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A joint initiative of Ludwig-Maximilians University’s Center for Economic Studies and the Ifo Institute
CESifo Conference Centre, Munich
Area Conferences 2012
CESifo Area Conference on
Global Economy
25 – 26 May
Gravity with Unemployment
Benedikt Heid and Mario Larch
CESifo GmbH · Poschingerstr. 5 · 81679 Munich, Germany
Tel.: +49 (0) 89 92 24 - 14 10 · Fax: +49 (0) 89 92 24 - 14 09
E-mail: [email protected] · www.CESifo.org
Gravity with Unemployment∗
Benedikt Heid
†
and Mario Larch
‡
May 23, 2012
Abstract
The gravity equation is the workhorse of international trade ow studies and has
been the basis for numerous evaluations of the trade and welfare impact of trade liberalization. However, its theoretical foundations have neglected labor market frictions.
We extend a standard structural gravity model by modeling these frictions within
a search and matching framework. Our framework allows counterfactual analysis of
changes in trade costs and labor market reforms on trade ows, prices, employment,
and welfare. We demonstrate that standard gravity models which neglect adjustments
on the labor market typically underestimate welfare eects of trade liberalization by
deriving a sucient statistic for welfare. We apply our methodology to evaluate the
trade eect of endogenous preferential trade agreements (PTA) for a sample of OECD
countries and reconsider the border puzzle. Our estimates imply that welfare eects
of PTAs are magnied when taking into account employment eects. However, some
countries experience higher unemployment and lower welfare after trade liberalization.
Keywords : International trade; gravity equation; trade costs; unemployment;
structural estimation
JEL-Codes : J60; F12; F13; F16
Funding from the DFG under project 592405 is gratefully acknowledged. We thank participants at
the GEP Postgraduate Conference 2012 for helpful comments. As always we have a property right on any
remaining mistakes and errors.
†
Aliations: University of Bayreuth and ifo Institute, Address: Universitätsstraÿe 30, 95447 Bayreuth,
Germany, Email: [email protected]
‡
Aliations: University of Bayreuth, CESifo, ifo Institute, and GEP at University of Nottingham.
Address: Universitätsstraÿe 30, 95447 Bayreuth, Germany, Email: [email protected]
∗
1 Introduction
The quantication of the welfare eects of trade liberalization is one of the core issues
in empirical international trade.
The workhorse models for evaluating trade policies all
feature a gravity equation for international trade ows which captures key stylized facts:
Trade increases with market size and decreases with distance. Despite the multitude of
theoretical underpinnings of the gravity equation all models so far assume perfect labor
markets. This implies that changes in real welfare neglect changes in the total number of
employed workers due to trade liberalization.
We propose the rst structural gravity model in international trade accounting for
imperfect labor markets. We derive a simple, structural framework that allows for
and employment
price
adjustments and show how counterfactual trade ow, GDP, employment,
and welfare changes can be calculated.
We therefore contribute to the vast literature
on structural gravity estimation by augmenting it by search and matching labor market
frictions.
We derive a simple sucient statistic for welfare, relating welfare changes to
employment changes, changes in the share of spending on domestic goods and the (partial)
import trade elasticity similar to Arkolakis et al. (2012).
Our applications show that welfare eects are substantially magnied when allowing for
imperfect labor markets. The additional richness of incorporating labor market frictions
comes at minimal cost:
function.
it only requires an estimate of the elasticity of the matching
Hence, our suggested framework can easily be applied in all elds where the
gravity equation has been used successfully.
We apply our Armington (1969) type model with a one-shot simplication of Pissarides
(2000) search and matching labor market frictions as discussed in Rogerson et al. (2005)
to two dierent data-sets. First, we use a sample of 28 OECD countries from 1950 to 2006
in order to evaluate the eects of preferential trade agreements (PTAs) and a hypothetical
labor market reform in the US. We nd that introducing PTAs as observed in 2006 implies
that on average, estimated GDP increases are roughly one third larger when accounting
for employment eects arising from imperfect labor markets. Countries with only slight
increases in GDP even see negative employment eects. These negative employment eects
translate into a magnication of the negative welfare eects predicted for those countries.
Our second counterfactual analysis assumes an improvement of labor market institutions in
the US. As expected, GDP and welfare increases in the US but also in all trading partners
due to positive spillover eects of the labor market reform.
We next use our methodology to reconsider the McCallum (1995) border puzzle accounting for employment eects. McCallum (1995) showed that trade between US states
and Canadian provinces is reduced by a factor of 22 in comparison to trade within a country. When comparing the GDP changes between the perfect and imperfect labor markets,
we see that on average, GDP changes are more than twice as large.
On average, US
states gain far less than Canadian provinces. Finally, turning to the welfare implications,
we calculate a doubling in the equivalent variation when comparing the perfect with the
imperfect labor market scenario, similar to the eect found for GDP.
Gravity models have been used successfully to explain observed trade ows.
has spurred the development of their theoretical underpinnings.
This
Anderson (1979) and
Bergstrand (1985) addressed the role of multilateral price eects on trade ows, while
more recent contributions by Eaton and Kortum (2002) and Anderson and van Wincoop
(2003) rened the theoretical foundations for the gravity equation to emphasize the importance of accounting properly for the endogeneity of prices. Fieler (2011) and Waugh (2010)
build on the former and stress the importance of non-homothetic preferences and asym-
1
metric trade costs, respectively. Anderson and Yotov (2010) elaborate on the incidence of
bilateral trade costs in the latter framework. All these frameworks emphasize that in order
to calculate the eects of a counterfactual situation taking into account general equilibrium
eects, one needs to take care of changes of GDP. To do so, one needs to calculate prices
in the counterfactual equilibrium.
produced are assumed xed In all these frameworks this is easy as ...quantities
(p. 190), Anderson and van Wincoop (2003). However, this
assumption is also very restrictive, as it implies that GDP and welfare changes do not
account for changes in the total number of employed workers.
Theoretical contributions have stressed the eects of trade liberalization with imperfect
labor markets.
Labor market frictions may arise due to fair wages or eciency wages
(Amiti and Davis (2012), Egger and Kreickemeier (2009)), minimum wages (Brecher (1974),
Davis (1998), Egger et al. (2011a)) or due to search and matching frictions (Davidson
et al. (1988), Davidson et al. (1999), Felbermayr et al. (2011a), Helpman and Itskhoki
(2010), Helpman et al. (2010)). One of the main ndings in this literature is that trade
liberalization is likely to reduce unemployment rates. Recently, Dutt et al. (2009) as well as
Felbermayr et al. (2011b) provide reduced-form evidence that more open economies have
lower unemployment rates on average.
1
The remainder of the paper is structured as follows: Section 2 presents the structural
gravity model accounting for employment eects.
It also includes a discussion of how
to calculate counterfactual employment, GDP, trade ow, and welfare changes.
Section
3 discusses the parameter estimation. Section 4 evaluates the eects of preferential trade
agreements and labor market reforms for a sample of 28 OECD countries. Section 5 revisits
the McCallum (1995) border puzzle. Section 6 presents robustness checks, and Section 7
concludes.
2 A gravity model with imperfect labor markets
In order to derive the gravity model with imperfect labor markets, we rst describe the
goods and labor market, and then derive the gravity equation given the assumptions about
the goods and factor market. Afterwards we discuss the comparative static analysis.
2.1 Goods market
j
The representative consumer in country
is characterized by the utility function
Uj .
We
assume goods that are dierentiated by country of origin following Armington (1969). The
quantity of purchased goods from country
i
is given by
qij ,
leading to the following utility
function
Uj =
" n
X
(1−σ)
σ
βi
#
qij
σ−1
σ
σ
σ−1
,
(1)
i=1
where
βi
n
is the number of countries,
σ
is the elasticity of substitution in consumption and
is a positive distribution parameter.
1
Another strand of the literature uses the quasi-natural experiment of the opening up of Japan in the
19th century to infer welfare gains from trade arising from sectoral reallocations (Bernhofen and Brown
(2005)). Artuc et al. (2010) infer welfare eects of trade shocks at the worker arising from sectoral
reallocation of workers in a structural dynamic framework. Both abstract from welfare eects due to
changes in the number of employed workers.
2
i to j
International trade of goods from
and
tij = 1
for
i = j
i
pij = pi tij .
such that all goods from
Prot maximization then implies that
> 1 for all i 6= j ,
price pi domestically.
imposes iceberg trade costs tij
sell at the same
Therefore, the representative consumer maximizes (1) subject to the budget constraint
ỹj =
n
X
pi tij qij ,
(2)
i=1
where
ỹj = yj (1 + dj ),
with
yj
denoting nominal income in country
j
of trade decit or surplus of country
j
and
dj
the share
in terms of GDP. The according demand for each
variety is given by
βi1−σ (pi tij )−σ
ỹj ,
Pj1−σ
qij =
(3)
where the CES price index is dened by
"
Pj =
n
X
#1/(1−σ)
(βi pi tij )1−σ
.
(4)
i=1
The value of aggregate exports from
i
to
j
can then be expressed as
xij
= pi tij cij =
βi pi tij
Pj
1−σ
ỹj .
(5)
In general equilibrium the total amount of exports corresponds to nominal income, i.e.
yi =
n
X
xij .
(6)
j=1
Assuming labor to be the only factor of production, GDP in a world with imperfect labor
markets is given by:
yi = wi (1 − ui )Li .
(7)
wi
We next describe the labor market, which determines wages
rate
and the unemployment
ui .
2.2 Labor market
We model the labor market using a one-shot version of the search and matching frame-
2
work (SMF, see Mortensen and Pissarides (1994) and Pissarides (2000)).
Search-theoretic
frameworks t stylized facts of labor markets in developed economies as e.g. the simulta-
3
neous existence of unlled vacancies and unemployed workers.
The labor market is characterized by frictions. All potential workers in country
have to search for a job, and rms post vacancies
2
Vj
at a unit cost of
cj Pj
j , Lj ,
(measured in
See Rogerson et al. (2005) for a survey of search and matching models including an exposition of the
simplied one-shot version. For recent trade models using a similar static approach see Keuschnigg and
Ribi (2009) and Helpman and Itskhoki (2010).
3
They are less successful in explaining the cyclical behavior of unemployment and vacancies, see Shimer
(2005). This deciency is not crucial in our case as we purposely focus on the steady state.
3
terms of the nal output good) in order to nd workers. The number of successful matches
Mj ,
between an employer and a worker,
is given by
the elasticity of the matching function and
4
mj
Mj = mj Lµj Vj1−µ ,
where
µ ∈ (0, 1)
is
measures the overall eciency of the labor
Mj /Vj = mj (Vj /Lj )−µ = mj ϑ−µ
j ,
1−µ
1−µ
and only a fraction of all workers will nd a job, Mj /Lj = mj (Vj /Lj )
= mj ϑj , where
ϑj ≡ Vj /Lj denotes the degree of labor market tightness in country j . This implies that
market.
Only a fraction of open vacancies will be lled,
5
the unemployment rate is given by
uj = 1 − mj ϑ1−µ
.
j
(8)
After a match has been established, the rm and the worker bargain over the match surplus.
The worker's surplus from the match is the dierence between the wage the worker earns
while being employed and the unemployment benets she receives when she is unemployed.
The unemployment benets are expressed as a fraction
Denote by
Jjo
γj
of the ongoing wage rate.
Jjv the value of
− Jjv ), i.e. by the
the value of expected prot from an occupied job and
v
expected prot from a vacant job. Jj is given by
−Pj cj +
Mj /Vj (Jjo
sum of negative of the cost of posting a vacancy and the probability of lling the vacancy
multiplied with the surplus of lling it.
Jjo
is given by
Jjo = pj − wj ,
of marginal revenues and marginal costs of an employed worker.
until all prot opportunities are exploited, hence
pj − wj = Pj cj Vj /Mj .
Jjv = 0
i.e. by the dierence
Firms post vacancies
in equilibrium. This implies that
Hence, the worker's wage has to be strictly smaller than the value
of output of the rm.
Rewriting, one nds the
job creation curve
wj = p j −
Pj cj
.
mj ϑ−µ
j
(9)
It is increasing in the value of output and decreasing in the expected costs of lling a
vacancy
Pj cj /(mj ϑ−µ
j ).
Following Stole and Zwiebel (1996), we use a generalized Nash bargaining solution to
determine the surplus splitting rule:
max
(wj − γj wj )ξj (Jjo − Jjv )1−ξj
(10)
⇒ max
(wj − γj wj )ξj (pj − wj )1−ξj ,
(11)
wj
wj
where the bargaining power of the worker is given by
ξj ∈ (0, 1) .
Note that both the
worker and the rm neglect the fact that in general equilibrium, higher wages lead to higher
unemployment benets, i.e. they both treat the replacement rate as exogenous. The rst
order conditions of the bargaining problem yield
for
wj
results in the
wage curve
wj =
wj − γj wj = ξj /(1 − ξj ) (pj − wj ).
ξj
pj .
1 + γ j ξj − γ j
Due to the one-shot matching, the wage curve does not depend on
wage increases in the value of output
replacement rate
pj ,
Solving
(12)
ϑj .
The bargained
in the worker's bargaining power
ξj
and in the
γj .
4
Note that we assume a constant returns to scale matching function in line with empirical studies, see
Petrongolo and Pissarides (2001).
5
Note that the matching eciency has to be suciently low to insure job nding rates and job lling
rates to be strictly between 0 and 1.
4
Combining the job creation and wage curves determines the equilibrium labor market
tightness as
ϑj =
where
Ωj :=
1−γj +γj ξj
1−γj +γj ξj −ξj
≥1
pj
Pj
1/µ cj
Ωj
mj
−1/µ
,
(13)
ξj
is increasing in the worker's bargaining power
and in the replacement rate
market tightness decreases and the unemployment rate increases when
Ωj
pj /Pj
increases. An increase of
Ωj
summarizes the eective bargaining power of workers.
mj
or
cj
γj .
Labor
decrease or
increases the marginal revenue of an additional worker
relative to the cost of posting the vacancy. Hence, rms will create more vacancies, thereby
increasing labor market tightness and lowering unemployment.
pj /Pj
The relative price
is determined via goods demand and supply. It therefor pro-
vides the link between the labor and goods market.
Specically, changes in trade costs
will aect the relative price, therefore inuence labor market outcomes. This can best be
seen by using equation (12) to replace wages
wj
and equations (8) and (13) to replace
uj
in equation (7)
ξj
yj =
pj mj
1 + γj ξj − γj
Given trade costs
tij ,
labor endowments
(5), (6) and (14) to solve for the
trade ows
xij ,
GDPs
yj
pj 's
Lj
pj
Pj
1−µ µ
cj
Ωj
mj
µ−1
µ
Lj .
(14)
and the parameters, we can use equations (4),
and subsequently for relative prices
and the unemployment rate
pj /Pj ,
wages
wj ,
uj .
2.3 Derivation of the gravity equation
In order to derive the gravity equation in our setting we rst use equation (6) that summarizes the general equilibrium nature of our model and implies market clearing, i.e.
yi =
n
X
xij =
j=1
n X
βi tij pi 1−σ
Pj
j=1
1−σ
ỹj = (βi pi )
θj ≡
βi pi and dening y W =
θ̃j ≡ ỹj /ỹ W , we can write
yi ỹj
xij = W
y
P
j
tij
Πi Pj
Πi ≡ 
n X
tij 1−σ
j=1
Pj
yj , ỹ W =
P
j
ỹj
ỹj .
(15)
and income shares
1−σ
where

Pj
j=1
Solving for scaled prices
yj /y W and
n X
tij 1−σ
,
(16)
1/(1−σ)
θ̃j 
.
(17)
Substituting equilibrium scaled prices into equation (4), we obtain
Pj ≡
n X
tij 1−σ
i=1
Πi
!1/(1−σ)
θi
.
(18)
Note that this system of equations exactly corresponds to the system given in equations
(9)-(11) in Anderson and van Wincoop (2003) or equations (5.32) and (5.35) in Feenstra
(2004) assuming balanced trade,
di = 0
for all
5
i,
even when labor markets are imperfect.
If trade costs are symmetric, i.e.
tij = tji ,
and trade is balanced
Πi = Pi
(see AvW). This
is what Anderson and van Wincoop (2003) assumed throughout. Bergstrand et al. (2012)
relaxed this assumption and we follow their approach here.
The intuition for this results is that in equation (16) GDPs appear. Observed GDPs
already take care of the actual number of employed peoples.
total spending is total production.
achieved by
Hence, it still holds that
The only dierence is that now total production is
employed workers, not all workers, as is assumed with perfect labor markets.
We summarize this result in the following implication:
Implication 1 The estimation of trade costs is unchanged when allowing for imperfect
labor markets.
An immediate consequence of Proposition 1 is that parameter estimates of the gravity
equation are not aected by allowing for imperfect labor markets. But then the question
arises whether imperfections on the labor market matter at all for the evaluation of trade
policies? The answer is yes, they do matter in the counterfactual analysis, to which we
turn next.
2.4 Comparative statics
As pointed out in Proposition 1, the gravity equation derived from our model does not
dier from the standard gravity equation (see for an overview Feenstra (2004)). The secret
of the power of our approach lies in the counterfactual analysis.
As Anderson and van Wincoop (2003) emphasize in Appendix B, in order to calculate
the counterfactual situation without borders, one needs to take into account that income
and spending shares
θi
and
θ̃i
change. In doing so, one needs to calculate prices in the
borderless equilibrium. In the framework of Anderson and van Wincoop (2003) assuming
perfect labor markets, this is easy as ...quantities produced are assumed xed (p. 190).
