Productivity differentials and firm strategy in Italian manufacturing:
some evidence
Enrico Tundis
Graduate School of Social Sciences, University of Trento
Enrico Zaninotto
Department of Computer and Management Sciences, Univerity of Trento
Preliminary draft
June 1, 2012
Abstract
This paper studies the dynamics of the productivity of a sample of Italian manufacturing
firms over the period 1996-2006. The breakdown of productivity growth into a
technlogical and an efficiency component permits to gauge clearer evidence of the
increasing dispersion of firm performance over time, with some firms that achieve
technological advances and move the best-practices frontier, and other firms that
apparently seem to not move from their positions and get further away from the frontier.
Moreover, the analysis suggests how observed productivity heterogeneity may be
eventually related to different firm strategies, mostly associated to different
management of workforce. The first evidence put forward reinforces the idea of a
dualism between two groups of firms that compete either through innovation or cost,
particularly labour cost.
1. Introduction
Earlier studies on the economic slowdown that has characterized Italy since mid nineties
gave a pessimistic view about the future of the Italian productive system. In the face of
new challenges, manufacturing and perhaps the entire economy seemed inert and to
move towards its decline (see Faini, 2004 and Onida, 2004 among others). Recent
studies, however, suggest a more complex picture.
The competitive environment faced by Italian manufacturing has changed
radically since the mid nineties due principally to the emergence of countries with low
labour cost (especially China) and to the process of European integration, culminating
with the introduction of the euro (Brandolini and Bugamelli, 2009). One hypothesis put
forward is that the adoption of the euro, by eliminating competitive devaluation often
used in the past, has had a profound impact on the Italian productive system populated
by firms with very different characteristics, independently on the geographical location
and sectoral specialization. These heterogeneous firms would react in different ways to
external to the firm changes: some firms were able to face the new “competitive game”,
while others went through a low growth path. In this regard, Dosi et al. (2011) suggest
“Turbulence underneath the big calm”. By analyzing a sample of over 100,000 firms in
all economic sectors, they found an increase of the dispersion of labor productivity
between 1989 and 2004, giving rise to a kind of neo-dualism among firms. Bugamelli,
Schivardi and Zizza (2010) reach similar conclusions. Looking at labour productivity as
indicator of firm restructuring they argue that the euro adoption would not affect so
much the reallocation of firms across sectors, but had principally a within firm effect,
forcing firms to internal changes. Boeri and Garibaldi (2007) argue instead that the
origin of the decline in labour productivity and the increase of its dispersion is relate to
the labor reforms and the establishment of a stratified model of labour market, with a
rigid and a flexible component.
This study fits in with this strand of research with two contributions. First, the
study looks at total factor productivtity instead of labour productivity. Specifically, by
using the Malmquist index and its decomposition it considers productivity dynamics as
stemming from two different mechanisms: how much closer or farther away firms gets
to the best-practice frontier and the extent to which the best-practice firms are changing
(improving or deteriorating) their positions in the input-output space over time,
allowing a comparison among the evaluated firms. The results that emerge give further
confirmation of the underlying heterogeneity of firm behaviour. In particular, the first
part of the study shows a discontinuity of behaviors after the adoption ot the euro,
highlighting the gap between firms that contribute to technological advancement, and
firms that worsen their performance and move away from the frontier.
Moreover, after classifying firms into categories based on their productivity
dynamics, the second part of the study explores the relationship between firm belonging
to one category and a set of firm characteristics, in particular the cost and composition
of workforce, and financial constraints. Firms belonging to less dynamic group, i.e.
those firms characterized by slower productivity growth, appear to use labour of lesser
quality and draw from flexible labor market more extensively then other firms.
Although preliminary, the results are consistent with the idea that some firms have
taken advantage of the emergence of two tier labour market (Boeri and Garibaldi,
2007).
The paper is organized as follows: section 2 presents the productivity estimation
strategy; section 3 decribes the database; section 4 presents the results emerging from
the analysis of productivity growth and its decomposition. Finally, section 5 tries to
isolate some factors that characterize different classes of performance.
2. Measuring and decomposing Total Factor Productivity
This paper uses a non-parametric approach in the frontier framework as estimation
strategy. Specifically, it is employed the DEA approach (Cooper et al, 1978; Banker et
al., 1984) since it shows some caracteristics that make this technique very appealing for
the analysis. First, DEA yields estimates of efficiency and an estimator of the
production frontier (Kneip et al., 1998, 2008; Simar and Wilson, 2008). Second, when
!rms are likely to employ different technologies, DEA estimates are among the most
robust (Van Biesebroeck, 2007). Besides, this technique does not make a priori
assumptions on the shape of frontier function and establishes a best-practice frontier
among the observed firms based on direct comparison process. Finally, in the DEA
framework it is possible to obtain measure of Total Factor Productivity change by
means of the Malmquist index (Fare et al., 1992, 1994). This index computes firm
productivity change over time directly from input and output data and allows
meaningful decompositions of productivity dynamics between a technological
2
component – related to best-practices frontier shift – and a component linked to
efficiency improvements – related to firms distance from the frontier.
In this frontier framework, the shape of the frontier and consequently the
estimated productivity depends on the choice of the production set. One possibility is to
employ contemporaneous frontiers, i.e., production sets are constructed at each point in
time from the observations at that time only. In this case, production sets can expand or
contract from one year to another and outward – technical progress – as well as inward
– technical regress – shift of the frontier can occur with respect to the base time period
considered. However, a single intertemporal production set by using the full dataset, or
a sequential frontier by using accumulate data until the baseline year (Tulkens and
Vanden Eeckaut, 1995) can be alternatively constructed. In both cases inward shift of
the frontier is not allowed.
As in the the original Malmquist TFP approach (Färe et al., 1992, 1994) and
the majority of Malmquist TFP application in the relevant literature (Heshmati, 2003),
this study employs the contemporaneous frontier approach allowing for upward as well
as inward shift of the frontier. Indeed, this choice is particularly useful since it allows to
observe how best-practices firms and firms below the frontier move with respect to each
other.
2.1. The Malmquist index
Consider a firm producing a vector of outputs, y ! "+M , from a vector of inputs,
x ! "+S . Assume a convex production possibility set with freely disposable inputs and
outputs. Then, the output distance function1 can be de!ned on the technology
T = {( x, y ) : x!can produce y} as (Shepard, 1970):
(
+
! y$
D ( x, y ) = inf )! > 0 : # x, & ' T ,
! *
" !%
-
(1)
This distance function is relative to each firm and can be interpreted as the potential
increase of output that can be achieved by the firm that uses a given amount of inputs.
In particular the scalar " # (0,1] identify the potential expansion of the output y such
that the production possibility ( x, y " ) lies on the efficient frontier T at time. Therefore
a firm will be efficient at time t (lay on the frontier) iff D ( x, y ) = 1 .
Since !
the production possibilities T in (1) is not known, it must be estimate it in
order to obtain estimates
of the distance. To overcome this issue, we use the Data
!
Envelopment Analysis estimator. The DEA production set assuming Constant Return to
Scale (CRS) (Cooper et al, 1978) can be described by:
N
N
%'
)'
T̂CRS = &( x, y ) : " ! j y jm ! ym ,!!m = 1,..., M;!" ! j x js ! xs ,!s = 1,..., S;! ! # $+N *
('
+'
j=1
j=1
(2)
and assuming Variable Return to Scale (VRS) by (Banker et al 1984):
1
An input-oriented distance function can be simmetrically defined. In this paper we present however only
the output-oriented case.
3
N
N
N
%'
)'
T̂VRS = &( x, y) : " ! j y jm ! ym ,!!m =1,..., M;!" ! j x js ! xs ,!s =1,..., S;!" ! j =1,!! # $+N * (3)
'(
'+
j=1
j=1
j=1
where in both cases T̂ is an estimate based on the observed data of the true production
set T. Consistent estimators of D ( x, y ) defined in (1) can then be obtained by
substituting the true, but unknown, production set T whit the estimator T̂ (Simar and
Wilson, 2008). As practical matter, estimates of D ( x, y ) , assuming CRS, can be
computed by solving a linear program. Specifically, the distance of a firm from the
empirical production frontier, is estimated by solving the following linear programming
model:
#N
'
p
k
%" " j y jm ! ! yim ,!!m = 1,..., M, %
% j=1
%
1
=
max
$
( p, k = t, t + *t
N
!
