Konstantinos Kavouridis
S1667319Msc. International Economics and Business
Supervisor: Dr. Bart Los
UNIVERSITY OF GRONINGEN
THE NETHERLANDS
CONTENTS
LIST OF FIGURES
4
LIST OF TABLES
4
1. INTRODUCTION
6
2. PRODUCTIVITY AND EFFICIENCY
10
2.1 Productivity
10
2.2 Efficiency
11
2.3 Technical Efficiency
13
3. LITERATURE REVIEW
17
3.1 Building Hypotheses
19
4. THE STOCHASTIC FRONTIER ANALYSIS
22
4.1 Method of Moments
24
5. DEA VERSUS SFA
30
6. DATA SPECIFICATION
33
6.1 Time Period
33
6.2 Size of Firms
33
6.3 List of European Countries
34
6.4 Specification of Variables
36
6.5 Methodology Specification
39
7. EMPIRICAL RESULTS
43
7.1 Coefficients of Production Frontier
43
7.2 Frontier’s Intercept and Indicators of Inefficiency
46
7.3 Technical Efficiency
49
7.4 Testing Hypotheses
51
8. LIMITATIONS – FUTURE RESEARCH
55
9. CONCLUSIONS
57
Acknowledgements
List of Figures
Figure 1: Production frontier
11
Figure 2: Productivity and Efficiency
12
Figure 3: Farrell’s Depiction of Technical Efficiency
15
Figure 4: normal-half normal distribution
26
Figure 5: Stochastic Frontier Analysis
31
Figure 6: Overall Mean Technical Efficiency
52
List of Tables
Table 1: List of European Countries
35
Table 2: Consumer Price Inflation rates from 2001 to 2005
37
Table 3: Descriptive Statistics
38
Table 4: Correlation Test
40
Table 5: Coefficients of Production Frontier per year
44
Table 6: Efficiency Indicators and Frontiers’ Intercept
47
ABSTRACT
1.
INTRODUCTION
After decades of socialist planning, the energy sector in the Central Eastern European transition economies applied substantial market-oriented reforms which started in the middle of the 1980s and ended at the beginning of the new century. During this transition period, the energy sector has been reformed, causing social reactions particularly with reference to mergers and acquisitions, mostly because companies reduced the number of employees (Newbery, 1994). In addition to the increase of the unemployment rate, transition from planned to market economy led to a new market economy with characteristics such as rapid price liberalization, removal of price controls and direct subsidies, and creation of a large private sector since new firms started to operate and in the same time state owned enterprises where in the privatization process.
The last decade of the previous century was characterized as a tough reform period from socialist structures towards market economies. Since the late 1980s small enterprises in most transition economies have been rapidly privatized through local auctions while in the following years there was an excessive privatization period of medium and large state owned enterprises. In the recent years, a competitive market has been established in almost all transition economies and firms operate under new regulations. Hence, firms have to look beyond the traditional business characteristics in order to meet new challenges such as the increasingly competitive and internationalized environment.
Although the main objective of most reforms was the need to improve the economic efficiency of sectors by introducing private capital, liberalizing markets and introducing new regulatory institutions, however, developing countries suffer from serious institutional weaknesses, meaning that planned reforms may not produce their intended benefits. In addition to that, little is known about the competitiveness of major sectors, and whether differences between Eastern and Western European companies prevail (Cullmann et al., 2006).
traditionally focused on business concepts that affect firm performance as an answer to the question of why some firms perform better than others.
In order to detect differences in firm performance the terms of productivity and efficiency have been introduced. In the field of economic analysis, most authors agree today that productivity is the ability displayed by production factors to produce. When variations in this ability do occur then they are deemed productivity gains or losses (Thiry and Tulkens, 1985). On the other hand, efficiency has emerged as a powerful tool towards understanding whether some firms produce more output than other firms using the same amount of input or if there are firms which use less input in order to produce the same amount of output (Koopmans, 1951).
A similar explanation of technical efficiency refers to the ability of a firm to minimize input use in the production of a given output, or the ability to obtain maximum output from a given input. In fact not all producers are always so successful in solving their optimization problems, while they do not always succeed in utilizing the minimum inputs required to produce the outputs they choose to produce given technology at their disposal. Therefore not all producers are technically efficient. (Kumbhakar, 2000)
Efficiency literature has developed substantially over the latest decades producing a large number of studies using different quantitative techniques in order to succeed in estimating the efficiency of a firm. The most favorable and common methods which can lead to the estimation of technical efficiency are the Data Envelopment Analysis (DEA) and the Stochastic Frontier Analysis (SFA). The former is a non-parametric approach which estimates technical efficiency using programming techniques while the latter is a parametric approach which estimates technical efficiency with the application of econometric techniques. Both of them have advantages and disadvantages analytically described in the theoretical part of this study while this study prefers the use of SFA instead of DEA given the advantage that technical efficiency is distinguished from both statistical noise and measurement errors which can not be estimated using programming techniques. However, both techniques are commonly used in major sectors for both developed and developing countries.
from the centrally planned economy to the liberalized economy leads to an increase in a firm’s performance, while performance was usually measured in an ad hoc way such as by labor productivity or growth in sales. For instance, Halpern and Korosi (2001) show that in the Hungarian corporate sector increasing competition has led to a gradual improvement in efficiency while the aim of their study was to investigate the link between competition and efficiency for the Hungarian corporate sector during various phases of the transition process. Another similar study was conducted by Funke and Rahn (2002) who compared the performance of firms between countries with transition and developed economy. They reached the conclusion that the Eastern German firms were significantly less efficient than those in Western Germany. A number of other studies are presented in the chapter 3 most of which support the hypothesis that most sectors in developed countries are more efficient than in transition countries. On the other hand, there is a limited number of studies such as Martin and Parker (1997), Boubakri and Cosset (1999), Yunos and Hawdon (1997) which have provided mixed results on the relation between efficiency of firms and competition during the privatization and the post privatization period for both transition and developed countries.
Testing the hypothesis that sectors in developed countries appear to be more efficient than those in developing ones, in a recent study by Cullmann et al. (2006), technical efficiency of Eastern European electricity firms was estimated in order to provide evidence on whether the efficiency of firms would explain any possible development of individual companies and would facilitate any further analysis which combines firms’ performance and reforms of the transition economies. However, since the dataset was small, general conclusions could not be provided and therefore the authors suggested that future research or expansion of their study should be based on a more dynamic comparative analysis of efficiency measures in Central and Eastern Europe, using cross sectional data or time series from 1995 until 2005.
in order to conclude first on whether industries in transition countries are as efficient as their Western counterparts and second testing on whether the relative efficiency of the electricity sector in European developing countries has been improved through time.
