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J.A. Mañez1, M.E. Rochina-Barrachina1 and J.A. Sanchis-Llopis1
University of Valencia and ERICES
This paper estimates a dynamic model of a firm’s decision to export and invest in R&D, in which
we allow past export and R&D experience to endogenously affect productivity. In our empirical
strategy we proceed in two steps: in the first step, using as starting point the traditional control
approach method to estimate total factor productivity, we consider a more general process driving
the law of motion of productivity in which we recognise the potential role that export and R&D
experience might have in shaping future firms’ productivity, and test whether this assumption
holds; in the second step, we estimate a bivariate dynamic model of the firm’s decision to invest
in R&D and export, in which we analyse the linkages among investing in R&D, exporting and
productivity. Using a representative sample of Spanish manufacturing firms for the period 19902009 we find that both export and R&D positively affect future productivity, which will drive more
firms to self-select in those activities.
Key words: export experience, R&D experience, endogenous Markov, Total Factor Productivity,
learning-by-exporting, returns to innovation, GMM, dynamic bivariate probit.
1. Introduction.
The relation between exports and productivity has been extensively studied.1 Using rich micro
data sets from a wide range of different countries, this research has consistently found that
exporters are generally more productive than non-exporters. This empirical finding could be due
to a process of self-selection of the more productive firms into export markets (Melitz, 2003)
and/or from potential productivity gains accruing to firms from participation in export markets
(learning-by-exporting).2 However, Aw et al. (2011) point out a missing piece in this analysis:
firms carrying out some investments in R&D or technology adoption could increase both
productivity and the propensity to export, i.e. that the productivity export link could be conditioned
by firms’ R&D activities. In this line, works such as Bernard and Jensen (1997), HallwardDreimeier et al. (2002), Baldwin and Gu (2003), Aw et al. (2007, 2008), Damijan et al. (2008),
Mañez et al. (2009a), Lileeva and Trefler (2010), Bustos (2011), and Iacovone and Javorcik
(2012), find support to this correlation between exporting and firm’s R&D activities that could also
have an impact on productivity.
Also the relationship between R&D investments and productivity has been object of
widespread analysis. There is a large tradition within the Industrial Organization literature that
studies the direction of causality between both activities. The common finding of higher average
productivity of R&D firms over non-R&D firms could be again the result of either a process of selfselection (only the more productive firms can afford the sunk costs associated to R&D activities,
see Sutton, 1991, and Mañez et al., 2009b)3 and/or the result of the productivity returns to R&D
See Greenaway and Kneller (2007a) and Wagner (2007, 2012) for thorough reviews of this literature.
Silva et al. (2010) provide a detailed survey of the learning-by-exporting literature. Further, Martins and Yang (2009)
provide a meta-analysis of 33 empirical studies. Singh (2010) concludes that studies supporting self-selection
overwhelm studies supporting learning-by-exporting.
Some support for self-selection into R&D activities can be found, among others, in Hall (2002), who uses a financial
constraint argument, González and Jaumandreu (1998), González et al. (1999) and Máñez et al. (2005).
investments.4 However, a missing piece in this relationship is whether exporting influences R&D
investments. Filling this gap, Bustos (2011), in a context of a trade model with heterogeneous
productivity firms, predicts that during trade liberalization periods, both old and new exporters
upgrade technology faster than non-exporters. Further, using data for Argentina she detects that
new exporters were not more technology intensive than non-exporters before liberalization, but
upgraded technology faster as they entered export markets during the liberalization period. In the
same line, Atkinson and Burstein (2010) and Constantini and Melitz (2008) develop models that
show, also in a context of heterogeneous productivity firms, how trade liberalization can raise the
returns of R&D and thus lead to future endogenous productivity gains. Furthermore, productivity
gains for firms from participating into export markets could also arise from (among others): growth
in sales that allows firms to profit from economies of scale, knowledge flows from international
customers that provide information about innovations reducing costs and improving quality, or
from increased competition in export markets that force firms to behave more efficiently. These
productivity gains could allow firms to reach the minimum R&D threshold and so to start
performing R&D.
All in all, a crucial implication of these works is that R&D and export decisions are
interrelated, and both activities may endogenously have an effect on firms’ future productivity.
Thus, the empirical work presented in this paper is related both to the literature analysing whether
There are, at least, three strands in the literature supporting a positive relationship between R&D and firms’
productivity growth. The first is based on the well-known R&D capital stock model of Griliches (1979, 1980) that
analyses the relationship between R&D investments and productivity growth (see Griliches, 2000, for a survey). The
second strand in the literature rendering theoretical support to the relationship between R&D and productivity growth
is the active learning model (Ericson and Pakes, 1992, 1995, Pakes and Ericson, 1998). According to this model,
R&D investments contribute to improve firms’ productivity over time. Finally, endogenous growth theory is the third
strand of the literature stressing the importance of R&D for productivity growth (see, e.g., Romer, 1990, and Aghion
and Howitt, 1992).
export market participation has a positive impact on productivity and the effect of firms’ R&D
activities on productivity. However, instead of analysing the impact of exporting and performing
R&D separately, we jointly analyse the linkages among R&D, exports and productivity.
Furthermore, we recognise the fact that the R&D and exporting thresholds, identified in previous
analyses, are not necessarily exogenous but determined by previous firms’ exporting and R&D
For this purpose we estimate a dynamic model of R&D investment and exporting, in
which we allow past export and R&D experience to endogenously affect productivity, using data
for Spanish manufacturing firms over the period 1990-2009. In the first part of our analysis, using
as starting point the traditional control approach TFP (total factor productivity) estimation method
(Olley and Pakes, 1997, Levinshon and Petrin, 2003), we consider a more general process
driving the law of motion of productivity in which we recognise the potential role that both export
and R&D experience might have in shaping future firms’ productivity. Moreover, in the
specification of the production function we acknowledge that firms with different export and R&D
strategies (i.e., only exporters, only R&D firms, firms that both invest in R&D and export and firms
that neither perform R&D nor export) may have different demands of intermediate inputs
(materials). Further, we incorporate these features into the generalized method of moments
(GMM) framework proposed by Wooldridge (2009). Lastly, we test whether the assumption of
endogenizing the law of motion for productivity holds, estimating a dynamic model in which we
regress firms’ productivity on lagged productivity and lagged export/R&D firms’ strategies.
