Efficiency and productivity change across the economic sectors in Lithuania (2000-2010): the dea-multimoora approach.
Balezentis, Tomas ; Misiunas, Algimantas ; Balezentis, Alvydas 等
JEL Classification: C44, C61, D24, M21.
Introduction
Productivity is considered as the key factor for competitiveness in
the long run (European Commission 2011). Indeed, it also guarantees
non-inflatory growth and thus provides a momentum for increase in real
income. It is due to Latruffe (2010) that measures of competitiveness
can be broadly classified into neoclassical ones and strategic
management ones. The neoclassical approach analyses competitiveness from
the viewpoint of international trade flows, whereas the strategic
management theories focus on the specific factors of competitiveness.
These factors encompass, for instance, profitability, productivity, and
efficiency. It is, therefore, important to analyse the trends in
productivity and efficiency in order to make reasonable strategic
management decisions. Furthermore, this study will focus on the
strategic management approach rather than neoclassical one.
One can speak of efficiency when comparing the actual level of
productivity with the yardstick one. In case one knows the foremost,
ideal goal of production, he can speak of effectiveness, albeit it does
seldom occur in the real life. The measurement of efficiency, therefore,
involves the benchmarking practice. The relative measurement of
efficiency - benchmarking - is an important issue for both private and
public decision makers to ensure the sustainable change. It is due to
Jack and Boone (2009) that benchmarking might create motivation for
change; provide a vision for what an organization can look like after
change; provide data, evidence, and success stories for inspiring
change; identify best practices for how to manage change; create a
baseline or yardstick by which to evaluate the impact of earlier
changes.
Frontier techniques are those most suitable for efficiency and
productivity analysis (Murillo-Zamorano 2004; Margono et al. 2011;
Bogetoft, Otto 2011; Bojnec, Latruffe 2011; Atici, Ulucan 2011;
Hajiagha et al. 2013). These methods can be grouped into parametric and
nonparametric as well as into deterministic and stochastic ones. This
study employs a deterministic non-parametric method, data envelopment
analysis, which requires no a priori specification of the functional
form of the underlying production function. Furthermore, productivity
indices are employed to analyse the changes in productivity. The two
seminal methods are usually employed, namely Malmquist and Luenberger
productivity indices (Ippoliti, Falavigna 2012; Tohidi et al. 2012).
On the other hand, the efficiency can be analysed at various
levels, namely at the firm, sector, and nation level. The assessment of
inter-sectorial patterns of efficiency provides a rationale for
strategic management for both private and public decision makers.
Indeed, the comparison of efficiency across different sector of
Lithuanian economy has been by the means of financial ratios (Balezentis
et al. 2012). Therefore, there is a need for further studies on the
area. Our study aims at analysing the productive efficiency across
different sectors of Lithuanian economy by the means of the Malmquist
productivity index. It is worth to be noted, that the latter method has
not been applied for analysis of the Lithuanian economy.
The economic research often involves multiple conflicting
objectives and criteria (Zavadskas, Turskis 2011). In our case, we have
different efficiency and productivity change indicators. Accordingly the
multi-criteria decision making method MULTIMOORA (Brauers, Zavadskas
2006, 2010, 2011) is employed to summarize these indicators and provide
an integrated ranking of the economic sectors.
The rest of the paper is structured as follows. Section 1 presents
the measures of efficiency as well as Malmquist productivity index. The
following Section 2 gives the preliminaries for data envelopment
analysis. The multi-criteria decision making method MULTIMOORA is
described in Section 3. Finally, the last section discusses the results
of the research.
1. Productive technology and Malmquist index
This section presents the main concepts of efficiency and
productivity. The first sub-section describes the very definition of
efficiency, whereas the second one presents the Malmquist productivity
index. The Malmquist productivity index enables to quantify the changes
in firm-specific efficiency as well as global shift in the production
frontier.
1.1. Measures of efficiency
In order to relate the Debreu-Farrell measures to the Koopmans
definition of efficiency, and to relate both to the structure of
production technology, it is useful to introduce some notation and
terminology (Fried et al. 2008). Let producers use inputs x =
([x.sub.1],[x.sub.2], ..., [member of] [[R].sup.m.sub.+] to produce
outputs y = ([y.sub.1], [y.sub.2], ..., [y.sub.n]) [member of]
[[R].sup.m.sub.+]. Production technology then can be defined in terms
of the production set:
T = {(x,y)|x can produce y}. (1)
Thus, Koopmans efficiency holds for an input-output bundle (x, y)
[member of] T if, and only if, (x', y')[??]T for (-x',
y') [greater than or equal to] (-x, y).
Technology set can also be represented by output correspondence
set:
O(x) = { y |(x, y)[member of] T} . (2)
The isoquants or efficient boundaries of the sections of T can be
defined in radial terms as follows (Farrell 1957). Every y [member of]
[R.sup.n.sub.+] has an input isoquant:
isoI(y) = {x|x [member of] I(y), [lambda]x[??]I(y), [lambda] <
1}. (3)
Similarly, every x [member of] [R.sup.m.sub.+] has an output
isoquant:
isoO(x) = {y|y [member of] O(x), [lambda]x [??] O(x), [lambda] >
1}. (4)
In addition, DMUs might be operating on the efficiency frontier
defined by Eqs. (3)-(4), albeit still use more inputs to produce the
same output if compared to another efficient DMU. In this case the
former DMU experiences a slack in inputs. The following subsets of the
boundaries I(y) and O(x) describe Pareto-Koopmans efficient firms:
effO(x) = {y|y [member of] O(x), y' [??] O(x),[for all]y'
[greater than or equal to] y, y' [not equal] y}. (5)
Note that effO(x) [subset or equal to] isoO(x) [subset or equal to]
O(x).
There are two types of efficiency measures, namely Shepard distance
function, and Farrell distance function. These functions yield the
distance between an observation and the efficiency frontier. Shepard
(1953) defined the following output distance function:
DO(x, y) = min{[theta]|(x, y/[theta]) [member of] O(x)}. (6)
Similarly, the following equations hold for the Farrell
output-oriented measure:
TEO(x, y) = max{[phi]|(x, [phi]y) [member of] O(x)}; (7)
TEO(x, y) = 1/[D.sub.o](x, y), (8)
where: T[E.sub.o](x, y) [greater than or equal to] 1 for y [member
of] O(x), and T[E.sub.o](x, y) = 1 for y [member of] isoO(x).