2 . PRODUCTIVITY AND EFFICIENCY
As it was pointed out in the introduction, the aim of this study is to estimate the relative efficiency across European developed and transition economies. In order to proceed to a further and deeper analysis it is essential to provide analytical information on the concept of efficiency and productivity as well as to explain why efficiency is important, what the impact on real world phenomena is and finally to convince why this study prefers to estimate efficiency instead of productivity.
2.1
Productivity
In the field of economics analysis, most authors agree today that productivity is “the ability displayed by production factors to produce” (Thiry and Tulkens, 1988). In an early study, Vincent (1968) proposed a general definition of productivity as “the ratio between production and the production factors that realized it, or between production and some of the factors that originated it”. In fact, an efficient use of resources in the production of goods will improve productivity since more goods will be produced with the same resources or maintaining the same level of production with fewer resources.
Productivity can be explained by the production function and its shifts. As a matter of fact production function is defined as the relationship assumed to exist between the quantities of the inputs used and of the outputs that may be obtained as a result (Thiry and Tulkens, 1988). In the case of only one factor being considered, for instance labour, capital, or any other input, then productivity is called partial. As an example, when the production volume expressed as turnover or added value is compared with the quantity of labour involved then instead of partial productivity we use the term of labour productivity.
Figure 1: Production frontier
Source: Thiry and Tulkens, 1988
The production function, which can be considered as the simple relationship between inputs and outputs, is also possible to be considered as a frontier, delineating the limits of what an enterprise can achieve. Then the production function specifies the maximum quantities of realizable output, given any level of inputs and for any level of output, the minimum quantities of inputs needed for producing. Figure 1 shows that if function f0 is considered as a frontier then all points on or below such as
B, C, D, must be realizable whereas point E can not be realizable. The new production frontier indicates the existence of inefficiency if a firm operates below the frontier. On the other hand, a firm will be efficient if it operates on the production frontier.
2.2
Efficiency
There is a formal difference between productivity and efficiency. In fact, productivity relies essentially on a ratio between inputs and outputs. On the other hand, efficiency expresses the distance between the quantities of outputs and inputs considered, and the quantities defining by the frontier (Thiry and Tulkens, 1988). Such a distinction can be represented in Figure 2 which is an output oriented figure with one input variable (X) and one output variable (Y). In the following production function points C and D represent firms which produce YC output with the use of XC
input and firm D produces YD output with the use of XD input. Firms C, D produce
different amount of output using different amount of input. However, both firms appear to have the same productivity ratio since OYC / OXC = OYD / OXD. On the
other hand firm C is less efficient contrary to firm D since firm C could have produced a higher amount of output with the same use of input XC.
Figure 2: Productivity and Efficiency
2.3
Technical Efficiency
As previously stated, firm outputs may lie below the frontier for a variety of reasons such as the existence of random shocks in the production process and the fact that firms are less technical efficient (Aigner and Chu, 1968). In fact firms which are inefficient indicate that they could have produced more output using the same amount of inputs.
A well known and widely used approach comes from Farrell (1957) who distinguishes the efficiency of firms into allocative and technical efficiency. Allocative efficiency is defined as a failure to choose the optimal combination of inputs while technical efficiency is defined as the failure to achieve the maximum possible output from the use of inputs. A similar definition of technical efficiency is provided by Koopmans (1951) who explains that technical efficiency refers to the ability to minimize input use in the production of a given output, or the ability to obtain maximum output from a given input.
In respect to this concept, this study estimates technical efficiency in a major sector such as the electricity, gas and water supply sector in order to provide evidence on the relative performance of firms both in developing and developed countries. Since this study prefers to estimate efficiency instead of productivity it is essential to provide reasons underlying this decision. Although productivity is one of the most commonly used measures for analysing performance of firms or industries, it only gives a partial picture of performance. A common assumption that is used in estimating production functions is that producers who operate on their production functions appear to be technically efficient.
improve their market position since they can increase their profits producing more outputs with the same amount of inputs.
In addition to the latter, efficient firms face lower cost of production, improved quality of products and higher profits. Therefore such firms can compete with success not only in the domestic but in the global market too (Agarwal, 2001). Moreover, efficiency is not just a concept of nice graphical and mathematical tricks but an important source of under-performance. Daly et al. (1985) suggest that the major discrepancy between UK and German plants is not the lack of capital but the inability to exploit that capital due to poor skills of both operatives and management. Thus, capital intensive firms with a high degree of inefficiency indicate the existence of major operatives and management problems. Thus, the efficiency of a firm is an essential indicator in order to avoid such operatives and management problems.
In the real world it is highly important for firms to be efficient and we can imagine the advantages not only for economy but also for nature. For example, an efficient production unit operating in a major sector such as the electricity, gas and water supply sector, would exploit fewer resources in order to produce the same amount of outputs. This latter view indicates the necessity of this analysis to provide evidence on the relative performance of firms operating in the European Union since firms will detect their inefficient use of inputs and will adjust their level of production using inputs simply more efficiently. Moreover Coelli et al. (2005) supported that efficiency can be applied to firms in the private sector in producing goods or to service industries such as hotels and restaurants or to non profit organizations such as schools and hospitals. Therefore, efficiency is a concept which can provide evidence for different types of organizations, firms or services and describe real world phenomena.
So far what have been discussed concerning the efficiency theory are the definition and the distinction between productivity and efficiency. As mentioned in the introduction, this study estimates the efficiency of firms in the electricity, gas and water supply sector for both developed and developing market economies. However, in order to provide such estimation, it is important that theory on the appearance of technical efficiency in a single input-output case based on Farell’s concept be provided.
Farrell’s concept of production frontier is depicted in figure 3 as an output orientated graph and shows how technical efficiency can be measured. The horizontal axis represents the inputs (X) and the vertical shows the output (Y). As explained in figure 1, all the input-output values which are below the production frontier mean that firms do not attain the maximum possible output with the use of input. Point A produces output (y) using input (x) and technical efficiency is given by the ratio of the output (y) to the frontier output (y*) using the same level of inputs (x).
Figure 3: Farrell’s Depiction of Technical Efficiency
Source: Battese and Coelli, 1992
methodological distinction engages parametric and non parametric approaches. Such distinction involves the assumption that the distance between the observed situation and those specified by the production functional form correspond only to inefficiencies or to inefficiencies tied to the statistical error term (Thiry and Tulkens, 1988).
