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© 2014 Nicolaus Copernicus University. All rights reserved.  
http://www.dem.umk.pl/dem 

D Y N A M I C  E C O N O M E T R I C  M O D E L S  
DOI: http://dx.doi.org/10.12775/DEM.2014.002  Vol. 14 (2014) 29−49 

Submitted June 25, 2014  ISSN 
Accepted December 23, 2014 1234-3862 

 Natalia  Drzewoszewska* 

Searching for the Appropriate Measure of Multilateral 
Trade-Resistance Terms in the Gravity Model  

of Bilateral Trade Flows 

A b s t r a c t. The aim of the paper is to compare different approximations of multilateral 
trade-resistance in the gravity model and the influence of their use on estimation results for 
models of EU-trade. Three synthetic variables: for bilateral trade costs, exporter’s and import-
er’s remoteness are used as an alternative for including time-varying country effects. Results 
indicate significant impact of those variables but not wholly compatible with the theory. 
Estimated coefficients of trade determinants, including Euro’s effects, have expected values 
in both approaches only if the FE estimator is applied. 

K e y w o r d s: international trade, panel data, gravity model, multilateral trade-resistance 
terms, bilateral trade costs, globalization in the XXI century, Euro‘s effect  

J E L Classification: F10, F14, F15, C23, C24, C26. 

Introduction 

 The gravity model is a common tool for analyzing the flows of interna-
tional trade. The characteristics of panel data allow for taking into considera-
tion unit specific effects with regard to territorial units covered by the study, 
as well as time effects referring to the years under analysis. Therefore, 

                                                 
* Correspondence to: Natalia Drzewoszewska, Nicolaus Copernicus University, Depart-

ment of Statistics and Econometrics, ul. Gagarina 13a, 87-100 Toruń, e-mail: natalia-
drzewoszewska@gmail.com.  

This paper was written during the author's research stay at  the Chair of Statistics and 
Econometrics at Justus Liebig University Giessen. The author would like to thank Prof. Dr. 
Peter Winker for the work conditions, his encouragement and helpful suggestions. 



Natalia Drzewoszewska 

DYNAMIC ECONOMETRIC MODELS 14 (2014) 29–49 

30

it assists in controlling for unobserved heterogeneity, which could not be 
accounted for by explanatory variables in the model, which is useful for such 
a macroeconomic study. An additional incentive for using the gravity model 
is that the necessary data is relatively easily available. Estimation results of  
a majority of studies described hereinafter are quite similar for the main 
variables in the model – differences come from the different test samples and 
different time periods, as well as from different estimation methods used in 
the research. 
 Focusing on theoretical assumptions of the model can easily explain the 
inaccuracy of some empirical trade analyses based on the gravity model. 
According to the theory of Anderson and van Wincoop (2003), decisions 
about international trade essentially depend on the relative trade costs, which 
are however not easy to measure. One of the aims of this study is to identify 
the best measure of these costs, which will cover the multilateral trade-
resistance, both for exporter and importer. Estimated panel gravity models 
include typical explanatory variables: national income, measure of bilateral 
distance and the set of dummy variables for common border, common lan-
guage and access to the sea. Additionally, considering the utility of the 
gravity model by the test of trade-agreement effect, in former analysis there 
were the dummy variables used to describe the participation in The Econom-
ic and Monetary Union (Micco et al., 2002, 2003; Maliszewska, 2004).  
 Another purpose is the analysis of the international trade between EU 
countries, which create an integrated, relatively homogenous area, where 
such variables like tariffs or rates of exchange that do not have to be includ-
ed in the model. Globalization is often defined as the growing integration of 
economies and societies around the world1 “mainly by free trade and free 
capital mobility, but also by easy or uncontrolled migration” (Daly, 1999), 
“leading to the notion of a borderless global or planetary economy” (Avi-
nash, 2000), which makes the European Union a great example of the glob-
alized economies. 
 Globalization in the XXI century is a specific time – there are deeper and 
broader changes in the global economy – spread of the “New Economy” as 
well as the new information and communication technology (ICT), what is 
pointed out in recent studies (Ramos and Ballell, 2009; Farhadi et al., 2012; 
García-Muñiz  and  Vicente, 2014). Friedman describes 1999 as the year of 
the Internet, when the globalization started a new era, opened for outsourc-
ing, offshoring and other new activities changing the global trade structure 

                                                 
1 Definition used by The World Bank Group, 2001. 



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31

(Friedman, 1999). That is the reason choosing 1999  the starting year of the 
analyzing time period. 
 Three research hypotheses were put forward within the framework of the 
carried out objective. The first assumes that the travel time between cen-
troids of countries is a good base for approximation of bilateral trade costs. 
Following the second hypothesis, bilateral trade flows increase if exchange 
partners are members of the Eurozone. The third hypothesis assumes that 
synthetic variables of bilateral costs and remoteness are accurate approxima-
tion of multilateral trade-resistance terms for EU countries. 
 Two first parts of the paper discuss the theoretical assumptions of the 
gravity model for trade flows and the problems with its estimation. The third 
focuses on the description of the new measures for multilateral trade-
resistance terms. The final part presents the results of conducted research.   

