The Gravity Model and Trade Efficiency: A Stochastic Frontier Analysis of Potential Trade
The objective of this research is to study and analyze the export of wooden furniture from developing nations to the EU market, with a focus on India. The research will examine marketing strategies and factors influencing future scenarios of wooden furniture exportation, as well as the impact of technology and market growth on the economy.
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This paper assesses potential trade against a maximum level of trade feasible for the group of 10 new member states (NMS) using a stochastic frontier approach to estimating the gravity equation. The findings indicate a high degree of East West trade integration close to two thirds of frontier estimates, suggesting a low degree of trade resistances.
The Gravity Model and Trade Efficiency: A Stochastic Frontier Analysis of Potential Trade
The objective of this research is to study and analyze the export of wooden furniture from developing nations to the EU market, with a focus on India. The research will examine marketing strategies and factors influencing future scenarios of wooden furniture exportation, as well as the impact of technology and market growth on the economy.
Added on 2023-06-15
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D I S C U S S I O N P A P E R S
I N
E C O N O M I C S
No. 2013/4 ISSN 1478-9396
THE GRAVITY MODEL AND TRADE
EFFICIENCY: A STOCHASTIC FRONTIER
ANALYSIS OF POTENTIAL TRADE
GEETHA RAVISHANKAR
MARIE STACK
DEC 2013
D I S C U S S I O N P A P E R S
I N
E C O N O M I C S
No. 2013/4 ISSN 1478-9396
THE GRAVITY MODEL AND TRADE
EFFICIENCY: A STOCHASTIC FRONTIER
ANALYSIS OF POTENTIAL TRADE
GEETHA RAVISHANKAR
MARIE STACK
DEC 2013
2
DISCUSSION PAPERS IN ECONOMICS
The economic research undertaken at Nottingham Trent University
covers various fields of economics. But, a large part of it was grouped
into two categories, Applied Economics and Policy and Political
Economy.
This paper is part of the new series, Discussion Papers in
Economics.
Earlier papers in all series can be found at:
http://www.ntu.ac.uk/research/research_at_ntu/academic_schools/nbs
/working_papers.html
Enquiries concerning this or any of our other Discussion Papers should
be addressed to the Editors:
Dr. Marie Stack, Email: marie.stack@ntu.ac.uk
Dr. Dan Wheatley, Email: daniel.wheatley2@ntu.ac.uk
Division of Economics
Nottingham Trent University
Burton Street, Nottingham, NG1 4BU
UNITED KINGDOM.
DISCUSSION PAPERS IN ECONOMICS
The economic research undertaken at Nottingham Trent University
covers various fields of economics. But, a large part of it was grouped
into two categories, Applied Economics and Policy and Political
Economy.
This paper is part of the new series, Discussion Papers in
Economics.
Earlier papers in all series can be found at:
http://www.ntu.ac.uk/research/research_at_ntu/academic_schools/nbs
/working_papers.html
Enquiries concerning this or any of our other Discussion Papers should
be addressed to the Editors:
Dr. Marie Stack, Email: marie.stack@ntu.ac.uk
Dr. Dan Wheatley, Email: daniel.wheatley2@ntu.ac.uk
Division of Economics
Nottingham Trent University
Burton Street, Nottingham, NG1 4BU
UNITED KINGDOM.
3
The Gravity Model and Trade Efficiency:
A Stochastic Frontier Analysis of Potential Trade
ABSTRACT
The opening up process of the eastern European countries is characterised by an
increasing degree of trade integration with their Western neigbouring countries.
Typically, the degree of East West trade integration is assessed by comparing actual trade
volumes with potential trade volumes projected from the gravity model parameters
estimated for a group of countries that best represent normal trade relations. This
approach, however, does not compare trade levels against a maximum level of trade
feasible for the group of eastern European countries. This paper by using a stochastic
frontier specification of the gravity model is able to identify the efficiency of trade
integration relative to maximum potential levels. The findings, based on a panel data set
of bilateral exports from 17 Western European countries to the 10 new member states
over the 1994 2007 period, indicate a high degree of East West trade integration close to
two thirds of frontier estimates, suggesting a low degree of trade resistances.
