The Gravity Model and Trade Efficiency: A Stochastic Frontier Analysis of Potential Trade

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.

DISCUSSION PAPERS
IN
ECONOMICS
No. 2013/4 ISSN 1478-9396
THE GRAVITY MODEL AND TRADE
EFFICIENCY: A STOCHASTIC FRONTIER
ANALYSIS OF POTENTIAL TRADE
GEETHA RAVISHANKAR

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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

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

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

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 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)
where t
ijTRADE are the bilateral trade flows between countries i and j over a given
time period t ; t
iGDP and t
jGDP denote the economic size of both countries; ijDIST is
the geographic distance between their economic centres; and t
iGDPPC and t
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 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 degree to which actual output falls short of potential output. Analogously, SFA can be
used to define a trade frontier whereby inefficient trade performance refers to the degree
to which actual trade falls short of the maximal, frontier level of trade. This is achieved
by modifying the conventional gravity model (equation 1), as follows:
)exp()exp(),,,,,,( t
ij
t
ij
t
ijij
t
j
t
iij
t
j
t
i
t
ij uvXZGDPPCGDPPCDISTGDPGDPfTRADE  (2)
where bilateral trade and its determinants are defined as above and the error term, t
ij , in
equation (1) is now comprised of two parts, viz., a two sided error element, t
ijv ,
representing statistical noise due to measurement error and a one sided inefficiency
element, t
iju , representing a measure of trade performance. Whereas the former term is
assumed to follow a normal distribution, ),0(~ 2
v
t
ij Niidv  , as is typical of the
conventional gravity specification, the latter term, t
iju , is assumed to be distributed
independently of the random error and the regressors. This one sided inefficiency
component is a non negative random variable representing technical inefficiency (TE)
and can identify the degree to which observed trade levels deviate from the maximal
possible. Taking a value between zero and unity, a value of zero would imply that the
actual and potential trade levels coincide while values tending towards unity would
indicate scope to raise actual trade levels nearer maximum levels. These deviations from
the maximal trade level can occur due to multilateral resistances (Anderson and van

Following Aigner et al. (1977), equation (2) is operationalised as a pooled frontier wherein the
parameter values are obtained by maximum likelihood estimation (MLE). Along with the gravity model
parameters, estimates for the variance of the composed error term, 222
uv   , and the ratio of the
standard deviation of the inefficiency component to the standard deviation of the random error component,
vu  , are also generated. The latter assesses the degree of inefficiency relative to the random error
and when statistically significant, justifies the use of the SFA approach. A further test for the presence of
technical efficiency in the model is undertaken via a one sided likelihood ratio (LR) test of the null
hypothesis, 0: 2
0 uH  , against the alternative, 02
0 u:H  . Failure to reject the null hypothesis
leads to the SFA model to reduce to an OLS model.
Following parameter estimation, the point estimates of inefficiency can then be obtained as the
mean of the conditional distribution of u given  (Jondrow et al. 1982):





 


 2
2
)~(
exp
)~(2
1
)(
),(
)( 



 u
f
uf
uf
vv
)(
)(
)(











v
t
ij
v
t
ij
v
t
ij
t
ij
t
ij z
z
zuE 


(3)
where uv
t
ij
t
ijz  2
 and (.) and (.) are the standard normal density and cumulative
distribution functions, respectively. The technical efficiency (TE) estimates for each country pair are then
determined as )exp( t
ij
t
ij uTE  .
The full model specification of trade determinants between the Western European countries and
the new EU member states is specified as follows:
tttt COLLOCKDGDPPCDISTGDPGDPEXP  

relative terms as the absolute difference in the logged values of GDP per capita income levels,
tj
t
i
t
ij GDPPClnGDPPClnDGDPPC  , as a proxy for differences in consumption patterns. The
vector of time invariant explanatory variables, ijZ , comprises a binary coded dummy for landlocked
countries, jLOCK , and a dummy denoting common colonial ties, ijCOL , as an indicator for institutional
proximity. The vector of time varying explanatory variables, t
ijX , refers to the real exchange rate for both
countries, t
iRER and t
jRER , to capture currency price movements. Two additional dummies account for
the EU accession of eight new member states in 2004, t
ijEU 04 , and the later accession of Bulgaria and
Romania in 2007, t
ijEU 07 . All non dummy variables in equation (4) are estimated in logarithmic form.
In its basic form, the standard gravity equation posits that bilateral trade increases with national
income and declines with the distance between them. 4 Larger countries tend to trade more, consistent with
the conduct of much of intraindustry trade between the advanced countries (Helpman and Krugman 1985),
hence the GDP coefficients for both countries should be positively signed. Countries located within close
proximity incur lower transport costs which boosts trade, implying the distance coefficient, ijDIST , should
be negatively signed.
In the augmented version of the gravity model, the separate roles for per capita
income identified by Bergstrand (1989) are merged by Gruber and Vernon (1970) into
the per capita income differential as an indirect way of testing the Linder (1961)
hypothesis. Although Linder presented no formal model, the demand based theory
suggests that if an importing country’s aggregated preferences for goods are similar to an

