On Measuring the Welfare Gains from Trade under
Consumer Heterogeneity
Sergey Nigai∗
ETH Zurich
June, 2012
Abstract
I develop a multi-country model of international trade with heterogeneous consumers and non-homothetic
preferences. I use the model to quantify the bias in the conventional estimates of gains from trade calculated
under the assumption of a representative consumer. The model predicts heterogeneous income and price
effects that are translated into consumer-specific welfare gains and further quantified in a counterfactual
trade liberalization experiment. I find that conventional measures, such as the average real income per
capita, are adequate welfare measures mostly for consumers in the right tail of the income distribution. This
measure overestimates the gains from global trade liberalization by up to 9% and 88% for the median and
the poorest consumer, respectively. In terms of the aggregate country-level welfare gains, the measurement
error is between -6% and 8% in the utilized experiment.
Keywords: International trade; Income distribution; General equilibrium model.
JEL-codes: F11; F14; Q43; Q48.
∗
ETH Zurich, Weinbergstrasse 35, 8092 Zurich, Switzerland; E-mail: [email protected]; Telephone: +41
44 632 9360
1
1
Introduction
An overwhelming majority of economists believe that free international trade is welfare
enhancing. In fact, this conventional wisdom may have been the least disputable one in the
profession.1 The general public, however, seems to have mixed feelings towards globalization,
with many people consistently opposing free trade policies. Surveys often indicate that up
to half of the population views free trade as potentially harmful.2 What is the reason for
this large gap between one of the most robust theoretical and empirical results in economics
and general perception of the public?
I argue that the reason for this disparity stems from the assumption of a representative
consumer. I show that this assumption is a source of large measurement errors in the
estimates of welfare gains from trade for certain consumer groups. For that, I build a multicountry model of trade with non-homothetic preferences and heterogeneous consumers, and
demonstrate that welfare gains from trade in a counterfactual global trade liberalization
experiment largely differ both qualitatively and quantitatively across individuals.
The model predicts that under trade liberalization different consumer groups experience
heterogeneous changes in their total nominal incomes and consumer price indices. This heterogeneity must be taken into account when evaluating welfare gains because measures based
on aggregate income and aggregate price indices, such as average real income per capita, may
(under)overstate gains from trade by up to (13%) 88% depending on the consumer group
and the country. In terms of aggregate welfare, the differences between changes in average
real income per capita and changes in true aggregate gains are between -6% and 8%.
Differences in the consumption patterns across consumers are the first source of heterogene1
The survey data among economists across different periods show that on average only about 5% of
economists believe that tariffs do not reduce welfare. See Alston, Kearl and Vaughan (1992), Poole (2004)
and others.
2
According to the survey conducted by the Pew Research Center in 2010, only 35% of respondents agreed
that free trade agreements such as NAFTA and WTO policies are good for the United States. In fact, 44%
of the respondents indicated that they consider free trade agreements to be bad for the United States.
2
ity3 in welfare gains from trade. The poor and the rich consume different bundles of goods.
For example, an abolishment of import tariffs on luxury cars and premium wines will have
positive price effects on the rich, but will offer no gains to the poor, whose consumption
baskets do not include those goods. The non-homothetic preference structure that I employ
here allows calculating unique price indices based on the expenditure shares of each individual. I use these price indices to deflate the nominal income of each consumer and calculate
adequate estimates of the welfare gains.
Consumers also differ in terms of their nominal incomes. I assume that each country has a
unique distribution of physical capital, so that the factor returns are distributed unevenly
across individuals.4 On the other hand, total government transfers such as foreign aid and
tariff revenues are distributed equally among all consumers. Trade liberalization affects factor
prices and government transfers which exert heterogeneous income effects. Depending on
the relative shares of factor returns and government transfers in total income, each consumer
faces a potential trade-off between change in factor prices and the size of tariff revenues in
case of a trade liberalization.
Recently, non-homothetic preferences have been reintroduced into the models of international
3
Fajgelbaum, Grossman and Helpman (2011) formulate a model with non-homothetic preferences, horizontal and vertical product diffentiation. They show that income distribution, in terms of the numeraire
good, remains unchanged after a trade liberalization episode but not in terms of real consumption. Two
empirical case studies discuss the bias from calculating welfare gains using a price index common to all
consumers. Porto (2006) calculates welfare gains for different consumer groups in Argentina from joining
MERCOSUR. Recently, Broda and Romalis (2009) have argued that welfare gains for low-income groups in
the US have been underestimated by using the price index of a representative consumer. The authors also
argue that around 50% of the documented increase in income inequality in the US between 1994 and 2005
is due to the problem of using a uniform price index.
4
Another way to introduce heterogeneity in incomes is to account for heterogeneous wages associated
with heterogeneous profits across firms in the presence of labor marker frictions (see Egger and Kreickermeier,
2009; Helpman, Itskhoki and Redding, 2010; Davis and Harrigan, 2011 and others). For example, Davis and
Harrigan (2011) introduce labor market frictions into Melitz (2003) model and show while trade liberalization
raises the average wage in their model, it negatively impacts workers that had relatively high wages in
the pre-trade equilibrium. Several empirical studies point to the heterogeneous income effects from trade
liberalization. Artuc, Chaudhuri and McLaren (2010) use a dynamic labor adjustment model and estimate
how trade liberalization affects different types of workers. McLaren and Hakobyan (2010) use US Census
data to estimate local welfare effects for heterogenous workers from joining NAFTA. Helpman, Itskhoki
and Redding (2008, 2010) explore the link between wages, income inequality and unemployment in general
equilibrium models of trade with heterogenous firms and workers.
3
trade (for example see Markusen, 2010; Simonovska, 2010; Fieler, 2011). The authors show
that non-homotheticity plays an important role in explaining bilateral trade patterns across
several margins. However, these papers are mainly concerned with consumer heterogeneity
across countries and not within a single country. In that sense, they still evaluate potential
welfare gains through the lens of a representative consumer which, as I argue, can be a source
of large bias.
I recognize the importance of large differences in the consumption patterns across countries
in explaining bilateral trade flows. I also add an additional dimension – differences in the
consumption patterns within a single country. Besides identifying differences in welfare gains
from trade of consumers within each country, this approach also delivers quantitative predictions documented in the empirical literature but currently missing in computable general
equilibrium work. The model provides the missing two-way link between international trade
and within-country income inequality (for example see Goldberg and Pavcnik 2004, 2007;
Harrison, McLaren and McMillan, 2010). On the one hand, the distribution of income shapes
import demand schedules, so that developing countries with relatively high income inequality and low average income are likely to import a higher share of manufacturing goods than
countries with low income inequality and low average income. On the other hand, trade
liberalization raises income inequality through heterogeneous income and price effects on
average.
In the next section, I illustrate the fundamental problem with current approaches that quantify welfare gains using aggregate measures such as average real income per capita. I present
the model in Section 3. In Section 4, I estimate the parameters of the model and describe
the calibration procedures. Section 5 discusses novel predictions of the model that are consistent with a number of empirically established facts. I conduct a counterfactual trade
liberalization experiment to assess the validity of conventional welfare metrics and evaluate
consumer-specific welfare gains in Section 6. The last section offers a brief conclusion.
4
2
Consumer heterogeneity and measures of welfare
Let d = 1, . . . , D denote the type of consumer in country i and let Yid denote his total nominal
income. Suppose there are g = 1, . . . , G different goods available for consumption. Let sg,id
P
be the share of income that consumer d spends on good g, so that G
g=1 sg,id = 1. The shares
sg,id vary across consumers and depend on the individual income level Yid . For example,
poor consumers spend a larger share of their income on food relative to rich consumers. The
welfare of consumer d in country i is then measured as:
ωid =
Yid
sg,id
, where Pid = ΠG
g=1 pgi .
Pid
(2.1)
Here, Pid is d’s price index calculated using a country-specific vector of prices pgi and
consumer-specific expenditure shares sg,id .5
Next, consider the average real income per capita:
D
Ȳi
1 X
sgi
ȳi =
, where Ȳi =
Yid and Pi = ΠG
g=1 pgi .
Pi
Li d=1
(2.2)
Here, Li is the total number of consumers in i and sgi is the country-specific expenditure
share on good g. Two sources of the measurement error about welfare in models assuming
homogenous consumers are immediately clear. First, under consumer heterogeneity average
nominal income Ȳi differs from individual total income Yid . Second, depending on the level
of income, consumer d’s expenditure shares sg,id also deviate from country-level expenditure
shares sgi .
Let me define the measurement error (meid ) for consumer d in i as follows:
meid ≡ 100 ×
ȳi
Yid Pi
− 1 = 100 ×
−1 .
ωid
Ȳi Pid
5
(2.3)
Broda, Leibtag and Weinstein (2009) discuss the importance of using consumer-type specific price
indices such as Pid here.
5
Here, meid measures by how much (in percent) ȳi overestimates true welfare of consumer d.
It is clear from (2.3) that meid will be especially high for consumers whose income deviates
relatively more from the mean and for countries with higher income inequality across different
d’s. In a representative consumer framework Yid = Ȳi and Pid = Pi , so that (2.3) collapses
to meid = 0. This is assumed in conventional models of trade. It turns out that the model
used in this paper suggests that the range and the mean of meid are extremely large. Hence,
if one evaluates welfare gains from trade liberalization without accounting for consumer
heterogeneity, one will overestimate the gains for some consumers and underestimate them
for others. For instance, rich consumers would benefit if trade liberalization led to a reduction
