%Paper: ewp-dev/9609001
%From: wolfgang@econ.wisc.edu
%Date: Mon, 9 Sep 96 16:41:48 CDT

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\begin{document}

\author{Wolfgang Keller \\
%EndAName
Department of Economics\\
University of Wisconsin-Madison\thanks{
1180 Observatory Drive, Madison WI 53706. Email: wkeller@facstaff.wisc.edu.
An earlier version of this paper circulated under the title: ''International
R\&D Spillover and Intersectoral Trade Flows: Do they Match?''. I thank
seminar audiences at Colorado-Boulder, UW-Madison, the NBER Summer
Institute, Purdue, and Yale, especially R.Evenson, Z.Griliches, J.Harrigan,
K.Maskus, T.N.Srinivasan, and M.Thursby. I also thank C.Langer for providing
data on trade flows, and M.Craw for the US import input-output data.}}
\title{Trade and the Transmission of Technology}
\date{This version: September 1996}
\maketitle

\begin{abstract}
\noindent 
This paper studies the role of trade, both domestically as well as
internationally, as a channel of technology transmission. A model is
presented in which R\&D investments towards product innovations trigger
total factor productivity growth at the industry level. If the new products
are exported to other industries, the return to the R\&D investments does in
part spill over to these industries. The model predicts that total factor
productivity levels are positively related to both own-, and the domestic
and foreign industry R\&D\ investments of the trade partners. Using data on
trade relations between OECD country sectors, effective R\&D stocks are
constructed which should pick up technology flows that are trade-related.
The empirical results, which are comparative to a benchmark model where
trade relations play no role, find generally only weak support for the
notion that the transmission of technology is trade-related; more
specifically, they point more towards domestic than to international trade.
At the same time, the results suggest that the adopted approach might not be
powerful enough to identify trade-related technology flows, which has
implications for other areas of research which have used analogous
approaches before.
\end{abstract}

\section{Introduction}

The question of whether goods trade at arm's length contributes to the
transmission of new technologies is both old and new: it is an old question
in a closed-economy context, because there exist many studies which examine
whether research and development (R\&D) investments--creating technology--in
one industry affect productivity also in other industries. These other
industries are often, at least in part, identified through input-output
relations--trade as channel of transmission--between industries (see e.g.,
Griliches 1984). In the open-economy context, however, the idea that trade
might be contributing to the international transmission of technology has
been emphasized particularly recently.

There has been no consensus for a long time on the question why, on average,
outward-oriented economies grow more rapidly (see, e.g., World Bank 1987,
Rodrik 1995). Two important issues were the following: First, if the trade
models were static, and markets were competitively (as was the case in most
of them), then they predicted static gains from trade which were very small
compared to the real-world differences in productivity growth between the
average open and protectionist countries. However, once models predicting
positive productivity growth rates even in the long-run (e.g., Romer 1990)
were placed into an open-economy context, changes in the trade regime could
have both long-run and large growth effects.

Another issue was: how is trade contributing to productivity growth?
According to one view, trade is affecting a country's growth rate through
its effects on domestic resource allocation. One problem with this view is
that trade is predicted to generate the same growth effects as other
influences which alter the domestic resource allocation. Specifically, a
purely domestic tax-and-subsidy policy can achieve exactly what trade
achieves. An alternative view, therefore, holds that international trade
directly affects productivity growth because it is transmitting
technological knowledge from country to country (Rivera-Batiz/Romer 1991,
Grossman/Helpman 1991). In those models, if R\&D investment creates new
technology in form of a construction design for a new intermediate product,
and this product is traded internationally, the receiving country can
benefit from employing the new, imported intermediate good without having
first to invent the construction design by itself. In this sense, importing
a foreign intermediate good allows to capture its R\&D-, or
'technology-content'.\footnote{%
Note that direct technology spillovers (in the sense of the employed
intermediate good revealing anything about its construction design to this
industry's R\&D entrepreneurs) are not necessary for the importing country
to experience productivity gains.} For given primary resources, in this
model, productivity is increasing in the range of different intermediate
goods which are employed, because these are assumed to be imperfect
substitutes for each other. The model's predictions is that TFP is
positively affected by the country's own, as well as R\&D investments made
by trade partners.

It is clear from this, however, that the framework is open to another
interpretation: that it captures the process of technology transmission
between different sectors within one economy. This model could well serve as
a theoretical underpinning of the empirical analyses in the closed-economy
studies referred to earlier. Indeed, as an empirical matter, this model
might even be a better description of technology diffusion within an economy
than across economies. This paper, therefore, attempts to provide a unified
and balanced approach in analyzing the importance of trade for the
transmission of technology along these lines both internationally as well as
domestically.

Earlier work in an international setting includes Eaton/Kortum (1996),
Coe/Helpman (1995), and Coe, Helpman, and Hoffmaister (1995). In the latter
two papers, the authors use country-level data to examine whether countries
productivity levels (or growth rates) are positively affected by domestic as
well as import-share weighted foreign R\&D investments. Because Coe/Helpman
and Coe et al. find that to be true, they suggest, contrary to the results
obtained by Eaton/Kortum (1996) using a different framework, that imports
are important vehicles for the international diffusion of technology. The
research on input-output related spillover effects closed-economy
industry-analysis can be traced back to Terleckyj (1974), and a good
overview is provided by the papers in Griliches (1984).

This paper departs from earlier work in several respects: First, I will be
using industry-level data also on international transactions, as opposed to
the country-level data employed by Coe/Helpman (1995), Coe et al. (1995),
and Eaton/Kortum (1996). It has been argued that studies employing aggregate
data are likely to miss much of the technology flows, because the diversity
of sectoral characteristics as well as the very nature of technology
diffusion confound any inferences from that data (e.g., Branstetter 1996).
Using two- or three-digit industry level data should reduce this problem.
Secondly, and related to the first, the usage of industry-level data allows
to integrate the recent emphasis on the open-economy relations with earlier
work, in particular by Terleckyj (1974) and Scherer (1984), which had
stressed domestic intersectoral technology transmission. The advantage of
this is that all market transactions predicted by the theoretical model,
both domestic as well as international, are considered, as opposed to only
focusing on a subset of those.

Third, I compare the empirical performance of the R\&D-driven growth and
intermediates inputs trade model with estimates from a benchmark model where
technology transmission is unrelated to goods trade. This comparison has
rarely been made.\footnote{%
The approach taken here differs from Keller (1996a), who uses Monte-Carlo
techniques to evaluate the claim of Coe/Helpman (1995) that international
R\&D\ spillovers are trade-related.} It is used to assess exactly how
important trade is in the relation of R\&D investments on the one, and
productivity growth on the other hand. Further, this comparative approach
encompasses both the domestic as well as the international elements of the
technology-transmission-is-trade-related hypothesis. Therefore, it might be
possible to find out whether technology transmission is brought about
through trade relatively more in the domestic, rather than in the
international context (or vice versa).

Lastly, a more general point of this paper is that it is advocating a simple
comparison analogous to the one proposed below to evaluate the empirical
importance of any specific weighting matrices which have been used in a
variety of contexts: apart from the papers mentioned so far, for instance,
Jaffe (1986) and Park (1995) have constructed matrices of technological
distance between sectors in work on technological diffusion and spillovers,%
\footnote{%
Also Branstetter (1996) builds partly on Jaffe (1986).} Englander, Evenson,
and Hazanaki (1988) construct technology flow matrices which are similar in
spirit, and Bartelsman, Caballero, and Lyons (1994) have used input-output
matrix weights in search of so-called customer- and supplier driven
externalities. In any of these analyses, a test analogous to what is being
proposed here might prove useful.

The remainder of the paper is as follows. In the next section, I develop the
benchmark model. Section 3 then describes the R\&D-driven growth and
intermediate inputs model, first for a closed-economy, and then extending it
to an international context. In section 4, I describe the data which will be
used. Section 5 gives the estimation results and the comparison of the
benchmark and trade-relations models, and section 6 concludes.

\section{The Benchmark Model}

Consider a model with $I$ different countries, $i=1,...,I$, and $J$
different goods, indexed by $j$, $j=1,...,J$. Output is being produced
according to a Cobb-Douglas production function which includes both domestic
as well as foreign R\&D capital stocks (time subscripts are dropped for
better readability) 
\[
q_{ij}=A\,_{ij}\left( b_{ij}^p\right) ^\nu \left( b_{-ij}^p\right) ^\mu
\,l_{ij}^\alpha \,k_{ij}^{1-\alpha }\,\,\,,\,\,0<\alpha <1,
\]
where $q_{ij}$ is output, $A_{ij}$ is a constant, $b_{ij}^p$ denotes the
domestic cumulative R\&D stock, $b_{-ij}^p$ is an aggregator of foreign
cumulative R\&D stocks, $l_{ij}$ are labor services, and $k_{ij}$ denotes
physical capital.\footnote{%
The presentation of the theory assumes that $\alpha _{ijt}=\alpha ,\forall
i,j,t$; however, as described in the appendix, the data is constructed by
using labor shares which vary by country, industry, and over time.} A
priori, one would expect both $\nu $ and $\mu $ to be positive: higher R\&D
stocks, irrespective of whether domestically or foreign, increase, ceteris
paribus, domestic output. For specificity, assume that $b_{-ij}$ is just the
sum of the foreign cumulative R\&D stocks in industry $j$%
\begin{equation}
b_{-ij}^p=\sum_{h\neq i}b_{hj}^p,\,\,\forall i,j.  \label{bp-}
\end{equation}
Define an index of TFP, $f_{ij}$, as $f_{ij}=\frac{q_{ij}}{l_{ij}^\alpha
\,k_{ij}^{1-\alpha }\,}.$Then, substituting and taking logs, one has 
\begin{equation}
\ln f_{ij}=\ln A_{ij}+\nu \ln b_{ij}^p+\mu \ln b_{-ij}^p.  \label{lnF}
\end{equation}
Adding a random disturbance with mean zero, $\varepsilon _{ij}$, equation (%
\ref{lnF}) predicts that in a OLS regression 
\begin{equation}
\ln f_{ij}=\alpha _{ij}+\beta ^d\ln b_{ij}^p+\beta ^f\ln
b_{-ij}^p+\varepsilon _{ij},  \label{bench}
\end{equation}
the coefficient $\hat \beta ^d$ is an estimate of the domestic elasticity, $%
\nu $, and the coefficient $\hat \beta ^f$ is an estimate of the structural
parameter $\mu $.

\section{R\&D-Driven Growth and Intermediate Inputs Trade}

Alternative to the benchmark model just laid out, I now consider a typical
model of the Grossman/Helpman, Romer variety, in which long-run growth is
endogenously driven by R\&D investments, and technology is being transmitted
via trade in intermediate inputs. I develop a closed-economy version first.

