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1
Transfer Prices and Import and Export Price Indexes: Theory and Practice
1
March 18, 2005.
Discussion Paper 05-08,
Department of Economics,
University of British Columbia,
Vancouver, Canada, V6T 1Z1.
W. Erwin Diewert
Department of Economics
University of British Columbia
Vancouver, Canada, V6T 1Z1
Email:diewert@econ.ubc.ca
William F. Alterman
Division of International Prices
Bureau of Labor Statistics
2 Massachusetts Avenue, N. E.
Washington DC 20212
Email: alterman_w@bls.gov
Lorraine Eden
Department of Management
Texas A&M University
TAMU 4221
College Station, Texas 77843-4221
Email: leden@tamu.edu
Abstract
Currently over one-third of U.S. trade in goods takes place between related parties. The
valuation of these goods has been subject to much controversy and criticism over the
years, as companies have been accused of over or under valuing these goods in order to
minimize business taxes and/or import duties. A myriad of rules and regulations
developed (in the case of the United States) by both the Internal Revenue Service as well
as the Customs Service deal with these valuations. For the purpose of calculating the
1
A preliminary version of this paper was presented at the SSHRC Conference on Price
Index Concepts and Measurement held at the Fairmont Waterfront Hotel, Vancouver
Canada, June 30-July 3, 2004. The first author thanks the SSHRC for financial support.
The authors thank Ted To for helpful comments. The opinions expressed in this paper do
not necessarily reflect the views of the Bureau of Labor Statistics.
2
export and import price indexes, however, the question we attempt to answer is,
“Conceptually, what is the ideal import/export price the Bureau of Labor Statistics should
be collecting in those instances where a transaction is between related parties.” We
demonstrate that the ideal price for incorporation into these price indexes may be very
difficult to calculate, and that the selection of an alternative arms length transaction may
be a more fruitful approach.
Key words
Transfer price, export and import price indexes, measurement issues, taxation of traded
goods.
Journal of Economic Literature Classification Codes
C8, C42, C43, C81, C82, F10, H25.
1. Introduction
The main purpose of this paper is to suggest a theoretical foundation for determining
what is the appropriate price a statistical agency (like the Bureau of Labor Statistics)
should seek from domestic establishments that engage in international trade with an
affiliated establishment abroad. Such a price is called a transfer price. Should such a
price be the same price that the related party reports to the relevant domestic trade
authority such as the U. S. Customs Service for the U. S.? Or should it be the price that is
reported to the domestic tax authority such as the Internal Revenue Service for the U. S.
case? Or should it be a cost based price? Or should it be a market based price for similar
trades with unaffiliated establishments? Finally, suppose that the conceptually perfect
transfer price cannot be collected for practical reasons. In this situation, what are the
practical alternatives for the price collector and can they be ordered in terms of their
desirability? These are the questions that we will attempt to answer in this paper.
What makes a transfer price different from a price for an international trade transaction
between two unrelated firms? When there is a international transaction between say two
divisions of a multinational enterprise (MNE), then the value of the transaction to the
exporting division will be equal to the value of the transaction for the importing division
and when the MNE works out its profits worldwide for the quarter where the transaction
took place, the export value will equal the import value and hence will cancel out, leaving
the MNE’s overall profits unchanged, no matter what price it chooses to value the
transaction.
2
Hence, at first glance, it appears that the firm could choose the transfer
price for the transaction to be practically anything.
3
However, in a world where there are
2
This assertion requires the proviso that there are no trade taxes on the transaction and
that business income tax rates are equal in both countries.
3
Thus this situation is very different than that where the trade takes place between
unaffiliated firms. In the latter case, the price for the transaction is very meaningful: an
3
taxes on international transactions and where the rates of business income taxation differ
across countries, then as we shall see below, the situation is actually worse: in this
situation, the multinational will have definite financial incentives to choose strategically
the transfer price to minimize the amount of taxation paid to both jurisdictions. It is this
element of strategic choice that casts doubt on the usefulness of simply collecting transfer
prices just as if they were ordinary prices between unrelated parties.
However, if we choose to question reported transfer prices, what type of price should
replace them? This question will be addressed in section 13 of this paper.
Before the transfer price problem is directly addressed, some background information
detailing the importance and complexity of pricing intra-firm trade will be found in
section 2. It will be followed by a brief overview in section 3 of some of the purposes
that indexes of export and import prices might be used. In section 4, we look at some
alternative pricing concepts that could be used to describe import and export prices that
could be used in a national index of import or export prices.
In section 5, we define in a preliminary fashion the four main types of transfer price that
have been considered in the theoretical literature on transfer prices. In this section, the
transfer price problem is studied in the context of two affiliated establishments in two
countries trading a single commodity. In section 6, we consider the simplest case where
there are no trade taxes, business income taxes do not exist (or are the same in the two
jurisdictions) and there is an external market price for the traded commodity. In section
7, we consider the case where there are no trade or business income tax distortions but an
external market for the internationally traded commodity does not exist. In sections 8-10,
the analysis is extended to the case where the rates of business income taxation differ in
the two countries (section 8), to the case where the rate of business taxation are the same
but there are trade taxes (section 9) and finally to the situation where there are both trade
taxes and differing rates of business income taxation (section 10). Although this
framework is rather simple, most of the complexities of transfer pricing can be illustrated
using it.
Sections 11 and 12 look at “practical” approximations to the theoretical transfer price in
the context of a single commodity traded internationally between related establishments.
Section 13 looks at the main question that we are attempting to answer, namely, what are
the practical alternatives for collecting transfer prices and can they be ordered in terms of
their desirability? This section concludes with some additional discussion of what can be
done at the central office in order to obtain improved transfer prices.
The theory presented in sections 6-12 assumes that the importing and exporting
establishments behave competitively; i.e., they take the prices of nontraded commodities
as being fixed parameters beyond their control. An Appendix considers how the
increase in the negotiated price will increase the profits of one firm and decrease the
profits of the other firm.
4
theoretical results are changed when this assumption is relaxed.
2. Background
The need to calculate accurately prices of goods in intra-firm trade is not just an abstract
one. In calendar 2000, the latest year that the data are available, the Bureau of Economic
Analysis reported that $241 billion (or 31 percent) of export goods and $452 billion (or
37 percent) of imports were between related parties. During the past 20 years these
percentages have tended to fluctuate somewhat. The value for exports has ranged
between 31 and 40 percent, while the comparable range for imports is between 37 and 44
percent. Regardless of the actual percentage, intra-firm shipments continue to represent a
substantial portion of U.S. trade.
4
It should be noted that the characteristics of intra-firm trade could be different from trade
between unrelated parties. For example, in 2001, only 13 percent of exports to both
China and Korea were intra-firm, while 41 percent of sales to Mexico were between
related parties. On the import side, fully 74 percent of U.S. imports from Japan were
related party trade, while the comparable figure for China was just 18 percent. Similar
differences crop up when looking at the data by industry, with especially high proportions
of intra-firm trade in transportation equipment, computers and chemicals.
5
Even within
intra-firm trade their can be significant differences. For U.S. multinationals, 65 percent
of their exports in 1999 consisted of intermediate products exported to overseas affiliates
for further processing or assembly. In contrast, for foreign multinationals 76 percent of
their shipments to the U.S. in 1998 were finished goods ready for final sale.
6
Given
these types of variations, simply excluding intra-firm trade when constructing export and
import price indexes would not be appropriate.
Because of the significant international taxation aspects of world trade, the pricing of
goods in intra-firm trade has become a major issue, both politically as well as
administratively. It has been contended that companies do indeed price these goods in
order to maximize corporate profits. Using BLS price data, a recent paper found
evidence that “there is a strong and statistically significant relationship between
countries’ tax rates and the prices of intra-firm imports and exports exchange with those
countries.”
7
A Federally funded study released in October 2002 by Professors Simon J.
Pak and John S. Zdanowicz, estimated that corporations saved $53.1 billion in 2001 by
over or under invoicing goods in intra-firm trade. Although these and earlier studies
were not without their critics, politicians and academics alike are taking a closer look at
4
The percentage figures constructed using the BLS price data (which uses a separate
survey compared to the data produced by the U.S. Customs Service or BEA) are similar.
5
These data are from the Bureau of the Census (2002). Although the Census data is not
considered as accurate as data from BEA, the aggregate numbers are fairly consistent.
6
The best article on the value of intra-firm trade was published in 1997 by the Bureau of
Economic Analysis; see Zeile (1997). In addition, more recent data is available directly
from BEA.
7
See Clausing (2001).
5
these and other possible practices used by multinationals to minimize corporate taxes.
8
From an administrative standpoint, the pricing of U.S. goods in international trade must
serve two masters: The Internal Revenue Service (IRS) and the U.S. Customs Service.
9
While Federal—and most foreign--regulations call for the use of an arm’s length
standard in valuing intra-firm trade, these two agencies historically have worked
independently in deriving values for intra-firm trade, in part because they have differing
objectives.
10
Tariff officials, who are attempting to maximize duty assessments, will tend
to want to raise the value of imported goods, while the IRS will have a tendency to want
to lower the value of imports in order to maximize the amount of domestic profits.
11
Furthermore, while Customs values tend to be finalized comparatively quickly, final
valuations associate with IRS audits and subsequent court procedures can drag on for
years.
12
The laws, procedures and documentation covering transfer prices are
complicated and substantial. Both agencies devote significant resources to pricing intra-
firm trade. This brief summary of the US situation, of course, does not even address the
transfer price regulations associated with other countries.
13
Because of this complexity, corporations can end up devoting substantial resources to
8
This study was funded at the behest of Senator Byron Dorgan (Democrat, North
Dakota) who has been critical of both multinationals as well as the Treasury Department.
Pak and Zdanowicz (2002) is an executive summary of this study. For Senator Dorgan’s
comments, see Dorgan (2002). For an example of ongoing attempts by Congress to
address other multinational practices for reducing taxes (such as incorporating in a low
tax jurisdiction), see Freedman (2002).
9
Note that, in general, the valuation of transactions between domestic buyers and sellers
are not subject to the same government scrutiny. This is for two reasons: first, the vast
majority of these transactions are between unrelated parties; and second, the tax
implications of these transactions are minimal. An official of the Bureau of the Census,
which is responsible for collecting data on domestic shipments from manufacturers, did
confirm that companies oftentimes had problems valuing shipments between plants that
were within the same firm, particularly when the item was an intermediate good which
would undergo further processing prior to being sold. Unfortunately, the Bureau of the
Census does not publish separate totals for related and unrelated value of domestic
shipments. (as per conversation with Judy M. Dodds, May 25
th
, 2004).
10
Under an Arm’s Length Standard, the transfer price should equal the price that would
be settled on if the two trading firms were unrelated.
11
See Eden (1998; 395-96) for further details.
12
See Eden (1998; 684) for mention of 4 cases that each dragged on for over a decade.
13
It should also be noted that export data do not receive nearly the same scrutiny as
import data from the U.S. Customs Service. In fact, since 1990 the U.S. has used data
supplied by Statistics Canada to estimate U.S. exports to Canada. In 1986 undocumented
U.S. exports to Canada were equivalent to 22.4 percent of the published value; see Mozes
and Oberg (2002).
6
valuing intra-firm trade.
14
In a recent survey, fifty-nine percent of multinationals
indicated that they had undergone an audit of their transfer pricing practices in 2001.
15
Increasingly multinational traders avail themselves of any number of accounting firms
that specialize in assisting corporations in navigating the multitude of both domestic and
foreign regulations associated with pricing intra-firm trade. In the early 1990s, in order
to minimize the disagreements between importers and the IRS, the IRS introduced
Advanced Pricing Agreements (APA) whereby a company could voluntary meet with the
IRS and negotiate a transfer pricing method that would stand for a fixed length of time,
usually five years. While designed to streamline the process, it nonetheless, has added
more complexity to the pricing process.
16
Since individual APAs are considered
confidential, it is not clear how they are constructed and how often they are used. The
limited evidence available, however, indicates that APAs cover a significant portion of
U.S. trade.
17
Furthermore, there is a concern that companies are able to use APAs to
minimize taxes. Consequently, the U.S. Senate Committee on Finance has requested the
IRS investigate and report back to Congress on the effectiveness of the APA program.
18
Some of the companies which have publicly announced that they make use of APAs
include Ford Motor Company, Apple Computer Incorporated, Sony Corporation of
America and Intel Corporation.
All of this serves to emphasize both the importance of transfer pricing as well as the
difficulty in estimating these prices. Since transfer prices are used in export and import
price indexes, the next section will review some of the purposes and uses of these
indexes.