in prices of luxury goods. On the other hand, poor consumers would not gain much because
they do not consume any luxury goods in the first place. However, looking at the reduction
in a common price index driven solely by the decrease in the price of luxury goods, one may
wrongly conclude that trade liberalization is beneficial for all consumers. The measurement
errors in terms of quantified aggregate gains from trade are also large.
I use a general equilibrium model of trade calibrated to real data on Yid and Pid and show that
under a counterfactual trade liberalization meid ’s are very large, especially for consumers in
the left tail of the income distribution.
3
Model
The production side of the model is in the spirit of Eaton and Kortum (2002). There are
N countries in the world. Each country i = 1 . . . N is endowed with Li units of labor and
Ki units capital. Each country hosts a measure of heterogeneous firms in three sectors:
agricultural, manufacturing and non-tradable. Manufacturing and agricultural goods can be
traded subject to sector-specific iceberg trade costs from country n to country i – τm,in and
τa,in respectively.6 The factors of production are assumed to be completely mobile across
6
The usual triangularity (non-arbitrage) assumption applies.
6
sectors but not countries.
I introduce consumer heterogeneity in the spirit of Mayer (1984) by assuming that each
household owns a unit of labor and d units of capital.7 Households vary according to their
endowment of capital and can be of type d = 1, ..., D. Here, d stands for the decile in the
capital distribution.8 The distribution of capital is assumed to be exogenous, stationary and
country-specific. Hence, households are homogeneous within a decile in any country i but
not across countries and/or deciles.
The preference structure is non-homothetic which ensures that differences in the level of real
income are mapped into the differences in consumption patterns of consumers across deciles
and countries. Depending on the level of real income, some consumers may choose not to
consume (or consume little) of certain goods. Both the extensive and intensive margins of
import demand are important in this context.
A large class of general equilibrium models of trade deliver identical predictions in terms
of welfare gains from trade (see Arkolakis, Costinot and Rodriguez-Clare, 2010). The two
necessary conditions for this remarkable result are a CES demand system and a structural
gravity equation. This model deviates in two major ways from such an approach: consumer
heterogeneity and non-homothetic preferences. The combination of these two guarantees
that the predictions of the model here differ from the canonical models of trade (Eaton and
Kortum, 2002; Anderson and van Wincoop, 2003; Bernard, Jensen, Eaton and Kortum,
2003; Melitz, 2003) and provides novel quantitative insights about the welfare gains from
trade liberalization at both individual and aggregate levels.
7
There are alternative ways to introduce heterogeneity in workers. Differences in abilities (Blanchard and
Willmann, 2011), skill intensities (Costinot and Vogel, 2010) or distribution of human capital endowments
(Bougheas and Riezman, 2007) are all viable options. The solution of the model does not depend on the
interpretation of capital, kid . Here, I interpret capital as physical capital without loss of generality.
8
I use deciles to approximate the distribution of capital simply because no data are available on a more
disaggregated level. On the other hand, I find that using less disaggregated measures such as quartiles or
quintiles would convolute the differences between the poor and the rich to the point when income inequality
is no longer as important (for example see Fieler, 2011).
7
3.1
Households
Households of type d in country i maximize consumption of the non-tradable good, cni , the
tradable manufacturing good, cmi , and the tradable agricultural good, cai , according to the
following nested Stone-Geary utility function:
α
1−α
U = (cβni c1−β
s.t. yid = cni pni + cmi pmi + cai pai ,
mi ) (cai − µ)
(3.1)
where pni , pmi , and pai are prices of the non-tradable, manufacturing, and agricultural goods,
respectively. Let me denote labor as li and capital as ki , then total per-capita income of a
household of type d in i is yid = (li wi + kid ri ) + vi , where wi is the wage rate, ri is the capital
rental rate, and vi are total per-capita transfers.9
The utility function in (3.1) captures non-homotheticity of preferences through the term µ,
which can be interpreted as a subsistence level of income10 . As long as yi,d > µpa the value
of final demands of type-d consumers in country i are given by:
cai,d pai = (1 − α)yid + αµpai ,
(3.2)
cni,d pni = αβ(yid − µpai ),
(3.3)
cmi,d pmi = α(1 − β)(yid − µpai ),
(3.4)
yid
whenever yid ≤ µpa . The demand equations
pai
in (3.2)-(3.4) can be normalized by total income of consumers of type d to get expenditure
cai,d pai
shares in that decile. For instance, consumer of type d in country i spends sai,d ≡
yid
on agricultural goods.
and cni,d pni = cmi,d pmi = 0, and cai,d pai =
For a given distribution of yid , I also derive country-level income shares spent on non9
Total per capita transfers subsume tariff and tax revenues, and transfers from other countries including
foreign aid.
10
For further discussion of Stone-Geary preferences refer to Markusen (2010).
8
tradables, tradables and agricultural goods – sni , smi , and sai – respectively, which are
defined as follows:
PD
sni =
d=1 cni,d pni
;
P
D
y
id
d=1
PD
smi =
d=1 cmi,d pmi
;
PD
y
id
d=1
PD
sai =
d=1
P
D
cai,d pai
d=1 yid
,
(3.5)
1 PD
yid as the average level of real income per capita. This will
D d=1
turn out to be useful in subsequent sections.
Let me also define ȳi =
3.2
Production
I model production in the spirit of Eaton and Kortum (2002) because multi-country Ricardian11 models calibrated to real data mimic both aggregate trade flows and average levels of
real income per capita with high accuracy.12 This allows me to provide clear quantitative
predictions in the counterfactual section that have straightforward interpretations relative
to the benchmark data.
Each country is endowed with a fixed measure of capital and labor. Besides these two factors
of production, firms in all sectors employ Spence-Dixit-Stiglitz (SDS hereafter) aggregates of
the non-tradable and manufacturing goods, and firms in the agricultural sector also employ
the SDS aggregate of the agricultural goods.13 This way of modeling sectoral production is
consistent with the data in input-output tables.
Non-tradable sector
Let ni be the output of the non-tradable good, mi , the quantity of the manufacturing ag11
Although, the model here departs from the conventional Ricardian models in terms of consumer heterogeneity and non-homothetic preferences, the production structure specified here is identical to the one
specified in Eaton and Kortum (2002).
12
For example, see Alvarez and Lucas (2007) or Egger and Nigai (2012).
13
Consistent with the literature and the OECD classification I classify industries in three broad sectors:
Agricultural goods, Manufacturing goods and Non-tradable goods. The SDS aggregates are produced according to a conventional CES technology with the elasticity parameters 1−σa and 1−σm for the agricultural
and manufacturing sectors respectively.
9
gregate and ai , the quantity of the agricultural aggregate. I assume that each country has
a unit measure of firms in the non-tradable sector producing identical non-tradable output
using constant-returns-to-scale technology:
ni = (liν ki1−ν )φ (n%i mi1−% )1−φ ,
(3.6)
accordingly the price of the non-tradable good is:
1−φ
,
pni = Γn (wiν ri1−ν )φ (p%ni p1−%
mi )
(3.7)
where Γn is a sector-specific constant.
Manufacturing sector
Each country hosts a measure of firms each producing a unique variety with a productivity
drawn from a Fréchet distribution. The productivity is a realization of a random variable
zmi distributed according to:
−θm
Fmi (zmi ) = exp(−λmi zmi
),
(3.8)
where λmi is a country-specific productivity parameter and θm is a dispersion parameter
which is common across all countries. Each firm in the sector employs labor, capital, nontradable and manufacturing aggregates in the following way:
)1−ξ ,
mi (q) = zmi (q)(liν ki1−ν )ξ (nζi m1−ζ
i
(3.9)
where q denotes different varieties of the manufacturing goods. The probabilistic representation of technologies allows me to derive the average variable cost of a producer of a
manufacturing variety in country i:
10
ν 1−ν ξ ζ 1−ζ 1−ξ
m
κmi = Γm λ−θ
) (pni pmi ) ,
mi (wi ri
(3.10)
where Γm is a sector-specific constant. The average variable cost κmi along with the sectorspecific iceberg trade costs τm,i` and the ad-valorem tariff rate tm,i` are sufficient to derive
the aggregate price of tradables in i as follows:
pmi =
N
X
!− θ1
m
(κ` τm,i` tm,i` )−θm
.
(3.11)
`
Agricultural sector
Similar to the firms in the tradable sector, firms in the agricultural sector each produces
a unique variety with a total factor productivity parameter drawn from a country-specific
productivity distribution:14
−θa
Fai (zai ) = exp(−λai zai
).
(3.12)
The respective expression of the production function of a producer of an agricultural variety
h in i is:
ai (h) = zai (h)(liν ki1−ν )γ (ni mρi a1−−ρ
)1−γ .
i
(3.13)
An important feature of the production of agricultural goods is their dependence on the
aggregate agricultural input. This is not the case for the firms in the non-tradable and
manufacturing sectors.15 This modeling choice is consistent with the data on the production
inputs in the three sectors. The price of the agricultural aggregate can be expressed using
14
The productivity distributions of the tradable and agricultural sectors are identical in terms of the
family class but not the underlying parameters. I estimate the parameters for each of them in the following
sections.
15
This approach is consistent with Caliendo and Parro (2011) who use input-output tables to account
for the inter-dependence of industries. My formulation uses information from the input-output tables in a
similar way but on a more aggregate level.
11
average variable cost in i’s partner countries, κan , iceberg trade costs specific to that sector,
τa,in , and an import tariff ta,in :
pai =
N
X
!− θ1
a
(κa` τa,i` ta,in )
−θa
.
(3.14)
`
3.3
International trade
International trade occurs in the manufacturing and agricultural sectors. Firms producing identical varieties in different countries compete vis-á-vis each other given geographical
and policy barriers to trade. The probabilistic representation of technologies permits the
derivation of trade shares in a straightforward way:
(κmn τm,in tm,in )−θm
xm,in = PN
,
−θm
` (κm` τm,i` tm,i` )
and
(κan τa,in ta,in )−θa
xa,in = PN
−θa
` (κa` τa,i` ta,i` )
(3.15)
Trade shares, however, are not sufficient to close the model. It is necessary to derive total
spending of each country on both manufacturing and agricultural goods and specify the market clearing conditions. To do this I derive i’s total absorption capacities of manufacturing
and agricultural goods, respectively. Let Yni , Ymi , and Yai be the total sectoral output of the
non-tradable, manufacturing, and agricultural goods, respectively, and let Dni , Dmi , Dai be
net imports in the respective sectors. Consistent with Bernand, Eaton, Jensen and Kortum
(2003), I define total absorption in a sector as total output plus net imports. The absorption,
however, is nothing but the sum of intermediate and final demands. Hence, the following
identity must hold:

 
 
Yni
Dni
(1 − φ)%

 
 

 
 
Ymi  + Dmi  =  (1 − ξ)ζ

 
 
Yai
Dai
(1 − γ)
(1 − φ)(1 − %)
(1 − ξ)(1 − ζ)
(1 − γ)ρ
 
Yni
sni

 

 
+




0
Y
0
  mi  
(1 − γ)(1 − − ρ)
Yai
0
0

0
smi
0


Yi
 
 
0   Yi  ,
 
sai
Yi
0
(3.16)
here Yi is total income of consumers in i. Let fni , fmi and fai be the ratio of the absorption
12
capacities of the non-tradable, manufacturing and agricultural sectors, respectively, to total
expenditures in i, then (3.16) can be reformulated as follows:





 Yni   Dni  fni 0
  
 
Y  + D  =  0 f
mi
 mi   mi  
  
 
Yai
Dai
0
0
 
0  Yi 
 
 
0
 Yi  .
 
fai
Yi
(3.17)
Here fni , fmi and fai are functions of production parameters, sectoral trade imbalances, and
country-level consumption shares, defined by consumption shares of consumers of each type
d in i. The latter depend on both the average level of income per capita and the level of
income in different deciles in each country.
To close the model, I assume that total imports, IMi , equal total exports, EXi up to a
country-specific constant Di 16 :
Di = EXi − IMi , where
IMi = (Li wi + Ki ri + Li vi )
EXi =
N
X
(3.18)
N
X
(fmi xm,in + fai xa,in ) ,
(3.19)
n=1
(Ln wn + Kn rn + Ln vn ) (fmn xm,ni + fan xa,ni ) .
(3.20)
n=1
The central difference of (3.18) from the Ricardian models with homothetic preferences
and/or homogeneous consumers is in terms fmi and fai . In those models, the shares are
assumed to be constant across all countries and consumers. On the contrary, here fmi
and fai can be viewed as a link between the non-homotheticity of preferences, consumer
heterogeneity, and total import demand.
16
Closing the model in this way is in the spirit of Dekle, Eaton and Kortum (2007), where Di is an
exogenous deficit constant observed in the data
13
4
Calibration
I calibrate the model to 92 countries in the world.17 The reference year for all the data is
1996. I describe the data sources in the Appendix.
For the counterfactual experiment I need to calibrate the parameters of the utility function
and the production functions in the three sectors. I also need to estimate θm and θa . I solve
for the counterfactual values in the spirit of Dekle, Eaton and Kortum (2007) and do not
have to estimate λmi , λai , τm,in , and τa,in since those are taken as primitives (constants) in
the model.
4.1
Parameters of the utility function
Calculating β, which governs the ratio of the consumption of non-tradable to manufacturing
goods, is straightforward given the data on households’ spending. This share is constant
across countries and does not vary much with the average level of per-capita income. This is
confirmed in the left panel of Figure 1 where I plot the ratio of the total non-tradable consumption in each country to the total manufacturing consumption. It is then straightforward
to infer the value of β from the following:
P
N
1 X pni d cni,d
β
P
=
1−β
N i=1 pmi d cmi.d
(4.1)
The calculated average is (1.96) with a standard deviation of (0.62) which implies β = 0.38.
Estimating the remaining two parameters α and µ is more challenging because, unlike β, the
share of income spent on agricultural goods is not constant across countries and is consistently
17
The limitations of the data do not allow me to extend the sample further. However, the 92 countries
in the sample include all large countries in the world. Hence, the calibrated model is very close to reflecting
the world in economic terms. The sum of GDP’s of the 92 countries in the sample constituted to about 93%
of total world GDP in 1996.
14
correlated with real income of an average household in country i. The relationship18 is
seemingly non-linear as shown in the right panel of Figure 1 where I plot the ratio of total
consumption in agricultural goods to the remaining expenditures.
Figure 1: Expenditure Ratios versus real Average Real Income per Capita
The reason for this strong relationship is the non-homotheticity of household preferences.
This has been well documented in the literature.19 Modeling this relationship using StoneGeary preferences has two advantages. First, the utility function leads to tractable linear
demand functions. Second, the parameters of the utility function have straightforward and
intuitive interpretation.20
Calibrating α and µ is a non-standard optimization problem. To estimate these parameters,
I minimize the squared distance between country-level expenditure shares predicted by the
model as described in (3.5) in Section 3.1:
18
This is the maximum number of observations of the data in Penn World Tables. Benchmark year 1996.
Fieler (2010) introduces non-homothetic preferences into a Ricardian Eaton-Kortum type model. Simonovska (2010) links non-homotheticity to the concept of pricing to market using a unique dataset for the
OECD countries. Markusen (2010) demonstrates that non-homothetic preferences can resolve many puzzles
of international economics.
20
Tombe (2012) uses Stone-Geary preferences to explain trade patterns in food products between poor
and rich countries. A minor departure of this paper from the literature is in the specification of the utility
function – a nested functional form which is easier to calibrate and interpret.
19
15
min
N
X
α,µ
(sai − sai (α, µ))2 s.t. α ∈ [0, 1],
(4.2)
i=1
where sai are the data and sai (α, µ) is the function of α and µ, which given the value of β
and the data on yid and pai , is calculated as in (3.5). Solving (4.2) yields α = 0.8860 and
µ = 0.0017. The fit of calibration is good, the correlation between the predicted and actual
sai is 0.92.21
4.2
Parameters of the production functions
The only parameter common to all three production functions is the capital-labor ratio
parameter ν. Consistent with the literature in macroeconomics and international trade (for
example, see Gollin, 2002), I set ν = 0.67.
The rest of the production parameters are calculated using input-output tables as follows.
The parameters {φ, ξ, γ} govern the share of value added in the non-tradable, manufacturing
and agricultural sectors, respectively. I calculate them as a ratio of value added to the total
output in the respective sector. Similarly, the parameters {%, ζ, , ρ} are calculated from the
ratio of total non-tradable input to total manufacturing input. Cross-country averages and
standard deviations of the production parameters are provided in Table 1.
Table 1: Production parameters
mean
std.deviation
N
φ
0.5474
0.0574
39
ξ
0.2919
0.0363
39
γ
0.4995
0.1101
39
%
0.6822
0.1046
39
ζ
0.3154
0.0842
39
0.2780
0.0778
39
ρ
0.3829
0.1243
39
Notes: The parameters were calculated using the data on Argentina, Australia, Austria, Belgium, Brazil, Canada,
Chile, China, Czech Rep., Denmark, Estonia, Finland, France, Germany, Greece, Hungary, India, Indonesia, Ireland,
Italy, Japan, Korea, Mexico, Netherlands, New Zealand, Norway, Poland, Portugal, Romania, Slovakia, Slovenia,
Spain, Sweden, Switzerland, Turkey, UK, USA, Vietnam. The data for other countries in the sample were unavailable.
I estimate the trade elasticities in the manufacturing and the agricultural sectors – θm and
21
For this calibration exercise and throughout the rest of this paper, all income values are normalized
such that the average real income per capita in the USA is unity.
16
θa – using the data on trade flows and tariffs. Let Xm,in denote manufacturing trade flow
from n to i. Normalize trade flows by the value of domestic sales to get a familiar structural
gravity equation:
Xm,in
=
Xm,ii
κn τm,in tm,in
κi
θm
where τm,in = (τm,i τ̃m,in τm,n ).
(4.3)
I assume total trade costs τm,in to be log-additive with tariffs and consist of an exporterspecific asymmetric component – τm,n , an importer specific asymmetric component – τm,i ,
and a symmetric component τ̃m,in . Consistent with the literature, I proxy for the symmetric
component of trade costs τ̃m,in using a distance measure and an adjacency dummy.22 The
two asymmetric trade cost components will be captured by respective country-specific fixed
effects. I estimate the following stochastic version of (4.3):
Xm,in
= exp[log(exn ) + log(imi ) − θm log(tm,in ) − θm log(τ̃m,in )] + errorin , (4.4)
Xm,ii
where imi and exn are catch-all importer and exporter fixed effects, respectively. Notice that
the coefficient on tariffs between i and n identifies θm .23 I estimate θa using data on Xa,in
and ta,in in the same fashion. I chose to estimate (4.4) in levels rather than in logs to avoid
the problem of zeros.24 The trade data for the 92 countries include a considerable number of
zeros and dropping those may lead to inconsistent marginal effects. In practice, I maximize
the respective Poisson Pseudo Maximum Likelihood function as advocated by Santos Silva
and Tenreyro (2006). The estimates are θ̂m = 6.53(1.23) and θ̂a = 12.07(1.16)
22
25
.
The coefficients on distance and adjacency variables have the expected signs and due to the solution
strategy are of no particular interest, hence not reported.
23
Caliendo and Parro (2011), Ramondo and Rodriguez-Claire (2009), Egger and Nigai (2011, 2012) use
tariffs to identify the elasticity of trade. The critique of Simonovska and Waugh (2011) is not particularly