In the second part or our empirical analysis we estimate a dynamic discrete choice model
of exporting and R&D in which we characterize the firms’ joint dynamic decisions as depending
on their prior export and R&D experience, productivity, and firms’ capital stocks. Therefore, the
estimated dynamic bivariate probit model accounts for the existence of sunk costs in both
activities and the self-selection/continuation in the performance of them depending on
productivity, which, as pointed out by the first part or our empirical analysis, also depends on past
exporting and R&D decisions taken by firms and influencing future paths of productivity. The
estimation method also takes into account the potential simultaneity in the two firms’ decisions, as
well as the endogeneity of initial conditions for state variables (Wooldridge, 2005).
Our approach is closely related to that followed by Aw et al. (2011). Like this study, we
first estimate firms’ TFPs to recover the parameters driving the TFP dynamics over time and,
then, use these estimated TFPs as regressors in a dynamic bivariate model on R&D and export
decisions. However, although closely related, the empirical analysis in our study differs at some
points, as it will be explained in detail in Section 2.
To anticipate our results, we find that both exporting and R&D activities have a positive
effect on firms’ future productivity. Therefore, firm’s productivity levels before they start exporting
or investing in R&D are not necessarily exogenous when analysing self-selection into exporting or
into R&D. These productivity levels should be considered as endogenous as firm’s past choices
about exporting and performing R&D may result in productivity gains, allowing firms to surpass
the exporting or R&D productivity thresholds. Second, we find that sunk costs are relevant both
for exporting and performing R&D activities, although larger for exporting than for R&D (differently
to Bustos, 2011, and Aw et al., 2011). Third, our results suggest the existence of a phenomenon
of self-selection/continuation of the high productivity firms into exporting and R&D activities. This
is reinforced by the effect of these activities on future firms’ productivity. Fourth, we find that
investing in R&D in the past has a positive direct and significant effect on the likelihood of
exporting. Similarly, exporting in the past has a positive and significant effect on the probability to
engage in R&D. This probably suggests that each decision also affects future returns from the
other activity.
The remainder of the paper is organized as follows. Section 2 summarises the related
literature. Section 3 describes the data and presents some relevant descriptive statistics. Section
4 is devoted to explain the main features of the production function estimation method and how
do we obtain TFP estimates. In Sections 5 and 6 we discuss the main results from our analysis.
Finally, Section 7 concludes.
2. Related literature.
The theoretical context of our analysis is related to three streams of the literature: the
microeconomic literature that analyses the relationship between exporting and productivity, the
stream that studies the relationship between R&D and productivity, and to more recent papers
that investigate altogether the linkages among R&D, exports and productivity.
The recent papers that analyse only the relationship between exports and productivity or
between R&D and productivity have followed a quite similar methodological approach. This
considers a general process driving the law of motion of productivity in which it is recognised the
potential role that the export or R&D experience might have in shaping future firms’ productivity.
Traditionally, the empirical strategy has been to look at whether a productivity estimate, typically
obtained as the residual of a production function, increases as a result of firms exporting or
performing R&D activities. But for such an estimate to make sense, past export experience or
past R&D experience should be allowed to impact future productivity. Yet some previous studies
(implicitly) assume that the productivity term in the production function specification is just an
idiosyncratic shock while others assume that an exogenous Markov process governs this term. It
is this sort of assumptions, often critical to obtain consistent estimates (Ackerberg et al., 2006),
what make these analyses of the relationship between exports or R&D and productivity to lack
internal consistency.
As for the analysis of the relationship between exports and productivity, Van Biesebroeck
(2005) is probably the first study to extend the estimation framework developed by Olley and
Pakes (1996) to include lagged export participation status as a state variable in the estimation of
productivity. Somehow differently, De Loecker (2010) allows the law of motion for productivity to
depend on past export status over time. Following suit, although with some differences, the
recent papers by De Loecker and Warzyniski (2011) and Manjón et al. (2013) also allow for past
export experience to impact future productivity.
As regards the relationship between R&D and productivity, to the best of our knowledge,
the first paper endogenizing the law of motion for productivity allowing past R&D experience to
affect future productivity is Doraszelsky and Jaumandreu (2010). Añón et al. (2011) and Añón
and Manjón (2009) also use the same methodology to analyse multinationality and foreignness
effects in the returns to R&D on productivity.
Finally, some recent papers recognise the joint role of exporting and performing R&D as
productivity enhancing activities. Bustos (2011), Lileeva and Trefler (2010), Mañez et al. (2009a),
Aw et al. (2007, 2008) and Damijan et al. (2008) find evidence about exporting being correlated
with innovation and also about some linkages among exporting, innovation and productivity.
Within this literature, the theoretical works by Constantini and Melitz (2008) and Atkeson and
Burstein (2010) show how trade liberalization increases R&D returns and, therefore, creates
incentives for firms’ R&D investments, with the subsequent effect on productivity growth.
Liberalization of trade regimes may lead firms to bring forward the decision to innovate, in order
to be ready for future participation in the export market.
Very likely, the paper more related to our work is Aw et al. (2011). This paper estimates a
dynamic structural model for a firm’s decision to invest in R&D and export, allowing the two
decisions to endogenously affect future productivity (through an endogenous Markov process for
the evolution of productivity over time, in line with De Loecker, 2010, and Doraszelsky and
Jaumandreu, 2010). In their model, a firm increases its expected profits from exporting by
investing in R&D and exporting also contributes positively to the returns to R&D investments.
