A Stochastic Frontier Analysis on Firm-level Total Factor
Productivity and Technical Efficiency in Korea
Sunyoung Jung*, Hak K. Pyo**

Abstract

The conventional index number approach to the analysis of total factor productivity cannot
distinguish between a shift of production function (technical progress) and a movement along a
production function (technical efficiency). This paper attempts to separate technical efficiency fromthe productivity measurement using the econometric approach based on the stochastic frontier
production models. This study will be limited to the models that take firms’ heterogeneity into accountbecause most of the available panel data consist of a large cross-section and relatively short timeseries. To the extent that firms’ production is characterized by heterogeneous production conditions,estimation techniques that do not account for unobserved heterogeneity lead to biased efficiency
estimates. The sources of total factor productivity growth are decomposed into technical progress, thechanges in technical efficiency, the changes in allocative efficiency, and the scale effects by using theestimated parameters in the stochastic-frontier production models.

Keywords: Productivity decomposition, Technical efficiency, Stochastic frontier production model*

Fellow at World Class University Program, School of Economics, Seoul National University, Seoul
151-746, Korea. Tel: +82-10-8787-2808. E-mail: trust124@hanmail.net. Corresponding author.
**

Professor, School of Economics, Seoul National University, Seoul 151-746, Korea. Tel: +82-2-8806395. Fax: +82-2-886-4231. E-mail: pyohk@plaza.snu.ac.kr.

1

I. Introduction
Productivity is an important indicator that represents the growth of each economic agent. Byutilizing data on productivity by country or industry as the OECD database or EU KLEMS, theproductivities of several countries are compared and large-scale researches are actively conducted inorder to consistently discuss productivity measures and computing methodologies. Japan’s RIETI has
developed the Japan Industrial Productivity Database (JIP Database) and is carrying out researches on
productivity and other activities that could improve statistical data by initiating projects that promote
the productivity of several industries or firms. Korea also, with the Korea Productivity Center as thecentral figure, has been building up a Korea Industrial Productivity Database (KIP Database). Until
today, productivity analysis by industry has been predominant. However, many researchers analyzing
productivity point out that the existing approaches are quite limited because they do not reflect thecharacteristics of a firm, which is the standard unit that makes actual decisions and implements
economic activities. Existing approaches are limited to either establishment-level analysis orcomparative analysis on the industry unit. It is necessary, therefore, to analyze productivity using thefirm-level micro data.
In researches on firms, what has been actively researched recently, together with researches on
productivity, is the analysis on technical efficiency of a firm. Inefficiency occurs from a firm’s
external and internal factors. A firm should begin by striving to identify such internal factors of
inefficiency in order to eliminate these factors and thereby enhance its competitiveness and achieve
long-run growth. This is why it is necessary to analyze the efficiency of Korean firms and researcheson the determinants that promote efficiency.
The objectives of this paper are to discuss empirical and theoretical issues related to identifying
and estimating the sources of firms’ productivity growth and technical efficiency in terms of2

econometric approaches. By its construction, the index number analysis approach, which is themainstay methodology of productivity analysis, cannot distinguish between a production function
shift, which means technical progress, and a movement along a production function, which meanschanges in technical efficiency. The econometric approach is a flexible technique not only for
identifying the sources of productivity growth but also for considering the technical efficiency offirms by explicitly specifying the underlying production (or cost or profit) structure. Therefore, thispaper attempts to separate technical efficiency from the productivity measurement using the
econometric approach, especially the stochastic frontier production models. By using stochastic
frontier models, technical efficiency can be directly estimated, and the estimated parameters of theunderlying structure are used to derive an index of total factor productivity growth.
In the following Section II, we describe the Kumbhakar (2000) method and adopted stochastic
frontier models for the decomposition of TFP. Then Section III presents the results of an empiricalanalysis including econometric results with the summary description of database. Finally, wesummarize conclusions in Section IV.