D̂pCRS ( x k , y k )
%
%
p
k
%" " j x js ! xis ,!!!!!!s = 1,..., S %
& j=1
)
(4)
where D̂pCRS ( x k , y k ) is the estimated distance of a firm at time k = t, t+!t from the CRS
frontier at time p = t, t+!t. Estimates of distance assuming VRS can be computed
(Banker et al., 1984):
#N
'
p
k
! ! yim
,!!m = 1,..., M, %
%" " j y jm
% j=1
%
%N
%
%
%
1
p
k
= max $" " j x js ! xis ,!!!!!!s = 1,..., S ( p, k = t, t + *t
VRS
!
D̂p ( x k , y k )
% j=1
%
%N
%
%" " j = 1
%
%& j=1
%)
(5)
For each firm, the Malmquist index represents productivity changes between two
period, t and t+!t. This index can be derived as the ratio of distances from the CRS
production frontier – composed by the best-practice in the observed set of firms – in
each period. The link between the calculated distances and TFP change is as follows:
Malmquistt = !TF̂Pt =
D̂tCRS ( x t+!t , y t+!t )
D̂tCRS ( x t , y t )
(6)
This is the ratio between the distance of the firm in period t+!t from the frontier in
period t and the distance in period t from the frontier in period t+!t. It is also possible to
define the Malmquist index with respect to the frontier at time t+!t as follow:
4
Malmquistt+!t = !TF̂Pt+!t =
CRS
D̂t+!t
( x t+!t , yt+!t )
(7)
CRS
D̂t+!t
(xt , yt )
Fare et al. (1994) defined a Malmquist index as geometric average between the two
indexes defined in (4) and in (5) as follows:
1
" D̂ CRS ( x , y ) D̂ CRS ( x , y ) %2
Malm = $ t CRS t+!t t+!t ! t+!tCRS t+!t t+!t '
D̂t+!t ( x t , y t ) '&
$# D̂t ( x t , y t )
(8)
The index can be decomposed as follows:
1
D̂ CRS ( x , y ) # D̂ CRS ( x , y ) D̂ CRS ( x , y ) &2
Malm = t+!tCRS t+!t t+!t " % tCRS t+!t t+!t ! tCRS t t (
D̂t ( x t , y t )
%$ D̂t+!t ( x t+!t , y t+!t ) D̂t+!t ( x t , y t ) ('
!!!!!!!!!!=!EffCh "!TeCh
(9)
where productivity change is splitted into two parts. The first part is the ratio of the
distances of a firm from the frontier at two different time and shows how much closer
(or farther away) a firm gets to the best-practice frontier. It will be higher (lower) than
unity if there has been an increase (decrease) in ef!ciency. The second part can be
considered as a proxy of the shifts in the empirical production frontier (i.e., the growth
rate of technological progress), from t to t+!t and points out to the extent to which the
best-practice firms are changing their performance (improving or deteriorating),
allowing a comparison to the evaluated firms.
Efficiency change (EffCh) can be further decomposed as follows (Fare et al.
1994):
VRS
CRS
D̂t+!t
x t+!t , y t+!t ) # D̂t+!t
x t+!t , y t+!t ) D̂tVRS ( x t , y t ) &
(
(
((
EffCh =
" %% VRS
! CRS
D̂tVRS ( x t , y t )
$ D̂t+!t ( x t+!t , y t+!t ) D̂t ( x t , y t ) '
!!!!!!!!!!!!!!!=!PEffCh " SEffCh
(10)
where PEffCh and SEffCh are measures of pure efficiency change – efficiency change
with respect to the VRS frontier – and change in scale efficiency, respectively. Values
higher (lower) than unity indicate an increase (decrease) of the related quantities.
While pure efficiency change and scale efficiency change are related to Variable
Return to Scale (VRS) frontiers movements between two different periods, TeCh
variation still refers only to Constant Returns to Scale (CRS) frontier shifts over time.
Wheelock and Wilson (1999) observed that if a generic firm in the input-output space
remains fixed between time t and t+!t, and the only change that happens is in the VRS
estimate of technology, the TeCh component, as measured in previous equations, will be
equal to unity indicating no change in technology – since the only way for TeCh to
change is if the CRS estimate of the technology changes. Such being the case, the CRS
estimate of the technology is then statistically inconsistent. Since the VRS estimator is
always consistent (Kneip et al., 1998), a further decomposition of Technological change
is proposed by introducing also VRS estimates:
5
1
" D̂VRS ( x , y ) D̂VRS ( x , y ) %2
TeCh = $ tVRS t+!t t+!t tVRS t t ' (
$# D̂t+!t ( x t+!t , y t+!t ) D̂t+!t ( x t , y t ) '&
1
" D̂CRS ( x , y ) D̂VRS ( x , y ) D̂CRS ( x , y ) D̂VRS ( x , y ) %2
t
t+!t
t+!t
t
t
t
' (11)
!!!!!!!!!!!!!!!!(!$ tCRS t+!t t+!t
! tCRS t t
VRS
VRS
$# D̂t+!t ( x t+!t , y t+!t ) D̂t+!t ( x t+!t , y t+!t ) D̂t+!t ( x t , y t ) D̂t+!t ( x t , y t ) '&
!!!!!!!!!!=!PTeCh ( STeCh
where TeCh is further decomposed into Pure Technical Changes – PTeCh – and Scale
Technical Changes, i.e. changes in the scale of technology – STeCh. The first
component is the geometric mean of two ratios that measure the shift in the VRS
frontier estimate relative to the firm’s position at times t and t+!t. When PTeCh is
greater than unity, it indicates an expansion in pure technology, i.e., an upward shift of
the VRS estimate of the technology. STeCh provides information regarding the shape of
the technology. It describes the change in returns to scale of the VRS technology
estimate at two fixed points, which are the firm’s locations at times t and t+!t. When
STeCh is greater than unity, this indicates that the technology is moving farther from
CRS and the technology is becoming more and more convex. On the contrary, when
this index is less than unity it suggests that the technology is moving toward CRS; the
index equal to unity suggests no changes.
Besides, different decomposition of technological change is possible. Technical
progress, in fact, can be independent or dependent on the change of the composition of
input used and/or output produced by the firms. Therefore, technical change component
can be rewritten as follows (Fare and Grosskopf, 1996):
1
# D̂CRS ( x , y ) D̂CRS ( x , y ) &2
t+!t
t
( "
TeCh = CRS
" % tCRS t+!t t+!t t+!t
CRS
D̂t+!t ( x t+!t , y t+!t ) %$ D̂t+!t ( x t+!t , y t+!t ) D̂t ( x t+!t , y t ) ('
D̂tCRS ( x t , y t )
1
# D̂CRS ( x , y ) D̂CRS ( x , y ) &2
t
t
t
t+!t
t
(
!!!!!!!!!!!!!!!!"!% t+!t
CRS
CRS
%$ D̂t ( x t , y t ) D̂t+!t ( x t+!t , y t ) ('
!!!!!!!!!!=!MaTeCh " ObTeCh " IbTeCh
(12)
MaTeCh (Magnitude Tchnical Change) is related to Hicks-neutral technical change. If
the magnitude effect is greater (lower) than unity, it means that output of the same
composition but greater (lower) in terms of volume is obtained with the same input mix.
IbTeCh (Input Biased Technical Change) refers to a non-neutral shift in the bestpractice production frontier due to different input mix, while ObTeCh (Output Biased
Technical Change) refers to a non-neutral shift in the best-practice production frontier
due to different output mix. Values of ObTeCh (or IbTeCh) greater than unity indicate
that the biased technical change amplifies the TFP growth, and values of ObTeCh (or
IbTeCh) less than one signify that the biased technical change shrinks the TFP growth.
