XXXIII CONFERENZA ITALIANA DI SCIENZE REGIONALI
DO SUBSIDISED NEW FIRMS SURVIVE LONGER? EVIDENCE FROM A
COUNTERFACTUAL APPROACH
Guido PELLEGRINI1, Teo MUCCIGROSSO2
ABSTRACT
This study assesses the impact of public subsidies on the lifetime of new firms in the
manufacturing sector by implementing an accurate micro-econometric evaluation of their
causal effect. Analyses consider subsidies allocated by the main regional policy in Italy, the
Law 488/1992, during the period 1996-2009 in the South of Italy. The novelty of the paper is
the use of a counterfactual approach based on a quasi-experimental design, named Regression
discontinuity design (RDD), with high internal validity. Moreover, the paper integrates for the
first time the RDD approach in the survival analysis framework. The results show constantly
higher default risk probability in subsidised start-ups relative to non-subsidised ones:
statistically significant difference in terms of lifetime in favour of the treated firms emerges,
with particular evidence at the seventh years of life (about 30%). Afterwards the discrepancy
decreases. As a robustness proof, we applied the classical survival analysis to a matched
sample: the previous results are basically confirmed.
Università degli Studi “La Sapienza” di Roma, Dipartimento di Scienze Sociali, Piazzale Aldo Moro 5, 00185,
Roma, e-mail: [email protected].
2
Istituto Nazionale di Statistica (ISTAT), Via Depretis 74/B, 00147, Roma, e-mail: [email protected]. The
views expressed in the article are those of the authors and do not involve the responsibility of ISTAT.
1
1
1. Introduction
This paper provides a new and statistically robust evaluation of the impact of capital subsidies
on the lifetime of start-ups in the South of Italy. In this analysis, we consider Law 488/1992
(L. 488), which is the primary regional policy instrument in Italy devoted to the creation and
support of industrial firms and job creation in less-developed areas through private
investment. In the years from 1996 (the first operative year) to 2007, this law financed 44,000
projects, granting over 2.3 billion Euros in subsidies. The total amount of subsidised
investments was 87 billion Euros, 70% of which were in Southern Italy (Mezzogiorno). An
important part of these projects were start-ups (around 30%).
Based on the presumptions that new firms contribute positively to regional economic
development and that financing constraints cause under-investment, one of the main
objectives of L. 488 is to prevent sub-optimal investment at the start-up of ex ante efficient
firm projects. New firms with start-up assistance in form of capital subsidies are expected to
invest more, to perform better and to have higher survival chances than they would in case of
constrained entry. Therefore, the L. 488 allocates the financial resources using a set of
indicators that (almost in one case) are in favour of start-ups. However, to our knowledge, no
empirical research has investigated the impact of L. 488 subsidies on growth and survival
chances of newborn firms.
The main aim of this paper is to use a quasi-experimental design based on the Rubin causal
model (Rubin, 1974) to investigate whether L. 488 affected the industrial structure of the
Mezzogiorno in terms of creation and survival chances of start-ups. As for other policy
interventions, policy evaluation of incentives to start-ups must contend with problems of
isolating the effects of subsidies from the confounding effects induced by other factors.
Endogenous participation and high selection bias in the program require implementing an
accurate micro-econometric evaluation of their causal effects, but studies in this direction are
rare, primarily because of the difficulty of achieving credible identification (Criscuolo et al.,
2012).To overcome these problems, we fully exploit the unique procedure for the allocation
of subsidies dictated in L. 488. Each year, subsidies are allocated to a broad range of
investment projects through regional “calls for tenders”. In each regional “call for tender”, the
investment projects are ranked on the basis of a score that depends on a number of (known)
characteristics of both the project and the firm. Projects receive subsidies according to their
position in the ranking until the financial resources granted to each region are exhausted.
The presence of sharp discontinuities in the L. 488 rankings allows us to use a quasiexperimental method based on a Regression Discontinuity Design (henceforth RDD)
approach, able to identify the causal effect of subsidy on start-ups’ lifetime. In a RDD
approach, we can estimate the policy effect if the treatment is determined by whether an
observed forcing variable exceeds a known cut-off point. In the L. 488 case, the critical
assumption is that selection to the “treatment” (the subsidy) is determined uniquely by the
2
forcing variable (the score of the project in the regional ranking). The selection mechanism of
L. 488 guarantees that this assumption is compelling, being the allocation of the subsidies
based only on the forcing variable (the score). Average (local) policy effects are then
estimated by comparing the lifetime of the group of subsidised start-ups just above the
threshold with the lifetime of the group of start-ups that applied for the incentives but were
not financed just below the threshold. We claim that non financed start-ups (called “not
treated” firms), with a score just below the threshold are a very good comparison group to
those just above the threshold (called “treated” firms) and describe a valid “counterfactual
scenario: if “treated” start-ups are similar to “non-treated” start-ups (around the threshold), we
do not need any controls and any models to consistently detect the effects of subsidies on
firms’ lifetime.
In recent years, researchers have shown an increased interest in the evaluation of the impact
of public subsidies to private firms. With regard to manufacturing, the evaluations have
produced contradictory results. For example, the impact of capital subsidies on employment is
equivocal (Gabe and Kraybill, 2002). Some authors suggest that regional capital incentives
can induce additional investment in subsidised firms (Daly, Gorman, Lenjosek and McNevin,
1993; Faini and Schiantarelli, 1987; Harris, 1991; Schalk and Untied, 2000; Bondonio and
Greenbaum, 2007; Criscuolo, Martin, Overman and Van Reenen, 2012), whereas others argue
that intertemporal substitution effects prevail (Bronzini and De Blasio, 2006). Furthermore,
minor or negative effects of the subsidies on efficiency and productivity have been detected
(Lee, 1996; Bergstrom, 1998; Harris and Trainor, 2005; Criscuolo, Martin, Overman and Van
Reenen, 2012).