1.2. The Malmquist productivity index
Measurement of the total factor productivity (TFP) of a certain DMU
involves measures for both technological and firm-specific developments.
As Bogetoft and Otto (2011) put it, firm behaviour changes over time
should be explained in terms of special initiatives as well as
technological progress. The benchmarking literature (Coelli et al. 2005;
Bogetoft, Otto 2011; Ramanathan 2003) suggests Malmquist productivity
index being the most celebrated TFP measure. Hence, this section
describes the preliminaries of Malmquist index.
Fare et al. (2008) firstly describe productivity as the ratio of
output y over input x. Thereafter, the productivity can be measured by
employing the output distance function of Shepard (1953):
[D.sup.t.sub.0](x, y) = min{[theta]: (x, y/ [theta]) [member of]
[T.sup.t]}, (9)
where [T.sup.t] stands for the technology set (production
possibility set) of the period t. This function is equal to unity if and
only if certain input and output set belongs to production possibility
frontier.
The Malmquist productivity index (Malmquist 1953) can be employed
to estimate TFP changes of single firm over two periods (or vice versa),
across two production modes, strategies, locations etc. In this study we
shall focus on output-oriented Malmquist productivity index and apply it
to measure period-wise changes in TFP. The output-oriented Malmquist
productivity index due to Caves et al. (1982) is defined as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)
with indexes 0 and 1 representing respective periods. The two terms
in brackets follows the structure of Fisher's index. Consequently a
number of studies (Fare et al. 1992, 1994; Ray, Desli 1997; Simar,
Wilson 1998; Wheelock, Wilson 1999) attempted to decompose the latter
index into different terms each explaining certain factors of
productivity shifts. Specifically, Fare et al. (1992) decomposed
productivity change into efficiency change (EC or catching up) and
technical change (TC or shifts in the frontier):
[M.sub.o] = EC x TC, (11)
where:
EC = [D.sup.1.sub.o] ([x.sup.1], [y.sup.1])/[D.sup.0.sub.o]
([x.sup.0], [y.sup.0]) (12)
and
TC = [([D.sup.0.sub.o] ([x.sup.1], [y.sup.1]) [D.sup.0.sub.o]
([x.sup.0], [y.sup.0])/ [D.sup.1.sub.o] ([x.sup.1], [y.sup.1])
[D.sup.1.sub.o] ([x.sup.0], [y.sup.0])).sup.1/2]. (13)
EC measures the relative technical efficiency change. The index
becomes greater than unity in case the firm approaches frontier of the
current technology. TC indicates whether the technology has progressed
and thus moved further away from the observed point. In case of
technological progress, the TC becomes greater than unity; and that
virtually means that more can be produced using fewer resources. Given
the Malmquist productivity index measures TFP growth, improvement in
productivity will be indicated by values greater than unity, whereas
regress--by that below unity.
An important issue associated with the decomposition a la Fare et
al. (1992) is that of returns to scale. In this case Eqs. (9)-(13)
represent distance functions relying on the assumption of the constant
returns to scale (CRS) rather than variable returns to scale (VRS). As a
result the efficiency change component, EC, catches both the pure
technical efficiency change and scale change. The latter two terms were
defined by Fare et al. (1994) who offered the decomposition of the
Malmquist productivity index under assumption of VRS. Indeed,
macro-level studies do often assume the underlying production technology
as a CRS technology.
The following Fig. 1 presents a graphical interpretation of the
input Malmquist productivity index. Here, the point A denotes an initial
production plan in period t, whereas point B stands for another
production plan during period t + 1. Meanwhile, the two isoquants, isoOt
and isoOt+1, represent the efficient technology during periods t and t +
1, respectively. The two points A and B are projected onto efficiency
frontiers at the points At and Bt or At+1 and Bt+1 depending on the
reference period. After achieving the full efficiency, a decision making
unit (DMU) would move from point A towards point At. The change in
inputs, however, makes the DMU to move along the efficiency frontier
towards point Bt. It is the technological innovation that makes the
frontier shift and thus the point Bt+1 is achieved. Meanwhile, the DMU
experiences certain technical inefficiency and remains operating in
point Bt+1. The Malmquist productivity index quantifies both the
frontier shift and inefficiency change.
Specifically, the two components of the Malmquist productivity
index, EC and TC, can be explained in terms of Fig. 1. The Malmquist
productivity index can be obtained as follows (Fare et al. 2008):
[M.sub.o] = [([0d/0e/0a/0b] [0d/0f/0a/0c]).sup.1/2]. (14)
Similarly, its components for efficiency change and technical
change are given by:
EC = 0d/0f/0a/0b; (15)
TC = [([0d/0e/0d/0f] [0a/0b/0a/0c]).sup.1/2] (16)
[FIGURE 1 OMITTED]
2. Preliminaries for Data Envelopment Analysis
The distance functions used in the computations of the Malmquist
productivity index (cf. Section 2) can be obtained by the virtue of the
frontier methods. In this study we are to employ the non-parametric
deterministic method, viz. Data Envelopment Analysis (DEA).
DEA is a nonparametric method of measuring the efficiency of a
decision-making unit (DMU) such as a firm or a public-sector agency (Ray
2004). The very term of efficiency was initially defined by Debreu
(1951) and then by Koopmans (1951). Debreu discussed the question of
resource utilization at the aggregate level, whereas Koopmans offered
the following definition of an efficient DMU: A DMU is fully efficient
if and only if it is not possible to improve any input or output without
worsening some other input or output. Due to similarity to the
definition of Pareto efficiency, the former is called Pareto-Koopmans
Efficiency. Finally, Farrell (1957) summarized works of Debreu and
Koopmans thus offering frontier analysis of efficiency and describing
two types of economic efficiency, namely technical efficiency and
allocative efficiency (indeed, a different terminology was used at that
time). The concept of technical efficiency is defined as the capacity
and willingness to produce the maximum possible output from a given
bundle of inputs and technology, whereas the allocative efficiency
reflects the ability of a DMU to use the inputs in optimal proportions,
considering respective marginal costs (Kalirajan, Shand 2002). However,
Farrell (1957) did not succeed in handling Pareto-Koopmans Efficiency
with proper mathematical framework.
