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\author{Wolfgang Keller\thanks{%
\thinspace \thinspace \thinspace 1180 Observatory Drive, Madison, WI 53706;
email: wkeller@facstaff.wisc.edu.} \\
%EndAName
Department of Economics\\
University of Wisconsin-Madison}
\date{March 26, 1996}
\title{Are International R\&D Spillovers Trade-related?\\
Analyzing Spillovers among Randomly Matched Trade Partners\thanks{%
\thinspace \thinspace \thinspace This paper was originally presented on
April 9, 1996 at the International Economics workshop at
UW-Madison.\thinspace I would like to thank, without implication, David Coe
and Chiwha Kao for the provision and discussion of the data files, and
Steven Durlauf, Robert Staiger, as well as seminar participants for comments.%
}}
\maketitle

\begin{abstract}
\noindent In this paper, I analyze recent findings by Coe and Helpman (1995)
of trade-related international R\&D spillovers. I show generally that
randomly created bilateral trade shares also give rise to large estimated
international R\&D spillovers; often, in fact, to larger estimated spillover
effects which are more precisely estimated than by employing the 'true'
bilateral trade shares. This casts some doubt on the earlier results in the
literature.
\end{abstract}

\section{Introduction}

The recent development of theories of endogenous technological change, in
particular by Romer \cite{romer90} and Aghion/Howitt \cite{aghhow}, have
triggered new work on the relations of trade, growth, and technological
change in open economies. Most important is the monograph by Grossman and
Helpman \cite{gh91}. These authors embed the new theories in multi-sector,
multi-country general-equilibrium models 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 embodied in intermediate inputs: If
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 improved
through the R\&D efforts of its trade partner.

Even before the advent of the models of endogenous technological change, a
vast literature had developed which related domestic R\&D expenditures to
total factor productivity (TFP) growth. The particular contribution of the
new models of trade and growth therefore lies in the testable hypotheses one
can derive with regard to trade and openness. Coe and Helpman \cite{chelp}
have recently attempted to test one of these. These authors suggest that the
following testable prediction can be derived and tested empirically: Ceteris
paribus, if one country imports to a large degree from other countries which
have accumulated high levels of technological knowledge, it should exhibit
higher productivity levels than if it would import less from 'high-tech'
countries.

At the center of the analysis by Coe-Helpman is what the authors call the
''foreign stock of knowledge''. This variable is constructed as a weighted
sum of the cumulative R\&D expenditures of a country's trading partners. The
weights are given by the bilateral import shares.\footnote{%
This is in analogy to the R\&D-total factor productivity literature; since
Terleckyj \cite{terl74}, several authors have related R\&D expenditures in
industry $i\neq j$ to the TFP growth of industry $j$, where for instance
input-output coefficients serve as weights.} According to Coe-Helpman, their
analysis

\begin{quotation}
''underlines the importance of the interaction between international trade
and foreign R\&D'' (p.860).
\end{quotation}

Coe and Helpman conclude their analysis by stating that

\begin{quotation}
''not only does a country's total factor productivity depend on its own R\&D
capital stock, but, as suggested by the theory, it also depends on the R\&D
capital stocks of its trade partners.'' (p.875).
\end{quotation}

Hence, Coe and Helpman argue that their analysis supports the view that
international R\&D spillovers are trade-related. The present paper
investigates this claim.

\section{Theory and Empirical Implementation by Coe-Helpman}

Coe and Helpman's \cite{chelp} empirical specification is derived from
models which have endogenized the process of technological change. I will
give here only a sketch of one type of model (the horizontally
differentiated-inputs specification). Assume that final output $y$ is
produced according to 
\begin{equation}
y=A\,k^\alpha d^{1-\alpha },\,\text{ with }0<\alpha <1,  \label{outp}
\end{equation}
where $A$ is a constant, $k$ are capital services, and $d$ is a composite
input consisting of horizontally differentiated varieties $x(s)$%
\[
d=\left( \int_0^nx(s)^{1-\alpha }\,ds\right) ^{\frac 1{1-\alpha }}. 
\]
Here, $n=n(t)$ is the range of intermediate inputs existing in this economy
at time $t$ (ignoring integer constraints). Because intermediates enter
symmetrically, if only one unit of labor is needed to create a unit of any $%
x(s)$, it will be the case that $l$, the total labor employed in the
production of intermediate goods, will be given by 
\[
l=n\,\bar x,\text{ } 
\]
where $\bar x$ is the equilibrium quantity of intermediates employed.
Substituting in (\ref{outp}) gives 
\[
y=A\,k^\alpha n^\alpha l^{1-\alpha }. 
\]
Hence, if one defines $\log \,F=\log \,y-\alpha \,\log \,k-(1-\alpha )\log
\,l$ as the log TFP level, one obtains that 
\begin{equation}
\log \,F=\log \,A+\alpha \log \,n.  \label{pred}
\end{equation}
This says that the log TFP level should be positively related to the range
of intermediate inputs existing at that time.

