1
R&D, Spatial Spillovers and Productivity Growth: Evidence
from Dynamic Panel
Wen-Cheng Lu, Jong-Rong Chen,* Chia-Ling Wang
Abstract
This paper investigates the relationship between R&D stock and productivitygrowth, while taking into account the effect of spatial spillovers. We propose ahomogeneous dynamic panel data model and three heterogeneous dynamic panel datamodels to consider the individual effect as well as endogenous. We also distinguishbetween the estimated long-run and short-run results. Our results indicate that boththe R&D stock and R&D spatial spillovers positively affect productivity growth in theshort-run as well as in the long-run.
Key words: Industrial cluster, dynamic panel data model, R&D spatial spillovers,productivity growth.
JEL classification code: L63, O30, R10, D24
* Corresponding author: Graduate Institute of Industrial Economics, National Central University,Taiwan 320. Tel: 886-3-4227791, Fax: 886-3-4226134, E-mail: [email protected].
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1. Introduction
The purpose of this paper is to recognize the importance of technological
accumulation and to evaluate its contribution to productivity growth in the context of
spatial spillover effects. R&D behavior may be enhanced by the location of R&D
facilities such as Silicon Valley or Taiwan’s Hsinchu Science-based Industrial Park.
Total factor productivity (TFP), which measures productivity improvements generated
from technical progress and changes in efficiency, has been a commonly-used
indicator of the role of the state of technology on input productivity. Many economists
have found that R&D serves as the main engine of technological progress and
productivity growth. In particular, a firm’s investment plays an important role in TFP
growth. The R&D expenditures of individual firms contribute to the sustained
long-run growth of an economy (Grossman and Helpman, 1990a, 1990b; Romer,
1990). Based on this view, individual firms invest in R&D in order to acquire private
knowledge that increases their productivity and profit. During the process, the private
technology of individual firm spills over to other firms and becomes social knowledge
that gives rise to an external effect in promoting the productivity of all firms. R&D
spatial spillover effect is mainly viewed as externality. In the previous studies, the
spatial spillover effects can be divided into two categories: Marshall-Arrow-Romer
externality and Jocobs externality. No matter what kind of externality, Geographic
location for R&D is very important.
The size of the external effect depends on the technological characteristics and the
respective locations of firms. Because the spillover effects can’t be observable, we
measure them by their properties of accessibility and R&D intensity. Accessibility
reflects the interaction between firms in the neighborhood while R&D intensity
described by R&D stock. In particular, if the distance between firms is smaller, the
external effect will be larger. In other words, the size of spillover effect is captured by
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industrial clustering. In this paper, we use the industrial cluster multiplied by the R&D
stock of other firms to measure the spatial spillovers.
In this paper, we study the relationship between productivity growth and R&D
stock while considering the spatial spillovers. Our reasons for studying this issue are
as follows. First, productivity growth may reflect different states of technology. As
technology accumulates over time, using the R&D stock to represent different states
of technology is more suitable. Firms may need to engage in persistent and long-run
R&D investment. Secondly, it is important to emphasize that the concept of
geographical space may also be defined in an economic sense with distance in terms
of economic connections (e.g., TFP growth, bilateral trade). Many papers have used
economic theory to predict very specific forms of spatial correlation. In this study, we
use the latitude and longitude data to calculate the distance from the center of the
latitude and longitude. The distance stands for the industrial cluster effects from
which we can then estimate the R&D spillover effects.
