This note proposes the segregation of independent endogenous and exogenous
components of tax penalty probability to introduce a formal demonstration that
enforcement and tax penalties are negatively related with income shifting. JEL
F23; H26.Comment: 8 page

Rathke, Alex Augusto Timm

English

arXiv

This note proposes the segregation of independent endogenous and exogenous components of tax penalty probability to introduce a formal demonstration that enforcement and tax penalties are negatively related with income shifting

Munich RePEc Personal Archive

Munich Personal RePEc ArchiveNote on tax enforcement and transferpricing manipulationRathke, Alex Augusto TimmSchool of Economics, BA and Accounting, University of São Paulo,BrazilApril 2015Online at https://mpra.ub.uni-muenchen.de/65337/MPRA Paper No. 65337, posted 30 Jun 2015 15:16 UTCNote on tax enforcement and transfer pricing manipulation  Alex A. T. Rathke School of Economics, BA and Accounting, University of São Paulo, Brazil E-mail: alex.rathke@usp.br  Keywords: income shifting; transfer pricing; tax enforcement, tax penalty.  JEL codes: F23; H26.  Abstract: This note proposes the segregation of independent endogenous and exogenous components of tax penalty probability to introduce a formal demonstration that enforcement and tax penalties are negatively related with income shifting.  I. Introduction Recent studies on tax avoidance emphasize the effects of tax enforcement against income shifting in multinational enterprizes (MNEs). They argue that enforcement creates a tax cost if noncompliance exists, and countries present different levels of fiscal stringency that affects MNEs’ tax planning1. The Organization for Economic Co-operation and Development (OECD) also highlights tax enforcement to restrain transfer pricing manipulation (OECD, 2013), explaining that governments’ enforcement influences the effectiveness of tax rules. In particular, the general premise is that enforcement increases the probability of imposition of fines whether MNEs manipulate transfer prices, forcing MNEs’ compliance. Although current literature recognizes the                                                           1 See Lohse and Riedel (2013) and Beuselink et al. (2014) for recent empirical findings. relevance of tax enforcement, it typically takes the stringency effect as an assumption, and few studies effectively specify the penalty cost function in the analysis2. This note uses the model of tax costs of transfer pricing manipulation to verify the premise of tax enforcement effect on income shifting. The proposed model segregates the penalty probability in two independent components: an endogenous and an exogenous component with respect to MNE. The model embodies a specification of the endogenous probability in accordance with standard conditions in literature, and applies this specification to demonstrate formally that enforcement and penalties have a negative relation with income shifting. It shows that the magnitude of tax differential shapes the optimal level of transfer pricing manipulation, but enforcing tax effectiveness reduces this magnitude.  II. The model Consider a MNE with two divisions in different countries (i = 1,2) producing (xi) and selling (si) domestically. Division 1 exports part of its output (m) to division 2, charging a transfer price p. Using one set of books, MNE’s pretax profits πi = Ri(si) – Ci(xi) are  π1 = R1(s1) – C1(s1 + m) + pm     and     π2 = R2(s2) – C2(s2 – m) – pm  with x1 = s1 + m and x2 = s2 – m. For an income tax rate ti on each country, MNE’s after tax profits are Π = (1 – t1)π1 + (1 – t2)π2.  If t1 ≠ t2, MNE has incentive to shift profits from high-tax to low-tax country via intrafirm trades (Yoshimine and Norrbin, 2007): if t2 > t1, profits increase if p increases – the HighTP case; if t1 > t2, profits increase if p decreases – the LowTP case. In order to discourage income shifting, countries impose                                                           2 e.g. Amerighi (2008) specifies the penalty function, but does not limit upward threshold as 1. limitations in setting transfer prices and levy a penalty if MNEs do not comply with these rules. The widely accepted criterion focuses in the OECD guidelines, which determine that transfer prices must correspond to the arm’s length price shaped by free trades. Assume the harmed country i settles a penalty Ψi whether the difference between p and the arm’s length price w causes profits to be shifted away from it. The probability α of imposition of Ψi depends on the extent of the difference p – w. Additionally, assume that imposition of Ψi is related with country i’s tax enforcement level θi, evaluated in a standard range 0 ≤ θi ≤ 1, positively related with governments’ taxation effectiveness and not influenced by MNE’s decisions. For a unitary penalty φi > 0, the expected tax cost of transfer pricing manipulation is  Ψi = φimαθi + 0m(1 – α)θi = φimαθi      (1)  MNE’s objective function becomes ϕ = Π – Ψi (i = 2 for HighTP, and i = 1 for LowTP). For θi > 0, transfer pricing manipulation implies Ψi > 03. Thus, MNE maximizes profits when achieves equilibrium between reduced overall taxation and expected tax penalty.  