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\begin{document}

\author{Wolfgang Keller\thanks{
1180 Observatory Drive, Madison, Wi 53706; email: wkeller@facstaff.wisc.edu.}
\\
%EndAName
Department of Economics\\
University of Wisconsin-Madison}
\title{Trade Patterns, Technology Flows, and Productivity Growth\thanks{
I would like to thank, without implicating them, Robert Evenson, Zvi
Griliches, Elhanan Helpman, Rody Manuelli and T.N. Srinivasan for helpful
comments on an earlier draft.}}
\date{This Version: January 1997. First Version: June 1996}
\maketitle

\begin{abstract}
\noindent 
This paper presents a model of international trade in differentiated
intermediate goods. Because intermediates are invented through costly R\&D
investments, employing foreign intermediates implies sharing the return to
R\&D with the inventor country. I first derive a relation of how domestic
productivity is related to foreign R\&D investments. In the subsequent
empirical analysis, industry level data for eight OECD countries between
1970-91 is used to estimate that relation. The robustness of interpreting
empirical findings is emphasized, to which effect I employ Monte-Carlo
techniques, and the part of international R\&D spillovers that is related to
trade is quantified. I find evidence, first, that domestic and foreign R\&D
affect productivity differently, in contrast to assuming symmetric effects.
Second, the productivity effects resulting from R\&D vary substantially by
which country conducts the R\&D. Third, I find that the composition of a
country's import partners does not significantly affect the estimated effect
from foreign R\&D, indicating a large component in the benefit from foreign
R\&D which is not related to trade. Lastly, I estimate that international
trade contributes about 20\% to the total productivity effect from foreign
R\&D.
\end{abstract}

\newpage\setcounter{page}{1}

\section{Introduction}

The recent development of theories of endogenous technological change, in
particular by Romer (1990) and Aghion and Howitt (1992), have triggered new
work on the relations of trade, growth, and technological change in open
economies (Grossman and Helpman 1991, Rivera-Batiz and Romer 1991a). In
these papers, the authors embed the recent theories in multi-sector
general-equilibrium 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 research
and development (R\&D) expenditures create new intermediate goods which are
different (the horizontally differentiated inputs model) or better (the
quality ladder model) from those already existing, and if these are also
exported to other economies, then the importing country's productivity is
increased through the R\&D efforts of its trade partner.

The impact of receiving a new input in the importing country might take
various forms. First of all, there is the direct effect of employing a
larger range of intermediate inputs in final output production: For a given
amount of primary resources, output is increasing in the range of
differentiated inputs (Ethier 1982). To the extent that the importing
country succeeds in not paying in full for this increase-in-variety, it is
reaping an external, or, ''spillover'' effect. Secondly, the import of
specialized inputs might facilitate learning about the product, spurring
imitation or innovation of a competing product.

In this paper, I will use data on the G-7 group of countries plus Sweden to
evaluate these mechanisms. The traded goods here are machinery inputs for
manufacturing industries; these inputs are usually differentiated and
imperfect substitutes, as in the Ethier-Romer model. In addition, they are
often highly specialized for a particular industry, implying that the
elasticity of substitution between machinery produced for two different
industries is negligible.\footnote{%
See Keller (1996a) for an analysis focusing on inter-industry relations.}

In this setting, I ask whether productivity growth in a particular industry
of an importing country is increased by the R\&D investments--leading to a
larger variety of differentiated machinery--of its trade partners. It is
clear that the pattern of trade in intermediate inputs is a central element
of this technology spillovers hypothesis. Both the 'increasing variety' as
well as the 'reverse-engineering' effects discussed above are tied to arm's
length market transactions of goods. This is in contrast to many other
possibilities by which technological knowledge can diffuse and which do not
rely on arm's length transactions per se.\footnote{%
See Griliches (1979) and Nadiri (1993) for more discussion, and the latter
paper for a recent survey.}

One hypothesis concerns the composition of imports by partner country:
Countries which import to a larger extent from high-knowledge countries
should, all else equal, import on average more and better differentiated
input varieties than countries importing largely from low-knowledge
countries. Consequently, this should lead to a higher TFP level in the
former importing countries. Second, for a given composition of imports, this
effect is likely to be stronger, the greater the overall import share of a
country is. A number of papers have recently attempted to assess the
importance of imports in transmitting foreign R\&D into domestic industries,
spurring total factor productivity (TFP), including Coe and Helpman (1995),
Coe et al. (1995), Evenson (1995), Keller (1996a, 1996b), as well as
Lichtenberg and van Pottelsberghe (1996).\footnote{%
The papers by Park (1995), Bernstein and Mohnen (1994), and Branstetter
(1996) are also estimating international R\&D spillovers, but do not contain
an explicit argument with respect to international trade.} In Coe and
Helpman (1995), the authors find a significantly positive correlation
between TFP levels and a trade-weighted sum of partner country R\&D stocks,
where bilateral import shares serve as weights. The interpretation of this
finding is not clear, though, because Keller (1996b), using the same data,
finds that the composition of countries' imports plays no particular role in
obtaining this correlation: Alternatively weighted R\&D stocks--where import
shares are created randomly--also lead invariably to a positive correlation
between foreign R\&D and the importing country's R\&D, and the average
correlation is often larger than when foreign R\&D is weighted using
observed import shares.

While making the point that the Coe and Helpman (1995) results do not depend
on the observed patterns of imports between countries, it does not imply
that R\&D spillovers are unrelated to international trade. For instance,
these papers use aggregate import data to compute the trade share weights
for a given importing country. Overall import relations between countries,
however, might be a very poor measure of intermediate inputs trade
relations. Another interpretation of the findings by Keller (1996b) is that
the characteristics of the data and the data generating process call for a
different, and perhaps more general, econometric specification in the first
place. Moreover, even if trade is not all what is driving international R\&D
spillovers, it is necessary to quantify the effect of trade in order to
assess its relative importance.