3. Import and Export Price Indexes: Purposes and Uses
There are many purposes for national import and export price indexes. In this section, we
list seven of the major uses and purposes.
14
The IRS, at the behest of Senate Committee on Appropriations, even contracted for a
study assessing the cost to business of filing the paperwork associated with intra-firm
trade; see Schulman, Ronca and Bucuvalas, Inc. (2001).
15
The survey indicated that the rate for was even higher when looking at just U.S. trade;
see Ernst and Young (2001).
16
APAs can still be very detailed and a number of companies such as Ernst and Young,
and Deloitte & Touche advertise their services extensively. For example, see Deloitte
and Touche (2002), which is essentially an advertisement, detailing their services.
17
During the first 10 years of its existence (1991-2001) 349 APA agreements were
executed; see Internal Revenue Service (2002; 8). In 2001 alone, however, 77
applications for an APA were filed, indicating that this practice is becoming more
prevalent over time. A report by the General Accounting Office stated that the 10 percent
of the major multinationals had an approved APA, but that this 10 percent accounted for
42 percent of the dollar value of the intercompany transactions included in their analysis
(2002).
18
“Grassley, Baucus Launch Review of Whether Certain Multinationals Pay Fair Share
of Taxes,” Press Release, December 22, 2003.
7
(a) Calculation of a Country’s Terms of Trade
A country’s terms of trade is defined as an index of export prices divided by an index of
import prices. To illustrate this concept, assume for simplicity that there is only one
exported commodity that has price p
x
t
in period t and one imported commodity into the
country that has price p
m
t
in period t. Then the terms of trade for the country, comparing
the prices in period 0 with those of period t, is defined as follows:
(1) TT(0,t) ≡ [p
x
t
/p
x
0
]/[p
m
t
/p
m
0
] .
Thus the terms of trade is the rate of increase in export prices going from a base period to
the current period divided by the corresponding rate of increase in import prices. If the
terms of trade is greater than 1, we say that there has been an improvement in the
country’s terms of trade while if TT(0,t) is less than 1, we say that there has been a
deterioration in the terms of trade. An improvement in the terms of trade means that a
country can now purchase additional units of the imported commodity in exchange for a
single unit of the export commodity as compared to the situation in the base period; i.e.,
foreigners offer are now willing to exchange more imports in exchange for a constant
amount of exports compared to the base period. Hence, the home country is now better
off.
19
A country’s terms of trade index is sometimes viewed as an index of the country’s
competitive success in foreign markets. Thus if a country is able to sell its products at
higher prices in foreign markets so that its terms of trade increases, then this could be
viewed as an improvement in the country’s competitiveness.
20
(b) Measurement of National Real Output and Productivity
The output of a country is defined in nominal terms as the familiar C + I + G + X - M
(consumption plus investment plus government expenditures plus exports minus imports)
and in order to define real output, each component of national output has to be deflated
by a price index. Hence, a major use for the export and import price index is to act as
deflators for two major components of national output so that accurate estimates of real
GDP can be constructed. The national productivity of a country is defined as either real
output divided by labor input (labor productivity) or as real output divided by real input
(multifactor or total factor productivity). Thus import and export price indexes are a
necessary input into the construction of national productivity indexes.
19
Thus an improvement in a country’s terms of trade acts in much the same manner as a
productivity improvement, which corresponds to a situation where more output can be
produced with the same amount of input.
20
On the other hand, if the country exports mainly primary products, then world
commodity prices may simply fluctuate exogenously and the country’s terms of trade
may not say much about the country’s competitiveness in international markets.
8
(c) Measures of National Inflation
Central banks require broad indexes of price change or general inflation so that they can
undertake monetary policy. Two of the most frequently used indexes of general inflation
are the Consumer Price Index and the GDP deflator.
21
In order to construct the GDP
deflator, price indexes for exports and imports are required.
(d) Model Building and Forecasting
Price indexes for exports and imports are required for a wide variety of macroeconomic
models. More generally, disaggregated models of the economy may require price indexes
for a wide variety of components of the exports and imports of a country. Business and
government economists are often required to provide forecasts for specific classes of
exports and imports in real terms (or they may be asked to forecast future trends in the
prices of these components) and price indexes for these components of exports and
imports are vital building blocks into their models.
(e) Indexation of Contracts
An exporter may sign a contract to deliver units of a commodity to a foreign purchaser on
a long-term basis. Alternatively, a domestic producer may sign a long-term contract with
a foreign supplier in order to ensure delivery of a vital input into the producer’s
production process. It may be difficult to determine what a “fair” price for the
commodity is for periods that are far off and hence these long-term contracts may use a
component of the export or import price index in order to index future prices. Similarly,
in the regulatory context, a domestic power company that has to import fuel may be able
to pass on part of its costs to demanders by using a formula that involves the import price
index for fuel. In all of these indexation uses, it is important that the relevant import or
export price index be fairly comprehensive and representative of actual transactions for
that component.
(f) Monitoring Trade Legislation and Trade Agreements
Export and import price indexes can be used to track the effects of various trade policies.
For example, the U. S. Department of Commerce may impose a punitive tariff on a
21
It could be argued that the GDP deflator is not the best index of inflation since import
prices enter this index with negative weights. Hence if import prices increase, other
things remaining constant, the GDP deflator will decrease. This is a rather
counterintuitive property for a measure of general price change. Thus a more appropriate
indicator of general inflation might be the deflator for C + I + G + X. Note that a price
index for exports will still be required for this inflation index. A price index for imports
will be required in order to construct an input price index for the economy. The input
price index will be required in order to construct an index of multifactor productivity for
the economy but it could also serve as a useful measure of general inflation. See Diewert
(2002; 12) for further discussion on these points.
9
certain class of imports (e.g., softwood lumber imports from Canada) in retaliation for
perceived unfair trade practices. The import price index for the affected commodity can
then be monitored in order to determine whether the foreign exporters are absorbing the
tariffs or passing them on to U. S. importers. Similarly, if the government decides to
subsidize the exports of a domestic industry, then the relevant export price index could be
used to determine whether these exports become more competitive in foreign markets.
At times, export and import price indexes play a role in negotiating trade agreements in
specific commodity areas.
(g) Replacement Cost Accounting
If a domestic firm uses replacement cost accounting and it has used imports of foreign
machines and equipment in its production process, then it could use the import price
index for the relevant class of imports as a price index to escalate the initial purchase
cost.
From the above list of uses for the components of the export and import price indexes, it
can be seen that a modern economy cannot do without these indexes. They are a key
input into the national system of economic statistics and they have many other private
and public uses.
4. Pricing Concepts
In this section, we make some observations on the interaction of the uses of the export
and import price indexes with alternative definitions for the price of an export or the price
of an import.
22
We consider the problem of determining the price for an imported commodity. The
problem is that there are several plausible price concepts that can be used in order to
price an imported commodity. Consider the problem of importing a particular good from
a foreign factory. There is a starting price for this good: the selling price for this good at
the foreign factory. This is known as the (output) factory gate price. To this initial price,
we need to add transportation costs to ship the good to the port of export in the foreign
country plus insurance costs for the inland transportation in the foreign country. Call the
resulting price the private opportunity cost export price. Once the good is at the port of
export, there may be export subsidies, domestic commodity taxes or additional export
taxes that must be paid. After adjusting for government tax and subsidy payments, the
resulting price is called the water’s edge export price or the free along side export price.
From the viewpoint of the importing country, this price is also known as the free on
board import price. This price represents the price that the exporting country is charging
international purchasers of the commodity at the exit port of the exporting country. This
water’s edge export price is the sum of the private opportunity costs of producing the
commodity and shipping it to the export port plus government net taxes that the exporting
22
For additional material on this topic, see Eden (2001) and Eden and Rodriguez (2004).
10
country sees fit to impose on foreign purchasers of the commodity. This is not the end of
the story. To the water’s edge export price, we need to add international shipping and
insurance charges to get the commodity to the port of entry of the importing country.
The resulting price is called the water’s edge import price. Again, this is not the end of
the story. We now can add any applicable domestic commodity taxes and import tariffs
to the price (less import subsidies if any) in order to obtain the post tariff import price or
the import for consumption price. Finally, we can add to this price, transportation costs
to ship the good from the port of entry in the home country to the importing
establishment plus the associated insurance costs for the inland transportation in the home
country. Call the resulting price the (input) factory gate price.
The International Price Program of the Bureau of Labor Statistics attempt to collect the
water’s edge export price as its pricing concept for exports (which is the domestic output
factory gate price plus domestic inland transportation costs plus U. S. tax and subsidy
adjustments). For imports, it attempts to use the foreign water’s edge export price (which
is the foreign output factory gate price plus foreign inland transportation costs plus
foreign tax and subsidy adjustments). Thus, essentially the same pricing concept is used
for both exports and imports.
23
This treatment of export and import prices seems to be
appropriate if our major purpose is to measure a country’s terms of trade; i.e., what do
countries offer us for their exports compared to what we offer foreigners for our exports,
exports and imports being priced in a symmetric manner. However, for many of the
other purposes listed in section 3 for the import and export price indexes, this treatment
will only be approximately “correct”. For purposes (b) and (c), if we are using the
economic approach to price and quantity indexes, then the appropriate import pricing
concept is either the input factory gate price (since this is the price actually paid for the
use of the imported commodity by the importing establishment) or the post tariff import
price (since this is the price paid for the use of the imported commodity by the
consolidated U.S. production sector, including the domestic transportation sector).
Similarly, the appropriate export pricing concept is the output factory gate price plus
government subsidies since this is the actual revenue received by the producing
establishment for producing a unit of the commodity. If we consolidated the exporting
establishment with the domestic transportation sector, then the appropriate export pricing
concept from the viewpoint of the economic approach to index number theory would be
the output factory gate price plus government subsidies plus domestic transportation and
insurance costs which is equal to the private opportunity cost export price plus export
subsidies.
24
23
In practice, BLS will accept nearly any price basis that the respondent reports is the
basis consistently used in transactions for that particular good. The major exception is
on imports where the Bureau will not use prices that include a duty value that cannot be
removed.
24
We mention these complications because as noted above, in order to deal with transfer
prices in the context of index number theory, it is necessary to use the economic approach
to index number theory. However, the economic approach to index number theory
requires that the prices used be the prices that firms actually get for their sales of products
and the prices that they actually pay out for their inputs. For an exposition of the
11
Unfortunately, an implication of the above paragraph is that, in theory, more than one
export and import index will be required in order to meet the needs of all users of
international price indexes. The use of water’s edge prices for imports and exports is
suitable if the main purpose of the index is to calculate the country’s terms of trade. For
all other uses that use an economic modeling approach that assumes that firms maximize
profits or minimize costs, the post tariff price for an imported commodity and the private
opportunity cost plus subsidies price for an exported commodity would be the most
suitable pricing concepts. If in addition, the effects of domestic trade taxes and subsidies
on international trade were to be modeled, then it would also be essential to collect
information on taxes paid or subsidies received by domestic exporting and importing
establishments. However, it must be recognized that collecting this additional
information may place a heavy burden on respondents and price collectors. Indeed, in
reality, The Bureau is very limited--both from a legal standpoint, as well as a burden
standpoint--in how much additional information can be collected. Like nearly all BLS
data collection efforts, the IPP is a voluntary Program and currently approximately 20
percent of the establishments in any given sample refuse to cooperate. The most
frequently cited reason for this refusal is burden on the respondent. In addition, any
attempt to collect additional information on a regular basis would require approval from
the Office of Management and Budget.
5. Alternative Transfer Pricing Concepts
There are four main theoretical concepts for a transfer price.
25
These concepts are:
• the external market or arm’s length transfer price
26
;
• the efficient transfer price;
• the profit maximizing transfer price and
economic approach to export and import price indexes, see Alterman, Diewert and
Feenstra (1999). These theories draw heavily on the theory of the output price index; see
Fisher and Shell (1972), Samuelson and Swamy (1974; 588-592), Archibald (1977; 60-
61) and Diewert (1980; 461) (1983; 1055).
25
Diewert (1985) considers other transfer pricing concepts but for our purposes, they are
not important. Some of these alternative concepts will be mentioned in footnotes below.
