HIAS-E-124

Transportation Infrastructure and Trade

Han Zheng (a), Li Hongtao (b)(a) Hitotsubashi Institute for Advanced Study, Hitotsubashi University(b)
The University of Tokyo

October 2022

Hitotsubashi Institute for Advanced Study, Hitotsubashi University
2-1, Naka, Kunitachi, Tokyo 186-8601, Japan
tel:+81 42 580 8668 http://hias.hit-u.ac.jp/
HIAS discussion papers can be downloaded without charge from:https://hdl.handle.net/10086/27202
https://ideas.repec.org/s/hit/hiasdp.html

Transportation Infrastructure and Trade∗
Han Zheng†
Li Hongtao‡
October 20, 2022

Abstract
This paper offers a variant of the Ricardian model able to structurally interpret theestimate of country-specific variable—transportation infrastructure. Guided by thisnew theoretical framework, this paper shows that transportation infrastructure enhances international trade more than internal trade. Further quantitative analysis
suggests 10% increase in transportation infrastructure induces 3.9% increase in real
income and more than 95% of the gains concentrate on the infrastructure improving
country. This paper also suggests that transportation infrastructure improvement
increases real income mostly through internal trade cost reduction. All the above
results suggest that better infrastructure leads to sizable gains providing additional
empirical support to policies aiming to improve transportation infrastructure.
Keywords: Gravity model, Transportation infrastructure, Internal trade cost
JEL Codes: F10, F14∗

We wish to thank Kenichi Ueda, Taiji Furusawa, Yoichi Sugita, Hirokazu Ishise, Daisuke Fujii, andKonstantin Kucheryavyy for providing useful comments at the various stages of this paper and two
anonymous referees for their constructive comments. All remaining errors and omissions are our sole
responsibility. Han Zheng is supported by JSPS Grant-in-Aid for Early-Career Scientists(KAKENHI),
Project Number JP22K13380. Li Hongtao is supported by WINGS-GSDM Designing Future Society
Fellowship, Project Number 150201SP01.
†
Hitotsubashi Institute for Advanced Study, Hitotsubashi University, 2-1 Naka, Kunitachi, Tokyo
186-8601, Japan. Email address: hanzheng211@gmail.com.
‡
Graduate School of Public Policy, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 1130033, Japan. Email address: li-hongtao@g.ecc.u-tokyo.ac.jp.

1

Introduction

Job creations and investment payoff are two common pros for infrastructure investment
discussed in economics literature while relatively few literature analyze how infrastructure
affects trade flows. The scarcity of research is partly because of the nondiscriminatory
feature of transportation infrastructure as a country-specific variable, which precludes
the identification of transportation infrastructure out of country-specific fixed effect in
the popular fixed effect gravity specification. However, this paper capitalizes on themethodology devised by Beverelli et al. (2018) and finds that the infrastructure boosts
international trade more than internal trade. Further quantitative counterfactual exercise
shows that 10% transportation infrastructure increase induces sizable 3.9% increase inreal income. This provides solid support to President Biden’s Bipartisan Infrastructure
Law by arguing this Law can lead to higher trade openness.
It is commonly believed that a better infrastructure can lead to both lower international and internal trade costs, where the international trade refers to the trade flows
crossing the country border while the internal trade is defined conversely, regardless ofwhether those trade flows are inter-industry or not. Further academic evidence confirms
this intuition—Jaworski et al. (2022) find a significant impact of the US highways on
both internal and international trade flows. However, whether infrastructure primarily
facilitates international trade or internal trade is a question of significance, because thisheterogeneous impact affects expenditure share on domestically produced goods which
is one of the sufficient statistics on real income. To provide analysis for this question,
this paper proposes a variant of the Eaton and Kortum (2002) framework, capable ofidentifying the country-specific variable separately from the country-specific fixed effect,to estimate how much infrastructure can affect the trade cost and the gains from trade.
Contrary to an intuitive statement that infrastructure benefits internal trade more thaninternational trade since domestically produced goods seem to have unfettered accessto internal transportation infrastructure, the empirical results show that better infrastructure boosts international trade more than internal trade, rendering infrastructure afavorable policy instrument to effectively elevate the trade openness. Further quantitative
analysis reinforces the aforementioned claim and finds infrastructure improvements cangenerate sizable gains and the infrastructure improving country reaps more than 95% of
its gains.
Another noteworthy merit of this framework is that it can be readily applicable to assess the impact of other more convoluted country specific factors, e.g., institution quality,
political party turnover, on both international trade and internal trade flows.
The internal trade cost is the same across countries is a convenient assumption imposed in international trade literature, whereas little evidence is shown to warrant thisassumption. On the contrary, intuitions and both anecdotal and academic evidence hint

1

at the opposite—transportation infrastructure and investment exhibits considerable variations across countries. Several recent studies also analyze the presence and implicationof the internal trade cost, such as Allen and Arkolakis (2014), Ramondo et al. (2016),
Kerem Coşar and Fajgelbaum (2016), Atkin and Donaldson (2017) and Allen and Arkolakis (2022). Unlike the aforementioned studies, this paper attempts to estimate theimpact of internal infrastructure on both international and internal trade flows using a
popular fixed effect gravity specification. In addition, building on the empirical specification proposed by Beverelli et al. (2018), this paper provides a framework capable ofstructurally interpreting the estimate on country-specific variables, such as infrastructure
which affects both internal trade and international trade.
Figure 1: Total Inland Transport Infrastructure Expenditure over GDP

Note: The data comes from the OECD Database. The y-axis is the total inland transport infrastructure
expenditure percentage points out of GDP.

Suspecting that the infrastructure should affect trade cost across time and be motivated by the real-time infrastructure investment difference shown in Figure 1, this paperbuilds a theoretical model, a variant of Eaton and Kortum (2002), to accommodate thefact that infrastructure affects both the international trade cost and the internal tradecost. The theoretical model yields a novel welfare formula predicting that the change in
the internal trade cost works as a multiplier, amplifying the traditional gains from trade.
This modification is not only quantitative important but also qualitative crucial, because
the quantitative analysis section shows that there are sizable gains in real income evenwhen domestic goods expenditure share increases. More importantly, this formula provides a theoretical foundation to structurally estimate a country-specific internal trade
cost component. Based on the new framework, this paper offers a structural interpretation of the coefficient in front of the infrastructure measure. Using an estimation method2developed by Beverelli et al. (2018), this paper finds that a better infrastructure boosts
international trade flow more than internal trade flow, a result, though odd at first sight,
which suggests that there might be an economy of scale in the domestic distribution, thatis exports and imports have to go through several major ports or nodes for clearance,
whereas internal goods flow has no such requirements. Another possible explanation isthat countries provide more favorable shipping policies to exports and imports to foster international trade. Additionally, this result also implies that, other than the twochannels through which people commonly perceive infrastructure investments to yield
benefits, creating jobs and investment returns, infrastructure investment has the potential to levitate trade openness, which in turn yields higher gains from trade.
The most related literature which study the effect of infrastructure on international
trade using the gravity model are the following. Feenstra and Ma (2014) examine how
the port efficiency, part of transportation infrastructure, affects the extensive margin of
trade and confirm a significant positive impact. A new index of infrastructure is createdin Donaubauer et al. (2016a), and it is used to study various issues in Donaubauer
et al. (2016b), Donaubauer et al. (2015), and Rehman et al. (2020). Using the newindex of infrastructure, Donaubauer et al. (2015) find a country’s endowment with overall
infrastructure to be positively associated with more intensive trade relations and theeffects of infrastructure prove to be non-linear. Similar to his work, We further investigate
the effects of infrastructure on international and internal trade and results show that
better infrastructure boosts international trade more than internal trade. Rehman et al.
(2020) show that infrastructure positively improves exports while negatively affecting
trade deficit. They use fully modified least squares (FMOLS) and dynamic ordinary
least square (DOLS) estimator to deal with endogeneity issues by adding the leads andlags, while we use the Poisson Pseudo Maximum Likelihood Estimator for Structural
Gravity Models, whose solutions define the exporter and importer specific multilateralresistance terms.
Admittedly, this paper is by no means the first paper to discuss the internal trade cost
and the domestic infrastructure. Other than the studies mentioned before, Donaldson
and Hornbeck (2016) and Donaldson (2018) analyze, respectively, the impact of the US
railroad networks and the railroad construction project during the Indian colonial period,
both of which find a significant, positive impact on welfare measures. Banerjee et al.
(2020) find access to domestic transportation infrastructure has a positive causal effecton per capita GDP levels in China. Using detailed Chinese custom data, Fan et al.
(2021) develop a route choice model and embed it into an input-output multi-sector
trade model to evaluate the massive expressway construction program in China, finding
positive welfare gain. Recently, using a newly assembled sub-country regional bilateral
trade data set, under a causal inference framework, Santamaria et al. (2020) unveil asignificant Border effect, unexplained by usual geographical proxies, such as distance. As3

an intermediate measure to find how the theoretical cost of living measures altered by thevariety of goods, Cavallo et al. (2021) discover that the internal trade cost constructedby the margins, captured by the transportation sector and the various taxes, is positively
correlated with trade openness which frequently and positively correlates with the percapita income.1
The following section presents a theoretical model capable of dealing with factors
affecting the internal trade cost and the international trade cost, simultaneously. Section
3 builds a roadmap from the theory to the empirical counterparts and offers a structuralinterpretation to the coefficient of the infrastructure proxy. Section 4 describes the data
sources and briefly discusses their merits. Section 5 presents the estimation results and a
discussion ensues. Section 6 considers several counterfactual situations and assesses boththe qualitative and quantitative importance of the new welfare formula. Section 7 reports
robustness check. The final section concludes.

2

Theoretical Framework

The section presents a theoretical framework as a variant of Eaton and Kortum (2002)(thereafter the EK model) with roundabout production. However, the qualitatively same
results shown here can also be derived under the Anderson-Wincoop or Melitz-Chaneysettings.2
As in Alvarez and Lucas (2007), the tradable sector produces intermediate goods.
Each country sources each variety of intermediate goods from different countries andcombines them into a CES composite used to produce both intermediate goods andfinal goods which is non-traded. The consumers derive utility from the consumption ofcompetitively sold final goods. The production technology of each variety of intermediate
goods is given asqi (ω) = zi (ω)li (ω)β mi (ω)1−β(1)where li (ω) is the labor and mi (ω) is the intermediate aggregate. zi (ω) is drawn independently from Type-2 Gumbel distribution F (z) = P (zi (ω) ≤ z) = exp(−Ti z −θ ). Because
1Many other noteworthy studies mainly analyze the relations between domestic infrastructure andbut not confined to real income. For example, using the rich road network data for Peru, Volpe Martincus
et al. (2017) confirm the positive effect from the expansion of road network on firms’ export and job
growth; Ma and Tang (2020) study the migration within China through the transportation infrastructureand discover the welfare impacts of migrations crucially hinge on the extensive margin of trade—the entry
and exit of firms; Li and Ma (2021) finds better domestic infrastructure contributes to the rapid spread of
Covid-19 in the early stage of the global pandemic; Felbermayr and Tarasov (2022) emphasize the uneven
distribution of transportation infrastructure inside countries arising from the endogenous infrastructure
investment decisions could account for a significant portion of the border effect.
2
Cavallo et al. (2021) arrive at a similar formula as in equation (8) with the Melitz-Chaney heterogeneous firm framework. The only difference between this model and theirs is that the goods variety holds
to be constant.