In this paper, therefore, I plan to address several of these issues. First
of all, I conduct an analysis of R\&D, imports, and TFP at a two- and three
digit industry level. At this level of aggregation, one is much more likely
to observe trade flows embodying new technology than at a country-level.
Secondly, I present estimation results for both TFP level as well as TFP
growth rate specifications, addressing some of the open questions concerning
characteristics and time series properties of the data. Thirdly, I extend
the Monte-Carlo analysis conducted by Keller (1996b), showing how these type
of experiments are related to estimating a general spillovers effect from
foreign R\&D. With this, it is, fourthly, possible to determine whether
there exists a trade-related part of internationally R\&D\ spillovers; I
find that this is the case, and it is estimated to be about 20\% of the
total benefit derived from foreign R\&D.

The remainder of the paper is as follows. In the next section, I describe
the model which motivates the empirical analysis below. Section 3 contains a
discussion of the characteristics and construction of the data. In the
following section 4, the basic empirical results are presented, and
contrasted with those from the corresponding Monte-Carlo experiments. The
following section discusses how general international R\&D\ spillovers
estimates are related to the Monte-Carlo experiments, and how they can be
empirically separated from trade-related effects. Section 6, finally,
concludes.

\section{The Model}

This section will give a theoretical background for the empirical analysis
presented below. I emphasize the empirical implementation of these models;
for more on this type of models, see, e.g., Grossman and Helpman (1991) and
Rivera-Batiz and Romer (1991a, 1991b).

Assume that the final good $j,$ $j=1,...,J,$ in country $v,$ $v=i,h,...,V,$
at time $t$ is produced according to 
\begin{equation}
y_{vjt}=A_{vj}\,l_{vjt}{}^{\alpha _{vj}}d_{vjt}{}^{1-\alpha _{vj}},\,\text{
with }0<\alpha _{vjt}<1,\forall v,j,t,  \label{outp}
\end{equation}
where $A_{vj}$ is a constant, $l_{vjt}$ are labor services used in sectoral
final output production, and $d_{vjt}$ is a composite input consisting of
horizontally differentiated intermediate products $x$ of variety $s.$ For a
specific country $i,$ $d_{ijt}$ is defined as 
\begin{equation}
d_{ijt}=\left( \gamma _{ijt}^i\int_0^{n_{ijt}^i}x_{ijt}^i(s)^{1-\alpha
_{it}}\,ds+\gamma _{hjt}^i\int_0^{n_{hjt}^i}x_{hjt}^i(s^{\prime })^{1-\alpha
_{hj}}\,ds^{\prime }+...+\right) ^{\frac 1{1-\alpha _{ijt}}}.  \label{int}
\end{equation}
Here, $x_{ijt}^i(s)$ denotes the quantity of an intermediate of variety $s$
used in sector $j,$ where the country in which the intermediate is produced
is given by the subscript, and the superscript denotes the country where the
intermediate is employed. Similarly, $n_{ijt}^i$ gives the range of
domestically produced intermediate goods utilized in country $i$'s good $j$
production, and the $n_{wjt}^i,$ $w\neq i,$ give the ranges of imported
goods. We think of the $x$'s as differentiated capital goods. Assume that
all varieties are different, and that $\gamma _{ijt}^i=1,\forall i,j,t;$ the 
$\gamma _{wjt}^i$ are functions to be defined below. Note that only inputs
of type $j$ are productive in the sector $j$ of any country, corresponding
to the often highly specialized nature of machinery inputs for particular
industries.

Concentrating on inputs utilized in country $i$'s sector $j$ at time $t,$
let $p_i$ and $p_w$ denote the rental prices which are asked by the
producers of intermediate input variety $x_i,$ respectively $x_w$. It
follows from (\ref{outp}) and (\ref{int}) that the first order conditions
for choosing $x_i$ and $x_w$ are 
\begin{equation}
p_i=(1-\alpha _i\,)\,\,x_i{}^{-\alpha _i}L^{\alpha _i}  \label{pi}
\end{equation}
and 
\begin{equation}
p_w=(1-\alpha _w)\,\gamma _w\,x_w{}^{-\alpha _w}L^{\alpha _i},\forall w\neq
i.  \label{pw}
\end{equation}
Intermediate goods producers are monopolists who choose the profit
maximizing quantity $x$, given the inverse demands in (\ref{pi}) and (\ref
{pw}). The production technology for all intermediates produced in one
country is the same. In any country, one unit of any intermediate in sector $%
j$ is produced linearly by using one unit of the local good $j.$ This leads
to a constant-markup formula for the price of intermediates from country $v$
(where I have dropped the index of any particular variety because they are
produced, and enter (\ref{outp}), symmetrically) 
\begin{equation}
p_v=\frac{r_v}{1-\alpha _v},\forall v,  \label{pv}
\end{equation}
where $r_v$ is the interest rate prevailing in country $v.$ Assume, for
simplicity, that the functions $\gamma _w$ are given by $\gamma
_w=x_w^{\alpha _w-\alpha _i}\frac{(1-\alpha _i)^2\,r_w}{(1-\alpha _w)^2\,r_i}%
,\forall w\neq i;$ then, using (\ref{pv}) and (\ref{pi}), (\ref{pw}), it can
be shown that all intermediates, whether domestically produced ($x_i$) or
imported ($x_w$), are employed at the same level, $x_i$.

In equilibrium, there will be trade in intermediate goods in this model.
Define capital $k_i$ as foregone consumption. This will be equal to the
resources needed to produce the quantity $n_ix_i$ of the domestic varieties,
plus the resources to obtain the foreign intermediates, $\sum_wn_wx_w,w\neq
i $. A unit of domestic intermediates, selling at price $p_i,$ buys $p_i/p_w$
units of an intermediate of country $w\neq i$. Hence, if trade is balanced, $%
\sum_w\frac{p_w}{p_i}n_wx_w$ units of domestic intermediates must be
exported in order to obtain the quantity $\sum_wn_wx_w$ of foreign
intermediates. It follows that capital $k_i$ is given by 
\begin{equation}
k_i=n_ix_i+\sum_{w\neq i}\frac{p_w}{p_i}n_wx_w=(n_i+\sum_{w\neq i}\frac{p_w}{%
p_i}n_w)\,x_i.  \label{k}
\end{equation}
In a situation where the interest rates are equalized internationally at
rate $r,$\footnote{%
In the symmetric version of this model which can be shown to have a stable
balanced growth path, $r$ will be equalized in equilibrium.} we have, from (%
\ref{k}) and (\ref{pv}), that 
\begin{equation}
x_i=\frac{k_i}{\left[ n_i+\sum_{w\neq i}\mu _wn_w\right] },  \label{xi}
\end{equation}
and $\mu _w\equiv \left( \frac{1-\alpha _i}{1-\alpha _w}\right) $.