negative coefficient for the per capita income differential, t
ijDGDPPC , suggesting trade
is positively related to consumers with similar per capita incomes and therefore having
similar consumption patterns, indicates support for the Linder hypothesis. On the other
hand, a positive coefficient will ensue if trade is driven more by differing per capita
incomes consistent with the Heckscher Ohlin model (1919, 1933) of relative factor
abundance.
The dummies included in equation (4) are equal to unity if the new member countries are
landlocked, jLOCK , or if the EU countries share a history of colonial ties, ijCOL . Opposing trade
effects are expected for the respective dummy coefficients. As the overland costs of transporting goods
tends to be higher than shipping costs, landlocked countries located in the heart of Europe tend to be
disadvantaged in trade terms because of their geographical position. In contrast, past governance of another
country can boost present economic links because a coloniser may well have contributed to the state of the
institutions of the colonised.
Motivated by the gravity model derived by Bergstrand (1985), which explicitly includes an
exchange rate index to account for location dependent trade costs, the real exchange rate for both countries,
t
iRER and tjRER , is included to capture the trade effect of currency price movements. Micco et al.
(2003) include the RER for both countries against the US dollar to control for valuation effects, arguing
that a depreciation of the US dollar exchange rate can lower the US dollar value of intra eurozone trade.
The real exchange rate can also be interpreted as a measure of national competitiveness. An increase in the
US real exchange rate (implying a depreciation of the US dollar) improves price competitiveness with
consequential beneficial effects on US exports in foreign markets, but with detrimental effects on US

additional countries joined in 2007. In a similar vein, Aitken (1973) examined the trade effects of the
dummy variables denoting the European Economic Community (EEC) and the European Free Trade
Association (EFTA) over the period 1951 1967 to assess the importance of regional integration within a
gravity model framework.
The panel data set consists of bilateral export flows from 17 Western European
countries comprising the 14 established EU countries (Belgium and Luxembourg are
treated as a single country) and three EFTA member countries5 to 10 new member states6
over the period 1994 to 2007. The sample period covers the transformation phase from
communism to EU accession and ends in 2007 to avoid the effects of the global financial
crisis leading to very abnormal trade flows.
The data sources are as follows. Nominal export flow data, denominated in US
dollars at constant 2000 prices, are obtained from the Direction of Trade Statistics
(DOTS), International Monetary Fund (IMF). The export data are expressed in real terms
based on US producer prices (2000 = 100), sourced from the International Financial
Statistics (IFS), IMF. Data on GDP and GDP per capita at constant 2000 US dollars are
from the World Development Indicators (WDI), World Bank. The geographic distance,
measured in kilometres between the economic centres of the trading partner countries, are
from the CEPII as are the colonial and the landlocked dummies.
Nominal exchange rates are official exchange rates in local currency units (LCU)
per US dollar, sourced from the WDI, World Bank. The exchange rates for each country

i and j vis a vis the US dollar are expressed as a ratio of goods prices abroad to
domestic prices where prices refer to consumer prices (2000 = 100), obtained from the
IFS, IMF. The summary statistics for the model variables are shown in Table 1.
[Insert Table 1 here]
3. EMPIRICAL RESULTS
3.1 Gravity Model Estimates
Table 2 presents the results for the stochastic frontier specification of the gravity model
of exports from 17 Western European countries to 10 new member states estimated by
maximum likelihood over the 1994 2007 period. Column (1) shows the results for the
baseline model (equation 4). Column (2) augments the baseline model with time specific
effects to control for common shocks affecting all countries in the sample. Column (3)
additionally includes country specific effects capturing varying country characteristics
among the new member states. Interacting the specific effects in columns (2) and (3),
column (4) allows for variation of country characteristics over time. Baier and Bergstrand
(2007) have previously highlighted the benefits of using country time interactions to
account for time variation of multilateral trade resistances.
[Insert Table 2 here]
Two tests confirm the appropriateness of the SFA approach to estimating the gravity model. In
rejecting the null hypothesis, 0: 2
0 uH  , against the alternative, 02
1 u:H  , the likelihood ratio