4

of perfect competition and a constant return to scale, the factory price is given as:
wiβ Pi1−βcipi (ω) ==β
1−βzi (ω)β (1 − β)zi (ω)
wβ P 1−β(2)wβ P 1−βi ii iwhere ci = β β (1−β). Pi is the price index of intermediate aggregate. Similar
1−β =γ
to the intermediate goods sector, the production technology of the final goods sector isdeterministic Cobb-Douglas type meaning:

wiβ Pi1−β
pF = ββ (1 − β)1−β(3)

The c.i.f price for any price is given as:pij (ω) =p (ω)t τ t∀i ̸= jp (ω)ti=j

i· ij ·j

i
i

ii

(4)

where τij is the standard iceberg trade cost and t·j is the trade cost stemming from theimporting country’s infrastructure condition, which applies unanimously to the goods
from every exporting country. Similarly ti· is the trade cost stemming from the exporting
country’s infrastructure condition. tii is the internal trade cost from this country’s infrastructure. This country-specific internal trade cost is reminiscent of what Han (2021)
has convincingly shown that the internal trade cost at the country level is a functionof country size and the trade cost between the basic geographical units defined in that
paper. The basic geographical unit is a swathe of area within a country satisfying thesethree requirements: equal labor endowment, equal technology level, and equal price index. The heterogeneity in tii across countries reflects the innate differences in the trade
costs between basic geographical units. Notice that the above formulation of prices acrosscountry pairs lies at the very core of this new extension of the EK model, because it allows
a country-specific infrastructure to affect both internal trade and international trade heterogeneously. This heterogeneous impact on internal trade and international trade mightreflect the economy of scale in shipping or the nonlinear pricing phenomenon in shipping
as highlighted in Han and Fujii (2020). Normally, the effect of country-specific variables is precluded from an estimation even when only using the international trade flows
in a fixed effect estimation approach, as the country-specific variables will be perfectly
collinear with the country-specific fixed effects.3 The same procedure as in EK yields the3

Fixed effect estimation approach of the gravity model is preferred here because it is consistent with abroader class of trade models, including Melitz and Ottaviano (2008) and Han and Fujii (2020). However,
several other versions of gravity specifications not using the fixed effect to control multilateral resistanceterms permit analyzing the effect of country-specific variables such as infrastructure, and institution
quality. One notable example is Donaubauer et al. (2018) use a weighted average of all bilateral trade
costs to control for multilateral resistance terms and embed it into a traditional gravity model with GDP

5

trade share of country j’s expenditure on country i’s goods as:4

πij =



P

Ti (ci ti· τij t·j )−θ−θ]+Tj (cj tjj )−θs̸=j [Ts (cs ts· τsj t·j )∀i ̸= j
P

Ti (ci tii )−θ
−θ
T
(c
t
]+Tj (cj tjj )−θs̸=j [ s s s· τsj t·j )

i=j

(5)

with price index Pi given as:
(
)−1/θ
i
Xh
Pi = ATi (ci ti· τij t·j )−θ + Tj (cj tjj )−θ

(6)

i̸=j

1/(1−σ), a constant of parameters. Equation (5) immediately gives
where A = Γ θ+1−σθ
the trade flow from country i to country j as multiplication of trade share and country
j’s total expenditure:
Xij = πij Xj ∀i, j,(7)where Xj is country j’s total expenditure. When i = j, similar to the definition in Ramondo et al. (2016), Xjj are the domestic absorption and also the internal trade flows
including both inter-industry trade and intra-industry trade within one country’s boundary. This variant incorporates two new components into the country’s competitivenessmeasure Ti (ci ti· τij t·j )−θ : ti· and t·j , which function the same way as τij —higher costlower competitiveness, except both are country specific rather than pair specific. Somestraightforward substitutions yield the following:5
wj
=B
pF

Tj
πjj tθjj

! 1−β
θβ
,

(8)

where πjj is also dubbed absorption rate in trade literature and B is a collection of constants including A, γ. Following Ramondo et al. (2016) and Han (2021), the technology
parameter Tj can be sensibly parameterized as Tj = ϕj Lj where Lj is country j’s laborendowment and ϕj is called innovation intensity measuring how creative on average each
personnel can be in country j. Then equation (8) can be alternatively written as:
wj
=B
pF

ϕj Lj
πjj tθjj

! 1−β
θβ
.

(9)

to represent economy sizes. Their results show that higher infrastructure quality in both pair countries
tends to increase trade flows between them. However, their approach might suffer from omitted variablebiases because it could miss some country specific forces captured by country specific fixed effects but
not able to be exhausted in their enumeration of variables included.
4
Curious readers can refer to Eaton and Kortum (2002) or Dekle et al. (2008) for details in derivation.
5
The derivation procedure strictly follows Han (2021)’s cookbook steps.

6

Following Dekle et al. (2008), the hat algebra version of equation (8) is given as:6
ŵj
=
p̂F

! 1−β
θβ

T̂j
π̂jj
| {z

t̂jj

− 1−β
β

.

(10)

}

ACR formula

Equation (10) looks very similar to the famous ACR formula in Arkolakis et al. (2012)
where the ACR formula only contains the first parenthesis in equation (10). However, it
extends what Arkolakis et al. (2012) claim: the welfare measure not only depends on two
sufficient statistics, trade elasticity and the absorption rate change, but also the internal
trade cost change. A simple thought experiment would illustrate the intuition behind
this equation. A negative shock devastates the infrastructure lifting up the trade costto both internal trade and international trade rendering the absorption rate somewhat
unchanged. The formula endorsed by Arkolakis et al. (2012) would predict a small welfarechange or even higher welfare in case internal trade shrinks more than international
trade proportionately, completely silencing the adverse impact of the negative shock.
The internal trade cost change component in equation (10) will adjust the gains frominternational trade by the internal trade conditions.7 More importantly, equations (8)and (10) are useful to structurally estimate the country specific components of the internal
trade cost, where the standard gravity estimation falls short. Additionally equation (10)is reminiscent of the theoretical framework in Ramondo et al. (2016) and Han (2021)
where the regional level EK setting is aggregated into a country level EK setup. Their
welfare formula is similar to equation (10), under the assumption that the regions are
all symmetric. Meanwhile, Ramondo et al. (2016)’s results show that the symmetricassumption is not restrictive at all, reassuring the validity of equation (10).86

The detailed derivation is provided in the Appendix D.
Another way to show the comparative statics of t̂jj on the real income change is to combine thedirect effect from t̂jj and indirect effect from π̂jj , as t̂jj affects π̂jj as well. It is straightforward to showthat the net effect of t̂jj on real income change is negative, meaning higher t̂jj leads to a lower real
income change. However, this simplistic discussion of the impact from t̂jj on the real income change
does not provide much valuable insight, because this paper allows infrastructure to affect not only theinternal trade cost but the international trade cost as well, both of which affects the absorption rate.
Therefore, a discussion of t̂jj conditional on the absorption rate change serves the purpose of this paper
better.
8
One may argue that the ACR formula has already included the effects of internal trade cost change
because its effects can be attributed to the change of technology as a residual. This kind of argument
has a logic like national accounting in growth literature. However, this claim is not very well grounded
for the following two reasons. First, careful inspection of equation (5) reveals that the technology
parameter has partial trade elasticity one, whereas the internal trade cost parameter has partial tradeelasticity θ meaning the variation on the internal trade cost parameter could be used to estimated tradeelasticity. Second, though sounds like the logic used in national accounting, they are essentially different.
National accounting reduces all the unknown elements affecting production to a technology parameter
after netting out all the known production factors. However, the immediate attribution of change in
the internal trade cost to the change in technology does not help in understanding what constitutes thetechnology parameter. As a matter of fact, Han (2021) shows that in a parsimonious trade model withroundabout production, after filtering out the effect of internal trade cost, the technology parameter can
7

7

3

From Theory to Empirics

This section offers a road map from the theoretical framework to our empirical specifications. More importantly, it provides insights on how to structurally interpret thecoefficients estimated and explains why the same coefficient appears regardless eitherside of the country specific infrastructure proxy is used in estimation.
Inspection on equation (5) reveals that the standard fixed effect gravity model isplagued by the econometric difficulty of the perfect collinearity. The country-specifictrade cost ti· and t·j would be absorbed into the country-specific fixed effect. Fortunately,
Beverelli et al. (2018) provide hints at how the country-specific trade cost can be estimatedindirectly using the internal trade flows. Built upon their results, the following derivation
demonstrates how the effects can be estimated and their theory-consistent interpretation.
The trade flow equations can be written as follows which comes from equation (7):Xij = exp ln−θ
Ti c−θ
i ti·



i
Xh
−θ
Ts (cs τsj t·j )
t−θ
− ln
j·

!

!
+ ln Xj + ln (tj· τij t·j )

−θ

s

(11)




!


i
Xh



−θ
−θ
−θ
−θ
−θ
 . (12)
−
ln
T
(c
τ
t
)
t
+
ln
X
+
ln
(τ
t
)
Xjj = exp 
ln
T
c
t
s
s
sj
·j
j
jj
jj
j
j·
j
j·

|
{z
}


s
expj
|
{z
}
impj

Notice that the first term of the above equation system is exporting country specific andthe second and third terms are importing country specific, which respectively will becontrolled for using exporter country fixed effect expi and importer country fixed effectimpj in the cross-section empirical setting.9 τij is the standard iceberg trade cost able
to be captured by bilateral trade proxies or country pair fixed effect and τjj is one as
usual. Notice that t−θ
i· is an exporting country-specific term which will be absorbed into
i’s exporter fixed effect as in equation (11). And because of the existence of exporter fixed
effect in internal trade flow observations, the same i’s exporter fixed effect appearing in its
own internal trade observation contains an effect from t−θ
j· which shouldn’t appear in theinternal trade flow observation as in equation (12). To balance this effect, the second termin equation (12) has to contain t−θ
j· which in turn will appear in the importer fixed effectin equation (11) because of the very same importer fixed effect in both international trade
flow and internal trade flow observations and, as a result, the fourth term in equation
be well approximated by R&D data.
9This paper is using panel data, therefore the expi and impj fixed effects will be transformed into
the exporter-time fixed effect expi,t and the importer-time fixed effect impj,t in this paper’s empirical
specifications.

8

(11) will have to contain both effects stemming from the importer’s infrastructure t−θj·−θ
and t·j .
To proceed, parametric assumptions are imposed on the country-specific trade cost—they are power functions on the infrastructure proxy for expository simplicity:10
tjj = IN Fja ,t·j = IN Fjb ,tj· = IN Fjc .

(13)

Then the trade flow equations become:
Xij = exp (expi + impj − θ (b + c) ln (IN Fj ) + BT Pij × η) ,(14)

Xjj = exp (expi + impj − θa ln IN Fj ) ,where BT Pij is used to capture τij . Notice that θa ln IN Fj is importer specific and will beabsorbed into impj . Therefore, in the specification in equation (15), what the coefficientin front of ln(IN Fj ) × Border will capture is θ(b + c − a), namely the infrastructure’s
effect on the international flow relative to the internal flow:
Xij = exp (impi + expj + Border + ln(IN Fj ) × Border + BT Pij × η)∀i, j,(15)

where Border is a dummy variable taking values of 1 for the international trade flows
and 0 for the internal trade flows. The inclusion of a Border dummy follows Beverelli
et al. (2018) and also Han (2021) shows compelling evidence that the Border effect is anindispensable part of internal trade cost and failing to include it might lead to biased
estimates.
An alternative way of reformulating the trade flow equation is given as follows:
i
Xh

−θ
−θ θ
Xij = exp ln Ti ci t·i − ln
Ts (cs τsj t·j )
tθ·j

!

