Tsukuba Economics Working Papers
No. 2009-006

Import Variety and Skill Premium in a Calibrated General Equilibrium Model:
The Case of Mexico
by
Manoj Atolia and Yoshinori Kurokawa
March 2009This version: March 2012

UNIVERSITY OF TSUKUBA
Department of Economics
1-1-1 Tennodai
Tsukuba, Ibaraki 305-8571
JAPANImport Variety and Skill Premium in a Calibrated General
Equilibrium Model: The Case of Mexico
Yoshinori Kurokawa
University of Tsukubaz

Manoj Atolia
Florida State Universityy

March 27, 2012

Abstract
It can be theoretically shown that imports of new foreign varieties— an increase in
the extensive margin of imports— can be a possible channel for increased skill premiumin wages. No past studies, however, have quanti…ed how much of the increase in skill
premium can be accounted for by the increase in the extensive margin. This paper formulates a static applied general equilibrium model and then calibrates it to the Mexican
input-output matrix for 1987. In the calibrated model, our numerical experiments showthat the extensive margin growth in Mexican manufactured imports from the U.S. canaccount for up to approximately 15 percent of the actual increase in skill premium in
Mexico from 1987 to 1994. It indicates that the increase in import variety reinforced
the increase in Mexican skill premium that was caused by the Mexican export side.
Keywords: Extensive margin, Import variety, Skill premium, Variety-skill complementarity, Applied general equilibrium, Mexico
JEL Classi…cations: F12, F16

We are grateful to Pedro Amaral, Cristina Arellano, Michele Boldrin, Winston Chang, Fumio Dei, Koichi
Hamada, Katsuhito Iwai, Toru Kikuchi, Paul Klein, Michihiro Ohyama, Terry Roe, Esteban Rossi-Hansberg,
and Yoshimasa Shirai for their suggestions and encouragement. We wish to thank seminar participants at
the Trade and Development Workshop at Minnesota, SUNY-Bu¤alo, Tsukuba, TUJ, Sophia, Hosei, NTU,
Sinica, Osaka, Tokyo, Keio, YNU, the Spring 2009 Midwest International Economics Meetings, the 2009
JEA Annual Spring Meeting, the 2009 FESAMES, the 2010 Midwest Macro Meetings, the Hitotsubashi
COE Trade Workshop for Young Researchers, and the IEFS Japan Annual Meeting 2010 for their usefulcomments. We also thank Kim Strain for her careful correction of our English. However, the remaining errors
are exclusively ours. This paper previously circulated under the title "Variety Trade and Skill Premium ina Calibrated General Equilibrium Model: The Case of Mexico."y
Department of Economics, Florida State University, Tallahassee, FL 32306, USA. Tel.: +1-850-644-7088.
Email: matolia@fsu.edu.
zFaculty of Humanities and Social Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan.
Tel.: +81-29-853-7426. Email: kurokawa@dpipe.tsukuba.ac.jp.

11Introduction

By extending the well-known model of variety trade in intermediate goods advanced by
Ethier (1982), it can be theoretically shown that imports of new foreign varieties— an increase in the extensive margin of imports— can be a possible source of an increase in therelative wage of high-skilled to low-skilled workers— the skill premium.1 An increase inimport variety increases the number of inputs used by the …nal goods and thus widens
the gap between the marginal products of high-skilled and low-skilled workers through thevariety-skill complementarity.2 This raises the relative demand and thus relative wage ofhigh-skilled to low-skilled workers and generates the skill premium.
This variety-skill complementarity mechanism is compatible with the spirit of the Oring model of Kremer (1993), which shows that higher skill workers will use more complex
technologies that incorporate more inputs.3 The mechanism is also compatible with thehistorical facts in regards to production organization emphasized by Mitchell (2005) if thevariety of inputs is interpreted as the variety of tasks which workers need to handle.4 During
the …rst half of the twentieth century, the spread of mass production required workers to
perform a single routine task on the assembly line. On the other hand, during the second
half of the century, the introduction of ‡exible machine tools required workers to handle awide variety of tasks in each batch. Thus, as the tasks shifted from a single routine task toa wide variety of tasks, the required skill shifted from low skill to high skill.
Hence, this variety-skill complementarity mechanism is intuitively appealing. However,this next poses a quantitative challenge since no past studies have quanti…ed how much of
the increase in skill premium is accounted for by the change in the extensive margin.5 This
paper formulates a static applied general equilibrium model and calibrates it to Mexican
data for 1987 to quantify the impact of the extensive margin growth in Mexican manufactured imports from the U.S. on the skill premium in Mexico.6 Here, applied generalequilibrium analysis is de…ned to be the numerical implementation of general equilibrium
1
Ethier’s (1982) model is an intermediate-good version of Krugman’s (1979) model of variety trade in…nal goods.
2
Kurokawa (2011) formalizes the hypothesis of variety-skill complementarity. Dinopoulos et al. (2009)
also link variety trade to wage inequality. Their model, however, modi…es the standard one-sector varietytrade model by introducing quasi-homothetic preferences for varieties and non-homothetic technology in the
production of each variety, thus relating an increase in the output of each variety— not an increase in thenumber of variety— to an increase in the relative demand for high-skilled labor by each variety.
3
Blanchard and Kremer (1997) de…ne the index of complexity which relates the increased number of
inputs to more complexity in production processes.
4
Task-based models (e.g. Grossman and Rossi-Hansberg, 2008; Acemoglu and Autor, 2010) de…ne a skill
as a worker’s endowment of capabilities for performing various tasks.
5
Although Kurokawa (2011) has provided several numerical examples to show that the variety-skill complementarity mechanism can be potentially important, it does not produce a more comprehensive quantitative analysis since its purpose is to use a simple model to highlight the existence of such a mechanism.
6
Due to data constraint, here we use data from 1987. Fortunately, however, Mexico acceded to theGeneral Agreement on Tari¤s and Trade (GATT) in 1986 and signed a framework agreement on trade andinvestment with the U.S. in 1987.

2

models calibrated to data (Kehoe and Kehoe, 1994; Kehoe and Prescott, 1995).7
We use a static applied general equilibrium model which allows us to perform a fullscale calibration.8 There are two countries and three sectors— primaries, manufactures,and services. While primaries and services are produced under constant returns and perfect competition, manufactures are di¤erentiated goods produced under increasing returns
and monopolistic competition. The production of each good uses high- and low-skilledworkers, primaries, services, and a variety of manufactures. The technology in each sector
displays the variety-skill complementarity mentioned above. Primaries and manufactures
are tradable goods, while services are non-tradable goods. In each country, a representative consumer with homothetic preferences consumes these primaries, manufactures, andservices. While our model speci…cation is very general, in this paper, we are interested inassessing the impact of the growth in the extensive margin of manufactured imports on
the skill premium in Mexico— a small country relative to the U.S. Thus, for our numericalanalysis, we specialize the model to a small open economy.
We calibrate our theoretical model to the Mexican input-output matrix for 1987. It is
worth noting that as will be shown in the matrix, much of output is services which are
non-traded and trade is not balanced in the data, which can be captured by our calibrated
model. In this calibrated model, we conduct numerical experiments to see how much of theincrease in Mexican skill premium can be accounted for by the extensive margin growthin Mexican manufactured imports from the U.S. Here, the growth in the extensive margin
is measured by the growth in what Kehoe and Ruhl (2009) call the "least traded goods."
Kehoe and Ruhl classify the set of goods which accounts for only 10 percent of trade as theleast traded goods.
Figure 1 plots the 1987-2000 data on the growth in the least traded goods in Mexican
manufactured imports from the U.S. for 1987 and on the growth in the relative wage of highskilled to low-skilled labor in Mexican manufacturing industries.9 Figure 1 reveals that theleast traded goods that account for 10 percent of Mexican manufactured imports from the
U.S. in 1987 account for 19.5 percent in 1994. This indicates that over this period, Mexico
started importing U.S. manufactured goods that it had not imported before or had imported
7

See Kehoe and Kehoe (1994) and Kehoe and Prescott (1995) for the discipline and history of applied
general equilibrium analysis. While we use it for the Mexican economy, Kehoe et al. (1988) and Kehoe etal. (1995) use a static applied general equilibrium model for the Spanish economy to analyze the impact of
the reforms implemented in 1986 to accompany Spain’s entry into the European Community (EC).
8
Our model extends Bergoeing and Kehoe’s (2003) applied general equilibrium model by distinguishinghigh- and low-skilled labor, thus relating an increase in extensive margin into an increase in skill premium.
9
The data for the least traded goods growth are the Standard International Trade Classi…cation (SITC)(revision 2) 4-digit manufacturing data from the OECD International Trade by Commodities Statistics(ITCS). See Kehoe and Ruhl (2009) for the detailed procedure used to construct Figure 1. The data for
the Mexican relative wage is from the Encuesta Industrial Mensual (EIM) [Mexican Monthly Industrial
Survey] conducted by the Instituto Nacional de Estadística Geografía e Informática (INEGI). Here, we use
non-production and production workers as an index for high-skilled and low-skilled workers (Berman et al.,
1994; Robertson, 2004). We calculate the Mexican relative wage by …rst calculating the monthly income perperson of non-production relative to production labor. The annual average is then produced by averaging
this monthly relative wage.

