This paper proposes an iterative procedure for testing periods of technical progress and periods of technical regress. We apply this methodology to the French food industry.productivity, efficiency, technical change, food industry, Productivity Analysis,

Bontemps, Christophe

Nauges, Celine

Requillart, Vincent

Simioni, Michel

French

Research Papers in Economics

Technical Change vs Efﬁciency Change:
Performance of Food Industries over Time
Christophe Bontemps, Céline Nauges, Vincent Réquillart & Michel Simioni
Toulouse School of Economics (INRA-GREMAQ, INRA-LERNA), France
Introduction
Question: What are the respective contributions of technical change and efﬁciency change in the
evolution of the TFP of an industry ?
Usual approach:
1. Specifying a distance function: Do(x;y) = minfj (x;y=) 2 Production setg
with x 2 R
p
+ (inputs), and y 2 R
q
+ (outputs)
2. Computing Malmquist indices to assess the relative weights of efﬁciency change and technical
change in productivity growth from the base period b to the current period c.
3. Implementing the two previous steps using DEA scores.
Problem: Deﬁnition of the production set of the current period ?
This procedure is generally implemented using the following production sets:
1. Contemporaneous production set:
TCon
c =
(
(x;y)j y 
X
i
zicYic; x 
X
i
zicXic; all zic  0
)
2. Using sequential production set à la Diewert (1980):
TSeq
c =
(
(x;y)j y 
c X
=b
X
i
ziYi; x 
c X
=b
X
i
ziXi; all zi  0
)
3. Implementing window DEA:
TWin
c =
(
(x;y)j y 
c+w X
=c w
X
i
ziYi; x 
c+w X
=c w
X
i
ziXi; all zi  0
)
Limits:
1. Contemporaneous: Generally, b and c consecutive periods
2. Sequential: Implicit assumption of technical progress
3. Window DEA: Ambiguous treatment of technical change (c   w  b  c + w ?).
Aim of the paper: To propose an iterative procedure for testing periods of technical progress and
periods of technical regress.
Related literature:
1. Tulkens, H. and P. Vanden Eeckaut (1995) ! General discussion on technical progress/regress.
2. O’Donnell et al. (2009) ! Metafrontier analysis
Methodology
Testing procedure: Based on an iterative procedure, i.e. for t = 0;:::;T where T  c   b,
(a) Compute the efﬁciency scores of ﬁrms present the current year c using
(b) The Forward Increasing Production Set:
TFIPS
c =
(
(x;y)j y 
b+t X
=b
X
i
ziYi; x 
b+t X
=b
X
i
ziXi; all zi  0
)
(c) Or the Backward Increasing Production Set
TBIPS
c =
(
(x;y)j y 
c X
=c t
X
i
ziYi; x 
c X
=c t
X
i
ziXi; all zi  0
)
(d) Test the equality of each pair of two consecutive efﬁciency distributions.
(e) If equality rejected ! Detection of technical regress or progress.
(f) Regress or progress ? : see the following example.
Howtoidentify“technicalregress”? Asimulationexercise.
Generation of a dataset of N = 100 ﬁrms with one input and one output for 3 different years using:
yt = x0:5  expf 0:25  (t   1)g=(1 + ut)
with xt  U[0;1] and ut  N +(0:2;0:25) as illustrated in Figure 1.
Figure 1 : Simulating technical regress over time
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Firms Year 3
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Figure 2 : Forward Increasing Production Sets (FIPS) and DEA frontiers
in the case of technical regress.
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Pooling Firms Year 1
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Pooling Firms Year 1, Year 2 & Year 3
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Figure 3 : Backward Increasing Production Sets (BIPS) and DEA frontiers
in the case of technical regress.
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Firms Year 3, Year 2 & Year 1
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Selected Paper prepared for presentation at the Agricultural & Applied Economics Association 2010 Joint Annual Meeting, Denver, Colorado, July 25-27, 2010
Figures2and3illustrateshowthemethodologyworks. Eachﬁgureprovidesthesampleofobservation
used in order to estimate the production frontier and its DEA estimates. These estimates do not shift
when using FIPS while they shift up with BIPS.
Figure 4 reports the efﬁciency distributions. With the FIPS (Figure 4b), the efﬁciency scores do not
change with the pooling, while with the BIPS (Figure 4c) the efﬁciency scores decrease when pooling
backward annual observations. This pattern clearly reveals the presence of technical regress over the
3 years. The same simulation exercice, but with technical progress, emphasizes a symmetric pattern
of FIPS and BIPS efﬁciency distributions.
Figure 4 : Distribution of DEA based efﬁciency scores :
(a) of ﬁrms each year (b) of ﬁrms in Year 3 (c) of ﬁrms in Year 3
on their contaporaneous frontiers on FIPS frontiers on BIPS frontiers
0.4 0.5 0.6 0.7 0.8 0.9 1.0
Scores distribution of firms on their own frontiers
Y
e
a
r
s
Year 1
Year 2