The modern version of DEA originated in studies of A. Charnes, W.
W. Cooper and E. Rhodes (Charnes et al. 1978, 1981). Hence, these DEA
models are called CCR models. Initially, the fractional form of DEA was
offered. However, this model was transformed into input- and
output-oriented multiplier models, which could be solved by means of the
linear programming (LP). In addition, the dual CCR model (i.e.
envelopment program) can be described for each of the primal programs
(Cooper et al. 2007; Ramanathan 2003).
Unlike many traditional analysis tools, DEA does not require to
gather information about prices of materials or produced goods, thus
making it suitable for evaluating both private- and public-sector
efficiency. Suppose that there are j = 1, 2, t, N DMUs, each producing r
= 1, 2, m outputs from i = 1, 2, n inputs. Hence, DMU t exhibits
input-oriented technical efficiency [[theta].sub.t], whereas
output-oriented technical efficiency is a reciprocal number
[[theta].sub.t] = 1/[[phi].sub.t]. The output-oriented technical
efficiency [[phi].sub.t] may be obtained by solving the following
multiplier DEA program:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)
[[phi].sub.t] unrestricted.
In Eq. (17), coefficients [[lambda].sub.j] are weights of peer
DMUs. Noteworthy, this model presumes existing CRS, which is rather
arbitrary condition. CRS indicates that the manufacturer is able to
scale the inputs and outputs linearly without increasing or decreasing
efficiency (Ramanathan 2003). Whereas the CRS constraint was considered
over-restrictive, the BCC (Banker, Charnes, and Cooper) model was
introduced (Banker et al. 1984). The CRS presumption was overridden by
introducing a convexity constraint [N.summation over (j = 1)]
[[lambda].sub.j] = 1, which enabled to tackle the VRS. The BBC model,
hence, can be written by supplementing Eq. (17) with a convexity
constraint [N.summation over (j = 1)] = 1.
The best achievable input can therefore be calculated by
multiplying actual input by technical efficiency of certain DMU. On the
other hand, the best achievable output is obtained by dividing the
actual output by the same technical efficiency [[theta].sub.t] =
1/[[phi].sub.t], where [[phi].sub.t] is obtained from Eq. (17). The
difference between actual output and the potential one is called slack.
In addition it is possible to ascertain whether a DMU operates under
increasing returns to scale (IRS), CRS, or decreasing returns to scale
(DRS). CCR measures gross technical efficiency (TE) and hence resembles
both TE and scale efficiency (SE); whereas BCC represents pure TE. As a
result, pure SE can be obtained by dividing CCR TE by BCC TE.
Noteworthy, technical efficiency describes the efficiency in converting
inputs to outputs, while scale efficiency recognizes that economy of
scale cannot be attained at all scales of production (Ramanathan 2003)
3. The MULTIMOORA method
In order to summarize the different efficiency and productivity
indicators obtained by the means of DEA and Malmquist productivity
index, one can employ a multi-criteria decision making method. The
MULTIMOORA method will be applied to perform an integrated assessment of
efficiency across the Lithuanian economic sectors. This section, hence,
briefly presents the MULTIMOORA method and the Dominance theory.
Chakraborty (2011) compared the six celebrated MCDM methods, viz.
MOORA, AHP, TOPSIS, VIKOR, ELECTRE, and PROMETHEE in terms of
computational time, simplicity, mathematical calculations, stability,
and information type. The ELECTRE and PROMETHEE methods can be described
as those of partial aggregation (Scharlig 1985). These methods require
moderate calculations which include some subjectivity in choosing
preference functions etc. The TOPSIS method relies solely on the
reference point approach; however, it defines both the positive and the
negative ideal solutions for comparison of the alternatives. The
Analytical Hierarchy process (AHP) is time consuming. The VIKOR method
utilizes both value measurement (complete aggregation) techniques and
reference point approach. However, it mixes the results provided by
these techniques and thus might provide some inconsistent ranking. The
comparison of Chakraborty (2011) attributed MOORA with the best ratings
against all of criteria save information type, given MOORA cannot handle
mixed-type information. The fuzzy MULTIMOORA as well as other MCDM
methods, however, does enable one to perform the data fusion by
involving linguistic variables. An interested reader could consult the
paper by Brauers and Zavadskas (2012) which defines the set of
robustness conditions which are met by the MULTIMOORA method.
Accordingly we will employ the MULTIMOORA method for comparison of the
economic sector performance.
The MULTIMOORA method begins with a response matrix X where its
elements [x.sub.ij] denote ith alternative of jth objective (i = 1, 2,
..., m and j = 1, 2, ..., n). The method consists of three parts, viz.
the Ratio System, the Reference Point approach, and the Full
Multiplicative Form.
The Ratio System of MOORA. Ratio system employs the vector data
normalization by comparing alternative of an objective to all values of
the objective:
[x.sup.*.sub.ij] = [w.sub.j] [x.sub.ij]/[square root of
([m.summation over (i = 1)][x.sup.2.sub.ij])], (18)
where [x.sup.*.sub.ij] denotes ith alternative of jth objective and
[w.sub.j] is weight of the jth criterion, [[summation].sub.j][w.sub.j] =
1. In the absence of negative values, these numbers belong to the
interval [0; 1]. These indicators are added (if desirable value of
indicator is maximum) or subtracted (if desirable value is minimum).
Thus, the summarizing index of each alternative is derived in this way:
[y.sup.*.sub.i] = [g.summation over (j = 1)] [x.sup.*.sub.ij] -
[n.summation over (j = g + 1)] [x.sup.*.sub.ij], (19)
where g = 1, 2, n denotes number of objectives to be maximized.
Then every ratio is given the rank: the higher the index, the higher the
rank.