II. The Stochastic Frontier Production Models and Decomposition
of TFP
Kumbhakar (2000) addresses the estimation and decomposition of TFP change using micro panel
data in a parametric framework. The Solow (1957) measure of productivity change, and thus the index
number analysis approach, is widely used for measuring TFP, but this approach is nothing but theindex of technical change when the constant returns to scale (CRS) production technology and perfect
efficiency are assumed. If efficiency change is omitted from the analysis, its omission will lead to an3

overstatement of the unexplained residual. Kumbhakar (2000) focuses on the parametric econometricmodeling of production systems and the estimation of TFP changes from the empirical production,
cost, and profit functions. Furthermore, TFP change is decomposed into the technical-change, scaleeconomies, and technical- and allocative-inefficiency components. The contributions of the technicaland allocative-inefficiency effects are separately identified and estimated.
Starting with the deterministic production frontier,yit = f ( xit , t ; β ) exp(−uit ), i = 1, 2,..., N , t = 1, 2,..., T(1)

where yit is the output for firm i at time t , f ( xit , t ; β ) the deterministic stochastic production
frontier with the technology parameter vector to be estimated, xit an input vector, t a time trend
serving as a proxy for technical change, and uit ≥ 0 the technical inefficiency. Totally differentiating
the logarithm y in equation (1) with respect to time1,

d ln f ( x, t ) du
−
dt
dt
du
= TP + ∑ ε j x j −
dt
j

y =

where ε j =(2)∂ ln f ( x, t ). A conventional Divisia index of productivity ( TFP ) change is defined∂ ln x jas the difference between the rate of change in the output and the rate of change in the input quantity
index, and so

 = y − ∑ S x
TFP
j j

(3)

j

1

For simplicity, the “ it ” subscripts will be omitted from this point onward.

4

where S j denotes the observed expenditure share of input j . By inserting equation (3) inequation (2), the growth of TFP can be represented asy =d ln f ( x, t ) dudu
 + ∑ S x−= TP + ∑ ε j x j −
= TFP
j j
dt
dt
dt
j
j

 = TP − du + ∑ (ε − S ) x
∴TFP
j
j
j
dt
j
= TP −

where RTS =

∑ε

(4)

du
+ ( RTS − 1)∑ λ j x j + ∑ (λ j − S j ) x j
dt
j
j

j

denotes the returns to scale and λ j = ε j /∑ ε = ε / RTS . Thus, in
k

j

k

j

equation (4), TFP growth can be decomposed into technical change (TC), technical-efficiencychange (TE), scale effects (SE), and allocative-efficiency change (AE).
Many literatures show that recent domestic researches attempt to analyze productivity by
applying Kumbhakar (2000). However, despite the fact that care should be taken in measuring
technical efficiency, since the characteristics of Kumbhakar (2000)’s methodology are such that theresults of productivity analyses are affected depending on how the method of measuring the estimatedvalue of changes in technical efficiency is designed, this fact has not been sufficiently taken into
account. The limitations of such literatures are summarized as follows. First, as mentioned previously,
the stochastic frontier models that are used in the existing literatures are very limited. Table 1 showsthat all, except Lee and Pyo(2007), estimated efficiency by employing Battese and Coelli(1992). Thisis only a part of stochastic frontier models that are already known. The model itself has existing
limitations. Existing models have continued to be improved and more rational models have continued
to be developed, but these have seldom been reflected in domestic researches. Second, it is necessary
to establish and accurately use stochastic frontier models that are suitable to the given research5

objectives and to the characteristics of data being used. The frequently used Battese and Coelli (1992)
model, for instance, has the advantages of estimating the changes of time-varying efficiency being
taken into account. However, it is limited in that efficiency of all sample firms demonstrates the sametime-varying pattern. By using the cross-section data models in the analysis using panel data, it
sometimes commits error because it cannot utilize the advantages that panel data have.

6

Table 1 Empirical Studies on Korea’s TFP Decomposition Using Kumbhakar (2000)
Study

Kim and Han (2001)

Kang and Park(2004)

Han(2005)

Industry

Manufacturing

Total Industry

Manufacturing

Period1980-1994

1995-2002

1986-2000

Cross-section

508
Listed Companies

2223
Firms

358
Listed Companies

Observati
ons

6,203

17,784

5,370

Production
Technology

Translog
Function

Stochastic Frontier
Model

Battese and Coelli(1992)

Translog
Function

Battese and Coelli(1992)

Translog
Function

Battese and Coelli(1992)

7

Dependent
Variable

Value-added

Sales

Sales

Time-varying
Component

Results○z Productivity growth was driven
mainly by technical progressz Changes in technical efficiency
had a significant positive effectz Allocative efficiency had anegative effect.