\subsection{Domestic Intersectoral Trade}

Assume that good $z_j$ is produced according to 
\begin{equation}
z_j=A_j\,l_j^\alpha d_j^{1-\alpha },  \label{outp}
\end{equation}
where $A_j$ is a constant, $l_j$ are labor services used in final output
production, and $d_j$ is a composite input consisting of horizontally
differentiated goods $x$ of variety $s.$ Specifically, $d_j$ is given by 
\begin{equation}
d_j=\left( \int_0^{n_j^{de}(s)}x_j(s)^{1-\alpha }\,ds\right) ^{\frac
1{1-\alpha }}.  \label{int}
\end{equation}
The variable $n_j^{de}$ denotes the range of intermediate inputs which are
employed in this sector (ignoring integer constraints). Distinguish $n_j^{de}
$ from $n_j^p,$ the range of intermediate inputs produced in any sector $j$;
the latter is increased by entrepreneurs devoting resources to R\&D. Denote
with $\phi _j^p$ the flow of R\&D expenditures in sector $j$. Let the
blueprints of new inputs be created simply according to $\dot n_j^p=\,\phi
_j^p.$ These resources could be in form of labor services which have an
alternative use in the output sector.\footnote{%
This presentation does not fully account for those; see, e.g., Romer (1990)
for a complete description.} If designs never become obsolete, the stock of
intermediate inputs produced in sector $j$ at time $T$ is equal to $%
n_j^p(T)=\int_{-\infty }^T\,\dot n_j^p(t)dt=\int_{-\infty }^T\phi _j^p(t)\,dt
$, that is, proportional to the cumulative R\&D resources at time $T$.
Define, as in the benchmark case, $n_j^p(T)\equiv b_j^p(T).$

Assume that one unit of any intermediate good requires one unit of sectoral
output. Then, if capital $k_j$ is defined as cumulative foregone sectoral
output, this will be equal to $k_j=\int_0^{n_j^p(s)}\,x_j(s)\,ds.$ In a
symmetric equilibrium, all intermediates $x$ are produced at the same level,
so that $k_j=n_j^px_j.$ Rearranging for $x$, and substituting into (\ref{int}%
) leads to the following expression for output\footnote{%
Here, $A_j^{^{\prime }}=A_j\left( n_j^{de}/n_j^p\right) ^{1-\alpha }.$ In
the following, I will ignore the term $\left( n_j^{de}/n_j^p\right)
^{1-\alpha }$, expecting that this will not crucially affect the estimation
below.} 
\[
z_j=A_j^{^{\prime }}\,\left( n_j^{de}\right) ^\alpha l_j^\alpha
\,\,k_j^{1-\alpha }, 
\]
Defining another index of TFP, $f_j^{*},$ as $f_j^{*}=\frac{z_j}{l_j^\alpha
\,k_j^{1-\alpha }},$and taking logs results in 
\begin{equation}
\ln f_j^{*}=\ln A_j^{^{\prime }}+\alpha \ln n_j^{de}.  \label{lnfs}
\end{equation}
Note that in equation (\ref{lnfs}), $f^{*}$ is positively related not to the
range of intermediates which have been invented in sector $j$ ($n_j^p$), but
those which are employed there ($n_j^{de}$). Empirically, I intend to
approximate the range of intermediates employed as the weighted average of
the ranges of intermediates of all sectors, where the weights are given by
the input-output relations of the sectors (see Terleckyj 1974) 
\[
n_j^{de}=\sum_{v=j}^J\omega _{jv}n_v^p,\,\,\forall j. 
\]
Let ${\bf \Omega }$ be the matrix of observed input-output coefficients,
with a typical element $\omega _{jv}$%
\[
{\bf \Omega }=\left[ 
\begin{array}{cccc}
\omega _{jj} & \omega _{jv} & \omega _{jw} & \cdots \\ 
\omega _{vj} & \omega _{vv} & \vdots & \vdots \\ 
\vdots & \vdots & \ddots & \vdots \\ 
\cdots & \cdots & \cdots & \ddots
\end{array}
\right] 
\]
In terms of observables, this means that the effective domestic R\&D stock
which affects TFP in sector $j$ is 
\[
b_j^{de}={\bf \Omega }_j\,{\bf b}_v^p,\text{ }v=j,...,J\text{, }\forall j. 
\]
Here, ${\bf \Omega }_j,$ of dimension ($1xJ$), is the $j$th row of ${\bf %
\Omega ,}$ and ${\bf b}_v^p$ is of dimension ($Jx1$). Hence, $b_j^{de}$ is
an input-output weighted average of the cumulative R\&D stocks of all
sectors $v$. Substituting, this leads to 
\begin{equation}
\ln f_j^{*}=\ln A_j^{^{\prime }}+\alpha \ln b_j^{de}=\ln A_j^{^{\prime
}}+\alpha \ln {\bf \Omega }_j{\bf \,b}_v^p  \label{lnf2}
\end{equation}

\subsection{International Trade}

By looking at a single country, so far the productivity effects resulting
from foreign R\&D have been ignored. With the possibility of international
trade, however, output producers in country $i$'s sector $j$ can employ
intermediates from other countries $h$ in addition to those from other
domestic sectors, $v\neq j$.\footnote{%
This will happen in equilibrium. Analytic results for the symmetric
two-country case are derived, e.g., in Keller (1996b).} Therefore, let $%
d_{ij}^{+}$ be 
\begin{equation}
d_{ij}^{+}=\left( \int_0^{n_{ij}^e(s)}x_{ij}(s)^{1-\alpha }\,ds\right)
^{\frac 1{1-\alpha }}.  \label{int2}
\end{equation}
Here, $n_{ij}^e$ is the range of intermediates employed in country $i$'s
sector $j$, with $n_{ij}^e\geq n_{ij}^{de}\geq n_{ij}^p$. Intermediates can
come from abroad, or from other sectors, or both. In a fully symmetric model
where all intermediates are different from one another, and traded to the
same extent, any of these types of intermediates will have the same
productivity effects for the importing industry.\footnote{%
Define again the sectoral capital stock as foregone consumption of good $j$.
Then $k_{ij}=k_{ij}^{ij}+k_{ij}^{-i-j},$ that is, the domestic capital stock
can be split into resources which are used to produce $ij$ intermediates
(superscript $ij$), or into those which are--in form of intermediate
inputs--used to exchange for inputs which are not produced in country $i$,
or not in sector $j$, or neither (superscript $-i-j$). If the country-sector 
$ij$ intermediate varieties are all produced at the equilibrium level $%
\tilde x_{ij}$, then $k_{ij}^{ij}=n_{ij}^p\tilde x_{ij},$ and $%
k_{ij}^{-i-j}= $ $\left( I\times J-1\right) k_{ij}^{ij}.$ Therefore, $%
k_{ij}=\left( I\times J\right) n_{ij}^p\tilde x_{ij}$, or, $k_{ij}=n_w\tilde
x_{ij}$, where $n_w$ is the world range of available intermediate goods.}
But suppose there is heterogeneity across $i$ and $j$. At the same time, we
can approximate the domestic capital stock with 
\[
k_{ij}=n_{ij}^e\bar x_{ij},
\]
where $\bar x_{ij}$ is the new equilibrium level when all varieties $s$ of
this intermediate are produced at the same level. Upon substitution, one
obtains\footnote{%
Here, $A_{ij}^{+}=A_{ij}\left( n_{ij}^e/n_{ij}^p\right) ^{1-\alpha }.$} 
\[
z_{ij}^{+}=A_{ij}^{+}\,\left( n_{ij}^e\right) ^\alpha l_{ij}^\alpha
\,\,k_{ij}^{1-\alpha },\,\,\,\forall i,j.
\]
If $f_{ij}^{+}$ is defined as $f_{ij}^{+}=\frac{z_{ij}^{+}}{l_{ij}^\alpha
\,k_{ij}^{1-\alpha }},$ then one obtains 
\begin{equation}
\ln f_{ij}^{+}=\ln A_{ij}^{+}+\alpha \ln n_{ij}^e,\,\,\,\forall i,j.
\label{lnfp}
\end{equation}
As an empirical matter, it appears that the degree to which intermediates
are used in sector $ij$ differs significantly by whether the intermediate is
of domestic or foreign origin. This not alone for reasons of transport costs
related to distance, but also because of other implicit or explicit trade
barriers such as tariffs, exchange rate risk, etc. This leads to a
specification which allows for two separate coefficients, 
\[
\ln f_{ij}^{+}=\ln A_{ij}^{+}+\alpha _1\ln n_{ij}^{de}+\alpha _2\ln
n_{ij}^{-de},\,\,\,\forall i,j.
\]
Here, $n_{ij}^{-de}$ denotes the range of intermediate goods which are
employed in sector $ij$ and imported from abroad. As argued above, the range
of domestic intermediates employed in any sector $ij$ will be related to the
cumulative R\&D investments of all domestic sectors, with intersectoral
input-output relations serving as weights: $n_{ij}^{de}={\bf \Omega }_{ij}%
{\bf \,b}_{iv}^p,v=j,...,J,\,\,\forall i,j.$ Then, define ${\bf n}_{Ij}^{de}$
as the ($Ix1$) vector of variables $n_{ij}^{de}$ from all $I$ countries.

As far as the intermediates originating from abroad, a natural way of
modeling these market transactions is to utilize bilateral import shares as
weights (e.g., Coe/Helpman 1995); these are conceptually identical to the
input-output relations capturing domestic trade transactions. Let $m_{ihj}$
be the bilateral import share of country $i$ from country $h$ for industry $j
$. Then, let $m_{iij}=0$, $\forall i$, ${\bf M}_{ji}$ the ($1xI$) vector of
import relations of country $i$'s sector $j$, and let ${\bf M}_j$ be the
matrix which collects these bilateral import shares for sector $j$. 
\[
{\bf M}_j=\left[ 
\begin{array}{cccc}
0 & m_{hij} & \cdots  & \cdots  \\ 
m_{ihj} & 0 & \vdots  & \vdots  \\ 
m_{ih^{\prime }j} & \vdots  & 0 & \vdots  \\ 
\vdots  & \vdots  & \vdots  & \ddots 
\end{array}
\right] 
\]
Further, let $c_{ij}$ denote sector $ij$'s bilateral import share-weighted
sum of foreign R\&D , 
\[
c_{ij}={\bf M}_{ji}\,{\bf n}_{Ij}^{de}.
\]
Denote the ($13x1$) vector of all these variables $c_{ij}$ in country $i$ by 
${\bf c}_{iJ}.$