JEL Classification: C33, F14, F15
Keywords: Gravity model, Potential trade, Efficiency scores
The Gravity Model and Trade Efficiency:
A Stochastic Frontier Analysis of Potential Trade
ABSTRACT
The opening up process of the eastern European countries is characterised by an
increasing degree of trade integration with their Western neigbouring countries.
Typically, the degree of East West trade integration is assessed by comparing actual trade
volumes with potential trade volumes projected from the gravity model parameters
estimated for a group of countries that best represent normal trade relations. This
approach, however, does not compare trade levels against a maximum level of trade
feasible for the group of eastern European countries. This paper by using a stochastic
frontier specification of the gravity model is able to identify the efficiency of trade
integration relative to maximum potential levels. The findings, based on a panel data set
of bilateral exports from 17 Western European countries to the 10 new member states
over the 1994 2007 period, indicate a high degree of East West trade integration close to
two thirds of frontier estimates, suggesting a low degree of trade resistances.
JEL Classification: C33, F14, F15
Keywords: Gravity model, Potential trade, Efficiency scores
4
1. INTRODUCTION
Not unlike the drive to increase trade between the established European Union (EU)
member countries as part of a customs union, the opening up process of the eastern
European countries began with trade integration. Strong bilateral trade links were formed
in advance of formal EU entry. After the Council for Mutual Economic Assistance
(CMEA) system1 was dissolved in the early 1990s, a new era of trade expansion was
ushered in, culminating in the Western European countries becoming the main trading
partners for the excommunist countries.
Figure 1 plots each new EU member country’s share of world trade (exports plus
imports) with the Western European countries. By 1994, Western Europe had already
become important trading partners for the group of ten, implying an almost immediate
release of economic ties from the former Soviet Union. Trailing behind its counterparts,
Lithuania was initially the slowest to open up its trade links, but increased its trade shares
by 1.5 times within a decade. Slovakia experienced an even more dramatic reorientation
of trade westwards, rising by two thirds to its peak levels in 2003. Conducting about half
of its trade with the Western countries in 1993, the trade shares for Bulgaria and Romania
depict an almost parallel trend, but with the latter maintaining a ten per cent lead over the
former. Much like Bulgaria’s path, the trade shares for Estonia and Latvia have ended up
like they started albeit with some variation in between. The trade shares for the top four
ranking countries, namely the Czech Republic, Hungary, Poland and Slovenia remain
relatively stable at around 65 per cent throughout the period.
[Insert Figure 1 here]
1 The CMEA system, also known as COMECON, was formed in 1949 to co-ordinate economic
development and industrial production between the Soviet Union and its member countries.
1. INTRODUCTION
Not unlike the drive to increase trade between the established European Union (EU)
member countries as part of a customs union, the opening up process of the eastern
European countries began with trade integration. Strong bilateral trade links were formed
in advance of formal EU entry. After the Council for Mutual Economic Assistance
(CMEA) system1 was dissolved in the early 1990s, a new era of trade expansion was
ushered in, culminating in the Western European countries becoming the main trading
partners for the excommunist countries.
Figure 1 plots each new EU member country’s share of world trade (exports plus
imports) with the Western European countries. By 1994, Western Europe had already
become important trading partners for the group of ten, implying an almost immediate
release of economic ties from the former Soviet Union. Trailing behind its counterparts,
Lithuania was initially the slowest to open up its trade links, but increased its trade shares
by 1.5 times within a decade. Slovakia experienced an even more dramatic reorientation
of trade westwards, rising by two thirds to its peak levels in 2003. Conducting about half
of its trade with the Western countries in 1993, the trade shares for Bulgaria and Romania
depict an almost parallel trend, but with the latter maintaining a ten per cent lead over the
former. Much like Bulgaria’s path, the trade shares for Estonia and Latvia have ended up
like they started albeit with some variation in between. The trade shares for the top four
ranking countries, namely the Czech Republic, Hungary, Poland and Slovenia remain
relatively stable at around 65 per cent throughout the period.