!
+ ln Xj + ln (ti· τij t·i )−θ

s

i
Xh

−θ
−θ θ
Xjj = exp ln Tj cj t·j − ln
Ts (cs τsj t·j )
tθ·j

!

(16)

!
+ ln Xj + ln (τjj tjj )

−θ

.

s

Similar to the above analysis, the fourth term in the above equation contains both
10

The true components of tjj , t·j and tj· could potentially include confounding differential trade costterms other than infrastructure proxy. The existence of other differential trade cost terms introduces
additional country specific border fixed effect in its empirical specification. However, when estimating
using symmetric pair fixed effect to capture bilateral trade cost the method endorsed by Baier andBergstrand (2007), the flexible specification of bilateral trade cost subsumes the country specific Bordereffect situation. That is one of the reasons symmetric pair fixed effect specification is favored when
picking the preferred estimates in the later section.

9effects from the exporter side ti· and t·i and its empirical counterpart is given as:
Xij = exp (expi + impj − θ (b + c) ln (IN Fi ) + BT Pij × η) ,Xjj = exp (expi + impj − θa ln IN Fi ) .

(17)

θa ln IN Fi will be absorbed into expi , leaving the coefficient of IN Fi capturing the relative
effect θ(b + c − a). The above analysis predestines that regardless of which side’s measureis used, the estimate of the infrastructure will be the same and its interpretation willbe the exporting and importing effects combined, relative to the internal effect, whichis confirmed in the robust analysis section. This analysis confirms what Beverelli et al.
(2018) discovered and their interpretation.

4

Data Description and Summary Statistics

This section discusses the data sources and their merits, then followed by a summary ofstatistics of several variables of interest.

4.1

Data Description

Trade Flows — The trade flow data is from the ITPD-E Database.11 The ITPD-E contains consistent data on international and domestic trade for 243 countries, 170 industries,
and 17 years. The time period covered by the dataset includes the years from 2000 until
2016, the most recent year for which data across all sectors are available. The dataset
is constructed using reported administrative data and intentionally excludes information
estimated using the statistical technique to preserve the authenticity of the data. The
data are constructed at the industry level covering the broad sectors of agriculture, mining and energy, manufacturing, and services which means the ITPD-E describes nearlycompletely the traded sectors of each economy.
About the construction of the international trade data, the dataset uses importerreported values which are considered more reliable than data on exports, for goods trade.
Also, the authors of this dataset use exports reported by partner countries to fill the values
whenever they are missing from the importer side. For service trade, it uses services trade
data provided by the exporter side, since services export data are collected by mandatory
surveys and are more accurate than from the importer side. Each observation in theoriginal ITPD-E Database documents the bilateral trade value of one industry in one
particular year. Therefore, this database has no information about how the imported
goods are used meaning the imported materials should be the aggregate value used by all
11

Its link is given as https://www.usitc.gov/data/gravity/itpde.htm. Its detailed procedure ofconstruction and comparison with other frequently used trade databases are well documented in Borchert
et al. (2021).

10

the industries. Therefore, the trade value should contain both inter-industry trade andintra-industry trade. Because the analysis in this paper is at the country level and to
map the industry level trade value in the data to the country level model in the paper,
the industrywise trade flows are aggregated to obtain country level trade flows throughsumming the trade values of all the industries for each bilateral country pair. Relative
to the other trade flow database, the most outstanding advantage is that it contains
internal trade flows whenever possible and its computation uses gross production rather
than GDP as the reference sum, which is more consistent with the roundabout structureof production in reality. The database’s construction does not rely on an imputation
using the gravity method, therefore, the database is suitable for gravity estimation. The
details of trade data used for quantitative analysis will be separately presented in the
Appendix F.
We compared ITPD-E with other trade and production datasets to highlight its merits. Compared with World Bank’s TPP, ITPD-E covers data post 2004 and includes
significantly more countries. Also, ITPD-E covers the complete economy while TPP only
covers data from manufacturing industries. Compared with CEPII’s TradeProd which
covers manufacturing industries for over 150 countries from 1980 to 2006, ITPD-E covers
a larger set of countries and more recent years. GTAP dataset covers the entire economiesof 121 countries like ITPD-E. However, its data only covers 2004, 2007, 2011, and 2014
specific years. GTAP’s reliance on statistical models to fill missing values renders it more
appropriate for simulation than estimation. ITPD-E is not balanced and constructed fromadministrative data to preserve the authenticity of the raw data so that it is suitable for
estimation. Compared with WIOD, which covers 56 industries from 2000 to 2014, ITPDE covers more countries and wider industries. Similarly to the GTAP, WIOD heavily
relies on economic models to fill the missing values. Therefore, compared to other frequently used trade datasets, ITPD-E generally covers wider countries and industries witha longer time span including more recent years. Its construction accesses the accurate
administrative data making it suitable for estimation.
Bilateral Trade Proxies — The proxies come from the CEPII website, which covers
bilateral distance, common language, border continuity etc. over 225 countries. The merits of the distance proxies constructed there are twofold: first, it computes intra-national
distances in the same manner as international distances; second, it offers several versionsof bilateral distances, including population weighted distances taking into account all thecities in a typical country. Therefore, the distance component of the internal trade cost
can be accounted for and the internal distance is also used to approximate the internal
trade cost in several studies.12
Regional Trade Agreement — The regional trade agreement dummy comes from the12

See Yotov (2012), Agnosteva et al. (2019), Ramondo et al. (2016), Beverelli et al. (2018) and Heidet al. (2021).

11

Mario Larch’s Regional Trade Agreements Database.13 It covers 516 Regional Trade
Agreement (RTA) notified to WTO from year 1950 to 2019. Dummies separating thetype of trade agreements, such as currency union, free trade agreement, and economic
integration agreement, are also included. Because the primary focus of this study is not
the impact of various RTAs, we include only the RTA dummy to control for bilateral
trade policies’ induced impact.
Infrastructure Proxy — As the main variable of interest, several types of infrastructure variables are collected from various sources to ensure the robustness of our main
result. First, we pick the sum of the total length of the railroad and the paved road as
the infrastructure proxy.14 It measures how extensive one country’s distribution network
is. Considering the innate heterogeneity of the country’s territorial size, a transportation
density measure is also constructed to check the robustness. The railroad length is fromthe United Nations’ World Development Indicator Database and the road length is fromthe OECD Transport Database. Second, an alternative measure of infrastructure proxyis the index composite constructed in Donaubauer et al. (2016a), where an unobserved
component model is employed in order to structurally clump together multiple highly
correlated infrastructure measures. Donaubauer et al. (2016a) categorize those infrastructure measures into four board categories—transportation, ICT, energy, and financial
infrastructure and assemble indices for each of these categories and a total index. In the
Appendix A, we experiment with each of these sub-indices and find the robustness of ourempirical results.
Institution Control — Numerous studies have analyzed the impact of institutional
quality on bilateral trade flows and trade patterns.15 Despite their vastness, their main
message is simple and clear—better institution in the pair countries generally leads tohigher trade flows. More importantly, Beverelli et al. (2018), the most similar paper
to ours in terms of methodology concludes that institution has a differential impact oninternational trade flow and internal trade flow. In light of those literature, in the robustness analysis, we decide to include institutional variables as a control to obviate theomitted variable bias. Following Beverelli et al. (2018), we use the institutional quality
indices from the World Bank’s World Governance Indicators which contain the follow13

It can be downloadable from the following website https://www.ewf.uni-bayreuth.de/en/
research/rta-data/index.html.
14Though the railroad and road transportation are substitutes for goods delivery, the sum of bothtransportation modes more accurately represents the country’s total transportation investment intensity
than either component, under the assumption that a country would invest in both modes until their
marginal benefits equalize.
15
See Anderson and Marcouiller (2002), Levchenko (2007), Tang (2012), Manova (2013), Francois andManchin (2013), Nunn and Trefler (2014), Beverelli et al. (2018) and Demir and Hu (2020). Samadi andAlipourian (2021) has suggested several indicators in the literature to measure the quality of institutions
from different dimensions. We select World Bank’s Worldwide Governance Indicators, WGI for short, asa candidate to measure the quality of institutions. Beverelli et al. (2018) also choose WGI as one of theoptions.

12

ing categories: Voice and Accountability, Political Stability and Absence of Violence,
Government Effectiveness, Regulatory Quality, Rule of Law and Control of Corruption.
However, a structurally composite indicator over those categories is not available. As acompromise, we use the simple arithmetic average as the aggregate index.
Innovation Intensity — Han (2021) has convincingly shown in a model with heterogeneous internal trade cost, the R&D data can approximate innovation intensity quite
well. Drawing upon this insight, we use the number of researchers per million populationfrom the World Bank’s World Development Indicator database as the innovation intensity proxy. This data set documents the annual number of researchers engaged in certain
activities, such as developing concepts and theories, and creating software of operational
methods. Though this database has another innovation intensity measure—percentage
point of expenditure on R&D activities out of GDP, the number of researchers is adopted
as it is more consistent with the parameterization of Ti = ϕi Li .
Other Variables — All the other variables are from Penn World Table 9.1 such as real
income, GDP, GDP per capita, population, and employment. Its coverage spans fromyear 1950 to 2017 and its construction and features are well documented in Feenstra et al.
(2015). The preferred real income measure is real GDP estimated from the expenditureapproach suitable for comparison across countries and years.

4.2

Summary Statistics

The following Table 1 provides descriptive statistics of interesting variables used in our
regression study. Given the trade flows are measured in million US dollars, the max valueof trade flow seems overly large. However, this abnormally large number exactly testifies
to the validity of this data set, because this data set contains internal trade flows andlarge countries generally absorb the majority of productions domestically. Moreover, theinternal trade flows are computed using the value of gross production rather than GDP
as reference sum, which further enlarges the size of internal trade flows. The observationthat attains this highest trade flow on record is the internal trade of the US in 2008.
The infrastructure proxy in length has a relatively low number of observations because
the OECD Transport Database only provides paved road data for OECD countries andpartner countries. However, we prefer this proxy when we quantitatively interpret theresults, because the other infrastructure index does not permit a structural interpretation consistent with the theory provided. Both the infrastructure index and the WGIinstitution index have its mean around 0 and the standard deviation 1, because bothare an index composite clumping several measures together using the unobserved components model method. This method generally assumes the underlying true variables
across countries follow the standard normal distribution. The negative values of thoseproxies prevent a theoretically consistent interpretation of their coefficients, however, the13signs of their coefficients have qualitative meanings. As for innovation intensity, there isa huge disparity among countries with the lowest record in this sample from Lesotho andthe highest record from Denmark.
Table 1: Descriptive Statistics
Count
Trade Flows (Million US$)Infrastructure Length (km)Infrastructure Index
Institution WGIInnovation Intensity

Mean

St. Dev.