As for Italy specifically, the ex-post impact evaluation of L. 488 in the manufacturing sectors
has been thoroughly investigated. Some studies present evidence that L. 488 has a positive
effect on either investment (Ministero dell’Industria, del Commercio e dell’Artigianato, 2000)
or employment (Pellegrini and Carlucci, 2003; Carlucci and Pellegrini, 2005). L. 488 also
generates a time substitution effect, as financed firms tend to significantly decrease
investment activity in the years following the programme (Bronzini and De Blasio, 2006).
Bernini and Pellegrini (2011) recently showed that growth in output, employment and fixed
assets, but not in TFP, are higher in the subsidised firms.
There are some empirical studies that attempt to evaluate the effectiveness of public subsidies
or government credit guarantees to entrepreneurs/start-ups in industrialized countries. The
studies on subsidies include Lerner (1998) for the United States, Fukanuma, Nemoto and
Watanabe (2008) for Japan, Pfeiffer and Reize (2000) for Germany, Battistin, Gavosto and
Rettore (2001) for Italy and Crépon and Duguet (2004) for France. However, there are very
few studies that explore the impact of public subsidies on the lifetime of old and new firms.
Rare examples are the papers of Battistin, Gavosto and Rettore (2001), Crépon and Duguet
(2004) and Prantl (2005). Battistin, Gavosto and Rettore (2001) evaluate an Italian
3
programme which promotes youth entrepreneurship by issuing substantial benefits to
candidate entrepreneurs selected through a screening process and by providing them with
some training. They adopt a weighted propensity score matching method in order to build up
an hazard function for subsidized and not subsidized new firms. They show that previous
results favourable to the programme badly overstated its effectiveness. Crépon and Duguet
(2004) evaluate the impact of bank loans and start-up subsidies on the survival of new firms.
They use the propensity score matching in the case of multiple treatments and evaluate the
difference between the survival functions of treated and not treated new firms. The results
show that start-up subsidies increase significantly the survival of the firms created by former
unemployed people, while they have no effect on the survival of the firms created by former
employed people. Prantl (2005) examines federal German policies that assist new firms with
subsidized medium - or long - term loans. She adopts a difference-in-difference strategy that
builds on the standard common trend assumption, controlling for influences coming from
unobservable characteristics, and combines difference calculation with propensity score
matching to take into account common support requirements and observable heterogeneity.
Short-run effect estimates suggest that start-up assistance is used right away to increase startup investment in assisted firms, but employment remains initially unchanged. Long-run effect
estimates indicate that additional employment growth follows after some time and early-stage
turnover among assisted start-ups is reduced without distorting the long-run selection process.
In all these studies the analysis of the effect of public subsidies on the survival of subsidized
new firms is based on a counterfactual approach, using propensity score matching and DID.
However, the assumptions behind these techniques are strong and basically untestable; in fact
the DID relies on the parallel trend assumption, while the matching estimator relies on the
conditional independence assumption.3 The use of the sharp RDD for each region in each one
of the call-for-tenders analysed allows to overcome these identification assumptions: the
method is locally equivalent to a random sampling procedure, and the internal validity
(around the cut-off) is high (Lee and Lemieux, 2010). However, the use of RDD in the
framework of survival analysis requires to develop new techniques and new instruments to
adapt the RDD analysis in this context. To our knowledge, no empirical research has
investigated the survival chances of newborn firms by the RDD approach.
The paper has been organised in the following way: the next section describes the evaluation
method we propose and the L. 488 procedures in more detail; section 3 presents the new
dataset we built up; the results of the empirical analysis and their robustness are discussed in
section 4. Finally, we briefly conclude and define some path for future research.
3
See, inter alia, Blundell and Costa Dias (2009) for the description of the diff-in-diffs, of the matching estimator
and of the diff-in-diffs matching estimator.
4
2. A new methodological approach for survival analysis using the RDD
The evaluation of the effect of incentives on the lifetime of the new firms in a counterfactual
framework has been achieved in the previous literature by using the classical methodology for
the survival analysis (Battistin, Gavosto, Rettore, 2001; Crépon and Duguet, 2004). On the
other hand the specific context of our study leads us to consider alternatives to overcome
some limitations of databases and exploit the best features of the RDD approach.
As a matter of fact the data are not so rich to be enough confident for defining a
counterfactual scenario exploiting the conditional independence assumption, and therefore
using a matching approach and a classical survival analysis. Moreover, the presence of callfor-tender lists and a cut-off introduce the possibility to take advantage of the quasiexperimental design for regression discontinuity.
Survival analysis aims to estimate the probability to register an event in a specific time. In our
context the event we observe is the default status of a firm. If we use classical survival
analysis, we get results in terms of a comparison between the group of subsidized firms and
the non-subsidized ones, but the selection bias cannot be completely eliminated using
matching in our data. Therefore, we used a matching approach and a classical survival
analysis only as a robustness proof.
