EFFICIENCY CONVERGENCE IN TRANSITION ECONOMIES:1991-2002 A NON-PARAMETRIC FRONTIER APPROACH Prof. Dr. Recep Kök Dokuz Eylül University, Department of Economics, Buca-İzmir e-mail: [email protected]Doç. Dr. Ertuğrul Deliktaş Ege University, Department of Economics, Bornova-İzmir e-mail: [email protected].edu.tr ABSTRACT This study based on panel data for 47 countries (25 transition countries and 22 OECD countries) examines efficiency convergence based on regression of average annual efficiency growth on initial levels of efficiency in transition economies during 1991-2002. Efficiency levels and average efficiency growth is calculated by Data Envelopment Analysis (DEA) and then regression analysis is applied to estimate β –convergence. Efficiency change indices of trasition economies indicate that the poor transition economies are catching up the rich countries or the best-practice world production frontier. β -convergence also justifies this finding. Because the estimated convergence coefficient for transition economies, β, is (-0.0498) . Keywords: Convergence or catch-up, efficiency, transition economies, OECD countries, and data envelopment analysis. 1. Introduction By the end of 1991, the Soviet Union had disolved into independent states or economies and these economies are now called transition economies . The underlying economic reason of the transition from planned economies to market-based economies is the ever worsening economic efficiency in the planned period or communist regime. Therefore, the expectation was that economic efficiency would increase in market-based econmies and less productive economies would grow faster than more productive countries (Deliktaş and Balcilar 2002). This is an important subject to be tackled for economists and policy makers. In the other words, are less productive economies or transition economies catching up to their more productive or developed economies. Do initially less productive or less efficient economies have greater efficiency changes than the most efficient ones? These questions should be answered by looking at per capita growth performance or efficiency growth performance of economies. Three major strands of literature can be identified on the analysis of economic performance of nations. The first, and most typical, approach focuses on growth in real per capita income or real GDP per capita. This indicator can be considered as a proxy for the standard of living achieved in a country.
Transcript
EFFICIENCY CONVERGENCE IN TRANSITION ECONOMIES:1991-2002 A NON-PARAMETRIC FRONTIER APPROACH
Prof. Dr. Recep Kök
Dokuz Eylül University, Department of Economics, Buca-İzmir
The second approach is to examine the extent of convergence achieved by the poor countries and
measure disparities in the global distribution of income. The third and recent approach, which is also
used in our paper, is to consider productive efficiency performance based on multi factor productivity
measures based on the concept of total factor productivity and its components, such as technical
efficiency change and technical change (Rao et al. 1998b). This third approach is also related to
convergence. Because change in technical efficiency level is an indicator of catching up or
convergence to the best-practice production frontier. This frontier is determined by both 25 transition
countries and 22 OECD countries in this study. Thus, convergence can be measured across transition
countries, and between transition countries and OECD countries.
The main aim of our study is to investigate the hypothesis of convergence or efficiency progress
based on the initial technical efficiency level and average annual efficiency change in 25 transition
countries for period 1991-2002 and secondly is to determine some probable sources of technical
efficiency progress, such as foreign aid, foreign direct investment, degrees of democratization and
political stability.
The remainder of this paper is organized as follows: Section 2 identifies convergence and
literature on convergence. Section 3 includes efficiency and efficiency growth rates which are utilized
to estimate β- convergence in this study based on Malmquist total factor productivity index. Section 4
describes data that is used. Section 5 presents the basic methodology used, namely Data envelopment
analysis, (DEA) and regression analysis. Section 6 reports the results of the empirical analysis and
finally, section 7 presents conclusion of the study.