The Reference Point of MOORA. Reference point approach is based on
the Ratio System. The Maximal Objective Reference Point (vector) is
found according to ratios found in Eq. (18). The jth coordinate of the
reference point can be described as [r.sub.j] = max [x.sup.*.sub.ij] in
case of maximization. Every coordinate of this vector represents maximum
or minimum of certain objective (indicator). Then every element of the
normalized response matrix is recalculated and final rank is given
according to deviation from the reference point and the Min-Max Metric
of Tchebycheff:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (20)
The Full Multiplicative Form and MULTIMOORA. Brauers and Zavadskas
(2010) proposed MOORA to be updated by the Full Multiplicative Form
method embodying maximization as well as minimization of purely
multiplicative utility function. Overall utility of the ith alternative
can be expressed as dimensionless number:
[U'.sub.i] = [A.sub.i]/[B.sub.i], (21)
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] denotes
the product of objectives of the ith alternative to be maximized with g
= 1, n being the number of objectives to be maximized and where
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] denotes the product
of objectives of the ith alternative to be minimized with n - g being
the number of objectives (indicators) to be minimized. Thus MULTIMOORA
summarizes MOORA (i.e. Ratio System and Reference point) and the Full
Multiplicative Form. Brauers and Zavadskas (2011) proposed the dominance
theory to summarize the three ranks provided by different parts of
MULTIMOORA.
Absolute Dominance means that an alternative, solution or project
is dominating in ranking all other alternatives, solutions or projects
which are all being dominated. This absolute dominance shows as rankings
for MULTIMOORA: (1-1-1). General Dominance in two of the three methods
is of the form with a < b < c < d:
(d-a-a) is generally dominating (c-b-b);
(a-d-a) is generally dominating (b-c-b);
(a-a-d) is generally dominating (b-b-c);
and further transitiveness plays fully.
Transitiveness. If a dominates b and b dominates c than also a will
dominate c. Overall Dominance of one alternative on the next one. For
instance (a-a-a) is overall dominating (b-b-b) which is overall being
dominated, with (b-b-b) following immediately (a-a-a) in rank
(transitiveness is not playing). Absolute Equability has the form: for
instance (e-e-e) for 2 alternatives. Partial Equability of 2 on 3 exists
e. g. (5-e-7) and (6-E-3). Despite all distinctions in classification
some contradictions remain possible in a kind of Circular Reasoning. We
can cite the case of:
Object A (11-20-14) y Object B (14-16-15);
Object B (14-16-15) y Object C (15-19-12); but
Object C (15-19-12) y Object A (11-20-14).
Here, the operator [??] represents a General Dominance. In such a
case the same ranking is given to the three objects.
4. Results of the research
The research relies on National Accounting data provided by
Statistics Lithuania (2012). We have used the aggregates for 35 economic
activities (NACE 2 classification), see Table A1 in Appendix A for
details. The data cover the period of 2000-2010.
The gross value added generated in certain sector was chosen as the
output variable, whereas intermediate consumption, remuneration, and
fixed capital consumption were treated as inputs. The latter three
indicators enable to tackle the total factor productivity and thus are
usually employed for productivity analysis (Piesse, Thirtle 2000). The
FEAR package (Wilson 2010) was employed for the analysis.
Firstly, the VRS technical efficiency scores were estimated by
employing the output oriented DEA model as described in Section 2. The
following Fig. 2 presents these estimates for years 2000 and 2010. The
weighted average was obtained by weighting the efficiency scores by the
value added generated in the respective sector during the base year. As
the results suggest, the mean efficiency increased from 0.79 in 2000 up
to 0.85 in 2010. These efficiency scores imply that there was a 21% gap
in output for 2000 which decreased to 15% in 2010 given technological
frontier of those periods. Note that the contemporaneous technological
frontier is defined by the efficient DMUs viz. economic sectors, and
these gaps are therefore incomparable in absolute terms. The application
of Malmquist index will enable to identify the shifts of the efficiency
frontier. As one can note, the four sectors remained operating on the
efficiency frontier during 2000-2010: pharmaceutical products (C21),
wholesale and retail trade (G), real estate activities (L), and
education (P).
As in 2000, the whole manufacturing sector (activities C22 to C33)
and utility services (D and E) exhibited the lowest values of technical
efficiency ranging between 0.32 and 0.49. Most of these sectors,
however, experienced the steepest increase in efficiency amounting to
some 50% of the initial efficiency scores and thus graduated the group
of the worst performing sectors. Meanwhile the most significant decrease
in efficiency was observed for the primary sector (A and B). This
indicates the need for modernization in these sectors. Anyway, it may
also be related to the overall transformation of the economy. Scientific
research and development (M72) was specific with particularly high
decrease in efficiency probably caused by rising compensations for
employees.
The Malmquist index given by Eqs. (9)-(13) was employed to examine
the productivity changes across different economic sectors. Initially,
we estimated the shift in productivity between years 2000 and 2010 (Fig.
3). As one can note, the most significant increase in productivity was
observed for pharmaceutical (C21) and chemical (C20) production. Indeed,
these industries were positively affected by the investments and market
enlargement following the accession to the European Union. Similar
trends were also exhibited in sectors of electronics (C26), machinery
(C28), and transport equipment (C29, C30). Although the scientific
research sector (M72) was specific with the decreased efficiency score,
it enjoyed an increase in productivity. At the other end of spectrum,
the two primary sectors (A and B) demonstrated a tremendous decrease in
productivity. Specifically, the agricultural sector was specific with
decrease of 40%, whereas mining and quarrying with that of some 23%.
Publishing industry (J58-J60) was also experiencing the decreasing
productivity: the Malmquist index for that sector suggested that
productivity there dropped by some 28% thanks to decreasing sectoral
efficiency. Indeed, cancellation of value-added tax exemptions might
have caused the efficiency decrease in the latter sector.
[FIGURE 2 OMITTED]
The decomposition of the Malmquist index enables to identify the
underlying reasons in productivity change. As Fig. 3 suggests, the
increase in productivity of the pharmaceutical sector was driven by both
inner innovation (efficiency change) and shift in the production
frontier (technology change). As for chemical sector, these two factors
have a positive effect, however catch-up effect was stronger. In
general, the technology effect was positive for all sectors with
exception of public administration (O) and education (P) which were
subject to a negative shift in the efficiency frontier (i.e. the
reference sector exhibited higher efficiency in 2010).