pertinent to the methodology here because: (i) I do not use price data for identification of the trade elasticity
and (ii) the results for manufacturing sector are reasonably close to Simonovska and Waugh (2011) and other
estimates in the literature. For example see Donaldson, Costinot and Komunjer (2012).
24
For example, see Baldwin and Harrigan (2011) or Chor (2010).
25
Standard errors in parenthesis are based on Eicker-White sandwich estimates and are robust to heteroskedasticity of an unknown form.
17
The values of θm and θa suggest that differences in technology and factor prices are relatively
larger and more important for trade in the agricultural sector. This is consistent with Tombe
(2012) who points our that the productivity gap between rich and poor countries is especially
pronounced in agriculture.
4.3
Benchmark distribution of capital
I use the data on the distribution of income to calibrate the model to the observed levels of
heterogeneity across consumers. The benchmark level of real income is:
yid = (li wi + ri kid ) + vi ,
(4.5)
here capital ownership, kid , is the only source of heterogeneity. Total government transfers,
vi include foreign aid, credits and tariff revenues. I calculate vi as the sum of the current
account balance (net of trade deficit) and tariff revenues given benchmark levels of tariffs
tm,in and ta,in .26 I, then, use the data on the income distribution in each country to pin down
the values of kid .
5
Predictions of the model
General equilibrium models of trade often fail to predict two stark relationships between
trade and income that are evident in the data: (i) trade increases in income per capita, and
(ii) trade and within-country income inequality are correlated. Many recent papers have
tackled the former issue by incorporating non-homothetic preferences into trade models. My
approach is consistent with previous work and provides predictions in line with the data.
The latter issue, however, has been largely ignored in general equilibrium analysis of trade.
26
All values here are in real terms per capita.
18
Numerous empirical studies have suggested that trade liberalization episodes have been characterized by a substantial increase in income inequality. For an excellent overview of recent
advances in the research of trade and inequality refer to Goldberg and Pavcnik (2004, 2007).
In addition, a number of empirical papers have found a considerable amount of evidence in
support of Linder’s (1961) hypothesis – countries with similar income distributions tend to
trade more. I introduce within country differences in capital owned by households, which,
together with a non-homothetic preference structure, link income inequality to total import
demand. The model delivers predictions in line with the empirical findings on trade and
income inequality.
5.1
Trade and per-capita income
It is a well established fact that total bilateral trade increases with per capita incomes of
both exporter and importer. Hence, it is essential for a model to provide clear-cut predictions
with respect to this relationship. Fieler (2011) criticizes conventional trade models because
they predict that trade increases in total income, regardless of the distribution of population
relative to average income. On the other hand, the data suggest that trade increases in real
income per capita rather than population. The model here captures this feature of the data
well and is not subject to Fieler’s critique.
To illustrate that the model does provide predictions consistent with empirical findings
consider the following. Recall that Xm,in and Xa,in are total trade flows from n to i in
manufacturing and agricultural goods, respectively. These can be decomposed into the
supply and demand effects.
Xm,in =
×
fmi
×
Yi
,
xm,in
|{z}
|{z}
| {z }
supply side expenditure share market size
|
{z
}
demand side
19
(5.1)
and a similar expression for Xa,in . Notice that xm,in depends only on technology and relative
factor prices, and is independent of the structure of preferences. However, fmi , the share
of aggregate expenditure Yi spent on tradables depends on smi .27 To see the argument in a
simple way assume that yi,d > µpa for all d. Then we can decompose total bilateral imports
of i from n from (5.1) as follows:
PD
Xm,in = Φxm,in ×
D
Lid (yid − µpai ) X
×
Lid yid = Φxm,in × Li × (ȳi − µpai ),
PD
d=1 Lid yid
d=1
d=1
(5.2)
where Φ is a constant. The model predicts that bilateral imports Xm,in are increasing in
average real income per capita, ȳi faster than in the population Li , ceteris paribus. The same
holds for trade flows in agricultural goods.
5.2
Income inequality and trade
Trade models based on the assumption of a representative consumer fail to capture the
strong link between the income distribution and international trade. A number of empirical
papers (for example, see Bernasconi, 2011) have found strong evidence of a correlation of
within-country income distribution similarities across countries and bilateral trade. This
goes back to Linder’s (1961) hypothesis of overlapping demands. The present model delivers
predictions consistent with that hypothesis.
For simplicity, in (5.2) I reduced total country demand to a function of total population,
average income per capita and prices. To do that I assumed that yi,d > µpai for all i, d. Of
course, in reality yid ≤ µpai for some i, d. This is where the distributional effects begin to
matter.
Suppose, I endowed all countries in the world with the distribution of capital observed in
the United States while keeping the average level of real income per capita unchanged. If
27
Input share parameters are assumed to be constant across all countries. Hence, the change in fmi is
proportional to the change in smi .
20
inequality were an insignificant determinant of import demand schedules, one would not see
significant changes in fmi (the same holds for fai and fni ). On the other hand, if one observed
large changes in country-level import demand solely due to changes in the distribution of
income, he could conclude that the model captures the link between income inequality and
trade.
I conduct the following thought experiment to illustrate how income distribution shapes
import demands at a given level of average income. I use the data on the distribution of
real income in the USA and set yid in all other countries so that the distribution of income
is exactly the same as in the USA. I keep the levels of average real income unchanged. In
Figure 2, I plot changes in fmi versus the average real income per capita.
Figure 2: Income Inequality and Import Demand
Poor countries, where income inequality is relatively more pronounced, would spend a lower
share of their total expenditure on manufacturing if they had less income inequality. This
may seem counter-intuitive but at a given level of average real income, poor countries that
exhibit relatively more income inequality must also have a higher import demand. The
intuition behind is as follows. Positive demand for manufacturing goods can be realized only
if at least one consumer in i has an income higher than the subsistence level. In very poor
countries, an equal distribution of income would imply that no consumer has enough income
21
to buy manufacturing goods. On the other hand, very high inequality could allow the richest
households to have positive import demand. The results displayed in Figure 8 with regard
to the impact of income inequality on trade is in line with the earlier empirical evidence
(see Goldberg and Pavcnik, 2004; 2007) and the theoretical argument proposed by Linder
(1961).28 This effect is completely missing in trade models with a representative consumer.
The model also has strong predictions with regard to the reverse effect, i.e., the effect of
trade on income inequality. I discuss this link in the context of a counterfactual global trade
policy liberalization scenario in Section 6.3.
To understand the mechanics behind the link between income inequality and trade, consider a
hypothetical case of two countries with different income distributions and identical otherwise.
For simplicity assume that d = {1, 2, 3}. Total income, population and all prices in both
countries are equal to unity. Incomes are distributed as {0.3, 0.3, 0.4} in country 1 and as
{0.1, 0.1, 0.8} in country 2. Further assume that µpai = 0.2 in both countries. In that case
total demands for manufacturing in countries 1 and 2, respectively, are:
1
1
1
× (0.3 − 0.2) + × (0.3 − 0.2) + × (0.4 − 0.2) = 0.13
3
3
3
1
1
1
=
× 0 + × 0 + × (0.8 − 0.2) = 0.2,
3
3
3
fm1 × Y1 =
(5.3)
fm2 × Y2
(5.4)
This is a simple example of how countries that are different with respect to their income
distribution only can have very different import demand schedules.
In that sense, the model here is substantially different from other trade models with nonhomothetic preferences. For example, Fieler (2011) provides a brief discussion of the role of
income distribution in shaping international trade flows. She finds that income inequality
has a very small impact, if any, on import demand schedules. The reason for this is twofold.
First, she uses quintiles of the income distribution so that differences between the richest and