26
This price corresponds to Eden’s (1998; 37) (2001; 32) Comparable Uncontrolled
Price concept for a transfer price. Eden (2001; 32) follows U. S. Internal Revenue
Service conventions and further distinguishes an external CUP (also referred to as an
external comparable) as the price set between two unrelated parties for the same or
similar product sold under the same or similar circumstances) and an internal CUP (also
referred to as an internal or in-house comparable) where the multinational enterprise
simultaneously buys or sells the same or similar product with an unrelated party. The IRS
recommends internal comparables as preferable to external comparables for income tax
purposes (Feinschreiber, 2004; 4). This concept for a transfer price also roughly
corresponds to the U. S. Customs Service transactions value concept for a transfer price;
see Eden (2001; 35-36).
12
• the economic transfer price that is suitable for collection by a statistical agency.
The first concept for a transfer price is feasible if there is a well-defined external market
price for the traded commodity where units can be bought or sold at a common price (let
us call it ‘w’). Then the transfer price for the commodity is just this price w. This is the
arm’s length transfer price.
The second concept for a transfer price arises if there is no external market for the
commodity that is traded between two production units (or establishments) of a
multinational that are located in different countries. The efficient transfer price is
generated by solving a joint profit maximization problem involving the two
establishments and it is a Lagrange multiplier, or shadow price, which corresponds to the
constraint that says the output of the producing establishment must equal the input of the
purchasing establishment. If there are no tax distortions
27
, then this transfer price can
also be generated by setting up two profit maximization problems for the two
establishments involving the traded commodity being sold by one unit at the price w say
and being purchased by the other production unit at the price w. This artificial price is
then varied so that the supply of the one establishment equals the demand of the other
establishment and the resulting transfer price is called the optimal decentralized transfer
price.
28
If there are no tax distortions and the establishments take all other input and
output prices as fixed, this transfer price will also be a socially efficient one.
The profit maximizing transfer price is the third main concept for a transfer price. With
no taxes on trade and no taxation of business income in the two jurisdictions, the profit
maximizing transfer price
29
is the same as the efficient transfer price. But with tax
distortions in either of the two jurisdictions, then the profit maximizing transfer price will
generally be different from the efficient transfer price. In fact, with tax distortions and no
constraints on the behavior of the multinational, the profit maximizing transfer price will
usually be zero or an arbitrarily large number. However, usually, the tax authorities will
not allow such extreme transfer prices and they will either impose a transfer price or the
multinational will choose a strategic transfer price that the tax authorities will accept.
27
We also need to rule out increasing returns to scale in both establishments in order to
get the existence of the decentralized transfer price.
28
This concept of a transfer price is also called an arm’s length transfer price by
Hirshleifer (1956); see also Diewert (1985; 61). Under the no tax distortions assumption
and a no increasing returns to scale assumption for each establishment, this second
concept for a transfer price is equal to Diewert’s (1985; 49-66) efficient, arm’s length and
decentralized transfer price concepts. Note that the external market transfer price is also
efficient and in fact, multinational profits will always be greater (or at least not less than)
in the situation where an external market for the product exists than the situation where
no such market exists.
29
The profit maximizing transfer price is indeterminate under these conditions; it could
be any positive price since it cancels out of the objective function of the multinational’s
global profit maximization problem.
13
The economic transfer price that is suitable, in theory, for collection by a statistical
agency will in all cases be a marginal cost (for the exporting establishment) or a marginal
revenue (for the importing establishment). In the case of no tax distortions, the economic
transfer price will coincide with the external market transfer price or the efficient transfer
price.
In sections 6-10 below, we consider how these concepts for a transfer price can be
defined for the case where there are only two establishments of a multinational trading in
a single commodity. This very simple framework will suffice to illuminate the problems
involved in constructing transfer prices.
6. Transfer Pricing when an External Market Exists
Assume that establishment 1 in country 1 imports the commodity from establishment 2 in
country 2. Let x
1
≥ 0 denote the total quantity of the commodity used by establishment 1
and let x
2
≥ 0 denote the production of the commodity by establishment 2. In this
section, we will assume that there are no tax distortions in order to simplify the analysis.
Suppose that establishment 1 has a technology set S
1
which is defined to be a set of
feasible net output vectors
30
, y
1
, that can be produced if the amount x
1
of the imported
commodity is available. Suppose further that the establishment faces the positive vector
of prices p
1
for these net outputs. Then the net revenue function of establishment 1, r
1
,
can be defined as follows
31
:
(2) r
1
(p
1
,x
1
) ≡ max
y
{p
1
⋅y : (y,x
1
) belongs to S
1
}
where p
1
⋅y ≡ Â
i=1
I
p
i
1
y
i
is the inner product between the vectors p
1
and y. Thus r
1
(p
1
,x
1
) is
the net revenue establishment 1 can achieve if it faces the price vector p
1
for its outputs
and non x inputs and it has available for use x
1
units of the imported commodity.
Suppose now that establishment 2 has a technology set S
2
which is defined to be a set of
feasible net input vectors
32
, z
2
, that can be used to produce the amount x
2
of the
30
If the ith component of y
1
is positive, then the ith commodity is an output produced by
the establishment while if the ith component of y
1
is negative, then the ith commodity is
an input used by the establishment.
31
See Diewert (1974; 133-146) (1993; 165-169) for the properties of net revenue or
profit functions. It should be noted that definition (2) assumes competitive behavior on
the part of the firm in the y markets. However, this assumption is not essential for our
analysis. The firm could be behaving in a monopolistic or monopsonistic manner in these
other markets but the revenue function as a function of the amount of imported
commodity x can still be defined; see Diewert (1993; 169-174) for alternative methods
for defining the revenue function in this case.
32
If the ith component of z
2
is positive, then the ith commodity is an input used by the
establishment while if the ith component of z
2
is negative, then the ith commodity is an
output produced by the establishment.
14
commodity that is exported to establishment 1 or which is sold on the general market.
Suppose further that this establishment faces the positive vector of prices p
2
for these net
inputs. Then the net cost function for establishment 2, c
2
, can be defined as follows
33
:
(3) c
2
(p
2
,x
2
) ≡ min
z
{p
2
⋅z : (z,x
2
) belongs to S
2
}.
Thus c
2
(p
2
,x
2
) is the minimum net cost establishment 2 can achieve if it faces the price
vector p
2
for its net inputs and it is asked to produce x
2
units of the commodity which can
be exported to establishment 1 or sold on the general market.
Given that the multinational faces the price w > 0 for the x commodity, the
multinational’s joint profit maximization problem is:
(4) max
x’s
{r
1
(p
1
,x
1
) - c
2
(p
2
,x
2
) - w[x
1
- x
2
]}.
If r
1
and c
2
are differentiable with respect to their x arguments, then the first order
necessary conditions for x
1*
and x
2*
to solve (4) are:
(5) ∂r
1
(p
1
,x
1*
)/∂x = w ;
(6) ∂c
2
(p
2
,x
2*
)/∂x = w.
Equation (5) says that at an optimal allocation of resources between the two
establishments, the marginal revenue generated by the last unit of x that is used by
establishment 1 should be equal to the external market price of the x commodity, which is
w. Equation (6) says that at an optimal allocation of resources between the two
establishments, the marginal cost of establishment 2 for producing the last unit of x
should be equal to the external market price of the x commodity, which is again w.
The second order sufficient conditions for x
1*
and x
2*
to solve (4)
34
are conditions (5) and
(6) and the following conditions:
(7) ∂
2
r
1
(p
1
,x
1*
)/∂x
2
< 0 ;
(8) ∂
2
c
2
(p
2
,x
2*
)/∂x
2
> 0.
Condition (7) says that marginal revenue is falling and condition (8) says that marginal
cost is increasing. Basically, these two conditions rule out increasing returns to scale in
both establishments in a neighborhood of the optimal allocation.
If x
2*
> x
1*
, then the multinational sells x
2*
- x
1*
units of the internationally traded
commodity to the external market while if x
2*
< x
1*
, then the multinational purchases x
1*
- x
2*
units of the internationally traded commodity from the external market.
33
See Diewert (1993; 167) for the properties of net cost or joint cost functions.
34
Actually, conditions (7) and (8) only guarantee that x
1*
and x
2*
locally maximize (4)
but if conditions (7) and (8) hold for all x
1
> 0 and x
2
> 0, then we will have a global
maximum for (4).
15
The external market case is relatively easy to deal with empirically: the external market
price w is the appropriate transfer price for statistical agencies to use to value the
transactions between the two production units of the multinational.
35
We turn now to the more difficult case where no such external market exists.
7. Transfer Pricing with no External Market, Trade or Profit Taxes
If no external market for the internationally traded good exists, then the amount
demanded by establishment 1, x
1
, must equal the amount supplied by establishment 2, x
2
.
Thus replacing x
1
and x
2
in (4) by a common x leads to the following (efficient) global
multinational profit maximization problem:
(9) max
x
{r
1
(p
1
,x) - c
2
(p
2
,x)}.
The first order necessary condition for x
**
to solve (9) is:
(10) ∂r
1
(p
1
,x
**
)/∂x = ∂c
2
(p
2
,x
**
)/∂x ≡ w**
The first equation in (10) says that at an optimal allocation of resources between the two
establishments, the marginal revenue generated by the last unit of x that is used by
establishment 1 should be equal to the marginal cost of establishment 2 for producing the
last unit of x. We have defined this common marginal cost and marginal revenue as w**.
We note that the allocation of resources generated by the solution to problem (9) will not
in general be equal to the solution to problem (4) unless the solution to (4) had the
property that x
1*
= x
2*
, so that there were no external sales or purchases of x at this
solution to (4).
The second order sufficient conditions for x
**
to solve (9) are conditions (10) and the
following condition:
(11) ∂
2
r
1
(p
1
,x
**
)/∂x
2
- ∂
2
c
2
(p
2
,x
**
)/∂x
2
> 0.
Condition (11) is actually weaker that our earlier second order conditions (7) and (8): the
new condition is consistent with increasing returns to scale in one of the two
establishments.
35
This is what is called a Comparable Uncontrolled Transfer Price (CUP) in the business
literature on transfer pricing. “The CUP method looks for a comparable product to the
transaction in question, either in terms of the same product being bought or sold by the
MNE in a comparable transaction with an unrelated party, or the same or similar product
being traded between two unrelated parties under the same of similar circumstances.”
(Eden 1998; 37). Obviously, the same concept is applicable in a tax distorted context as
well.
16
In order to obtain an interpretation for the transfer price w** defined by (10), consider the
following constrained maximization problem, which is equivalent to (9):
(12) max
x’s
{r
1
(p
1
,x
1
) - c
2
(p
2
,x
2
) : x
1
- x
2
= 0}.
It turns out that w** is the optimal Lagrange multiplier for the constraint in (12). Hence
following Diewert (1985; 51), we may use Samuelson’s (1947; 132) standard
interpretation for a Lagrange multiplier and interpret the efficient transfer price w** as
the marginal increase in the worldwide net output of the multinational firm (valued at the
reference prices p
1
and p
2
) due to an exogenous gift to the multinational of a marginal
unit of the intermediate input. Note that Copithorne (1976; 346) used the term
opportunity cost transfer price in place of our term, efficient transfer price.
If our earlier second order conditions (7) and (8) are satisfied globally, then we can show
that the efficient allocation of resources, i.e., the x
**
solution to (9) can be decentralized if
we use the w** defined by (10) as a transfer price. Consider the following profit
maximization problems for establishments 1 and 2 using the transfer price w**:
(13) max
x
{r
1
(p
1
,x) - w**x};
(14) max
x
{w**x - c
2
(p
2
,x)}.
It can be seen that the first order necessary conditions for (13) and (14) are:
(15) ∂r
1
(p
1
,x
**
)/∂x - w** = 0 ;
(16) w** - ∂c
2
(p
2
,x
**
)/∂x = 0.
It can be seen that (15) and (16) are equivalent to the conditions (10), which are the first
order conditions for x** to solve (9). The second order sufficient conditions for (13) and
(14) are:
(17) ∂
2
r
1
(p
1
,x
**
)/∂x
2
< 0 ;
(18) - ∂
2
c
2
(p
2
,x
**
)/∂x
2
< 0
and these conditions will hold if our earlier second order conditions (7) and (8) hold
globally. Thus under stronger conditions on the technology of establishments 1 and 2
i.e., no increasing returns to scale in either establishment), we have shown that the
efficient transfer price is also the decentralized arm’s length transfer price introduced by
Hirshleifer (1956) that equates the supply of establishment 2 to the demand of
establishment 1.
