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RAND Journal of Economics
Vol.
36,
No.
4, Winter 2005
pp. 930950
Barriers
to
innovation
and
subsidy
effectiveness
Xulia
Gonzfilez*
Jordi
Jaumandreu**
and
Consuelo Paz6*
We
explore the effects of subsidies by means of a model of firms' decisions about performing
R&D when some government
support
can be expected.
We estimate it with data on about 2,000
performing
and nonperforming
Spanish
manufacturing
firms. We
compute
the subsidies required
to induce R&D
spending,
we detect
the
firms that would cease to
perform
R&D without
subsidies,
and assess the change in the privately financed effort.
Results suggest that subsidies stimulate
R&D and some
firms would stop performing
in their absence, but most actual subsidies go to
firms that would have
performed
R&D otherwise.
We
find no crowding
out of private
funds.
1. Introduction
a Public sectors of all industrialized countries
spend
considerable
amounts of money
to support
commercial
R&D in manufacturing
firms.
Firms apply
for research
grants,
and agencies choose
the research to be funded. The economic justification
for these programs
lies in the presumed
failure of the market
to provide incentives to firms to allocate enough resources to innovative
activities
(Arrow,
1962;
Nelson, 1959). Positive externalities
affecting
other
firms
and consumers
induce a divergence
between the social and private
returns of such activities.
Despite the spread
of these subsidies,
the evidence of their
effects on firms' behavior remains
relatively
modest and controversial
(see, for example,
the survey
on microeconometric evidence
by Klette, Moen, and Griliches
(2000))'. Researchers are currently
trying
to determine
whether
subsidies stimulate
R&D, in the sense that firms undertake
projects that otherwise would not
have been carried
out, and also whether public funds crowd out the companyfinanced
R&D
expenditure.
The most recent firmlevel
econometric studies still offer conflicting
answers.
* Universidade de Vigo; xgzlez@uvigo.es, cpazo@uvigo.es.
**
Universidad Carlos
III
de Madrid;
jordij@eco.uc3m.es.
We are grateful to Manuel Arellano, Isabel Busom, Raquel Carrasco,
Miguel Delgado, Bronwyn Hall, Rupert
Harrison,
LarsHendrick
Rller, Peter
Zemsky,
and the audiences
at the 2nd CEPR
Conference on Applied IO (Lisbon,
2000) and at Universidad
Carlos
III
de Madrid for their
suggestions.
We
thank the Editor,
Ariel Pakes,and
two anonymous
referees for useful comments
that have
greatly improved
the
article.
We
acknowledge
support
from
projects
SEC20000268
and BEC200202527 (CICYT
and
FEDER),
and
PGIDT03PXIC300014PN
(Xunta
de Galicia).
1 See also the related works by Hall and Van
Reenen (2000) on fiscal incentives, David, Hall, and Toole (2000)
on public/private
R&D, and
the interesting
account of the Israeli
experience by Trajtenberg
(2002).
930 Copyright
? 2005, RAND.
GONZALEZ, JAUMANDREU,
AND
PAZO / 931
Wallsten
(2000) estimates a simultaneous model of expenditure
and
funding
for a sample
of
U.S. firms
and
claims
that,
controlling
for
the
endogeneity
of grants,
no effort effect
is detected and
that a full crowdingout
effect is present.
Busom (2000) estimates effort equations
for a Spanish
sample
divided into subsidized and nonsubsidized
firms,
controlling
for selectivity,
and
concludes
that full crowdingout
effects cannot be ruled out for 30% of the firms and partial crowding
out
may be important.
In contrast,
Lach (2002) estimates the relative
increase
in R&D expenditures
of subsidized versus
nonsubsidized
firms
using panel data
on a sample
of Israeli
companies,
and
finds
that
small firms
enjoy a positive (dynamic)
total
effect, whereas
this effect fades in the larger
firms. Almus and Czarnitzki
(2003) also compare
the average
effort of subsidized East German
firms with the effort of similar (in probability
of subsidy) nonsubsidized firms in a matched
sample, obtaining
a significant
difference of four
percentage
points.
The heterogeneity
of the results
mirrors
the diversity
of methods and
approaches
for dealing
with the two problems
that must
be addressed
in order to make estimates
convincing, namely,
the
selectivity
of subsidy
receivers and the endogeneity
of subsidies.
Furthermore,
available datasets
often impose severe limits on addressing
these problems.
For example, many samples include
only R&D performers
and many show a reduced
time dimension.
This article aims to explore the effects of commercial R&D subsidies by focusing on the
modelling
of firms'
decisions when some government support
can be expected:
whether or not to
carry
out R&D projects,
and the associated level of R&D effort (R&D expenditure
over sales).
It tries to shed light on the questions of interest
by constructing
a simple but explicit structural
framework to explain why and how the firms' investments can ultimately
be inhibited,
and by
employing a sample of highly heterogeneous
firms (R&D performers,
subsidized or not, and
nonperformers)
to identify the model parameters.
From the estimates we derive profitability
thresholds and gaps for expenditure
on innovative
activities for every firm. For nonperforming
firms, we then compute the trigger subsidies required
to induce R&D spending. Among the
performing
firms, we detect those that would move back across the profitability
threshold and
cease to carry
out R&D if subsidies were eliminated.
In addition,
we assess subsidy efficiency
for
the performing
firms.
The model considers each firm as a productdifferentiated
competitor capable of shifting
the demand for its product by enhancing
product quality
through
R&D.2 Demand
characteristics,
technological opportunities,
and setup
costs of R&D projects
interact to determine
the attainable
innovative outcomes and a spending
profitability
threshold.
Below this threshold,
R&D costs are
not completely
recovered
by means of the sales increment. Firms then find it more
profitable
not
to undertake
innovative
activities,
but this decision can change
if expected
subsidies
(the fraction
of expenditure
that is expected to be publicly supported)
reduce the cost of R&D. The same
framework
explains how performing
firms take expected grants
into account when determining
the size of planned
R&D expenditures.
This framework
naturally
leads to a Tobittype
modelling of a censored
variable,
which we
will call "optimal
nonzero
effort,"
for estimating
the model
parameters
and,
particularly,
the effect
of subsidies. But subsidies are
presumably granted
by agencies according
to the effort
and
perfor
mance of firms,
and hence are the result of selection and are endogenous.
We estimate
expected
subsidies and
use them in explaining
effort
by applying
methods for dealing with selectivity and
endogeneity
in a context
that
allows for autocorrelated
errors.
To estimate the
model,
we use an
unbalanced
panel
of more than
2,000 Spanish
manufacturing
firms observed during
the period 19901999. The data come from a random
sample drawn
by
industries and size strata,
and hence results can be claimed to be valid for the whole industry.
During
the period,
several
commercial
R&D subsidy programs
accounted for the primary
source
of support
for innovations.
Firm sample
behavior
is, however,
heterogeneous.
About 25% of the
firms with more than 200 workers,
and about 80% of the firms below this size, do not report
2 Innovative
investments
shift the demand for the firm
product
instead of the production
function.
The model can
be taken as a variant
of the classical Griliches
(1979) R&D "capital"
framework.
SRAND 2005.
932 / THE
RAND
JOURNAL
OF ECONOMICS
carrying
out formal R&D. Furthermore,
only a fraction
of performing
firms,
increasing
with firm
size, obtain subsidies.
The results contribute
a series
of interesting empirical
findings.
On the one hand,
a significant
proportion
of nonperforming
firms
is estimated as "stimulable"
by financing
sensible fractions of
their
expenses,
and some real
R&D investments
are estimated
to depend,
in fact,
on the anticipated
public support.
But at the same
time, most actual subsidies are
detected
going to firms that
would
have performed
innovative activities
even had they not received
the subsidy.
On the other
hand,
subsidies seem to induce
only a very slight change
in the level of private
expenditures
chosen by
the firms that would, in any case, perform
innovative
activities, but no crowding
out of private
funds or inefficient use of subsidies
is observed. On the whole, Spanish manufacturing
subsidies,
which amount to 45% of R&D expenditure,
are estimated
to increase
total R&D expenditure
by 8%. Half of this effect comes from the firms stimulated
to perform
R&D, which are mainly
small firms.
Thus,
the results
suggest
that
market
failures3
do matter and that subsidies can play a
role, and play it effectively,
in stimulating
R&D activities.
However,
they also suggest that most
subsidies
in fact go to firms
that would have perfomed
R&D anyway
and
therefore
actual
public
policy may, in part,
be neglecting
the inducing
dimension of public support.
The article is organized
as follows. In Section 2 we describe the data and the main facts
on innovation activities and subsidies. Section 3 explains our modelling of the firms' R&D
decisions. Section 4 presents
the estimation
procedure
and explains how the results are used to
measure
subsidy effects. In Section 5 we report
the results,
in Section 6 the subsidy
effects, and
the conclusions are in Section 7. Two Appendixes
detail the econometrics
and
the data.
2. Data and description
m The basic dataset is an unbalanced
panel of Spanish manufacturing
firms surveyed
during
the 1990s.4 At the beginning of the survey, firms with fewer than 200 workers were sampled
randomly
by industry
and size strata,
retaining
5%. Firms
with more than 200 workers were all
requested
to participate,
and
the answers
initially represented
approximately
a selfselected 60%
of firms within this size.5 Our
particular
sample
includes a total of 2,214 firms,
observed
during
the period 19901999, selected according
to data
availability.