3 . LITERATURE REVIEW
Over the last two decades, both developed and developing countries have been subjected to restructuring, increasing competition and privatizing of state-owned firms in almost every sector. Evidence supports that this shift in ownership (from state-owned to private-state-owned hands) has resulted in a significant increase on the efficiency of firms and the quality of production (Svcjnar, 2002). However, only few studies have been more cautious about the results of privatization and competition on firm performance especially in the recent years.
In an early comparison of electricity production in 27 developing countries in 1987, using the DEA analysis Yunos and Hawdon (1997) concluded that the public sector suppliers performed as well as the private sector companies; even though in none of the countries studied had effective competition been introduced. Similar evidence was provided by Martin and Parker (1997) who examined whether 11 UK firms which had been privatized between 1981 and 1988 had their performance been improved after divestment. Results showed that fewer than half of the British firms performed better after being privatized and several firms improved their performance prior to being privatized. Furthermore, Boubakri and Cosset (1999) examine the pre versus post privatization performance of 16 African firms which had been privatized through public share offering during 1989-1996. Results showed a significant increase in capital spending by privatized firms, but only insignificant changes in efficiency.
immediate effect on the productive efficiency and on the profitability of the industrial firms since the profitability of firms have been increased during that time period. In addition to that, large firms which were created under the centrally planned system suffered from inefficiencies that were alleviated by the breakups. However what is yet to be researched is whether these differences in firm’s efficiency have been converged or diverged in the following years.
In the middle of the 1990’s, as even more new firms appeared in the market, competition between private and state-owned firms forced them to improve their management in order to become more efficient. Halpern and Korosi (2001) searched the relationship between competition and efficiency for the Hungarian corporate sector during various phases of the transition process. In order to estimate the efficiency of firms the Stochastic Frontier Analysis was applied. Results showed a gradual improvement in mean efficiency especially in the recent years. As a matter of fact, since mean efficiency scores in various sectors are quite similar, from 1990 to 1991 efficiency showed a substantial drop while in the following years efficiency showed rapid growth until 1994 and remained almost stable (small decline) until 1997.
Such results can be explained due to the fact that in the early years of transition, firms had to adjust their production on the realities of the new market conditions. In the following years, since that adjustment had been completed, firms were able to produce more efficiently. In addition to that, the overall picture of corporate performance supported that in the first years transitional crisis was characterised by huge inefficiencies but in the following years the positive developing of performance is confirmed due to the initial painful and deep microeconomic restructuring and macroeconomic adjustment.
Results supported that technical efficiency of the distribution companies has been increased during the transition period; yet, doubtful still remains whether the same conclusions could be drawn testing more developing countries. Such expansion was proposed by authors in the last part of their study since they recommended that a conduction of a dynamic comparative analysis with neighboring transition countries, such as the Czech Republic, Slovakia and Hungary would provide more and significant evidence. This study aims to fill that gap including more developing countries from the Central Eastern Europe.
3.1
Building Hypotheses
Previous studies such as Lizal et al. (2001), Svcjnar (2002), Halpern and Korosi (2001) and Cullmann and Hirschhausen (2006), supported that firms which operate in countries with transition economy produce more efficiently since the transition period. However, such hypothesis was tested for an early transition period providing results from the beginning of 1990’s until almost the beginning of the new century. In fact, it is highly interesting whether firms in transition economies retain their development of their performance from the end of the last decade until the recent years. Since Cullmann and Hirschhausen (2006) had mentioned that it is still unclear whether sectors in countries with transition economy will have their efficiency level increased, this study provides evidence on that by testing the following hypothesis on a more recent time period.
HYPOTHESIS 1
“Firms operating in transition economies are expected to improve the efficiency of the electricity, gas and water supply sector from 2000 until 2005”
may have increased their performance in order to compete with success in the new market economy.
Despite the fact that previous studies have claimed that privatization in transition economies has led to an increase on the efficiency of firms, challenging still remains whether firms in transition countries are more or less efficient compared to those in developed countries. A first attempt comes from Funke and Rahn (2002) who estimate firms’ efficiency in both East and West Germany using Stochastic Frontier Analysis and exploring micro data from 1994 to 1998. Adopting a translog frontier model the authors estimate firm’s efficiency in three sectors and provide evidence when comparing results of mean efficiency scores between Eastern and Western Germany.
Results supported that relative efficiency of Eastern Germany have increased substantially over the period 1994-1998 providing support for the Hypothesis one. In addition to that, firms in Eastern Germany are significantly less efficient than firms operating in Western Germany but the overall difference was reducing year by year. However, it is quite unclear if the same conclusion can be drawn when comparing firms from Eastern Europe to those from Western Europe especially in the recent years.
Both previous studies indicate plenty of positive dynamic effects that arose from privatization during transition. In particular, changing ownership from state to private alters the residual control rights raising the incentives for the new owners to invest in a new and more recent technology. Such investment is very important especially for countries with transition economy, since state-owned enterprises lacked of innovation due to the communist rule. Furthermore, private ownership will be associated with higher price-cost margins which may be associated by cheaper ways of producing and of higher product quality, reflecting in higher prices. If these new technologies diffuse easily and hence spillovers to other firms are substantial, welfare may improve (Cullmann et al, 2006).
Challenged this time by Cullmann et al (2006) who proposed to test a larger sample of firms in order to provide evidence on a European cross country comparison of firms’ efficiency in the electricity sector, this study test for the hypothesis that in the post-privatization period, especially from the beginning of the new century until the recent time, firms which operate in countries with transition economies even if they have improved their efficiency they will still less efficient compared with firms in the Western countries.
HYPOTHESIS 2
“Firms in Central-Eastern European countries with transition economy are expected to be more inefficient compared to firms in Western Europe”
4 . THE STOCHASTIC FRONTIER ANALYSIS [1]
Since the hypotheses have been conducted, then it is essential to discuss the methodology of estimation firms’ efficiency. Stochastic frontier analysis as the approach which this study applies was proposed by Aigner et al. (1977) and by Meeusen and Van den Broeck (1977). This method is called Stochastic Frontier Analysis due to the fact that it concerns the estimation of the production frontier and which can be succeeded with the use of econometric knowledge. In fact, stochastic frontier offers the opportunity to extract both estimates of technical inefficiency and random shocks that affect a producer output.
