1. hobbies and interests
2. magic and illusion

WHY DO SOME FIRMS PERSISTENTLY PERFORM R&D ACTIVITIES?*
JUAN A. MÁÑEZ-CASTILLEJOa, MARÍA E. ROCHINA-BARRACHINAb,
AMPARO SANCHIS-LLOPISb AND JUAN A. SANCHIS-LLOPISb
Universitat de València and LINEEX
Abstract
This paper analyses the determinants of persistence in the firms’ decision to
undertake R&D activities using firm level panel data. We estimate three
discrete time (grouped data) proportional hazard models accounting for
unobserved individual heterogeneity. The data used is a panel of Spanish
manufacturing
firms
drawn
from
the
Encuesta
sobre
Estrategias
Empresariales, for the period 1990-2000. Our findings provide evidence
supporting the existence of dynamic increasing returns to R&D activities. We
also find that a number of firm and industry characteristics affect the firms’
persistence in undertaking R&D activities.
Key words: R&D activities, persistence, discrete time survival models
JEL classification: C41, L60, O31.
*
Financial support from the Ministry of Science and Technology in Spain, Project
number SEC2002-03812, is gratefully acknowledged. We would also like to thank
Fundación SEPI for providing the data.
a
Corresponding author: Juan A. Máñez-Castillejo, Universitat de València, Facultad
de Economía, Departamento de Economía Aplicada II, Avda. de los Naranjos s/n,
46022 Valencia (Spain); telephone: 0034 963828356, fax: 0034 963828354, e-mail
address: [email protected].
b
Universitat de València, Facultad de Economía, Departamento de Economía Aplicada
II, Avda. de los Naranjos s/n, 46022 Valencia (Spain).
1
1.- INTRODUCTION
Understanding whether innovation is persistent or not at the firm level is an
important issue, not only for the analysis of technical progress and economic
growth (Barro and Sala-i-Martin, 1995) but also for the theories of industrial
dynamics and evolution (Jovanovic, 1982; Nelson and Winter, 1982; Ericson
and Pakes, 1995; Dosi et al., 1995). From a theoretical point of view, there are
a number of models suggesting that firm’s innovative behaviour should exhibit
persistence. According to Nelson and Winter (1982), innovation persistence is
the result of a “success-breeds-success” process: innovative success generate
profits that may be reinvested in future R&D activities. According to this
theory, past innovations raise the probability to innovate again. The
cumulative nature of the learning process (Rosenberg, 1976, Nelson and
Winter, 1982) may also cause persistence: the generation of knowledge is
based on previous knowledge and affects future research. According to this
view, innovative activities are subject to dynamic increasing returns in the form
of learning-by-doing, learning-to-learn or scope economies, which produce
persistence (Cohen and Levinthal, 1989). Finally, innovative persistence may
also result from firm organisational capabilities, such as the establishment of
an R&D department, the purchasing of specific assets, and/or the hiring and
training of specialized workforce, which are sunk costs that firms may spread
over a period of time.
However, in spite of the theoretical arguments suggesting innovation
persistence, existing empirical studies conclude that firms’ innovative
persistence is in general rather weak, and that only a reduced number of firms
innovate in a persistent way (Geroski et al., 1997; Crépon and Duguet, 1997;
Malerba and Orsenigo, 1999; Cefis and Orsenigo, 2001; Cefis, 2003).
Nonetheless, this conclusion could be biased by the measures of innovation
used to evaluate firms’ innovative persistence. Indeed, these studies use the
number of patents and/or major innovations as the measurement of
innovation. The main problems of using these measures is that they focus on
the generation and the introduction of new technology, and that they could be
the result of firms’ strategies aimed at preserving market leadership and/or
knowledge intellectual protection (Duguet and Monjon, 2004). Thus, they are
somehow related to innovative leadership rather than innovative behaviour per
2
se. In addition, these measures underestimate the number of innovative firms
and so the persistence of innovative behaviour.1
This paper differs from previous studies in that we analyse firms’
innovative persistence by focusing on the input side on innovation, and in
particular, we investigate to what extent firms undertake R&D activities in a
persistent way.2 Thus, in this paper persistency in innovative behaviour
measures to what extent firms are continuously engaged in R&D activities.
The aim of this paper is to investigate the determinants of the
persistence of firms in undertaking R&D activities. In particular, we analyze
the determinants of the length of a period uninterrupted realization of R&D
activities (which we will call R&D spell, henceforth). We analyze the factors
conditioning whether a firm invests on R&D activities in a continuous way by
testing the theoretical predictions that have been proposed in the literature as
sources of persistency. Our main interest lies on testing the hypothesis of
dynamic increasing returns to innovation, or the also called hypothesis of
“success-breeds-success” (Nelson and Winter, 1982). We use for this purpose
a representative sample of the population of Spanish manufacturing for the
period 1990 to 2000. The dataset is drawn from the Encuesta sobre
Estrategias Empresariales (ESEE, henceforth), a survey carried out annually
since 1990 that provides detailed information at the firm level. We consider
both firms that are in the sample in 1990 and firms that are incorporated to
the sample along the above referred period to maintain its representativiness.
We use survival methods to study firm persistency in R&D activities.
The models we use take into account that in our dataset survival times have
been grouped into intervals of time. Although the underlying transition
process between undertaking and not undertaking R&D happens in a
continuous form we only observe these transitions on a yearly basis. Thus
R&D spell lengths can be measured as a set of positive integers (number of
years). The models we use are also adequate in presence of right-censored
observations and easily handle time-varying explanatory variables. In order to
avoid left censoring problems, we only consider those R&D spells that start in
See Patel and Pavitt (1995) for a discussion of the measurement of technological activity, and
Griliches (1990) for a discussion of patents.
2 According to Cefis and Orsenigo (2001), sustained innovative persistence needs to be
supported by a systematic and continuous process of accumulation of resources and
competencies, so that persistence in carrying out these activities might be even more important
than the size of R&D expenditures.
1
3
our observation window (from 1990 to 2000).
3
Furthermore, our estimation
methods have two distinctive features with respect to previous analysis of R&D
persistency. First, they allow a fully non-parametric specification of the
baseline hazard function allowing a full identification of the effect of survival
time on duration of R&D spells. Second, the estimation of both parametric and
non-parametric survival models with unobserved heterogeneity allows a robust
test for the presence of unobserved individual heterogeneity.
The contribution of this paper to existing literature is threefold. First,
this paper is the first attempt to investigate innovation persistence from an
input point of view, and in particular, persistence in the decision to invest in
R&D activities. Secondly, we analyse innovation persistence using survival
methods. To the best of our knowledge, only Geroski et al. (1997) use survival
analysis to investigate innovation persistence, but their analysis is from the
point of view of the output (they analyse the persistence in obtaining patents
and/or major innovations). Third, in our econometric analysis, our fully non
parametric specification of the baseline hazard and the fact of controlling for
R&D
spells
unobserved
heterogeneity
(both
parametrically
and
non-
parametrically) allows fully understanding of the patterns of duration
dependence. Once we control for observed spell characteristics, persistence in
R&D activities could be due both to the fact that the longer the R&D spell the
lower the hazard rate (negative duration dependence), and to the existence of
unobserved spell characteristics that cause persistency such as unobserved
firm organisational capabilities, purchasing of specific assets, etc.
Our results give support to the hypothesis that R&D activities
experience dynamic economies of scale (“success-breeds-success” hypothesis).
In particular, R&D intensity and innovation results are important drivers of
persistence in R&D activities. These results may be considered as giving
support to industry dynamic models where the main source of dynamics
arises from firms’ active learning (e.g. Ericson and Pakes, 1995). However, our
data do not exhibit negative duration dependence, i.e., the probability of
ending a firm’s period undertaking R&D activities (which we will call R&D
spell) do not decrease with the duration of the period. Nonetheless, we obtain
that
unobserved
heterogeneity
is
important,
probably
indicating
that
persistence is more linked to individual unobserved heterogeneity than to
negative duration dependence. This result is consistent with industry dynamic
3
Our sampling scheme is commonly named Inflow sample with follow up (see Jenkins, 2004)
4
models of passive learning (Jovanovic, 1982), in which dynamics is driven by
inherent and fairly constant characteristics of the firm (natural endowments,
managerial abilities, etc.). We also find that firm size, R&D employment, and
export activities affect the continuity in the performance of R&D activities.
A number of policy implications arise from the analysis of the
determinants driving the persistence of firms’ innovative behaviour. By
identifying those factors that increase the propensity of firms to perform R&D
activities over a long period of time, we would be able to suggest new
institutional
arrangements
and/or
policy
measures
to
strength
firms
incentives to undertake innovation activities in a continuous way.