III. Specification of α and optimal transfer pricing manipulation To design a fair specification for θi is quite a complex task because the assessment of tax enforcement involve country-level institutional factors that are difficult to measure4. Nonetheless, a specification for α appears to be simpler and is useful for the analysis. Standard model assumes the expected tax penalty as a continuous function f(p – w),                                                           3 Transfer pricing manipulation implies ϕΨ < 0. 4 Some studies create measures of tax enforcement based on rules’ characteristics, e.g. Lohse et al.  (2012). twice differentiable and satisfying f(p = w) = 0, sign fp = sign(p – w) and fpp > 05. Following Kant (1990), assume P to be a limiting price that triggers penalty with certainty, i.e. α increases as p gets closer to P. Henceforth, α can be specified as:  α = (p – w)r(P – w)r      (2)  where r represents curve’s convexity. Logically, α infers: - for HighTP, w < p < P implies 0 < α < 1, w ≥ p implies α = 0, and p ≥ P implies α = 1; - for LowTP, w > p > P implies 0 < α < 1, w ≤ p implies α = 0, and p ≤ P implies α = 1.  Equation (2) has interesting characteristics. First, it is continuous and satisfies the standard conditions for all r > 1 (Proof in Appendix). Second, it implies that w is shaped by free trade forces. Tax authorities use w as a parameter, but do not have power to influence it. Third, P – w is the range of acceptable arm’s length prices, so p can be hold as tax compliant within it (OECD, 2013).  Specification of α as in Equation (2) allows the segregation of penalty probability in two independent components: α represents the endogenous component with respect to MNE, while θi represents the exogenous component. MNE can influence Ψi because variations in p cause changes in α, despite of straight impacts on income shifting. On the other hand, tax authorities are able to increase penalty probability by enforcing audit procedures and strengthening their interpretation of what is an acceptable arm’s length price, although these actions cannot influence α because it cannot affect directly the comparative parameters w or P.                                                           5 (Double) subscripts denote first (second) derivatives with respect to indicated variables. The equilibrium between the level of transfer pricing manipulation and the corresponding manipulation cost can be found differentiating ϕ with respect to p. Assuming r = 2 for simplification, the first-order condition is  ϕp = t2 – t1m – 2p – wP – w2 φiθim = 0      (3)  Clearly, the difference between p and w denotes the transfer price manipulation. Rearranging Equation (3) leads to  (p – w) = (t2 – t1)2φiθi(P – w)2     (4)  The term (t2 – t1)/2φiθi reflects the influence of enforcement and unitary penalty on the tax differential, which is the income shifting motivation. Enforcement and penalties are negatively related with income shifting incentive and discourage transfer pricing manipulation, i.e. increase (decrease) in θi or φi causes a decrease (increase) in p – w. The same relation is obtained for the more complex cases where both countries impose income taxation under residence-based principle and for partially owned affiliates6. From the analysis, the following proposition arises:  Proposition: Assuming tax costs of transfer pricing manipulation as Ψi = f(θi,φi), tax enforcement θi and tax penalty φi are negatively related with income shifting. Proof: See Appendix.                                                           6 Models of residence-based taxation and partially owned affiliates show the same negative relation between income shifting and tax enforcement (and penalty). Unpublished analysis is available from the author on request.  