indicating that the level of inefficiency is 1.08 times that of the random error. A similar result is found
consistently across the estimated models in support of the SFA approach.
Regarding the core gravity parameter estimates, the positive and significant
coefficient estimates for GDP suggest larger countries trade more. Trade related costs,
however, reduce the volume of trade as indicated by the distance coefficients. In support
of the Heckscher Ohlin model the per capita income difference coefficients suggest factor
endowments are sufficiently different between Western Europe and the new EU member
countries, although its declining magnitude and significance suggests the gap is closing
over time.
With the exception of column (3), the trade inhibiting effect of geographical
characteristics is apparent across all specifications for the landlocked countries (the
Czech Republic, Hungary and Slovakia). The negative effect becomes insignificant when
country time interactions are introduced in column (4), suggesting the partition effects of
geography diminish over time. In contrast, historical colonial links (between Austria vis à
vis the Czech Republic and Slovenia; Germany and Poland; and Sweden and Estonia)
increase bilateral trade flows, but not significantly.
The sustained depreciation of the dollar after the launch of the euro suggests
valuation effects (Micco et al., 2003) and/or volume effects transmitted via changes to the
terms of trade negatively affect European exports. A similarly negative coefficient for the
importing countries’ RER is shown in columns (3) and (4), not surprising given the new

Finally, the positive and in general significant coefficient estimates for the EU
dummies confirm the trade enhancing effect of regional integration. The relatively higher
magnitude for the EU07 dummy suggests the efficiency gains of regional integration are
stronger for the two newest member countries. Overall, the results for the preferred
stochastic frontier specification of trade determinants provide a reasonable approximation
of the factors governing bilateral trade patterns between Western Europe and the new
member states over the 1994 2007 period.
3.2 Trade Efficiency Scores
The trade efficiency scores for each bilateral pair of countries associated with the preferred stochastic
frontier specification (column 4), averaged over the years 1994 2007, are shown in Table 3. A zero value
for the one sided term, t
iju , indicates the inefficiency term reduces to the random noise component thereby
rendering actual and maximum trade levels coincident. More realistic is a non zero value for the
inefficiency term, t
iju , indicating deviations of actual trade from frontier estimates and hence, scope for
further trade integration. Point estimates of technical efficiency (TE) are then obtained for each bilateral
pair as )exp( t
ij
t
ij uTE  . High efficiency scores suggest trade between two countries is close to their
maximum trade potential whereas low efficiency scores indicate deviations of actual trade from frontier
estimates, implying scope for further trade integration.
[Insert Table 3 here]
Most country pairs exhibit a high degree of trade integration, but with some
notable exceptions. The highly integrated countries include the big four (Czech Republic,

programme of liberalisation. At the same time, mixed efficiency scores are also in
evidence, depending on the partner country. For example, while attaining relatively high
efficiency scores vis à vis many Western partners, Hungary and Slovakia perform poorly
against others – Greece, Iceland and Norway in particular.
Several features characterise the high mean efficiency scores. First, geographical
proximity plays a key role. Close trade alliances are in evidence, for example, between
the Baltics (Estonia, Latvia and Lithuania) and the Nordic countries (Denmark, Finland
and Iceland); between Austria and the two latest accession countries; between Greece and
Bulgaria; and between Italy and Romania. Second, the new members tend to perform best
vis à vis the smaller and more open economies (Belgium and the Netherlands).
Finally, the contribution of regionalism to trade patterns is also apparent.
Although bilateral trade agreements are in force between the EU and the individual
EFTA member countries, the mean efficiency scores tend to be higher vis à vis the EU15
– Iceland and Norway are particularly low in comparison. Some exceptions to this pattern
among the EU15 exist. Together with the UK, lower than average trade performance
between the 10 new member countries and Greece is evident, perhaps not unrelated to its
declining competitiveness over time.
On the whole, the efficiency scores are consistent with the rapid reorientation of
trade towards Western Europe, with each new member state achieving close to two thirds
of frontier estimates over the 1994 2007 period. The high efficiency scores suggest a low

and Pentecost 2010). 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.
4. CONCLUSIONS
The breakup of the Soviet Union ushered in a new era of trade expansion between the
excommunist countries and their Western neigbouring countries. In anticipation of a
reorientation of CEE trade towards Western Europe, early studies sought to quantify the
volume of trade likely to prevail in an East–West trade direction assuming full economic
liberalisation. Typically, the degree of East–West trade integration is assessed by
comparing actual trade volumes with potential trade volumes using the gravity model
parameters that fit a model of a normal country’s geographic patterns. This approach,
however, does not gauge trade levels against a maximum level of trade feasible for the
group of eastern European countries.
Using a stochastic frontier approach to estimating the gravity equation for a panel
of exports from 17 Western European countries to the 10 new EU member countries over
the transformation period of 1994 2007, the efficiency of East–West trade integration is
identified relative to maximum potential levels. If two countries achieve an efficient level
of trade, they will operate on the trade frontier and thus reach their maximum trade
potential otherwise deviations from the trade frontier indicate inefficient levels of trade,

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.

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Figure 1 Trade Shares with the EU and the EFTA Countries
a Source: Direction of Trade Statistics, International Monetary Fund.