Previous studies usually focused on the domestic/foreign R&D stock in relation to
TFP at the country level and only rarely at the firm level.1 This paper expects that the
results at the firm level may be different from those at the country level. The research
at the country level cannot explain the industrial situation and the country-wide data
are aggregate data that may result in the loss of important information regarding
microeconomic units. The firm’s R&D stock in terms of its own R&D and other
firms’ R&D stocks plays an important role in TFP growth because of the R&D
1 According to the country evidence, domestic productivity depends not only on domestic but also onforeign R&D (Hayami and Ruttan, 1985; Johnson and Evenson, 1999). Domestic international R&Dspillovers play an important role in the productivity issue. If we ignore international spillovers, wewill overestimate productivity growth and the rates of return to research (Alston and Pardey, 2001).Gutierrez and Gutierrez (2003) find that total factor productivity is strongly influenced by domesticand foreign R&D spending in the agricultural sector. They also show that geographical factors matterand that the countries located in temperate zones benefit more from technological spillovers thancountries located in tropical zones. Based on the country evidence, we can conclude that thedomestic R&D stock and foreign R&D stock are both very closely related to TFP growth, and thatthe spillover effect is important for estimating TFP in relation to this.
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accumulation characteristics and R&D uncertainty. The R&D spatial spillover effects
are unobserved and influence each firm in a given industry through intra-industry (or
inter-industry) sales and geographical location. Whatever the benefit of intra-industry
sales or geographical location, R&D spillover effects are involuntary and viewed as
externalities. The main reason for these relationships in recent papers has to do with
the external economies that a firm faces. (Hoogstra, et al., 2004; Campi, et al., 2004;
Honjo, 2004)
This paper addresses the empirical relationship between a firm’s R&D stock, the
R&D stocks of other firms with their spatial spillover effects and TFP growth for the
electronic firms over the period 1991-2002. More specifically, this paper contributes
the following:
(1) Many of the previous studies viewed the firm structure as being homogeneous. In
other words, thefirm’s structure in a given industry is seen as being the same and
these parameters are estimated in the panel. Such an approach may lead to a
biased conclusion because previous studies did not consider the heterogeneity
between firms. In the paper, we propose the adoption of three heterogeneous
dynamic panel data models that consider both the individual effects and
endogenous. We also distinguish between long-run and short-run estimated
results.
(2) Spatial spillover effects are composed of industry clusters and the R&D stock.
Recently, spillover effects resulting from R&D stocks and industry clusters have
been viewed as an R&D external effect. We have applied the relative distance
among firms as a measure of industrial clustering. Industrial clustering may affect
a firm’s R&D behavior.We investigate the relationship between a firm’s R&D
stock and the R&D stocks of other firms through spatial spillover effects.
The remainder of the paper is organized as follows. In Section 2, we present a brief
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review of the empirical literature. In Section 3, we define the variables and describe
empirical models. The empirical results are discussed in Section 4. Finally, we
conclude with a summary of our results.
2. Previous Empirical Studies
In this paper, we begin by examining the relationship between the R&D stock and
productivity, with a view to investigating the relationship between the firm’s R&D
stock, the other firms’ R&D stocks with their spatial spillover effects and productivity
growth at the firm level. Since R&D expenditure may reduce a firm’s average cost
and promote the firm’s productivity, productivity may be seen as being connected
with the firm’s R&D behavior. Recently, many empirical studies have dealt with the
relationship between R&D expenditure/R&D capital and productivity growth.
Audretsch and Feldman (1996) find that industries with high levels of innovative
activity have a greater tendency to cluster. Raut (1995) estimates the effects of
individual R&D expenditures and industry-wide R&D spillovers on the individual
firm’s productivity growth. Raut (1995) also uses the R&D capital of a firm as a
factor of production. He finds that the R&D spillover is a highly significant
determinant of productivity growth that has an insignificant effect on own R&D
capital due to the non-reporting problem.
Bernstein and Mohnen (1998) empirically investigate bilateral spillovers between
the U.S. and Japan and show that international spillovers exist from the U.S. to Japan.