Throughout this study, the estimation of technical efficiency is based on the assumption that producers produce only a single output due to stochastic frontier’s restriction. Thus, stochastic frontier production function is defined by the following equation:
Y
i= f (x
i; β) exp (ε
i)
(4.1)ε
i= (ν
i– u
i), u
i> 0
(4.2)Y
i is the single outputf(x
i; β)
is the production functionε
i=(ν
i– u
i),
is the error termν
i is the random error with zero mean and it is associated with the random factors such as measurement errors in production, weather, industrial action, factors which are not under the control of a firm.u
i is the term which refers to technical inefficiency.Since the error term has two components, the stochastic production frontier model is often referred to as a “composed error” model. The noise component (
ν
i) is assumed to be identically distributed asν
~ N (0,s ) with zero mean and (v22
v
s )
variance, while
(u
i)
is a non-negative component distributed asu
~ N (0,s ) with u2 zero mean and (s ) variance.u2The estimation approach starts with the use of ordinary least squares (OLS) in order to estimate the parameters of the model. Even though the constant term (β0) can
not be estimated sufficiently due to the fact that the error term has not zero mean {E( ˆi
e ) = - E( ˆu ) ≤ 0} therefore OLS can not provide estimates of technical efficiency. i
Since the constant parameter can not be estimated directly from OLS, then there is a need to apply an additional approach which can lead to the estimation of the constant parameter and then to the estimation of technical efficiency. Meeting the last goal, it requires the use of distributional assumptions for both error components which lead to the application one of the two common methods such as the maximum likelihood and the method of moments.
Both methods are widely used in order to estimate a producer’s technical efficiency. This study prefers to use method of moments instead of maximum likelihood since with the use of the first method once we can obtain “good” estimates when there is a large dataset [2]. As a matter of fact, this study applies a large dataset
which will be described later in this study.
4 .1 Method of Moments
Method of moments is a highly technical orientated method. This method is a modern and widely used estimation technique in econometrics and it can be applied to cross-sectional problems, time-series problems and panel data settings. The intuition behind this method is the fact that offers highly consistence estimators under very general conditions. Unlike for other techniques, with the use of method of moments it is possible to obtain consistency of the estimators without making distributional assumptions and can allow for arbitrary heteroskedasticity. In addition, when other techniques have consistency problems on applying large data sample, method of moments offers consistency of results when applying large data sample (Hill et al. 2001).
As mentioned before, the production frontier can be estimated with the use of method of moments following two different parts. In the first part OLS is used in order to generate consistent estimates of the all parameters describing the structure of the production frontier, apart from the intercept. Then distributional assumptions are invoked in order to obtain consistent estimates of the intercept and the parameters which describe the structure of the two error components. This estimation procedure is known as the Modified Ordinary Least Squares and the major difference between MOLS and OLS is that in the MOLS procedure the intercept parameter is shifted up (“modified”) under the assumed distribution.
When the first step is accomplished then the so-called “JLMS” technique is used to estimate technical efficiency of each producer. The JLMS technique is a method to extract the information that the error term (εi) contains on technical
efficiency of each producer (ui) depending on the distributional assumptions.
However, there is no doubt that the use of different distributional assumptions may lead to different results of technical efficiency and therefore it is essential to provide evidence on which distributional assumption should be applied.
123 U.S. electric utilities, using different distributional assumptions each time for the efficiency term.
He reported a sample mean of efficiencies of 0.87 (half normal), 0.90 (exponential), 0.89 (truncated normal), and 0.89 (gamma). Then Greene supported that it is able to choose any possible distribution assumption since there are insignificant differences among results of technical efficiency using different distributional assumptions. In addition, Ritter and Simar (1997b) had proposed to use a relatively simple distribution such as half-normal or exponential in order to proceed further in the estimation of efficiency. In fact, that study applies method of moments in order to estimate firms’ efficiency with the use of normal – half normal distribution for the error components.
Assuming that the stochastic production frontier model takes the log-linear Cobb-Douglas form then the stochastic production frontier is given in the following equation:
ln y
i= β
0+ Σβ
nln x
ni+ ν
i- u
i (4.3) Rewriting the above equation in order to get zero mean and constant variance for the error term, the initial production frontier (3) adjusted in the following form:ln y
i= [β
0–Ε(u
i)] + Σβ
nln x
ni+ ν
i– [u
i- E(u
i)]
(4.4) Sinceu
i follows half normal distribution then:
Ε(
uˆi) =
2p sˆu (4.5)V (
uˆi) = [(π-2)/π]
ˆ2u
s (4.6)
In the first part of the method of moments, OLS can be used in order to obtain consistent estimates for the model parameters. Then it is necessary to apply distributional assumptions on the components of the error term (2).
u
i follows a half-normal distribution with zero mean,u
i~ Ν
+(0,σ
u2)
The normal-half normal distribution contains two parameters,
σ
u andσ
ν. Figure 4 provides three different normal-half normal distributions for 3 different combinations ofσ
uandσ
ν.Figure 4: normal-half normal distribution
Source: Kumbhakar and Lovell, 2000
Both variances of error components are the unknown variables which have to be estimated. Thus, the very next issue involves the estimation of these two variances. For this to be achieved, it is essential that both the second and third central moments of the model be estimated using the OLS residuals.
m
2(e) = [1/(N-k)]
2 1 N i i e =å
(4.7)m
3(e) = [1/(N-k)]
3 1 N i i e =å
(4.8)
Whenever m3 < 0 value of the third central moment is negative, OLS residuals
are negatively skewed and imply the presence of technical inefficiency. With the use of the second and the third central moment, both variances σ2
ν and σ2υ can be
estimated following the relationship between central moments and variances.
ˆ2 u s
=
2/3 3 2 / (1 4 / ) m p p æ ö ç ÷ -è ø(4.9)
ˆ2 n s
= m
2– [(π-2)/π]
ˆ2 u s(4.10)
After all one way to explore information of the relative contribution of both noise and technical efficiency term to the error term can be achieved by measuring the ratio of the efficiency estimated variance to the noise estimated variance.
2 2
ˆ
u/
ˆ
nl
=
s
s
(4.11)When lamda parameters is almost zero l ®0 (either ˆ2
n
s gets high value
contrary to ˆ2
u
s or ˆ2
u
s gets almost zero value), then the symmetric error component
dominates the one-sided error component in the determination of the error term. In this case the production function model has no technical inefficiency. In other words, technical efficiency gets the maximum value which is equal to one. On the other hand, whenever the ratio gets extremely large valuel ® ¥ (due to the fact that either
2
ˆu
s ® ¥ or ˆ2 0
n
s ® ), then the one sided-error component dominates the symmetric
error component in the determination of the error term.
Another indication of existence of technical efficiency is the gamma parameter which is the ratio between the estimated variation of efficiency to the sum of the variations of efficiency and noise terms. When this ratio is close to zero then there is indication of highly efficient firm, but when the ratio is close to one then there is indication of highly inefficient sector.