Min

566570 1997.801 104128.3
04864570031209203 3320.798
1477.0090378 1.005249 -1.760078
3011 -.0338481 .9144237 -2.449376
1340
2014.32
1957
5.91

Max
18844254
7155777
3.216129
1.969566
8065.89

Note: This table only includes variables of interest. The second row corresponds to the infrastructure measure constructed by summing railroad length and paved road length. The third row
is the index constructed in Donaubauer et al. (2016a). The fourth row is the institutional index
available from World Bank’s World Governance Indicator database. The fifth row is the numberof researchers engaged in certain activities per million people from the World Bank’s World Development Indicator database.

5

Empirical Findings

This section first presents the empirical results in augmented gravity estimation motivated by equation (15) and establishes the result that infrastructure boosts international
trade more than internal trade. Then comes the analysis that estimates the elasticity of
infrastructure on internal trade, which shows better infrastructure is conducive to higher
internal trade flows. A discussion of better infrastructure’s impact on real income showsthat though the traditional gains from trade decrease according to the ACR formula, thereal income increases because equation (10) shows that the effect from absorption ratechange has to be adjusted by the change of internal trade cost.

5.1

Augmented Gravity Estimation

Notice that though the previous analysis establishes that the coefficient in front of theinfrastructure proxy captures the relative effect of the export side and import side combined over the internal trade cost, it does not preordain that the effect should be positiveor negative, or even significant. Either way could happen even if the infrastructure has apositive impact on trade flow is well established. The exact empirical model is given as
follows:log Xij,t = α × Border + ρ × IN Fj,t × Border + η × BT Pij+ impi,t + expj,t + ϵij,t14∀i, j,(18)

where Xij,t is the bilateral trade flow at time t; Border is the border dummy taking value
1 for international trade flows, to signify any bilateral trade barrier either tangible orintangible because of the traversing of the country borders; IN Fj,t × Border, as elaborated in section 3, measures how much the infrastructure improvement enhances theinternational trade relative to the internal trade with positive ρ meaning the infrastructure improvement facilitates the international trade more than the internal trade; BT Pij
stands for the standard bilateral trade cost proxies used in gravity literature such as
distance, common language etc.; impi,t is the importer-year fixed effect to control all theimporter specific factors; expj,t is the exporter-year fixed effect to control all the exporter
specific factors; ϵij,t is the error term.
The benchmark results of the above empirical model using the total length of the railroad and paved road as infrastructure proxy are tabulated in Table 2 and all specifications
are estimated with both importer-time and exporter-time fixed effects implemented. The
first column offers the results from the standard log-linear gravity estimation. Almost all
the estimates on the bilateral trade proxies lie within the one standard error range fromthe estimates in the meta analysis of Head and Mayer (2014). Column (2) confirms the validity and reliability of the data set and the PPML estimates located within a reasonable
range from the ones in Santos Silva and Tenreyro (2006). The third and fourth column
estimate equation (18) using bilateral trade proxies with different methods and both ofthem confirm a positive and significant effect of the infrastructure measure comparable
to the size of the RTA across different specifications. The Border dummy capturing the
average unexplained internal trade cost exerts a considerable impact on the trade flows.
Column (5) shows the result with a symmetric country pair fixed effect using the PPML
estimate. The effect of the infrastructure is still positive under a specification so rich in
fixed effects and its impact is stable across all the specifications, ranging from 0.25 to
0.65. Contrary to the assumption Cavallo et al. (2021) made that the domestic trade costs
impact unanimously on domestically produced goods and imported goods, Column 3 to
5 suggest the domestic trade costs, at least for the portion proxied by the combination ofroad length and railroad length, are very likely to affect goods discriminatively. Because
the symmetric country pair fixed effects specification is flexible enough to subsume country specific Border effect specification as mentioned in Footnote 10 and able to capture all
the observed or even unobserved components of symmetric trade cost, an approach advocated by Baier and Bergstrand (2007). In addition, estimates of PPML automaticallyP
P
P
P
satisfy the add-up constraints: i X̂ij = i Xij = Ej , j X̂ij = j Xij = Yi , according
to Fally (2015). The estimate in column (5) is picked as our preferred estimate. Having
said that, however, viewing equation (18) as a reduced form estimation might suggest an
upward bias of the estimate on the infrastructure interaction term because of the reverse
causality. For example, higher trade generally leads to higher welfare and rich countries
already have much better domestic market access meaning the infrastructure built is for15the purpose of promoting international market access. Therefore, failing to control forthe relative effect of the size and welfare status of the country might bias the estimates
upward, even though the country-time fixed effect has controlled the unanimous effect.
So we conduct the exercises taking care of the size of countries in the Appendix B and findrobust estimates using infrastructure indices. Also reassuringly even smaller estimates do
not affect the main implications in the quantification analysis as shown in the working
paper version of this paper.
Table 2: Augmented Gravity Estimations with Infrastructure(1)
Inter OLS

(2)Inter PPML

INF×BorderDistance
Contiguity
Language
ColonyRTA−1.570∗∗∗(0.016)0.717∗∗∗(0.088)0.731∗∗∗(0.033)0.902∗∗∗(0.085)0.515∗∗∗(0.027)−0.742∗∗∗(0.030)0.300∗∗∗(0.059)0.161∗∗(0.065)0.161∗∗(0.082)0.304∗∗∗(0.055)13.751∗∗∗(0.146)4560660.734

15.223∗∗∗(0.272)629336

BorderConstants
Observations
R2
Pseudo R2Country Pair FE
Importer-Time FE
Exporter-Time FE

No
Yes
Yes

0.946
No
Yes
Yes

(3)
INF OLS(4)
INF PPML(5)
INF Pair PPML

0.556∗∗∗(0.124)−1.277∗∗∗(0.053)0.218(0.150)0.393∗∗∗(0.090)0.949∗∗∗(0.119)0.418∗∗∗(0.069)−9.744∗∗∗(1.559)15.738∗∗∗(0.399)
95319
0.818

0.276∗∗∗(0.039)−0.571∗∗∗(0.042)0.455∗∗∗(0.080)0.486∗∗∗(0.087)−0.034(0.100)0.309∗∗∗(0.084)−7.399∗∗∗(0.573)18.783∗∗∗(0.269)1068380.650∗∗∗(0.146)12.741∗∗∗(0.364)106397

0.992
No
Yes
Yes

0.998
Yes
Yes
Yes

No
Yes
Yes

0.251∗∗∗(0.040)Note: Standard errors clustered at country pair level are reported in parenthesis.
The dependent variable is the bilateral trade flows in PPML estimation and log trade flows in OLS estimations. The total length of the railroad and the paved road is selected as the infrastructure proxy. INF is
short for infrastructure and FE is short for fixed effect.
∗p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

Because of the relatively low observations of total length infrastructure proxy, we
corroborate our primary results using the infrastructure index constructed in Donaubauer
et al. (2016a), which is tabulated in Table 3. Generally, the results are preserved whenusing the infrastructure index as the proxy instead. The estimated coefficients are positive
across most specifications, though in the PPML estimation with symmetric pair fixed16effect it is not precisely estimated. Another noteworthy point is that the coefficients of
the infrastructure index under the OLS estimation method in column 1 are similar tothe ones in Donaubauer et al. (2018) using the same infrastructure index in a traditional
gravity model specification. This similarity cross-validates the validity of the results
shown here. Further robustness check using sub-indices of the infrastructure index isoffered in the Appendix A.
Table 3: Augmented Gravity Estimations with Infrastructure Index

INF Index×BorderDistance
Contiguity
Language
ColonyRTA
BorderConstants
Observations
R2
Pseudo R2Country Pair FE
Importer-Time FE
Exporter-Time FE(1)
INF OLS(2)
INF PPML(3)
INF Pair OLS(4)
INF Pair PPML

1.577∗∗∗(0.199)−1.444∗∗∗(0.020)0.843∗∗∗(0.093)0.754∗∗∗(0.038)0.865∗∗∗(0.092)
0.482∗∗∗(0.033)−4.134∗∗∗(0.189)16.768∗∗∗(0.219)2375600.749

0.455∗∗∗(0.043)−0.575∗∗∗(0.049)0.426∗∗∗(0.076)0.480∗∗∗(0.064)−0.094(0.097)0.128∗(0.073)−4.337∗∗∗(0.184)18.436∗∗∗(0.309)3132430.493∗∗∗(0.187)−0.033(0.076)0.116∗∗∗(0.036)−0.097(0.068)0.610∗∗∗(0.033)2364720.864

14.001∗∗∗(0.027)305287

NO
Yes
Yes

0.989
NO
Yes
Yes

Yes
Yes
Yes

0.998
Yes
Yes
Yes

Note: Standard errors clustered at country pair level are reported in parenthesis.
The dependent variable is the bilateral trade flows in PPML estimation and log trade flows in
OLS estimations. The infrastructure index is selected as the infrastructure proxy. INF is shortfor infrastructure and FE is short for fixed effect.
∗p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01.

Therefore, we can safely conclude that better infrastructure tend to affect trade flows
heterogeneously—it boosts international trade flows more than internal trade flows, whichanswers the question posited by Coughlin and Novy (2021) whether infrastructure primarily facilitates within-Border trade or cross-Border trade.16 Several economic mechanisms
16
On the contrary, Fan et al. (2021) generate opposite result—infrastructure facilitate internal tradeflows more than international flows. The methodology used and the entity of focus could be the causeof different results. Fan et al. (2021) exploit the cross-time variation of the expressway expansion in one

17could potentially be behind this observation. First, generally more infrastructure stocks
are dedicated to facilitating internal trade than international trade reflecting the general assumption that internal trade cost is one with international trade cost bigger thanone. If the marginal infrastructure improvement exhibits diminishing return, given thesame degree of infrastructure improvement, internal trade flows will respond less thaninternational trade flows. This could cause the phenomenon that marginal infrastructure
improvement facilitates more international trade flows than internal trade flows. Second, it is well known that there exists the economy of scale at the port level, see e.g.,
Clark et al. (2004), whose the economy of scale story could similarly hold in shipping
because exports and imports need to be transported to several major ports and nodes
for declaration or clearance. This would tend to create more international trade flows
than internal trade flows given the same level of infrastructure improvement and reinforce
the heterogeneous effects discussed above. The exact cause and economic mechanism are,unfortunately, out of the realm of this paper and can be a very promising venue for future
research.
An additional exercise of replacing the importer side infrastructure measure withthe exporter side infrastructure measure is also performed as the robustness analysis,
confirming the same coefficient obtained as claimed in section 3. This duality presents
researcher options to maximize the information used in the trade flow data, that is theimporter side infrastructure can be used when the countries with infrastructure data havemore accurate and more observations.

5.2

Elasticity on Internal Trade

It turns out to be quite challenging to obtain infrastructure’s elasticity directly from thetrade flows, because the other elements that constitute internal trade cost are unobserved.
As a theory consistent roundabout solution, we capitalize on equation (9) and draw on
the result in Han (2021) that after controlling for internal trade cost term, the innovation
technology term ϕi can be well approximated by R&D data. The logic of recovering
process is similar to the indirect least squares, but different from the indirect least squares,
the structural empirical equation directly comes from the theory. The log transformationof equation (9) is given as follows:

log

wj
pF


+

1−β
1−β
1−β
1−β
log(πjj ) = C +log(ϕj ) +log(Lj ) −log(tjj ), (19)
θβ
θβ
θβ
β

single country China, whereas this study utilizes the cross-country variations to estimate the transport
infrastructure to trade cost elasticity. Therefore, their results are not expected to be applicable to othercountries, because of the idiosyncrasies of China. Despite those differences, reassuringly, both studies
yield similar quantitative results, which will be discussed in the section 6.

