Volatility Due to Offshoring: Theory and Evidence

Abstract:
This paper develops a theoretical model to study the second moment properties of global
offshoring. It offers an explanation for the stylized fact that offshoring industries in Mexico
experience fluctuations in employment that are twice as volatile as the corresponding
industries in the U.S. The model features an extensive margin of offshoring that responds
endogenously to shocks in demand, and transmits those shocks across borders.
JEL classification: F4, F1

1

I. Introduction
International trade is being transformed by offshoring, the arrangement whereby firms
contract to carry out particular stages of production abroad. This especially is true for the U.S. andMexico. Offshoring accounts for nearly half of Mexico’s exports, with Mexican employment inexport assembly plants engaged in offshoring growing ten-fold from 0.12 million in 1980 to 1.2
million in 2006. While Mexican officials hail the export assembly plants for their contribution toeconomic growth, some complain that the sector is fickle and subject to excessive volatility.1 The
assembly plants, known as maquiladoras, are seen as a channel by which the U.S. exports to Mexico
a portion of its employment fluctuations over the business cycle.
While a growing number of papers model the effects of offshoring on the wage structure, theenvironment, and other outcomes, ours is among the first to examine the second-moment properties
of offshoring, which are at the heart of concerns expressed by policy makers. Bergin, Feenstra, andHanson (2009) document that maquiladora industries in Mexico associated with U.S. offshoring havefluctuations in employment that are twice as volatile as the corresponding industries in the U.S. Thisfinding is based on data covering Mexico’s four largest offshoring industries, apparel, transportationequipment, computers and electronics, and electrical machinery, which are matched to their U.S.
counterparts at the three digit level. Across offshoring industries, the standard deviation of
employment in Mexico is 2.2 times higher than in the U.S.2
One conjecture might be that high volatility in Mexican offshoring industries simply reflects
higher volatility in the Mexican economy overall. However, employment volatility for aggregate
manufacturing in Mexico is actually lower than in the U.S. A second conjecture might be that labormarket institutions differ between the countries, such that it is easier to hire and fire employees in
1

See for example the news account of how the Mexican car industry is highly susceptible to fluctuations in demandfor American brand automobiles in Dickerson (2005).
2
See column (1) of table 4 for the values reported in Bergin, Feenstra and Hanson (2009), which are standard
deviations computed from monthly data that are seasonally adjusted and HP-filtered in logs over the range 1996:12005:12.

2

Mexico. Yet, when Botero et al. (2004) rank countries in terms of job security laws restricting thehiring and firing of workers, Mexico ties for the most regulated among the 85 countries in thesample, whereas the U.S. ranks as the fifth least regulated economy, a finding consistent with Mexico
having lower aggregate employment volatility.3
In this paper, we offer an alternative explanation for differential volatility in countries
engaged in offshoring. We develop a model of global production sharing where the offshoring
decisions of firms respond to macroeconomic shocks. The model relies on a continuum of productsin the offshoring sector, and for each product an endogenous number of varieties. This structure
combines the Dornbusch-Fisher-Samuelson (1977) framework with the monopolistic competition
model, as also done by Romalis (2004). Production in the offshoring sector requires two activities: afixed-cost activity that occurs in the high-wage home country, representing headquarter andmanagerial costs, and a variable-cost activity representing assembly work that can be done at homeor offshored to a low-wage foreign country. The offshoring sector is embedded in a two country,
general equilibrium macroeconomic model, which also includes a homogeneous traded good in eachcountry.
A key feature of the model is that the point along the product continuum at which firms in thehome country begin to offshore the variable-cost activity to the foreign country is endogenously
determined as firms compare the unit-labor costs across borders. When the home country has a boom
in demand, the fact that home wages tend to be procyclical alters the offshoring decision of somefirms.4 Since home workers become relatively more expensive to hire, firms that previously had not

3

In Mexico, labor unions are active in maquiladoras and other manufacturing establishments, Collective bargaining
agreements in maquiladoras appear to be less restrictive than in the rest of Mexican manufacturing, in that jobclassifications tend to be wider and firms tend to have greater leeway in establishing pay-for-performance schemes(Fairris, 2003). At the same time, the decline in unionization in Mexican manufacturing, which has been ongoingsince the 1980s, is less evident among maquiladoras. The net effect of more flexible collective bargaining
agreements but more stable union presence is relatively small differences in labor relations between maquiladoras
and other Mexican manufacturing firms.
4
Huang et al. (2004) survey recent evidence confirming procyclicality of wages in the U.S. in the postwar period,
unconditionally as well as conditional on demand shocks.

3

offshored any production now find it profitable to do so. This shift in the extensive margin acts as a
powerful mechanism for the international transmission of shocks, whereby U.S. producers shiftunusually high levels of production abroad during a domestic economic boom, and the reverse duringa recession. Numerical examples, by way of stochastic simulation under demand and supply shocks,
indicate that the mechanism provides a potential explanation for the extra volatility in Mexican
offshoring. Even when the shock is a purely domestic one, the simulation shows that it is amplified in
its transmission abroad, so that it has a greater impact on the offshoring industries in the low-wageforeign country than on the domestic counterpart industries.
There are two reasons in our model why the shocks to home demand are amplified in theireffect abroad. First, the foreign offshoring sector, representing maquiladoras in Mexico, has smaller
total employment than in the U.S. Any given shift in employment therefore has an amplified effecton foreign volatility. Second, as just noted, home wages are procyclical with home demand shocks. A
home demand shock that raises demand in the offshoring industry will tend to raise employment
disproportionately in the foreign country, since offshoring activity is shifted in that direction at thesame time that employment is growing due to increased demand. In contrast, the shift in offshoring
activities offsets part of the employment increase at home.
To motivate the theoretical approach and help calibrate the model, the paper begins byproviding novel empirical evidence on movements in the extensive margin of offshoring trade, theentry and exit of new goods. We collect data on Mexican exports at key U.S. ports of entry
associated with offshoring, which record both the value of exports and the number of productclassifications exported. We find that at a monthly frequency changes in the extensive margin are astatistically significant channel of adjustment in trade.
The paper most closely related to ours is Burstein, Kuz and Tesar (2008), which studies thereal business cycle implications of offshoring. Our paper differs from theirs in its focus on volatility
rather than cross-country correlations in macroeconomic variables, and in its focus on the

4maquiladora sector. We are also distinct in modeling offshoring in a manner consistent with recent
developments in trade theory, emphasizing a high degree of substitution between production in
Mexican plants and their U.S. counterparts.5
The next section presents empirical results on the extensive margin, which serve as
motivation for our theory. Section 3 presents the theoretical model, analytical results are in section 4,
with simulation results in section 5. Conclusions are given in section 6.