3

only in small quantities, thus indicating that the variety of Mexican manufactured imports
from the U.S. increased. The …gure also reveals that the growth in the least traded goods
was highly correlated with the growth in the relative wage in Mexico over 1987-2000. In fact,
the correlation between these two series was high, 0.926, over the period. As can be seen,
the extensive margin of manufactured imports was drastically growing before the North
American Free Trade Agreement (NAFTA) was enacted in 1994, and it became stable after
the NAFTA. Similarly, the Mexican skill premium was also drastically increasing before the
NAFTA and became stable (with a slight decrease) after the NAFTA.10
Since our interest is in the impact of an increase in the extensive margin of manufactured
imports on rising skill premium, our numerical experiments will focus on the period 19871994, when both the extensive margin of manufactured imports and the skill premium
were drastically increasing.11 By restricting ourselves to this period, we give the varietyskill complementarity mechanism a best chance to account for the rising skill premium in
Mexico. Speci…cally, we assess how much of the increase in Mexican skill premium canbe accounted for by the extensive margin growth in Mexican manufactured imports fromthe U.S. over the period. We …nd that the relative wage of high- to low-skilled labor canincrease by up to approximately 6.5 percent if the extensive margin of manufactured imports
increases according to the data. Hence, the growth in the extensive margin of manufactured
imports over 1987-1994 can raise Mexican skill premium by up to approximately 6.5 percent.
On the other hand, the data show that Mexican skill premium increased from 2.021 to2.899 over 1987-1994, which is a 43.4 percent increase. Thus the results indicate that theextensive margin growth in Mexican manufactured imports from the U.S. can account for
up to approximately 15 percent of the change in Mexican skill premium over 1987-1994.
We, therefore, illustrate that the extensive margin of manufactured imports is possibly achannel signi…cantly contributing to the increase in wage inequality in Mexico.12
Of course, various mechanisms which can explain the increase in Mexican skill premium
have been proposed and empirically tested (e.g. Cragg and Epelbaum, 1996; Revenga,
1997; Hanson and Harrison, 1999; Feliciano, 2001; Esquivel and Rodríguez-López, 2003;
Robertson, 2004; Verhoogen, 2008).13 As shown by these past studies, both technological
10

Esquivel and Rodríguez-López (2003) also show the same movements of Mexican wages. Robertson(2004) argues, using the Mexican Industrial Census, that the Mexican skill premium declined from 1994 to1998.
11Note that the variety-skill complementarity can be also compatible with the 1994-2000 data in that theskill premium did not show an increasing trend when import variety did not show an increasing trend during
the period 1994-2000.
12
It should be noted that here we look at Mexican trade with the U.S. alone. Our results, however, would
be little changed even if Mexican trade with other trade partners of Mexico is also included. This is because
Mexico’s principal trade partner is by far the U.S., which in 1994 supplied 69 percent of Mexico’s imports
and attracted 85 percent of its exports. In 1994, Japan provided 6 percent of Mexico’s imports, Germany 4
percent, Canada 2 percent, and France 2 percent. Canada was the second largest destination for Mexican
products, accounting for 2 percent of exports. Outside the NAFTA, no individual country absorbed morethan 2 percent of total Mexican exports.
13
There are also many notable empirical/quantitative studies on U.S. wage inequality. One set of studies
highlights the in‡uence of skill-biased technological change (e.g. Katz and Murphy, 1992; Berman et al.,4change and trade can a¤ect skill premium through di¤erent channels. This paper focuseson their e¤ects through the extensive margin of manufactured imports. While many otherfactors can also potentially cause import variety to increase, Kehoe and Ruhl’s (2009) data
analysis suggests that the extensive margin growth is primarily driven by these two factors,
namely, trade liberalization or structural change, and not by the usual turbulence of businesscycles. Thus, in the case of Mexico, the increase in import variety could be a result of tradeliberalization in Mexico or of technological change in the U.S. increasing the number ofvarieties produced there. The results of this paper are independent of these underlying
causes of the increase in import variety.14
Thus our paper makes the following contributions to the literature on Mexican wage
inequality. First, our paper would be the closest and a good complement to Verhoogen(2008). The extensive margin of exports has recently been proven useful in understanding
heterogeneous …rms export patterns (e.g. Melitz, 2003). Upon application of it, Verhoogen(2008) shows that only the most productive plants in Mexico enter the export market
and produce a better-quality good for export than for the domestic market, thus requiring
paying high wages to both white-collar and blue-collar employees, but especially to whitecollar employees. Thus, while Verhoogen (2008) focuses on the role of the extensive marginof exports in understanding Mexican skill premium, we look at the role of the extensive
margin of imports.
Second, we show the possibility that this import variety channel is quantitatively important. It indicates that the increase in import variety reinforced the increase in Mexican skill
premium that was caused by the Mexican export side (Verhoogen, 2008). Thus the e¤ects
on Mexican skill premium of the extensive margin overall might be more important thanbelieved. Third, from a methodological viewpoint, while static applied general equilibrium
models have been used in trade studies, in particular, for analyses of the impact of the
NAFTA, ours is a …rst application to the analysis of Mexican wage inequality.15
The rest of this paper is organized as follows. In Section 2, we formulate our static
applied general equilibrium model. Section 3 calibrates the model to the Mexican inputoutput matrix for 1987. Using the calibrated model, we present our numerical experiments
1994; Berman et al., 1998; Katz and Autor, 1999; Krusell et al., 2000). Another set of studies concentrates
on the e¤ect of trade (e.g. Borjas and Ramey, 1994; Krugman, 1995; Feenstra and Hanson, 1996; Krugman,
1998; Harrigan and Balaban, 1999; Xu, 2003; Zhu and Tre‡er, 2005; Burstein and Vogel, 2010). Anotherset of studies analyzes the relative e¤ect of trade vs. technological change within a uni…ed framework (e.g.
Feenstra and Hanson, 1999).
14
Our exercise avoids the pitfalls pointed out by Deardor¤ and Hakura (1994) as it can be interpreted
as answering either of the following two questions that they suggest are theoretically meaningful: (1) what
have been the e¤ects on skill premium of trade liberalization over 1987-1994 through the extensive marginof trade; or (2) what have been the e¤ects in Mexico of increases in product variety in the U.S. over thesame period to the extent that they have been transmitted through the increase in the extensive margin of
trade.
15
Kehoe (2005) evaluates the performances of three of the most prominent static applied general equilibrium models used to predict the impact of the NAFTA: the Brown-Deardor¤-Stern model of all three North
American economies, the Cox-Harris model of Canada, and the Sobarzo model of Mexico. See, for example,
Francois and Shiells (1994) for applied general equilibrium models of the impact of the NAFTA.

5

in Section 4. Finally, Section 5 summarizes main results and mentions future research.

2

The Model

Consider a world in which there are two countries: country 1 and country 2. In eachcountry j, j = 1; 2, there are three types of goods, a primary good that is tradable andhomogeneous, varieties of a manufactured good that are tradable and di¤erentiated by the…rm that produces them, and a service good that is homogeneous and non-tradable. The
varieties of the manufactured good are combined to produce a composite manufactured
good. Each country j has a given endowment of high-skilled labor and low-skilled labor,
H j and Lj .16
A representative consumer in country j solves the problem of maximizingjp log cp +jm log cm +js log cs ;

(1)

j j
j
L
H j + wL
wH

(2)

subject toj j
qpj cjp + qm
cm + qsj cjs

cjp ; cjm ; cjs

0:Here, cjp is the consumption of the primary good and qpj is its price; cjm is the consumptionjis its price; cjs is the consumption of the serviceof the composite manufactured good and qmjj
good and qsj is its price; and wH
and wLare the wages for the high- and the low-skilledlabor. The composite manufactured goods is a CES aggregate of di¤erent varieties givenbycjm =where parameter ;

Z

Dw

1

(cjmz ) dz;

(3)

< 1; governs the elasticity of substitution, 1= (1two di¤erentiated varieties in the interval Dw =0; n1 + n2), between anyof the varieties of the manu-

factured good produced throughout the world. On the other hand, note that the elasticity
of substitution between primaries, services, and composite manufactures is 1.
Both the primary and the service good in country j are produced according to constantreturns production functions
ypj =
ysj =
16

h

j
"
p ap bp (xm;p ) + (1hj"s as bs (xm;s ) + (1bp ) (Hpj )"

"

+ (1

ap ) (Ljp )bs ) (Hsj )"

"

+ (1

as ) (Ljs )

i p1

i s1

(xjp;p ) p2 (xjs;p ) p3 ; (4)(xjp;s ) s2 (xjs;s ) s3 ; (5)It should be noted that by introducing primary and service goods in the present paper, we have generalized Kurokawa’s (2011) model that has only manufactured goods produced by high- and low-skilled labor.
In addition, we have also allowed trade in …nal goods which is absent in Kurokawa’s model.

