\/PS I8\
POLICY RESEARCH WORKING PAPER 1831
How Trade Patterns As a factor influencing
productivity, a country's own
and Technology Flows research and development to
Affect Productivity Growth generate new technology is
more important than that of
the average foreign country.
It is generally difficult to
Wolfgang Keller separate the effect of
importing intermediate goods
with embodied technology
from the effect of other
channels of international
technology transmission.
According to this study,
international trade contributes
20 percent of the total effect
on productivity from foreign
research and development
investments.
The World Bank
Development Research Group
September 1997
l POLICY RESEARCH WORKING PAPER 1831
Summary findings
Earlier studies of spiliovers from international research First, .the productivity effects of foreign R&D vary
and development (R&D) suggest how economies benefit substantially, depending on which country is conducting
from R&D conducted abroad. To the extent that the R&D. The quality of newly created technology
countries importing new technologies do not pay in full varies.
for the increased variety in intermediate inputs in Second, as a factor influencing productivity, a
production, they are reaping an external, or spillover, country's own R&D is more important than that of the
effect. average foreign country. It is difficult to separate the
Keller analyzes a particular mechanism through which effect of importing intermediate goods with embodied
economies benefit from foreign R&D. He estimates the technology from a more general spillover effect; often
extent to which a country benefits from imports of both are present.
intermediate goods that embody new technology - the Third, in Keller's sample of industrial countries,
result of foreign investments in R&D. He distinguishes international trade contributes about 20 percent of the
this mechanism from others unrelated to international total effect on productivity from foreign R&D
trade. investments. Keller conjectures that this effect could be
Using industry-level data for eight OECD countries higher for less industrialized countries importing from
(Sweden and the G-7 countries) bet-een 1970 and 1991, OECD countries, but he stresses that alternative
he estimates the underlying model of trade and growth. mechanisms (such as foreign direct investment) should be
This empirical analysis leads to several findings about included when estimating the effects of international
spillovers from international R&D. trade in the international diffusion of technology.
This paper -a product of the Development Research Group - is part of a larger effort in the group to analyze the impact
of trade, technology, and foreign direct investment on growth in developing countries. Copies of the paper are available
free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Jennifer Ngaine, room NS-056,
telephone 202-473-7947, fax 202-522-1159, Internet address jngaine@worldbank.org. September 1997. (34 pages)
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about
development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The
papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this
paper are entirely those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, or the
countries they represent.
Produced by the Policy Research Dissemination Center
How Trade Patterns and Technology Flows
Affect Productivity Growth
Wolfgang Keller
University of Wisconsin and NBER*
Keywords: International R&D spillovers, intermediate goods trade, embodied technical change,
Monte Carlo estimation.
JEL classification: F12, F2, 03, 04, C15.
An earlier version of this paper was presented at the conference "Trade and Technology Diffusion:
The Evidence with Implications for Developing Countries," in Milan, Italy, jointly sponsored by the
Fondazione Eni Enrico Mattei and the International Trade Division of the World Bank, April 1997.
The paper has also benefited from the comments of Robert Evenson, Zvi Griliches, Elhanan
Helpman, Juergen Jerger, Sam Kortum, Rody Manuelli, and T. N. Srinivasan, as well as participants
of presentations at the Econometric Society meetings, January 1997, in New Orleans, and the
Universities of Berlin (Humboldt), Bonn, Freiburg, and Tilburg.
* 1180 Observatory Drive, Madison, WI 53706; e-mail: wkeller@ssc.wisc.edu.
1. Introduction
The recent development of theories of endogenous technological change, in par-
ticular by Romer (1990) and Aghion and Howitt (1992), have triggered new work
on the relations of trade, growth, and technological change in open economies
(Grossman and Helpman 1991, Rivera-Batiz and Romer 1991a). In these papers,
the authors embed the recent theories in multi-sector general-equilibrium mod-
els to analyze the impact of both trade in intermediate as well as final goods
on long-run growth. Technology diffuses in this framework through being em-
bodied in intermediate inputs: If research and development (R&D) expenditures
create new intermediate goods which are different (the horizontally differentiated
inputs model) or better (the quality ladder model) from those already existing,
and if these are also exported to other economies, then the importing country's
productivity is increased through the R&D efforts of its trade partner.