The RDD well fits the aim to identify a policy impact by separating the effect of other factors
influencing the outcome under analysis. It develops as a quasi-experimental design to
compare two groups, which units are treated by a policy action depending on the “forcing
variable” values that assume these units. Given a cutoff point, if units marginally above
(below) it are treated, units non-treated marginally below (above) the cutoff point represent a
good comparison to the firsts. When we measure a significant discontinuity in the conditional
expectation of the outcome at the cutoff point, it can be interpreted as evidence of a causal
effect of the treatment. In particular, as Lee (2008) shows, the RDD is equivalent to a local
random assignment around the cutoff. For this evidence, inferences which are drawn from a
well-implemented RDD are comparable, in terms of internal validity, to the findings obtained
from randomized experiments, such as matching on observables, difference-in-differences and
instrumental variables. Other strength is related to the overcoming of the model specification
problems, like the variables identification and the choice of the functional form (Hahn et al.,
2001).
We use the RDD approach to estimate the effects of incentives connected to the L. 488 in
term of lifetime for the new firms in the South of Italy that built a new plant. In our analysis,
as shown above, we consider nine national call-for-tenders by regions. For each of them we
have a rank considering all the accepted projects presented by the applying firms. The
incentives are distributed only to the firms with highest scores in accordance with the
5
financial availability of government grants4. This framework presents a multiplicity of cutoff
points (by call-for-tenders and regions) and consequently a multiplicity of treated groups and
control groups. In order to aggregate in a unique sample of treated and not treated new firms,
we standardize the scores by Region and call-for-tender. This transformation allows to
identify a unique forcing variable X with the standardized score. Accordingly, the cutoff point
is standardized equal to zero, the treated firms are those with a standardized score greater or
equal zero, the non treated firms are those with a standardized score less than zero and the
forcing variable is measured in standard deviation units. For the firm i at a specific time t, the
outcome Yi is represented by a dummy variable that is equal to zero when the firm presents a
default, is equal to one if it survives.
If we consider that a firm receives a grant only when their score is above the threshold and we
define a non treated firm when the score is below the cutoff point, then we have RDD in the
case of “sharp design”. The treatment assignment W is a deterministic function of the forcing
variable X:
Wi  1X i  c,
(1)
where c is the cutoff point. All firms with a standardized score of at least c are in the
treatment group and all firms with a forcing variable value less than c are in the control group.
Let Yi(1) and Yi(0) the potential outcomes of the firm i, where Yi(1) represent the survival at
the time t and Yi(0) is a default at the same time t. The average causal effect of the treatment
at the discontinuity point is for the sharp RDD (Imbens and Lemieux, 2008):
 SRD  EYi 1  Yi 0 | X i  c .
(2)
Under the assumption of the continuity of the conditional regression functions, that is
EY 0 | X  x and EY 1 | X  x
(3)
are continuous in x, we have that
 SRD  lim EYi | X i  x  lim EYi | X i  x .
x c
(4)
xc
The estimator consists in the difference of two (parametric or non parametric) regression
functions at that point.
4
As mentioned before, a firm is defined granted over the analysis period when receives subsidies not later of two
years from its establishment. We excluded firms that received subsidies only when they were already “old”
firms, therefore firms older than two year, for not defiling the control group.
6
Given the absence of units Xi = c for whom we observe Yi(0), we consider units close to the
cutoff point. The answer to the question about how much close to the threshold have to be the
units is suggested by the contribution of Imbens and Kalyanaraman (2009), that presents a
data-dependent method for choosing an asymptotically optimal bandwidth in the case of a
RDD.
Our design is a cross sectional type: at the time t we point out per each firm i a survival status
or a default status. If we consider a series of cross sections over the analysis period, we can
verify the potential significance of a different probability to survive by the subsidized firms
with respect to the non subsidized ones. It is just this idea that represents the methodological
and applicative innovation to the method: having the possibility to observe the difference of
the two regression functions over time at the cutoff point, we measure the “jump” along the
experimental period to study the behavior of treated units whit respect to the counterfactual
scenario, that is the non treated units just below the threshold.
In theory the sharp RDD estimator of the difference of two regression functions at a point
over a temporal support is
 SRD (t )  
t b
lim EY t  | X t   x   lim EY t  | X t   x dt .
t  a xt c
t
t
xt c
(5)
For the linearity property of the integral is
 SRD (t )   lim EY t  | X t   xt dt   lim EY t  | X t   xt dt .
t b
t b
t  a xt c
t  a xt c
(6)
The uniform convergence of difference between the two limits let us write
 SRD (t )  lim

t b
xt  c t  a
EY t  | X t   xt dt  lim

t b
xt c t  a
EY t  | X t   xt dt .
(7)
When we consider the dependency from the time, the estimator consists in the difference of
the limits of the integrals of both the regression functions at a point.
In practice, the best approximation we can obtain using the above formulation it is a sequence
of cross sections by each day over the analysis period. This discrete function is a very
satisfactory solution to approximate the continuous function, but we show that the analysis of
yearly cross sections is enough to have a clear answer of the phenomenon.
Often in the empiric analysis there is not a deterministic function like W. In this case we
define RDD in the “fuzzy design” configuration, where the probability of receiving the
7
treatment need not change from zero to one at the cutoff. Therefore the probability of
assignment to the treatment is not univocal above or below the threshold:
lim Pr Wi  1 | X i  x   lim Pr Wi  1 | X i  x  ,
x c
xc
(8)
where is not necessary requiring the jump to equal 1. It can be several situations where some
treated units are among the non treated ones, above or below the threshold, and vice versa.
How show Imbens and Lemieux (2008), “in this design we interpret the ratio of the jump in
the regression of the outcome on the covariate to the jump in the regression of the treatment
indicator on the covariate as an average causal effect of the treatment”.
