This paper explores the distribution of the technical efficiencies across German manufacturing industries and looks at the association of technical efficiency to other economic categories. Aggregating 1995 to 2001 firm-level data yields an unbalanced panel with 241 cross-sections (industries). While the unbalanced nature of the data precludes some time-varying specifications, one can estimate the parameters of a time-invariant fixed-effects model. With only one industry being fully efficient, the rest perform poorly, having an efficiency mode of .32. To account for outliers 7 industries were dropped from the sample (a 2.9% reduction of the sample). In the smaller sample, the estimated mode of technical efficiency is .78. The distribution of TE is only slightly positively skewed, contrary to the rationale for using a one-sided distribution for the efficiencies. This problem has been noticed by other researchers, and so far the only solution proposed has involved changing the assumed distribution for the technical efficiencies. However, since fixed-effects estimation does not assume a particular distribution for the firm level inefficiencies, our purified-of-outliers scores of technical efficiencies can be trusted and used as endogenous variable in further analysis.

Oleg Badunenko

English

Research Papers in Economics

The Potential Determinants of
German Firms' Technical E±ciency:
An Application Using Industry Level Data
by
Oleg Badunenko¤ and Andreas Stephany
March, 2004
Abstract
Stochastic Frontier Analysis is employed to calculate technical e±ciencies of German ¯rms at
the industry level. The data come from the German Cost Structure Census of manufacturing for
the period 1995-2001. This survey is conducted by the German Federal Statistical O±ce (Statis-
tisches Bundesamt). Aggregating 1995 to 2001 ¯rm-level data yields an unbalanced panel with 241
cross-sections (industries). While the unbalanced nature of the data precludes some time-varying
speci¯cations, one can estimate the parameters of a time-invariant ¯xed-e®ects model. With only
one industry being fully e±cient, the rest perform poorly, having a technical e±ciency mode of 0.32.
To account for this outlier, one industry is dropped from the sample. In the reduced sample, the
estimated mode of technical e±ciency is 0.64.
The scores of technical e±ciencies are negatively correlated to concentration indices, positively
related to new ¯rm formation and human capital proxy. The analysis shows that technical e±ciency
is not related to sales growth, R&D expenditures, capital intensity, proportion of East German ¯rms
in the industry and size of the ¯rm. The straightforward continuation of this analysis is making use
of available ¯rm-level data.
¤PhD Student, European University Viadrina, Faculty of Economics, Gro¼e Scharrnstra¼e 59, 15230 Frankfurt Oder,
Germany. E-Mail: badunenko@euv.®o-de; Phone: +49 335 5534 2943.
yJunior Professor of Economics, European University Viadrina, Faculty of Economics and Management Stud-
ies, Gro¼e Scharrnstra¼e 59, 15230 Frankfurt Oder, Germany, URL: http://oekonometrie.euv-frankfurt-o.de, E-Mail:
astephan@euv.®o-de; Phone: +49 335 5534 2203, Fax: +49 335 5534 2279.2
Introduction
Analysis of a ¯rm activity on a industry level involves comparison of its performance relative to that
of others. By the same token, using frontier methodologies, the performance of each industry can be
measured relative to 'best-practice' frontier, which is constructed based on the performance of other
industries in the economy.
This paper focuses on the cost e±ciency of ¯rms at the industry-level; due to the lack of data on
the input prices, the basic production frontier model is employed, which is estimated based on the
assumption that ¯rms are maximizing output, given inputs1.
The usefulness of the frontier approach to the measuring e±ciency of industries is twofold. Firstly, it
provides managers of the ¯rms with answers to the questions regarding cost minimization, organization
and distribution systems. Secondly, frontier methodology o®ers guidance to regulators and policy makers
as for solving and mitigating problems in particular industry and economy in general.
Concept of in-E±ciency
On the following ¯gure hypothetical one input (y) { one output (x) production process is depicted.
Figure 1: Explanation of in-E±ciency concept: one-input-one-output case
One particular industry uses x input intensity and produces output y. It can be well seen that within