6
3. Data and descriptive analysis
The primary source of the data is the Bureau Van Dijk’s AIDA database, which
provides detailed information on the financials, geographical localization, number of
employees and local units for a large sample of limited liability Italian firms. From the
original collection of data it was selected a sub-sample of single-location manufacturing
firms, which were continuously active during the period 1996-2006. Since the original
employment figures were missing for several firms, data were supplemented with
information on workforce from the National Institute of Social Security (INPS). From
this additional source it is obtained the yearly average number of employees for all
firms in the sample. Moreover the data allow to decompose workforce into white and
blue collars as well as between full and part-time contracts for the eleven years covered
in this analysis.
In the end, the empirical analysis exploits an original dataset containing
information on 7,712 (84.832 observation) Italian manufacturing firms over the period
1996-2006. The database represents a unique collection of data for Italy and allows to
deepen the understanding of the dynamics of incumbent firms on a relatively long
period of time. Moreover, by dealing with single-location firms it allows to work at a
level of analysis that is as close as possible to the single establishment level.
Furthermore, focusing on single-location firms, changes such as mergers, acquisitions
and divestitures affect only marginally the group of firms in the sample. Besides, it is
neutralized the spurious effect stemming from the intra-group reallocation of equipment
and personnel.
The industry distribution of our data set generally reflects the distribution of
firms descripted by the ISTAT “8° Censimento Industria e Servizi” in 2001 – the mid
point in the observation period (See Table A1 in Appendix A).
3.1. Input and output variables
Input and output variables are constructed from balance sheet data, with the exception
of data on labour. The raw data were correct and deflated in order to obtain real values.
In this study we have used sectoral deflators constructed by using ISTAT data.
Output is measured by the amount of revenues from sales and services at the end
of the year, net of inventory changes and changes to contract work in progress; labor
input is measured as the total number of employees at the end of the year. Two
intermediate inputs are considered: (a) costs of raw materials consumed and goods for
resale (net of changes in inventories) and (b) cost of services; capital stock estimate in a
given year is proxied by applying a modified perpetual inventory method on nominal
value of tangible !xed assets over the period analysed (See Appendix C for further
details on the estimation procedure).
All monetary measures are expressed in thousands of euros and have been
de"ated by the proper industry level index. The deflator for the turnover variable was
constructed by processing the time series of national production. The deflator for
intermediate inputs is constructed using a weighted deflators of production, with
weights calculated as the average of the column coefficients of input/output matrix for
the year 2001 of a set of Italian regions.
Table A2 in appendix A shows descriptive statistics on the variables of input and
output for 2006, the final year of observation in our data set.
7
3.2. Outliers treatment
Several authors addressed the problem of the presence of outliers in nonparametric
efficiency estimation (Wilson, 1993, 1995; Simar, 2003; Banker and Chang, 2006). In
fact, DEA produces efficiency scores by comparing the input/output combination of
each firm with respect to a piecewise linear frontier obtained as convex combinations of
the best performing firms in the set. This implies that measurement errors for those
observations defining the frontier could cause distortions in the measured efficiency for
the entire population.
In order to detect outliers, we carried a !rst analysis to check the impact of each
single observation on the distances of the nearest !rms – whose distance depended from
that particular observation – using a method based on the concept of leverage, that is the
effect produced on the efficiencies of all the other firms when the observed firm is
removed from the dataset (Stosic and Sampaio de Souza, 2005). Afterwars,
observations with a wider impact on nearest !rms are discarded from the final
calculation (see Appendix B for detail on outlier detection procedure).
4. The dynamics of productivity
The distances from the estimated industry frontier at 2-digit level are calculated for each
firm and combined to construct and decompose Malmquist indexes. Specifically, we
calculate annual growth rate of quantities of interest for each firm and afterwards we
take weighted average of annual growth rates for each industry, rather than estimates
related to individual firm, accounting for the relative importance of each observation
whose productivity index is entering into the average (Zelenyuk, 2006).
As first exercise, we compare the annual gowth rates of productivity among
industries for the entire period 1996-2006 (Table 1). Some observations are immediate.
Productivity, with the exception of few industries such as Machinery equipment and
Electronics, shows annual growth rates below 1% everywere. In the majority of
industries, the annual growth rate is less than 0.5% and in some industries is even
negative. Furthermore, the two components – efficiency change and technological
change – behave differently in determining productivity trends (Table A4 in the
appendix A). There are industries, such as Textile and Wearing, Leather, Metal
products, and Electronics, where, on average, technology improves and efficiency
declines, while there are others, such as Paper and Chemical industry, where the
opposite occurs. Finally there are industries in which both components show positive
sign, as in the Machinery and Transportation equipments. Then, the whole period is
splitted into three subperiods: 1996-2000, 2000-2003, 2003-2006. This breakdown
allows to capture three different phases: the entrance into the euro area (1999), the
negative cycle centered on 2001, and the period before the current crisis, respectively.
Two facts emerge. First, productivity shows a negative trend in all industries in the
first period (Table 1). On the contrary, the central and final periods show a general
increase of productivity. Second, the sign of the two components of productivity growth
changes radically among subperiods (Figure 1).
8
Table 1. Malmquist index and its decomposition into Efficiency Change (EffCh) and
Technological change (TeCh). Entire period and subperiods.
Industry
Food and beverages
Textile and wearing
Leather
Wood
Paper and printing
Petroleum
Chemical
Rubber and plastic mat.
Non-met. mineral prod.
Fabricated metal prod.
Machinery and equipment
Electronics
Tansportation equipment
Other manufacturing
Subperiod
1996-2006
1.069
0.353
-0.004
0.268
0.090
-1.004
-0.032
0.490
0.068
0.273
1.019
1.224
0.558
0.196
1996-2000
2000-2003
2003-2006
-0.849
-0.355
-1.001
-0.068
-1.579
-4.327
-1.223
0.041
-0.702
-0.218
-0.510
0.500
-1.010
-0.628
1.624
0.823
0.860
0.975
1.908
8.473
1.794
1.738
0.391
1.239
0.767
1.200
0.523
0.055
6.992
1.007
1.295
0.479
0.765
-4.522
-0.164
0.050
1.144
0.346
3.544
2.652
2.631
1.649
In the first subperiod, uniformly in all sectors, there is a sort of “technological
regression” (negative sign of TeCh). The downward frontier shift is however partly
offset by efficiency gains. We interpret this evidence as a general inability of bestpractices firms to reach at the end of the period the best production combinations
formerly obtained. Moreover, this could be indicative of the pervasive difficulty of the
entire productive system associated to increased competitive pressure arising from the
introduction of the euro. Under these circumstances, firms seek a recovery of
competitiveness in terms of efficiency, being on average closer to the frontier.
Shifting the focus to the other subperiods, productivity grows in all industries
driven primarily by technological advancement – indicated by the outward shift of the
frontier that in some cases is strengthened by improved efficiency – during the second
subperiod2. Clearer is the trend that occurs in subperiod 2003-2006, the exit from the
2001 crisis, where technological change keeps on to be positive while everage
efficiency decreases. This evidence suggests a process of technological advancement
that involves only part of the observed firms, principally those closer to the frontier,
while part of firms lags behind. Figure 2 clarifies this dynamic plotting the evolution of
the probability density of estimated efficiencies, i.e. distances from the frontier, in the
particular case of Electronics industry in the first and last subperiods respectively. At
the end of the first subperiod (year 2000) efficiency distribution has shifted to the right
indicating a generalized increase of average efficiency. The evolution changes
drastically in the second subperiod (2003-2006), in which the leftward shift of the
distribution indicates a widespread loss of efficiency for many firms.
2
The coincidence with the cycle should be considered with caution, given the particular sensitivity of
observations to start and end points of the cycle.
9
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5
Figure 1. Technological Change (TeCh) and Efficiency Change
(EffCh). Subperiods: 1996-2000 and 2003-2006.
2006
3
Density
2
1
0
0
1
2
Density
3
4
2003
2000
4
1996
0.5
0.6
0.7
0.8
Efficiency
0.9
1.0
0.5
0.6
0.7
0.8
Efficiency
0.9
1.0
Figure 2. Kernel density estimation of efficiency in the Electronics industry.
Our results are in line with other studies. Aiello, Pupo and Ricotta (2009) found
increases of productivity starting from 2003, after the fall occurred between 1996 and
2003. Moreover, after the introduction of the euro, there is evidence of a profound
process of firm restructuring in the Italian manufacturing in terms of technological
content, quality, etc. (Rossi, 2006; Brandolini and Bugamelli, 2009; Bugamelli,
Schivardi and Zizza, 2010; De Nardis, 2010) that support the evidence of an increase of
productivity dispersion. An increase of labour productivity dispersion of firms is also
recognized in Dosi et al. (2011) mostly before 2000.