1. Theory of the Gravity Model of Bilateral Trade Flows 

 The first gravity equation was based only on empirical research of Tin-
bergen (1962). Inspired by Newton's law of universal gravitation, author 
presented following “traditional” gravity equation for trade2: 

,321
0

 oddood DXXY   (1) 

where: odY  – volume of trade flow from country o (origin) to country d (des-

tination), do X,X  – national income of countries o and d (GNP volumes), 

odD – physical distance between the two countries. 
 More generally, we can describe the gravity model by four forces:  
G – external (global) factors expressing “gravitational constant”, although it 
is only held constant in the cross-section, oS , dM – specific factors of origin 

and destination factors expressing their “masses”, and od – negative factors 
expressing the trade costs, with the following form: 

,0 oddod MSGY   (2) 

 The gravity model with panel data structure can be written in following 
logarithmic form: 

,,,3,2,10, todtodtdtotod εDXXY    (3) 

                                                 
2 This equation implies that exports have a constant elasticity with respect to each of three 

explanatory variables – what means that a 1 per cent increase in the GNP of country d always 
results in an increase of 

2  per cent in the exports of the supplying country o. 



Natalia Drzewoszewska 

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32

where:  Nod ,...,2,1, , tod ,Y – flow values (log) between regions o,d – 

object’s number3, t=1,2,...,T – number of time period, t,oX , t,dX – explana-

tory variables values (log) respectively for origin and destination regions, 

t,odD  – bilateral trade costs, including distance between regions (log), 

3210 ,,,  – structural parameters of the model4, tod ,ε  – random compo-

nent.  
 Tinbergen (1962) also extended his model for 18 developed countries by 
dummy variables of common border, Commonwealth preference and Bene-
lux preference and, in the second case, by the Gini coefficient of export 
commodity concentration. Further research of econometricians was expand-
ed by additional variables and effects, like time effects or country pair ef-
fects. Nevertheless, the gravity equation still needed the theoretical assump-
tions, which became a key issue in the following years. The theory of gravity 
model was proposed by Anderson (1979), Bergstrand (1989), Deardoff 
(1998), Eaton-Kortum (2002) and Anderson and van Wincoop (2003). The 
last one was named as “the final structural gravity equation” and it passes 
now for the most accurate description of reality. The most important part 
relates to the relative trade costs, which are included in the model as multi-
lateral trade-resistance (MTR) terms. Namely, these two terms measure the 
exporter's and importer's joint average trade resistance (in terms of trade 
barriers), which each of them faces to all their other potential trading part-
ners. For instance, if there is a rise in trade barriers between importing coun-
try d and all its other possible trading partners (inward MTR rises), the rela-
tive price of the exporting country o’s products will decrease and trade flows 
between o and d will increase. Likewise, if outward MTR rises, overall de-
mand on o’s exported products will slow down, thus reducing the price oP , 
which, under conditions of the constant trade barriers, will consequently 
increase trade flows between both countries. The new structural gravity 
equation takes the form of:  

,
1 















do

od
W

do
od P

t

X

XX
EXPORT  (4) 

                                                 
3 In case of panel gravity models, which analyze trade flows, a pair of regions represents 

an object (unit), namely  d,oi  . For N analyzed regions  NN 2
 objects are included in 

the study, i.e. pairs of trading partners. 
4 Prediction that 11  , 12   leads to the unit-income-elasticity model, what was often 

assumed by researchers in the studies. 



Searching for the Appropriate Measure of Multilateral Trade-Resistance Terms… 

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33

with: 
outward (exporter’s) multilateral trade-resistance: 

  ,
1

1
W
d

o d

od
o

X

X

P

t














  (5) 

and inward (importer’s) multilateral trade-resistance: 

  .
1

1
W
o

o o

od
d

X

Xt
P 


















 (6) 

where: oX , dX  – national income values of both trading countries, WX – 

World’s income, odt – trade cost factor reflecting bilateral trade resistance 
between country o and d,  – elasticity of substitution. 
 The conception of multilateral trade-resistance of trading countries is 
intuitively convincing since all the countries have a lot of potential alterna-
tive trading partners and relationships with them that influence the bilateral 
trade-resistance. Hence the trade impediments between countries should not 
be approximated only by the bilateral trade costs. Moreover, the import and 
export of more developed and wealthy countries should be easier, which is 
also expressed in the above form of gravity equation by implementing the 
income shares in the total World income. Omitting the theoretically motivat-
ed MTR terms in the gravity models leads to the systematic bias in coeffi-
cient estimates of bilateral trade-cost variables. This form of gravity model, 
acclaimed to be the most accurate one because of using relative differences 
between countries, was easily expanded to describe another foreign flows, 
namely migration flows (Anderson, 2011). 

2. Difficulties with Empirical Research Based on the Gravity 
Model of Trade Flows Using Panel Data 

 The multiplicative nature of the gravity equation, quality of available 
database, characteristics of panel data or the big amount of missing data 
yield many potential problems with a solid empirical analysis. Among the 
biggest problems occurring by estimating the panel data gravity models are5: 
 multitude of zero-observations (log-linearization is not feasible in these 

cases), 

                                                 
5 More problems with trade data are presented in Feenstra et al. (2001). For essential ref-

erence on panel-data models see Hsiao (2003). 