An imported good classified as belonging to sector $j,$ however, will not
necessarily also be used in sector $j$ of the importing country.\footnote{%
The Standard International Trade Classification (SITC) is partly product-,
partly process-oriented, but certainly not mainly 'use'-oriented.} The
matrix which captures those market relations is the import input-output
matrix, which might be significantly different from the input-output matrix
describing economy-wide domestic trade relations. Let $\gamma _{ijv}$ denote
the share of country $i$'s imports of the $j$ intermediate which go to the $v
$ industry, where $i=1,...,I$, and $\,j,v=1,...,J.$ Let ${\bf \Gamma }_{ij}$
be the ($1x13$) vector whose elements are the import input shares of
industry $j$ from all industries $v,v=1,...,J$, and call ${\bf \Gamma }_i$
the corresponding matrix of all import input-output relations of country $i$%
. 
\[
\,{\bf \Gamma }_i=\left[ 
\begin{array}{cccc}
\gamma _{ijj} & \gamma _{ijv} & \cdots  & \cdots  \\ 
\gamma _{ivj} & \gamma _{ivv} & \vdots  & \vdots  \\ 
\vdots  & \vdots  & \ddots  & \vdots  \\ 
\vdots  & \vdots  & \vdots  & \ddots 
\end{array}
\right] 
\]
With these definitions, the range of foreign intermediates employed in
sector $ij$, $n_{ij}^{-de},$ is given by 
\begin{equation}
n_{ij}^{-de}={\bf \Gamma }_{ij}\,{\bf c}_{iJ},\forall i,j\text{,}
\label{nmde}
\end{equation}
With a mean-zero random disturbance $\varepsilon _{ij},$ this leads to the
following estimating equation 
\begin{equation}
\ln f_{ij}^{+}=\alpha _{ij}+\beta ^\delta \ln \left( {\bf \Omega }_{ij}{\bf %
\,b}_{iv}^p\right) +\beta ^\varphi \ln \left( {\bf \Gamma }_{ij}\,{\bf c}%
_{iJ}\right) +\varepsilon _{ij},\,\,\,\forall i,j,v=1,..,J.  \label{eq}
\end{equation}
It is clear from above that the foreign variable $n_{ij}^{-de}={\bf \Gamma }%
_{ij}\,{\bf c}_{iJ}$ depends potentially on $7x13$ foreign cumulative R\&D
stocks, and the domestic variable depends potentially on $13$ cumulative
R\&D stocks. However, if $\omega _{hjj}=1$, $\forall j,$ and $\omega _{hjv}=0
$, $\forall j\neq v,$ then $b_{ij}^{de}=b_{ij}^p$ because economy-wide
intersectoral relations are non-existing. Denote this particular situation
with ${\bf \Omega }_i={\bf \Omega }_i^B$. Further, if international import
relations are symmetric, then $m_{ihj}=m$, $\forall i,h,j$.\footnote{%
If the number of countries in the sample is equal to $\upsilon $, then
symmetric import relations imply that the import share $m$ from any country
equals $m=1/\upsilon $.} In that case, the R\&D investments in all partner
countries are weighted evenly. In this situation of symmetric trade
patterns, let ${\bf M}_j={\bf M}_j^B$. Finally, $\gamma _{ijj}=1,$ $\forall j
$, and $\gamma _{ijv}=0,\forall j\neq v,$ then commodities of the $j$-type
are only imported by the $j$ industry, $\forall j$. Let ${\bf \Gamma }_i^B$
denote that situation: 
\begin{equation}
\begin{array}{cc}
{\bf \Omega }_i^B={\bf \Gamma }_i^B=\left[ 
\begin{array}{cccc}
1 & 0 & \cdots  & 0 \\ 
0 & 1 & \ddots  & \vdots  \\ 
\vdots  & \ddots  & \ddots  & \ddots  \\ 
0 & 0 & \ddots  & 1
\end{array}
\right] ;\, & {\bf M}_j^B=\left[ 
\begin{array}{cccc}
0 & m & \cdots  & m \\ 
m & 0 & \ddots  & \vdots  \\ 
\vdots  & \ddots  & \ddots  & \ddots  \\ 
m & m & \ddots  & 0
\end{array}
\right] ,\forall i,j.
\end{array}
\label{3mat}
\end{equation}
Note that in the case where ${\bf \Omega }_i^B{\bf ,M}_j^B,$ and ${\bf %
\Gamma }_i^B$ hold simultaneously, one has 
\begin{equation}
\begin{array}{ccccc}
n_{ij}^{de}=b_{ij}^{de}=b_{ij}^p,\forall i,j, &  & \text{and} &  & 
n_{ij}^{-de}=\sum_{h\neq i}^Ib_{hj}^p,\forall i,j.
\end{array}
\label{3ten}
\end{equation}
This, however, is the same as in the benchmark model above:\footnote{%
This is despite the fact that above, the foreign R\&D variable is obtained
by summing over all foreign sector $j$'s cumulative R\&D stocks, whereas in (%
\ref{eq}), one sums over $m=1/\upsilon $ times these same R\&D stocks; this
will affect only the intercepts $\alpha _{ij}$, but not the coefficients of
interest $\beta ^\delta $ and $\beta ^\varphi .$} Through the domestic
channel, productivity is solely affected through own-industry R\&D ($b_{ij}^p
$), and the effect of foreign R\&D\ on domestic TFP is appropriately
captured by summing over all foreign same-industry R\&D stocks, because
neither economy-wide- (${\bf \Omega }_i$) nor imports intersectoral (${\bf %
\Gamma }_i$), nor international trade patterns (${\bf M}_j$) play any role.
In the following empirical analysis, I will not only compare whether a
specification based on actual input-output and international trade relations
performs better than the benchmark, (${\bf \Omega }_i^B{\bf ,M}_j^B,{\bf %
\Gamma }_i^B$)-model, but also ask whether the transmission of technology is
more closely related to domestic, as opposed to international trade, by
imposing the structure of intersectoral and international trade (i.e., ${\bf %
\Omega }_i{\bf ,M}_j,$and ${\bf \Gamma }_i$) step-by-step.

Before turning to this, I will outline the basic characteristics of the data.

\section{Data}

This paper uses data for eight OECD countries and the years 1970-1991 (for
more details, see the appendix). The countries are Canada, France, Germany,
Italy, Japan, Sweden, the United Kingdom, and the United States; hence, the
G-7 group plus Sweden. I use industry classification with thirteen two- to
three-digit manufacturing industries according to the UN\ International
Standard Industrial Classification (ISIC).\footnote{%
These are: (1) ISIC (adjusted revision 2) 31 Food, beverages, and tobacco;
(2) ISIC 32 Textiles, apparel, and leather; (3) ISIC 33 Wood products and
furniture; (4) ISIC 34 Paper, paper products and printing; (5) ISIC 351+352
Chemicals and drugs; (6) ISIC 353+354 Petroleum refineries and products; (7)
ISIC 355+356 Rubber and plastic products; (8) ISIC 36 Non-metallic mineral
products; (9) ISIC 37 Basic metal industries; (10) ISIC 381 Metal products;
(11) ISIC 382+385 Non-electrical machinery, office and computing equipment,
and professional goods; (12) ISIC 383 Electrical machines and communication
equipment; and (13) ISIC 384 Transportation equipment.} A TFP (index) is
constructed using the Structural Analysis industrial (STAN) database of the
OECD (1994) by first calculating the growth of TFP as the difference between
output and factor-cost share weighted input growth. Then, the level of TFP
is normalized to 100 in 1970 for each of the $8x13$ time series. In Table
A.1, I show summary statistics on the TFP data.

As defined above, the unobservable technology stock variable $n$ is
identified with the sectoral cumulative R\&D stocks, derived from OECD
(1991) data on private R\&D expenditures. This data covers all intramural
business enterprise expenditures. Summary statistics on this data are given
in Table A.2. The R\&D stocks are derived from the R\&D expenditure series
using the perpetual inventory method.

Constructing the import-weighted foreign R\&D capital stocks as described
above requires data on bilateral import flows. These are obtained from the
World Trade Data Base of the Hamburg Institute of Economic Research (HWWA).
It is clear from the construction of the $n$ variable that the origin of a
given country's imports (together with the R\&D efforts there) determines
the size of the productivity effect in the domestic economy. In Tables A.3-1
and A.3-2, I show a subset of these bilateral import shares by sector (for
sectors ISIC 31 and ISIC 384).

The input-output matrix ${\bf \Omega }_i$ of the U.S. economy is employed
for all countries in the sample; it is derived from the benchmark
input-output Table 2 ('use of commodities by industry') published in U.S.
Department of Commerce (1991). The 13x13 matrix of input-output coefficients
can be found in Table A.4. The input-output matrix for imports, ${\bf \Gamma 
}_i{\bf ,}$ is also derived from US data, and assumed to be the same for all
countries. It is based on unpublished material of the U.S. Department of
Commerce (1996) on the use of commodities by industry in the import sector.%
\footnote{%
This data was collected for the 1987 benchmark survey. I thank Michael Craw
at the BEA for providing it to me.} I have aggregated the 525 x 505 matrix
up to the 13 x 13 industry classification used in this paper;\footnote{%
The bilateral trade shares matrices ${\bf M}_j$ are averaged over time
(1972-91); the input-output matrix ${\bf \Omega }_i$ reflects the relations
in the U.S. economy in the benchmark year of 1980, and the import
input-output matrix ${\bf \Gamma }_i$ is for the benchmark year of 1987.}
the result is shown in Table A.5.

\section{Estimation Results}

In Table 1, I show results of estimating (\ref{eq}), here reproduced for
convenience, by OLS. 
\[
\ln f_{ij}^{+}=\alpha _{ij}+\beta ^\delta \ln \left( {\bf \Omega }_{ij}\,%
{\bf b}_{iv}^p\right) +\beta ^\varphi \ln \left( {\bf \Gamma }_{ij}\,{\bf c}%
_{iJ}\right) +\varepsilon _{ij},\,\,\,\forall i,j,v=1,..,J.
\]
These regressions have fixed effects for countries and industries included.
I denote the domestic variable, with coefficient $\beta ^\delta ,$ by
n(dom), and use n(for) for the foreign variable. A coefficient which is
significantly different from zero at a 5(10)\% level is labeled with $^{**}$(%
$^{*}$).

{\small 
\[
\fbox{$
\begin{tabular}{lcccc}
\multicolumn{5}{c}{Table 1} \\ 
\multicolumn{5}{c}{Dependent Variable: Log of TFP index; 2288 observations}
\\ \hline\hline
\multicolumn{1}{l|}{} & \multicolumn{1}{c|}{$%
\begin{array}{c}
\text{Benchmark:} \\ 
{\bf \Omega }_i^B{\bf ,M}_j^B{\bf ,\Gamma }_i^B
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
\text{Plus I/O:} \\ 
{\bf \Omega }_i,{\bf M}_j^B{\bf ,\Gamma }_i^B
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
\text{Plus Imports:} \\ 
{\bf \Omega }_i{\bf ,M}_j{\bf ,\Gamma }_i^B
\end{array}
$} & $%
\begin{array}{c}
\text{Plus: Imp-I/O} \\ 
{\bf \Omega }_i{\bf ,M}_j{\bf ,\Gamma }_i
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{$%
\begin{array}{c}
\text{ln n(dom)} \\ 
\text{(s.e.)}
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.022^{**} \\ 
(0.006)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.027^{*} \\ 
(0.015)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.109^{**} \\ 
(0.014)
\end{array}
$} & $%
\begin{array}{c}
0.045^{**} \\ 
(0.016)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{$%
\begin{array}{c}
\text{ln n(for)} \\ 
\text{(s.e.)}
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.385^{**} \\ 
(0.012)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.373^{**} \\ 
(0.018)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.244^{**} \\ 
(0.016)
\end{array}
$} & $%
\begin{array}{c}
0.332^{**} \\ 
(0.018)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{$%
\begin{array}{c}
\text{F-statistic} \\ 
\text{(21, 2266)}
\end{array}
$} & \multicolumn{1}{c|}{$112.04$} & \multicolumn{1}{c|}{$114.1$} & 
\multicolumn{1}{c|}{$99.43$} & $107.48$ \\ \hline
\multicolumn{1}{l|}{R$^2$} & \multicolumn{1}{c|}{$0.509$} & 
\multicolumn{1}{c|}{$0.514$} & \multicolumn{1}{c|}{$0.48$} & $0.499$
\end{tabular}
$}
\]
}There are four regressions: first, the benchmark model which does not
incorporate information on either the domestic or the international actual
trade relations (with ${\bf \Omega }_i^B,{\bf M}_j^B,$ and ${\bf \Gamma }_i^B
$). For the regression in the third column of Table 1 (I/O), I have set $%
{\bf \Omega }_i$ to the observed intersectoral input-output relations, while
keeping ${\bf M}_j^B,$ and ${\bf \Gamma }_i^B$; this affects both the
cumulative domestic and foreign R\&D stock variable. In the next column, I
have, {\it in addition}, set the bilateral import shares to their observed
values, but kept ${\bf \Gamma }_i^B$. The regression in the last column of
Table 1 finally also imposes the observed import input-output relations, $%
{\bf \Gamma }_i.$ As the results in Table 1 show, all coefficients are
estimated to be significantly different from zero at a 10\% level, and seven
out of eight at a standard 5\% level. Looking at the point estimates, it is
clear that those of column two, three, and five are similar, with a
coefficent $\beta ^\delta $ of 2.2 to 4.5\%, and the foreign coefficient $%
\beta ^\varphi $ with 33.2\% to 38.5\%. Only the specification which imposes
the domestic input-output patterns, ${\bf \Omega }_i,$ together with the
international trade relations, ${\bf M}_j$, differs substantially, with a $%
\beta ^\delta $ of 10.9\%, and a foreign estimated elasticity of 24.4\%.