given 'best-practice' technology T this particular industry produces ine±ciently. With current input
intensity x, when e±ciently, it could have produced y¤. The distance between y¤, the potential output,
and y, the observed output, stands in the literature for the ine±ciency.
1This de¯nition is referred to as output-oriented frontier.3
Methodology: Time-Invariant Technical E±ciency
The survey of nowadays applied frontier methods to measure the e±ciency maybe found in Kumbhakar
and Lovell (2000). In this paper the simplest version of existing panel data e±ciency models, the
¯xed-e®ects model (Schmidt and Sickles, 1984) is employed.
A general Cobb-Douglas production frontier with time-invariant technical e±ciency can be written
as follows:
lnYit = ¯0 +
X
n
¯n lnCnit + vit ¡ ui (1)
where vit represents random statistical noise, and ui ¸ 0 represents technical e±ciency; i = 1;:::;I
and t = 1;:::;T. Note that technical e±ciencies remain constant over time. For the purpose of our
analysis we make the following assumptions: (i) vit are assumed to be iid (0;¾2
v) and uncorrelated with
the regressors, and (ii) no distributional assumption is made on the ui, and the ui's are allowed to be
correlated with the regressors or with vit.
The ui's are ¯xed e®ects and, therefore, are industry speci¯c intercept. With simple substitution
¯0i = ¯0 ¡ ui we apply OLS (Least Squares Dummy Variables, LSDV { from here and after) to the
modi¯ed equation (1):
lnYit = ¯0i +
X
n
¯n lnCnit + vit (2)
After LSDV estimation2 we obtain c ¯0i
3. The maximum of industry speci¯c ¯xed e®ects will suggest
the most e±cient industry. The ui are proposed to be estimated as in (3)4 and producer speci¯c technical
e±ciencies as in (4):
b ui = max
i
(c ¯0i) ¡ c ¯0i (3)
TEi = exp(¡ b ui) (4)
In this framework at least one industry is 100% e±cient and others' e±ciency scores are measured
relative to technically e±cient industry (or industries).
Data and Variables De¯nition
In this paper the data of the German Cost Structure Census of manufacturing for the period 1995-2001 is
utilized. This survey is conducted by the German Federal Statistical O±ce (Statistisches Bundesamt).5
It comprises almost all large German manufacturing ¯rms with 500 or more employees. Firms with 20-
499 employees are included as a random sample which is representative for the respective size category
and industry. Firms with less than 20 employees are not sampled.
Output Output is measured by gross production, which comprises the turnover plus the net change of
the stock of ¯nal products. We exclude turnover from activities that are classi¯ed as miscellaneous
such as license fees, commissions, rents and leasing, etc. because we assume that such revenue
can only be inadequately explained by means of a production function.
2The estimates of the ¯n's are consistent as either I ! 1 or T ! 1 and the consistency property does not require
that the ui's be uncorrelated with regressors.
3The estimates of ¯0i are consistent as T ! 1, however consistency property requires both I ! 1 and T ! 1.
4The ui's are ensured to be positive to satisfy our assumption.
5The ¯rms are obliged to participate in the survey and are not eligible to disclose any required information.4
Cost Structure The cost structure census contains information for a number of input categories. These
categories are payroll, employers' contribution to the social security system, fringe bene¯ts, ex-
penditure on material inputs, self-provided equipment and goods for resale, energy, external wage-
work, external maintenance and repair, tax depreciation of ¯xed assets, subsidies, rents and leases,
insurance costs, sales tax, other taxes and public fees, interest payments as well as "other" costs
such as license fees, bank charges, postage or expenses for marketing and transport.
Constructing cost groups Within this structure ¯ve following cost categories were aggregated:
material inputs (intermediate material consumption plus commodity inputs plus energy consump-
tion), labor compensation (salaries and wages plus employer's social insurance contributions), user
cost of capital (depreciation plus rents and leases), external services (external services and external
contract work) and other inputs related to production (e.g., transportation services, consulting or
marketing). All input and output data series were de°ated using the producer price index for the
respective industry.