Define a standard measure of total factor productivity (TFP) 
\[
\log F_{vjt}=\log y_{vjt}-\alpha _{vj}\log l_{vjt}-(1-\alpha _{vj})\log
k_{vjt},\forall v,j,t. 
\]
The output term $\log y_{vjt}$ is given by $\log A_{ij}+\alpha _{ij}\log
l_{ijt}+(1-\alpha _{ij})\log d_{ijt},$ with 
\[
\begin{array}{ccc}
\log d_{ijt} & = & \frac 1{1-\alpha _{ij}}\log \left[
n_{ijt}\,x_{ijt}^{1-\alpha _{ij}}+\sum_w\gamma
_w\,n_{wjt}\,x_{wjt}^{1-\alpha _{wj}}\right] \\ 
&  &  \\ 
& = & \frac 1{1-\alpha _{ij}}\log \left[ \frac{k_{ijt}^{1-\alpha _{ij}}}{%
\left[ n_{ijt}+\sum_{w\neq i}\mu _{hj}\,n_{wjt}\right] ^{1-\alpha _{ij}}}%
\left( n_{ijt}+\sum_wn_{wjt}\,\mu _{wj}^2\right) \right] .
\end{array}
\]
On substitution, one has for the TFP index 
\begin{equation}
\log F_{ijt}=\log A_{jt}+\log \left[ \frac{n_{ijt}+\sum_w\mu _{wj}^2\,n_{wjt}%
}{\left[ n_{ijt}+\sum_{w\neq i}\mu _{wj}\,n_{wjt}\right] ^{1-\alpha _{ij}}}%
\right] .  \label{lf}
\end{equation}
Equation (\ref{lf}) shows that the log-level of TFP is a function of the
ranges of intermediate goods which are employed in the importing country; $%
n_{ijt}$ gives the domestic range, and the $n_{wjt}$ are the foreign ranges.

As a benchmark case, consider a model where countries are perfectly
symmetric. Then, one has that $\mu _w=1,\forall w\neq i.$ Further, given the
CES structure and symmetry across intermediates, any sector of any country
will demand all intermediate inputs which are available worldwide, so that $%
n_{ijt}$ and $n_{wjt},$ the ranges of intermediates employed in country $i,$
are now equal to the ranges produced in countries $i$ and $w.$ Under these
circumstances, 
\begin{equation}
\log F_{ijt}=\log A_{jt}+\alpha _{ij}\log \left[ n_{ijt}+\sum_{w\neq
i}n_{wjt}\right] =\log A_{jt}+\alpha _{ij}\log n_{gjt},  \label{gl}
\end{equation}
where $n_{gjt}$ is the range of intermediates which is produced for the
sector $j$ globally.

The ranges of intermediate varieties are increased through devoting
resources to R\&D (Romer 1990). Although these ranges are not observed,
under certain assumptions on depreciation and obsolescence, the ranges are
equal to the respective cumulative R\&D spending, $S_v$, which itself is
observable. In the symmetric model with $V$ countries, the variable $n_g$ in
equation (\ref{gl}) will be equal to $V\times S_v$.

For the case where countries are asymmetric in size and with respect to R\&D
spending, and, consequently, intermediates are neither traded symmetrically
nor to the same degree, it is critical to know the relation between
countries' cumulative R\&D spending $S_v,$ and the ranges employed in
country $i$, $n_v^i$. The relation of TFP and the ranges of intermediates
employed can in general be written as (industry subscript suppressed) 
\begin{equation}
F_i=\Psi \left( A_i;n_i^i;n_w^i\right) =\Phi \left(
A_i;S_i,m_i^i,m_i;S_w,m_w^i\right) ,\forall i,w\neq i,  \label{gf}
\end{equation}
where $m_i$ is country $i$'s overall import share, $m_i^i$ is the weight the
country's own R\&D receives, and $m_w^i$ is country $i$'s import share from
country $w\neq i$. One can think of the import shares in (\ref{gf}) as being
related to the likelihood of receiving a new type of foreign intermediate.
This is certainly so in the extreme case when $m_w^i=0.$\footnote{%
Of course, even with $m_v^i=0,$ a country can obtain foreign knowledge which
is not embodied in goods.} Other than that, there is no necessary link
between the level of imports and the number of newly introduced intermediate
goods types in the local economy. Especially if one also considers indirect
effects, in particular the possibility that importing leads to local
learning through reverse engineering and the subsequent invention of new
inputs, it is clear that the volume of imports can be a very bad measure of
the increase in varieties which are available domestically.\footnote{%
An alternative view is implemented by Klenow and Rodriguez (1996) who
postulate that the number of different intermediate good varieties is
related to the number of different trade partners a country has. Also note
that in the fully symmetric model, the level of the intermediate $x_i$ does
not enter in determining the productivity effect, see (\ref{gl}). In that
model, as the number of countries rises, the value of bilateral imports
actually falls with the equilibrium level $x_i$. A paper which considers
some asymmetries between intermediates from different countries is
Rivera-Batiz and Romer (1991b).} Despite these considerations, however, it
is likely that the number of new varieties employed from a partner country
is positively, although presumably not linearly, related to the import
volume from that country.\footnote{%
In Grossman and Helpman (1991), Ch.6.5, the authors discuss several reasons
of why this should be the case.}

\section{Data}

This study employs data for eight OECD countries in six economic sectors
according to the International Standard Industrial Classification (ISIC) as
well as the Standard International Trade Classification (SITC), for the
years 1970-1991. The included countries are Canada, France, Germany, Italy,
Japan, Sweden, the United Kingdom, and the United States; hence, the G-7
group plus Sweden.\footnote{%
See the appendix for more details on data sources and the construction of
the variables.}

I use the following breakdown by sector (adjusted revision 2): (1) ISIC 31
Food, beverages, and tobacco; (2) ISIC 32 Textiles, apparel, and leather;
(3) ISIC 341 Paper and paper products; (4) ISIC 342 Printing; (5) ISIC
36\&37 Mineral products and basic metal industries; (6) ISIC 381 Metal
products. All sectors belong to ISIC class 3, that is, manufacturing. In
these sectors, the reliability and comparability of the measurement of
inputs and outputs is high compared to non-manufacturing sectors.