18

where C is a constant composite. As indicated in Footnote 10, it is very likely otherfactors other than the infrastructure condition affect the internal trade cost. Therefore,
this equation motivates the following empirical specification:log(RealGDPj,t ) +1−βlog(πjj,t ) = m × R&Dj,t + n × Employj,tθβ+ r × IN Fj,t + t̃jj + ϵj,t ,(20)

where RealGDPj,t is the real GDP data from the Penn World Table 9.1; πjj,t is thedomestic goods expenditure share also called absorption rate calculated from the ITPDE data; R&Dj,t is the number of researchers engaged in certain activities per million
people from World Bank’s World Development Indicator database and Employj,t is thenumber of employment from the Penn World Table 9.1; IN Fj,t is our variable of interestand the infrastructure proxy used in this paper; t̃jj represents other factors of the internal
trade cost which will be controlled by country fixed effect. Infrastructure as an elementof internal trade cost does not preclude other unobserved factors from influencing theinternal trade cost, which suggests this specification should be estimated with country
fixed effect. Failing to account for the internal trade cost fixed effect would render theestimates endogenous and biased downward, because countries are supposed to reduce
their internal trade cost across various methods up to the equalized marginal value.
The estimation of the above equation requires us to take a stand on the values of βand θ. Following Waugh (2010) we pick β = 0.33 and Simonovska and Waugh (2014)
estimate the value of trade elasticity from 4 to 8. We pick θ = 8 which together with
β = 0.33, according to equation (19) implies the coefficient a should roughly equal to0.25.17 Moreover, equation (19) presents another testable prediction that the coefficientson innovation intensity and employment are roughly the same, namely m = n which will
be tested later on. The estimation results are tabulated in Table 4 which also reports theP-value of testing the equality of coefficients on R&D and employment m = n.
The column 1 estimates the specification using heteroscedastic robust OLS. As anticipated, because of the presence of other unobserved internal trade cost components,
the erratic behavior of infrastructure proxy suggests that failing to control other unobserved internal trade cost components downward bias the estimate. Column 2 reports a
specification adding a country specific fixed effect to control unobserved internal trade
cost terms and any country specific terms. The coefficient on innovation intensity is similar to the coefficient on employment. The statistical test does not reject the hypothesisthat those two coefficients are the same. Moreover, the estimated coefficient is close to
0.25 confirming the validity of our specification. Moving to column 3, the positiveness17

Several notable studies, e.g., Eaton and Kortum (2002) and Allen and Arkolakis (2014), pick θ = 8
as their preferred value. In fact, the following analysis shows that the estimation result is insensitive tothe value of θ.

19and statistical significance of infrastructure persist when the infrastructure index is used.
Even in situations where different values are assigned to θ to which plenty of results intrade literature are sensitive, most of the results are preserved. Column 4 displays theresults under θ = 6. The estimate on infrastructure proxy remains positive and significant. Its value is close to the ones in column 2. The coefficients on innovation intensityand employment are very close to each other and pass the equality test.
Another possibility of endogeneity comes from reverse causality. The government
would improve infrastructure conditions to facilitate trade when it anticipates an economic boom. As Francois and Manchin (2013) point out, it is particularly hard to finda satisfactory instrument to obviate the reverse causality concern. In light of Arellano
and Bond (1991), we use the two period lag of infrastructure proxy as an instrument for
infrastructure. This instrument would be valid when the contemporary shocks on real
income would not be correlated with the infrastructure condition one period ahead. Then
we apply the two stage least squares and report the results in the last column of Table
4. The 2SLS results are similar to the ones using plain fixed estimation in column 2.
Both results are positively significant at 1% level, except that the point estimate on infrastructure length is slightly higher, which does not qualitatively change our result. The
statistic tests on the equality of the coefficients on innovation intensity and employment
are not rejected. To further ensure the exclusion restriction, we also conduct the 2SLS
using 10 period lag as the instrument and report both first stage and second stage resultsin the Appendix C, confirming the results using the 2 period lag in column 5. However,the 2SLS using the 10 period lag drops most of the observations and the estimates might
suffer from the weak instrument problem. So we decide to pick the estimates under 2SLS
using the 2 year lag as our preferred estimates. Additionally, the working paper versionof this paper shows that the estimates are robust to the inclusion of institutional control.
To summarize, we can safely conclude that better infrastructure enhance the real income
and internal trade, echoing the results in Allen and Arkolakis (2014), Donaldson andHornbeck (2016), Donaldson (2018) and Fan et al. (2021).
From the estimates of our preferred specification column 5, the internal trade elasticity
of infrastructure can be recovered as 1.604, which corresponds to θa in section 3. Together
with the preferred coefficient 0.650 in Table 2, the elasticity of infrastructure on importing
trade flows and exporting trade flows combined namely θ(b + c) equals to 2.254. Because
there is no systematic evidence showing the cross country variation of infrastructure
affects importing flows and exporting flows heterogeneously, following Fan et al. (2021),
we impose the assumption that to the same extent infrastructure enhances both tradeflows, which results in θb = 1.127. The qualitative repercussions from this assumption
would not be altered if the discriminatory impacts of infrastructure on both flows are
not overly unbalanced. The relative magnitude of θa and θb decides the direction ofabsorption rate change with respect to the unit increase of infrastructure. Here, the20Table 4: Internal Trade Elasticity from Real Income
(1)
OLS

(2)
LengthINF Length

0.014(0.027)0.326∗∗∗(0.117)INF Index

0.089∗∗∗(0.033)0.647∗∗∗ 0.364∗∗∗ 0.230∗∗∗ 0.324∗∗∗ 0.346∗∗∗(0.036) (0.048) (0.027) (0.057) (0.060)
0.042∗
0.407∗∗ 1.063∗∗∗ 0.297
0.405∗∗(0.022) (0.161) (0.084) (0.192) (0.191)
4.776∗∗∗ 2.711∗∗ 5.882∗∗∗ 2.876∗(0.392) (1.354) (0.181) (1.618)

R&D Intensity
Employment
Constant
Observations
R2
m = n P-valueCountry Fixed Effect

469
0.599
0.000
No

469
0.926
0.819
Yes

(3)
Index

(4)
Theta

(5)
2SLS

0.351∗∗ 0.401∗∗∗(0.139) (0.120)

619
0.987
0.000
Yes

469
0.899
0.904
Yes

420
0.783
Yes

Note: Standard errors in parentheses
The dependent variable is the log of real GDP per capita adjusted by the absorption
rate. R&D Intensity means researcher count engaged in certain activities in per
million people. INF length is the infrastructure proxy constructed using summation oflength of railroad and paved road. INF Index is the infrastructure index constructedby Donaubauer et al. (2016a). R&D, Employment, INF length are in their log values.
Other indices are in their level values.
∗
p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

21

estimation result implies domestic goods expenditure share also known as the absorption
rate will increase from better infrastructure, meaning the traditional gains from trade will
be dampened according to the ACR formula due to better infrastructure. Though seems
odd at the first sight, equation (10) shows that the traditional gains from trade haveto be adjusted by the change of internal trade cost. The better infrastructure reduces
internal trade cost meaning domestically produced goods are more competitive and higher
expenditure share on the low cost goods naturally leads to higher real income, although
the absorption rate appears to increase.
Moreover, the results of the above two subsections combined have important ramifications. It implies that a better infrastructure tends to increase trade openness, increasing
both export and import. This opens the door to additional benefits associated withhigher trade openness, such as increasing mobility of the international capital flow andhigher effectiveness of the financial market, which has been shown extensively by growthand finance literature.

6

Quantitative Analysis

Given the elasticity estimated in the previous sections, this section provides several quantitative exercises, highlighting the importance of internal trade cost in assessing thechange of real income. The first counterfactual scenario is to increase the transport
infrastructure worldwide by 10%, within which two situations are considered. The firstsituation is to assess the resulting effects using all the estimates we preferred in the previous sections. The second situation is assuming the infrastructure is not affecting theinternal trade cost, whose purpose is twofold. On one hand, it provides a conservative result to the elasticity estimation on internal trade because of the lack of ideal instruments,on the other hand, it provides square contrast between the traditional ACR formula andthe welfare formula advocated in this paper. The second counterfactual exercise is to compare the counterfactual changes if the 10% increase in transport infrastructure happenedin either China or the United States, in light of the recently passed the US infrastructure
bill. The details of the data used in this section are delegated into Appendix F.

6.1

10% Worldwide Infrastructure Increase

Table 5 displays the absorption rate change and real income change under two different
scenarios. The columns on the left correspond to the counterfactual situation where all
the elasticities are specified as we preferred in the previous sections. Meanwhile, thespecification of the two columns on the right is largely the same except that the elasticityof transportation infrastructure on the internal trade cost is taken as 0.
Though it is a worldwide uniform increase of transport infrastructure, its impact is22

Table 5: Cross Countries Comparison of Absorption Rate and Real Income Change

a = 0.201

a=0

ISOCodeAbsorption

Real Income

Absorption

Real Income

ARE
ARG
AUS
AUT
BEL
BRA
CAN
CHE
CHN
COL
DEU
EGY
ESP
FRA
GBR
GRC
IDN
IND
IRN
ITA
JPN
KOR
MEX
MYS
NGA
NLD
PAK
PHL
POL
RUS
SAU
SWE
THA
TUR
TWN
UKR
USA
VEN
XTW
ZAF

0.981
0.993
0.992
0.983
0.975
0.995
0.988
0.983
0.993
0.992
0.987
0.986
0.989
0.990
0.991
0.986
0.990
0.992
0.990
0.991
0.994
0.988
0.990
0.978
0.983
0.987
0.990
0.983
0.986
0.991
0.984
0.986
0.980
0.991
0.982
0.983
0.994
0.990
0.986
0.991

1.047
1.044
1.044
1.046
1.049
1.043
1.045
1.046
1.044
1.044
1.045
1.046
1.045
1.045
1.044
1.046
1.045
1.044
1.045
1.044
1.043
1.045
1.045
1.048
1.047
1.045
1.045
1.047
1.046
1.044
1.046
1.046
1.047
1.044
1.047
1.047
1.043
1.045
1.046
1.044

0.933
0.976
0.972
0.940
0.912
0.983
0.957
0.941
0.974
0.971
0.955
0.950
0.960
0.964
0.966
0.949
0.965
0.971
0.962
0.967
0.979
0.957
0.962
0.923
0.938
0.955
0.965
0.939
0.950
0.969
0.944
0.948
0.929
0.966
0.936
0.939
0.980
0.964
0.950
0.967

1.018
1.006
1.007
1.016
1.024
1.004
1.011
1.016
1.007
1.007
1.012
1.013
1.010
1.009
1.009
1.013
1.009
1.008
1.010
1.009
1.005
1.011
1.010
1.020
1.016
1.012
1.009
1.016
1.013
1.008
1.015
1.014
1.019
1.009
1.017
1.016
1.005
1.009
1.013
1.009

The wage level in country NGA is normalized to be the same as factual level as
country NGA has the lowest export value to China in year 2007.