2 2 2
ˆ
u/ (
ˆ
nˆ
u)
g s
=
s s
+
(4.12)Furthermore, as soon as the variances
(
s ) and (ˆu22
ˆn
s ) are estimated, then it is
possible to obtain consistent estimate of the intercept (b ) for stochastic frontier ˆ0
production (eq. 4).
0
ˆ
b
= OLS intercept +
2p sˆu (4.13)So far, all parameters of the stochastic frontier model have been estimated. The final step of the method of moments consists of the application of the JLMS technique in order to obtain each producer’s technical efficiency. In fact, any information on the error term concerning technical efficiency (
u
i), can be obtained from the conditional distribution assumptions ofu
givenε
. Jondrow et al. (JLMS, 1982) proved that in case that technical efficiency follows half-normal distributionu
i~ Ν
+(0, σ
u2
)
then the conditional distribution ofu
givenε
is:2 * * 2 * * * ( , ) ( / ) ( ) ( ) 1 exp / 1 2 2 f u f u f u e e e m m s s ps = é ù ì - ü æ ö = × í- ý ê- F -ç ÷ú î þ ë è øû (4.14) 2 2 2 * 2 2 u v u v s s s s s × = + (4.15) 2 * 2 2 u u v s m e s s =-+ (4.16) ()
F is the standard normal cumulative distribution function. Since ( / )f u e is distributed as *
(
2)
*, *
m s
N then the estimation of technical efficiency can be estimated by the Battese and Coelli (1988) point estimator:
However Olson et al. (1980) have pointed out two major drawbacks with the use of the method of moments approach.
Failure Type 1
Despite the fact that the third central moment of the OLS disturbances should be negative, there is a possibility that it will be positive. This case can be appeared when the variance of the efficiency term ( ˆ2
u
s ) is negative, suggesting that the initial
model is not well-specified. If the model is not re-specified by changing the functional form or the variables of the ( ; )f xi b , then it is unavoidable to set
2
ˆu
s = 0, which
provide zero inefficiency. Consequently, the gap between the production function and the production frontier is very small and as a result the level of inefficiency is too small (almost zero value), which occurs only in highly efficient industries.
Failure Type 2
The second disadvantage arises when the third central moment is negative and receives high absolute value, resulting on the estimated variance of the noise term being negative (s < ). In this case we assume that ˆn2 0 ˆ2
0 n
s = which infers that there is
no noise in the data.
5 . DEA VERSUS SFA
The estimation of production frontier can be succeeded with the use of Stochastic Frontier Analysis (SFA) and Data Envelopment Analysis (DEA). This study supports the use of stochastic frontier due to the fact that technical inefficiency is independently from other external disturbances since the error term contains both technical efficiency and noise components. In fact, SFA has been previously presented and DEA as a commonly used method has to be discussed too.
The intuition behind DEA was to construct a piece-wise surface (or frontier) over the data with the use of linear programming methods. The DEA efficient frontier is composed of those undominated firms and piecewise linear segments that connect the set of input/output combinations of these firms. In fact DEA calculates a discrete piece-wise frontier determined by a set of firms which have the ability to utilize the same volume of inputs and produce the same or higher amount of outputs. Therefore, technical efficiency can be measured from the distance between the outer value and the production value while each firm can only be compared to firms on the frontier (Bauer et al. 1997) under the assumption that all deviations from the efficient frontier respond to inefficiencies. Aigner and Chu (1968) have considered the idea of deterministic production frontier using a parametric frontier function of the Cobb-Douglas equation.
On the other hand, the Stochastic Frontier Analysis requires statistical methods in order to fit a frontier. The major issue of this approach is to identify the relationship between outputs and inputs allowing two types of deviation from this relationship. The first one is the statistical noise such as measurement errors and unfavourable operational conditions and the second type of deviation is the inefficiency term. These two types of deviation can be explained in the following figure.
Figure 5: Stochastic Frontier Analysis
Source: Chote et al. (2003)
Both methods the Stochastic Frontier Analysis and the Data Envelopment Analysis are common techniques whenever the efficiency of firm needs to be estimated. What makes the DEA more preferable is the fact that as Jacobs (2000) supports in his study “…non statistical approaches such as DEA have the disadvantage of assuming no statistical noise, but have the advantage of being no-parametric and requiring few assumptions about the underlying technology. On the other hand, the SFA has the attraction of allowing for statistical noise, but it also has the disadvantage of requiring strong assumptions as to the form of the frontier”. Consequently, the DEA is preferred where measurement error is unlikely to pose much of a threat and where the assumptions of production theory are in question. Furthermore, the DEA allows the use of multiple outputs, contrary to the SFA which allow only one output in the frontier model and does not require the explicit specification of functional form and so imposes very little structure on the shape of the efficient frontier (Bauer et al., 1997).
DEA leads to higher inefficiency score contrary to the SFA which separates measurement errors from efficiency (Bauer et al., 1997).
6 . DATA SPECIFICATION
This study explores cross-sectional data of medium size firms for seven developing countries on Central Eastern Europe with transition market economy and nine developed market economies from Western Europe. In order to proceed on the estimation of technical efficiency first it is essential to provide information on the dataset and the kind of variables.
First of all, this study explores financial data from the Amadeus Database, collected by the consultancy Bureau van Dijk. The Amadeus Database consists of companies’ accounts reported to national statistical offices for European companies when the total volume of turnover or assets is at least $1.2 million Dollars. Moreover, Amadeus provides standardized financial data for both European private and public companies, and is compiled from several well-established national information collectors.
6 .1 Time Period (2000-2005)
One of the advantages of this database is the opportunity to explore financial data and ratios from all European countries for all sectors for the last 10 years. However, financial data are less detailed from 1996 until 1999. Consequently, this study explores data for a period of six years from 2000 until 2005. Even though, this study estimates technical efficiency for all medium size firms which fulfill the following financial restrictions.
6 .2 Size of Firms
The first restriction involves size of firms. The aim of this study is to estimate the level of technical efficiency for medium size firms. Such firms can be distinguished by adopting size restrictions similar to those laid out in the Fourth E.U. Directive, which require firms to meet at least one of the following criteria in every year:
The Fourth EU Directive classifies small and medium sized companies depending on the above three criteria: balance sheet, net turnover and average number of employees. Based on this directive, firms which do not fulfill one of the above criteria are excluded from the dataset. Furthermore, in order to compare firms with similar size the dataset excludes firms with total volume of turnover higher than one billion EURO since the similar restriction has been applied by Halpern and Korosi (2001) who defined as large firms those firms which has number of employees higher than 500 or value of fixed assets greater than 1bn or sales of volume greater than 1.5bn. Since in the volume of turnover includes the volume of sales therefore in order to provide similar data restriction this study excludes firms with volume of turnover higher than 1bn. Euro.