II. Empirical Motivation
The theoretical model developed in the following section will imply that changes in
employment by offshoring industries are driven in part by adjustment at the extensive margin. The
mechanism we have in mind is one in which aggregate shocks alter Mexican wages relative to U.S.
wages, inducing an endogenous shift in the extent of production activities U.S. firms offshore to
Mexico. If such a mechanism is operative, we should see entry and exit among the assembly plants in
Mexico that produce intermediate goods and services for U.S. industry. There is abundant anecdotal
evidence of such plant turnover. During the U.S. economic expansion of the 1990s, the number ofmaquiladoras in Mexico grew from 1,600 to 3,700. Delphi, a large U.S. manufacturer of auto parts,
expanded its operations in Mexico to include six assembly plants. As U.S. economic growth slowedin 2001 and 2002, over 700 Mexican maquiladoras closed shop.6 Delphi shut down two of its
Mexican maquiladoras, leaving the other four in operation.7 Similar expansion and contraction in

5

Burstein, Kurz, and Tesar (2008) develop a dynamic model of trade in intermediate inputs whose respective
outputs are assumed to be complements in production, whereas we model international production in terms ofoffshoring of variable cost activities that are highly substitutable. Our formulation draws on the offshoring model inFeenstra and Hanson (1996, 1997). For other work on intermediate inputs and business cycle synchronization see
Kose and Yi (2001, 2006) and Ambler, Cardia, and Zimmerman (2002).
6
See “The Decline of the Maquiladora: The Government Isn’t Moving to Rescue a Troubled Industry,” Business
Week, April 29, 2002.
7
See Victoria Hirshberg, “Delphi to Consolidate Reynosa, Mexico, Operations,” Texas Knight Ridder/Tribune
Business News, July 23, 2004.

5

Mexican assembly plants is evident among firms that produce TV sets, cell phones, computer
printers, and other goods.8
More formal evidence of adjustment at the extensive margin comes from examining data on thenumber of products that Mexico exports to the U.S. We use the Harmonized System (HS) importdata for the U.S., at a monthly frequency, and focus on the three largest land border crossings:
Laredo, El Paso and San Diego. Table 1 summarizes the average number of HS 10-digit products
crossing at each location per month in the four offshoring industries identified above. For example,
there are 300 or more types of apparel items being imported at Laredo and San Diego each month,and a smaller number of items in other offshoring industries. We also report the mean number ofmonths that HS products in each industry are exported each year, ranging from 5.8 months forapparel items in El Paso, to 9.0 months for transport equipment in Laredo.
These summary statistics show that there are many ‘zeros’ in the data, i.e. many instanceswhere an HS product is not exported some month. That fact is also illustrated by Figure 1, whichgraphs the log number of HS products per month, after deseasonalizing and HP filtering. The
standard deviation of these series (reported in Table 1), averaged across industries is 3.6%. Some of
the fluctuation in the number of HS products will reflect products that are exported at irregularintervals during the year. But we also expect that some fluctuation is systematic: visually, there
appears to be a fall in the number of HS products in 2002, at the time when employment in both
Mexico and the U.S. fell substantially. That impression is confirmed by the correlations between thenumber of HS products and U.S. manufacturing employment reported in Table 1, which are nearly
all positive and often exceed 0.25.
Beyond confirming that the range of products exported from Mexico is procyclical with U.S.
employment, we wish to determine the degree to which there is a systematic component to its
8

See Mary Jordan, “Mexican Workers Pay for Success,” Washington Post, June 20, 2002; Elizabeth Malkin, “A
Boom along the Border,” The New York Times, August 26, 2004; and Diane Lindquist, “Slight Gain in Output
Cheers Mexico’s Beleaguered Maquiladora Industry,” San Diego Union-Tribune, March 11, 2004.

6

fluctuation.9 We evaluate this relationship along the lines of Eaton, Kortum and Kramarz (2004),
using the identity:

zit ×

Eit Eit≡× Et ,zit
Et(1)

where zit denotes the number of HS products exported from Mexico in industry i, month t, and aparticular border crossing, Eit is the value of exports for that industry i and border crossing in montht, and Et is total exports at that border crossing in month t. From this identity we specify two
regression equations:ln zit = α 0 + α1 ln

Eit+ α 2 Et + ε it
Et

(2)

and

ln

Eit
E
= β 0 + β1 ln it + β 2 Et − ε it .
zit
Et

(3)

where (Eit/ zit) is the average value of Mexican exports per HS product. By the logic of least squares,

αl 0 + βl 0 = 0, αl 1 + βl 1 = 1, and αl 2 + βl 2 = 1 . The relative magnitude of the coefficients identifies how
aggregate shocks affect the number of products (the extensive margin) and exports per product (theintensive margin).
The results from these regressions are shown in columns (1) and (2) of Table 2. All series havebeen deseasonalized and HP filtered, and then are pooled across the four offshoring industries, with
controls included for industry fixed effects. In column (1), the estimate for α1 is 0.07, which isstatistically significant, and for α2 is 0.10, which is also significant. The first coefficient shows thatthe number of HS products in each industry responds to a shift in Mexican exports towards thatindustry. In that sense, the number of products provides an avenue of adjustment. For an increase in

9

Alessandria, Kaboshki and Midrigan (2007) argue that large devaluations leads to systematic changes in the rangeof goods exported, also using the monthly 10-digit HS data for the United States.

7

overall exports (the second coefficient), the number of HS products in the industry also responds by amodest amount.
A problem with using the number of HS products as a measure of adjustment is that the HSclassification is quite arbitrary: the classifications are determined more by the need to distinguishtariffs for various items than by any consideration of the value of exports for each product, whichmight be very small or very large. To address that problem, we consider instead a measure of theextensive margin of exports used by Hummels and Klenow (2005). Let Jikt denote the set of 10-digit
Harmonized System exports from Mexico to the U.S. in industry i, at border crossing k, and month t.
The extensive margin of exports is a sales-weighted count of the number of products in the set Jikt,
relative to the number in a “common” set Jik, which we define as the products exported every monthwithin the year. Then the extensive margin is defined as:10

EM ikt ≡ ∑ pijk xijk / ∑ pijk xijk ,j∈J ikt(4)j∈J ikwhere pijk xijk is the value of exports for product j in industry i, summed across locations other thanborder crossing k, and averaged over months within each year. By measuring the value of exports atborder crossing other than k, and averaging over time, we avoid endogeneity between total monthly
exports at each border crossing and the values appearing in (4).
To determine the systematic component of the fluctuations in the extensive margin, we follow
Hummels and Klenow (2005) in defining the intensive margin of exports IM ikt by:

EM ikt × IM ikt =∑ pijkt xijkt ,(5)

j∈ J ikt

10

From Feenstra (1994), this formula is the correct way to count the number of products for a CES consumer, in thatthe welfare gain to the consumer from having products in Jikt that are not in Jik is proportional to the log of EM, withthe factor of proportionality depending on the elasticity of substitution between products. Hummels and Klenow(2005) were the first to refer to this formula as the extensive margin of exports.

8

where the right-hand side is the total exports in industry i, border crossing k and month t. Let us
rewrite total exports as Shareikt × Exportkt, where Shareikt is the share of industry i in the total exports
Exportkt at that border crossing. Then we have the identity:

EM ikt × IM ikt = Shareikt × Exportkt.
From this identity we specify the two regression equations:ln EM ikt = α 0 + α1 ln Shareikt + α 2 Export kt + ε ikt ,(6)

ln IM ikt = β 0 + β1 ln Shareikt + β 2 Export kt − ε ikt .

