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Discussion Papers
Redistributive Income Taxation under
Outsourcing and Foreign Direct Investment
Thomas Aronsson Umeå University, Sweden
and
Erkki Koskela
University of Helsinki and HECER
Discussion Paper No. 296 May 2010
ISSN 1795-0562
HECER – Helsinki Center of Economic Research, P.O. Box 17 (Arkadiankatu 7), FI- 00014 University of Helsinki, FINLAND, Tel +358-9-191-28780, Fax +358-9-191-28781, E-mail info-hecer@helsinki.fi, Internet www.hecer.fi
Redistributive Income Taxation under
Outsourcing and Foreign Direct Investment*
Abstract
This paper deals with optimal income taxation under labor outsourcing and FDI. We show how the optimal income tax response to the joint effect of outsourcing and FDI depends on whether FDI is complementary with, or substitutable for, domestic labor.
JEL classification: D60, H21, H23, H25, J31
Keywords: outsourcing, foreign direct investment, optimal nonlinear taxation
Thomas Aronsson
Department of Economics Umeå University SE – 901 87 Umeå SWEDEN
e-mail: thomas.aronsson@econ.umu.se
Erkki Koskela
Department of Economics University of Helsinki
P.O. Box 17 (Arkadiankatu 7) FI-00014 University of Helsinki FINLAND
e-mail: erkki.koskela@helsinki.fi
* Aronsson would also like to thank The Bank of Sweden Tercentenary Foundation, The Swedish Council for Working Life and Social Research, and The Swedish National Tax Board for research grants. Koskela thanks Academy of Finland (grant No. 1217622) for financial support and Department of Economics, Umeå University, for good hospitality.
1. Introduction
In the process of globalization, international outsourcing and foreign direct investment (FDI) have become increasingly important aspects of production and industrial organization.
International outsourcing is meant to imply that some production stages - typically low-skilled labor intensive production – is carried out by a foreign partner (or a subsidiary located abroad), whereas FDI implies that firms invest part of their capital stock abroad instead of domestically (a process that may, or may not, be directly associated with outsourcing). A large empirical literature has examined the distributional consequences of outsourcing, where the common message is that international outsourcing leads to more wage- inequality by increasing the skill-premium in countries that outsource production abroad.1 The (more scarce) literature dealing with the distributional consequences of FDI conveys a similar message.2
Yet, the literature dealing with the implications of globalization for optimal income taxation is surprisingly small. The purpose of this note is to analyze the simultaneous effects of outsourcing and FDI for the optimal use of redistributive income taxation. The analysis is based on the two-type optimal income tax model (developed in its original form by Stern 1982 and Stiglitz 1982), which is here modified to allow for outsourcing of low-skilled labor intensive production as well as FDI. Our study focuses on a country whose firms outsource production and invests part of its capital stock abroad (outward FDI). As such, the present study extends the recent paper by Aronsson and Koskela (2009), who examined the optimal income tax response to outsourcing without FDI. This extension is well motivated, because outsourcing and FDI jointly affect the domestic wage-distribution and, therefore, also the incentives underlying redistributive policy.
2. The Model
There are two types of consumers: a low-ability type (i 11) and a high-ability type (i 22).
This distinction refers to productivity, meaning that the high-ability type is more productive
1 See, e.g., Feenstra and Hanson (1999), Hijzen et al. (2005), Hsieh and Woo (2005) and Ge ishecker and Gö rg (2008).
2 See, e .g., Choi (2006), who finds that both inward and outward FDI leads to increased inequality measured by the GINI coeffic ient.
and faces a higher before-tax wage rate than the low-ability type. As the number of individuals of each such type is not important, it will be normalized to one. The utility function facing ability-type i is given by
( , )
i i i
uii u c z( , )( , )( , )ii ii u u c z( , ) ui u c z( , )i i uii u c z( , )( , )ii ii
ui u c z( , )( , ) i i (1)
where c is consumption and z leisure. Leisure is defined as a time endowment less the hours of work, l. Let wi denote the before-tax hourly wage rate and T w l( i i) the income tax payment faced by ability-type i. The individual budget constraint can then be written as
( ) 0
i i i i i
w li ii i T w l((( i ii i))) cii 000 w l T w l( ) c 0 w li i T w l( i i) ci 0 w li ii i T w l(( i ii i)) cii 00
w li i T w l(( i i)) ci 00 . (2)
The first order condition for work hours becomes (subindices denote partial derivatives)
(1 '( )) 0
i i i i i
c z
u wccii ii(1(1(1(1(1(1 T w l'('('('('('( i ii i)))))))))))) uzzii 000000 u wi i(1(1(1 T w l'('('( i i)))))) ui 000 u wci i(1(1(1(1 T w l'('('('( i i)))))))) uzi 0000
u wc (1(1 T w l'('( )))) uz 00 (3)
where T w l'( i i) is the marginal income tax rate.