If both the domestic and the foreign variables are included in one
regression, there are six distinct regressors in addition to the fixed
effects: two distinct domestic variables: imposing ${\bf \Omega }_i,$ or $%
{\bf \Omega }_i^B$, and four distinct foreign variables, corresponding to
the n(for) variables of columns 3-5 in Table 1.{\small \ }From these
results, given in Table 2, {\small 
\[
\fbox{$
\begin{tabular}{lccc}
\multicolumn{4}{c}{Table 2} \\ 
\multicolumn{4}{c}{Dependent Variable: Log of TFP index; 2288 observations}
\\ \hline\hline
\multicolumn{1}{l|}{} & \multicolumn{1}{c|}{S1} & \multicolumn{1}{c|}{S2} & 
S3 \\ \hline
\multicolumn{1}{l|}{$%
\begin{array}{c}
\text{ln n(dom-}{\bf \Omega }_i^B\text{)} \\ 
\text{(s.e.)}
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
-0.002 \\ 
(0.008)
\end{array}
$} & \multicolumn{1}{c|}{} &  \\ \hline
\multicolumn{1}{l|}{$%
\begin{array}{c}
\text{ln n(dom-}{\bf \Omega }_i\text{)} \\ 
\text{(s.e.)}
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.041^{**} \\ 
(0.02)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.036^{**} \\ 
(0.015)
\end{array}
$} &  \\ \hline
\multicolumn{1}{l|}{$%
\begin{array}{c}
\text{ln n(for-}{\bf \Omega }_i^B{\bf ,M}_j^B{\bf ,\Gamma }_i^B\text{)} \\ 
\text{(s.e.)}
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.145^{**} \\ 
(0.049)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.146^{**} \\ 
(0.045)
\end{array}
$} & $%
\begin{array}{c}
0.125^{**} \\ 
(0.044)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{$%
\begin{array}{c}
\text{ln n(for-}{\bf \Omega }_i{\bf ,M}_j^B{\bf ,\Gamma }_i^B\text{)} \\ 
\text{(s.e.)}
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.249^{**} \\ 
(0.067)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.226^{**} \\ 
(0.049)
\end{array}
$} & $%
\begin{array}{c}
0.28^{**} \\ 
(0.043)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{$%
\begin{array}{c}
\text{ln n(for-}{\bf \Omega }_i{\bf ,M}_j{\bf ,\Gamma }_i^B\text{)} \\ 
\text{(s.e.)}
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.005 \\ 
(0.04)
\end{array}
$} & \multicolumn{1}{c|}{} &  \\ \hline
\multicolumn{1}{l|}{$%
\begin{array}{c}
\text{ln n(for-}{\bf \Omega }_i{\bf ,M}_j{\bf ,\Gamma }_i\text{)} \\ 
\text{(s.e.)}
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
-0.029 \\ 
(0.074)
\end{array}
$} & \multicolumn{1}{c|}{} &  \\ \hline
\multicolumn{1}{l|}{$%
\begin{array}{c}
\text{F-statistic} \\ 
\text{(degrees of freedom)}
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
96.55 \\ 
(25,2262)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
109.84 \\ 
(22,2265)
\end{array}
$} & $%
\begin{array}{c}
114.58 \\ 
(22,2266)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{R$^2$, adjusted} & \multicolumn{1}{c|}{$0.511$} & 
\multicolumn{1}{c|}{$0.511$} & $0.510$
\end{tabular}
$} 
\]
}one sees that when included into the same regression, there is no support
for the domestic R\&D variable which does not incorporate intersectoral
relations: n(dom-${\bf \Omega }_i^B$) is insignificant$.$ The input-output
channeled domestic R\&D stock performs better, with a point estimate of
4.1\% which is significant at a 5\% level. Of the foreign R\&D variables,
two are not significantly different from zero: the variable which
incorporates both domestic input-output relations and bilateral import
relations, n(for-${\bf \Omega }_i{\bf ,M}_j,{\bf \Gamma }_i^B$), and the
n(for-${\bf \Omega }_i{\bf ,M}_j,{\bf \Gamma }_i$) variable which, in
addition, builds on the input-output relations between sectors in the
importing economy.{\small \ } Specifications S2 and S3 show that there is an
independent effect of foreign R\&D on domestic TFP in industry $ij\,$both
via the sum of cumulative R\&D in the exact same sectors of other countries
[n-for(${\bf \Omega }_i^B{\bf ,M}_j^B{\bf ,\Gamma }_i^B$)], and through the
sum of cumulative foreign R\&D which takes the intersectoral relations there
into account [n-for(${\bf \Omega }_i{\bf ,M}_j^B{\bf ,\Gamma }_i^B$)]. Among
these two, specification S3 shows that the latter is largest in magnitude
(0.28 versus 0.125) while at the same time more precisely estimated, with a
t-statistic of 6.48, as opposed to a t-statistic of 2.82 for the former. It
is important to note, however, that international trade plays no role in the
construction of the latter two variables.

For several reasons, of which not the least is the uncertainty associated
with the estimates for the 1970 R\&D capital stocks, might not be optimal to
correlate the levels of TFP and cumulative R\&D.\footnote{%
It is critical to know the time-series properties of the variables' data
generation process (especially stationarity versus non-stationarity of the
R\&D\ and TFP series), as this affects the choice of asymptotic theory to be
used. Unfortunately, the available tests suffer generally from low
statistical power; nevertheless, see, e.g., Coe et al. (1995). The paper by
Griliches/Lichtenberg (1984) contains further discussion on level versus
growth specification in this context.} Therefore, I have estimated the
relation between TFP on the one side, and domestic as well as foreign R\&D
on the other, also using a growth specification. Let $\hat x$ denote the
average annual growth rate of any variable $x$. The growth specification is
as follows: 
\begin{equation}
\hat f_{ij}^{+}=\alpha _{ij}+\beta ^\delta \left( \hat b_{ij}^{de}\right)
+\beta ^\varphi \left( {\bf \Gamma }_{ij}\,{\bf \hat c}_{iJ}\right)
+\varepsilon _{ij},\,\,\,\forall i,j.  \label{df}
\end{equation}
The third term on the right-hand side of equation (\ref{df}) constitutes a
weighted average of R\&D growth in the importing country's partner countries.%
\footnote{%
Here the variable ${\bf \hat c}_{iJ}$ is the $(13x1)$ vector consisting of $%
\hat c_{ij}={\bf M}_{ij}{\bf \hat b}_{Ij},$ and ${\bf \hat b}_{Ij}$ denotes
the ($13x1$) vector of the $\hat b_{ij}^{de}$ variables. Hence, the matrices 
${\bf M}_i$ and ${\bf \Gamma }_j$ channel growth rates, instead of taking
log differences of (${\bf \Gamma }_i{\bf \,c}_{iJ}$).} Analogously to Table
1, the results for the growth specification (\ref{df}) can be seen in Table
3 (industry- and country fixed effects included): {\small 
\[
\fbox{$
\begin{tabular}{lccc|c}
\multicolumn{5}{c}{Table 3} \\ 
\multicolumn{5}{c}{Dependent Variable: Annual Average Growth of TFP} \\ 
\multicolumn{5}{c}{Two subperiods (1970-80; 1981-91); 208 observations} \\ 
\hline\hline
\multicolumn{1}{l|}{} & \multicolumn{1}{c|}{$%
\begin{array}{c}
\text{Benchmark:} \\ 
{\bf \Omega }_i^B{\bf ,M}_j^B{\bf ,\Gamma }_i^B
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
\text{Plus I/O:} \\ 
{\bf \Omega }_i,{\bf M}_j^B{\bf ,\Gamma }_i^B
\end{array}
$} & $%
\begin{array}{c}
\text{Plus Imports:} \\ 
{\bf \Omega }_i{\bf ,M}_j{\bf ,\Gamma }_i^B
\end{array}
$ & $%
\begin{array}{c}
\text{Plus: Imp-I/O} \\ 
{\bf \Omega }_i{\bf ,M}_j{\bf ,\Gamma }_i
\end{array}
$ \\ \cline{2-5}\cline{1-1}
\multicolumn{1}{l|}{$%
\begin{array}{c}
\hat b_{ij}^{de} \\ 
(s.e.)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.171^{**} \\ 
(0.049)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.248^{*} \\ 
(0.15)
\end{array}
$} & $%
\begin{array}{c}
0.28^{**} \\ 
(0.128)
\end{array}
$ & $%
\begin{array}{c}
0.515^{**} \\ 
(0.126)
\end{array}
$ \\ \cline{2-5}\cline{1-1}
\multicolumn{1}{l|}{$%
\begin{array}{c}
{\bf \Gamma }_{ij}\,{\bf \hat c}_{iJ} \\ 
(s.e.)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.452^{**} \\ 
(0.087)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.564^{**} \\ 
(0.171)
\end{array}
$} & $%
\begin{array}{c}
0.552^{**} \\ 
(0.158)
\end{array}
$ & $%
\begin{array}{c}
0.128 \\ 
(0.143)
\end{array}
$ \\ \cline{2-5}\cline{1-1}
\multicolumn{1}{l|}{$%
\begin{array}{c}
\text{F-statistic} \\ 
\text{(21, 186)}
\end{array}
$} & \multicolumn{1}{c|}{$4.94$} & \multicolumn{1}{c|}{$4.4$} & $4.48$ & $%
3.72$ \\ \cline{2-5}\cline{1-1}
\multicolumn{1}{l|}{R$^2$} & \multicolumn{1}{c|}{$0.358$} & 
\multicolumn{1}{c|}{$0.332$} & $0.336$ & $0.296$
\end{tabular}
$}
\]
}The estimated coefficient on the foreign variable, ${\bf \Gamma }_{ij}\,%
{\bf \hat c}_{iJ},$ in column five of Table 3 is seen to be not
significantly different from zero. Out of the other three regressions, the
coefficients in the benchmark specification are estimated with the smallest
standard errors. However, note that the estimated coefficients of both the
domestic and the foreign variables are higher in columns three and four,
compared to the benchmark specification in column two. This is interesting
in an errors-in-variables context: The results are consistent with an
interpretation which considers the benchmark model as one where the
variables are measured with error, compared to the model which employs the
'true' data (effective R\&D stocks) of columns three or four, because errors
in variables tend to bias the estimated coefficient downwards. According to
this interpretation, the benchmark model correlates high R\&D growth
industries frequently to not-high TFP growth sectors, resulting in
relatively low estimates on $\hat b_{ij}^{de}$ and ${\bf \Gamma }_{ij}\,{\bf %
\hat c}_{iJ}$. But, if the R\&D\ expenditures are, through the trade
matrices, allocated to the sectors where in fact they are effective, then
the estimated relation between R\&D and TFP, as measured by the size of the
point estimates, is stronger. However, one problem with this interpretation
is that the benchmark model accounts for more of the variation in TFP growth
rates then the specifications incorporating trade relations, and more
importantly, the coefficients in the benchmark model are also more precisely
estimated than in the trade-relations specifications.

The results presented in Table 4 are obtained, analogously to the Table 2
results, through including in the first step all six regressors (two
domestic, and four foreign), together with the country and industry fixed
effects, into the estimating equation.