The estimator is
 FRD 
lim E Yi | X i  x   lim E Yi | X i  x 
xc
xc
lim E Wi | X i  x   lim E Wi | X i  x 
xc
.
(9)
xc
There are reasons to consider a fuzzy design in our analytic context, related to the effect of ex
post changes in the rank, exclusions and revocations. These changes can cause a systematic
distortion in our estimates. In order to take into account all this causes of rank changing (that
we excluded in the sharp design, losing the 25% of the observations) we implemented also a
fuzzy design and we consider the results of the fuzzy design as robustness proof of our
analysis based on the sharp design.
The question is how to exploit the RDD in the context of survival analysis. Born in the
medical and biological research field (Barclay, 1958; Cox and Oakes, 1984), survival analysis
found large application in the social sciences too. In this study we refer to the main tools of
this branch of statistics (Hosmer and Lemeshow, 1999; Therneau and Grambsch, 2000;
Cleves, Gould and Gutierrez, 2002).
Let T the survival time variable. The cumulative distribution function of T is
F t   PT  t  , t  0
(10)
where F(t) is continuous on the right, that is lim F u   F t  .
u t
Considering a single unit, F(t) represents the probability of a failure event before time t. If T
is continuous, the density probability function is
f t  
dF t 
,
dt
F t    f u du
t
(11)
0
8
Survival function S(t) points out the probability to survive at a default event at the time t:
 
S t   P(T  t )  1  F t 
 
(12)
where F t   lim F u .
u t
S(t) is a non-decreasing function, with S(0)=1. Given a random variable T, we have S(∞)=0,
that is we have for sure a failure event in an infinite period of observation. If T is continuous,
we have
f t   

S t    f u du
t
,
dS t 
dt
(13)
That shows a correspondence between f t  and S t  .
The main tool of the survival analysis is the Kaplan-Meier estimator (also called product limit
estimator), that allows to estimate the probability for a sample of units to survive at the time t.
Let the conditional survival probability over time t i  estimated with the ratio ni  d i  / ni ,
where ni are the units at risk and di is the number of failure events (or defaulted units). The
Kaplan-Meier estimate, that represents the unconditional probability to survive at the time t, is
ni  d i
ni .
t i t
Ŝ t   
(14)
Instead the hazard function is defined as the default rate at time t conditional on survival until
time t or later,
 t   lim
h 0
Pt  T  t  1 | T  t  f t 
S ' t 
d log S t 



PT  t 
S t 
S t 
dt
(15)
The hazard is interpretable as the expected number of events per individual per unit of time.
Comparison between distribution of treated group and non-treated group functions is the final
step of the counterfactual approach applied at the survival analysis. Null hypothesis is a non
significant difference between the distributions estimator (i.e.: survival function, hazard
function, etc.) of two defined samples. The most common tests to verify the significance of
this hypothesis are the Wilcoxon and the Logrank tests.
9
3. Samples of selected firms and their features
The analysis is based on a new dataset that exploits the administrative archive collected by
Italian Ministry of Economic Development, that supervised the implementation of the
incentives related to the Law 488/1992.
We select a set of new firms suitable for our analysis. First of all, we consider only firms with
a “new” plant located in the Mezzogiorno. The definition of “new plant” we adopted
considers only plants constituted no more than two years after the first call-for-tender they
applied for. If the firm has never been subsidised, we consider the first call-for-tender it
participated. Second, we analyse only call-for-tenders related to the industrial sector (Table 1).
Table 1 – Law 488/1992 call-for-tenders (Industrial sector)
N. of Call-for-tender
L. 488/92
(Industrial Sector)
1
2
3
4
8
11
14
17
31
Year
1996
1997
1998
1999
2001
2002
2003
2004
2006
Date of
Publication of the list
20/11/1996
30/06/1997
16/07/1998
18/02/1999
09/04/2001
12/02/2002
23/06/2003
19/12/2004
19/03/2007
Source: Gazzetta Ufficiale della Repubblica Italiana.
The main variables available to describe the plants are: the region where new plant has been
built, the sector (NACE Rev.2), the dimension in terms of employees.
In Table 2 we present the regional distribution of new plants. There is a strong presence of
plants in the regions of “Convergence” Objective 2007-2013 of the EU Cohesion policy
(about 90% of the firms examined). Campania has the most part of firms, followed by Puglia,
Calabria and Sicilia. The remaining 10% of firms is distributed on the other regions of South
of Italy (Abruzzo, Molise, Basilicata and Sardegna), which are under the “Competitiveness
and employment” Objective.
10
Table 2 – Distribution of new firms by region
Region of
production unit
Treatment
group
Control
group
Total
Treatment
group
83
32
1,257
866
189
939
816
163
4,345
1.9
0.8
33.2
19.3
3.5
17.3
20.1
4.0
100.0
Control
group
n.
Abruzzo
Molise
Campania
Puglia
Basilicata
Calabria
Sicilia
Sardegna
Total
36
15
635
368
66
331
383
76
1,910
Total
%
47
17
622
498
123
608
433
87
2,435
1.9
0.7
25.5
20.5
5.1
25.0
17.8
3.6
100.0
1.9
0.7
28.9
19.9
4.3
21.6
18.8
3.8
100.0
Source: our processing on Ministry of Economic Development data.
We measure the firm dimension by splitting the sample in three dimensional classes of
employees. The composition by dimension (Table 3) reflects the Italian manufacturing
structure, showing a presence of small firms of about 98 per cent. Medium firms are 0.9 per
cent for the treatment sample and 2.3 per cent for the control sample. Firms with over 250
employees are the 0.6 per cent of total units.