The impact of receiving a new input in the importing country might take
various forms. First of all, there is the direct effect of employing a larger range
of intermediate inputs in final output production: For a given amount of primary
resources, output is increasing in the range of differentiated inputs (Ethier 1982).
To the extent that the importing country succeeds in not paying in full for this
increase-in-variety, it is reaping an external, or, "spillover" effect. Secondly, the
import of specialized inputs might facilitate learning about the product, spurring
imitation or innovation of a competing product.
In this paper, we will use data on the G-7 group of countries plus Sweden
to evaluate these mechanisms. The traded goods here are machinery inputs for
manufacturing industries; these inputs are usually differentiated and imperfect
substitutes, as in the Ethier-Romer model. In addition, they are often highly
specialized for a particular industry, implying that the elasticity of substitution
between machinery produced for two different industries is negligible.1
In this setting, we ask whether productivity growth in a particular industry of
an importing country is increased by the R&D investments-leading to a larger va-
riety of differentiated machinery-of its trade partners. It is clear that the pattern
of trade in intermediate inputs is a central element of this technology spillovers
hypothesis. Both the 'increasing variety' as well as the 'reverse-engineering' ef-
fects discussed above are tied to arm's length market transactions of goods. This
is in contrast to many other possibilities by which technological knowledge can
'See Keller (1996a) for an analysis focusing on inter-industry relations.
1
diffuse and which do not rely on arm's length transactions per se.2
One hypothesis concerns the composition of imports by partner country: Coun-
tries which import to a larger extent from high-knowledge countries should, all else
equal, import on average more and better differentiated input varieties than coun-
tries importing largely from low-knowledge countries. Consequently, this should
lead to a higher TFP level in the importing countries. Second, for a given compo-
sition of imports, this effect is likely to be stronger, the greater the overall import
share of a country is. A number of papers have recently attempted to assess
the importance of imports in transmitting foreign R&D into domestic industries,
spurring total factor productivity (TFP), including Coe and Helpman (1995), Coe
et al. (1995), Evenson (1995), Keller (1996a, 1996b), as well as Lichtenberg and
van Pottelsberghe (1996).3 In Coe and Helpman (1995), the authors find a sig-
nificantly positive correlation between TFP levels and a trade-weighted sum of
partner country R&D stocks, where bilateral import shares serve as weights. The
interpretation of this finding is not clear, though, because Keller (1996b), using
the same data, finds that the composition of countries' imports plays no particu-
lar role in obtaining this correlation: Alternatively weighted R&D stocks-where
import shares are created randomly-also lead invariably to a positive correlation
between foreign R&D and the importing country's TFP, and the average corre-
lation is often larger than when foreign R&D is weighted using observed import
shares.
While making the point that the Coe and Helpman (1995) results do not de-
pend on the observed patterns of imports between countries, it does not necessar-
ily follow that R&D spillovers are unrelated to international trade. For instance,
these papers use aggregate import data to compute the trade share weights for
a given importing country. Overall import relations between countries, however,
might be only a very poor measure of intermediate inputs trade relations. An-
other interpretation of the findings by Keller (1996b) is that the characteristics
of the data and the data generating process call for a different, and perhaps more
general, econometric specification in the first place. Moreover, even if trade is not
all what is driving international R&D spillovers, the effect of trade needs to be
quantified in order to assess its relative importance.
2See Griliches (1979) and Nadiri (1993) for more discussion, and the latter paper for a recent
survey.
3The papers by Park (1995), Bernstein and Mohnen (1994), and Branstetter (1996) are also
estimating international R&D spillovers, but do not contain an explicit argument with respect
to international trade.