23

Figure 2: Cross Country Real Income Changequite diverse across countries in both scenarios with small countries generally having
higher real income change than large countries. Figure 2 plots the real income change
against country size for the situation of a = 0.201. The fitted blue line shows a clear
downward sloping trend confirming the conventional wisdom that small countries generally benefit more than large countries in the uniform trade liberalization with the highest
gain for Belgium almost 13% higher than the lowest for Brazil.
When compared across two scenarios, several noteworthy points emerge. First, boththe absorption rate change and real income change exhibit lower variance across countries when the transport infrastructure’s internal trade cost elasticity is in place. Almost
all regions have real income increases around 4.5%. The likely reason behind this phenomenon is that the incremental on the internal trade flow because of the reduction of theinternal trade cost is the deciding component of the overall impact. Although transport
infrastructure has roughly similar elasticity on both importing trade flows and internal
trade flows according to our estimates, just as Waugh (2010) points out, the factual absorption rate is roughly the same regardless of the country size and generally higher than
0.5 meaning more than half of the expenditures goes to domestic goods producers. Given
the sheer size of the factual absorption rate and its rough homogeneity across countries,
the incremental of the internal trade flow is likely to inherit the dominant role in shaping
the real income gain. The second noteworthy point can be obtained from comparing theabsorption rate across the two scenarios. It is clear that both situations imply the gains
24

from openness and the reduction of absorption rate is uniformly smaller in the situation
where the internal trade cost reduces. According to the ACR formula, the situation wherea = 0.201 should have lower real income gains whereas the model in this paper implies
higher real income gains in all the countries and regions, a crucial difference between
this model and the ACR formula. As equation (10) implies, the gains from the changeof absorption rate have to be adjusted by the internal trade cost change to arrive at
the real income change. It is possible that one country could have the absorption ratechange higher than 1 and the real income gain at the same time. Intuitively, though thiscountry seems to be “more closed from the world” and relies more on its own production,
it can actually be better off from consuming more of the more competitive domestically
produced goods. In addition to the qualitative difference between the model in this paper
and the classical ACR formula, the third point highlights the quantitative difference. The
scenario where a = 0.201 has much higher real income gains compared with the scenario
where a = 0, with 5 times higher on average. The lowest is Belgium being 2.06 times
higher and the highest is Brazil with 10.10 times higher.
Table 5 also provides conservative quantitative results where the causality effect of
infrastructure on internal trade flows is not properly identified due to the lack of an
appropriate instrument. The mean of the real income gain for the situation where a = 0
is 1.16%, with Belgium being the highest having 2.4%.

6.2

10% Infrastructure Increase in China vs. USA

Table 6 and Table 7 present the key changes for the counterfactual increase of transport
infrastructure in either China or the US. Those two tables share many things in common. The most striking and crucial message comes in the absorption rate change. The
unilateral trade cost reduction resulting from the increase in infrastructure decreases all
the countries’ absorption rate by a similar magnitude in both cases. Yet, the gains inreal income are the highest for the country itself. This result echos the key difference between this model and the ACR formula described in the theory section and the previous
counterfactual exercise—the gains from openness has to be adjusted by the internal trade
cost change to arrive at the real income change. The second noteworthy point is that thegains from better infrastructure densely concentrate on the country itself, though better
infrastructure facilitates both internal and international trade flow. The gains reaped by
the infrastructure improving country are around 4.2% under both situations, which are
more than one hundred times higher than the benefits spilling over to its trading partners.
However, the gains for the infrastructure improving country are fairly sizable given theycome from merely a 10% increase in the infrastructure. This echoes the result in Fan
et al. (2021) where shutting down the international trade channel will only marginallydiminish the gains from the domestic infrastructure improvement. Interestingly, despite25the differences in methodology, this study implies similar size welfare gain as Fan et al.
(2021). 50, 000 km expressway is roughly 13%, close to this exercise, increase of theinfrastructure measure used in this paper and yields 5.1% welfare gains which are alsotantamount in size to the gains of this exercise. The third insight appears when comparing this counterfactual analysis with the previous one where worldwide infrastructure
is increased by 10%. The improvement on the country’s own infrastructure contributes
more than 95% of its total gains, which echos the last point—the infrastructure improving
country reaps most of its gains.
Despite the above similarity, there are differences when zooming in on particularcountries. For example, the US is the major trading partner for Canada and Mexico.
They benefit one order higher than other countries from 10% improvement in the US’s
infrastructure. On the contrary, 10% improvement in China’s infrastructure benefits
other countries to the roughly same extent except for Chinese Taipei who also has China
as its major trading partner.
To summarize, several salient points stand out in the entire quantitative analysis.
First, transport infrastructure improvement can generate sizable real income gains. Second, the infrastructure improving country reaps almost the entirety of the gains fromtrade. Third, the gains from absorption rate change are much smaller than the gains
directly from the internal trade cost change. Failing to account for the change of the internal trade cost will result in underestimating the real income change by several orders.
Slightly lower estimates of a, b, and c—the trade elasticities will not qualitatively neither
quantitatively change the above results, as has been shown in the working paper versionof this paper.

7

Robustness Analysis

The section provides several types of robustness checks. First, we show the prediction insection 3 is valid meaning regardless of either side of the infrastructure proxy is employed,
the estimates always capture the export and import side combined relative to internal
trade. Second, we show our main results in Table 2 are robust to the inclusion of institutional variables whose impact numerous studies have found to be significant on tradeflows. The third robustness check is to show our main results are robust to infrastructure
proxy accounting for the country’s geographical size. It further shows that the results
remain valid even when infrastructure is proxied by the railroad or paved road separately.

7.1

Estimations with Infrastructure of Exporter Side

Table 8 displays the estimation results with bilateral trade proxies using OLS and PPML
as showcasing and validates the analysis in Section 3. The 1 and 3 columns show the26

Table 6: 10% Increase of Transport Infrastructure in China

ISOcodeWage

Price Index

Absorption

Real Income

ARE
ARG
AUS
AUT
BEL
BRA
CAN
CHE
CHN
COL
DEU
EGY
ESP
FRA
GBR
GRC
IDN
IND
IRN
ITA
JPN
KOR
MEX
MYS
NGA
NLD
PAK
PHL
POL
RUS
SAU
SWE
THA
TUR
TWN
UKR
USA
VEN
XTW
ZAF

1.00047
1.00037
1.00068
1.000221.00027
1.00032
1.00008
1.00039
1.04998
1.00006
1.00028
1.000101.000141.00019
1.000131.000131.000481.00035
1.00080
1.000141.00090
1.001510.99996
1.00119
1.00000
1.00009
1.00034
1.001441.00009
1.00023
1.00065
1.00025
1.001141.00009
1.00252
1.00009
1.00005
1.00018
1.00049
1.00032

0.99993
1.00015
1.000311.000131.00000
1.000150.99979
1.000170.987170.99990
1.00006
0.99980
1.000021.00008
1.00000
1.00000
1.00008
1.00008
1.000141.000031.000481.00055
0.999811.000150.999710.99989
0.99996
1.000470.99998
0.99994
1.000111.00008
1.00033
0.99995
1.00092
0.999810.999830.99996
1.00004
1.00004

0.99857
0.999410.99902
0.999760.999310.99957
0.999250.999430.99920
0.999560.999410.999210.99968
0.99969
0.99966
0.99964
0.99894
0.99929
0.99826
0.99969
0.998900.99746
0.99961
0.997270.999220.999490.99901
0.997470.999710.999220.99857
0.99956
0.99787
0.99962
0.995790.99926
0.999420.999420.998800.99925

1.000361.00015
1.00025
1.00006
1.00018
1.000111.00019
1.000141.04219
1.000111.00015
1.00020
1.00008
1.00008
1.00009
1.00009
1.00027
1.00018
1.000441.00008
1.00028
1.000641.000101.00069
1.00020
1.000131.00025
1.000641.000071.00020
1.000361.000111.000541.000101.001071.00019
1.00015
1.00015
1.000311.00019

The wage level in country NGA is normalized to be the same as factual level.

27

Table 7: 10% Increase of Transport Infrastructure in the US

ISOcodeWage

Price Index

Absorption

Real Income

ARE
ARG
AUS
AUT
BEL
BRA
CAN
CHE
CHN
COL
DEU
EGY
ESP
FRA
GBR
GRC
IDN
IND
IRN
ITA
JPN
KOR
MEX
MYS
NGA
NLD
PAK
PHL
POL
RUS
SAU
SWE
THA
TUR
TWN
UKR
USA
VEN
XTW
ZAF

0.99835
0.99820
0.99823
0.99849
0.99852
0.99827
1.000310.99855
0.99887
0.99889
0.998440.99862
0.99838
0.998400.99850
0.99835
0.99850
0.99856
0.99837
0.998420.99849
0.99851
1.000310.99897
1.00000
0.99838
0.99892
0.99875
0.99830
0.998390.998810.99849
0.99877
0.99834
0.998810.998391.04795
1.00050
0.99870
0.998450.99798
0.997990.997990.99825
0.99808
0.99806
0.99818
0.998130.99857
0.99823
0.99818
0.998100.99824
0.998220.99820
0.99811
0.99832
0.99834
0.99824
0.99828
0.99827
0.99809
0.99829
0.998210.99869
0.998130.99855
0.998070.99820
0.99825
0.998140.99823
0.99825
0.99820
0.998120.99823
0.98533
0.99923
0.99820
0.998240.999030.999450.999380.99937
0.99884
0.99946
0.99437
0.99889
0.999210.998280.99930
0.998630.999610.99952
0.999210.999350.999510.999400.99964
0.999620.999410.99887
0.99467
0.99798
0.99655
0.999350.99903
0.998210.999730.99965
0.998220.99932
0.998630.99962
0.998170.99957
0.99936
0.99666
0.998700.99943

1.00025
1.000141.00016
1.00016
1.000291.000141.00143
1.00028
1.00020
1.000441.00018
1.00035
1.000101.000121.00020
1.00016
1.000131.00015
1.00009
1.000101.00015
1.000291.001361.00051
1.00088
1.000171.00025
1.00045
1.000071.00009
1.00045
1.000171.00035
1.000101.00047
1.000111.04215
1.00085
1.00033
1.00014

The wage level in country NGA is normalized to be the same as factual level.