To sum up, the efficient transfer price w** was defined as the solution to equation (10);
i.e., we need to find an x** such that marginal revenue in establishment 1 is equal to
marginal cost in establishment 2 so that ∂r
1
(p
1
,x
**
)/∂x = ∂c
2
(p
2
,x
**
)/∂x and then this
common value is the appropriate transfer price w**. This efficient transfer price is an
appropriate price for a statistical agency to collect for the traded commodity if it can be
identified. From the viewpoint of production theory, the efficient transfer price will have
17
the same standing as the observable external prices p
1
of the establishment in country 1 or
the observable external prices p
2
of the establishment in country 2.
8. Transfer Pricing with Profit Taxes and No External Market
We now consider the multinational’s profit maximization problem in the case where there
is no external market for the commodity (as in the previous section) and there are no
trade taxes but there are differential rates of business income taxation in the two
jurisdictions. Let the rate of business income taxation in country 1 be T
1
and in country 2
be T
2
where the numbers T
i
are fractions between 0 and 1. If the multinational chooses
the transfer price w > 0, then the multinational’s global profit maximization problem is
now:
(19) max
x,w
(1-T
1
){r
1
(p
1
,x) - wx} + (1-T
2
){wx - c
2
(p
2
,x)}
= max
x,w
(1-T
1
)r
1
(p
1
,x) - (1-T
2
)c
2
(p
2
,x) + (T
1
-T
2
)wx
Comparing (19) with the profit maximization problem (9) in the previous section, we see
that there are two differences:
• The differential rates of business income taxation, T
1
and T
2
, lead to a difference
between the terms (1-T
1
)wx and (1-T
2
)wx and so the terms involving the transfer
price w no longer cancel out as they did in (9) and
• The multinational now is now able to choose the transfer price w as well as the
level of international trade in the intermediate input x; i.e., instead of just
maximizing with respect to x, the firm now maximizes with respect to x and w.
In order to solve the firm’s intercountry profit maximization problem, it is necessary to
consider two cases, depending on whether the rate of taxation in country 1 is higher than
in country 2 or not.
36
Case 1: Country 1 (the Importing Country) Is the Low Tax Country
In this case,
(20) T
1
< T
2
and the importing country is the low business income tax jurisdiction. If we look at the
second line of (19), we see that the term (T
1
-T
2
)wx is negative if w > 0 and x > 0. Note
also, that this is the only term where w appears. Hence to maximize overall profits, the
multinational will want to choose w to be as small as possible. This will make profits in
the low tax country (country 1) as big as possible compared to profits in the high tax
country (country 2). If there are no constraints on the multinational, the optimal choice
36
If the rates of business income taxation are exactly the same so that T
1
= T
2
, then (19)
is equivalent to (9) in the previous section and it does not matter what the firm chooses as
its transfer price. The efficient transfer price w** is still defined by (10) in this case.
18
of w would be:
37
(21) w = 0.
However, the tax authorities in country 2 will almost certainly object to the solution w =
0. A reasonable hypothesis in the case where losses can be carried forward to offset
taxable income in future periods might be that the tax authorities in country 2 insist that
the transfer price be high enough so that profits are zero in country 2. This leads to the
following constraint on w:
38
(22) wx = c
2
(p
2
,x).
Adding (22) as a constraint to the multinational’s profit maximization problem (19) leads
to the following global profit maximization problem:
(23) max
x,w
{(1-T
1
)r
1
(p
1
,x) - (1-T
2
)c
2
(p
2
,x) + (T
1
-T
2
)wx : wx = c
2
(p
2
,x)}
= max
x
{(1-T
1
)r
1
(p
1
,x) - (1-T
2
)c
2
(p
2
,x) + (T
1
-T
2
)c
2
(p
2
,x)} eliminating w
= max
x
{(1-T
1
)r
1
(p
1
,x) - (1-T
1
)c
2
(p
2
,x)} canceling terms
= (1-T
1
) max
x
{r
1
(p
1
,x) - c
2
(p
2
,x)}.
The last line of (23) shows that the multinational’s global profit maximization problem
under the zero profits constraint in the high tax country is equivalent to the efficient profit
maximization problem defined by (9) in the previous section. Hence if the high tax
country imposes a zero profits constraint on the transfer price, the multinational will end
up making an efficient allocation of resources between the two countries. However,
although the allocation of resources will be globally efficient in this case, the transfer
price w*** that the multinational chooses in this case will usually be higher than the
efficient transfer price w** defined by (10) in the previous section. In order to establish
this result, we need to assume that when the allocation of resources is efficient and the
efficient transfer price w** is used, both establishments make positive profits; i.e.,
assume:
39
(24) r
1
(p
1
,x**) - w**x** > 0 ; w**x** - c
2
(p
2
,x**) > 0.
However, instead of choosing the efficient transfer price w**, the multinational chooses
the profit maximizing transfer price w***, which is consistent with (22) when x = x**;
i.e., w*** satisfies the following equation:
37
In this case, the multinational would choose x to satisfy (1 -T
1
)∂r
1
(p
1
,x)/∂x -
(1-T
2
)∂c
2
(p
2
,x)/∂x = 0, which would not lead to the efficient allocation defined in the
previous section.
38
This method for choosing a transfer price is known as the cost plus method in the
transfer pricing literature; see Eden (1998; 42).
39
If there is constant returns to scale for establishment 1, then the first inequality in (24)
becomes an equality; if there is constant returns to scale for establishment 2, then the
second inequality in (24) becomes an equality.
19
(25) w*** ≡ c
2
(p
2
,x**)/x**.
Comparing (25) with the second equation in (24), we see that the profit maximizing
transfer price w*** will be less than the efficient transfer price w** defined by (10); i.e.,
we have:
(26) w*** < w**.
The result (26) was established under the hypothesis that the tax authorities in country 2
had enough knowledge about establishment 2’s costs to be able to impose the zero profits
constraint (22) on the transfer price. If the tax authorities do not have this knowledge,
then there will be an incentive for the multinational to choose an even lower transfer
price than w*** in order to transfer profits out of the high tax jurisdiction.
In general, we can sum up the results for the case where (20) holds by stating that the
chosen transfer price will generally be lower than the efficient transfer price and that it
will no longer be the case that the chosen transfer price equals marginal cost in the
exporting country or marginal revenue in the importing country. Hence the chosen
transfer price will no longer represent true opportunity costs in the two countries and
hence is not a suitable price to be collected if we are applying the economic approach to
index number theory.
40
Case 2: Country 2 (the Exporting Country) Is the Low Tax Country
In this case,
(27) T
1
> T
2
and the exporting country is the low business income tax jurisdiction. If we look at the
second line of (19), we see that when (27) holds, the term (T
1
-T
2
)wx is positive if w > 0
and x > 0. As before, note that this is the only term where w appears. Hence to
maximize overall profits, the multinational will want to choose w to be as large as
possible. This will make profits in the low tax country (country 2) as big as possible
compared to profits in the high tax country (country 1). If there are no constraints on the
multinational, the optimal choice of w would be a very large number. However, the tax
authorities in country 1 may object to this arbitrarily large solution for w, since it would
make taxable income in country 1 arbitrarily negative. A reasonable hypothesis in the
40
In the case where country 2 imposes the zero profits constraint (22), the “correct” price to collect from
the viewpoint of the economic approach to index number theory is the efficient transfer price w** defined
by (10). In the general case where the business income tax authorities in one or both countries impose the
arbitrary transfer price w
b
on the multinational, the firm will choose the x
b
that solves max
x
(1-T
1
)r
1
(p
1
,x)
- (1-T
2
)c
2
(p
2
,x) + (T
1
-T
2
)w
b
x. In the differentiable case, x
b
will satisfy the first order condition
(1-T
1
)∂r
1
(p
1
,x
b
)/∂x - (1-T
2
)∂c
2
(p
2
,x
b
)/∂x = (T
1
-T
2
)w
b
. The economic transfer price that should be
collected by the statistical agency in country 1 is the marginal revenue ∂r
1
(p
1
,x
b
)/∂x and the economic
transfer price that should be collected by country 2 is the marginal cost ∂c
2
(p
2
,x
b
)/∂x.
20
case where losses can be carried forward to offset taxable income in future periods might
be that the tax authorities in country 1 insist that the transfer price be low enough so that
profits are zero in country 1. This leads to the following constraint on w:
41
(28) wx = r
1
(p
1
,x).
Adding (28) as a constraint to the multinational’s profit maximization problem (19) leads
to the following global profit maximization problem:
(29) max
x,w
{(1-T
1
)r
1
(p
1
,x) - (1-T
2
)c
2
(p
2
,x) + (T
1
-T
2
)wx : wx = r
1
(p
1
,x)}
= max
x
{(1-T
1
)r
1
(p
1
,x) - (1-T
2
)c
2
(p
2
,x) + (T
1
-T
2
) r
1
(p
1
,x)} eliminating w
= max
x
{(1-T
2
)r
1
(p
1
,x) - (1-T
2
)c
2
(p
2
,x)} canceling terms
= (1-T
2
) max
x
{r
1
(p
1
,x) - c
2
(p
2
,x)}.
The last line of (29) shows that the multinational’s global profit maximization problem
under the zero profits constraint in the high tax country is equivalent to the efficient profit
maximization problem defined by (9) in the previous section. Hence, if the high tax
country imposes a zero profits constraint on the transfer price, the multinational will be
induced to make an efficient allocation of resources between the two countries.
However, although the allocation of resources will be globally efficient in this case, the
transfer price w**** that the multinational chooses in this case will usually be higher
than the efficient transfer price w** defined by (10) in the previous section. In order to
establish this result, we need to assume that when the allocation of resources is efficient
and the efficient transfer price w** is used, both establishments make positive profits;
i.e., assume again that (24) holds. Instead of choosing the efficient transfer price w**,
the multinational now chooses the profit maximizing transfer price w****, which is
consistent with (28) when x = x**; i.e., w**** satisfies the following equation:
(30) w**** ≡ r
1
(p
1
,x**)/x**.
Comparing (30) with the first equation in (24), we see that the profit maximizing transfer
price w**** will be greater than the efficient transfer price w** defined by (10); i.e., we
have:
(31) w**** > w**.
The result (31) was established under the hypothesis that the tax authorities in country 1
had enough knowledge about establishment 1’s costs to be able to impose the zero profits
constraint (28) on the transfer price. If the tax authorities do not have this knowledge,
41
This method for choosing a transfer price is roughly equivalent to the resale price
method that is described in the transfer pricing literature as follows: “Under the resale
price method, the tax auditor looks for firms at similar trade levels that perform similar
distribution functions (i.e., a functional comparable). The RP method is best used when
the distributor adds relatively little value to the product so that the value of its functions is
easier to estimate.” Lorraine Eden (1998; 40).
21
then there will be an incentive for the multinational to choose an even higher transfer
price than w**** in order to transfer profits out of the high tax jurisdiction.
In general, we can sum up the results for the case where (27) holds by stating that the
chosen transfer price will generally be higher than the efficient transfer price and that it
will no longer be the case that the chosen transfer price equals marginal cost in the
exporting country or marginal revenue in the importing country. Hence the chosen
transfer price will no longer represent true opportunity costs in the two countries and
hence is not a suitable price to be collected if we are applying the economic approach to
index number theory.
The above results rely somewhat on the ability of the tax authorities in the two
jurisdictions to be able to determine either the appropriate cost in the exporting country or
the appropriate net revenue or markup in the importing country. Needless to say, in
actual practice, it is difficult to determine costs or markups accurately. In the cost
context, Eden describes the situation as follows:
“In order to use the cost plus method, the tax authority or MNE
[Multinational Enterprise] must know the accounting approach adopted by
the unrelated parties. For example, what costs are included in the cost
base before the mark-up over costs is calculated? Is it actual cost or
standard cost (costs which have been standardized for cyclical
fluctuations in production as in the example in Box 1.5)? Are only
manufacturing costs (cost of goods sold, which includes labour, overhead
costs, including depreciation, and material input costs) included or is the
cost base the sum of manufacturing costs plus some portion of operating
costs (i.e., selling, general and administrative (SG&A) expenses and R&D
costs)? Lorraine Eden (1998; 42-43).
There are additional problems in allocating the cost of capital to various products,
including the problem of picking an appropriate benchmark rate of return to the firm’s
equity capital. Moreover, the problems involved in allocating joint costs over multiple
outputs are difficult indeed.
The main message that has been delivered in this section is this: when there are
differential rates of business income taxation in the two countries where two units of a
multinational engage in international trade, then the transfer prices that are reported by
the multinational are unlikely to represent true opportunity costs. Hence if the statistical
agency is using the economic approach to index number theory, these reported transfer
prices will generally be biased (and the direction of bias is indicated above).