In addition, the Malmquist productivity indices were computed for
each period of the two subsequent years between 2000 and 2010. The
results indicate that the total factor productivity had been decreasing
during 20O3-20O6 and has been recovering since 20O8 (Fig. 4). The
analysis of the cumulative change in the total factor productivity
implies that the productivity has never been decreased below the level
of 2000 and had reached its peak in 20O7 when the accumulated growth
since 2000 reached some 6%. As for the whole period of 2000-2010, the
accumulated growth rate was some 4%. Furthermore, the cumulative change
in total factor productivity has never been below the value unity what
indicates that the Lithuanian economy was rather persistent throughout
the economic downturns.
In order to better understand the driving forces of change in total
factor productivity, the mean values of the Malmquist components are
depicted in Fig. 5. As one can note, the overall productivity (i.e.
shifts in the production frontier) were generally downwards until 20O5
and has been following an opposite trend afterwards. Meanwhile, the
catch-up effect exhibited an inverse movement: firm-specific increase in
productivity had been increasing until 20O5 and decreasing ever since.
The results imply that the recent economic downturn negatively affected
the firm-specific innovations, whereas the overall productivity of the
economy has increased possibly due to appropriate managerial decisions.
The reported results also imply that efficiency and changes in
productivity varied across the economic sectors throughout 2000-2010.
The steep increases in productivity, however, do not necessarily
mean that a certain sector is operating efficiently in relative terms.
One thus needs to take into account the level of efficiency as well as
productivity changes when performing a robust comparison. Furthermore,
these indicators and indices are time-variant and thus might fluctuate
in a wider or tighter range. Indeed, higher variation of these
indicators is associated with higher risk and uncertainty in respective
economic sectors. To cap it all, there is a dichotomy between efficiency
and productivity as well as between mean values and variation of the
analysed criteria. The multi-criteria decision making method MULTIMOORA
will therefore be employed to simultaneously consider these criteria
identifying different objectives:
1. the mean technical efficiency score for 2000-2010 (to be
maximized);
2. coefficient of variation of the technical efficiency scores (to
be minimized);
3. the mean change in total factor productivity for 2000-2010 (to
be maximized);
4. coefficient of variation of change in total factor productivity
(to be minimized).
The presented set of indicators has the following implications.
First, a sector specific with high values of technical efficiency might
be experiencing decreasing total factor productivity and thus require
certain managerial and institutional measures to be taken. Second, a
sector exhibiting increasing total factor productivity might still
remain an inefficient one. Third, a high variance in these indicators
indicates high volatility of performance and should also attract certain
attention. The initial data are given in Table A2, Appendix A.
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
The initial decision matrix (Table A2, Appendix A) was normalized
by the virtue of Eq. (18). Subsequently, the economic sectors were
ranked according to the Ratio System approach, cf. Eq. (19). The
normalized values were also employed to rank the economic sectors upon
the Reference Point approach, cf. Eq. (20). Finally, zero values in the
initial decision matrix were changed into 0.001 and thus Eq. (21) was
applied to order the economic sectors according to the Multiplicative
Form approach. Thus, each of economic sectors was attributed with the
three ranks. The dominance theory, therefore, was employed to aggregate
these ratings. Table 1 presents all of the discussed ranks.
The results indicate that the best performing sectors in terms of
efficiency and productivity were those of wholesale and retail trade,
real estate activities, education, hospitality, health,
telecommunications, transport, legal services, accounting, advertising.
Therefore, the services sector seems to be that most developed in
Lithuania. Indeed, some of them, viz. education, hospitality, and health
sectors, can prevail by providing services for foreign visitors and thus
generating substantial revenues. Meanwhile, transport, legal services,
accounting, and advertising sectors rely both on local and international
customers. Finally, real estate, telecommunications, and trade sectors
are mainly focused on domestic market and thus on the development of the
remaining economic sectors in Lithuania.
The manufacturing sector followed the services. Pharmaceutical,
wood, food, and furniture production exhibited the best performance
amidst the manufacturing activities. Indeed, these sectors received
substantial foreign investments and thus modernized their production
technologies. Therefore, these sectors can be considered as those
constituting the core of the Lithuanian economy. The construction sector
was also attributed with rather high rank. The textile, metallurgy,
machinery, transport equipment, and rubber industry operated less
efficiently. Accordingly, certain fiscal and institutional measures
should be considered to improve the situation in the latter sectors.
The multi-criteria analysis also suggested that the worst
performing sectors were those of IT services, electrical equipment,
agriculture, computer products, and electrical equipment. IT-related
industries are likely to face the competition of the developing
countries. Finally, financial and insurance activities as well as
scientific research (R&D) were placed at the very bottom. Indeed,
the last two sectors were peculiar with rather high volatility of the
efficiency indicators. As for the financial sector, these findings are
almost imminent in the presence of the economic downturn. However,
R&D sector should be appropriately supported in order to create a
basis for prospective activities. As European Commission (2011)
reported, the Lithuanian knowledge-intensive business sectors, namely IT
and R&D, are specific with one of the largest backward dependence on
the imported materials among the EU Member States. Therefore, this
dependence should be reduced in order to maintain efficiency as well as
competitiveness.
Conclusions
The paper presented a multi-criteria framework for estimation of
productive efficiency across economic sectors. The research was based on
national accounting data. The data envelopment analysis was employed to
estimate efficiency in terms of an output indicator (value added) and
input indicators (intermediate consumption, capital consumption, and
remunerations). The productivity change was quantified by employing the
Malmquist index.
The results suggest that the mean efficiency increased from 0.79 in
2000 up to 0.85 in 2010. Specifically, the four sectors remained
operating on the efficiency frontier during 2000-2010: pharmaceutical
products, wholesale and retail trade, real estate activities, and
education. The Malmquist productivity index was applied to estimate the
productivity change. As for the whole period of 2000-2010, the
accumulated growth rate of the total factor productivity was some 4%. It
is evident, that the economic crisis of 2007-2008 accelerated growth in
the total factor productivity.