The data on imports of machinery comes from the OECD \textit{Trade by
Commodities} statistics, OECD 1980. I have tried to identify machinery
imports which will with high likelihood be utilized exclusively in one of
the above manufacturing industries. These commodity classes are (Revision 2)
SITC 727: Food-processing machines and parts, providing inputs to the ISIC\
31 industry; SITC 724: Textile and leather machinery and parts
(corresponding to ISIC 32); commodity class SITC 725: Paper \& pulp mill
machinery, machinery for manufacturing of paper (corresponding to ISIC 341);
commodity class SITC 726: Printing \& bookbinding machinery and parts
(corresponding to ISIC 342); commodity classes 736 \& 737: Machine tools for
working metals, and metal working machinery and parts (corresponding to ISIC
381); and, by SITC classification, Revision 1, commodity classes 7184 \&
7185: Mining machinery, metal crushing and glass-working machinery
(corresponding to ISIC 36 \& 37). The bilateral trade relations for these
SITC classes are given in full in Tables A-1 to A-6 in the appendix.

Data from the OECD (1991) on R\&D expenditures by sector is utilized to
capture the ranges of intermediate inputs, $n_v$. This data covers all
intramural business enterprise expenditure on R\&D. Because none of these
industries has a ratio of R\&D expenditures to GDP of more than $0.5\%$, it
is reasonable to assume that insofar as their productivity benefits from
R\&D at all, it will be to a large extent due to R\&D performed outside the
industry. However, there is no internationally comparable data on machinery
industry R\&D towards products which are used in specific industries.
Therefore, I assume that R\&D expenditures towards a sector $j$'s machinery
inputs is a certain constant share of the R\&D performed in the country's
non-electrical machinery sector (ISIC 382), where all specialized new
machinery inputs are likely to be invented.\footnote{%
This constant share is the share of an industry in employment in total
manufacturing employment, over the years 1979-81.} R\&D stocks are derived
from the R\&D expenditure series using the perpetual inventory method,%
\footnote{%
Hence, there is no variation in the proportional change of the R\&D stock of
industry $j$, and industry $j+1$ between time $t$ and $t+1$, for any given
country $i$. Any differential effect on TFP in sectors $j$ and $j+1$ of an
importing country is therefore due to differences in the patterns of
bilateral trade, the main focus of the paper.} and descriptive statistics on
the cumulative R\&D stocks are given in the appendix, Table A-7.

The TFP index is constructed using the \textit{Structural Analysis
Industrial (STAN) Database} of the OECD (1994). The share parameter $\alpha $
is, by profit maximization of the producers, equal to the ratio of total
labor cost to production costs. As emphasized by Hall (1990), using
cost-based rather than revenue-based factor shares ensures robustness of the
TFP index in the presence of imperfect competition, as in the model sketched
above. Building on the integrated capital taxation model (see Jorgenson 1993
for an overview), I construct cost-based labor shares. The parameter $\alpha 
$ above then is the share of labor in total production cost. The variable $l$
is the number of workers engaged, directly from the \textit{STAN} database.
The measure of $y$ is gross production, which also comes from the \textit{%
STAN} database. The growth of the TFP index $F$ is the difference between
output and factor-cost share weighted input growth, with the level of the $F$%
's normalized to 100 in 1970 for each of the $8\,x\,6$ time series. In Table
A-8 of the appendix, I show summary statistics for the TFP data.

\section{Estimation Results}

In this section, I will present estimation results for different
specifications of the function $\Phi $(.) above. The following section
discusses TFP level estimation results, whereas below, I present estimation
results for TFP growth rate regressions.

\subsection{TFP Level Specification}

Consider, as a specification of the function $\Phi
(A_{ij};S_{ijt}^d;m_{ij}^i;S_{wjt}^d;m_{wj}^i)$ above, the following 
\begin{equation}
\log F_{ijt}=\alpha _0+\mu d_j+\delta d_v+\sum_v\beta _v\left( m_{vj}^i\log
S_{vjt}^d\right) +\varepsilon _{ijt},  \label{l8}
\end{equation}
where $d_j$ and $d_v$ are industry-, and country- fixed effects,
respectively. In this specification, the TFP level in any industry is a
function of cumulative R\&D in all eight countries, with a domestic weight ($%
m_{ij}^i$) set to one, and the weights of the partner countries given by the
bilateral import shares ($\sum_wm_{wj}^i=1,\forall i$); the
country-elasticities $\beta _v$ are constrained to be the same across
importing countries.\footnote{%
The specification differs from Coe and Helpman's (1995) in that I allow the
R\&D elasticity to vary by country, whereas Coe and Helpman estimate one
parameter for the whole set of partner countries, which changes across
observations. In addition, here, the import shares enter linearly, not in
logs. The specification can be thought of being derived from a reduced form
expression for TFP of the form $F_{ijt}=A_{ij}\Pi _v\left( S_{vjt}^d\right)
^{\beta _v\,m_{vjt}^i}e^{\varepsilon _{ijt}}.$}

According to (\ref{l8}), the import composition matters for the TFP level of
a country, with the import-share interacted R\&D stocks capturing the
technology inflows into that country. However, (\ref{l8}) implies that two
countries with the same import composition, but different overall import
shares, should benefit to the same degree from foreign R\&D--which is
unlikely. Following Coe and Helpman (1995), we can model this through an
interaction of the overall import share, $m_{ij},$ with the R\&D variable%
\footnote{%
For the own R\&D effect, $m_{ij}$ is chosen such that $m_{ij}\,m_{ij}^i\log
S_{ijt}^d=\log S_{ijt}^d,$ i.e., $m_{ij}$ then equals one.} 
\begin{equation}
\log F_{ijt}=\alpha _0+\mu d_j+\delta d_v+\sum_v\beta _v\left(
m_{ij}\,m_{vj}^i\log S_{vjt}^d\right) +\varepsilon _{ijt}.  \label{l8i}
\end{equation}
I will refer to a specification without the overall import share, as in (\ref
{l8}), as $NIS,$ whereas a specification with the overall import share is
referred to as $IS$. Results for the specifications (\ref{l8}) and (\ref{l8i}%
) are given in Table 1, with standard errors in parentheses; a $^{**}(^{*})$
denotes significantly different from zero at a 5(10)\% level.