We assume that entrepreneurs invest in R\&D ($r(t)$), which expands the
available range of designs for new intermediate inputs: $\dot n(t)=a\,r(t),$%
where $a$ is a constant. If designs never become obsolescent, the stock of
intermediate inputs available at time $T$ is 
\begin{equation}
n(T)=\int_{-\infty }^T\,\dot n(t)dt=a\,\int_{-\infty }^Tr(t)\,dt\equiv
a\,S^d(T),  \label{nT}
\end{equation}
that is, it is proportional to the cumulative R\&D expenditures, $S^d(T)$.
Hence, for a single country, by substituting (\ref{nT}) into (\ref{pred}),
we arrive at the prediction that the log TFP level is positively related to
the country's cumulative R\&D expenditures 
\[
\log \,F=\mu +\alpha \log S^d, 
\]
where $\mu \equiv \log A+\alpha \log a.$ International trade among several
countries allows to import newly developed intermediates from abroad. If all
intermediates worldwide would be tradable to the same degree, then any
country's TFP level would depend solely on the world's cumulative R\&D
expenditures. Because the tradability of intermediates differs, though, Coe
and Helpman \cite{chelp} suggest that a foreign knowledge stock variable for
any country $i,$ $S_i^f,$ be constructed as follows: 
\begin{equation}
S_i^f=\sum_{h\neq i}\left( \frac{m_{hi}}{m_i}\,S_h^d\right) ,\,\forall \,i.
\label{nf}
\end{equation}
Here, $m_{hi}$ are the bilateral imports of country $i$ from country $h,$
and $m_i$ are total imports of country $i.$ Hence, the construction of the
variable $S_i^f$ weights the cumulative R\&D expenditures of country $i$'s
trading partners by their bilateral import share with country $i.$ Coe and
Helpman \cite{chelp} mention several effects trade can have, ranging from
learning about new technologies and production processes to learning about
new organizational methods to the direct import of goods and services
developed by trade partners. In this way the specification captures the
notion that the domestic economy will reap, ceteris paribus, more
international spillovers if it trades relatively more with countries which
have invested heavily in R\&D, and hence have large domestic knowledge
stocks, $S^d.$ \footnote{%
Clearly, some of these effects are not unique to trade in goods. Foreign
direct investment, for instance, can result in the same. Similarly, not all
of these effects are related to the volume of trade; see below.}

Coe and Helpman's first specification is therefore given by 
\begin{equation}
\log \,F_i=\beta _{0i}+\beta _1\log S_i^d+\beta _2\log \,S_i^f+\varepsilon
_i,\,\forall i,  \label{basic1}
\end{equation}
where $\varepsilon _i$ is an error term. Taking this a step further, these
authors argue that for a given composition of a country's trade partners, it
should be the case that the domestic economy benefits more from R\&D
activities abroad the higher are overall imports relative to GDP; let $s_i$
denote the import share of country $i.$ This argument presupposes that there
are some productivity effects which are tied to the volume of trade
(especially some of the learning effects mentioned above).\footnote{%
These effects are not captured by the model as sketched above; see
Grossman/Helpman \cite{gh91}, Ch.6.5, for more on this.} Hence, Coe and
Helpman's second specification is therefore 
\begin{equation}
\log \,F_i=\beta _{0i}+\beta _1\log S_i^d+\beta _2\,\left( s_i\log
\,S_i^f\right) +\varepsilon _i,\,\forall i.  \label{basic2}
\end{equation}
In the Coe-Helpman sample, there are 21 OECD countries plus Israel, for the
years 1971-90, making a total of 440 observations. The authors present three
regressions in the paper: The one given in (\ref{basic1}), a second one
augmenting (\ref{basic1}) with an additional effect for the G 7 countries,
and the equation (\ref{basic2}). In Table 1, I reproduce the Coe-Helpman
results (their Table 3) as a first step. Each of the following regressions
includes unreported country-specific intercepts.\bigskip