Additional Information Further industry-level information available in the Cost Structure Census in-
cludes6 (i) Competition Rate (Her¯ndahl Concentration Index), (ii) Sales Growth, (iii) New Firm
Formation Rate (mean annual number of new ¯rms per employee at the 3-digit industry level
1992-2000 (%), (iv) R&D Expenditures, (v) Capital Intensity (mean annual depreciations plus
expenditures for rents and leases over sales at industry level), (vi) Human Capital Intensity (num-
ber of employees with a university degree divided by number of untrained employees (%), (vii)
Proportion of East German Firms (proportion of ¯rms with headquarter in East Germany over
all ¯rms (%)), (vii) Average Firm Size (log of mean number of employees in respective industry
from 1992 to 2000).
Results
In the preceding analysis it is implicitly assumed that all ¯rms, and, therefore, industries face the same
environment. Consequently, all the deviations from the frontier are only due to ine±ciency.
Technical E±ciencies
The ¯rst step in calculating technical e±ciency scores involves Least Squares Dummy Variables esti-
mation. With all industries included in estimation, one outlier (tobacco industry) drives all the results:
this industry is e±cient, while the technical e±ciency score's mode of the rest is only 0.32. Without this
outlier, there are yet few e±cient industries and technical e±ciency score's mode of the rest increases
up to 0.64. Additional dropping of outliers does not change the results considerably, i.e. as dropping
of tobacco industry. In spite the fact that additional dropping of the outliers may yield better distri-
bution of technical e±ciencies it reduces the sample, which might make further analysis disadvantaged.
Therefore, only one outlier7 is decided to be dropped.
6The method of proxy construction is pointed in the parentheses.
7The output of the regression and resulted technical e±ciencies indices' distribution for the full sample maybe found
in Appendix.5
Table 1. { Fixed-E®ects regression, LSDV
lnProdit = ¯0i + lnMatit + lnLabit + lnExtit + lnCapit + lnOthit + vit
Number of groups = 236
Number of obs = 1573
Overall R2 = 0.9953
lnProd Coef. Std. Err. t p-value [95% Conf. Interval]
lnMat 0.5366338 0.00847 63.36 0.000 0.5200177 0.5532498
lnLab 0.185674 0.0122416 15.17 0.000 0.1616591 0.2096889
lnExt 0.087042 0.0055375 15.72 0.000 0.0761789 0.0979051
lnCap 0.0642858 0.0094572 6.80 0.000 0.0457333 0.0828384
lnOth 0.1049571 0.0075441 13.91 0.000 0.0901575 0.1197566
cons 1.646474 0.0711816 23.13 0.000 1.506834 1.786114
F test that all ui = 0: F(235;1332) = 39:60 Prob > F = 0:0000
Table 1 indicates that all the coe±cients are signi¯cant at all conventional levels and that the regression
is ¯tted good.
Further, technical e±ciency scores are calculated using equation (4). The summary statistics of
obtained technical e±ciencies scores that are presented in Table 2, indicate low level of technical ef-
¯ciency. Speci¯cally, industries could have produced, on average, the same level of output using only
65% of inputs they actually used.
Table 2. { Sample Statistics: E±ciency Measure
variable # obs mean st. d. min max
TE 236 .6517072 .0674251 .3502355 1
On the following ¯gure histogram and Kernel8 density estimates of technical e±ciencies scores of
236 industries are shown:
0
2
4
6
8
D
e
n
s
i
t
y
.4 .6 .8 1
Technical Efficiencies, without Outlier
0
2
4
6
8
1
0
D
e
n
s
i
t
y
.4 .6 .8 1
Technical Efficiencies, without Outlier
Figure 2: Histogram and Kernel density estimate for technical e±ciency produced using equation (4)
The distribution of TE (Figure 2) is only slightly positively skewed, contrary to the rationale for
using a one-sided distribution for the e±ciencies. This problem has been noticed by other researchers
(e.g. Carree, 2002), and so far the only proposed solution involves changing the assumed distribution
8We choose Gaussian normal kernel, with optimal bandwidth by Silverman (1986).6
of the ui's in equation (1). However, since LSDV estimation does not assume a particular distribution
for the ¯rm level ine±ciencies, our puri¯ed-of-outliers scores of technical e±ciencies can be trusted and
used as endogenous variable in further analysis.
Correlates of Technical E±ciencies
In this subsection regression analysis is used to determine whether the e±ciency scores are related to
characteristics of industries, de¯ned and described in section Data and Variable De¯nition, in Additional