(7)

and

l = 0, αl 1 + β
l = 1, and αl 2 + β
l = 1.
Again, by the logic of least squares, αl 0 + β
01
2The results from these regressions are in the last two columns of Table 2. The coefficient α1,
which indicates how the extensive margin responds to the export of industry i, rises from 0.07 to
0.13. It remains highly significant, indicating that the extensive margin responds systematically tochanges in total industry exports. The coefficient α2 falls slightly from 0.10 to 0.09 and remains
significant, indicating that the extensive margin also responds systematically to changes to overall
exports at that border crossing. We conclude that the changes in the extensive margin – measured byeither the number of maquiladora plants in Mexico or the range of product crossing the border – aremargins of adjustment that respond at a monthly frequency. We now turn to a model that emphasizes
these margins of adjustment.

III. Theoretical Model
A. Pricing and Product Variety in the Offshoring Sector

Consider a model of two countries, labeled home and foreign. The offshoring relationship in
the model is characterized by the home country offshoring to the foreign country, so that home may
be thought of as representing the U.S. and foreign as representing Mexico. We will scale the quantity

9variables coming from the foreign country by its relative size: if the share n of the world population
resides at home and 1-n in the foreign country, then we scale foreign quantities by (1-n)/n. Foreign
variables will be denoted by an asterisk *.
Each country has two sectors. The first is a standard homogeneous good whose production is
specific to that country; this country-specific sector will be subscripted by H for the home produced
good and F for the foreign produced good, or by X when referring to a composite of the home andforeign homogenous goods in the consumption bundle. The second sector consists of differentiatedproducts that are multinational, subscripted by M, in that they can be produced using factors in either
country. This sector represents the aggregate of the four industries listed in the empirical section
above, and it sometimes will be referred to as the offshoring sector. There is a continuum of productsin this sector indexed by z ∈ [0,1] , and for each z, there is free entry of firms who then produce N(z)differentiated varieties of good z. The model follows Romalis (2004) in combining a continuum of
products z in the M sector along with multiple varieties N(z) of each product.
Production in the offshoring sector involves a fixed cost activity as well as a variable cost
activity. The fixed cost, B, represents headquarters and R&D services, and is paid every period. It is
assumed here to be uniform across goods and takes place in the home country, due to the assumptionthat it is sufficiently more productive in these activities. The variable cost activity has a unit labor
input requirement that differs by product, and follows the function aMt ( z ) = exp ( az + bt ) in the homecountry. The foreign country has a corresponding function, and the relative unit-labor requirement
function between the two countries will be specified as,

A( z ) =aMt ( z ) exp ( az + bt )== exp ( ad z + bdt ) ,*( z ) exp ( a* z + bt* )aMtwhere a d ≡ a − a * and bdt ≡ bt − bt* . By ordering of the products z, we assume that A(z) is decreasing
in z, i.e. products are arranged by increasing order of home comparative advantage, so that a d < 0 . It10follows that those offshoring activities below some cutoff z 't will be produced in the foreigncountry, while those activities above z 't will be done at home. The cutoff activity z 't is determinedby the equality of unit-labor costs in the two countries, or given the wages Wt and Wt* , by:A( z 't ) =

Wt *
.
Wt

(8)

Overall home-country demand in this multinational sector is specified as,
1

ln DMt = ∫ ln d Mt ( z )dz ,(9)0

where d Mt ( z ) is the demand for a product z. The market for each z is assumed to be monopolisticallycompetitive, with demand for a product specified as a CES aggregate over individual varieties i,σσ −1⎡ Nt ( z )⎤ σ −1d Mt ( z ) = ⎢ ∫d Mt ( z , i ) σ di ⎥ .
0⎣⎦

The composite multinational good DMt will serve as the numeraire.
To determine the number of firms we make use of zero profits for each product z. Since theprice of the multinational good is taken as numeraire, the revenue earned from home plus foreign*(1 − n) / n] / N t ( z ) . To obtainsales of each variety in a symmetric equilibrium equals [ DMt + DMt

profits, equal to revenue minus variable costs, we divide by the elasticity of demand, σ. Setting thisequal to fixed costs BWt, we then solve for the number of products. Under our assumptions that the
fixed cost and weight in demand are uniform across varieties, the number of firms likewise isuniform across varieties, so Nt does not vary with z:* ⎛1− n ⎞DMt + DMt⎜⎟
⎝ n ⎠.
Nt =
σ BWt

(10)

11

The overall labor demand in the multinational sector at home includes labor used for the fixed
cost activity, LBt, as well as the variable cost activity, LMt, for activities not offshored ( zt > z 't ); labordemand abroad includes just variable cost activity for offshored activities ( zt < z 't ), so that:⎛* ⎛1− n ⎞ ⎞⎜ DMt + DMt ⎜ n ⎟ ⎟⎝⎠⎟LBt = N t B = ⎜
σ Wt
⎜
⎟
⎜
⎟
⎝
⎠

(11)

⎛
* ⎛1− n ⎞ ⎞⎜ DMt + DMt ⎜ n ⎟ ⎟⎝⎠ ⎟ σ −1 1− z 'LMt = ⎜
(
)(
t )
σ Wt
⎜
⎟
⎜
⎟
⎝
⎠

(12)

⎛
* ⎛1− n ⎞ ⎞DMt + DMt⎜⎟⎟⎜
⎛1− n ⎞ *⎝ n ⎠ ⎟ σ −1 z '
⎜
L
=
Mt
(
) t
⎜
⎟
σ Wt*
⎜
⎟
⎝ n ⎠
⎜
⎟
⎝
⎠

(13)

B. Production in the Rest of the Economy

The remainder of the model follows a standard open macroeconomy specification. The
country-specific sector in the home country is a perfectly competitive market for the homogeneous
traded good with production function:
YHt =

LHt
,
aHt

(14)

where LHt is labor in the home country-specific sector and aHt is its unit labor input requirement.
Profit maximization by producers in this sector implies,
Wt =

pHt
,
aHt

(15)

where pHt is the relative price of the home domestic good in terms of the multinational good
numeraire. Analogous conditions apply to the foreign country’s homogeneous good.

C. Households

12Household preferences in the home country are represented by an instantaneous utility functionof consumption ( Ct ), which is a composite of goods in the three sectors, and overall labor ( Lt ):
1
1
1−φ
1+ µ
Ct −
Lt
1−φ
1+ µ
where

Ut =

χ

1
χ −1 ⎞ χ −1
1
χ −1
⎛
χ
χ
χ
Ct = ⎜ (1 − α ) C Xt + α ( CMt ) χ ⎟
⎜
⎟
⎝
⎠

η

1
η −1 ⎞η −1⎛ η1 η −1
C Xt = ⎜ θ CHt η + (1 − θ )η CFt η ⎟⎜⎟⎝⎠In each period t, the economy experiences one of finitely many events, st . We denote bys t = ( s0, ..., st ) the history of events up through and including period t. All variables referred to so far

are implicitly functions of the states of nature in period t (e.g., YHt ≡ YH ( s t ) ). We assume complete
contingent asset markets, as discussed more fully in Chari, et al. (2002). In period t, consumers ineither country purchase state-contingent assets in units of the numeraire good, denoted by
Bt +1 ≡ B ( s t +1 ) , which bear a return of exactly one unit of the numeraire good in period t+1 if states t +1 occurs. They purchase these assets at the prices V ( s t +1 | s t ) , which denotes the price of one unit of

the numeraire good at s t +1 in units of the numeraire good at state s t . The budget constraint facing thehome household in period t is therefore:t +1
PC| s t )B ( s t +1 ) = Wt Lt + Bt − Gt ,t t + ∑V ( ss t +1

where Pt is the price index of the home country consumption basket in terms of the numeraire good,and Gt is government spending. Analogous conditions apply for the foreign country.
Labor is mobile between sectors within a country, and between fixed and variable cost
activities within the home offshoring sector, but there is no labor mobility between countries,
meaning each country has a single but distinct equilibrium wage rate.