{\footnotesize 
\begin{tabular}{c}
\fbox{%
\begin{tabular}{l|c|cc}
\multicolumn{4}{l}{TABLE 1} \\ \hline\hline
& \multicolumn{1}{c}{} & \multicolumn{1}{c}{} &  \\ 
\multicolumn{4}{l}{TFP estimation results (pooled data; 440 observations)}
\\ \hline
&  & \multicolumn{1}{|c|}{} &  \\ 
& (i) & \multicolumn{1}{|c|}{(ii)} & (iii) \\ 
&  & \multicolumn{1}{|c|}{} &  \\ 
$\log \,S^d$ & $0.097\,\, 
\begin{array}{c}
\left[ 0.097\right]
\end{array}
$ & \multicolumn{1}{|c|}{$0.090\,\,\, 
\begin{array}{c}
\left[ 0.089\right]
\end{array}
$} & $0.078\,\,\, 
\begin{array}{c}
\left[ 0.078\right]
\end{array}
$ \\ 
&  & \multicolumn{1}{|c|}{} &  \\ 
G7$*\log \,S^d$ &  & \multicolumn{1}{|c|}{$0.135\,\,\, 
\begin{array}{c}
\left[ 0.134\right]
\end{array}
$} & $0.157\,\,\, 
\begin{array}{c}
\left[ 0.156\right]
\end{array}
$ \\ 
&  & \multicolumn{1}{|c|}{} &  \\ 
$\log \,S^f$ & $0.092\,\,\, 
\begin{array}{c}
\left[ 0.092\right]
\end{array}
$ & \multicolumn{1}{|c|}{$0.060\,\, 
\begin{array}{c}
\left[ 0.060\right]
\end{array}
$} &  \\ 
&  & \multicolumn{1}{|c|}{} &  \\ 
$s*\log \,S^f$ &  & \multicolumn{1}{|c|}{} & $0.289\,\,\, 
\begin{array}{c}
\left[ 0.294\right]
\end{array}
$ \\ 
&  & \multicolumn{1}{|c|}{} &  \\ 
$R^2$ & $0.630 
\begin{array}{c}
\left[ 0.558\right]
\end{array}
$ & \multicolumn{1}{|c|}{$0.683 
\begin{array}{c}
\left[ 0.621\right]
\end{array}
$} & $0.706 
\begin{array}{c}
\left[ 0.651\right]
\end{array}
$%
\end{tabular}
}
\end{tabular}
{\small \bigskip\ } }

For comparison, I have given Coe-Helpman's results in hard brackets.%
\footnote{{\footnotesize In this table, I follow Coe-Helpman who do not give
standard errors, because they think of their regressions as cointegrating
equations. In that case the conventional standard errors are biased and not
asymptotically normal. Solely for the record: All coefficients are
significantly different from zero at a 5\% level if the conventional
standard errors are used.}} Note that there are differences in the $R^2$ of
the regressions; the $R^2$ of the regressions presented here is higher than
in Coe-Helpman. There are also very small differences in the point estimates
of the coefficients; the largest on the variable $s*\log \,S^f$, which is $%
0.294$ in Coe-Helpman, whereas it is $0.289$ in regression (iii) presented
here. These discrepancies are most likely due to data revisions immediately
preceding the publication of Coe and Helpman's paper, which I could not
incorporate so far. However, the point estimate differences are, in any
case, very small.\footnote{%
I am using data which was provided by David Coe to Chihwa Kao; I thank the
latter for transferring the data electronically to me.}

\section{The Monte-Carlo Approach: Simulating Bilateral Trade Shares}

In evaluating the hypothesis that international R\&D spillovers are
trade-related, the foreign knowledge stock variable $S^f$ constructed by
Coe-Helpman is of central interest. A country's R\&D benefit from abroad is
taken to be a weighted average of these foreign countries' R\&D efforts,
where the weights are given by the bilateral import shares. I call this
matrix $BTS$; the values for 1990 are reproduced from Coe-Helpman in Table
2. For instance, 29.94\% of the US imports came from Canada, as opposed to
only 1.07\% of Germany's. In consequence, the level of the Canadian
cumulative R\&D expenditure should be much more relevant to the US than it
is for Germany. Further, international R\&D spillovers are expected to be
large if a country imports primarily from 'high-knowledge' economies within
this sample of developed countries.