U.S. R&D capital accumulation leads productivity growth and reduces average cost in
Japan. Coe and Helpman (1995), among other researchers, state that
commercially-oriented innovation efforts that respond to economic incentives are the
major engine of technological progress and productivity growth. Coe and Helpman
(1995) argue that a country’s productivity depends on its own R&D efforts as well as
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the R&D efforts of its trading partners. Using data from 21 OECD countries plus
Israel during 1971-1990, they find that both domestic and foreign R&D capital stocks
have important effects on TFP. Kao, et al. (1999) studied the issue of international
R&D spillovers and the effect of domestic and foreign R&D capital stocks. Madden
and Savage (2000) applied these methods to a sample of OECD and Asian economies
from 1980 to 1995 to determine the extent to which total factor productivity was
related to domestic and foreign R&D activity, trade, and information technology and
telecommunications (ITT). They found that the benefits of R&D could spill over to
other countries through trade. Branstetter (2001) has estimated the size of
international spillovers using micro-level data. He shows that technological
externalities can generate persistent growth differentials. Bottazzi and Peri (2003) use
European regional data to test for the existence of spatial spillovers of R&D. They
find that R&D spillovers exist and localized only within a distance of 300 km.
Doubling R&D spending in a region would increase the output of new ideas in other
regions within 300 km only by 2-3%.
In sum, spatial spillover effect plays an important role in the issue of productivity
growth and R&D as many previous papers shown.
3. Theoretical and empirical framework
3.1 The measure of TFP and the spatial spillover effect
A firm will choose a location that maximizes profit. When a location is determined,
the way in which that firm is clustered with other firms and its spatial R&D spillover
effect will affect its productivity. The firm’s spatial spillover effect may be calculated
in terms of its relative distance from other firms. The regional stock of human capital
is a suitable means of explaining persistent regional differences and determines the
firm’s ability to absorb and use new technology. Geographical clustering and
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knowledge diffusion may also contribute to regional growth, with geographical
clustering playing an important part in the R&D spillover effect. At the same time, the
R&D spillover effect may have an effect on TFP.
TFP is measured as follows:
LKYTFP log)1(logloglog , (1)
where it is assumed that the production function is of a Cobb-Douglas form in which
logarithms are taken on both sides of the equation. Term K denotes capital
accumulation, L is the firm’s hired amount of employees, and Y is final output.
However, firms within a given industry often face different internal and external
environments and are able to obtain or absorb distinct spillover effects. Bernstein
(1989) constructed a model for seven Canadian industries based on Equation (2). He
argued that it is implausible for every firm to be able to gain equally from the
aggregate stock of knowledge. To account for the different abilities of firms to
internalize other firms’ knowledge, Bernstein (1989) provides the following indicator:
N
ijjiji KwS , (2)
where jK is R&D stock, iS is the spillover effect of firm i, and ijw represents
the absorptive ability of firm i. Equation (2) is characterized by the weights, ijw ,
which represent firm i’s ability to internalize pieces of firm j’s stock of knowledge.
The larger these weights are, the more that firm i can gain from firm j’s stock of
knowledge. There are many suggestions for the calculation of spillover effects that
can be found in the literature: (1) Distance in technology space. Jaffe (1986),
Adam (1990), Inkmann and Pohlmeier (1995) belong to this classification. (2)
Geographical distance. Beise and Stahl (1999) use the inverse of the geographical
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distance between firms i and j to calculate the weights ijw . (3) Direct measures
based on innovation survey data.
In this paper, we use the latitude and longitude of a firm to define the firm’s
position. Our method involves finding the center of gravity and computing the
distance of every firm from the core. Head and Mayer (2002) use the weighted
latitude and longitude of each firm to estimate the center of gravity in a given industry.
The purpose in using weighted latitude and longitude is to exhibit the effect of firm
size on industrial clustering. We thus exploit the latitude and longitude data of the
firms and their distance from the industry center to estimate the industry cluster and
the R&D spillover effects. Within this framework, we assume that the more that an
industry is clustered; the greater will be the R&D spillover effects. Similarly, a firm
near the center of gravity will have larger R&D spillover effects.
