Advanced Science and Technology Letters
Vol.114 (Business 2015), pp.86-89
http://dx.doi.org/10.14257/astl.2015.114.17
Allocative Efficiency of Global Steel Firms
Seok-Young Lee
Department of Business Administration, College of Social Sciences, Sungshin Women’s
University, 2 Bomun-ro 34da-gil, Seongbuk-gu, Seoul, 02844, Korea
136-742, Korea, [email protected]
Abstract. I explore allocative efficiency of global steel firms employing Data
Envelopment Analysis (DEA). Based on a panel dataset for global steel firms
over the period 1997-2011, I report that the means (medians) of aggregate
technical and allocative, technical, and allocative efficiency scores are 0.716
(0.702), 0.787 (0.772) and 0.913 (0.929) respectively. I empirically investigate
whether given input prices for labor, material and other overhead resources,
global steel firms choose inputs to be the least cost mix. Empirical results
indicate that global steel firms exhibit insignificant allocative inefficiency.
1
Introduction
Most previous studies have primarily concentrated on analyzing overall technical
efficiency (Charnes et al. 1978), pure technical efficiency (Banker et al. 1984), and
scale efficiency in the global steel industry to find out what drives inefficiency.
However, there are not many studies on allocative efficiency of global steel firms.
Therefore, the objective of this study is to investigate whether given input prices for
labor, material and other overhead resources, global steel firms choose inputs to be
the least cost mix.
This study applies data envelopment analysis (DEA) in estimating efficiency
scores. First, I employ the input-oriented one-input one-output variable returns to
scale DEA model of Banker et al. (1984) to estimate the aggregate technical and
allocative efficiency scores of the different observations (j, t) for firm j = 1,…..,J, and
year t = 1,……,T. For this efficiency model, the single input is total expenses that
comprise labor cost, material cost, and other overhead costs, and the single output is
total revenue. The aggregate technical and allocative efficiency ̂ kt
observation k in period t is obtained from the following linear program:
of an
ˆ Agg  min 

kt
kt
(1)
Agg
subject to
T
J

t 1
T

 jt x jt   kt x kt ,
j 1
J

t 1
 jt y jt  y kt  0 ,
j 1
ISSN: 2287-1233 ASTL
Copyright © 2015 SERSC
Advanced Science and Technology Letters
Vol.114 (Business 2015)
T
J

t 1

jt
 1 ,  jt , 
kt
 0
j 1
where x jt is the quantity of the input consumed by DMUjt , y jt the quantity of the
output produced by DMUjt,  jt the weight placed on DMUjt data, x kt and y jt are
quantities of an input and an output for DMUkt being evaluated. Here i=1; r=1, 2, 3; j,
k=1,…, J and t=1,….., T. The linear program is solved for each observation (j, t).
Second, I also employ the input-oriented three-input one-output variable returns to
scale DEA model of Banker et al. (1984) to estimate the technical efficiency scores of
the different observations (j, t) for firm j = 1,…..,J, and year t = 1,……,T. For this
efficiency model, the three inputs are (i) labor cost, (ii) material cost, and (iii) other
overhead costs, and the single output is total revenue. The technical efficiency ̂ kt is
obtained from the following linear program:
Te
ˆ Te  min 