○z Since financial crisis,
restructuring mainly depended on
an increase in the total factor
productivity by reducing
employment and selling assets
without significant increase in
TFP.

○

z The Contribution of technicalprogress was higher than that oftechnical efficiency improvementin the TFP growth.
z The industries withhigher(lower) rate of technicalchange experienced thelower(higher) rate of technicalefficiency change.

Lee and Pyo(2007)

Total Industry

1984-1997

32
Industries

448

Translog
FunctionLee(2006)

Gross Output○

z Productivity growth was driven
mainly by changes in technicalefficiency in 1980s.
z Productivity growth was driven
mainly by technical progress in1990s.

Pai(2007)IT
Manufacturing

1992-2004

Establishments

21,681

Translog
Function

Battese and Coelli(1992)

Value-added○z The productivity growth of IT
manufacturing was driven
mainly by technical progress.
z Poor technical and allocative
efficiency hindered the
productivity growth.

Kang and Lee(2008)

Port-Logistics
Industry

1990-2003

10
Industries

140

Translog
Function

Battese and Coelli(1992)

Value-added○z The main component of TFP
growth is not efficiency change
but technical progress.

8

As previously stated, many stochastic frontier models have been developed for the estimation oftechnical efficiency, and it is important to choose the most appropriate model or the one that is mostsuitable for the purpose of analyzing the available data. This study was limited to the consideration of
the models that take into account firms’ heterogeneity because the used data consist of a large crosssection and relatively short time series. Also due to the short time series, the models that consider thetime-varying pattern of technical efficiency were excluded in this analysis even though such models
are currently the state-of-the-art models. All the models are based on the specification given inequation (5).

yit = α 0 + x'it β − uit + vit , i = 1, 2,..., N , t = 1, 2,..., T(5)This model postulates that the error term vit − uit , is made up of both the statistical-noise term

vit , a two-sided error term representing the usual statistical noise found in any relationship, and of the
one-sided error term uit ≥ 0 representing technical inefficiency. The frontier is α 0 + x it 'β + vit ,which is stochastic because it includes vit .
The differences among the alternative models are related to the assumptions imposed on thestochastic components. Table 2 summarizes the five models that are used in this paper. The first model
is a fixed-effects model following Schmidt and Sickles (1984). This model can be defined as below.

yit = α i + x'it β + vit , α i = α 0 − uiyit = max(α i ) + x'it β + vit + [α i − max(α i )]= a + x'it β + vit − ui , ui = max(α i ) − α i ≥ 0

(6)

(7)

The most efficient firm’s ui in the sample is 0, and the estimated efficiency in this model is not
an absolute but a relative value. The fixed-effects specifications are estimated as “within” estimators
9without any additional distributional assumption regarding α i since they are treated as firm constants.
Model 2 is the Pitt and Lee (1981) model specified in line with the Mundlak (1978) formulation.
Pitt and Lee (1981) introduced the maximum-likelihood estimator in equation (5) by making someassumptions. They take distributional assumptions on two error terms, vit ~ i.i.d N (0, σ v2 ) andui ~ i.i.d N + (0, σ u2 ) , and ui , vit and xi are independent of each other. Basically, the approach ofMundlak (1978) involves modeling the correlation of unobserved heterogeneity with the regressors inan additional equation, under the assumption that the unobserved environmental-production factors
are correlated with the group means of the explanatory variables. To explicitly account for thiscorrelation, the following auxiliary regression can be introduced (Mundlak, 1978):αi = γ X i + δi , X i =1 Ti∑ X it , δ i ~ N (0, σ δ2 )Ti i =1(8)