The data
provide
information on the total R&D
expenditures
of the
firms,
including
intramural
expenditures,
R&D contracted
with laboratories or research
centers,
and technological
imports,
that is, payments for licensing or technical assistance. We consider a firm to be performing
technological
or innovative
activities
when it reports
some R&D expenditure.
Our central
interest
lies in the firms' R&D expenditures
and their
technological
effort, defined as the ratio of R&D
expenditures
to firm sales. To explain these variables,
we use the extensive information on the
firms' activities covered
by the survey
and the data
on subsidies.
During
the 1990s, subsidies as
a whole were the main public incentive
available
for manufacturing
firms to undertake research
programs.
Our subsidy measures
refer to the total amount of public financing
received for each
firm
under
different
program headings.6
Sample
and
variable details are
given in Appendix
B. In
what follows, we summarize some facts about R&D expenditures
and granted
subsidies.
Table
1 and
the first two columns of Table
2 report
the
degree
to which
Spanish
manufacturing
firms
engage in formal
R&D activities.
Table 1 shows that
the probability
of undertaking
R&D
3
We refer to situations
in which some R&D investment
is not carried out due to its cost, but the addition
of the
net consumer
surplus
increase derived
from the investment would give a positive global surplus.
4 The survey was sponsored
by the Spanish Ministry
of Industry
under the name "Encuesta sobre Estrategias
Empresariales"
(Survey
on Firm
Strategies,
available at www.funep.es/esee/esee.asp).
5 To preserve representation, samples of newly created
firms were added
every subsequent year. Exits from the
database
come from both death
and attrition,
but they can be distinguished,
and attrition
was maintained under sensible
limits. 6 Namely,
the
European
Framework
program,
which
reached
a very
small
number
of firms;
the
Ministry
of Industry
programs,
which include the subsidies granted
by the specialized agency CDTI (Center for Industrial
Technological
Development),
and the technological
actions of regional governments.
? RAND 2005.
GONZALEZ,
JAUMANDREU,
AND PAZO / 933
TABLE 1 R&D Activities and R&D Effort (Yearly Averages of Nonzero
Efforts)
<200 Workers >200 Workers
Total R&D Effort Total
R&D Effort
Firms
with R&D Without With Firms with R&D Without With
Year (%) Subsidies Subsidies (%) Subsidies Subsidies
1990 17.3 2.3 4.5 76.6 1.7 4.2
1991 18.8 2.2 4.8 75.0 1.7 4.3
1992 18.0 2.1 5.6 71.4 1.7 3.8
1993 18.9 2.1 4.0 70.1 1.8 3.6
1994 19.6 2.0 4.0 74.4 1.9 3.4
1995 20.2 1.6 4.2 69.3 1.5 4.1
1996 20.4 1.9 4.4 72.1 1.6 3.3
1997 22.3 1.9 3.8 71.3 1.8 3.3
1998 25.6 1.6 4.3 74.4 1.7 3.4
1999 26.0 1.6 4.2 77.0 1.4 4.1
activities
increases
sharply
with size7 (average probability
is 21% for firms
with fewer than
200
workers
and 73% for firms with more than 200 workers).
This probability,
which shows some
procyclical
features,
has been increasing
slightly over time for the smallest firms. The first
two
columns
of Table 2 adopt
another
perspective
by distinguishing
stable and
occasional
performers
during
the period.
Stable R&D performers
are firms
that
report
R&D expenditures every
year they
remain in the sample. Occasional
performers
are those firms that
report
R&D expenditures only
some of the years they remain in the sample. Stable performance
of R&D activities is strongly
correlated
with size, while occasional
performance
shows an inverted
Ushaped
relationship.
Expenditures among the R&D performers
are unequal, with a high probability
that the
observed
amounts exceed nonnegligible positive values, which suggests
the involvement of setup
costs. Figure 1 depicts the (standarized)
distributions of the logs of firms' expenditures,
keeping
the corresponding expenses in thousands of euros as labels.8 Both distributions tend to fit the
standardized
normal very well, and hence expenses can be taken as lognormal. The vertical
dashed lines point out the modes of the lognormal distributions,9 with values of about
4 and 54
TABLE 2 R&D Activities and Subsidies During the Period 19901999
Firms Granted at Least One Year Subsidy/R&D Expenditures Total
R&D Effort
Firms
with R&D (%) (% of R&Dperformers) (in %,
granted
firms) (averages
of nonzero
efforts)
Stable Occasional Stable Occasional All Stable Occasional All Without With
Firm
Size Performersa Performersb Performersa Performersb Performers Performersa Performersb Performers Subsidies Subsidies
<20 workers 4.1 20.3 31.0 9.9 13.5 69.9 65.3 67.5 2.2 4.9
2150 11.2 23.6 31.7 16.7 21.5 49.5 57.0 53.1 2.0 3.8
51100 19.1 36.3 43.3 24.6 31.0 53.9 26.0 42.4 1.7 5.0
101200 39.1 28.2 31.6 17.5 25.7 29.5 75.8 38.1 1.6 3,9
201500 54.1 31.7 52.7 26.6 43.1 23.0 47.1 26.6 1.7 3.7
>500 69.0 20.7 54.3 23.7 47.3 15.0 42.4 17.3 1.8 3.8
aFirms
reporting
R&D expenditures
every observed
year.
bFirms
reporting
R&D expenditures
some of the observed
years.
7 In all tables, "size"
reflects the first
year the firm
is in the sample.
8 Representation
is based on the standarized
values of the data after dropping
2.5% of the values at each tail.
Heterogeneity
is likely to influence
the variance
of the distribution
by mixing the typical
expenditure
amounts
of different
activities
(some of them very low).
9 If x ,lognormal (pt,
a2), mode(x) = eU22. According to their means and standard
deviations, we assume
distributions to be lognormal(3.85, 1.572) and (6.15, 1.472).
? RAND 2005.
934 / THE RAND
JOURNAL OF
ECONOMICS
FIGURE 1
THE DISTRIBUTION OF R&D EXPENDITURES
Up to 200 workers
14.
S12
1022
> 10
0,8
0
) 6
0 4
S2
a.
2 10 47 226 1083
R&D
expenses, thousands of euros (logscale)
More
than 200 workers
14 
) I
C 12
0
> 10
0)
a 8
o, 4
S2
25 108 466 2020 8754
R&D
expenses, thousands of euros (logscale)
thousand
euros. Take these values as a descriptive
measure
(among those possible) of "critical"
expenditure
values (associated
probabilities
of observing
lower expenditures
are small, 5.8 and
7.1%,
respectively).
To assess their
importance
in relative
terms,
we average
observed minimum
industry
sales over a breakdown of manufacturing
in 110 industries.
Absolute critical expendi
tures
divided by average
minimum
sales give rough
critical values for R&D effort of 1.9 and .8
percentage points, respectively.
Absolute critical
expenditures
for the smallest firms are smaller,
but they appear
to be higher
in relative terms.
Table 2 reports
the main facts about grants.
Columns 3 to 5 show that only a fraction of
R&D performers
receive subsidies and that
the proportion
of subsidized firms
tends to increase
with firm
size and stable
performance. Figure
2 depicts the distribution of the subsidy amounts.
Many subsidies are small, but the spread
is also important.
Columns
6 to 8 of Table
2 show that
the typical subsidy
covers between 20% and 50% of R&D expenditures
and also that the rate of
subsidized
expenditure
is inversely
related
to firm
size (particularly
for the stable
performers).
Table 1 and the two final columns of Table 2 also provide a first look at the relationship
between subsidies and effort, based on the comparison
of the R&D effort of subsidized and
nonsubsidized
performers'
data. Both tables show a positive association
between the granting
of
subsidies and
R&D
effort,
during
the period
as a whole and from
year
to year.
The data
show more
than
"additionality"
in the sense that
subsidized efforts minus the part
of these efforts
attributable
to subsidies are
higher
than
nonsubsidized
efforts.
Figure
3 provides
a first
look at the relationship
between the privately
financed
expenditure
and
the amount
of the subsidy
for subsidized
firms.'0
FIGURE 2
THE SIZE DISTRIBUTION OF SUBSIDIES
28 Up to 200 workers
. 24
20 96.4%
of values shown
21 20
16
o 12
S8
CD
2 4
50 100 150 200 250 300 350 400
Subsidies,
thousands of euros
28 More than 200 workers
28
 24
20  82.2%
of values shown
2 20
(D
0 16
0
o 12
IS 8
2
4
50 100 150 200 250 300 350 400
Subsidies,
thousands of euros
0o
Representation
is carried out by dropping
the subsidies
higher
than their associated
yearly
R&D expense values
(see Section 5) and 2.5% of subsidy
values at each tail.
? RAND 2005.