2
In this paper, therefore, we address several of these issues. First of all, the
analysis of R&D, imports, and TFP is conducted at a two- and three digit industry
level. At this level of aggregation, one is much more likely to observe trade
flows embodying new technology than at a country-level. Secondly, we present
estimation results for both TFP level as well as TFP growth rate specifications,
addressing some of the issues related to characteristics and time series properties
of the data. Thirdly, we extend the Monte-Carlo analysis conducted by Keller
(1996b), showing how these type of experiments are related to estimating a general
spillover effect from foreign R&D. With this, it is, fourthly, possible to determine
whether there exists a trade-related part of internationally R&D spillovers; we
find that this is the case, and it is estimated to be about 20% of the total benefit
derived from foreign R&D.
The remainder of the paper is as follows. In the next section, we describe
the model which motivates the empirical analysis below. Section 3 contains a
discussion of the characteristics and construction of the data. In the following
section 4, the basic empirical results are presented, and contrasted with those
from the corresponding Monte-Carlo experiments. The following section discusses
how general international R&D spillovers estimates are related to the Monte-Carlo
experiments, and how they can be empirically separated from trade-related effects.
Section 6, finally, concludes.
2. The Model
This section will give a theoretical background for the empirical analysis presented
below. We emphasize the empirical implementation of these models; for more
on this type of models in general, see, e.g., Grossman and Helpman (1991) and
Rivera-Batiz and Romer (1991a, 1991b).
Assume that the final good j, j = l,...,J, in country v, v-i, h,..., V, at time
t is produced according to
Yvjt = Avj lvjtatdvjtl-Uj with 0 < avjt < 1,Vv,j,t, (2.1)
where Avj is a constant, lVjt are labor services used in sectoral final output pro-
duction, and dvjt is a composite input consisting of horizontally differentiated
intermediate products x of variety s. For a specific country i, dijt is defined as
ijt (fJt Xit(s)' ds + | Xhjt (Sd)-adahi ds' + ) l- . (2.2)
3
Here, xi (s) denotes the quantity of an intermediate of variety s used in sector j,
where the country in which the intermediate is produced is given by the subscript,
and the superscript denotes the country where the intermediate is employed. Sim-
ilarly, ni gives the range of domestically produced intermediate goods utilized in
country i's good j production, and the n,,t, w $4 i, give the ranges of imported
goods. We think of the x's as differentiated capital goods. Assume that all va-
rieties are different. The YWjt are functions to be defined below. Note that only
inputs of type j are productive in the sector j of any country, corresponding to
the often highly specialized nature of machinery inputs for particular industries.
Concentrating on inputs utilized in country i's sector j at time t, let pi and
pw, denote the rental prices in terms of sectoral output which are asked by the
producers of intermediate input variety xi, respectively xw. It follows from (2.1)
and (2.2) that the first order conditions for choosing xi and xz, are
Pi a(1-ci ) Ai xi-i clia (2.3)
and
Pus = (1- o,,) -y,,Aw xt, Vw zi. (2.4)
Intermediate goods producers are monopolists who choose the profit maximizing
quantity x, given the inverse demands in (2.3) and (2.4). The production tech-
nology for all intermediates produced in one country is the same. In any country,
one unit of any intermediate in sector j is produced linearly by using one unit
of the local good j. This leads to a constant-markup formula for the price of in-
termediates from country v (where we have dropped the index of any particular
variety because they are produced, and enter (2.1), symmetrically)
PV= Ia V (2.5)
where rv is the interest rate prevailing in country v. Assume, for simplicity, that
the functions yYw (.) are given by 7, = X,___i V_W _ 4 i; then, using (2.5)
and (2.3), (2.4), it can be shown that all intermediates, whether domestically
produced (xi) or imported (xw), are employed at the same level, xi.
In equilibrium, there will be trade in intermediate goods in this model. Define
capital ki as aggregate capital in country i. This will be equal to the resources
needed to produce the quantity nixi of the domestic varieties, plus the resources
to obtain the foreign intermediates, Ewu, n,,,x w :& i. A unit of domestic interme-
diates, selling at price pi, buys Pi/P,, units of an intermediate of country w 7& i.