Turning to production, the representative firm uses four variable inputs : domestic labor of each ability-type, l1 and l2; outsourcing, m; and FDI, I . By slightly extending the production- model used in Koskela and Stenbacka (2010), we write the production function as follows;
1 2
( , , )
y F l1 m l I2 y F l( m l I, , ) y F l((11 m l I, , ), , )22 y F l((111 m l I, , ), , )222 y F l( m l I, , ) y F l((11 m l I, , ), , )22
y F l(11 m l I, , )22 (4)
where y denotes output, while 00 is a parameter. The variable m is interpretable as an intermediate good bought from a foreign partner; alternatively, this good may be manufactured domestically by use of low-skilled labor (this process is embedded in the production function). The production function is increasing and strictly concave in each of its three separate arguments – i.e. FFFllll11 000, Fl2 00, FI 00 , and FFFl ll ll ll ll l1 11 11 11 1 000, Fl l2 2 00, FII 00 , where
1 1
l l m
l l m
l1 l1 m l1 l1 m l11 l11 m l1 l1 m l1 l1 m
l l m - and the technology is characterized by constant returns to scale. We also assume that the two types of domestic labor are technical complements in the sense that
1 2 0 Fl ll ll l1 21 21 2 0 Fl l
Fl l 0. This formulation means that increased outsourcing leads to higher wage- inequality.
Whether FDI is a technical complement or technical substitute to domestic labor is subject to debate, and we consider both these scenarios below.3 In Case I, domestic labor and FDI are technical substitutes in the sense that FFFl Il Il Il Il I1111 000 and Fl I2 00, whereas Case II implies that domestic labor and FDI are technical complements such at FFFl Il Il Il Il I1111 000 and Fl I2 00.4 Case I is interpretable to reflect market-seeking (horizontal) FDI, and Case II to reflect cost-saving (vertical) FDI. In each such case, our main results will be derived on the assumption that increased FDI leads to increased domestic wage- inequality.5 However, as the effect of FDI on the wage distribution is uncertain to some extent, we also discuss how results are modified if increased FDI instead leads to less domestic wage-inequality.
There is also a cost associated with outsourcing, ( )( )( )( )mm , and FDI, q I( ), each of which is increasing and convex in its argument. The first order conditions can be written as
1
1 2 1
( , , ) 0
F ll (((( 111 m l I, , ), , ), , ), , )222 w111 0000 F l(( 11 m l I, , ), , )22 w11 00 F l(( 11 m l I, , ), , )22 w11 00 F l(( 11 m l I, , ), , )22 w11 00 F l((( 111 m l I, , ), , ), , )222 w111 000 F l(( 11 m l I, , ), , )22 w11 00 F ll1(( 11 m l I, , ), , )22 w11 00 F l1 m l I w F l1( m l I, , ) w 0 F ll ( m l I, , ) w 0 F ll (( m l I, , ), , ) w 00
F l( m l I, , ) w 0 (5)
2
1 2 2
( , , ) 0
F ll (((111 m l I, , ), , ), , )222 w222 000 F l((11 m l I, , ), , )22 w22 00 F l(((111 m l I, , ), , ), , )222 w222 000 F l((11 m l I, , ), , )22 w22 00
F l(11 m l I, , )22 w22 0 (6)
1
1 2
( , , ) m( ) 0
F lll 1 m l I2 m F l( m l I, , ) ( )m 0 F l((11 m l I, , ), , )22 ( )( )m 00 F ll (11 m l I, , )22 ( )m 0 F ll (((((1 m l I, , ), , ), , ), , ), , )2 mm( )( )( )( )( )m 00000 F l((11 m l I, , ), , )22 ( )( )m 00 F l(((11 m l I, , ), , ), , )22 m( )( )( )m 000 F lll1((( m l I, , ), , ), , ) m( )( )( )m 000 F l1 m l I m F l1( m l I, , ) ( )m 0 F ll ( m l I, , ) ( )m 0 F ll (( m l I, , ), , ) ( )( )m 00
F l( m l I, , ) ( )m 0 (7)
1 2
( , , ) ( ) 0
I I
F lI(1 m l I, , )2 q II( ) 0 F l( m l I, , ) q I( ) 0 F lI( m l I, , ) q II( ) 0 F lII(( m l I, , ), , ) q III( )( ) 00 F lI((( m l I, , ), , ), , ) q II( )( )( ) 000 F l((11 m l I, , ), , )22 q I( )( ) 00 F lI(11 m l I, , )22 q II( ) 0 F lII(( m l I, , ), , ) q III( )( ) 00 F lII(((1 m l I, , ), , ), , )2 q III( )( )( ) 000 F l((11 m l I, , ), , )22 q I( )( ) 00 F lI(11 m l I, , )22 q II( ) 0 F lII(( m l I, , ), , ) q III( )( ) 00