The multi-criteria analysis suggests that the best performing
sectors were those of wholesale and retail trade, real estate
activities, education, hospitality, health, telecommunications,
transport, legal services, accounting, advertising. The manufacturing
sector followed the services. Pharmaceutical, wood, food, and furniture
production exhibited the best performance amidst the manufacturing
activities. The multi-criteria analysis also suggested that the worst
performing sectors were those of IT services, electrical equipment,
agriculture, computer products, and electrical equipment. The fiscal and
administrative easing should be designed for suchlike prospective
sectors as R&D and IT which exhibited rather low performance.
Furthermore, the excessive dependence of the latter sector should be
reduced.
The carried out research, though, has some limitations. First, the
selection of inputs and outputs is of crucial importance for DEA.
Therefore, further studies should attempt to employ different sets of
indicators for a more robust estimation of efficiency scores. Indeed,
the currently available datasets prevented us from analysing physical
quantities of energy etc. involved in the production process. Second,
DEA is applicable to homogeneous decision making units. It is obvious
that different economic activities are associated with rather different
productive technologies. Therefore, the econometric analysis (e.g.
stochastic frontier analysis) could be employed to tackle the
heterogeneity existing among the economic sectors.
Further research should aim at employing different datasets and
methods. Specifically, different types of the total factor productivity
indices, namely Luenberger, Hicks-Moosteen, and extensions thereof,
could be employed for the analysis. In addition sequential indices are
likely to be more suitable for longitudinal productivity analysis.
APPENDIX A. ABBREVIATIONS AND INITIAL DATA FOR MULTI-CRITERIA
ASSESSMENT
Table A1. Aggregates of statistical classification of
economic activities (NACE Rev. 2) used in the research
NACE code Economic activity
A Agriculture, forestry and fishing
B Mining and quarrying
C10_TO_C12 Manufacture of food products,
beverages and tobacco
C13_TO_C15 Manufacture of textiles, wearing apparel,
leather and related products
C16_TO_C18 Manufacture of wood, paper,
printing and reproduction
C20 Manufacture of chemicals
and chemical products
C21 Manufacture of basic pharmaceutical
products and pharmaceutical preparations
C22_C23 Manufacture of rubber
and plastics products
C24_C25 Manufacture of basic metals and
fabricated metal products,
except machinery
C26 Manufacture of computer,
electronic and
optical products
C27 Manufacture of electrical equipment
C28 Manufacture of machinery
and equipment n.e.c.
C29_C30 Manufacture of transport equipment
C31_TO_C33 Manufacture of furniture; jewellery,
musical instruments, toys
D Electricity, gas, steam
and air conditioning supply
E Water supply; sewerage,
waste management and
remediation activities
F Construction
G Wholesale and retail trade;
repair of motor vehicles
and motorcycle
H Transportation and storage
I Accommodation and
food service activities
J58_TO_J60 Publishing, motion picture,
broadcasting activities
J61 Telecommunications
J62_J63 IT services
K Financial and insurance activities
L Real estate activities
M69_TO_M71 Legal and accounting activities;
activities of head offices
M72 Scientific research and development
M73_TO_M75 Advertising and market research;
other professional activity
N Administrative and support
service activities
O Public administration and defence;
compulsory social security
P Education
Q86 Human health activities
Q87_Q88 Residential care activities;
social work activities
without accommodation
R Arts, entertainment
and recreation
S Other service activities
Table A2. Decision matrix for multi-criteria decision making
1. Mean 2. CV 3. Mean TFP 4. CV
TE (TE) change (TFP)
MAX MIN MAX MIN
A 0.739 0.180 0.953 0.169
B 0.775 0.160 0.957 0.094
C10_TO_C12 0.665 0.124 1.013 0.081
C13_TO_C15 0.676 0.171 0.985 0.087
C16_TO_C18 0.666 0.095 0.999 0.101
C20 0.731 0.302 1.076 0.180
C21 1.000 0.000 1.126 0.209
C22_C23 0.665 0.176 1.014 0.122
C24_C25 0.502 0.151 1.038 0.088
C26 0.407 0.249 1.054 0.144
C27 0.500 0.205 0.985 0.103
C28 0.580 0.144 1.022 0.123
C29_C30 0.614 0.190 1.031 0.101
C31_TO_C33 0.639 0.139 1.022 0.067
D 0.634 0.169 1.030 0.113
E 0.419 0.062 1.017 0.073
F 0.756 0.161 0.997 0.070
G 1.000 0.000 0.986 0.038
H 0.932 0.102 1.005 0.060
I 0.844 0.066 0.992 0.036
J58_TO_J60 0.585 0.115 0.967 0.098
J61 0.951 0.079 1.000 0.076
J62_J63 0.741 0.165 1.005 0.177
K 0.684 0.273 1.035 0.196
L 1.000 0.000 0.994 0.050
M69_TO_M71 0.956 0.067 1.022 0.118
M72 0.945 0.149 1.003 0.339
M73_TO_M75 0.833 0.094 1.035 0.059
N 0.626 0.121 1.030 0.106
O 0.805 0.051 0.997 0.103
P 1.000 0.000 0.998 0.095
Q86 0.796 0.036 0.997 0.077
Q87_Q88 0.633 0.230 1.018 0.135
R 0.513 0.140 0.999 0.125
S 0.857 0.167 0.951 0.169
Caption: Fig. 1. The output Malmquist productivity index
Caption: Fig. 2. Technical efficiency scores across economic
sectors, 2000 and 2010
Caption: Fig. 3. Malmquist productivity index across economic
sectors, 2010 Compared to 2000
Caption: Fig. 4. Changes in the mean total factor productivity
(TFP) during 2000-2010
Caption: Fig. 5. Decomposition of the Malmquist productivity index
for 2000-2010
doi: 10.3846/20294913.2013.881431
Acknowledgments
This research was funded by the European Social Fund under the
Global Grant measure (VP1-3.1-SMM-07-K-03-002).