[Insert Figure 1 here]
1 The CMEA system, also known as COMECON, was formed in 1949 to co-ordinate economic
development and industrial production between the Soviet Union and its member countries.
5
A two stage gravity approach to projecting East West trade volumes is the usual
route to assessing bilateral trade performance. In the first stage, the gravity model of trade
is estimated for a group of countries that best represent normal trade relations. In its basic
form, the standard gravity equation explains bilateral trade as a function of the economic
size of two countries and the distance between them (Tinbergen 1962; Pöyhönen 1963).
The augmented version additionally includes income per head for both countries and
other trade impeding or trade stimulating factors (Bergstrand 1989).
In the second stage, the gravity model parameters that fit a model of a normal
country’s geographic trade patterns are used to project the expected trade flows in an East
West direction. The trade flows predicted by the model can then be compared with actual
trade flows to assess the likelihood for future expansion or depletion of trade links
between a pair of countries. Whereas a value in excess of unity suggests remaining
potential for trade growth, a value of less than unity suggests trade potential is already
exhausted. In this way, the potential to actual trade ratios are informative as to the degree
of East West trade integration under normal conditions.
The two stage approach to trade projections pervades the empirical literature (see,
for example, Baldwin 1994; Gros and Gonciarz 1996; Stack and Pentecost 2010). In
assuming full economic liberalisation, these studies define East West potential trade in
terms of the sample average, usually the Western European countries. In other words, the
mean effects of trade determinants are estimated, implying potential trade is assessed
using the mean predicted values as a benchmark (Armstrong et al., 2008). The predictive
ability of the gravity model, however, declines as the year of the inserted values
increasingly departs from the historical average. Moreover, these studies do not gauge
A two stage gravity approach to projecting East West trade volumes is the usual
route to assessing bilateral trade performance. In the first stage, the gravity model of trade
is estimated for a group of countries that best represent normal trade relations. In its basic
form, the standard gravity equation explains bilateral trade as a function of the economic
size of two countries and the distance between them (Tinbergen 1962; Pöyhönen 1963).
The augmented version additionally includes income per head for both countries and
other trade impeding or trade stimulating factors (Bergstrand 1989).
In the second stage, the gravity model parameters that fit a model of a normal
country’s geographic trade patterns are used to project the expected trade flows in an East
West direction. The trade flows predicted by the model can then be compared with actual
trade flows to assess the likelihood for future expansion or depletion of trade links
between a pair of countries. Whereas a value in excess of unity suggests remaining
potential for trade growth, a value of less than unity suggests trade potential is already
exhausted. In this way, the potential to actual trade ratios are informative as to the degree
of East West trade integration under normal conditions.
The two stage approach to trade projections pervades the empirical literature (see,
for example, Baldwin 1994; Gros and Gonciarz 1996; Stack and Pentecost 2010). In
assuming full economic liberalisation, these studies define East West potential trade in
terms of the sample average, usually the Western European countries. In other words, the
mean effects of trade determinants are estimated, implying potential trade is assessed
using the mean predicted values as a benchmark (Armstrong et al., 2008). The predictive
ability of the gravity model, however, declines as the year of the inserted values
increasingly departs from the historical average. Moreover, these studies do not gauge
6
trade performance against a maximum possible level of potential trade defined by a
stochastic frontier.
This paper assesses potential trade against a maximum level of trade feasible for
the group of 10 new member states (NMS) using a stochastic frontier approach to
estimating the gravity equation. Specifically, a trade frontier representing the maximum
possible level of bilateral trade is constructed for a panel of exports from 17 Western
European countries to the new EU member countries over the 1994 2007 period, covering
the transformation phase from communism to EU accession. The efficiency scores are
then generated from this frontier specification of the gravity model. If two countries
achieve an efficient level of trade, they will operate on the trade frontier and will realise
their maximum trade potential otherwise deviations of observed trade levels from the
trade frontier indicate inefficient levels of trade, implying scope for further trade
expansion. The frontier specification of the gravity model is similar in approach to that
used by Drysdale et al. (2000) who consider China’s trade efficiency, Kalirajan and
Singh (2008) who conduct a comparative analysis of export potential for China and India
and Armstrong et al. (2008) who compare trade performance in East Asia and South
Asia.