GONZALEZ,
JAUMANDREU,
AND PAZO / 935
FIGURE 3
PRIVATE
R&D EXPENDITURES AND SUBSIDIES
Up to 200 workers
10
o 9
'•o 8
.. 7
7*
S4 * * II
0 1 2 3 4 5 6 7 8 9 10
Log of subsidy
11
More than 200 workers
10 *
27 *"
a
9
"
0r 7
6, 6
2
012345678910
0 1 2 3 4 5 6 7 8 9 10
Log
of subsidy
According to the figure, private expenses tend to show a unit elasticity with respect to public
funds.
Therefore,
the data
suggest nonnegative
and even
positive
R&D effects of subsidies.
However,
this could be the consequence
solely of other
omitted
variables or because of the twoway nature
of the relationship:
firms
with more R&D are
more likely to receive subsidies,
and the larger
the
subsidies, the higher the R&D expenses. Only the development
of an econometric
analysis can
provide
further
insight into this relationship, by providing
evidence as to how these data
patterns
can be interpreted
in terms
of "causal"
effects.
3. A model with barriers to R&D
N R&D with setup costs. Let R(x) be firm net revenue as a function of R&D expenditure
(subindexes
are
dropped
for simplicity)." R&D affects
revenue
positively
at a nonincreasing
pace,
i.e., aR/ax > 0 and a2R/laX2 0, but
only if x surpasses
setup
costs F. To decide the pertinence
and level of R&D expenditures,
the firm
maximizes the expected profits E[R(x)  (1  p) x],
where p is the fraction of R&D expenditure
that is subsidized,
and E indicates the expectation
over p values.12 We allow for public funds
to be associated
with either
a higher
or lower level of
expenditure
efficiency13
by means of parameter
#.
Equilibrium
admits
the straightforward
representation
of Figure
4. Isoprofit
curves are
linear
with a slope equal to the (expected)
effective cost of R&D, E[(1  p)#], and the firm's
decision
is dictated
by the maximum
of two ordinates,
the profit
no corresponding
to x = 0 and a profit
as
fi or 12, say, associated
respectively
with x* or x*. Define I as the expenditure
level that
makes
the firm
indifferent
to performing
R&D or not (the tangent
of R at this point, not shown in the
figure,
crosses the yaxis at no).
Under fairly general conditions there is an effort by both performing
and nonperforming
firms, which we will call optimal nonzero effort, that can be summarized in the (Dorfman
and
Steiner
(1954)type) unique
expression
x* xaq p aq
p*q* q x / p E[(1 p)) (1)
p*q* q 8x q p
" Net revenue
can be, for example, R(x) = max(p  c)q(p, x), where p stands for output price, c for (constant)
marginal
cost, and q the demand
for the firm's
output.
12
Firms
have subjective
conditional distributions
of probability,
which depend
on their beliefs about the chance of
success in the search for a subsidy
program,
and on the likelihood
of being granted
a subsidy
by the agency.
13
On the one hand, public funding often gives access to other facilities or advantages
(e.g., access to public
laboratories and researchers).
On the other hand,
public funds can be mainly viewed as easing liquidity
constraints and
allowing for less financing
discipline, which implies less expenditure
efficiency.
C RAND 2005.
936 / THE RAND
JOURNAL OF
ECONOMICS
FIGURE
4
THE DETERMINATION
OF EQUILIBRIUM
AND PROFITS
fl(xeq) = max{1f(x*), n(0)}
R(x)
R(x)
n,
no
I I I
n2
F
*
x
xi
x
and that will be observed
if it surpasses
the
threshold effort
which
corresponds
to y.14 Formula
(1) shows
that
optimal
nonzero effort increases with the elasticity
of demand with
respect
to
R&D
expenditure
and with the
degree
of market
power
(the
inverse of the
price elasticity).
The
numerator can be decomposed
into the elasticity
of demand with
respect
to quality
(demand
conditions)
and the
elasticity
of quality
with
respect
to R&D
(technological
opportunities).
"Lack
of appropriability,"
as
a factor that
discourages
R&D,
can
be
easily
discussed in this
framework.15
(Expected)
subsidies
have
two
different
potential
effects:
they
can induce firms
to perform
R&D
and
they
can enhance the R&D of the firms that would
perform
innovative activities
in any
case.
o Econometric model. Let
e* and
i stand
for
the
logs
of optimal
nonzero
effort
and
threshold
effort,
respectively. Starting
from
(1) we assume
e* =  5
In(1
 pe)
+ zl1 + w (2)
e= zf•2
+ u2 (3)
pe = E(plz) = g(zp,X
), (4)
where e* is observed only when e*  i > 0, pe is the expectation
for p, and w represents
an
autocorrelated error of the form w, = y wt1 + 81t (for simplicity, time subindexes are used
only when needed
to avoid
confusion).
We assume that
(sE,
u2) is bivariate
Normal,
with
zero
mean,
independent
of z and
z,p
(Zl
is a subset of z), and
serially
independent,
with
V(el) = 0•
V(u2) = 22,
and Cov(e1, u2) = 012.
The effort
equation
(2) is obtained
by taking logs in (1), substituting In[1
 E(pJzp)]
for
In
E[(1  p) I ZP],'6
and letting Zl stand for the vector of variables
that determine the value
of the (log of) elasticities.
Expected
subsidies enter the effort
equation
in the
way they
appear
in the firstorder
condition
(1), but elasticities are
endogeneous
unobservable variables
that
we
replace
with a set of reducedform
determinants,17
(i.e., exogenous
or predetermined
variables
14
R&D
level
expenditures
x and
R&D effort
x
/pq can be used
interchangeably
because the
model
and
assumptions
imply
that effort increases
monotonically
with
x for
a given
firm.
15
For
example,
high
knowledge
spillovers
mean
a high
likelihood
of a rapid matching
of product
innovations
by
rival
firms,
and
hence
a lower
(net)
demand
elasticity
with
respect
to
quality.
For
given
F, this
increases
the
likelihood
of
an
optimal
nonzero effort below
the
threshold effort.
16
An expansion
of (1  p)# around
E(p) shows that
In E[(1  p)#] L P In[1
 E(p)] + In[1
+ (1/2)5(P  1)c2v],
where
cv is the coefficient of variation
of (1  p), i.e., cv = [var(l  p)]1/2/E(1  p). The second term of this expression
is likely
to be small,
of order
(1/2)P(P
 1)E(p2)
and,
under certain
circumstances,
constant.
17
We
assume the standard
account
of determinants of innovative
activities
to
be
underlying
these
elasticities.
See,
for
example,
Pakes
and
Schankerman
(1984),
Cohen
and
Levin
(1989),
or Cohen
(1995).
C RAND 2005.
GONZALEZ,
JAUMANDREU,
AND PAZO / 937
with respect to (E1, U2)).18 The autocorrelated
disturbance w takes into account that we are not
likely to be able to fully specify optimal
nonzero effort
determinants.
Equation
(3) models thresholds.
We take
firms
as having
idiosyncratic
stochastic
thresholds,
which can be presumed
to be a function of the same
variables that
determine
e* and
perhaps
others
of the same kind (z contains at least all variables
in zl). The coefficients give the height of the
"barriers"
to the profitability
of R&D. Here
we are
assuming
that the error term
u2 is independent
and identically
distributed over time.
Equation
(4) states
our
assumption
that the unobservable
firms'
expectations
pe can
be related
to observable
data
through
the function
g(zp, k), with zp such that (e1, u2) is independent
of zp.
The function
gives the financial
support
each firm
presumes
it can obtain
given its characteristics
and the allocations
observed from agencies. Notice that
we make the strong
assumption
that
we
observe all variables relevant for the expectation.
In particular, any agency evaluation of firm
conditions is anticipated
through
firm attribute indicators.
The function is likely to be highly
nonlinear,
and zp is (possibly) only partially overlapping
with z.
Equations (2)(4) define a rather standard
(typeII or thresholds) Tobit model.19
R&D
performance,
and hence observation of e*, is determined
by the sign of e*  i (selectivity or
decision equation).
Amemiya (1985) discusses alternative
identification conditions
of this model
(see also Maddala
(1983) and Wooldridge
(2002)). One of these conditions
is the availability
of
at least one variable that enters the equation
for the censored variable but can be excluded on
theoretical
grounds
of the thresholds
equation.
This condition
arises
naturally
in our
model,
where
expected subsidies
can be safely excluded from the determinants
of thresholds.20 But the model
also has some nonstandard
features.
First, disturbances
of the effort equation are assumed to be autocorrelated.
This implies
that predetermined
variables are likely to be correlated with these disturbances. To ensure
consistency, the effort equation must then be specified in the pseudodifferenced
form e =
yet l
 (ln(1  pe)  y In(1  p1))
+ (Zlt  YZit1)pI + elt, and this raises the difficulty that
the latent variable
e*, only partially
observable,
also becomes an explanatory
variable.
Second, we have the unobservable pe. Observed subsidies p are granted by agencies
according
to, among other things, the contemporary
effort and performance
of firms
and hence
are presumably
endogenous (their values are likely to be correlated
with the random
term el
and hence with u2). Our
framework
assumes, however,
that
relevant subsidies are the subsidies
expected in advance
by firms, pe, which can be expressed
in terms of a set zp of exogenous or
predetermined
variables. But because pe is unobservable,
we need to substitute
the generated
regressor
g(zp, X) for the expectation.