The rest of the paper is organised as follows. Section 2 describes the
data and section 3 discusses the determinants of the persistence in firms’
R&D activities. Section 4 describes the methodology to be used and section 5
presents the results. Finally, section 6 concludes.
2.- DATA .
In order to explore the factors determining the continuity of firms in
undertaking R&D activities we begin by exploring the patterns of R&D
activities by firms. The dataset has been built up using information from the
Encuesta sobre Estrategias Empresariales (ESEE), which is an annual survey
of Spanish manufacturing firms sponsored by the Ministry of Industry and
carried out since 1990. The ESEE is a representative sample of the population
of Spanish manufacturing firms classified by industry and size that provides
broad information at the firm level.4
The unit of observation in this study is the R&D spell. We denote an
R&D spell as the uninterrupted realization of R&D activities for a given
number of years.5 A spell is considered as starting in year j if the firm did not
The sampling procedure of the ESEE is as follows. Firms with less than 10 employees are not
included from the survey. Firms with 10 to 200 employees were randomly sampled by industry
and size strata (according to 21 different productive activities and 4 size intervals), holding
around a 4% of the population in 1990. All firms with more than 200 employees were requested
to participate, obtaining a participation rate around 60% in 1990. Important efforts have been
made to minimise attrition and to annually incorporate new firms with the same sampling
criteria as in the base year so that the sample of firms remains representative of the Spanish
manufacturing industry over time (see http://www.funep.es for further details).
5 In order to consider that a firm carries out R&D activities in a given year we require two
conditions, namely that the firm declares to undertake R&D activities and that the firm has a
positive expenditure in R&D.
4
5
undertake R&D in year j-1 but it undertakes in year j. Analogously, a spell is
computed to end in year T when this is the first year in which the firm
declares not to carry out R&D after a series of one or more consecutive years
in which the firm declares to undertake R&D. Thus, in this paper persistency
in innovative behaviour measures to what extent firms are continuously
engaged in R&D activities.
Some features of this dataset make it suitable to examine the
determinants of firms’ persistence in R&D activities using survival methods.
First, it is comprised by a representative sample of the population of Spanish
manufacturing firms classified by industries and size categories in 1990 and
by annually incorporated new firms so that the sample of firms remains
representative of the Spanish manufacturing industry over time. All these
firms are followed up to 2000.
Some of the firms in the sample declare to
undertake R&D activities the first year they appear in the sample, so that we
do not know whether this is the starting year of their R&D spell or this spell
started one more years before. Should we had included these spells in the
analysis we would incur in a problem of left-censoring that would lead to
underestimate the duration of the R&D spells. To avoid this problem of leftcensoring, we only include the spell of a given firm in the analysis if we know
the exact year in which the spell initiates, e.g. we include in the analysis a
spell that starts in year j if we know that the firm to which corresponds the
R&D spell did not carried out R&D in (j-1). Therefore, as we do not consider
spells already going on in 1990, the first R&D spells in our sample start in
1991.
Secondly, the ESEE provides broad information on characteristics at
the firm level on a yearly basis, which may help to unravel the factors driving
the length of R&D spells.
Thirdly, this survey also allows identifying firms that continue
undertaking R&D, quit this activity or stop answering the survey over the
observation window (1990-2000). We exclude from the analysis those spells
corresponding to firms that fail along the observation window. As for many of
these spells the end of the R&D spell is own firm failure, their consideration
could bias the results of our analysis.
After applying the above mentioned criteria we end up with a sample of
1296 observations corresponding to 481 R&D spells, 48% of which ended
during the sample period. The mean and median duration of these spells are
6
4.57 and 3 years, respectively. Moreover, the non-parametric estimate (using
the Kaplan-Meier estimator) of the survival function (figure 1) shows that 50%
of the R&D spells endure more than 3 years, and that at least 27% of them
last more than 10 years.
[ Insert Figure 1 about here]
The 481 R&D spells correspond to 383 firms. Out of these firms, 285
experienced one R&D spell, 78 two R&D spells and 10 three R&D spells. As it
could be expected in our ten-years period of analysis, mean durations of R&D
spells decrease with the number of spells by firm. Thus, whereas mean spell
duration for a firm with just one spell is 4 years, for firms with two or three
spells it is two years.
3.- THE DETERMINANTS OF R&D PERSISTENCE.
Economic theory suggests that innovation activity is an inherently dynamic
process so that a number of factors may explain why firms should undertake
R&D activities in a continuous way, that is, why one should expect to find
persistence in the innovation behaviour of firms. For the purposes of this
paper, a number of factors may help to explain the duration of an R&D
episode/spell. They include dynamic economies of scale, appropriability
conditions, firm’s internal capabilities, product market competition and
business cycle conditions, among others. In what follows we deal with these
factors in turn, using related theoretical models to establish testable
hypothesis.
6
[ Insert table I about here]
H1: Innovation activities are subject to “dynamic increasing returns to
scale”.
According to this hypothesis, innovation activities are subject to
dynamic increasing returns, in the form of learning-by-doing or learning-tolearn effects (Cohen and Levinthal, 1989). Dynamic economies of scale may
also be explained by the argument that “success-breeds-success” (Nelson and
Winter, 1982): innovation success produces profits that can be reinvested by
the firm in R&D activities. The existence of dynamic economies of scale is also
6
See Table I for a definition of the variables used in our empirical analysis.
7
consistent with industry dynamic models of active learning (Ericson and
Pakes, 1995, Pakes and Ericson, 1998). According to these models, firms learn
from their experience and knowledge accumulation and so their abilities to
succeed in a market (or, in our case, to perform R&D activities) improve as
time goes by.
To test for the presence of dynamic increasing returns in R&D activities,
we use the following three hypotheses:
H1.a. The higher the firm’s R&D intensity, the longer the R&D spell.
According to this hypothesis, we look at the relationship between R&D
INTENSITY (measured by the R&D expenditures to sales ratio) at the
beginning and during the R&D spell, and the length of the R&D spell.
Dynamic economies of scale may arise from two sources. First, R&D
expenditures may be considered as sunk costs that firms may be interested in
spread over a period of time (Cohen and Klepper, 1996). Second, learning-bydoing and learning-to learn effects may derive from the accumulation of
innovation effort and knowledge, so that research today generates new
opportunities to research tomorrow (Rosenberg, 1976; Nelson and Winter,
1982). Therefore, we expect higher R&D effort to be related to a higher length
of the R&D spell.
H1.b. The R&D spell is longer for those firms with innovation results.
The idea behind this hypothesis is the “success-breeds-success”
argument of Nelson and Winter (1982) explained above. We will look at the
relationship between the innovations results obtained by the firm during the
R&D spell, and the length of the spell. Due to the cumulative nature of the
learning process, R&D activities are likely to be built upon previous innovation
results, giving rise to learning-by-doing and learning-to learn effects that are
expected to extend the length of the R&D spell. In order to capture firms
innovation results, we use the interaction of two variables: the variable R&D
RESULTS (which captures whether the firm has obtained at least one
innovation result in year j, either a patent, a utility model, a product
innovation or a process innovation), with the variable IND_TECHNOLOGY
(indicating whether the firm produces in a low, medium or high technological
intensity industry, see table II for industrial classification). These variables
may also be considered as capturing technological opportunities, that is, the
8
possibility of converting research resources into new products or superior
production techniques, which are also positively related to the probability to
perform innovation activities (Scherer, 1965; Lunn and Martin 1986; Cohen
and Levinthal, 1989).
[ Insert table II about here]
H1.c. R&D spells exhibit “negative duration dependence”.
According to this hypothesis, the probability that the R&D spell will end
at some given time falls as the length of the spell raises. We are interested in
measuring the sign and amount of the relationship between the length of an
R&D spell and the probability that the R&D spell will end at some time t. Since
firms perform R&D activities during the spell, this effectively measures the
relationship between within-spell accumulation of innovation knowledge and
the likelihood that the R&D spell will not continue (a sort of innovation
learning curve). Therefore, “negative duration dependence” captures dynamic
effects generated within the R&D spell. In order to control for this effects, we
estimate a non-parametric baseline hazard function that will allow us fully
understanding of the patterns of duration dependence.
H2. The length of the R&D spell rises with firm’ appropriability
conditions.
The incentives to undertake R&D activities in a continuous way depend
also on the extent to which the results from these activities can be
appropriated by the firm or easily diffused within or across industries. The
higher the degree of appropriability of the innovation output, the higher will be
the incentives to invest in R&D (Levin et al., 1987, and Levin,1988). However,
a low degree of appropriability may have two opposite effects on innovation.