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 error terms in the usual log-linear form of the gravity equation are heter-
oscedastic (which violates the assumption that error term should be sta-
tistically independent from the regressors, using OLS-method after the 
log-linearization leads to inconsistent estimates of the elasticity of inter-
est, the NLS estimator is in turn very inefficient, as it ignores the hetero-
scedasticity), 

 variance of the error term is not constant (NLS estimator is not optimal) 
 trade data are suffering from rounding errors (that leads to the bias of 

estimates), 
 MTR terms should be included in the gravity model of bilateral flows, 

but they are not directly observable. 
 There are many potential methods that can more or less overcome the 
foregoing problems. One way with the first problem is dropping the pairs 
with zero from the trade-data set, what allows for using OLS estimation 
method. Another way is to keep these observations by adding a constant to 
zero-observations, for instance ( 1ijY ) and use again OLS method, what can 

be found in Martinez-Zarzoso (2007), Westerlund and Wilhelmsson (2009), 
or use tobit model for panel data (Soloaga and Winters, 2001; Baldwin and 
DiNino, 2006; Tripathi and Leitão, 2013). However, all three of these meth-
ods lead to inconsistent estimates (especially by tobit models, where estima-
tion results depend on the chosen constant). To avoid this problem, Santos 
Silva and Tenreyro (2006) proposed the use of PPML (Poisson pseudo max-
imum likelihood) estimator6 in levels, which not only deals with zero-value 
observations, but also can be easily adapted in models with endogenous re-
gressors, providing unbiased estimates in the presence of heteroske-dasticity, 
where all observations are weighted equally. 
 The choice of an accurate estimation method in face of all the problems 
connected with the gravity model is never infallible; hence the common way 
is to use several estimation methods, appropriate to considering case of 
study. Every estimator has pros and cons7 and the inference based on the 
only one method is not advisable. Even using the Hausman test by pointing 
out the right version of model between RE and FE is not practiced since the 
form of both models is not the same (the lack of constant variables in FE-
model) and the assumption about individual fixed effects between trading 

                                                 
6 Previously authors used the gamma PML (GPML), which gave good results, but is very 

sensitive to measurement errors – as it gives an extra weight to the noiser observations. The 
PPML method was originally proposed by McCullagh and Nelder (1989). 

7 Details about majority of estimation methods of gravity model are presented by Gómez-
Herrera (2013). 



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35

pairs in this case seems to always be the right one. However, the readiness of 
researchers to know the coefficients by constant variables leads to imple-
menting more estimation methods. The comparison of the coefficients gives 
an answer to the questions asked in the hypotheses of the research. Interest-
ing research of Gómez-Herrera (2013) includes a comparison of many esti-
mation methods (truncated OLS, OLS ( 1ijY ), tobit, probit – with Heck-

man’s approach8, RE, FE and PPML), where gravity model, despite of  
physical distance and dummies (common border, common language, same 
country and participation in trade agreements)9 among regressors, included 
also exporter and importer time varying effects. The results of comparison of 
several techniques with a dataset covering 80% of World trade induce to 
choose the Heckman sample selection model as the preferred estimation 
method within nonlinear techniques when data are heteroskedastic, but this 
approach is preferred when the data also contain a significant proportion of 
zero observations – what is natural by analyzing 80% of the World trade.  
 The need of using MTR terms is the result of new structural gravity 
equation proposed by Anderson and van Wincoop (2003), which logarithmic 
form is following: 

,,,4

,4,3,2,10,

todtd

totodtdtotod

ε
π

P

tXXEXPORT








 (7) 

where: 31   . 
 There are two ways to take MTR on board in the gravity model: 1) creat-
ing synthetic variables for both countries – remoteness10 – or: 2) including 
time-varying individual effects for both countries in the gravity model (the 
dummy variables identifying the exporter and importer) 11.  

                                                 
8 See Bikker and de Vos (1992), Linders and de Groot (2006), Martin and Pham (2008). 

9 The formula to compute the effect of dummy-variables is following:   %ibe 1001  , 

where ib  is the estimated coefficient. 
10 Wei (1996) defined as the log of GDP-weighted average distance to all other countries. 
10 The use of simulation method allows to obtain MTR as well. However, because of the 

complex calculation problem, this method is rarely taken into consideration by researchers. 
Anderson and van Wincoop (2003) used non-linear programming to include MTR terms, 
assuming that elasticity of substitution equal to 8 . However, Feenstra (2002) showed that 
it is possible to apply importer and exporter fixed effects to obtain approximately similar 
results. Alternatively, Baier and Bergstrand (2009) introduced variables of MR approxima-
tions which produce consistent estimates, using Taylor approximation. This approach were 
used also by  Behar and Nelson (2012). 



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36

 The first method faces a problem with the choice of the right form of the 
variable. The implementing of physical distance is not enough to approxi-
mate bilateral costs, used then in the remoteness variable, since it doesn’t 
cover the whole trade costs, is not time-varying and forces to take the as-
sumption about symmetric bilateral trade costs. There also appeared to be 
another calculation problems, for instance the measure of inter-distance by 
the formula proposed by Head and Mayer (2002)12. The literature provides 
a lot of ways to calculate bilateral trade costs. The most common way, de-
spite using only physical distance, is to create bilateral costs-equation by 
implementing dummy variables, such as common border, common language, 
landlocked and others, namely13: 

  ._...exp 32
1 dummiesotherlanguageborderdt odododod  

   (8) 

 However, the equation above is still difficult to calculate and provides 
still constant and symmetric variable for both countries of the trading pair. 
The calculation of time-varying bilateral trade costs is possible through us-
ing the time-varying specific variables in the equation with some specific 
weights, like: 

 ,...ln ,,33,22,11,
s

tnodn
s

tod
s

tod
s

todtod xwxwxwxwt   (9) 

where: nw – weights, s
t,nodx – standardized values of regressors14.  