{\small 
\[
\fbox{$
\begin{tabular}{lcccc}
\multicolumn{5}{c}{Table 4} \\ 
\multicolumn{5}{c}{Dependent Variable: Average annual TFP growth} \\ 
\multicolumn{5}{c}{Two subperiods (1970-80, 1981-91); 208 observations} \\ 
\hline\hline
\multicolumn{1}{l|}{} & \multicolumn{1}{c|}{S1} & \multicolumn{1}{c|}{S2} & 
\multicolumn{1}{c|}{S3} & S4 \\ \hline
\multicolumn{1}{l|}{$%
\begin{array}{c}
\text{ln n(dom-}{\bf \Omega }_i^B\text{)} \\ 
\text{(s.e.)}
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.247^{**} \\ 
(0.059)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.192^{**} \\ 
(0.059)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.171^{**} \\ 
(0.049)
\end{array}
$} & $%
\begin{array}{c}
0.132^{**} \\ 
(0.055)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{$%
\begin{array}{c}
\text{ln n(dom-}{\bf \Omega }_i\text{)} \\ 
\text{(s.e.)}
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.422^{**} \\ 
(0.135)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
-0.054 \\ 
(0.085)
\end{array}
$} & \multicolumn{1}{c|}{} & $%
\begin{array}{c}
0.151^{**} \\ 
(0.034)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{$%
\begin{array}{c}
\text{ln n(for-}{\bf \Omega }_i^B{\bf ,M}_j^B{\bf ,\Gamma }_i^B\text{)} \\ 
\text{(s.e.)}
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
1.113^{**} \\ 
(0.258)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.583^{**} \\ 
(0.223)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.452^{**} \\ 
(0.087)
\end{array}
$} &  \\ \hline
\multicolumn{1}{l|}{$%
\begin{array}{c}
\text{ln n(for-}{\bf \Omega }_i{\bf ,M}_j^B{\bf ,\Gamma }_i^B\text{)} \\ 
\text{(s.e.)}
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
-0.774^{*} \\ 
(0.415)
\end{array}
$} & \multicolumn{1}{c|}{} & \multicolumn{1}{c|}{} &  \\ \hline
\multicolumn{1}{l|}{$%
\begin{array}{c}
\text{ln n(for-}{\bf \Omega }_i{\bf ,M}_j{\bf ,\Gamma }_i^B\text{)} \\ 
\text{(s.e.)}
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.123 \\ 
(0.358)
\end{array}
$} & \multicolumn{1}{c|}{} & \multicolumn{1}{c|}{} &  \\ \hline
\multicolumn{1}{l|}{$%
\begin{array}{c}
\text{ln n(for-}{\bf \Omega }_i{\bf ,M}_j{\bf ,\Gamma }_i\text{)} \\ 
\text{(s.e.)}
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
-0.037 \\ 
(0.052)
\end{array}
$} & \multicolumn{1}{c|}{} & \multicolumn{1}{c|}{} &  \\ \hline
\multicolumn{1}{l|}{$%
\begin{array}{c}
\text{F-statistic} \\ 
\text{(degrees of freedom)}
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
5.35 \\ 
(25,182)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
4.72 \\ 
(22,185)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
4.94 \\ 
(21,186)
\end{array}
$} & $%
\begin{array}{c}
4.47 \\ 
(21,186)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{R$^2$, adjusted} & \multicolumn{1}{c|}{$0.344$} & 
\multicolumn{1}{c|}{$0.283$} & \multicolumn{1}{c|}{$0.285$} & $0.261$
\end{tabular}
$}
\]
}The most notable result of specification S1 is that of the foreign R\&D\
variables now only the simple sum of unweighted R\&D growth [n(dom-${\bf %
\Omega }_i^B{\bf ,M}_j^B{\bf ,\Gamma }_i^B$)] enters significantly, with a
large point estimate of $1.1$. None of the foreign R\&D variables which
incorporate trade relations are significantly different from zero at a 5\%
level. Further, specification S2 shows that in this 'testing-down' approach,
only the unweighted sum of own-industry domestic R\&D [n(dom-${\bf \Omega }%
_i^B$)] and the unweighted foreign R\&D growth [n(dom-${\bf \Omega }_i^B{\bf %
,M}_j^B{\bf ,\Gamma }_i^B$)], that is, the benchmark specification, enter
with positive at significant coefficients (as seen in regression S3).
Although specification S4 shows that there is an independent effect from
R\&D\ in domestic trade partner sectors, the results presented in Table 4
clearly do not point to trade as playing, either domestically or
internationally, an important role in the transmission of technology.\newpage%
\ 

\section{Conclusions}

A model of R\&D-driven growth has been developed which predicts that
technology, created through R\&D\ investments, is transmitted to other
sectors by being embodied in intermediate goods demanded by these sectors.
This occurs both domestically as well as internationally. I have then tried
to estimate the importance of trade relations for technology transmission by
comparing regressions results in which variables are constructed
incorporating domestic and international trade relations with results in
which the variables employed did not incorporate those relations. The
estimation results in Table 1 and 2 suggest that domestic trade relations
might have an identifiable and significant role in the transmission on
technology. Further, in Table 3 there is limited evidence also for the
importance of international trade relations in this process. Overall,
however, this evidence is weak, and based on these estimation results, no
clear case can be made that trade plays an important role in the
transmission of technology. One explanation of these results might be that
the approach used is not powerful enough to accomplish what it is supposed
to accomplish. After all, it might not be possible to fully capture the
domestic and international trade-relatedness of technology flows by
channeling a multiplicity of R\&D stocks through various weighting matrices
at the same time when only few (two in this case) parameters are estimated. 

For one, using the weighting matrices might not generate sufficient
variation between the trade-imposed versus the no-trade-imposed R\&D
variables (which are noisy and possibly collinear to begin with). For
another, this problem is likely to be exacerbated by the extent to which
productivity effects of some R\&D inflows differ much from those generated
by other sector's or country's R\&D, but the estimation constrains them to
be the same. Future research should be directed at both of these issues:
finding, alternative to embodied R\&D spending, measures which are related
to both trade and technological transmission, such as patents.\footnote{%
This would imply to consider the Eaton/Kortum (1996) result that trade,
especially imports, are not important in the international diffusion of
technology as preliminary.} Short of that, it might prove useful to
concentrate on the part of trade which is conceptually close to the
intermediate inputs trade modeled above, namely trade in specialized
intermediate products, for instance, machinery for certain industries.
Secondly, short of a structural estimation, the analysis should perhaps
allow for a richer structure of potentially different spillover effects from
various domestic and international sources. 

At the same time, given the data and methodology employed in this paper, the
comparison of the results from the R\&D-driven growth and intermediate
inputs trade model with the findings for the benchmark model does pose the
question whether earlier results which were building on similar
weighting-type matrices can be upheld if an analogous comparison with a
benchmark model would be made.

\newpage\ \pagestyle{empty}

\begin{thebibliography}{99}
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\bibitem{jaffe}  Jaffe, A.B (1986), ''Technological Opportunity and
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\bibitem{jl}  Jorgenson, D.W., and R.Landau (1993b), ''Appendix'' in
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\bibitem{mans}  Mansfield, E. (1984), ''Comment'' on the paper by Scherer,
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\end{thebibliography}

\appendix

\section{Appendix}

\subsection{Labor, physical capital, and gross production}

For these variables, the OECD (1994) STAN database is the basic source. It
provides internationally comparable data on industrial activity by sectors,
primarily for OECD countries. The STAN figures there are not the submissions
of the member countries to the OECD, but the OECD estimates based on them,
which try to ensure greater international comparability. See OECD (1994) for
the details on adjustments of national data.

In constructing the TFP variable, I consider only inputs of labor and
physical capital. Data on labor inputs $l$ can be extracted directly from
the STAN database--the number of workers engaged. This includes employees as
well as the self-employed, owner proprietors and unpaid family workers. The
physical capital stock data is not available in that data base, but gross
fixed capital formation in current prices is. I first convert the investment
flows into constant 1985 prices. The deflators used for that are output
deflators, because investment goods deflators were unavailable to me. The
capital stocks are then estimated using the perpetual inventory method,
with--suppressing the industry subscripts-- 
\begin{equation}
\begin{array}{ccc}
k_{it} & = & (1-\delta _i)\,k_{it-1}+inv_{t-1},\,\,\text{for }%
t=2,...,22,\,\,i=1,...,8 \\ 
& \text{and} &  \\ 
k_{i1} & = & \frac{inv_{i1}}{(g_i+\delta _i)}\text{ \thinspace , }i=1,...,8,
\end{array}
\label{kstock}
\end{equation}
where $inv$ is gross fixed capital formation in constant prices (land,
buildings, machinery and equipment), $g$ is the average annual growth rate
of $inv$ over the period 1970-1991, and $\delta $ is the rate of
depreciation. I use country-specific depreciation rates, taken from
Jorgenson/Landau (1993b), Table A-3 
\[
\frame{$
\begin{array}{lccccl}
\text{Canada: 8.51\%} &  &  &  &  & \text{Japan: 6.6\%} \\ 
\text{France: 17.39\%} &  &  &  &  & \text{Sweden: 7.7\%} \\ 
\text{Germany: 17.4\%} &  &  &  &  & \text{United Kingdom: 8.19\%} \\ 
\text{Italy: 11.9\%} &  &  &  &  & \text{United States: 13.31\%}
\end{array}
$ } 
\]
The numbers, which are used throughout, are estimates for machinery \&
manufacturing in the year 1980.

The parameter $\alpha _{ijt}$ is the share of the labor in total production
costs. Following the approach by Hall (1991), the $\alpha _{ijt}$'s are not
calculated as the ratio of total labor compensation to value added (the
revenue-based factor shares), but cost-based factor shares are constructed
which are robust in the presence of imperfect competition. For this I use
the framework of the integrated capital taxation model of King and Fullerton
(see Jorgenson 1993 and Fullerton/Karayannis 1993) and data provided in
Jorgenson/Landau (1993b). The effective marginal corporate tax rate $\tau $
is given by the wedge between before-tax ($p$) and after-tax rate of return (%
$\rho $), relative to the former 
\begin{equation}
\tau =\frac{p-\rho }p.  \label{met}
\end{equation}
Here, the variable of interest is $p$, the user cost of capital. It will be
a function of the statutory marginal tax rate on corporate income, available
investment tax credits, the rates of depreciation, etc.

In the case of equity financing, the after-tax rate of return will be $\rho
=\chi +\pi ,$ where $\chi $ is the real interest rate, and $\pi $ is the
rate of inflation. Jorgenson (1993) tabulates the values for the marginal
effective corporate tax rate, $\tau ,$ in Table 1-1. According to the
''fixed-r'' strategy, one gives as an input a real interest rate $\chi $ and
deduces $\tau .$ In this case, I use a value of $\chi =0.1$, which, together
with the actual values of $\pi $ allows, using equation (\ref{met}) to infer
the user cost of capital, $p$. From Jorgenson's Table 1-1 on $\tau $, I use
the values on ''manufacturing'' (the 1980 values given are used for
1970-1982 in my sample, the 1985 values for 1983-1986, and Jorgenson's 1990
values are used for 1987-1991). This certainly introduces an error; in
addition, the Jorgenson Table 1-1 is derived from a ''fixed-p'' approach, as
opposed to the ''fixed-r'' approach employed here. Further, the results
depend on the chosen real interest rate, $\tau $ varies by asset type, and $%
\rho $ is a function of the way of financing (equity versus debt primarily).
Hence, there are, due to unavailability of more detailed data, several
shortcomings in the construction of the cost-based factor shares. But, first
of all, the chapter by Fullerton/Karayannis (1993) presents a sensitivity
analysis in certain dimensions. Second, I have myself experimented with
different values for the real interest rate, and found that the basic
results presented above do not depend on a particular value of that.
Finally, the cost-based aprroach has the advantage of using all data on the
user cost of capital compiled in Jorgenson/Landau (1993a) while at the same
time being robust to deviations from perfect competition.

Having obtained the series on the user cost of capital $p$ and $k$, $\alpha $
is given by 
\begin{equation}
\alpha =\frac{w\,l}{w\,l+p\,k},  \label{ws}
\end{equation}
where $wl$ are the constant price labor costs. Labor and capital inputs
together with the factor shares allow to construct a Thornqvist index of
total inputs $I_t$%
\begin{equation}
\begin{array}{ccc}
\ln \left( \frac{I_{ijt}}{I_{ijt-1}}\right)  & = & \frac 12*\left[ \alpha
_{ijt}+\alpha _{ijt-1}\right] \ln \left( \frac{l_{ijt}}{l_{ijt-1}}\right) 
\\ 
& + & \frac 12*\left[ (1-\alpha _{ijt})+(1-\alpha _{ijt-1})\right] \ln
\left( \frac{k_{ijt}}{k_{ijt-1}}\right) .
\end{array}
\label{torn}
\end{equation}
This gives a series of growth of total factor input. The TFP growth series
is obtained by substracting total input from output growth. A value of 100
in 1970 is chosen for each of the $8x13$ time series, for all industries $j$
and countries $i.$

\subsection{Data on R\&D}

The raw data on R\&D expenditures comes from OECD (1991). It is more patchy
than the series on output, investment, and employment. This is not so much a
problem of the sectoral breakdown, because the national statistical offices
do collect their R\&D data along the lines of the two- or three-digit ISIC
classification. But R\&D surveys were not conducted annually in all
countries over the entire sample period. In the United Kingdom, for
instance, they were held only every third year until well into the 1980s. In
Germany, R\&D data is collected only bi-annually. This required to estimate
about 25\% of the all the R\&D expenditure data, which is done by
interpolation.

The construction of the technology stock variables $n$ is based on data on
total business enterprise intramural expenditure on R\&D ($r$), in constant
1985 US \$, and it uses the OECD purchasing power parity rates for
conversion. The OECD code for this series is BERD, given in Table 9B of OECD
(1991). Also here, I use the perpetual inventory method to construct
technology stocks, assuming that (industry and country subscripts are
suppressed) 
\begin{equation}
\begin{array}{ccc}
n_t & = & (1-\delta )\,n_{t-1}+r_{t-1},\,\,\text{for }t=2,...,22 \\ 
& \text{and} &  \\ 
n_1 & = & \frac{r_1}{(\lambda +\delta +0.1)}\text{ \thinspace .}
\end{array}
\label{techst}
\end{equation}
The rate of depreciation $\delta $ is set at $0.05,$ and $\lambda $ is the
average annual growth rate of $n$ over the period of 1970-1991. Preliminary
analysis using other values for the rate of depreciation, such as $0$, or $%
0.1$, showed that this does not alter the estimation results qualitatively.
The denominator in the calculation of $n_1$ is increased by $0.1$ in order
to obtain positive estimates of $n_1$ throughout.