Equation (4) implies that the extent of tax differential determines the amount of MNE’s price manipulation, but countries are able to toughen tax compliance actions in order to discourage this strategy. Higher enforcement levels and greater tax fines generate two effects. First, increasing θi causes probability of imposition of unitary penalty φi to increase; as a consequence, the optimal p get closer to w, and MNE is forced to reduce transfer pricing manipulation (be more tax compliant) in order to restore equilibrium; the same occurs when φi increases. This is called “spillover effect”, being an increase in compliance independent of revenues generated directly from tax audits themselves (Alm, 2012). Second, Equation (4) suggests that countries could manage both φi and θi with intentions to recover evaded tax revenues, i.e. more tax prosecutions and greater fines effectively reduce MNE net profits. This is called “deterrent effect” of higher enforcement. Equation (4) also shows that the range of acceptable arm’s length prices is positively related with transfer pricing manipulation: the extent of (P – w)2 represents a whole spectrum of alternatives where p can be approved for tax purposes7, and MNE may hold defense chances against tax inspections whether p does not reach P.  IV. Conclusion This note introduces a formal demonstration that enforcement and tax penalties are negatively related with income shifting. The extent of tax differential defines the optimal size of transfer pricing manipulation, but strengthening tax effectiveness reduces this extent. While there are few studies that determine formally the function of                                                           7 Expanding (compressing) range (P – w)2 formally creates more (less) opportunities for transfer pricing manipulations. Nonetheless, because w is the main parameter for valuation of p, changes in w generate different results for HighTP and LowTP. penalty cost, this note proposes the segregation of independent endogenous and exogenous components for the analysis. The specification of the endogenous probability presented here is expected to be more comprehensible with respect to MNEs’ income shifting decisions, since it aims to approximate the realistic link between MNEs’ transfer prices and arm’s length criterion. Yet, the model maintains function’s premises as stated in literature and infers results in line with empirical findings. This analysis intends to provide a simple and credible enhancement to existing literature and to spark further insights in income shifting research.  References Alm, J. (2012) Measuring, explaining, and controlling tax evasion: lessons from theory, experiments, and field studies. International Tax and Public Finance, 19, 54-77. Amerighi, O. (2008) Transfer pricing and enforcement policy in oligopolistic markets, in Foreign Direct Investment and the Multinational Enterprise, MIT Press, Mass, Cambridge, pp. 117-154. Beuselinck, C., Deloof, M. and Vanstraelen, A. (2014) Cross-jurisdictional income shifting and tax enforcement: evidence from public versus private multinationals. Review of Accounting Studies, 1-37. Kant, C. (1990) Multinational firms and government revenues. Journal of Public Economics, 42, 135-147. Lohse, T. and Riedel, N. (2013) Do Transfer Prices Laws Limit International Income Shifting? Evidence from European Multinationals. Working Paper 13/07, Centre for Business Taxation, Oxford University. Lohse, T., Riedel, N. and Spengel, C. (2012) The increasing importance of transfer pricing regulations - a worldwide overview. Working Paper 12/27, Centre for Business Taxation, Oxford University. OECD, J. (2013) Action Plan on Base Erosion and Profit Shifting. Yoshimine, K. and Norrbin, S. C. (2007) The effect of the corporate tax rate on the trade balance. Applied Economic Letters, 14, 343-347.  Appendix Proof of conditions satisfied by α. Tax literature agrees on the following assumptions: expected tax penalty = f(p – w), f(p = w) = 0, sign fp = sign(p – w) and fpp > 0 for all p ≠ w. Equation (2) shows that, for all r > 1:   α(p = w) = 0   αp = r(p – w)r – 1(P – w)r    > 0 for HighTP< 0 for LowTP   and  αpp = (r2 – r)(p – w)r – 2(P – w)r  > 0   for both HighTP and LowTP  Proof of Proposition. Since θi and φi run for the same direction within Ψi, let Gi represent the effect of both variables (Ψi = mαGi). Assume α as specified in Equation (2). For the equilibrium in Equation (4), taking (p – w) = f(Gi), the first-order condition with respect to Gi gives  (p – w)G = – t2 – t1rGi2P – wr(r – 1) t2 –  t1rGiP – wr1 – 1r – 1 < 0  for both HighTP and LowTP. If α = 1 (p ≥ P in HighTP or p ≤ P in LowTP), manipulation cost Ψi is not a function of p. Differentiating ϕ with respect to Gi gives ϕG = – ΨG < 0.  