Table 3 – Distribution of firms by employment dimension
Firm size
Treatment
group
Control
group
Total
Treatment
group
n.
Big (>250 employees)
Medium (10-249 employees)
Small (0-9 employees)
Total
7
17
1,886
1,910
Control
group
Total
%
19
55
2,361
2,435
26
72
4,247
4,345
0.4
0.9
98.7
100.0
0.8
2.3
97.0
100.0
0.6
1.7
97.7
100.0
Source: our processing on Ministry of Economic Development data.
The treated and not treated groups of new plants show some differences related to the
classification of the activities5 (Table 4). The treatment group and the control group are very
similar for the share of the aggregations “Manufacture of rubber and plastics products, and
other non-metallic mineral products” (6.8% on total units) and “Other professional, scientific
and technical activities” (6.9% on total units). Shares differ less than 5% in “Manufacture of
basic metals and fabricated metal products, except machinery and equipment” and “IT and
other information services”. Most significant differences (almost 10% of share) is shown in
“Manufacture of food products, beverages and tobacco products” and “Manufacture of
5
There are activities that seem not properly related to the industrial sector, but this is the revision effect of the
Statistical classification of economic activities in the European Community (NACE Rev. 2 is the new revised
version of the NACE Rev. 1 and of its minor update NACE Rev. 1). For example, firms classified as “IT and
other information services” in accordance with NACE Rev. 2 were classified in the industrial sector according to
NACE Rev. 1.
11
textiles, apparel, leather and related products”. The lack of the sector mark is very high in the
control group (33 per cent), but not in the treated group (6 per cent).
Table 4 – Distribution of firms by activity (Classification NACE Rev. 2)
Activity (NACE Rev.2)
Treatment
group
Control
group
Total
Treatment
group
n.
Control
group
Total
%
Manufacture of rubber and plastics
products, and other non-metallic mineral
products
150
146
296
7.9
6.0
6.8
Manufacture of food products,
beverages and tobacco products
241
109
350
12.6
4.5
8.1
Manufacture of textiles, apparel, leather
and related products
263
105
368
13.8
4.3
8.5
Manufacture of basic metals and
fabricated metal products, except
machinery and equipment
177
123
300
9.3
5.1
6.9
Other professional, scientific and
technical activities
121
177
298
6.3
7.3
6.9
Other manufacturing activities
157
135
292
8.2
5.5
6.7
IT and other information services
193
170
363
10.1
7.0
8.4
Other non-manufacturing activities
494
665
1159
25.9
27.3
26.7
n.a.
114
805
919
6.0
33.1
21.2
1,910
2,435
4,345
100.0
100.0
100.0
Total
Source: our processing on Ministry of Economic Development data.
We conclude that the treated and the not treated are very similar. This is not enough to assert
the absence of sample selection: a counterfactual approach requires to use a statistical robust
method that deals with the selection problems.
12
4. Empirical evidences
The default of a firm is the event we analyze. In the data set we observe five default statuses:
winding-up, bankruptcy, shutdown, inactivity and cutback. For interpreting the results in a
more suitable way we reclassify some of them: the first two statuses, showing a similar
condition, were grouped in a unique status that considers the winding-up and the declaration
of a bankruptcy together; we dropped the firms with suspended activity, because they are very
few. The firms that closed down their activity are divided in two groups: the firms that closed
down definitively and the firms that closed down for merging, conversion or transfer. The last
ones (1.3% of total firms examined) are excluded from the analysis because the event is not
considered as a negative event (Asquith, Bruner and Mullins, 1983; Lubatkin, 1983 and
1987). As foreseeable, the treatment sample shows a presence of active firms during the
whole analysis period significantly higher with respect to the control sample. On the other
hand, the shares of inactivity and cutback status are higher for the not treated group (Table 5).
The analysis period is of almost 15 years, from the constitution of the first new plant till April
2009, when data were collected.
Table 5 – Distribution of firms by status (April 2009)
Firm status
(April 2009)
active
inactive
winding-up/bankruptcy
cutback (definitively)
Sub-total
cutback (merging /transf.)
Total
Treatment
group
1,485
67
232
95
1,879
31
1,910
Control
group
n.
1,247
463
230
468
2,408
27
2435
Total
Treatment
group
2,732
530
462
563
4,287
58
4,345
77.7
3.5
12.1
5.0
98.4
1.6
100.0
Control
group
Total
51.2
19.0
9.4
19.2
98.9
1.1
100.0
62.9
12.2
10.6
13.0
98.7
1.3
100.0
%
Source: our processing on Ministry of Economic Development and Infocamere data.
As explained in the methodological section, the outcome is a Bernoulli variable Yi that
indicates the survival of a firm i at the time t. For illustrating our idea about the application of
the regression discontinuity design we plot the relation between the forcing variable
(standardized score by Region and call-for-tender) and the survival rate of the firms by
lifetime. The survival rate is calculated on intervals (bins) of the forcing variable domain
sufficiently wide to consider a consistent number of firms. Referring to a sharp design, the
aim is to find an evidence of a discontinuity at the cutoff point between treated and nontreated firms. Therefore it is useful estimate two non-parametric polynomial regression model
on both sides of the cutoff, being interesting examine the behaviour around the threshold. If
we find a significant jump level with the threshold at the lifetime l, we can assert that the
difference between the right limit and the left limit of the two non-parametric polynomial
13
regressions with respect to the cutoff point is the policy effect in terms of survival rate when
the firms reach the l-years age. Testing a succession of cross-sections along time axis, we can
evaluate the presence of significance of the policy. We carried out these non-parametric
estimations at every lifetime year after the fifth6. This preliminary approach shows a first
evidence of a higher survival rate of the treated firms with respect to the non-treated ones for
the whole period considered (Figure 1).