On the one hand, low appropriability has a disincentive effect on R&D
activities because firms are unable to appropriate the benefits of their
investments (Arrow, 1962, and Spence, 1984). On the other hand, when
appropriability is low spillovers among firms are high and in order to take
advantage of these spillovers firms may need to develop sufficient “absorptive
capacity”, which implies own innovation activities (Cohen and Levinthal,
1990). To proxy for APPROPRIABILITY conditions we calculate the ratio
9
between total number of patents in the firm’s industry and the total number of
firms innovating in that industry.
H3. The length of the R&D spell rises with firm’ internal capabilities.
The decision to persistently undertake R&D activities is also associated
with
firm
internal
capabilities;
these
can
be
both
observable
and
unobservable. To account for unobservable characteristics, we control for spell
unobserved heterogeneity in our estimation model, which is due in most of the
cases to firms’ unobserved heterogeneity caused by factors such as firms’
organisational capabilities or managers’ ability. To account for observable
characteristics we control for firm size, specialized R&D workforce, and the
nature of R&D activities to be developed by firms. Relating to the association
between firm’s SIZE and R&D investment, there is a considerable amount of
literature (Schumpeter, 1942; Kamien and Schwartz 1982; Acs and Audretsch,
1987; and Cohen and Levin, 1989, for a review). The exploitation of economies
of scale and scope, larger market size, lower risk, higher appropriability
possibilities, etc., are the usual arguments used to support a positive
association between firm size and innovative activities. The empirical results
are mixed but in general they suggest a positive association, although not
necessarily linear.7 In order to control for firm’ size we use the number of
employees (without considering R&D related workforce) and expect this
variable to have a positive and non-linear effect on the length of the R&D spell.
Having R&D specialized workforce is expected to raise the probability of
both undertaking R&D activities and the length of the R&D spell. We therefore
consider the possible effect of the number of R&D related employees by using
the variable R&D EMPLOYEES.
We also consider that firm’ product DIVERSIFICATION may affect
positively to the duration of the R&D spell, since firms with a high degree of
product diversification may spread their R&D results among their different
products (Chen,1996), and so they may have higher incentives to undertake
R&D activities in a persistent way. According to Schmoockler (1962), the
incentives to invest in R&D is supposed to depend positively on the economic
opportunities faced by firms, that is, the market possibilities to exploit
innovation results.
In order to check for non-linearities in the relation between size and the probability to invest in
R&D, we measure size using a set of six dummy variables according to the number of employees
(see Table I for details).
7
10
In addition, we include a variable to control for the foreign content of
the firm’s physical capital (FOREIGN PHYSICAL EQUIPMET) in order to check
whether foreign technology incorporated in machinery increases technology
absorption and stimulates R&D activities, and so whether it positively affects
the continuity in performing R&D activities.
Finally, we also consider the nature of innovation activities undertaken
by the firm. Firms may perform R&D activities internally within the firm, or
they may contract these activities externally to the firm. Since internal R&D
activities involve both higher set up costs and effort than their external
contract, we expect INTERNAL R&D activities (as compared to EXTERNAL
R&D) to affect positively to the duration of the R&D spell.
H4. The length of the R&D spell is affected by firm’ market competition.
We expect the duration of the R&D spell to be influenced by product
market
conditions.
The
literature
on
industrial
organization
remains
controversial on whether market power encourages or inhibits firms from
undertaking R&D activities. According to Schumpeter (1942), ex ante market
power generates financial means to innovate and reduces risk levels. However,
following Arrow (1962) the incentives to innovate are higher in competitive
markets because the expected incremental rents from innovating are higher as
compared to monopoly conditions. There is empirical evidence on the existence
of an inverted U-shaped relationship between competition and innovation, so
that the incentives to innovate are higher when market competition is neither
too low nor too high (see, e.g. Scherer, 1967; or more recently, Aghion et al.,
2004, and references therein). In order to capture the degree of product
market competition, we use two variables, namely, a dummy variable
capturing whether the firm claims to enjoy a significant MARKET SHARE, and
the dummy variable EXPORTER indicating that the firm is an exporting firm.
We consider that exporting firms may need to innovate to face a higher
competitive pressure in international markets (Kleinschmidt and Cooper, 1990
and Kotable, 1990). In addition, according to Cohen and Levinnthal (1989),
foreign markets may facilitate the transfer of technology and so stimulate
firms R&D activities.
H5. The length of the R&D spell depends upon the business cycle
conditions.
11
We include time-specific effects in order to capture macro-level changes
in R&D conditions and institutional factors that are common across firms,
such as R&D policy variations, the business cycle, credit-market conditions,
etc.
4. ECONOMETRIC METHODOLOGY.
Before presenting the methodology we should point out that our sampling
process has been one of inflow sampling with right censoring in which we
sample out all spells for which we do not know their exact starting year.
Hence, we do not have left censoring in our sample. However, there are R&D
spells that have not completed their duration by the end of the sample period.
Additionally to the incidence of right-censoring, some of the covariates used to
explain the duration of R&D spells vary over time (time-varying covariates).
The consideration of time-varying covariates allows overcoming the limitation
arising from considering firm characteristics previous to the beginning of the
period analyzed or at the time of entry as the unique determinants of the firm
survival probability across time (see Mata et al., 1995). We consider time as a
discrete variable, not because it is intrinsically discrete but because the data
is provided on a yearly basis (grouped or banded survival times into number of
years performing R&D). Then, our spell lengths are positive integers and we
should use econometric models capturing the particular nature of our dataset.
Although for some firms we have multiple R&D spells, we assume they are
independent, which allows estimation by pooling the spells.
Discrete time proportional hazard models
In what follows, this section relies heavily on Jenkins (2004), who significantly
improves the understanding, both from a theoretical and an applied point of
view, of survival analysis.
Our intervals of time are of unit length (a year). Then, the interval
boundaries are the positive integers j=1, 2, 3, 4,…, and the interval j is
( j − 1, j ] .
An R&D spell of a firm can either be complete ( ci = 1 ) or right censored
( ci = 0 ). A firm i censored spell contributes to the likelihood function with the
12
discrete time survivor function (the probability of survival until the end of
interval j):
j
Si ( j ) = Pr (Ti > j ) = ∏ (1 − hik ) ,
(1)
k =1
{
}
where Ti = min Ti * , Ci* , being Ti * some latent failure time and Ci* some latent
(
)
censoring time for firm i, and hik = Pr k − 1 < Ti ≤ k Ti > k − 1
is the discrete
hazard (the probability of ending the spell in interval k conditional to the
probability of survival at the beginning of this interval). A firm i completed
spell contributes to the likelihood with the discrete time density function (the
probability of ending the spell within the jth interval):
fi ( j ) = Pr ( j − 1 < Ti ≤ j ) = S ( j − 1) − S ( j ) =
hij
1 − hij
j
∏ (1 − h ) .
(2)
ik
k =1
Using (1) and (2), the whole likelihood function is
n
L = ∏  Pr ( j − 1 < Ti ≤ j )   Pr (Ti > j ) 
ci
1− ci
i =1
 h
ij
= ∏ 

−
1
hij
i =1 

n



ci
j

k =1


∏ (1 − hik )
(3)
and the log likelihood
n
 h
log L = ∑ ci log  ij
 1− h
i =1
ij

 n j
 + ∑∑ log (1 − hik )
 i =1 k =1
(4)
Allison (1984) and Jenkins (1995, 2004) show that (4) can be rewritten
as the log likelihood function of a binary dependent variable yik with value of
one if the firm i spell ends in year k, and zero otherwise:
j
n
 h
log L = ∑∑ yik log  ik
i =1 k =1
 1 − hik
j
n
 n j
+
−
=
h
log
1
( ik ) ∑∑  yik log hik + (1 − yik ) log (1 − hik ).
 ∑∑
i =1 k =1
 i =1 k =1
(5)
This implies that discrete time hazard models can be “easily” estimated by
binary dependent variable models. A prerequisite is the reorganization of data
in the following way. For individual 1 of the sample, leaving R&D activities in
year four, we have:
13
Table III: Data organization.
Identifier of individual
Spell interval identifier Created binary
for the individual (j)
dependent variable (new
censoring variable)
1
1
0
1
2
0
1
3
0
1
4
1
If the individual had not exited the state at the end of the sample period
then the binary dependent variable created would have been a 0 also for the
fourth year and this would have been an individual censored spell. An
uncensored spell of an individual has as many rows as periods until the spell
ends. A censored spell of an individual has as many rows as periods up to the
end of the sample period. The re-organization of data in Table III will affect
every individual in the sample. This allows not only an “easy” estimation
method for discrete time hazard models but also it is the way of incorporating
time-varying covariates in the analysis. The way the data should be reorganised coincides with the long version re-organisation of data in panel data
sets.
The next step for estimation is the choice of the functional form of hik .
As we are interested in a proportional hazard specification with groupedinterval data8, the complementary log-log is the appropriate one. This is a
discrete time representation of an underlying continuous time proportional
hazard θ ( t , xit ) = θ 0 ( t ) exp
β0 + xit β 9
.