F lI(( m l I, , ), , ) q II( )( ) 00 (8)
where subindices denote partial derivatives. Since the decision-problem facing the government will be written in terms of l1 and l2, it will be convenient to solve equations (7) and (8) for m and I, respectively, as functions of l1 and l2. These functions can be writte n as
1 2
( , ) m m l l( , )( , )111 222 m m l l( , ) m m l l( , )( , )11 22
m m l l( , )11 22 (9a)
3 Based on cross-country data, Feldstein (1995) and Desai et a l. (2005) find that domestic investment tends to decline in response to outward FDI (in what appears to be a one-to-one relationship). If domestic labor and domestic capital are technical co mple ments, then this would suggest that domestic labor and foreign direct investment ought to be treated as technical substitutes in the production function set out above. However, by focusing solely on U.S. mu ltinationals, Desai et al. find the opposite relationship between domestic investment and outward FDI; na mely, that increased FDI in other coun tries by U.S. multinationals tends to increase the domestic investment as well.
4 See a lso the overview artic le by Crino (2009), who argues that outward FDI appears to be substitutable for domestic labor, although the effect is relat ively sma ll.
5 See, e.g ., Choi 2006. Note that Choi focuses on the GINI coeffic ient instead of on wage-inequality (which is the measure used here).
1 2
( , ) I I l l( , )( , )111 222 I I l l( , ) I I l l( , )( , )11 22
I I l l( , )11 22 . (9b)
With the assumptions made above, one can show that equation (9a) implies mmm///// lll1111 00000 and / 2 0
m// l222 00 m/ l 0
m/ l 0. For equation (9b), the comparative statics results depend on whether FDI is complementary with, or substitutable for, domestic labor. If domestic labor and FDI are technical substitutes (Case I), we have III///// lll1111 00000 and III///// lll2222 00000; if they are technical complements (Case II), we obtain III///// lll1111 00000 and III///// lll2222 0.0.0.0.0.
3. Optimal Income Taxation
We analyze Pareto efficient taxation by assuming that the government maximizes the utility of the low-ability type subject to a minimum utility restriction for the high-ability type. The minimum utility restriction for the high-ability type is given by (for minimum utility u2)
2 2 2 2
( , ) u2222 u c z( ,( ,2222 2222)) u2222 u u c z( , ) u
u u c z( , ) u . (10)
The informational assumptions are conventional. The government knows the income of each individual, while ability is private information. By following much earlier literature in assuming that redistribution means income transfers from the high-ability to the low-ability type, one would like to prevent the high-ability type from becoming a mimicker. The self- selection constraint that may bind then becomes
2 ( ,2 2) ( ,1 1) ˆ2
u2 u c z( ,2 2) u c H( ,1 l1) u2 u2 u c z2 2 u c H1 l1 u2 u2 u c z( ,2 2) u c H( ,1 l1) u2 u22 u c z( ,( ,22 22)) u c H( ,( ,11 l11)) u22 u22222 u c z( ,( ,22222 22222)) u c H( ,( ,11111 l11111)) uˆ22222 u2 u c z2 2 u c H1 l1 u2 u222 u c z222 222 u c H111 l111 uˆ222 u22 u c z( ,22 22) u c H( ,11 l11) uˆ22 u22 u c z( ,( ,22 22)) u c H( ,( ,11 l11)) u22
u22 u c z( ,22 22) u c H( ,11 l11) u22 (11)
where uˆ2 denotes the utility of the mimicker, and w ww ww w1111111/////// 2222222 1111111 is the relative wage rate. The mimicker faces the same income and consumption point (a nd, therefore, pays as much tax as) the low-ability type. As the mimicker is more productive than the low-ability type, he/she spends more time on leisure. By using the first order conditions for the firm, one can write is a function of l1, l2, m and I, i.e.