28
In terms of the quantitative predictions of the model I calculate the squared distance between benchmark
Gini-coefficients for each pair of countries and correlate it to the total trade. The correlation is −0.11 which
suggests that countries that are more similar in terms of the income distributions trade relatively more.
22
the poorest consumers are not as pronounced as here. Second, Stone-Geary preferences have
a discontinuity at the level of subsistence so that both the extensive and intensive margins of
consumption are important. Preferences specified in Fieler (2011) are continuous in a sense
that each consumer always spends some part of her income on each type of good.29
6
Counterfactual experiment
For the counterfactual experiment, it is useful to express the model in relative changes. Let
a denote benchmark and a0 counterfactual values of some variable, then the relative change
is b
a = a0 /a. This approach is particularly convenient because one may assume that the
primitives of the model, τin and λi , do not respond to indirect shocks and one can conduct
counterfactual experiments without having estimated these unobservable fundamentals.30
In the counterfactual experiment, I globally eliminate all import tariffs to assess the effect of
this hypothetical policy on real income, welfare and income distribution. Tariffs are asymmetric in the outset, hence for this counterfactual exercise I reduce tariffs in an asymmetric
manner:
t0a,in = 1 and t0m,in = 1 such that b
ta,in = (ta,in )−1 ; b
tm,in = (tm,in )−1 for all i, n.
(6.1)
which effectively means zero MFN-tariffs for all countries in both tradable sectors. I list
expressions for the counterfactual values of all variables and describe the solution algorithm
and the data in the Appendix.
For the comparative static experiment I choose three outcomes of interest: average real
incomeȳi ,31 welfare (decile-specific ωid and aggregate Wi ), and the within-country income
29
This is a well-known property of any CES-related demand system.
See Dekle, Eaton and Kortum (2007), Caliendo and Parro (2011), Egger and Nigai (2011)
31
Real income may be measured in many different ways, here I stick to the conventional definition, i.e.,
real income is a ratio of nominal income to a country-specific price index.
30
23
distribution.
6.1
Trade liberalization, real income and welfare
Conventional wisdom suggests that trade liberalization on average has positive aggregate
effects in terms of real income. First, let me consider the effect of a complete elimination of
tariffs on the average real income per capita as parameterized for the year 1996. I plot the
counterfactual change in ȳi against its initial values in Figure 3.
Figure 3: Trade Liberalization and Real Income Per Capita
The results in Figure 3 are consistent with the large body of literature on the effects of trade
liberalization. Numerous empirical and theoretical works found that trade liberalization
leads to higher income per capita on average, much more so for small economies. Smaller
countries gain relatively more because with lower barriers they are able to specialize on the
production of goods where productivity is high. In this experiment, bigger countries lose a
little in terms of the average real income per capita. The reason for this is twofold. First, the
initial tariff matrices are asymmetric and developing countries initially face relatively higher
24
tariffs. Accordingly, they benefit relatively more from trade liberalization.32 Second, in the
counterfactual equilibrium rich countries face tougher competition from poor countries that
start exporting relatively more through specialization. In general, the results of the counterfactual exercise, as far as changes in the average real income per capita are concerned, are
very much in line with both the empirical literature and other computable general equilibrium models of trade (for example, see Alvarez and Lucas, 2007). The exact counterfactual
results for all countries and all relevant variables are in Tables 3-4 in the Appendix.
Next, let me examine whether average real income per capita is an adequate metric for the
evaluation of welfare effects of trade liberalization for different type of consumers. For each
ω0
decile d in each country i, I calculate counterfactual change, ω
bid = id .
ωid
In Figure 4, I plot welfare changes of the 1st , 5th and 10th deciles of the distribution of
consumers in each country against the change in the average real income per capita. The
results of the counterfactual exercise for all deciles are in Tables 3-4.
Figure 4: Change in Average Real Income per Capita versus Change in Welfare (by decile)
If average real income per capita were an adequate measure of welfare for all types of consumers the scatter points would lie on the 45 degree line in all three panels. Serious deviations from the 45 degree line suggest that ȳi is not an appropriate metric for some consumer
groups. Figure 4 shows that as one goes from the richest to the poorest households, average
32
As a sensitivity check, I conduct a counterfactual exercise which reduces trade costs symmetrically by
the same margin. In that case, all countries gain but smaller countries still gain relatively more. The results
are available upon request.
25
real income per capita becomes less and less relevant. Notice that changes in welfare and
average real income per capita are practically identical for the decile of consumers with the
highest income per capita. The relationship is much weaker for consumers in the 5th decile
of the distribution (although still positive). Finally, the left panel of the figure suggests that
changes in the average income per capita and changes in welfare for the poorest income
groups are largely unrelated.
To formally show that average income per capita is not a good predictor of welfare gains (at
least for some consumer groups) I run the following regression:
ω
bid = πd yb̄i + errorid .
(6.2)
If ȳi were a good measure of welfare gains then πd would be close to unity. The results in
Table 2 suggest that this is true only for the highest and second highest deciles. For all other
deciles the estimate of πd is considerably different from unity, with high standard errors and
low explanatory power.
Table 2: Measurement Bias
π̂d
-0.26
0.27
0.4
0.49
0.57
0.64
0.72
0.79
0.87
1.02
d = 10
d=9
d=8
d=7
d=6
d=5
d=4
d=3
d=2
d=1
std.error
0.47
0.14
0.11
0.09
0.08
0.07
0.06
0.05
0.04
0.03
R2
0.01
0.06
0.19
0.35
0.49
0.63
0.75
0.86
0.93
0.97
max
88.15
16.83
11.21
9.32
8.64
8.08
6.22
4.35
2.68
1.01
min
-11.33
-8.48
-7.13
-6.24
-5.59
-4.95
-4.34
-3.68
-2.87
-2.88
mean
2.34
1.05
0.85
0.71
0.61
0.49
0.36
0.24
0.1
-0.14
std. dev.
12.73
4.6
3.59
2.97
2.52
2.12
1.73
1.34
0.97
0.59
s+
d
0.49
0.58
0.61
0.64
0.66
0.67
0.67
0.65
0.57
0.42
Notes: Standard errors are robust to an unknown form of heteroskedasticity. The number
of observations for each regression is 92.
For each decile d in each country i, I also calculate the measurement error meid . Recall,
that I defined it as:
26
meid ≡ 100 ×
yb̄i
−1 .
ω
bid
(6.3)
Expression in (6.3) measures by how much changes in the average real income per capita
overpredict changes in decile-specific welfare. I plot meid in Figure 5.
Figure 5: Measurement Errors (by deciles)
The dispersion of med is considerably higher for relatively poor consumers. For the poorest
decile the measurement errors are in the interval [−11%, 88%] with relatively equal shares of
of positive (overprediction) errors and negative (underprediction) errors. I report the share
of positive measurement errors, denoted by s+
d , along with the other descriptive statistics in
Table 2.
The range of med becomes smaller as one goes from the poorest to the richest consumer. The
range is between [-5%,8%] for the median consumer and between [-3%,1%] for the richest
consumer, respectively. The same tendency holds for the dispersion of errors measured in
terms of the standard deviation. The statistics in Table 2 suggest that overall med is small
for d = 1, hence yb̄i is a good measure of welfare for very rich consumers.
There is an inverse U-shaped relationship between s+
d and d. Average real income per
capita tends to overestimate the gains from trade for consumers in the middle of the income
27
distribution. However, this measure underestimates the gains for consumers in the right
tail of the income distribution. The reason for this are differences in the relative price and
nominal income effects that vary across different deciles.
Policy makers may be interested in targeting certain consumer groups when considering trade
liberalization policy. However, it may also be useful to have a measure of aggregate welfare
gains of a country. As is well known, this is not an easy task. Welfare effects are largely
heterogeneous across different consumer groups which makes evaluating overall welfare gains
quite challenging. One way to proceed is to assume a simple, yet intuitive, unweighted
utilitarian social welfare function33 such that the social welfare is the sum of utility measures
P
across different deciles of consumers: Wi =