6 .3 List of European Countries
The second restriction engages the number of countries which belong to the dataset. As a matter of fact this study is willing to explore as many countries as possible in order to estimate technical efficiency across firms from all European countries. However, this thought can not be accomplished due to the fact that there are firms in few countries which do not publish their financial statements.
Starting with countries which include either no firms at all or few large state-owned firms with accounting data unavailable and operating in the electricity, gas and water supply sector are Belarus, Cyprus, Ireland, Latvia, Luxemburg, Moldova, Montenegro, Greece, Iceland, Ireland and Liechtenstein. Consequently, those countries have to be excluded from the sample.
Further limitation appears when extracting data of firms from the Database. In the case of Austria, only 3 out of 11 firms provide all data while the remaining 8 firms include missing values for 2000 and 2001.
the countries which subjected into this limitation are Austria, Bosnia, Denmark, Estonia, Slovakia Slovenia have to be excluded from the sample. Such problem appears in most studies when extracting financial data, for example a similar study by Cullmann et al. (2006) is also constrained by data availability especially for the Eastern European countries which are still among the developing countries of Europe (Cullmann et al., 2006).
Last limitation appears for Hungary, Norway and the Russian Federation due to the fact that even if firms provide information in most financial data, however the majority of them do not provide information on the number of employees. This variable is a major variable for that study consequently those countries can not be included in the sample.
To sum up, when excluding all firms which subjected into previous limitations and considering the fact that a small reduction of the number of firms which do not provide financial statements can not alter the conditions and characteristics of the electricity, water supply and gas sector for further research, all the remaining countries which include few firms with missing values are provided in the table 1. These European countries are divided into two groups: the developing countries with transition economy and the countries with developed economy:
Table 1: List of European Countries
DEVELOPED
COUNTRIES DEVELOPING COUNTRIES
Belgium Bulgaria
Finland Croatia
France Czech Republic
In efficiency analysis the choice of the right variable and the selection of an appropriate model are crucial. The literature is rather heterogeneous on which variables should be preferred as the inputs and which variables as the outputs.
The very first step in carrying out the assessment of firm’s efficiency is the identification of the input-output variables. Thanassoulis (2001) argued that “measuring efficiency may be a reflection of a failure to incorporate the right variables and the right constraints and to specify the right economic objective of a production unit”. In order to determine which the right variables are, it is essential to review other studies. Prior (2002) provides a review of the variables used in the analysis of frontier efficiency in the time period from early 1990 till 2002 and among output variables the most frequently applied in studies are sales and revenue (Huang and Liu (1994), Athanassopoulos and Ballantine (1995) and Zhang and Zhao (2001)). Similar study which has used profit before tax and market capitalization of enterprise as outputs has been conducted by Thore, et al. (1994). Furthermore, studies which test for the efficiency of firms in the context of transition, apply single aggregate output namely as gross value of production (turnover). Such studies have been conducted by Piesse and Thirtle (2000) and Hill and Kalirajan (1993).
In case of inputs, there are also studies which estimate efficiency with the use of different type of inputs. As an example, Hill and Kalirajan (1993) used accounting variables such as the cost of employees, material costs and value of investments. Piesse and Thirtle (2000) used operating costs and fixed assets while Ahuja and Majumdar (1998) used fixed assets and the number of employees as inputs.
Considering all previous studies, two of the most common outputs are the number of revenues and number of sales as well as number of employees and number of assets as inputs. Both variables, annual number of revenue as turnover and total assets are measured in terms of thousands of EURO while the Amadeus Database has already converted values from domestic to the European currency (Euro). However Amadeus Database does not provide further details on the converting prices from domestic currency to European currency, not even all similar studies which extract and use their dataset from the Amadeus Database.
1. Firm’s total number of revenues in constant values per year 2. Firm’s total number of employees per year.
3. Total Assets in constant values per year in constant values per year
According to the Amadeus Database all financial values are measured as current prices. However, since most quantitative studies explore financial data in constant prices, it is essential to construct price indices to deflate the values in order to allow for comparisons among variables over time. Although the number of employees is a constant value, both the annual total number of revenue and annual total number of assets have to be transformed into constant prices for every country starting from 2000 until 2005.
In order to construct price indices to deflate the series it is essential to use price deflators. This study uses consumer price inflation rates in order to deflate the data. In fact, consumer price index is the main guide for economies in order to compare a consistent base of products from year to year, focusing on products that are bought and used by consumers on a daily basis. The consumer price index can provide insight to investors on where to invest as they are aware of the inflation rate. On the other hand, the consumer price index is volatile from month to month and cannot be predicted. The annual price inflation index for all countries is explored from International Monetary Funds Database (World Economic Outlook Database, October 2007) and is presented in Table 2.
Country 2001 2002 2003 2004 2005 Belgium 2,4 1,6 1,5 1,9 2,3 Bulgaria 7,5 5,8 2,3 6,1 4,4 Croatia 4,9 1,7 1,8 2,1 3 Czech Republic 4,7 1,8 0,1 2,8 2 Finland 2,7 2 1,3 0,1 1 France 1,8 1,9 2,2 2,3 1,9 Germany 1,9 1,4 1 1,8 1,9 Italy 2,3 2,6 2,8 2,3 2,2 Netherlands 5,1 3,9 2,2 1,4 1,4 Poland 5,5 1,9 0,8 3,5 2,2 Romania 34,5 22,5 15,3 11,9 8,8 Serbia 91,1 21,2 11,3 9,5 15,4 Spain 2,8 3,6 3,1 3,1 3,2 Sweden 2,7 2 2,3 1,1 0,8 Switzerland 1 0,6 0,6 0,8 1,3 Ukraine 12 0,8 5,2 9 14,2
Source: International Monetary Funds, World Economic Outlook Database, October 2007
Most transition countries have experienced high inflation or hyperinflation due to the fact that the communist system has been disintegrated. Countries such as Poland, Bulgaria and Romania had their consumer price inflation been exceeded 200 percent at least one year between 1990 and 1993 while the Russia Federation and Ukraine had experienced at least one year with inflation rates higher than 2000 percent. From the beginning of the new century especially by 2001, in most transition countries, inflation rates were in single digits. In particular Table 2 shows that Serbia, Romania and Ukraine have been subjected into hyperinflation especially in Serbia inflation has reached almost 90 %. Such hyperinflation indicates that it is essential to use constant prices instead of current prices since the prices year by year differ significantly. On the other hand in most developed countries the inflation rate is almost constant between 0.5 and 3 with Switzerland having the lowest inflation rate of all. After deflation descriptive statistics of the variables are presented in the following Table 3.