Note on tax enforcement and transfer pricing manipulation

Munich Personal RePEc Archive

MPRA
Munich Personal RePEc Archive
Note on tax enforcement and transfer
pricing manipulation
Alex Augusto Timm Rathke
School of Economics, BA and Accounting, University of Sa˜o Paulo,
Brazil
April 2015
Online at http://mpra.ub.uni-muenchen.de/65337/
MPRA Paper No. 65337, posted 30. June 2015 15:16 UTC
Note on tax enforcement and transfer pricing manipulation 
 
Alex A. T. Rathke 
School of Economics, BA and Accounting, University of São Paulo, Brazil 
E-mail: alex.rathke@usp.br 
 
Keywords: income shifting; transfer pricing; tax enforcement, tax penalty. 
 
JEL codes: F23; H26. 
 
Abstract: This note proposes the segregation of independent endogenous and 
exogenous components of tax penalty probability to introduce a formal demonstration 
that enforcement and tax penalties are negatively related with income shifting. 
 
I. Introduction 
Recent studies on tax avoidance emphasize the effects of tax enforcement against 
income shifting in multinational enterprizes (MNEs). They argue that enforcement 
creates a tax cost if noncompliance exists, and countries present different levels of fiscal 
stringency that affects MNEs’ tax planning1. The Organization for Economic Co-
operation and Development (OECD) also highlights tax enforcement to restrain transfer 
pricing manipulation (OECD, 2013), explaining that governments’ enforcement 
influences the effectiveness of tax rules. In particular, the general premise is that 
enforcement increases the probability of imposition of fines whether MNEs manipulate 
transfer prices, forcing MNEs’ compliance. Although current literature recognizes the 
                                                          
1 See Lohse and Riedel (2013) and Beuselink et al. (2014) for recent empirical findings. 
relevance of tax enforcement, it typically takes the stringency effect as an assumption, 
and few studies effectively specify the penalty cost function in the analysis2. 
This note uses the model of tax costs of transfer pricing manipulation to verify the 
premise of tax enforcement effect on income shifting. The proposed model segregates 
the penalty probability in two independent components: an endogenous and an 
exogenous component with respect to MNE. The model embodies a specification of the 
endogenous probability in accordance with standard conditions in literature, and applies 
this specification to demonstrate formally that enforcement and penalties have a 
negative relation with income shifting. It shows that the magnitude of tax differential 
shapes the optimal level of transfer pricing manipulation, but enforcing tax effectiveness 
reduces this magnitude. 
 
II. The model 
Consider a MNE with two divisions in different countries (i = 1,2) producing (xi) and 
selling (si) domestically. Division 1 exports part of its output (m) to division 2, charging 
a transfer price p. Using one set of books, MNE’s pretax profits πi = Ri(si) – Ci(xi) are 
 
π1 = R1(s1) – C1(s1 + m) + pm     and     π2 = R2(s2) – C2(s2 – m) – pm 
 
with x1 = s1 + m and x2 = s2 – m. For an income tax rate ti on each country, MNE’s after 
tax profits are Π = (1 – t1)π1 + (1 – t2)π2.  If t1 ≠ t2, MNE has incentive to shift profits 
from high-tax to low-tax country via intrafirm trades (Yoshimine and Norrbin, 2007): if 
t2 > t1, profits increase if p increases – the HighTP case; if t1 > t2, profits increase if p 
decreases – the LowTP case. In order to discourage income shifting, countries impose 
                                                          
2 e.g. Amerighi (2008) specifies the penalty function, but does not limit upward threshold as 1. 
limitations in setting transfer prices and levy a penalty if MNEs do not comply with 
these rules. The widely accepted criterion focuses in the OECD guidelines, which 
determine that transfer prices must correspond to the arm’s length price shaped by free 
trades. 
Assume the harmed country i settles a penalty Ψi whether the difference between p and 
the arm’s length price w causes profits to be shifted away from it. The probability α of 
imposition of Ψi depends on the extent of the difference p – w. Additionally, assume 
that imposition of Ψi is related with country i’s tax enforcement level θi, evaluated in a 
standard range 0 ≤ θi ≤ 1, positively related with governments’ taxation effectiveness 
and not influenced by MNE’s decisions. For a unitary penalty φi > 0, the expected tax 
cost of transfer pricing manipulation is 
 
Ψi = φimαθi + 0m(1 – α)θi = φimαθi      (1) 
 
MNE’s objective function becomes ϕ = Π – Ψi (i = 2 for HighTP, and i = 1 for LowTP). 
For θi > 0, transfer pricing manipulation implies Ψi > 0
3. Thus, MNE maximizes profits 
when achieves equilibrium between reduced overall taxation and expected tax penalty. 
 