13

Households maximize the expected discounted sum of current and future instantaneous utility
defined above, using the discount factor β , subject to the budget constraint.11 The first orderconditions for this problem imply the following. Risk-sharing equates nominal marginal utilities ofconsumption apart from a constant of proportionality,
φ
PC
t t
=ω ,
P*t Ct*φ(16)

where ω is a constant indicating the relative per-capita wealth of the home country in the initial asset
allocation. Relative demands for the domestic and multinational goods are:CMt
α ⎛ PMt ⎞=⎜⎟C Xt (1 − α ) ⎝ PXt ⎠

−χ

(17)
−η

and,

CHt ⎛ θ ⎞ ⎛ PHt ⎞=⎜⎟⎟⎜CFt ⎝ 1 − θ ⎠ ⎝ PFt ⎠where,

PXt = (θ PHt1−η + (1 − θ ) PFt1−η )1−η .

(18)1Note that the law of one price holds, so the relative prices PHt and PFt apply to the goods markets inboth countries. The labor supply is,
Lµt =

Wt −φ
Ct .
Pt

(19)

Corresponding conditions apply for the foreign country.

D. Market Clearing and Equilibrium

Exogenous government consumption, Gt , is introduced to capture shocks to demand. It is
assumed that the home government allocates demand between homogeneous domestic anddifferentiated multinational good in the same fashion as consumers, except that among homogenous

As the discount factor β is assumed identical across countries, it cancels out of the risk sharing condition (16),and does not appear in the other equations of the model.
11

14

⎛P ⎞
goods it consumes only the home and not the foreign good. This implies GMt = α ⎜ Mt ⎟
⎝ P ⎠

−χ

Gt ,

−χ

⎛P ⎞
⎛P ⎞
GXt = (1 − α ) ⎜ Xt ⎟ Gt and GHt = GXt ⎜ Xt ⎟ . This holds analogously for the foreign government’s⎝ P ⎠⎝ PHt ⎠

demand. We then define the home country demand for the multinational sector noted in thepreceding section as DMt = CMt + GMt . The market clearing condition for the homogeneous good ofhome country is:⎛1− n ⎞ *CHt + ⎜⎟ CHt + GHt = YHt .
⎝ n ⎠

(20)

Equilibrium in the labor market requires that overall labor supply equal the sum of labordemands across sectors:
Lt = LHt + LMt + LBt ,(21)

L*t = L* Ft + L*Mt .

(22)

The general equilibrium is a sequence of 19 endogenous variables: Lt , L*t , LHt , L*Ft ,**LBt , LMt , L*Mt , Wt , Wt * , N t , CHt , CHt, CFt , CFt* CMt , CMt, PHt , PFt , and z 't , which are determined by thelabor-supply condition (19), relative demand for the multinational and home country-specific goods(17) and (18), labor demand for the country-specific sector (14) and the multinational sector (12), themarket clearing condition for the country-specific sector (20), the market clearing condition for labor(21), and the foreign counterparts for each of these. In addition, there is the marginal offshoring
condition (8), the risk sharing condition in (16), the zero profit condition (10), labor demand for fixed
cost labor (11), and the normalization of the price of the numeraire good DMt (as described in the
Appendix).

E. Shocks

15

The model will include shocks both to demand and supply, entering through the additive
demand terms ( Gt and Gt* ) and the unit labor requirement terms ( aHt and aFt* ). Both types of shocks
are specified as first order autoregressions in log deviations from their respective means:

( )

( )

( )

( )

⎡ log ( aHt ) − log aH ⎤⎡ log ( aHt −1 ) − log aH ⎤⎢⎥ =ρ ⎢⎥ + ⎡ε aHt ⎤ , where ⎡ε aHt ⎤ ~N ⎛ ⎡0 ⎤ ,σ ⎞⎜⎢ ⎥ a ⎟
a
⎢ε ⎥
⎢ε ⎥
⎢
⎢
*
* ⎥
*
* ⎥
⎣ aFt ⎦
⎝ ⎣0 ⎦⎠⎢⎣ log ( aFt ) − log aF ⎥⎦⎢⎣ log ( aFt −1 ) − log aF ⎥⎦ ⎣ aFt ⎦

( )

and:

( )

⎡ log ( Gt ) − log G ⎤⎡ log ( Gt −1 ) − log G ⎤⎢⎥ =ρ ⎢⎥ + ⎡ ε Gt ⎤ , where ⎡ ε Gt ⎤ ~N ⎛ ⎡ 0 ⎤ ,σ ⎞ .
⎜⎢ ⎥ G ⎟
G
⎢ε ⎥
⎢ε ⎥
⎢
⎢
*
* ⎥
*
* ⎥
⎣ G*t ⎦
⎝ ⎣0⎦⎠⎢⎣ log ( G t ) − log G ⎥⎦⎢⎣ log ( G t −1 ) − log G ⎥⎦ ⎣ G*t ⎦

( )

( )

We do not compute a separate set of Solow residuals for the offshoring sector of each country, as thismight end up replicating the higher volatility in the Mexican offshoring sector in a purely mechanicalway. Instead, we consider two cases of how a country’s domestic productivity shocks affect theoffshoring sector. One case simply assumes that productivity moves proportionately in the domestic**
and offshoring sectors within each country: a~Mt ( z ' ) = a~Ht , a~Mt
( z ' ) = a~Ft
, where tildes indicate log

deviations from means. This specification implies that the relative cost schedule A(z) shifts in
response to productivity shocks. The other case differs in that it holds the A(z) schedule fixed,
assuming that productivity shocks in a country’s offshoring sector are perfectly transmitted to the**( z ' ) = a~Ht + a~Ft
. This specification is similar to that
other country’s offshoring sector: a~Mt ( z ' ) = a~Mt

assumed in Burstein et al. (2008), and is also consistent with Berman, Bound and Machin (1998) who
argue that technology shocks spread quickly to other countries. We take this second specification as
our benchmark, although we shall report results for the first case as well.