4
Hence, if trade is balanced, E En,x,,, units of domestic intermediates must be
exported in order to obtain the quantity E,, n,xW of foreign intermediates. It
follows that ki is given by
ki = nixi + E Pnwxw = (nj + E -nw) xi. (2.6)
w#i Pi w˘i Pi
In a situation where the interest rates are equalized internationally at rate r,4 we
have, from (2.6) and (2.5), that
xi= ki (2.7)
[ni + Ew:i pwnw s
and lw ( )
Define a standard measure of total factor productivity (TFP)
log Fjt = log Yvjt - aj log ljt - (1- avj) log kjt, Vv, j, t.
The output term log yjt is given by log Ai + aij log lijt + (1 - ij) log dijt, with
logdc4t = lct* log [nijt ijt f+Ewynwjt x3t jt
| 1 log I (nijt + wnwjt w)
- {~~~nj +w0 A~hj nlwjt]1az
On substitution, one has for the TFP index
log Fijt = log Ajt + log njt + EW /2 j nwjt ] (2.8)
[nijt + Ew,i U> nwjt 1aj
Equation (2.8) shows that the log-level of TFP is a function of the ranges of
intermediate goods which are employed in the importing country; nijt gives the
domestic range, and the nwjt are the foreign ranges.
As a benchmark case, consider a model where countries are perfectly syminet-
ric. Then, one has that ,uw = 1,Vw =A i. Further, given the CES structure and
4In the symmetric version of this model which can be shown to have a stable balanced growth
path, r will be equalized in equilibrium.
5
synunetry across intermediates, any sector of any country will demand all inter-
mediate inputs which are available worldwide, so that n,jt and nwjt, the ranges
of intermediates employed in country i, are now equal to the ranges produced in
countries i and w. Under these circumstances,
log Fijt = log Ajt + aij log ±ijt + E nwjt j= log Ajt + aij log ngjt, (2.9)
where ngjt is the range of intermediates which is produced for the sector j globally.
The ranges of intermediate varieties are increased through devoting resources
to R&D (Romer 1990). Although these ranges are not observed, under certain
assumptions on depreciation and obsolescence, the ranges are equal to the respec-
tive cumulative R&D spending, Sv, which itself is observable. In the symmetric
model with V countries, the variable ng in equation (2.9) will be equal to V x S,.
For the case where countries are asymmetric in size and with respect to R&D
spending, and, consequently, intermediates are not traded symmetrically, it is
critical to know the relation between countries' cumulative R&D spending Sv,
and the ranges employed in country i, n'. The relation of TFP and the ranges
of intermediates employed can in general be written as (industry subscript sup-
pressed)
Fi = @(Ai;n ;n.,;) = 4 (Ai; Si,m,mm; S.,,,n ,z,w =4 i, (2.10)
where mi is country i's overall import share, m' is the weight the country's own
R&D receives, mu, is country i's import share from country w :8 i, and 'I (.) and
4 (.) are unknown functions. One can think of the import shares in (2.10) as being
related to the likelihood of receiving a new type of foreign intermediate. This is
certainly so in the extreme case when m, = 0.5 Other than that, there is no
necessary link between the level of imports and the number of newly introduced
intermediate goods types in the local economy. Especially if one also considers
indirect effects, in particular the possibility that importing leads to local learning
through reverse engineering and the subsequent invention of new inputs, it is
clear that the volume of imports can be a very bad measure of the increase in
varieties which are available domestically.6 Despite these considerations, however,
it is likely that the number of new varieties employed from a partner country is
50f course, even with mt = 0, a country can obtain foreign knowledge which is not embodied
in goods.
6An alternative view is implemented by Klenow and Rodriguez (1996) who postulate that
6
positively, although presumably not linearly, related to the import volume from
that country.7
3. Data
This study employs data for eight OECD countries in six economic sectors ac-
cording to the International Standard Industrial Classification (ISIC) as well as
the Standard International TRade Classification (SITC), for the years 1970-1991.