The estimation strategy employed enables to deepen the analysis by isolating the
effect of scale and input composition on productivity change. The evidence is that
10
increases of efficiency in the first subperiod have occurred simultaneously through a
reduction of pure inefficiencies and a recovery of scale (Table A5 in the appendix A).
Conversely, similar trends are not so clear and pervasive afterwards. This gives
additional evidence of two different stories between what took place at the beginning of
the observed period and what happened subsequently. The evolution of average size of
firms further support this idea. The average number of employees increased between
1996 and 2000, again substantially in all sectors, but subsequently stabilized (Table A6
in the appendix A). The average size expressed in terms of nominal turnover follows the
same pattern, although less evident, till 2003 and then grows in the last period.
Looking at the best-practices frontier, it is evident how in the first period the two
components – pure and scale technological change – determine the downward shift of
best-practices frontier in different manner depending on the industry, while in the last
subperiod a general upward shift of the frontier pravails (Table A7 in the appendix A).
At the same time, frontier generally tends to modify its shape with a movement towards
the constant return to scale (negative sign of growth rate of STeCh). Further insighs
come from the analysis of the nature of technological progress (table A8 in the appendix
A). The apparent technological regression observed during the first subperiod is
principally due to Hicks-neutral shift. This fact reinforces the idea that the downward
shift of the frontier is the effect of a general reduction of the use of production factors
due to a crisis of competitiveness. On the contrary, the outward shift of the frontier in
subsequent periods is both Hicks-neutral and input biased. A plausible interpretation of
this evidence is that during the years around the crisis of 2001 some firms have
undertaken a process of restructuring with gains of competitiveness and better use of
production factors. It would be also the effect of an increased production flexibility due
to the introduction of ICT.
5. Productivity and firm strategy
The evidence put forward above suggests a generalized attempt to reduce inefficiency as
first reaction of firms to increased competition. Afterwards, some firms significantly
have changed their structure in terms of inputs used and that have gone through new
technological paths. Technological advances, however, has not been uniform among
firms. In fact, part of firms apparently seem to not move from their positions and get
further away from the frontier.
This section explores the hypothesis that firms have implemented different
strategies to cope with increased competition. If it would be the case the observed
increasing productivity dispersion could be related to the different modes of adaptation
to the new economic conditions that firms followed. The underlying idea is that firms
seek to adopt differet strategies to gain production flexibility to cope with external
changes, drawing in different ways on labour market with different effect on
performance (Michie and Sheehan, 2001, 2003; Arvanitis, 2005; Kleinknecht et al.,
2006).
Two main kinds of organizational flexibility firm can achieve. First, functional
or internal flexibility, that is the ability to redeploy workers from one task to another,
which require higher skills. Second, numerical or external flexibility, that is the ability
to adjust the size of its workforce to fluctuations in demand by using workers who are
not their regular, full-time employees. In fact, part of observed firms would have chosen
11
a cost-cutting strategy – a “low road” – putting, for instance, employees onto short-term
contracts and/or part-time working, and accepting less skilled labour as solution to cope
with the new competitive environment. In contrast, more dynamic firms would have
chosen higher skilled labour to achieve a quality or value added advantage over
competitors – they would go through the “high road”. Here, the interest is mainly in
highliting some characteristics that may distinguish different “classes” of firms
performance.
To set off the analysis it seems usefull to create meaningful categories of
performance. For this purpose, estimated productivity and efficiency so far illustrated,
are used in a descriptive sense, that is as an indicators of a “residual” due to not
observed factors. This residual can be explained both by esternal condition – industry
affiliation, different access to external inputs due to location factors, etc. – and factors
such as firms’ characterisitcs and different use of inputs – e.g., different factor costs if
firms have access to input markets with different cost or quality. Then, firms are
grouped, for each of the three periods, with respect to the industry average value of two
variables: the level of efficiency at the beginning of each period and the dynamics of
productivity observed in the same period. Figure 3 presents the obtained classifications.
Productivity change t+!t
Efficiency level t
Low
High
Low
High
Laggards (1)
Static Leader (2)
N. obs:
Period1 = 1439
Period2 = 1572
Period3 = 1693
Climbers (3)
N. obs.:
Period1 = 2468
Period2 = 2242
Period3 = 2090
N. obs.:
Period1 = 2193
Period2 = 2303
Period3 = 2275
Dynamic leader (4)
N. obs.:
Period1 = 1247
Period2 = 1230
Period3 = 1289
Figure 3. Firms categories
The dynamic leaders are firms closer to the technological frontier at the beginning of the
period, which improve their productivity mainly through innovative strategies rather
than efficiency improvements. The static leaders are firms close to the frontier, but with
low productivity growth and therefore that tend, over time, to move away from the
frontier. The climbers are firms with low initial efficiency, but that move rapidly
towards the frontier and sometimes induce its shift. Productivity growth for these firms
may be particularly fast as they can act on two factors: efficiency gains related to
imitative processes and independent technological advancements. Finally the laggards
are firms with low initial efficiency and low productivity growth, which nevertheless
continue to be observed in the market throughout the period.
A multinomial logit regression model is estimated in order to isolate some
significant relatioships between a set of explanatory variales and the category:
12
" 4
%
P ( y = j | x ) = exp ( x!k ) $1+ ! exp ( x! j )'
$# j=2
'&
(13)
j = 2, 3, 4 rapresent the categories defined and x represents explanatory variables and
controls. Obviously, for the reference category (1) we have:
4
"
%
P ( y = 1| x ) = 1! $1+ ! exp ( x! j )'
$# j=2
'&
(14)
Two groups of variables are considered. The first group relates to the composition of the
workforce and it contains a measure of unit labor cost (labour cost), the ratio between
white and blue collars (skill ratio), and the share of part-time contracts on total
employment (partime). The other variable is related to financial constraints (cash flow).
We also considered the size – log of employees – and age – log of age – of firms. Table
2a,b shows mean and standard deviation and correlation matrix of the explanatory
variables.
Table 2a. Descriptive statistics
Variable
Labour cost
skill_ratio
partime
cash flow
size
age
Laggards
Avg
20.7
0.46
0.043
393.0
54.5
22.5
Std
5.2
1.42
0.060
723.0
52.9
12.4
Static leader
Avg
23.8
0.66
0.037
649.8
47.5
21.7
Std
7.4
2.53
0.053
1246.6
52.8
13.2
Climbers
Avg
20.0
0.47
0.041
327.7
53.0
21.1
Dyn. leaders
Std
5.6
1.28
0.058
576.6
49.6
12.4
Avg
23.8
0.88
0.039
564.3
44.0
20.9
Std
7.5
3.51
0.056
1151.8
46.6
12.7
Table 2b. Correlation matrix
Correlation matrix
Variable
Labour cost
skill_ratio
partime
cash flow
size
age
Labour cost
1
0.167*
-0.141*
0.225*
0.147*
0.256*
skill_ratio
partime
cash flow
size
age
1
0.034*
0.078*
-0.009
0.007
1
-0.075*
-0.065*
0.038*
1
0.597*
0.092*
1
0.158
1
* significativity 5%
Table 3 presents the estimated model using different sets of explanatory variables. The
estimates refer to the log-odds ratio, i.e. the logarithm of the ratio of the probability of
being in the category j over the probability of being in the baseline category. All models
control for financial constraints, firm size, firms age, and include dummy variables to
take into account periods, industry and the geographic area effects. Models differ
13
essentially for the introduction of control variables that allow refining the assumptions
about the cost of labor.
Model 1 takes into account only the unit cost of labor. It should be noted,
however, that different labor cost may represent either different quality of labour
employed, or, in the presence of a segmented labor market, may result from labour of
the same quality but at a lower price. This hypothesis is consistent with the idea of twotier labor market (Boeri and Garibaldi, 2007). But, while in the former case the
omission of an unobservable factor – the use of a single quality instead of two quality of
labour force – can result in production inefficiency due to the use of labour of lower
quality, in the latter case should imply only allocative inefficiency if firms do not adjust
the composition of production factors, and then should affect only what part of the bestpractices frontier will be refence for each firm.