IV. Analytical Results

Some important intuition can be gained into relative volatilities across countries by using thelabor demand conditions for the variable cost activity in (12) and (13). Denote the world demand for16w*
the multinational good as DMt≡ [ DMt + DMt(1 − n ) / n ] , and replace Wt in (23) by Wt * / A( zt' ) using(8), to obtain:⎛ Dw ⎞⎛ σ −1⎞
LMt = ⎜ Mt* ⎟ (1 − z 't ) A ( zt' ) ⎜⎟⎝ σ ⎠⎝ Wt ⎠(23)⎛ D w ⎞ ⎛ n ⎞⎛ σ − 1 ⎞L*Mt = ⎜ Mt* ⎟ z 't ⎜⎟⎜⎟⎝ Wt ⎠ ⎝ 1 − n ⎠⎝ σ ⎠(24)

We focus on the variable cost activity in these equations, as our data apply to production workers in
the two countries.12 Recalling A( zt' ) = exp( a d z t' + bdt ) with a d < 0 , let us further focus on demand
shocks by treating bdt as constant. Then taking natural logs of (23)-(24) and using a first-orderapproximation for ln z t' and for ln(1 − z t' ) , we can compute the variances:2
w ⎞⎤⎡ ' ⎛ DMt
⎡ ⎛ D w ⎞⎤ ⎡ 1
⎡ 1
⎤
⎤
'
⎜
⎟⎥ + ⎢
var(ln LMt ) = var ⎢ln⎜⎜ Mt
var(
)
2
cov
,
ln
a
z
a
z
−
−
−
⎢ t ⎜ * ⎟⎟⎥ , (25)td⎥d⎥
⎢ (1 − z ' )
* ⎟
⎣
⎦
⎦
⎢⎣
⎢⎣ ⎝ WMt ⎠⎥⎦ ⎣ (1 − z ' )⎝ WMt ⎠⎥⎦

and,

w ⎞⎤
w ⎞⎤
⎡ ⎛ DMt⎡ ' ⎛ DMtvar( zt' )
2
*
⎜
⎟
⎜
+
cov ⎢ zt , ln⎜ * ⎟⎟⎥ .
var(ln LMt ) = var ⎢ln⎜ * ⎟⎥ +
2
(
'
)
z
(
'
)
W
z
⎝ WMt ⎠⎦⎥⎣⎢ ⎝ Mt ⎠⎦⎥
⎣⎢

(26)

Thus, the variance of employment in the multinational sector depends on the variance ofworld demand relative to the foreign wage; on the variance of the offshoring margin zt' measured
relative to an ‘adjusted’ size of the offshoring sector, {[1 /(1 − z ' )] − a d } at home and (1 / z ' ) abroad;and also on the covariance between zt' and world demand.

12

The choice to exclude fixed cost labor from the U.S. total potentially works against our model’s ability to generate
the desired lower volatility in the U.S. But this measure is the appropriate comparison to the data, which measureemployment of production workers. Simulation results are nearly identical if we include fixed cost labor, as (12)–(14) indicate that Wt LMt is proportional to Wt ( LMt + LBt ) , including fixed costs at home, for fixed z'.

17

The covariance term in (25)-(26) will generally be positive for home demand shocks, since
an increase in home demand raises the offshoring margin zt' but also lowers the foreign wage Wt* .13
Notice that the covariance enters with a positive sign in (26) but a negative sign in (25): as more
offshoring activities are shifted abroad, that will tend to offset the variance in home employment in
the offshoring industry, but enhance it abroad, because the procyclical nature of zt' will amplify the
impact abroad of the demand shocks. Therefore, a positive covariance between world demand for themultinational good and the offshoring margin will shift variance towards the foreign country. Thissituation is clearly relevant for the U.S./Mexico case we study, as the U.S. is the primary demander
for offshored goods both in the data and in our simulation due to its larger population and wealth.
The volatility in employment also depends on the size of the offshoring sector in the twocountries, adjusted by a d < 0 which determines the slope of the A(z ) schedule. Provided that{[1 /(1 − z ' )] − a d } < (1 / z ' ) , which is easily satisfied in our calibration, then the volatility of

employment in the foreign country will magnified by the variance in zt' . This occurs simply because
the shift of a given amount of employment from home to foreign will have a greater percentage
impact abroad when the foreign country has a smaller offshoring sector. So for this reason, also, theforeign country will experience greater volatility.
Our model also includes supply shocks in the two countries, but their impact is sensitive to how
the shocks are specified. In our benchmark case we hold fixed the A(z) schedule. In that case, supply
shocks in the homogeneous goods turn out to have minimal impact on the offshoring margin z',
relative wages, or other endogenous variables. This finding follows from a little-known result in theinternational macro literature. Consider our model without the offshoring sector, so that it is a twogood Ricardian model with complete asset markets, and assume Cobb-Douglas preferences over the
13

With bdt constant, it is readily shown from (A3) in the Appendix that any increase in the home wage due todemand shocks must be matched by a decrease in the foreign wage, since both are measured relative to the price ofthe multinational good which is the numeraire. Therefore, home demand shocks raise Wt and lower Wt* .

18homogeneous goods from each country. Then it turns out that the technology shocks have no impact
at all on relative wages. The reason is that a positive productivity shock to, say, the home good, will
reduce its price on international markets but increase its demand by the same percentage amount, so
the implied relative labor demand across countries is unchanged. Relative labor supply is alsounchanged due to complete asset markets, so the equilibrium relative wage does not change.14
Adding the offshoring sector but with a fixed A(z) schedule leads to nearly the same result.
However, when we allow the A(z) schedule to respond to technology shocks, then a rise inhome productivity shifts the A(z) schedule down compared to a given relative wage, inducing a fall inoffshoring. This “in-sourcing” behavior implies a negative correlation between employment in thehome and foreign offshoring activity, and is counterfactual given the positive correlations observedin the data. This is one benefit of using our benchmark specification of productivity shocks, where
the A(z) schedule is held fixed by assuming transmission of productivity across countries within theoffshoring sector.

V. Numerical Experiment

A. Calibration
We calibrate the model to monthly data for the U.S. and Mexico. Parameter choices are
summarized in Table 3. We have already argued that the magnitude of z ' is important. Taking theratio of (12) and (13) indicates that z ' can be calibrated to match the Mexican share of production
labor earnings in the offshoring sector.
14

The result that neutral technology shocks have no impact on the relative wage in a two-sector model with large
countries and Cobb-Douglas preferences is noted by Krugman (2000), in a model with fixed labor endowments.
Using labor choice and complete asset markets, Devereux and Engel (2001) obtain a factor-price equalization result
under the assumption that labor enters the utility function linearly. Our assumptions are weaker, since labor entersutility with a power. Combining (16) and (19) we readily obtain ( Lt / L*t ) µ = (Wt / Wt* ) , which is the relative labor
supply schedule. Relative labor demand in the two-sector Ricardian economy is obtained by combining (14) with
Cobb-Douglas preferences , LHt / LFt = a Ht Y Ht / a Ft Y Ft = ( a Ht / a Ft )( p Ft / p Ht ) . Then substituting for prices from(15) we have, LHt / LFt = ( a Ht / a Ft )( a FtWFt / a HtWHt ) = (WFt / WHt ) . This proves that both relative labor demandand supply do not depend on the technology shocks, so neither does the equilibrium relative wage.