\subsection{Data on import flows, economy-wide-, and imports input-output
relations}

Data on import flows for 1972, and 1975-91, in ISIC format, comes from the
HWWA institute in Hamburg. The HWWA data base, in turn, relies on UN
Commodity Trade Statistics, up to 1981, and the OECD Foreign Trade by
Commodities Statistics, from 1982 onward. Because this data originally is in
the Standard International Trade Classification (SITC) of the United
Nations, a conversion to the ISIC scheme is necessary. I implicitly use the
HWWA conversion scheme; it takes account of the three revisions the SITC
classification has been undergoing during the period of observation. Langer
(1986) describes the HWWA conversion from SITC to ISIC in some detail, and
also shows that the differences to the OECD's conversion scheme are minor.
Bilateral import shares are formed, and a subset of them are reported in
Table A.3-1 and A.3-2.

The sources of the economy-wide input-output relations in the ${\bf \Omega }%
_i$ matrix is for the year 1980, from U.S. Department of Commerce (1991),
whereas the imports input-output data (${\bf \Gamma }_i$), derived from 1987
data, draws on unpublished data as described in the text. The ${\bf \Omega }%
_i$ matrix is given in Table A.4, and ${\bf \Gamma }_i$ is given in Table
A.5.\newpage\ 

{\scriptsize $\fbox{$%
\begin{tabular}{lcccccc|c|c|c|c}
\multicolumn{11}{c}{Table A.1} \\ 
\multicolumn{11}{c}{Total Factor Productivity Index Summary Statistics} \\ 
\multicolumn{11}{c}{By Industry and By Country} \\ \hline\hline
\multicolumn{1}{l|}{ISIC} & \multicolumn{1}{c|}{1970} & \multicolumn{1}{c|}{
1980} & \multicolumn{1}{c|}{1991} & \multicolumn{1}{c||}{$
\begin{array}{c}
\text{Average } \\ 
\text{Annual } \\ 
\text{Growth} \\ 
\text{1970-91 (\%)}
\end{array}
$} &  & \multicolumn{1}{c|}{} & 1970 & 1980 & 1991 & $
\begin{array}{c}
\text{Average } \\ 
\text{Annual } \\ 
\text{Growth} \\ 
\text{1970-91 (\%)}
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{31} & \multicolumn{1}{c|}{800} & \multicolumn{1}{c|}{
1056.6} & \multicolumn{1}{c|}{982.0} & \multicolumn{1}{c||}{1.0} &  & 
\multicolumn{1}{c|}{CAN} & \multicolumn{1}{c|}{1300} & \multicolumn{1}{c|}{
1837.4} & \multicolumn{1}{c|}{1990.3} & \multicolumn{1}{c}{2.0} \\ \hline
\multicolumn{1}{l|}{32} & \multicolumn{1}{c|}{800} & \multicolumn{1}{c|}{
1070.6} & \multicolumn{1}{c|}{1290.0} & \multicolumn{1}{c||}{2.3} &  & 
\multicolumn{1}{c|}{FRA} & \multicolumn{1}{c|}{1300} & \multicolumn{1}{c|}{
2405.1} & \multicolumn{1}{c|}{2871.7} & \multicolumn{1}{c}{3.8} \\ \hline
\multicolumn{1}{l|}{33} & \multicolumn{1}{c|}{800} & \multicolumn{1}{c|}{
1044.7} & \multicolumn{1}{c|}{1206.8} & \multicolumn{1}{c||}{2.0} &  & 
\multicolumn{1}{c|}{GER} & \multicolumn{1}{c|}{1300} & \multicolumn{1}{c|}{
1927.8} & \multicolumn{1}{c|}{2221.5} & \multicolumn{1}{c}{2.6} \\ \hline
\multicolumn{1}{l|}{34} & \multicolumn{1}{c|}{800} & \multicolumn{1}{c|}{
1004.0} & \multicolumn{1}{c|}{1138.0} & \multicolumn{1}{c||}{1.7} &  & 
\multicolumn{1}{c|}{IT} & \multicolumn{1}{c|}{1300} & \multicolumn{1}{c|}{
2058.0} & \multicolumn{1}{c|}{3372.0} & \multicolumn{1}{c}{4.5} \\ \hline
\multicolumn{1}{l|}{351/2} & \multicolumn{1}{c|}{800} & \multicolumn{1}{c|}{
1376.6} & \multicolumn{1}{c|}{1768.5} & \multicolumn{1}{c||}{3.8} &  & 
\multicolumn{1}{c|}{JAP} & \multicolumn{1}{c|}{1300} & \multicolumn{1}{c|}{
2398.4} & \multicolumn{1}{c|}{2892.5} & \multicolumn{1}{c}{3.8} \\ \hline
\multicolumn{1}{l|}{353/4} & \multicolumn{1}{c|}{800} & \multicolumn{1}{c|}{
2014.2} & \multicolumn{1}{c|}{1958.3} & \multicolumn{1}{c||}{4.3} &  & 
\multicolumn{1}{c|}{SWE} & \multicolumn{1}{c|}{1300} & \multicolumn{1}{c|}{
1936.5} & \multicolumn{1}{c|}{1836.9} & \multicolumn{1}{c}{1.6} \\ \hline
\multicolumn{1}{l|}{355/6} & \multicolumn{1}{c|}{800} & \multicolumn{1}{c|}{
1158.4} & \multicolumn{1}{c|}{1346.4} & \multicolumn{1}{c||}{2.5} &  & 
\multicolumn{1}{c|}{UK} & \multicolumn{1}{c|}{1300} & \multicolumn{1}{c|}{
1513.4} & \multicolumn{1}{c|}{2220.0} & \multicolumn{1}{c}{2.5} \\ \hline
\multicolumn{1}{l|}{36} & \multicolumn{1}{c|}{800} & \multicolumn{1}{c|}{
1084.6} & \multicolumn{1}{c|}{1356.2} & \multicolumn{1}{c||}{2.5} &  & USA & 
\multicolumn{1}{c|}{1300} & \multicolumn{1}{c|}{1641.6} & 
\multicolumn{1}{c|}{1978.2} & \multicolumn{1}{c}{2.0} \\ 
\cline{1-5}\cline{7-11}\cline{6-7}
\multicolumn{1}{l|}{37} & \multicolumn{1}{c|}{800} & \multicolumn{1}{c|}{
1150.5} & \multicolumn{1}{c|}{1516.7} & \multicolumn{1}{c||}{3.0} &  & 
\multicolumn{5}{c}{} \\ \cline{1-5}
\multicolumn{1}{l|}{381} & \multicolumn{1}{c|}{800} & \multicolumn{1}{c|}{
1046.8} & \multicolumn{1}{c|}{1182.8} & \multicolumn{1}{c||}{1.9} &  & 
\multicolumn{5}{c}{} \\ \cline{1-5}
\multicolumn{1}{l|}{382/5} & \multicolumn{1}{c|}{800} & \multicolumn{1}{c|}{
1261.4} & \multicolumn{1}{c|}{1967.0} & \multicolumn{1}{c||}{4.3} &  & 
\multicolumn{5}{c}{} \\ \cline{1-5}
\multicolumn{1}{l|}{383} & \multicolumn{1}{c|}{800} & \multicolumn{1}{c|}{
1323.1} & \multicolumn{1}{c|}{2093.4} & \multicolumn{1}{c||}{4.6} &  & 
\multicolumn{5}{c}{} \\ \cline{1-5}
\multicolumn{1}{l|}{384} & \multicolumn{1}{c|}{800} & \multicolumn{1}{c|}{
1126.7} & \multicolumn{1}{c|}{1577.1} & \multicolumn{1}{c||}{3.2} &  & 
\multicolumn{5}{c}{}
\end{tabular}
$}$ }

{\scriptsize \bigskip\ \bigskip\ }

{\scriptsize $\fbox{$%
\begin{tabular}{lc|c|c|ccc|c|c|c|c}
\multicolumn{11}{c}{Table A.2} \\ 
\multicolumn{11}{c}{R\&D Stock Summary Statistics} \\ 
\multicolumn{11}{c}{By Industry and By Country; 1985 US \$} \\ \hline\hline
\multicolumn{1}{l|}{ISIC} & \multicolumn{1}{c|}{1970} & 1980 & 1991 & 
\multicolumn{1}{c||}{$
\begin{array}{c}
\text{Average } \\ 
\text{Annual } \\ 
\text{Growth} \\ 
\text{1970-91 (\%)}
\end{array}
$} &  & \multicolumn{1}{c|}{} & \multicolumn{1}{c|}{1970} & 1980 & 1991 & $
\begin{array}{c}
\text{Average } \\ 
\text{Annual } \\ 
\text{Growth} \\ 
\text{1970-91 (\%)}
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{31} & \multicolumn{1}{c|}{6390.7} & \multicolumn{1}{c|}{
15424.7} & \multicolumn{1}{c|}{30092.5} & \multicolumn{1}{|c||}{7.4} &  & 
\multicolumn{1}{c|}{CAN} & \multicolumn{1}{c|}{4930.9} & \multicolumn{1}{c|}{
10435.5} & \multicolumn{1}{c|}{22820.6} & \multicolumn{1}{c}{7.3} \\ \hline
\multicolumn{1}{l|}{32} & \multicolumn{1}{c|}{4744.6} & \multicolumn{1}{c|}{
7482.3} & \multicolumn{1}{c|}{9816.1} & \multicolumn{1}{|c||}{3.5} &  & 
\multicolumn{1}{c|}{FRA} & \multicolumn{1}{c|}{25216.9} & 
\multicolumn{1}{c|}{60913.3} & \multicolumn{1}{c|}{112246.8} & 
\multicolumn{1}{c}{7.1} \\ \hline
\multicolumn{1}{l|}{33} & \multicolumn{1}{c|}{1794.4} & \multicolumn{1}{c|}{
3211.0} & \multicolumn{1}{c|}{4798.0} & \multicolumn{1}{|c||}{4.7} &  & 
\multicolumn{1}{c|}{GER} & \multicolumn{1}{c|}{41545.6} & 
\multicolumn{1}{c|}{98871.5} & \multicolumn{1}{c|}{193959.4} & 
\multicolumn{1}{c}{7.3} \\ \hline
\multicolumn{1}{l|}{34} & \multicolumn{1}{c|}{4112.3} & \multicolumn{1}{c|}{
9058.7} & \multicolumn{1}{c|}{14966.6} & \multicolumn{1}{|c||}{6.2} &  & 
\multicolumn{1}{c|}{IT} & \multicolumn{1}{c|}{7807.3} & \multicolumn{1}{c|}{
19329.5} & \multicolumn{1}{c|}{45193.6} & \multicolumn{1}{c}{8.4} \\ \hline
\multicolumn{1}{l|}{351/2} & \multicolumn{1}{c|}{55698.7} & 
\multicolumn{1}{c|}{133493.4} & \multicolumn{1}{c|}{259920.6} & 
\multicolumn{1}{|c||}{7.3} &  & \multicolumn{1}{c|}{JAP} & 
\multicolumn{1}{c|}{37341.0} & \multicolumn{1}{c|}{106730.8} & 
\multicolumn{1}{c|}{284083.3} & \multicolumn{1}{c}{9.7} \\ \hline
\multicolumn{1}{l|}{353/4} & \multicolumn{1}{c|}{11104.7} & 
\multicolumn{1}{c|}{22640.8} & \multicolumn{1}{c|}{37347.5} & 
\multicolumn{1}{|c||}{5.8} &  & \multicolumn{1}{c|}{SWE} & 
\multicolumn{1}{c|}{6674.0} & \multicolumn{1}{c|}{15234.3} & 
\multicolumn{1}{c|}{25765.8} & \multicolumn{1}{c}{6.4} \\ \hline
\multicolumn{1}{l|}{355/6} & \multicolumn{1}{c|}{6757.1} & 
\multicolumn{1}{c|}{16073.8} & \multicolumn{1}{c|}{29553.5} & 
\multicolumn{1}{|c||}{7.0} &  & \multicolumn{1}{c|}{UK} & 
\multicolumn{1}{|c|}{39067.6} & 76971.6 & \multicolumn{1}{c|}{121302.8} & 
\multicolumn{1}{c}{5.4} \\ \hline
\multicolumn{1}{l|}{36} & \multicolumn{1}{c|}{5080.6} & \multicolumn{1}{c|}{
11319.5} & \multicolumn{1}{c|}{23585.0} & \multicolumn{1}{|c||}{7.3} &  & 
\multicolumn{1}{c|}{USA} & \multicolumn{1}{|c|}{248541.0} & 517898.8 & 
\multicolumn{1}{c|}{950958.3} & \multicolumn{1}{c}{6.4} \\ 
\cline{1-5}\cline{7-11}\cline{6-7}
\multicolumn{1}{l|}{37} & \multicolumn{1}{c|}{13472.5} & \multicolumn{1}{c|}{
26591.0} & \multicolumn{1}{c|}{41960.1} & \multicolumn{1}{|c||}{5.4} &  & 
\multicolumn{5}{c}{} \\ \cline{1-5}
\multicolumn{1}{l|}{381} & \multicolumn{1}{c|}{5115.6} & \multicolumn{1}{c|}{
11939.9} & \multicolumn{1}{c|}{23450.6} & \multicolumn{1}{|c||}{7.3} &  & 
\multicolumn{5}{c}{} \\ \cline{1-5}
\multicolumn{1}{l|}{382/5} & \multicolumn{1}{c|}{48366.7} & 
\multicolumn{1}{c|}{131.561.1} & \multicolumn{1}{c|}{303919.1} & 
\multicolumn{1}{|c||}{8.8} &  & \multicolumn{5}{c}{} \\ \cline{1-5}
\multicolumn{1}{l|}{383} & \multicolumn{1}{c|}{104071.0} & 
\multicolumn{1}{c|}{221154.1} & \multicolumn{1}{c|}{425524.1} & 
\multicolumn{1}{|c||}{6.7} &  & \multicolumn{5}{c}{} \\ \cline{1-5}
\multicolumn{1}{l|}{384} & \multicolumn{1}{c|}{14415.7} & 
\multicolumn{1}{c|}{296435.0} & \multicolumn{1}{c|}{551396.9} & 
\multicolumn{1}{|c||}{6.4} &  & \multicolumn{5}{c}{}
\end{tabular}
$}$ \ }