Further, the returns to each activity also depend on firms’ productivity, what contributes to self-
selection of the most productive firms into those activities. Finally, undertaking R&D or
participating in export markets contributes to future productivity, reinforcing the self-selection
Similarly to Aw et al. (2011), we first estimate firms’ TFPs to recover the parameters
driving the TFP dynamics over time, and use these estimated TFPs as regressors in a dynamic
bivariate model on R&D and export decisions that explicitly accounts for the correlation between
firms’ R&D and exporting decisions. However, we differ from them in several respects. First,
although they also consider a general process driving the law of motion for productivity that
recognises that both export and R&D experience may affect future productivity, in their structural
model they do not consider the possibility of different intermediate input demands according to
firms’ exporting and R&D strategies as we do. In their structural model, intermediate inputs
(materials) demand depends only on capital stocks and productivity. Second, when modelling the
dynamic decisions to export and invest in R&D, due to the short time span of their data, they treat
the firm’s capital stock as fixed over time. At difference, we allow the capital to evolve following a
deterministic dynamic law of motion. Finally, following their fully structural model they use a
sequential approach for TFP estimation. First, they estimate by OLS a domestic revenue function
(that uses the inverted demand of materials to proxy for productivity), from where they get an
estimated function that captures the combined effect of capital and productivity on domestic
revenue. Then, they use the fitted values of this function as dependent variables of a second step
regression (estimated by nonlinear least squares) that allows them to incorporate the
endogenous law of motion for productivity with respect to past export and R&D experience. In
contrast, we estimate simultaneously by a GMM-system (as proposed by Wooldridge, 2009) two
convenient transformations of the firm’s production function, incorporating on each of them the
demand of materials inversion for productivity and the endogenous law of motion for productivity,
3. Data and descriptive analysis.
The data used in this paper are drawn from the Spanish firms’ manufacturing survey (ESEE) for
the period 1990-2009. This is an annual survey sponsored by the Spanish Ministry of Industry
and carried out since 1990 that is representative of Spanish manufacturing firms classified by
industry and size categories.5 It provides exhaustive information at the firm level, and its panel
nature allows following firms over time.
The sampling procedure of the ESEE is the following. Firms with less than 10 employees
were excluded from the survey. Firms with 10 to 200 employees were randomly sampled, holding
around 5% of the population in 1990. All firms with more than 200 employees were requested to
participate, obtaining a participation rate around 70% 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 over time.6
We have a sample of 36,436 observations corresponding to 4,603 firms. From this
sample, to estimate TFP and to analyse the impact of export and R&D strategies on TFP, we
sample out those firms that fail to supply relevant information in any given year. Further, as our
TFP estimation method requires that firms supply information for at least three consecutive years,
we remove all firms that do not accomplish this criterion. After cleansing the data we end up with
a sample of 18,457 observations corresponding to 2,182 firms.
The two variables of interest in this work (exporting and R&D statuses) are obtained from
the survey using the following questions. As for the firm’s export status the relevant question is:
“Indicate whether the firm, either directly, or through other firms from the same group, has
exported during this year (including exports to the European Union)”. For the R&D status the
We have data at industry 2-digit NACE level.
See http://www.funep.es/esee/sp/presentacion.asp for further details.
question we use is: “Indicate if during this year the firm has undertaken or contracted any R&D
Figure 1 plots the evolution between 1990-2009 of the proportion of firms only exporting,
only undertaking R&D activities, both exporting and doing R&D and neither exporting nor doing
R&D. We observe that exporting is a more frequent activity among Spanish firms than engaging
in R&D activities. Further, whereas the proportion of firms exporting has increased significantly
over the period (from 34.07% in 1990 to 57.59% in 2009), the percentage of firms engaged in
R&D activities has only slightly increased (from 21.25% in 1990 to 26.11% in 2009). It is also
important to highlight that the proportion of firms that both export and undertake R&D activities
has steadily increased (from 14.06% in 1990 to 23.47% in 2009). This supports the idea that
exporting and R&D are related activities, although from these figures we cannot disentangle the
dynamics behind this relationship.
In Table 1, we report the cross-sectional distribution of exporting, undertaking R&D and
performing both activities averaged over all years (panel A), and the conditional probabilities of
exporting according to R&D status and vice versa (panels B and C). In our sample, we find that
34.20% of the observations correspond to firms that neither export nor engage in R&D. The
proportion of observations that correspond to firms that perform R&D but do not export is 4.31%,
that corresponding to firms that only export is 29.98% and, finally, the one that corresponds to
firms conducting both activities is 31.52%. Both in panels B and C we observe that firms engaged
in one of the two activities have a higher probability to start the other one than firms that do not
perform any of them.
Table 2 reports transition rates from each combination of export and R&D status in year t
to the corresponding one in t+1. Some features clearly emerge from these rates. First, there is
significant persistence in each status over time. Almost 90% of the firms that neither export nor
perform R&D continued in that status in t+1. Analogously, the empirical probability of being in the
same status between t and t+1 is 59.63%, 83.19% and 88.13% for performing only R&D, only
exporting and performing both activities, respectively. This can be the result of both high sunk
costs of entering a new activity and a high degree of persistence in the underlying sources of
profit heterogeneity (such as productivity).
Second, firms that already perform R&D (export) are more likely to start exporting
(performing R&D) than firms that do neither. In particular, if a firm does not perform either activity
in t it has a 7.26% probability of starting to export in t+1, which is lower than the 15.61% that
corresponds to firms engaged only in R&D activities in t. Similarly, the probabilities to start
performing R&D in t+1 that correspond to firms that do neither activity in t and firms that only
export in t are 3.65% and 10.75%, respectively.
Third, firms engaged in both activities in year t are less likely to abandon any of the two
activities than firms only performing one of them. Firms that undertake both activities have a
10.58% probability of quitting R&D and a 1.92% probability of leaving export markets. In
comparison, firms that only perform R&D have a 28.90% probability of stopping this activity, while
firms that only export have a 6.48% probability of leaving the export markets.
All in all, this evidence suggests the need to jointly model the firm decision to export and
to engage in R&D activities.