1 2
( , , , )l l m I ( , , , ) ( , , , )l l m I ( , , , )1 2 ( , , , ) ( , , , )l l m I ( , , , )1 2 ( , , , )l l m I11 22
( , , , )1 2 . (12)
With equation (4) at our disposal, it is straight forward to show that //// mm 0000. As empirical evidence suggests that outward FDI also contributes to increased wage-inequality, i.e.
/ I 0
/ 0
/ I 0
/ 0, this implies additional (implicit) restrictions on the production function. For / I 0
/ 0
/ I 0
/ 0 to hold, Case I must imply that FDI is at least as substitutable for low-skilled labor as it is for high-skilled labor; in Case II, it follows that FDI is a stronger complement to high- skilled than to low-skilled labor.
By using ( i i) 0
iT w l((( i ii i))) 000
iT w lT w lT w l((((((( i ii i))))))) 0000000 together with the private budget constraints and the objective function of the firm, we can write the budget constraint faced by government as follows;
1 2
( , , ) i ( ) ( ) 0
i
F l1 m l I2 c m q I F l( m l I, , ) c ( )m q I( ) 0 F l(( 11 m l I, , ), , )22 c ( )( )m q I( )( ) 00 F l(( 111 m l I, , ), , )222 c ( )( )m q I( )( ) 00 F l( m l I, , ) c ( )m q I( ) 0 F l(( 11 m l I, , ), , )22 c ( )( )m q I( )( ) 00 F l( 11 m l I, , )22 ci ( )m q I( ) 0 F l( m l I, , ) c ( )m q I( ) 0 F l((( m l I, , ), , ), , ) ci ( )( )( )m q I( )( )( ) 000
F l(( m l I, , ), , ) ci ( )( )m q I( )( ) 00 . (13)
The Lagrangean is given by
1 2 [ 2 ˆ2] [ (1 , , )2 i ( ) ( )]
i
L u u [u u ] [ (F l m l I, , ) c ( )m q I( )]
L u u [u u ] [ (F l m l I, , ) c ( )m q I( )]
L u1 u2 [u2 u2] [ (F l1 m l I, , )2 c ( )m q I( )]
L u1 u2 u2 u2 F l1 m l I2 c m q I L u1111 u2222 u2222 uˆ2222 F l1111 m l I2222 c m q I L u1 u2 u2 u2 F l1 m l I2 c m q I L u1 u2 [u2 u2] [ (F l1 m l I, , )2 c ( )m q I( )]
L u11 u22 [[u22 u22]] [ ([ (F l11 m l I, , ), , )22 c ( )( )m q I( )]( )]
L u111111 u222222 [[u222222 uˆˆ222222]] [ ([ (F l111111 m l I, , ), , )222222 c ( )( )m q I( )]( )]
L u1111 u2222 [u2222 uˆˆ2222] [ (F l1111 m l I, , )2222 ci ( )m q I( )]
L u u [u u ] [ (F l m l I, , ) c ( )m q I( )]
L u u [[[u u ]]] [ ([ ([ (F l m l I, , ), , ), , ) ci ( )( )( )m q I( )]( )]( )]
L u u [[u u ]] [ ([ (F l m l I, , ), , ) ci ( )( )m q I( )]( )] (14)
where , and are Lagrange multipliers. To shorten the notation, let mm and II denote the welfare effect following an increase in outsourcing and FDI, respectively. By using the first order conditions of the firm and the assumptions underlying the wage-distribution, we have
ˆ2 1 0
m z
L u l
m m
L 0
m L u lz
2 1 0 u lˆ2 1 u lˆ2 1 u lˆ
m z
m m 0
m z
m u lz
m u lz
m z
ˆ2 1 0
I z
L u l
I I
L 0
I L u lz
2 1 0 ˆ u l2 1 u lˆ2 1 u lˆ
I z
I I
I z
I I
I z 0
I z
I z
I I
I z
I u lz
I u lz
I z
I I
I z
I I
I z .
