods, another for royalties, a third for services, each priced on its own. The objection sounds rigorous,…
In U.S. Corporate Profits, 1950–2024 (Springer, 2026), I estimated the operating profit markup of 71 leading U.S. corporations with a bivariate regression, . The slope is the markup on operating costs, and the operating margin follows from it by indirect…
1. The question you will be asked A reviewer can ask why we run a regression when every other consulting firm reports the median and the interquartile range of a profit level indicator (PLI). The PLI (or ratio statistics) answers…
1. The IRS set carries everything The Commissioner’s expert tested six concentrate manufacturers, the Supply Points (tested parties), in Brazil, Chile, Costa Rica, Ireland, Mexico and Swaziland. A seventh, in Egypt, was adjusted in the taxpayer’s favor and drops out…
1. Two objects, one name A reader noted that ratio is among the oldest constructions in mathematics, and takes my article to argue that ratios are invalid or biased. My article makes no such claim. My issue focus on the…
Abstract Let for and let denote the ratio indicator. We show that the arithmetic mean of overstates the slope by exactly , where is the harmonic mean of ; that the -th quantile of overstates by exactly , where is…
Thin capitalization rules ask a single question in two different ways. The older way looks at the balance sheet and asks whether the borrower carries more debt than its equity supports. The newer way looks at the income statement and…
For applied transfer-pricing work, I prefer the conventional econometric formulation because every step is visible, reproducible, and open to challenge. Regulatory support for using regression analysis is found in Section 1.482-1(e)(2)(iii)(B), which says that reliability may be increased through application…
Introduction A prior post on this blog recommended HC3 standard errors for the reduced-form markup equation estimated on transfer pricing benchmark sets. It stated the estimator and left two questions unanswered, both of the kind that surface under examination rather…
Introduction Another post traced the ownership of transfer pricing data from Disclosure, Inc. in Bethesda through Primark and Thomson to Ryan in Dallas. That was a history of corporations. This one is a history of a practice, and it is…
A transfer pricing comparables set is small. Thirty independent companies is a generous count; eight to fifteen comparables are common. Each contributes three fiscal years, so the pooled regression runs on fewer than 45 annual observations and often on fewer…
Ordinary least squares (OLS) produce two things: an estimate of the intercept and slope coefficients, and an estimate of their uncertainties. The coefficient estimates are sound, based on matrix algebra inversion. The standard errors rest on an assumption that is…
1. Reliable PLI The interquartile range is not an estimator. A benchmark set of n comparables produces a distribution of ratios : operating margin, markup, return on assets. If the underlying relation is , then and the ratio carries a…
1. The Apparent Contradiction Two positions I have defended appear, at first sight, to pull in opposite directions. First: corporate profits and asset bases are understated because research and development (XRD), advertising (XAD), and software development outlays are expensed as…
1. The System in Three Equations Start from the GDP expenditure identity, collect autonomous expenditure as and decompose it into its mean and its fluctuation, . Close the identity with two behavioral equations, both linear in lagged income: consumption with…
1. The Complaint A commentator objected that stating unit price is proportional — or log-proportional — to unit labor cost (ULC) confuses correlation with causation. The objection deserves a serious answer, because the aphorism it invokes is usually deployed as…
1. The Apparent Contradiction Two positions I have defended appear, at first sight, to pull in opposite directions. First: corporate profits and asset bases are understated because research and development (XRD), advertising (XAD), and software development outlays are expensed as…
1. Two Ratios, One Regime Change Plot two ratios from FRED over 1950-2025. The first is private nonresidential equipment investment as a share of GDP: it has oscillated within a narrow band, roughly 5 to 7 percent, for four decades,…
Discussions of crude oil’s forward curve start the same way — plot , call it contango or backwardation. Contango is , and backwardation is the reverse . This ratio construction is a mistake, and it is the same PLI (profit…
Purpose This note derives the combined profit split method when each member of a controlled group has its own profit-per-payroll coefficient. The purpose is to show that variable entity-level coefficients do not defeat a simple payroll-based profit split. They collapse…
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…
1. Introduction In transfer-pricing analysis and corporate-profit studies, the objective of regression analysis is estimating a meaningful slope coefficient rather than predicting the dependent variable. This distinction has implications for how rival operating profit specifications are selected and evaluated. A…
A controlled party’s reported operating profit is the residual of the intercompany prices under audit examination. Where transfer prices have been set to move income across borders, the reported operating profits are distorted. I’ve developed an internal benchmark for each…
Two regressions are implicit in transfer pricing benchmarking: the linear regression of operating profits on revenue, and the double-log regression of the same two variables. Each produces a slope coefficient. The two coefficients have different meanings, different units, and answer…
The contrived linear function , with the zero intercept specified in the U.S. and OECD transfer pricing guidelines, is a special case of a much more general structural form: the power function, Two questions arise the moment one fits (1)…
The term prewhitening sounds arcane and likely worse. The word belongs to a long-standing optical metaphor in spectral analysis that predates its econometric usage. This note sets out the etymology, the formal statistical content, and the specific procedure introduced by…
1. The Geometric Distributed-Lag Model Like research and development, advertising is a risk-taking investment. The economic rationale is straightforward: a campaign launched in period t builds brand awareness and consumer loyalty that generate revenue and operating profit in the current…
1. Introduction Transfer pricing analysis for intangible-intensive corporations requires structural econometric models, not ratio-based profit level indicators (PLIs). The standard operating margin and the Berry ratio are quotients of accounting aggregates. When the underlying structural relationship has a nonzero intercept…
Compared with the Additive and Multiplicative Rivals
The Harmonic Mean Bias in Ratio-Based Profit Level Indicators
Why Induced Heteroscedasticity Compounds the Intercept Bias
This article shows that ratio-based profit level indicators (PLIs)—including return on assets (ROA), Berry ratio, and operating margin—are biased estimators of the structural profit rate when the underlying relationship between...