kt
kt
(2)
subject to
T
J

t 1
T

 jt x ijt  
t 1
 jt y jt  y kt  0 ,
j 1
J

t 1
x ikt , i =1, 2, 3
J

T
kt
j 1

jt
 1 ,  jt , 
kt
 0
j 1
Third, I measure allocative efficiency ̂ kt of an observation k in period t by
All
dividing aggregate allocative and technical efficiency ̂ kt
Agg
by technical efficiency
̂ kt as in Banker and Maindiratta (1998).
Te
2
Data and Descriptive Statistics
I consider 30 global steel firms for each of 15 years from 1997 to 2011, resulting in a
total of 450 firm-year observations. All data used in this study are obtained from
World Steel Dynamics published in 2013. All monetary value items have been
deflated to 2000 US dollars.
Table 1 presents descriptive statistics on output, inputs, and efficiency scores. The
mean of allocative efficiency scores is 0.9133 and the median is 0.9266. The lower
and upper quartiles for allocative efficiency scores for the pooled data are 0.8870 and
0.9625 respectively.
Copyright © 2015 SERSC
87
Advanced Science and Technology Letters
Vol.114 (Business 2015)
Table 1. Descriptive statistics for pooled data (N=450)
Description
Output
Revenues
Labor cost
Material
Inputs
cost
Overhead
cost
Aggregate
technical
and
allocative
Efficiency eff.
Technical
eff.
Allocative
eff.
Mean
5,759.56
649.38
Std. Dev.
8,057.89
912.81
Q1
1,649.85
198.22
Median
3,327.47
377.38
Q3
6,245.86
4,167.08
6,043.01
1,075.12
2,306.89
4,628.24
447.25
593.13
111.50
268.66
522.47
0.7160
0.1035
0.6426
0.7023
0.7738
0.7868
0.1170
0.6984
0.7719
0.8640
0.9133
0.0648
0.8870
0.9266
0.9625
748.14
Note: Outputs and inputs are expressed in million dollars.
3
Empirical Results
Table 2 reports each efficiency scores for each of 15 years from 1997 to 2011. For the
pooled data, the means of aggregate technical and allocative, technical, and allocative
efficiency scores are 0.716, 0.787 and 0.913, respectively, suggesting that there exist
a significant level of inefficiency and still room for improvement. The aggregate
technical and allocative efficiency score and the technical efficiency score indicate the
highest 0.807 and 0.879 respectively in 2005. However, allocative efficiency score
exhibits the highest 0.928 in 2001. The aggregate technical and allocative efficiency
score and the technical efficiency score indicate the lowest 0.645 and 0.697,
respectively in 2001, and the allocative efficiency score 0.893 in 2008.
Table 2. Mean (median) of efficiency scores by year
Year
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
88
Sample
size
30
30
30
30
30
30
30
30
30
30
30
30
Aggregate technical
and allocative eff.
0.678 (0.674)
0.671 (0.662)
0.665 (0.655)
0.686 (0.663)
0.645 (0.645)
0.684 (0.676)
0.704 (0.662)
0.805 (0.800)
0.807 (0.793)
0.788 (0.782)
0.786 (0.767)
0.779 (0.764)
Technical eff.
Allocative eff.
0.757 (0.735)
0.738 (0.743)
0.737 (0.707)
0.743 (0.716)
0.697 (0.691)
0.749 (0.730)
0.779 (0.758)
0.870 (0.875)
0.879 (0.895)
0.870 (0.849)
0.867 (0.856)
0.876 (0.896)
0.904 (0.924)
0.913 (0.925)
0.908 (0.921)
0.926 (0.948)
0.928 (0.929)
0.917 (0.924)
0.904 (0.927)
0.924 (0.922)
0.919 (0.919)
0.908 (0.916)
0.909 (0.920)
0.893 (0.909)
Copyright © 2015 SERSC
Advanced Science and Technology Letters
Vol.114 (Business 2015)
2009
2010
2011
Pooled
30
30
30
450
0.642 (0.637)
0.700 (0.690)
0.699 (0.707)
0.716 (0.702)
0.698 (0.674)
0.765 (0.752)
0.776 (0.771)
0.787 (0.772)
0.924 (0.937)
0.918 (0.910)
0.904 (0.916)
0.913 (0.929)
Figure 1 depicts average efficiency scores for each year from 1997 to 2011.
1
0.8
0.6
0.4
0.2
0
Technical eff.
Aggregate technical and allocative eff
Allocative eff
Fig. 1. Trends of efficiency scores
References
1. Banker, R.D., A. Charnes, and W.W Cooper, Some Models for Estimating Technical and
Scale Inefficiencies in Data Envelopment Analysis. Management Science, 30 (9) (1984),
1078-1092.
2. Banker, R.D. and A. Maindiratta, Nonparametric Analysis of Technical and Allocative
Efficiencies in Production. Econometrica, 56 (6) (1998), 1315-1332.
3. Banker, R.D., H. Chang, and R. Natarajan, Estimating DEA Technical and Allocative
Inefficiency Using Aggregate Cost or Revenue Data. Journal of Productivity Analysis 27 (2)
(2007), 115-121.
4. Charnes, A., Cooper, W. W., Rhodes, E., Measuring the Efficiency of Decision Making
Units. European Journal of Operations Research, 2(6) (1978), pp. 429-444.
5. World Steel Dynamics: Financial Dynamics of International Steelmakers, World Steel Dynamics
Inc., Englewood Cliffs, New Jersey, USA (2013).
Copyright © 2015 SERSC
89