4. Estimating
the model and measuring
subsidy effects
M Estimation procedure. Estimation
is carried out through
a twostep procedure:
first we
estimate the conditional expectation of subsidies, and then we estimate the Tobit model, by
maximumlikelihood methods. Let us explain
these steps in turn.
To estimate the unobserved variable pe = E(p zp) = g(zp, X), we decompose the
expectation
as follows:
pe = E(p I
Zp)= P(p > 0 Izp)E(p I
zp,
p > 0), (5)
where P(p > 0 I zp) stands for the conditional
expectation
of receiving
a grant
and
E(p I zp, p >
0) for the
expected
value of the subsidy
conditional
on zp and
its granting.
This allows us to use two
18 Some variables are
taken
to be predetermined
in the sense that
(e8t, u2t) is assumed
to be uncorrelated
with their
current and
past values but feedback
effects from
lagged errors
are not ruled
out. Predetermined
variables
include
lagged
values of endogenous
variables.
19
Econometric
models of censored variables with stochastic thresholds date back to Gronau
(1973) and Nelson
(1977).
20
This
happens
because
thresholds
for
profitable
technological
activities
are defined
in terms
of
the total
expenditure
needed, independently
of its composition.
0 RAND 2005.
938 / THE RAND
JOURNAL OF
ECONOMICS
natural
"rationality"
or "correctness"
restrictions
on the expectations
to estimate the E(p I zp)
function. On the one hand, we assume that firms that effectively receive a subsidy are able to
forecast the amount
of the subsidy
up to a zero mean
error.
Accordingly,
we use the subsample
of
observations
in which firms are granted
a subsidy
to consistently
estimate the parameters
of the
granting
conditional
expected subsidy
function. On
the other
hand,
we assume that firms
correctly
forecast the probability
of getting
a subsidy
(which obviously is not the same as anticipating
that
they are going to receive a subsidy). Consequently,
we use the grants observed in the whole
sample to estimate
the conditional
probability
function.21 The expected subsidy
function
can be
computed
from estimates
on these two expectation
functions.
We specify P(p > 0  zp) by means of a probit of parameters
X1. We also assume
In
p I (zp, p > 0)  N(zpX2,
a 2) to estimate E(p z, p > 0). Using the estimated
parameters,
expected subsidies are then computed
as pe = 4(zpX1)exp(zpX2
+ (1/2)V2) for all firms in the
sample.
Substituting
pe for pe in the effort equation, we can estimate the Tobit model by partial
maximum
likelihood. The likelihood is based on the specification
of the joint density associated
with E1
and v2 = 81  u2 (which are the disturbances of the pseudodifferences
of the effort
equation
and
the disturbances of the decision equation;
see Appendix
A). The allowance
for serial
correlation
in the disturbances
of the effort
equation
has come at the price of the presence
of the
partially
unobservable variable
e_1I among the explanatory
variables
of both equations.
We are
going to explore
the results and
insights provided by approaching
this problem
in three
ways (see
Appendix
A for details).
If disturbances of (2) are assumed not to be autocorrelated
(y = 0), the terms in e*,
disappear,
and
parameters , fl1, and i2 can be estimated
by applying
standard
partial
maximum
likelihood methods. We
call this model
I. Estimates of this model
will show,
as expected,
evidence
of simultaneity
bias.
Autocorrelated errors
(y : 0) imply that we must include the laggedlatent
variable
e*_.
But the value of e*1 is not observed
for many
firms'
data
points (when observed
effort
at t  1 is
zero). Estimates must then rely on the remaining
data
points, which constitute an (exogenously
selected) sample consisting
of the firms'
observations
with
positive
effort at t  1.22
Selection here
is exogenous because observability
of e*1 is not related
to (elt, u2t). This is model I. The main
problem with this estimate is the small proportion
of observations of current
nonperformance
("zeros"),
which in addition correspond only to firms that discontinue
R&D at precisely that
moment
("stopping
zeros").
Consistency
is reached at a high price in estimation
efficiency.
We assume that
efficiency in estimation
can be improved by using more "zeros?'
One way
is to reformulate the model in such a manner that we do not need to observe the laggedlatent
variable. This can be accomplished by using a pseudodifferences
transformation
of the decision
equation,
which
amounts
to examining
the sign of the
pseudodifference
(e  et)  y (e_ 1
 et
1).
This sign is always
right
(it agrees
with the sign of e*  t) when the sign of e*  i changes
from
one period
to the other,
but it must be assumed to be right
when positive and
negative
differences
e*  i tend to remain
unchanged.
The assumption
is more likely if y is not very large,
but if it
does not hold, its violation will be a source of bias in estimation.
This is model III. We expect
it to contribute
a large reduction
in variance
with a negligible bias. On the estimation
side, the
decision equation
of this model shows a composite
disturbance
including
u2t1. This implies that
any endogenous variables
included among the predetermined
should be lagged twice to avoid
correlation
with this disturbance,
and
that we induce
some autocorrelation
in the likelihood score.
Models I to III are estimated
using partial
maximumlikelihood estimators with a generated
regressor; these estimators solve max6
>i Et log Lit(O, ). Asymptotic standard
errors are
computed taking into account the variance of X and possible correlations between the scores at
different
periods
of time (see, for example,
Wooldridge,
2002). Maximumlikelihood estimation
21 A more structural
approach
to the probability
function is unfortunately prevented
by the fact that we cannot
separately identify the sample
of applying
firms.
22 See Arellano, Bover, and
Labeaga (1999) for an application
of this solution in a different
context.
SRAND 2005.
GONZALEZ,
JAUMANDREU,
AND
PAZO / 939
is carried out through
a grid covering the values of the disturbances
correlation coefficient r,
beginning
at r = 0 (see Nawata and Nagase, 1996). Models in pseudodifferences
are estimated
performing
a combined
grid over the r and y values.
o Measuring profitability gaps and subsidy effects. After the estimation
of the model, we
are
ready
to compute
individual
optimal
nonzero effort
and
threshold
estimates,
then use them
to
assess the effects of subsidies. We will do this relying on the nonstochastic
components
of the
equations,
that is, evaluating
the relationships
at the (zero) expected value of the disturbances.
Let us distinguish
between these gaps and the gaps that
average
the unobserved
heterogeneity.23
The model predicts
R&D performance using the first
gaps, and we choose to base our measures
on these gaps. We also report
values for the second gap measure.
Let us define
profitability
gaps. These are the difference between the optimal
nonzero
effort
in the absence of subsidy and threshold effort. If negative, they provide
the R&D effort wherein
the firm falls short of undertaking
profitable
innovative activities. If positive, they provide the
R&D effort that the firm would make, in the absence of subsidies, in addition to the minimum
profitable
amount.
We compute
them as exp(zfll)  exp(zf82).
Given
estimated
profitability
gaps,
we can
evaluate the
(actual
and
potential)
roles of subsidies
in the performance
of innovative activities.
Let us first focus on trigger
subsidies.
We define them
as the value of the pe's that would induce
nonperforming
firms to undertake innovative activities
(by filling their
negative profitability
gaps). They can be estimated as the values of pe that solve
the equations
f In(1
 pe)+ z(f1  •2) = 0 for observations for which this
expression,
evaluated
at the estimated
expected subsidy,
is negative.
Let us now evaluate the role of a subsidy withdrawal. Some firms are likely to be
carrying
out innovative activities because the support
effect of the expected subsidy fills in the
negative profitability
gap that would exist in its absence. We identify the observations at which
P In(1  '?) + z(•i  12) > 0 but with z(8i  12) < 0 (negative
profitability gap).
The above refers to the ability of subsidies to induce firms (potentially
or effectively) to
invest in R&D. But how, according
to the model, do subsidies change the expenditure
of firms
that
perform
innovative
activities?
First,
notice
that
R&D expenditures
are
expanded
in the model
to increment
sales, and, therefore,
the rate of change in effort constitutes
a lower bound for the
rate of change in expenditure.24
Second, changes in effort depend on subsidies in a complex
way, because all the elasticities in (1) may change with the firm's
equilibrium.
We will use an
approximate
measure of the change in effort that becomes exact in the simplest case in which
elasticities remain
constant.
Call E(pe) total effort with subsidy and e(O)
total effort in its absence. Write (1  pe)e(pe)
for private
effort when R&D is subsidized.
It is easy to check that
(1  pe)E(pe) e(O) = [(1  pe)(l) 1]0 if 051.
e(o)
Therefore,
if subsidy efficiency 0 is unity,
private
effort will remain the same, which means that
privately
financed
expenditures
will increase
at the same pace as sales. In contrast,
if P exceeds
unity,
the subsidy will increase
private
effort, and total effort will be higher
than the sum of the
public fraction and the private
effort without subsidy. If P were less than unity, private
effort
would be reduced. Other studies take the value of the derivative of private
expenses with respect
to subsidy
(see Wallsten
(2000) or Lach
(2003)). With sales controlled
for,
this derivative amounts
to a linear
partial
effect (independent
of the subsidy
value and
without
demandinduced
effects).25
23 E[exp(e*)  exp(J) I z, w = u2 = 0] = exp[E(e*  F)],
which gives the level values
corresponding
to the (zero)
expected value of the disturbances,
and E[exp(e*)  exp() I z], which also averages
the unobserved
heterogeneity.