From Table 1, we see that all countries' R\&D stocks are estimated to have a
significant and positive influence on the TFP level of the importing
country. The magnitude of these effects, however, varies substantially,
with, e.g. for the second specification, a low for Germany with 1.9\%, and a
high for R\&D from Sweden, with 27.6\%. The specifications account for a
third to one half of the variation of TFP levels across countries, with the
higher $R^2$ for the $NIS$ specification. The result that high stocks of
scaled foreign R\&D are associated with high domestic levels of TFP is
interesting, but does not say much about the importance of the fact that the
scaling variables are the observed bilateral import shares. Interpreting
these shares as the probability that the importing country receives new
intermediate inputs from a partner country, a natural question to ask is how
the estimated parameters would look like if we had employed a different set
of probability weights, corresponding to different import patterns. This is
what the following Monte-Carlo experiments show.

Here, I intend to address two different questions: First, is there support
for the hypothesis that there is a distinction between effects on TFP
resulting from foreign as opposed to domestic R\&D? Second, conditional on
the effect from domestic R\&D on TFP, is there evidence to assume that the
composition of intermediate imports trade matters for TFP growth across
sectors?

\subsubsection{Domestic and International Inputs: does it matter how much
from where?}

In the Monte-Carlo experiments which follow, I will exchange trade partners
randomly. Let $b$ denote a specific Monte-Carlo replication, $b=1,...,B$.
For a given importing country, say $i,$ I exchange the observed bilateral
shares randomly. This means that any bilateral import share in replication $%
b,$ $\sigma _{vj}^i(b),$ is equal to\footnote{%
For a given industry and importing country, I draw eight numbers from a
uniform distribution with support $[0,1]$. These are matched with the eight
(that is, including 'imports' from own) observed 'import' shares to form a $%
8\times 2$ matrix. This matrix is then sorted in ascending order on the
random number column. In this way, the probability that any trade share $%
\sigma _{vj}^i(b)$ is equal to the value $m_{vj}^i,$ all $v,$ is equal to
1/8. A new sequence of trade relations (the eight numbers from the uniform
distribution with support $[0,1]$) is drawn for every importing country and
every industry, making a total of $8\times 6=48$ independent sequences.} 
\begin{equation}
\sigma _{vj}^i(b)= 
\begin{array}{c}
\left\{ 
\begin{array}{c}
m_{ij}^i\text{ with }\Pr =\frac 18 \\ 
\vdots \\ 
m_{Vj}^i\text{ with }\Pr =\frac 18
\end{array}
\right. \text{ },\forall v,j.
\end{array}
\label{mr}
\end{equation}
Because $m_{ij}^i=1$ and $\sum_wm_{wj}^i=1,$ it holds that $\sum_v\sigma
_{vj}^i(b)=2.$ Note that in setting up this experiment, I ignore the
distinction between the domestic weights $m_{ij}^i,$ and bilateral import
shares $m_{wj}^i,$ $w\neq i$. Hence, the experiment allows to see whether,
conditional on the ex-ante chosen value for $m_i^i=1$ and the specification
of $\Phi ,$ it is important to distinguish between embodied technology in
intermediate inputs from domestic, on the one hand, versus from foreign
producers, on the other. The equations are 
\begin{equation}
\log F_{ijt}=\alpha _0+\mu d_j+\delta d_v+\sum_v\beta _v\left( \sigma
_{vj}^i(b)\log S_{vjt}^d\right) +\varepsilon _{ijt},\forall b,  \label{l8r}
\end{equation}
for the specification without the overall import share ($NIS$), and, for the 
$IS$ specification: 
\begin{equation}
\log F_{ijt}=\alpha _0+\mu d_j+\delta d_v+\sum_v\beta _v\left(
m_{ij}\,\sigma _{vj}^i(b)\log S_{vjt}^d\right) +\varepsilon _{ijt},\forall b.
\label{l8ir}
\end{equation}
The results are shown in Table 2, second and fifth result columns. In the
table, I report the average slope estimate $\beta _v(\bar b)$ from $B=1000$
replications, as well as the standard deviation of $\beta _v(\bar b)$ (in
parentheses) and the average $R^2.$

One sees that the Monte-Carlo experiments result in coefficient estimates
which are in 75\% of the cases statistically indistinguishable from zero. In
particular, for the model (\ref{l8r}), this is true for half of the
coefficient estimates, and for the model (\ref{l8ir}), it is true for all
countries' estimates. The average $R^2$ in column two, with $0.522,$ is
larger than for the corresponding observed-data regression. This is somewhat
surprising, but the finding could well be spurious. Overall, the result that
parameter estimates tend to be not significantly different from zero in the
Monte-Carlo experiment implies that if intermediate input usage (from abroad
and domestically) is determined randomly, the effect of R\&D on the
importing sector's TFP is not statistically different from zero. Therefore,
it helps to know which intermediates come from the domestic, as opposed to
foreign economies if one wants to predict an importing sector's TFP level.%
\footnote{%
Obviously, this depends on how large a weight the domestic R\&D variable
receives (here, its weight is equal to one).}

The next experiment control for the domestic R\&D effect and asks whether
the composition of imports matters for domestic TFP levels.