Next, we identify some stylized facts about exporters and firms engaged in R&D activities
using a simple regression analysis (see Table 3). The objective is to explore the relationship
between exporting and R&D strategies (exporting only, performing R&D activities only or both)
and some basic firm’s characteristics. In particular, we estimate the following reduced form
log( y it ) = β0 + β1Export it + β2R & Dit + β3Bothit + controlsit + eit
where the dependent variable yit is alternatively sales, capital and intermediate materials per
worker, and size (as measured by the number of employees). The variables Exportit, R&Dit, and
Bothit capture firms’ export and R&D strategies. Thus, Exportit is equal to one if the firm i only
exports in t (and zero otherwise), R&Dit is equal to one if the firm i only undertakes R&D activities
in t (and zero otherwise), and Bothit is equal to one if the firm i both exports and engages in R&D
activities in t (and zero otherwise). We also control for size and size squared (except for the size
regression), industry and year dummies.
The differences (in %) between firms with different exporting/R&D strategies for each of the
four considered firm characteristics are computed from the estimated coefficients β as
100(exp(β)-1). It is possible to observe in Table 3 that regardless of their combined export/R&D
strategy, firms that only export, only perform R&D or undertake both activities simultaneously, are
larger, more capital and materials intensive and have higher labour productivity than firms that
neither undertake R&D nor export.
Analogously, the joint consideration of the estimates in Table 3 and the pairwise tests in Table
4 also suggests that firms that both export and undertake R&D activities are significantly bigger,
more capital and intermediate materials intensive and have larger labour productivity than firms
that only export or only perform R&D. As for the comparison between the firms that only export
and only perform R&D, our estimates and pairwise tests suggest that firms that only export are
larger, have a higher labour productivity and are more material intensive than firms that only
perform R&D. However, we do not find any significant difference between these two types of
firms in terms of capital intensity.
Consequently, when estimating productivity it seems important to acknowledge the significant
differences between firms that do not perform R&D or export, firms that only export, firms that
only perform R&D and firms that undertake both activities. We do this by considering that each of
the four groups of firms has a different demand function for intermediate materials. As pointed out
by De Loecker (2007, 2010), this might be an important refinement in the analysis of the effects of
firms’ strategies on productivity.
4. Production function and TFP estimation.
We assume that firms produce using a Cobb-Douglas technology:
y it = β 0 + β l l it + β k k it + β m mit + µt + ω it + ηit
where yit is the natural log of production of firm i at time t, lit is the natural log of labour, kit is the
natural log of capital, mit is the natural log of intermediate materials, and µt are time effects. As for
the unobservables, ω it is the productivity (not observed by the econometrician but observable or
predictable by firms) and ηit is a standard i.i.d. error term that is neither observed nor predictable
by the firm.
It is also assumed that capital evolves following a certain law of motion that is not directly
related to current productivity shocks (i.e. it is a state variable), whereas labour and intermediate
materials are inputs that can be adjusted whenever the firm faces a productivity shock (i.e. they
are variable factors).7
Under these assumptions, Olley and Pakes (1996, hereafter OP) show how to obtain
consistent estimates of the production function coefficients using a semiparametric procedure;
see also Levinshon and Petrin, (2003, hereafter LP), for a closely related estimation strategy.
However, here we follow Wooldridge (2009), who argues that both OP and LP’s estimation
methods can be reconsidered as consisting of two equations which can be jointly estimated by
GMM: the first equation tackles the problem of endogeneity of the non-dynamic inputs (that is, the
The law of motion for capital follows a deterministic dynamic process according to which k it = (1− δ )k it−1 + Iit−1 .
Thus, it is assumed that the capital the firm uses in period t was actually decided in period t-1 (it takes a full
production period for the capital to be ordered, received and installed by the firm before it becomes operative).
Labour and materials (unlike capital) are chosen in period t, the period they actually get used (and, therefore, they
can be a function of ωit). These timing assumptions make them non-dynamic inputs, in the sense that (and again
unlike capital) current choices for them have no impact on future choices.
variable factors); and, the second equation deals with the issue of the law of motion of
productivity. Next we consider each in detail.
Let us start considering first the problem of endogeneity of the non-dynamic inputs.
Correlation between labour and intermediate inputs with productivity complicates the estimation
of equation (2), because it makes the OLS estimator biased and the fixed-effects and
instrumental variables methods generally unreliable (Ackerberg et al., 2006). Both OP and LP’s
methods use a control function approach to solve this problem, by using investment in capital and
materials, respectively, to proxy for “unobserved” firm productivity.
In particular, the OP’s method assumes that the demand for investment in capital,
i it = i k it ,ω it , is a function of firms’ capital and productivity. To circumvent the problem of firms
with zero investment in capital, the LP’s method uses the demand for materials (intermediate
inputs), mit = m ( k it ,ωit ) , instead, as a proxy variable to recover “unobserved” firm’s productivity.
Since we follow this last approach, we concentrate on the demand of materials hereafter.8
Therefore, when estimating productivity using these general versions of OP and LP in a
sample where some firms do not participate in foreign markets, others do, and some firms do not
perform R&D, while others do, it is assumed that the demand of intermediate materials for the
different types of firms according to their exporting and R&D statuses is identical. However,
heterogeneity in these firms’ strategies may influence the demand of intermediate inputs.
Therefore, analogously to De Loecker (2007, 2010), when analysing the effects of exporting on
firms’ productivity, we consider different demands of intermediate materials for only exporters,
only R&D performers, performers of both activities and non-performers. Thus, we write the
demand of materials as:
Both the investment of capital demand function and the demand for intermediate materials are assumed to be
strictly increasing in ωit (in the case of the investment of capital this is assumed in the region in which iit>0). That is,
conditional on kit, a firm with higher ωit optimally invests more (or demands more materials).
mit = mS k it ,ω it
where we include the subscript S to denote different demands of intermediate inputs for the
different firms’ strategies (categories) according to exporting and R&D statuses. Since the
demand of intermediate materials is assumed to be monotonic in productivity, it can be inverted
to generate the following inverse demand function for materials:
ω it = hS k it ,mit
where hS is an unknown function of kit and mit. Then, substituting expression (4) into the
production function (2) we get:
y it = β 0 + β l l it + β k k it + β m mit + µt + hS k it ,mit + ηit
Finally, by explicitly considering the four different demand functions for intermediate
materials, our first estimation equation for the production function is:
y it = β l l it + µt +1(NP)HNP k it ,mit
+1(E)HE k it ,mit +1(R & D)HR&D k it ,mit +1(BOTH)HBOTH k it ,mit + ηit
where 1(NP), 1(E), 1(R&D) and 1(BOTH) are indicator functions that take value one for nonperformers, only exporters, only R&D performers and performers of both activities, respectively.