However, this assumption is also very restrictive, as it implies that GDP and welfare
changes are solely due to changes in (real) prices. Hence, whereas a change in a country's
GDP only translates into price changes in the perfect labor market framework, our model
leads to
price and quantity
adjustments. When GDP falls, unemployment will rise, which
in turn will impact wages. In essence, our model allows labor market variables to aect
income. Hence, in the proper counterfactual analysis assuming perfect or imperfect labor
markets matters.
We derive and discuss in turn counterfactual (un)employment, GDP, and trade ows.
Afterwards we discuss how to calculate welfare and derive a sucient statistics for welfare
along the lines of Arkolakis et al. (2012).
2.4.1 Counterfactual (un)employment
Noting that the
p's are not observed, we follow Anderson and van Wincoop (2003) and use
equation (15) to solve for scaled prices as follows:
yj
(βj pj )1−σ = P 1−σ
tji
n
i=1
where
j ≡ θj Πσ−1
.
j
replacing
ϑ
Pi
=
ỹi
yW
yW
σ−1
θ
Π
=
j ,
j j
ỹ W
ỹ W
We then use the denition of
ui
given in equation equation (8),
by the expression given in equation (13) and
6
(19)
Ξj = mj
cj
m j Ωj
µ−1
µ
and
κ̂j =
Ξcj /Ξj ,
we may write:
1 − uci
= κ̂j
1 − ui
pci
pi
1−µ 1−µ
Pi
Pic
µ
µ
.
(20)
Pj1−σ =
Noting from the derivation of equation (19) and the fact that
P
1−σ
i tij i (see
Appendix A) that we can express the ratios of the prices and price indices as functions of
i ,
we end up with
1 − uci
= κ̂j
êj ≡
1 − ui
1−µ
c µ(1−σ)
j
j
1−σ
i tij i
P 1−σ
i tij,c i,c
P
!
1−µ
µ(1−σ)
.
(21)
Note that employment changes are homogeneous of degree zero in prices, implying that
the normalization does not matter for the employment eects.
In contrast to the setting assuming perfect labor markets, our framework allows for
employment eects. We summarize in the following implication:
Implication 2 Whereas in the setting with perfect labor markets employment eects are
zero by assumption, the employment eects in our gravity system with imperfections on the
labor market are given by:
ecj
1−µ
c µ(1−σ)
j
= κ̂j
j
1−σ
i tij i
P 1−σ
i tij,c i,c
P
!
1−µ
µ(1−σ)
(1 − ui ) .
When data on replacement rates and unemployment rates for all countries are available,
we can also calculate counterfactual changes in the unemployment rate.
2.4.2 Counterfactual GDP
We next derive counterfactual GDPs. Dening
Ξj = mj
cj
mj Ωj
µ−1
µ
, we can write equation
(14) as:
ξj
yj =
pj
1 + γ j ξj − γ j
Now take the ratio of counterfactual GDP,
parameters and constants, like
yjc
yj
where
= κ̂j
ξj , γj , Ξj
pcj
pj
and
Lj ,
pj
Pj
1−µ
µ
Ξj Lj .
(22)
yj ,
while noting that all
stay constant:
µ
j
Pjc
1−µ
and observed GDP
pc 1−µ
= κ̂j
µ
pcj
pj
µ1
Pj
Pjc
! 1−µ
µ
,
(23)
κ̂j = Ξcj /Ξj .
Using again (19) and the fact that
ŷj ≡
with
yjc
pj
Pj
D̂W ≡
yjc
yj
y W,c ỹ W
ỹ W,c y W
= D̂W
1
1−σ
1
1−σ
Pj1−σ =
1−σ
i tij i (see Appendix A), we can write
P

 1−µ
µ(1−σ)
P 1−σ
1
c µ(1−σ)
j


i tij i
κ̂j
.
 P 1−σ 
j
c
c
i
i tij
(24)
indicating the endogenous change in the world trade decit
to keep trade decit GDP shares
dj 's
constant.
7
It equals one in the case of balanced
yj , tij and tcij , we can solve counterfactual GDPs, yjc , as soon as
c
we have j , j , σ and µ. Even with imperfect labor markets we just need one additional
parameter alongside σ , namely, µ, the elasticity of the matching function, in order to
trade.
Hence, given
calculate counterfactual GDPs.
P1 =
P1c
data-set.
= 1,
6
In order to ensure a common numéraire, we normalize
i.e. GDP changes are in terms of the price level of the rst importer in the
If we assume balanced trade and if
µ = 1, we end up in the case of perfect labor markets
employed by AvW, i.e.
yjc
=
yj
1
c 1−σ
j
.
j
(25)
We summarize our ndings in the following implication:
Implication 3 Counterfactual GDPs are given by:
1
1−σ
imperfect labor markets:
yjc
perfect labor markets:
1
1−σ
yjc = D̂W
=
D̂W
c j
κ̂j j
c 1
j
1
µ(1−σ)
1−σ
j
1−σ
i tij i
P c 1−σ c
i
i tij
P
1−µ
µ(1−σ)
yj .
( )
yj .
We can now go a step further and disentangle the change in GDP in changes due to
real price changes and changes due to employment changes as follows:
ŷj
=
=
=
D̂W
1
1−σ
D̂W
1
1−σ
D̂W
1
1−σ
κ̂j p̂j êj
1
c µ(1−σ)
j
κ̂j
j
1−σ
i tij i
P 1−σ c
i tij,c i
P
µ
1−µ
c µ(1−σ)
c µ(1−σ)
j
j
κ̂j
j
j
|
{z
} |
price change
with
p̂j
!
1−µ
µ(1−σ)
1−σ
i tij i
P
!
1−σ
i tij,c i,c
P
{z
employment change
1−µ
µ(1−σ)
,
(26)
}
denoting the price change. Taking logs, we can attribute the share of log change
in GDP divided by
D̂W
1
1−σ
,
ŷj? ,
due to changes in institutions, prices and employment
as follows:
1=
ln κ̂j
ln p̂j
ln êj
+
+
.
ln ŷj? ln ŷj? ln ŷj?
Let us focus on country 1 for a moment. As we use its price index
(27)
P1
as our numéraire,
the last expression in brackets of equation (26) is equal to one for country 1. Then, the
equation simplies to the change in
κj
(which is solely driven by changes in exogenous
parameters) and to two terms which are equal except their exponents: The price change
term is risen to the power of
µ
and the employment change term to the power of
Hence, the relative importance of price and employment changes only depends on
1 − µ.
µ. If µ
approaches zero, the labor market rigidities vanish, and the total GDP change is due to the
price change, as in models assuming perfect labor markets. With any value of
6
µ
between
As mentioned in footnote 12 in AvW, the solution of the multilateral resistance terms adopts a particular normalization. In general this applied normalization may vary between the baseline MRTs and
the counterfactual MRTs. In order to ensure the same normalization for the baseline and counterfactual
scenario, we normalize P1 = P1,c = 1.
8
zero and one, the share of the GDP change attributable to the price change is
share due to the employment change
1 − µ.
Hence, with
µ = 0.5,
µ
and the
half of the change in
GDP is due to the price change and the other half due to the employment change.
2.4.3 Counterfactual trade ows
With estimates of tij , data on
yi
and a value for
ows as:
where
Πi
xij y W
=
yi ỹj
and
Pj
σ , we can calculate (scaled) baseline trade
tij
Πi P j
1−σ
,
(28)
are given by equations (17) and (18), respectively.
With counterfactual GDPs given by (24), we can calculate counterfactual trade ows
as
!1−σ
tcij
Πci Pjc
xcij y W,c
=
yic ỹjc
,
(29)
where
Πci

n
X

=
j=1
Pjc
θ̃jc 
n c 1−σ
X
tij
=
i=1
1/(1−σ)
!1−σ
tcij
Pjc
Πci
,
(30)
!1/(1−σ)
θic
,
(31)
c
c
c
c
i ỹi .
i yi and θ̃j = ỹj /
c
c
Note that Pj and Pj are homogeneous of degree one in prices while Πi and Πi are homoW
c W,c /(y c ỹ c )
geneous of degree minus one. Hence, scaled trade ows xij y /(yi ỹj ) and xij y
i j
and
θjc = yjc /
P
P
are homogeneous of degree zero in prices.
In other words, they do not depend on the
normalization chosen.
Due to direct eects of trade costs changes via tij and non-trivial changes in
Πi
and
Pj
it is theoretically ambiguous whether trade will change more or less assuming imperfect
labor markets in comparison with the baseline case with perfect labor markets. This will
also become obvious when we present our results for trade ow changes of the empirical
examples in Section 5.2.
2.4.4 Calculating welfare eects
The equivalent variation in percent can in our framework be expressed as follows:
EVi =
ỹi?,c PPic − ỹi?
i
ỹi?
=
ỹi?,c Pi
Pi
− 1 = ỹˆi? c − 1.
ỹi? Pic
Pi
(32)
We next derive a similar sucient statistics for the welfare eects of trade liberalization
as Arkolakis et al. (2012).
to serve the own market,
We therefore consider a foreign shock that leaves the ability
τjj ,
unchanged as in Arkolakis et al. (2012). Additionally, we
follow their normalization and set labor in country
j , wj
equal to one and assume balanced
trade. We then come up with the following sucient statistics (see Appendix B for the
derivation):
9
Implication 4 Welfare eects of trade liberalization in our model with imperfect labor
markets can be expressed as
1
1−σ
Ŵj = êj λ̂jj
.
Hence, welfare depends on the employment change,
expenditures
λ̂jj
and the partial elasticity of imports with respect to variable trade costs,
given in our case by
1/(1−σ)
Ŵj = λ̂jj
êj , the change in the share of domestic
1/(1 − σ).
Note that in the case of perfect labor markets
êj = 1
and
, which is exactly equation (6) in Arkolakis et al. (2012).
Assuming that
λ̂jj
is observed, assuming imperfect or perfect labor markets would lead
to dierent welfare predictions. The dierence in the welfare change is given by
êj .
Hence,
assuming perfect labor markets neglects the eects on employment and the welfare eects
thereof. Recent empirical ndings suggest that trade liberalization lowers unemployment
(see Dutt et al. (2009) and Felbermayr et al. (2011b)).
Hence, falling trade costs will
increase welfare due to to a decreasing share of domestic expenditures and increasing
employment. The sucient statistics of Arkolakis et al. (2012) neglects the employment
eect and therefore likely underestimates the welfare eects of trade liberalization.
3 Parameter estimation
Having laid out our structural model and described how to obtain counterfactual GDPs,
trade ows, employment levels and welfare, we next describe our estimation strategy for
the gravity variables and the key parameters needed for the counterfactual analysis, the
elasticity of substitution,
σ,
and the elasticity of the matching function,
µ.
3.1 Estimating the gravity variables
We start by writing (16) in stochastic form as follows
zij ≡
where
εij
xij
= exp k − (1 − σ) ln tij − ln Πi1−σ − ln Pj1−σ + εij ,
yi yj
(33)
is a random disturbance term or measurement error of exports, assumed to be
identically distributed and mean-independent of the remaining terms of the right-hand side
of equation (33).
We employ country-specic importer and exporter xed-eects to control for the outward and inward MRT terms
Πi and Pj , respectively, as was already suggested by Anderson
7
and van Wincoop (2003) and Feenstra (2004).
We then solve for the multilateral resistance
terms based on the xed eects trade friction parameter estimates.
Additionally to estimating equation (16) log-linear, we also use the approach suggested
by Santos Silva and Tenreyro (2006) and estimate the multiplicative version of the model
using PPML.
7
Egger and Larch (2012) show that even in the US-Canada example of Anderson and van Wincoop
(2003), a disadvantage of the structural approach as compared to xed eects estimation is that correlation
between trade friction variables in the model and unobserved country/region-specic determinants leads to
inconsistent parameter estimates and, hence, to inconsistent estimates of the impact of trade frictions such
as international borders on bilateral trade. They show that the AvW model produces biased parameter
estimates according to a Hausman test.
10
3.2 Estimating σ
There are many possible ways to estimate
to obtain estimates for
σ
σ.
However, Bergstrand et al. (2012) show how
within their proposed framework with a production structure
without relying on additional data. We show here that their approach which only relies on
trade ows and observed baseline variables is still applicable, even when assuming imperfect
labor markets. We therefore follow this approach in order to obtain an estimate for
σ.
First, note that we can rewrite trade ows as given in equation (5) by using equation
(12) as follows:
xij =
βi (1 − γi + ξi )wi tij
ξi P j
1−σ
yj .
(34)
Estimation of equation (16) using observable determinants of bilateral trade costs generates
estimates
1−σ 8
td
ij .
We next substitute
analogue to generate
x̂mj .
wi = yi /[(1 − ui )Li ],
we end up with
1−σ
td
ij
in equation (16) to generate
1−σ
x̂ij , td
mj
in its
Using observations on unemployment rates and observing that
xij =
βi (1 − γi + ξi )yi tij
ξi (1 − ui )Li Pj
Taking ratios of predicted trade ows
x̂ij
and
x̂mj ,
1−σ
yj .
(35)
we end up with:
1−σ td
x̂ij
βi (1 − γi + ξi )yi ξm (1 − um )Lm 1−σ
ij
=
.
1−σ
x̂mj
βm (1 − γm + ξm )ym ξi (1 − ui )Li
td
mj
(36)
Now we are left with an equation with only observables and parameters. Hence, we can
solve for
σ:

1−σ
x̂ij td
βi (1 − γi + ξi )ξm yi (1 − um )Lm
mj 

/ ln
σ = 1 − ln
.
1−σ
βm (1 − γm + ξm )ξi ym (1 − ui )Li
x̂ td

(37)
mj ij
yi , ym , Li , Lm , ui and um are observables.9 We can then calculate n2 (n − 1) such
values of σ by using all combinations i, j , and m (m 6= i). As a measure of central tendency,
we use the average value of all positive estimates of σ as our (summary) estimate. Standard
10
errors for σ are obtained via bootstrapping.
Assuming that labor market parameters and β 's are equal, this simplies to:
where
t1ij−σ
x̂ij
= [
−σ
x̂mj
t1mj
[
yi (1 − um )Lm
ym (1 − ui )Li
8
1−σ
.
(38)
1−σ
For instance, in the AvW context, td
would be determined by the exponentiated value of
ij
\
\
[(1 − σ)ρ] ln dij + [(1 − σ) ln bU S,CA ]Borderij .
9
Alternatively, we can use the predicted Y s from the model. We show in our empirical results that the
correlation coecient between observed and predicted Y s is 0.992.
10
Standard errors for all other parameters are the analytical standard errors of the corresponding models.
However, the bootstrapped standard errors of those parameters are very similar to the analytical ones.
11
3.3 Estimating µ
The other crucial parameter for our counterfactual analysis is the elasticity of the matching
function,
µ.
A rst attempt to estimate
and
Ωj
µ
is to assume that labor market variables, such as
mj , cj
are identical across countries.
Then
1 − uj = Ξj
Noting that we observe
uj
pj
Pj
1−µ
µ
=Ξ
pj
Pj
1−µ
µ
.
(39)
in the baseline, we may take ratios for two countries and the
log of this ratio to obtain:
ln
1 − uj
1 − um
=
⇒µ =
Using
(βj pj )1−σ = θj Πσ−1
= j
j
and
pj Pm
p m Pj
1
.
1−uj
p
1 + ln 1−um / ln pmj PPmj
1−µ
ln
µ
Pj1−σ =
1 + (1 − σ) ln
(40)
Pn
1−σ
i=1 tij i , we can reformulate as follows:
µ =
1−uj
1−um
1
/ ln
(41)
Pn d
1−σ
j
i=1 tim i
m Pn d
1−σ
i=1 tij i
n2 (n=1) such values of µ by using all combinations j, m, and m(m 6= j).
2
From those values we can then calculate n (n=1) µ's. As a (summary) estimate of µ, we
use the average of all estimated values of µ within the unit interval. Standard errors for µ
We then calculate
are obtained via bootstrapping.
4 Preferential trade agreements and labor market frictions
We now turn to evaluate the trade eects of preferential trade agreements and labor market
11
reforms in a sample of 28 OECD countries for the years 1950 to 2006.
are taken from Head et al. (2010), available from the CEPII
12
website.
The trade data
In order to obtain an estimable gravity equation as given in (33), we have to parametrize
trade costs. We follow the literature and proxy
tij
by a vector of trade barrier variables in
the following way
t1−σ
ijτ = exp(β1 P T Aijτ + β2 ln DISTij + β3 CON T IGij + β4 COM LAN Gij ),
DISTij
is bilateral distance, CON T IGij is a dummy variable indicating whether countries i and j
are contiguous, and COM LAN Gij indicates whether two countries share a common ocial
13 The data for the P T A's are constructed from the notications to the World
language.
where
P T Aijτ
(42)
is an indicator variable of preferential trade agreement membership,
11
The 28 countries are Australia, Austria, Belgium, Canada, Czech Republic, Denmark, Finland, France,
Germany, Greece, Hungary, Iceland, Ireland, Italy, Japan, Korea, Netherlands, New Zealand, Norway,
Poland, Portugal, Slovak Republic, Spain, Sweden, Switzerland, Turkey, United Kingdom, and United
States.
12
13
http://www.cepii.fr/anglaisgraph/bdd/gravity.htm.
We do not use common colonizer indicators or similar variables regularly used in the literature as these
have hardly any variation in the employed OECD sample.
12
Trade Organization (WTO) and were augmented and corrected by using information from
PTA secretariat webpages. The remaining geography variables are taken from the CEPII
geography data-set. Table 1 gives summary statistics of the data.
[Table 1 about here.]