 Substantial weakness of this approach is the problem of appropriate 
weights. Taking the arbitrary weights does not seem to be correct in face of 
the differences between countries and non-theoretical or empirically-based 
assumptions. 
 The use of the second method – time-varying individual effects – seems 
to be easier, however, it increased the dimension of the estimated matrix 
causing calculating problems and does not allow for incorporating specific 
variables for countries into the model due to collinearity, what leads to 
a bias15. 

                                                 
12 In this study, the author proposed the approximation of the inter-distance based on liter-

ature, namely ≈ square root of land surface*0,4.  
13 See Baier and Bergstrand (2009); Baldwin and Taglioni (2006). 
14 For more details about the method, see Drzewoszewska et al. (2013). 
15 Likewise, the inclusion of the exporter and importer dummies in the model means that 

inclusion of time invariant exporter and importer characteristics is not possible in this case. 
See Ruiz and Vilarrubia (2007). 



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DYNAMIC ECONOMETRIC MODELS 14 (2014) 29–49 

37

 Facing the problems above, there is no standard way to incorporate MTR 
in the gravity model so far. In the literature, there is a lot of research with 
exporter and importer effects in gravity model of bilateral trade flows, e.g. 
Rose and Wincoop (2001), Baltagi (2003), Ruiz and Vilarrubia (2007). The 
popular practise is to include country-pair effects as well, eg. Glick and Rose 
(2002), Baltagi (2003), Micco et al. (2003), Fratianni and Hoon-Oh (2007), 
Fidrmuc (2008), Bussière and Schnatz (2009). Furthermore, using time ef-
fects in the gravity model is a common issue now, as it replaces global cir-
cumstances, shocks, ect. Another way could be spatial modeling – in the 
research of FDI Fernández-Avilésa et al. (2012) proposed a simple FDI-
based measure of financial distance with the use of spatial techniques. 
 The remoteness variables for exporting and importing countries used in 
foregoing studies have different formulas, are both time-varying (Baldwin 
and Taglioni, 2006) and fixed (Fidrmuc, 2001; Ruiz and Vilarrubia, 2007). 
For instance, Head (2003) calculates remoteness as a country’s average 
weighted distance from its trading partners, where weights are the partner 
countries’ shares of world GDP. 
 The physical distance between trading countries approximates bilateral 
trade costs since the first application of gravity model. The coefficient of this 
variable in estimated models is always negative in all the empirical analysis, 
what makes it a common measure used by researchers. However, the trade 
costs are created primarily by transport costs, which are depended on the 
quality of transport infrastructure, tariffs, prices, as well as on the distance. 
An alternative measure of bilateral trade costs for UE countries is prosed in 
the empirical part of this study. 

3. A New Measure of Remoteness  

 The new formula of remoteness variables, proposed in this study, allows 
for using time-varying bilateral costs, which according to the strong assump-
tion in Anderson and van Wincoop (2003) theory are symmetric. Besides, 
using the distance between countries to describe their bilateral costs leads to 
the constant remoteness, which is another unreal assumption. The formulas 
of three synthetic variables – bilateral costs t,odt , exporter’s remoteness 

t,odREM  and importer’s remoteness t,doREM – are following: 

,
_' ,

,
tod

od
tod OPENNESSSIMPORTER

DISTANCE
t   (10) 

where: 



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38

 .
_

_'
,

,,
,

td

tdotod
tod IMPORTTOTAL

EXPORTEXPORT
OPENNESSSIMPORTER


  (11) 

 Bilateral trade costs (10) became time-varying in this approach, which 
suits better to reality – trading costs are not constant over time and the psy-
chical distance, especially in the era of globalization XXI century, does not 
lower the trade flows as much as 50 years ago. Here the distance between 
countries, measured by travel time between the centroids of trading coun-
tries, is divided by share of bilateral trade exchange in the total import of 
importing country. Moreover, this method reflects the theoretical signifi-
cance of importer’s demand in the final amount of bilateral trade flows. 

Importer’s demand is also underlined by the following form of export-
er’s remoteness variable: 

,
_, ,

,
, 




dok ttk

tok
tod INCOMEWORLDINCOME

t
REMOTENESS  (12) 

which is the sum of  bilateral costs divided by importer’s income share in the 
World’s total income. It is expected that a relatively richer importing country 
will have a larger overall demand, hence the export to this country will be 
relatively easy (exporter’s remoteness is smaller then).  
 In this approach, importer’s remoteness variable includes analogously 
the exporter’s income share in the World’s total income as a weight in the 
weighted average: 

.
_, ,

,
, 




dok ttk

tkd
tdo INCOMEWORLDINCOME

t
REMOTENESS  (13) 

 However, the denominator of importer’s remoteness variable above un-
derlines exporter’s condition, what (being still potential good weight) does 
not play substantial role in the demand of importing country16. Potentially 
better weight would be a share of bilateral export from the importer in his 
total export, since it better expresses importer’s condition and also reflects 
the interrelation with his trading partner. Hence, an alternative measure for 
importer’s remoteness is the following:  

                                                 
16 In macroeconomic theory, import is defined as a function of the domestic absorption A 

(total demand for all final marketed goods and services) and the real exchange rate  , taking 
the form of: ),A(fI  . See Burda and Wyplosz (2005). 