To show this let us start with the evaluation of
a continuous survivor function at the end of interval j:
j
j
β +x β
β +x β
S ( j , xij ) = exp  − ∫ θ ( ε , x ) d ε  = exp  − exp 0 ij ⋅ ∫ θ 0 ( ε ) d ε  = exp  − exp 0 ij H j  ,
0
 0



(6)
where H j =
∫
j
0
θ 0 ( ε ) d ε is the integrated baseline hazard evaluated at the end
of interval j. The baseline survivor function at j is
This specification leads to the most well known duration models based on a specification of the
hazard function. It is often used to describe the relation between the empirical exit rate and
covariates in a concise way.
9 From here onwards we already incorporate explicitly the role of explanatory variables in the
survival analysis. Also notice that in our notation we are considering the possibility of timevarying covariates, assumed to be constant within a given interval.
8
14
S0 ( j ) = exp ( − H j ) .
(7)
Using (6) the discrete time hazard can be written as
(
h ( j , xij ) ≡ h j ( xij ) = Pr j − 1 < Ti ≤ j T > j − 1, xij
=
(
Pr j − 1 < Ti ≤ j xij
(
Pr Ti > j − 1 xij
)
)
) = S ( j − 1, x ) − S ( j, x ) = 1 − exp  H
ij
S ( j − 1, xij )
(
ij
j −1
− H j ) exp
β0 + xij β
(8)
where rearranging terms and taking logs, we get
(
)
β +x β
log 1 − h j ( xij )  = ( H j −1 − H j ) exp 0 ij ⇒ log − log 1 − h j ( xij )  = β 0 + xij β + log ( H j − H j −1 )
(9)
The discrete time baseline hazard for interval j is
1 − h0 j = exp ( H j −1 − H j )
(10)
then
(
)
j
log − log 1 − h0 j  = log ( H j − H j −1 ) = log  ∫ θ 0 ( ε ) d ε  = γ j ,
 j −1

(11)
where γ j is the interval baseline hazard which specification allows testing for
the type of duration dependence. Substituting (11) back into (9):
(
)
log − log 1 − h j ( xij )  = β 0 + xij β + γ j ⇒ h j ( xij ) = 1 − exp  − exp ( β 0 + xij β + γ j )  , (12)
implying
that
our
discrete
log ( − log ( ⋅) ) ≡ c log log ( ⋅)
once
time
we
hazard
have
has
been
assumed
that
isolated
the
from
a
underlying
continuous hazard has a proportional form. For this reason this discrete time
proportional hazard model is known as a cloglog model.
When the underlying continuous proportional hazard is a Weibull
model, the corresponding discrete one would specify γ j = (α − 1) ln ( j ) in (12).10
However, in estimation we treat the baseline hazard non-parametrically by
creating 10 interval-specific dummy variables (one for each spell year at risk),
as the longer observed spell in our data set is 10 years. However, we can only
estimate 8 dummy variables because we do not observe any spell completion
either in years 8 and 10. The non-parametric approach allows γ j to vary from
one interval to another.
10
Where the parameter (α-1) controls for duration dependence on a Weibull specification.
15


Incorporating unobserved heterogeneity the cloglog model in (12)
becomes
(
)
log − log 1 − h j ( xij )  = β 0 + xij β + γ j + ui ⇒ h j ( xij ) = 1 − exp  − exp ( β 0 + xij β + γ j + ui ) 
(13)
being ui ≡ ln (ν i ) , where vi originally enters multiplicatively on the underlying
continuous hazard function θ ( t , xit ) = θ 0 ( t ) exp β0 + xit β ν i . Usually the distribution
chosen for ν is a Gamma distribution with unit mean and variance σ 2 to be
estimated from the data, as well as distributed independently from t and x
(Meyer, 1990). This random variable is assumed to be positive. The null
hypothesis of variance equal to zero can be tested. Under the null, unobserved
heterogeneity is not important and the estimated model will be the model
without individual unobserved heterogeneity. The contribution to the sample
likelihood for a censored observation with spell length j intervals is
(
)
jth
interval
S j , xij β 0 , β , σ 2 , and the contribution of someone who exits the state in the
is
(
) (
)
S j − 1, xij β 0 , β , σ 2 − S j , xij β 0 , β , σ 2 ,
where
S ( j , xij vi ) =  S ( j , xij )  .
vi
Alternatively,
parametrically.
one
Heckman
may
and
treat
Singer
unobserved
(1984)
heterogeneity
allowed
for
an
non-
arbitrary
distribution for the individual heterogeneity term. They did this by assuming
that there is a number of different types of individuals (or “mass points” in the
distribution of individual heterogeneity) and we only can assign individuals to
different types according to probabilities. This is reflected in the hazard
function incorporating an extra term allowing for different intercepts for
different types. For instance, if one assumes a model with two types (type=1,
2), then the hazard will be
h j ,type ( xij ) = 1 − exp  − exp ( mtype + β 0 + xij β + γ j )  ,
where mtype
(14)
characterises the discrete points of support of a bivariate
distribution (“mass points”), with mtype =1 normalized to zero and the probability
of belonging to type 1 is p1 = 1 − p2 . Mass point 2 equals mtype = 2 + β 0 .
All the individual contributions to the likelihood function will be a
mixture of contributions assuming type1 individual and type2 individual. This
16
mixture will weight contributions of the two types according to the
corresponding associated probabilities ( p1 , p2 ) to the “mass points”.
The above discrete time proportional hazard models may be estimated
in
Stata.
The
complementary
loglog
without
unobserved
individual
heterogeneity may be estimated using the cloglog stata command. The
complementary loglog model with Gamma distributed unobserved individual
heterogeneity may be estimated using Jenkins´s written program pgmhaz8.11
Finally, a model with non-parametric unobserved individual heterogeneity may
be estimated using Jenkins´s hshaz program.12
Not controlling for unobserved heterogeneity when it is important may
have the following effects. First, the degree of negative duration dependence in
the hazard is over-estimated. This is the result of a selection process according
to which firms with unobserved heterogeneity correlated with higher exit rates
finish the spell more rapidly. Then, as time goes by we have more firms with
low v in the group of surviving firms, which implies a lower hazard and so the
underestimation of the true hazard. Secondly, the β parameters are underestimated. Then, they do not have anymore an interpretation as the
proportionate response of the hazard to a change in a given covariate.
However, some empirical results indicate that the more flexible the baseline
hazard
the
less
important
are
the
effects
of
unobserved
individual
heterogeneity (Dolton and van der Klaauw, 1995).
5. RESULTS.
a) Non-parametric tests
In order to better understand the effects of the explanatory variables used
in the analysis, we carry out non-parametric tests for the equality of survival
functions across the r groups in which a number of explanatory variables
classify the R&D spells. These tests are extensions of non-parametric rank
tests to compare two or more distributions for censored data. Under the null
hypothesis, there is no difference in the survival rate of each of the r groups at
An up-to-date Stata program elaborated by S. Jenkins that implements this estimator is
available from http://fmwww.bc.edu/RePEc/bocode/p or, inside Stata, typing ssc install
pgmhaz8. An initial version of the program was presented in Jenkins (2001).
11
12 A Stata program elaborated by S. Jenkins that implements this estimator is available from
http://fmwww.bc.edu/RePEc/bocode/h , or inside Stata, typing ssc install hshaz.
17
any of the exit times and the t-statistic distributes as χ 2 with r-1 degrees of
freedom. At any exit time, the contribution to the t-statistic is obtained as a
weighted standardised sum of the difference between the actual and expected
number of exits for each of the r groups (Cleves et al., 2004).
In table IV we present the results for the log-rank and Wilcoxon tests of
equality of R&D spell duration across groups by explanatory variables.13 Our
results indicate that there are remarkable differences in the survival prospects
across groups of R&D spells for each of the variables considered (except for the
variable accounting for product diversification).
Thus, focusing on the variables related to the existence of dynamic
increasing returns, we get that R&D spells corresponding to firms with high
and medium R&D intensity and obtaining innovation results enjoy better
survival
prospects
(at
5%
level
of
significance)14
than
R&D
spells
corresponding to firms with low R&D intensity and not obtaining any
innovation result. In addition, firms operating in high and medium
technological intensity industries enjoy longer R&D spells than firms operating
in low technological intensity industries (at 5% level of significance). The
magnitude of these differences can be seen by comparing the mean survival
times by group shown in the last column of Table IV.15
With respect to the extent to which the results from the innovative
activities can be appropriated by the firm or easily diffused within or across
industries we get that spells belonging to firms operating both in low and high
appropriability sectors enjoy significant higher survival prospects (at the 5%
level). The longer duration of the R&D spells in high appropriability sectors is
consistent with the argument of Levin et al. (1987) and Levin (1988), that the
higher the appropriability of the innovation output the higher will be the
incentives to invest in R&D. The longer duration of R&D spells in low
appropriability sectors is in line with the idea that when appropriability is low
spillovers among firms are high and in order to take advantage of these
13 We have also carried out the Peto-Peto-Prentice test obtaining similar results. The differences
among these test lie on the weights assigned to the differences between actual and predicted
number of exits by group. The weight at each distinct failure time is 1 for the long-rank test,
whereas it is the number of R&D spells at risk for the Wilcoxon test. See Cleves et al. (2004) for
further details.