As is well known in the literature, countries do not randomly sign PTAs.
Recently,
Baier and Bergstrand (2004), Baier and Bergstrand (2007), Baier and Bergstrand (2009),
Magee (2003), Egger et al. (2008), Egger et al. (2011b), Anderson and Yotov (2011) allowed
for PTAs to be endogenous to trade in an econometric sense and showed that the exogeneity
assumption is harmful for quantifying the eects of regional trade agreements. In order
to avoid the potential endogeneity we follow Baier and Bergstrand (2007) and Anderson
and Yotov (2011) and use a two-step estimation approach to obtain consistent estimates
of trade cost coecients. In a rst step, we estimate equation (33) including (directional)
bilateral xed eects, i.e. we estimate
zijτ = exp (k + β1 P T Aijτ + ϕiτ + φjτ + νij + εij ) ,
where
ϕiτ
and
φjτ
(43)
are exporter- and importer-time varying xed eects and
14
constant (directional) bilateral xed eects.
tilateral resistance terms
Πi
and
Pj ,
Note that
ϕiτ
and
φjτ
νij
is a time-
control for the mul-
and the bilateral xed eects also capture the time-
invariant geography variables. In a second step we re-estimate equation (33) in order to
obtain estimates for the coecients of the time-invariant geography variables,
β2
to
β4 .
We therefore only use exporter- and importer-time varying xed eects and constrain the
coecient of
P T A, β1 ,
to the estimate of the rst step,
β̂1 .
We follow Wei (1996) and
Anderson and van Wincoop (2003) and set the internal distance in a country
i, DISTii ,
to one quarter of the distance to the closest neighboring country.
4.1 Estimation results
Concerning the estimation, we present results estimating log-linearized trade ows by OLS
as well as the Poisson pseudo-maximum-likelihood (PPML) estimator for the trade ows
in levels following the recommendation by Santos Silva and Tenreyro (2006). Results are
shown in Table 2.
[Table 2 about here.]
Columns (1)-(4) present results using bilateral xed eects, i.e. assuming symmetric
trade costs
tij = tji .
Columns (5)-(8) allow for asymmetric trade costs, i.e.
by employing directional bilateral xed eects.
specications.
zijτ .
tij 6= tji ,
Each of these two blocks presents four
Columns (1) and (5) report OLS estimates for logged scaled trade ows
Column (2) and (6) present PPML estimates for the scaled trade ows in levels
to control for heteroskedasticity and zero trade ows.
columns (1) and (5) for unscaled trade ows
xijτ .
Columns (3) and (7) reproduce
Finally, columns (4) and (8) present
PPML estimates for unscaled trade ows. The slightly larger number of observations for
unscaled trade ows stems from the fact that GDP data are not available for all countries
in all years where we have trade data and control variables.
Our estimates reproduce well-known results from the empirical trade literature. Distance is a large obstacle to trade, whereas contiguity, a common language and PTAs spur
14
We report results for regressions including bilateral xed eects, i.e. νij = νji , and directional bilateral
xed eects, i.e. νij 6= νji .
13
trade. Comparing the results from columns (1)-(4) with those of columns (5)-(8) reveals
that allowing for asymmetric trade costs does not change our parameter estimates substantially. Comparing with PPML estimates shows a clear pattern. While distance coecients
are smaller in absolute values with PPML, all other coecients are larger. The dierences
are larger for estimates using scaled trade rather than unscaled trade ows.
Note that
in the case of specications using unscaled trade ows, GDP eects are captured by the
time-varying importer- and exporter-xed eects.
Hence, those specications implicitly
allow for non-unitary GDP coecients.
PTAs increase trade by 30.60% (column (3)) to 40.64% (column (8)) when neglecting
general equilibrium eects. The general equilibrium eects will be taken into account in
the comparative static results, to which we turn next.
4.2 Comparative static results
We perform two counterfactual experiments in our OECD sample. First, we evaluate the
eects of PTAs. Therefore we take PTAs as observed in 2006 and contrast it with a counterfactual situation without any PTAs. Second, we evaluate a hypothetical improvement
of labor market institutions in the US. In all scenarios we assume that trade is balanced
multilaterally.
4.2.1 Introducing PTAs as observed in 2006
Our rst counterfactual experiment evaluates the eects of introducing PTAs as observed
in 2006 from a counterfactual situation with no PTAs in place. We base our counterfactual
analysis on parameter estimates from column (6) of Table 2.
[Table 3 about here.]
The results can be found in Tables 3, 4, and 5. Table 3 is organized as follows: The
rst column (1) labeled AvW %GDP gives the percentage change in nominal GDP in
terms of the price index of Australia for the baseline case of perfect labor markets. Column
(2) labeled SMF %GDP gives the same change for our gravity model using a search and
matching framework. Columns (3) and (4) use equation (26) and decompose the change
in nominal GDP of column (2) due to the price and employment changes.
Column (5)
reports the percentage change in the employement share for the case of imperfect labor
markets. Finally, columns (6) and (7) report the equivalent variation (EV) for the case of
perfect and imperfect labor markets, respectively.
Table 3 reveals that all countries gain in terms of GDP when introducing PTAs as
observed in 2006. This translates into an average gain in terms of GDP of 0.89% when
assuming perfect labor markets. The average GDP gain increases by 29% to 1.15% when
accounting for employment eects.
Hidden behind these average eects is substantial
heterogeneity. While some countries gain substantially more than the average, e.g. Canada
with a gain of 2.80%, countries like the US experience a very modest increase of 0.60%.
The decomposition of (log) GDP in (log) price and (log) employment changes highlights
that for many countries in the sample, roughly one third of the increase in GDP is driven
by the increase in employment. Countries with only slight increases in GDP see negative
employment eects, as can be seen in in column (5) of Table 3. We graphically illustrate
the employment eects in Figure 1.
These negative employment eects translate into a
magnication of the negative welfare eects predicted for those countries in comparison
with the assumption of perfect labor markets, see columns (6) and (7). In general, welfare
14
eects are magnied when taking into account employment eects.
For example, the
standard welfare estimate for Canada is about two thirds of the welfare eect when taking
into account labor markets imperfections.
[Figure 1 about here.]
Tables 4 and 5 report goods trade changes for perfect and imperfect labor markets, respectively. Trade changes are heterogeneous across importers and exporters. To summarize
this heterogeneity, we present moments of calculated trade ow changes across all destination countries for all exporters. Both tables report the minimum and maximum changes,
alongside with the 2.5%, 25%, 50%, 75% and 97.5% quantiles. Comparing numbers across
columns for each row reveals the heterogeneity amongst importers, while comparing numbers across rows for each column highlights the heterogeneity across exporters.
In general, we see that for every country there are both positive and negative bilateral
trade ow changes. By and large, median trade ow changes tend to be larger for small
(e.g., Austria and Switzerland) and remote (e.g., Korea and Japan) countries. For example,
the introduction of PTAs as observed in 2005 implies that the change in trade ows for the
UK is larger than 12.77% for 25% of all countries importing goods from the UK. Turning
to the trade ow results of our model with imperfect labor markets given in Table 5, we
nd a similar pattern for trade ow changes. Again, changes are heterogeneous both across
importers and exporters and again small and remote countries experience larger changes.
The implied trade ow changes dier from the case with perfect labor markets, even though
they are very similar in magnitude.
[Table 4 about here.]
[Table 5 about here.]
4.2.2 Evaluating the eects of a labor market reform in the US
Our second counterfactual experiment evaluates the eects of a labor market reform in
the US which improves their labor market institutions. We implement this reform by a
3% increase in
κ
for the US, i.e. changing
κ
from 1 to 1.03 for the US. Note that with
our framework we do not have to be explicit about the specic changes in labor market
institutions.
[Table 6 about here.]
The results can be found in Tables 6 and 7. Table 6 is organized as Table 3.
Table 6 reveals that all countries gain in terms of GDP when improving US labor market
institutions. This highlights the positive spill-over eects, recently suggested theoretically
by Egger et al. (2011a) and Felbermayr et al. (2009), and documented empirically in a
reduced-form setting in Felbermayr et al. (2009).
Trivially an evaluation of any change
of labor market institutions cannot be analyzed when assuming perfect labor markets.
Therefore, columns (1) and (6) are uninformative in this setting. The decomposition of
(log) GDP in (log) price and (log) employment changes highlights that in the US prices
fall and all GDP increases are brought about by employment increases.
In the trading
partner countries of the US the positive GDP eects are composed of roughly 60-80% of
price changes and 20-40% changes in employment.
This is also reected in the relative
magnitudes of the employment changes reported in column (5) of Table 6. We graphically
15
illustrate the employment eects in Figure 2.
Concerning welfare, obviously US prots
the most from its improvements in labor market institutions with an increase in welfare
of 2.94%. However, importantly all other countries also gain, with the highest gains for
Canada with 0.19%.
[Figure 2 about here.]
Table 7 summarizes the trade eects.
A labor market reform in the US spurs trade
changes across the whole sample. Eects of exports of the US range between -1.42% and
0.12%.
Eects across other exporters range between -1.43% for Australia to 1.05% for
Belgium and Switzerland. On average, 50% of trade ow changes are larger than 0.55%.
The size pattern of the spill-over eects of labor market reforms in the US clearly depend
on the distance and trade volumes between the corresponding countries and the US.
[Table 7 about here.]
5 The US-Canadian border puzzle and labor market frictions
We next use our methodology to reconsider the McCallum (1995) border puzzle accounting
for employment eects. McCallum (1995) showed that trade between US states and Canadian provinces is reduced by a factor of 22 in comparison to trade within a country. This
has spawned a vast literature on estimating border eects, which is too numerous to be
15
discussed here.
Most notably, Anderson and van Wincoop (2003) made much progress in
solving McCallum's border puzzle by showing that accounting for multilateral resistance
terms reduces this eect to a factor of 1/5 to 1/2.
While the subtleties of the price eects have now been widely acknowledged, the literature so far has abstracted from employment eects. We therefore turn to the classical
data-set used by McCallum (1995) and Anderson and van Wincoop (2003) to reconsider
the border eect and quantify the employment eects of counterfactually abolishing the
US-Canadian border.
For reasons of comparison we use data for the same 30 US states and 10 Canadian
16
provinces alongside an aggregate of OECD countries labeled ROW for the year 1993
as
in Anderson and van Wincoop (2003). We also follow their specication of the trade costs
function, which is given by
t1−σ
= exp(β1 ln DISTij + β2 BORDERij ),
ij
where
DISTij
is again bilateral distance and
BORDERij
(44)
is a dummy variable indicates
whether a trade ow crosses the US-Canadian border.
5.1 Estimation results
We present results of our estimates for 6 dierent specications in Table 8. Column (1)
reproduces the parameter estimates of Table 6, column (viii) using xed eects to control
for the multilateral resistance terms. Column (2) estimates the gravity model as given in
equation (16) multiplicatively using PPML on the same 1,511 observations as in column
(1).
This controls for the heteroskedasticity, a typical feature of trade ow data.
reduces the estimated coecient for
15
16
BORDER
from
−1.551
in column (1) to
For an in-depth review of this literature see Anderson and van Wincoop (2004).
For a detailed description of the data-set see Anderson and van Wincoop (2003).
16
This
−0.981.
Assuming
σ = 5,
this implies a partial equilibrium tari equivalent of the US-Canadian
border of 47.37% and 27.79%, respectively.
17
Hence, accounting for heteroskedasticity by
estimating the gravity equation in multiplicative form more than halfs the estimate of the
partial border eect.
In column (3) we include the 49 zero trade ows, leading to a total of 1,560 observations.
Compared to column (2), estimates hardly change.
The coecient of the border
dummy even slightly decreases. In column (4) we include internal trade ows for states
and provinces. As internal trade ows are not readily available, we follow Anderson and
Yotov (2012) and calculate them as
yi −
Pn
j6=i xij . Using xed eects, we end up with
somewhat larger distance and border eects as compared to column (1). Column (5) reproduces results with the PPML. Now, distance coecients get much larger and the border
eect much smaller. Finally, column (6) includes both, zero trade ows and internal trade,
leaving estimates virtually unchanged compared to column (5). Our preferred specication
(6) implies a partial equilibrium tari equivalent of the border barrier of 22.26%.
5.2 Comparative static results
[Table 8 about here.]
[Table 9 about here.]
Our counterfactual experiment abolishes the US-Canadian border. We base our counterfactual analysis on parameter estimates from column (1) of Table 8. Further, following
Anderson and van Wincoop (2003), we add one aggregate region consisting of 20 OECD
18
countries labeled ROW and assume balanced trade.
value for the elasticity of substitution
use standard values for both and set
µ = 0.75,
Additionally, we have to chose a
σ and the elasticity of the matching function µ. We
σ = 5 as in Anderson and van Wincoop (2003) and
as proposed in Hall (2005). We provide robustness results with respect to these
parameter values in the Appendix.
The results can be found in Tables 9, 10, and 11. Table 9 is organized as follows: The
rst column (1) labeled AvW %GDP gives the percentage change in nominal GDP in
terms of the price index of Alabama for the baseline case of perfect labor markets. Column
(2) labeled SMF %GDP gives the same change for our gravity model using a search and
matching framework. Columns (3) and (4) use equation (26) and decompose the change in
nominal GDP of column (2) due to the price and employment changes. Column (5) reports
the percentage change in the employement share for the case of imperfect labor markets.
We graphically illustrate the employment eects in Figure 3. Finally, columns (6) and (7)
report the equivalent variation (EV) for the case of perfect and imperfect labor markets,
respectively.
Table 9 reveals that all states and provinces gain both in terms of GDP and equivalent
variation. This result holds irrespective of whether we consider perfect or imperfect labor
markets. When comparing the GDP changes between the perfect and imperfect labor markets, we see that on average, GDP changes are more than twice as large. On average US
states gain far less than Canadian provinces, in line with standard predictions of new trade
theory models of larger gains for smaller regions/countries. This result is even magnied
when considering search and matching labor market frictions. The decomposition of (log)
GDP in (log) price and (log) employment changes highlights that in the US GDP changes
17
This is calculated as exp(BORDER/(1 − σ)).
We dier from the optimization routine used in Anderson and van Wincoop (2003) by solving the
system of multilateral resistance terms for all regions including ROW.
18
17
are predominantly brought about by price changes, whereas the increase in GDP of Canadian provinces depends relatively more on changes in employment. This reects the fact
that the reduction in trade costs due to the abolition of the US-Canadian border leads to a
bigger change in the domestic price index in the smaller country. This leads to a relatively
larger reduction in real vacancy posting costs in Canada, explaining the larger importance
of employment changes. In line with this fact, are the larger employment changes stated
in column (5). Finally, turning to the welfare implications, we calculate a doubling in the
equivalent variation when comparing the perfect with the imperfect labor market scenario,
similar to the eect found for GDP.
[Figure 3 about here.]
[Table 10 about here.]
[Table 11 about here.]
Tables 10 and 11 reports goods trade changes for perfect and imperfect labor markets, respectively.
Trade changes are heterogeneous across importers and exporters.
To
summarize this heterogeneity, we present moments of calculated trade ow changes across
all destination countries for all exporters.
Both tables report the minimum and maxi-
mum changes, alongside with the 2.5%, 25%, 50%, 75% and 97.5% quantiles. Comparing
numbers across columns for each row reveals the heterogeneity amongst importers, while
comparing numbers across rows for each column highlights the heterogeneity across exporters.
In general, we see that for every region there are both postive and negative
bilateral trade ow changes.
By and large, trade ow changes are larger for exporting
Canadian provinces.
Interestingly, this pattern is reversed for the largest quantiles. For example, the abolition of the border implies that the change in trade ows for the state of New York is
larger than 80.50% for 25% of all regions importing goods from New York.
Turning to
our model with imperfect labor markets, we nd a similar pattern for trade ow changes.
Again, changes are heterogeneous both across importers and exporters and again Canadian
provinces experience larger changes. Even the implied trade ow changes dier from the
case with perfect labor markets, albeit similar in magnitude.
6 Robustness checks
In order to check the sensitivity of our results, we perform two sets of robustness checks.
First, we allow for trade imbalances following Dekle et al. (2007). Second, as we have to
set (or estimate) the unobserved parameters for the elasticity of substitution and of the
matching function,
σ
and
µ,
we provide results for dierent values of those parameters.
6.1 Controlling for trade imbalances
Our framework can easily accommodate trade imbalances following Dekle et al. (2007).
With trade balance,
ỹj = yj
and
θ̃j = θj .
19
GDP and total spending dier.
However, as soon as we allow for trade imbalances,
In Tables 12, 13 and 14 we reevaluate the eects of
preferential trade agreements when allowing for trade imbalances. By and large our results
are hardly eected by trade imbalances. The biggest dierence is in the decomposition of
19
We set the trade imbalance for the aggregate of OECD countries (ROW) equal to 0.
18
the GDP change. The price change share is smaller when accounting for trade imbalances.
Aggregate average welfare eects are literally the same.
In Tables 15 and 16 we recalculate the eects of the hypothetical US labor market
reform. Average GDP, employment and welfare eects are literally unchanged.
We also report results from counterfactually erasing the US-Canadian border taking
into account trade imbalances in Tables 17, 18, and 19. Whereas GDP changes are somewhat larger for Canada and slightly smaller for the US when controlling for trade imbalances, welfare eects remain very similar.
[Table 12 about here.]
[Table 13 about here.]
[Table 14 about here.]
[Table 15 about here.]
[Table 16 about here.]
[Table 17 about here.]
[Table 18 about here.]
[Table 19 about here.]