In the following, I will compare the estimation results of Coe and Helpman
with those obtained from assigning bilateral trade partners randomly.%
\footnote{%
See also Ben-David (1995), who has used a random-country-grouping-method to
the question of trade and income convergence. He shows that there is more
income convergence in groups formed on the basis of trade interaction than
in random groupings of countries.} That is, rather than constructing the
foreign knowledge stock variable $S^f$ using the observed bilateral trade
share matrix $BTS$, I use random trade share matrices (denoted $RTS$) and
re-do the Coe-Helpman regressions (i)-(iii). For each Monte Carlo experiment
I obtain one matrix $RTS$ of 22 x 22 random elements constructed in the
following way: 440 (22 x 22) elements of a matrix $\Gamma $ are drawn from a
uniform distribution using the (pseudo) random number generator of the GAUSS
package.\footnote{%
I use a seed value which is updated during the process; the initial seed
value is 26875.} I then set the diagonal elements of $\Gamma ,$ $\gamma
_{ii},\forall i,$ equal to zero. In the next step the sum of each column is
calculated, $\gamma _{\bullet \,i}=\sum_{h\neq i}\gamma _{hi}.$ Finally,
shares $\sigma _{hi}$ are formed by 
\begin{equation}
\sigma _{hi}=\frac{\gamma _{hi}}{\gamma _{\bullet \,i}},\,\text{ }\forall
h,\,i,  \label{sig}
\end{equation}
with $\sum_h\sigma _{hi}=1,\,\forall i.$ The 22 x 22 matrix containing the
random shares $\sigma _{hi}$ is denoted $RTS$, the random trade share matrix.%
\footnote{%
Coe-Helpman (\cite{chelp}) use bilateral trade shares which are varying from
year to year from 1971 to 1991. Therefore I will also present results below
for the case where the $RTS$ matrix is re-build every year.}

With the $RTS$ matrix (and the variable $S^d$) in hand, I calculate the
variable $S^f,$ and then run the Coe-Helpman regressions (i)-(iii). For each
of the regressions, I conduct 1000 experiments; the following Table 3
reports the average estimated coefficient and the average estimated standard
error (in brackets).\bigskip 