\subsubsection{Does the TFP performance reflect the composition of
intermediate imports?}

I now constrain the Monte-Carlo experiments such that only the composition
of the international demand is randomized. That is, the results are
conditional on the domestic R\&D effect: $\theta _{vj}^v(b)=1,\forall v,b.$
For all $w\neq i,$ we have 
\begin{equation}
\theta _{wj}^i(b)=m_{qj}^i\text{ with }\Pr =\frac 17,\text{ }q\in
V\,\,\backslash \,i,\forall w,j.  \label{a7}
\end{equation}
The $\theta _{wj}^i(b)$ are constructed such that $\sum_w\theta
_{wj}^i(b)=1, $ that is, any observed trade share is assigned only once. The
two specifications, for a given country $i,$ are 
\begin{equation}
\log F_{ijt}=\alpha _0+\mu d_j+\delta d_v+\sum_v\beta _v\left( \theta
_{vj}^i(b)\log S_{vjt}^d\right) +\varepsilon _{ijt},\forall b,  \label{l7r}
\end{equation}
and 
\begin{equation}
\log F_{ijt}=\alpha _0+\mu d_j+\delta d_v+\sum_v\beta _v\left(
m_{ij}\,\theta _{vj}^i(b)\log S_{vjt}^d\right) +\varepsilon _{ijt},\forall b.
\label{l7ir}
\end{equation}
The results of these two experiments, for $B=1000,$ are shown in result
columns three and six of Table 2. The parameter estimates now are, in 75\%
of the cases significantly different from zero and positive. In addition,
these coefficients are sometimes smaller, and sometimes larger than those
obtained employing observed import shares: no clear pattern can be detected.
Moreover, the regressions which employ randomly exchanged import shares
account for a comparable part of the variation in TFP levels as the
observed-data regressions.

The fact that it is not necessary to impose the observed import shares to
estimate significant international R\&D spillovers confirms the result of
Keller (1996b) that one cannot test the hypothesis of the R\&D-trade-TFP
link simply by examining whether the parameter estimates are positive, or
how high the $R^2$ of these regressions is. Obviously, the regression
results are invariant to some degree to whatever weights the R\&D\ stocks
are interacted with. This would be trivially so if the R\&D stocks of
different countries are equal in size and move together over time. However,
as shown in Table A-7 in the appendix, there are considerable differences in
the cumulative R\&D stocks of different countries. In addition, Figure 1
shows that the R\&D stocks of different countries exhibit neither growth at
approximately the same rates, nor do they rise and fall simultaneously.%
\footnote{%
The average annual rate of growth of the R\&D stock estimates ranges from
3.64\% for the Canada to 11.88\% for Italy; and the standard deviation of
these growth rates for different four-year subperiods across countries
ranges from a low of 2.87\% (1978-82) to a high of 5.15\% (1970-74).}
Therefore, this explanation, at least in its extreme form, cannot be the
reason for the finding of fairly invariant parameter estimates.

Another interpretation of the results in Table 2 is that what the
regressions pick up is mainly a strong general effect from foreign R\&D;
that is, although imports are in part related to international technology
flows, this effect is overshadowed by the general R\&D spillover effect.
This is discussed further in section 5 below. A third interpretation is that
much of the estimated correlation is spurious, perhaps the consequence of
interpolation in the data, or due to the time-series properties of the data
generation process. It is the latter point which I intend to address first,
by presenting results from a TFP-R\&D growth specification. This is
appropriate if the benchmark capital stocks for physical capital (underlying
the TFP variable) as well as for the R\&D capital stocks have been estimated
with an error, as is very likely; further, the growth specification is also
preferred in the case of unobserved, time-invariant heterogeneity among the
industries.\footnote{%
The data generation process underlying the variables, especially whether
they are integrated of order one or less, also influences the choice of
specification. However, the unit root and cointegration tests I have
conducted fail to settle this issue in the present context.}

\subsection{TFP Growth Estimation}

The TFP growth specifications corresponding to (\ref{l8}) and (\ref{l8i})
above are, for an importing country $i,$%
\begin{equation}
\frac{\Delta F_{ijt}}{F_{ijt}}=\alpha _0+\sum_v\beta _v\left( m_{vj}^i\,%
\frac{\Delta S_{vjt}^d}{S_{vjt}^d}\right) +\varepsilon _{ijt},  \label{g8}
\end{equation}
where $\frac{\Delta x}x$ denotes the average annual growth rate of any
variable $x,$ and $m_{vj}^v=1,\forall v,j,$ The specification including the
overall import share is now given by 
\begin{equation}
\frac{\Delta F_{ijt}}{F_{ijt}}=\alpha _0+\sum_v\beta _v\left(
m_{ij}\,m_{vj}^i\,\frac{\Delta S_{vjt}^d}{S_{vjt}^d}\right) +\varepsilon
_{ijt},  \label{g8i}
\end{equation}
where, again, the value of the import share from $i,\,m_{ij},$ is set equal
to one, $\forall i,j.$ Dividing the period of observation into five
subperiods of approximately four years each, these regressions have 240
observations; the results are shown in Table 3, result columns one and three.

All slope coefficients are estimated to be positive, although only in the
model which includes the overall import share, $IS,$ all estimates are
significantly different from zero at a 5\% level. The latter appears to be
the preferred specification in this class of models, which is in line with
the arguments given above, as well as with findings in Coe and Helpman
(1995).

The results of the corresponding Monte-Carlo experiments are shown in result
columns two and four of Table 3. Contrary to the TFP level regressions
above, only the results conditional on the effect from domestic R\&D are
shown in Table 3. The specifications are, for an importing country $i,$%
\begin{equation}
\frac{\Delta F_{ijt}}{F_{ijt}}=\alpha _0+\sum_v\beta _v\left( \theta
_{vj}^i(b)\frac{\Delta S_{vjt}^d}{S_{vjt}^d}\right) +\varepsilon
_{ijt},\forall b,  \label{g8r}
\end{equation}
and 
\begin{equation}
\frac{\Delta F_{ijt}}{F_{ijt}}=\alpha _0+\sum_v\beta _v\left( m_{ij}\,\theta
_{vj}^i(b)\,\frac{\Delta S_{vjt}^d}{S_{vjt}^d}\right) +\varepsilon
_{ijt},\forall b.  \label{g8ir}
\end{equation}
For each of these two experiments, I conduct $B=1000$ replications. Again,
all Monte-Carlo based coefficients are estimated to be significantly above
zero, confirming the earlier results from TFP level regressions. Moreover,
now, the mean estimates from the Monte-Carlo experiments are very similar to
the coefficients in the corresponding observed-trade share regression. For
instance, a 95\% confidence interval for the coefficient of Canada in $IS,$ (%
\ref{g8ir}), is given by $0.427\pm 2\times 0.022$. Given that this interval
also includes the estimate for the import-weighted R\&D effect from Canada
when employing observed data (with $0.415$), this implies that the Canadian
trade-related R\&D effect is statistically not different from a randomized
Canadian R\&D effect, as captured by the average Monte-Carlo estimate. In
the following section, I will show how the latter is related to a general
spillover effect from foreign R\&D, and determine whether there is a
marginal contribution of international trade.