6.2 Dierent parameter values for counterfactual analysis
We check the sensitivity of our results to variations in the elasticity of substitution,
well as the elasticity of the matching function
average eects.
µ.
σ,
as
For expositional brevity, we only present
In Tables 20 and 21 we present robustness checks for the US-Canadian
border trade sample (without and with correcting for trade imbalances), whereas we present
results for the OECD sample in Tables 22 and 23. Clearly, our GDP, employment and EV
eects depend on the values of
σ and µ.
When the elasticity of substitution increases, GDP,
employment and EV changes get smaller. This is due to the fact that varieties are higher
substitutes, making trade less important. Hence, abolishing the US-Canadian border leads
to smaller predicted gains in terms of GDP, employment and welfare.
µ also show a clear pattern. Lower
µ indicate higher GDP, employment and welfare changes. Lower µ corresponds to
labor market imperfections. When µ approaches 1 we end up in the case of perfect
Changes in the elasticity of the matching function
values of
larger
labor markets.
[Table 20 about here.]
[Table 21 about here.]
[Table 22 about here.]
[Table 23 about here.]
19
7 Conclusion
The gravity equation is the workhorse of international trade ow studies and has been
the basis for numerous evaluations of the trade and welfare impact of trade liberalization.
However, its theoretical foundations have neglected labor market frictions.
We extend a standard structural gravity model by modeling these frictions within a
search and matching framework. Our framework allows counterfactual analysis of changes
in trade costs and labor market reforms on trade ows, prices, employment, and welfare.
We apply our developed structural model to two dierent data-sets.
First, we use
a sample of 28 OECD countries from 1950 to 2006 in order to evaluate the eects of
preferential trade agreements (PTAs) and a hypothetical labor market reform in the US.
We nd that introducing PTAs as observed in 2006 leads to a signicant magnication
of GDP increases when accounting for employment eects.
Countries with only slight
increases in GDP even see negative employment eects. These negative employment eects
translate into a magnication of the negative welfare eects predicted for those countries.
Our second counterfactual analysis assumes an improvement of labor market institutions
in the US. Again, average welfare eects are doubled when taking into account employment
eects. US GDP increases roughly ten times more than GDP of the other countries. While
the US prots the most from its improvements in labor market institutions with an EV of
2.94%, all trading partners also experience an increase in welfare due to positive spill-over
eects.
We next use our methodology to reconsider the McCallum (1995) border puzzle accounting for employment eects. McCallum (1995) showed that trade between US states
and Canadian provinces is reduced by a factor of 22 in comparison to trade within a
country. When comparing the GDP changes between the perfect and imperfect labor markets, we see that on average, GDP changes are more than twice as large. On average US
states gain far less than Canadian provinces. Finally, turning to the welfare implications,
we calculate a doubling in the equivalent variation when comparing the perfect with the
imperfect labor market scenario, similar to the eect found for GDP.
As our developed approach does not need any information of the labor market besides
the elasticity of the matching function, it can easily be applied in all elds where the
gravity equation has been applied successfully previously.
20
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23
A Derivation of asymmetric multilateral resistance equations
Using equation (17), we can write
n
X
Π1−σ
=
i
σ−1
t1−σ
θ̃j .
ij Pj
(45)
j=1
Dene
Pj = θ̃j Pjσ−1 ,
wich leads to
Π1−σ
=
i
n
X
1−σ
tij
Pj .
(46)
1−σ σ−1
tij
Πi θ i .
(47)
j=1
Similarly, equation (18) can be written as
Pj1−σ
n
X
=
i=1
Dene
i = θi Πσ−1
i
leads to
Pj1−σ
=
n
X
t1−σ
ij i .
(48)
t1−σ
ij Pj .
(49)
i=1
Now divide equation (46) by
Π1−σ
i
1 = Πσ−1
i
n
X
j=1
Using again
i = θi Πσ−1
i
leads to
1=
n
i X 1−σ
tij Pj .
θi
(50)
j=1
And therefor to
θi − i
n
X
t1−σ
ij Pj = 0.
(51)
j=1
1−σ
Similarly, divide equation (48) by Pj
1=
Pjσ−1
n
X
t1−σ
ij i .
(52)
i=1
Using again
Pj = θ̃j Pjσ−1
leads to:
1=
n
Pj X
θ̃j
And therefore to:
θ̃j − Pj
t1−σ
ij i .
(53)
t1−σ
ij i = 0.
(54)
i=1
n
X
i=1
Equations (51) and (54) lead to a system of
unknowns
i
and
2n
Pj .
24
equations that can be solved for the
2n
B Sucient statistics for welfare in the trade model with
imperfect labor markets
Dening real income as
Wj ≡ ỹj /Pj
and taking the log-derivative leads to
d ln Wj = d ln ỹj − d ln Pj .
yj
is given by
yj = wj (1 − uj )Lj .
Hence, the log-derivative of
yj
can be written as
uj
uj
d ln uj = −
d ln uj ,
1 − uj
1 − uj
= d ln wj −
d ln yj
(55)
where the second expression on the right-hand side follows by choice of numéraire. Noting
that
ỹj = yj (1 + dj )
dj
hP
and taking
The log-derivative of
Pj =
as constant, it holds that
n
1−σ
i=1 (βi pi tij )
i
1
1−σ
d ln ỹj = d ln yj .
is given by
!
n
X
βi pi tij 1−σ
βi pi tij 1−σ
=
d ln pi +
d ln tij .
Pj
Pj
d ln Pj
i=1
Using
xij =
βi pi tij
Pj
1−σ
ỹj
λij = xij /ỹj =
and dening
d ln Pj =
n
X
βi pi tij
Pj
1−σ
, we can simplify to
λij (d ln pi + d ln tij ) .
(56)
i=1
p = 1−γξii+ξi wi , it also holds that d ln pi = d ln wi .
Pn i
d ln Pj = i=1 λij (d ln wi + d ln tij ). Combining terms leads to
Noting that
Hence, we can also write:
n
d ln Wj = d ln yj − d ln Pj = −
X
uj
d ln uj −
λij (d ln wi + d ln tij ) .
1 − uj
(57)
i=1
Taking the ratio of
λij
and
λjj
we can write
λij
=
λjj
Noting that
dtjj = 0
βi pi tij
βj pj tjj
by assumption and that
1−σ
wj
.
is the numeraire, so that
dwj = dpj = 0,
the log-change of this ratio is given by:
d ln λij − d ln λjj = (1 − σ) (d ln tij + d ln pi ) .
Combining this with equation (56) leads to:
d ln Pj
=
1
1−σ
n
X
λij d ln λij − d ln λjj
i=1
n
X
!
λij
.
i=1
Pn
Pn
Pn
Pn
, it follows that
i=1 λij = 1 and d
i=1 λij =
i=1 dλij = 0.
Pn ỹj = i=1 xijP
n
dλ
=
0
.
Using
these
facts,
the
above
expression
simplies
Hence,
λ
d
ln
λ
=
ij
ij
i=1
i=1 ij
Noting that
to:
d ln Pj
= −
1
d ln λjj .
1−σ
25
The welfare change can than be expressed as follows
d ln Wj
= −
uj
1
d ln uj +
d ln λjj .
1 − uj
1−σ
Integrating between an initial situation and a counterfactual situation we end up with
ln Ŵj
= ln eˆj +
1
1−σ
ln λ̂jj .
Taking exponents leads to
1
Ŵj
where
ej = 1 − uj
1−σ
= êj λ̂jj
,
is the share of employed people. When we move from any observed level
of trade to autarky,
λcjj = 1,
which simplies the expression to
1
= êj (λjj )− 1−σ .
Ŵj
Note, however, that unequal to the case with perfect labor markets considered in Arkolakis
et al. (2012), even this expression needs information about counterfactual GDP or at least,
with balanced trade, employment levels.
C Minimum wages within the search and matching framework
In this appendix we show how minimum wages can be introduced in our search and matching framework. Basically, a binding minimum wage will replace the bargaining of workers
and rms that are matched.
We rst consider the bounds for a binding minimum wage. A minimum wage below
the wage that a rm and a worker would bargain is not binding, hence not relevant. The
wj ,
is therefore given by the wage
ξj
pj .
1 + γ j ξj − γ j
(58)
lower bound for a binding minimum wage, denoted by
curve (12)
w j = wj =
The upper bound for a minimum wage, denoted by
wj ,
is given by the job's output, as
w j = pj .
wj < w̃j < wj .
longer relevant. ϑj can be
rms would not be able to recover vacancy posting costs. Hence,
A well dened equilibrium with binding minimum wage
With a given binding minimum wage, the wage curve is no
w̃
exists if
solved by using the job creation curve given in (9)
Pj cj
⇒
mj ϑ−µ
j
pj − w̃j 1/µ cj −1/µ
ϑj =
,
Pj
mj
w̃j = pj −
which corresponds to equation (13).
GDP in country
j
(59)
can be derived by replacing
uj
using equations (8) and (59):
yj = w̃j mj
pj − w̃j
Pj
1−µ 26
µ
cj
mj
µ−1
µ
Lj ,
(60)
which corresponds to equation (14).
Counterfactual employment can be calculated using the denition of
tion (8). Then, replacing
mj
cj
mj
µ−1
µ
and
ϑ
ui
given in equa-
by the expression given in equation (59) and dening
ˆ j = Ξ̃c /Ξ̃j ,
κ̃
j
Ξ̃j =
we get
1 − uci
ˆj
= κ̃
1 − ui
pci − w̃j
pi − w̃j
1−µ µ
Pi
Pic
1−µ
µ
.
(61)
Assuming that nominal minimum wages are indexed to prices, we can express it as share
of prices, i.e.
w̃j = ξj pj .
Then the last expression simplies to
1 − uci
ˆj
= κ̃
1 − ui
pci
pi
1−µ µ
Pi
Pic
1−µ
µ
,
(62)
which exactly corresponds to equation (20) besides the replacement of
κ̂j
by
ˆj .
κ̃
Hence,
when assuming that labor market institutions do not change, we can proceed as with
bargained wages to calculated employment eects.
Note that in the case of binding minimum wages, all GDP changes are due to employment changes. Hence, counterfactual GDP changes correspond to employment changes.
Counterfactual trade ows and welfare can be calculated as in the case with bargained
wages.
D Eciency wages within the search and matching framework
In this appendix we show how eciency wages in the spirit of Stiglitz and Shapiro (1984)
can be introduced in our search and matching framework. Basically, the no-shirking condition will replace the bargaining of workers and rms that are matched.
We rst derive the asset value for a shirker
earns wage
wj
with eort
ej .
ns
and a non-shirker
s.
The non-shirker
ns
Hence, the asset value in our one-shoot framework is given
by
Ejns = wj − ej .
A shirker
s
also earns wage
wj
(63)
but does not show any eort
ej .
However, a share of
dj
of
shirkers is detected by rms and gets red, which leads to unemployment. Noting that in
unemployment the worker earns
γ j wj ,
the asset value for a shirker can be written as
Ejs = wj + d(Uj − Ejs ) ⇒ Ejs =
The no shirking-condition
E ns ≥ E s
wj + dj γj wj
.
1 + dj
leads in equilibrium to
E ns = E s .
(64)
Hence, using
Equations (63) and (64), the wage can be written as:
wj =
1 + dj
ej .
1 − γj
Hence, as in the case of bargaining, wages can be solved without knowledge of
(65)
ϑj . ϑj
can
be solved by using the job creation curve given in (9)
1 + dj
Pj cj
ej = pj −
⇒
1 − γj
mj ϑ−µ
j
mj
1 + dj
µ
ϑj =
pj −
ej .
Pj cj
1 − γj
27
(66)
Now assume that eort
ej
can be expressed in terms of prices
pj
as
e j = ξj p j .
Then we
can simplify equation (66) to:
ϑj =
with
Ω̃j =
pj
Pj
1/µ cj
Ω̃j
mj
−1/µ
,
(67)
1−γj
1−γj −(1+dj )ξj , which corresponds to equation (13).
GDP in country
j
uj
can be derived by replacing
using equations (8) and (67), and
wj
by using equation (65):
1 + dj
ej mj
yj =
1 − γj
pj
Pj
1−µ µ
cj
Ω̃j
mj
µ−1
µ
Lj ,
(68)
which corresponds to equation (14).
Counterfactual employment can be calculated using the denition of
tion (8), replacing
and
ui
given in equa-
ϑ by the expression given in equation (67) and dening Ξ̃j = mj
cj
mj Ω̃j
µ−1
ˆ j = Ξc /Ξj
κ̃
j
1 − uci
ˆj
= κ̃
1 − ui
pci
pi
1−µ µ
Pi
Pic
1−µ
µ
.
(69)
which exactly corresponds to equation (20) besides the replacement of
κ̂j
by
ˆj .
κ̃
Hence,
when assuming that labor market institutions do not change, we can proceed as with
bargained wages to calculated employment eects.
Counterfactual GDPs can be calculated by using again
1 + dj
yj =
ξj pj mj
1 − γj
Dening
Ξj = mj
cj
mj Ω̃j
µ−1
µ
pj
Pj
Now take the ratio of counterfactual GDP,
parameters and constants, like
yj
where
κ̂j = Ξcj /Ξj .
µ
cj
Ω̃j
mj
which leads to:
µ−1
µ
Lj ,
(70)
, we can write :
1 + dj
yj =
ξj p j
1 − γj
yjc
1−µ ej = ξj pj ,
= κ̂j
yjc
ξj , γj , dj , Ξj
pcj
pj
pj
Pj
1−µ
µ
Ξj Lj ,
and observed GDP
and
Lj ,
pc 1−µ
j
µ
Pjc
pj
Pj
1−µ
= κ̂j
µ
(71)
pcj
pj
yj ,
while noting that all
stay constant:
µ1
Pj
Pjc
! 1−µ
µ
,
(72)
This exactly correspond to equation (23). Hence, we can calculated
counterfactual GDP as in the case with bargained wages according to equation (24).
Similarly, counterfactual trade ows and welfare can be calculated as in the case with
bargained wages.
28
µ
E A Ricardian gravity model with imperfect labor markets
following Eaton and Kortum (2002)
j
The representative consumer in country
is again characterized by the utility function
As in Eaton and Kortum (2002) we assume a continuum of goods
of individual goods is denoted by
q(k),
k ∈ [0, 1].
Uj .
Consumption
leading to the following utility function
Z
1
σ−1
σ
σ
σ−1
,
(73)
is the elasticity of substitution in consumption.
Again, international trade of
Uj =
q(k)
dk
0
where
σ
i
goods from
j
to
imposes iceberg trade costs
tij > 1
for all
i 6= j ,
and
tij = 1
for
i = j.
Countries dier in the eciency with which they can produce goods. We denote country
i's
k ∈ [0, 1] as zi (k). Denoting input costs in country i as ci ,
j in country i is then ci /zi (k).
account, delivering a unit of good k produced in country i
eciency in producing good
the cost of producing a unit of good
Taking trade barriers into
to country
j
costs
pij (k) =
Assuming perfect competition,
bought good
k
from country
pij (k)
i.
ci
zi (k)
tij .
(74)
is what consumers in country
where to buy. Hence, the price they actually pay for good
all sources
j
would pay if they
In an international economy, consumers can select from
k is pj (k), the lowest price across
i:
pj (k) = min {pij (k); i = 1, · · · , N } ,
where
n
(75)
denotes the number of countries.
i's
Let country
k be the realization of an
−Ti z −θ , where T
distribution Fi (z) = e
i
eciency in producing good
drawn Fréchet random variable with
independently
is the location
parameter (also called state of technology by Eaton and Kortum (2002)) and
θ
governs
the variation within the distribution and thereby also the comparative advantage within
the continuum of goods.
Fi (z)
Plugging in Equation (74) in
Noting that the distribution of prices for
P r[Pj ≤ p] = 1 −
Qn
i=1 [1
− Gij (p)],
−θ
leads to:
θ
Gj (p) = 1 − e−Φj p ,
where
Φj =
θ
Gij (p) = P r[Pij ≤ p] = 1 − e−[Ti (ci tij ) ]p .
which a country j buys is given by Gj (p) =
leads to
(76)
−θ
i=1 Ti (ci tij ) .
Pn
The probability that country
i provides good k
at the lowest price to country
j
is given
by (see Eaton and Kortum (2002), page 1748):
πij =
Ti (ci tij )−θ
.
Φj
(77)
With a continuum of goods between zero and one this is also the fraction of goods that
country
j
buys from country
that country
j
i.
Eaton and Kortum (2002) show that the price of a good
actually buys from any country
exact price index is given by
Pj =
−1/θ
γΦj , with
function.
29
i
is also distributed
γ= Γ
1
1−σ
θ+1−σ
θ
Gj (p),
where
and that the
Γ is the Gamma
j buys from country i, πij is also the fraction of its
i (xij ) due to the fact that the average expenditures
The fraction of goods that country
expenditures on goods from country
per good do not vary by source. Hence,
Ti (ci tij )−θ
Ti (ci tij )−θ
yj = Pn
y ,
−θ j
Φj
k=1 Tk (ck tkj )
xij =
where
yj
is country
j 's
(78)
total spending.
Exporters total sales (including home sales) are equal to exports total spending and
are simply given by:
n
X
yi =
xij = Ti c−θ
i
n
X
t−θ
ij
j=1
Solving for
Ti c−θ
i
j=1
leads to:
Ti c−θ
i =
Replacing
Ti c−θ
i
yi
t−θ
ij
j=1 Φj yj
(79)
.
(80)
Pn
in Equation (78) with this expression leads to:
xij
=
Φj
− θ1
Pj = γΦj
Using
yj .