Further, the unknown functions H in (6) are proxied by second-degree polynomials in their
respective arguments.
With the specification in equation 6, the difference in the inverse demand function of firms
with different productivity enhancing strategies arises not only from differences in the coefficients
of kit and mit but also by the fact that each inverse demand function includes a dummy variable
capturing the corresponding firm’s strategy or combination of strategies. This is not equivalent to
introduce the set of dummies identifying different strategies as additional inputs in the production
function, as each one of these dummies is interacted with all the terms kit and mit in its
corresponding polynomial. For example, introducing an R&D only dummy as an input in the
production function will cause at least two problems. First, an identification problem, as we will
need another estimation step to identify the parameter associated to that variable. Second,
implies that a firm can substitute any input with R&D performance at constant unit elasticity (see
De Loecker, 2007, 2010, for similar arguments applied to export dummies).
Notice, however, that we cannot identify βk and βm from (6). This is achieved by the
inclusion of a second estimation equation in the GMM-system that deals with the law of motion for
The standard OP/LP’s approaches consider that productivity evolves according to an
exogenous Markov process:
( )
ω it = E ⎡⎣ω it ⎤⎦ + ξ it = f ω it−1 + ξ it
where f is an unknown function that relates productivity in t with productivity in t-1 and ξit is an
innovation term uncorrelated by definition with kit. However, this assumption neglects the
possibility of previous exporting and R&D experience to affect productivity. Consequently, here
we consider a more general (endogenous Markov) process in which previous exporting and R&D
history can influence the dynamics of productivity:
ω it = E ⎡⎣ω it ω it−1 ,Eit−1 ,R&Dit−1 ,BOTH it−1 ⎤⎦ + ξ it = f ω it−1 ,Eit−1 ,R&Dit−1 ,BOTH it−1 + ξ it
where Eit-1, R&Dit-1 and BOTHit-1 indicate whether the firm, in period t-1, choses to only export, to
only perform R&D, or to do both activities, respectively. Obviously, the reference category is not
performing any of these activities.
Let us now rewrite the production function in (2) using (8) as:
y it = β 0 + β l l it + β k k it + β m mit + µt + f ω it−1,Eit−1,R&Dit−1,BOTH it−1 + ξ it + ηit
Further, since ω it = hS k it ,mit , we can rewrite f ω it−1 ,Eit−1 ,R&Dit−1 ,BOTH it−1 as:
f ω it−1,Eit−1,R&Dit−1,BOTH it−1 = f ⎡⎣ hS k it−1,mit−1 ,Eit−1,R&Dit−1,BOTH it−1 ⎤⎦
= FS k it−1,mit−1 = 1(NP)FNP k it−1,mit−1 +1(E)FE k it−1,mit−1
+1(R&D)FR&D k it−1,mit−1
) +1(BOTH)F ( k
with F being unknown functions to be proxied by second degree polynomials in their respective
arguments. As before, the firms’ strategy dummies are used to define the polynomials and are
also included as dummy variables in the corresponding polynomials.
Lastly, substituting (10) into (9), our second estimation equation for the production function is
given by:
y it = β 0 + β l l it + β k k it + β m mit + µt
+1(NP)FNP k it−1 ,mit−1 +1(E)FE k it−1 ,mit−1 +1(R&D)FR&D k it−1 ,mit−1
+1(BOTH)FBOTH k it−1 ,mit−1 + uit
where uit=ξit+ηit is a composed error term.
Wooldridge (2009) proposes to estimate jointly the system of equations (6) and (11) by
GMM using the appropriate instruments and moment conditions for each equation. Ackerberg et
al. (2006) showed that there exists an identification problem with a first step estimation of variable
inputs coefficients (affecting the labour input) in previous methods relying on a two-step
estimation procedure (OP and LP), and derived a mixture of OP and LP’s approaches to solve
the problem. However, theirs is still a two-step estimation procedure. More recently, Wooldridge
(2009) has argued that both OP and LP’s estimation methods can be reconsidered as consisting
of two equations which can be jointly estimated by GMM in a one-step procedure. This joint
estimation strategy has the advantages of increasing efficiency relatively to two-step procedures,
making unnecessary bootstrapping for the calculus of standard errors, and also solving the
aforementioned identification problem. By this method we obtain, for each one of the 9
considered industries,9 both the coefficient estimates of the production function (shown in Table
A.1. in the Appendix) and firms’ productivity estimates as:
ˆ s = y − βˆ l − βˆ k − βˆ m − µˆ
l it
k it
m it
Following Doraszelski and Jaumandreu (2010) we group the 20 industries in which the ESEE classifies firms into 9
industries. The aim is to get enough observations to carry out industry-by-industry estimations.
ˆ s is the estimated log of the TFP for firm i at time t, for industry s.
where tfp
5. Estimation of the endogenous dynamic evolution of the TFP process over time.
In this section, we aim to recover the implicit parameters in the endogenous Markov process in
(8) to check whether our assumption of considering a more general Markov process, in which we
allow past export and R&D to affect future productivity, holds. Therefore, the main point at this
stage of our analysis is the specification of the transition process for the state variable TFP, ωit ,
in expression (8).