The efficiency scores suggest a high degree of East West trade integration, with
each new member state achieving on average two thirds of frontier estimates over the
1994 2007 period. The high efficiency scores indicate a low degree of trade resistances.
The main exceptions to the broad pattern of high integration levels suggest greatest
potential for trade expansion vis à vis Greece, Iceland, Norway and the UK.
trade performance against a maximum possible level of potential trade defined by a
stochastic frontier.
This paper assesses potential trade against a maximum level of trade feasible for
the group of 10 new member states (NMS) using a stochastic frontier approach to
estimating the gravity equation. Specifically, a trade frontier representing the maximum
possible level of bilateral trade is constructed for a panel of exports from 17 Western
European countries to the new EU member countries over the 1994 2007 period, covering
the transformation phase from communism to EU accession. The efficiency scores are
then generated from this frontier specification of the gravity model. If two countries
achieve an efficient level of trade, they will operate on the trade frontier and will realise
their maximum trade potential otherwise deviations of observed trade levels from the
trade frontier indicate inefficient levels of trade, implying scope for further trade
expansion. The frontier specification of the gravity model is similar in approach to that
used by Drysdale et al. (2000) who consider China’s trade efficiency, Kalirajan and
Singh (2008) who conduct a comparative analysis of export potential for China and India
and Armstrong et al. (2008) who compare trade performance in East Asia and South
Asia.
The efficiency scores suggest a high degree of East West trade integration, with
each new member state achieving on average two thirds of frontier estimates over the
1994 2007 period. The high efficiency scores indicate a low degree of trade resistances.
The main exceptions to the broad pattern of high integration levels suggest greatest
potential for trade expansion vis à vis Greece, Iceland, Norway and the UK.
7
The layout of this paper is as follows. Section 2 sets out the gravity model
specification, distinguishing between the conventional gravity equation and the stochastic
frontier gravity equation. The data sources and the expected coefficient signs are also
given in this section. The results in Section 3 are split between the gravity model
coefficient estimates and the efficiency scores of potential trade. Section 4 concludes.
2. MODEL SPECIFICATION AND DATA
2.1 The Gravity Equation
The gravity model specification for calculating trade volumes (Baldwin 1994; Gros and
Gonciarz 1996; Nilsson 2000) is typically of the following form:t
j
t
iij
t
j
t
i
t
ij GDPPCGDPPCDISTGDPGDPTRADE 543210
t
ij
K
k
t
ijk
G
g
ijg XZ
11
(1)
wheret
ijTRADE are the bilateral trade flows between countriesi andj over a given
time periodt ;t
iGDP andt
jGDP denote the economic size of both countries;ijDIST is
the geographic distance between their economic centres; andt
iGDPPC andt
jGDPPC are
the respective countries’ per capita income levels capturing factor endowments in the
exporting country and consumption patterns in the importing country. Equation (1) also
includes a vector of time invariant explanatory variables,ijZ ; a vector of time varying
trade stimulating and trade resisting variables,t
ijX ; and the error term,t
ij
.
East West trade projections of trade flows for the countries of interest typically
use the gravity model parameters estimated for a group of countries that best represent
normal trade relations. The main drawback to this approach is that the potential to boost
The layout of this paper is as follows. Section 2 sets out the gravity model
specification, distinguishing between the conventional gravity equation and the stochastic
frontier gravity equation. The data sources and the expected coefficient signs are also
given in this section. The results in Section 3 are split between the gravity model
coefficient estimates and the efficiency scores of potential trade. Section 4 concludes.