Information description.
The output of the regression is presented in Table 3. The independent variables do not account for
the signi¯cant share in the variation of technical e±ciency measure.
Table 3. { OLS regression
TEi = ¯0i + X¯ + ²i
Number of obs = 236
F(8;227) = 4:99, Prob > F = 0:0000
Adj. R2 = .12
Tech. E®. Coef. Std. Err. t p-value [95% Conf. Interval]
her¯ndahl -.0958505 .0354733 -2.70 0.007 -.1657496 -.0259515
sales growth .1514117 .1284603 1.18 0.240 -.1017154 .4045389
new ¯rm 5.267175 1.570813 3.35 0.001 2.171936 8.362413
r&d -.2346449 .2878304 -0.82 0.416 -.8018058 .3325161
cap -.1976795 .1808955 -1.09 0.276 -.5541286 .1587695
hum cap .2381159 .0791692 3.01 0.003 .0821154 .3941164
east .0003808 .0004095 0.93 0.353 -.0004261 .0011877
size -.0045804 .006763 -0.68 0.499 -.0179066 .0087458
cons .633303 .0518139 12.22 0.000 .5312053 .7354007
However, Her¯ndahl Concentration Index is negatively related, while new ¯rm formation and human
capital are positively related to the technical e±ciency; and signi¯cantly so. Additionally, F-statistic
indicates that multiple regression equation is statistically signi¯cant.
These ¯ndings suggest that improving competition (that is, reducing concentration) has a potential
to increase technical e±ciency. By the same token, foundation of new ¯rms and increasing the number
of employees with university degree would facilitate technical e±ciency improvement.
Summary and Conclusions
German industries in the sample during 1995-2001 time span are characterized by quite low level of
technical e±ciency. The scores of technical e±ciency are negatively related to concentration indices and
positively related to new ¯rm formation and human capital proxies.
Performed analysis reveals that (i) R&D expenditures, (i) capital intensity, (iii) proportion of east
German ¯rms and (iv) size of the ¯rm do not have in°uence on technical e±ciency. This does not
seem to be plausible in the real world. However, this analysis is based on the aggregated data, and the
aggregation might have disclosed important properties of the data. That is why, the prospect for the
future research would be the same analysis, but with ¯rm-level data.References
[1] Aly, Hassan Y.; Grabowski, Richard; Pasurka, Carl; Rangan, Nanda \Technical, Scale, and Al-
locative E±ciencies in U.S. Banking: An Empirical Investigation. " The Review of Economics and
Statistics, Vol. 72, No. 2. (May, 1990), pp. 211-218.
[2] Carree, Martin A. \Technological Ine±ciency and the Skewness of the Error Component in Stochas-
tic Frontier Analysis. " Economic Letters, 77, 2002, pp. 101-107.
[3] Kumbhakar, Subal C.; Lovell, C.A.Knox. Stochastic Frontier Analysis, Cambridge University Press,
2000
[4] Schmidt, P., and Sickles R.C. \Production Frontiers and Panel Data " Journal of Business and
Economic Statistics, 2:4 October 1984, pp. 367-74.
[5] Silverman B.W. Density Estimation: for Statistics and Data Analysis, Chapman and Hall, London,
1986.8
Appendix
Table A1 Fixed-E®ects regression
lnProdit = ¯0i + lnMatit + lnLabit + lnExtit + lnCapit + lnOthit + vit
Number of groups = 237
Number of obs = 1580
Overall R2 = .9931
lnProd Coef. Std. Err. t p-value [95%Conf. Interval]
lnMat .5338688 .0085244 62.63 0.000 .5171462 .5505914
lnLab .1882965 .0123227 15.28 0.000 .1641227 .2124703
lnExt .0858638 .0055798 15.39 0.000 .0749178 .0968099
lnCap .0644981 .0095362 6.76 0.000 .0457906 .0832056
lnOth .1056842 .0075993 13.91 0.000 .0907763 .1205921
cons 1.657035 .0717926 23.08 0.000 1.516196 1.797873
F test that all ui = 0: F(236;1338) = 58:82 Prob > F = 0:0000
0
5
1
0
1
5
D
e
n
s
i
t
y
.2 .4 .6 .8 1
Technical Efficiencies, Full Sample
0
5
1
0
1
5
2
0
D
e
n
s
i
t
y
.2 .4 .6 .8 1
Technical Efficiencies, Full Sample
Figure 3: Histogram and Kernel density estimate for technical e±ciency produced using equation (4)

and Allocative E±ciencies in U.S. Banking: An Empirical Investigation. &quot;

Density Estimation: for Statistics and Data Analysis,

Production Frontiers and Panel Data &quot;

Stochastic Frontier Analysis,

Technological Ine±ciency and the Skewness of the Error Component in Stochastic Frontier Analysis. &quot;

The potential determinants of German firms' technical efficiency: An application using industry level data

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The potential determinants of German firms' technical efficiency: An application using industry level data

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