Discussion Papers In Economics
And Business

Nonlinear Effects of the Transport Costs on
the Wage Inequality
Yuichiro Matsumoto
Discussion Paper 18-07

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANNonlinear Effects of the Transport Costs on
the Wage Inequality
Yuichiro Matsumoto
Discussion Paper 18-07

March 2018

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANNonlinear Effects of the Transport Costs on
the Wage Inequality∗
Yuichiro Matsumoto†
March 6, 2018

Abstract
This paper examines how transport costs affect wage inequality. Goods
produced by the unskilled must pay higher transport costs because they have
low market values. Reduction in transportation cost changes the relative
wage. At first, only the skilled gains from the transportation improvement.
Then the unskilled also gains from international trade. Therefore, transportation development causes Kuznets curve.

JEL Classification Codes: F16; J31; L91; O11; R1
Keywords: Alchian-Allen Hypothesis; Kuznets Curve; Trade Liberalization; Transportation Infrastructure; Wage Inequality∗†

I am grateful to the seminar participants at Osaka University.
Osaka University email:u847103e@ecs.osaka-u.ac.jp

1

Introduction

Transportation has a sizable impact on the economy. Railroads in colonial India
increased the agricultural income more than 17 percent (Donaldson (2010)). Donaldson and Hornbeck (2016) suggested that if all the US railroads in 1890 had been
removed, the agricultural land value would have decreased by 60 percent. The regions with the top 25th percentile transportation infrastructures have 68 percent
larger trade volume than the median regions (Limao and Venables (2001)). It istrue that the economists realize the importance of the transportation.
However, less attention has been paid to the fact that gains from the transportation are different across workers. The costs for transportation are more costly formore cheap goods because the physical properties such as the mass determine
the transportation costs (Alchian and Allen (1972); Hummels and Skiba (2004);
Irarrazabal et al. (2015); Lugovskyy and Skiba (2015)). This fact is importantfor income distribution because cheap goods are often produced by the unskilled(Verhoogen (2008)). Then, higher trade burden reduces the unskilled wage.1
The purpose of this study is to show that this natural presumption leads toa somewhat unexpected result. To see this, we cite the following fact: if thetransport costs are extremely high or low, the cost difference does not matter forinequality because transport costs are not used in these cases. This result suggests
1

Admittedly, many previous studies examined the implication of sector specific trade costs forthe goods demand and the industrial structure. Feenstra (1988) examined the idea that importquotas increase the import of the high quality goods. Hanson and Xiang (2004) showed that
agglomeration force is strong for the sector with high transport costs. However, as I know, theeffect for factor demands is not examined before.

1the nonlinear effect of transport costs for wage inequality.
Main results are summarized as follows. First, transportation development
causes Kuznets curve (Kuznets (1955)). Interestingly, similar, although distinct,
nonlinear behavior was observed in Banerjee et al. (2012): the access of transportation infrastructures improves the middle-class income at the expense of theincome of the other classes. It also indicates that the sufficient investment fortransportation may reduce inequality.
Second, the effect of the trade liberalization depends on the relative importshares (Arkolakis et al. (2012)). It also implies that the size of the effect isnonlinear—the effect magnifies: with low openness, the effect of trade for inequality is low; as openness increases, however, the effect of the trade becomessizable.
To make the point clear, section 2 uses the iceberg specification of the transport
costs. However, this specification does not incorporate the idea that cheap goods
values cause the high transport costs. Then, section 3 modifies the specificationof transport costs. In this case, the absolute level of the skill premium matters
because it determines the market value of the goods. Section 4 concludes.

2

Model

Consider the economy with M + 1 countries. For tractability, we assume symmetric countries, which is a reasonable assumption because the factor difference
is not so important. Indeed, international trades mainly occurs between similar2

countries (Krugman (2000); Waugh (2010)). 2
The final goods Yi in country i is produced by the technology:
1

−1

1

−1



Yi = (βs Ysi  + βu Yui  ) −1(1)

where Ysi and Yui denote the composite skill and unskilled intensive goods respectively.  > 1 denotes the elasticity of substitution across goods with different
skill intensity. Composite goods Yhi are produced by internationally differentiatedgoods (Armington (1969)):

Yhi ≡ (

M
X

ρ−1

ρ

yhijρ ) ρ−1

(2)

j=0

where yhij is the quantity of the intermediate goods sold from country j to i.
All markets are competitive, which implies
βs Psi 1−
Psi Ysi= ()
Pui Yuiβu Pui
phii 1−ρphii yhii=()
phij yhij
phij

(3)

where phij is the price of yhij . Phi is the price indexes
X 1−ρ 1
Phi ≡ (
phij ) 1−ρ

(4)

j
2

Moreover, even unskilled abundant developing countries—in contrast to the prediction offactor proportion theory—increased wage inequality after liberalization (Goldberg and Pavcnik(2007); Verhoogen (2008)).