Using (8), expression (9) can be rewritten as:
y it = β 0 + β l l it + β k k it + β m mit + µt + ω it + ηit
= β 0 + β l l it + β k k it + β m mit + µt + E ⎡⎣ω it ω it−1,Eit−1,R&Dit−1,BOTH it−1 ⎤⎦ + ξ it + ηit
from where, by (11), we can write our estimation equation of interest as:
ˆ s = y − β̂ l − β̂ k − β̂ m − µ̂
l it
k it
m it
= β 0 + E ⎡⎣ω it ω it−1 ,Eit−1 ,R&Dit−1 ,BOTH it−1 ⎤⎦ + ξ it + ηit + ε it
If we specify the conditional expectation in the above expression as,
E ⎡⎣ω it ω it−1 ,Eit−1 ,R&Dit−1 ,BOTH it−1 ⎤⎦ = α 1ω it−1 + α 2Eit−1 + α 3R&Dit−1 + α 4BOTH it−1
we get our final estimation equation of interest:
ˆ = β + α ω + α E + α R&D + α BOTH + s + τ
1 it−1
2 it−1
where τ it = ξit + ηit + ε it is a composite error. We have explicitly included in estimation a set of
industry dummies, si, to account for the fact that in the regression analysis we pool all industries’
TFP estimates. Positive estimates for α2, α3 and α4 should be interpreted as evidence of
learning-by-exporting and/or positive returns of R&D to productivity. Furthermore, a positive
estimate for α1 implies that current productivity will carry forward to the future.
In Table 5 we present and compare the estimates resulting from estimating equation (16)
by OLS, panel data random effects and System-GMM. Regardless of the estimation method used
we obtain positive and significant estimates for α2, α3 and α4 suggesting that exporting,
performing R&D or both activities jointly in the past has a positive direct effect on current
productivity. More specifically, the estimate of α2 suggests that past only exporters have
productivity that is between 2.2% to 3.8% higher (in the OLS and System-GMM estimations,
respectively). The direct impact of R&D on productivity is slightly smaller (differently to Aw et al.,
2011), as the extra productivity for firms that undertake R&D activities only ranges from 1.8% in
the OLS estimation to 3.3% in the System-GMM one. Finally, firms that undertake both activities
simultaneously have the highest productivity, as they have a productivity that is between 4.4%
and 5.4% higher.
Therefore, our a priori of considering a more general process for the law of motion of
productivity allowing past export and R&D experience to affect productivity seems to be
adequate. Further, the positive coefficients of α2 and α3 suggest that both the export and
productivity thresholds, determining self-section into these activities, are endogenous to firms’
R&D and export decisions. For instance, when a firm that neither exported or performed R&D
starts exporting, its incorporation to the export markets could lead to an increase in productivity
that would make more likely that the firm surpasses the minimum productivity threshold required
to perform R&D activities (i.e., the probability that the firms self-select to perform R&D activities
increases). Additionally, the estimate for α1 is also positive and significant, meaning that there is
a clear relationship between current and past productivity.
6. Dynamic exporting and R&D decisions.
Finally, we use our TFP estimates, which are robust to the endogenous firms’ exporting and
performing R&D choices, as regressors explaining the firm joint decisions to export and to invest
in R&D in a dynamic bivariate probit model. We also account for sunk costs firms have to incur to
undertake either of the two activities.
Our estimation equations are quite similar to the reduced-form model implied by the
dynamic structural model in Aw et al. (2011). Firms entering export markets will face costs
associated with entering foreign markets that may be sunk in nature. For instance, non-exporting
firms have to research foreign demand and competition, establish marketing and distribution
channels, and adjust their product characteristics to meet foreign tastes and/or fulfil quality and
security legislation of other countries. Additionally, the development of R&D activities may involve
not only creating an R&D department, purchasing specific physical assets, hiring or training
specialized workforce, but also collecting information on new technologies, organizational
changes and adjustments to new technologies, among others. These are costs that in turn may
be considered, at least partly, as sunk costs. All these arguments imply that the firm’s past export
and R&D statuses should be considered as state variables in the firm´s export and R&D
decisions, respectively.
Within this framework, a firm will decide to export (perform R&D) in year t whenever the
current increase to gross operating profits associated with the decision to export (engage in R&D)
plus the discounted expected future returns from being an exporter (R&D performer) in year t
exceed sunk costs.
Further, as the value function of a firm that decides to export can be affected by its
optimal R&D decision and vice versa (as theoretically justified by the structural model in Aw et al.,
2011), our joint likelihood will also include the firm’s past R&D status when explaining the current
probability to export and past export status when explaining the probability to perform R&D. This
is the case, when there are non-negligible sunk exporting (R&D) costs and/or exporting (R&D)
affects productivity. Notice that if productivity evolves endogenously depending on past exporting
and R&D decisions, the firm’ payoffs from exporting (R&D) depend positively on how much past
exporting (R&D) increases future productivity (this is explicitly recognised in equation 15).
Therefore, in our framework, the net benefits from exporting and performing R&D are increasing
in productivity. This argument endogenizes the well-known self-selection mechanism10 in the
literature, given that R&D/export firm’s choices increase future productivity and, therefore, would
positively influence the likelihood of firms’ being self-selected or continuing in such activities in the
future. This is why we also include the firm’s estimated productivity in our specification of the joint
likelihood of exporting and investing in R&D.
Therefore, our empirical model of the joint likelihood of exporting and performing R&D will
be specified in terms of sunk costs (proxied by the lagged export and R&D status in the
respective choice equations) and a reduced-form group of variables proxying for the payoffs to
each activity. Among them we find as especially relevant: the opposite lagged choices in each
equation, estimates of TFP, and firms’ capital stock. Therefore, we are primarily considering that
relevant firm’s variables affecting profits for each export and R&D strategy are the vector of state
variables: k it−1 ,ω it−1 ,Eit−1 ,R&Dit−1 . In econometric terms, the model is a dynamic discrete choice
model of the export and R&D decisions, in which the choice probabilities in year t are conditioned
on the previous vector of state variables for that year:
⎪ 1
Eit = ⎨
⎪ 0
⎪ 1
R&Dit = ⎨
⎪ 0
γ 0E Ei ,t−1 + γ 1E R & Di ,t−1 + γ 2ETFPi ,t−1 + γ 3E k i ,t−1 + β E X it−1 + µtE + siE + ε itE ≥ 0
γ 0R&D R & Di ,t−1 + γ 1R&D Ei ,t−1 + γ 2R&DTFPi ,t−1 + γ 3R&D k i ,t−1 + β R&D X it−1 + µtR&D + siR&D + ε itR&D ≥ 0
where γ 0 identifies sunk costs for each one of the two considered activities, γ 1 accounts for the
fact that performing one activity enhances the likelihood of starting the other activity, γ 2 allows for
I.e., that more productive firms are more likely to export and perform R&D.
a self-selection/continuation mechanism to be in work, γ 3 allows for a direct effect of the capital
stock state variable in determining firm’s exporting and R&D choices, β is the parameter vector
for other relevant firm/market characteristics affecting profits in each activity, µt is a vector of time
dummies accounting for macro conditions and si is a vector of industry dummies. Finally, εit, is
an error term for which we assume that has two components, a permanent firm-effect (α i ) and a
transitory component (uit).