References
Atici, K. B.; Ulucan, A. 2011. A multiple criteria energy decision
support system, Technological and Economic Development of Economy 17(2):
219-245. http://dx.doi.org/10.3846/20294913.2011.580563
Balezentis, A.; Balezentis, T.; Misiunas, A. 2012. An integrated
assessment of Lithuanian economic sectors based on financial ratios and
fuzzy MCDM methods, Technological and Economic Development of Economy
18(1): 34-53. http://dx.doi.org/10.3846/20294913.2012.656151
Banker, R. D.; Charnes, A.; Cooper, W. W. 1984. Some models for
estimating technical and scale inefficiencies in data envelopment
analysis, Management Science 30(9): 1078-1092.
http://dx.doi.org/10.1287/mnsc.30.9.1078
Bogetoft, P.; Otto, L. 2011. Benchmarking with DEA, SFA, and R.
International Series in Operations Research and Management Science, Vol.
157. Springer. 352 p.
Bojnec, S.; Latruffe, L. 2011. Farm size and efficiency during
transition: insights from Slovenian farms, Transformations in Business
& Economics 10(3): 104-116.
Brauers, W. K. M.; Zavadskas, E. K. 20O6. The MOORA method and its
application to privatization in a transition economy, Control and
Cybernetics 35: 445-469.
Brauers, W. K. M.; Zavadskas, E. K. 2010. Project management by
MULTIMOORA as an instrument for transition economies, Technological and
Economic Development of Economy 16(1): 5-24.
http://dx.doi.org/10.3846/tede.2010.01
Brauers, W. K. M.; Zavadskas, E. K. 2011. MULTIMOORA optimization
used to decide on a bank loan to buy property, Technological and
Economic Development of Economy 17(1): 174-188.
http://dx.doi.org/10.3846/13928619.2011.560632
Brauers, W. K. M.; Zavadskas, E. K. 2012. Robustness of MULTIMOORA:
a method for multi-objective optimization, Informatica 23(1): 1-25.
Caves, D. W.; Christensen, L. R.; Diewert, W. E. 1982. The economic
theory of index numbers and the measurement of input, output, and
productivity, Econometrica 50(6): 1393-1414.
http://dx.doi.org/10.2307/1913388
Chakraborty, S. 2011. Applications of the MOORA method for decision
making in manufacturing environment, International Journal of Advanced
Manufacturing Technology 54(9-12): 1155-1166.
http://dx.doi.org/10.1007/s00170-010-2972-0
Charnes, A.; Cooper, W. W.; Rhodes, E. 1978. Measuring the
efficiency of decision making units, European Journal of Operational
Research 2(6): 429-444. http://dx.doi.org/10.1016/O377-2217(78)90138-8
Charnes, A.; Cooper, W. W.; Rhodes, E. 1981. Evaluating program and
managerial efficiency: an application of data envelopment analysis to
program follow through, Management Science 27(6): 668-697.
http://dx.doi.org/10.1287/mnsc.27.6.668
Coelli, T. J.; Rao, D. S. P.; O'Donnell, C. J.; Battese, G. E.
20O5. An introduction to efficiency and productivity analysis. Springer.
349 p.
Cooper, W. W.; Seiford, L. M.; Tone, K. 20O7. Data envelopment
analysis: a comprehensive text with models, applications, references and
DEA-Solver software. 2nd ed. Springer. 490 p.
Debreu, G. 1951. The coefficient of resource utilization,
Econometrica 19(3): 273-292. http://dx.doi.org/10.2307/1906814
European Commission. 2011. European Competitiveness Report 2011.
Commission staff working document SEC(2011) 1188. Luxembourg:
Publications Office of the European Union.
http://dx.doi.org/10.2769/30346
Fare, R.; Grosskopf, S.; Lindgren, B.; Roos, P. 1992. Productivity
changes in Swedish pharmacies 1980-1989: a non-parametric Malmquist
approach, Journal of Productivity Analysis 3(1-2): 85-101.
http://dx.doi.org/10.1007/BF00158770
Fare, R.; Grosskopf, S.; Margaritis, D. 20O8. Efficiency and
productivity: Malmquist and more, in Fried, H. O.; Lovell, C. A. K.;
Schmidt, S. S. (Eds.). The Measurement of Productive Efficiency and
Productivity. New York, Oxford University Press, 522-621.
http://dx.doi.org/10.1093/acprof:oso/9780195183528.003.0005
Fare, R.; Grosskopf, S.; Norris, M.; Zhang, Z. 1994. Productivity
growth, technical progress, and efficiency change in industrialized
countries, American Economic Review 84: 66-83.
Farrell, M. J. 1957. The measurement of technical efficiency,
Journal of the Royal Statistical Society, Series A 120(3): 253-281.
http://dx.doi.org/10.2307/2343100
Fried, H. O.; Lovell, C. A. K.; Schmidt, S. S. 20O8. Efficiency and
productivity, in Fried, H. O.; Lovell, C. A. K.; Schmidt, S. S. (Eds.).
The Measurement of Productive Efficiency and Productivity. New York,
Oxford University Press, 3-91.
http://dx.doi.org/10.1093/acprof:oso/9780195183528.003.0001
Hajiagha, S. H. R.; Akrami, H.; Zavadskas, E. K.; Hashemi, S. S.
2013. An intuitionistic fuzzy data envelopment analysis for efficiency
evaluation under ucertainty: case of a finance and credit institution, E
+ M Ekonomie a Management (1): 128-137.
Ippoliti, R.; Falavigna, G. 2012. Efficiency of the medical care
industry: evidence from the Italian regional system, European Journal of
Operational Research 217(3): 643-652.
http://dx.doi.org/10.1016/j.ejor.2011.10.010
Jack, L.; Boone, J. 20O9. Sustainable change and benchmarking in
the food supply chain, in Jack, L. (Ed.). Benchmarking in Food and
Farming. Gower, 1-8.
Kalirajan, K. P.; Shand, R. T. 20O2. Frontier production functions
and technical efficiency measures, Journal of Economic Surveys 13(2):
149-172. http://dx.doi.org/10.1111/1467-6419.00080
Koopmans, T. C. 1951. An analysis of production as an efficient
combination of activities, in Koopmans, T. C. (Ed.). Activity Analysis
of Production and Allocation. Cowles Commission for Research in
Economics, Monograph No. 13. New York: Wiley.