d ωi,d . Is ȳi a good measure of the overall
social welfare gains? In Figure 6, I plot counterfactual changes in the average real income
per capita versus changes in the measure of aggregate welfare – Wi .
Figure 6: Change in Average Real Income per Capita versus Change in Total Welfare
Figure 6 suggests that average real income per capita is a noisy measure of the aggregate
welfare. The range of the measurement error is between −6% and 8%. On average, changes
in real income per capita tend to be larger than changes in aggregate welfare. The share
33
The results are even stronger for some other measures of social welfare such as Rawlsian welfare function.
28
of positive errors is s+ = 0.58 which suggests that ȳi is likely to overpredict true aggregate
welfare gains.
6.2
On the mechanics of heterogeneous welfare effects
Welfare gains of poor consumers largely differ from the predictions based on the change in
average real income per capita. For example, according to Figure 3 consumers in Mexico
and Chile on average should gain approximately 2.5% and 1% in welfare, respectively. The
effects are reversed for the poorest consumers in both countries. Welfare of poor consumers
in Mexico and Chile actually falls by about 20% and 5% respectively. This is depicted in
Figure 7 where I plot welfare gains of the poorest consumer groups (lowest decile of per-capita
income) in all countries.
Figure 7: Trade Liberalization and Welfare (for the 10th Decile)
What exactly drives these differences? To understand the mechanics behind, I conduct an
additional experiment. Up to this point, I assumed that trade liberalization takes place
instantaneously. However, in order to understand the main drivers of the results, it is useful
to consider liberalization as a gradual process. Let ς be a step function such that ς =
(0, ..., 20), each step is a discrete jump from the benchmark towards full trade liberalization.
Hence, at ς = 0 the model is exactly as in the benchmark case, and at ς = 20 the model is
29
0,ς
exactly as in the case of full trade liberalization. Let t0,ς
a,in and tm,in be the counterfactual
values of tariffs at step ς in the agricultural and manufacturing sectors, respectively. I define
them as follows:
t0,ς
a,in = ta,in −
ς
(ta,in − 1)
20
and
t0,ς
m,in = tm,in −
ς
(tm,in − 1) for all i, n.
20
(6.4)
For each step ς, I calculate the counterfactual change (in percent) in Yid , Pid , and ωid . Notice
that one can decompose34 welfare gains ∆ωid (hereafter ∆ denotes change in %) into the
nominal income effect, ∆Yid , and the price effect – ∆Pid as:
∆ωid = ∆Yid − ∆Pid
(6.5)
In Table 2, I argued that changes in average income per capita do not reflect individual
welfare gains of poor consumers. In fact, if one employs ωid instead of ȳi as a measure of
welfare the effects are reversed for many countries in the sample. For example, counterfactual
change in ȳi in Chile is positive (around 1 % in Figure 3). On the other hand, Figure 7
suggests that the poorest decile in Chile loses in terms of welfare (around 5%). What drives
this large difference? I use the decomposition in (6.5) to answer this question. The model
predicts that real returns to labor and capital increase by 3% in Chile. At the same time,
zero-MFN tariffs imply that consumers lose all of the tariff revenues. This trade-off is good
for those who own a lot of capital and bad for those who own little.
Higher labor and capital costs increase prices of agricultural goods by relatively more.35 Poor
consumers spend most of their income on agricultural goods. Hence, the price effect has an
additional negative effect on their welfare. In Figure 8, I plot total welfare gains, income and
price effects for the 1st , 5th and 10th deciles in Chile for each counterfactual step ς. Notice
34
35
Log-linearize (2.1) and multiply both sides by 100 to get (6.5).
That the home bias is larger in the agricultural sector than in manufacturing is a well-documented fact.
30
Figure 8: Step-wise Trade Liberalization: Price and Income Effects
that as countries start reducing tariff revenues, consumers in the poorest decile lose in terms
of the nominal income and prices. This happens because they own very little capital so that
the increase in the price of that factor cannot compensate for losses in tariff revenues. Hence,
their total welfare gains are strictly negative. Consumers in the median decile own enough
capital to have positive total nominal income effects. But their decile-specific price index
increases relatively more. As a result, their total welfare gains are negative. Finally, the
richest households in Chile own enough capital so that their income effect overcompensates
the increase in the price index. This leads to positive welfare gains. It bears noting that the
price effects are strongest for the poorest consumer group.
6.3
Trade liberalization and income distribution
The purpose of this section is to demonstrate that the model delivers quantitative predictions
consistent with the empirical literature in terms of the effect of trade liberalization on income
inequality. The empirical evidence suggests that, during the last quarter of the twentieth
century, many developing countries experienced acute increase in the income inequality part
31
of which can be attributed to higher trade (see Goldberg and Pavcnik, 2004; 2007).36 Does
the model provide credible predictions in that respect?
To answer this question I have to measure real income per capita of different consumer groups
in a way consistent with the empirical literature. For that, I use decile-specific income yid
measured as a ratio of total nominal income of consumers of type d in country i deflated by
the country-specific price index:
yid =
Yid
sai smi sni .
Lid pai pmi pni
(6.6)
I use the benchmark and counterfactual values of yid to calculate the Gini-coefficient, denoted
by Gi in the pre and post-liberalization periods. I plot the results of the counterfactual
experiment in Figure 9.37
Figure 9: The Effect of Trade Liberalization on the Distribution of Income
Global liberalization of trade increases inequality for most countries. The majority of devel36
A notable exception from numerous case studies conducted on the subject is Porto (2006) who estimates
distributional effects of joining MERCOSUR for Argentina. The author uses household survey data and
shows that on average joining MERCOSUR had positive effects on welfare of poor and middle-income
consumers and reduced inequality. My results do not contradict Porto’s findings. To simulate the natural
experiment examined in Porto (2006), I conduct a separate counterfactual exercise. I reduce import tariffs
set by Argentina only. The model predicts that inequality in Argentina decreases by 2.2%.
37
I repeated the exercise using alternative measures of inequality such as the percentile ratio. The results
turn out to be quantitatively robust to those manipulations.
32
oping countries experiences an increase in income inequality. The effects in the rich countries
are less pronounced.
Essentially, the effects of trade liberalization on the distribution of real income can be decomposed into changes in nominal income and changes in common price index as illustrated
in Section 6.2. It is intuitive that a reduction in income inequality must come from either
higher income of consumers in the left tail of the distribution or equivalently lower income
of consumers in the right tail of the distribution. As I argued, trade liberalization is likely to
raise income of the rich and reduce income of the poor which leads to the increase in income
inequality as in Figure 9.
7
Conclusion
I have developed a multi-country model of trade with non-homothetic preferences and heterogeneous consumers. The model reflects empirically established facts in a few novel dimensions. For instance, the model features a strong link between income inequality within
countries and trade which has been missing in quantitative models of trade.
Perhaps, one of the most important features of the model is its ability to predict large
heterogeneity of consumption patterns of different consumer groups within a country. I
argue that this heterogeneity must be taken into account when evaluating welfare gains from
trade. I show that conventional measures thereof do not capture true welfare gains for poor
and middle-income consumers and tend to introduce a measurement error in the magnitude
between -6% and 8% of aggregate welfare gains.
Admittedly, one of the caveats of the model is the assumption of an exogenous and stationary capital distribution. However, in a multi-country framework endogenous accumulation
and/or the non-stationary distribution of capital would complicate the model significantly.
I leave this for future research.
33
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37
Appendix
7.1
Data
The reference year for all the data is 1996. Trade data are from Feenstra, Lipsey, and Bowen
(1997). I aggregate industry-level trade flows into manufacturing and agriculture trade.
Trade deficit constants Di , Dai and Dmi are calculated as total imports minus total exports