{\footnotesize $
\begin{array}{c}
\fbox{%
\begin{tabular}{lllllll}
\multicolumn{7}{l}{TABLE 3} \\ \hline\hline
&  &  &  &  &  &  \\ 
\multicolumn{7}{l}{TFP estimation results (pooled data; 440 observations)}
\\ \hline
\multicolumn{1}{l|}{} &  & \multicolumn{1}{l|}{} &  & \multicolumn{1}{l|}{}
&  &  \\ 
\multicolumn{1}{l|}{} & \multicolumn{2}{|c|}{(i)} & \multicolumn{2}{|c|}{(ii)
} & \multicolumn{2}{|c}{(iii)} \\ 
\multicolumn{1}{l|}{} & \multicolumn{1}{c}{$BTS$} & \multicolumn{1}{c|}{$RTS$
} & \multicolumn{1}{c}{$BTS$} & \multicolumn{1}{c|}{$RTS$} & 
\multicolumn{1}{c}{$BTS$} & \multicolumn{1}{c}{$RTS$} \\ 
\multicolumn{1}{l|}{} &  & \multicolumn{1}{l|}{} &  & \multicolumn{1}{l|}{}
&  &  \\ 
\multicolumn{1}{l|}{$\log \,S^d$} & \multicolumn{1}{c}{$%
\begin{array}{c}
0.097 \\ 
(0.009)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.028 \\ 
(0.011)
\end{array}
$} & \multicolumn{1}{c}{$%
\begin{array}{c}
0.090 \\ 
(0.008)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.034 \\ 
(0.010)
\end{array}
$} & \multicolumn{1}{c}{$%
\begin{array}{c}
0.078 \\ 
(0.008)
\end{array}
$} & \multicolumn{1}{c}{$%
\begin{array}{c}
0.048 \\ 
(0.008)
\end{array}
$} \\ 
\multicolumn{1}{l|}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c|}{} & 
\multicolumn{1}{c}{} & \multicolumn{1}{c|}{} & \multicolumn{1}{c}{} & 
\multicolumn{1}{c}{} \\ 
\multicolumn{1}{l|}{G7$*\log \,S^d$} & \multicolumn{1}{c}{} & 
\multicolumn{1}{c|}{} & \multicolumn{1}{c}{$%
\begin{array}{c}
0.135 \\ 
(0.016)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.097 \\ 
(0.016)
\end{array}
$} & \multicolumn{1}{c}{$%
\begin{array}{c}
0.157 \\ 
(0.015)
\end{array}
$} & \multicolumn{1}{c}{$%
\begin{array}{c}
0.158 \\ 
(0.014)
\end{array}
$} \\ 
\multicolumn{1}{l|}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c|}{} & 
\multicolumn{1}{c}{} & \multicolumn{1}{c|}{} & \multicolumn{1}{c}{} & 
\multicolumn{1}{c}{} \\ 
\multicolumn{1}{l|}{$\log \,S^f$} & \multicolumn{1}{c}{$%
\begin{array}{c}
0.092 \\ 
(0.016)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.157 \\ 
(0.013)
\end{array}
$} & \multicolumn{1}{c}{$%
\begin{array}{c}
0.060 \\ 
(0.015)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.126 \\ 
(0.014)
\end{array}
$} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} \\ 
\multicolumn{1}{l|}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c|}{} & 
\multicolumn{1}{c}{} & \multicolumn{1}{c|}{} & \multicolumn{1}{c}{} & 
\multicolumn{1}{c}{} \\ 
\multicolumn{1}{l|}{$s*\log \,S^f$} & \multicolumn{1}{c}{} & 
\multicolumn{1}{c|}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c|}{} & 
\multicolumn{1}{c}{$%
\begin{array}{c}
0.289 \\ 
(0.041)
\end{array}
$} & \multicolumn{1}{c}{$%
\begin{array}{c}
0.337 \\ 
(0.030)
\end{array}
$} \\ 
\multicolumn{1}{l|}{} &  & \multicolumn{1}{l|}{} &  & \multicolumn{1}{l|}{}
&  &  \\ 
\multicolumn{1}{l|}{$R^2$} & \multicolumn{1}{c}{$0.630$} & 
\multicolumn{1}{c|}{$0.703$} & \multicolumn{1}{c}{$0.683$} & 
\multicolumn{1}{c|}{$0.728$} & \multicolumn{1}{c}{$0.706$} & 
\multicolumn{1}{c}{$0.749$} \\ 
\multicolumn{1}{l|}{} &  & \multicolumn{1}{l|}{} &  & \multicolumn{1}{l|}{}
&  & 
\end{tabular}
}
\end{array}
${\small \bigskip } }

\setcounter{page}{8}The estimates of central interest are the coefficients
on $\log \,S^f$ and $s*\log \,S^f.$ From Table 3 it is clear that the
regressions based on simulated data generate (on average) larger estimated
foreign R\&D spillovers, as well as a better fit in terms of $R^2.$ This
does not support the argument that the actually observed trade patterns are
behind the estimated international R\&D spillovers. Figure 1 shows a
histogram of the experiment (i), $RTS,$ in Table 3.

Further inspection of Table 3 shows that in the regressions based on
simulated data the elasticity of the cumulative domestic R\&D expenditures ($%
S^d$) is estimated to be smaller than in the Coe-Helpman regressions. One
wonders, therefore, whether the larger estimated coefficients on $S^f$ using
random shares is just a mirror image of that effect. Therefore, I conduct
the following two-step simulations: In step one, I regress the log TFP on
country-specific effects and the (log) $S^d$ variable.\footnote{%
When the G 7 dummy is part of the specification, also this variable is
included in the first-step regression.} I then subtract the fitted value of
that regression from log TFP, and employ the result as dependent variable in
the step two-regression on the $\log \,S^f$ variable, either created using
the 'true' trade shares ($BTS$) or random shares ($RTS$). The results of
this can be seen in Table 4.\bigskip