In the following section, we assume that either business income taxation is absent in the
two countries or that the rates are equal and we focus on the distortions induced by trade
taxes.
9. Transfer Pricing with Trade Taxes and No External Market
22
We now consider the multinational’s profit maximization problem in the case where there
is no external market for the commodity (as in the previous sections) and there are no
business income taxes but there are trade taxes We assume that the importing country
(country 1) imposes a specific tax or tariff at the rate t
1
and an ad valorem tax at the rate
t
1
42
on each unit of x that is imported. We assume that the exporting country (country 2)
imposes a specific tax at the rate t
2
and an ad valorem tax at the rate t
2
43
on each unit of x
that is exported. If the multinational chooses the transfer price w > 0, then the
multinational’s global profit maximization problem is now:
(32) max
x,w
{r
1
(p
1
,x) - w(1+t
1
)x - t
1
x} + {w(1-t
2
)x - t
2
x - c
2
(p
2
,x)}
= max
x,w
r
1
(p
1
,x) - c
2
(p
2
,x) - (t
1
+ t
2
)x - w(t
1
+t
2
)x.
Comparing (32) with the no tax profit maximization problem (9) in section 7, we see that
there are two differences:
• The ad valorem trade tax rates, t
1
and t
2
, and the specific trade taxes, t
1
and t
2
,
lead to the terms (t
1
+ t
2
)x and w(t
1
+t
2
)x in the objective function. In particular,
the terms involving the transfer price w no longer cancel out as they did in (9) and
• The multinational now is now able to choose the transfer price w as well as the
level of international trade in the intermediate input x; i.e., instead of just
maximizing with respect to x, the firm now maximizes with respect to x and w.
In order to solve the firm’s global profit maximization problem, it is necessary to
consider two cases, depending on whether the ad valorem trade taxes are jointly positive
(this is the usual case) or jointly negative
Case 1: Ad Valorem Trade Taxes Are Jointly Positive
In this case,
(33) t
1
+ t
2
> 0.
If we look at the second line of (32), we see that the term - w(t
1
+t
2
)x is negative in this
case. Note also, that this is the only term where w appears. Hence to maximize overall
profits, the multinational will want to choose w to be as small as possible. If there are no
constraints on the multinational, the optimal choice of w would be w = 0.
44
However, the
trade tax authorities in at least one of the countries would almost certainly object to the
solution w = 0. It is difficult to specify what transfer price the border tax officials will
42
If the imports are subsidized by country 1, then t
1
and t
1
are negative or zero.
43
If the exports are subsidized by country 2, then t
2
and t
2
are negative or zero.
44
In this case, the multinational would choose x to satisfy ∂r
1
(p
1
,x)/∂x - ∂c
2
(p
2
,x)/∂x = (t
1
+ t
2
), which would not lead to the efficient allocation defined in section 7 unless the sum
of the specific taxes were equal to zero; i.e., unless (t
1
+ t
2
) = 0.
23
impose;
45
hence, we will assume that it is some positive number, say w
b
> 0. With this
exogenous choice for the transfer price w, the multinational’s profit maximization
problem (32) becomes:
(34) max
x
r
1
(p
1
,x) - c
2
(p
2
,x) - (t
1
+ t
2
)x - w
b
(t
1
+t
2
)x.
If the revenue and cost functions are differentiable and if x
b
solves (34), then the
following first order condition will be satisfied:
(35) ∂r
1
(p
1
,x
b
)/∂x - ∂c
2
(p
2
,x
b
)/∂x = (t
1
+ t
2
) + w
b
(t
1
+t
2
).
If by chance, the sum of the trade distortion terms on the right hand side of (35) is equal
to zero so that
(36) (t
1
+ t
2
) + w
b
(t
1
+t
2
) = 0,
then it can be seen that the solution to (34) is the efficient solution x** to (9); i.e., under
assumption (36), we will have x
b
= x** and using (35), we will also have
(37) ∂r
1
(p
1
,x
b
)/∂x = ∂c
2
(p
2
,x
b
)/∂x ≡ w**
so that marginal revenue and marginal cost in the two establishments will be equal to the
efficient transfer price w**. However, even in the case where (36) holds, it will not
generally be the case that the imposed transfer price w
b
is equal to w**. Hence, in
general:
(38) ∂r
1
(p
1
,x
b
)/∂x ≠ w
b
; ∂c
2
(p
2
,x
b
)/∂x ≠ w
b
.
In the general case where (t
1
+ t
2
) + w
b
(t
1
+t
2
) ≠ 0, then it will still be the case that the
inequalities in (38) will hold; i.e., in this case, it would only be by chance that we would
find that marginal revenue or marginal cost in the two establishments equal the border
authorities’ acceptable transfer price w
b
. Since the economic approach to index number
theory requires that the transfer price in establishment 1 be set equal to the marginal
revenue ∂r
1
(p
1
,x
b
)/∂x and the transfer price in establishment 2 be set equal to the marginal
cost ∂c
2
(p
2
,x
b
)/∂x, it can be seen that the transfer price that is acceptable to the border tax
authorities will not usually be an acceptable one for statistical purposes.
Case 2: Ad Valorem Trade Taxes Are Jointly Negative
In this case,
45
The border tax authorities will usually not have access to the information possessed by
the tax authorities in the two countries and so it will be difficult for them to impose the
zero profits constraint on either establishment as in the previous section. The transfer
price w
b
may not actually be imposed by the border trade authorities but it must be
acceptable to them.
24
(39) t
1
+ t
2
< 0.
If we look at the second line of (32), we see that the term - w(t
1
+t
2
)x is positive in this
case. Note, as in the previous case, that this is the only term where w appears. Hence to
maximize overall profits, the multinational will want to choose w to be as large as
possible. If there are no constraints on the multinational, the optimal choice of w would
be an arbitrarily large. However, the trade tax authorities in at least one of the countries
would almost certainly object to this solution and so again, they will impose some
acceptable transfer price w
b
> 0. With this exogenous choice for the transfer price w, the
multinational’s profit maximization problem (32) becomes (34) and the rest of the
analysis proceeds as in the previous case. Thus there is little difference in this case
compared to the previous case except in the present case, the multinational will want to
choose an acceptable transfer price w
b
that is as large as possible, whereas in the previous
case, the multinational wanted to choose an acceptable transfer price that was as small as
possible. In either case, it can be seen that the transfer price that is acceptable to the
border tax authorities will not usually be an acceptable one for statistical purposes.
10. Transfer Pricing with Trade and Profit Taxes and No External Market
We now consider the multinational’s profit maximization problem in the case where there
is no external market for the commodity (as in the previous sections) and there are
business income taxes as well as trade taxes. Using the definitions of the tax variables
made in the previous 2 sections, if the multinational chooses the transfer price w > 0, then
the multinational’s global profit maximization problem is now:
(40) max
x,w
(1-T
1
){r
1
(p
1
,x) - w(1+t
1
)x - t
1
x} + (1-T
2
){w(1-t
2
)x - t
2
x - c
2
(p
2
,x)}
= max
x,w
(1-T
1
)r
1
(p
1
,x) + (1-T
2
)c
2
(p
2
,x) - {[1-T
1
]t
1
+ [1-T
2
]t
2
}x
+ wx{[T
1
-T
2
] - (t
1
+t
2
) + [T
1
t
1
+T
2
t
2
]}
Comparing (40) with the no tax profit maximization problem (9) in the section 7, we see
that as usual, there are two differences:
• The ad valorem trade tax rates, t
1
and t
2
, the specific trade taxes, t
1
and t
2
, and the
income tax rates, T
1
and T
2
, lead to the terms {[1-T
1
]t
1
+ [1-T
2
]t
2
}x and
wx{[T
1
-T
2
] - (t
1
+t
2
) + [T
1
t
1
+T
2
t
2
]} in the objective function. In particular, the
terms involving the transfer price w no longer cancel out as they did in (9) and
• The multinational now is now able to choose the transfer price w as well as the
level of international trade in the intermediate input x.
In order to solve the firm’s global profit maximization problem, it is necessary to
consider two cases, as usual.
Case 1: Tax Gap Is Negative
In this first case, the term involving wx is negative; i.e., we assume that:
25
(41) [T
1
-T
2
] - (t
1
+t
2
) + [T
1
t
1
+T
2
t
2
] = [T
1
-T
2
] - [(1-T
1
)t
1
+ (1-T
2
)t
2
] < 0.
Note that sufficient conditions for condition (41) to hold are:
(42) T
1
- T
2
< 0 ;
(43) (1-T
1
)t
1
+ (1-T
2
)t
2
> 0.
Condition (42) means that the business income tax rate in country 1 (the importing
country) is less that the income tax rate in country 2 (the exporting country) and so (42)
corresponds to case 1 in section 8 above. Condition (43) says that an income tax adjusted
sum of the ad valorem trade taxes is positive. This condition corresponds roughly to case
1 in section 9 above.
46
Thus case 1 in the present section corresponds to a situation
where either the business income tax rate in the importing country is lower than in the
exporting country or income tax adjusted ad valorem trade taxes are positive or both
conditions (42) and (43) hold. In any case, if condition (41) holds, in order to maximize
overall profits, the multinational will want to choose w to be as small as possible. As
usual, if there are no constraints on the multinational, the optimal choice of w would be w
= 0. However, the trade tax authorities and the income tax authorities in at least one of
the countries would almost certainly object to the solution w = 0. It is difficult to specify
what transfer price the border tax officials will impose in the present situation.
47
Hence,
we will assume that it is some positive number, say w
b
> 0. With this exogenous choice
for the transfer price w, the multinational’s profit maximization problem (40) becomes:
(44) max
x
(1-T
1
)r
1
(p
1
,x) + (1-T
2
)c
2
(p
2
,x) - {[1-T
1
]t
1
+ [1-T
2
]t
2
}x
+ w
b
x{[T
1
-T
2
] - (t
1
+t
2
) + [T
1
t
1
+T
2
t
2
]}.
If the revenue and cost functions are differentiable and if x
b
solves (44), then the
following first order condition will be satisfied:
(45) (1-T
1
)∂r
1
(p
1
,x
b
)/∂x - (1-T
2
)∂c
2
(p
2
,x
b
)/∂x = [1-T
1
]t
1
+ [1-T
2
]t
2
+ w
b
{[T
1
-T
2
] - (t
1
+t
2
) + [T
1
t
1
+T
2
t
2
]}.
In this case, the economic transfer price in the importing country is the marginal revenue
∂r
1
(p
1
,x
b
)/∂x. The economic transfer price in the exporting country is the marginal cost
∂c
2
(p
2
,x
b
)/∂x. Only by chance would these transfer prices be equal to the transfer price
46
It corresponds exactly to case 1 in section 9 if T
1
= T
2
so that the business income tax
rates in the two countries are equal.
47
The border tax authorities will usually not have access to the information possessed by
the tax authorities in the two countries and so it will be difficult for them to impose the
zero profits constraint on either establishment as in the previous section. The transfer
price w
b
may not actually be imposed by the border trade authorities but it must be
acceptable to them.
26
that is acceptable to the border tax authorities, w
b
.
48
Hence, in general:
(46) ∂r
1
(p
1
,x
b
)/∂x ≠ w
b
; ∂c
2
(p
2
,x
b
)/∂x ≠ w
b
.
Since the economic approach to index number theory requires that the transfer price in
establishment 1 be set equal to the marginal revenue ∂r
1
(p
1
,x
b
)/∂x and the transfer price in
establishment 2 be set equal to the marginal cost ∂c
2
(p
2
,x
b
)/∂x, it can be seen that the
transfer price that is acceptable to the border tax authorities w
b
will not usually be an
acceptable one for statistical purposes.
Case 2: Tax Gap Is Positive
In the second case, the term involving wx is positive; i.e., we assume that:
(47) [T
1
-T
2
] - (t
1
+t
2
) + [T
1
t
1
+T
2
t
2
] = [T
1
-T
2
] - [(1-T
1
)t
1
+ (1-T
2
)t
2
] > 0.
Note that sufficient conditions for condition (47) to hold are:
(48) T
1
- T
2
> 0 ;
(49) (1-T
1
)t
1
+ (1-T
2
)t
2
< 0.