in the respective sector. Data on total GDP, average real GDP per capita, and current
account balance are from the World Bank’s World Development Indicators (WDI) database.
The data on the aggregate expenditure shares sai , smi and sni , and on pai are from the
Penn World Tables.38 The input-output tables are from the OECD’s Structural Analysis
(STAN) database. Distance and adjacency data are from the Centre d’Études Prospectives
et d’Informations Internationales (CEPII). Bilateral tariff data are from the Market Access
Map Database (MacMap) which provides tariff data at the HS2 sectoral level. I calculate
the average import tariff using the classification identical to the one used for the aggregation
of the trade data. Whenever, tariff data were missing in the MacMap database I used tariff
data provided by Mayer, Paillacar and Zignago (2008). Data on the distribution of income
are from UN-WIDER World Income Inequality Database (WIID). If missing, the data were
taken from Klaus and Squire (1996), and/or Milanovic and Yitzhaki (2001).
7.2
Results of the counterfactual experiment
I report all results of the counterfactual experiment in Tables 3-4.
38
Expenditure and price data were not available for all countries in the sample. If missing, the observations
were imputed using average real income and price regressions where pai is a dependant and ȳi explanatory
variable.
38
39
yi10
-0.47
-2.59
1.36
10.13
-2.25
4.29
10.99
5.24
3.83
-0.95
7.52
9.46
-10.46
-9.97
-5.28
-6.03
-34.18
-0.58
0.48
7.70
0.13
-3.67
-4.93
12.34
-1.50
20.57
0.57
8.65
-0.34
-6.01
0.09
0.22
5.06
6.61
2.29
0.87
-40.39
-1.06
9.25
1.72
0.74
3.50
19.77
3.65
-18.48
0.35
ISO
ARG
AUS
AUT
BDI
BEL
BEN
BFA
BGD
BOL
BRA
BRB
CAF
CAN
CHE
CHL
CHN
CIV
CMR
COL
CYP
DEU
DNK
DOM
DZA
ECU
EGY
ESP
ETH
FIN
FJI
FRA
GBR
GHA
GMB
GRC
GTM
GUY
HND
HTI
HUN
IDN
IND
IRL
IRN
ISL
ISR
-0.49
-1.00
-0.02
8.86
-1.62
2.82
8.39
3.65
2.04
-0.89
5.34
5.81
-5.62
-3.23
-3.51
0.16
-3.13
-0.06
0.04
5.01
-0.58
-1.32
-2.60
8.88
-0.63
17.81
-0.40
6.66
-0.99
-1.47
-0.70
-0.63
3.89
4.52
0.56
0.10
-4.34
-1.59
6.92
0.34
-0.10
2.53
-5.41
1.77
-6.97
-0.75
yi9
-0.29
-0.91
-0.44
8.52
-1.29
2.48
7.14
3.24
1.51
-0.70
4.60
4.45
-4.29
-2.87
-2.65
1.92
-0.40
0.36
0.10
4.12
-0.83
-1.29
-1.37
7.31
-0.15
16.17
-0.68
6.03
-1.17
0.77
-0.91
-0.88
3.75
4.29
0.04
0.09
1.78
-1.25
5.90
-0.03
-0.21
2.35
-1.81
1.19
-3.85
-0.89
yi8
-0.16
-0.86
-0.68
8.32
-1.25
2.32
6.19
3.01
1.20
-0.55
4.16
3.57
-3.57
-2.57
-2.02
3.08
0.66
0.63
0.18
3.49
-0.98
-1.19
-0.49
6.21
0.16
14.97
-0.85
5.64
-1.25
2.04
-1.00
-0.99
3.74
4.35
-0.26
0.13
4.99
-0.77
5.08
-0.24
-0.23
2.28
-0.56
0.84
-2.69
-0.92
yi7
-0.09
-0.81
-0.85
8.17
-1.15
2.25
5.36
2.85
0.98
-0.46
3.81
2.88
-3.06
-2.28
-1.50
3.89
1.17
0.82
0.28
2.99
-1.07
-1.10
0.20
5.35
0.40
14.01
-0.97
5.36
-1.30
3.08
-1.06
-1.06
3.79
4.55
-0.48
0.21
7.25
-0.26
4.35
-0.38
-0.21
2.27
0.01
0.59
-2.03
-0.93
yi6
-0.02
-0.70
-0.96
8.08
-1.02
2.22
4.58
2.74
0.81
-0.38
3.53
2.28
-2.64
-2.00
-1.05
4.57
1.53
0.98
0.39
2.56
-1.14
-1.00
0.78
4.63
0.61
13.10
-1.05
5.14
-1.33
3.99
-1.10
-1.10
3.86
4.86
-0.65
0.28
8.86
0.31
3.67
-0.48
-0.16
2.28
0.34
0.40
-1.52
-0.92
yi5
0.04
-0.60
-1.06
8.00
-0.95
2.22
3.78
2.65
0.67
-0.31
3.28
1.80
-2.26
-1.76
-0.63
5.13
1.79
1.10
0.49
2.16
-1.19
-0.90
1.31
3.95
0.79
12.25
-1.10
4.95
-1.35
4.74
-1.08
-1.10
3.94
5.19
-0.79
0.36
10.06
0.91
2.97
-0.55
-0.09
2.31
0.48
0.23
-1.16
-0.92
yi4
0.10
-0.48
-1.15
7.92
-0.90
2.25
2.94
2.58
0.53
-0.25
3.03
1.39
-1.87
-1.56
-0.22
5.64
1.97
1.19
0.60
1.74
-1.23
-0.85
1.82
3.27
0.96
11.36
-1.14
4.76
-1.37
5.54
-1.13
-1.14
4.02
5.61
-0.92
0.44
10.97
1.61
2.27
-0.61
0.00
2.35
0.63
0.08
-0.86
-0.91
yi3
0.15
-0.38
-1.24
7.85
-0.81
2.32
2.05
2.51
0.39
-0.21
2.74
1.02
-1.46
-1.38
0.22
6.15
2.16
1.26
0.73
1.28
-1.28
-0.86
2.34
2.49
1.13
10.31
-1.19
4.56
-1.37
6.35
-1.13
-1.15
4.12
6.11
-1.06
0.53
11.95
2.47
1.49
-0.66
0.11
2.40
0.74
-0.08
-0.59
-0.89
yi2
0.19
-0.28
-1.36
7.75
-0.54
2.47
0.76
2.41
0.17
-0.22
2.24
0.49
-0.83
-1.00
0.83
6.89
2.37
1.33
0.93
0.29
-1.32
-0.85
3.12
1.17
1.39
8.51
-1.24
4.23
-1.32
7.69
-1.14
-1.13
4.32
6.77
-1.27
0.65
14.18
4.20
0.61
-0.67
0.30
2.46
0.85
-0.34
-0.25
-0.87
yi1
0.13
0.03
-1.38
7.63
-0.26
2.68
0.33
2.29
-0.03
-0.37
1.80
0.19
0.05
-0.53
0.85
7.31
2.41
1.22
0.85
-1.20
-1.27
-0.73
3.38
-0.33
1.34
7.32
-1.26
3.97
-1.16
8.29
-1.05
-1.09
4.47
6.74
-1.46
0.57
14.54
4.94
0.21
-0.55
0.38
2.49
0.91
-0.57
0.16
-0.86
ȳi
-0.68
-2.62
1.45
8.36
-2.12
2.59
10.16
4.28
3.24
-1.36
7.85
8.96
-10.40
-9.83
-5.64
-8.95
-34.31
-1.14
0.09
8.03
0.22
-3.53
-5.95
12.40
-2.14
19.21
0.69
6.96
-0.25
-6.11
0.17
0.31
3.44
5.88
2.43
0.26
-39.12
-3.30
10.53
1.86
0.38
1.74
0.00
3.58
-18.12
0.63
ωi10
-0.60
-1.00
0.02
7.07
-1.56
1.98
7.53
2.66
1.65
-1.07
5.49
5.28
-5.60
-3.18
-3.70
-1.68
-3.37
-0.66
-0.11
5.15
-0.54
-1.27
-3.10
8.89
-0.90
16.71
-0.35
4.95
-0.96
-1.54
-0.66
-0.59
2.25
3.77
0.61
-0.18
-1.96
-2.53
8.13
0.40
-0.32
1.41
-5.34
1.72
-6.85
-0.61
ωi9
% change relative to the benchmark
-0.35
-0.91
-0.42
6.72
-1.26
1.90
6.29
2.24
1.30
-0.82
4.70
3.91
-4.28
-2.84
-2.78
0.62
-0.43
-0.26
0.00
4.21
-0.81
-1.26
-1.70
7.32
-0.32
15.42
-0.65
4.32
-1.15
0.73
-0.89
-0.85
2.09
3.53
0.08
-0.08
3.51
-1.83
7.08
0.01
-0.37
1.50
-1.76
1.16
-3.79
-0.80
ωi8
-0.21
-0.86
-0.67
6.51
-1.23
1.91
5.34
2.00
1.07
-0.62
4.22
3.03
-3.56
-2.55
-2.11
2.18
0.69
0.34
0.11
3.55
-0.96
-1.17
-0.71
6.22
0.05
14.46
-0.83
3.93
-1.24
2.01
-0.99
-0.98
2.97
3.58
-0.24
0.02
6.23
-1.13
6.24
-0.22
-0.35
1.68
-0.53
0.82
-2.65
-0.87
ωi7
-0.11
-0.81
-0.84
6.37
-1.14
2.01
4.51
2.49
0.90
-0.51
3.85
2.34
-3.05
-2.27
-1.56
3.31
1.20
0.61
0.24
3.03
-1.06
-1.09
0.06
5.36
0.32
13.67
-0.95
3.65
-1.30
3.06
-1.05
-1.05
3.32
3.78
-0.47
0.13
8.08
-0.49
5.51
-0.37
-0.29
1.86
0.03
0.58
-2.01
-0.90
ωi6
Table 3: Results of the Counterfactual Experiment
-0.03
-0.70
-0.96
6.28
-1.02
2.10
3.73
2.45
0.77
-0.42
3.55
1.74
-2.64
-2.00
-1.09
4.26
1.55
0.85
0.36
2.58
-1.14
-1.00
0.70
4.63
0.56
12.92
-1.04
3.43
-1.33
3.97
-1.10
-1.10
3.63
4.73
-0.64
0.24
9.38
0.18
4.57
-0.47
-0.20
2.07
0.35
0.39
-1.51
-0.91
ωi5
0.03
-0.60
-1.06
6.19
-0.95
2.22
3.50
2.56
0.65
-0.33
3.29
1.89
-2.26
-1.76
-0.65
5.08
1.80
1.04
0.47
2.15
-1.19
-0.90
1.28
3.95
0.77
12.19
-1.10
3.23
-1.35
4.74
-1.08
-1.10
3.90
5.15
-0.79
0.34
10.31
0.87
3.45
-0.56
-0.10
2.27
0.48
0.23
-1.17
-0.92
ωi4
0.10
-0.48
-1.16
6.11
-0.90
2.36
2.68
2.67
0.54
-0.25
3.01
1.25
-1.88
-1.57
-0.22
5.83
1.98
1.20
0.60
1.72
-1.24
-0.85
1.84
3.27
0.96
11.42
-1.15
4.33
-1.37
5.54
-1.13
-1.14
4.17
5.63
-0.93
0.45
11.01
1.64
2.44
-0.62
0.02
2.49
0.62
0.08
-0.87
-0.92
ωi3
0.16
-0.37
-1.25
8.00
-0.82
2.56
2.07
2.82
0.42
-0.20
2.71
1.05
-1.47
-1.40
0.24
6.59
2.17
1.32
0.74
1.24
-1.29
-0.87
2.41
2.48
1.16
10.50
-1.20
4.92
-1.38
6.37
-1.14
-1.16
4.46
6.18
-1.07
0.55
11.74
2.56
1.39
-0.68
0.16
2.73
0.72
-0.08
-0.61
-0.92
ωi2
0.22
-0.28
-1.37
10.83
-0.57
2.90
1.09
3.07
0.22
-0.19
2.18
0.74
-0.84
-1.02
0.87
7.75
2.37
1.47
0.96
0.21
-1.34
-0.87
3.27
1.17
1.45
8.87
-1.26
6.05
-1.33
7.72
-1.15
-1.15
4.93
6.87
-1.29
0.70
13.39
4.40
0.31
-0.71
0.42
3.08
0.81
-0.32
-0.29
-0.91
ωi1
-0.12
-0.90
-0.41
7.29
-1.20
2.25
4.83
2.82
1.15
-0.48
4.60
2.57
-3.76
-2.73
-1.42
2.84
0.54
0.67
0.38
4.15
-0.87
-1.22
-0.11
6.52
0.32
14.32
-0.71
4.81
-1.11
2.64
-0.84
-0.81
3.44
5.12
0.00
0.28
6.65
-0.51
5.04
0.13
-0.05
2.05
-0.02
0.90
-2.89
-0.65
Wi
1.50
-3.33
2.78
6.39
-3.94
1.61
1.04
4.44
2.88
0.70
5.15
-4.69
-23.39
5.03
3.82
32.18
6.45
1.87
1.12
4.77
2.44
4.76
3.83
11.66
3.27
11.58
3.41
4.89
1.40
1.09
1.97
2.27
0.79
1.90
4.50
1.35
26.48
-4.28
1.92
2.02
1.02
2.26
2.14
6.42
17.36
2.80
Gi
40
yi10
-4.22
0.94
-0.74
3.44
-3.87
1.73
7.15
-0.21
-19.46
4.96
2.77
3.68
-8.77
8.93
13.40
-2.81
-1.08
-0.22
6.54
-6.26
5.07
0.97
-0.04
4.87
1.89
4.89
-1.62
3.77
4.57
3.39
2.22
-0.19
9.64
4.32
6.09
0.92
8.71
4.95
4.93
0.82
-0.05
4.53
1.40
-3.15
3.48
ISO
ITA
JAM
JPN
KEN
KOR
LKA
MAR
MDG
MEX
MLI
MOZ
MWI
MYS
NER
NGA
NIC
NLD
NOR
NPL
NZL
PAK
PER
PHL
PNG
PRT
PRY
ROM
RWA
SEN
SLE
SLV
SWE
SYR
TCD
TGO
THA
TUN
TUR
TZA
UGA
URY
VEN
ZAF
ZMB
ZWE
-1.44
0.66
-1.52
2.47
-1.55
2.32
5.44
-0.60
-8.77
3.04
2.89
2.49
-5.26
5.77
9.55
-2.92
-0.51
-0.87
4.37
-3.05
3.57
0.15
-0.67
4.80
0.25
3.09
-1.97
2.49
3.13
2.11
0.91
-0.58
7.51
2.25
4.58
2.37
6.53
2.83
3.88
0.26
-0.19
2.22
0.35
-1.87
2.47
yi9
-1.29
1.12
-1.83
2.60
-1.00
2.99
4.98
-0.48
-5.23
2.42
3.39
2.25
-3.04
4.36
8.09
-2.46
-0.67
-1.03
3.67
-2.44
3.18
0.10
-0.48
4.72
-0.24
2.57
-1.94
2.31
2.78
1.96
0.62
-0.82
6.80
1.56
4.27
3.28
5.80
2.13
3.72
0.23
-0.03
1.50
0.16
-0.86
2.57
yi8
-1.24
1.58
-1.93
2.77
-0.77
3.46
4.72
-0.33
-3.28
2.02
3.89
2.16
-1.39
3.45
7.11
-2.04
-0.70
-1.09
3.23
-2.07
2.96
0.12
-0.20
4.58
-0.52
2.26
-1.88
2.27
2.62
1.94
0.47
-0.94
6.36
1.14
4.14
4.65
5.33
1.68
3.67
0.25
0.10
1.07
0.08
-0.08
2.80
yi7
-1.23
2.02
-1.96
2.91
-0.63
3.87
4.54
-0.19
-1.94
1.73
4.42
2.11
0.08
2.76
6.36
-1.66
-0.74
-1.12
2.91
-1.73
2.83
0.14
0.14
4.49
-0.70
2.05
-1.81
2.26
2.54
1.97
0.39
-1.02
6.02
0.83
4.08
5.89
4.98
1.36
3.65
0.28
0.20
0.77
0.04
0.54
3.06
yi6
-1.17
2.49
-1.95
3.06
-0.59
4.25
4.40
-0.03
-0.92
1.50
4.96
2.10
1.40
2.22
5.71
-1.27
-0.72
-1.13
2.65
-1.39
2.74
0.17
0.49
4.42
-0.85
1.89
-1.72
2.28
2.50
2.03
0.33
-1.06
5.74
0.59
4.07
7.07
4.70
1.09
3.68
0.34
0.29
0.53
0.03
1.07
3.33