The estimation of equation (17) poses an “initial conditions” problem as we do not
observe prior period choices for E and R&D for the first year the firms are in the dataset. To solve
this problem we follow Wooldridge’s (2005) method that proposes to model the distribution of the
unobserved effects, α i , conditional on the initial value of the state variables, i.e. the vector
SV1 = k1 ,ω 1 ,E1 ,R&D1 , and the other controls in the model in all time periods (we call this vector
of controls X i ):11
α i = α 0 + α 1SVi1 + α 2 X i + ai
where ai (SVi 1 , X i ) ∼ Normal ( 0,σ a2 ) . Thus, SVi1 and X i are added as additional explanatory
variables in each time period t in the two equations in (17).
In Table 6 we report the bivariate probit estimation results. We present two different sets
of results that differ in the set of variables included as other controls in the vector X (this affects
both to equations 17 and 18). The variables included as regressors in both specifications are
lagged export and lagged R&D dummies, firm’s productivity, log capital stock, and a set of year
and industry dummies. In columns 1 and 2 only firm’s size and log age are included in vector X.12
Following Mundlack (1978) and Chamberlain (1984) we use time-averages for this vector, i.e., X i = T −1 ∑ X it .
Table A.2. in the Appendix provides detailed information on all the variables involved in estimation of the two firm’s
choices; any nominal variable has been deflated using specific industry deflators according to 20 sectors of the
In columns 3 and 4 we extend our specification including firm’s age and size and other potentially
relevant firm/market characteristics in vector X (see Máñez et al., 2004, 2006, 2008, 2009a,
2009b). The bivariate probit model allows the error terms of the two choices to be correlated (at
the bottom of Table 6 it can be seen that these correlations are positive and statistically
Results are very robust to either the more parsimonious or the extended specification.
First, sunk costs are high both for exporting and for R&D decisions, but larger for exporting (in Aw
et al., 2011, they are larger for R&D). Second, previous exporting (R&D) decisions increase the
likelihood of future R&D (exporting) decisions. Third, previous productivity has a positive impact
on the performance of both activities, being the magnitude of the effect similar in both decisions.
The same holds for the capital stock variable.
Overall, all relevant variables are highly significant, have the expected signs, and are
robust to distinct specifications and to the controls for initial conditions of state variables and
mean linear projections on variables in the vector X. Our reduced-form regressions confirm that
our refined estimation measure for TFP is relevant for explaining firms’ exporting and performing
R&D decisions. Most of our results are in line with the ones in Aw et al. (2011).
To assess the fit of the bivariate model we calculate the predicted strategies pursued by
firms according to their characteristics and the transition patterns between the choices. In Table 7
we report the percentage of firms for which our model predicts the same strategy than the actual
one. In general, we see that our model replicates quite well the actual patterns of export an R&D
decisions (the overall fit being 88.34%). We get that our model predicts 92.44% of firms
undertaking neither activity, 90.17% of firms engaged in both, 84.62% of firms only exporting, and
68.37% of firms only doing R&D.
NACE-93 classification. In estimation, explanatory variables are lagged one period. The main reason is that variables
should be observable to firms when taking their decisions in period t.
In Table 8, we report the transition patterns of firms’ export and R&D strategies. In
general, we see that the predicted transition rates for the four strategies perform quite well, and
are similar to the empirical transition rates observed in the data. The predicted transitions also
confirm the interdependence of the two strategies. We can observe that firms engaged in one of
the activities in year t have a higher probability to start the other one than firms that do not
perform any of those. Thus, a firm not engaged in any activity in year t has a predicted probability
of 5.7% of exporting, whereas this probability is 10.27% for firms undertaking R&D. Similarly, a
firm not doing any activity in year t has a 2.42% probability of doing R&D only, whereas an
exporting firm has a 9.25% probability of starting this activity.
7. Conclusions.
In this paper we analyse the dynamic linkages among exports, R&D and productivity.
Furthermore, we recognise that the R&D and exporting thresholds are not necessarily exogenous
but determined by previous firms’ exporting and R&D experience.
We investigate this tenet using a two-step strategy. In the first step, we use a CobbDouglas production function to estimate firms’ productivity by GMM. In particular, in the
specification of the production function we consider that only exporters, only R&D firms, firms that
perform both activities and firms that perform neither of them have different demands of
intermediate materials. We also assume that firms’ expectations about their future productivity
depend not only on their current productivity but also on their past export and R&D experience.
Further, we test whether the assumption of past export experience and R&D affecting current
productivity holds. In a second step, we estimate a bivariate dynamic model of the firms’ decision
to invest in R&D and export, that: i) explicitly recognises the correlation between firms’ R&D and
export decisions; ii) accounts for the role for sunk costs (proxied by firms’ past R&D and export
decisions), and iii) past productivity to account for the self-selection mechanism to be in work.
As expected, we find that productivity evolves endogenously according to firms’ export
and R&D decisions, as shown by the evidence of a direct positive effect of past exporting and
R&D on firms’ future productivity. Therefore, firm’s productivity levels before they start exporting
or investing in R&D should be considered as endogenous as firm’s past choices about exporting
and performing R&D may result in productivity gains, allowing firms to surpass the exporting or
R&D productivity thresholds.
Second, our estimates suggest that sunk costs are important both for investing in R&D
and exporting. In the case of Spanish manufacturing, sunk costs for exporting are slightly higher
than those for investing in R&D. Notwithstanding, the fact that the proportion of exporting firms is
higher than that of firms performing R&D, may point out that the difference between the net
returns of exporting and performing R&D, more than compensates the higher sunk costs. Third,
we find evidence of a phenomenon of self-selection of the high-productivity firms into exports and
R&D activities, which is reinforced by the effect of exporting and R&D on future firms’ productivity.