Condition (48) means that the business income tax rate in country 1 (the importing
country) is greater that the income tax rate in country 2 (the exporting country) and so
(48) corresponds to case 2 in section 8 above. Condition (49) says that an income tax
adjusted sum of the ad valorem trade taxes is negative. This condition corresponds
roughly to case 2 in section 9 above. Thus case 2 in the present section corresponds to a
situation where either the business income tax rate in the importing country is greater
than in the exporting country or income tax adjusted ad valorem trade taxes are negative
or both conditions (48) and (49) hold. In any case, if condition (47) holds, in order to
maximize overall profits, the multinational will want to choose w to be as large as
possible. If there are no constraints on the multinational, the optimal choice of w would
be an arbitrarily large. However, the tax authorities in at least one of the countries would
almost certainly object to this solution and so again, they will impose some acceptable
transfer price w
b
> 0. With this exogenous choice for the transfer price w, the
multinational’s profit maximization problem (40) becomes (44) and the rest of the
analysis proceeds as in the previous case. Thus there is little difference in this case
compared to the previous case except in the present case, the multinational will want to
choose an acceptable transfer price w
b
that is as large as possible, whereas in the previous
case, the multinational wanted to choose an acceptable transfer price that was as small as
possible. In either case, it can be seen that the transfer price that is acceptable to the tax
authorities will not usually be an acceptable one for statistical purposes.
48
Recall that in this case, the multinational will try to choose the acceptable transfer price
w
b
to be as small as possible so there will be a tendency for the economic transfer prices
to be above w
b
.
27
In the following sections, we turn our attention to the problem of estimating the economic
transfer prices, ∂r
1
(p
1
,x
b
)/∂x and ∂c
2
(p
2
,x
b
)/∂x.
11. Constructing an Economic Transfer Price for Exports
In this section, we consider the problem of how to construct an approximation to the
economic transfer price for the exporting country.
49
In the following section, we will
consider the problem of how to construct an approximation to the economic transfer price
for the importing country.
50
In the case of no tax distortions, the economic transfer price
will coincide with the external market transfer price or the efficient transfer price.
Suppose that the producing establishment has a constant returns to scale technology
51
;
i.e., if all inputs are doubled, then output is also doubled. Then the net cost function
defined by (3) will have the following decomposition
52
:
(50) c
2
(p
2
,x) = c
2
(p
2
,1)x for all x > 0 ;
i.e., the total establishment 2 cost of producing x units of the traded intermediate input,
c
2
(p
2
,x), is equal to the cost of producing one unit of the traded commodity, c
2
(p
2
,1),
times the number of units produced, x.
Let the observed net input vector for the exporting establishment 2 during the period
under consideration be z
2b
and let x
b
be the establishment’s observed output of x during
the same period. Then under the assumption that the establishment is cost minimizing
during the period, the observed total cost of producing x
b
is:
(51) c
2
(p
2
,x
b
) = p
2
⋅z
2b
.
Now differentiate (50) with respect to x and we find that the marginal cost of x is the
following constant for all x > 0:
(52) ∂c
2
(p
2
,x)/∂x = c
2
(p
2
,1) for all x > 0
= c
2
(p
2
,1)x
b
/x
b
= c
2
(p
2
,x
b
)/x
b
using (50)
= p
2
⋅z
2b
/x
b
using (51).
Thus under the assumption of a constant returns to scale technology, the unknown
marginal cost ∂c
2
(p
2
,x
b
)/∂x which occurs in (45) and which we have identified as the
economic transfer price for the exporting establishment, w
e
say, is exactly equal to the
49
Recall that this transfer price is the marginal cost ∂c
2
(p
2
,x
b
)/∂x.
50
Recall that this transfer price is the marginal revenue ∂r
1
(p
1
,x
b
)/∂x.
51
Technically, this means that the set S
2
which appears in (3) is a cone. This means that
if (z
2
,x
2
) belongs to S
2
and the scalar l is greater than 0, then (lz
2
,lx
2
) also belongs to S
2
.
52
See Diewert (1993; 120).
28
observable total cost of producing x
b
units, c
2
(p
2
,x
b
) = p
2
⋅z
2b
, divided by the output
produced, x
b
; i.e.,
(53) w
e
≡ p
2
⋅z
2b
/x
b
.
Thus we have an observable exact estimator for the economic transfer price ∂c
2
(p
2
,x
b
)/∂x
defined in the previous section.
It is clear that the transfer price w
e
defined by (53) is a cost based estimate which is very
close to the Cost Plus method for estimating transfer prices described in Eden (1998; 42)
(2002; 33).
53
Some limitations on using (53) as a practical transfer price should be kept in mind. These
limitations are:
• It was necessary to assume constant returns to scale in production for the
exporting establishment in order to derive (53).
• The result works only if the exporting establishment is producing only one
product that is subject to transfer pricing.
• The desired transfer price is to be representative for a reference week or month.
However, typically, establishment accounting data are only available on a
quarterly basis
54
and so the w
e
defined by (53) can only be a average of several
economic transfer prices that are applied to the weeks or months in the quarter.
The last two limitations provide significant difficulties for statistical agencies that might
want to use the cost based transfer price defined by (53) as an export price in their export
price index, since typically establishments produce many products or models and hence,
the assumption that the establishment produces only one product that is subject to transfer
pricing is rather unlikely to hold. Similarly, if the statistical agency must produce an
export price index every month that is not subject to revision, then it cannot wait for
accounting data to become available some months later than the current period.
12. Constructing an Economic Price for Imports
Suppose now that the importing establishment has a constant returns to scale
53
“The method starts with the costs of production, measured using recognized accounting
principles, and then adds an appropriate markup over costs. ... Are only manufacturing
costs (costs of goods sold, which includes labour, overhead costs, including depreciation
and material input costs) included or is the cost base the sum of manufacturing costs plus
some portion of operating costs (i.e., selling general and administrative (SG&A)
expenses and R&D costs)? The larger the cost base (i.e., the more items put below the
line and thus into the cost base), the smaller should be the profit markup, or gross margin,
over costs.” Lorraine Eden (1998; 42-43).
54
Managerial accounting data may be available for shorter time intervals.
29
technology.
55
Then the net revenue function defined by (2) will have the following
decomposition:
(54) r
1
(p
1
,x) = r
1
(p
1
,1)x for all x > 0 ;
i.e., the establishment 1 net revenue that can be raised if x units of the traded intermediate
input are available, r
1
(p
1
,x), is equal to the net revenue that can be raised if 1 unit of the
traded intermediate input is available, r
1
(p
1
,1), times the number of intermediate units
purchased, x.
Let the observed net output vector for establishment 1 during the period under
consideration be y
1b
and let x
b
be the establishment’s observed imports of x during the
same period. Then under the assumption that the establishment is maximizing net
revenues during the period, the observed establishment net revenue excluding any charge
for the imports of x is:
(55) r
1
(p
1
,x
b
) = p
1
⋅y
1b
.
Now differentiate (54) with respect to x and we find that the marginal revenue for an
extra unit of x is the following constant for all x > 0:
(56) ∂r
1
(p
1
,x)/∂x = r
1
(p
1
,1) for all x > 0
= r
1
(p
1
,1)x
b
/x
b
= r
1
(p
1
,x
b
)/x
b
using (54)
= p
1
⋅y
1b
/x
b
using (55).
Thus under the assumption of a constant returns to scale technology, the unknown
marginal revenue for establishment 1, ∂r
1
(p
1
,x
b
)/∂x which occurs in (45) and which we
have identified as the economic transfer price for the importing establishment, w
i
say, is
exactly equal to the observable total net revenue (excluding any cost for the imports) that
establishment 1 can raise provided it imports x
b
units, p
1
⋅y
1b
, divided by the amount
imported, x
b
. Hence if we define the observable transfer price for the importing
establishment w
i
as the last expression on the right hand side of (56) so that
(57) w
i
≡ p
1
⋅y
1b
/x
b
,
then under the constant returns to scale assumption for establishment 1, we have an
observable exact estimator for the efficient transfer price ∂r
1
(p
1
,x
b
)/∂x defined in
equation (45) in section 10.
It can be seen that the transfer price for the importing establishment, w
i
defined by (57),
is a revenue based estimate, which is somewhat related to the Resale Price method for
55
Technically, this means that the set S
1
which appears in (2) is a cone. This means that
if (y
1
,x
1
) belongs to S
1
and the scalar l is greater than 0, then (ly
1
,lx
1
) also belongs to S
1
.
30
estimating transfer prices described in Eden (1998; 40) (2001; 33).
56
If the imported
commodity is distributed to domestic demanders in substantially unchanged form, then w
i
is essentially the average selling price of the commodity to the demanders less the per
unit costs of selling and distribution. However, if the commodity is substantially
transformed by the importer before it is sold to third parties, then w
i
is the average selling
price of the transformed commodity less the per unit costs of manufacturing, distribution
and selling.
Some limitations (similar to the limitations on using (53) in the previous section) on
using (57) as a practical transfer price are:
• It was necessary to assume constant returns to scale in production for the
importing establishment in order to derive (57).
• The result works only if the importing establishment is using only one input that is
subject to transfer pricing.
• The desired transfer price is to be representative for a reference week or month.
However, typically, establishment accounting data are only available on a
quarterly basis and so the w
i
defined by (57) can only be a average of several
economic transfer prices that are applied to the weeks or months in the quarter.
In spite of the above limitations, in section 13, we recommend that a modification of this
net revenue method for constructing a transfer price be used in a wide variety of
circumstances. If the commodity is not substantially transformed by the importing
establishment, then the modification is to use the importer’s selling price of the
commodity to third parties as a proxy for the transfer price.
57
This price will move
proportionally to the net revenue transfer price w
i
provided that per unit manufacturing,
distribution and selling costs of the imported commodity are a constant proportion of the
selling price to third parties. This method will not work well if the imported commodity
is substantially transformed by the importer and the imported good makes up a small
fraction of the cost of the finished good.
If data on both the importing and exporting establishment are available, then we could
56
“If the chosen firm is the importer (distributor), the government estimates the normal
gross profit margin earned by unrelated distributors performing the same or similar
functions to the related party (contract distributors) and subtracts this gross return from
the retail price to find the transfer price. This method is called the resale price (RP)
method (Eden 2001; 33). Thus in (57), the estimated transfer price is based on the net
revenues of the actual importing firm, not comparable importing firms (which may not
exist).
57
This same method can be used in the context of an exporting establishment that exports
a commodity only to affiliated establishments abroad. A proxy for the exporter’s transfer
price to a particular foreign establishment could be foreign (importing) establishment’s
selling price of the commodity to unrelated parties. However, the collection of this latter
price would entail price collectors working in the foreign country or the cooperation of
the foreign statistical agency in collecting the relevant prices.
31
calculate both the cost based estimate for the exporting establishment’s transfer price w
e
and the revenue based estimate for the importing establishment’s transfer price w
i
.
However, if we assume constant returns to scale in production for both the exporting and
importing establishments, then the profit maximization problem defined by (44) breaks
down; i.e., with constant returns to scale in both establishments, (44) becomes, using (50)
and (54):
(58) max
x
(1-T
1
)r
1
(p
1
,x) + (1-T
2
)c
2
(p
2
,x) - {[1-T
1
]t
1
+ [1-T
2
]t
2
}x
+ w
b
x{[T
1
-T
2
] - (t
1
+t
2
) + [T
1
t
1
+T
2
t
2
]}
= max
x
[(1-T
1
)r
1
(p
1
,1) + (1-T
2
)c
2
(p
2
,1) - {[1-T
1
]t
1
+ [1-T
2
]t
2
}
+ w
b
{[T
1
-T
2
] - (t
1
+t
2
) + [T
1
t
1
+T
2
t
2
]}]x.
Thus the multinational’s objective function is linear in x under the assumption of
constant returns to scale in both the importing and exporting establishment. Hence if
(59) (1-T
1
)r
1
(p
1
,1) + (1-T
2
)c
2
(p
2
,1) - {[1-T
1
]t
1
+[1-T
2
]t
2
}
+ w
b
{[T
1
-T
2
] - (t
1
+t
2
) + [T
1
t
1
+T
2
t
2
]} > 0,
then the optimal x solution to (58) is x = +•. If on the other hand,
(60) (1-T
1
)r
1
(p
1
,1) + (1-T
2
)c
2
(p
2
,1) - {[1-T
1
]t
1
+[1-T
2
]t
2
}
+ w
b
{[T
1
-T
2
] - (t
1
+t
2
) + [T
1
t
1
+T
2
t
2
]} < 0,
then the optimal x solution to (58) is x = 0. Thus the assumption of constant returns to
scale in both establishments is not consistent with the existence of a finite positive x
solution to our global profit maximization problem unless the inequalities (59) or (60)
hold as equalities, which is a knife edge case unlikely to hold in practice.