The included countries are Canada, FRance, Germany, Italy, Japan, Sweden, the
United Kingdom, and the United States; hence, the G-7 group plus Sweden.8
We use the following breakdown by sector (adjusted revision 2): (1) ISIC 31
Food, beverages, and tobacco; (2) ISIC 32 Textiles, apparel, and leather; (3) ISIC
341 Paper and paper products; (4) ISIC 342 Printing; (5) ISIC 36&37 Mineral
products and basic metal industries; (6) ISIC 381 Metal products. All sectors
belong to ISIC class 3, that is, manufacturing. In these sectors, the reliability
and comparability of the measurement of inputs and outputs is high compared to
non-manufacturing sectors.
The data on imports of machinery comes from the OECD Trade by Commodi-
ties statistics, OECD 1980. We have tried to identify machinery imports which
will with high likelihood be utilized exclusively in one of the above manufacturing
industries. These commodity classes are (Revision 2) SITC 727: Food-processing
machines and parts, providing inputs to the ISIC 31 industry; SITC 724: Textile
and leather machinery and parts (corresponding to ISIC 32); commodity class
SITC 725: Paper & pulp mill machinery, machinery for manufacturing of paper
(corresponding to ISIC 341); commodity class SITC 726: Printing & bookbind-
ing machinery and parts (corresponding to ISIC 342); commodity classes 736 &
737: Machine tools for working metals, and metal working machinery and parts
(corresponding to ISIC 381); and, by SITC classification, Revision 1, commodity
classes 7184 & 7185: Mining machinery, metal crushing and glass-working ma-
the number of different intermediate good varieties is related to the number of different trade
partners a country has. Also note that in the fully symmetric model, the level of the intermediate
xi does not enter in determining the productivity effect, see (2.9). In that model, as the number
of countries rises, the value of bilateral imports actually falls with the equilibrium level xi.
A paper which considers some asymmetries between intermediates from different countries is
Rivera-Batiz and Romer (1991b).
7In Grossman and Helpman (1991), Ch.6.5, the authors discuss several reasons of why this
should be the case.
8See the appendix for more details on data sources and the construction of the variables.
7
chinery (corresponding to ISIC 36 & 37). The bilateral trade relations for these
SITC classes are given in Tables A-1 to A-6 in the appendix.
Data from the OECD (1991) on R&D expenditures by sector is utilized to
capture the ranges of intermediate inputs, n,. This data covers all intramural
business enterprise expenditure on R&D. Because none of these industries has a
ratio of R&D expenditures to GDP of more than 0.5%, it is reasonable to assume
that insofar as their productivity benefits from R&D at all, it will be to a large
extent due to R&D performed outside the industry. However, there is no interna-
tionally comparable data on machinery industry R&D towards products which are
used in specific industries. Therefore, we assume that R&D expenditures towards
a sector j's machinery inputs is a certain constant share of the R&D performed
in the country's non-electrical machinery sector (ISIC 382), where all specialized
new machinery inputs are likely to be invented.9 R&D stocks are derived from the
R&D expenditure series using the perpetual inventory method,'0 and descriptive
statistics on the cumulative R&D stocks are given in the appendix, Table A-7.
The TFP index is constructed using the Structural Analysis Industrial (STAN)
Database of the OECD (1994). The share parameter a is, by profit maximiza-
tion of the producers, equal to the ratio of total labor cost to production costs.
As emphasized by Hall (1990), using cost-based rather than revenue-based factor
shares ensures robustness of the TFP index in the presence of imperfect competi-
tion, as in the model sketched above. Building on the integrated capital taxation
model (see Jorgenson 1993 for an overview), we construct cost-based labor shares.
The parameter a above then is the share of labor in total production cost. The
variable I is the number of workers engaged, directly from the STAN database.
The measure of y is production, which also comes from the STAN database. The
growth of the TFP index F is the difference between output and factor-cost share
weighted input growth, with the level of the F's normalized to 100 in 1970 for
each of the 8 x 6 time series. In Table A-8 of the appendix, summary statistics
for the TFP data are shown.
9This constant share is the share of an industry in employment in total manufacturing em-
ployment, over the years 1979-81.
l°Hence, there is no variation in the proportional change of the R&D stock of industry j, and
industry j + 1 between time t and t + 1, for any given country i. Any differential effect on TFP
in sectors j and j + 1 of an importing country is therefore due to differences in the patterns of
bilateral trade, the main focus of the paper.