19(1 − n )Wt* L*Mt =nWt LMt

zt'
1 − zt'(27)

Averaging over our data for earnings in the four offshoring industries at the end of our sample
indicates a share of 0.06.
The U.S. unit cost schedule in the offshoring sector is characterized by the two parameters,a and the mean of b . First, we calibrate the level of this schedule at the steady state margin to be thesame as for the overall U.S. manufacturing sector, which is normalized to unity (that is,a M ( z ' ) ≡ exp( az '+ b) = a H = 1 ). Second, we replicate the observation in Bernard et al. (2003) that thestandard deviation of log U.S. plant sales is 1.67. This is sufficient to pin down both scheduleparameters.15
Similarly, two pieces of information are needed to pin down the two parameters ad and bd in
the cross-country relative unit cost schedule, A( zt ) = exp( a d z t + bdt ) . First, we calibrate the level ofthis schedule at the steady state offshoring margin to our data. The average weekly rate of payment toworkers for the four offshoring industries in the data set is 8 times higher in the U.S. than in Mexico,
implying that A(z ' ) =1/8 (and hence bd = ln(0.125) − a d z ' ) . Secondly, we calibrate the slope of theschedule at the steady state margin, by using estimates from Eaton and Kortum (2002) of thevariation within the distribution of productivity across a continuum of goods.16 They show that theirdistribution implies a relative distribution of unit labor input requirements across two countries ofA( z ) = (T1 / T2 )1 / θ [(1 − z ) / z ]1 / θ , where θ is the parameter characterizing variation in the distribution

within the continuum of goods, and T1 and T2 characterize the absolute technology advantage of thecountries over the whole continuum. This is analogous to the relative cost schedule of Dornbusch et
15

In particular, given that the schedule is defined over the unit interval, and if we identify firm size with sales,
which depends on price and the elasticity σ , the constant value a can be computed as −1.67(12)0.5 / σ . Then bt

varies with overall productivity shocks as bt = log(aHt ) − az .
Their estimates are based upon bilateral import shares and price differences for 50 manufactured products, most ofwhich coincide with offshoring industries.
1620

al. (1976), and thereby analogous to our own A(z) schedule. Given their preferred estimate of θ at
8.28, and since the ratio T1 T2 is pinned down by our calibration above that A( z ' ) = 1 / 8 , this issufficient information to pin down the desired slope as A' ( z ' ) = −0.2677 , and hence
ad = A' ( z ' ) / A( z ' ) = –2.14.

The fixed cost, B, enters the model only jointly as a product with N, the number of firms, where
NB represents the total fixed costs paid by an industry in labor units. Domowitz, et al. (1988) report
estimates of the size of fixed costs for a range of U.S. industries as a share of industry output. Threeof these correspond to the industries we use (apparel, electronic equipment, and transportationequipment), and the average among these indicates a share of 0.11. Equations (10) and (12) imply
that this share can be written as WBN / WLM = 1 /[1 + (σ − 1)(1 − z ' )] . Given calibration of z ' above,
matching the fixed cost share necessarily pins down the calibration of σ at 9.5.
The relative wealth parameter ω is chosen to imply a ratio of per-capita consumption of the
U.S. to Mexico in steady state that matches the data, which the Penn World tables indicate is 4.3 in
2000. The parameter n is calibrated to reflect the 74 percent share of the U.S. in the combined
population of the two countries. Calibrations of standard preference parameters are taken from thebusiness cycle literature. The labor supply elasticity is set at unity, µ =1. The curvature parameter is
set at φ =2. The elasticity of substitution between home and foreign goods is calibrated at thecommon value of unity, η = 1.17 We assume a higher elasticity, χ =2, between the homogeneous andmultinational good.
The remaining preference parameters are calibrated to reflect the relationship between U.S. andMexican aggregates. The home bias parameters reflect the share of import expenditures in GDP,

θ =0.88, θ * =0.71. The four U.S. industries classified as offshoring industries in the data set represent
24% of total U.S. manufacturing, so the offshoring share parameter is calibrated at α = 0.24 . The
17

Bergin (2006) estimates a value near unity for this elasticity using macroeconomic data.

21

relative weight on the home country in the complete asset market allocation (ϖ ) is calibrated toreplicate the ratio of U.S. to Mexican per capita consumption. The steady state levels of the additive
consumption terms ( G and G * ) are calibrated at 15% of total demand, representing the share ofgovernment purchases in U.S. gross national expenditure during our sample range.
The mean unit labor requirement in Mexico’s domestic sector ( a F ) is calibrated to imply asteady state of the model consistent with the assumption above that the Mexican wage is 1/8 that of
the U.S. Productivity shock parameters are estimated from a first-order autoregression on Solow
residuals, computed from monthly manufacturing data from our sample range.18 Regarding demand
shocks, since there is no monthly series available for government consumption, total government
spending from IFS is used. Linear trends are removed from the log of each series before fitting it to
the first-order autoregressive processes used for all shocks above. See Table 3 for exact values.

B. Numerical Results

Simulations consist of solving the model numerically in its original nonlinear form for 120
periods of random draws of shocks. The first 20 periods are dropped, and the remaining 100 periods
are HP filtered and used to compute moments. This process is repeated 1000 times, and we report the
average of moments over the replications. These simulated moments are compared to the moments
for actual data computed in Bergin, Feenstra and Hanson (2009).
Results for the benchmark case of the model are summarized in column (2) of Table 4; actual
moments for Mexico and the U.S. are in column (1). Although the focus of our study is on theoffshoring sector, it is reassuring for our general calibration of shocks that the volatilities for overall
manufacturing employment are in the neighborhood of what is observed in the aggregate data,
including the fact that overall employment volatility is somewhat higher in the U.S. than in Mexico.
18

We follow the convention in Glick and Rogoff (1995) of computing Solow residuals by setting the labor share at
0.6 and assuming a constant capital stock. Resulting estimates are almost identical if we assume a labor share ofunity, as implied by the production function in the model above.

22

Of primary interest is the fact that the calibrated model can easily generate double the volatility in theoffshoring sector of Mexico relative to the corresponding U.S. sector. The standard deviation of
employment for Mexican offshoring, 4.5%, is remarkably close to that in the data at 4.4%; theemployment volatility in U.S. offshoring is somewhat underestimated compared to the data, 1.5%
and 2.0%, respectively.19
We next evaluate the model’s implications for extensive margin movement. For a measure of
the standard deviation of zt' , we use the number of HS products exported from Mexico, which
averaged 3.6%. A somewhat smaller number of 2.9% is obtained in the benchmark simulation. This
indicates that our explanation for Mexican volatility does not rely upon an unreasonably high degreeof firms switching their offshoring decision. Further evidence on the extensive margin comes from
Bergin, Feenstra, and Hanson (2009), who present data on the number of plants operating eachmonth in the maquiladora sector. The monthly standard deviation in the number of plants (logged,
deseasonalized and HP filtered) ranged between 2.1 percent for electrical machinery to 5.2 percent
for apparel, with an average of 3.1 percent over the four industries. These results can be compared tothe theoretical model either as the number of plants Nt, or to N t zt' , which is the product of plants pergood and the mass of offshored goods. The standard deviations for Nt and N t zt' implied by the model
simulation encompass the standard deviation on the number of plants from the data.20
Regarding employment correlations, all are positive as in the data, indicating positive
comovement between the offshoring sectors of both countries. This coincides with our intuition
provided earlier, for how demand shocks in particular should generate volatility in the Mexican
19

The model does not replicate the volatility of the wage-based real exchange rate across countries, however. The
standard deviation of log W*/W in the simulation is 0.48; in data, the standard deviation of log sw*/w, where s is thenominal exchange rate and w and w* are wage indexes from IFS, is 4.22 for our sample range. The failure to explain
volatility of real exchange rates of various types is common to our class of models that exclude nominal shocks andnominal rigidities. This property is not a result of endogenous offshoring dampening relative wage volatility, as thevolatility of the relative wage is likewise small, 0.87, when we suspend the A(z) schedule and hold z' fixed.
20
If the maquiladora plants all produced a single product, then it would be appropriate to measure their number by
N t z t' ; but if the plants all produce the full range of products, then their number should be measured by Nt.