2. Convergence
Convergence is known as the tendency for two or more economies to become more similar in terms of
per capita income, growth rate or efficiency growth or such similar measure. Convergence may be
defined as catch-up by low efficiency economies to higher efficiency economies. Islam (2003)
identifies some of different ways in which convergence has been understood:
a) Convergence within an economy vs. convergence across economies;
b) Convergence in terms of growth rate vs. convergence in terms of income level;
c) Unconditional (absolute) convergence vs. Conditional convergence ;
d) β- convergence vs. σ- convergence ;
e) Global convergence vs. local or club-convergence;
f) Income convergence vs. total factor productivity (TFP) convergence;
g) Deterministic convergence vs. stochastic convergence.
In this study we preferred the way of β- convergence using the initial efficiency level and
efficiency change indices of transition economies. Convergence in terms of growth rate vs.
convergence in terms of income level requires what is called β- convergence. There exist β-
convergence in a cross-section of economies, if poor or low efficiency economies tend to grow faster
than wealthy ones ore higher efficiency ones. Through the international diffusion of knowledge and
technology, low productivity and low-income countries have the opportunity to adopt the techniques
of the leader and hence catch-up with the higher productivity countries (Taskin, Zaim 1997).
Efficiency change is also an indicator of a country s performance in adapting the global technology,
and therefore represents the catch-up factor (Rao and Coelli 1998b).
β- convergence indicates that there should be a negative correlation between the initial income
level (efficiency level in our study) and the subsequent growth rate. The coefficient of the initial
efficiency level variable in these regressions (β) is supposed to pick up the negative correlation. That
is, the convergence is judged by the sign of coefficient of β. This follows from the assumption of
diminishing returns, which imply higher marginal productivity of capital is in a capital-poor country.
With similar savings, poorer countries will, therefore, grow faster (Islam 2003).
In neoclassical growth models as presented Solow (1956), a country’s per capita growth rate
tends to be inversely related to its starting level of output or income per person. If economies are
similar in respect to preferences and technology, then poor economies grow faster than the rich ones.
Thus there is a force that promotes convergence in levels of per capita product and income (Barro and
Sala-i- Martin 1992). However, Quah (1993a), Friedman (1994) emphasized that a negative (β) does
not necessarily imply a reduction in dispersion among countries. And the sign of (β) convergence
should be evaluated directly by looking at the dynamics of dispersion of income level or growth rates
across countries (σ- convergence, which is standard deviation of the cross-sectional distribution of
either income level or growth rate).
In the literature, there is extensive empirical evidence of β-convergence of per capita income or
productivity. Abromovitz (1986), Baumol (1986), and Maddison (1987) found evidence of
convergence in per capita income levels for a group of industrialized countries. Baumol and Wolf
(1988) detected similar results for a larger group of countries. Using cross-section regressions, Barro
(1991), Barro and Sala-i -Martin (1992), Mankiw et al. (1992) found convergence in levels of per
capita product and income. They argue that countries and regions are converging, or catching up, since
initially poor areas grow faster than their richer counterparts. On the other hand, Dowrick and Nguyen
(1989) studied TFP- convergence using a cross-section regression and their results support TFP-
convergence in a sample of fifteen for OECD countries (Islam 2003). Yigit and Kutan (2004) use a
stochastic endogenous growth model to investigate the impact of European Union integration on
convergence and productivity growth and their results support convergence.
Wolff (1991) and Dollar and Wolff (1994) examined TFP-convergence using time-series data in
order to get the TFP level indices across countries. TFP level indices obtained were used to check for
TFP-level convergence. For this, the subsequent TFP growth indices regressed on initial TFP levels.
Dougherty and Jorgenson (1996,1997) and Wolff, employing this methodology to the G-7 countries,
found evidence of TFP-convergence.
Alternatively, Fare et al. (1994) studied convergence by examining the changes in efficiency
obtained from the decomposition of the Malmquist productivity index in OECD countries for period
1979-1988. Bernard and Jones (1996) examined TFP-convergence in the manufacturing industry for
14 OECD countries for period 1970-1987 and their major finding is that manufacturing shows little
evidence of multifactor productivity convergence. Taskin and Zaim (1997) found that the inverse
relationship between the mean efficiency change index and the initial per capita income level for a
group of high- and low- income countries for the period 1975-1990.