14 For the R&D intensity variable we get a Wilcoxon text significant at the 17.7% level. For the
Peto-Peto-Prentice we obtain a significant difference at the 6.5% level.
15 These mean duration have been calculated taking into account only the R&D spells
completed along the years of the sample.
18
spillovers firms may need to develop sufficient “absorptive capacity”, which
implies own innovation activities (Cohen and Levinthal, 1990).
As for firms’ internal capabilities, R&D spells corresponding to firms
large in size, with a high number of R&D employees, and undertaking only
internal or both internal and external R&D activities (as opposed to
contracting
R&D activities externally) endure significantly better survival
chances than R&D spells corresponding to firms with different characteristics.
We further find that R&D spells of firms with a high percentage of foreign
physical equipment last longer (at the 1% level of significance). This could
indicate that the foreign technology incorporated in machinery is a
complement to technology from own R&D that increases firm’s propensity to
undertake R&D activities.
Finally, regarding to the variables used to proxy market competition, we
obtain that the higher the market share of a firm the longer its R&D spells,
and that also exporting firms experience longer R&D spells.
[Insert table IV about here]
b) Estimation results
Table V shows estimation results for three discrete time proportional
hazard model based on the Prentice-Gloecker (1978) model. In the first column
we present the estimates of a complementary log-log (cloglog) model (model 1)
that does not considers any potential unobserved individual heterogeneity; in
the second column we present the result of a cloglog model assuming a
gamma distribution for an included individual heterogeneity term (model 2);
finally, in column 3 we present the estimates of a cloglog that includes a
discrete
mixture
distribution
to
summarise
unobserved
individual
heterogeneity non-parametrically as proposed by Heckman and Singer (1984)
(model 3). The three estimators include a non-parametric specification for the
shape of the baseline hazard function that allows fully identification of the
pattern
of
duration
dependence.
When
using
a
fully
non-parametric
specification for the baseline hazard function one must drop from the sample
the observations corresponding to survival years without events (i.e. without
spell completions) as the hazard cannot be estimated for these years (exactly
19
as with the non-parametric baseline hazard in the continuous time Cox
model). We do not have any event in survival years 8 and 10, thus after
dropping the data for these survival years the size of the estimation data get
reduced to 1250 observations that correspond to 481 spells. For the same
reason, and as explained in the methodological section, we cannot include in
the estimation the dummy variables corresponding to survival years 8 and 10
(d8 and d10).
It should also be mentioned that as the observational unit of our analysis
is the R&D spell, in our estimations we consider unobserved individual
heterogeneity at the spell level. Notwithstanding, most of the causes
underlying spell unobserved heterogeneity come from the unobserved
characteristics of the firms producing the R&D spell. Although in our sample
we observe firms with more than one R&D spell, for the estimation we consider
the spells belonging to a single firms as independent. In any case, it should be
taken into account that almost 60% of the firms in the sample show only one
R&D spell.
As in any proportional hazard specification, a unit change in a covariate
leads to a proportional shift on the hazard rate. Moreover, the assumption of
proportionality has been tested using the tests proposed by Grambsch and
Therneau (1994). The null hypothesis that the hazard rates are proportional
cannot be rejected.
Both for models 2 and 3 the tests for individual heterogeneity do not
allow us to reject the null hypothesis that individual unobserved heterogeneity
is not relevant. For model 2 (parametric specification by a Gamma
distributional assumption) we reject the null hypothesis that the unobserved
heterogeneity variance component ( σ 2 ) is equal to zero (p-value for the
likelihood ratio test is 0.049), indicating statistically significant unobserved
heterogeneity.16 For model 3 (non-parametric treatment through “two masspoints”) we reject the null that the mass-point for type 2 is statistically no
different to the mass-point for type 1 (the coefficient of the mass-point for type
2 is -2.455 with p-value 0.003),17 what means that there is unobserved
individual heterogeneity. The above mentioned results suggest that for our
16 This likelihood ratio tests whether the gamma variance is equal to zero. The reference to a
χ2(01) is due to the fact that this test is a “boundary” test that takes account of the fact that the
null distribution is a 50:50 mixture of a chi-squared (d.f.=0) variate (which is a point mass at
zero) and a chi-squared (d.f.=1) (see Gutiérrez et al., 2001, and Jenkins, 2004) .
17 In this estimation method we set mass point for type 1 spells equal to zero and estimate the
second mass point.
20
particular analysis we should mainly rely on the results of the models
including unobserved heterogeneity (models 2 and 3).
[Insert Table V about here]
It should be also mentioned that with the aim of capturing possible
non-linear effects of the covariates on duration, all covariates in our model are
introduced as sets of dummy variables.
The fact that both specifications accounting for unobserved individual
heterogeneity yield similar results indicates that our results are robust to any
specification
controlling
for
unobserved
spell
heterogeneity.
However,
comparison of the estimates of model 1 with models 2 and 3 estimates reveals
that the coefficients of the covariates (excluding those that correspond to our
non-parametric baseline hazard function) in the models that account for
unobserved spell heterogeneity are slightly larger in absolute value. These
differences are not unexpected as Jenkins (2004) shows that not accounting
for unobserved heterogeneity attenuates the magnitude of the impact of
covariates on the hazard rate.
Nonetheless
the
results
of
the
two
estimations
accounting
for
unobserved heterogeneity are very similar, our preferred model is model 3 as it
does not impose any parametric distribution to unobserved heterogeneity.
Thus, we will focus our analysis on the results of this estimation.
Notwithstanding, if there is any relevant difference between the estimates of
model 2 and 3, we will take notice of it.
Analysing the patterns of duration dependence
Figure 2 shows the predicted discrete hazard rates obtained from a
cloglog model without unobserved heterogeneity (model 1), a cloglog model
with gamma distributed heterogeneity (model 2) and a cloglog model in which
unobserved heterogeneity is treated non-parametrically assuming that there
are two types of individuals (model 3). In all cases, the discrete hazard rates
shown correspond to a representative spell for which all covariates except the
ones capturing duration dependence have been set at sample mean values.18
18 As in our analysis all the covariates are included as sets of dummy variables, to characterise
the representative spell we follow a two stage procedure. First, we calculate the mean value of
the continuous variable that we have used to create the corresponding set of dummy variables;
21
Additionally, as we do not observe any event for the eight and the tenth years
of survival we set the discrete hazard rates of these survival years equal to
zero. For the gamma distributed unobserved heterogeneity model, discrete
hazard rates are predicted assuming that the unobserved heterogeneity
component is set equal to its mean. For model 3, we have represented both the
discrete hazard rates that correspond to Type 1 spells (mass-point 1) and to
Type 2 spells (mass-point 2), taking into account that mtype=1 has been
normalized to zero and mtype=2 estimate is -2.455.
Observation
in
Figure
2
of
predicted
discrete
hazard
rates
corresponding to the model without unobserved heterogeneity (model 1)
suggest that they decrease from survival years 1 to 3, then they slightly
increase up to survival year 5, and then they decrease again up to survival
year 7 (the predicted discrete hazard rate in survival year 9 is very similar to
the one corresponding to survival year 7). However the magnitude of these
increases and decreases is very small as it shows that the highest discrete
hazard rate (corresponding to survival year 1) is 0.172 and the lowest 0.046
(corresponding to survival year 9). To check the significance of these increases
and decreases we carry out pairwise comparisons of the duration dependence
coefficients. These suggest that not all these increases and decreases are
significant, as only the coefficient associated to the survival year 1 is
significantly smaller in absolute value to the other duration dependence
coefficients.
Thus, the results of these pairwise comparisons indicate that
after initial decrease in the hazard rates (from survival years 1 to 2), these stay
constant along the period of analysis. Hence, in the estimation that does not
take into account frailty we do not find evidence of negative duration
dependence.
Discrete hazard rates corresponding to model 2 and type 1 spells of
model 3 (the probability that a spell belongs to type 1 is 0.812 with a p-value
close to 5%) are for every survival year, except for survival year 1, above model
1 predicted hazard rates. This result is not unexpected as not controlling for
unobserved heterogeneity overestimates the extent to which hazard rates
decrease with survival time as it was explained in the methodological section.