24 The change
in expenditure
may be conceptually
decomposed
in the sum of two changes:
the change
due to sales
and the change in effort. An assessment of the sales effect of subsidies would be possible only with a more complete
specification
of the demand.
25
We can compute
an average
subsidy
effect of this type by evaluating
at some point
the first
term
of the righthand
side of the identity
below (where S is a shorthand for sales): (1pe)x(e)x() = pe)(pe)(o) + 6(o) s(pe)s(o)
pex(pe)0 pee(pe) pe,(pe) S(pe )
? RAND 2005.
940 / THE RAND
JOURNAL OF ECONOMICS
5. Empirical specification and results
m Expected subsidies. We estimate the unobservable
firms'
expectations
pe using the probit
and OLS specification
of (5). Recall that we want to predict the expected outcome by means
of a set of variables that can be considered
exogenous or, at least, predetermined.
This will be
explained
in the following section. Details on all the employed
variables can be found in Appen
dix B.
First
of all, subsidies
tend
to persist
over
time. This
persistence
can
be based either on projects
spread
over several
years or the renewal
of grants
by particular
firms.
To pick up persistence,
we
specify both equations
as dynamic,
including
the dependent
variable
(the subsidy dummy
and the
log of the subsidy) suitably
lagged. We consider
two alternative
specifications
of the equations:
we will use in turn
the dependent
variables,
lagged one and two periods.
On the other
hand,
the
subsidy
can be zero for the (one or two periods) lagged values. Hence, this variable is included
in
OLS regressions
split in two: a variable
taking
the value of the log of the subsidy
when positive
and zero when the subsidy
is zero, and a dummy
that takes the value one when this is the case.26
We use the same set of additional variables to estimate
both equations.
We first include a
series of the firm's
characteristics
that
may enhance
the willingness to apply
and/or
the eligibility
of firms:
their size, age, an indicator of the degree of technological sophistication,
and capital
(in equipment goods and machinery) growth.
We then include three indicators of situations
for
the firm
that can turn
out to be significant
to granting
agencies for politicoeconomic
reasons: a
dummy characterizing
whether the firm is a domestic exporter,
a dummy denoting
whether
the
firm has foreign
capital,
and another
indicating
whether the firm is likely to have
significant
market
power. A number of these variables
are considered
predetermined
and always included lagged
one period;
others are assumed to be strictly exogenous or predetermined
longer in advance.27
Finally, we add three sets of dummy variables to account for sectorial heterogeneity
(industry
dummies),
differences
in regional
support
policies (region
dummies),
and
changes
over time (time
dummies).
Table
3 reports
the results
of the estimation. Results
are sensible and turn out to be similar in
the two specifications (dependent
variables
lagged once and
twice). The goodness of fit of probit
models is checked using the explained percentage
of ones and zeros when the critical value is
suitably
selected (samples
have only about 8% of ones). The OLS model explains
approximately
50% of the variance
of the observed subsidies' values.
Persistence
turns
out to be significant.
Industry
dummies
tend to reveal
heterogeneity
across
manufacturing. Region dummies show a significantly greater probability
of subsidies for two
particular
regions. Although
the characterization of the granting process is not the main
target
of
these estimations,
the estimated
equations
seem good enough to provide
a stylized summary
of
it: the large, mature,
technologically sophisticated
and
expanding
firms,
as well as the domestic
exporters,
are more likely to obtain grants
for their innovative
activities, but agencies seem to
apply some criteria
in expenditure
coverage favoring the relatively small, new, domestic, and
competitive
firms.
Computed
expected
subsidies are sensible.
Average probability
is near
8%,
average expected
subsidy
conditional on its granting
28%,
and
average expected
subsidy
about
2%,
with a standard
deviation of 4%.28
Only
a negligible
number of predictions
for
expected
conditional
values
slightly
surpasses 100%,
and no prediction
of expected subsidy
lies outside the relevant interval
(with a
maximum value of 59%).
o Tobit model. Let us now detail the specifications
of equations (2) and (3). According
to the model, there are three main types of variables to be considered:
indicators of market
26
In addition, a small number of sample subsidy values (33) are higher than their associated yearly R&D
expenditures.
We assume
that this reflects
simple accounting imperfections
in the time allocation of subsidies.
27
Exceptionally,
the capitalgrowth
variable, already
in differences,
will be alternatively
used contemporaneously
and lagged once to avoid losing extra data
points.
28 These are the values obtained
using the last two columns of Table 3.
? RAND 2005.
GONZALEZ,
JAUMANDREU,
AND PAZO / 941
TABLE
3 Estimates of the Equations
P(p > 0 I y) and E(ln p I
p > 0, y)
Dependent
Variable:
(indicator
function
and log of) p
Equations
with Endogenous
Variables
Lagged
Once (r = t  1) Lagged Twice (r = t  2)
Probability
Equationa Subsidy Equationa Probability
Equationa Subsidy Equationa
Constant 2.83 (12.7) .40 (1.3) 2.62 (11.4) .67 (1.7)
Abnormal
subsidy dummyb .79 (3.8) 2.12 (14.5) .45 (1.8) 2.33 (14.1)
1(pr > 0)c 1.89 (23.9) 1.47 (15.4)
ln[l(pr > 0)pr + l(p, = 0)]c .38 (8.3) .28 (5.2)
l(p, = 0)c .58 (5.1) .41 (3.2)
Sizet1 .04 (4.3) .02 (2.7) .05 (3.4) .02 (1.8)
Age .04 (2.6) .08 (3.3) .05 (2.5) .12 (3.3)
Technological
sophistication 2.48 (5.7) .48 (.8) 2.94 (6.0) .50 (.6)
Capital
growth+,, .18 (3.3) .16 (1.1) .09 (1.2) .32 (1.5)
Domestic exporter
dummyt_1 .47 (7.8) .14 (1.3) .50 (7.3) .26 (1.7)
Foreign capital dummy .17 (2.3) .37 (3.1) .17 (2.0) .40 (2.5)
Firm
with market
power dummytl .03 (.5) .10 (1.2) .01 (.2) .06 (.6)
Industry, region and
time dummiesd included included included included
a .96 1.02
Estimation
method Probit OLS Probit OLS
Number
of firms 2,214 321 1,916 270
Number of observations 9,455 727 7,241 571
Correctly
predicted
observationse
O's .84 .81
l's .83 .81
R2 .51 .49
a Coefficients and tratios
(standard
errors robust to heteroskedasticity
and serial
autocorrelation).
b
Dummy
to account for a total of 33 subsidy
coverages
higher
than
yearly expenditure.
Included in probit
estimations dated at t  1 and
t  2, respectively,
and in OLS at t.
c (.) stands
for the indicator
function.
d17 industry
dummies, 2 particular
region dummies (Navarre
and Basque Country),
and yearly dummies for periods 19921999 and
19931999 respectively.
e Using .055 and .065 as critical values respectively.
power/competition
conditions,
variables
used to reflect the sensitivity
of demand with respect
to
product quality
and
product
quality
with respect
to R&D expenditure,
and variables
employed
to
approximate
setup
costs and
the heterogeneity
of thresholds
among
firms.
Obviously,
no variable
can claim
to pick
up exclusively
the effects of one of these headings,
but it seems
useful to classify
them in order to summarize
the empirical
effects.
With the important
exception of expected subsidies, it must be admitted
that the same
variables can play a role in explaining the optimal nonzero efforts and the thresholds. This
happens
partly
because we have to rely on proxies, but also because thresholds tend to depend
on the same factors as effort. However,
we will find it both statistically
acceptable
and useful to
impose some exclusion constraints on the effort
equation.
The main variables
included in both equations
are: the firms' market
share and a dummy
variable representing
concentrated markets (both lagged one period) as indicators
of market
power/competition
conditions;
the advertising/sales
ratio (lagged) and average
industry patents
(excluding the patents obtained
by the firm) as indicators of a high sensitivity of demand with
respect
to product
quality
and/or
product
quality
with respect
to R&D;
and a dummy
variable that
takes the value one for the firms with (lagged) negative
cash flow, to represent
serious financial
difficulties
in carrying
out innovation
activities.
Six variables are
included
exclusively in the decision
equation
to account
for setup
costs. The
list consists
of the
following
indicators:
presence
of foreign capital,
location
in regions
in which
the
? RAND 2005.
942 / THE RAND JOURNAL
OF ECONOMICS
TABLE
4 The Effect of Public
Funding
on R&D Decisions:
Alternative Estimates of the
Thresholds Model
Dependent
Variable:
(log of and indicator
of) R&D effort
Estimation
Method: Maximum Likelihood
Model
I Model I Model II Model HIa Model IIIba
Levels Levels Pseudodiffs. Pseudodiffs. Pseudodiffs.