III. Specification of α and optimal transfer pricing manipulation 
To design a fair specification for θi is quite a complex task because the assessment of 
tax enforcement involve country-level institutional factors that are difficult to measure4. 
Nonetheless, a specification for α appears to be simpler and is useful for the analysis. 
Standard model assumes the expected tax penalty as a continuous function f(p – w), 
                                                          
3 Transfer pricing manipulation implies ϕΨ < 0. 
4 Some studies create measures of tax enforcement based on rules’ characteristics, e.g. Lohse et al.  
(2012). 
twice differentiable and satisfying f(p = w) = 0, sign fp = sign(p – w) and fpp > 0
5. 
Following Kant (1990), assume P to be a limiting price that triggers penalty with 
certainty, i.e. α increases as p gets closer to P. Henceforth, α can be specified as: 
 
α = (p – w)
r
(P – w)r      (2) 
 
where r represents curve’s convexity. Logically, α infers: 
- for HighTP, w < p < P implies 0 < α < 1, w ≥ p implies α = 0, and p ≥ P implies α = 1; 
- for LowTP, w > p > P implies 0 < α < 1, w ≤ p implies α = 0, and p ≤ P implies α = 1.  
Equation (2) has interesting characteristics. First, it is continuous and satisfies the 
standard conditions for all r > 1 (Proof in Appendix). Second, it implies that w is shaped 
by free trade forces. Tax authorities use w as a parameter, but do not have power to 
influence it. Third, P – w is the range of acceptable arm’s length prices, so p can be hold 
as tax compliant within it (OECD, 2013).  
Specification of α as in Equation (2) allows the segregation of penalty probability in two 
independent components: α represents the endogenous component with respect to MNE, 
while θi represents the exogenous component. MNE can influence Ψi because variations 
in p cause changes in α, despite of straight impacts on income shifting. On the other 
hand, tax authorities are able to increase penalty probability by enforcing audit 
procedures and strengthening their interpretation of what is an acceptable arm’s length 
price, although these actions cannot influence α because it cannot affect directly the 
comparative parameters w or P. 
                                                          
5 (Double) subscripts denote first (second) derivatives with respect to indicated variables. 
The equilibrium between the level of transfer pricing manipulation and the 
corresponding manipulation cost can be found differentiating ϕ with respect to p. 
Assuming r = 2 for simplification, the first-order condition is 
 
ϕ
p
 = t2 – t1m – 2
p – w
P – w2 φiθim = 0      (3) 
 
Clearly, the difference between p and w denotes the transfer price manipulation. 
Rearranging Equation (3) leads to 
 
(p – w) = (t2 – t1)
2φ
i
θi
(P – w)
2
     (4) 
 
The term (t2 – t1)/2φiθi reflects the influence of enforcement and unitary penalty on the 
tax differential, which is the income shifting motivation. Enforcement and penalties are 
negatively related with income shifting incentive and discourage transfer pricing 
manipulation, i.e. increase (decrease) in θi or φi causes a decrease (increase) in p – w. 
The same relation is obtained for the more complex cases where both countries impose 
income taxation under residence-based principle and for partially owned affiliates6. 
From the analysis, the following proposition arises: 
 
Proposition: Assuming tax costs of transfer pricing manipulation as Ψi = f(θi,φi), tax 
enforcement θi and tax penalty φi are negatively related with income shifting. 
Proof: See Appendix. 
                                                          
6 Models of residence-based taxation and partially owned affiliates show the same negative relation 
between income shifting and tax enforcement (and penalty). Unpublished analysis is available from the 
author on request. 
 Equation (4) implies that the extent of tax differential determines the amount of MNE’s 
price manipulation, but countries are able to toughen tax compliance actions in order to 
discourage this strategy. Higher enforcement levels and greater tax fines generate two 
effects. First, increasing θi causes probability of imposition of unitary penalty φi to 
increase; as a consequence, the optimal p get closer to w, and MNE is forced to reduce 
transfer pricing manipulation (be more tax compliant) in order to restore equilibrium; 
the same occurs when φi increases. This is called “spillover effect”, being an increase in 
compliance independent of revenues generated directly from tax audits themselves 
(Alm, 2012). Second, Equation (4) suggests that countries could manage both φi and θi 
with intentions to recover evaded tax revenues, i.e. more tax prosecutions and greater 
fines effectively reduce MNE net profits. This is called “deterrent effect” of higher 
enforcement. 
Equation (4) also shows that the range of acceptable arm’s length prices is positively 
related with transfer pricing manipulation: the extent of (P – w)2 represents a whole 
spectrum of alternatives where p can be approved for tax purposes7, and MNE may hold 
defense chances against tax inspections whether p does not reach P. 
 