8
4. Estimation Results
In this section, we will present estimation results for different specifications of the
function 4'(.) above. The following section discusses TFP level estimation results,
whereas below, estimation results for TFP growth rate regressions are shown.
4.1. TFP Level Specification
Consider, as a specification of the function (Aij; Sidt; m'; Sd,t; m J) above, the
following
log Fijt = ao + tddj + 8d± + E3A (m7t log S' ') + eijt, (4.1)
where dj and dv are industry-, and country- fixed effects, respectively. In this
specification, the TFP level in any industry is a function of cumulative R&D in
all eight countries, with a domestic weight (m' ) set to one, and the weights of
the partner countries given by the bilateral import shares (Z", m j = 1, Vi); the
country-elasticities /J are constrained to be the same across importing countries.1
According to (4.1), the import composition matters for the TFP level of a
country, with the import-share interacted R&D stocks capturing the technology
inflows into that country. Howvever, (4.1) implies that two countries with the
same import composition, but different overall import shares, should benefit to
the same degree from foreign R&D-which is unlikely. Following Coe and Helpman
(1995), we can model this through an interaction of the overall import share, mij,
with the R&D variable'2
log Fijt = oz + ,udj + 6d, + E 3 (mij Mi j log Sd t) + Eijt (4.2)
We will refer to a specification without the overall import share, as in (4.1), as
NIS, whereas a specification with the overall import share is referred to as IS.
Results for the specifications (4.1) and (4.2) are given in Table 1, with standard
errors in parentheses; a **(*) denotes significantly different from zero at a 5(10)%
level.
llThe specification differs from Coe and Helpman's (1995) in that we allow the R&D elasticity
to vary by country, whereas Coe and Helpman estimate one parameter for the whole set of
partner countries, which changes across observations. In addition, here, the import shares enter
linearly, not in logs. The specification can be thought of being derived from a reduced form
expression for TFP of the form Fijt = AijII3 (Sd')3_ X m eeijt.
'2For the own R&D effect, mij is chosen such that mijm3 logSi = logS i.e., mid then
equals one.
9
From Table 1, we see that all countries' R&D stocks are estimated to have a
significant and positive influence on the TFP level of the importing country. The
magnitude of these effects, however, varies substantially, with, e.g. for the second
specification, a low for Germany with 1.9%, and a high for R&D from Sweden,
with 27.6%. The specifications account for a third to one half of the variation of
TFP levels across countries, with the higher R2 for the NIS specification. The
result that high stocks of scaled foreign R&D are associated with high domestic
levels of TFP is interesting, but does not say much about the importance of
the fact that the weighing variables are the observed bilateral import shares.
Interpreting these shares as the probability that the importing country receives
new intermediate inputs from a partner country, a natural question to ask is how
the estimated parameters would look like if we had employed a different set of
probability weights, corresponding to different import patterns. This is what the
following Monte-Carlo experiments show.
Here, we intend to address two different questions: First, is there support
for the hypothesis that there is a distinction between effects on TFP resulting
from foreign as opposed to domestic R&D? Second, conditional on the effect
from domestic R&D on TFP, is there evidence to assume that the composition of
intermediate imports trade matters for TFP across sectors?
4.1.1. Domestic and International Inputs: does it matter how much
from where?
In the Monte-Carlo experiments which follow, we will exchange trade partners
randomly. Let b denote a specific Monte-Carlo replication, b = 1, ..., B. For a given
importing country, say i, we exchange the observed bilateral shares randomly.
This means that any bilateral import share in replication b, 'j (b), is equal to13
mz with Pr=
˘vj(b) = 4 ,Vv,j. (4.3)
I mVvithr = P
13For a given industry and importing country, eight numbers are drawn from a uniform
distribution with support [0, 1]. These are matched with the eight (that is, including 'imports'
from own) observed 'import' shares to form a 8 x 2 matrix. This matrix is then sorted in
ascending order on the random number coluni. In this way, the probability that any trade share
or (b) is equal to the value m' , all v, is equal to 1/8. A new sequence of trade relations (the
eight numbers from the uniform distribution with support [0, 1]) is drawn for every importing
country and every industry, making a total of 8 x 6 = 48 independent sequences.