23

offshoring sector.21 Our model has a somewhat stronger correlation of the range of products zt' with
U.S. employment than obtained from the data, however.
w
At the bottom of Table 4 we report the theoretical covariance between zt' and ln( DMt/ Wt* ) .

That covariance is positive in our benchmark results in column (2), reflecting the procyclical natureof the extensive margin of offshoring. From our results in (25)-(26), that positive covariancecombined with the smaller size of the offshoring sector in the foreign country ( z ' = 0.06), bothcontribute to higher volatility of employment abroad.
Columns (3)-(6) indicate the results obtained when just one of the four shocks is used. These
results reveal that the home demand shock is the most important driver of the amplified volatility in
the Mexican offshoring sector. Column (7) confirms the analytical claim above that our main result
depends crucially on endogenous movement in the offshoring margin. Mexican employment
volatility falls to a level much closer to the U.S for offshoring sector earnings when z' is held fixed.
The theoretical model did not attempt to represent the complex dynamics of firm entry, inwhich it is reasonable to think there are substantial delays between a decision to enter and actuallycommencing production. Nor does the theory model the sunk cost of entry, which might discourage
entry in response to transitory shocks. We test whether the modeling of this feature could bequantitatively relevant for the issue at hand, by modeling it in its most extreme form. Column (8) of
Table 4 reports simulation results for the case where the number of firms is held constant. The results
are almost the same as the benchmark case. Since modeling the most extreme form of sluggishness infirm entry has a quantitatively small impact on the results, it would seem that modeling theintermediate cast of realistic entry dynamics is not warranted. One might also consider modeling an
adjustment cost discouraging switching in the offshoring decision, which is more likely to affect our

21

Note that a positive demand shock in the U.S. has two effects: the rise in demand directly raises firm entry andemployment in the U.S., but at the same time the rise in relative wage induced by the shock leads some entry andemployment to be shunted to Mexico.

24

results, given that endogenous movement in the offshoring sector is behind the cross-country
difference in volatilities. But given that the standard deviation of the offshoring margin in ourbenchmark case is close to that in the data, there appears to be no empirical motivation for
introducing such an adjustment cost in this model.
When the relative productivity schedule A(z) is made flatter, where the slope A ' ( z ') = -0.1,
column (9) shows that Mexican volatility rises. A flatter distribution implies greater movement in theoffshoring margin z.
As the analytical result identified the mean of the offshoring margin as important for our result,column (10) reports results for the case of an equal split of goods between the U.S. and Mexico, z ' =0.5. In this case there is much less volatility in the foreign offshoring sector than found with ourbenchmark calibration, though volatility there still exceeds that found in the home offshoring sector.
The reason why foreign volatility is higher even with equal-sized offshoring industries in the twow/ Wt* ) still adds to the volatility ofcountries is that the covariance between zt' and ln( DMtemployment abroad, but offsets it at home, as shown by (25)-(26).
Finally, we study alternative specifications of the supply shock that are allowed to shift the A(z)schedule in the offshoring sector, as discussed previously. In column (11) this is found to further
amplify the volatility in the Mexican offshoring sector to remarkably high values. But this comes atthe cost of implying strong negative correlations between the offshoring sectors of both countries.
This arises from the fact, as discussed previously, an increase in U.S. relative productivity exceeding
the increase in the U.S. relative wage induces U.S. firms to “in-source” activity previously allocatedto Mexico.

VI. Conclusions

Global production sharing is responsible for a substantial portion of world trade and is the25primary means through which many developing countries engage in international commerce. Whilethe expansion of export assembly operations have lead to impressive rates of employment growth inChina, Eastern Europe, Mexico, and elsewhere, the implications of global production sharing for thevolatility of economic activity has only recently attracted scholarly attention. In the case of Mexico,the country’s offshoring industries experience fluctuations in economic activity that are twice asvolatile as the corresponding industries in the U.S. (Bergin, Feenstra, and Hanson, 2009). In thispaper, we find that fluctuations in offshoring employment in Mexico result in part from adjustment at
the extensive margin, as products enter and exit trade between the two countries.
To account for differences in U.S. and Mexican employment variability, we develop atheoretical model in which heterogeneous firms in a high wage country (the U.S.) are free to enterand exit offshoring relationships with firms in a low wage country (Mexico). Shocks that change
U.S.-Mexico relative wages induce U.S. firms to alter which products they offshore to Mexico.
Adjustment in the offshoring margin is the main mechanism through which U.S. shocks become
amplified in Mexico. Stochastic simulations show that the model matches the empirical regularities
observed in U.S. offshoring to Mexico. For Mexico, one consequence of economic integration with
the U.S. appears to be greater variability in its manufacturing employment.

26

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28

Appendix

Labor demand at home is obtained by integrating over the fixed costs B for every productz ∈ [0,1] , and the variable labor input requirement a Mt ( z ) y t (z ) for those products z ∈ [ z ' t ,1] :
1

1

0

zt'

Lt = ∫ BN t dz + ∫ a Mt ( z ) y t ( z ) N t dz .

(A1)

The number of varieties Nt appearing in the first integral of (A1) is obtained from (10). For thesecond integral, we multiply the labor input requirement ay t (z ) by the wage Wt, and further multiply*
by the markup σ /(σ − 1) , to obtain the expenditure [CMt + CMt(1 − n) / n] / N t on each variety. So the*expression inside the second integral of (A1) equals [CMt + CMt(1 − n) / n](σ − 1) / σ Wt , which is

integrated over z ∈ [ zt' ,1] to yield (11).
*For foreign labor demand we integrate the variable labor input requirement a Mt(z ) yt* ( z ) forz ∈ [0, zt' ] :zt'*(z ) yt* ( z ) N t dz .
L = ∫ a Mt
*
t

(A2)

0

Multiplying the labor input requirement a * y t* ( z ) by the wage Wt* , and further multiplying by the*markup σ /(σ − 1) , we again obtain the expenditure [CMt + CMt(1 − n) / n] / N t on each variety. So the*expression inside the integral of (A2) equals [CMt + CMt(1 − n) / n](σ − 1) / σ Wt* , which is integrated

over z ∈ [0, z ' t ] to yield (12).
Finally, the price index for multinational goods is:*a2⎛ σ ⎞ ⎛a −a⎞**+ln PMt = z 't ln Wt + (1 − z 't ) ln Wt + ln ⎜⎟ ( z 't ) + bt − bt z 't + + bt ,⎟ ⎜2
⎝ σ −1⎠ ⎝ 2 ⎠(is set equal to unity to close the model.