(Total
sample) (Latent
lag (Latent
lag (Differenced (Differenced
Variables Parameters observed) observed) differences) differences)
R&D
decision
equationb
Constant' 4.74 (14.1) 4.27 (10.8) 5.18 (6.0) 4.72 (9.2) 5.11 (13.9)
Expected subsidyd f 2.38 (7.1) 2.00 (4.6) 1.00 (2.0) 1.18 (3.9) 1.07 (2.0)
Other
variables;
size and
industry
dummiese (see
Table
5)
R&D
decision
equationb
Constantc 2.14 (8.8) .12 (.4) .33 (.9) 4.36 (7.9) 4.86 (8.0)
Expected subsidyd 8 = /la 6.05 (5.4) 1.17 (1.3) .25 (2.0) 4.69 (5.9) 5.11 (5.0)
Other
variables;
size
and
industry
dummiese (see
Table
5)
ar 1.36 1.39 .91 .95 .94
a .39 1.71 3.91 .25 .21
alv .07 2.15 .14 .03 .01
y .69 .50 .52
r .14 .90 .04 .11 .05
Number of firms 2,214 849 849 1,891 1,396
Number of observations 9,455 2,532 2,532 6,891 5,076
Loglikelihood .989340 1.731081 1.454862 .780667 .773197
Correctly predicted
observationsf
O's .74 .90 .90
1's .74 .75 .76
a
Endogenous
variables
used to
predict
subsidies have been
lagged
twice.
b
Coefficients and tratios
(standard
errors corrected
for
twostage
estimation and correlation
in
the
score).
c
Firm with
fewer than
20 workers,
18th
industry.
d Generated
regressorIn(l  pe).
e Additional
set of variables common
to all
versions of the model. Includes
17
industry
dummies and 5 size dummies
(see
Table
5).
f For model
II,
predictions
for
the
critical value
which
equals
the
predicted percentages.
Modified critical values
predictions give .83 in
models
lia and IIIb.
accumulation of private
and
public technological
assets ensures
higher spillovers
(geographical
opportunities), capital growth,
a market
that has been in recession, a product highly sensitive to
quality controls, and employment
of highly skilled workers.
All these variables are
likely to be
associated
with
lower setup
expenses,
and
some of them also with a high sensitivity
of the demand
with respect
to quality.
In addition, in both equations we include a set of dummy variables of size (number
of
employees) to control for any remaining
threshold size effect. Moreover,
we include a set of 18
sector
dummies
to control for permanent
differences
arising
from activities.
Table 4 reports
the results of carrying
out the estimation of the different versions of the
model. Samples change for two reasons, according
to the estimated version: the "usable" time
observations29
and the exogenous
selections
performed
in each case. Variables,
on the other
hand,
are
always kept
the same (although lags used to predict
expected
subsidies are different for
model
IIIb).
29
Levels estimation
including
lagged
variables
requires
dropping
the first observation of each firm from
regression,
pseudodifferences require dropping the first two observations,
and pseudodifferenced
equations using a regressor
generated employing variables
lagged twice require
dropping
the first
three observations.
? RAND 2005.
GONZALEZ, JAUMANDREU,
AND
PAZO / 943
Expected
subsidy
is included
in the form  In(1
 pe), and it would be surprising
to obtain
a
6 estimate
very far
from
unity when estimating
consistently.
In fact, the sequence
of estimates
in
Table
4 strongly
confirms
what we expect from theory.
Estimates
in levels (model I) show clear
signs of bias, both when they are carried out with the unselected sample and when the selected
sample
used next
to obtain
a consistent estimate
is employed.
The
extremely large
P
coefficient
can
be attributed to the correlation
between
the generated regressor
and
an autocorrelated disturbance.
The estimate of model
II supports
the
presence
of autocorrelated
disturbances
(y = .69) and
shows
a dramatic
change in the coefficient value, which falls to unity with autocorrelated
residuals
controlled
for. However,
as discussed above, model II provides a consistent estimate but at the
price
of constraining
the sample
to observations
for which the latent variable
past
value
is observed.
This induces a considerable
loss of efficiency, which is in fact apparent
in the a estimate and
the variancescovariances of the remaining
parameter
estimates
(not shown in the table). Model
II uses scarcely a fourth of the available observations and includes a scant 13%
of zeroeffort
observations.
Model
III
provides
an
interesting
alternative for the estimation of parameter
P. The
parameter
estimate
is sensible when the subsidy
regressor
is generated
using both the onelag and the two
lags alternatives,
but model IIIb implies a more judicious choice from the point of view of the
assumptions
(subsidies lagged twice are expected to be orthogonal
to the first lag of u2). In
addition,
the preserving
sign assumption,
on which the model transformation and
consistency
are
based, holds ex post in 96.5% of the cases. Moreover,
coefficients are sensible (see Table 5 and
comments
below) and fit is good. We take this model as our
preferred
estimate,
and we will base
our economic discussion on its parameter
estimates.
Does the modelling of uncertainty really make a difference
in estimations?
To check this,
we alternatively
estimate models II and
IIIb
using the simple
prediction
of subsidy
values for the
firms
obtaining
subsidies and zeros for the rest. This can be interpreted
as the relevant
variable
in case firms are
certain about
the subsidy
and the only problem
is endogeneity.
The P parameter
drops
to .60 and .69, respectively. Uncertainty
about
subsidies
is probably
a key question
outside
of the largest
firms.
Table 4 (bottom)
reports
the results of comparing
the models' predictions
with the actual
observations
in the sample. All models except for model II behave sensibly,
even when keeping
the standard .5 critical value for prediction.30
Table 5 shows all the results of model estimation. Let us interpret
the estimates. Market
power clearly influences effort and thresholds,
although
the effect of the firm's
market share
is
somewhat
imprecisely
estimated.
In any
case, the impact
of market
share
must be balanced
against
the degree
of rivalry.
For any given market
share,
R&D effort
is greater
when the environment
is
more
competitive.
This is consistent with
the evidence of inverted
Ushaped relationships
between
product
market
competition
and innovative activities (see, e.g., Aghion et al., 2005).31
Market
power also seems to have the same type of impact on thresholds.
On the other hand, spread
patent protection
emerges as a good indicator
of technological
opportunities
that show a positive
impact
on effort. Nevertheless,
it also performs
as an indicator
of the corresponding setup costs
of innovative
activities,
increasing
thresholds.
Although
less precisely
estimated,
there
appear
to
be two additional effects. The advertising/sales
ratio seems to perform weakly as an indicator
of
demand
sensitivity,
increasing
effort, and tight firm financial constraints increase thresholds.
Finally, the inclusion of the list of firm characteristics
to pick up threshold effects shows
that the presence of foreign capital, the benefits stemming
from geographical
spillovers, a high
product sensitivity to quality, and the presence of highly skilled labor reduce thresholds.
The
similar effect of the recessive market
dummy
can be interpreted
as controlling
for the impact
on
30 For model II, highly unbalanced
in terms of ones and zeros, it is better to compute prediction
with an adjusted
critical value
that
equals
the
prediction
outcomes.
The rest of the models
can also be compared
in terms of adjusted
critical
values (see the table's footnote f).
31 We additionally experimented
with the introduction of the variable
representing competition changes, which
was never
fully significant
and
did not change the main estimation results.
? RAND 2005.
944 / THE RAND JOURNAL
OF ECONOMICS
TABLE
5 The Effect of Public
Funding
on R&D Decisions:
Estimate
of the Thresholds
Model (PseudoDifferences,
Endogenous Lagged
Twice)
Dependent
Variable:
(log of and indicator function
of) R&D effort
Estimation Method: Maximum Likelihood
Variables Parametersa R&D Effortb R&D Decisionb Thresholdb
Constantc 5.11 (13.9) 4.86 (8.0) 4.10 (5.9)
Expected
subsidyd b,
8 = l/r 1.07 (2.0) 5.11 (5.0)
Market
sharet_
l .27 (1.4) .22 (1.0) .22 (1.2)
Concentrated market
dummy, .17 (2.1) .20 (2.7) .21 (2.5)
Advertising/sales
ratiot1 1.12 (1.1) 2.81 (1.7) .53 (.5)
Average
industry
patents .12 (3.9) .12 (2.5) .09 (2.5)
Negative cash flow dummyt1 .08 (1.0) .19 (2.7) .12 (1.4)
Foreign capital
dummy .45 (2.6) .09 (1.4)
Geographical
opportunity dummy .73 (4.0) .15 (1.6)
Capital
growtht,_ .02 (.2) .00 (.2)
Recessive market
dummyt1 .12 (2.2) .02 (1.4)
Quality
controls
dummy .81 (8.3) .17 (1.7)
Skilled labor
dummy .89 (6.6) .19 (1.7)
Size dummies:
2150 workers .19 (.8) .76 (4.8) .03 (.1)
51100 workers .22 (.6) 1.20 (4.9) .04 (.1)
101200 workers .23 (.8) 2.48 (10.2) .28 (.7)
201500 workers .05 (.2) 3.11 (12.6) .70 (1.5)
>500 workers .22 (.8) 4.19 (12.2) .66 (1.1)
Industry
dummies included included included
al, a, r2 .94 .21 .97
tlr, a12 .01 .89
y = .52
r = .05
a Unless otherwise stated,
the first column estimates refer to parameters
f,, the second to parameters
82, and the third to parameters
02.
Third column estimates are
based on P2 = f1  r82,
and standard
errors
are
computed
from the delta method.
b Coefficients
and
tratios
(standard
errors
corrected
for twostage
estimation and correlation
in the score).