IV. Conclusion 
This note introduces a formal demonstration that enforcement and tax penalties are 
negatively related with income shifting. The extent of tax differential defines the 
optimal size of transfer pricing manipulation, but strengthening tax effectiveness 
reduces this extent. While there are few studies that determine formally the function of 
                                                          
7 Expanding (compressing) range (P – w)2 formally creates more (less) opportunities for transfer pricing 
manipulations. Nonetheless, because w is the main parameter for valuation of p, changes in w generate 
different results for HighTP and LowTP. 
penalty cost, this note proposes the segregation of independent endogenous and 
exogenous components for the analysis. The specification of the endogenous probability 
presented here is expected to be more comprehensible with respect to MNEs’ income 
shifting decisions, since it aims to approximate the realistic link between MNEs’ 
transfer prices and arm’s length criterion. Yet, the model maintains function’s premises 
as stated in literature and infers results in line with empirical findings. This analysis 
intends to provide a simple and credible enhancement to existing literature and to spark 
further insights in income shifting research. 
 
References 
Alm, J. (2012) Measuring, explaining, and controlling tax evasion: lessons from theory, 
experiments, and field studies. International Tax and Public Finance, 19, 54-77. 
Amerighi, O. (2008) Transfer pricing and enforcement policy in oligopolistic markets, 
in Foreign Direct Investment and the Multinational Enterprise, MIT Press, 
Mass, Cambridge, pp. 117-154. 
Beuselinck, C., Deloof, M. and Vanstraelen, A. (2014) Cross-jurisdictional income 
shifting and tax enforcement: evidence from public versus private 
multinationals. Review of Accounting Studies, 1-37. 
Kant, C. (1990) Multinational firms and government revenues. Journal of Public 
Economics, 42, 135-147. 
Lohse, T. and Riedel, N. (2013) Do Transfer Prices Laws Limit International Income 
Shifting? Evidence from European Multinationals. Working Paper 13/07, Centre 
for Business Taxation, Oxford University. 
Lohse, T., Riedel, N. and Spengel, C. (2012) The increasing importance of transfer 
pricing regulations - a worldwide overview. Working Paper 12/27, Centre for 
Business Taxation, Oxford University. 
OECD, J. (2013) Action Plan on Base Erosion and Profit Shifting. 
Yoshimine, K. and Norrbin, S. C. (2007) The effect of the corporate tax rate on the 
trade balance. Applied Economic Letters, 14, 343-347. 
 
Appendix 
Proof of conditions satisfied by α. Tax literature agrees on the following assumptions: 
expected tax penalty = f(p – w), f(p = w) = 0, sign fp = sign(p – w) and fpp > 0 for all p ≠ 
w. Equation (2) shows that, for all r > 1:  
 
α(p = w) = 0  
 
αp = 
r(p – w)
r – 1
(P – w)
r    > 0 for HighTP
< 0 for LowTP
   and 
 
αpp = (r
2 – r)
(p – w)
r – 2
(P – w)
r  > 0   for both HighTP and LowTP 
 
Proof of Proposition. Since θi and φi run for the same direction within Ψi, let Gi 
represent the effect of both variables (Ψi = mαGi). Assume α as specified in Equation 
(2). For the equilibrium in Equation (4), taking (p – w) = f(Gi), the first-order condition 
with respect to Gi gives 
 
(p – w)
G
 = – 
t2 – t1
rGi
2
P – wr
(r – 1) t2 –  t1
rGi
P – wr
1 – 
1
r – 1
 < 0 
 
for both HighTP and LowTP. If α = 1 (p ≥ P in HighTP or p ≤ P in LowTP), 
manipulation cost Ψi is not a function of p. Differentiating ϕ with respect to Gi gives ϕG 
= – ΨG < 0. 
 


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