where X it is the vector of the explanatory variables and γ a vector of the parameters to be
estimated. The model 2 specification can avoid the heterogeneity bias and at the same time gives
reasonable estimates of inefficiency. Moreover, other time-invariant explanatory variables can also be
included in the model.
Model 3 is a pooled-frontier model in which the firm-specific effect is assumed to be zero. Thus,
the sample is considered a series of cross-sectional subsamples pooled together. This model is basedon the original production frontier model proposed by Aigner et al. (1977). Unlike models 1 and 2,
model 3 can estimate time-varying efficiency.
Model 4 is the “true” fixed-effects model, which contains α i , representing the additional firmspecific effects and thus, the unobservable heterogeneity of firms. Strictly speaking, the application of
fixed effects to the stochastic-frontier model, primarily that of Schmidt and Sickles (1984), is a10reinterpretation of the linear-regression model with fixed effects, not of the frontier models. Following
Greene (2005), the “true” fixed-effects model is specified as

yit = α i + x 'it β + vit − uit(9)This model is estimated by maximum likelihood. Unlike the usual fixed-effects specification, in
which the fixed effects are interpreted as inefficiency, the fixed effects in Greene’s model represent
the unobserved heterogeneity.
Finally, model 5 is the “true” random effects model following Greene (2005) and modified by
the Mundlak (1978) specification. As with the fixed-effects model, the random-effects model,
especially that of Pitt and Lee (1981), can be improved into

yit = α i + x 'it β + vit − uit

α i ~ N (0, σ α2 )(10)This model not only includes a firm-level source of heterogeneity ( α i ), which is potentiallycorrelated with the explanatory variables but also allows for a time-varying inefficiency term. The
Mundlak (1978) adjustment is also applied to model 2, as given in equation (8). The improved
random-effects model can estimate time-varying efficiency.

11

Table 2 Econometric Specification: Stochastic-Frontier Models
Model 1[FE]

Model 2
[RE (MLE) with
Mundlak’s Formulation]

Model 3Model 4

[Pooled (ALS)][“True” FE]

αi = γ X i + δi

Firm-specificComponent α i
Fixed

Xi =

1 Ti
∑ X itTi i =1

ε itInefficiency

Error

i.i.d (0, σ ε2 )max{αˆ i } − αˆi[“True” RE with
Mundlak’s Formulation]αi = γ X i + δi
None

Fixed

δ i ~ N (0, σ δ2 )RandomModel 5Xi =1 Ti
∑ X itTi i =1

δ i ~ N (0, σ δ2 )ε it = uit + vit

ε it = uit + vit

ε it = uit + vit

ε it = uit + vit

uit ~ N + (0, σ u2 )uit ~ N + (0, σ u2 )uit ~ N + (0, σ u2 )uit ~ N + (0, σ u2 )vit ~ N (0, σ v2 )vit ~ N (0, σ v2 )vit ~ N (0, σ v2 )vit ~ N (0, σ v2 )E[ui | ui + vit ]E[uit | uit + vit ]E[uit | uit + vit ]E[uit | δ i + ε it ]12

III. Empirical Results
3.1 Data and Descriptive Statistics
This study uses data from Survey of Business Structure and Activities, which consists of unified
firm-level micro panel data including even information on management activities for policymaking by
the government and for firms’ business strategy establishment, as well as basic information. The
purpose of conducting Survey of Business Structure and Activities2 is to provide basic data for thefirm of various economic policies for businesses by examining the actual conditions of firms’
management strategies and the changes in their industrial structure, through a comprehensive surveyof diverse economic activities, such as the diversification, globalization, and affiliation of thecountry’s business firms. The first survey was conducted in 2006, and the same survey will be
conducted every year. The database for three consecutive years (2005-2007) has been built.
For analysis purposes, the industrial sectors to be used are summarized in Table 3. Since eachindustrial sector has a different set of characteristics, estimating the same production structure in all
the sectors seems unreasonable. Therefore, it is assumed that all firms can be classified into four
sectors. In this case, the firms within the same sector have common production parameters to be
estimated, and the production structure between the sectors is different.
Table 3 Sectoral Classification
Code

Sector1
Manufacturing2
3
4ServiceICT(Computer, Manufacture of Communication
Equipment)
Other Manufacturing/Mining/ Electricity, Gas andWater Supply
Producer Service
Non-producer Service

Table 4 shows the descriptive statistics of the variables that were used for the estimation of thestochastic-frontier production functions.
2

Report on Business Structure and Activities (2007).