)

(A3)

29

Table 1: U.S. Harmonized System Imports from Mexico, 1996–2006

Laredo, TX
Mean Number of HS Products
Mean Number of Months a HS Product is
Imported Per Yeara
Std. Dev. Log Number of HS Products b
Correlation of Number of HS Products
and U.S. Manufacturing Employment c
El Paso, TX
Mean Number of HS Products
Mean Number of Months a HS Product is
Imported Per Yeara
Std. Dev. Log Number of HS Products b
Correlation of Number of HS Products
and U.S. Manufacturing Employment c
San Diego, CA
Mean Number of HS Products
Mean Number of Months a HS Product is
Imported Per Yeara
Std. Dev. Log Number of HS Products b
Correlation of Number of HS Products
and U.S. Manufacturing Employment c

ApparelElectrical
MachineryComputer &Electronics

Transport
Equipment

384.0

219.2

258.6

140.5

6.9
2.64

8.9
2.14

7.5
3.10

9.0
2.94

0.28

0.32

0.07

0.31

162.6

137.0

208.3

53.4

5.8
4.99

8.9
2.43

7.8
2.60

7.8
5.66

0.05

0.04

0.12

0.30

299.8

129.6

237.0

53.2

6.3
3.38

8.3
3.86

7.5
3.39

7.0
6.18

-0.01

0.28

0.25

0.12

Notes:
a. Averaged over HS products and over the years 1996–2006.
b. The log number of HS products has been deseasonalized and HP filtered, and the standard deviation ismultiplied by 100.
c. The number of HS products and U.S, manufacturing employment are in logs, and are deseasonalized
and HP filtered.
Source:Bureau of the Census, 1996-2006, U.S. Exports and Imports of Merchandise on CD-ROM [machinereadable data file], Washington, D.C.

30

Table 2: Adjustment in the Maquiladora Industry: Extensive Margins

(3)
(2)
(1)
No. of HS Sales per Extensive
Products HS Product Marginof Exports(4)
Intensive
Marginof Exports

Industry share ofexports
at border crossing

0.071(0.021)

0.929(0.021)

0.131(0.025)0.869(0.025)

Total exports
at border crossing

0.103(0.027)0.897(0.027)0.085(0.025)0.915(0.025)

R2
N

0.02
1584

0.77
1584

0.04
1584

0.70
1584

Notes:

Columns (1) and (2) show regressions of either the number of HS products imported by the U.S. permonth, or the average import sales per HS product, on the industry share of imports at that bordercrossing and total imports from Mexico at that border crossing. Columns (3) and (4) show regressions of
the extensive margin of Mexican exports (which is a weighted count of the number of HS products) andthe intensive margin of Mexican exports (which is the industry sales divided by the extensive margin), on
the same independent variables. The sample is the four offshoring industries in Mexico, exporting to threeland border crossings, with data at a monthly frequency from 1996:1 to 2006:12. All variables are in logs,
expressed in real terms, deseasonalized, and HP filtered. All regressions include controls for industry
fixed effects, which are not shown. Standard errors (clustered by industry) are in parentheses.

31

Table 3. Calibration of model Parameters

Preferences

θ
θ*
α
σ
η
χ
µ
φ

home bias in U.S.

0.88

G

home bias in Mexico
offshoring expenditure shareelasticity between varieties
elasticity, multinational and domestic goods
elasticity, home and foreign goods
labor supply elasticity
risk aversion
relative size of U.S.
relative wealth of U.S.
US mean government demand

0.71
0.24
9.5
1
2
1
2
0.74
24.5
0.186

G*

Mexican mean government demand

0.0432nϖTechnology
aH

US steady state unit cost

1

aF*
z'
a
b
ad

Mexican steady state unit costoffshoring margin
US offshoring slope parameter
US offshoring level parameter
relative cost slope parameter

4.22
0.06
-0.6090.0365-2.14

bd

relative cost level parameter-1.95

Shock processes⎡ 6.42 x10−5

σa = ⎢⎣ −4.67 x10−6⎡ 7.68 x10−3

σG = ⎢⎣ 4.02 x10−3−4.02e − 2 ⎤⎡ 0.9310.961 ⎥⎦
⎣ 7.38e − 3−4.67 x10−6 ⎤⎥1.87 x10−4 ⎦ρa = ⎢

4.02 x10−3 ⎤⎥2.36 x10−2 ⎦ρG = ⎢⎡ −0.0549 0.379 ⎤⎥⎣ −0.368 0.424 ⎦32Table 4. Model Simulation for Production Worker Employment in the Offshoring Sector(1)
Mexicanor U.S.
data(2)Benchmark
case

(3)
U.S.
demandshock(4)
Mexicodemand
shock

(5)
U.S.
supplyshock(6)
Mexicosupply
shock

(7)
Fixed
z'

(8)
Fixed
N

(9)
FlatterA’(z)b(10)(11)
cz ' = 0.5 Altern.
supplyShocksd

4.44
2.04
0.89
1.15
2.21
0.77

4.54
1.52
0.94
1.22
3.01
0.77

3.80
0.59
0.48
0.90
6.45
0.53

2.63
0.56
0.57
0.66
4.77
0.87

0.59
0.27
0.39
0.44
2.15
0.90

1.86
1.21
0.26
0.20
1.54
1.29

2.15
1.62
0.88
1.24
1.34
0.71

4.45
1.56
0.93
1.20
2.90
0.78

5.63
1.46
1.02
1.21
3.90
0.84

1.40
0.76
1.00
1.17
1.85
0.85

12.89
1.22
1.28
1.20
10.66
1.07

0.51
0.78
0.64
0.76
0.18

0.73
0.93
0.46
0.50
0.71

0.98
0.99
0.97
1.00
0.99

0.36
0.86
0.19
0.94
0.49

1.00
1.00
1.00
0.99
1.00

1.00
0.96
-0.79
-0.62
-0.55

0.96
0.81
0.27
0.56
0.00

0.72
0.93
0.45
0.49
0.70

0.61
0.98
0.58
0.45
0.71

0.83
0.99
0.93
0.78
0.84

-0.35
0.71
0.78
0.73
0.23

3.61

2.86

2.58

1.99

0.25

0.53

0.00

2.79

4.15

0.54

13.10

⎧
1.66
0.80
0.61
3.14 ⎨
⎩
4.09
3.37
2.31
σ (N z')4
Addendum: covariance (x10 )cov (z',D W /W* )a
0.33
0.25
0.09
Notes:a
All variables are in logs except for z' in this expression.
bA'(z ) = -0.1.
cHolding the slope A'(z) constant at its benchmark value of -0.2677.
dA(z) distribution shifted by productivity shocks.

0.30

1.25

1.62

0.00

1.68

0.82

1.12

0.55

1.77

1.62

2.79

5.34

1.22

13.50

0.01

0.06

0.00

0.32

0.50

0.07

-0.30

Standard deviations (%):σ (L*M)
σ (LM)σ (L*)σ (L)
σ (L*M)/ σ (LM)σ (L*)/ σ (L)Correlations:corr (L*M ,L M )corr (L* ,L )corr (L*M ,L* )corr (L M ,L)corr (z',L)Margin movements (%):σ (z')σ (N)33Figure 1: The Number of HS Products Over Years(Ave. over 3 ports; Log values, seasonally adjusted, HP filtered)
NAICS 315

NAICS 334
.05

.05

0
0

-.05

-.05
-.1
1996

1998

2000

2002

2004

2006

1996

1998

2000

Date

2002

2004

2006

2004

2006

Date

NAICS 335

NAICS 336

.05

.1

.05

0

0

-.05

-.05

-.1
1996

1998

2000

2002

Date

2004

2006

1996

1998

2000

2002

Date