OECD Covid-19 TP Guidance: Considering Econometrics-Based Approaches for Estimating CPM/TNMM Adjustments—Part 2 of 2

March 26, 2021, 7:00 AM

This part of the article continues the exposition of how econometrics-based approaches can be used to perform a “comparability adjustment” to the benchmark range of profitability results derived from independent companies under an application of the CPM/TNMM. As discussed in the OECD Guidance, for a year in which a taxpayer is subject to an industry-wide or economy-wide adverse economic shock (e.g., as has been caused by the pandemic for several businesses), a “standard” application of the CPM/TNMM to benchmark the profitability level for a ‘“routine” entity (e.g., distributor or manufacturer) may misstate the appropriate level of profitability.

The first part of the article outlined the challenge presented by “atypical” economic conditions in relation to a CPM/TNMM analysis and provided an overview of econometric approaches that can help address these challenges by estimating “comparability adjustments” and classified these approaches into two categories. The first part concluded with a discussion of the approach falling into the first of the two categories of approaches—i.e., ‘OL-based approaches.’ In this second part, we discuss the second category—i.e., IO-based approaches—in more detail and illustrate the application of both approaches using actual data on independent routine distributors.


In general, the approaches within this category effectively involve the following general estimation equation (where t denotes year and i denotes a specific firm/company) using panel data on the relevant comparables:

Equation 2

PLIit = αi + βASit + γ1Xit + γ2Xit-j + εit

In the estimation equation above, the PLI of interest (e.g., OM) is the dependent variable and the “adverse shock” variable (ASit) is the independent variable of interest. The “adverse shock” variable is intended to identify a year in relation to company i when the company is viewed as being subject to economic conditions comparable—ideally, in terms of the nature as well as severity of those conditions—to those affecting the tested party in the shock year(s).

Equation 2 presents a “fixed effects” (FE) specification for the estimation equation. As an alternative, a random effects specification may be tried and compared with the FE specification. If the specification includes lagged values of the PLI as an independent variable, dynamic panel data models may be considered.

The ASit variable is an indicator variable that takes on the value 1 in years identified as representing a comparable “adverse shock” for company i and 0 otherwise. The (vector of) contemporaneous and/or lagged independent variables Xit and Xit-1 are control variables. These are variables that are viewed as potentially influencing the PLI independently (with the selection of such variables in the estimation equation being informed by transfer pricing practice and the relevant empirical literature).

The coefficient estimate for β is the key output of interest from this exercise. The estimate measures how the comparables’ PLI in “adverse shock” years differed from their average PLI levels. For instance, if the average PLI (e.g., OM) for the comparables in the sample over the time period covered in the panel data was 5% , a (statistically significant) coefficient estimate of negative 2% for β would imply that the comparables’ PLI was (on average) 40% (i.e., 2% divided by 5%) lower during “adverse shock” year(s) relative to their average (i.e., “normal”) levels.

Note again that this relationship is estimated and applicable for the sample over the historical period covered by the panel data used. This estimated sample-wide historical relationship then can be used to make an adjustment (e.g., negative 40% in the example) to the applicable unadjusted benchmark range derived from the comparables. This is where the unadjusted range would be the applicable arm’s-length range but for the effect of the present economic conditions on the tested party.

The reliability of the above application is inherently dependent on how the variable ASit in Equation 2 is defined and specified. Ideally, ASit would be specified in a way that would identify instances when the comparables experienced circumstances that were similar in both type and severity to the shock year(s) impacting the tested party. We discuss different variants of the general estimation equation in Equation 1 that differ in the specification of the variable ASit below.

Economy or Industry-based Measures Used to Infer Adverse Economic Conditions

Under this variant of Equation 2, ASit is based on an economy-wide or industry-wide measure such that the presence of adverse economic conditions can be inferred from such a measure. For instance, a dummy variable “Rec2009” is a version of the ASit variable in Equation 1 that is 1 for all companies during the year 2009 and zero otherwise (i.e., in years considered “normal”). This is under the premise that all companies in the sample experienced adverse economic conditions in 2009 as a result of the 2008-09 recession and such conditions are comparable in relation to each of the comparable companies viz-a-viz those being experienced by the tested party in the shock year(s).

Alternatively, the dummy variable “IndustryDeclinet” is a version of the ASit variable in Equation 1 that is 1 for years when the comparables’ industry (e.g., U.S. wholesale and distribution) experienced a decline in output (e.g., as measured by sales) relative to the prior year (and zero in other ‘normal’ years).

The specification of the ASit variable based on economy-wide or industry-wide measures have the advantage of being (relatively) exogenous measures. However, they may represent fairly blunt approximations of ASit for purposes of the estimation equation in Equation 1 in that they may not account for whether the company in question truly experienced an economic environment comparable to that experienced by the tested party in the current shock year(s)—e.g., when the adverse conditions translate into a significantly depressed demand for products but such an effect is not uniform across subsectors, markets, channels, regions, time periods, etc.