In order to gain clearer interpretation of the results, Models 2 and 3 introduce,
respectively, the ratio of white over blue collars that approximates the importance of
upstream and downstream activities (Bugamelli et al., 2010), and the ratio of part-time
contracts over total employees, which can be considered a measure of the use of flexible
labor market (Arvanitis, 2005). Finally, in Model 4 introduces an interaction term
between labor costs and times.
As it can be seen in all models (Table 3), with reference to the probability of
being a laggard, cash flow is positively associated with an increased probability of
being leaders and reduces the probability of being a climber. Then the leaders will take
advantage of less restrictive financial conditions, regardless of their productivity
dynamics. However, the effect of cash flow, although statistically significant, is very
low. The unit cost of labor acts in the same direction in all models: a higher cost of
labor is associated to higher probability of being into the groups of firms close to the
frontier (leaders) with respect to laggards. The effect is quite significant in terms of
variation. The ratio of white over blue collars in Model 2 appears to act in the expected
direction, and is particularly significant in explaining the probability of belonging to the
group of dynamic leaders. The effect of this variable still persist in Model 3, after
introducing the share of part-time contracts over the total number of employees. This
latter variable reduces the probability of belonging into each of the categories with
respect to laggards. The group of inefficient firms that do not increase productivity
seem therefore to use more extensively labour flexibility. Finally, it should be pointed
out that size significantly reduces the probability of being a leaders and reduces the
probability of belonging to each of the different classes with respect to the laggards (but
in terms of marginal effects, the effects of age are negative, once again, only for
leaders).
14
Table 3. Multinomial logit estimates (log-odds ratios) . Reference category: Laggar
Model 1
Variables
labour cost
skill ratio
Static leaders
Climbers
Model 2
Dyn. leaders
0.11806*** -0.02078*** 0.12209***
(0.004)
(0.004)
(0.004)
!
!
!
Static leaders
Climbers
Model 3
Dyn. leaders
0.11806*** -0.02283*** 0.11913***
(0.004)
(0.004)
(0.005)
0.03292*
0.02984
0.05720***
(0.018)
(0.019)
(0.018)
!
!
!
partime
!
!
!
period 2 * labour cost
!
!
!
!
!
!
period 3 * labour cost
!
!
!
!
!
!
cash flow
age
size
Statistics
Osservazioni
Log-likelihood
McFadden's Adj R2
Nagelkerke R2
LR !2 (dgr of freed.)
estimates refer to log-odds ratio
Standard errors in parenthesys
*** p<0.01, ** p<0.05, * p<0.10
Dyn. leaders
Static leaders
Climbers
Dyn. leaders
0.11672*** -0.02403*** 0.11783***
(0.004)
(0.004)
(0.005)
0.03586*
0.03254*
0.06005***
(0.018)
(0.019)
(0.018)
-0.75662**
-0.65536*
-0.70499
(0.385)
(0.353)
(0.436)
!
!
!
0.12662***
(0.007)
0.03631*
(0.019)
-0.75431*
(0.385)
-0.01678*
(0.009)
-0.00976
(0.009)
0.00088***
(0.000)
-0.37407***
(0.037)
-0.96332***
(0.036)
0.00273
(0.007)
0.03374*
(0.019)
-0.71834**
(0.353)
-0.03858***
(0.009)
-0.04252***
(0.009)
-0.00030***
(0.000)
-0.14653***
(0.036)
0.13546***
(0.033)
0.13823***
(0.007)
0.06071***
(0.018)
-0.72638*
(0.437)
-0.03883***
(0.010)
-0.02247**
(0.010)
0.00084***
(0.000)
-0.44027***
(0.042)
-1.02293***
(0.040)
!
Climbers
!
!
0.00088*** -0.00031*** 0.00085***
(0.000)
(0.000)
(0.000)
-0.37521*** -0.14342*** -0.44413***
(0.037)
(0.036)
(0.041)
-0.96826*** 0.13308*** -1.03350***
(0.035)
(0.032)
(0.039)
0.00088*** -0.00030*** 0.00084***
(0.000)
(0.000)
(0.000)
-0.37386*** -0.13428*** -0.43571***
(0.037)
(0.036)
(0.042)
-0.95791*** 0.13997*** -1.01723***
(0.035)
(0.033)
(0.040)
0.00088*** -0.00030*** 0.00084***
(0.000)
(0.000)
(0.000)
-0.36909*** -0.12989*** -0.43112***
(0.037)
(0.036)
(0.042)
-0.96107*** 0.13753*** -1.02017***
(0.036)
(0.033)
(0.040)
yes
yes
yes
yes
yes
yes
yes
yes
yes
dummies periods
dummies industry
dummies location
constant
Static leaders
Model 4
2.12999***
(0.165)
0.87758***
(0.161)
21,258
-26569.454
0.076
0.207
4562.546 (66)
1.68603***
(0.186)
2.07361***
(0.167)
0.84948***
(0.163)
21,030
-26297.17
0.075
0.205
4474.089 (69)
1.64763***
(0.189)
2.13194***
(0.170)
0.89974***
(0.165)
21,030
-26294.682
0.075
0.205
4479.07 (72)
yes
yes
yes
1.70268***
(0.192)
1.96952***
(0.197)
0.42065**
(0.188)
21,030
-26274.224
0.075
0.207
4519.98 (78)
1.31008***
(0.221)
To get a better idea of the impact of explanatory variables on the probability of
belonging to a particular class, Table 4 presents, for Model 3 and 4, the marginal effects
of variables on the probability of belonging to each category.
Table 4. Marginal effects
Model 3
Variables
Model 4
Laggards
Static leaders
Climbers
Dyn. leaders
period 2 * labour cost
-0.0109***
(0.0006)
-0.00687**
(0.0030)
0.122**
(0.0542)
!
0.0209***
(0.0006)
0.00148
(0.0021)
-0.0640
(0.0658)
!
-0.0218***
(0.0007)
0.000424
(0.0024)
-0.0310
(0.0616)
!
0.0118***
(0.0004)
0.00497***
(0.0012)
-0.0265
(0.0514)
!
period 3 * labour cost
!
!
!
!
labour cost
skill ratio
partime
cash flow
age
size
dummies periods
dummies industry
dummies location
-7.23e-05*** 0.000172*** -0.000187*** 8.75e-05***
(6.39e-06)
(6.17e-06)
(8.01e-06)
(4.05e-06)
0.0502*** -0.0441*** 0.0289*** -0.0350***
(0.0054)
(0.0059)
(0.0058)
(0.0046)
0.0956***
-0.164***
0.169***
-0.101***
(0.0049)
(0.0057)
(0.0056)
(0.0043)
yes
yes
yes
Laggards
Static leaders
-0.0141*** 0.0195***
(0.0010)
(0.0010)
-0.00700**
0.00142
(0.0030)
(0.0021)
0.126**
-0.0566
(0.0542)
(0.0659)
0.00515***
0.00204
(0.0013)
(0.0013)
0.00430*** 0.00303**
(0.0013)
(0.00137
-7.26e-05*** 0.000172***
(6.38e-06)
(6.18e-06)
0.0520*** -0.0431***
(0.0055)
(0.0059)
0.0961***
-0.164***
(0.0049)
(0.0057)
Climbers
Dyn. leaders
-0.0181***
(0.0011)
0.000593
(0.0024)
-0.0432
(0.0617)
-0.00452***
(0.0014)
-0.00682***
(0.0015)
-0.000187***
(8.02e-06)
0.0264***
(0.0058)
0.169***
(0.0056)
0.0128***
(0.0007)
0.00498***
(0.0012)
-0.0265
(0.0515)
-0.00267***
(0.0010)
-0.000511
(0.0010)
8.79e-05***
(4.06e-06)
-0.0352***
(0.0046)
-0.101***
(0.0043)
yes
yes
yes
It is now clearer that the skill ratio affects mainly the extreme categories, with a
significant increase ot the probability of being a dynamic leaders and reduces the
probability of being a laggard. This aspect seems particularly significant in light of the
positive role that investment in upstream phases (e.g., design and product design) and
downstream (e.g., marketing and sales) seems to have on firms competitiveness
(Bugamelli et al. 2010). Moreover, it should be noted the sign of the interaction terms
between labour cost and periods (Model 4). The marginal effect of changes in labour
cost (Table 4), although negative in all periods, shows a different trend over time
regarding the effect on the probability of belonging to categories 1 and 3. In the first
case there is a trend towards a reduction of the negative impact while in the second case
there is an amplification of the negative effect. This seems to suggest that after the
phase of adaptation to the euro, climbers actually follow a pattern of reduction in unit
labour cost with respect to leaders.