Φj
to replace
Φj
xij
t−θ
ij −θ
Pn tij
j=1 Φj
yi yj .
yj
in both terms of the denominator leads to:
t−θ
ij
−θ Pn
=
γ θ Pj
yi yj .
t−θ
ij
j=1 γ θ P −θ yj
j
Dening

− 1
θ
−θ
n X
tij


Πi =
θj
,
Pj
j=1
and noting that we can express
Pj
=
γ
−θ
Φj
− 1
θ
=
γ
Pj
also as follows:
−θ
n
X
!− 1

θ
−θ
Ti (ci tij )
= γ −θ
i=1
i=1
=
n X
tij −θ
i=1
where
θj = yj /y W
Πi
with
−θ
by
θ

,
θ
θi
yW =
1−σ
t−θ
il
l=1 Φl yl
Pn
− 1
!− 1
,
P
j
yj .
xij
Replacing
t−θ
ij yi
n
X
Then we can write:
=
yi yj
yW
tij
Πi P j
−θ
.
we end up with exactly the same system as in the AvW model.
Hence, our approach can be applied to both worlds with the only dierence that the
interpretation diers and the roles of
θ
and
σ
30
have to be exchanged.
E.1 Counterfactual GDP in the Eaton and Kortum (2002) framework
with perfect labor markets
Assuming that there are no intermediates and one unit of the nal good is produced with
one unit of labor,
ci = wi .
Noting that
yi
Ti wi−θ =
t−θ
ij
Pn
j=1 Φj
Solving for
wi
yi = wi Li
=
Pn
yj
j=1 γ
θ
θi
and using again
tij
Pj
−θ
= γ −θ θi Πθi .
θj
leads to:
1
−1
wi = γTiθ θi θ Π−1
i .
yic /yi = wic /wi ,
Noting that the change in GDP is given by
yic
yi
where
1
1
γTiθ (θic )− θ (Πci )−1
=
1
θ
−1
γTi θi θ Π−1
i
leads to
1
=
(θic )− θ (Πci )−1
−1
θi θ Π−1
i
c − 1
θ
,
= i
i
i = θi Πθi .
E.2 Counterfactual GDP in the Eaton and Kortum (2002) framework
with imperfect labor markets
We assume that there are no intermediates and
with one unit of labor for the rm.
zi
units of the nal good
k
are produced
For simplicity, we omit the product index
following. Denoting the net price earned by the producer by
k
in the
the total surplus
zi pi − wi and
the worker's by wi − bi . Nash bargaining leads to wi − bi = ξi (zi pi − wi ). Using bi = γi wi
and combining leads to wi = ξi /(1 − γi + ξi )zi pi = ξi /(1 − γi + ξi )ci .
of a successful match is given by
zi pi − bi ,
pi = pij /tij ,
while the rm's rent is given by
Firms create vacancies until all rents are dissipated. The free entry (zero prot) condition is given by
Mi /Vi (zi pi − wi ) = Pi ci .
wi = z i p i −
Rewriting leads to the job creation curve
Pi ci
Pi ci
.
−µ = ci −
m i ϑi
mi ϑ−µ
i
(81)
Using the job creation and wage curve, labor market thightness
ϑi =
Noting that
yi = wi (1 − ui )Li
ci
1/µ ci
Ωi
mi
ca be expressed as:
−1/µ
.
(82)
and using again
yi
Ti c−θ
=
i
Solving for
ci
Pi
ϑ
t−θ
ij
j=1 Φj yj
=
Pn
Pn
j=1
γθ
θi
tij
Pj
−θ
= γ −θ θi Πθi .
θj
leads to:
1
−1
ci = γTiθ θi θ Π−1
i .
c
Noting that the change in GDP is given by yi /yi
wi
by
yic
yi
ξi /(1 − γi + ξi )ci
1
(1 − uci )γTiθ (θic )− θ (Πci )−1
(1 −
= (1 −
− ui )wi ]
and replacing
leads to
1
=
(83)
uci )wic /[(1
1
θ
−1
ui )γTi θi θ Π−1
i
1
=
(1 − uci ) (θic )− θ (Πci )−1
−1
(1 − ui )θi θ Π−1
i
31
(1 − uci )
=
(1 − ui )
c − 1
θ
i
,
i
where
i = θi Πθi .
For the change in employment exactly the same relationship as in the main text holds.
Hence, we end up with

− 1−µ
µθ
P
1
−θ
t
i
ci − µθ 
yic

i ij
= κ̂i
.
 P −θ 
yi
i
c
c
t
i
ij
i
32
(84)
33
(.1,5]
(.005,.1]
(.0025,.005]
(0,.0025]
(-.0025,0]
[-.01,-.0025]
No data
Figure 1: Employment eects of counterfactually incepting PTAs as observed in 2006.
34
(.07,2.98]
(.04,.07]
(.03,.04]
(.01,.03]
[0,.01]
No data
Figure 2: Employment eects of a hypothetical labor market reform in the US (κ̂U S
= 1.03).
35
Figure 3: Employment eects of counterfactually abolishing the US-Canadian border.
Table 1: Summary statistics
Mean
xij (cur. mn US$)
GDP (cur. mn US$)
PTA
ln(DIST )
CON T IG
COM LAN G
Std. Dev.
Min.
Max.
N
2,048.991
8,950.166
0
348,420.6
38,313
386,072.995
1,143,571.923
126.99
13,201,819
43,372
0.237
0.425
0
1
44,688
7.863
1.213
4.201
9.880
44,688
0.077
0.266
0
1
44,688
0.074
0.262
0
1
44,688
Notes :
Summary statistics for the OECD sample from 1950 to 2006. The 28 countries included are Australia,
Austria, Belgium, Canada, Switzerland, Czech Republic, Germany, Denmark, Spain, Finland, France, United
Kingdom, Greece, Hungary, Ireland, Iceland, Italy, Japan, Korea, Netherlands, Norway, New Zealand, Poland,
Portugal, Slovak Republic, Sweden, Turkey, and United States. Data are taken from Head et al. (2010) which
can be downloaded from http://www.cepii.fr/anglaisgraph/bdd/gravity.htm.
36
37
tijτ
tijτ
36,945
X
37,741
X
X
(0.010)
(0.023)
(0.857)
0.655***
(1.451)
0.663***
22.734***
(0.019)
20.897***
0.308***
(0.016)
(0.049)
0.274***
0.769***
(0.019)
(0.030)
0.386***
0.276***
(0.019)
(0.027)
(0.009)
0.097***
-0.669***
-1.050***
zijτ
ln zijτ
(3)
37,493
X
(0.006)
0.657***
(0.428)
21.198***
(0.017)
0.267***
(0.019)
0.387***
(0.019)
0.116***
(0.010)
-1.041***
ln xijτ
OLS
(4)
38,313
X
X
(0.021)
0.682***
(1.284)
18.100***
(0.019)
0.332***
(0.017)
0.150***
(0.018)
0.414***
(0.010)
-0.816***
xijτ
PPML
(5)
36,945
X
(0.006)
0.663***
(0.405)
20.899***
(0.014)
0.274***
(0.019)
0.386***
(0.019)
0.097***
(0.009)
-1.050***
ln zijτ
OLS
(6)
37,741
X
X
(0.024)
0.655***
(1.670)
22.719***
(0.016)
0.311***
(0.049)
0.769***
(0.030)
0.275***
(0.027)
-0.669***
zijτ
PPML
(7)
37,493
X
(0.006)
0.653***
(0.405)
21.172***
(0.015)
0.276***
(0.019)
0.387***
(0.019)
0.115***
(0.010)
-1.040***
ln xijτ
OLS
(8)
38,313
X
X
(0.021)
0.683***
(1.353)
18.028***
(0.013)
0.341***
(0.017)
0.151***
(0.018)
0.414***
(0.010)
-0.813***
xijτ
PPML
Results for a gravity model of normalized trade ows between 28 OECD countries between 1950 and 2006 estimated by ordinary least squares
(OLS) and Poisson pseudo-maximum-likelihood (PPML). zij are trade ows standardized by importer and exporter GDPs. ln DIST is distance between
exporting and importing country, CON T IG is an indicator variable equal to 1 if the exporting and importing countries i and j share a common border,
COM LAN G is an indicator variable equal to 1 if the exporting and importing country share a common ocial language, and P T A is an indicator variable
equal to 1 if the exporting and importing country have signed a preferential trade agreement. All regressions control for multilateral resistance terms
(MRTs) via exporter and importer xed eects. (Robust) standard errors in parentheses, *** p <0.01, ** p <0.05, * p <0.1. Standard errors for σ and µ
are bootstrapped using 200 replications.
Notes :
N
asymmetric
symmetric
zero trade
µ
σ
Estimated elasticities
P T Aijτ
First stage
COM LAN Gij
CON T IGij
ln DISTij
Second stage
(2)
PPML
(1)
OLS
Table 2: Estimation results for gravity model for the OECD sample, 1950-2006
Table 3: OECD sample, Comparative static eects of PTA inception in 2006
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
share %GDP SMF
SMF
SMF
AvW
SMF
AvW
SMF
%GDP
%GDP
% ln(p̂)
% ln(ê)
%ê
∆u
%EV
%EV
Australia
Austria
Belgium
Canada
Czech Republic
Denmark
Finland
France
Germany
Greece
Hungary
Iceland
Ireland
Italy
Japan
Korea
Netherlands
New Zealand
Norway
Poland
Portugal
Slovak Republic
Spain
Sweden
Switzerland
Turkey
United Kingdom
United States
1.27
1.35
1.39
1.72
1.31
1.26
1.19
1.16
1.09
1.17
1.26
1.15
1.22
1.11
0.59
0.60
1.24
0.68
1.22
1.25
1.20
1.29
1.12
1.21
1.42
1.16
0.98
0.62
1.91
2.09
2.16
2.80
2.00
1.90
1.75
1.69
1.57
1.71
1.91
1.68
1.82
1.59
0.53
0.56
1.87
0.72
1.82
1.88
1.78
1.95
1.61
1.80
2.22
1.70
1.34
0.60
65.48
63.98
63.40
59.82
64.68
65.60
67.09
67.77
69.39
67.58
65.53
67.95
66.37
69.06
111.38
108.92
65.84
95.20
66.33
65.79
66.78
65.09
68.74
66.62
63.00
67.71
73.06
103.98
34.52
36.02
36.60
40.18
35.32
34.40
32.91
32.23
30.61
32.42
34.47
32.05
33.63
30.94
-11.38
-8.92
34.16
4.80
33.67
34.21
33.22
34.91
31.26
33.38
37.00
32.29
26.94
-3.98
0.66
0.75
0.79
1.12
0.70
0.65
0.57
0.54
0.48
0.55
0.65
0.53
0.61
0.49
-0.06
-0.05
0.64
0.03
0.61
0.64
0.59
0.68
0.50
0.60
0.82
0.55
0.36
-0.02
-0.62
-0.71
-0.72
-1.05
-0.65
-0.62
-0.53
-0.49
-0.43
-0.50
-0.60
-0.52
-0.58
-0.46
0.06
0.05
-0.61
-0.03
-0.59
-0.55
-0.54
-0.59
-0.46
-0.55
-0.78
-0.50
-0.34
0.02
1.27
1.43
1.51
2.18
1.35
1.24
1.10
1.03
0.91
1.05
1.25
1.03
1.17
0.93
-0.12
-0.10
1.22
0.06
1.17
1.22
1.13
1.30
0.96
1.14
1.57
1.04
0.68
-0.06
1.91
2.18
2.29
3.27
2.05
1.89
1.67
1.58
1.39
1.60
1.90
1.56
1.77
1.43
-0.18
-0.14
1.85
0.10
1.78
1.86
1.71
1.98
1.46
1.74
2.38
1.59
1.04
-0.07
Average
0.89
1.15
87.51
12.49
0.26
-0.24
0.49
0.76
Notes :
Counterfactual analysis based on parameter estimates from column (6) of Table 2. AvW
gives results assuming perfect labor markets. SMF are results for the gravity model using a search
and matching framework for the labor market.
38
Table 4: Heterogeneity of comparative static eects in percent of PTA inception, OECD
sample with perfect labor markets in 2006
Heterogeneity of goods trade changes in %
Min.
2.50%
25%
50%
75%
97.5%
Max.
Australia
Austria
Belgium
Canada
Czech Republic
Denmark
Finland
France
Germany
Greece
Hungary
Iceland
Ireland
Italy
Japan
Korea
Netherlands
New Zealand
Norway
Poland
Portugal
Slovak Republic
Spain
Sweden
Switzerland
Turkey
United Kingdom
United States
-31.46
-32.65
-33.20
-33.63
-32.01
-31.24
-30.13
-29.65
-28.64
-29.79
-31.30
-29.59
-30.68
-28.85
-20.08
-20.27
-31.03
-21.63
-30.69
-31.09
-30.36
-31.66
-29.05
-30.46
-33.63
-29.72
-26.87
-15.13
-30.62
-31.42
-31.98
-33.55
-30.77
-29.98
-28.85
-28.36
-27.33
-28.51
-30.04
-28.30
-29.41
-27.55
-19.11
-19.20
-29.77
-20.68
-29.42
-29.83
-29.09
-30.41
-27.76
-29.19
-32.41
-28.43
-25.54
-15.03
-24.11
-1.54
-2.14
-31.28
-0.60
0.52
2.15
2.86
4.33
2.64
0.44
3.64
1.34
4.02
-11.69
-11.72
0.83
-13.23
2.03
0.75
1.81
-0.09
3.72
1.66
-1.46
3.45
6.91
-12.03
-23.09
2.15
1.31
-30.36
3.12
4.29
5.89
6.62
8.15
6.39
4.20
6.79
5.05
7.82
-10.46
-10.24
4.52
-12.07
5.13
4.52
5.54
3.66
7.52
5.38
1.17
6.60
10.82
-10.65
-21.48
4.06
3.21
-28.90
5.05
6.25
7.97
8.49
10.05
8.35
6.16
8.80
7.11
9.72
-8.82
-1.01
6.57
-10.23
7.21
6.48
7.61
5.60
9.41
7.45
2.67
8.68
12.77
-8.82
19.36
7.85
6.96
3.34
8.87
10.11
11.89
12.67
14.22
12.43
10.02
21.67
11.01
13.94
2.58
23.42
10.45
15.11
19.77
10.35
11.52
9.44
13.61
11.36
14.70
21.45
14.70
17.65
19.62
8.31
7.42
8.31
9.34
10.58
12.37
13.14
14.76
12.90
10.48
23.46
11.48
14.42
2.67
23.46
10.91
18.13
21.54
10.82
12.00
9.91
14.09
11.83
16.38
23.23
14.76
19.62
Average
-29.09
-27.95
-2.39
0.71
2.87
12.87
13.78
Notes :
Counterfactual analysis based on parameter estimates from column (6) of
Table 2.
39
Table 5: Heterogeneity of comparative static eects in percent of PTA inception, OECD
sample with imperfect labor markets in 2006
Heterogeneity of goods trade changes in %
Min.
2.50%
25%
50%
75%
97.5%
Max.
Australia
Austria
Belgium
Canada
Czech Republic
Denmark
Finland
France
Germany
Greece
Hungary
Iceland
Ireland
Italy
Japan
Korea
Netherlands
New Zealand
Norway
Poland
Portugal
Slovak Republic
Spain
Sweden
Switzerland
Turkey
United Kingdom
United States
-31.28
-32.60
-33.17
-33.59
-31.96
-31.18
-30.05
-29.59
-28.59
-29.72
-31.24
-29.48
-30.58
-28.79
-19.84
-20.04
-30.98
-21.47
-30.61
-31.02
-30.28
-31.60
-28.98
-30.39
-33.59
-29.63
-26.77
-15.20
-30.48
-31.38
-31.96
-33.51
-30.73
-29.93
-28.79
-28.32
-27.30
-28.45
-29.99
-28.20
-29.32
-27.50
-18.91
-19.02
-29.73
-20.56
-29.35
-29.78
-29.02
-30.36
-27.69
-29.13
-32.38
-28.36
-25.44
-15.11
-24.11
-1.76
-2.38
-31.22
-0.82
0.32
1.96
2.62
4.08
2.44
0.23
3.50
1.20
3.80
-11.54
-11.70
0.60
-13.28
1.83
0.54
1.63
-0.30
3.53
1.46
-1.68
3.27
6.74
-12.08
-23.07
1.93
1.07
-30.28
2.91
4.09
5.72
6.42
7.93
6.23
4.00
6.66
4.93
7.63
-10.42
-10.20
4.32
-12.09
4.94
4.32
5.39
3.44
7.35
5.21
0.99
6.42
10.69
-10.69
-21.48
3.89
3.02
-28.84
4.89
6.09
7.82
8.30
9.84
8.21
6.00
8.71
7.02
9.54
-8.76
-0.88
6.39
-10.27
7.04
6.33
7.48
5.44
9.25
7.30
2.45
8.52
12.65
-8.89
19.50
7.68
6.78
3.57
8.72
9.96
11.76
12.49
14.03
12.29
9.86
21.75
10.92
13.78
2.81
23.53
10.27
15.26
19.80
10.21
11.40
9.28
13.48
11.21
14.66
21.49
14.53
17.80
19.76
8.16
7.24
8.54
9.19
10.44
12.25
12.98
14.59
12.78
10.35
23.57
11.41
14.27
2.91
23.57
10.75
18.27
21.59
10.69
11.89
9.76
13.97
11.70
16.37
23.30
14.59
19.76
Average
-29.01
-27.88
-2.54
0.57
2.75
12.81
13.74
Notes :
Counterfactual analysis based on parameter estimates from column (6) of
Table 2.