6where 0 < ai ; bi < 1;i > 0; and 0 < ik < 1 are sector-speci…c parameters with i1 + i2 +j
i3 = 1 and xh;i refers to factor h used in sector i. The composite manufactured inputs are

xjm;p =

Z

Dw

Z

1

xjmz;p dz

andxjm;s =

1xmz;s dz

:

(6)

Dw

In contrast, the technology for producing manufactured goods exhibits increasing returns
to scale because of the presence of …xed costs. Speci…cally, every manufacturing …rm z;
z 2 Dw , has the production function
j
ymz
= max

8
>
<
>
:

m

2

n
j
"
a
4 m bm (xm;mz ) + (1(1jbm ) (Hmz)"
am ) (Ljmz )where as in other sectors 0 < am ; bm < 1;Also,
xjm;mz =ZDwom > 0; 0 <

"

3 m1

+ 5

(xjp;mz ) m2 (xjs;mz ) m3

mk < 1; and9>=F; 0 ;
>
;

(7)
m1 +

m2 +

m3 = 1:

1

xjmz 0 ;mz

dz

0

;

(8)

and F > 0 is the level of …xed costs in terms of output.
Thus, in each sector, production requires primaries, services, and a composite good as
inputs. The composite input is produced by combining the manufactured good, high-skilledlabor, and low-skilled labor with a nested-CES technology, where substitution parameters "andare the same across all sectors. The nested-CES speci…cation allows us to introduce

variety-skill complementarity in production in the most natural and parsimonious manner.
This is achieved by setting " <which makes the varieties of manufactured goods relatively

more complementary to high-skilled labor than to low-skilled one.17
jjj; qpj ; qsj ; ymz + F ) be the solution to the cost minimization problem
; wL
; wH
Let c~jmz (qmfor manufacturing …rm z: As the manufacturing sector produces output using a nested-CES
technology with primaries, services, and a composite input made from manufactured good,high-skilled labor, and low-skilled labor as inputs, the cost function can be written in termsof the sub-cost functions as follows:jjjc~jmz qm
; wH
; wL
; qpj ; qsj ; ymz + Fjjj= c~jmz c~jA;m qm
; wH
; wL
; qpj ; qsj ; ymz + F ;jjj= c~jmz c~jA;m c~jB;m qm
; wH
; wL
; qpj ; qsj ; ymz + F ;
! m1
"
#
m2
m3
c~jA;m
ymz
qp
1
qs
=
(9)
;
+F
m1
m2
m3
m

17

Kurokawa (2011) formalizes the hypothesis of variety-skill complementarity. As mentioned in the introduction, the number of inputs plays a related role in the O-ring model of Kremer (1993), which shows thathigher skill workers will use more complex technologies that incorporate more inputs.

7where z 2 D1 = 0; n1 or z 2 D2 = n1 ; n1 + n2 ; and the sub-cost functions are
c~jA;mc~jB;m

1

1

j
j
j
qm
; wH
; wL

=

j
j
qm
; wH

c~jB;m

1

am
1
1 "

=

j
j
qm
; wH

+ (1

"

j
qm

bm

1

1 "

1

+ (1

am )

j
wL

1

;(10)

1 "
"

"
1 "

j
wH

bm ) 1 "

1
1

:

(11)

Thus we can write c~jmz (:) as a linear function of ymz + F :jjjc~jmz qm
; wH
; wL
; qpj ; qsj ; ymz + F= Gj (ymz + F ) ;z 2 Dj ;j = 1; 2:(12)

The …rms in the manufacturing sector are monopolistic competitors and face a downwardjsloping demand curve and manufacturing …rm z 2 Dw in country j sets its price qmz
tomaximize pro…ts:

max

j
j
mz = qmz ymz

Gj (ymz + F ) ;(13)

taking all other prices as given.
Let us derive the demand for each variety z. The demand by the consumer in country
j for the domestic variety z 2 Dj and the foreign variety z 2 D j is:
cjmz
cjmz

=

=

j
qmz
j
qm

qmzj
j
qm

!
!

1
1

j j
j
L
H j + wL
wH

m

j
qm
1
1

j
j j
wH
H j + wL
L

m

j
qm

;

z 2 Dj ;(14);

z 2 D j;(15)

jis the price in country j of variety z 2 Dj and qmzj the price in country
where qmz

variety z 2 D

j.

j of

j
One can show that qm
can be written as an exact consumption-based

price index of the prices of individual varieties as follows:
j
qm
=

Z

Dj

j
(qmz
)

dz +

1

Z

1

D

j

(qmzj )

1

dz

:

(16)

Hence, the total consumption demand for variety z 2 Dj faced by the …rm is:cjmz + cmzj =

j
qmz
j
qm
j
qmz

qmj

!
!

1
1

m

j
qm
1
1

m

+

wHj H j + wL j L jqmj

1= Eqmz1jj j
wH
H j + wLL

z 2 Dj ;;8

j = 1; 2;(17)where
E=

m

j
j j
wH
H j + wL
L
j
(qm
)

+

wHj H j + wL j L jm(qmj )

1

:

(18)

1

j
Thus the total consumption demand varies with price qmz
with elasticity

1= (1). Onecan show that the same holds true for the total input demand by …rms for variety z 2 Dj .
Thus the total consumption and input demand for variety z can be expressed as1

ymz = T qmz1

z 2 Dj ;;j = 1; 2;(19)

for some constant T > 0:Hence, given the number of varieties, the pro…t of manufacturing …rm z can be rewritten
as:
1
j
j
mz = qmz T qmz

1

Gj T qmz1

1

Gj F:

(20)

The …rst order condition for pro…t maximization with respect to qmz then gives:
qmz =

Gj

;

z 2 Dj ;j = 1; 2:(21)

Gj (ymz + F ) = 0;(22)

z 2 Dw :(23)

Further, by the zero pro…t condition for this qmz :
G
j
mz =

j

ymz

we obtain
j
ymz
=

1

F;

j
j
j
; and quantities cjp ;; wLDe…nition 1 An equilibrium is a vector of prices qpj , qsj , qmz, wHj; xjmz;p ; xjp;p ; xjs;p ; Hpj ; Ljp ; xjmz;s ; xjp;s ; xjs;s ; Hsj ; Ljs ; xjmz;mz ; xjp;mz ; xjs;mz ;cjs ; cjmz ; ypj ; ysj ; ymz
j; Ljmz ; z 2 Dj ; j = 1; 2; an interval Dw = [0; n1 + n2 ]; and a measure of manufacturingHmz…rms for each country D1 = 0; n1 and D2 = n1 ; n1 + n2 such that

1. Given the prices, the consumption plans cjp ; cjmz ; cjs solve the utility maximization
problem of consumer j;
2. Given factor prices, the production plans (including the factor demands) for the primary and service good satisfy the conditions for zero pro…t and cost minimization;j
3. Given factor prices and demand, price qmz
and production plans (including the factor

demands) of the manufacturing …rm z in country j maximize pro…ts and minimize
costs;
4. Every manufacturing …rm z 2 Dw earns zero pro…ts;
9

5. The markets for goods clear,
P2

j=1

cjp + xjp;p + xjp;s +Z

Djxjp;mz dz

Z

=

P2

j
j=1 yp ;xjs;mz dz = ysj ; j = 1; 2;
Dj
2
3
R
j
j
j
j
cmz + xmz;p + xmz;s + Dj xmz;mz 0 dz 0 +j4
5 = ymz; j = 1; 2;Rjj
cmzj + xmz;p+ xmz;s+ D j xjmz;mz 0 dz 0
cjs + xjs;p + xjs;s +

(24)
(25)
(26)

6. The factor markets clear,
Hpj +

Z

Ljp +

Dj

Z

j
Hmz
dz + Hsj

Dj

= Hj;

j = 1; 2;(27)

Ljmz dz + Ljs = Lj ;j = 1; 2;(28)

7. The number of available varieties for consumption is the number of varieties produced,
Dw = D1 [ D2 :3

Calibration of the ModelIn the previous section, we have laid out the model in the two-country setting. We, however,are interested in assessing the impact of the growth in the extensive margin of manufactured
imports on the skill premium in Mexico— a small country relative to the U.S. Thus, inour simulations, we will concentrate on the small open economy case. Therefore, we will
omit country superscripts from this section onwards. The details of solving the model are
standard and have been relegated to Appendix A.
We calibrate the model to the input-output matrix for Mexico for the year 1987 to test
the ability of the model to account for the rise in skill premium in Mexico over the period
1987-1994. The choice of 1987 comes from data constraint. However, this is not a serious
limitation since Mexico acceded to the GATT in 1986 and signed a framework agreementon trade and investment with the U.S. in 1987.