The latitude and longitude data are obtained from the Industry, Commerce and
Service (ICS) Census conducted by the Directorate-General of Budget, Accounting
and Statistics (DGBAS) in Taiwan. The purpose of the database development is to
meet the increasing demand for national censuses and academic research. The ICS
census is designed to collect basic data on economic activities such as the operational
status of an industry, the commerce and services sectors, the distribution of resources,
major equipment, capital utilization, economic structure, changes in sales and
production, and other relevant matters. To estimate the center of gravity, we assemble
the information on the latitude and longitude for each village and define the
geographical position of the various firms. By exploiting the differences in terms of
the latitude and longitude, we can estimate the real degree of industrial clustering. The
latitude and longitude are calculated as follows
9
ix
xxi longpconlong (3)
xix
xi latpconlat
, (4)
where iconlong and iconlat represent the center of longitude and latitude in a
given industry, respectively, and xlong and xlat stand for the longitude and latitude
of a firm, respectively. Term xp is the share of employees in the industry as a whole.
The distance from the center of longitude and latitude to firm x is shown as follows
360(min()2958.57/()2958.57/((6370 COSlatCOSconlatCOSARCOSdist xixi
)2958.57/()2958.57/))(, ixixi conlatSINlongconlonglongconlong
)2958.57/( xlatSIN . (5)
Finally, the industrial cluster effects are expressed as
xii dist
m1
. (6)
We use im to measure the industrial cluster effects. When the extent of the clustering
is higher, xidist is smaller, and the firm in the neighborhood of the industry core
absorbs more spillover effects and has a significant effect on productivity. In addition,
im multiplied by other firms’ R&D stocks ( ftiS , ) is used to measure R&D spatial
spillovers ( ftii Sm , ). A diagram of the relations between industrial gravity and
industrial members is shown in Figure 1.
3.2 Estimation of parameters using the dynamic panel data method
For simplicity, we design a dynamic panel data model to describe the relationship
between a firm’s own R&D capital stock and the R&D capital stock of other firms
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taking into consideration the spatial spillover effects and TFP growth as follows
titiftidtiti TFPSmSTFP ,1,21, log)log(loglog
Ni ,,2,1 Tt ,,2,1 , (7)
where tiTFP , and 1, tiTFP are the TFP growth rates at times t and 1t ,
respectively, dtS is the firm’s own R&D stock, f
tii Sm , is the R&D spatial spillover
effect and ftS represents the R&D stocks of other firms. 1 and 2 denote the
elasticities of the firm’s own R&D and the R&D spatial spillovers.
In equation (8), i stands for the individual effects and is different across firms.
, 1 and 2 are homogeneous, implying that the lagged dependent variables and
exogenous variables have the same effects on the dependent variables. Due to the
endogenous (i.e. where the expectations regarding the explanatory variables and
residuals are not equal to zero), the OLS estimation procedure may lead to biased
estimators. It is clear that such an equation (7) is very restrictive, since it particularly
implies that causality does not exist for any individual. We adopt the econometric
procedure of Ahn and Schmidt (1995) and Baum, et al. (2002) to eliminate individual
specific effects to estimate parameters. The presence of such heterogeneity can result
in serious mis-specification biases in the subsequent estimation that imposes
homogeneous parameter values. In particular, if the dynamics are heterogeneous
across firms and they are assumed to be equal, Pesaran and Smith (1995) show that
estimates will be biased and inconsistent.
We apply the following simple heterogeneous dynamic model proposed by Pesaran
and Smith (1995):
titiitiiti xTFPTFP ,1,1,, Ni ,,2,1 Tt ,,2,1 (8)
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with its coefficients i and i varying across groups according to the following
random coefficients model:
iiH 10 : , ii 2
where fti
dtiti SmiSx 1,1,1, , , and ),( 21 ii . i1 and i2 are assumed to
have zero means and constant covariances. The model introduces parameter
heterogeneity through the short-run coefficients i and i and long-run parameters
)1( i
i
. There is a sizeable literature on the small sample bias of the least
squares estimators of the short-run slope coefficients i and i . Many earlier
econometric studies provide an estimation method to obtain a consistent parameter
estimate for short-run parameters on the small sample: (1) the Mean group estimator
of Pesaran and Smith (1995); (2) the Pooled mean group estimator of Pesaran, et al.