13

Table 4 Variable Definition and Descriptive Statistics

Variables

Observ
ationsMeanStandard
Deviation

Min
imu
m

Maximum

Fractionof
Variance
due tothe“Between”
Variatio
n3

Y
K
L
M

29,808143,477.8

1,395,764.0

0.6

117,000,000.0

0.987

29,80829,80829,80844,908.4
284.5
108,490.8

430,460.8
1,392.3
964,666.6

0.8
3.0
0.9

29,000,000.0
85,813.0
72,000,000.0

0.993
0.992
0.985

Gross
OutputCapital
Labor
Materials(Note: Unit: Gross Output, Capital, Materials: Million won, Labor: Person)

The standard deviation indicates a high degree of heterogeneity among the firms in the sample.
The last column of the table presents the fraction of the variance of each variable due to the variation
between the different firms. The figures indicate that all the variables under consideration show asignificant variation between the firms rather than within the firms. Therefore, it can be concluded
that this dataset is more similar to cross-sectional data rather than time series. This finding justifies theuse of models involving heterogeneity.

3.2 Testing for the Separability of the Production Function
Prior to analysis for the estimation of technical efficiency, it is necessary to define the functional
form for the production function. In the real production process, output is produced using the inputs ofcapital, labor, and intermediate materials. The value-added function, however, consists of theaggregate indices of heterogeneous inputs: capital and labor. This means that the value-added function
should not be affected by the change in the intermediate inputs. To use the value-added function foranalysis purposes, it has to be assumed that the value-added function, which is the function of only

3

“Within”

variation

and“between”

variationaredefinedas∑∑ ( x − x )iji∑∑ ( x − x ) = ∑ n ( x − x) , respectively. Here, x represents each variable.
i

i

j

j

2

i

i

2

i

14

j

i

2

and

capital and labor, is independent of the input of intermediate materials. This assumption is referred toas the separability of the real value-added function from the gross output. If the result of theseparability test does not accept this assumption, then the studies on the value-added function areincorrect, and gross output as a measure of output is the proper concept.
The translog gross output production function with three inputs can be specified as follows:

ln yit = α 0 + ∑ α j ln xijt +j1∑∑ β jl ln xlit ln x jit + vit
2 j l

(11)

j , l = L, K , M
where the subscripts i and t are the individual firms ( i = 1, 2,..., N ) and the time
( t = 1, 2,..., T ), respectively; yit the output; and xijt the input factors; and where the subscripts jand l are the labor ( L ), capital ( K ), and intermediate materials ( M ). vit is the typical statisticalerror term with N (0, σ v2 ) .
Following Pyo and Ha (2007), if β km = βlm = 0 in equation (11), then the translog gross output
production function can be expressed as equation (12). Thus, the separability assumption can be
accepted by the data.

log Q = Y (log K , log L) + G (log M )(12)

The test statistics for the fixed- and random-effects models are summarized in Table 5. Since all
the test statistics are sufficiently beyond the critical values at the 1% significant level, the hypothesisof separability is rejected. Therefore, based on these results, it may be inferred that the value-addedfunction-based productivity analysis may be incorrect and that it is more appropriate to use gross
output as an output measure.

15

Table 5 Test Statistics of the Separability Test
LR Test Wald Test
Fixed-Effects Model

3170.94

1068.82

Random-Effects Model-

3907.29

3.3 Estimation of the Technical Efficiency and Comparison of the Alternative
Models4
The translog stochastic-frontier function that was used in the estimation can be specified as
equation (13). The function consists of one output, three inputs, and two error terms. Since the periodthat the data pertain to is very short (three years), the time variable is not considered in the analysis.

ln yit = α 0 + ∑ α j ln xijt +j1∑∑ β jl ln xlit ln x jit + vit − uit
2 j l

(13)

j , l = L, K , M
where the subscripts i and t are the individual firms ( i = 1, 2,..., N ) and the time
( t = 1, 2,..., T ), respectively; yit the output; and xijt the input factors; and where the subscripts jand l are the labor ( L ), capital ( K ), and intermediate materials ( M ). The statistical-noise term vi
is a two-sided error term that follows N (0, σ v2 ) and that represents the usual statistical noise foundin any relationship, and ui ≥ 0 is a one-sided error term representing technical inefficiency. In thispaper, it is assumed that vit is independent of uit , and if necessary, it is also assumed that uit
follows N (0, σ u2 ) + . In the first two models (1 and 2), the firm’s inefficiency is assumed to beconstant over time, thus captured by the firm-specific effects. In models 3, 4, and 5, on the other hand,the firm’s inefficiency can vary over time. In these models, the skewed stochastic-error term isinterpreted as inefficiency. In all the models, except for the fixed-effects model, it is assumed that the4

The estimation results of the production function’s parameters can be obtained by email on request from the author.