In the end, it seems that laggard firms are on average characterized by higher age
and adopt a defensive strategy, using labour of lesser quality and drawing from flexible
labor market more extensively then other firms3. The climbers seem to use a mixture of
strategies to reach the frontier, based on the servitization strategy and the use of less
qualified labour. Leader firms, regardless of the dynamics of productivity, are younger,
smaller, use more skilled labor and tend to be more tertiarized.
3
This evidence is coherent with Lucidi and Kleinknecht (2009), who found that Italian manufacturing
!rms with a high share of "exible workers, lower costs of labour experienced signi!cantly lower rates of
labour productivity growth from 2001 to 2003.
The negative effect of firm size seems to be in constrast with a substantial
proportion of the literature that shows a positive relationship between size and
productivity. However, it is possible that in the periods examined, firms have
experienced a process of downsizing. Moreover, we have seen how, in the first period,
the increase in efficiency is also due to scale effects. As a consequence, it is likely that
attempts to gain efficiency through adjusting the scale of production, in terms of
number of employees, have hampered productivity improvement through the shift of the
frontier. This result is indeed coherent with Hall et al. 2008. In fact, by analysing a
panel of SMEs Italian manufacturing firm in the period 1995-2003, they found that
larger and older firms were less productive.
A final remark is necessary. Our exercise can only give some insights on the
strategic nature of the observed productivity heterogeneity. Although the explanatory
variables used are the level at the beginning of each period, concerns about endogeneity
(cash flow, in the first place) still remain. The evidence put forward should be
considered then only in a descriptive sense, nevertheless it suggests that the strategic
nature of the observed heterogeneity has a foundation and that different groups of firms
actually pursue differet strategy to adapt to new market conditions.
6. Conclusions
Earlier studies on the Italian economic slowdown pointed to a generalized failure of the
productive system to meet the challenges posed by the increasing globalization of
markets. The analysis presented in this work suggests however that behind this
generalized economic slowdown there could be high heterogeneity of firm behaviour.
The evidences we presented are consistent with that obtained in related studies
carried out with different methodologies. The approach we follow allows to isolate
more precisely the component of productivity growth due to technological change.
What emerges is evidence of a growing dualism. On the one hand some firms show
sustained positive productivity dynamics, but at the same time, there is evidence that
part of the system fails to keep pace with the group of innovators, with a consequent
efficiency loss. In the latter part of the work it is questioned whether this dynamic may
be related to different patterns of strategic adaptation.
The evidence reported reinforce the hypothesis that firms follow different paths
of adaptation and that different use of labour play decisive role in this process. Labour
market reforms implemented in Italy in the ‘90s have indeed dramatically reduced the
cost of use, and perhaps the quality, of newly hired workers. We hypothesized that part
of the productive system has taken advantage of the emergence of a dualistic labour
market. The availability of flexible labour, less expensive but also less skilled, has been
for some categories of firms an easy solution to face competition. In contrast, more
efficient and dynamic (dynamic leaders) firms have a higher unit cost of labour, are
more outsourced, use less flexible labour, are younger and smaller. It is nevertheless
difficult to assess the long run effectiveness of these different modes of adaptation. The
first evidence we have, however, encourages a more careful analysis of this hypothesis.
Finally, the nature of the analysis, based on a sample of firms along 11 years,
can only observe firms that have survived and do not say anything about the effect of
entry and exit on productiviy growth. In fact, it is known that firms turnover is a key
17
factor in explaining productivity growth (Bartelsman, Scarpetta and Hartiwanger,
2009): it would be necessary to move also in this direction to gauge better
understanding on the origins of the long stagnation of productivity in Italy.
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municipalities: correcting nonparametric frontier measurement for outliers.
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Princeton University Press.
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Operational Research, 80, 474 - 499.
Wheelock D.C., Wilson P.W. (1999). Inefficiency and productivity change in U.S.
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Zelenyuk, V. (2006), Aggregation of Malmquist productivity indexes. European
Journal of Operational Research, 174, 1076–1086
19
APPENDIX A
Table A1. Number of Firms and Employment for industries. Year, 2001
Firms
a
Industry
Food and beverages
Textile and wearing
Leather
Wood
Paper and printing
Petroleum
Chemical
Rubber and plastic mat.
Non-met. mineral prod.
Fabricated metal prod.
Machinery and equip.
Electronics
Tansportation equipment
Other manufacturing
Manufacturing
a)
ISTAT
Number
%
8,328
7.2
13,929
12.0
4,869
4.2
3,281
2.8
9,838
8.5
352
0.3
3,797
3.3
5,993
5.2
6,399
5.5
20,545
17.7
15,879
13.7
11,291
9.7
2,697
2.3
8,716
7.5
115,914 100.0
Employees
Ns. Database
Number
%
564
7.3
911
11.8
365
4.7
204
2.6
479
6.2
22
0.3
309
4.0
492
6.3
433
5.6
1,445
18.7
1,137
14.7
574
7.4
161
2.1
616
7.9
7.712
100.0
ISTAT
Number
220,922
352,291
113,573
56,284
178,708
24,192
197,340
175,330
175,035
503,712
498,507
344,198
253,778
174,104
3,267,974
a
%
6.8
10.8
3.5
1.7
5.5
0.7
6.0
5.4
5.4
15.4
15.3
10.5
7.8
5.3
100.0
Ns. Database
Number
%
25,404
6.2
51,645
12.6
19,971
4.8
9,071
2.2
21,419
5.2
1,045
0.2
17,313
4.2
26,858
6.5
21,676
5.3
77,814
19.0
62,991
15.3
31,104
7.6
10,691
2.6
32,288
7.8
409,290 100.0
Values refer to entire population
Table A2. Input and output variables. Year 2006
Industry
Food and beverages
Textile and wearing
Leather
Wood
Paper and printing
Petroleum
Chemical
Rubber and plastic mat.
Non-met. mineral prod.
Fabricated metal prod.
Machinery and equipment
Electronics
Tansportation equipment
Other manufacturing
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
Turnover
(Th !)
Labour
Services
(mgl !)
Row Mat.
(Th !)
15,669.5
25,117.2
9,109.3
13,017.2
10,510.2
13,650.8
8,185.0
9,979.3
8,662.5
9,640.1
26,414.5
42,909.3
18,540.3
38,739.3
10,846.8
16,665.0
10,014.8
14,122.2
13,774.9
55,741.7
11,097.2
16,495.7
9,987.7
16,243.5
14,649.7
28,463.5
8,868.7
11,117.8
44.31
55.56
50.33
65.79
45.70
48.80
43.38
40.97
43.94
40.79
51.24
70.51
59.50
75.74
54.77
71.06
49.65
59.21
54.73
63.06
56.81
66.52
52.98
52.34
63.88
70.80
49.52
49.03
2,652.3
4,747.6
2,941.1
4,488.2
2,647.6
3,554.8
1,749.4
2,824.6
2,155.0
2,611.1
2,561.3
3,856.4
4,234.7
12,159.0
2,055.2
2,981.7
2,429.3
4,190.4
2,292.0
4,576.7
2,245.3
3,246.3
1,936.2
2,102.5
2,836.3
4,474.4
2,141.6
3,332.0
10,263.4
18,072.1
3,931.2
6,346.0
5,899.3
8,682.2
4,425.8
5,586.4
3,979.7
5,698.8
18,993.9
37,197.5
9,706.4
18,641.5
5,898.8
10,270.9
4,704.8
6,737.6
8,215.4
50,413.3
5,601.1
9,926.1
5,138.7
12,652.7
8,344.9
21,173.8
4,647.5
6,582.7
Tangible
fix. assets
(Th !)