2. MODEL SPECIFICATION AND DATA
2.1 The Gravity Equation
The gravity model specification for calculating trade volumes (Baldwin 1994; Gros and
Gonciarz 1996; Nilsson 2000) is typically of the following form:t
j
t
iij
t
j
t
i
t
ij GDPPCGDPPCDISTGDPGDPTRADE 543210
t
ij
K
k
t
ijk
G
g
ijg XZ
11
(1)
wheret
ijTRADE are the bilateral trade flows between countriesi andj over a given
time periodt ;t
iGDP andt
jGDP denote the economic size of both countries;ijDIST is
the geographic distance between their economic centres; andt
iGDPPC andt
jGDPPC are
the respective countries’ per capita income levels capturing factor endowments in the
exporting country and consumption patterns in the importing country. Equation (1) also
includes a vector of time invariant explanatory variables,ijZ ; a vector of time varying
trade stimulating and trade resisting variables,t
ijX ; and the error term,t
ij
.
East West trade projections of trade flows for the countries of interest typically
use the gravity model parameters estimated for a group of countries that best represent
normal trade relations. The main drawback to this approach is that the potential to boost
8
trade is defined relative to the sample average rather than in terms of a maximum level
feasible for a given pair of trading partners. Measuring trade potential against mean
predicted values can be problematic because the predictive ability of the gravity model
declines as the year of the inserted values increasingly deviates from the sample average.2
Under the stochastic frontier analysis (SFA) approach, the gravity equation of
trade determinants identifies the trade frontier. The resulting frontier levels of trade, i.e.
the maximum possible level of trade for a given bilateral trading pair, is impacted by a
random error term which can be positive or negative thereby allowing the stochastic
frontier trade level to vary about the deterministic part of the gravity equation. Observed
trade levels can then be compared against this frontier level of trade for each bilateral
trading pair to assess the scope for trade expansion. The next section provides a detailed
exposition of this approach.
2.2 The Gravity Equation estimated using Stochastic Frontier Analysis
Developed independently by Aigner et al. (1977) and Meeusen and van den Broeck
(1977), stochastic frontier analysis (SFA) has been used extensively in the assessment of
firm performance. In its traditional application, SFA specifies a production frontier
representing the maximum output that can be produced from a given level of inputs.
Fully efficient firms operate on the frontier such that observed and frontier levels of
output coincide, while (technically) inefficient firms operate at a point within the frontier,
signifying a shortfall between the observed and the maximum possible levels of output.
The latter thus implies scope for further expansion of outputs given current input bundles.
Therefore, in the case of a production function, technically inefficient production refers to
2 This is because the width of the confidence intervals is smallest when the inserted values are equal to the
historical average but widens sharply – and thereby increases the prediction error of the regression – as the
inserted values depart from the sample mean.
trade is defined relative to the sample average rather than in terms of a maximum level
feasible for a given pair of trading partners. Measuring trade potential against mean
predicted values can be problematic because the predictive ability of the gravity model
declines as the year of the inserted values increasingly deviates from the sample average.2
Under the stochastic frontier analysis (SFA) approach, the gravity equation of
trade determinants identifies the trade frontier. The resulting frontier levels of trade, i.e.
the maximum possible level of trade for a given bilateral trading pair, is impacted by a
random error term which can be positive or negative thereby allowing the stochastic
frontier trade level to vary about the deterministic part of the gravity equation. Observed
trade levels can then be compared against this frontier level of trade for each bilateral
trading pair to assess the scope for trade expansion. The next section provides a detailed
exposition of this approach.
2.2 The Gravity Equation estimated using Stochastic Frontier Analysis
Developed independently by Aigner et al. (1977) and Meeusen and van den Broeck
(1977), stochastic frontier analysis (SFA) has been used extensively in the assessment of
firm performance. In its traditional application, SFA specifies a production frontier
representing the maximum output that can be produced from a given level of inputs.
Fully efficient firms operate on the frontier such that observed and frontier levels of
output coincide, while (technically) inefficient firms operate at a point within the frontier,
signifying a shortfall between the observed and the maximum possible levels of output.
The latter thus implies scope for further expansion of outputs given current input bundles.
Therefore, in the case of a production function, technically inefficient production refers to
2 This is because the width of the confidence intervals is smallest when the inserted values are equal to the
historical average but widens sharply – and thereby increases the prediction error of the regression – as the
inserted values depart from the sample mean.
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