16

firm’s technical efficiency is not correlated with the explanatory variables.
At first, a Hausman test of the null hypothesis that the firm-specific effects are uncorrelated withthe explanatory variables was conducted in the fixed-effects model. The test statistic yieldedχ 2 (9) = 553.50 and the null hypothesis was rejected. Therefore, the specifications that do not allow
for these correlations may produce biased and inconsistent results. Thus, the random-effects models,
which assume no correlation between the firm-specific effects and the explanatory variables, can besaid to be too restrictive and to provide inferior estimates. On the other hand, the fixed-effects model
can be expected to produce unbiased and consistent estimates of the stochastic-production-function
parameters.
If the inefficiency is believed to be persistent, the models with time-invariant inefficiency, suchas models 1 and 2, may be more relevant. In the case, however, of the panel data with large crosssections and short time series, the incidental-parameter problem may occur, and therefore, model 2
can be said to be more suitable than model 1. The heterogeneity bias is expected to be relatively low
in models 2 and 5, which directly control the correlation between the individual effects and the
explanatory variables although they are random-effects models. A test of the null hypothesis that the
Mundlak terms are jointly equal to zero is rejected for both models with the Mundlak (1978)
adjustment. The values of the likelihood ratio statistic for each industrial sector are 129.0, 919.0,
550.4, and 64.1 for the random effects with the Mundlak (1978) adjustment. Thus, for models 2 and 5,
the Mundlak (1978) adjustment is useful in obtaining consistent results. In fact, the estimators ofmodel 2 are almost identical to the fixed-effects estimators of model 1 (the “within” estimators), andare thus unbiased. If the time-varying pattern of inefficiency is assumed, models 3, 4, and 5 are morereasonable. Since model 3 does not consider the characteristics of the panel data, it is inferior to theother models. As shown above, the results of the Hausman test are rejected, and the fixed-effects
model is more relevant than the random-effects model. It can be concluded intuitionally, however, thatmodel 5 is the best model for the examination of efficiency using the panel data employed in thisanalysis because the possibility of the incidental-parameter problem is intrinsic to model 4, and model17

5 combined with the Mundlak (1978) adjustment takes care of the fact that technical inefficiency iscorrelated with the explanatory variables. In sum, model 5 can be said to be the best model for theexamination of efficiency using the panel data employed in this analysis, for the following threereasons: (1) this model can consider the time-varying pattern of efficiency; (2) heterogeneity can betaken into account; and (3) the estimated parameters are unbiased and consistent.
Table 6 provides a summary of the weighted averages of the estimated efficiency measures using
different models for each industrial sector. The efficiency scores are taken to be equal to theinefficiency scores ( 1 − exp(−uit ) ) obtained from the regression model. The share of each firm’s sales
to a sector is used as the weight. An examination of the result will reveal that each model has adifferent estimated-efficiency score. The estimated-efficiency score using the Schmidt and Sickles(1984) method shows very unrealistic values compared with the other models’ results. This seems tobe due to the features of the Schmidt and Sickles (1984) model. Since in this model, relative technicalefficiency is estimated rather than absolute technical efficiency, the wider the gap is, the smaller theefficiency that is estimated. Especially, a problem arises when the maximum efficiency is an outlier.
Based on the results obtained from all the models, except for model 1, the Schmidt and Sickles (1984)
method, the estimated technical efficiency ranges from 77% to 86%. Moreover, the results indicatethat the introduction of the Mundlak (1978) adjustment, in which the correlation between the
explanatory variables and firm-specific heterogeneity is accounted for in the models, can decrease theheterogeneity bias. In fact, compared to the other models, model 5, which considers the heterogeneity
bias and firm-specific heterogeneity, shows the highest estimates of technical efficiency, and among
the sectors, the estimate of the producer service sector is the highest.