40
Table 6: OECD sample, Comparative static eects of a 3% increase of
(1)
(2)
(3)
κ
in US in 2006
(4)
(5)
(6)
(7)
(8)
share %GDP SMF
SMF
SMF
AvW
SMF
AvW
SMF
%GDP
%GDP
% ln(p̂)
% ln(ê)
%ê
∆u
%EV
%EV
Australia
Austria
Belgium
Canada
Czech Republic
Denmark
Finland
France
Germany
Greece
Hungary
Iceland
Ireland
Italy
Japan
Korea
Netherlands
New Zealand
Norway
Poland
Portugal
Slovak Republic
Spain
Sweden
Switzerland
Turkey
United Kingdom
United States
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.12
0.05
0.04
0.16
0.05
0.05
0.06
0.05
0.05
0.06
0.05
0.07
0.06
0.05
0.05
0.06
0.05
0.10
0.06
0.05
0.06
0.05
0.06
0.06
0.04
0.06
0.07
2.94
64.21
92.16
97.90
58.87
88.14
86.68
82.17
89.08
88.99
83.22
85.50
74.23
78.21
85.90
84.40
83.34
90.60
67.18
82.30
85.81
80.60
86.12
82.50
83.89
98.41
81.20
74.89
-1.34
35.79
7.84
2.10
41.13
11.86
13.32
17.83
10.92
11.01
16.78
14.50
25.77
21.79
14.10
15.60
16.66
9.40
32.82
17.70
14.19
19.40
13.88
17.50
16.11
1.59
18.80
25.11
101.34
0.04
0.00
0.00
0.07
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.02
0.01
0.01
0.01
0.01
0.00
0.03
0.01
0.01
0.01
0.01
0.01
0.01
0.00
0.01
0.02
2.98
-0.04
0.00
0.00
-0.06
-0.01
-0.01
-0.01
0.00
0.00
-0.01
-0.01
-0.02
-0.01
-0.01
-0.01
-0.01
0.00
-0.03
-0.01
-0.01
-0.01
-0.01
-0.01
-0.01
0.00
-0.01
-0.02
-2.84
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.12
0.01
0.00
0.19
0.02
0.02
0.03
0.01
0.01
0.03
0.02
0.05
0.04
0.02
0.02
0.03
0.01
0.09
0.03
0.02
0.03
0.02
0.03
0.02
0.00
0.03
0.05
2.94
Average
0.00
1.12
51.79
48.21
1.11
-1.06
0.00
1.11
Notes :
Counterfactual analysis based on parameter estimates from column (6) of Table 2. AvW
gives results assuming perfect labor markets. SMF are results for the gravity model using a search
and matching framework for the labor market.
41
Table 7: Heterogeneity of comparative static eects in percent of a 3% increase of
OECD sample with imperfect labor markets in 2006
Heterogeneity of goods trade changes in %
Min.
2.50%
25%
50%
75%
97.5%
Max.
Australia
Austria
Belgium
Canada
Czech Republic
Denmark
Finland
France
Germany
Greece
Hungary
Iceland
Ireland
Italy
Japan
Korea
Netherlands
New Zealand
Norway
Poland
Portugal
Slovak Republic
Spain
Sweden
Switzerland
Turkey
United Kingdom
United States
-1.43
-0.57
-0.50
-1.43
-0.62
-0.64
-0.72
-0.61
-0.61
-0.70
-0.66
-0.92
-0.81
-0.65
-0.68
-0.70
-0.58
-1.23
-0.72
-0.66
-0.75
-0.65
-0.71
-0.69
-0.50
-0.74
-0.90
-1.42
-1.32
-0.46
-0.40
-1.43
-0.51
-0.54
-0.62
-0.50
-0.50
-0.59
-0.55
-0.82
-0.70
-0.55
-0.57
-0.59
-0.48
-1.13
-0.61
-0.55
-0.65
-0.54
-0.61
-0.58
-0.39
-0.63
-0.80
-1.31
-0.15
0.69
0.75
-0.75
0.63
0.61
0.53
0.65
0.64
0.55
0.59
0.37
0.48
0.60
0.57
0.55
0.67
0.06
0.53
0.59
0.50
0.60
0.53
0.56
0.75
0.51
0.39
-0.13
-0.08
0.78
0.85
-0.69
0.73
0.71
0.64
0.74
0.74
0.66
0.69
0.43
0.55
0.69
0.67
0.66
0.76
0.12
0.64
0.69
0.60
0.70
0.64
0.66
0.85
0.62
0.45
-0.07
-0.02
0.84
0.90
-0.62
0.79
0.78
0.70
0.80
0.80
0.72
0.76
0.50
0.61
0.77
0.74
0.72
0.82
0.18
0.70
0.77
0.67
0.77
0.71
0.73
0.91
0.68
0.52
0.00
0.11
0.99
1.04
-0.50
0.93
0.91
0.83
0.95
0.94
0.85
0.89
0.62
0.74
0.90
0.87
0.85
0.97
0.31
0.83
0.90
0.80
0.90
0.84
0.86
1.04
0.81
0.64
0.12
0.11
0.99
1.05
-0.50
0.93
0.91
0.83
0.95
0.95
0.85
0.89
0.62
0.74
0.90
0.87
0.85
0.97
0.31
0.83
0.90
0.80
0.90
0.84
0.86
1.05
0.81
0.65
0.12
Average
-0.78
-0.68
0.46
0.55
0.62
0.75
0.75
Notes : Counterfactual analysis based on parameter estimates from column (6) of
Table 2.
42
κ in US,
Table 8: Estimation results for gravity model of US-CAN trade in the Anderson and van
Wincoop (2003) sample
ln DIST
BORDER
(1)
(2)
(3)
(6)
OLS
PPML
PPML
OLS
PPML
PPML
zij
zij
ln zij
zij
zij
-1.252***
-1.328***
-1.353***
-1.411***
-1.934***
-1.942***
(0.0368)
(0.0420)
(0.0430)
(0.0292)
(0.0418)
(0.0409)
-1.551***
-0.981***
-0.962***
-1.562***
-0.807***
-0.804***
(0.0589)
(0.0823)
(0.0835)
(0.0603)
(0.122)
(0.121)
X
X
zero trade
N
R2
ln L
(5)
ln zij
internal trade
MRTs
(4)
X
X
X
X
X
X
X
X
X
1511
1511
1560
1551
1551
1600
0.664
0.898
0.897
0.744
0.999
0.999
-1841
-0.002
-0.002
-1957
-0.014
-0.014
Notes : Results for a gravity model of normalized trade ows between 30 US states and 10 Canadian provinces
in 1993 estimated by ordinary least squares (OLS) and Poisson pseudo-maximum-likelihood (PPML) on the
sample used in Anderson and van Wincoop (2003). zij are trade ows standardized by importer and exporter
GDPs. BORDER is an indicator variable equal to 1 if a trade ow between regions i and j crosses the
US-CAN border. Intra-trade indicates whether inter-state/inter-provicincial trade is included. All regressions
control for multilateral resistance terms (MRTs) via exporter and importer xed eects. (Robust) standard
errors in parentheses, *** p <0.01, ** p <0.05, * p <0.1.
43
Table 9: US-CAN sample, Comparative static eects of erasing the US-CAN border
ROW
Alabama
Arizona
California
Florida
Georgia
Idaho
Illinois
Indiana
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Missouri
Montana
New Hampshire
New Jersey
New York
North Carolina
North Dakota
Ohio
Pennsylvania
Tennessee
Texas
Vermont
Virginia
Washington
Wisconsin
Alberta
British Columbia
Manitoba
New Brunswick
Newfoundland
Nova Scotia
Ontario
Prince Edward Island
Quebec
Saskatchewan
Total average
US average
CAN average
Notes :
(1)
(2)
(3)
(4)
(5)
(6)
(7)
AvW
SMF
share %GDP SMF
SMF
AvW
SMF
%GDP
%GDP
% ln(p̂)
% ln(ê)
%ê
%EV
%EV
1.75
1.16
1.28
1.04
1.11
1.16
1.88
1.17
1.29
1.31
1.13
2.85
1.17
1.28
1.68
1.46
1.20
2.34
1.94
1.32
1.33
1.25
2.11
1.37
1.38
1.23
1.10
2.75
1.27
1.90
1.44
2.42
1.42
1.63
1.19
1.31
1.40
2.63
1.43
1.63
1.67
1.36
4.25
1.43
1.61
2.29
1.94
1.49
3.40
2.72
1.68
1.70
1.57
3.04
1.78
1.79
1.53
1.31
4.05
1.59
2.65
1.89
75.00
88.97
84.59
95.39
91.63
89.31
73.39
88.64
84.45
83.87
90.32
66.47
88.73
84.87
76.08
79.86
87.35
69.29
72.77
83.65
83.39
85.72
70.96
82.11
81.91
86.44
91.66
67.03
85.20
73.27
80.45
25.00
11.03
15.41
4.61
8.37
10.69
26.61
11.36
15.55
16.13
9.68
33.53
11.27
15.13
23.92
20.14
12.65
30.71
27.23
16.35
16.61
14.28
29.04
17.89
18.09
13.56
8.34
32.97
14.80
26.73
19.55
0.60
0.16
0.25
0.05
0.11
0.15
0.69
0.16
0.25
0.27
0.13
1.40
0.16
0.24
0.54
0.39
0.19
1.03
0.73
0.27
0.28
0.22
0.87
0.32
0.32
0.21
0.11
1.32
0.23
0.70
0.37
1.75
0.43
0.70
0.15
0.30
0.41
2.04
0.45
0.71
0.76
0.36
4.25
0.45
0.69
1.58
1.10
0.52
3.07
2.17
0.78
0.80
0.63
2.55
0.90
0.92
0.58
0.29
4.00
0.67
2.07
1.05
2.42
0.62
1.00
0.22
0.44
0.60
2.80
0.65
1.01
1.07
0.52
5.74
0.64
0.97
2.19
1.56
0.75
4.19
2.97
1.10
1.12
0.89
3.54
1.27
1.29
0.83
0.44
5.37
0.94
2.83
1.48
8.87
5.67
14.54
11.65
14.76
8.68
9.49
12.98
6.77
13.50
14.20
8.91
23.59
18.74
23.92
13.89
15.22
20.92
10.74
21.84
58.59
60.59
57.25
57.78
57.23
58.67
58.37
57.51
59.68
57.42
41.41
39.41
42.75
42.22
42.77
41.33
41.63
42.49
40.32
42.58
5.65
3.42
9.47
7.52
9.61
5.52
6.08
8.41
4.20
8.78
18.46
10.79
32.81
25.37
33.38
17.99
20.00
28.76
13.39
30.10
24.60
14.41
43.63
33.65
44.34
23.98
26.61
38.11
17.88
40.00
1.86
1.28
8.72
2.58
1.60
13.95
82.93
86.49
58.88
17.07
13.51
41.12
0.66
0.24
5.54
2.05
0.68
18.18
2.79
0.96
24.21
Counterfactual analysis based on parameter estimates from column (1) of Table 8. We
set σ = 5 as in Anderson and van Wincoop (2003) and µ = 0.5. AvW gives results for the
Anderson and van Wincoop (2003) estimates assuming perfect labor markets. SMF are results
for the gravity model using a search and matching framework for the labor market.
44
Table 10: Heterogeneity of comparative static eects in percent of erasing the US-CAN
border, US-CAN sample with perfect labor markets
Heterogeneity of goods trade changes in %
Min.
2.50%
25%
50%
75%
97.5%
Max.
ROW
Alabama
Arizona
California
Florida
Georgia
Idaho
Illinois
Indiana
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Missouri
Montana
New Hampshire
New Jersey
New York
North Carolina
North Dakota
Ohio
Pennsylvania
Tennessee
Texas
Vermont
Virginia
Washington
Wisconsin
-11.51
-8.90
-9.43
-8.33
-8.63
-8.86
-12.07
-8.93
-9.46
-9.55
-8.75
-15.69
-8.93
-9.42
-11.17
-10.24
-9.07
-14.00
-12.31
-9.60
-9.64
-9.29
-13.03
-9.84
-9.88
-9.19
-8.62
-15.69
-9.37
-12.12
-10.13
-11.27
-8.65
-9.19
-8.09
-8.39
-8.62
-11.83
-8.68
-9.22
-9.31
-8.51
-14.85
-8.69
-9.17
-10.93
-9.99
-8.83
-13.77
-12.08
-9.35
-9.40
-9.05
-12.79
-9.60
-9.64
-8.95
-8.38
-14.62
-9.13
-11.88
-9.89
-5.04
-2.42
-3.00
-1.82
-2.14
-2.39
-5.63
-2.46
-3.03
-3.13
-2.27
-10.01
-2.46
-2.98
-4.67
-3.67
-2.61
-7.71
-5.89
-3.17
-3.22
-2.85
-6.66
-3.43
-3.48
-2.74
-2.13
-9.52
-2.93
-5.69
-3.61
-4.23
-1.50
-1.98
-0.89
-1.21
-1.46
-4.83
-1.53
-2.02
-2.11
-1.34
-9.24
-1.54
-1.96
-3.86
-2.85
-1.68
-6.92
-5.10
-2.16
-2.20
-1.87
-5.87
-2.42
-2.47
-1.82
-1.20
-8.76
-1.91
-4.89
-2.74
68.98
73.97
72.95
74.89
74.48
74.04
67.92
73.91
72.89
72.72
74.25
60.14
73.90
72.98
69.63
71.42
73.64
64.23
67.46
72.64
72.56
73.21
66.09
72.17
72.10
73.41
74.50
61.00
73.07
67.82
71.61
255.21
265.70
263.54
267.97
266.76
265.84
252.98
265.57
263.42
263.06
266.28
236.62
265.55
263.62
256.58
260.33
265.00
245.22
252.00
262.89
262.73
264.10
249.13
261.92
261.75
264.52
266.80
238.42
263.81
252.77
260.74
264.38
275.14
272.93
277.47
276.22
275.28
262.09
275.01
272.80
272.44
275.74
245.31
274.99
273.00
265.78
269.63
274.43
254.13
261.09
272.26
272.09
273.50
258.14
271.26
271.09
273.93
276.27
247.15
273.20
261.88
270.05
Alberta
British Columbia
Manitoba
New Brunswick
Newfoundland
Nova Scotia
Ontario
Prince Edward Island
Quebec
Saskatchewan
-63.50
-57.64
-71.68
-67.82
-71.68
-63.17
-64.53
-69.67
-59.77
-70.36
-63.32
-57.43
-70.88
-67.66
-71.02
-63.00
-64.36
-69.52
-59.58
-70.21
198.33
246.23
131.42
163.03
129.22
200.97
189.91
147.89
228.80
142.27
219.30
270.57
147.69
181.53
145.33
222.13
210.30
165.32
251.92
159.30
222.01
273.71
149.79
183.91
147.42
224.86
212.93
167.57
254.91
161.50
224.73
276.87
151.90
186.31
149.50
227.61
215.57
169.83
257.90
163.71
225.24
277.47
152.30
186.76
149.90
228.13
216.07
170.26
258.47
164.13
Total average
US average
CAN average
-23.94
-10.34
-65.98
-23.65
-10.05
-65.70
40.37
-3.92
177.81
45.83
-3.01
197.34
102.52
71.19
199.86
245.73
259.85
202.39
252.86
269.14
202.87
Notes :
Counterfactual analysis based on parameter estimates from column (1) of Table 8.
We set σ = 5 as in Anderson and van Wincoop (2003) and µ = 0.5.
45
Table 11: Heterogeneity of comparative static eects in percent of erasing the US-CAN
border, US-CAN sample with imperfect labor markets
Heterogeneity of goods trade changes in %
Min.
2.50%
25%
50%
75%
97.5%
Max.