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39

.
_, ,,

,
, 




dok tdtdk

tkd
tdo EXPORTTOTALEXPORT

t
REMOTENESS (14) 

 Comparison of the estimated coefficient’s sign of both above importer’s 
remoteness synthetic variables would give an answer if the second form, 
more economically justifiable, contains a better approximation of inward 
multilateral resistance. According to the theoretical assumptions of Anderson 
and van Wincoop (2003), the MTR terms should have a positive impact on 
bilateral trade flows.  
 According to the theory, estimation results of models with remoteness 
synthetic terms and models with countries time-varying specific effects 
should have similar estimates of the rest of the variables. This could confirm 
that the created synthetic variables are a good approximation of MTR, which 
allows for estimation of their exact influence, also giving an opportunity to 
use more estimators, like PPML or HT. The model to compare has the fol-
lowing form: 

,,,5

,43,2,10,

todtod

todttdtotod

εX

tIIIEXPORT








  (15) 

where: t,dt,o ,II  – time-varying individual effects, tI – time effects, t,odt – 

bilateral trade costs, t,odX – set of dummies for the trading pair. 

 An easier way to estimate MTR can be the assumption that MTR is con-
stant over time, what allows for using only fixed individual effects for both 
countries, with lower dimension of the estimating matrix. However, this 
assumption is advisable in the case of relatively short time period, so it is not 
considered in this study.  

4. Gravity Model of Bilateral Trade Flows for EU Countries  
in the Period of 1999–2011 – Empirical Results  

 The data used in this study consists of a sample of 25 EU countries, with 
the following database-sources: Comtrade/OECD, WDI and Google Maps 
application. In order to analyze the trade in the era of globalization XXI 
century, the chosen time period of research is opened by “the year of the 
Internet” and includes the last year of available data. Variables included in 
the analysis are presented in Table 1. 
 The first step of research was to look for an alternative variable that 
could replace the physical distance in the traditional gravity model. As 
a matter of fact, the physical distance is considered as a good approximation 



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40

of bilateral trade costs, however it does not take into account the quality of 
transport infrastructure, which varies over the countries and influence on the 
time and costs of transportation. The use of the time travel between centroids 
of countries became possible owing to free Google Map application, which 
time-data was downloaded on 14.03.201417. 

Table 1. Variables included in the analysis of international trade flows 

Variable Definition 
Measure 

unit 
Source 

EXPORT 
Export flows in current prices from origin country to 

destination country 
USD 

Comtrade/OECD 

GNI Gross National Income in current prices18 USD WDI 

DIST Great circle distance between the national centroids km 
Author’s calcula-

tion 
TRAVEL Travel time by road between the national centroids19 hour Google Maps 

border 
1 if two trading countries share a common border and 

0 otherwise 
dummy 
variable 

 

language 
1 if two trading countries share a common language 

and 0 otherwise 
dummy 
variable 

 

sea 
1 if at least one from both trading countries is not 

landlocked and 0 otherwise 
dummy 
variable 

 

OneEMU 
1 if the importer belongs to The Economic and Mone-
tary Union but the exporter does not and 0 otherwise 

dummy 
variable 

 

BothEMU 
1 if both of the trading countries in the pair are mem-

bers of The Economic and Monetary Union and 0 
otherwise 

dummy 
variable 

 

   

                                                 
17 Generally, Google Maps application offers a route planner for traveling by foot, car, bi-

cycle (beta test), or with public transportation. It does not include the information about cur-
rent traffic in its calculation (this is a property of another application - the Google Traffic). 
Reproducing the calculation in a short time period gives equal results of the travel time by car 
between two chosen locations. Google created the application in 2005, hence it is impossible 
to find a data with the measurement of travel time across last 13 years. However, the regular 
collecting of the data generated by Google Maps could be successfully used in the future 
research. 

18 The use in the study GNI instead of GDP variable is intentional, as it measures income 
received by a country both domestically and from overseas. In fact, there is considered the 
output from the citizens and companies of a particular nation, regardless of whether they are 
located within its boundaries or overseas. The first empirical research provided by the author 
of the gravity equation – Tinbergen (1962) included similar measure, namely GNP. 