(1999); (3) the Bayesian estimator of Hsiao and Tahmiscioglu (1997); and (4) the
bias-corrected method of Kiviet and Phillips (1993) to estimate the short-run slope
coefficients. The long-run parameters can be obtained by indirectly deriving from the
short-run parameters or directly estimated through the long-run approach. Therefore,
we apply the following methods to estimate the long-run parameters: (1) The OLS
method is used to estimate the short-run slope coefficients and to derive the long-run
parameters. (2) The bias-corrected method of Kiviet and Phillips (1993) is used to
estimate the short-run slope coefficients and to construct the long-run parameters. (3)
The bootstrap bias-corrected method of Pesaran and Zhao (1999), who proposed a
bootstrap bias-corrected method to directly estimate i, is used to show that the next
source of potential bias is due to the non-linearity of i in terms of i and i.
3.4 Data description
The firms’ operational dataare derived from the Taiwan Economic Journal (TEJ)
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database. There are 90 firms covering 10 years (1992-2002) in our sample. To define
the spatial relationship between firms, we must have longitude and latitude data. The
longitude and latitude data are obtained from the Industry, Commerce, and Service
(ICS) Census provided by the Directorate-General of Budget, Accounting and
Statistics (DGBAS). The basic statistics are listed in Table 1.
4. Empirical Results
In this paper, we use the dynamic panel data method for a sample of Taiwanese
electronics companies that are listed on the Taiwan stock exchange. The success and
excellent performance of Taiwan’s electronics industry has attracted worldwide
attention. There are several science parks in Taiwan, in which firms are integrated
both horizontally and vertically. While this is conducive to a firm’s R&D, it does not
mean that there is no technology diffusion or R&D spillovers. Distance from the
center of gravity is adopted to measure the industrial cluster. The data used are
suitable for investigating the issue of TFP growth and R&D stock.
The dynamic panel data model has already been mentioned as equation (8). The
estimation results are presented in Table 2. Model 1 is expressed by equation (8) and
we test the robustness of our model in order to estimate Model 2 and Model 3 as
follows:
tiitdititi STFPTFP ,1,11,, Ni ,,2,1 Tt ,,2,1 (Model 2)
tiitfiititi SmTFPTFP ,1,21,, Ni ,,2,1 Tt ,,2,1 (Model 3)
In Model 1, we find that the lag-one period TFP growth rate has a negative effect on
the current TFP growth rate. dS and fi Sm have a positive effect on the current
TFP growth rate. This means that the TFP growth rate for firm i converges over
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time. dS and fi Sm play important roles in TFP growth. To maintain the TFP
growth, we have to accumulate R&D effort. Model 2 and Model 3 also exhibit the
same results. 1 and 2 measure the effect of the short-run R&D stock on TFP
growth. In Table 2, we can find that the short-run effects are both positive and
significant. In previous empirical studies such as Pesaran and Smith (1995), we can
study the heterogeneous panel data and estimate different slopes for the explanatory
variables across firms. The heterogeneous model has a short-run slope that varies
across firms and that is used to derive the long-run effects. As mentioned in Section 3,
there are two long-run effects associated with TFP growth—the long-run effect from
diS to TFP growth and also that from fi Sm to TFP growth. In this paper, there are
three estimation methods used to obtain the long-run effects. In a recent paper, Judson
and Owen (1999) recommended the corrected fixed estimator of Kiviet (1995) as the
best choice for balanced macro-panels, with GMM being the second best choice, and
for long panels, the computationally simpler Anderson and Hsiao (1982) estimator. In
this paper, we use the OLS procedure, the bias-corrected estimator of Kiviet and
Phillips (1993), and the bootstrap bias-corrected method of Pesaran and Zhao (1999)
to estimate the long-run effects. The long-run effects are shown in Table 4. It can be
shown that the long-run effects are positive and significant and the conclusion is
similar to that for the short-run effects. The results are similar to those of Raut (1995).