3.1

Data

The input-output matrix for Mexico for 1987 is given in Appendix B. This matrix contains
the information on the factor costs in each sector (Xh;i ) where i stands for sector and hstands for the factor; the value of output for each sector, Yi ; the value of exports andimports for each sector, EXi and IMi ; and the value of consumption of each good, Ci . Allof the steps to construct this input-output matrix and the sources of the data are shownin Appendix B. Note that we do not have data on the break-up of the cost share of labor10between low-skilled and high-skilled labor for the primary and service sectors for Mexico.18
In the benchmark simulations, we assume the share to be the same as in the manufacturingsector. In an alternative scenario, we use the break-up for Chile for 1992.
As shown in the matrix, much of output is services which are non-traded, and trade is
not balanced in the data. We can also see that the gross value added in each sector equals
its factor paymentsYi =Ph Xh;i ;i = p; m; s;(29)

and that the total use of each good equals its net supplyPk Xi;k + Ci = Yi + IMi

3.2

CalibrationEXi

i = p; m; s:(30)

We begin our calibration by choosing the values of the three substitution parameters in themodel, , , and ". The parameter

governs the elasticity of substitution, 1= (1), among

varieties. Recall that the elasticity of substitution between the primaries, the services, andthe manufactures is already set to 1. We set
substitution among varieties, 1= (1= 19=29, which means that the elasticity of), is 2:9. This is in accordance with evidence on theelasticity of substitution across varieties of intermediate goods estimated by Klenow andRodríguez-Clare (1997).19
Parametersand " set the elasticity of substitution between the varieties and low-skilledlabor and between the varieties and high-skilled labor, respectively. Due to the uncertainty
about these elasticities, we set

and " as free parameters. Here, as a benchmark case, wechoose the elasticity of substitution for low-skilled labor to be 2 and for high-skilled labor tobe 0.5.20 This implies= 1=2 and " =analysis for a variety of values of

1. In Section 4.2, we will do an extensive sensitivity

and " and report the range for skill premium rather

than a point estimate. Therefore, the choice of benchmark values of these two substitution
parameters does not a¤ect the results that we report.
We next calibrate the rest of the model’s parameters to match the input-output matrix
18

As will be noted in footnote 30 in Section 4.3, though the Encuesta Nacional de Empleo Urbano (ENEU)[National Urban Employment Survey] conducted by the INEGI has data for the primary and service sectors
in Mexico, unfortunately it is not consistent with the data that we use for skill premium and input-output
matrix.
19
Klenow and Rodríguez-Clare (1997)’s estimate, though based on Costa Rican data, is in line withestimates of substitutability in the trade and industrial organization literatures (see Feenstra, 1995).
20
Although our focus is on variety-skill complementarity, it is worth noting that a number of studies
report evidence on capital-skill complementarity. For example, see Griliches (1969), Berndt and Christensen(1974), Fallon and Layard (1975), and Brown and Christensen (1981). As Krusell et al. (2000) document,
the majority of the estimates for the elasticity of substitution between low-skilled labor and capital lie
between 0.5 and 3 whereas most estimates of the elasticity of substitution between high-skilled labor andcapital are below 1.2, and as they note, “several are near zero.”This capital-skill complementarity hypothesis
was …rst formalized by Griliches (1969). Goldin and Katz (1998) document the importance of capital-skill
complementarity during the period 1909-1929. Lindquist (2005) has recently replicated the research by
Krusell et al. (2000) for Sweden.

11

for Mexico for 1987. We begin this calibration by setting
E = Cp + Cm + Cs :(31)

Further, given that there are productivity parameters in the production functions, we canonly normalize all domestic goods prices to 1, i.e., we set
qp = qm = qs = 1:

(32)

Further, we can also independently set the wage rates. Hence, without loss of generality,
let21
wL = wH = 1:
The calculation of

0

(33)

s is straightforward in our case
i =

Ci
;
E

i = p; s; m:

For factor h, de…ne the cost share of that factor in sector i as
price of factor h = p; s; m; L; H.22

(34)h;i and denote by wh theThen, from the demand functions derived above, we geth;i (qm ; wH ; wL ; qp ; qs ) =wh xh;i (qm ; wH ; wL ; qp ; qs ):c~i (qm ; wH ; wL ; qp ; qs )(35)

Then, b0i s can be solved from the following equations
m;i

=

H;i

Xm;i
;
XH;i

i = p; s; mz:(36)

Each of these equations has only one unknown, bi . Note that here we are using the fact
that

Xm;mz
Xm;m
=
:
XH;mz
XH;m

(37)

Similarly, a0i s solve the following equations
m;i + H;i=

L;i

Xm;i + XH;i;XL;ii = p; s; mz:(38)

Recall, as we do not have data on the break-up of the cost share of labor between low-skilled
and high-skilled labor for the primary and service sectors, in the benchmark calibration we
set

H;i = L;i =23
H;m = L;m ; i = p; s.

21

It does not matter how big wH is in relation to wL . Normalizing prices/wages at one only changes theunits of goods and labor, but does not change the results in terms of percent changes.
22
For example, wm = qm , wp = qp ; and ws = qs .
23
In Section 4.3, for the primary and service sectors, we will use the break-up in Chile in 1992.

12

0 s are easy to calculate as well
i

The

i1

=

i2

=

i3

=

Xm;i + XH;i + XL;i
;
Yi
Xp;i
; i = p; s; mz;
YiXs;i; i = p; s; mz:
Yi

i = p; s; mz;

(39)
(40)
(41)

With all goods prices (qp ; qm ; qs ) and factor prices (wH ; wL ) normalized to 1, factor costs
equal factor demands, and it is easy to calibrate

p and

(4

i . Furthermore, by labor market clearing,5) in which the only remaining unknown iss by using the production functions

the supply of low-skilled and high-skilled labor is simply equal to the factor payments ofeach labor.
P

L =
H =
3.2.1

i=p;m;s XL;i ;(42)

i=p;m;s XH;i :

(43)

P

Remaining Calibration

To complete the calibration we still need to …nd values for
qmz ; qmz ;m ; n; n ; xmz ; xmz :(44)

We begin with the composite of the domestic traded varieties which can be expressed as
xmz =

Ym

EXm
Ym EXm
=
;
1
qmz
n
q

(45)

mz

which in turn yields24
xmz =

xmz
n

1

=

Ym

EXm
nqmz

:

(46)

Similarly,
xmz =

xmz
(n )

1

=

IMm
:
n qmz

Since varieties are aggregated using a CES aggregator, it is easy to see from (14or (A:9

15)A:10) that the relative demand for the domestic and foreign varieties is
xmz
=
xmz

24

(47)

qmz
qmz

We could have obtained this directly using symmetry.

13

1
1

:

(48)

Further, from the price index of the manufactured good (A:12), we have11

qm = nqmz

1+ n qmz;(49)

which can be simpli…ed using (48). For this, we use (48) to obtainnnqmz xmz=
n qmz xmz
n

qmz
qmz

1

=

Ym

EXm
;
IMm

(50)

which can be used to write (49) as
1

qmz

qm = (n )1= (n )

qmz

"(

n
n

Ym

qmz
qmz

1

EXm
+1
IMm

)

#

1

+1

1

:

(51)

Finally, we impose the normalizationn + n = 100;(52)

and calibrate the ratio of varieties produced in Mexico and the U.S.
n
n

(53)

using the employment data. It can be shown that in the model, the ratio n=n equals
the ratio of the total labor compensations in the Mexican and U.S. manufactures (XH;m +XL;m )=(XH;m + XL;m ), which is approximately 3=97 in the data for 1987.
It is possible to solve (21), (4648) ; and (5153) for qmz ; qmz ;m ; n; n ; xmz ; andxmz . In order to complete the calibration of the model, we check the calibration by ensuringthat all markets actually clear. The resulting calibration of the model is summarized inTable 1, and Table 2 lists the initial steady state values of the key variables.

4

Extensive Margin and Skill Premium

We have calibrated the static applied general equilibrium model to the Mexican economy.
In the calibrated model, we quantitatively evaluate the ability of the variety-skill complementarity mechanism to account for the rise in skill premium in Mexico over the period
1987-1994. To do so, we change the number of foreign varieties— the extensive margin of
manufactured imports— in the calibrated model as in the Mexican data from 1987 to 1994.
Here, as we have seen in Figure 1, the growth in the extensive margin is measured by the14growth in what Kehoe and Ruhl (2009) call the "least traded goods."25 Kehoe and Ruhl
classify the set of goods which accounts for only 10 percent of trade as the least traded
goods. As shown in Figure 1, the least traded goods that account for 10 percent of Mexican
manufactured imports from the U.S. in 1987 account for 19.5 percent in 1994, which is a 95
percent increase in the extensive margin of manufactured imports. This indicates that overthis period, Mexico started importing U.S. manufactured goods that it had not imported
before or had imported only in small quantities, thus indicating that the variety of Mexican
manufactured imports from the U.S. increased.
It is worth noting that the method by Kehoe and Ruhl (2009) used in our paper formeasuring the extensive margin is di¤erent from methods used in the few previous studiesof the extensive margin. Hummels and Klenow (2005) and Broda and Weinstein (2006), forexample, classify a good as not traded if the value of trade is zero, and Evenett and Venables(2002) classify a good as not traded if its yearly value of trade is less than or equal to 50,000
1985 U.S. dollars, regardless of the country to be studied.26 In Kehoe and Ruhl’s de…nitionof a non-traded good, on the other hand, goods with very small but non-zero amounts oftrade can also be considered, and the actual dollar value of the 10 percent cuto¤ can di¤er
across countries. Thus non-traded goods in a country are determined based on the relative
importance of goods in the country’s trade. In fact, this country-variant method by Kehoeand Ruhl has been widely used. Mukerji (2009) and Sandrey and van Seventer (2004), forexample, use the method to measure the extensive margin of trade as does our paper.
Before presenting the results, here we brie‡y sketch the procedure for solving for the0
0 , n0 , q 0 , q 0 , w 0 , w 0 , y 0 , and y 0 ,new equilibrium. To obtain the new values of qmz
; qmz
s
m
p
s
H
L

we solve zero pro…t conditions (A:11) for the primary and the service sectors; the pro…tmaximization condition (21) for a representative domestic variety; the price index (49) for
the domestic composite manufactured good, qm ; market clearing conditions (4243) for thetwo types of labor; the market clearing condition for the non-traded service good (25); theconsumer’s budget constraint (A:2); and the market clearing condition for a representative
foreign variety (26). In the consumer’s budget constraints, total net exports adjust freely
in the new equilibrium.