Blank
spaces
stand for exclusion
restrictions.
C
Firm with fewer than 20 workers,
18th
industry.
d Generated
regressor
 ln(1  pe).
the (sales relative)
threshold of an abnormally
low value of sales. In addition,
some effect of scale
seems to remain
(larger
sizes tend to experience
smaller
thresholds).
6. Profitability
gaps and subsidy effects
m Figure 5 depicts the distribution
of the estimated
profitability gaps (see also the numbers
in the web Appendix).
Positive gaps represent
about 30% and their mean is around
.4%,
while
the absolute value of the negative
gaps mean
is about .8%.
Positive gaps show less heterogeneity
(90%
lie in the (0,1) interval),
with an important
mass of values concentrated
at
relatively
uniform
departures. Negative gaps show a greater heterogeneity
(less than 73% lie in the ( 1,0) interval),
which includes,
however,
a significant
number of firms
presenting relatively
small gaps.32
Table 6 further details gap heterogeneity
by reporting
the distribution of trigger
subsidies
for the nonperforming
firms. Subsidies required
to induce firms to engage in R&D are smaller
for the largest
firms and
bigger for the smallest ones. With an expected
funding
of less than 10%
of R&D expenditures,
almost 50% of the big nonperforming
firms will switch to performing
innovative activities. In contrast,
inducing 30% of the small firms to carry out R&D implies
32 In the distribution
exp(zfi + (1/2)v~i(w))  exp(zP2 + (1/2)v"t(u2)) = 1.83 exp(zSl)  1.61 exp(zM2), positive
gaps represent
about
35%,
with a mean
of .8%,
and
the average
of negative gaps gives an absolute
value of about 1.1%.
? RAND 2005.
GONZALEZ, JAUMANDREU,
AND
PAZO / 945
FIGURE
5
THE DISTRIBUTION OF PROFITABILITY
GAPS
10
8
7
o 5
)4
c3 2
0.1 2 1 0 1 2 3
Profitability
gaps
(%)
expected support
accounting
for up to 40% of the expenses, and inducing one firm out of two
would require financing up to 50% of the expenses.
Table 6 also reports
the impact
of subsidy
withdrawal on performing
firms and the expected
subsidies that characterize
the firms that presumably abandon R&D. Interestingly enough,
subsidy
withdrawal would induce the cessation of innovative activities
in a significant
number of
performing
observations
(93 observations,
about 6% of all positive gap observations),
particularly
among the smallest firms (almost 14%). More than half of the deterred
firms show expected
subsidies lower than 10%,
but some small firms show expected funding to be more important.
These results
suggest that not all funding
is allocated
to firms that
have positive profitability
gaps
and would carry
out R&D activities even in the absence of public financing,
thus indicating
that
some part
of public financing
does, in fact, stimulate R&D activities.
Finally, our preferred
point estimate for parameter
?f (1.07) implies that subsidies induce
only modest increases
in privately
financed effort. This impact
grows with the size of the subsidy,
but the increase
in private
effort for subsidies
running
from 20% to 60% is by about 2% to 7%.33
This is, however,
only a lower bound
for the increment
in private
expenses, which does not try to
disentangle
the sales growth
effect of the innovative activities.
In any case, there
is no evidence
of funding
crowding
out, displacement,
or slackness.
What is implied,
then,
by our model with
regard
to the overall effect of subsidies on Spanish
manufacturing?
Because our
sample
has a known
representativeness,
this can be roughly
computed
from the following exercise.
Take
(predicted)
R&D expenditures
in the presence
of subsidies
and
in the absence of subsidies. We will distinguish
between firms
whose R&D performance
decision
is not affected
by subsidies and firms that
begin carrying
out R&D thanks to subsidies.
We build
manufacturing aggregate
numbers
(for
the whole period).34
The numbers
say that
aggregate
R&D
expenditure
increases
by about 8% as the
result of subsidies.35
Interestingly enough,
total
expected
subsidies (observed
subsidies)
amount
to 4.4% (5%) of total R&D expenditure.
Hence subsidies
are
helping to increase
total expenditure by slightly more than
their amount.
The 8% increment can be decomposed in two parts: 4.4% comes from the increase in
expenditures
of firms that would perform
R&D in any case, and 3.6% comes from the R&D
contributed
by firms
that
the model predicts
to be nonperformers
in the absence of subsidies. It is
interesting
to further
decompose these numbers
according
to firm size. The percentage
increase
33 These numbers
imply a low value for the derivative
of private expenses with respect
to subsidies. For pe = .3,
our estimate
gives a value of .06, positive (no crowding
out) but small.
34
We add
up the values for firms with 200 and
fewer workers
multiplied
by 20 (the sample
of these firms amounts
to roughly 5% of the population)
and for firms with more than 200 workers
multiplied
by 2 (the sample includes on
average
more or less half of the population).
35
We
compute
a rough
standard error of .2 associated with the
aggregrate
number
8%
by applying
the delta
method,
taking
the weighting scheme as fixed.
0 RAND 2005.
946 / THE RAND JOURNAL OF ECONOMICS
TABLE 6 Subsidies
Required
to Engage
in R&D and the Impact
of Subsidy
Withdrawal
Impact
of Subsidy
Withdrawalb
Subsidies
Required
to Engage
in
R&DI (Number
of observations and
percentage
from
(Percentages
of observations
by subsidy
values) performing
observations)
<200 Workers >200 Workers <200 Workers >200
Workers
Trigger Subsidy
Values Subsidy
Values 
(%) % Cumulated % % Cumulated % (%) Stop Doing
R&D % Stop
Doing
R&D %
010 3.3 3.3 48.7 48.7 010 29 6.8 24 2.0
1020 6.0 9.3 41.3 90.0 1020 5 1.2 10 .9
2030 8.1 17.4 6.9 96.9 2030 14 3.3
3040 13.3 30.7 2.5 99.4 3040 7 1.6
4050 22.4 53.1 0.6 100.0 4050 2 .5
5060 29.5 82.6 5060 2 .5
6070 17.4 100.0
Number of observations 3,321 160 59 (13.8%) 34 (2.9%)
Median
subsidy 48.9 10.1 11.0 4.0
aFirms
with
negative gaps
even
with
currently expected subsidy.
bFirms
that run into
negative
gaps
when
expected subsidy
is not accounted for.
in the
R&D of the smallest firms
(< 200 workers)
is higher,
10.8%,
with a contribution of the
firms stimulated to perform
R&D
as high
as 6.9%.
The
percentage
increase
in the
R&D of the
largest
firms
(> 200
workers)
is 5.9%,
with a component
due to the
switching
firms of only
.9%.36
Subsidies
during
the
period
are thus
estimated
to increase total R&D
expenditure
by more than
their
amount,
with almost half of the effect
coming
from the firms stimulated to perform
R&D,
which
are
mainly
small firms.
7. Summary
and conclusions
a The evidence
of
the
impact
of subsidies on firms' decisions
regarding
R&D remains
relatively
modest
and
controversial.
This
article tries to contribute
a series of findings,
based on a model
of firms'
decisions
estimated
with a representative
panel sample
of more
than
2,000 Spanish
manufacturing
firms. The decision of whether
or not to spend
on R&D emerges
from the
comparison
of optimal
nonzero effort with the effort needed to
reach
some
profitability
(threshold
effort).
We focus
on the
impact
of the
expected
subsidy
(or
fraction of effort
that is expected
to
be publicly supported)
on this
comparison,
and
on the level
of expenditure
chosen.
The
model
is
estimated
using
a censored
variable
regression,
with methods
that
attempt
to avoid
selectivity
and
endogeneity
biases,
taking
into account
autocorrelated
errors.
We find
that
nonperformance
of innovative activities
can
effectively
be traced back to the
presence
of optimal
efforts
below
the
profitability
thresholds
(that
is, negative
profitability gaps).
Small
firms
experience
the greatest
negative profitability
gaps,
but
negative gaps
also affect
a
proportion
of large
firms.
Subsidies
are
potentially
effective in inducing
firms to invest. We estimate
that
almost
half
of large nonperforming
firms
could
be induced to perform
innovative
activities
by financing
less
than 10% of their
R&D,
and one out
of three
small
nonperforming
firms
by financing up
to 40%
of their
expenses.
We obtain evidence that
actual
subsidies
do,
in
fact,
play
a
part,
even if a
modest
one. Some small
firms' R&D
performing
observations
are estimated to depend
on the
(expected)
subsidy,
in the sense that no R&D would be observed in its absence. But it must be realized
that
subsidies
go mainly
to firms
that would have
performed
innovative activities
anyway.
This
fact,
which can
be seen as the result of a proper
selection
of applicants
and
riskaversion
practices
of
agencies, suggests
that
public policy
tends to neglect
the
inducing
dimension of public
support.
36
Standard
errors associated
with 10.8% and 5.9% are .35 and .23 respectively.
C RAND 2005.
GONZALEZ, JAUMANDREU,
AND
PAZO / 947
On the other
hand,
subsidies seem to induce
only a very slight change in the level of private
expenditures
chosen by the firms that would, in any case, perform innovative activities. Our
estimate implies that if projects
were not subsidized,
they would basically be carried out at the
smaller size implied
by the absence of public
funds. However,
this also implies that no crowding
out of private
funds or inefficient use of subsidies
is observed.