58
The analysis in this section and the previous one can be summarized as follows: in
practice, it will not be possible for the price statistician to estimate economic transfer
prices with any degree of accuracy even in the simplest case where the exporting and
importing establishments are trading only a single commodity. In the many commodity
case, the difficulties are even greater: econometric techniques would have to be
employed
59
and different econometricians would come up with very different transfer
prices; i.e., the issue of reproducibility of the estimates would become important.
58
An alternative way around this difficulty would be to relax the assumption of price
taking behavior on the part of the multinational. This relaxation introduces other
formidable difficulties for the price statistician who wishes to use the economic approach
to index number theory; see Frisch (1936). See the Appendix for a discussion of the
implications of price making behavior for the efficient transfer price.
59
We would have to estimate econometrically the cost function c
2
(p
2
,x,t) and the revenue
function r
1
(p
1
,x,t), where x is now a vector of traded commodities. Note that each
function is now a function of time t as well in order to allow for the possibility of
technical progress.
32
12. Which Transfer Prices Can Be Usefully Collected?
As one can see, the validity of using transfer prices, either one reported by the respondent
or one constructed by from outside, is rather suspect. The price associated with a
transaction between unaffiliated parties reveals very useful information. In this situation,
one party wishes to make the price as small as possible while the other party wishes to
make it as large as possible. For the minimizing party (the importer), the price should not
exceed the marginal revenue that can be generated by the last unit of the imported
commodity. For the maximizing party (the exporter), the price should not be less than
the full marginal cost of producing the last unit of the sale. However, the transfer price
that is used to value international trades between affiliated establishments in general tells
us nothing about marginal costs and marginal revenues: this transfer price will be chosen
strategically by a profit maximizing multinational in order to maximize its global after-
tax profits. Hence, in general, it will not be useful for a statistical agency to collect such
a strategically chosen transfer price. Nor would it be easy to construct one. What then
should be collected?
(a) Recommended Transfer Pricing Methods for Profit and Trade Tax Purposes
For income taxation and customs valuation purposes, the OECD Transfer Pricing
Guidelines (OECD, 1995) recommend MNEs and national tax authorities follow the
arm’s length standard, that is, set the transfer price equal to the price that two unrelated
parties would negotiate when trading the same or substantially similar products under the
same or substantially similar circumstances.
All OECD countries, and many non-OECD member countries, follow the OECD
Guidelines by requiring MNEs to report their transfer prices using the best method (that
is, the most appropriate method given the facts and circumstances) selected from a set of
acceptable transfer pricing methods (Eden, 1998; Feinschreiber, 2004). Key to selection
of the best method is the concept of comparability. Transactions are considered
comparable when their “economically relevant characteristics” are the same, or if they
differ, the differences have no material impact on the results. The attributes of a
transaction that can affect comparability are (OECD, 1995, Chapter I. paragraphs 1.15-
1.17):
• Specific characteristics of the traded product (e.g., weight, quality, product
maturity, whether intangibles are bundled with tangibles)
• Functions performed by the parties to the transaction (e.g., manufacturing,
distribution, purchasing, marketing)
• Contractual terms of the transaction (e.g., warranties, rights, payment and credit
terms)
• Economic circumstances of the parties (e.g., wholesale versus retail level,
geographic location and relative size of the markets, market competition)
• Business strategies of the parties (e.g., market penetration strategies)
In practice, since internal and external transactions are unlikely to be exact comparables,
33
the OECD Guidelines recommend that material differences be identified, quantified and
adjusted for in determining the arm’s length transfer price. Moreover, since transfer
pricing is not an exact science, the Guidelines recommend that transfer prices be set
inside a range of acceptable arm’s length prices, called the arm’s length range.
The arm’s length transfer price can be measured using either an internal comparable or
external comparable to the intra-firm transaction. An internal or in-house comparable is
a product traded by the MNE on both the internal and external markets, under
substantially the same or similar circumstances. For example, a Ford affiliate might buy
an auto part from a sister subsidiary and also buy the same part from an arm’s length
supplier such as TRW. An external comparable is a transaction, similar to the intra-firm
transaction, which occurs between two unrelated firms. For example, the transfer price
for an auto part traded between two Ford affiliates could be proxied by an arm’s length
transaction between TRW and General Motors.
Tax authorities typically view an internal or in-house comparable where the MNE sells
(buys) the same product from an unaffiliated firm as it sells (buys) in-house as having a
higher degree of comparability, in general, than an external comparable. There is a higher
probability that the facts and circumstances are the same or similar (or, alternatively, a
lower probability of potential errors and omissions) for in-house comparables, and thus,
the “economically relevant characteristics of the transaction” are more likely to be the
same.
There are five acceptable transfer pricing methods for income tax purposes: comparable
uncontrolled price (CUP), the cost plus method, the resale price (minus) method, the
transactional net margin method (TNMM)
60
and the profit split method. Customs
authorities typically require merchandise imports to be priced using one of three methods:
transaction value (equivalent to CUP), computed value (similar to cost plus) or deductive
value (similar to resale price). Most national tax authorities, but not all (e.g., the U.S.),
rank these methods, with CUP for income tax purposes and transaction value for customs
valuation being preferable to the others because they most closely fulfill the conditions
required by the arm’s length standard.
The reasoning developed by income tax and customs valuation authorities should have
relevance for other statistical agencies. While their purposes in collecting transfer prices
may not be the same, the agencies share a desire for pricing to reflect economically
relevant characteristics of the market. We follow this line of reasoning below, in
developing recommendations for selecting transfer prices to be used in international price
index programs.
(b) Recommended Transfer Pricing Methods for the International Price Program
60
In the United States, TNMM is replaced by the comparable profit method (CPM). The
IRS argues that the two methods are basically equivalent. Others argue there are
recognizable differences. See Eden (1998) and Feinschreiber (2004).
34
The primary goal of the BLS International Price Program (IPP) is “to produce accurate
and timely price indexes for both U.S. exports and imports” (BLS IPP Manual, Chapter I,
“Overview of the International Price Program”, p. 3). The Manual states (p.7):
To ensure uniformity and to create indexes which show pure price changes
in “the real world” the IPP uses actual transaction prices from reporters
whenever possible. Actual transaction prices provide the most accurate
reflection of prices faced by buyers and sellers in item markets.
Because the IPP produces indexes rather than actual prices, the statistical agency’s goals
are somewhat different from those of income tax and customs authorities. First, in the
case of taxes and tariffs, the relevant agencies do want to know the exact price paid or
payable in order to determine the applicable tax on the transaction or profits from the
transaction. The arm’s length standard is designed to ensure that the MNE sets a transfer
price that proxies the price that would be selected by unrelated firms. Second, customs
and tax authorities are interested in a particular firm and taxing its transactions or profits.
For the BLS export and import price index calculations, on the other hand, actual
transaction prices are required as the first step in calculating price changes of product
groups (ELIs, entry level items) aggregated across firms. Thus, movements in prices are
more important than the level of prices, and representative firms and transactions are
more important than any individual firm or transaction. Thus, the appropriate transfer
pricing methods for calculating international price indexes may differ somewhat from
those for paying income taxes and customs duties, even if all three statistical agencies
adhere to the arm’s length standard. We explore this below.
Case 1: Exports
For an exporting establishment, we recommend the following ordering of alternative
collection strategies, in order of their merit, starting with the best method first. The
ranked methods are:
a. Internal Comparable: If the same or a sufficiently similar product is sold by the MNE
affiliate, under the same or substantially similar circumstances, to an unaffiliated third
party during the reference period, use that price
61
for the sales of the commodity to
affiliated parties rather than the transfer price. Where the same product is exported
under the same circumstances to both affiliated and unaffiliated firms, we have an
exact internal comparable (or exact internal CUP).
62
Where the circumstances are
61
It may be necessary to make adjustments for transport costs and alternative tax
treatments.
62
For example, suppose Ford-US exports finished cars to an affiliated distributor in
Germany and to an arm’s length distributor in France. If wholesale trade between France
and Germany in finished cars is unrestricted, it may be possible to use the arm’s length
price in France, adjusted for material differences, to proxy for the transfer price to the
German affiliate.
35
sufficiently similar and differences can be identified, quantified and adjusted, we
have an inexact internal comparable(or inexact internal CUP). It does not matter
whether the unaffiliated sales are domestic or international for most purposes, as long
as differences can be identified, quantified and adjusted for. Exact comparables are,
of course, preferable to inexact comparables, where they exist.
b. Externally Referenced Comparable: If alternative (a) is not available, but there is a
recognized domestic or international exchange (e.g., the London Metal Exchange, the
Chicago Mercantile Exchange) that trades in the product, use the price on the
exchange for the reference period, making any necessary adjustments to ensure that
the economically relevant characteristics of the transactions are sufficiently similar. It
does not matter whether the reference exchange is domestic or international for most
purposes, as long as differences can be identified, quantified and adjusted for.
63
c. External Comparable: If alternatives (a) and (b) are not available, attempt to find a
foreign or domestic market price for the product traded between two unaffiliated
traders under the same or substantially similar circumstances, and make adjustments
for any material differences.
64
It does not matter whether the external transaction is
domestic or international for most purposes, as long as differences can be identified,
quantified and adjusted for.
d. Downstream (and Upstream) Internal Transactions: If alternatives (a), (b) and (c) are
not available, then attempt to collect the first arm’s length price of a downstream
product that uses the intermediate good as a major input. In the simplest case, the
exported good will be a finished good and the downstream sale will be to arm’s
length distributors.
65
In more complex cases, the intra-firm transaction will be in
unfinished parts or subassemblies that undergo further processing in the foreign
affiliate prior to final sale. If the final product is sold through different channels to
many downstream buyers, possibly located in different countries, it may be difficult
to trace and identify appropriate transactions for comparison purposes. In such cases,
63
The primary differences are likely to be additional costs for transportation, insurance
and foreign currency transactions.
64
Such prices may be available from the country’s Producer Price Index program or from
industry sources. Note that this strategy might imply a cooperative collection strategy
with other countries.
65
For example, if GM-US exports finished cars to GM-Germany, collect the downstream
selling price from GM-Germany to an unaffiliated GM dealer in Germany and adjust for
any differences in price movements due to differences in the trade levels. This is similar
to the resale price method (for tax purposes) and the deductive method (for customs duty
purposes) where an arm’s length gross profit margin is deducted from the final market
price to determine the transfer price. The key difference is that the export price index is
not interested in calculating the gross margin, per se, but rather in whether movements of
the downstream price to the arm’s length distributor in Germany is a good proxy for
movements in the transfer price of exported finished cars from the U.S. parent to its
German affiliate.
36
it may be easier to trace downstream transactions in the U.S. (domestic) market, and,
even in this situation there may be many buyers at different arm’s length prices. The
closer the exported product is to final sale, the more likely it should be to obtain
downstream internal comparables.
66
e. Declared Transfer Price: If none of the above alternatives is available, the
international price program should collect the exporting firm’s listed transfer price
along with a brief description of its type. The data collector should also determine if
the transfer price is market-based or cost-based. If the latter, the collector should
identify whether a profit component is attached or not (the “plus” in cost plus, as
compared to standard or actual cost without any “plus”).
67
Case 2: Imports
For an importing establishment, we suggest the following ordering of alternative
collection strategies, in order of their merit:
a. Internal Comparable: If the same commodity is purchased from an unaffiliated third
party during the reference period, then use that price
68
for the purchases of the
commodity from affiliated parties rather than the transfer price. It does not matter
whether the unaffiliated purchases are domestic or international for most purposes.
Where the same product is imported under the same circumstances from both an
affiliated and an unaffiliated firm, we have an exact internal comparable. Where the
circumstances are sufficiently similar and differences can be identified, quantified
and adjusted, we have an inexact internal comparable. It does not matter whether the
unaffiliated purchases are domestic or international for most purposes, as long as
differences can be identified, quantified and adjusted for. Exact internal comparables
are, of course, preferable to inexact internal comparables, where they exist.
b. Externally Referenced Comparable: If alternative (a) is not available, but there is a
66
It may also be possible to determine an arm’s length price by going upstream from the
intrafirm transaction. This would be appropriate only in cases where little additional
value is added in moving to the downstream stage. This situation resembles the cost plus
method, whereby a gross profit margin for arm’s length firms is added to costs to
determine the transfer price. For the IPP, the relevant question is whether upstream costs
move in a similar fashion to costs of the intrafirm product. For example, the Producer
Price Index might be a relevant substitute for some intrafirm transactions where there are
no external comparables.