\section{Separating Trade-related from General R\&D Spillovers}

\subsection{Monte-Carlo Experiments and General Foreign R\&D Spillovers}

Consider the average of a particular off-diagonal element across the $B$
simulations, $\sigma _w^i(\bar b)=\frac 1B\sum_b\sigma _w^i(b)$. Because the
exchanging of $m_w^i$ is i.i.d., as $B\rightarrow \infty ,$ this average
will be the same for all, $\sigma _w^i(\bar b)=$ $\sigma (\bar b),\forall
i,w.$ Further, with 7 trade partners for any importing country, given that $%
7\times $ $\sigma (\bar b)=1,$ we have that $\sigma (\bar b)=1/7.$ Hence,
for any partner country's R\&D variable across all $B$ replications, we have 
\[
\frac 1B\sum_b\left( \sigma _w^i(b)\frac{\Delta S_{wj}^d}{S_{wj}^d}\right) =%
\frac{\Delta S_{wj}^d}{S_{wj}^d}\,\frac{\sum_b\sigma _w^i(b)}B=\sigma (\bar
b)\frac{\Delta S_{wj}^d}{S_{wj}^d}. 
\]
Therefore, across all $B$ replications, the average regressors are just the
average annual growth rates, $\frac{\Delta S_{wj}^d}{S_{wj}^d},w\neq i,$
multiplied by $\sigma (\bar b)=1/7$ for all partner countries, and simply $%
\frac{\Delta S_{ij}^d}{S_{ij}^d}$ as the own-country R\&D variable. Note,
however, that the coefficients reported from the Monte-Carlo experiments are
averages across the OLS estimates from $1000$ replications, not OLS
estimates from employing the average regressors. Nevertheless, as I show in
the appendix, the two will be very similar under certain circumstances, both
because the regression equation is linear and because the trade weights
enter the specification linearly. The Monte-Carlo based estimates can then
be viewed as estimating general R\&D spillover effects. In Table 4, I
present the following general R\&D spillover regression 
\begin{equation}
\frac{\Delta F_{ijt}}{F_{ijt}}=\alpha _0+\sum_v\beta _v\left[ m_{ij}\left(
\sigma (\bar b)\,\frac{\Delta S_{vjt}^d}{S_{vjt}^d}\right) \right]
+\varepsilon _{ijt}.  \label{g1i}
\end{equation}
For convenience, I have reproduced the corresponding Monte-Carlo based
results from Table 3. Comparing these two regressions, it is clear that the
Monte-Carlo averages indeed estimate the general R\&D spillover effect; the
maximum relative difference between the estimated parameters in columns four
and five is 2\% ($18.5\%$ versus $18.9\%$ in the case of Sweden).\footnote{%
The estimated standard deviations in these two regressions are not
comparable.}

\subsection{Estimating the Trade Component of International R\&D Spillovers}

The previous section suggests a direct way of assessing whether there is a
marginal international R\&D spillover which is related to international
trade. Consider the following regression: 
\begin{equation}
{\large \frac{\Delta F_{ijt}}{F_{ijt}}=\alpha _0+\sum_v\beta _v^I\left[
m_{ij}\,\sigma (\bar b)\frac{\Delta S_{vjt}^d}{S_{vjt}^d}\right]
+\sum_v\beta _v^{II}\left[ m_{ij}\left( m_{vj}^i-\sigma (\bar b)\right) \,%
\frac{\Delta S_{vjt}^d}{S_{vjt}^d}\right] +\varepsilon _{ijt},}  \label{both}
\end{equation}
Regressors with parameters $\beta ^I$ measure the general R\&D spillover
effect, and the $\beta ^{II}$ coefficients estimate the marginal
trade-related effect, if any. In particular, if there is no separate effect
of international R\&D which works through international trade, then the
coefficients $\beta ^{II}$ will be equal to zero, and the regression (\ref
{both}) will explain as much of the variation in TFP growth rates as the
general R\&D spillover specification (\ref{g1i}). The result of this
comparison is seen in Table 5. The specification allowing for an additional
trade-related R\&D spillovers effect explains more of the variation in TFP
growth rates, with an adjusted $R^2$ of 9.6\%, versus 7.8\% in the
specification which captures solely the general R\&D spillovers effect.
Therefore, the marginal effect of trade contributes a little less than 20\%
to the overall spillovers effect.\footnote{%
I have considered analogous regressions to (\ref{both}) for the growth
specification without the overall import share ($NIS$), as well as for the
TFP level regressions $NIS$ and $IS$ to check the robustness of this
finding. In the level $NIS$ specification, I estimate a contribution of
trade to the overall R\&D spillover of 7.8\%; in the $IS$ specification, it
is 26.5\%. In these cases, the restricted regression setting the $\beta
^{II} $ coefficients to zero is rejected at all standard levels of
significance. In the growth specification $NIS,$ however, no significant
marginal trade-related R\&D\ spillover effect is estimated. Hence, while not
perfectly robust, generally, the trade mechanism is estimated to contribute
significantly to the overall benefit from foreign R\&D, and it is in the
order of 20\% in the preferred specification presented in Table 5.}

The $\beta ^{II}$ point estimates in Table 5 can be interpreted as follows:
The negative coefficient for Canada, for instance, means that industries
which had imported overproportionately (that is, more than $1/7$ per cent)
from Canada have experienced on average a lower rate of TFP growth. The
effect is estimated to be positive for France and Japan, and negative for
all other countries; however, it is only in the case of Canada significantly
different from zero at a 5\% level.