3

Then, we consider the intermediate goods. Following Epifani and Gancia(2008), we assume that intermediate goods are produced only by sector-specificlabors. For each sector, unit labor requirement is one. In addition, exporters mustpay θh τp units of iceberg transport cost and τt units of the wasted tariff. The
transport cost is low for high quality goods: θs < θu . Then prices arephii = wh ,phij = (1 + θh τp )(1 + τt )whi 6= j(5)where wh denotes the wage of the sector h. By symmetry, we omit the subscripti.
Now we see the distribution of revenues. They are distributed to the inputs:

Phi Yh = wh Lh(6)

where Lh is the labor force h within a country.
Consequently, we can obtain the equilibrium skill premium ω ≡ wwus . From(3), (4), (5) and (6),ω = (1−
Lu 1 + M̂ (1 + θs τp )1−ρ 1−ρ
))(Ls 1 + M̂ (1 + θu τp )1−ρ(7)where M̂ ≡ M (1 + τt )1−ρ is a measure of openness, which is large when tariff τt
is low or there are many trade partners M .
Before proceeding, it is instructive to note that the transport cost is extremely
high or low, the skill premium is unaffected by it: limτp →0 ω = limτp →∞ ω =4

( LLus )1/ . This result is obtained because transport costs are not used in these cases.
This result indicates that some nonlinearity exists.

2.1

Trade Liberalization

The effect of trade liberalization isd log ωd log M̂
where

=

−1
M̂ (1 + θs τp )1−ρM̂ (1 + θu τp )1−ρ(−)>0
(ρ − 1) 1 + M̂ (1 + θs τp )1−ρ 1 + M̂ (1 + θu τp )1−ρM̂ (1+θh τp )1−ρ
1+M̂ (1+θh τp )1−ρ=P
j6=i phij yhijPj phij yhij

(8)is the sectoral import share. The importshare is higher for the skill intensive sector, which is roughly consistent with theempirical facts (Bernard and Jensen (1995); Bernard et al. (2012)). Then, trade
costs increases inequality (See also Figure 1). The trade liberalization is more
beneficial for the labor who works in the sector where more goods is exported.
The size of the effect is also suggestive. High trade costs implies the negligiω
ω= limτP →∞ ddlnlnM̂
= 0. With negligible
ble impact of liberalization: limM̂ →0 ddlnlnM̂

trade volume, the effect of trade for wage inequality is also negligible. Moreover,as the trade volume expands by trade liberalization, the effect of the interregional
trade is increasing. Indeed, we can show that the size of the effect of trade liberalization expands if the import share of skill intensive goods is lower than 0.5 (seeappendix). Hence, policymakers must carefully handle with information from theprevious liberalization to evaluate the effect of the additional liberalization.

5

Wage inequality

TariffFigure 1: Trade liberalization and wage inequality.

2.2

Transportation Costs and Kuznets Curve

The effect of the transportation technology is much more complicated: − 1 Y M̂ (1 + θh τp )−ρ∂ log ω=∂τp

1 + M̂ (1 + θh τp )1−ρh(9)

· (θu (1 + θs τp )ρ − θs (1 + θu τp )ρ − M̂ (θs − θu ))However, it can be shown that ω(τp ) has inverted U shape, which is reminiscentof Kuznets curve (See Figure 2). This is because θu (1 + θs τp )ρ − θs (1 + θu τp )ρ −M̂ (θs − θu ) is decreasing in τp . At first, the transport development is beneficial
only for skilled labors, who suffer from relatively low trade barriers. Then, unskilled labors also gains from trade by the further reduction of transport costs.

6

Skill Premium

Transport Costs
Figure 2: Transport cost and wage inequality.

3

Non Iceberg Specification

We have used the iceberg specification. However, it does not fully incorporate
the idea that the cheap goods suffer from relatively high trade burdens. Then, we
assume that τp units of the final goods is used to export one units of intermediate
goods. Then, (5) is changed tophii = wh ,phij = (1 + τt )(wh + τp )for i 6= j

(10)where we normalize the final goods to one. Here, the transport cost is specified
symmetrically across sectors. Nevertheless, when ws > wu , transportation iscostly for the unskilled.
Revenue distribution and resource constraint are changed because: (i) somerevenue is distributed to final goods sector as transportation cost; (ii) labor is only
7

used for the production of intermediate goods. Then, we replace (6) with

Ph Yh =

X

phij xhij ,

Lh =

X

j

xhij

(11)

j

The second equation denotes the resource constraint.
Now we can obtain two equations which determine the equilibrium. The firstis the equation for the final goods price:X1−1( (βh (wh1−ρ + (wh + τp )1−ρ ) 1−ρ ) 1− = 1