19 Great circle distance algorithm was used in the calculation. 



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DYNAMIC ECONOMETRIC MODELS 14 (2014) 29–49 

41

Table 2. Traditional gravity model of trade flows for EU-25 countries20 in 1999– 
–2011 with physical distance between centroids as approximation of bilat-
eral trade costs  – results for alternative estimation methods 

Model A OLS ( 1ijY ) RE FE HT Tobit ( 1ijY ) PPML 

lnGNI_o –0.13 1.30*** 1.30*** 1.30*** 1.97*** 0.76*** 
lnGNI_d 0.52*** 1.05*** 1.05*** 1.05*** 0.58*** 0.74*** 
lnDIST –1.23*** –1.50***  –1.50*** –1.51*** –0.98*** 

OneEMU –0.24 0.08 0.08 0.08*** –0.16* –0.15*** 
BothEMU 0.25** 0.14*** 0.14*** 0.14*** 0.15* –0.02 

border 0.21 0.13  0.13 0.05 0.21*** 
language –0.38 –0.07  –0.06 –0.34 0.47*** 

sea 0.21 0.33***  0.33*** 0.33* 0.08** 
TE Yes Yes Yes Yes Yes Yes 
CE Yes Yes No Yes Yes No 

Constant 20.70*** –30.40*** –40.40*** –32.50*** –35.40*** –11.60*** 
Number of state 600 504 504 504 600 504 

Observations 7800 6533 6533 6533 7800 7800 
R2     0.777    

Note: TE – time effects, CE – country effects (separately for exporter and importer); *** p<0.01, ** 
p<0.05, * p<0.1. 

Table 3. Traditional gravity model of trade flows for EU-25 countries in 1999–2011 
with travel time between centroids as approximation of bilateral trade costs 
– results for alternative estimation methods 

Model B OLS ( 1ijY ) RE FE HT Tobit ( 1ijY ) PPML 

lnGNI_o –0.13 1.30*** 1.30*** 1.30*** 1.96*** 0.75*** 
lnGNI_d 0.52*** 1.05*** 1.05*** 1.05*** 0.59*** 0.73*** 

lnTRAVEL –1.39*** –1.76***  –1.76*** –1.77*** –1.03*** 
OneEMU –0.26* 0.07 0.08 0.07*** –0.19** –0.19*** 
BothEMU 0.27** 0.15*** 0.14*** 0.15*** 0.17* –0.09*** 

border 0.21 0.09  0.09 0.01 0.19*** 
language –0.40 –0.13  –0.13 –0.42* 0.38*** 

sea 0.25 0.35***  0.35*** 0.35** 0.09*** 
TE Yes Yes Yes Yes Yes Yes 
CE Yes Yes No Yes Yes No 

Constant 16.30*** –35.40*** –40.40*** –38.30*** –40.40*** –15.00*** 
Number of state 600 504 504 504 600 504 

Observations 7800 6533 6533 6533 7800 7800 
R2     0.777    

Note: TE – time effects, CE – country effects (separately for exporter and importer); *** p<0.01, ** 
p<0.05, * p<0.1. 

                                                 
20 The sample includes all EU countries without Malta and Cyprus. 



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42

 Validity of replacing physical distance by travel time in the gravity mod-
el was checked by comparison of estimation results of two models: with 
distance as approximation of bilateral trade costs (Model A) and with travel 
time respectively (Model B).  
 Tables 2 and 3 show that the gravity model with travel time estimated 
with several estimation methods – OLS ( 1ijY ), RE, FE, HT, tobit ( 1ijY ) 

and PPML – gives similar estimates of other variables as the model includ-
ing physical distance. The influence of travel time is significant and still 
negative in all cases, as expected. Hence, the travel time between centroids 
of trading countries is replacing the physical distance in the gravity model in 
this study. 
 Different results for the dummy variable describing the participation of 
only the importing country in EMU have different estimates, however nega-
tive signs occur only by the most naïve methods – namely OLS and tobit 
model, where zero-export flows are replaced by the value of 1. Unexpected 
signs occur by PPML method, however, the estimated models do not include 
country effects, which can lead to the bias in estimates. 
 Despite improving the gravity equation by introducing the variable 
which covers the influence of physical distance and the quality of road infra-
structure, the variable of travel time remains still constant, what does not 
represent the whole reality. Then the second step of the research is to create 
a time-varying synthetic variable describing bilateral trade cost according to 
the formula (10) and afterwards use it in the next synthetic variables: export-
er’s and importer’s remoteness, according to (12), (13) – Model 1 – and ac-
cording to (12), (14) – which reflects Model 221. All synthetic variables were 
used in the gravity model (7), with and without fixed country effects for 
exporter and importer. The most similar estimates, with higher R2 coeffi-
cients as well, were obtained in the models including time and country ef-
fects, whose estimation results are shown in Table 4.  
  

                                                 
21 The share in World income in remoteness variable was counted in two ways: through 

dividing by the total income of UE-25 countries as well as by the total World income. As 
expected, the estimation results in both cases were almost identical estimates, including the R2 
coefficient of estimated FE-model (90%), where the only differences were exposed by the 
constant.  