Latruffe, L. 2010. Competitiveness, productivity and efficiency in
the agricultural and agri-food sectors. OECD Food, Agriculture and
Fisheries Working Papers, No. 30, OECD Publishing.
http://dx.doi.org/10.1787/5km91nkdt6d6-en
Malmquist, S. 1953. Index numbers and indifference surfaces,
Trabajos de Estatistica 4(2): 209-242.
http://dx.doi.org/10.1007/BF03006863
Margono, H.; Sharma, S. C.; Sylwester, K.; Al-Qalawi, U. 2011.
Technical efficiency and productivity analysis in Indonesian provincial
economies, Applied Economics 43(6): 663-672.
http://dx.doi.org/10.1080/00036840802599834
Murillo-Zamorano, L. R. 20O4. Economic efficiency and frontier
techniques, Journal of Economic Surveys 18(1): 33-45.
http://dx.doi.org/10.1111/j.1467-6419.2004.00215.x
Piesse, J.; Thirtle, C. 2000. A stochastic frontier approach to
firm level efficiency, technological change, and productivity during the
early transition in Hungary, Journal of Comparative Economics 28(3):
473-501. http://dx.doi.org/10.1006/jcec.2000.1672
Ray, S. C. 2004. Data envelopment analysis: theory and techniques
for economics and operations research. Cambridge University Press. 353
p. http://dx.doi.org/10.1017/CBO9780511606731
Ray, S. C.; Desli, E. 1997. Productivity growth, technical
progress, and efficiency change in industrialized countries: comment,
American Economic Review 87: 1033-1039.
Ramanathan, R. 20O3. An introduction to data envelopment analysis:
a tool for performance measurement. Sage Publications. 201 p.
Scharlig, A. 1985. Decider sur plusieurs criteres. Lausanne:
Presses Polytechniques Romandes. 304 p.
Shepard, R. W. 1953. Cost and production functions. Princeton, New
Jersey: Princeton University Press. 104 p.
Simar, L.; Wilson, P. W. 1998. Productivity growth in
industrialized countries. Discussion Paper #9810, Institut de
Statistique, Universite Catholique de Louvain, Louvain-la-Neuve,
Belgium.
Statistics Lithuania. 2012. Indicator database [online], [cited 1
September 2012]. Available from Internet: http://db1.stat.gov.lt/
Tohidi, G.; Razavyan, S.; Tohidnia, S. 2012. A global cost
Malmquist Productivity index using data envelopment analysis, Journal of
the Operational Research Society 63: 72-78.
http://dx.doi.org/10.1057/jors.2011.23
Wheelock, D. C.; Wilson, P. W. 1999. Technical progress,
inefficiency, and productivity change in U.S. banking, 1984-1993,
Journal of Money, Credit, and Banking 31(2): 212-234.
http://dx.doi.org/10.2307/2601230
Wilson, P. W. 2010. FEAR 1.15 User's Guide. Clemson
University, Clemson, South Carolina.
Zavadskas, E. K.; Turskis, Z. 2011. Multiple criteria decision
making (MCDM) methods in economics: an overview, Technological and
Economic Development of Economy 17(2): 397-427.
http://dx.doi.org/10.3846/20294913.2011.593291
Tomas BALEZENTIS is a Junior Research Fellow at the Lithuanian
Institute of Agrarian Economics and a PhD student in Vilnius University.
He received Student scientific paper award (2011) from the Lithuanian
Academy of Sciences and Presidential Scholarship (2012). He has
published over 50 peer-reviewed papers on multi-criteria decision
making, benchmarking, and quantitative methods.
Algimantas MISIUNAS, PhD in social sciences, is an Associate
Professor at the Department of Quantitative Methods and Modelling in
Vilnius University. His scientific interests cover areas of
macroeconomic analysis, macroeconomic models, forecasting of economic
processes, and informal economy.
Alvydas BALEZENTIS holds PhD (HP) in Management and Administration
and is a Professor at the Institute of Management in Mykolas Romeris
University. While working at the Parliament of the Republic of
Lithuania, Ministry of Agriculture, and Institute of Agrarian Economics
he contributed to creation and fostering of the Lithuanian rural
development policy at various levels. His scientific interests cover
areas of innovatics, strategic management, sustainable development, and
rural development. Tomas BALE2ENTIS (a), Algimantas
MISIUNAS (b), Alvydas BALE2ENTIS (c)
(a) Lithuanian Institute of Agrarian Economics, V. Kudirkos g. 18,
03105 Vilnius, Lithuania
(b) Vilnius University, Sauletekio al. 9, 10222 Vilnius, Lithuania
(c) Mykolas Romeris University, Valakupiu g. 5, 10101 Vilnius,
Lithuania
Received 15 May 2012; accepted 09 September 2012
Table 1. Ranks of the economic sectors provided by the
different parts of the MULTIMOORA method
Economic Ratio Reference Multiplicative Final Rank
sector System Point Form (MULTIMOORA)
G 1 1 1 1
L 2 2 2 2
P 3 5 3 3
I 4 4 5 4
Q86 5 3 6 5
J61 6 7 7 6
M73_TO_M75 8 8 8 7
H 7 12 9 8
O 9 6 10 9
M69_TO_M71 10 11 11 10
C21 11 29 4 11
E 12 9 12 12
C16_TO_C18 13 10 14 13
C10_TO_C12 14 15 16 14
C31_TO_C33 15 16 13 15
F 16 21 15 16
J58_TO_J60 17 13 18 17
N 18 14 17 18
B 19 20 19 19
C13_TO_C15 20 25 20 20
C24_C25 21 19 21 21
C28 22 18 23 22
D 23 24 22 23
R 24 17 26 24
C29_C30 25 28 24 25
C22_C23 26 26 25 26
S 27 23 27 27
J62J63 29 22 28 28
C27 28 30 29 29
A 30 27 30 30
Q87_Q88 31 31 31 31
C26 32 32 35 32
C20 33 34 33 33
K 34 33 34 34
M72 35 35 32 35