{\footnotesize $
\begin{array}{c}
\fbox{%
\begin{tabular}{l|ll|ll|ll}
\multicolumn{7}{l}{TABLE 4} \\ \hline\hline
& \multicolumn{1}{l}{} &  & \multicolumn{1}{l}{} &  & \multicolumn{1}{l}{} & 
\\ 
\multicolumn{7}{l}{Two-step TFP estimation results;} \\ 
\multicolumn{7}{l}{second step shown (pooled data; 440 observations)} \\ 
\hline
& \multicolumn{1}{|c}{} & \multicolumn{1}{c|}{} & \multicolumn{1}{|c}{} & 
\multicolumn{1}{c|}{} & \multicolumn{1}{|c}{} & \multicolumn{1}{c}{} \\ 
& \multicolumn{2}{|c}{(i)} & \multicolumn{2}{|c|}{(ii)} & 
\multicolumn{2}{|c}{(iii)} \\ 
& \multicolumn{1}{|c}{$BTS$} & \multicolumn{1}{c|}{$RTS$} & 
\multicolumn{1}{|c}{$BTS$} & \multicolumn{1}{c|}{$RTS$} & 
\multicolumn{1}{|c}{$BTS$} & \multicolumn{1}{c}{$RTS$} \\ 
& \multicolumn{1}{|c}{} & \multicolumn{1}{c|}{} & \multicolumn{1}{|c}{} & 
\multicolumn{1}{c|}{} & \multicolumn{1}{|c}{} & \multicolumn{1}{c}{} \\ 
$\log \,S^f$ & \multicolumn{1}{|c}{$%
\begin{array}{c}
0.037 \\ 
(0.010)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.043 \\ 
(0.007)
\end{array}
$} & \multicolumn{1}{|c}{$%
\begin{array}{c}
0.023 \\ 
(0.009)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.029 \\ 
(0.007)
\end{array}
$} & \multicolumn{1}{|c}{} & \multicolumn{1}{c}{} \\ 
& \multicolumn{1}{|c}{} & \multicolumn{1}{c|}{} & \multicolumn{1}{|c}{} & 
\multicolumn{1}{c|}{} & \multicolumn{1}{|c}{} & \multicolumn{1}{c}{} \\ 
$s*\log \,S^f$ & \multicolumn{1}{|c}{} & \multicolumn{1}{c|}{} & 
\multicolumn{1}{|c}{} & \multicolumn{1}{c|}{} & \multicolumn{1}{|c}{$%
\begin{array}{c}
0.118 \\ 
(0.026)
\end{array}
$} & \multicolumn{1}{c}{$%
\begin{array}{c}
0.132 \\ 
(0.020)
\end{array}
$} \\ 
& \multicolumn{1}{|c}{} & \multicolumn{1}{c|}{} & \multicolumn{1}{|c}{} & 
\multicolumn{1}{c|}{} & \multicolumn{1}{|c}{} & \multicolumn{1}{c}{} \\ 
$R^2$ & \multicolumn{1}{|c}{$0.031$} & \multicolumn{1}{c|}{$0.070$} & 
\multicolumn{1}{|c}{$0.014$} & \multicolumn{1}{c|}{$0.040$} & 
\multicolumn{1}{|c}{$0.044$} & \multicolumn{1}{c}{$0.093$}
\end{tabular}
}
\end{array}
${\small \bigskip
} }

\setcounter{page}{10}As one sees from Table 4, (1) the average point
estimate using random bilateral shares in this two-step analysis is always
larger than in the corresponding regression using the observed trade shares;
(2) the average estimated standard error is smaller, and (3) the random
share variable accounts for more of the variation left in the (purged) log
TFP levels. This result does not depend on the fact that the random share
regressions reported in Table 4 use time-invariant random shares for each
experiment, corresponding to using the same bilateral trade shares for all
years 1971-90.\footnote{%
The corresponding point estimates (standard errors) are for the regressions
(i)-(iii) when the shares are newly drawn every year: (i) $\log
S^f:\,\,0.043 $ $(0.007),$ $R^2=0.070$; (ii) $\log S^f:\,\,$ $0.029$ $%
(0.007),$ $R^2=0.040; $ (iii) $s*\log S^f:\,0.132$ $(0.020),$ $R^2=0.093.$
Beyond the 3-digit level which is reported here, the standard errors of the
estimates using time-varying random shares are slightly smaller.}

In Figure 2, I show a frequency distribution of the 1000 experiments
underlying regression (i), $RTS$. The plot underlines the point which is
already clear from the mean estimate given in the table, that the random
share-constructed variable results generally in a higher estimated foreign
spillovers effect. However, looking at Figure 3, which shows the 99\%
confidence region of the experiment, the estimate resulting from the 'true'
trade shares can also be thought of being a draw in the random share
experiment.