4.1

Numerical Experiment - Extensive Margin and the Skill Premium

In this experiment, as mentioned above, we increase the number of foreign varieties nby 95 percent as in the Mexican data over 1987-1994. Thus it is anticipated that theincreased availability of varieties would raise the demand for the high-skilled labor relative25

Klenow and Rodríguez-Clare (1997) measure import variety by the number of countries from which agiven product is imported.
26
According to Kehoe and Ruhl (2009), there is no absolute concept of zero in trade statistics. For
example, export shipments from the U.S. (import shipments to the U.S.) are, in general, required to bereported only if the value of the shipment is greater than 2,500 U.S. dollars (2,000 U.S. dollars). A good
could have trade with a number of shipments smaller than this limit and be reported as having zero trade.
The minimum reporting level tends to vary across countries.

15

to that of the low-skilled labor since the high-skilled labor is more strongly complementary
to varieties than the low-skilled labor. This, in turn, will lead to the rise in the wage ofthe high-skilled labor relative to that of the low-skilled labor— the skill premium. In otherwords, the increase in the available number of foreign varieties will lower the price of thecomposite manufactured input, which in turn will raise the relative wage of the high-skilledlabor through the variety-skill complementarity mechanism.
This indeed is the case as shown by the new equilibrium for the year 1994 in Table 2.
The number of imported varieties n rises from 97 to 189.15, which is a 95 percent increasein the number of foreign varieties. The price index of the composite manufactured good falls
from 1 to 0.8952. As a result, we can see that the wage of the high-skilled labor increases
from 1 to 1.0377 and that of the low-skilled labor decreases from 1 to 0.9972. Thus therelative wage wH =wL increases from 1 to 1.0406, which is a 4.06 percent increase.
Other changes in the equilibrium are also worth noting. While qmz does not change in
the new equilibrium, qmz does fall, in this case, from 1.9422 to 1.8947. While the numberof imported varieties n increases, the quantity of each imported variety xmz actually
falls from 4.17 to 3.34. This is an interesting and important point in variety-trade models
emphasized by Ethier (1982). When the increased number of varieties become available,
it is optimal to spread existing imports over these varieties to gain from the diversity of
inputs. However, this also reduces the price of the composite input which then increases its
usage. This increase in usage tends to mitigate the fall in quantity of each imported variety
but does not completely o¤set it.
The e¤ect on skill premium of the extensive margin growth in manufactured imports
seems to be small compared to the data. The data show that the Mexican skill premiumincreased from 2.021 to 2.899 during the period 1987-1994, which is a 43.4 percent increase.
Thus the extensive margin growth in Mexican manufactured imports from the U.S. accounts
for approximately 9.4 percent of the change in Mexican skill premium over 1987-1994. It
should be noted that here we have looked at Mexican trade with the U.S. alone. Our results,
however, would be little changed even if Mexican trade with other trade partners of Mexico
is also included. This is because Mexico’s principal trade partner is by far the U.S., which
in 1994 supplied 69 percent of Mexico’s imports and attracted 85 percent of its exports.
It should be also noted that one of the most salient characteristics of the Mexican
economy is maquiladoras. This export-processing sector imports intermediate inputs andthen assembles them into …nal goods in a similar way as modeled in this paper. In fact, ourassumption (manufactured imported inputs and high-skilled workers are complements) can
be compatible with the observations in maquiladoras emphasized by Feenstra and Hanson(1997): both the imports from the U.S. and the demand for high-skilled workers increasedin maquiladoras.27
27

Of course, low-skilled workers would be used more intensively than high-skilled workers in maquiladoras,
but it is still possible that the demand for high-skilled workers increases more than that for low-skilled workers(complementarity). In fact, our experiments successfully capture both the intensity and the complementarity.

16

4.2

Sensitivity Analysis

The results obviously depend on the values of the two substitution parameters in the model," and . We thus do an extensive sensitivity analysis for a variety of values of " andandreport the range for skill premium rather than a point estimate. Given the uncertainty
about these elasticities, the sensitivity analysis can test the robustness of our quantitative
results. It can also provide an estimate of the upper bound on the amount of rise in skill
premium in Mexico that can be accounted for by the extensive margin growth in Mexican
manufactured imports from the U.S.
Recall that the benchmark numerical experiment in Section 4.1 has set " =1 and= 1=2. This means that the elasticity of substitution between the varieties and high-skilledlabor, 1= (1"), is 1=2 and that between the varieties and low-skilled labor, 1= (1

), is

2.
Here, we do our sensitivity analysis for two sets of value of " andso that the twoelasticities of substitution take extreme values. Table 3 reports the results of the numericalexperiment in which " =3 and= 3=4, that is, the elasticity of substitution between thevarieties and high-skilled labor is 1=4 and that between the varieties and low-skilled labor is
4. The rise in skill premium is still small but is stronger (a 5.17 percent increase) comparedto the benchmark case (the 4.06 percent increase). We can now account for 11.9 percent of
the actual rise in skill premium.
In Table 4, we further increase the di¤erence in the elasticities by letting " =9 and= 9=10; the elasticity of substitution between the varieties and high-skilled labor is 1=10
and that between the varieties and low-skilled labor is 10. As we can see, the results indicatethat the skill premium now increases slightly more (a 5.49 percent increase). We can now
account for 12.7 percent of the actual rise in skill premium.
Qualitatively, these results are as expected. A more negative value of " (a smaller
elasticity of substitution between the varieties and high-skilled labor) and a greater valueof(a greater elasticity of substitution between the varieties and low-skilled labor) areaccompanied by a larger increase in skill premium. Quantitatively, however, all of theseincreases (4.06, 5.17, and 5.49 percent) do not make a signi…cant di¤erence in that they arearound 10 percent of the actual increase of 43.4 percent. In fact, it can be shown that in our
numerical experiments, the upper bound for the increase in skill premium is approximately
13 percent of the actual increase of 43.4 percent. However, the choice of elasticities ofsubstitution may make a greater di¤erence when the rise in skill premium is initially moresigni…cant in the benchmark case.
It is worth noting that besides the manufacturing sector, the service sector also expands
whereas the primary sector shrinks when the elasticity of substitution between the varieties
and high-skilled labor is small (" =

3 and

9).

17

4.3

Sectoral Variation in Skill Intensity of Employment and Skill Premium

In the previous sections, we might have underestimated the increase in skill premium dueto the increase in the extensive margin of manufactured imports. In the new equilibrium,
manufacturing and service sectors can expand at the expense of the primary sector. Thereis overwhelming evidence that manufacturing and service production is more skill intensive
than the production of primaries (see Atolia, 2007).28 In fact, recent evidence in Bussolo etal. (2002) indicates that the service sector is the most skill-intensive sector followed by the
manufacturing.29 The upshot of these facts is that as manufactures and services expand,their resulting resource allocation further raises the relative demand of high-skilled laborthrough the Heckscher-Ohlin mechanism.
Due to lack of data on the skill intensity of employment in the primary and service sectors
for Mexico, we have so far assumed the skill intensity to be the same as in manufacturing.30
However, as the above discussion shows, this is not an innocuous assumption and mightlead us to underestimate the e¤ect of the growth in the extensive margin of manufactured
imports on skill premium. The only virtue of this assumption is that it does not demand
any additional data. It can, however, be argued that this virtue is also its weakness since
it forces us to ignore evidence available on sectoral di¤erences in skill intensity, albeit fromother similar countries.
To rectify this shortcoming of the previous analysis, in this subsection we allow sectoraldi¤erences in the skill intensity of employment. In particular, we use the evidence in Bussolo
et al. (2002) on the skill intensity of employment in Chile for 1992.31 They provide thesectoral break-up of employment into seven categories. We present results for two di¤erent
ways of aggregating these categories into high- and low-skilled employment.
In the …rst case, we aggregate workers by their skill level: managers and professionals,
technicians, administrative workers, and skilled blue collar workers comprise the high-skilled
28