Figure 1 – Survival rate: succession of cross-sections applying one-side local linear regressions at cut-off
Source: our processing on Ministry of Economic Development data.
Given these results, we can verify what happen when we carry out the RDD with the variable
Yi as the outcome variable. For this aim is very important choose an appropriate bandwidth to
balance accuracy and bias. We took advantage of the contribution of Imbens and
Kalyanaraman (2009) that presents a data-dependent method for choosing an asymptotically
optimal bandwidth in the case of a RDD. The RDD has been estimated using different kernel
functions (Epanechnikov, Gaussian) and bandwidths larger and smaller with respect to the
optimal bandwidth for test the robustness of the results. Standard errors are estimated by a
bootstrap procedure. The results are very clear and highly significant. Actually, the difference
between the survival probability of the subsidised firms and the non-subsidises ones at each
lifetime is positive and statistically significant (Table 6).
6
The incentives of Law 488 are confirmed only if the new plants reach the age of five years at least.
14
Table 6 – Sharp RDD (non parametric estimates using optimal and different kernel types): Estimation of
the differences between treated and non treated firms.
Estimation
Lifetime
(years)
5
6
7
8
9
10
11
12
13
Epanechnikov
kernel
0.10
(0.017)***
0.25
(0.03)***
0.30
(0.032)***
0.27
(0.035)***
0.17
(0.037)***
0.10
(0.042)**
0.111
(0.041)***
0.07
(0.036)*
0.05
(0.015)***
Gaussian
kernel
0.10
(0.017)***
0.25
(0.029)***
0.30
(0.037)***
0.26
(0.033)***
0.16
(0.044)***
0.09
(0.039)**
0.106
(0.04)***
0.07
(0.033)**
0.05
(0.014)***
Notes: Bootstrapped standard errors in brackets.
One-side local linear regressions at cut-off are estimated. Optimal bandwidth, 50 replications;
*, **, ***: significant at 10%, 5%, 1% level, respectively.
Source: our processing on Ministry of Economic Development data.
So we can plot this difference over time: when the firms are five years old, the probability to
survive of a treated firm is 0.1 points higher; between seven and height years the difference
shows their maximum values (0.25-0.3 points); after a seven years lifetime we register a
decreasing of this difference, pointing out just a flex point between ages of 10 and 11 years.
The confidence interval is clearly higher than 0 in every year of analysis. (Table 6 and Figure 2).
15
Figure 2 – Sharp RDD estimate: difference of survival probability between treated and non treated firms
0.40
Sharp RDD estimate
(difference T-NT survival probability)
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
5
6
7
8
9
10
11
12
13
lifetime (years)
Notes: Thin lines bound the 95% confidence interval. One-side local linear regressions at cut-off are estimated. Optimal
bandwidth, 50 replications;
Source: our processing on Ministry of Economic Development data.
The results are confirmed by comparing the RDD estimations with the survival rate empirical
functions, defined through a progressive reduction of the analyzed sample around the cutoff
point. As a matter of facts, we register that the survival rate came closer to the sharp RDD
estimator when we consider a smaller fraction of the standardized score, that is include a
small bandwidth in the cut-off neighbourhood (Figure 3).
Figure 3 – RDD estimate vs Survival rate difference of treated and non-treated firms with different
samples around the cut-off.
40
Difference T-NT firms
35
30
25
20
15
10
5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
lifetime (years)
RD estimate (*100)
Inf RD (95% c.i.)
Sup RD (95% c.i.)
Diff. Surv. rate T/nT (SD*0.4)
Diff. Surv. rate T/nT (SD*0.6)
Diff. Surv. rate T/nT (SD*0.8)
Diff. Surv. rate T/nT (SD*1)
Diff. Surv. rate T/nT (SD*3)
Source: our processing on Ministry of Economic Development data.
16
14
The empirical survival rate functions well fit the RDD estimation, particularly for the values of the
lifetime less than seven years. Survival rate does not adequately capture the presence of an indefinite
dynamics of the survival probability at the 10th and 11th years, where the RDD approach shows the
flex point. However, this gap is reduced remarkably when we consider the firms related to the half
standard deviation of the forcing variable, showing all the values in the 95 per cent confidence interval
of the RDD estimates.
4.1.Robustness proofs
As Imbens and Lemieux (2009) explain, we can assess our results employing several
specification tests among the main robustness proofs. We show some evidences about two
key tests. These tests looking for possible discontinuities in the conditional density of the
forcing variable (the standardized score achieved in the call-for-tender list). It is related to the
possibility of manipulating the forcing variable. Lee (2008) shows that if there is not full
control over the forcing variable, variation in treatment status will be randomized in a
neighbourhood of the cutoff. In this case, the RDD can be considered being “as good as” a
local randomly assignment. We present the histogram of the distribution of standardized
scores to verify this aspect (Figure 4). There is no evidence of some differences around the
cutoff point, also using different bin sizes. A more formal test of manipulation related to the
continuity in the density of the forcing variable is presented by McCrary (2008).
300
200
0
100
Frequency
400
500
Figure 4 – Distribution of standardized scores by region and call-for-tender
-10
-5
0
punt_stdscore
Standardized
5
Source: our processing on Ministry of Economic Development data.
17
10
We show a kernel estimate of the standardized score with 95 percent confidence bands
(Figure 5). The weak discontinuity around the cutoff point is not statistically significant.