3. Efficiency and Efficiency Growth
Convergence requires the identification of the most productive countries in order to construct a
behavioral reference or benchmark or best practice frontier for the rest of economies. The distance that
separates it from the best practice frontier explains the relative performance of one economy. If that
distance becomes smaller over time it is said that there is a convergence. This is in contrast to the
traditional approach of measuring TFP growth for one economy exclusively on the basis of the
country’s past performance. Growth and convergence are closely related but not identical concepts so
are efficiency and productivity. Productivity is a ratio of the amount of outputs obtained to the amount
of inputs used, without regard to the efficiency of inputs utilization (Arcelus and Arocena 2000).
According to Farrel (1957), economic efficiency is divided into two parts: technical efficiency
and allocative efficiency. Technical efficiency reflects the ability of a firm to produce maximal output
from a given set of inputs at a certain time period while allocative efficiency reflects the ability of a
firm to use the inputs in optimal proportions, given their respective prices and the production
technology.
A decision-making unit or a firm exhibits production efficiency when it cannot produce more of
any output without decreasing some other output or increasing some other input. Efficiency is a
relative concept. Efficiency or performance of a firm must be compared with a standard or norm,
which indicates the firm is fully technically efficient. The full efficient firms determine the production
frontier. Efficiency levels of firms may increase, decrease or become constant over time.
Growth in efficiency change is an indicator of industry or country’s performance in adapting
technology (Rao and Coelli 1998) and it is also an indicator of the level of catch-up and convergence
among the countries (Deliktaş and Balcilar, forthcoming). Convergence may be broadly defined as the
tendency for two or more economies to become more similar, be they in terms of per capita incomes,
growth rates or total factor productivity growth (TFP growth). Total factor productivity growth is
decomposed into two factors: efficiency change and technical change.In the other words, the
predominance of efficiency change (or catch-up) as a source of TFP growth (Rao and Coelli 4/98).
Efficiency change, which is one of the main parts of TFP growth, can be identified by the Figure 1
illustrating the distance functions and Malmquist productivity index under the case of constant returns
to scale. ( Karadağ, et al , forthcoming).
Y
٠
(xt,yt)
٠ ٠
(xt+1,yt+1)
Rt
Rt+1
f e d c b a 0
X Figure 1. The Output Distance Functions and Malmquist Productivity Index
Suppose one input is used to produce one output and there exist two technologies, namely, tR
and 1+tR or “the best production frontiers” in the periods (t) an (t+1) . The distance functions are
shown as , and in the
figure. Thus the efficiency change (EC) and technical change (TC) can be expressed as follows,
bayxD ttt 0/0),(0 = feyxD tt
t 0/0),( 111
0 =+++ ceyxD tt
t 0/0),( 110 =++
EC = ,00
00
ab
fe
(1)
TC = ,00
00 2/1
bd
cf
(2)
Following FÄRE et al., 1994, Malmquist index of productivity change between period t and t+1 is
defined as
,),(),(
),(),(
2/1
10
110
0
111
01,0
= +
+++++
+
ttt
ttt
ttt
ttt
tt
yxDyxD
yxDyxD
M (3)
where denotes the distance from the period t observation to the period t+1 technology. ),(10 ttt yxD +
Efficiency and technical changes are the two components of TFP change (see Fare et al.,
1994, for pioneering studies) as defined below:
Efficiency Change (EC) = ,),(
),(
0
111
0
ttt
ttt
yxDyxD ++
+
(4)
Technical Change (TC) = ,),(
),(),(
),(2/1
10
0
111
0
110
+
+++
++
ttt
ttt
ttt
ttt
yxDyxD
yxDyxD
(5)
Hence productivity change defined in equation 4 becomes
.1,0 TCECM tt ⋅=+ (6)
When there is an increase in the level of productivity from period t to t+1 then . 11,0 >+ttM
4.Data
Malmquist productivity index requires data on input and output quantities or shares for production.