Table 1 Summary Statistics
Variable Mean Standard
deviation
Minimum Maximum No. of obs
Exports 18.82 2.21 5.32 24.37 2359
Exporter GDP 26.26 1.27 22.65 28.36 2380
Importer GDP 23.96 0.98 22.11 26.14 2380
Distance 7.15 0.63 4.09 8.22 2380
GDP per capita difference 1.70 0.61 0.38 × 10–2 3.26 2380
Landlocked 0.30 0.46 0.00 1.00 2380
Colony 0.02 0.15 0.00 1.00 2380
Exporter RER 5.11 1.25 3.90 9.15 2370
Importer RER 6.95 1.91 3.77 10.25 2363
EU-2004 0.19 0.39 0.00 1.00 2380
EU-2007 0.02 0.11 0.00 1.00 2380

Table 2 A Stochastic Frontier Specification of EU and EFTA–NMS Export Determinants
Regressors (1)a (2)a (3)a (4)a
Exporter GDP 0.90**
(0.02)
0.87**
(0.02)
0.88**
(0.02)
0.87**
(0.02)
Importer GDP 0.83**
(0.02)
0.81**
(0.02)
0.85**
(0.22)
0.98**
(0.08)
Distance –1.47**
(0.03)
–1.49**
(0.03)
–1.55**
(0.03)
–1.54**
(0.03)
GDP per capita difference 0.29**
(0.04)
0.34**
(0.04)
0.07
(0.06)
0.09
(0.06)
Landlocked –0.26**
(0.04)
–0.28**
(0.04)
1.51**
(0.50)
–0.17
(0.80)
Colony 0.10
(0.10)
0.09
(0.10)
0.03
(0.09)
0.03
(0.09)
Exporter RER –0.12**
(0.02)
–0.15**
(0.02)
–0.11**
(0.02)
–0.10**
(0.02)
Importer RER 0.03**
(0.01)
0.07**
(0.01)
–0.80**
(0.16)
–0.07
(0.36)
EU-2004 0.44**
(0.04)
0.11
(0.07)
0.07
(0.07)
0.29**
(0.09)
EU-2007 0.78**
(0.14)
0.33**
(0.15)
0.28*
(0.15)
0.86**
(0.29)
Intercept –13.83**
(0.70)
–13.13**
(0.68)
–8.55*
(5.03)
–15.33**
(2.80)
b 1.08**
(0.04)
1.18**
(0.04)
1.22**
(0.03)
1.30**
(0.04)
u2
 c –1.05**
(0.09)
–1.03**
(0.09)
–1.10**
(0.09)
–1.07**
(0.09)
No. of obs 2332 2332 2332 2332
2 d 250** 290** 300** 310**

27
Table 3 Efficiency Score Estimates from the Stochastic Frontier Specification of the Gravity Model, 1994-2007a
AUT BEL DNK FIN FRA DEU GRC IRL ISL ITA NLD NOR PRT ESP SWE CHE UKK
BGR 0.75 0.80 0.71 0.68 0.68 0.78 0.82 0.63 0.34 0.65 0.79 0.19 0.61 0.63 0.72 0.67 0.53
CZE 0.63 0.79 0.52 0.78 0.64 0.63 0.47 0.81 0.22 0.74 0.76 0.67 0.60 0.80 0.79 0.61 0.58
EST 0.66 0.82 0.81 0.46 0.55 0.69 0.26 0.72 0.70 0.75 0.81 0.55 0.58 0.68 0.76 0.51 0.55
HUN 0.58 0.83 0.56 0.80 0.66 0.80 0.25 0.77 0.20 0.65 0.80 0.17 0.74 0.74 0.77 0.61 0.53
LVA 0.60 0.81 0.78 0.72 0.53 0.67 0.33 0.59 0.82 0.73 0.80 0.67 0.54 0.63 0.67 0.64 0.52
LTU 0.41 0.80 0.80 0.71 0.54 0.65 0.28 0.43 0.91 0.70 0.76 0.57 0.55 0.72 0.68 0.55 0.48
POL 0.53 0.83 0.63 0.72 0.70 0.63 0.37 0.74 0.66 0.79 0.81 0.61 0.59 0.79 0.72 0.64 0.56
ROM 0.78 0.81 0.53 0.42 0.77 0.80 0.62 0.69 0.20 0.83 0.80 0.33 0.50 0.64 0.70 0.65 0.62
SVK 0.12 0.82 0.61 0.78 0.69 0.81 0.33 0.71 0.24 0.74 0.79 0.37 0.66 0.80 0.76 0.62 0.47
SVN 0.77 0.76 0.60 0.72 0.79 0.79 0.44 0.64 0.23 0.76 0.77 0.42 0.37 0.79 0.80 0.47 0.42
a Efficiency scores are derived from the parameter estimates of the preferred specification, column 4, Table 2.

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