Year 3
0.3 0.4 0.5 0.6
Scores of Year 3 firms relative to FIPS
Y
e
a
r
s
Year 3 on Frontier(Year1)
Year 3 on Frontier(Year1+Year2)
Year 3 on Frontier(Year1+Year2+Year3)
0.2 0.4 0.6 0.8 1.0
Scores of Year 3 firms relative to BIPS
Y
e
a
r
s
Year 3 on Frontier(Year3)
Year 3 on Frontier(Year3+Year2)
Year 3 on Frontier(Year3+Year2+Year1)
Application to French Food Industries (1996-2006)
Data
We use data from an accounting survey (Enquête Annuelle d’Entreprise) which provides the following
information at the ﬁrm level: Production in value (Y), Stock of Capital (K), Labor (L) both in volume
(number of employees) and value, and Materials expenditures (M) in value. We use annual data
over the 1996-2006 period. Firms are classiﬁed with respect to their main production, using a 4-digit
classiﬁcationlevel(41foodindustries). Valuesareconvertedinvolumeusingappropriatepriceindices
obtained from the French National Statistical Institute. We consider the value of production excluding
trade activities. Materials expenditures are net of stock variation. Finally, the stock of capital is
estimated at constant prices rather than historical prices. In this paper, we select two food industries
(chicken meat industry and cheese industry) based on the number of ﬁrms (about 200 ﬁrms in each
industry) and their economic importance (respectively 5 and 8% of total food industry production).
Results
We perform FIPS and BIPS computation using data on cheese and chicken meat industries over the
period [1996, 2006]. We then estimate DEA frontiers on these production sets and compute the efﬁ-
ciency scores of 2006 ﬁrms data relative to those frontiers (Figure 5 and 6).
Figure 5 : Distribution of DEA based efﬁciency scores for the Cheese industry :
a) Firms in 2006 on FIPS frontiers b) Firms in 2006 on BIPS frontiers
.6 .7 .8 .9 1 1.1
189 firms in 2006
secteur 155C: Fabrication de fromages
Efficiency of Firms in 2006
when computed on FIPS Frontiers
(Outside values graphed out)
FIPS1996
FIPS1997
FIPS1998
FIPS1999
FIPS2000
FIPS2001
FIPS2002
FIPS2003
FIPS2004
FIPS2005
FIPS2006
.6 .7 .8 .9 1
189 firms in 2006
secteur 155C: Fabrication de fromages
Efficiency of Firms in 2006
when computed on BIPS Frontiers
(Outside values graphed out)
BIPS1996
BIPS1997
BIPS1998
BIPS1999
BIPS2000
BIPS2001
BIPS2002
BIPS2003
BIPS2004
BIPS2005
BIPS2006
Figure 6 : Distribution of DEA based efﬁciency scores for the Chicken Meat Industry :
a) Firms in 2006 on FIPS frontiers b) Firms in 2006 on BIPS frontiers
.2 .4 .6 .8 1 1.2
151 firms in 2006
secteur 151C: Production de viandes de volailles
Efficiency of Firms in 2006
when computed on FIPS Frontiers
(Outside values graphed out)
FIPS1996
FIPS1997
FIPS1998
FIPS1999
FIPS2000
FIPS2001
FIPS2002
FIPS2003
FIPS2004
FIPS2005
FIPS2006
.2 .4 .6 .8 1
151 firms in 2006
secteur 151C: Production de viandes de volailles
Efficiency of Firms in 2006
when computed on BIPS Frontiers
(Outside values graphed out)
BIPS1996
BIPS1997
BIPS1998
BIPS1999
BIPS2000
BIPS2001
BIPS2002
BIPS2003
BIPS2004
BIPS2005
BIPS2006
Results from the visual inspection of the evolution of efﬁciency score distribution can be conﬁrmed
using tests of equality of densities (Li, Maasoumi & Racine, 2009).
Table 1 : Test of equality of consecutive efﬁciency distribution distribution (Chicken meat)
FIPS BIPS
Null Hypothesis Test (Tn Value) Null Hypothesis Test (Tn Value)
... ... ... ...
H0 : F
2001 = F
2000 Not Rejected (-0.581) H0 : B
2002 = B
2001 Not Rejected (-2.105)
H0 : F
2002 = F
2001 Not Rejected (-0.403) H0 : B
2002 = B
2001 Not Rejected (-2.435)
H0 : F
2003 = F
2002 Reject (4.838 ) H0 : B
2003 = 2002 Not Rejected (-2.235)
H0 : F
2004 = F
2003 Not Rejected -3.022) H0 : B
2004 = B
2003 Reject (14.161)
H0 : F
2005 = F
2004 Not Rejected (-1.166) H0 : B
2005 = B
2004 Reject (9.027)
H0 : F
2006 = F
2005 Not Rejected (-3.225) H0 : B
2006 = B
2005 Reject (5.12)
Conclusion
The distributions show that the cheese industry seemed to have experienced technical regress over the
whole period (Figure 5). Thus, the distribution of efﬁciency scores under the FIPS procedure does not
signiﬁcantly change over the period while it changes when using the BIPS procedure. On the chicken
meat industry, we observe a period of technical progress from 1996 to 2002 and technical regress from
2003 to 2006 (Figure 6). The consecutive distribution tests performed on the FIPS and BIPS for the
Chicken meat industry (Table 1) conﬁrm a clear-cut technical regress pattern on the period [2003-
2006]. Technical regress might be a consequence of higher constraints exerted on the industry such as
environmental or sanitary constraints that might have increased the cost of production over time.

Technical Change vs Efficiency Change: Performance of Food Industries over Time

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