Thus the input and output quantities or real values used in this study is based on data set related to the
each country. The data was mainly obtained from World Development Indicators 2004 (WDI)
published by the World Bank. The data covers the time period of 1991-2002 for 47 countries (25
transition and 22 OECD countries) and includes 564 observations in total.
Aggregate output (Q) is measured by real GDP (constant 1995 US dollars) for each country.
Inputs used in our model are labor (L) and, capital (K). Labor input is measured as the total labor
force. The capital stock for each country was cumulatively calculated from gross capital formation
(constant 1995 US dollars) by taking 1989 as the base year.
Following variables are considered as conditions that can explain efficiency growth among
transition economies. Indices of democratization and political stability taken from Kaufman et al.
(1999), foreign direct investment (percent of GDP), foreign aid (percent of GDP) economic
liberalization, the distance from Dusseldorf, time under communist regime, and human capital
(secondary school enrolment).
5. Methodology
In this study, we use the Malmquist index methods described in Fare et all (1994) to analyse
efficiency and efficiency change of transitional and OECD economies or in total.. Secondly, we
estimate β-convergence based on regression of base year efficiency level for transition economies on
the average efficiency change for transition economies for period 1991-2002.
Data envelopment analysis
Malmquist approach uses data envelopment analysis (DEA) methods to construct a pice-wise linear
production frontier over the data (input and output quantities of transition economies in our study) .
Efficiency measures are then calculated relative to this surface. The frontier surface is constructed by
the solution of a squence of linear programming problems. The linear programming problem must be
solved NT times in order to provide a value of φ for each country in the sample.
The DEA method was developed by Charnes et al., 1978, Lovell (1993), Ali and Seiford
(1993), Lovell (1994), Charnes et al., 1995, and Seiford, 1996, give the comprehensive review of this
method. Also, panel data applications of DEA method are widely used in the literature (see for
example, Milán and Aldaz, 2001; and Sıngh et al., 2000).
DEA can be either input-oriented or output-oriented. In the former case, the DEA methods
defines the frontier by seeking the maximum possible proportional reduction in input usage with a
given level of output for each economy. In the latter case, the DEA methods seeks the maximum
proportional increase in output production with a given set of inputs. These two approaches give the
same technical efficiency scores when constant returns to scale (CRS) technology is assumed,
however, they may give different efficiency scores when variable returns to scale (VRS) technology is
assumed. In this study we assume a CRS technolgy and output-oriented approach.
Malmquist TFP index might not correctly measure TFP changes when variable returns to scale
(VRS) assumed for the technology. Therefore it is important to impose constant returns to scale (CRS)
on any technology which is used to estimate distance functions regarding the calculation of Malmquist
TFP index (Karadağ et.al, forthcoming)1 .
The choice an appropriate orientation is not as curical as it is in the case of econometric
estimation. Given that linear programming dose not suffer from statistical problems as simultaneous
equation bias (Coelli et al. 1998).
We have preferred an output-orientation (Kök, Deliktaş 2004) because we believe that the
main challenge of transition or developping economies is to maximize output from given set of inputs,
rather than to decrease input usage.
1 There also exists some contrary argument on this subject. See BALK, 2001, for details.
The output-oriented DEA model for the i-th country is as follows:
,max , φλφ
St. 0 ≥+− λφ Yyit ,
0 ≥− λXxit ,
0 ≥ λ , (7)
where,
yi is a Mx1 vector of output quantities for the i-th country;
xi is a Kx1 vector of input quantities for the-i-th country;
Y is a NxM matrix of output quantities for all N countries;
X is a NxK matrix of input quantities for all N countries;
λ is a Nx1 vector of weights; and
φ is a scalar and takes a value greater than one or equal to one. φ-1 is the proportional increase
in outputs that could be achieved by the i-th country with a given inputs. 1/φ defines technical
efficiency score, which varies between zero and one, with a value of one indicating any point on the
frontier.