28

results for OLS and PPML estimations for the exporter side infrastructure proxy and the
2 and 4 columns display the results using the importer side infrastructure proxy. The
coefficients of infrastructure proxies confirm that they capture the relative effect regardlessof which side’s measure is used. The estimates of the infrastructure are the same andtheir interpretation is that the exporting and importing effect combined, relative to theinternal effect. The same results are obtained when estimating using other alternative
methods, such as PPML with pair fixed effect.
Table 8: Augmented Gravity Estimations with Infrastructure of Exporter side
(1)
EXP OLS
EXP INF×Border

0.409∗∗∗(0.128)IMP INF×BorderDistance
Contiguity
Language
ColonyRTA
BorderConstants
Observations
R2
Pseudo R2Country Pair FE
Importer-Time FE
Exporter-Time FE(2)
IMP OLS−1.251∗∗∗(0.069)0.420∗∗∗(0.104)0.333∗∗∗(0.114)0.038(0.125)0.487∗∗∗(0.089)−8.105∗∗∗(1.574)18.715∗∗∗(0.449)
17406
0.912
No
Yes
Yes

(3)
EXP PPML(4)
IMP PPML

0.196∗∗∗(0.045)0.409∗∗∗(0.128)−1.251∗∗∗(0.069)0.420∗∗∗(0.104)0.333∗∗∗(0.114)0.038(0.125)0.487∗∗∗(0.089)−8.105∗∗∗(1.574)18.693∗∗∗(0.448)
17406
0.912
No
Yes
Yes

−0.627∗∗∗(0.051)0.394∗∗∗(0.089)0.563∗∗∗(0.102)−0.101(0.110)0.107(0.097)−6.119∗∗∗(0.663)19.215∗∗∗(0.324)17409

0.196∗∗∗(0.045)−0.627∗∗∗(0.051)0.394∗∗∗(0.089)0.563∗∗∗(0.102)−0.101(0.110)0.107(0.097)−6.119∗∗∗(0.663)19.213∗∗∗(0.324)
17409

0.994
No
Yes
Yes

0.994
No
Yes
Yes

Note: Standard errors clustered at country pair level are reported in parenthesis.
The 1st row shows the results for the infrastructure proxy of the importer side and the
2nd row shows the results for the infrastructure proxy of the exporter side. These results
are not the same as the results in Table 2, because we drop some observations withmissing values of either the infrastructure proxy of the exporter or importer side andestimate only with observations that have both of them. The main goal of this exercise
is to verify our analysis at the end of section 3. FE is short for fixed effect.
∗p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

29

7.2

Robustness to Institutional Control

After including the interaction term of the WGI index and border dummy as institutional
control, Table 9 displays that most of the coefficients of the infrastructure proxy are
significantly positive and slightly smaller than the ones in Table 2 dissipating the concernthat infrastructure can easily succumb to omitted variable biases. Those slightly smaller
estimates will not quantitatively change our quantitative results which have been shownin the working paper version. As a side note, Table 9 also shows that the signs ofcoefficients of the institution are unstable in the estimations we conduct. The method
in Beverelli et al. (2018) having the institution as the only variable of interests without
controls can lead to omitted variable bias, while the estimation with infrastructure as the
only dependent variable has higher immunity.
Table 9: Augmented Gravity Estimations with Institutions

INF×Border
WGI×Border
Observations
R2
Pseudo R2Country Pair Fixed EffectImporter-Time Fixed EffectExporter-Time Fixed Effect

(1)
(2)
(3)
OLS
PPML Pair OLS
0.490∗∗∗ 0.260∗∗∗ 0.039(0.101) (0.038)(1.205)0.808∗∗∗ 0.326∗∗∗ 0.602(0.259) (0.071)(0.608)
89437
99867
89261
0.819
0.925
0.992
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes

(4)
Pair PPML
0.369∗∗(0.184)−0.607∗∗∗(0.143)
99396
0.998
Yes
Yes
Yes

Note: Standard errors clustered at country pair level are reported in parenthesis.
Total length of the railroad and the paved road is selected as infrastructure proxy. WGI
index is the institution quality index from World Bank’s World Governance Indicator
database. The standard gravity variables such as distance are not reported here.
∗p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01.

7.3

Alternative Proxies for Infrastructure

To account for the intrinsic heterogeneity in the country size, in Table 10, we present
the results in which we use the paved road, railroad, and infrastructure density, as theproxy of infrastructure, respectively. Table 10 implies that results similar to our main
result can be obtained regardless of what out of those three proxies we pick. However,it reports a negative coefficient of the length of the railroad from PPML estimation withsymmetric pair fixed effect, although reassuringly it is insignificant. This might comefrom the lack of variations in the railroad length variable. A sensible explanation is thatthe geomorphic feature of some countries is not suitable to have more railroads built,
whereas paved road is more adaptable to various geomorphic features.
30

31
121210
0.998
Yes
Yes
Yes

121892
0.992
No
Yes
Yes

108486
0.814

No
Yes
Yes

(5)
PPML

No
Yes
Yes

95319
0.818
0.992
No
Yes
Yes

1068380.477∗∗∗ 0.211∗∗∗(0.138) (0.050)

(4)
OLS

0.998
Yes
Yes
Yes

106397−0.124(0.131)(6)
Pair PPML

Railroad(8)
PPML0.703∗∗∗ 0.232∗∗∗(0.244) (0.052)
95319
106838
0.818
0.992
No
No
Yes
Yes
Yes
Yes

(7)
OLS

0.998
Yes
Yes
Yes

0.650∗∗∗(0.146)106397(9)
Pair PPML

Total Length Desity

Note: Standard errors clustered at country pair level are reported in parenthesis.
The independent variables are the log of the length of the paved road, the length of the railroad, and the total length of the paved road and therailroad per area, respectively. The standard gravity variables such as distance are not reported here. FE is short for fixed effect.
∗p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01.

Observations
R2
Pseudo R2Country Pair FE
Importer-Time FE
Exporter-Time FE

INF Density×Border

INF Rail×Border

INF Paved×Border

(1)
(2)
(3)
OLS
PPML Pair PPML
0.455∗∗∗ 0.256∗∗∗
0.896∗∗∗(0.130) (0.037)(0.154)

Paved Road

Table 10: Augmented Gravity Estimations with Alternative Proxies for Infrastructure8Conclusion

Motivated by cross-country differences in the domestic infrastructure investment, thispaper attempts to estimate how much infrastructure can affect the trade cost and thegains from trade and it proposes a variant of the EK framework, capable of identifying thecountry-specific variable separately from the country-specific fixed effect. This framework
can be widely applicable to assess the impact of other country specific factors, e.g.,
institution quality, political party turnover, on both international trade and internal tradeflows. The proposed theoretical model enables the structural interpretation of coefficientson infrastructure and explains why regardless of whichever side’s infrastructure is used,the estimate would be the same. Moreover, this theoretical model offers a new welfare
formula that better aligns with intuition when the variable of interest affects both theinternational trade cost and the internal trade cost. Proven by the quantitative evidence,
failing to account for the impact of infrastructure improvement on internal trade cost in
the welfare formula will not only quantitative but also qualitative misinterpret the gains
from trade.
Guided by the theoretical model, the empirical results show that better infrastructure
boosts international trade more than internal trade and it has a non-negative impact oninternal trade. Further quantitative analysis shows that 10% transportation infrastructure increase induces a sizable 4.2% increase in real income and more than 95% of total
gains concentrate on the infrastructure improving country itself. All the above results
make infrastructure improvement a favorable policy instrument.
An interesting venue to extend this paper is to embed this framework into a broader
setting and assess the relative importance of several interesting factors in shaping theworld trade flows and real income changes in a comparative way.

Acknowledgements
We are thankful to Dr.Julian Donaubauer for providing us with the complete dataset of
Global Infrastructure Index.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal
relationships that could have appeared to influence the work reported in this paper.

32

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37

AppendicesA

Augmented Gravity Estimations with Sub-indicesof Infrastructure

Table 11 and 12 showcase the results when we estimate with sub-indices in Donaubauer
et al. (2016a) using PPML and OLS with symmetric pair fixed effect. The coefficientsof those sub-indices are positive and most of them remain significant. These results are
consistent with the results in Table 3 showing our results are not driven by the aggregationof sub-indices.
Table 11: PPML Estimations with Sub-indices of Infrastructure(1)
PPML
INF Tran×Border

(2)
PPML

(3)
PPML

0.389∗∗∗(0.038)0.274∗∗∗(0.044)

INF Com×Border

0.143∗∗∗(0.046)INF En×Border
INF Fin×Border
Observations
Pseudo R2Country Pair Fixed EffectImporter-Time Fixed EffectExporter-Time Fixed Effect

(4)
PPML

321889
0.989
No
Yes
Yes

330789
0.988
No
Yes
Yes

272238
0.988
No
Yes
Yes

0.589∗∗∗(0.047)304552
0.989
No
Yes
Yes

Note: Standard errors clustered at country pair level are reported in parenthesis.
Independent variables from the 1st to the 4th row are sub-indices of the infrastructure index constructed by Donaubauer et al. (2016a) interacted with borderdummy. Their categories are transportation, communication, energy, and financial infrastructure, respectively. The standard gravity variables such as distanceare not reported here.
∗p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01.

B

Augmented Gravity Estimations with Real GDP
and Real GDP per capita

As Frankel and Romer (1999) and Feyrer (2019) point out there exist reverse causality between trade and income which complicates the identification of the positive effect of tradeon income, in the same vein, it is reasonable to have a concern that missing GDP in the38

Table 12: Pair Fixed Effect OLS Estimations with Sub-indices of Infrastructure

INF Tran×Border(1)
Pair OLS
0.001(0.106)

INF Com×Border(2)
Pair OLS(3)
Pair OLS

0.184(0.136)
0.766∗∗∗(0.212)INF En×Border
INF Fin×Border
Observations
R2
Country Pair Fixed EffectImporter-Time Fixed EffectExporter-Time Fixed Effect(4)
Pair OLS

240427
0.862
Yes
Yes
Yes

246360
0.860
Yes
Yes
Yes

211831
0.874
Yes
Yes
Yes

0.199∗(0.109)231638
0.866
Yes
Yes
Yes

Note: Standard errors clustered at country pair level are reported in parenthesis.
Independent variables from the 1st to the 4th row are sub-indices of the infrastructure index
constructed by Donaubauer et al. (2016a) interacted with border dummy. Their categories
are transportation, communication, energy, and financial infrastructure, respectively. The
standard gravity variables such as distance are not reported here.
∗p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01.

estimation could cause omitted variable bias. To alleviate this concern, we run tests that
include Real GDP and Real GDP per capita. However, the simple inclusion of Real GDP
and Real GDP per capita introduces another complexity—multicollinearity between RealGDP and the length of transportation infrastructure. Table 13 shows the result of the estimation including GDP instead of the proxy of infrastructure. As anticipated, the highly
significant coefficient on Real GDP indicates the high correlation between Real GDP and
the length of transportation infrastructure causes spurious positive causal interpretation.
Moreover, when both Real GDP and the length of transportation infrastructure are included as shown in the first two columns of Table 14, the coefficients of the proxy of
infrastructure become negative and not significant, which is exactly the typical symptomof multicollinearity issue. The same difficulty persists when the additional variable RealGDP per capita is included as shown in the first two columns of Table 15.
The underlying cause of the strong correlation between Real GDP and the lengthof transportation infrastructure is unknown and hard to identify. One possible reason
is that the relatively small observations of the length of transportation infrastructure
as documented in the data description section compromises its efficiency as a proxy fortransportation infrastructure. As a potential remedy, we use another proxy which has
much larger observations—the infrastructure index to redo all the exercises as before
whose results are shown in the last two columns of Table 14 and 15. The positive coefficient on the infrastructure index remains significant and persistent across different
39specifications confirming the main result that the infrastructure facilitates international
trade more than internal trade.
As a side note, all the above exercises are of reduced form. The specification in themain content of this paper is derived from the structural gravity model. The structural
gravity model implies we should not find a significant relative effect from Real GDP between international trade and internal trade because all the effects from the size of theeconomy are subsumed in the country specific fixed effects. In the preferred specificationof pair fixed effect as in the last column of Table 14 and 15, where the unobserved differential internal trade costs are controlled for as mentioned in footnote 10, the coefficient on
Real GDP remains insignificant, echoing the implication of structural gravity model. To
summarize, despite the difficulty of the multicollinearity issue, we have enough reduced
form support for our results in the main content of this paper, and those results are also
backed up by our preferred pair fixed effect estimation from structural gravity theory.
Table 13: Augmented Gravity Estimations with GDP

GDP×Border
Observations
R2
Pseudo R2Country Pair Fixed EffectImporter-Time Fixed EffectExporter-Time Fixed Effect

(1)
(2)
(3)
(4)
OLS
PPML Pair OLS Pair PPML
0.787∗∗∗ 0.384∗∗∗ 0.782∗∗∗
1.300∗∗∗(0.101) (0.036)(0.205)(0.125)397819 519468
396947519468
0.748
0.853
0.985
0.996
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes

Note: Standard errors clustered at country pair level are reported in parenthesis.
Real GDP data are from Penn World Table 9.1. The first column shows the result fromthe OLS estimation. The second column shows the result from the PPML estimation.
The third column shows the result with a symmetric country pair fixed effect using the
OLS. The fourth column shows the result with a symmetric country pair fixed effect using
the PPML. The standard gravity variables such as distance are not reported here.
∗p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01.