YEAR: 2000 N Minimum Maximum Mean DeviationStd. Op. Revenue 811 3517 959650 86974,86 132950,3 T. Assets 811 1335 5316685 206370,9 442445,1
Employees 811 50 27836 821,06 1832,17
YEAR: 2001 N Minimum Maximum Mean DeviationStd. Op. Revenue 913 2774,07 952931,7 89503,91 138223,9 T. Assets 913 2229,38 9792766 182117,5 458656,4
Employees 913 50 17422 851,47 1590,51
YEAR: 2002 N Minimum Maximum Mean DeviationStd. Op. Revenue 1017 2546,49 947557,54 94616,87 140081,32
T. Assets 1017 2220,51 3422610,31 185190,96 351159,29 Employees 1017 50,00 16053,00 831,54 1557,67
YEAR: 2003 N Minimum Maximum Mean DeviationStd. Op. Revenue 1073 2132,78 861605,68 94477,89 135555,39
T. Assets 1073 1645,37 4604088,07 188260,11 393402,12 Employees 1073 50,00 15504,00 822,03 1526,63
YEAR: 2004 N Minimum Maximum Mean DeviationStd. Op. Revenue 1212 2193,96 996035,70 97241,67 173576,70
T. Assets 1212 2062,28 16538018,1 198273,68 597367,19 Employees 1212 50,00 35301,00 786,63 1769,58
YEAR: 2005 N Minimum Maximum Mean DeviationStd. Op. Revenue 1282 1826,58 844582,02 94744,84 138695,98
T. Assets 1282 1206,31 3986473,53 179692,76 365555,78 Employees 1282 50,00 14881,00 682,81 1359,34 (Note: Operating Revenues and volume of total assets are measured in thousands of EURO)
Studying Table 3 and considering the discussion in data exploitation, the number of observations is increased year by year, as it was expected due to the fact that in the early years many firms have not published their financial accounts. Therefore the minimum number of observations appears in 2000 (811). Since 2000 more and more firms disclosed their financial accounts and the maximum number of observations appears in 2005 (1282).
by year and indicate that observations did not face large deviations in the sample. Finally, the results of standard deviation indicate that in 2004, the number of operating revenue and volume of total assets appears to be more “spread out” from the mean value. Results of standard deviation (less than 2004) for the remaining years indicate that observations seem to be close to the mean value.
6 .5 Methodology Specification
In order to explore this dataset with the application of Stochastic Frontier Analysis it is essential to define the production function. This study applies the Cobb-Douglas production function applying two independent variables, the volume of total assets as capital input and the total number of employees as labour input. On the other hand there is one independent variable the annual total number of operating revenues.
Practically, most empirical studies in accounting and finance using cross-sectional data may come to grips with the problem of highly correlated data across firms. Since this study is exploring financial data, it is appropriate to test whether data are correlated or not since correlated data may be an indication of multicollinearity between independent variables.
As a matter of fact, it is necessary to test on the existence of multicollinearity in the model because stochastic frontier analysis would not provide correct results first for technical efficiency term due to the fact that technical efficiency depends on the regression residuals which depend on the best estimated model. Since the initial model will not be the “best” one model then residuals will provide insufficient measures for the estimation of the second and the third central moment of the methodology. In addition to that, coefficients of both independent variables will be incorrect since the estimated model will include both independent which are correlated and such coefficients will provide insufficient information on the estimated production frontier.
The analysis of the data was carried out with the aid of the Statistical Package for Social Sciences (SPSS 15.0). Correlation results for the independent variables per year are provided in the following Table 4.
T. Assets
2000 T. Assets 2001 T. Assets 2002 T. Assets 2003 T. Assets 2004 T. Assets 2005 N. Employees 2000 0,39 N. Employees 2001 0,21 N. Employees 2002 0,2 N. Employees 2003 0,18 N. Employees 2004 0,31 N. Employees 2005 0,14
Notes: Correlation score between volume of total assets and number of Employees is provided using SPSS 15.0
** Correlation is significant at the 0.01 level (2-tailed).
Results from the above tables, in almost all cases, indicate weak positive relationship between the total assets and the number of employees. The maximum correlation score exists in 2000 (0.39) and the minimum score appears in 2005 (0.14). Indication of multicollinearity between independent variables appears when the correlation score is higher than 0.4. However, the maximum correlation score of this study’s data is almost 0.4 for 2000.
Since there is no indication of multicollinearity between both independent variables, this study provides information on the production function. Starting with the production function this study applies the Cobb –Douglas equation.
1 2
0
a a
Y a K L
=
(6.1)Applying logarithms in both sides the initial Cobb-Douglas equation transformed in the following form as it was described in section 5. Then method of moments is applied in order to provide estimates for all coefficients of the production frontier.
0 1 2
( )
( )
( ) (
)
The appearance of unusual observations is common in econometric techniques. These observations, in the “method of moments” approach leads to two different kinds of failures as it was explained previously in stochastic frontier session. The first and most common failure appears when sectors are totally efficient (TE = 1) and the second failure appears when the initial production function cannot be estimated correctly. In both cases the method of moments is not able to distinguish the most efficient or the most inefficient firms and drop them from the sample. In fact, residuals of the OLS regression can provide indication on which firms are highly efficient and which are highly inefficient, however it is not appropriate to reject these unusual observations due to the valuable information which may hide.
7 . EMPIRICAL RESULTS
The presentation of results is divided into two broad sections. In the first section, the model consisting of two inputs (volume of total assets and number of employees per firm) and one output (annual volume of revenue per firm) is estimated from year to year. When the estimation process is completed then the results of coefficients are presented in order to discuss the characteristics of the Stochastic Production Frontier and compare among results from similar studies. In the second part of this section, results of the mean technical efficiency for both European developed and developing countries are presented. Finally the discussion upon the Hypotheses of this study is provided in order to conclude on whether both hypotheses are supported or not. The estimation process starts from 2000 and ends in 2005.