Under CRS , it is obvious that the catching-up reflects the productivity change or change in the
components of TFP growth. The most productive country presents the highest ratio of average
productivity and it constitutes the reference for the rest. If the other countries increase their average
technical efficiency ratio more than the leader, they are considered to be “catching-up” to it (Arcelus
and Arocena 2000). For this, we follow standard methodology and regress each ecomoy’s annual
average efficiency growth indicies on the economiy’ initial efficiency level to estimate coefficient of
β- convergence. The classical definition of convergence refers to the log of real GDP per capita (Yigit
and Kutan 2004).
Regression
The form of the regression used in our study to estimate coefficient of β for each economy is given as
follows:
ii
T
tti
ti
Tεφββ
φφ
++=∑=
+1991
101
1
ln))(1(ln (8)
In our study, this equation is as follows:
iiii IDEMFDIFAIDTEEFCHii
εβββββ +++++=− 432)1991(10)20021991( )ln()ln( (9)
where, (EFCH)i denotes the average technical efficiency change for period 1991-2002 for each
trantition economy. The subscript (i) represents the i-th country; N is equal to 25 accordingly. (TE)i
denotes the initial technical efficiency level of each economy, FAID stands for foreign aid (percent of
real GDP), FDI denotes foreign direct investment (percent of real GDP), IDEM is an index of
democratization (average of political process, civil society, independent media, and governance and
public administration ratings by the Freedom House, and IPS represents an index of political stability
foe each country (Deliktaş and Balcilar, forthcoming).
The other explanatory variables mentioned in section 4 have been found statistically
insignificant and been omitted from regression.
6. Empirical Results
The initial GDP per capita and efficiency level index, Malmquist productivity index or total factor
productivity change (tfpch) index, and its components, namely efficiency change (effch) index and
tecnological change (techch) index are given in Table 1 over the 1991-2002 period for the transition
economies. For each index, except for the initial efficiency level index3, a value greater one indicates
an average annual progress in the performance of the economy while a value less than one indicates
regress or detoriation in performance. The efficiency change index4 which is greater one also shows
catch-up or convergence of economy to the best-practice production frontier.
3 The initial efficiency level indices indicates that the best practice frontier is determined by Georgia, Slovenia, and Turkmenistan and other countries are inefficient in respcet to the full efficient countries in 1991. 4 The country-specific graphical behavior of efficiency change over time is given in appendix .
Table 1: Initial efficiency, initial GDP per capita, and annual average changes for transition
Table 1 indicates that average annual technical efficiency change for 25 transition economies is 1.022
or 2.2% for period 1991-2002. In the same period, Uzbekistan has the greatest average growth rate of
technical change (14.3%). Secondly, Albania and Kazakhstan have average rates of growth of 9.7 and
7.3 percents in technical efficiency level, respectively. These countries are followed by Russia (5.5%),
Armenia (5.4%), Romania (6.6%), Latvia (3.7%), Ukraina (3.1%), Kyrgyzstan (2.4%), Macedonia
(1.9%), Bulgaria and Estonia (1.8%), Poland (1.5%), Slovak Republic (1.4%), and Azerbaijan 1.2%.
On the other hand, Moldova (-5.0%), Slovenia (11.8%), and Czech Republic (-1.1%) have
deterioration in performance while Georgia, Slovenia, and Turkmenistan have not experienced any
improvement and deterioration in performance over the period 1991-20025.
5 Although average annual technical efficiency growth rate for transition is greater one, average annaul total factor productivity growth rate is less than one. This is due to average annual tehnical regress in transition economies over the period 1991-2000.
The average annual efficiency growth rates in the OFSU countries, the MEE countries, and
Baltic countries are 3.29, 1.93, and 1.50 percents, respectively6. It is seen that the OFSU countries
have higher annual efficiency growth than those of MEE and Baltic countries for period 1991-2002.