(12)

h

The second is the equation for the relative labor demand. From (3), (4), (10)and (11),β/Ls
H(ws , τp )=(1 − β)/Lu
H(ws , τp )−ρwith H(w, τp ) ≡(w1−ρ + M̂ (w + τp )1−ρ ) 1−ρ
w−ρ + M̂ (w + τp )−ρ
(13)where M̂ ≡ M (1 + τt )1−ρ is trade openness. H is increasing in w (See appendix).
Then, (12) and (13) imply the negative and the positive relationship between ws
and wu respectively (see Figure 3).
The skill premium ω = wwus asymptotically reaches the value equivalent to1/Ls
the previous section: limτp →0 ω = limτp →∞ ω = ( ββus /L)  . This is because theutransport cost is not used in these cases.
/Ls
The relative factor scarcity ββus /L
is important for determining the skill preu

mium. From (13), skill premium is higher than one if and only if relative scarcity
is higher than one:βs /Lsβu /Lu≷ 1⇐⇒

ω ≷ 1. For this reason, we assume
8

ws
(13)

(12)
wu
Figure 3: The equilibrium (ws , wu )βs /Ls> 1, which produces endogenous trade barrier differences.
βu /LuFigure 4 plots computed values of ω(τp ).3 The left hand side of the figure
confirms the Kuznets curve. Moreover, in contrast to the previous section, withhigh transportation cost, the cost reduction implies lower wage inequality. Thismay be because some portion of the revenue is squeezed by the purchase of the
final goods as the transport cost. Admittedly, this result is slightly different fromthe previous section. However, at the right, the behavior of ω(τp ) is modest andnot so important because with high transport cost the effect of the trade is low.
(12) and (13) seem to be difficult to work analytically. However, if τp ≈ 0, we
3

We choose  = 2 to match the elasticity of substitution across labors (Acemoglu (1998);
Acemoglu and Autor (2011)) or across sectors with different skill intensities (Epifani and Gancia/Ls(2008)), and ρ = 6 to match the trade elasticity (Arkolakis et al. (2012)). We choose ββus /L= 200,usβs = βu = 0.5, and M̂ = 1. We also examine the parameters ρ = 4, 8, ββus /L/Lu = 2, 1600, βs =1 − βu = 0.2, 0.8, and M̂ = 0.1, 6.0. Although the quantitative result is changed considerably,theresult is not changed qualitatively.

9

4.65

Skill Premium

4.60

4.55

4.50

4.45
0.0

0.5

1.0

1.5
2.0
Transport costs

2.5

3.0

Figure 4: Skill Premium and Transportation Cost

can show ω(τp ) is increasing . From (13),H(1, wτps ) 
βs /Ls=ωβu /LuH(1, wτpu )

(14)

1

/Ls
Then, ω > ( ββus /L)  if and only if H(1, wτps ) < H(1, wτpu ). Since whτ(τp p ) ≈ 0 foruτp ≈ 0 and wτps < wτpu , it is only needed to show ∂τ∂p H(1, τp ) > 0 at τp = 0. This isindeed the case because ∂ log∂τH(1,0)=  1+M̂M̂ > 0.
p

10

4

Conclusion

This paper begins with the presumption that the unskilled intensive goods arehampered by higher transport cost by their low values. Although the model inthis paper is quite simple, many insights can be obtained: (i) The development of
the transportation infrastructure produces Kuznets curve; (ii) Trade liberalization
increases wage inequality and its effect is also increasing.
Moreover, these results have many policy implications. First, since the effectof the trade liberalization is nonlinear, the information from the previous liberalization may not be informative. Second, investments in the transportation infrastructure can change wage inequality. Especially, if the size of the investment issufficiently large, it can reduce wage inequality.

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A

2

ω
The Sign of d(lnd M̂
)2

What we want to show that if the skilled import share is lower than 50 percent,2ωthen d(lnd M̂
is positive. The first step is to write the import share of h intensive)2hsector as λ(xh ) ≡ xhx+1
where xh ≡ M̂ (1 + θh τp )1−ρ . Since λ0 (x) > 0, the skilledimport sharesλ(xh ) < 0.5 ⇐⇒ xh < 1

(15)

2

d log ω> 0 is satisfied if and only if
The next step is to see that d(lnM̂ )2φ(xs ) > φ(xu )(16)xwhere φ(x) ≡ (1+x)
2 . Then, we only need to show that if xu < xs ≤ 1, thenφ(xs ) > φ(xu ). This is indeed satisfied because φ0 (x) > 0 for x ≤ 1.

14

2

B

The Sign of ∂H
∂w

h(−ρ)
∂ log H= ( − ρ) h(1−ρ)+ ρ h(−ρ−1)
where h(ρ) ≡ wρ + (w + τp )ρ . It implies
∂w
h(−ρ)

∂H
>0
∂w

if h(−ρ − 1)h(1 − ρ) − h2 (−ρ) > 0

This condition is indeed satisfied because −ρ = 12 (−ρ − 1) + 12 (1 − ρ) and h is
2

ρ

ρ

2

w−log(w+τp ))h(ρ)
log convex: ∂ log= w (w+τpw) ρ(log> 0. Then, ∂H> 0.
∂ρ2+(w+τp )ρ
∂w

152