Abstract The perpetual inventory method (PIM) for estimating capital stock (PPENT) is attributed to Raymond Goldsmith (1951). Goldsmith provided conceptual descriptions without explicit algebraic derivations—a ceremonial citation. However, the extended PIM formula with geometrically declining weights is the standard solution…
1. Introduction Transfer pricing practice relies on ratio analysis. Operating profit divided by revenue, operating profit divided by total cost, operating profit divided by operating assets—these profit level indicators (PLIs) are ratios of the form m(i) = Y(i) / X(i).…
A complete statistical procedure for transfer pricing practitioners. Transfer pricing practice usually determines the arm’s length range using the interquartile range of the chosen profit indicator, defined as a ratio m(i) = Y(i)/X(i) across comparable companies.
Return on Assets and the Harmonic Mean
On May 23, 2017, the OECD released a draft of Action 8 of the Base Erosion and Profit Shifting (BEPS) plan, providing taxpayers and tax administrations with a new transfer pricing approach to measure hard-to-value-intangibles (HTVI):
From Equation Counting to Class Conflict: A Mathematical Reading of Political Economy
Analysts often work with ratios. Whether examining price-to-earnings ratios in finance or profit indicators in transfer pricing, the ratio m(i) = Y(i) / X(i) is often reported. However, this simple ratio masks a systematic bias that affects quartile estimates and other location parameters.
Controlling producer price inflation (PPI) doesn’t require austerity.
Using a less reliable (higher variance) adjusted profit indicator violates the scientific principle of minimizing measurement error. Avoiding error propagation is essential for producing credible and reproducible estimates.
The profit rate identity can be estimated as a dynamic framework using an autoregressive distributed lag (ARDL) model.
Some basic rules of differential calculus are useful for understanding economic discourse, such as discussions in business or financial media about U.S. economic performance.
This blog presents a basic analytical framework for understanding the relationship between GDP growth and public debt commitments. The Harrod-Domar principle, which posits that increased gross private domestic fixed non-residential investment drives GDP growth, does not apply to the recent GDP growth of many countries.
Microeconomics are detached from the reality of corporate profits behavior. Here, I explore the operating profits (before depreciation and amortization) of a major group of U.S. corporations (consolidated entities) that make up a large fraction of U.S. gross domestic product.
The operating profit margin (OMBD or OMAD) can be derived from the profit markup by indirect least squares (ILS). This is the most theoretically defensible and reliable operating profit indicator that can be obtained from comparable data.
U.S. 26 CFR 1.482-5(b)(4)(i-ii) claim that the “return on capital employed” (return on assets) is less sensitive to “functional differences” than the operating profit margin or the operating profit markup. This claim is based on the unrealistic premise that “capital flows” to equalize profit rates (return on assets) among companies in the same (or in different) industries by some "invisible hand."
Data suggest that “big oil” forms an oligopoly industry. Noise about oil and gas prices being determined by supply and demand is suspect.
Quartiles are the most elementary form of univariate (single variable) data summary, because no statistical technique beyond sorting and slicing (tagging) of the data is employed. Distributions of profit indicators have long tails, suggesting that the Median is a good measure for only 50% of the dataset.
Determining an arm’s length profit indicator (profit ratio) requires two equations, and not one equation, as prescribed in financial statement analysis textbooks. E.g., Bernstein (1993), Drake & Fabozzi (2012). An accounting critique of univariate profit ratios is found in Whittington (1986).
EdgarStat® contains an internal regression model to calculate the beta-risk coefficient of an individual enterprise stock price return compared to the return of the S&P 500 stock price (market) index. This stock price return regression model is known as CAPM.
Regression analysis yields more reliable profit indicators than the linear equation without intercept specified in US and OECD transfer pricing guidelines.
Dr. Ednaldo Silva illustrates why asset intensity adjustments to the Return on Assets profit indicator are redundant and unviable.
Notwithstanding its acceptance in Coca Cola Co. v. Commissioner of the IRS, Return on Assets is a controversial profit indicator to use in transfer pricing. At the very least it must be subject to economic analysis to corroborate a relationship between operating profit and operating assets.
Ad hoc adjustments are a risky endeavor in transfer pricing. Using regression analysis, we can test if asset intensity is relevant to explain the behavior of the operating profit markup or profit margin and calculate a reliable adjustment to the profit indicator.
The prevalent use of quartiles to determine profit indicators often results in a wide (unreliable range) and ad hoc assets adjustments. These problems can be solved by using regression analysis, which produces more defensible statistical ranges of the profit indicator resistant to audit scrutiny.