These findings indicate that the poor countries are catching up the rich countries. This argument can
also be supported by comparing transition economies to OECD countries. The average annual
efficiency change in 22 OECD countries has been measured as 0.991 for period 1991-20027 while that
of 25 transition countries is 1.022. These indices (appendix) clearly indicate that transition economies
or poor economies are converging the OECD countries.
On the other word, the results also show that the economies that have the lower initial efficiency
indices (or poor economies) have the highest technical efficiency growth rates or they catch-up the
best practice frontier at a faster rate than the economies that have the higher initial efficiency levels
(richer economies) This is a good indicator of convergence.
The robustness of convergence in transition economies is also justified by the significant negative
regression coefficient estimated by equation (9). The negative coefficient of the initial level of
technical efficiency level (TE), in equation 10, indicates β- convergence.
We have regressed, in equation (10), each economy’s average annual efficiency change index
on the economy’s initial efficiency level index to produce estimate of β-convrgence. The equation
shows that the coefficient on the initial levels is negative and strongly significant (t values are in
parenteheses). It also shows that initially less efficient or poor countries are catching up to the most
efficient countries over period 1991-2002. The signs of the coefficients of FAID, FDI investment and
index of democratization have a positive impact on efficiency change. The coefficients of FAID, FDI,
and IDEM are also statistically significant at 5% level.
β- convergence can also be justified the regression of each economy’s average annual efficiency
change index on the each economy’s initial GDP per capita.
)1654.3()5367.3(ln0328.02826.0)ln(
−−= itaGDPpercapiEFFCH
270.02 =R , (11) 027.10=− statisticF
6 The OFSU countries are Armenia, Azerbaijan, Belarus, Georgia,Kazakhstan, Kyrgyzstan, Moldova, Russian Federation, Tajikistan, Turkmenistan, Ukraina, Uzbekistan, and The MEE countries are Albania, Bulgartia, Crotia, Czech Republic, Hungary, Macedonia , Poland, Romania, Slovak Republic, Slovenia, 7 Fare et al. (1994) indicate that the average annual efficiency change index of 17 OECD countries is 0.998 over the period 1979-1988. Taskin and Zaim (1997) report that high income countries’ average annual efficiency change index is 0.999 over the period 1975-1990.
The negative sign of coefficient of initial GDP per capita points out β- convergence in transition
economies for period 1991-2002. This is consistent with the result of equation (10).
7. Conclusion
We have investigated convergence based on regression of average efficiency growth on initial levels
of efficiency in 25 transition economies during 1991-2002. We have used DEA in order to measure
the efficiency levels and average annual efficiency growth. The efficiency change indices indicate that
the economies that have the lower initial efficiency levels have the highest technical efficiency growth
rates. The OFSU countries are converging the MEE countries and Baltic countries The transition
countries are also catching up the OECD countries.
The robustness of convergence is also justified by the cross section econometric regression as
finding a negative coefficient of the initial level of technical efficiency level (β- convergence) or of the
initial level of GDP per capita. The signs of coefficients of foreign direct investment, foreign aid and
index of democratization indicate that they have a positive impact on efficiency change. The positive
sign of democratization indicates that the establishment of democratic institutions will tend to
accelerate the rate of economic efficiency growth. The positive signs of foreign aid and foreign direct
investment point out the more foreign aid and more foreing direct investment are the more efficiency
growth in transition economies. The impact of foreign direct investment on transition economies is
consistent with the literature. It is estimated that foreign direct investment has a positive effect on
labor productivity and output in Turkish manufacturing industry and also the foreing firms creates
positive spillover effects on productivity of local firms (Kök and et al. Türkiye İktisat Kongresi,
2004). Yigit and Kutan (2004) also indicate that the FDI causes the high productivity gains in Poland
and Hungary and the presence of foreing firms creates positive spillover effects on productivity of
local firms in Hungary.
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Appendix A
Table 2. Average annual changes in 47 countries over the 1991-2002 period Country effch techch pech sech tfpch
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