Notwithstanding, discrete hazard rates for type 2 spells of model 3, are lower
than the corresponding to models 1 and 2, and type 1 spells of model 3 as the
then, we set equal to 1 the dummy containing this mean value (the dummies take value of 1 for
a given range of values of the continuous variable).
22
negative mtype=2 estimate (-2.455) reduces the predicted hazard rates. In any
case, it should be taken into account that the probability of a spell being of
type 2 is much lower than the probability of being of type 1, 0.18819
and
0.812 respectively.
[ Insert figure 2 about here ]
Furthermore, both in models 2 and 3 all duration dependence
coefficients are not significantly different from zero (at 5% level) and are not
significantly different among them.20 Therefore, once we control for unobserved
heterogeneity, our results indicate that survival time itself plays no role in
explaining the duration of R&D spells.
On the basis of the survivor functions predicted by model 2 and type 1
spells of model 3, Figure 3 shows that approximately 50% of the innovative
spells endure more than 3 years, and that about 30% of them last more than
10 years.21 These high figures give an idea of the importance of persistence in
R&D activities.
[ Insert figure 3 about here ]
Dynamic increasing returns
Our results provide evidence supporting hypothesis one (H1), i.e., that
there are dynamic increasing returns to R&D activities. In particular, we
obtain a non-linear relationship between firms’ R&D intensity (measured as
the ratio of R&D expenditures over sales) and the expected length of the R&D
spell. Only those firms belonging to the “medium R&D intensity” group enjoy
R&D spells with longer survival prospects that those firms belonging to the
“low R&D intensity group” (the coefficient of the R&D INTENSITY2 is negative
and significant at 2% level). However, there is no difference between the
expected duration of the R&D spells of “high R&D intensity” firms and their
“low R&D intensity” counterparts (the coefficient of the R&D INTENSITY3 is
not significantly different from zero). However, we cannot distinguish between
the expected duration of firms belonging to the “medium and high R&D
intensity” groups. This result gives support to hypothesis H1.a, that is, that
With a p-value of 1%.
d3 is significantly different from zero at 6% level in the mass-points estimation.
21 These figures are much higher for type 2 spells in model 3, however they should not be as
representative as the probability of being a type 2 spell is only 18%.
19
20
23
there are learning by doing and learning-to-learn effects in R&D activities
(Rosenberg, 1976; Nelson and Winter, 1982).
The analysis of the interactions between the degree of technological
intensity of the firm industry and the R&D results obtained by the firm (either
in the form of patents and utility models or in the form of product and process
innovations) leads to a number of interesting results. Firstly, only in medium
technological intensity industries the expected duration of R&D spell of firms
that obtain innovation results is longer than the spells of firms that do not
obtain innovations. Both for low and high technological intensity industries we
cannot distinguish between the expected duration of firms obtaining and not
obtaining
innovations.
Second,
the
expected
length
of
R&D
spells
corresponding to firms not obtaining innovation results is independent of the
technological intensity of the industry they belong to. Third, the R&D spell
length prospects of firms obtaining innovations are better in medium and high
technological
intensity
industries
than
in
low-technological
industries.
However, there is no difference between the expected duration of the R&D
spells of firms obtaining innovations in medium and high technological
intensity industries. Thus, these results give support to hypothesis H1.b, and
in particular, to the argument that “success-breeds-success” (Nelson and
Winter, 1982). The results behind hypothesis H1.a and H1.b may also be
considered as giving support to industry dynamic models where the main
source of dynamics arises from firms’ active learning (Ericson and Pakes,
1995; Pakes and Ericson, 1998).
However, as we described above our data do not exhibits negative
duration dependence, indicating that the probability of ending of a firm’ R&D
spell does not decrease with the duration of the spell. Thus we cannot confirm
hypothesis 1.c. Nonetheless, in our data unobserved heterogeneity is
important, indicating that persistence is more linked to individual unobserved
heterogeneity than to duration dependence. This result is consistent with the
industry dynamic models of passive learning (Jovanovic, 1982), in which
dynamics is driven by inherent and fairly constant characteristics of the firm
(natural endowments, managerial abilities, internal capabilities, etc.).
In summary, our analysis provides evidence supporting the hypothesis
that increasing returns to scale in innovative activities are an important driver
of firms’ innovation persistence.
24
Appropriability conditions
As regards to appropriability conditions faced by R&D firms, our results
suggest that firms operating in an environment with high appropiability
conditions enjoy longer R&D spells as compared to industries with low
appropriability conditions (the reference cathegory).22 This result is consistent
with Geroski et al. (1997), who found that spillovers affects positively to the
length of the innovative spell, and is also in line with Levin et al. (1987) and
Levin (1988), who predict that the higher the degree of appropriability of the
innovation output, the higher will be the incentives to invest in R&D.
Firms’ internal capabilities
We now turn to analyse the impact of firm’s internal capabilities on
R&D spell duration. First, in relation to firm size and after controlling for all
other variables, we obtain that the R&D spells of larger firms have lower
chances of ending. The coefficients corresponding to all included size groups
(the excluded one is SIZE1, i.e. under 21 employees) are negative and
significant, except for the SIZE3 group (firms over 50 and below 101
employees). However, the impact of firm size on the length of the R&D spell is
not linear, as pairwise comparisons of the coefficients corresponding to
included groups suggest that only R&D spells of firms with more than 200
employees (SIZE 5 and SIZE6 groups) endure better survival prospects.23
Hence, the implication of our results on firm size are twofold: on the one hand,
they suggest that survival prospects of the R&D spells produced by the group
of the smallest firms are shorter than those spells that correspond to larger
firms; on the other hand, they suggest the existence of a size threshold as
there is no difference in the expected duration of the R&D spells of firms
employing between 21 and 200 workers but, nevertheless, the expected
duration of the R&D spells carried out by firms with more than 200 employees
is larger. This result is consistent with existing studies of innovation
persistence, who have also found that large firms show higher persistence in
innovative behaviour (Geroski et al., 1997; Cefis and Orsenigo, 2001; Cefis,
2003).
22 We also find significant differences between the coefficient of APPROPRIABILITY2 and
APPROPRIABILITY3, i.e. firms belonging to industries with medium and high appropriability
environments.
23 We obtain that, in absolute value, the negative coefficient of SIZE2, SIZE3 and SIZE4 are
significantly smaller than the coefficients of Size5 and Size6. However, the coefficients of SIZE5
and SIZE6 are not significantly different.
25
Second, as regards to the impact of the number of R&D employees on
the R&D spell duration, we obtain that, as expected, firms with larger R&D
departments experience R&D spells with longer survival prospects. However,
this relationship is not linear. The expected duration of the R&D spells of firms
that employ R&D workers is greater than the one of firms with no R&D
workers
(the
coefficients
of
both
R&D
EMPLOYMENT1
and
R&D
EMPLOYMENT2 are negative and significant, although the first one only at 9%
level). Nevertheless, the number of R&D workers does not seem to have an
impact on the expected duration of the innovative spell (the coefficients of R&D
EMPLOYEMENT1 and R&D EMPLOYMENT2 are not significantly different).24.
Third, in relation to product diversification, our results suggest that the
R&D spells corresponding to firms producing a larger number of products
have
higher
chances
of
ending
(the
coefficient
of
the
variable
DIVERSIFICATION is positive and significant). This finding is not in line with
Chen (1996), who argues that diversified firms have usually higher incentives
to perform R&D since they may spread their innovative results among all their
products.
Fourth and interestingly, we find that the internal/external nature of
R&D activities has an important impact on the length prospects of the R&D
spell. Our results suggest that firms undertaking both internal and external
R&D
activities
enjoy
better
innovative
survival
prospects
than
firms
contracting externally these activities. We also obtain that undertaking these
activities both internal and externally is significantly better for the R&D spell
length than doing these activities only internally.
Firms’ market competition
In relation to firm market share, we do not find that this variable affects
its expected R&D spell length. However, we find that firms’ export
participation extends R&D spell survival prospects (the coefficient of the
Exporter dummy variable is negative and significant). This result may indicate
that firms in more competitive markets have greater incentives to undertake
R&D
activities
in
a
continuous
way
in
order
to
maintain
market
competitiveness and the high quality standard products demanded in
international markets.
24 In the estimation of the model with gamma distributed unobserved heterogeneity, the
coefficient of R&D EMPLOYMENT2 is not significant at 10% level.
26
Business cycle
Regarding the year dummies introduced to capture for the business
cycle, we find that the larger probability of ending corresponds to 1991 (the
omitted year in the estimation). In addition, pairwise comparisons between
year dummies do not reveal any business cycle effect as in most cases the
coefficient of a given year is not significantly different to the coefficient of any
other year.