C

IV Estimations of Internal Trade Elasticity

Here we confirm the results in Table 4 using a longer lag of the total infrastructure length
as the instrument to further ensure exclusion restriction. The IV estimation results using
2 different lags as instruments are tabulated in Table 16. The first stage results hintthat both instruments are relevant to the infrastructure proxy, although the 10 year
lag is a bit less significantly correlated with the infrastructure proxy. This is intuitive
because as time elapses, the correlation tends to fade away and be diluted by othercontemporaneous shocks. The second stage results show both instruments indicate a40

Table 14: Augmented Gravity Estimations with GDP and Infrastructure Proxy(1)
PPML−0.052(0.065)

INF×Border(2)
Pair OLS−1.263(0.771)INF Index×Border
GDP×Border
Observations
R2
Pseudo R2Country Pair Fixed EffectImporter-Time Fixed EffectExporter-Time Fixed Effect0.400∗∗∗ 2.157∗∗∗(0.068)(0.392)106838
95163
0.923
0.993
No
Yes
Yes
Yes
Yes
Yes

(3)
PPML Index(4)
Pair OLS Index

0.338∗∗∗(0.041)0.264∗∗∗(0.032)302736

0.394∗∗(0.185)0.182(0.187)230486
0.866

0.989
No
Yes
Yes

Yes
Yes
Yes

Note: Standard errors clustered at country pair level are reported in parenthesis.
This table contrasts the results of including the infrastructure index to the ones using infrastructure
length. The real GDP data are from Penn World Table 9.1. Column 1 is the PPML estimation
including the total length. Column 2 is a symmetric country pair fixed effect using the OLS estimation including the total length. Column 3 is the PPML estimation including the infrastructureindex. Column 4 is a symmetric country pair fixed effect using the OLS estimation including theinfrastructure index. The standard gravity variables such as distance are not reported here.
∗p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

positive internal trade elasticity estimate with the 10 year lag identifying a slightly higher
effect. However, we tend to interpret the results using the 10 year lag with caution. First,
the 10 year lag reduces sample size significantly. It reduces the initial 469 observations
to 169 observations with around two-thirds dropped, which would significantly impair
the validity of the estimates. Second, the Kleibergen-Paap rk F statistic is smaller thanthe conventionally accepted value 10 suggesting a weak instrument. Third, the erratic
behavior of the coefficients on R&D and employment might imply the instrument isweak or under identified. Therefore, our final take is to appoint estimates from the IV
estimation with the 2 year lag instrument as our preferred estimates and use them in thequantitative analysis ensued.

D

Hat Algebra of General Equilibrium

Following Dekle et al. (2008), we define x̂ = x′ /x as the change of any equilibrium
variables x in its counterfactual x′ relative to its factual x. The labor market clear
condition in the equilibrium is given as:
wi Li = βwi Li + β

X
j

41

πij Xj ,(21)

Table 15: Estimations with GDP per Capita and Infrastructure Proxy

INF×Border

(1)
PPML
−0.045(0.068)(2)
Pair OLS−1.277∗(0.760)INF Index×Border
GDP×Border
GDP per Capita×Border
Observations
R2
Pseudo R2Country Pair Fixed EffectImporter-Time Fixed EffectExporter-Time Fixed Effect0.358∗∗∗ 2.469∗∗∗(0.072)(0.742)0.807∗∗∗ −0.361(0.122)(0.723)106838
95163
0.923
0.993
No
Yes
Yes
Yes
Yes
Yes

(3)
PPML Index(4)
Pair OLS Index

0.522∗∗∗(0.070)0.228∗∗∗(0.029)−0.245∗∗(0.103)2915750.346∗(0.193)−0.215(0.360)0.772(0.505)223095
0.869

0.990
No
Yes
Yes

Yes
Yes
Yes

Note: Standard errors clustered at country pair level are reported in parenthesis.
This table displays the results of including two types of infrastructure proxies, real GDP and real
GDP per capita. GDP data are from Penn World Table 9.1. Column 1 is the PPML estimation
including the total length. Column 2 is a symmetric country pair fixed effect using the OLS estimation including the total length. Column 3 is the PPML estimation including the infrastructureindex. Column 4 is a symmetric country pair fixed effect using the OLS estimation including theinfrastructure index. The standard gravity variables such as distance are not reported here.
∗p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

42

Table 16: IV Estimations Using Different Lags
Second StageINF Length
R&D Intensity
Employment

2 Year Lag

10 Year Lag

0.401∗∗∗(0.120)0.346∗∗∗(0.060)0.405∗∗(0.191)0.636∗∗(0.309)−0.240(0.180)0.862∗∗(0.362)First Stage
2 Lag Length

0.830∗∗∗(0.075)0.007(0.015)−0.050(0.083)0.302∗(0.158)0.056(0.062)−0.577∗(0.362)420
121.630
Yes

169
3.630
Yes

10 Lag Length
R&D Intensity
Employment
Observations
KP F-Statistic
Country Fixed EffectNotes: Standard errors in parentheses.
The dependent variable is the log of real GDP per capita
adjusted by the absorption rate. R&D Intensity means
researcher count engaged in certain activities in per million people. INF length is the infrastructure proxy constructed using summation of length of railroad and paved
road. INF Index is the infrastructure index constructed by
Donaubauer et al. (2016a). R&D, Employment, INF length
are in their log values. Other indices are in their level values.
∗
p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

43where the first term on the right denotes the demand for labor in the final goods sector
and the second term captures the labor demand in the intermediate goods sector. The
total expenditure on intermediate Xj consists of spending for intermediate and final goods
usage which are:1−β
(1 − β)2
wj Lj =
wj Lj .
ββ

Xj = (1 − β)wj Lj +(22)

The above two equations combined imply the following
wi Li =

X

πij wj Lj .

(23)

j

Several other relevant equations are inherited from the main text, which includes the unit
cost formula:wβ P 1−βci = i i ,(24)γ
the price index formula:

Pj = A(Xh

Ti (ci ti· τij t·j )

−θ

i

)−1/θ
+ Tj (cj tjj )−θ

,

(25)

i̸=j

the trade share formula:

πij =



P

Ti (ci ti· τij t·j )−θ−θT(c]+Tj (cj tjj )−θs̸=j [ s s ts· τsj t·j )∀i ̸= j
P

Ti (ci tii )−θ−θ]+Tj (cj tjj )−θs̸=j [Ts (cs ts· τsj t·j )

i=j

.

(26)

Given the variable set {Ti , Li , t′i· , t′·j }, equations (21) to (26) provide the panorama of the
new counterfactual general equilibrium. However, knowing Ti and Li would require much
more demanding data availability and a more precise model layout. Provided that therate of change is the focus of interest, a roundabout way is to solve the general equilibriumin the rate of change a.k.a hat algebra. The hat algebra version of the general equilibrium
is given as follows:ĉi = ŵiβ P̂i1−β
(
)−1/θ
X
−θ
P̂j =
πij (ĉi t̂ij )

(27)
(28)

i

(
π̂ij =
wi′ Li =ĉi t̂ij

)−θ

P̂j
X

πij′ wj′ Lj ,

j

44

(29)
(30)

π X

where δij := P ijπij jXj and tij := ti· τij t·j . After solving the general equilibrium in changes,j
the welfare change is given as in formula (10).

E

Computation Algorithm
1. Using equation (30) and factual values of πij to obtain factual values of wi Li ,2. Given initial guess of ŵi , equation (27) and (28) together can solve both ĉi and P̂i .
3. After knowing both ĉi and P̂i , equation (29) generates value of π̂ij .
4. Using π̂ij and factual values of πij to construct counterfactual πij′ and plugging backthe values of πij′ into equation (30) to obtain counterfactual values of wi′ Li .18
5. Dividing the counterfactual values wi′ Li by the factual values wi Li obtained in step
1, to get updated ŵi .
6. Repeat the step 2 to 5 with the updated ŵi until the values of ŵi converge.

One caveat is that the above equation system can only identify ŵi up to a scale, i.e.,
only the relative value of ŵi but not its absolute value is meaningful. Therefore, in thequantification exercise, additional restrictions are imposed to pinpoint the solution.

F

Data for Quantification

The data used for quantification analysis is from GTAP 8 Data Base, which is publicly
available online. The main motive for using GTAP data is that it has well-regularized
data values such that the adding-up constraints stipulated in Fally (2015) are satisfied
which complies better with the theoretical framework in this paper.
The original GTAP database consists of 129 regions and 57 sectors for year 2007. To
circumvent the computation limits and ensure bilateral trade data has nonzero entries
to guarantee the irreducibility and aperiodicity of the trade share matrix, we keep thehighest 39 regions in terms of real GDP and aggregate the rest of the regions into therest of the world(XTW). The 40 regions’ ISO codes and country names concordanceis given in Table 17. The complete data for quantitative exercises utilize the bilateral
trade flow data and domestic input-output data out of the GTAP database. The original
bilateral trade flow data contains bilateral sector level trade flows which we aggregate toobtain country level bilateral trade flows. As for the construction of country level internal
trade flows a.k.a absorption, we aggregate the entries of the domestic input-output flows′′
We choose to work on πij
rather than its hat algebra version π̂ij , because πij
is a stochastic matrix
which has guaranteed eigenvectors associated with eigenvalue 1. This would accelerate the iteration
process and minimize the approximation error during iteration.
18

45

across each pair sector. The resulting internal trade flows resemble more closely the grossexpenditure used in the theoretical framework, rather than a value-added term.
Table 17: Regions Concordance

ISOCodeRegion Name

ISOCodeRegion Name

ARE
ARG
AUS
AUT
BEL
BRA
CAN
CHE
CHN
COL
JPN
KOR
MEX
MYS
NGA
NLD
PAK
PHL
POL
RUS

United Arab Emirates
Argentina
Australia
Austria
BelgiumBrazilCanadaSwitzerland
China
ColombiaJapan
Republic of Korea
MexicoMalaysia
Nigeria
Netherlands
Pakistan
Philippines
PolandRussian Federation

DEU
EGY
ESP
FRA
GBR
GRC
IDN
IND
IRN
ITA
SAU
SWE
THA
TUR
TWN
UKR
USA
VEN
XTW
ZAF

Germany
Egypt
Spain
FranceUnited Kingdom
GreeceIndonesia
India
Iran (Islamic Republic of)
Italy
Saudi Arabia
SwedenThailandTurkeyChinese Taipei
UkraineUnited States
Venezuela (Bolivarian Republic of)Rest of the WorldSouth Africa

46