0
.1
Density
estimate
.2
.3
.4
.5
Figure 5 – McCrary Test’s, Density of the forcing variable at the cutoff (standardized score by regional
call-for-tenders)
-10
-5
00
Standardized score
5
10
Source: our processing on Ministry of Economic Development data.
4.2. Fuzzy design results
The loss of information due to the choice to not consider non-subsidised firms above the
standardized call-for-tenders threshold and subsidised firms with a standardized score below
the cutoff leads to carry out RDD estimates using the fuzzy design. It is important underline
that we can not realize the RDD fuzzy design in a unique solution as the sharp design because
the origin of the fuzzy shape is strictly connected to the single combinations constituted by a
region and a call-for-tender. Actually, we found subsidised firms among the non-subsidised
ones and vice versa because every call-for-tender is managed at regional level. Therefore we
are able to estimate fuzzy designs just for couple constituted by one region and one call-fortender. The limitation of this condition consists in the possibility to dispose of a number of
firms sufficiently high to develop the analysis. This weakness imposes a restriction on the
total units considered for the analysis. We verified that the fuzzy estimate is feasible only for
few combinations of region and call-for-tenders. An appreciable amount of firms refers to the
Regions Calabria and Campania for several call-for-tenders (n. 3, 4 and 8). The answer given
by the RDD estimation on these couples is not so clear to justify an agreement or a
disagreement with the sharp design results. Calabria region shows a non significance of the
18
fuzzy RDD estimates (Table 7), whereas Campania region (Table 8) presents significance
(call-for-tenders n. 3 and 8) and non significance (n. 8).
Table 7 – Fuzzy RDD for Calabria region
call-fortenders
lifetime
(years)
5
III
7
10
5
VIII
7
10
Wald
estim.
numer
denom
lwald
numer
denom
lwald
numer
denom
lwald
numer
denom
lwald
numer
denom
lwald
numer
denom
lwald
Coeff.
Boot. Std. Err.
-0.023
-0.205
0.111
0.154
-0.205
-0.750
0.385
-0.205
-1.876
0.052
-0.086
-0.610
-1.318
-0.086
15.391
0.000
-0.086
0.000
(0.079)
(0.105)**
(13.418)
(0.127)
(0.141)
(120.376)
(0.154)**
(0.099)**
(6.798)
(0.13)
(0.088)
(10.877)
(0.166)***
(0.082)
(45.388)
(0.06)
(0.084)
(4.407)
Source: our processing on Ministry of Economic Development data.
These results depend by the nature of the fuzzy design. We have to analyse the treatment
assignment variable Wi, that in the fuzzy design is not a deterministic function of the forcing
variable Xi, particularly it should be a random variable given Xi. This is the crucial point to
evaluate the validity of this approach. We can not affirm that the treatment for the firms with
a score below the threshold and the non-treatment for the firms with a score above the
threshold are assigned randomly. There are different situations by call-for-tender and by
region that lead to assume different behaviour for the assignment rules. Therefore, we pay
particular attention in considering the output of the fuzzy design. The conclusion on these
results can suffer of a systematic distortion due to the data generating process, differently
from the sharp design approach.
19
Table 8 – Fuzzy RDD for Campania region
call-fortenders
lifetime
(years)
5
III
7
10
5
IV
7
10
5
VIII
7
10
Wald
estim.
numer
denom
lwald
numer
denom
lwald
numer
denom
lwald
numer
denom
lwald
numer
denom
lwald
numer
denom
lwald
numer
denom
lwald
numer
denom
lwald
numer
denom
lwald
Coeff.
Boot. Std. Err.
-0.845
-0.719
1.175
-0.890
-0.719
1.238
-0.543
-0.719
0.756
0.546
-0.013
-41.675
0.546
-0.013
-41.675
0.546
-0.013
-41.676
0.009
-0.008
-1.194
-0.001
-0.008
0.124
0.000
-0.008
0.000
(0.001)***
(0.143)***
(0.541)**
(0.085)***
(0.143)***
(0.392)***
(0.136)***
(0.131)***
(0.280)***
(0.116)***
(0.101)
(0.172)***
(0.135)***
(0.079)
(0.179)***
(0.152)***
(0.093)
(0.201)***
(0.043)
(0.109)
(0.622)*
(0.108)
(0.128)
(12.324)
(0.038)
(0.122)
(0.575)
Source: our processing on Ministry of Economic Development data.
4.3. Classical survival analysis
Another robustness proof is provided by the classical survival analysis approach. We
developed an alternative approach as the RDD, just to overcome the limitations shown by the
data and benefit of particular properties for evaluating a binary treatment effect.
The results related to the main tool of the survival analysis, the Kaplan-Meier estimator (or
product limit estimator), gives an answer that supports very well the RDD estimates. We can
observe clearly as the survival probability through the whole period is higher for a subsidised
firm with respect a non subsidies one (Figure 6).
20
Figure 6 – Survival functions of subsidised and non-subsidised firms
0
.25
.5
.75
1
Kaplan-Meier survival estimates
0
5
10
15
enterprise life (years)
95% CI
treat = 0
95% CI
treat = 1
Source: our processing on Ministry of Economic Development data.
After a first development using the original samples, we refer to a scenario of exact statistical
matching for reducing the selection bias, applying to the control group the weights of the
treatment group covariates calculated on the treatment group. The new estimation shows
differences about survival probability lightly smaller. The subsidised firms show the
probability to reach an age of 5 years higher than 10% with respect to the non subsidised
ones, 20% at the age of 10 years ad 30% at 14 years (Table 9).