3,490.4
5,209.3
1,629.7
3,459.8
1,186.6
1,738.5
2,030.9
3,055.5
2,153.4
3,512.9
8,176.1
25,167.8
2,764.4
4,774.9
2,484.2
7,319.7
2,459.3
3,500.9
2,330.1
4,813.5
1,556.4
2,514.6
1,258.7
2,210.3
2,115.5
2,719.7
1,752.0
2,960.9
Table A3. Malmquist index and its decomposition into Efficiency Change (EffCh)
and Technological change (TeCh). Period 1996-2006.
1996-2006
Industry
Food and beverages
Textile and wearing
Leather
Wood
Paper and printing
Petroleum
Chemical
Rubber and plastic mat.
Non-met. mineral prod.
Fabricated metal prod.
Machinery and equipment
Electronics
Tansportation equipment
Other manufacturing
Malm
EffCh
TeCh
1.069
0.353
-0.004
0.268
0.090
-1.004
-0.032
0.490
0.068
0.273
1.019
1.224
0.558
0.196
0.050
-0.221
-0.171
0.226
0.534
-0.685
0.147
0.194
0.041
-0.033
0.143
-0.120
0.169
-0.175
1.018
0.574
0.167
0.043
-0.442
-0.326
-0.180
0.296
0.030
0.307
0.873
1.346
0.387
0.372
Table A4. Malmquist index and its decomposition into Efficiency Change (EffCh) and Technological
change (TeCh). Subperiod: 1996-2000, 2000-2003, 2003-2006
1996-2000
2000-2003
2003-2006
Industry
Food and beverages
Textile and wearing
Leather
Wood
Paper and printing
Petroleum
Chemical
Rubber and plastic mat.
Non-met. mineral prod.
Fabricated metal prod.
Machinery and equipm.
Electronics
Tansportation equipment
Other manufacturing
Malm
EffCh
TeCh
Malm
EffCh
TeCh
Malm
EffCh
TeCh
-0.849
-0.355
-1.001
-0.068
-1.579
-4.327
-1.223
0.041
-0.702
-0.218
-0.510
0.500
-1.010
-0.628
0.346
0.046
-0.106
0.636
1.228
-0.178
-0.165
0.887
0.677
0.654
0.636
0.703
0.197
0.201
-1.189
-0.400
-0.895
-0.701
-2.775
-4.155
-1.058
-0.835
-1.357
-0.864
-1.134
-0.200
-1.206
-0.826
1.624
0.823
0.860
0.975
1.908
8.473
1.794
1.738
0.391
1.239
0.767
1.200
0.523
0.055
0.311
-0.235
0.064
-0.641
0.876
-0.184
1.202
0.597
0.496
0.396
-0.058
0.258
0.768
-0.379
1.315
1.063
0.769
1.628
1.021
8.668
0.579
1.135
-0.104
0.841
0.830
0.948
-0.237
0.443
6.992
1.007
1.295
0.479
0.765
-4.522
-0.164
0.050
1.144
0.346
3.544
2.652
2.631
1.649
-0.511
-0.400
-0.401
0.596
-0.584
-1.587
-0.358
-1.078
-0.860
-1.305
-0.188
-1.622
-0.569
-0.349
7.509
1.408
1.676
-0.118
1.369
-2.959
0.194
1.143
2.033
1.667
3.740
4.337
3.209
2.005
Table A5. Efficiency Change (EffCh) and its decomposition into Pure Efficiency Change (PEffCh) and
Scale Efficiency Change (SEffCh). Subperiods: 1996-2000, 2000-2003, 2003-2006
1996-2000
2000-2003
2003-2006
Industry
Food and beverages
Textile and wearing
Leather
Wood
Paper and printing
Petroleum
Chemical
Rubber and plastic mat.
Non-met. mineral prod.
Fabricated metal prod.
Machinery and equipm.
Electronics
Tansportation equipment
Other manufacturing
EffCh
PEffCh
SEffCh
EffCh
PEffCh
SEffCh
EffCh
PEffCh SEffCh
0.346
0.046
-0.106
0.636
1.228
-0.178
-0.165
0.887
0.677
0.654
0.636
0.703
0.197
0.201
0.520
-0.215
-0.095
0.280
0.841
-0.069
-0.202
0.591
0.545
0.011
0.118
0.354
0.124
0.071
-0.170
0.268
-0.009
0.357
0.390
-0.108
0.040
0.303
0.133
0.646
0.521
0.361
0.084
0.134
0.311
-0.235
0.064
-0.641
0.876
-0.184
1.202
0.597
0.496
0.396
-0.058
0.258
0.768
-0.379
0.216
-0.129
0.122
-0.314
0.946
0.202
0.218
0.168
-0.021
0.186
0.299
-0.578
0.538
0.316
0.100
-0.100
-0.052
-0.323
-0.057
-0.385
0.991
0.432
0.522
0.216
-0.352
0.850
0.235
-0.686
-0.511
-0.400
-0.401
0.596
-0.584
-1.587
-0.358
-1.078
-0.860
-1.305
-0.188
-1.622
-0.569
-0.349
-0.412
-0.198
-0.486
0.336
-0.707
-0.208
0.194
-0.514
-0.857
-0.451
-1.025
-1.046
-0.150
-0.195
Tabla A6. Number of employee for different years
Year
Industry
Food and beverages
Textile and wearing
Leather
Wood
Paper and printing
Petroleum
Chemical
Rubber and plastic mat.
Non-met. mineral prod.
Fabricated metal prod.
Machinery and equipment
Electronics
Tansportation equipment
Other manufacturing
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
Avg
St.dev.
1996
2000
2003
2006
40.03
45.30
53.62
64.86
52.45
59.27
39.88
34.10
41.16
39.03
43.27
66.53
49.95
74.14
46.12
50.17
44.46
48.68
46.26
48.68
49.30
51.75
46.35
42.92
60.47
70.66
45.67
38.33
44.87
53.40
57.05
67.58
54.74
61.22
45.10
41.07
44.87
40.35
44.09
60.07
56.52
80.73
54.81
62.59
49.43
54.80
53.83
56.34
55.37
56.71
54.10
51.34
67.21
74.55
52.67
44.25
46.35
56.22
53.91
64.73
50.37
53.97
43.57
39.80
44.03
39.18
47.14
60.57
56.40
76.81
54.17
65.02
49.79
57.30
53.42
58.58
55.08
59.94
52.73
52.17
63.57
67.01
51.23
46.28
44.31
55.56
50.33
65.79
45.70
48.80
43.38
40.97
43.94
40.79
51.24
70.51
59.50
75.74
54.77
71.06
49.65
59.21
54.73
63.06
56.81
66.52
52.98
52.34
63.88
70.80
49.52
49.03
-0.096
-0.189
0.088
0.264
0.132
-1.382
-0.549
-0.562
0.000
-0.854
0.865
-0.580
-0.421
-0.149
Table A7. Technological Change (TeCh) and its decomposition into Pure Technological Change (PTeCh)
and Scale Technological Change (STeCh). Subperiod: 1996-2000, 2000-2003, 2003-2006
1996-2000
2000-2003
2003-2006
Industry
Food and beverages
Textile and wearing
Leather
Wood
Paper and printing
Petroleum
Chemical
Rubber and plastic mat.
Non-met. mineral prod.
Fabricated metal prod.
Machinery and equipm.
Electronics
Transportation equipm.