Raut (1995) uses panel data for a sample of Indian private manufacturing firms, in
which he considers correlation in the error terms and simultaneity in the determination
of output and input levels, but not the endogeneity of the dynamic panel data method.
Raut (1995) points out that the spillover R&D is a highly significant determinant of
productivity growth but that own R&D capital has an insignificant effect on the light
and petrochemical industries.
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5. Conclusion
In this paper, we also investigate the relationship between the R&D stock and the
R&D spatial spillover effects and TFP growth. R&D spillover effects have been
viewed as external economies and have been measured their contribution to TFP
(Madden and Savage, 2000; Raut, 1995). Previous studies measured the spillover
effects based on bilateral trade or sales. From the viewpoints of geographic, urban,
and regional economics, spatial correlations play an important role in analyzing
cross-firm TFP growth. From the viewpoint of a firm’s choice of location, different
locations may offer different external resources such as learning opportunities and
specifically-skilled workers. In this paper, we use the inverse of the distance between
a given firm and the center of gravity to measure the extent of the industrial clustering.
When the industrial squeeze is higher or the other firms’ R&D stocks are larger, the
spillover effects are larger. Furthermore, we propose three heterogeneous dynamic
panel data models to consider the individual effects and endogenous. We also
distinguish between the long-run and short-run estimated results. Our results indicate
that both the R&D stock and R&D spatial spillovers positively affect productivity
growth in the short run as well as in the long run.
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Table 1. Basic statistics
Variable Definition MeanStandarddeviation
TFP )ln()ln( 1,, titi TFPTFP 0.001 0.485
dSThe logarithm of own R&Dstock
11.513 2.442
fi Sm The logarithm of ( fii
Sd
1
) -0.783 0.697
Table 2. The results of the dynamic panel data model (dependent variable: productivity growth rate)
VariablesModel 1
(full model)Model 2 Model 3
Constant-0.040**
(-2.193)
-0.025**
(-2.116)
-0.032***
(-7.246)
1 tTFP-0.463***
(-5.527)
-0.539***
(-14.545)
-0.545***
(-22.435)
dtiS 1,
0.002**
(2.061)--
0.001**
(3.348)
ftii Sm 1,
1.265**
(2.055)
0.842**
(2.060)
--
1.“***”and“**” stand for significance at the 1 percent level and 5 percent level, respectively.
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Table 3. Long-run effects of the dynamic panel data model
Denote OLSKiviet-Phillips
(1993)estimator
Pesaran andZhao (1999)
Bootstrapbias-corrected
estimator
Long-run effect
from dtiS 1, to
TFP1
11 1
0.002**
(2.011)0.007***(2.567)
0.003(1.154)
Long-run effect
from ftii Sm 1,
to TFP2
22 1
0.003
(1.002)0.052*(1.731)
0.008***(2.667)
1.“***”, “**” and “*” stand for significance at the 1 percent level, 5 percent level and 10 percent
level, respectively.
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Figure 1. A diagram of relation of industrial gravity and industrial members
Geographicscope
Geographicscope
Industrialgravity
Industrialgravity
Note: As Figure 1 shows, the dotted line periphery is the geographic boundary. The left diagram has
more clusters than the right diagram. The industrial gravity is mentioned by the main text and the
distances between it and every industrial member measures the spatial spillover effects. When the
distances are smaller, it means highly-squeezed and more spatial spillover effects like the left diagram.
18
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