10
Because m'. = 1 and E m" - = 1, it holds that ,, oj (b) = 2. Note that in setting
up this experiment, we ignore the distinction between the domestic weights mi'j,
and bilateral import shares ml ,, w :& i. Hence, the experiment allows to see
whether, conditional on the ex-ante chosen value for m' = 1 and the specification
of 4), it is important to distinguish between embodied technology in intermediate
inputs from domestic, on the one hand, versus from foreign producers, on the
other. The equations are
log Fijt = ao + ,udj + 6d, + E pt (of,fj (b) log Sd t) + Eijt Vb, (4.4)
v~~~~~v
for the specification without the overall import share (NIS), and, for the IS
specification:
log Fijt = ao + ,udj + 6dv + E i j (ma3j 4(b) log sd t) + Eijt, Vb. (4.5)
V~~~~~~~V
The results are shown in Table 2, second and fifth result columns. In the table, the
average slope estimate 3v(b) from B = 1000 replications, as well as the standard
deviation of ,lv (b) (in parentheses) and the average R2 are reported.
One sees that the Monte-Carlo experiments result in coefficient estimates
which are in 75% of the cases statistically indistinguishable from zero. In particu-
lar, for the model (4.4), this is true for half of the coefficient estimates, and for the
model (4.5), it is true for all countries' estimates. The average R2 in column two,
with 0.522, is larger than for the corresponding observed-data regression. This is
somewhat surprising, but the finding could well be spurious. Overall, the result
that parameter estimates tend to be not significantly different from zero in the
Monte-Carlo experiment implies that if intermediate input usage (from abroad
and domestically) is determined randomly, the effect of R&D on the importing
sector's TFP is not statistically different from zero. Therefore, it helps to know
which intermediates come from the domestic, as opposed to foreign economies if
one wants to predict an importing sector's TFP level.14
The next experiment control for the domestic R&D effect and asks whether
the composition of imports matters for domestic TFP levels.
140bviously, this depends on how large a weight the domestic R&D variable receives (here,
its weight is equal to one).
11
4.1.2. Does the TFP performance reflect the composition of intermedi-
ate imports?
We now constrain the Monte-Carlo experiments such that only the composition
of the international demand is randomized. That is, the results are conditional
on the domestic R&D effect: n9j(b) = 1,Vv,b. For all w + i, we have
0,tj(b) = m' with Pr = 7, q C V \ i,Vw, j. (4.6)
The Oi (b) are constructed such that w , O.j (b) = 1, that is, any observed trade
share is assigned only once. The two specifications, for a given country i, are
log Fjt = ao + jdj+ + Ed ± >Zv (9' (b) log Sd ') + Eijt, Vb, (4.7)
v
and
log Fijt = ao + [tdj + Mdv + E 0, (mij O j(b) log Sdt) + Eijt, Vb. (4.8)
V~~~~j V
The results of these two experiments, for B = 1000, are shown in result columns
three and six of Table 2. The parameter estimates now are, in 75% of the cases
significantly different from zero and positive. In addition, these coefficients are
sometimes smaller, and sometimes larger than those obtained employing observed
import shares: no clear pattern can be detected. Moreover, the regressions which
employ randomly exchanged import shares account for a comparable part of the
variation in TFP levels as the observed-data regressions.
The fact that it is not necessary to impose the observed import shares to
estimate significant international R&D spillovers confirms the result of Keller
(1996b) that one cannot test the hypothesis of the R&D-trade-TFP link simply
by examining whether the parameter estimates are positive, or how high the
R2 of these regressions is. Obviously, the regression results are to some degree
invariant to whatever weights the R&D stocks are interacted with. This would
be trivially so if the R&D stocks of different countries are equal in size and move
together over time. However, as shown in Table A-7 in the appendix, there are
considerable differences in the cumulative R&D stocks of different countries. In
addition, Figure 1 shows that the R&D stocks of different countries exhibit neither
growth at approximately the same rates, nor do they rise and fall simultaneously.'5
"5The average annual rate of growth of the R&D stock estimates ranges from 3.64% for the
Canada to 11.88% for Italy; and the standard deviation of these growth rates for different
four-year subperiods across countries ranges from a low of 2.87% (1978-82) to a high of 5.15%
(1970-74).