{\scriptsize \bigskip\ \bigskip\ }

{\scriptsize $\fbox{$%
\begin{tabular}{lcccccccc}
\multicolumn{9}{c}{Table A.3-1} \\ 
\multicolumn{9}{c}{Bilateral Import Shares in Food , Beverages \& Tobacco
Manufacturing (ISIC 31)} \\ 
\multicolumn{9}{c}{Average over 1972-1991; in per cent} \\ \hline\hline
\multicolumn{1}{l|}{from / to} & \multicolumn{1}{c|}{CAN} & 
\multicolumn{1}{c|}{FRA} & \multicolumn{1}{c|}{GER} & \multicolumn{1}{c|}{IT}
& \multicolumn{1}{c|}{JAP} & \multicolumn{1}{c|}{SWE} & \multicolumn{1}{c|}{
UK} & USA \\ \hline
\multicolumn{1}{l|}{CAN} & \multicolumn{1}{c|}{0} & \multicolumn{1}{c|}{1.93}
& \multicolumn{1}{c|}{1.4} & \multicolumn{1}{c|}{0.67} & \multicolumn{1}{c|}{
14.46} & \multicolumn{1}{c|}{3.87} & \multicolumn{1}{c|}{7.07} & 35.2 \\ 
\hline
\multicolumn{1}{l|}{FRA} & \multicolumn{1}{c|}{8.33} & \multicolumn{1}{c|}{0}
& \multicolumn{1}{c|}{48.95} & \multicolumn{1}{c|}{39.4} & 
\multicolumn{1}{c|}{6.6} & \multicolumn{1}{c|}{17.13} & \multicolumn{1}{c|}{
35.78} & 17.5 \\ \hline
\multicolumn{1}{l|}{GER} & \multicolumn{1}{c|}{3.37} & \multicolumn{1}{c|}{
36.69} & \multicolumn{1}{c|}{0} & \multicolumn{1}{c|}{45.97} & 
\multicolumn{1}{c|}{3.64} & \multicolumn{1}{c|}{30.24} & \multicolumn{1}{c|}{
25.09} & 9.24 \\ \hline
\multicolumn{1}{l|}{IT} & \multicolumn{1}{c|}{3.6} & \multicolumn{1}{c|}{
24.99} & \multicolumn{1}{c|}{22.96} & \multicolumn{1}{c|}{0} & 
\multicolumn{1}{c|}{0.98} & \multicolumn{1}{c|}{7.78} & \multicolumn{1}{c|}{
15.03} & 12.26 \\ \hline
\multicolumn{1}{l|}{JAP} & \multicolumn{1}{c|}{2.6} & \multicolumn{1}{c|}{
0.53} & \multicolumn{1}{c|}{1.14} & \multicolumn{1}{c|}{0.14} & 
\multicolumn{1}{c|}{0} & \multicolumn{1}{c|}{0.57} & \multicolumn{1}{c|}{2.16
} & 5.84 \\ \hline
\multicolumn{1}{l|}{SWE} & \multicolumn{1}{c|}{2.0} & \multicolumn{1}{c|}{
0.66} & \multicolumn{1}{c|}{1.35} & \multicolumn{1}{c|}{0.89} & 
\multicolumn{1}{c|}{2.23} & \multicolumn{1}{c|}{0} & \multicolumn{1}{c|}{1.5}
& 1.54 \\ \hline
\multicolumn{1}{l|}{UK} & \multicolumn{1}{c|}{7.8} & \multicolumn{1}{c|}{
21.74} & \multicolumn{1}{c|}{8.94} & \multicolumn{1}{c|}{6.07} & 
\multicolumn{1}{c|}{7.53} & \multicolumn{1}{c|}{20.46} & \multicolumn{1}{c|}{
0} & 18.43 \\ \hline
\multicolumn{1}{l|}{USA} & \multicolumn{1}{c|}{74.63} & \multicolumn{1}{c|}{
13.46} & \multicolumn{1}{c|}{15.26} & \multicolumn{1}{c|}{6.86} & 
\multicolumn{1}{c|}{65.46} & \multicolumn{1}{c|}{19.95} & 
\multicolumn{1}{c|}{13.37} & 0
\end{tabular}
$}$ }

{\scriptsize \bigskip\ \bigskip\ }

{\scriptsize \ $\fbox{$%
\begin{tabular}{lccccc|c|c|c}
\multicolumn{9}{c}{Table A.3-2} \\ 
\multicolumn{9}{c}{Bilateral Import Shares in Transportation Equipment (ISIC
384)} \\ 
\multicolumn{9}{c}{Average over 1972-1991; in per cent} \\ \hline\hline
\multicolumn{1}{l|}{from / to} & \multicolumn{1}{c|}{CAN} & 
\multicolumn{1}{c|}{FRA} & \multicolumn{1}{c|}{GER} & \multicolumn{1}{c|}{IT}
& \multicolumn{1}{c|}{JAP} & SWE & UK & USA \\ \hline
\multicolumn{1}{l|}{CAN} & \multicolumn{1}{c|}{0} & \multicolumn{1}{c|}{0.5}
& \multicolumn{1}{c|}{0.38} & \multicolumn{1}{c|}{0.37} & 
\multicolumn{1}{c|}{0.79} & \multicolumn{1}{c|}{0.83} & \multicolumn{1}{c|}{
1.02} & \multicolumn{1}{c}{38.22} \\ \hline
\multicolumn{1}{l|}{FRA} & \multicolumn{1}{c|}{0.74} & \multicolumn{1}{c|}{0}
& \multicolumn{1}{c|}{43.57} & \multicolumn{1}{c|}{34.79} & 
\multicolumn{1}{c|}{3.51} & \multicolumn{1}{c|}{8.25} & \multicolumn{1}{c|}{
18.52} & \multicolumn{1}{c}{3.41} \\ \hline
\multicolumn{1}{l|}{GER} & \multicolumn{1}{c|}{2.06} & \multicolumn{1}{c|}{
43.93} & \multicolumn{1}{c|}{0} & \multicolumn{1}{c|}{44.37} & 
\multicolumn{1}{c|}{23.77} & \multicolumn{1}{c|}{47.77} & 
\multicolumn{1}{c|}{40.94} & \multicolumn{1}{c}{12.44} \\ \hline
\multicolumn{1}{l|}{IT} & \multicolumn{1}{c|}{0.23} & \multicolumn{1}{c|}{
17.38} & \multicolumn{1}{c|}{13.31} & \multicolumn{1}{c|}{0} & 
\multicolumn{1}{c|}{1.96} & \multicolumn{1}{c|}{3.49} & \multicolumn{1}{c|}{
6.64} & \multicolumn{1}{c}{1.69} \\ \hline
\multicolumn{1}{l|}{JAP} & \multicolumn{1}{c|}{7.26} & \multicolumn{1}{c|}{
7.05} & \multicolumn{1}{c|}{15.04} & \multicolumn{1}{c|}{2.09} & 
\multicolumn{1}{c|}{0} & \multicolumn{1}{c|}{13.94} & \multicolumn{1}{c|}{
13.85} & \multicolumn{1}{c}{37.26} \\ \hline
\multicolumn{1}{l|}{SWE} & \multicolumn{1}{c|}{0.53} & \multicolumn{1}{c|}{
2.95} & \multicolumn{1}{c|}{2.11} & \multicolumn{1}{c|}{2.02} & 
\multicolumn{1}{c|}{4.24} & \multicolumn{1}{c|}{0} & \multicolumn{1}{c|}{6.11
} & \multicolumn{1}{c}{2.29} \\ \hline
\multicolumn{1}{l|}{UK} & \multicolumn{1}{c|}{1.27} & \multicolumn{1}{c|}{
9.72} & \multicolumn{1}{c|}{12.77} & \multicolumn{1}{c|}{7.61} & 
\multicolumn{1}{c|}{6.59} & \multicolumn{1}{c|}{12.84} & \multicolumn{1}{c|}{
0} & \multicolumn{1}{c}{4.7} \\ \hline
\multicolumn{1}{l|}{USA} & \multicolumn{1}{c|}{87.9} & \multicolumn{1}{c|}{
18.47} & \multicolumn{1}{c|}{12.82} & \multicolumn{1}{c|}{8.75} & 
\multicolumn{1}{c|}{61.63} & \multicolumn{1}{c|}{12.88} & 
\multicolumn{1}{c|}{12.91} & \multicolumn{1}{c}{0}
\end{tabular}
$}$\ }