The government’s first order conditions for hours of work and consumption can be written as
1 2 1 1
1 1 1
ˆ 0
z z m I
m I
u u l w
l l l
m I
1 2 1 1
z z m I
u1 u2 l1 w1
u1z u2z l1 w1 m I
uz111z uˆz222z l111 w111 mm II 0 u1 u2 l1 w1
u111 uˆ222 l111 w111
u11z uˆ22z l11 w11 m I
uz11 uz22 l11 w11 m mm I II 0 u111 u222 l111 w111
u111 u222 l111 w111 u1 u2 l1 w1
u u l w
uz uz l w m I
uz uz l w m I
u1 u2 l1 w1 u1 u2 l1 w1 u1 u2 l1 w1 u11 u22 l11 w11 u1 u2 l1 w1
u1 u2 l1 1 w1 1 1
l1 l1 l1
l11 l11 l11
z z 1 m 1 I 1
l1 l1 l1
z z 11 m 11 I 11 0
z z 1 m 1 I 1
z z 11 m 11 I 11
l11 l11 l11
z z 1 m 1 I 1
l1 l1 l1
z z 1 m 1 I 1
z z 1 m 1 I 1
z z 11 m 11 I 11
z z 1 m 1 I 1
l1 l1 l1
z z 1 m 1 I 1
z z m I
uz uz l w m I
uzzzz uzzzz l w mmmm IIII
uz uz l w m I
l l l
z z m I
l1 l1 l1
l1 l1 l1
z z m I
l l l
z z 1 m 1 I 1
z z 1 m 1 I 1
l1 l1 l1
z z 1 m 1 I 1
z z 1 m 1 I 1
z z 1 m 1 I 1
z z m I
uzz uzz l 11 w mm 11 II 11 uzz uzz l 11 w mm 11 II 11
l l l
z z 1 m 1 I 1
z z 1 m 1 I 1
l1 l1 l1
z z 1 m 1 I 1 (15)
1 ˆ2 0
c c
u1c uc2 uc uc
uc111c uˆcc222 0 uc uc
uc uc (16)
2 2 1 2
2 1 1
( ) z ˆz m m I I 0
u u l w
l l l
m I
( ) 0
( ) 0
( ) 0
( ) 222 ˆ2 12 12 1 222 0
( ) 0
( ) z z m I 0
( ) z z m I 0
( ) 0
( )u u l w 0
( ) 0
( )u u l w 0
( ) 2 2 1 2 0
( )u22 u l2 12 1 w22 0
( ) 222 ˆ2 12 12 1 222 0 ( )u2222 u lˆˆ2 12 12 12 1 w2222 0
( ) 22 ˆ2 12 1 22 0
( ) z z m I 0
( )u u l w 0
( ) z z m I 0
( ) 0
( ) m I 0
( ) m I 0
( ) 0
( ) m I 0
( ) m I 0
( ) 2 2 1 2 0
( )u u l w 0
( ) 2 2 1 2 0
( )u22 u l2 12 1 w22 0
( ) 22 2 12 1 22 0
( ) 2 2 1 2 0
( ) 2 2 1 2 0
( )u u l w 0
( ) 2 2 1 2 0
( )u22 u l2 12 1 w22 0
( ) 2z z2 1 2 2 m 1 I 1 0
l2 l1 l1
l2 l1 l1
z z m I
l l l
z z 2 m 1 I 1
z z 2 m 1 I 1
l2 l1 l1
z z 22 m 11 I 11
( ) 2 1 1 0
( ) 2 1 1 0
( ) z z m I 0
( ) 2 1 1 0
( ) z z 22 m 11 I 11 0
( ) 22 11 11 0
l22 l11 l11
( ) 2 1 1 0
l2 l1 l1
( ) z z 222 m 111 I 111 0
l2 l1 l1
z z 22 m 11 I 11
( ) z z 22 m 11 I 11 0
( ) 2 1 1 0
l2 l1 l1
( ) z z 22 m 11 I 11 0
( ) 2 1 1 0
( ) z z m I 0
( ) z z m I 0
( ) 2 1 1 0
( ) z z 22 m 11 I 11 0
( ) 2 1 1 0
( )u u l w 0
( ) 0
( ) z z m I 0
( )u u l w 0
( ) z z m I 0
( ) 2 1 1 0
( ) z z 22 m 11 I 11 0
( )u u l 22 w 11 11 0
( ) z z 22 m 11 I 11 0
( ) z z 2 m 1 I 1 0
l l l
z z 2 m 1 I 1
z z 2 m 1 I 1
l2 l1 l1
z z 2 m 1 I 1
( ) z z m I 0
( ) 0
l l l
( ) z z m I 0
( ) 2 1 1 0
( ) z z 22 m 11 I 11 0
( ) 2 1 1 0
l2 l1 l1
( ) z z 22 m 11 I 11 0
( ) 2 1 1 0 (17)