Table 9 – Survival functions selected values (exact matching estimation)
Survival probability: P(T>t)
Lifetime
(years)
5
7.5
10
12
14
Treatment
group
Control
group
0.99
0.95
0.85
0.70
0.55
0.88
0.75
0.63
0.47
0.25
Difference
Treat.-Control
0.11
0.20
0.22
0.23
0.30
Source: our processing on Ministry of Economic Development data.
Two tests to verify the significance of the difference about the survival probability at the time
t are the Logrank test and the Wilcoxon test. Both these tests refuse the hypothesis that the
two groups of firms have the same survival function.
We resort to the hazard function to get the measure of the default rate at time t conditional on
survival until time t or later. In our case the hazard function values are higher for the non
21
subsidised firms for all the period examined. It is an analytic tool for evaluating the failure
possibility considering the age of the firms. While for the treated group the hazard function is
equal - or very close to - zero at the lifetime less than 5 years, for the non-treated group it
growths practically linear, showing a local maximum between 5 and 6 lifetime years, where
the expectation of failures is equal to 8 per cent. After a 7 years lifetime this function begins
again to grow, reaching almost 10 per cent of failures at the 10th years and showing a strong
rise afterwards, with a 30 per cent of default events at the 12th and 13th year. On the other
hand, the treatment group hazard function shows a non-decreasing monotonic trend, reaching
the maximum risk level at the 12th year equal to 13 per cent (Figure 7).
Figure 7 – Hazard functions (exact matching estimation)
0
.1
.2
.3
Smoothed hazard estimates
0
5
10
15
analysis time
treat = 0
treat = 1
Source: our processing on Ministry of Economic Development data.
Given these clear results, the estimation on the average lifetime of the firms over the
considered period is definitely in favour of subsidised firms with respect to the non subsidised
ones.
22
5. Conclusions
Policymakers help start-ups to survive and develop under the assumption that they contribute
positively to regional economic development and that their financing constraints can cause
under-investment. One of the main objectives of L. 488 is to prevent sub-optimal investment
at the start-up of ex ante efficient firm projects in less developed areas.
The increase in survival chance of new firms is a key element in every regional development
strategy. Long-lasting firms invest more, and increase human capital and net wealth of a
region. They are well rooted in the local economy, and are a source of job and income for the
local population. Therefore, the measure of the (positive) effect of a regional policy on the
survival rate of new firms is an essential information for policy makers in order to assess the
validity of the policy intervention.
Our study sheds new light on the impact of L. 488 subsidies on survival chances of newborn
firms. In the paper, we create an original and rich statistical dataset by matching two data
sources (an administrative archive and a balance sheet archive) in order to evaluate the effect
of operating public subsidies on firm survival. As the distribution of entrepreneurs who get
start-up subsidies is not random, we face a selectivity process depending on entrepreneurs’
characteristics. To control for this selection bias, we use a counterfactual approach based on a
quasi-experimental design, named Regression discontinuity design (RDD), with high internal
validity. Moreover, the paper integrates for the first time the RDD approach in the survival
analysis framework.
The empirical evidences we show is clear and robust: the new subsidised firms in
Mezzogiorno survive longer than the not subsidized ones, coeteris paribus. These results are
supported by the presence of a statistically differences in terms of lifetime at every time spam
we consider. Several robustness proofs confirm the results.
The results can be summarized in few sentences:
 At the same age, the subsidised firms always show a statistically significant higher
survival rate with respect to the non-subsidised ones.
 During the 15 years considered, the new subsidized firms reach a 5 years lifetime with a
probability almost equal to one (as a consequence of Law 488 regulations), and after show
the higher difference in terms of survival probability at the seventh years of life (about
30%). Afterwards this difference decreases (with the exception of an inflexion point
around the tenth year).
 Treated firms present at every age a next year default probability constantly lower that the
non-treated ones.
These findings discriminates against the view that entrepreneurs with start-up assistance by L.
488 merely lived on the grant to delay exit. The analysis suggests that one of the targets of L.
488 (increase the survival chances of newborn firms) has been achieved. The results are in
line with Crépon and Duguet (2004) for France and Prantl (2005) for Germany. However the
23
conclusions are different from Battistin, Gavosto and Rettore (2001). They found evidence
that a few months after the birth the subsidized new firms start dying at an increasing rate as
the amount of subsidies decreases, a pattern which is peculiar to subsidised firms. Their
interpretation of such evidence is that subsidised firms surviving chances depend on
subsidies. In our results the default probability of a subsidized new firm is lower that the nontreated one after 15 year the subsidy is provided (or after 10 years the subsidy is gone).
However, the central question posed by Battistin, Gavosto and Rettore (2001) is related to the
selectivity of the programme: “what matters for the success of such programmes is not how
effective the subsidy per se is in keeping firms alive but how well selected the beneficiaries
are. To prevent this dependence of firms on subsidies only ‘good’ firms should be
selected…”. This is true also in our case: the selection mechanism of L. 488 can choose the
new firms that have the best survival chance. Nevertheless, the use of the RDD exploiting the
unique procedure for the allocation of subsidies dictated in L. 488 allow us to thoroughly
control for selection bias, with a higher internal validity than matching or other quasiexperimental methods.
There are two aspects that are left out for future research: a methodological one related to the
integration of RDD in all survival analysis instruments; an empirical one, in which are
analysed the effects of L. 488 on survival chance of new firms in the long run, exploiting the
differences in subsidies’ intensity.
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