7 .1 Coefficients of Production Frontier
Table 5: Coefficients of Production Frontier per year
YEAR: 2000 Unstandardized Coefficients Sig. B Std. Error Std. Error
(Constant) 2,05 0,2 0
LN(T. Assets) 0,73 0,02 0
LN(Employees) 0,05 0,02 0,01
Dependent Variable: LN(Op. Revenue)
YEAR: 2001 Unstandardized Coefficients Sig. B Std. Error Std. Error
(Constant) 1,39 0,19 0
LN(T. Assets) 0,79 0,02 0
LN(Employees) 0,06 0,02 0
Dependent Variable: LN(Op. Revenue)
YEAR: 2002 Unstandardized Coefficients Sig. B Std. Error Std. Error
(Constant) 1,06 0,16 0
LN(T. Assets) 0,83 0,01 0
LN(Employees) 0,05 0,02 0
Dependent Variable: LN(Op. Revenue)
YEAR: 2003 Unstandardized Coefficients Sig. B Std. Error Std. Error
(Constant) 1,52 0,18 0
LN(T. Assets) 0,79 0,02 0
LN(Employees) 0,05 0,02 0,01
Dependent Variable: LN(Op. Revenue)
YEAR: 2004 Unstandardized Coefficients Sig. B Std. Error Std. Error
(Constant) 1,45 0,17 0
Ln(T. Assets) 0,79 0,01 0
Ln(Employees) 0,06 0,02 0
Dependent Variable: Ln(Op. Revenue)
YEAR: 2005 Unstandardized Coefficients Sig. B Std. Error Std. Error
(Constant) 1,54 0,17 0
Ln(T. Assets) 0,8 0,01 0
Ln(Employees) 0,03 0,02 0,13
Dependent Variable: Ln(Op. Revenue)
Notes: Table 5 presents all coefficient results for the estimated European Frontier as well as the level of significant in order to determine on whether the variables are significant or not. The estimated variables have been adjusted in logarithms followed the estimation process of the Cobb – Douglas equation.
independent variables offer valuable information first on the size of the effect that a variable is having on the dependent variable and second on the direction of this effect based on the sign of the coefficient. In fact coefficient with a positive sign indicates how much the dependent variable is expected to increase when the independent variable increases by one unit holding all the other independent variables constant. On the other hand, coefficient with a negative sign indicates how much the dependent variable is expected to decrease when the independent variable increases by one unit holding all the other independent variables constant.
Considering the previous analysis and studying the coefficients of the OLS regression two interesting points are mentioned. First there is a clear indication that all coefficients are significant (except of the number of employees in 2005) and due to the positive values, both of the variables contribute positively to the production of the output. Second coefficients of both independent variables indicate that the electricity, gas and water supply sector is more capital intensive than labor intensive due to the high value of capital coefficient compared to that of the labor coefficient.
As a matter of fact, according to Table 6, there is a small deviation of results of the estimated coefficients for all European Production Frontiers. The capital input indicates that the volume of total assets contributes from 73% to 83% in increase for the output when holding the labor variable constant. On the other hand, labor coefficient contributes only from 3% to 6% in increase of the output holding the capital constant.
Interesting still remains on whether the coefficients of the European Frontier are in the same direction with results from similar studies. However, any comparison of the coefficients among similar studies seems to be subjected into several limitations. First of all, most studies estimate Stochastic Frontiers for the beginning of 90’s or even earlier while this study estimate Stochastic Frontier for the recent years (2000 until 2005). In addition, most studies are focused on the estimation results of technical efficiency and do not provide information on the coefficients of the OLS regression analysis. Last, similar studies use different methodology (maximum likelihood instead of method of moments) for example Funke and Rahn (2002), Cullmann et al. (2006).
estimate technical efficiency of firms in the gas distribution sector in Argentina, coefficient results of the OLS regression analysis using panel data from 1993-1997 indicate that the elasticity of output with respect to labor input (0.45) is less than the elasticity of output with respect to capital input (0.5). Another panel data estimation using the Cobb-Douglas production function has been conducted by Agarwal (2001), who estimates technical efficiency and productivity growth in the central public sector enterprises in India in the 1990’s. OLS regression results indicate that capital coefficient (0.65) is higher than labor coefficient (0.26). Last, Halperin and Κorosi (2001) found that coefficient of capital is relatively low contrary to the coefficient of labor either using panel data or cross sectional data.
Previous results suggest that there is not a clear answer on whether the coefficient of capital should be higher than the coefficient of labor while in other studies the difference between those values is relatively low. However, estimated coefficients of the European Frontiers of this study are not in the same direction with results of previous studies since coefficient of labor is very low comparing with the coefficient of capital. Even though all coefficients of the European Frontiers have always positive sigh and such result is totally agree with the sigh of coefficients from all previous studies.
7 .2 Frontiers’ Intercept and Indicators of Inefficiency
In this part of this chapter the estimated results of the intercept parameter of the European Frontiers are provided. In addition to that, the variance of the estimation of the error component parameters and the indicators of the existence of inefficiency are presented. Finally, results of the intercept of the European Frontier are discussed in order to provide arguments upon the shifts of the European Stochastic Frontier from 2000 until 2005.
supporting that the efficiency results are more homogenous. In fact, in the early years the lamda parameter indicates that the sector includes highly inefficient firms while in the recent years the sector includes less inefficient firms since the lamda value is significant lower in 2002, 2004 and 2005.
Table 6: Efficiency Indicators and Frontiers’ Intercept
λ γ OLS
const interceptFrontier
2000 1,1 0,06 18,92 0,95 2,05 2,22 2001 0,99 0,1 9,44 0,9 1,39 1,54 2002 0,46 0,29 1,61 0,62 1,06 1,13 2003 0,69 0,21 3,29 0,77 1,52 1,63 2004 0,47 0,29 1,61 0,62 1,45 1,53 2005 0,55 0,29 1,62 0,65 1,54 1,63
Similar indications can be provided by the gamma parameter. In the early years the gamma parameter is close to 1.0 suggesting that the technical inefficiency effects on the European Frontier model are significant. In other words, such results support that the European Frontier model is appropriate since it can capture the inefficiencies across countries. In a similar study by Funke and Rahn (2002) estimated the gamma parameter for three different sectors and they supported that technical inefficiency effects is also significant since the gamma parameter is close to 1. In the recent years (2002, 2004 and 2005) the gamma parameter is lower than the early years, yet, inefficiency effects are still significant since the value of the gamma parameter is almost 0.65.
Since both the gamma and the lamda parameters are significant then the use of frontier production function has been justified (Halperin and Korosi, 2001). Using equation 5.13 of the methodology part of this study, the intercept of European Frontier can be estimated. Results of Table 6 indicate that there was a downward shift of production frontier from 2000 to 2002 since the intercept parameter in the early years was higher than the following two years while the production frontier show a slight increase in 2003 and remaining almost constant in 2004 and 2005.
At first we expected that the production frontier should be moved upward in this specific time period indicating that there was technological progress in this sector, however results seem to provide different conclusions. In fact it is highly important to
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