18

Table 6 Average Efficiency Scores by Technique: 2005-2007
Model 5Model 2

Observation

Model 1[FE]

[RE (MLE)

Model 3

with

[PooledMundlak’s(ALS)]

Model 4[“True” FE][“True” RE
withMundlak’s
Formulation]

Formulation]

ICT

3744

0.365

0.847

0.865

0.847

0.887

nonICT

16074

0.388

0.819

0.855

0.818

0.855

ProdServ

4080

0.072

0.608

0.665

0.653

0.919

Serv

5847

0.289

0.734

0.732

0.717

0.743

Total

29745

0.301

0.767

0.798

0.774

0.859

ICT

1248

0.363

0.841

0.861

0.847

0.896

nonICT

5358

0.388

0.818

0.847

0.810

0.844

ProdServ

1360

0.071

0.605

0.650

0.642

0.915

Serv

1949

0.288

0.733

0.735

0.722

0.742

Total

9915

0.302

0.766

0.792

0.770

0.854

ICT

1248

0.368

0.847

0.865

0.846

0.882

nonICT

5358

0.388

0.820

0.856

0.819

0.855

ProdServ

1360

0.073

0.613

0.672

0.660

0.919

Serv

1949

0.289

0.735

0.731

0.716

0.740

Total

9915

0.303

0.770

0.801

0.772

0.858

ICT

1248

0.369

0.851

0.869

0.848

0.883

nonICT

5358

0.389

0.820

0.861

0.823

0.864

ProdServ

1360

0.072

0.606

0.671

0.656

0.921

Serv

1949

0.289

0.734

0.730

0.713

0.746

Total

9915

0.299

0.766

0.801

0.775

0.863

2005

2006

2007

Table 7 contains the Spearman rank correlation coefficients, computed at the firm level, from thefive different estimation techniques. These coefficients show how close the rankings of the firms areto one another, using the full sample of firms. For the models with time-varying efficiency, theefficiency score is computed as the firm’s average efficiency score over the sample period. The resultshows that the use of different models leads to different rankings of estimated efficiency. Therefore, it
can be concluded that it is important to choose the most appropriate model or that which is mostsuitable for analysis purposes and considering the available data.
19

Table 7 Spearman Rank Coefficients
Model 1Model 2Model 3Model 4Model 5[FE]

[RE (MLE) with

[Pooled (ALS)][“True” FE][“True” RE with

Mundlak’s

Mundlak’s

Formulation]

Formulation]

Model 11Model 20.482

1Model 3

0.470

0.856

1

Model 4

0.326

0.332

0.675

1

Model 5-0.069

0.290

0.440

0.178

1

3.4 Decomposition of the Productivity Change Using the Stochastic-Frontier
Production ModelIn the previous section, several stochastic-production-frontier models were compared considering
the firms’ heterogeneity. Among these models, model 5, the “true” random-effects model with theMundlak (1978) adjustment, will be used in the analysis in this section, which will attempt todecompose productivity as model 5 is considered the most suitable model as far as the available data
and the purpose of analysis are concerned. The functional form of production to be used is the same asthat in the previous section. The translog stochastic-frontier function used in the estimation can be
specified as equation (13). Since the period that the data pertain to is very short (three years), the time
variable was not considered in the analysis. Therefore, among the effects, technical change (TC) is
assumed to be zero.

ln yit = α 0 + ∑ α j ln xijt +j1∑∑ β jl ln xlit ln x jit + vit − uit
2 j l

j , l = L, K , M
Table 8 shows the average output elasticity of each industrial sector for the period 2005-2007.
The estimate of returns to scale ( RTS ), which combines the output elasticity of the capital ( ε K ), oflabor ( ε L ), and of the intermediate outputs ( ε M ), shows an increasing return to scale (IRS) when it isgreater than 1, a constant return to scale (CRS) when it is equal to 1, and a decreasing return to scale
20