Other manufacturing
TeCh
PTeCh
STeCh
TeCh
PTeCh
STeCh
TeCh
PTeCh
STeCh
-1.189
-0.400
-0.895
-0.701
-2.775
-4.155
-1.058
-0.835
-1.357
-0.864
-1.134
-0.200
-1.206
-0.826
-1.042
0.171
-0.997
0.108
-1.755
-5.022
-0.134
0.174
-0.735
0.011
-0.415
0.537
0.138
-0.413
-0.096
-0.492
0.144
-0.742
-0.814
1.037
-0.638
-0.924
-0.530
-0.850
-0.680
-0.681
-1.096
-0.357
1.31
1.06
0.77
1.63
1.02
8.67
0.58
1.13
-0.10
0.84
0.83
0.95
-0.24
0.44
1.865
0.557
-0.746
1.004
0.789
8.555
1.631
1.420
0.353
1.052
0.552
2.015
-0.017
-0.161
-0.490
0.516
0.740
0.511
0.172
-0.031
-1.018
-0.262
-0.432
-0.252
0.284
-1.119
-0.214
0.614
7.509
1.408
1.676
-0.118
1.369
-2.959
0.194
1.143
2.033
1.667
3.740
4.337
3.209
2.005
1.604
1.642
0.873
2.142
-4.046
-0.350
1.202
2.716
1.152
5.095
4.465
3.222
2.018
-0.181
-0.004
-0.958
-0.727
1.120
0.610
-0.005
-0.650
0.560
-1.308
-0.027
-0.054
-0.050
Table A8. Technological Change (TeCh) and its decomposition into MaTeCh and Input Biased
Technological Change (IbTeCh). Subperiod: 1996-2000, 2000-2003, 2003-2006
1996-2000
2000-2003
2003-2006
Industry
Food and beverages
Textile and wearing
Leather
Wood
Paper and printing
Petroleum
Chemical
Rubber and plastic mat.
Non-met. mineral prod.
Fabricated metal prod.
Machinery and equipm.
Electronics
Transportation equipm.
Other manufacturing
TeCh
MaTeCh
IbTeCh
TeCh
MaTeCh
IbTeCh
TeCh
MaTeCh
IbTeCh
-1.189
-0.400
-0.895
-0.701
-2.775
-4.155
-1.058
-0.835
-1.357
-0.864
-1.134
-0.200
-1.206
-0.826
-1.558
-0.645
-1.213
-1.133
-3.061
-11.724
-1.842
-1.071
-1.790
-1.315
-1.343
-0.505
-1.830
-1.047
0.406
0.270
0.348
0.461
0.329
9.503
0.958
0.252
0.458
0.479
0.218
0.318
0.742
0.236
1.315
1.063
0.769
1.628
1.021
8.668
0.579
1.135
-0.104
0.841
0.830
0.948
-0.237
0.443
0.380
0.897
-0.252
1.004
0.689
4.349
0.311
0.918
-0.380
0.589
0.661
0.729
-0.850
0.188
0.958
0.183
1.045
0.641
0.353
4.129
0.279
0.237
0.283
0.265
0.171
0.220
0.655
0.275
7.509
1.408
1.676
-0.118
1.369
-2.959
0.194
1.143
2.033
1.667
3.740
4.337
3.209
2.005
-0.594
1.148
1.236
-0.657
1.071
-7.801
-0.231
0.918
1.774
0.290
3.396
3.459
2.414
1.593
9.473
0.266
0.780
0.577
0.353
5.914
0.449
0.236
0.266
1.421
0.347
0.870
0.789
0.416
APPENDIX B: Outliers detection strategy
We use a method based on the concept of leverage, that is the effect produced on the
efficiencies of all the other firms when the observed firm is removed from the dataset
(Stosic and Sampaio de Souza, 2005). The underlying idea is that outliers are expected
to display leverage much above the mean leverage. The leverage measure is then
calculated for each firm, and it is used to detect and to automatically eliminate outliers
from the dataset. Formally, the leverage is measured as the standard deviation of the
efficiency estimates relative to the full sample without the evaluated observation, and
the inefficiency estimates relative to the full sample. I order to calculate it, the most
straightforward possibility is to use jackknife resampling. One first applies DEA to each
of the firms using the unaltered, original dataset to obtain the set of efficiencies
{"k , k = 1,...,K} . Then a “leave-one-out” strategy is employed: one by one, each firm is
successively removed from the dataset, and each time the set of efficiencies
{"ki* , k = 1,...,K, k # i} is recalculated, where i=1,…,K indexes the removed firm.
!
Finally, the leverage of the i-th firm may then be defined as:
% ("
!
(17)
leveragei =
k= S L ,k$i
*
ki
# "k )
K #1
A higher leverage value provides evidence for an influential observation.
We perform the outlier procedure with respect to eahc year forntier at industry level.
This !
approach however is extremely computationally intensive. Therefore, as in Stosic
and Sampaio de Sousa (2005), we use a more efficient stochastic procedure, which
combines bootstrap resampling with the above jackknife strategy. In our procedure we
reduce the computational burden of the procedure proposed by Stosic and Sampaio de
Sousa by calculating the leverage only for those firms that are efficient given the
extracted subsample, while for inefficient firm the leverage is set to zero. This because
the elimination of an inefficient firm from the data set under analysis has no effect on
the efficiency of all other firms. The procedure is as follows1:
[1] Loop the following steps ([1.1]–[1.5]) B times and obtain estimates of the
B
leverage A = {lbi }b=1 "i # SLEff
[1.1] extract randomly without reemission a subset SL of cardinality
L from the original data set S of cardinality K
[1.2] calculate the efficiency " k #k $ SL
!
[1.3] partition SL = SLEff " SLIneff
[1.4] loop the following step ([1.3.1]) "j # SLEff
[1.4.1] remove firm the current firm j " SLEff and calculate the
!
efficiency {" ki* : k = 1,...,LIneff } where i is the removed firm.
!
[1.4] calculate the leverage !
!
!
1
The procedure has been implemented using the statistical package R.
(
**
li = )
*
*+0
% ("
k= S L ,k$i
*
ki
# "k )
K #1
&i ' SLEff
&i ' SLIneff
B
[2] calculate the average leverage li = " lbi n i , where ni is the number of time
b=1
!
firm i is extracted.
K
[3] calculate the global average leverage: l = " li K
i=1
!
The procedure requires the choice of the cardinality of the subsample extracted in each
iteration and the number of repetitions. Stosic and Sampaio suggest a cardinality that is
! dataset S and a number of repetitions that is
10-20% of the cardinality of the entire
greater or equal to 1000. In this paper we chose L=0,2 and B=1000. In order to take into
account the number of observations used, we define as threshold levarage the quantity
l log(K ) . Observation with average leverage greater than the threshold was omitted.
!
APPENDIX C: Capital stock estimation procedure
To obtain estimates of capital stock the procedure uses historical values of tangible
assets and adapts the perpetual inventory method. Specifically, the procedure assumes
that assets are purchased and then replaced over a certain period of time depending on
their estimated average duration.
The first step consists in estimating capital for the base year – the firs year. It is
assumed that assets in first year has been bought gradually over the past and then
replaced in subsequent years. For the base year, historical value of tangible assets is
divided for the estimated average duration and each portion is deflated using the
specific deflator for the related period. The estimated capital stock for the first year
(base) is as follow:
base
$k
kbase
1
kbase
1
kbase
1
1 '
base
k̂base =
!
+
!
+!+
!
=&
! #
)
d
deflbase
d
deflbase"1
d
deflbase"d % d
i=base"d defli (
where kbase is the historical value of tangible assets for base year, d it the average
assets duration calcuated at 2-digit level and defli is the deflator for year i. Deflators are
obtained by processing ISTAT data. In particular, given the unavailability of the
investments series at the 2-digit level, the deflator are common to all firms and are built
as the ratio of the monetary value of total investments at current prices, in a given year,
over the corresponding value in the chained series, and the base year is 2000.
For subsequent years, capital stock is splitted into two part: the estimated quantity of
capital that still survive at time t and the estimated new investment at time t. Thus for
year t the adjusted value of tangible assets kt is as follow:
"
"
k % (
k %+
kt = $ kt!1 ! t!1 ' + *kt ! $ kt!1 ! t!1 'dt!1 & )
dt!1 &,
#
#
where kt!1 is the historical value of tangible assets at time t-1 and dt!1 is the average
duration caculated for year t-1. Specifically first component of the right hand of
equation above represents the estimated volume of tangible assets that still survive at
time t, while the second component the estimated new investment at time t. Therefore,
the estimated stock of capital k̂t a time t is obtained as follows:
""
% "
"
k %
k %%
$ $ kt!1 ! t!1 ' t!1
' $ kt ! $ kt!1 ! t!1 ' '
dt!1 &
dt!1 & '
1 ' $
#
#
k̂t = $
()
+
$ (d !1)
' $
'
deflt
i=t!d defli
$
' $
'
#
& #
&