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43

Table 4. The structural gravity models of trade flows for EU-25 countries in 1999– 
–2011 with remoteness as an approximation of MTR – results of approach-
es 1 and 2 for alternative estimation methods 

Model 1 RE FE HT Tobit PPML 
lnGNI_o 0.424*** 0.468*** 0.428*** 0.425*** 0.286*** 
lnGNI_d 2.259*** 2.215*** 2.256*** 2.258*** 1.449*** 

lnBTC_od –0.690*** –0.659*** –0.687*** –0.689*** –0.587*** 
lnREM_od 1.103*** 1.068*** 1.100*** 1.102*** 0.642*** 

lnREM_1_do –0.523*** –0.515*** –0.523*** –0.523*** –0.326*** 
OneEMU 0.244*** 0.238*** 0.243*** 0.243*** 0.040* 
BothEMU 0.257*** 0.245*** 0.256*** 0.257*** –0.015 

border –0.085**  –0.078*** –0.083*** 0.038* 
language –0.078  –0.075 –0.078 0.181*** 

sea 0.072*  0.076* 0.073** –0.054** 
Constant –53.030*** –51.680*** –53.550*** –53.040*** –25.180*** 

Observations 6533 6533 6533 6533 6533 
Number of state 504 504 504 504  

R2    0.918    
Model 2      
lnGNI_o 0.484*** 0.546*** 0.494*** 0.486*** 0.256*** 
lnGNI_d 1.845*** 1.797*** 1.838*** 1.844*** 1.735*** 

lnBTC_od –0.638*** –0.596*** –0.632*** –0.637*** –0.622*** 
lnREM_od 0.757*** 0.710*** 0.750*** 0.756*** 0.960*** 

lnREM_2_do –0.260*** –0.248*** –0.259*** –0.260*** –0.457*** 
OneEMU 0.256*** 0.248*** 0.255*** 0.256*** 0.018 
BothEMU 0.292*** 0.275*** 0.290*** 0.292*** –0.031** 

border –0.005  0.008 –0.002 –0.066*** 
language –0.036  –0.029 –0.034 0.145*** 

sea 0.159***  0.169*** 0.161*** 0.087*** 
Constant –42.910*** –42.350*** –41.310*** –42.910*** –33.890*** 

Observations 5441 5441 5441 5441 5441 
Number of state 420 420 420 420 420 

R2    0.900    
TE Yes Yes Yes Yes Yes 
CE Yes No Yes Yes No 

Note: TE – time effects, CE – country effects (separately for exporter and importer); *** p<0.01, ** 
p<0.05, * p<0.1. 

 Table 4 does not show the fully expected results. Mainly, the coefficient 
of importer’s remoteness variable remains negative in all cases, although, 
due to the Anderson and van Wincoop’s theory, it covers trade barriers be-
tween importing country and all its other potential trading partners, so it is 
expected to have a positive influence on bilateral import flows from the one 
considering importer’s partner. The construction of synthetic remoteness 
variable as weighted average of bilateral costs of trade with other partners is, 
however specific – not such strongly connected with relative prices as in the 



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44

theoretical approach. In the case of the importer this remoteness could be 
interpreted more as the importer’s ability to import from other countries, 
which is not so opposite to the ability to bilateral import, seeing that trading 
goods are differentiated not only by their place of origin22 and the bilateral 
trade costs are not symmetric.   
 According to Table 4, none of border coefficients are positive, despite 
the PPML approach, which results in negative influence of sea access in-
stead. Model 2 with importer’s remoteness variable calculated with the for-
mula (14), gives more similar estimates for the most of coefficients by using 
different estimation methods, including PPML. However the weakness of 
Model 2 is a smaller number of state, caused by the importer’s remoteness 
synthetic formula, which dropped the observations with zero export values. 
Due to calculation problems in Stata software, the estimation of PPML mod-
el was possible only without the country effects, so the results remain biased, 
which can be the reason of the negative influence of BothEMU and border 
dummy variables. The different estimates of national incomes (comparing 
with empirical models of the traditional gravity equation) are the result of 
synthetic variables formulas, they remain however significantly positive.   

Table 5. The structural gravity model of trade flows for EU-25 countries in 1999– 
–2011 with time-varying country effects as an approximation of MTR 
terms (Model 3) 

Model 3 RE FE HT 
lnBTC_od –1.000*** –1.000*** –1.000*** 
OneEMU –0.030*** 0.177*** –0.260*** 
BothEMU –0.030*** 0.177*** –0.260*** 

border –0.845***  –0.839*** 
language –0.843**  –0.489 

sea 1.008***  1.070*** 
TE Yes Yes Yes 

CE (time-varying) Yes Yes Yes 
Constant 27.10*** 26.25*** 25.78*** 

Observations 6533 6533 6533 
Number of state 504 504 504 

R2    0.999  
Note: TE – time effects, CE – country effects (separately for exporter and importer); *** p<0.01, ** 
p<0.05, * p<0.1. 

                                                 
22 Anderson and van Wincoop (2003) assume that each country specializes in the produc-

tion of one good in the derivation to follow. As a matter of fact, in reality good specific trade 
resistance varies depending on the product class under consideration, what by estimation of 
model with aggregated data, like this used in the study, causes a large bias. See Anderson and 
van Wincoop (2004), Anderson and Yotow (2011). 



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DYNAMIC ECONOMETRIC MODELS 14 (2014) 29–49 

45

 In order to check if the created remoteness synthetic variables can be 
a good approximation of multilateral trade-resistance, the estimates of the 
models should be in phase with the estimates of models including time-
varying countries effects, which is the next step of study. The estimation 
results are presented below in Table 5. 
 The complexity of calculation (using Stata software) of the model with 
time-varying countries effects (Model 3) does allow only for the use of RE, 
FE and HT estimators. The FE-model gives the estimates only for time-
varying and non-specific country variables, however it seems to be the most 
accurate method since its extremely high coefficient of determination and 
the additional use of time-invariant pair effects, which absorb all time-
invariant determinants of bilateral trade costs, leading to relative small bias 
in the estimates. Furthermore, as the only one estimator, FE results with the 
same coefficients’ signs in all considering cases. According to these results, 
bilateral trade costs synthetic variable has a negative influence on the bilat-
eral and the EMU-effects are positive. 