This is the interpretation underlying Table 5, which presents the bilateral
trade shares for one particular of the 1000 runs of regression (i), $RTS$,
in Table 4: The shares presented in Table 5 result in an estimated
coefficient on the variable $\log S^f$ of 0.037, which is the same estimate
as is obtained on $\log S^f$ in a regression which builds on the observed
bilateral trade shares; see Table 4, regression (i), column $BTS$. The
upshot of this is that we can compare the observed trade shares $m_{hi}$ in
Table 2 with the random shares $\sigma _{hi}$ given in Table 5. For
instance, given the importance of the United States as a technological
leader in most fields throughout the period of observations, one would
certainly expect that the fact that Japan has imported most of its goods
from the USA (45.77\% in 1990) is important for assessing the importance of
trade for Japanese TFP growth - if the hypothesis of technological knowledge
embodied in imported goods is correct. However, we see from Table 5 that the
same elasticity with respect to $S^f,$ the foreign knowledge stock, is
estimated in a different world where Japan imports only 4.2\% of its goods
from the US. Or take Canada as another example: It has been importing most
of its goods from the US (in 1990: 75.93\%). But Table 5 shows that in
another world where Canada imports more from Portugal than from the US
(8.7\% versus 7.5\%), we estimate the same effect on the foreign knowledge
spillover term $\log S^f.$ This analysis clearly suggests that it is
problematic to infer from the Coe-Helpman findings that it is indeed trade
in goods which transmits international R\&D spillovers.\footnote{%
Note that Table 2 given only the shares for 1990, not for all years between
1971 and 1990, as does Table 5. Any distorting effect resulting from that,
however, is unlikely to be the major reason of why the matrices are as
dissimilar as in fact they are: Ireland, for instance, did not only import
most of its goods by far (44.55\%) from the UK in 1990, but also between
1971 and 1990. The corresponding value for $\sigma _{hi}$, though, is only
5.2\%.}\setcounter{page}{13}

\section{Conclusion}

In this paper, I showed that the finding of international R\&D spillovers is
not unique to an analysis which builds on observed bilateral trade shares;
the same qualitative results, and usually quantitatively more important, are
found in a systematic study where trade partners are matched at random. The
answer to the question posed in the title is therefore clear: We do not know
yet whether international R\&D spillovers are trade-related; the available
evidence, at any rate, does not provide strong support for the hypothesis.

No attempt has been made in this paper to address the original question:
What is (is there?) a relation of trade and international technology
diffusion? In order to make future progress on that question in the
framework of recent models of trade and growth, two questions need to be
addressed. First, if the estimation equation correctly corresponds to a
(recent trade-and-growth) structural model, would the empirical
implementation of Coe-Helpman allow to find conclusive evidence? Chances are
that it would not. For one, the constructed foreign knowledge stock, has, in
the light of the considerable uncertainty involved in calculating the
domestic R\&D stocks (leading to measurement errors), only a small chance of
fully and appropriately capturing the trade-relatedness of international
R\&D spillovers. It is conceivable that any signal which might be in the
bilateral trade shares is perfectly confounded through the noise in the
domestic R\&D stock variables. For another, it is the flows of total
merchandise trade which are used in this approach, not intermediate input
trade flows. Even though the countries in the sample are a rather homogenous
group (OECD plus Israel), this will introduce an error, the effects of which
are difficult to judge.

The second question which needs to be addressed: Is the estimation equation
indeed corresponding to the recent model(s) of trade and growth? It appears
that the link from structural model to the estimation equations so far is
not as tight as one would hope. For instance, already the construction of
the variable $S^f$ implies that spillovers are tied to the volume of
imports. The basic structural model underlying this analysis, however, would
predict that spillover effects are forthcoming whenever any quantity,
however small, of a new intermediate input is imported.\footnote{%
See Keller \cite{wo95} for more on this.}\setcounter{page}{15}

\bigskip 

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\end{document}