Fourth, we find that firms that perform one of the activities have a higher probability to start
performing the other. This suggests that firms’ decisions on one of the activities very likely affect
future returns of the other activity. 25
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Figure 1. Evolution of the export and R&D strategies, 1990-2009.
Only export
Only R&D
Table 1. Exports/R&D status and conditional probability of exporting.
Panel A: Export/R&D status
R&D only
Export only
Panel B: Conditional probability of exporting
Pr(Export=0|R&D=0) Pr(Export=1|R&D=0) Pr(Export=0|R&D=1) Pr(Export=1|R&D=1)
Panel C: Conditional probability of performing R&D
Pr(R&D=0|Export=0) Pr(R&D =1|Export =0) Pr(R&D=0|Export=1) Pr(R&D=1| Export =1)
Status year t
R&D only
Export only
Table 2. Annual transition rates for continuing firms.
Status year t+1
R&D only
Export only
Table 3. Differences across export and R&D strategies undertaken by firms.
Both export
and R&D
Sales per worker
Capital (net value) per worker
Materials per worker
Note: *** mean significance at the 1% level.
Table 4. Test of the differences across export and R&D strategies
undertaken by firms.
Sales per worker
Both vs. Export
Both vs. R&D
Export vs. R&D
Capital (net value) per worker
Both vs. Export
Both vs. R&D
Export vs. R&D
Materials per worker
Both vs. Export
Both vs. R&D
Export vs. R&D
Both vs. Export
Both vs. R&D
Export vs. R&D
Note: ***, ** mean significance level at 1% and 5% levels, respectively.
Table 5. Effect of Export and R&D strategies on TFP.
tfpit-1 (α1)
Eit-1 (α2)
R&Dit-1 (α3)
BOTHit-1 (α4)
N. observations
Number of firms
All estimations include industry dummies.
Robust p-values in parenthesis.
***, **, * mean significance level at 1%, 5% and 10% levels, respectively.
Table 6. Dynamic bivariate probit model estimations for the export and R&D decisions.
Market sharet-1
Expansive demandt-1
Recessive demandt-1
Number competitors 0-10t-1
Number competitors 10-25t-1
Number competitors >25t-1
Public salest-1
Initial conditions
Mean values
Mean age
Mean size
Mean foreign
Mean market share
Mean expansive demand
Mean recessive demand
Mean number compet. 0-10
Mean number compet. 10-25
Mean number compet. >25
Mean public sales
Mean appropriability
Log-likelihood: -5,593.8903
N observations: 14,023 (1960 firms)
ρ = 0.147 (s.e. = 0.043)
LR test ρ = 0, χ2(1) = 11.078
(0.042 )
Log-likelihood: -5,492.4247
N observations: 13,914 (1960 firms)
ρ = 0.147 (s.e. = 0.043)
LR test ρ = 0, χ2(1) = 11.252
1. All estimations include industry and time dummies.
2. Robust p-values in parentheses.
3. ***, ** and * mean significant at the 1%, 5% and 10% level of significance, respectively.
Table 7. Actual vs. predicted R&D and export patterns (%).
Only R&D
Only export
Only R&D
Only export
Status in t
Only R&D
Only export
Table 8. Actual vs. predicted transition rates (%).
Status in t+1
Only R&D
Only export
Table A.1. Production function estimates (by industry).
1. Metals and metal products
0.102*** (0.023) 0.288*** (0.007) 0.503*** (0.082)
2. Non-metallic minerals
0.050** (0.022) 0.118*** (0.005) 0.783*** (0.066)
3. Chemical products
0.112*** (0.043) 0.221*** (0.009) 0.685*** (0.114)
4. Agric. and ind. machinery
0.000 (0.043) 0.227*** (0.015) 0.584*** (0.170)
5. Transport equipment
0.043** (0.018) 0.220*** (0.007) 0.696*** (0.070)
6. Food, drink and tobacco
0.047** (0.020) 0.236*** (0.006) 0.627*** (0.059)
7. Textile, leather and shoes
0.052*** (0.016) 0.273*** (0.007) 0.603*** (0.064)
8. Timber and furniture
0.062 (0.046) 0.337*** (0.018) 0.631*** (0.134)
9. Paper and printing products 0.080*** (0.029) 0.313*** (0.012) 0.659*** (0.070)
Robust standard errors in parenthesis. Significance level: ***p<1%, **p<5% and * p<10%.
The production function estimates control for industry dummies.
Table A.2. Variables definition.
Dummy variable taking value 1 if the firm exports, and 0
Dummy variable taking value 1 if the firm invests in R&D, and 0
Total Factor Productivity.
Value of capital stock.
Number of years since the firm was born.
Dummy variable taking value 1 if the number of workers is
larger than 200.
Dummy variable taking value 1 if the firm’s capital is participated
by a foreign enterprise.
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.
Expansive demand
Dummy variable taking value 1 if the firm declares to face an
expansive demand.
Recessive demand
Dummy variable taking value 1 if the firm declares to face a
recessive demand.
Number of competitors 0-10 Dummy variable taking value 1 if the firm asserts to have less
than (or equal to) 10 competitors with significant market share in
its main market, and 0 otherwise.
Number of competitors 10-25 Dummy variable taking value 1 if the firm asserts to have more
than 10 and less than (or equal to) 25 competitors with
significant market share in its main market, and 0 otherwise.
Number of competitors > 25 Dummy variable taking value 1 if the firm asserts to have more
than 25 competitors with significant market share in its main
market, and 0 otherwise.
Public sales
Dummy variable taking value one if more than 25% of firm sales
go to the public sector and zero otherwise.
Ratio of the total number of patents over the total number of
firms that assert to have achieved innovations in the firms
industrial sector (20 sectors of the two-digit NACE-93
classification) (in %).
Year dummies
Dummy variables taking value 1 for the corresponding year, and
0 otherwise.
Industry dummies
Industry dummies accounting for 20 industrial sectors of the
NACE-93 classification.
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