It also should be noted that the OECD Guidance reference to industry-wide effects should be considered in the context of the specific functional and economic analysis. “In particular, the widespread effects of the Covid-19 pandemic in an industry or within an MNE group do not suffice to claim that a member of an MNE group has to bear the consequences of risks materialising as a result of the Covid-19 pandemic without an analysis of how the outcome of the economically significant risks controlled by the member of the group has been affected by the pandemic.” Paragraph 8, OECD Guidance.

Company-specific Outcomes Used to Infer Adverse Economic Conditions

Under this version of the estimation equation, the variable of interest ASit is identified based on an observed decline in some measure of the individual company’s output (or a proxy for such output). In particular, the premise underlying this approach is to infer that a company was subject to an adverse economic shock (similar to that impacting the tested party in the current shock year(s)) in a given year when a sharp decline—i.e., exceeding a pre-specified threshold—is observed in the company’s output relative to the prior year.

Specifying a relatively high (and comparable) threshold for the observed decline (e.g., 10%, 20%, etc.) in output as the basis for classifying a year for which the ASit variable takes on the value 1 is intended to achieve two objectives. First, to isolate those instances where the decline in output likely was driven by external forces impacting the wider industry and economy versus more “normal” market forces that the company may be subject to in periods of steady economic conditions. It may be argued that a marked decline in output is, by itself, an indication of ‘disequilibrium’ economic conditions that warrant comparability adjustments of the type facilitated by the approached covered in this article. Second, the selection and calibration of the threshold (e.g., 10% versus 25%) may enable better comparability between the shock year(s) experienced by the tested party and—in terms of the severity as experienced by the tested party (e.g., via depressed demand conditions)—the years/instances identified for the comparables when they are classified as being subject to similar economic conditions.

Ideally, the “output” measure used to identify the decline relative to the prior year would rely on a physical measure (e.g., volume or units). Note that the output measure is not used as an explanatory variable in its own right in the estimation of Equation 1. The output measure—in particular, an observed decline in such measure above a prespecified threshold—is used to identify a year in which a company is inferred to be subject to an adverse economic shock/environment. The causal link being estimated in Equation 1 is between the year when a company is (viewed as being) subject to an economic shock (i.e., ASit ) and the dependent variable (i.e., the PLI of interest). The relationship of interest is not, nor should it be interpreted as, between the output measure (used to identify the “shock year”) in its own right and the dependent variable.

Examples of possible proxies or substitutes for physical measures of output that may be used in alternative specifications of ASit together with possible pros and cons:

(1) AS_Salesit: Under this specification of ASit, a year in which a given company is viewed as being subject to adverse economic conditions comparable to the tested party in the shock year(s) is identified as one during which the sales revenues for the comparable in year are lower than in the prior year by an amount that exceeds a specified threshold (e.g., 15%). In this instance, sales are used as a proxy for product volume such that a marked decline in product volume relative to a prior year is taken as evidence of an adverse economic shock impacting the company.

(2) AS_COGSit: In this specification of ASit, the cost of goods sold (COGS) is used as the proxy for output in order to infer whether a company is subject an adverse shock in the current year—i.e., when the COGS in the current year is observed to be lower relative to the prior year by an amount greater than the specified threshold (e.g., 15%). COGS is defined as purchases plus starting inventory less closing inventory and can serve as a proxy for the products sold in a given year.

AS_Inventory Turnoverit: In this specification of ASit, the inventory turnover—specifically, an observed decline in such measure in the current year relative to the prior year by an amount exceeding a defined threshold—is used as the proxy for output in order to infer whether a company is subject an adverse shock in the current year. Inventory Turnover is defined as ratio of COGS to average inventory (for the year) and is a measure of how often inventory turns over the course of a year. A (marked) decline in this ratio can signal a significant decline in volumes sold.

(3) AS_CapacityUtilizationit: In this specification of ASit applicable to manufacturers, an estimate of the firm’s capacity utilization—specifically, an observed decline in such measure in the current year relative to the prior year (e.g., by 15% or more)—is used as the proxy for output in order to infer whether a company is subject an adverse shock in the current year. An approximation for capacity utilization that may considered for a manufacturer under this approach can be calculated as the ratio of (COGS – opening inventory + closing inventory) and average (net) plant, property and equipment (“PP&E”) for the year.

In principle, this specification of the ASit variable based on observed values of firm-specific variables may raise some endogeneity concerns (informally referred to as “chicken and egg” question) that may imply failure of the assumptions in the standard regression models and bias the estimate of β in Equation 1.