(DRS) when it is less than 1. The estimate of RTS for the ICT sector exhibits IRS, with a magnitudeof 1.253. This result is similar to that obtained by Pai (2007). On the other hand, the other sectors
exhibit DRS, with 0.92, 0.866, and 0.982 magnitudes, respectively.
The main findings of the present study are summarized in Table 9. Table 9 presents the changes
in technical efficiency (TE), scale effects (SC), allocative efficiency (AE), and total factor ) of each sector for 2005-2007. It is shown that the contributions of eachproductivity growth( TFP
factor to productivity growth differ according to the industrial sector. First, the estimate of TFP
growth in the producer service sector is negative, and the other sectors’ TFP growth is positive.
Second, in the case of the changes in technical efficiency, all the sectors, except for the ICT sector,
show positive growth. A poor contribution of technical efficiency to productivity growth in the ICT
sector was also shown in the study conducted by Pai (2007). Third, the changes in allocative
efficiency contribute positively to the productivity growth in all the sectors. Lastly, in the ICT sector,
the scale effect helps improve the firm’s productivity, but in the other sectors, it does not.
Table 8 Output Elasticities of the Input Factors
Observation

Capital

Labor

Materials

RTS

ICT

3,744

0.143

0.093

1.017

1.253

nonICT

16,074

0.042

0.061

0.823

0.926

ProdServ

4,080

0.105

0.066

0.695

0.866

Serv

5,847

0.034

0.060

0.888

0.982

total

29,745

0.077

0.069

0.848

0.994

Table 9 The Rate of Changes in Technical Efficiency (TE),
Scale Component (SC), Allocative Efficiency (AE), and Total Factor Productivity Growth
 )
( TFP


TFP

TE

AE

SC

ICT

0.025

-0.006

0.022

0.009

nonICT

0.006

0.010

0.013

-0.017

ProdServ-0.026

0.003

0.022

-0.052

Serv

0.001

0.004

0.013

-0.015

total

0.002

0.004

0.017

-0.01921

IV. Concluding Remarks
In this paper, we attempt to discuss empirical and theoretical issues related to identifying andestimating the sources of firms’ productivity growth and technical efficiency using micro level panel
datasets in Korea for the period of 2005-2007. In econometric approach, prior to analysis for theestimation of technical efficiency, it is necessary to define the functional form for the production
function. Based on the test statistics for the fixed- and random-effects models, the hypothesis ofseparability is rejected. Therefore, it may be inferred that the value-added function-based productivity
analysis may be incorrect and that it is more appropriate to use gross output as an output measure.
Many stochastic frontier models have been compared for the estimation of technical efficiency, and it
is important to choose the most appropriate model or the one that is most suitable for the purpose ofanalyzing the available data. In this analysis, the true random effects model with Mundlak’s
adjustment can be said to be the best model for the examination of efficiency using the panel data
employed in this study, for the following three reasons: (1) this model can consider the time-varying
pattern of efficiency; (2) heterogeneity can be taken into account; and (3) the estimated parameters areunbiased and consistent. The estimated technical efficiency ranges from 77% to 86%. Moreover, theresults indicate that the introduction of the Mundlak (1978) adjustment, in which the correlation
between the explanatory variables and firm-specific heterogeneity is accounted for in the models, candecrease the heterogeneity bias. In fact, compared to the other models, the true random effects modelwith Mundlak’s adjustment, which considers the heterogeneity bias and firm-specific heterogeneity,shows the highest estimates of technical efficiency, and among the sectors, the estimate of the
producer service sector is the highest.
Next, it is shown that the contributions of each factor to productivity growth differ according to
the industrial sector. First, the estimate of TFP growth in the producer service sector is negative, andthe other sectors’ TFP growth is positive. Second, in the case of the changes in technical efficiency, all
the sectors, except for the ICT sector, show positive growth. A poor contribution of technical22efficiency to productivity growth in the ICT sector was also shown in the study conducted by Pai(2007). Third, the changes in allocative efficiency contribute positively to the productivity growth inall the sectors. Lastly, in the ICT sector, the scale effect helps improve the firm’s productivity, but inthe other sectors, it does not.
There are many methodologies and approaches that analyze the productivity and efficiency offirms, but to derive significant results, it is very important to choose a methodology that fits the
purpose of the analysis and the data to be used in it. Since the results can be greatly affected by the
choice of classification criteria and models when analyzing the factors that determine productivity andefficiency, needless to say, care should be taken in choosing such classification criteria and models.

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