6. CONCLUDING REMARKS.
This paper has investigated the determinants of the persistence of firms
in undertaking R&D activities. Unless previous studies, that have focused on
firms’ innovation persistence by analysing the number of innovation results
obtained by firms (either patents and/or major innovations), we have
examined persistence from an input point of view, and in particular,
persistence in the firms’ decision to invest in R&D activities. Our main interest
has been testing the hypothesis of dynamic increasing returns to innovation,
or the also called hypothesis of “success-breeds-success” (Nelson and Winter,
1982).
In order to do so, we have used survival methods, including nonparametric tests and the estimation of three discrete time proportional hazard
models. The advantages of our estimation methods, as compared to previous
analysis of innovation persistence, is that they have allowed for a fully nonparametric estimation of the baseline hazard function, permitting a full
identification of the effect of survival time on the length of the R&D spell. In
addition, the estimation of both parametric and non-parametric frailty survival
models has allowed a robust test for the presence of unobserved individual
heterogeneity. We have used for this purpose a representative sample of the
population of Spanish manufacturing for the period 1990 to 2000. The dataset
has been drawn from the Encuesta sobre Estrategias Empresariales, a survey
carried out annually since 1990 that provides broad information at the firm
level.
Our findings may be considered as giving support to the hypothesis that
R&D activities are subject to dynamic economies of scale (“success-breedssuccess” hypothesis). In particular, R&D intensity and innovation results are
27
important drivers of persistence in R&D activities. These results may be
considered as giving support to industry dynamic models where the main
source of dynamics arises from firms’ active learning (e.g. Ericson and Pakes,
1995). Our data has not exhibited negative duration dependence, indicating
that the probability of ending a firm’ R&D spell do not decrease as the period
goes on. However, we have obtained that unobserved heterogeneity is
important, indicating that persistence is more linked to individual unobserved
heterogeneity than to duration dependence. This result is consistent with the
industry dynamic models of passive learning (Jovanovic, 1982), in which
dynamics is driven by inherent and fairly constant characteristics of the firm
(natural endowments, managerial abilities, etc.). We have also found that firm
size, R&D employment, the nature of R&D activities, and export activities
affect the continuity in the performance of R&D activities.
Our findings make an important contribution to the understanding of
the determinants of firms’ persistency in R&D activities. Furthermore, as it is
generally accepted that the achievement of innovations (both product and
process innovations) depends crucially on the persistency in the realization of
R&D activities, our results are susceptible to have important implications both
for public policy and firm managers. As for public policies, actions addressed
to increase firms’ R&D intensity, favouring the appropriability of the
innovations,
subsidizing
the
creation
of
R&D
departments
and
the
undertaking of internal R&D, or the participation of firms in the export
markets could have a positive impact on the persistency of R&D activities and
foster the achievement of innovations. As for managers, our results suggest
that although undertaking internal R&D (versus external contracting) and
creating an own R&D department may increase the sunk costs associated to
perform R&D, they are also factors that increase the propensity to perform
R&D persistently, and persistent R&D eases the achievement of innovation
that are the final aim of R&D activities.
28
Table I. Variable definitions
Duration
Spells duration in years
Dynamic increasing returns
R&D intensity
Variable taking value 1 if the firm R&D expenditure (including
imported technology) normalized by sales (in %) is lower than 0.5%,
value of 2 if the firm R&D expenditure is greater than 0.5% and lower
than 2.5%, and value of 3 if the firm R&D expenditure is greater than
2.5%.
R&D intensity1
Dummy variable taking value 1 if the firm R&D expenditure is lower
than 0.5% and 0 otherwise.
R&D intensity2
Dummy variable taking value 1 if the firm R&D expenditure is greater
than 0.5%, and lower than 2.5%, and 0 otherwise.
R&D intensity3
Dummy variable taking value 1 if the firm R&D expenditure is greater
than 2.5% and 0 otherwise.
R&D results
Dummy variable taking value 1 if the firm obtains at least an
innovation result (a patent, a utility model, a product innovation or a
process innovation), and 0 otherwise.
Ind_technology
Variable taking value 1 if the firm belongs to a low-technological
intensity industry, value 2 if the firm belongs to a mediumtechnological intensity industry, and value 3 if the firm belongs to a
high-technological intensity industry. (See table A.2. for the industry
classification).
Low_tech_R&D0
Dummy variable taking value 1 if the firm belongs to a lowtechnological intensity industry and does not have any innovation
result (a patent, a utility model, a product innovation or a process
innovation), and 0 otherwise.
Low_tech_R&D1
Dummy variable taking value 1 if the firm belongs to a lowtechnological intensity industry and has at least an innovation result
(a patent, a utility model, a product innovation or a process
innovation), and 0 otherwise.
Medium_tech_R&D0 Dummy variable taking value 1 if the firm belongs to a mediumtechnological intensity industry and does not have any innovation
result (a patent, a utility model, a product innovation or a process
innovation), and 0 otherwise.
Medium_tech_R&D1 Dummy variable taking value 1 if the firm belongs to a mediumtechnological intensity industry and has at least an innovation result
(a patent, a utility model, a product innovation or a process
innovation), and 0 otherwise.
High_tech_R&D0
Dummy variable taking value 1 if the firm belongs to a hightechnological intensity industry and does not have any innovation
result (a patent, a utility model, a product innovation or a process
innovation), and 0 otherwise.
High_tech_R&D1
Dummy variable taking value 1 if the firm belongs to a hightechnological intensity industry and has at least an innovation result
(a patent, a utility model, a product innovation or a process
innovation), and 0 otherwise.
Appropriability conditions
Appropriability
Variable taking value 1 if the firm total number of patents and utility
models over the total number of firms that assert to have achieved
innovations in the firm industrial sector (20 sectors of the two-digit
NACE-93 classification) belongs to the first tercile of the distribution,
29
value 2 if belongs to the second tercile of the distribution, and value 3
if belongs to the last tercile of the distribution.
Appropiability1
Dummy variable taking value 1 if the firm total number of patents
and utility models over the total number of firms that assert to have
achieved innovations in the firm industrial sector belongs to the first
tercile of the distribution, and 0 otherwise.
Appropiability2
Dummy variable taking value 1 if the firm total number of patents
and utility models over the total number of firms that assert to have
achieved innovations in the firm industrial sector belongs to the
second tercile of the distribution
Appropiability3
Dummy variable taking value 1 if the firm total number of patents
and utility models over the total number of firms that assert to have
achieved innovations in the firm industrial sector belongs to the third
tercile of the distribution
Firms’ internal capabilities
Size
Variable taking value 1 if the number of employees of the firm is lower
than 21, value 2 if the number of employees is greater than 20 and
lower than 51, value of 3 if the number of employees is greater than
50 and lower than 101, value of 4 if the number of employees is
greater than 100 and lower than 201, value of 5 if the number of
employees is greater than 200 and lower than 501, and value of 6 if
the number of employees is greater than 500. To calculate the
number of employees we do not account for R&D employment.
Size1
Dummy variable taking value 1 if the number of employees of the firm
is lower than 21 and 0 otherwise. We do not account for R&D
employment.
Size2
Dummy variable taking value 1 if the number of employees of the firm
is greater than 20 and lower than 51 and 0 otherwise. We do not
account for R&D employment.
Size3
Dummy variable taking value 1 if the number of employees of the firm
is greater than 50, and lower than 101and 0 otherwise. We do not
account for R&D employment.
Size4
Dummy variable taking value 1 if the number of employees of the firm
is greater than 100 and lower than 201 and 0 otherwise. We do not
account for R&D employment.
Size5
Dummy variable taking value 1 if the number of employees of the firm
is greater than 200 and lower than 501 and 0 otherwise. We do not
account for R&D employment.
Size6
Dummy variable taking value 1 if the number of employees of the firm
is greater than 500 and 0 otherwise. We do not account for R&D
employment.
R&D employees
Variable taking value 1 if the firm number of R&D employees is 0,
value of 2 if the number of R&D employees is greater than 0 and lower
than 11 and value of 3 if the number of R&D employees is greater
than 10.
R&D employees1
Dummy variable taking value 1 if the firm number of R&D employees
is 0 and 0 otherwise.
R&D employees2
Dummy variable taking value 1 if the firm number of R&D employees
is greater than 0 and lower than 11, and 0 otherwise.
R&D employees3
Dummy variable taking value 1 if the firm number of R&D employees
is greater than 10 and 0 otherwise.
Diversification
This variable tries to approximate the degree of differentiation of the
firm line of business. The ESEE provides information about the main
30
products offered by the firm that account for at least the 50% of its
total amount of sales. Using such information, this variable has been
defined as the number of products (from 1 to 5) that account for at
least this percentage.