Atolia (2007) shows, using numerical simulations, that the rise in wage inequality in Latin America canbe rationalized as a short-run response to trade liberalization. See also Robbins (1996) for discussions on
increased skill premium in Latin America.
29
Note, this implies that by assuming the skill intensity of employment to be the same as the manufacturingsector for all sectors, we have not overestimated the overall skill intensity of employment in the economy.
In fact, besides being the most skill-intensive sector, the service sector is also the biggest, accounting foralmost half of the total output of the economy.
30
Note that though the ENEU conducted by the INEGI has data for the primary and service sectors in
Mexico, unfortunately it is not consistent with the data that we use for skill premium and input-output matrix. While our data use a non-production/production classi…cation, the ENEU data use a post-secondary/no
post-secondary classi…cation. In fact, the share of non-production employment in the manufacturing sector
is 30 percent in our data, but the share of post-secondary in the manufacturing sector is 12 percent in the
ENEU data. On the other hand, the data in Bussolo et al. (2002), though Chilean data, classify workers
by skill level, and the share of skilled workers in the manufacturing sector is 28 percent in the Bussolo et al.
data. Thus, the Bussolo et al. data, though from Chile, are more consistent with our data.
31
Table 2 in their paper summarizes the structural features of the Chilean economy. They report theshares of gross output, value-added, total demand, trade ‡ows, and employment for 24 sectors and threeaggregate macro-sectors (primary, manufactures and services). These shares are calculated using the Social
Accounting Matrix for Chile in Alonso and Roland-Holst (1995).

18

category; commerical and service workers, un-skilled blue collar workers, and informal workers comprise the low-skilled. With this classi…cation, the ratio of (share of) high-skilledworkers in the primary sector to the manufacturing sector is 11/28. The number for theservice sector is 32/28. We recalibrate the model taking these sectoral skill intensity variations into account.
In the recalibrated model, the change is that as shown in Table 5, the growth in the extensive margin of manufactured imports over 1987-1994 gives rise to a 3.94 percent increasein skill premium for the benchmark values of " =1 and= 1=2, which is slightly smaller

than the 4.06 percent change in the absence of sectoral variations in skill intensity. This
3.94 percent increase is 9.1 percent of the actual 43.4 percent increase. In fact, by doing asensitivity analysis it can be shown that the upper bound of the increase in skill premium
is approximately 14 percent of the actual rise.
In the …rst case, the classi…cation of the workers as high- and low-skilled is not thesame across all sectors. We have followed the skill classi…cation of Bussolo et al. (2002)
for the primary and service sectors, whereas for the manufacturing sector, we have used
nonproduction-production classi…cation based on Mexican data. To avoid this problem, inthe second case, we aggregate employment in the primary and service sectors according to
the white and blue collar classi…cation of Bussolo et al. (2002) which corresponds moreclosely to the nonproduction-production classi…cation. As a result, now the ratios of highskilled workers in primaries and services are 22/48 and 49/48. In the recalibrated model, as
shown in Table 6 the skill premium now increases by 4.17 percent for the bencmark valuesof " =1 and= 1=2. This number (4.17 percent) is 9.6 percent of the actual observed

rise in skill premium. In fact, by doing a sensitivity analysis it can be shown that the upperbound of the increase in skill premium is approximately 15 percent of the actual rise in thissecond case.
Thus the above results indicate that in the previous sections, we have slightly underestimated the increase in skill premium due to lack of data on the skill intensity of employment
in the primary and service sectors for Mexico.

5

Conclusion

The main purpose of this paper has been to quantitatively evaluate the ability of thevariety-skill complementarity mechanism to account for the rise in skill premium in Mexico
over the period 1987-1994. The results of our numerical experiments indicate that theextensive margin growth in Mexican manufactured imports from the U.S. has the capabilityof accounting for up to approximately 15 percent of the change in Mexican skill premium
during this period. Here, we have illustrated the possibility that the growth in the extensive
margin of manufactured imports can signi…cantly contribute to the increase in Mexican skill
premium, indicating that the increase in import variety reinforced the increase in Mexican

19

skill premium that was caused by the Mexican export side (Verhoogen, 2008).
It may be noted that while the increase in the extensive margin of manufactured imports
is large, the rise in wage inequality in Mexico is modest in our experiments. A factor causing
this modesty is that in our model, the marginal products of both high- and low-skilled laborrise due to the increased number of inputs, but the former rises disproportionately morethan the latter. Thus the relative demand for high- to low-skilled labor does not rise as
much, thereby mitigating the rise in wage inequality.
Looking forward, we can say that this paper’s methodology can be used to derive further
quantitative implications. First, this paper has focused on the case where Mexico is a small
open economy. We can also extend our model to a two-country model.
Second, our model can be directly applied to countries other than Mexico. We cancalibrate our model to the input-output data for other countries and then quantify thee¤ects of the growth in the extensive margin of manufactured imports on skill premium ineach of them.
Third, this paper has focused on the extensive margin of manufactured imports. It
would also be interesting to introduce tari¤s into the model and then exogenously change
the tari¤s to change the intensive margin of manufactured imports— the import volumes ofexisting foreign varieties— in the model as in available data.
Finally, it would also be interesting to extend our model to a heterogeneous …rm trademodel. It may provide further insights on the rise in wage inequality due to the heterogeneous use of increasing import varieties.

20Appendix A - Solving the Model
To solve the model, we begin with the consumer’s problem.

Consumption
With the Cobb-Douglas utility function, the consumer’s optimal decision is to spend a
constant fraction

i of his income on good i = p; m; s. Thus utility maximization yields thefollowing demand functions for the consumption of the di¤erent goods:
ci (qi ; E) =

iE

qi

;

i = p; m; s;(A.1)

where E is the total consumption expenditure and qi is the price of good i. From (2), we
have that the consumption expenditure equals the wage income. However, with an eye on
calibration to data wherein a country may not have the balanced current account, we allow
for net exports (N X) and E to be given by
E = wH H + wL L

N X:

(A.2)

Accordingly, in the demand for each individual variety in (1415) ; wH H +wL L is replaced

by E.

Production
Turning to the production, we start with the primary and service sectors. Similar to (9),we can write the cost functions for the primary and service sectors as
c~i (qm ; wH ; wL ; qp ; qs ; yi ) = c~i (~cA;i (qm ; wH ; wL ) ; qp ; qs ; yi )= c~i (~
cA;i (~
cB;i (qm ; wH ) ; wL ) ; qp ; qs ; yi )i2
1 c~A;i (qm ; wH ; wL ) i1 qp
=
i1

i

i3

qs

i2

yi ; (A.3)

i3

where
1

1

c~A;i (qm ; wH ; wL ) =c~B;i (qm ; wH ) =

1

ai

1
1 "

bi

c~B;i (qm ; wH )
qm

"
1 "

+ (1

1

bi )

+ (1
1
1 "

wH

ai ) 1
"
1 "

1

wL

1

;

1 "
"

;

(A.4)

and, i = p; s:Using these cost functions, it is easy to derive the input demands using Shephard’s

21

lemma. For example, the demand of primaries isxp;i (qm ; wH ; wL ; qp ; qs ; yi ) =xp;mz (qm ; wH ; wL ; qp ; qs ; ymz + F ) =

~i
@~
ci
i2 c
=
;
i = p; s;
@qp
qp
@~
cmz
~mz
m2 c
=
;
@qp
qp

(A.5)
(A.6)

where the numerator is the factor payment to the primaries for the relevant good or variety,and the demand for service input isxs;i (qm ; wH ; wL ; qp ; qs ; yi ) =xs;mz (qm ; wH ; wL ; qp ; qs ; ymz + F ) =

@~
ci
~i
i3 c
=
;
i = p; s;
@qs
qs
~mz
@~
cmz
m3 c
=
;
@qs
qs

(A.7)
(A.8)

Similarly, we can derive the demand for low-skilled labor (Li (qm ; wH ; wL ; qp ; qs ; yi )) andhigh-skilled labor (Hi (qm ; wH ; wL ; qp ; qs ; yi )) and that of the composite manufactured input(xm;i (qm ; wH ; wL ; qp ; qs ; yi )) by di¤erentiating the cost function with respect to wL , wH , andqm . Finally, the input demand for a particular variety z of manufactures is11xmz;i =qmz
qm1

xmz;mz =qmz
qmxm;i ;

i = p; s;

(A.9)

1

xm;mz :

(A.10)

The condition for pro…t maximization by the …rms producing varieties has already been
derived (see (21)).32 Pro…t maximization by …rms implies that in the primary and service
sectors, price equals marginal cost which also equals the unit costqi =1c~A;i (qm ; wH ; wL )

i

i1

i1

qp
i2

i2

qs

i3

;

i = p; s:(A.11)

i3

Production and Use of Manufactures
The maximization problem for a …rm manufacturing a particular variety has already beensolved in Section 2. We now proceed to further derive the aggregate variables for the manufacturing sector or good. For this we begin by imposing symmetry in the manufacturingsector so that the price of all domestic varieties and hence their quantities produced aswell as domestically used are all the same. Similarly, the price and quantities used of theimported varieties are the same as well.
Let n be the number of domestic varieties and n be the number of foreign varieties.
Further, let xmz be the quantity of a representative variety that is domestically used and32

Even though the country is small, every …rm producing a variety z of manufactured good possesses
marketing power and faces same elasticity of demand in domestic and foreign markets. So, equation (21)still applies.