67
Most intermediate transfers are at mandated full costs for cost centers, and at full cost
plus a profit mark-up for profit centers (Feinschreiber, 2004, p. 18). It would also be
useful to know whether the affiliate had the responsibility for setting the transfer pricing,
either wholly or shared with its trading partner, or whether the transfer price was
mandated by the parent firm.
68
It may be necessary to make adjustments for transport costs and alternative tax
treatments.
37
recognized domestic or international exchange (e.g., the London Metal Exchange, the
Chicago Mercantile Exchange) that trades in the product, use the price on the
exchange for the reference period, making any necessary adjustments to ensure that
the economically relevant characteristics of the transactions are sufficiently similar. It
does not matter whether the reference exchange is domestic or international for most
purposes, as long as differences can be identified, quantified and adjusted for.
c. External Comparable: If alternatives (a) and (b) are not available, attempt to find a
foreign or domestic market price for the product traded between two unaffiliated
traders under the same or substantially similar circumstances, and make adjustments
for any material differences. It does not matter whether the external transaction is
domestic or international for most purposes, as long as differences can be identified,
quantified and adjusted for.
d. Downstream (and Upstream) Internal Transactions: If alternatives (a), (b) and (c) are
not available, then attempt to collect the first arm’s length price of a downstream
product that uses the intermediate good as a major input. In the simplest case, the
imported good will be a finished good and the downstream sale will be to arm’s
length distributors.
69
In more complex cases, the intra-firm transaction will be in
unfinished parts or subassemblies that undergo further processing in the U.S. affiliate
prior to final sale. It is possible in such cases that the final product will be sold
through different channels to many downstream buyers, not only in the U.S. but
abroad, making it difficult to trace and identify appropriate transactions for
comparison purposes. The closer the imported product is to the finished stage, the
more likely it should be to obtain downstream internal comparables. Again, similar
to the situation with exports, it may be possible to find arm’s length upstream prices
that can be used to replace the transfer price of the imported product (but this would
typically involve cooperation with statistical agencies in the exporting country
although internet search for prices is a possibility).
e. Declared Transfer Price: If none of the above alternatives is available, the
international price program should collect the importing firm’s listed transfer price
along with a brief description of its type. The data collector should also determine if
the transfer price is market-based or cost-based. If the latter, the collector should
identify whether a profit component is attached or not.
( c) Practical Issues in Selecting the Best Method
69
For example, if Toyota-Japan sells a finished car to Toyota-US, the IPP should collect
the selling price from Toyota-US to an unaffiliated Toyota dealer in the United States and
adjust for the difference in trade levels. While this looks similar to the resale price
method for tax and customs duty purposes, the key difference is that the import price
index is not interested in calculating the gross margin, per se, but rather in whether
movements of the downstream price to the arm’s length U.S. distributor is a good proxy
for movements in the transfer price of exported finished cars from Toyota-Japan to
Toyota-US.
38
We have outlined, and ranked, five methods for determining an acceptable transfer price
for constructing international price indexes: (a) internal comparable, (b) externally
referenced price, (c) external comparables, (d) downstream (and possibly upstream)
internal transactions, and (e) the declared transfer price. Our analysis and ranking were
theoretically driven. In this section, we discuss some issues of moving from theory to
practice.
First, note that the transfer pricing methods outlined above bear a close resemblance to
those recommended by the OECD Transfer Pricing Guidelines in that they stress the
importance of comparing economically relevant characteristics, and typically (but not
always) prefer internal to external comparables. In such cases, if the MNE states that its
transfer price does follow the same method as the IPP is attempting to collect, that
transfer price should be collected. For example, collection strategy (a), Internal
Comparables, is the top preferred method for intrafirm exports. If the MNE states that its
transfer price is based on an exact or inexact internal comparable, the transfer price
should be collected by the IPP.
Second, in comparing which collection strategy should be selected by the statistical
agency, the issues of feasibility and administrative costs are important considerations.
For example, suppose the MNE respondent states that its declared transfer price follows
method (b), an External Comparable on a Reference Exchange. While method (a),
Internal Comparable, is theoretically preferable, the costs and time involved in collecting
this information may outweigh the additional reliability. The statistical agency should, in
these situations, collect the declared transfer price that follows method (b), even where in
theory method (a) is preferable. Similarly, if the MNE’s transfer price is based on method
(c), accepting that transfer price may be preferable to the additional time and costs
involved in determining the arm’s length price using method (a) or (b).
70
Third, it might be thought that the multinational’s posted transfer price would be
acceptable for statistical purposes, provided that the multinational uses the same set of
transfer prices for both management and tax purposes. In a recent survey, Ernst and
Young (2001; 6) report that 77% of multinationals responding to their survey used the
same set of transfer prices for both purposes,
71
which seems encouraging at first glance
since transfer prices for managerial purposes should approximate economic transfer
prices based on opportunity costs. However, the same Ernst and Young survey also
reveals that these dual purpose transfer prices are frequently heavily influenced by tax
70
Moreover, given the reluctance of firms to share transfer pricing information when
compliance is voluntary, the statistical agency may fail to collect any price if the firm
perceives a request for detailed information as a ‘fishing expedition’ or something that
could potentially be used by another agency to collect more income or trade taxes.
71
“According to the 2001 survey responses, over three quarters of MNC parents (77%)
reported using the same set of transfer prices for both tax and management purposes.”
Ernst and Young (2001; 6).
39
considerations.
72
Thus, the existence of one – as opposed to two – sets of books is
insufficient justification for accepting the MNE’s stated transfer price for purposes of
calculating export and import price indexes. Rather, the key issue is whether the MNE
uses an economically acceptable transfer pricing methodology.
Fourth, although in most cases, strategy (a) will be preferred, there are circumstances
when this strategy may not be very reliable, such as:
• The sales to the unaffiliated parties are relatively small and sold at prices that are
“abnormally” high or low.
Lastly, if there are no sales to unaffiliated parties during the reference period, then
methods (b) or (c) should be used. However, these strategies can fail under some
circumstances:
• The exporting establishment may be shipping a proprietary product to units of a
multinational firm in other countries for further processing and there is no
openly traded market for the product anywhere in the world.
73
• The open market for trades in the product may be small and unrepresentative of
the bulk of the trades in the commodity or price movements in this open market
could be very volatile.
14. Conclusion
We have attempted to show above that in a world where there are taxes on international
transactions or where the rates of business income taxation differ across countries, then a
multinational enterprise has financial incentives to choose strategically a transfer price to
reduce the amount of taxation paid in the importing and exporting countries. This
strategically chosen transfer price will generally be very different from an economic
transfer price (based on opportunity costs) that would be suitable for an import or export
price index. Since international trade between affiliated units is somewhere in the
neighborhood of 30 to 40 percent of world trade, it can be seen that this problem of
determining appropriate transfer prices is a huge one.
Our first best alternative to the firm’s listed transfer price is an internal comparable; that
is, the average price paid to (for an imported commodity) or received from (for an
72
“Of those using the same transfer price, about half (52%) use a compromise between
satisfying tax requirements and achieving management/operational objectives, while a
quarter (26%) and a fifth (21%) base it primarily on tax management/operations
respectively.” Ernst and Young (2001; 6).
73
In this case, if the proprietary product is a major component of a product that is traded
between unaffiliated parties, then the price of this latter product could be used as a proxy
for the transfer price.
40
exported commodity) unaffiliated firms for the same commodity during the reference
period, if such unaffiliated purchases or sales exist. If there are no such unaffiliated
purchases or sales, then we recommend the use of an externally referenced comparable,
that is, the price of the commodity on a recognized exchange that trades in the
commodity if such an exchange exists. If no such exchange exists, then we recommend
attempting to find an external comparable price based on transactions between
unaffiliated traders. These three methods all focus on the price of the same product traded
by different firms. Where this is impossible, the price collector could look at downstream
prices, or potentially upstream prices, to see whether an economically acceptable price
can be found. Finally, if there are no internal or external comparables, at the same or
different levels of the value chain, the international price index should use the MNE’s
stated transfer price.
Our recommended strategy for the collection of transfer prices may appear to be
somewhat radical, given that we recommend that the multinational’s listed transfer prices
only be used as a last resort. Since the MNE must develop and use transfer prices that
meet the arm’s length standard, for both income tax and customs duty valuation purposes,
it is possible that the declared transfer price does satisfy one of the outlined methods for
the International Price Program. However, a multinational that is attempting to maximize
its after-tax profits has an incentive to choose relatively extreme transfer prices that will
reduce its tax liabilities, suggesting that the reported transfer price may not meet any of
the IPP’s best method tests outlined above. Even in this situation, both time and financial
constraints may change the ranking of the acceptable methods or make the MNE’s stated
transfer price the only practical alternative.
41
Appendix: Transfer Pricing in the Context of Noncompetitive Behavior
A considerable amount of international trade that is conducted by multinational firms
between affiliated establishments is in commodities that are proprietary; i.e., these
commodities are protected by patents or other barriers to entry. In this Appendix, we
extend our analysis to cover cases where the importing or exporting establishments have
potential monopoly power. We find below that the theoretical analysis presented above
in sections 6-10 for the competitive case goes through unchanged in the monopoly case,
except that the formerly “efficient” transfer prices must now be interpreted more
narrowly as “opportunity cost” transfer prices. However, the approximations to the
efficient transfer prices developed in sections 11 and 12, which are based on marginal
cost and marginal revenue, are no longer necessarily valid in the monopolistic case.
Consider the two-establishment framework that was presented in section 6 for the case of
a competitive importing and exporting establishment. The revenue function of the
importing establishment, r
1
(p
1
,x
1
), was defined by the competitive profit maximization
problem (2), where x
1
≥ 0 was the amount of the affiliate traded imported commodity and
p
1
≡ [p
1
1
,p
2
1
,…,p
I
1
] was defined as the positive vector of prices that the importing
establishment faced for its outputs and non-imported inputs. In the present
noncompetitive context, the fixed vector p
1
is now replaced by a vector of inverse (net)
demand functions d
1
≡ [d
1
1
(y
1
),d
2
1
(y
2
),…,d
I
1
(y
I
)]. Thus each (net) output price p
i
1
is
replaced by the inverse (net) demand function
74
d
i
1
(y
i
), which indicates how the selling
price changes as supply increases so that we have
75
(A1) p
i
1
= d
i
1
(y
i
) ; i = 1,2,…,I.
The counterpart to the competitive importing establishment’s profit maximization
problem (2) in section 6 above is now the following monopolistic profit maximization
problem:
(A2) r
1
(d
1
,x
1
) ≡ max
y
{Â
i=1
I
d
i
1
(y
i
) y
i
: (y
1
,y
2
,…,y
I
,x
1
) Œ S
1
}
where as before, S
1
is the importing establishment’s production possibilities set. Note
that this maximization problem is conditional on the amount imported, x
1
. Thus the
monopolistic net revenue function for the importing establishment, r
1
(d
1
,x
1
), depends on
x
1
, the amount imported from the foreign affiliate and the vector of (net) input demand
functions that the establishment faces in other markets.
76
The only difference between
74
If commodity i corresponds to an input, then d
i
1
(y
i
) is the inverse supply function that
the establishment faces in this market.
75
If the establishment has no monopoly or monopsony power with respect to its sales or
purchases of commodity i, then d
i
1
(y
i
) will be a constant and the establishment behaves
competitively in that market.
76
The net revenue function depends on the establishment’s production possibilities set S
1
as well so that it should be written as r
1
(d
1
,x
1
,S
1
) but since we hold S
1
constant
throughout our analysis, we have suppressed S
1
from the notation.
42
the monopolistic net revenue function r
1
(d
1
,x
1
) defined by (A2) and the competitive net
revenue function r
1
(p
1
,x
1
) defined by (2) in section 6 above is that the vector of inverse
demand functions d
1
has replaced the old fixed vector of (net) output prices p
1
.
We now turn our attention to the cost minimization problem of the exporting
establishment and we now allow for possible non-price taking behavior. The (net) cost
function of the exporting establishment, c
2
(p
2
,x
2
), was defined by the competitive cost
minimization problem (3), where x
2
≥ 0 was the amount of the affiliate traded commodity
produced by the establishment and p
2
≡ [p
1
2
,p
2
2
,…,p
J
2
] was defined as the positive vector
of prices that the exporting establishment faced for its inputs and non-exported outputs.
In the present noncompetitive context, the fixed vector p
2
is now replaced by a vector of
inverse (net) supply functions s
2
≡ [s
1
2
(z
1
),s
2
2
(z