Consider for instance, when the ASit variable is based on firm sales (i.e., AS_Salesit.) Simplistically put, since profit is a “component” of sales, identifying years during which a company is taken to be subject to an adverse shock based on a sharp decline in sales being observed (relative to the prior year) could mean that we necessarily may be identifying years when the company’s profits dropped (and in turn, caused the observed drop in sales that we use in this specification of ASit to identify adverse shock years). Since the dependent variable is a measure of profitability, this may lead to biased coefficient estimates under this specification.

Note however, that for “routine” entities such as are the subject of CPM/TNMM analyses, the profit component within sales is likely to be relatively small on average (e.g., relative to the “decline threshold” selected) thereby acting as a check on these concerns. The instrumental variable approach discussed below can further help address such endogeneity concerns in relation to this specification of ASit in Equation 1 when a suitable instrument and data on such instrument can be found. As the illustrative results based on the Distributor Reference Sample show, potential endogeneity does not appear to be impacting the magnitude and significant of the estimated coefficients of the ASit variable based on firm-specific measures.

Instrumental Variable (IV) Estimation

In light of the endogeneity concerns highlighted in section III.b.i. and as a possible way to combine the respective merits of the approaches in sections III.a and III.b, an instrumental variable (IV) estimation approach can be considered. Under this approach, an industry-wide variable used in section III. serves as an “instrument” for the ASit variable in III.b (e.g., AS_Salesit).

In essence, the IV estimation technique can be viewed as a two-stage estimation approach. For example, the IndustryGrowtht variable could be used as an instrument for AS_Salesit such that in the first stage, “predicted” values of AS_Salesit would be estimated based on the following estimation equation.

Equation 3

AS_Salesit = αi + δIndustryGrowtht + y1Xit + y2Xit-j + εit

The “predicted” values of AS_Salesit from the first-stage estimation (i.e., Equation 3 above) then would be used in place of the raw values in the second-stage estimation Equation 2.


In order to illustrate the approaches described above, the different specifications are applied to panel data covering (where available) the years from 2006 through 2019 for a set of 24 independent U.S. distributors to perform a comparability adjustment to the “but for” (i.e., pre-adjustment) arm’s-length range of results. For purposes of illustration, the applicable PLI is taken to be the OM and the pre-crisis arm’s-length range of OM results—assumed to be the interquartile range (IQR)—is assumed to be 2.5% to 7.5% with a median of 5%. Absent the crisis and the revised economic conditions impacting the tested party, the above would represent the arm’s-length benchmark under the CPM/TNMM for the tested party and is reproduced in Table 1.

Table 1: Unadjusted Arm’s-Length Benchmark OM

Table 2 shows certain summary statistics for the panel data used for purposes of illustrating the application of the approaches described above. The panel in this case is ‘unbalanced’ given that the number of years of data available is not the same for each company.

Table 2: Summary Statistics

The application of, and results from, the two categories of approaches described in this note are summarized in the following sections. Only the estimates for the coefficient of interest are presented while those for the different control variables are left out in the interest of brevity.

OL-Based Approach

The table below illustrates the application of the OL-based approach presented in the first part of the article. The coefficient estimate for β1 in Equation 1 was 0.95 (the estimate β2 for the interactive term was not found to be statistically significant). The estimated coefficient implies that for the firms in the sample, the average cost structure is such that a 1% change in sales revenues is associated with a 0.95% change in total costs with the concomitant implication for profits and profitability following.

Based on this relationship, an appropriate adjustment factor—based on the relevant scenario of a sales decline caused by the economic environment—can be imputed using a ‘baseline’ hypothetical P&L with an OM that corresponds to the average OM for the sample. The adjustment factor so derived for a given scenario can then be applied to the (unadjusted) arm’s-length range to derive the adjusted arm’s-length range of OM applicable for the relevant scenario.

Table 3: Adjustment Using OL-Based Approach

*Adjusted values for the lower quartile and upper quartile are calculated analogously to what is shown for the median above

IO-based Approaches with the PLI as the Dependent Variable

Table 4 below summarizes the estimated coefficients for the ASit variable under alternative specifications described in section III.b. Also shown in the table is the adjusted arm’s-length range based on the coefficient estimate derived under each alternative specification. The results shown for the ASit variable defined under the alternative specifications are as follows:

(1) Rec2009 is an indicator variable that is 1 for each company for the year 2009 and 0 otherwise (the coefficient for this variable was not found to be statistically significant.);

(2) IndustryDeclinet is an indicator variable that is one in a year for each company when IndustryGrowtht is less than one and zero otherwise. IndustryGrowtht represents the current-year sales for the U.S. wholesale industry divided by prior-year sales with such ratio being calculated using economic census data reported by the US Census Bureau;

(3) AS_Salesit is an indicator variable that is one for a given company in a year when its sales revenues are lower than prior-year revenues by 10% or more, and zero otherwise;

(4) AS_COGSit is an indicator variable that is one for a given company in a year when its COGS are lower than prior-year COGS by 10% or more, and zero otherwise;

(5) AS_InventoryTurnoverit is an indicator variable that is one for a given company in a year when its inventory turnover is lower than the prior year figure by 10% or more, and zero otherwise;

(6) In the IV specification, the IndustryGrowtht is used as an instrument for AS_Salesit.