ROW
Alabama
Arizona
California
Florida
Georgia
Idaho
Illinois
Indiana
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Missouri
Montana
New Hampshire
New Jersey
New York
North Carolina
North Dakota
Ohio
Pennsylvania
Tennessee
Texas
Vermont
Virginia
Washington
Wisconsin
-11.91
-9.10
-9.70
-8.44
-8.80
-9.06
-12.50
-9.14
-9.72
-9.82
-8.94
-16.25
-9.13
-9.66
-11.56
-10.58
-9.30
-14.55
-12.75
-9.85
-9.90
-9.53
-13.59
-10.12
-10.16
-9.43
-8.80
-16.25
-9.61
-12.54
-10.45
-11.63
-8.81
-9.42
-8.16
-8.52
-8.77
-12.22
-8.85
-9.44
-9.54
-8.66
-15.40
-8.84
-9.37
-11.29
-10.30
-9.02
-14.29
-12.47
-9.57
-9.62
-9.25
-13.33
-9.85
-9.88
-9.14
-8.51
-15.14
-9.32
-12.27
-10.18
-5.07
-2.27
-2.92
-1.57
-1.95
-2.23
-5.70
-2.31
-2.94
-3.04
-2.10
-10.31
-2.30
-2.87
-4.69
-3.64
-2.49
-7.92
-5.97
-3.08
-3.13
-2.73
-6.89
-3.37
-3.41
-2.62
-1.95
-9.75
-2.82
-5.75
-3.57
-4.19
-1.23
-1.79
-0.52
-0.91
-1.19
-4.83
-1.27
-1.81
-1.91
-1.06
-9.48
-1.26
-1.74
-3.81
-2.75
-1.45
-7.07
-5.10
-1.95
-2.00
-1.64
-6.02
-2.25
-2.29
-1.59
-0.90
-8.91
-1.69
-4.88
-2.61
67.86
73.21
72.07
74.27
73.78
73.29
66.74
73.14
72.02
71.84
73.51
58.60
73.16
72.15
68.52
70.39
72.83
62.82
66.26
71.78
71.69
72.39
64.64
71.26
71.19
72.59
73.79
59.58
72.25
66.65
70.63
251.64
262.86
260.46
265.46
264.05
263.02
249.29
262.70
260.36
259.99
263.48
232.23
262.75
260.63
253.03
256.93
262.05
241.08
248.30
259.84
259.67
261.14
244.91
258.76
258.61
261.55
264.06
234.30
260.83
249.11
257.44
260.99
272.51
270.04
275.18
273.73
272.68
258.58
272.35
269.95
269.56
273.15
241.07
272.39
270.22
262.41
266.42
271.67
250.15
257.56
269.41
269.23
270.74
254.08
268.30
268.15
271.16
273.74
243.19
270.42
258.40
266.95
Alberta
British Columbia
Manitoba
New Brunswick
Newfoundland
Nova Scotia
Ontario
Prince Edward Island
Quebec
Saskatchewan
-64.25
-58.39
-72.23
-68.44
-72.23
-63.93
-65.25
-70.23
-60.55
-70.94
-64.09
-58.21
-71.46
-68.30
-71.58
-63.77
-65.10
-70.10
-60.37
-70.81
193.96
242.13
128.31
159.51
126.34
196.56
185.70
144.79
224.40
138.96
215.80
267.55
145.28
178.79
143.15
218.59
206.92
162.98
248.50
156.72
218.73
270.95
147.55
181.38
145.41
221.54
209.77
165.42
251.73
159.10
221.74
274.46
149.89
184.04
147.73
224.59
212.70
167.93
255.06
161.55
222.36
275.18
150.37
184.59
148.20
225.21
213.30
168.45
255.75
162.05
Total average
US average
CAN average
-24.33
-10.64
-66.64
-24.02
-10.31
-66.38
39.50
-3.88
174.07
45.22
-2.86
194.43
101.13
70.23
197.16
242.69
256.63
199.97
250.00
266.11
200.55
Notes :
Counterfactual analysis based on parameter estimates from column (1) of Table 8.
We set σ = 5 as in Anderson and van Wincoop (2003) and µ = 0.5.
46
Table 12: OECD sample, Comparative static eects of PTA inception controlling for trade
imbalances in 2006
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
share %GDP SMF
SMF
SMF
AvW
SMF
AvW
SMF
%GDP
%GDP
% ln(p̂)
% ln(ê)
%ê
∆u
%EV
%EV
Australia
Austria
Belgium
Canada
Czech Republic
Denmark
Finland
France
Germany
Greece
Hungary
Iceland
Ireland
Italy
Japan
Korea
Netherlands
New Zealand
Norway
Poland
Portugal
Slovak Republic
Spain
Sweden
Switzerland
Turkey
United Kingdom
United States
1.43
1.48
1.53
1.91
1.44
1.38
1.30
1.27
1.22
1.27
1.39
1.27
1.35
1.22
0.65
0.66
1.39
0.75
1.36
1.37
1.32
1.42
1.22
1.33
1.56
1.27
1.07
0.69
2.09
2.24
2.33
3.03
2.15
2.04
1.89
1.82
1.71
1.83
2.05
1.81
1.98
1.72
0.59
0.61
2.05
0.79
1.98
2.02
1.92
2.11
1.73
1.93
2.39
1.83
1.43
0.67
67.09
65.41
64.86
61.52
66.07
66.98
68.40
69.05
70.64
68.86
66.88
69.23
67.64
70.27
110.65
108.36
67.25
95.38
67.66
67.15
68.07
66.45
69.97
67.95
64.44
68.99
74.24
103.70
32.91
34.59
35.14
38.48
33.93
33.02
31.60
30.95
29.36
31.14
33.12
30.77
32.36
29.73
-10.65
-8.36
32.75
4.62
32.34
32.85
31.93
33.55
30.03
32.05
35.56
31.01
25.76
-3.70
0.68
0.77
0.81
1.16
0.73
0.67
0.59
0.56
0.50
0.57
0.68
0.55
0.64
0.51
-0.06
-0.05
0.67
0.04
0.64
0.66
0.61
0.70
0.52
0.62
0.84
0.56
0.37
-0.02
-0.65
-0.73
-0.75
-1.08
-0.67
-0.64
-0.55
-0.51
-0.45
-0.52
-0.63
-0.54
-0.61
-0.47
0.06
0.05
-0.64
-0.03
-0.62
-0.57
-0.56
-0.61
-0.47
-0.57
-0.81
-0.51
-0.35
0.02
1.43
1.59
1.68
2.44
1.50
1.38
1.22
1.15
1.02
1.16
1.39
1.14
1.31
1.04
-0.13
-0.11
1.37
0.07
1.31
1.36
1.25
1.45
1.06
1.27
1.74
1.16
0.75
-0.06
2.09
2.35
2.49
3.56
2.22
2.05
1.81
1.71
1.52
1.73
2.07
1.69
1.94
1.56
-0.19
-0.15
2.04
0.11
1.95
2.01
1.86
2.15
1.58
1.88
2.58
1.72
1.12
-0.08
Average
0.98
1.25
87.94
12.06
0.27
-0.25
0.55
0.82
Notes :
AvW gives results assuming perfect labor markets. SMF are results for the gravity model
using a search and matching framework for the labor market.
47
Table 13: Heterogeneity of comparative static eects in percent of PTA inception, OECD
sample with perfect labor markets and controlling for trade imbalances in 2006
Heterogeneity of goods trade changes in %
Min.
2.50%
25%
50%
75%
97.5%
Max.
Australia
Austria
Belgium
Canada
Czech Republic
Denmark
Finland
France
Germany
Greece
Hungary
Iceland
Ireland
Italy
Japan
Korea
Netherlands
New Zealand
Norway
Poland
Portugal
Slovak Republic
Spain
Sweden
Switzerland
Turkey
United Kingdom
United States
-31.65
-32.41
-33.05
-33.89
-31.82
-31.04
-29.90
-29.38
-28.65
-29.46
-31.13
-29.37
-30.63
-28.70
-19.90
-20.09
-31.14
-21.60
-30.67
-30.84
-30.14
-31.48
-28.74
-30.27
-33.43
-29.48
-26.50
-15.26
-30.85
-31.17
-31.82
-33.81
-30.57
-29.78
-28.62
-28.09
-27.34
-28.16
-29.86
-28.08
-29.35
-27.40
-18.97
-19.06
-29.88
-20.69
-29.39
-29.57
-28.86
-30.22
-27.44
-28.99
-32.21
-28.19
-25.15
-15.15
-24.52
-1.42
-2.15
-31.52
-0.57
0.57
2.24
2.99
4.06
2.89
0.45
3.75
1.18
3.98
-11.56
-11.71
0.44
-13.43
1.85
0.87
1.88
-0.06
3.93
1.71
-1.40
3.59
7.21
-12.15
-23.53
2.33
1.36
-30.66
3.21
4.39
5.96
6.75
7.86
6.64
4.27
6.92
4.87
7.77
-10.49
-10.28
4.10
-12.29
4.97
4.70
5.60
3.73
7.72
5.41
1.13
6.76
11.11
-10.80
-21.93
4.14
3.15
-29.22
5.04
6.24
8.00
8.58
9.71
8.56
6.11
8.81
6.88
9.62
-8.90
-0.90
6.09
-10.46
6.95
6.55
7.63
5.57
9.57
7.44
2.68
8.74
13.02
-8.94
18.94
7.94
6.92
3.10
8.88
10.12
11.94
12.77
13.87
12.66
9.99
21.79
10.79
13.86
2.64
23.35
9.97
15.16
19.56
10.45
11.56
9.43
13.80
11.36
14.79
21.61
15.03
17.80
19.20
8.39
7.36
8.08
9.33
10.58
12.41
13.24
14.42
13.12
10.45
23.60
11.25
14.33
2.70
23.39
10.43
18.22
21.34
10.90
12.02
9.88
14.27
11.82
16.50
23.41
15.11
19.79
Average
-28.95
-27.81
-2.39
0.70
2.81
12.86
13.77
Notes :
Counterfactual analysis based on parameter estimates from column (6) of
Table 2.
48
Table 14: Heterogeneity of comparative static eects in percent of PTA inception, OECD
sample with imperfect labor markets and controlling for trade imbalances in 2006
Heterogeneity of goods trade changes in %
Min.
2.50%
25%
50%
75%
97.5%
Max.
Australia
Austria
Belgium
Canada
Czech Republic
Denmark
Finland
France
Germany
Greece
Hungary
Iceland
Ireland
Italy
Japan
Korea
Netherlands
New Zealand
Norway
Poland
Portugal
Slovak Republic
Spain
Sweden
Switzerland
Turkey
United Kingdom
United States
-31.46
-32.36
-33.01
-33.85
-31.77
-30.98
-29.83
-29.34
-28.61
-29.39
-31.07
-29.26
-30.52
-28.65
-19.66
-19.86
-31.09
-21.43
-30.59
-30.78
-30.06
-31.43
-28.67
-30.20
-33.40
-29.40
-26.39
-15.33
-30.70
-31.13
-31.80
-33.77
-30.53
-29.73
-28.56
-28.05
-27.31
-28.10
-29.82
-27.98
-29.26
-27.35
-18.77
-18.87
-29.84
-20.56
-29.33
-29.52
-28.79
-30.18
-27.37
-28.93
-32.19
-28.11
-25.05
-15.23
-24.52
-1.65
-2.39
-31.42
-0.79
0.36
2.03
2.75
3.81
2.68
0.23
3.60
1.03
3.75
-11.53
-11.64
0.20
-13.47
1.65
0.66
1.69
-0.29
3.72
1.50
-1.62
3.40
7.04
-12.20
-23.51
2.10
1.11
-30.58
2.99
4.18
5.79
6.53
7.63
6.46
4.05
6.78
4.75
7.57
-10.45
-10.25
3.89
-12.32
4.78
4.49
5.44
3.51
7.54
5.23
0.98
6.57
10.98
-10.84
-21.93
3.96
2.95
-29.15
4.87
6.08
7.85
8.38
9.49
8.41
5.95
8.72
6.79
9.44
-8.84
-0.77
5.91
-10.51
6.77
6.39
7.49
5.40
9.40
7.28
2.45
8.56
12.90
-9.01
19.09
7.77
6.73
3.34
8.71
9.97
11.80
12.59
13.68
12.51
9.83
21.88
10.70
13.69
2.87
23.45
9.79
15.31
19.59
10.29
11.43
9.26
13.66
11.21
14.75
21.65
14.86
17.96
19.34
8.23
7.18
8.31
9.17
10.44
12.28
13.07
14.23
12.99
10.30
23.72
11.18
14.17
2.95
23.50
10.26
18.36
21.40
10.76
11.90
9.72
14.14
11.69
16.49
23.49
14.93
19.93
Average
-28.87
-27.74
-2.55
0.55
2.69
12.80
13.72
Notes :
Counterfactual analysis based on parameter estimates from column (6) of
Table 2.
49
Table 15: OECD sample, Comparative static eects of a 3% increase of
κ in US controlling
for trade imbalances in 2006
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
share %GDP SMF
SMF
SMF
AvW
SMF
AvW
SMF
%GDP
%GDP
% ln(p̂)
% ln(ê)
%ê
∆u
%EV
%EV
Australia
Austria
Belgium
Canada
Czech Republic
Denmark
Finland
France
Germany
Greece
Hungary
Iceland
Ireland
Italy
Japan
Korea
Netherlands
New Zealand
Norway
Poland
Portugal
Slovak Republic
Spain
Sweden
Switzerland
Turkey
United Kingdom
United States
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.12
0.05
0.04
0.17
0.05
0.06
0.06
0.05
0.05
0.06
0.06
0.08
0.07
0.06
0.06
0.06
0.05
0.11
0.06
0.06
0.06
0.06
0.06
0.06
0.04
0.06
0.08
2.93
65.60
92.82
98.49
60.29
88.91
87.44
83.07
89.86
89.76
84.20
86.36
75.36
79.34
86.78
85.34
84.32
91.30
68.48
83.18
86.62
81.63
86.97
83.48
84.73
99.08
82.19
75.97
-1.46
34.40
7.18
1.51
39.71
11.09
12.56
16.93
10.14
10.24
15.80
13.64
24.64
20.66
13.22
14.66
15.68
8.70
31.52
16.82
13.38
18.37
13.03
16.52
15.27
0.92
17.81
24.03
101.46
0.04
0.00
0.00
0.07
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.02
0.01
0.01
0.01
0.01
0.00
0.03
0.01
0.01
0.01
0.01
0.01
0.01
0.00
0.01
0.02
2.98
-0.04
0.00
0.00
-0.07
-0.01
-0.01
-0.01
-0.01
-0.01
-0.01
-0.01
-0.02
-0.01
-0.01
-0.01
-0.01
0.00
-0.03
-0.01
-0.01
-0.01
-0.01
-0.01
-0.01
0.00
-0.01
-0.02
-2.84
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.12
0.01
0.00
0.20
0.02
0.02
0.03
0.02
0.02
0.03
0.02
0.06
0.04
0.02
0.02
0.03
0.01
0.10
0.03
0.02
0.03
0.02
0.03
0.03
0.00
0.03
0.05
2.93
Average
0.00
1.13
52.33
47.67
1.11
-1.06
0.00
1.11
Notes :
Counterfactual analysis based on parameter estimates from column (6) of Table 2. AvW
gives results assuming perfect labor markets. SMF are results for the gravity model using a search
and matching framework for the labor market.
50
Table 16: Heterogeneity of comparative static eects in percent of a 3% increase of
κ
in
US controlling for trade imbalances, OECD sample with imperfect labor markets in 2006
Heterogeneity of goods trade changes in %
Min.
2.50%
25%
50%
75%
97.5%
Max.
Australia
Austria
Belgium
Canada
Czech Republic
Denmark
Finland
France
Germany
Greece
Hungary
Iceland
Ireland
Italy
Japan
Korea
Netherlands
New Zealand
Norway
Poland
Portugal
Slovak Republic
Spain
Sweden
Switzerland
Turkey
United Kingdom
United States
-1.42
-0.54
-0.47
-1.41
-0.59
-0.62
-0.70
-0.58
-0.58
-0.67
-0.63
-0.91
-0.78
-0.62
-0.67
-0.69
-0.56
-1.22
-0.70
-0.63
-0.72
-0.62
-0.68
-0.67
-0.46
-0.71
-0.89
-1.41
-1.31
-0.43
-0.37
-1.41
-0.49
-0.51
-0.60
-0.47
-0.47
-0.57
-0.53
-0.80
-0.68
-0.52
-0.56
-0.58
-0.45
-1.11
-0.59
-0.52
-0.62
-0.52
-0.58
-0.56
-0.36
-0.61
-0.78
-1.31
-0.15
0.70
0.77
-0.74
0.65
0.62
0.54
0.66
0.66
0.57
0.60
0.37
0.49
0.61
0.57
0.55
0.68
0.05
0.54
0.61
0.52
0.62
0.55
0.57
0.78
0.52
0.39
-0.14
-0.09
0.81
0.87
-0.68
0.75
0.73
0.64
0.77
0.76
0.67
0.71
0.43
0.56
0.72
0.67
0.66
0.79
0.12
0.64
0.71
0.62
0.72
0.66
0.67
0.88
0.63
0.45
-0.08
-0.03
0.85
0.92
-0.62
0.80
0.78
0.70
0.81
0.81
0.73
0.77
0.50
0.62
0.78
0.74
0.72
0.83
0.18
0.71
0.77
0.68
0.78
0.72
0.74
0.93
0.69
0.52
-0.02
0.10
0.99
1.05
-0.50
0.93
0.91
0.82
0.95
0.95
0.85
0.89
0.62
0.74
0.90
0.86
0.84
0.97
0.30
0.83
0.90
0.80
0.90
0.84
0.86
1.05
0.81
0.64
0.10
0.10
0.99
1.06
-0.50
0.94
0.91
0.82
0.95
0.95
0.86
0.89
0.62
0.74
0.90
0.86
0.84
0.97
0.30
0.83
0.90
0.80
0.90
0.84
0.86
1.06
0.81
0.64
0.10
Average
-0.76
-0.65
0.47
0.56
0.62
0.75
0.75
Notes : Counterfactual analysis based on parameter estimates from column (6) of
Table 2.