12
Therefore, this explanation, at least in its extreme form, cannot be the reason for
the finding of more or less invariant parameter estimates.
Another interpretation of the results in Table 2 is that what the regressions pick
up is mainly a strong general effect from foreign R&D; that is, although imports
are in part related to international technology flows, this effect is overshadowed
by a general R&D spillover effect. This is discussed further in section 5 below. A
third interpretation is that much of the estimated correlation is spurious, perhaps
the consequence of interpolation in the data, or due to the time-series properties
of the data generation process. It is the latter point which I intend to address first,
by presenting results from a TFP-R&D growth specification. This would address
the problem if the benchmark capital stocks for physical capital (underlying the
TFP variable) as well as for the R&D capital stocks had been estimated with an
error, as is very likely; further, the growth specification is also preferred in the
case of unobserved, time-invariant heterogeneity among the industries.16
4.2. TFP Growth Estimation
The TFP growth specifications corresponding to (4.1) and (4.2) above are, for an
importing country i,
a__ o + ~ m2.Sjt+6i (4.9)
AFijt E Sjt
where ^ denotes the average annual growth rate of any variable x, and mv=
1, Vv, j, The specification including the overall import share is now given by
F = ac + B, (mi. mvj 5dv) + eijt, (4.10)
Fijt v tsj
where, again, the value of the import share from i, mij, is set equal to one, Vi, j.
Dividing the period of observation into five subperiods of approximately four years
each, these regressions have 240 observations; the results are shown in Table 3,
result columns one and three.
All slope coefficients are estimated to be positive, although only in the model
which includes the overall import share, IS, all estimates are significantly different
'6The data generation process underlying the variables, especially whether they are integrated
of order one or less, also influences the choice of specification. However, the unit root and
cointegration tests which have been conducted failed to settle this issue in the present context.
13
from zero at a 5% level. The latter appears to be the preferred specification in
this class of models, which is in line with the arguments given above, as well as
with findings in Coe and Helpman (1995).
The results of the corresponding Monte-Carlo experiments are shown in result
columns two and four of Table 3. Contrary to the TFP level regressions above,
only the results conditional on the effect from domestic R&D are shown in Table
3. The specifications are, for an importing country i,
4F = a + (0t,j(b) ) + eijt, (4.11)
Fijt vU v"j t
and
= ao+Z + ( S(b ASdjb Eb. (4.12)
For each of these two experiments, we conduct B = 1000 replications. Again, all
Monte-Carlo based coefficients are estimated to be significantly above zero, con-
firming the earlier results from TFP level regressions. Moreover, now, the mean
estimates from the Monte-Carlo experiments are very similar to the coefficients in
the corresponding observed-trade share regression. For instance, a 95% confidence
interval for the coefficient of Canada in IS, (4.12), is given by 0.427 ± 2 x 0.022.
Given that this interval also includes the estimate for the import-weighted R&D
effect from Canada when employing observed data (with 0.415), this implies that
the Canadian trade-related R&D effect is statistically not different from a ran-
domized Canadian R&D effect, as captured by the average Monte-Carlo estimate.
In the following section, we will show how the latter is related to a general spillover
effect from foreign R&D, and determine whether there is a marginal contribution
of international trade.
5. Separating Trade-related from General R&D Spillovers
5.1. Monte-Carlo Experiments and General Foreign R&D Spillovers
Consider the average of a particular off-diagonal element across the B simulations,
o,W(b) = B Eai ,(b). Because the exchanging of mu is i.i.d., as B -- oo, this
average will be the same for all, ou,(b) =(b), Vi, w. Further, with 7 trade partners
for any importing country, given that 7x u(b) = 1, we have that a(b) = 1/7.
14
Hence, for any partner country's R&D variable across all B replications, we have
1 E__ - i zX)swj ASd. Lb