On the whole, for Spanish manufacturing,
subsidies are estimated to increase total R&D
expenditure by slightly more than their amount,
with almost half of the effect coming from the
firms stimulated to carry
out R&D, which are
mainly small firms.
The employed framework,
despite its simplicity,
has turned out to be sensible in describing
profitability
gaps and exploring the impact of subsidies. Among others, two main questions
call for further research:
(1) the developing of dynamics (the different behavior of stable and
occasional performers,
the incurring
of sunk investments,
etc.), and (2) the modelling of the ex
post adjustments
of firms.
Appendix
A
N Econometric details follows.
O Model
I (levels's model). Let
us
write x for
 In(l
 pe),
z for the union of variable
sets
z and
zp,
and
assume that
/31
is written
including
the exclusion restrictions. If
y = 0,
equations
e* = fix
+
z l1 +1 and e*  = fix +
z(fl  2)+
v2,
where
v2 = 81
 U2
, are the structural
and
selectivity equations.
We observe
yl = e* if y2 = 1
[e*
 i > 0] = 1. The
partial
conditional likelihood for one
observation
may
be
written
L() = [P(y2 = 0I z)]12 [f(y1 I
Y2
= 1, z)P(y2 = 1 I
z)]
= [P(y2 = 0 z)]l2 [P(y2 = 1 1
y, z)f(yl I
z)]Y2.
Normality implies
yl I z , N(fx +zip1, a2) and
y2 = l[fx +
z(l1  2)+v2 > 0], with
v2 ' N(0, a2). Conditioning
on
Yl and
writing
(8, 82) = (1/o)(fl, 1
 2), Y2 = 1
[x +z82 +r(yl   zIfl1)/al +E2 > 0], with
E2 ^ N(0, 1  r2) and
r = orlv/(al
a). Notice that
a is identified
through
the relationship
between
8 and
P. The partial
conditional
loglikelihood
for an observation is
?(O)
= (1  y2) log(1  Q(8x + z82))
Y2[
(x+
zBs
2
+
r(
fix
z1fl)/
+
1

log
Yi

fix
ZI.
log
al.
(1
 r2)
1/2 rl
0 Model H (pseudodifferences with latent lag observed). If y ' 0, e* = ye*1 + fl + "1fl1 + 1l, where
xt = xt  y xt1. This equation
now includes a lag of the latent
variable,
and this is also the case for the decision equation,
which
becomnes
e*  = ye1+ + 1z2  u2 or
e* 
e
=e [+(y yl/)et/ i 
1YZlti1(f1/fl)+z(f1 
2)+v2 =
xc
+ z(fl  02)+
V2.
Under our serial independence
assumption,
et1 constitutes a variable uncorrelated
with (Elt, u2t), and hence a
sample selection based on a fixed rule involving et1 does not affect the consistency of the estimation.
Consequently,
we use twoyear subsequences
in which the laggedlatent
variable
is observed, i.e., all the twoyear subsequences
for
which the indicator of performance
takes the sequence
of values (1, 1) or (1, 0). The partial
likelihood for one observation
has the same general form as before, and our assumptions
now imply that yl I z  N(yet1 + fix + Zl1, al2),
Y2
= 1[c Z+
z(f1  2)+ V2
> 0],with v2 N(0, a2),and y2 = Il[SX'
+z82 +r(yl  y 1
e fx 1i 1)/oal
+82 > 0],
with E2 N N(0, 1  r2) and
r = a/(orlor). Notice that
Y2
is now given by a nonlinear model in the parameters,
but a is
again identified.
O Model III (differenced differences). Assume that
sign[(e*  et)  y(e*1  et1)] = sign(e  Ft). This is always
the case for subsequences
(1, 0) and (0, 1) and,
if y is not too large,
it is a sensible stationarity
assumption
for differences
e*  J which remain
positive or negative.
Take the set of subsequences
with a sequence
of values
(0, 0) or (1, 1) or (1, 0).
The selectivity equation
can be rewritten as (e*  it)  y(et*>  et1) = /# + (fi1  f2) + 81  u2, where the lagged
latent
is now not necessary.
This gives an estimable model (conditional
on y) where yl = et  ye1 is observed
when
Y2 = l[(e*  et)  y(et1  et1) > 0] = 1 (we have excluded the subsequences
(0, 1) because y2 = 1 but yl is
not observable).
The partial
likelihood, conditional
on y, may be written
similarly
to the other models. But notice that
v2t = Elt  u2t
+ YU2t1 (a lagged disturbance enters the composite
error
term)
and
hence endogenous
variables must be
lagged twice.
0 RAND 2005.
948 / THE RAND JOURNAL OF ECONOMICS
Appendix
B
m Variable definition and sample description. After
deleting
the firms'
data
points
for which some variable
needed
in the econometric
exercise is missing,
we retain a panel with 9,455 observations
(and
the lagged observations needed for
some variables).
In what follows, we briefly define the variables
employed. Table
B1 describes the sample. Descriptive
statistics are available
in the web Appendix
at www.rje.org/main/supmat.html.
Advertising/sales
ratio: advertising
and
promotional
expenditures
over sales.
Age: firms' average founding year (1975) minus the founding year of the firm
(in tens of years).
Average industry patents: yearly average
number of patents
registered
by the firms in the same industry
(excluding
the
patents registered
by the firm),
for a breakdown
of manufacturing
in 110 industries.
Capital
growth:
real growth
rate of an estimate of the firm's
capital
in equipment goods and
machinery.
Competition changes: dummy
variable that
takes
the value one if the firm
reports
that
a price variation has occurred
due
to market
changes.
Concentrated market:
dummy
variable that
takes
the value one if the firm
reports
that its main market
consists of fewer
than 10 competitors.
Domestic exporter:
dummy
variable that takes
the value one if the firm is domestic
(less than
50%
of foreign capital)
and
has exported during
the year.
Expected subsidy: computed
as the product
of the predicted probability
times the predicted
value.
Firm with market
power: dummy variable that takes the value one if the firm reports significant
market share and the
market has fewer than 10 competitors.
Foreign
capital: dummy
variable that
takes
the value one if the firm has foreign capital.
Geographical opportunities:
dummy variable
that takes the value one if the firm has its main plant in the autonomous
communities
of Madrid,
Catalonia,
or Valencia.
Industry
dummies: set of 18 industry
dummies.
Market share: market share
reported
by the firm
in its main market. Firms are asked to split their
total sales according
to
markets
and
report
their market shares.
If a firm
reports
that its share
is not significant,
market share
is set to zero.
Negative cash
flow: dummy
variable that takes the value one if sales minus
production
cost is negative.
Quality controls: dummy variable that takes the value one if the firm reports
that it carries out quality controls on a
systematic
basis.
Recessive market:
dummy
variable that takes the value one if the firm
reports
that its main market is in recession.
Region dummies:
set of 17 autonomous
community (regions)
dummies.
R&D effort: ratio of total R&D expenditures
to sales. Total R&D expenditures
include the cost of intramural
R&D
activities, payments for outside R&D contracts,
and expenditures
on imported technology (patent licenses and
technical
assistance).
R&D effort dummy: dummy
that takes the value one if effort is positive.
Skilled labor: dummy
that takes the value one if the firm
possesses highly qualified
workers
(engineers
and
graduates).
Size: number of employees (in hundreds).
Size dummies: set of 6 dummy
variables.
Subsidy:
ratio
of total public subsidies
to total R&D expenditures.
Subsidy
dummy: dummy
that takes the value one if the subsidy
is positive.
Technological sophistication: dummy
variable
that
takes the value one if the firm uses automatic
machines,
or robots,
or
CAD/CAM,
or some combination of these procedures,
multiplied by the ratio of engineers
and
university
graduates
to total personnel.
Time
dummies:
set of yearly dummy
variables.
? RAND 2005.
GONZALEZ,
JAUMANDREU,
AND PAZO / 949
TABLE
B1 Number of Firms
by Time
Spells
and Type
of R&D
Performers
Stable Performersb Occasional Performersc
Nonperformersa Mean Effort Mean Effort
Years
in Sample Firms Observations Firms Firms <200 >200 Firms <200 >200
1 298 298 145 112 3.1 2.5 41 .7 .3
2 503 1,006 287 129 2.6 3.1 87 .9 .6
3 319 957 159 74 2.0 2.1 86 .5 .3
4 186 744 84 56 2.7 2.2 46 .5 .4
5 193 965 81 54 2.4 3.3 58 .5 .5
6 170 1,020 83 39 2.3 2.4 48 .8 .6
7 136 952 67 27 2.8 2.7 42 1.0 .7
8 168 1,344 85 18 4.5 3.3 65 .6 .7
9 241 2,169 102 53 2.3 2.6 86 .6 .4
Total 2,214 9,455 1,093 562 2.6 2.7 559 .7 .5
a
Firms
reporting
zero R&D
expenditures
each observed
year.
b
Firms
reporting
positive
R&D
expenditures
each observed
year.
c
Firms
reporting positive
R&D
expenditures
some of the observed
years.
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