51
Table 17:
US-CAN sample, Comparative static eects of erasing the US-CAN border
controlling for trade imbalances
(1)
(2)
AvW
SMF
%GDP
%GDP
% ln(p̂)
1.74
1.15
1.26
1.08
1.05
1.15
1.86
1.20
1.32
1.34
1.11
2.81
1.18
1.18
1.60
1.46
1.21
2.26
1.83
1.36
1.18
1.28
2.11
1.40
1.38
1.25
1.07
2.58
1.24
1.57
1.45
2.39
1.40
1.60
1.25
1.25
1.40
2.60
1.46
1.67
1.70
1.34
4.19
1.43
1.51
2.20
1.94
1.49
3.30
2.60
1.73
1.54
1.59
3.04
1.81
1.79
1.55
1.28
3.86
1.56
2.31
1.91
Alberta
British Columbia
Manitoba
New Brunswick
Newfoundland
Nova Scotia
Ontario
Prince Edward Island
Quebec
Saskatchewan
12.16
5.33
15.57
13.48
15.48
10.10
12.69
14.18
9.99
15.40
Total average
US average
CAN average
2.02
1.25
11.25
ROW
Alabama
Arizona
California
Florida
Georgia
Idaho
Illinois
Indiana
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Missouri
Montana
New Hampshire
New Jersey
New York
North Carolina
North Dakota
Ohio
Pennsylvania
Tennessee
Texas
Vermont
Virginia
Washington
Wisconsin
Notes :
(3)
(4)
(5)
(6)
(7)
share %GDP SMF
SMF
AvW
SMF
% ln(ê)
%ê
%EV
%EV
75.00
88.84
84.57
95.52
91.36
89.26
73.43
88.82
84.72
84.11
90.18
66.12
88.82
83.93
75.77
79.98
87.46
69.08
71.80
84.06
81.92
85.90
71.11
82.47
82.07
86.53
91.48
66.05
85.15
69.94
80.62
25.00
11.16
15.43
4.48
8.64
10.74
26.57
11.18
15.28
15.89
9.82
33.88
11.18
16.07
24.23
20.02
12.54
30.92
28.20
15.94
18.08
14.10
28.89
17.53
17.93
13.47
8.52
33.95
14.85
30.06
19.38
0.60
0.16
0.25
0.06
0.11
0.15
0.69
0.16
0.26
0.27
0.13
1.41
0.16
0.24
0.53
0.39
0.19
1.01
0.73
0.28
0.28
0.23
0.87
0.32
0.32
0.21
0.11
1.30
0.23
0.69
0.37
1.75
0.43
0.69
0.15
0.30
0.42
2.03
0.45
0.72
0.77
0.36
4.25
0.45
0.69
1.54
1.10
0.52
3.01
2.16
0.79
0.80
0.64
2.55
0.90
0.92
0.59
0.30
3.94
0.66
2.05
1.05
2.41
0.63
1.00
0.23
0.44
0.60
2.78
0.66
1.03
1.09
0.53
5.75
0.64
0.98
2.14
1.56
0.75
4.11
2.96
1.11
1.12
0.90
3.54
1.27
1.29
0.84
0.44
5.30
0.93
2.81
1.49
17.66
8.56
24.60
20.59
24.52
15.32
18.57
22.04
14.04
23.85
65.99
59.14
59.33
61.84
59.06
62.82
65.39
60.41
68.86
60.82
34.01
40.86
40.67
38.16
40.94
37.18
34.61
39.59
31.14
39.18
5.69
3.42
9.37
7.41
9.40
5.45
6.08
8.21
4.18
8.75
18.61
10.78
32.38
24.96
32.56
17.73
20.00
28.01
13.33
29.99
24.79
14.39
43.06
33.10
43.25
23.63
26.62
37.12
17.81
39.86
2.74
1.58
16.58
83.17
86.27
64.82
16.83
13.73
35.18
0.66
0.24
5.53
2.05
0.68
18.14
2.78
0.96
24.15
Counterfactual analysis based on parameter estimates from column (1) of Table 8. We
set σ = 5 as in Anderson and van Wincoop (2003) and µ = 0.5. AvW gives results for the
Anderson and van Wincoop (2003) estimates assuming perfect labor markets. SMF are results
for the gravity model using a search and matching framework for the labor market.
52
Table 18: Heterogeneity of comparative static eects in percent of erasing the US-CAN
border, US-CAN sample with perfect labor markets and controlling for trade imbalances
Heterogeneity of goods trade changes in %
Min.
2.50%
25%
50%
75%
97.5%
Max.
ROW
Alabama
Arizona
California
Florida
Georgia
Idaho
Illinois
Indiana
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Missouri
Montana
New Hampshire
New Jersey
New York
North Carolina
North Dakota
Ohio
Pennsylvania
Tennessee
Texas
Vermont
Virginia
Washington
Wisconsin
-11.48
-8.86
-9.38
-8.57
-8.44
-8.88
-12.00
-9.09
-9.66
-9.73
-8.69
-15.71
-9.00
-9.02
-10.88
-10.29
-9.14
-13.71
-11.88
-9.84
-9.01
-9.45
-13.09
-10.02
-9.93
-9.33
-8.54
-15.07
-9.29
-10.76
-10.23
-11.33
-8.70
-9.23
-8.42
-8.28
-8.73
-11.85
-8.94
-9.51
-9.58
-8.54
-14.72
-8.85
-8.87
-10.73
-10.13
-8.99
-13.57
-11.73
-9.68
-8.86
-9.30
-12.94
-9.86
-9.78
-9.17
-8.38
-13.93
-9.14
-10.61
-10.08
-4.94
-2.20
-2.76
-1.89
-1.74
-2.22
-5.50
-2.44
-3.06
-3.13
-2.02
-9.79
-2.35
-2.37
-4.30
-3.66
-2.50
-7.34
-5.37
-3.24
-2.33
-2.83
-6.67
-3.44
-3.35
-2.70
-1.85
-8.79
-2.66
-4.17
-3.67
-3.95
-1.23
-1.68
-0.92
-0.77
-1.25
-4.52
-1.48
-1.98
-2.06
-1.05
-8.85
-1.38
-1.29
-3.30
-2.66
-1.53
-6.37
-4.38
-2.17
-1.27
-1.82
-5.70
-2.36
-2.27
-1.73
-0.88
-7.84
-1.58
-3.17
-2.60
75.60
80.80
79.76
81.07
81.64
80.76
74.56
80.35
79.21
79.07
81.13
66.65
80.52
80.48
76.79
77.97
80.24
71.18
74.81
78.86
80.50
79.63
72.41
78.51
78.68
79.87
81.44
68.49
79.94
77.03
78.08
276.00
287.14
284.91
288.35
288.93
287.04
273.78
286.16
283.72
283.43
287.84
256.83
286.54
286.44
278.54
281.08
285.95
266.53
274.31
282.99
286.49
284.63
269.18
282.23
282.59
285.15
288.51
260.77
285.30
279.06
281.31
291.37
302.97
300.65
304.23
304.84
302.87
289.07
301.95
299.41
299.11
303.70
271.42
302.34
302.25
294.02
296.66
301.73
281.52
289.62
298.65
302.30
300.36
284.28
297.86
298.23
300.90
304.40
275.52
301.06
294.56
296.90
Alberta
British Columbia
Manitoba
New Brunswick
Newfoundland
Nova Scotia
Ontario
Prince Edward Island
Quebec
Saskatchewan
-66.90
-54.68
-71.51
-68.78
-71.14
-63.69
-67.68
-69.72
-63.50
-71.29
-66.75
-54.48
-70.39
-68.64
-70.14
-63.53
-67.54
-69.59
-63.34
-71.17
156.67
251.41
120.95
142.08
121.84
181.54
150.65
134.78
183.04
122.61
175.16
276.72
136.86
159.52
137.83
201.82
168.70
151.69
203.43
138.64
178.03
280.65
139.33
162.23
140.31
204.97
171.50
154.32
206.59
141.13
180.28
283.73
141.27
164.35
142.25
207.43
173.70
156.37
209.07
143.08
181.11
284.87
141.99
165.14
142.97
208.35
174.52
157.14
210.00
143.81
Total average
US average
CAN average
-24.09
-10.25
-66.89
-23.85
-10.04
-66.56
35.37
-3.68
156.56
40.64
-2.67
175.04
102.32
78.01
177.91
256.42
281.19
180.15
268.41
296.78
180.99
Notes :
Counterfactual analysis based on parameter estimates from column (1) of Table 8. We
set σ = 5 as in Anderson and van Wincoop (2003) and µ = 0.5.
53
Table 19: Heterogeneity of comparative static eects in percent of erasing the US-CAN
border, US-CAN sample with imperfect labor markets and controlling for trade imbalances
Heterogeneity of goods trade changes in %
Min.
2.50%
25%
50%
75%
97.5%
Max.
ROW
Alabama
Arizona
California
Florida
Georgia
Idaho
Illinois
Indiana
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Missouri
Montana
New Hampshire
New Jersey
New York
North Carolina
North Dakota
Ohio
Pennsylvania
Tennessee
Texas
Vermont
Virginia
Washington
Wisconsin
-11.90
-9.09
-9.68
-8.79
-8.62
-9.11
-12.46
-9.34
-9.96
-10.03
-8.91
-16.27
-9.22
-9.27
-11.28
-10.66
-9.40
-14.27
-12.31
-10.13
-9.27
-9.72
-13.68
-10.33
-10.23
-9.60
-8.74
-15.62
-9.55
-11.21
-10.58
-11.71
-8.89
-9.49
-8.59
-8.43
-8.92
-12.27
-9.15
-9.77
-9.84
-8.72
-15.27
-9.03
-9.08
-11.09
-10.47
-9.21
-14.09
-12.13
-9.94
-9.07
-9.53
-13.49
-10.14
-10.04
-9.41
-8.54
-14.43
-9.36
-11.02
-10.39
-4.97
-2.02
-2.66
-1.70
-1.52
-2.04
-5.58
-2.29
-2.96
-3.04
-1.83
-10.06
-2.17
-2.22
-4.30
-3.63
-2.36
-7.53
-5.42
-3.14
-2.21
-2.70
-6.89
-3.36
-3.26
-2.57
-1.64
-8.98
-2.52
-4.23
-3.63
-3.90
-0.97
-1.48
-0.64
-0.46
-0.99
-4.51
-1.24
-1.79
-1.86
-0.77
-9.05
-1.12
-1.04
-3.22
-2.55
-1.31
-6.49
-4.35
-1.97
-1.03
-1.61
-5.84
-2.19
-2.09
-1.52
-0.59
-7.96
-1.34
-3.15
-2.46
74.48
80.05
78.87
80.27
80.97
80.00
73.36
79.55
78.32
78.18
80.40
65.13
79.77
79.68
75.70
76.93
79.42
69.77
73.66
77.98
79.69
78.79
70.96
77.58
77.77
79.03
80.74
67.11
79.13
75.84
77.08
272.18
284.06
281.56
285.33
286.03
283.97
269.81
282.99
280.37
280.07
284.81
252.24
283.47
283.27
274.80
277.42
282.72
262.14
270.43
279.66
283.30
281.39
264.67
278.80
279.21
281.90
285.54
256.46
282.10
275.09
277.74
286.96
299.31
296.72
300.63
301.37
299.22
284.50
298.21
295.48
295.17
300.10
266.23
298.70
298.50
289.69
292.41
297.92
276.53
285.14
294.74
298.53
296.54
279.16
293.85
294.27
297.07
300.85
270.62
297.28
289.99
292.75
Alberta
British Columbia
Manitoba
New Brunswick
Newfoundland
Nova Scotia
Ontario
Prince Edward Island
Quebec
Saskatchewan
-67.54
-55.49
-72.06
-69.38
-71.71
-64.43
-68.30
-70.29
-64.17
-71.84
-67.41
-55.32
-70.98
-69.26
-70.74
-64.30
-68.18
-70.17
-64.03
-71.73
153.10
247.03
117.87
138.79
118.86
177.32
147.15
131.69
179.37
119.57
172.43
273.52
134.51
157.02
135.57
198.49
166.02
149.38
200.70
136.34
175.50
277.73
137.15
159.91
138.23
201.86
169.02
152.19
204.08
139.00
178.08
281.27
139.37
162.35
140.46
204.69
171.54
154.55
206.93
141.24
179.09
282.66
140.24
163.30
141.33
205.80
172.53
155.47
208.05
142.12
Total average
US average
CAN average
-24.50
-10.58
-67.52
-24.24
-10.33
-67.21
34.57
-3.62
153.08
40.11
-2.52
172.40
101.00
77.06
175.47
253.27
277.71
178.05
264.85
292.72
179.06
Notes :
Counterfactual analysis based on parameter estimates from column (1) of Table 8. We
set σ = 5 as in Anderson and van Wincoop (2003) and µ = 0.5.
54
Table 20: US-CAN sample, Comparative static eects in percent of erasing the US-CAN
border for various parameter values
µ
σ
0.2
average %GDP
average %ê
average %EV
total
US
CAN
total
US
CAN
total
US
CAN
5
10
15
11.82
4.73
2.94
6.63
2.27
1.32
71.26
33.14
21.69
9.42
3.79
2.36
4.34
1.52
0.89
67.58
30.01
19.41
12.28
4.84
2.99
5.46
1.90
1.11
91.00
38.91
24.87
0.5
5
10
15
4.08
1.73
1.10
2.32
0.90
0.55
24.37
11.39
7.44
2.05
0.88
0.56
0.79
0.31
0.19
16.64
7.53
4.88
4.32
1.81
1.14
1.58
0.62
0.39
36.25
15.68
10.02
0.75
5
10
15
2.58
1.11
0.71
1.60
0.65
0.41
13.95
6.51
4.25
0.66
0.29
0.19
0.24
0.10
0.06
5.54
2.52
1.63
2.79
1.19
0.75
0.96
0.39
0.25
24.21
10.48
6.69
0.9
5
10
15
2.10
0.91
0.58
1.38
0.57
0.36
10.47
4.88
3.18
0.22
0.10
0.06
0.08
0.03
0.02
1.84
0.84
0.54
2.29
0.98
0.63
0.77
0.32
0.20
20.19
8.74
5.58
0.99
5
10
15
1.88
0.82
0.52
1.28
0.54
0.34
8.88
4.13
2.70
0.02
0.01
0.01
0.01
0.00
0.00
0.17
0.08
0.05
2.07
0.89
0.57
0.69
0.29
0.18
18.36
7.95
5.07
Notes : Table reports average changes in nominal GDP, employment, and the equivalent
variation for the gravity model using a search and matching framework for the labor
market with varying elasticity of substitution σ and the elasticity of the matching
function µ.
55
Table 21:
US-CAN sample, Comparative static eects of erasing the US-CAN border
controlling for trade imbalances for various parameter values
µ
σ
0.2
average %GDP
average %ê
average %EV
total
US
CAN
total
US
CAN
total
US
CAN
5
10
15
12.14
4.82
2.99
6.69
2.25
1.30
75.02
34.77
22.73
9.50
3.80
2.36
4.42
1.52
0.88
67.53
30.19
19.57
12.37
4.85
2.99
5.57
1.90
1.10
90.93
39.15
25.08
0.5
5
10
15
4.26
1.80
1.14
2.31
0.88
0.54
27.19
12.68
8.27
2.05
0.88
0.56
0.79
0.31
0.19
16.61
7.58
4.92
4.32
1.81
1.14
1.59
0.62
0.38
36.18
15.77
10.10
0.75
5
10
15
2.74
1.18
0.75
1.58
0.63
0.39
16.58
7.72
5.03
0.66
0.29
0.18
0.24
0.10
0.06
5.53
2.53
1.64
2.78
1.18
0.75
0.96
0.39
0.24
24.15
10.54
6.75
0.9
5
10
15
2.26
0.98
0.62
1.36
0.55
0.35
13.03
6.06
3.95
0.22
0.10
0.06
0.08
0.03
0.02
1.84
0.84
0.55
2.29
0.98
0.62
0.77
0.32
0.20
20.14
8.79
5.63
0.99
5
10
15
2.04
0.89
0.57
1.26
0.52
0.33
11.41
5.30
3.46
0.02
0.01
0.01
0.01
0.00
0.00
0.17
0.08
0.05
2.07
0.89
0.57
0.69
0.29
0.18
18.32
8.00
5.12
Notes : Table reports average changes in nominal GDP, employment, and the equivalent
variation for the gravity model using a search and matching framework for the labor
market with varying elasticity of substitution σ and the elasticity of the matching
function µ.
56
Table 22: OECD sample, Comparative static eects in percent of PTA inception for various
parameter values
µ
σ
average
%GDP
average
%ê
average
%∆u
average
%EV
0.2
5
10
15
16.76
7.13
4.53
11.90
5.00
3.16
-11.05
-4.63
-2.92
15.23
6.33
3.98
0.5
5
10
15
7.60
3.35
2.15
2.75
1.20
0.77
-2.55
-1.11
-0.71
5.66
2.44
1.55
0.75
5
10
15
5.75
2.55
1.64
0.90
0.40
0.25
-0.83
-0.37
-0.24
3.71
1.61
1.03
0.9
5
10
15
5.15
2.28
1.47
0.30
0.13
0.08
-0.27
-0.12
-0.08
3.07
1.34
0.85
0.99
5
10
15
4.89
2.16
1.39
0.03
0.01
0.01
-0.02
-0.01
-0.01
2.78
1.21
0.78
Notes : Table reports average changes in nominal GDP,
employment, and the equivalent variation for the gravity model using a search and matching framework for
the labor market with varying elasticity of substitution
σ and the elasticity of the matching function µ.
57
Table 23: OECD sample, Comparative static eects in percent of PTA inception controlling
for trade imbalances for various parameter values
µ
σ
average
%GDP
average
%ê
average
%∆u
average
%EV
0.2
5
10
15
16.68
7.11
4.51
11.91
5.00
3.16
-10.94
-4.61
-2.91
15.25
6.33
3.98
0.5
5
10
15
7.54
3.32
2.13
2.75
1.20
0.77
-2.54
-1.11
-0.71
5.67
2.44
1.55
0.75
5
10
15
5.69
2.52
1.62
0.90
0.40
0.25
-0.83
-0.37
-0.23
3.71
1.61
1.03
0.9
5
10
15
5.10
2.26
1.45
0.30
0.13
0.08
-0.27
-0.12
-0.08
3.07
1.34
0.85
0.99
5
10
15
4.83
2.14
1.37
0.03
0.01
0.01
-0.02
-0.01
-0.01
2.78
1.21
0.78
Notes : Table reports average changes in nominal GDP,
employment, and the equivalent variation for the gravity model using a search and matching framework for
the labor market with varying elasticity of substitution
σ and the elasticity of the matching function µ.
58