Recalling the classification given earlier, specifications (1) and (2) relate to economy or industry-based measures, specifications (3), (4), and (5) to company-specific outcomes, and specification (6) to IV estimates. “FE” denotes a fixed-effects specification.

Table 4: Estimation Results using IO-Based Approaches

* Bolded font indicates estimates that are significant at least at the 10% confidence level.


The OECD Guidance released in December 2020 notes the challenges of performing comparability analyses in the Covid-19 environment. This is on account of the impact of the pandemic on transactions between unrelated parties as well as the fact that transfer pricing analyses typically rely on historical data. In order to address these “information deficiencies,” the OECD Guidance discusses the use of statistical approaches like regression analysis among several “practical approaches.”

The approaches discussed in this two-part article are intended to address key considerations and facilitate an analysis and estimation of appropriate profitability benchmarks for a tested party adversely impacted by the economy-wide adverse economic shock resulting from the Covid-19 crisis. The approaches are relevant when suitably comparable data on potential comparable companies that reflect the impact of an adverse shock (similar to that experienced by the tested party) are not available or directly observable. We note that the approaches are not intended as an attempt to predict or forecast the comparables’ profitability levels in the shock year(s), but instead represent an attempt at deriving a more reliable range of profitability benchmarks based on the same set of independent comparable companies that have been used as benchmarks for the tested party using the comparables’ historical data.

The statistical methods discussed in this article draw from academic research published by various authors from different fields in economics and finance. This literature has valuable applications in a transfer pricing analysis attempting to address the comparability challenges created or exacerbated by the Covid-19 pandemic.

Each of these models is based on a set of assumptions which present inherent limitations and are inexact. The evaluation, selection, and application of these models therefore requires bespoke, thoughtful, and evidenced-based judgment. Ultimately, in addressing which combinations of methodologies and approaches best address the comparability issues and the informational constraints raised by the Covid-19 pandemic, priority should be given to clearly establishing how the arm’s-length test is met consistently with the rules and under the specific facts and circumstances.

The authors are principals in the transfer pricing group of PricewaterhouseCoopers’ Washington National Tax Services practice. The authors acknowledge helpful comments from, and discussions with, Joe Murphy, Paige Hill, Jozef Kavuliak, Sarita Mohapatra, Matt Haag, and David Ernick from PwC. All errors and omissions are our own. The views expressed in this article are solely the authors’ and should not be ascribed to any other person or institution.

This column does not necessarily reflect the opinion of The Bureau of National Affairs, Inc. or its owners.

Author Information

The authors are principals in the transfer pricing group of PricewaterhouseCoopers’ Washington National Tax Services practice. The authors acknowledge helpful comments from, and discussions with, Joe Murphy, Paige Hill, Jozef Kavuliak, Sarita Mohapatra, Matt Haag, and David Ernick from PwC. All errors and omissions are our own. The views expressed in this article are solely the authors’ and should not be ascribed to any other person or institution.


Below is a short list of published articles that provide some of the foundations in each stream of literature discussed in this article.

IO-Based Approaches

1. Bothwwell, J., T.Cooley and T.E. Hall (1984), “A New View of the Market Structure – Market Performance Debate,” Journal of Industrial Economics, 32: 397-417.
2. Comanor, W. and T. Wilson (1967), “Advertising, Market Structure and Performance,” Review of Economics and Statistics, 49: 423-440.
3. Liebowitz, S. (1982), “Measuring Industrial Disequilibria.” Southern Economic Journal, 49: 119-136.
4. Schmalensee, R. and R. Willig (1990), Handbook of Industrial Organization, Volume 2, Amsterdam; North-Holland.

OL-Based Approaches

1. Anderson, M., Banker, R. and D. Janakiraman, (2003) “Are selling, general, and administrative costs “sticky”?” Journal of Accounting Research 41.
2. Banker, R., D. Byzalov, S. Fang and Y. Liang (2018) “Cost management research,” Journal of Management Accounting Research. Fall2018, 30(3).
3. Lev, B., (1974) “On the Association between Leverage and Risk.” Journal of Financial and Quantitative Analysis, 9.
4. Mandelker, G.N., and S.G. Rhee (1984) “The Impact of Degrees of Operating and Financial Leverage on Systematic Risk of Common Stock.” Journal of Finance and Quantitative Analysis, 19.

Copyright 2021 Kartikeya Singh. Marco Fiaccadori. All rights reserved.

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