22

similarly de…ne xmz . Then we can write the price (qm ) of the composite manufactured
good that is used in production and for consumption as a use- or consumption-based price
index

1
1

1

qm = nqmz:+ n qmz(A.12)

It is instructive to rewrite this index as a combination of the price indices for the domestic
and foreign varieties11

qm = qmz

1

;

+ qmz

(A.13)

where
1

qmz ;

qmz = n(A.14)

is the price index for the domestically produced varieties and1

qmz = (n )qmz

(A.15)

is the price index for the foreign produced varieties. The corresponding quantity indices fortheir use in the domestic economy are1

xmz = n xmz ;xmz

1= (n ) xmz :23(A.16)(A.17)

Appendix B - Benchmark 1987 Mexican Data Set
The following is the input-output matrix for 1987 that is used to calibrate the model to the
Mexican economy. All the numbers in the matrix are in millions of U.S. dollars. The steps
following the matrix show the procedure for the construction of the input-output matrix
and the sources of the data.
Primaries

Manufactures

Services

Total

Xp;i

2; 712

13; 485

1; 53317; 730

Xm;i2; 836

23; 704

15; 939

42; 479

Xs;i1; 1908; 355

14; 874

24; 419Hi

9; 131

17; 068

37; 41463; 613Li

10; 756

20; 106

44; 075

74; 937

Yi

26; 625

82; 718

113; 835

223; 179

Ci

4; 64338; 793

89; 416132; 853

N Xi

4; 252

1; 4460

5; 698EXi

6; 626

13; 643IMi

2; 374

12; 197

Step 1. Intermediate input and total production. This 1987 matrix is constructed fromthe 1980 input-output table provided by the INEGI.
Step 2. Labor compensation. Yi

Xp;i

Xm;i

Xs;i in each sector. The compensationis then distributed into Hi and Li according to the INEGI’s EIM: wH H=wL L =4185=4930 in 1987.
Step 3. Net exports to the U.S. of primaries and manufactures. Source: The International
Trade Administration.
Step 4. Consumption. Get from Yi

Ci

Xi;p

Xi;m

Xi;s = N Xi . This consumption

C corresponds to c + i + g+net exports to the rest of the world except the U.S.
Notes
1. 1 peso = 1000 old pesos.
2. The nominal exchange rate in 1987 = 1.37818 MXP/USD. Source: The International
Financial Statistics (IFS).

24

References
Acemoglu, Daron and David Autor. "Skills, Tasks and Technologies: Implications
for Employment and Earnings." NBER Working Paper No. 16082, 2010.
Alonso, Esther V. and David W. Roland-Holst. "A Detailed Social Accounting
Matrix for Chile." Working Paper, Department of Economics, Mills College, 1995.
Atolia, Manoj. "Trade Liberalization and Rising Wage Inequality in Latin America:
Reconciliation with HOS Theory." Journal of International Economics, 2007, 71(2),pp. 467-494.
Bergoeing, Raphael and Timothy J. Kehoe. "Trade Theory and Trade Facts."
Federal Reserve Bank of Minneapolis Research Department Sta¤ Report No. 284,
2003.
Berman, Eli; Bound, John and Zvi Griliches. "Changes in the Demand for Skilled
Labor within U.S. Manufacturing: Evidence from the Annual Survey of Manufactures." Quarterly Journal of Economics, 1994, 109(2), pp. 367-397.
Berman, Eli; Bound, John and Stephen Machin. "Implications of Skill-Biased Technological Change: International Evidence." Quarterly Journal of Economics, 1998,
113(4), pp. 1245-1279.
Berndt, Ernst R. and Laurits R. Christensen. "Testing for Existence of an Aggregate
Index of Labor Inputs." American Economic Review, 1974, 64(3), pp. 391-404.
Blanchard, Olivier and Michael Kremer. "Disorganization." Quarterly Journal of
Economics, 1997, 112(4), pp. 1091-1126.
Borjas, George J. and Valerie A. Ramey. "Time Series Evidence on the Sources ofTrends in Wage Inequality." American Economic Review (Papers and Proceedings),
1994, 84(2), pp. 10-16.
Broda, Christian and David E. Weinstein. "Globalization and the Gains from Variety." Quarterly Journal of Economics, 2006, 121(2), pp. 541-585.
Brown, Randall S. and Laurits R. Christensen. "Estimating Elasticities of Substitution in a Model of Partial Static Equilibrium: An Application to U.S. Agriculture,
1947 to 1974," in Ernst R. Berndt and Barry C. Field, eds., Modeling and Measuring
Natural Resource Substitution. Cambridge, MA: MIT Press, 1981.
Burstein, Ariel and Jonathan Vogel. "Globalization, Technology, and the Skill Premium: A Quantitative Analysis." NBER Working Paper No. 16459, 2010.

25

Bussolo, Maurizio; Mizala, Alejandra and Pilar Romaguera. "Beyond Heckscher–
Ohlin: Trade and Labour Market Interactions in a Case Study for Chile." Journal of
Policy Modeling, 2002, 24(7-8), pp. 639-666.
Cragg, Michael I. and Mario Epelbaum. "Why Has Wage Dispersion Grown in
Mexico? Is It the Incidence of Reforms or the Growing Demand for Skills?" Journalof Development Economics, 1996, 51(1), pp. 99-116.
Deardor¤, Alan V. and Dalia S. Hakura.

"Trade and Wages – What Are theQuestions?" in Jagdish Bhagwati and Marvin H. Kosters, eds., Trade and Wages:
Leveling Wages Down? Washington, D.C.: AEI Press, 1994, pp. 76-107.
Dinopoulos, Elias; Syropoulos, Costas and Bin Xu. "Intraindustry Trade andWage-Income Inequality." Working Paper, Department of Economics, University of
Florida, 2009.
Esquivel, Gerardo and José A. Rodríguez-López. "Technology, Trade, and Wage
Inequality in Mexico before and after NAFTA." Journal of Development Economics,
2003, 72(2), pp. 543-565.
Ethier, Wilfred J. "National and International Returns to Scale in the Modern Theoryof International Trade." American Economic Review, 1982, 72(3), pp. 389-405.
Evenett, Simon J. and Anthony J. Venables. "Export Growth in Developing Countries: Market Entry and Bilateral Trade Flows." Working Paper, University of Bernand London School of Economics, 2002.
Fallon, Peter R. and Richard Layard. "Capital-Skill Complementarity, Income Distribution, and Output Accounting." Journal of Political Economy, 1975, 83(2), pp.
279-302.
Feenstra, Robert C. "Estimating the E¤ects of Trade Policy," in Gene M. Grossman
and Kenneth Rogo¤, eds., Handbook of International Economics, Vol. 3. Amsterdam:
North-Holland, 1995, pp. 1553-1596.
Feenstra, Robert C. and Gordon H. Hanson. "Foreign Investment, Outsourcing andRelative Wages," in Robert C. Feenstra, Gene M. Grossman and Douglas A. Irwin,eds., The Political Economy of Trade Policy: Papers in Honor of Jagdish Bhagwati.
Cambridge, MA: MIT Press, 1996, pp. 89-127.
Feenstra, Robert C. and Gordon H. Hanson.

"Foreign Direct Investment andRelative Wages: Evidence from Mexico’s maquiladoras." Journal of International
Economics, 1997, 42(3-4), pp. 371-393.