{\scriptsize \bigskip\ \bigskip\ }

{\scriptsize $\fbox{$%
\begin{tabular}{lccccc|cccccccc}
\multicolumn{14}{c}{Table A.4} \\ 
\multicolumn{14}{c}{Economy-Wide Input-Output Relations} \\ 
\multicolumn{14}{c}{US economy, 1980; 13x13 ISIC industries} \\ 
\multicolumn{14}{c}{Per cent of row commodity going to column industry} \\ 
\hline\hline
\multicolumn{1}{l|}{} & \multicolumn{1}{c|}{31} & \multicolumn{1}{c|}{32} & 
\multicolumn{1}{c|}{33} & \multicolumn{1}{c|}{34} & \multicolumn{1}{c|}{351/2
} & \multicolumn{1}{c|}{353/4} & \multicolumn{1}{c|}{355/6} & 
\multicolumn{1}{c|}{36} & \multicolumn{1}{c|}{37} & \multicolumn{1}{c|}{381}
& \multicolumn{1}{c|}{382/5} & \multicolumn{1}{c|}{383} & 384 \\ \hline
\multicolumn{1}{l|}{31} & \multicolumn{1}{c|}{96.19} & \multicolumn{1}{c|}{
1/16} & \multicolumn{1}{c|}{0.05} & \multicolumn{1}{c|}{0.56} & 
\multicolumn{1}{c|}{1.5} & \multicolumn{1}{c|}{0.33} & \multicolumn{1}{c|}{
0.01} & \multicolumn{1}{c|}{0.03} & \multicolumn{1}{c|}{0.01} & 
\multicolumn{1}{c|}{0.02} & \multicolumn{1}{c|}{0.12} & \multicolumn{1}{c|}{
0.02} & 0.02 \\ \hline
\multicolumn{1}{l|}{32} & \multicolumn{1}{c|}{0.15} & \multicolumn{1}{c|}{
74.72} & \multicolumn{1}{c|}{5.38} & \multicolumn{1}{c|}{8.88} & 
\multicolumn{1}{c|}{0.29} & \multicolumn{1}{c|}{0.11} & \multicolumn{1}{c|}{
2.18} & \multicolumn{1}{c|}{0.45} & \multicolumn{1}{c|}{0.35} & 
\multicolumn{1}{c|}{0.62} & \multicolumn{1}{c|}{1.42} & \multicolumn{1}{c|}{
0.44} & 5 \\ \hline
\multicolumn{1}{l|}{33} & \multicolumn{1}{c|}{5.37} & \multicolumn{1}{c|}{0}
& \multicolumn{1}{c|}{11.45} & \multicolumn{1}{c|}{9.16} & 
\multicolumn{1}{c|}{0} & \multicolumn{1}{c|}{0} & \multicolumn{1}{c|}{0} & 
\multicolumn{1}{c|}{4.44} & \multicolumn{1}{c|}{0.36} & \multicolumn{1}{c|}{0
} & \multicolumn{1}{c|}{4.08} & \multicolumn{1}{c|}{27.92} & 37.22 \\ \hline
\multicolumn{1}{l|}{34} & \multicolumn{1}{c|}{16.43} & \multicolumn{1}{c|}{
1.75} & \multicolumn{1}{c|}{0.57} & \multicolumn{1}{c|}{64.17} & 
\multicolumn{1}{c|}{5.07} & \multicolumn{1}{c|}{0.79} & \multicolumn{1}{c|}{
1.85} & \multicolumn{1}{c|}{1.97} & \multicolumn{1}{c|}{0.33} & 
\multicolumn{1}{c|}{1.65} & \multicolumn{1}{c|}{2.46} & \multicolumn{1}{c|}{
2.36} & 0.6 \\ \hline
\multicolumn{1}{l|}{351/2} & \multicolumn{1}{c|}{3.95} & \multicolumn{1}{c|}{
12.98} & \multicolumn{1}{c|}{0.23} & \multicolumn{1}{c|}{7.63} & 
\multicolumn{1}{c|}{41.19} & \multicolumn{1}{c|}{6.24} & \multicolumn{1}{c|}{
13.72} & \multicolumn{1}{c|}{2.65} & \multicolumn{1}{c|}{4.36} & 
\multicolumn{1}{c|}{1.54} & \multicolumn{1}{c|}{1.16} & \multicolumn{1}{c|}{
3.47} & 0.89 \\ \hline
\multicolumn{1}{l|}{353/4} & \multicolumn{1}{c|}{3.58} & \multicolumn{1}{c|}{
5.38} & \multicolumn{1}{c|}{1.29} & \multicolumn{1}{c|}{9.82} & 
\multicolumn{1}{c|}{10.42} & \multicolumn{1}{c|}{46.62} & 
\multicolumn{1}{c|}{1.27} & \multicolumn{1}{c|}{1.91} & \multicolumn{1}{c|}{
4.28} & \multicolumn{1}{c|}{3.84} & \multicolumn{1}{c|}{4.01} & 
\multicolumn{1}{c|}{2.68} & 4.88 \\ \hline
\multicolumn{1}{l|}{355/6} & \multicolumn{1}{c|}{13.48} & 
\multicolumn{1}{c|}{5.98} & \multicolumn{1}{c|}{2.43} & \multicolumn{1}{c|}{
8.2} & \multicolumn{1}{c|}{10.53} & \multicolumn{1}{c|}{1.08} & 
\multicolumn{1}{c|}{7.08} & \multicolumn{1}{c|}{0.86} & \multicolumn{1}{c|}{
1.83} & \multicolumn{1}{c|}{3.46} & \multicolumn{1}{c|}{12.1} & 
\multicolumn{1}{c|}{15.95} & 17.02 \\ \hline
\multicolumn{1}{l|}{36} & \multicolumn{1}{c|}{25.03} & \multicolumn{1}{c|}{
2.15} & \multicolumn{1}{c|}{1.12} & \multicolumn{1}{c|}{0.96} & 
\multicolumn{1}{c|}{4.78} & \multicolumn{1}{|c|}{2.65} & \multicolumn{1}{c|}{
2.33} & \multicolumn{1}{c|}{27.64} & \multicolumn{1}{c|}{3.49} & 
\multicolumn{1}{c|}{4.29} & \multicolumn{1}{c|}{7.68} & \multicolumn{1}{c|}{
8.83} & 9.05 \\ \hline
\multicolumn{1}{l|}{37} & \multicolumn{1}{c|}{0.01} & \multicolumn{1}{c|}{
0.05} & \multicolumn{1}{c|}{1.43} & \multicolumn{1}{c|}{1.47} & 
\multicolumn{1}{c|}{0.58} & \multicolumn{1}{|c|}{0.14} & \multicolumn{1}{c|}{
0.24} & \multicolumn{1}{c|}{0.24} & \multicolumn{1}{c|}{27.69} & 
\multicolumn{1}{c|}{29.81} & \multicolumn{1}{c|}{16.22} & 
\multicolumn{1}{c|}{9.57} & 12.55 \\ \hline
\multicolumn{1}{l|}{381} & \multicolumn{1}{c|}{17.83} & \multicolumn{1}{c|}{
2.54} & \multicolumn{1}{c|}{2.23} & \multicolumn{1}{c|}{2.29} & 
\multicolumn{1}{c|}{4.29} & \multicolumn{1}{|c|}{1.81} & \multicolumn{1}{c|}{
1.37} & \multicolumn{1}{c|}{0.78} & \multicolumn{1}{c|}{2.28} & 
\multicolumn{1}{c|}{16.88} & \multicolumn{1}{c|}{14.82} & 
\multicolumn{1}{c|}{9.53} & 23.24 \\ \hline
\multicolumn{1}{l|}{382/5} & \multicolumn{1}{c|}{1.23} & \multicolumn{1}{c|}{
2.5} & \multicolumn{1}{c|}{0.34} & \multicolumn{1}{c|}{2.65} & 
\multicolumn{1}{c|}{2.61} & \multicolumn{1}{|c|}{0.21} & \multicolumn{1}{c|}{
0.9} & \multicolumn{1}{c|}{0.9} & \multicolumn{1}{c|}{5.77} & 
\multicolumn{1}{c|}{7.07} & \multicolumn{1}{c|}{49.89} & \multicolumn{1}{c|}{
5.13} & 20.79 \\ \hline
\multicolumn{1}{l|}{383} & \multicolumn{1}{c|}{0.04} & \multicolumn{1}{c|}{
0.18} & \multicolumn{1}{c|}{0.06} & \multicolumn{1}{c|}{0.11} & 
\multicolumn{1}{c|}{0.1} & \multicolumn{1}{|c|}{0.03} & \multicolumn{1}{c|}{
0.23} & \multicolumn{1}{c|}{0.16} & \multicolumn{1}{c|}{1.63} & 
\multicolumn{1}{c|}{2.39} & \multicolumn{1}{c|}{24.41} & \multicolumn{1}{c|}{
57.61} & 13.04 \\ \hline
\multicolumn{1}{l|}{384} & \multicolumn{1}{c|}{0.07} & \multicolumn{1}{c|}{
0.12} & \multicolumn{1}{c|}{0.02} & \multicolumn{1}{c|}{0.21} & 
\multicolumn{1}{c|}{0.05} & \multicolumn{1}{|c|}{0.1} & \multicolumn{1}{c|}{
0.03} & \multicolumn{1}{c|}{0.03} & \multicolumn{1}{c|}{0.06} & 
\multicolumn{1}{c|}{0.14} & \multicolumn{1}{c|}{0.38} & \multicolumn{1}{c|}{
0.16} & 98.64
\end{tabular}
$}$ }

{\scriptsize \bigskip\ \bigskip\ }

{\scriptsize $\fbox{$%
\begin{tabular}{l|c|c|c|c|c|c|c|c|c|c|c|c|c}
\multicolumn{14}{c}{Table A.5} \\ 
\multicolumn{14}{c}{Import Sector Input-Output Relations} \\ 
\multicolumn{14}{c}{US economy, 1987; 13x13 ISIC industries} \\ 
\multicolumn{14}{c}{Per cent of row commodity going to column industry} \\ 
\hline\hline
& 31 & 32 & 33 & 34 & 351/2 & 353/4 & 355/6 & 36 & 37 & 381 & 382/5 & 383 & 
384 \\ \hline
31 & 96.85 & 0.66 & 0.01 & 0.56 & 1.4 & 0.2 & 0.02 & 0.03 & 0.02 & 0 & 0.2 & 
0.03 & 0.02 \\ \hline
32 & 0.12 & 79.25 & 5.78 & 1.9 & 0.26 & 0.16 & 1.74 & 0.31 & 0.05 & 0.03 & 
0.99 & 0.15 & 9.23 \\ \hline
33 & 0.22 & 0.59 & 65.63 & 1.43 & 0.08 & 0.33 & 0.56 & 1.22 & 0.56 & 1.06 & 
1.06 & 0.55 & 26.71 \\ \hline
34 & 2.03 & 0.3 & 0.15 & 90.49 & 3.12 & 0.02 & 1.2 & 0.74 & 0.04 & 0.19 & 1
& 0.6 & 0.13 \\ \hline
351/2 & 3.75 & 6.6 & 1.2 & 6.22 & 54.19 & 5.45 & 11.88 & 2.73 & 2.99 & 0.85
& 1.51 & 1.87 & 0.76 \\ \hline
353/4 & 2.41 & 1.35 & 2.41 & 8.44 & 6.26 & 63.6 & 1.21 & 1.35 & 3.28 & 4.54
& 1.67 & 1.34 & 2.14 \\ \hline
355/6 & 7.61 & 5.04 & 9.04 & 6.97 & 7.46 & 1.82 & 2.24 & 0.22 & 1.35 & 8.02
& 13.68 & 11.68 & 24.88 \\ \hline
36 & 3.18 & 0.44 & 4.71 & 0.34 & 4.85 & 0.65 & 2.32 & 38.62 & 6.64 & 5.57 & 
9.18 & 8.09 & 15.4 \\ \hline
37 & 0.01 & 0 & 1.95 & 0.19 & 0.19 & 0.03 & 0.3 & 0.48 & 38.13 & 32.2 & 9.31
& 9.69 & 7.53 \\ \hline
381 & 3.18 & 0.11 & 8.69 & 2.01 & 4.97 & 1.98 & 3.32 & 0.42 & 2.35 & 16.66 & 
15.68 & 6.81 & 33.82 \\ \hline
382/5 & 1.36 & 4.15 & 1.75 & 9.19 & 4.03 & 0.21 & 1.93 & 0.54 & 5.97 & 5.23
& 31.19 & 5.8 & 28.65 \\ \hline
383 & 0.01 & 0.01 & 0.33 & 0.09 & 0.05 & 0.02 & 0.26 & 0.09 & 0.71 & 0.8 & 
18.09 & 62.38 & 17.17 \\ \hline
384 & 0.03 & 0.01 & 0.31 & 0.11 & 0.02 & 0.06 & 0.02 & 0.02 & 0.03 & 0.07 & 
0.09 & 0.04 & 99.2
\end{tabular}
$}$ }

\end{document}