yi5
-1.18
2.95
-1.93
3.19
-0.51
4.63
4.30
0.14
-0.06
1.31
5.54
2.10
2.61
1.75
5.13
-0.88
-0.67
-1.12
2.43
-1.06
2.69
0.21
0.86
4.36
-0.99
1.76
-1.63
2.32
2.48
2.10
0.29
-1.09
5.50
0.38
4.08
8.23
4.46
0.87
3.74
0.40
0.38
0.33
0.05
1.54
3.58
yi4
-1.17
3.46
-1.90
3.33
-0.42
5.03
4.22
0.31
0.70
1.13
6.19
2.11
3.81
1.33
4.57
-0.44
-0.64
-1.13
2.22
-0.76
2.64
0.24
1.25
4.31
-1.10
1.64
-1.51
2.36
2.48
2.18
0.26
-1.10
5.24
0.19
4.12
9.37
4.22
0.65
3.81
0.47
0.46
0.14
0.11
1.98
3.80
yi3
-1.19
4.01
-1.85
3.46
-0.34
5.49
4.12
0.46
1.46
0.93
7.02
2.12
5.05
0.90
3.98
0.04
-0.61
-1.15
2.00
-0.48
2.62
0.28
1.68
4.25
-1.22
1.52
-1.36
2.41
2.50
2.27
0.24
-1.13
4.97
-0.02
4.20
10.46
3.97
0.42
3.91
0.56
0.55
-0.06
0.22
2.44
4.06
yi2
-1.18
4.94
-1.75
3.70
-0.16
6.51
3.98
0.69
2.48
0.62
9.13
2.21
6.95
0.24
3.03
1.03
-0.54
-1.08
1.62
-0.08
2.74
0.35
2.47
4.11
-1.40
1.35
-0.97
2.52
2.63
2.44
0.21
-1.09
4.48
-0.34
4.40
12.11
3.55
0.04
4.06
0.69
0.66
-0.36
0.45
3.16
4.48
yi1
-1.14
5.33
-1.48
3.73
0.21
6.90
3.83
0.82
2.69
0.39
10.74
2.19
7.72
-0.24
2.53
1.28
-0.28
-0.89
1.35
0.29
2.68
0.27
2.77
4.03
-1.55
1.17
-0.36
2.53
2.64
2.48
0.10
-0.99
4.10
-0.62
4.71
12.94
3.19
-0.28
4.30
0.60
0.72
-0.61
0.32
3.18
4.32
ȳi
-4.13
0.56
-0.61
1.98
-2.66
3.92
9.31
-1.01
-19.41
4.31
0.39
2.76
-9.03
8.53
13.76
-3.15
-0.94
-0.14
7.65
-6.31
4.46
1.06
-1.19
6.02
2.05
3.74
-1.53
3.14
3.37
3.02
1.88
-0.11
8.86
4.27
3.40
1.28
13.06
5.39
3.21
0.11
-0.25
4.51
1.17
-4.74
1.83
ωi10
-1.40
0.46
-1.46
0.97
-1.17
3.60
6.75
-1.44
-8.74
2.36
0.46
1.53
-5.41
5.34
9.85
-3.30
-0.46
-0.84
5.41
-3.07
3.17
0.19
-1.37
5.57
0.31
2.58
-1.93
1.82
2.48
1.70
0.84
-0.55
7.09
2.16
1.88
2.57
8.91
3.05
2.14
-0.49
-0.29
2.21
0.22
-3.52
0.79
ωi9
% change relative to the benchmark
-1.27
1.00
-1.79
1.09
-0.80
3.86
5.83
-1.33
-5.21
1.74
0.94
1.29
-3.14
3.92
9.25
-2.56
-0.63
-1.02
4.69
-2.45
2.87
0.13
-0.97
5.18
-0.20
2.30
-1.92
1.64
2.34
1.53
0.58
-0.80
6.53
1.46
2.87
3.43
7.34
2.27
1.97
-0.53
-0.09
1.50
0.06
-2.54
0.88
ωi8
-1.23
1.50
-1.91
2.04
-0.66
4.08
5.28
-1.19
-3.27
1.34
1.42
1.18
-1.46
3.00
7.47
-2.10
-0.68
-1.08
4.24
-2.08
2.73
0.13
-0.54
4.89
-0.49
2.08
-1.87
1.58
2.32
1.51
0.45
-0.93
6.17
1.03
3.22
4.75
6.33
1.77
2.69
-0.51
0.06
1.07
0.01
-1.78
1.99
ωi7
-1.22
1.97
-1.94
2.45
-0.58
4.28
4.90
-1.04
-1.93
1.04
1.93
1.14
0.03
2.32
6.60
-1.69
-0.72
-1.12
3.91
-1.74
2.66
0.15
-0.09
4.67
-0.69
1.94
-1.81
1.57
2.34
1.54
0.37
-1.01
5.90
0.71
3.53
5.96
5.58
1.41
3.02
-0.48
0.18
0.76
-0.01
-1.17
2.54
ωi6
-1.17
2.46
-1.94
2.81
-0.58
4.49
4.61
-0.35
-0.92
0.81
2.46
1.12
1.37
2.36
5.87
-1.29
-0.72
-1.12
3.56
-1.39
2.63
0.18
0.37
4.49
-0.85
1.83
-1.72
1.59
2.39
1.59
0.32
-1.06
5.67
0.75
3.82
7.10
4.99
1.12
3.36
-0.43
0.28
0.53
-0.01
0.12
3.00
ωi5
-1.18
2.94
-1.93
3.10
-0.53
4.71
4.35
0.01
-0.06
1.03
4.25
1.82
2.60
1.60
5.21
-0.89
-0.67
-1.12
2.87
-1.06
2.63
0.21
0.81
4.34
-0.99
1.74
-1.63
2.18
2.45
1.95
0.29
-1.09
5.47
0.38
4.10
8.24
4.48
0.87
3.70
-0.22
0.38
0.32
0.02
0.99
3.39
ωi4
Table 4: Results of the Counterfactual Experiment (continued)
-1.18
3.47
-1.91
3.40
-0.48
4.95
4.09
0.37
0.70
0.91
6.12
2.10
3.82
1.31
4.58
-0.44
-0.65
-1.13
2.35
-0.76
2.65
0.24
1.29
4.19
-1.11
1.66
-1.52
2.39
2.53
2.22
0.26
-1.11
5.27
0.20
4.41
9.35
4.01
0.63
4.05
0.27
0.47
0.14
0.10
1.79
3.72
ωi3
-1.20
4.03
-1.87
3.67
-0.43
5.24
3.84
0.69
1.46
0.92
7.85
2.45
5.07
0.99
3.92
0.05
-0.63
-1.15
1.81
-0.48
2.71
0.27
1.79
4.02
-1.23
1.56
-1.36
2.63
2.62
2.42
0.24
-1.13
5.04
0.02
4.78
10.43
3.52
0.38
4.45
0.67
0.57
-0.06
0.22
2.60
4.07
ωi2
-1.19
4.99
-1.78
4.13
-0.31
5.91
3.46
1.16
2.47
0.92
11.75
3.16
6.99
0.49
2.87
1.07
-0.56
-1.09
0.87
-0.07
3.02
0.34
2.69
3.76
-1.42
1.43
-0.99
3.04
2.91
2.75
0.22
-1.11
4.63
-0.28
5.45
12.04
2.69
-0.04
5.01
1.25
0.69
-0.36
0.48
3.84
4.63
ωi1
-1.41
2.18
-1.62
2.57
-0.83
4.47
5.60
-0.44
-2.25
1.65
2.86
1.91
-0.08
3.09
7.02
-1.55
-0.67
-0.93
3.85
-1.97
3.11
0.31
0.13
4.65
-0.25
2.31
-1.67
2.22
2.64
2.09
0.61
-0.84
6.44
1.21
3.51
6.24
6.77
1.97
3.23
0.06
0.20
0.97
0.30
-0.02
3.04
Wi
4.09
-3.25
1.13
1.40
0.13
-4.48
4.68
-0.48
19.19
0.92
-5.07
2.54
-0.50
3.58
5.38
-2.36
-0.30
1.10
5.98
-15.24
2.51
1.34
-1.48
-1.57
4.77
3.55
-0.64
2.23
2.30
1.79
3.35
1.62
5.10
10.39
1.41
-3.34
7.40
8.53
0.88
1.03
0.52
-7.99
1.06
4.27
1.46
Gi
7.3
Model solution: counterfactual experiment
Dekle, Eaton and Kortum (2007) proposed a way to solve for counterfactual values in Ricardian models by expressing the variables in relative changes and using real data. The
advantage of their solution algorithm is the fact that one does not have to estimate unobservable trade cost and technology primitives of the model.
In my counterfactual experiment I uniformly set all tariffs to unity. Given this exogenous
change and the data on real income and trade, I can solve for all other counterfactual values
as in Table 5.
Table 5: Benchmark and Counterfactual expressions
variable
pai
Benchmark
− 1
P
θa
N
−θa
pai =
(κ
τ
t
)
a`
a,i`
a,i`
`
pmi
pmi =
pni
1−φ
pni = Γn (wiν ri1−ν )φ (p%ni p1−%
mi )
1−φ
p0ni = pni (w
biν rbi1−ν )φ (b
p%ni pb1−%
mi )
xm,in
(κmn τm,in tm,in )−θm
xm,in = PN
−θm
` (κmn τm,i` tm,i` )
bmn b
xm,in (κ
tm,in )−θm
x0m,in = PN
−θm
b b
` xm,i` (κm` tm,i` )
(κan τa,in ta,in )−θa
xa,in = PN
−θa
` (κan τa,i` ta,i` )
1−ν
wi νk
+ 1 + vi
id
yid =
mi sni
(psaiai psmi
pni )
−θa
ban b
xa,in (κ
ta,in )
x0a,in = PN
b b −θa
` xa,i` (κa` ta,i` )
xa,in
yid
P
N
−θm
` (κ` τm,i` tm,i` )
vi
vi = ei + ȳi
ωi,d
ωid = yid
P
n (fmi xt,in tt,in
−
Counterfactual
− 1
P
θa
N
−θa
b
b
t
)
p0ai = pai
x
(
κ
a,i`
a,i`
a`
`
1
θm
p0mi = pmi
0 =
yid
+ fai xa,in ta,in )
mi sni
psaiai psmi
pni
sai,d smi,d sni,d
pai pmi pni
P
N
`
bm` b
tm,i` )−θm
xm,i` (κ
− 1
θt
w
bi yi,d + vi0
mi sni
pbsaiai pbsmi
pbni
vi0 = ei + ȳi0
0 = y0
ωid
id
0
0
0
n (fmi xt,in tt,in
P
0 x0
0
+ fai
a,in ta,in )
mi sni
pbsaiai pbsmi
pbni
sai,d smi,d sni,d
pbai pbmi pbni
Notes: Total per-capita transfers denoted as vi are calculated as a sum of tariff revenues and exogenous crosscountry transfers, ei (net of trade imbalances).
To solve for the counterfactual change in wages w
bi I use a market clearing condition as in
(3.18):
41
(w
bi Yi + Vi0 )
N
X
N
X
0
0 0
0
0
fmi
x0t,in + fai
xa,in − Di =
(w
bn Yn + Vn0 ) fmn
x0m,ni + fa,ni
x0a,ni
n=1
(7.1)
n=1
In practice, the solution algorithm boils down to finding a fixed point for a series of contraction mappings. For further discussion refer to Alvarez and Lucas (2007) and Dekle, Eaton
and Kortum (2007).
7.4
Derivation details (NOT FOR PUBLICATION)
Derivation of demand shares in (3.2)-(3.4)
Use the utility function and the budget constraint in (3.1) to formulate the lagrangian as
follows:
α
1−α
Lid = (cβni c1−β
− ϑ (yid − cni pni + cmi pmi + cai pai ) ,
mi ) (cai − µ)
(7.2)
the first-order conditions are as follows:
∂Lid
(1−β)α
(cai − µ)1−α = ϑpni
: αβcαβ−1
cmi
ni
∂cni
∂Lid
(1−β)α−1
(cai − µ)1−α = ϑpmi
: (1 − β)αcαβ
ni cmi
∂cmi
∂Lid
1−β α
) (cai − µ)−α = ϑpai
: (1 − α)(cβni cmi
∂cai
(7.3)
(7.4)
(7.5)
Take the ratio of (7.3) to (7.4) to establish the following relationship:
β cmi
pni
=
,
1 − β cni
pmi
(7.6)
and divide (7.3) by (7.5) to establish the following:
αβ
pni
(cai − µ)pai =
1−α
pai
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(7.7)
Recall that the budget constraint reads:
yid = cni pni + cmi pmi + cai pai ,
(7.8)
plug pmi cmi from (7.6) and pai cai from (7.7) into the budget constraint to get:
1−β
1−α
pni cni + pni cni +
pni cni = yid
β
αβ
(7.9)
Equation (7.9) can be simplified as follows:
1
pni cni + µpai = yid ,
αβ
⇒ pni cni = αβ(yid − µpai ).
(7.10)
I restrict the range of pni cni to [0; +∞), hence pni cni is positive whenever yid > µpai and zero
otherwise. The two remaining demand systems in (3.2)-(3.4) immediately follow.
Derivation of prices in (3.11) and (3.14)
Recall the production function of a variety q in i:
mi (q) = zim (q)(liν ki1−ν )ξ (nζi mi1−ζ )1−ξ ,
(7.11)
1−ξ
let vci = (wiν ri1−ν )ξ (pζni p1−ζ
. Then, we can rewrite the price of the variety q as:
mi )
p(q)mi = zim (q)vi ,
(7.12)
In the open economy equilibrium, each country shops around for the lowest price of each
variety q. In other words,
p(q)mi = min {zim (q)vc` τi` ti` } ,
`
43
(7.13)
Since zim (q) is distributed Frechet, zim (q)−θm is distributed exponential with mean λi . A
well known property of the exponential distribution is:
θ
p (q)mi ∼ exp
`=N
X
!
−θ
λ` (vc` τi` ti` )
(7.14)
`=1
Denote p̃ = pθ (q)mi and use change-of-variables formula to derive the pmi from the CES
specification:
m
p1−σ
mi
Z
= τi` ti`
1
p̃
1−σm
θ
vc` exp(−vc` p̃)dp̃,
0
⇒ pmi
⇒ pmi
− θ1
X
m
−θm
ν 1−ν ξ ζ 1−ζ 1−ξ
=
(Γm λmi (wi ri ) (pni pmi ) τi` ti`
,
!− θ1
N
m
X
=
(κ` τm,i` tm,i` )−θm
.
(7.15)
`
The same applies to the agricultural aggregate.
Derivation of trade shares in (3.15)
There is a mass of different varieties q. Hence, the trade share xm,in equals the probability
that n is the lowest cost supplier to i across the varieties. This probability can be derived
as:
xm,in
= P r zn (q)vn τin tin ≤ min (z` (q)vc` τi` ti` ) ,
`6=n
(7.16)
Use the properties of the exponential distribution and (7.15) to arrive at the expression for
trade shares:
(κmn τm,in tm,in )−θm
.
xm,in = PN
−θm
(κ
τ
t
)
m`
m,i`
m,i`
`
44
(7.17)
The same applies to the agricultural sector.
45