26

Feenstra, Robert C. and Gordon H. Hanson. "The Impact of Outsourcing andHigh-Technology Capital on Wages: Estimates for the United States, 1979-1990."
Quarterly Journal of Economics, 1999, 114(3), pp. 907-940.
Feliciano, Zadia M. "Workers and Trade Liberalization: The Impact of Trade Reforms
in Mexico on Wages and Employment." Industrial and Labor Relations Review, 2001,
55(1), pp. 95-115.
Francois, Joseph F. and Clinton R. Shiells, eds. Modeling Trade Policy: Applied
General Equilibrium Assessments of North American Free Trade. Cambridge, UK:
Cambridge University Press, 1994.
Goldin, Claudia and Lawrence F. Katz. "The Origins of Technology-Skill Complementarity." Quarterly Journal of Economics, 1998, 113(3), pp. 693-732.
Griliches, Zvi. "Capital-Skill Complementarity." Review of Economics and Statistics,
1969, 51(4), pp. 465-468.
Grossman, Gene M. and Rossi-Hansberg Esteban. "Trading Tasks: A Simple
Theory of O¤shoring." American Economic Review, 2008, 98(5), pp. 1978-1997.
Hanson, Gordon H. and Ann Harrison. "Trade Liberalization and Wage Inequality
in Mexico." Industrial and Labor Relations Review, 1999, 52(2), pp. 271-288.
Harrigan, James and Rita A. Balaban. "U.S. Wages in General Equilibrium: The
E¤ects of Prices, Technology, and Factor Supplies, 1963-1991." NBER Working Paper
No. 6981, 1999.
Hummels, David and Peter J. Klenow. "The Variety and Quality of a Nation’s
Exports." American Economic Review, 2005, 95(3), pp. 704-723.
Katz, Lawrence F. and David H. Autor. "Change in the Wage Structure and Earnings Inequality," in Orley C. Ashenfelter and David Card, eds., Handbook of Labor
Economics, Vol. 3A. Amsterdam: North-Holland, 1999, pp. 1463-1555.
Katz, Lawrence F. and Kevin M. Murphy. "Changes in Relative Wages, 19631987: Supply and Demand Factors." Quarterly Journal of Economics, 1992, 107(1),pp 35-78.
Kehoe, Patrick J. and Timothy J. Kehoe. "A Primer on Static Applied General
Equilibrium Models." Federal Reserve Bank of Minneapolis Quarterly Review, 1994,
18(1).
Kehoe, Timothy J. "An Evaluation of the Performance of Applied General Equilibrium
Models of the Impact of NAFTA," in Timothy J. Kehoe, T. N. Srinivasan, and John
27

Whalley, eds., Frontiers in Applied General Equilibrium Modeling: Essays in Honor
of Herbert Scarf. Cambridge, UK: Cambridge University Press, 2005, pp. 341-377.
Kehoe, Timothy J.; Manresa, Antonio; Noyola, Pedro J.; Polo, Clemente andFerran Sancho. "A General Equilibrium Analysis of the 1986 Tax Reform in Spain."
European Economic Review, 1988, 32(2-3), pp. 334-342.
Kehoe, Timothy J.; Polo, Clemente and Ferran Sancho. "An Evaluation of the
Performance of an Applied General Equilibrium Model of the Spanish Economy."
Economic Theory, 1995, 6(1), pp. 115-141.
Kehoe, Timothy J. and Edward C. Prescott. "Introduction to the Symposium: The
Discipline of Applied General Equilibrium." Economic Theory, 1995, 6(1), pp. 1-11.
Kehoe, Timothy J. and Kim J. Ruhl. "How Important Is the New Goods Margin
in International Trade?" Federal Reserve Bank of Minneapolis Research Department
Sta¤ Report No. 324, 2009.
Klenow, Peter J. and Andrés Rodríguez-Clare. "Quantifying Variety Gains from
Trade Liberalization." Working Paper, Graduate School of Business, University of
Chicago, 1997.
Kremer, Michael. "The O-Ring Theory of Economic Development." Quarterly Journalof Economics, 1993, 108(3), pp. 551-575.
Krugman, Paul R. "Increasing Returns, Monopolistic Competition, and International
Trade." Journal of International Economics, 1979, 9(4), pp. 469-479.
Krugman, Paul R. "Growing World Trade: Causes and Consequences." Brookings Papers on Economic Activity, 1995, (1), pp. 327-377.
Krugman, Paul R. "Trade and Wages, Reconsidered." Brookings Papers on Economic
Activity, 2008, (1), pp. 103-154.
Krusell, Per; Ohanian, Lee E.; Rios-Rull, Jose-Victor and Giovanni L. Violante.
"Capital-Skill Complementarity and Inequality: A Macroeconomic Analysis." Econometrica, 2000, 68(5), pp. 1029-1053.
Kurokawa, Yoshinori. "Variety-Skill Complementarity: A Simple Resolution of theTrade-Wage Inequality Anomaly." Economic Theory, 46(2), 2011, pp. 297-325.
Lindquist, Matthew J. "Capital-Skill Complementarity and Inequality in Sweden."
Scandinavian Journal of Economics, 2005, 107(4), pp. 711-735.
Melitz, Marc J. "The Impact of Trade on Intra-Industry Reallocations and Aggregate
Industry Productivity." Econometrica, 2003, 71(6), pp. 1695-1725.
28

Mukerji, Purba. "Trade Liberalization and the Extensive Margin." Scottish Journal of
Political Economy, 2009, 56(2), pp. 141-166.
Revenga, Ana. "Employment and Wage E¤ects of Trade Liberalization: The Case of
Mexican Manufacturing." Journal of Labor Economics, 1997, 15(3), pp. 20-43.
Robbins, Donald J. "Trade, Trade Liberalization and Inequality in Latin America andEast Asia: Synthesis of Seven Country Studies." Working Paper, Harvard Institutefor International Development, 1996.
Robertson, Raymond. "Relative Prices and Wage Inequality: Evidence from Mexico."
Journal of International Economics, 2004, 64(2), pp. 387-409.
Sandrey, Ron and Dirk van Seventer. "Has the New Zealand/Australian Closer
Economic Relationship (CER) Been Trade Widening or Deepening?" African Development and Poverty Reduction: The Macro-Micro Linkage, Forum Paper 2004, 2004.
Verhoogen, Eric A. "Trade, Quality Upgrading and Wage Inequality in the Mexican
Manufacturing Sector." Quarterly Journal of Economics, 2008, 123(2), pp. 489-530.
Xu, Bin. "Trade Liberalization, Wage Inequality, and Endogenously Determined Nontraded Goods." Journal of International Economics, 2003, 60(2), pp. 417-431.
Zhu, Susan C. and Daniel Tre‡er. "Trade and Inequality in Developing Countries: A
General Equilibrium Analysis." Journal of International Economics, 2005, 65(1), pp.
21-48.

29

Figure 1: Least traded goods growth in Mexican manufactured imports from U.S. andMexican skill premium, 1987-2000.

30

Preference parameters
p = 0:035
s = 0:673

m = 0:292

Technology: CES aggregator parameters
bp = 0:088
bs = 0:154
bm = 0:659
ap = 0:569
as = 0:591
am = 0:665
"= 1
= 12
= 19
29
Technology: productivity parameters
p = 3:688
s = 3:697
m = 3:697
Technology: cost shares
p1 = 0:853
p2 = 0:102
s1 = 0:856
s2 = 0:013
m1 = 0:736
m2 = 0:163
Endowments
L = 74936:415

p3 = 0:045
s3 = 0:131
m3 = 0:101

H = 63613:585

Manufactured varieties
F = 7472:059
n=3
n = 97qmz = 1:9422
qmz = 30:1432
xmz = 11; 855 xmz = 4:17

Table 1: The parameterization of the model.

31

"=

1; = 1=2
n
n
xmz
xmz
qmz
qmz
qm
qp
qs
wH
wL
wH =wLyp
ysym

Initial equilibrium

New equilibrium

1987

1994

3
97
11,8554.17
1.942230.1432111
1
11
26,625
113,835
82,7183.1705189.15
10,1873.34
1.894730.1432
0.8952
1
0.99551.03770.9972
1.0406
26,786
113,71385,284

Table 2: The results for the benchmark numerical experiment with epsilon = -1 and mu =(1/2).

32

Initial equilibrium"=

3; = 3=4
n
n
xmz
xmz
qmz
qmz
qm
qp
qs
wH
wL
wH =wLypysym

New equilibrium

1987

1994

3
97
11,8554.17
1.942130.1432111
1
11
26,625
113,835
82,7183.1577189.15
10,2263.36
1.896030.1432
0.8971
1
0.9956
1.0431
0.99181.051723,923
115,857
84,992

Table 3: The results for the numerical experiment with epsilon = -3 and mu = (3/4).

33

Initial equilibrium

"=

9
= 10

9;
n
n
xmz
xmz
qmz
qmz
qm
qp
qs
wH
wL
wH =wLypysym

New equilibrium

1987

1994

3
97
11,8554.17
1.942230.1432111
1
11
26,625
113,835
82,7183.1637189.15
10,2103.35
1.895230.1432
0.8961
1
0.99591.04510.99071.054924,843
115,128
85,122

Table 4: The results for the numerical experiment with epsilon = -9 and mu = (9/10).

34

1; = 21
n
n
xmz
xmz
qmz
qmz
qm
qp
qs
wH
wL
wH =wL
yp
ys
ym

"=

Initial equilibrium

New equilibrium

1987

1994

3
97
11,8554.17
1.942230.1432111
1
11
26,625
113,835
82,7183.1724
189.15
10,1453.38
1.906130.1432
0.89911
1.00481.04591.00631.039427,735112,975
85,848

Table 5: The results for the benchmark numerical experiment with sectoral variations inskill intensity: the …rst case.

35

1; = 21
n
n
xmz
xmz
qmz
qmz
qm
qp
qs
wH
wL
wH =wL
yp
ys
ym

"=

Initial equilibrium

New equilibrium

1987

1994

3
97
11,8554.17
1.942230.1432111
1
11
26,625
113,835
82,7183.1730189.15
10,1423.38
1.906530.1432
0.89921
1.0043
1.04761.00571.0417
27,583113,095
85,881

Table 6: The results for the benchmark numerical experiment with sectoral variations inskill intensity: the second case.

36