Foreign
Physical Variable taking value 1 if the firm average percentage of foreign
Equipment
physical equipment is 0, value of 2 if the average percentage of foreign
physical equipment is greater than 0 and lower than 51%, and value
of 3 if the average percentage of foreign physical equipment is greater
than 50%.
Foreign
Physical Dummy variable taking value 1 if the firm average percentage of
Equipment 1
foreign physical equipment is 0, and 0 otherwise
Foreign
Physical Dummy variable taking value 1 if the firm average percentage of
Equipment 2
foreign physical equipment is greater than 0 and lower than 51%, and
0 otherwise
Foreign
Physical Dummy variable taking value 1 if the firm average percentage of
Equipment 3
foreign physical equipment is greater than 50% and 0 otherwise.
R&D type
Variable taking value 1 if the firm undertakes only internal R&D,
value 2 if the firm only contracts R&D externally, and value 3 if the
firm both performs internal R&D and contracts R&D externally.
Internal R&D
Dummy variable taking value 1 if the firm undertakes only internal
R&D and 0 otherwise.
External R&D
Dummy variable taking value 1 if the firm undertakes only contracts
R&D externally and 0 otherwise.
Internal and
Dummy variable taking value 1 if the firm both performs internal R&D
external R&D
and contracts R&D externally, and 0 otherwise.
Firms’ market competition
Market share
Dummy variable taking value 1 if the firm asserts to account for a
significant market share in its main market, and 0 otherwise.
Exporter
Dummy variable taking value 1 if the firm declares to export a positive
amount and 0 otherwise.
Business cycle
Year dummies
Dummy variables taking value 1 for the corresponding year and 0
otherwise.
31
Table II Industrial technological
classification)
Industry
Meat industry
Food and tobacco
Beverages
Textiles and clothing
Leather and shoes
Timber
Paper industry
Printing and printing products
Chemical products
Rubber and plastic
Non metallic mineral products
Ferrous and non-ferrous metals
Metallic products
Industrial and agricultural machinery
Office machines
Electric and electronic machinery and
material
Vehicles, cars and motors
Other transport equipment
Furniture
Other manufacturing goods
intensity
(NACE-93
2-digits
industrial
Industrial technological intensity
Low
Medium
Low
Low
Low
Low
Low
Low
High
Medium
Low
Medium
Low
High
High
High
High
High
Low
Low
32
Table IV. Non-parametric tests of equality of survival functions and mean
duration by explanatory variables.
Log-rank
Wilcoxon
Mean duration
Dynamic increasing returns
R&D intensity
7.47
(0.024)
3.46
(0.177)
R&D intensity=1
3.83
R&D intensity=2
5.06
R&D intensity=3
5.10
R&D results
7.83
(0.005)
3.68
(0.055)
R&D results=0
1.79
R&D results=1
2.40
Industry
6.09
(0.047)
6.98
(0.031)
Ind_tech.=1
2.52
technological
Ind_tech.=2
2.81
intensity
Ind_tech.=3
3.12
(Ind_technology)
Appropriability conditions
Appropriability
7.94
(0.019)
7.13
(0.028)
Appropriability=1
2.04
Appropriability=2
1.60
Appropriability=3
1.85
Firms’ internal capabilities
Size
38.84 (0.000)
34.72 (0.000)
Size=1
1.94
Size=2
1.93
Size=3
2.10
Size=4
2.48
Size=5
3.08
Size=6
3.24
R&D employees
13.09 (0.001)
8.30
(0.016)
R&D employ.=1
1.80
R&D employ.=2
2.94
R&D employ.=3
3.96
Diversification
4.12
(0.389)
3.81
(0.432)
Diversification=1
2.69
Diversification=2
1.82
Diversification=3
1.62
Diversification=4
1.00
Diversification=5
1.50
Foreign Physical 14.90 (0.000)
12.09 (0.002)
Foreign Equip.=1
1.98
Equipment
Foreign Equip.=2
2.46
Foreign Equip.=3
2.69
R&D type
32.77 (0.000)
24.57 (0.000)
R&D internally=1
2.03
R&D externally=2
1.68
R&D internally &
2.43
externally=3
Firms’ market competition
Market share
9.48
(0.002)
9.68
(0.002)
Market share=0
2.13
Market share=1
2.59
Exporter
30.49 (0.000)
24.46 (0.000)
Exporter=0
1.97
Exporter=1
2.82
Notes:
1. Mean duration calculated considering only completed spells.
33
Table V. Maximum likelihood estimates for the discrete time proportional hazards models.
No Unobserved
Gamma unobserved
Two-mass points
heterogeneity
heterogeneity
estimates
Coefficient
p-value
Coefficient
p-value
Coefficient
p-value
R&D intensity2
-0.329
0.020
-0.418
0.020
-0.399
0.014
R&D intensity3
Low_tech_RD1
-0.102
0.599
-0.221
0.386
-0.254
0.268
-0.037
0.829
-0.061
0.772
-0.062
0.759
Medium_tech_RD0
-0.024
0.919
-0.206
0.516
-0.239
0.391
Medium_tech_RD1
-0.509
0.015
-0.706
0.015
-0.681
0.007
High_tech_RD0
-0.225
0.400
-0.437
0.230
-0.438
0.167
High_tech_RD1
-0.539
0.090
-0.808
0.053
-0.749
0.034
Aproppiability2
0.111
0.482
0.101
0.588
0.069
0.707
Aproppiability3
-0.314
0.072
-0.383
0.067
-0.417
0.038
Size2
-0.231
0.186
-0.386
0.121
-0.450
0.047
Size3
-0.081
0.722
-0.266
0.412
-0.362
0.221
Size4
-0.462
0.040
-0.740
0.034
-0.793
0.007
Size5
-0.704
0.003
-1.048
0.005
-1.102
0.000
Size6
-0.727
0.050
-1.131
0.029
-1.141
0.008
R&D employment2
-0.196
0.258
-0.281
0.189
-0.351
0.086
R&D employment3
-1.114
0.070
-1.299
0.053
-1.332
0.04
Diversification
0.211
0.078
0.308
0.073
0.334
0.03
Foreign physical equipment2
0.010
0.953
0.033
0.874
0.062
0.751
Foreign physical equipment3
-0.256
0.122
-0.297
0.168
-0.312
0.115
R&D internally
-0.080
0.617
-0.077
0.698
-0.107
0.558
R&D internally & externally
-0.647
0.002
-0.692
0.004
-0.685
0.002
Market share
-0.176
0.192
-0.207
0.228
-0.172
0.293
Exporter
Year 1992
-0.287
0.043
-0.395
0.046
-0.335
0.048
1.420
0.000
1.389
0.000
1.322
0.000
Year 1993
1.574
0.000
1.673
0.000
1.587
0.000
Year 1994
1.451
0.000
1.563
0.000
1.52
0.000
Year 1995
1.064
0.001
1.198
0.001
1.102
0.001
Year 1996
1.357
0.000
1.448
0.000
1.372
0.000
Year 1997
0.986
0.002
1.094
0.002
0.988
0.003
Year 1998
1.364
0.000
1.506
0.000
1.484
0.000
Year 1999
1.431
0.000
1.681
0.000
1.640
0.000
d1
-1.022
0.004
-0.595
0.237
-0.468
0.258
d2
-1.479
0.000
-0.815
0.193
-0.756
0.100
d3
-1.832
0.000
-1.023
0.153
-0.960
0.058
d4
-1.693
0.000
-0.722
0.372
-0.623
0.269
d5
-1.693
0.000
-0.621
0.479
-0.459
0.452
d6
-2.135
0.000
-0.980
0.323
-0.812
0.274
d7
-2.366
0.003
-1.227
0.279
-1.076
0.250
-2.407
0.024
-1.341
0.317
-1.216
0.304
d9
Log-likelihood
N. of observations
N. of spells
Test for unobserved individual
heterogeneity
-542.500
-541.130
-539.938
1250
1250
1250
480
480
480
LR
test
of
Gamma mtype1 = 0
variance=0
mtype2= -2.455 with
Chibar2(01)=2.742
p-value=0.003
p-value =0.049
34
Figures
0.00
0.25
0.50
0.75
1.00
Figure 1: Kaplan-Meier Survival estimate
0
1
2
3
4
5
6
Survival time
7
8
9
10
0
Predicted hazard rate, h(j)
.05
.1
.15
.2
Figure 2: Predicted discrete hazard rates, all estimations
0
2
4
Survival time
No unobs. heterogeneity
Discrete mixture type 1
6
8
10
Gamma unobserved heterogeneity
Discrete mixture type 2
.2
.4
S(j)
.6
.8
1
Figure 3: Predicted survivor function , all estimations
0
2
4
Survival time
No unobs. heterogeneity
Discrete mixture type 1
6
8
10
Gamma unobserved heterogeneity
Discrete mixture type 2
36
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