Table 6. Results of Hausman test, Sargan-Hansen test of overidentifying restrictions 
and the test for time effects 

Hausman test Chi-square p-value 
TE (time 
effects) 

CE 
(const) 

CE (time-
varying)* 

result 

Model 1 746.92 0.00 + – – FE 
Model 2 475.79 0.00 + – – FE 
Model 3 –16165.56 – + – + FE  
Model 3 760.99 0.00 + – – No answer** 

Test of overidentifying 
restrictions 

S-H statistic   
 

  

Model 1 2308.25 0.00 + – – FE 
Model 1 588.20 0.00 + + –  
Model 2 5195.58 0.00 + – – FE 
Model 2 4791.49 0.00 + + –  
Model 3 2597.88 0.00 + + – FE 
Model 3 2134.06 0.00 + – – FE 

Test for time effects  F statistic      
Model 1 286.85 0.00 + – – TE 
Model 2 158.96 0.00 + – – TE 
Model 3 2.6e+13 0.00 + – + TE 

Note: * Test of overidentifying restrictions (fixed vs random effects) for model with time effects (TE) and 
time-varying country effects (CE) is not feasible due to permanent presence of collinearity; ** “No 
answer” occurs when the matrix was not positive definite. 

 The results of Hausman test (Table 6), conducted for all three models, 
show that FE estimators is more preferred than RE. However, including 
time-varying country effects results in negative chi-square statistic. Due to 



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46

the investigation of Schreiber (2008), this result can happen only if H1 of the 
test is true – FE is consistent and preferred. Moreover, the results of Sargan-
Hansen test of overidentifying restrictions confirm the choice of FE estima-
tor. 

Conclusions 

 The purpose of this paper was to analyze the structural gravity model of 
trade flows with alternative approximations of multilateral trade-resistance 
terms. The empirical results of two synthetic variables – bilateral trade costs 
and exporter’s remoteness give significant and expected signs of coeffi-
cients. The sign of third created synthetic variable – importer’s remoteness – 
remains a problematic issue, since the estimates of importer’s remoteness do 
not respond to the theory of gravity model in any case. The theory of struc-
tural gravity equation assumes however symmetric trade barriers and lower 
differentiation of trade than is observed in the researching sample of EU 
countries, especially under conditions of globalization in the XXI century. 
Based on the estimation results for statistically preferred FE-model only, it 
can be concluded that the proposed synthetic remoteness variables are good 
measures of MTR since including them in the model gives similar results as 
the model with time-varying country effects. However, it did not allow for 
unequivocal verification of the third hypothesis.  
 All the results with alternative estimation methods provided grounds for 
the first research hypothesis verification, confirming the accuracy of using 
the bilateral trade costs synthetic variable, based on the travel time between 
country centroids and importer’s openness.  
 The conducted analysis did not allow for verification of the second re-
search hypothesis, according to which bilateral trade flows increase if ex-
change partners are members of Eurozone. Different signs of estimated 
dummies describing the membership in EMU, especially in models includ-
ing time-varying country effects, do not establish the accurate euro effect on 
the export flows between UE countries in the last 15 years. 
 The specificity of researched sample and time period has definitely in-
fluence the deviation from the theoretical suspicions. Among the problems 
still left open for consideration, the following should be mentioned: the ex-
tension of the research sample by other global-leading countries, the use of 
spatial effects and the use of synthetic trade costs and remoteness variables 
in the model with disaggregated data. 



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47

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Problem właściwego pomiaru multilateralnego oporu wobec handlu  
w panelowym modelu grawitacji 

Z a r y s  t r e ś c i. Celem artykułu  jest porównanie różnych metod aproksymacji multilate-
ralnego oporu wobec wymiany międzynarodowej w modelu grawitacyjnym. Analizie podda-
ny jest także ich wpływ na wyniki różnych metod estymacji modelu bilateralnych przepły-
wów handlowych w Unii Europejskiej w latach 1999-2011. Jako alternatywę dla zastosowa-
nia  w modelu zmiennych w czasie indywidualnych efektów dla kraju importera i eksportera, 
proponowane są trzy zmienne syntetyczne opisujące bilateralne koszty handlu, opór eksporte-
ra oraz opór importera. Tradycyjna miara odległości w modelu grawitacji, jaką jest dystans 
fizyczny, zastąpiony został czasem trwania podróży pomiędzy centroidami państw. Wyniki 
estymacji wskazują na istotny statystycznie wpływ proponowanych zmiennych, jednakże 
znak oceny parametru oporu importera nie odpowiada założeniom teoretycznym modelu 
grawitacji. Wpływ pozostałych zmiennych, w tym efekt strefy euro, jest  w pełni zgodny 
z oczekiwaniami jedynie w przypadku zastosowania estymatora FE. 

S ł o w a  k l u c z o w e: wymiana międzynarodowa, dane panelowe, model grawitacji, multi-
lateralny opór wobec handlu, koszty handlu bilateralnego, globalizacja XXI wieku, strefa 
euro.  