\section{Conclusion}

In this paper, I have examined the relation of trade patterns, technology
flows, and productivity growth. Along the lines of recent theory on
R\&D-driven growth and trade, a model has been developed where domestic TFP
is related to the number of varieties of differentiated inputs from abroad
which are employed domestically. Based on the hypothesis that these ranges
of varieties from partner countries are related to imports from those
countries, I estimate the relation between domestic as well as
import-weighted foreign R\&D and domestic TFP.

I find, first, that there is a lot of variation in the estimated TFP effects
from different countries' R\&D investments. Secondly, the findings suggest
that domestic and foreign R\&D investments are not perfect substitutes in
their effect on TFP. This implies that theoretical models of the type
discussed above need to incorporate factors which imply asymmetric effects
of domestic and foreign intermediate inputs embodying technology in order to
be consistent with the data. Third, I find that, conditional on the effect
of domestic R\&D on TFP, the composition of a country's imports does not
significantly affect the degree to which it benefits from foreign R\&D.
While there are several possible reasons for that, including the possibility
that the econometric specification is too limited to allow finding anything
else, I argue that it is primarily due to the presence of a strong general
spillover effect from foreign R\&D investments. This effect is unrelated to
international trade, driven perhaps by mechanisms such as foreign direct
investment, the relative importance of which still needs to be established.
For international trade, the analysis in this paper has allowed to quantify
its contribution to the total effect derived from foreign R\&D investments,
which is about 20\%.\newpage 

\pagestyle{empty}

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\appendix

\section{Import Flows Data}

The specialized machinery trade data comes from OECD (1980). See Table A-1
to A-6 for the absolute values of imports between the countries in US
dollars of 1980 and 1975, respectively: The import data I use for the first
five industries is from 1980, exactly in the middle of the period of
observation; for the sixth industry, I have been unable to obtain data for
1980 according to SITC Revision 2, so I have used data from 1975 for SITC
Revision 1. These tables are used to calculate the variable $m_{wj}^i,$ the
bilateral import shares of country $i$ with countries $w\neq i$ in sector $%
j. $

\section{Data on R\&D}

The raw data on R\&D expenditures comes from OECD (1991). It is more patchy
than the OECD data on output, investment, and employment, which is discussed
below. 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 included in the sample 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 variable $n$ is based on data on
total business enterprise intramural expenditure on R\&D ($rd$) for ISIC
sector 382 (non-electronical machinery), 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). I use the perpetual
inventory method to construct technology stocks, assuming that 
\begin{equation}
\begin{array}{ccc}
n_{it} & = & (1-\delta )\,n_{it-1}+rd_{it-1},\,\,\text{for }t=2,...,22 \\ 
& \text{and} &  \\ 
n_{i1} & = & \frac{rd_{i1}}{(g_i^n+\delta +0.1)}\text{ \thinspace .}
\end{array}
\label{techst}
\end{equation}
The rate of depreciation $\delta $ is set at $0.05,$ and $g^n$ is the
average annual growth rate of $n$ over the period of 1970-1989 (the year
endpoints for which there is data available for all countries). Preliminary
analysis using other values for the rate of depreciation such as $0$, or $%
0.1 $, shows that this does not influence the estimation results
considerably. The denominator in the calculation of $n_1$ is increased by $%
0.1$ in order to obtain positive estimates of $n_1$ throughout. As described
in the text, the industry-specific R\&D expenditures are derived by
splitting up the ISIC 382 stocks according to the employment share of a
particular industry in total manufacturing employment.

\section{Labor, Physical Capital, and Gross Production}

For these variables, the OECD (1994) \textit{STAN} database is the basic
source. It provides internationally comparable data on industrial activity
by sectors, primarily for OECD countries. This includes data on labor input,
on labor compensation, investment, production, and gross production for up
to 49 3-digit ISIC industries (revision 2). 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 $F$, I consider only inputs of labor and
physical capital (in particular, there is no data on quality-adjusted labor
input by industry). Data on labor inputs $l$ is taken directly from the 
\textit{STAN} database (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 database, 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
output deflators are derived from figures on value-added both in current as
well as constant 1985 prices, both included in the \textit{STAN} data base.
The capital stocks are then again 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^{inv}+\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), $g^{inv}$ 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 and Landau (1993), Table A-3 
\[
\frame{$
\begin{array}{ccc}
\text{Canada: 8.51\%} &  & \text{Japan: 6.6\%} \\ 
\text{France: 17.39\%} &  & \text{Sweden: 7.7\%} \\ 
\text{Germany: 17.4\%} &  & \text{United Kingdom: 8.19\%} \\ 
\text{Italy: 11.9\%} &  & \text{United States: 13.31\%}
\end{array}
$ } 
\]
These numbers, which are used throughout, are estimates for machinery in
manufacturing in the year 1980.

According to equation (\ref{outp}), $\alpha _{ijt}$ will be the share of the
labor cost in production. Following the approach by Hall (1990), the $\alpha
_{ijt}$'s are not calculated as the ratio of total labor compensation to
value added (the revenue-based factor shares), both of which is included in
the \textit{STAN} database, 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 and Karayannis 1993) and data provided in
Jorgenson and Landau (1993). The effective marginal corporate tax rate $\tau 
$ is given by the wedge between before-tax ($p_k$) and after-tax rate of
return ($\rho $), relative to the former 
\begin{equation}
\tau =\frac{p_k-\rho }{p_k}.  \label{met}
\end{equation}
For us, the variable of interest is $p_k$, 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 
\begin{equation}
\rho =\iota +\pi ,  \label{rho}
\end{equation}
where $\iota $ 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. Our approach then is the
so-called ''fixed-r'' strategy (''fixed-$\iota $'' in my notation), where
one gives as an input a real interest rate and deduces $\tau .$ In this
case, I use a value of $0.1$ for the real interest rate, which, together
with the actual values of $\pi $ allows, using equations (\ref{met}) and (%
\ref{rho}) to infer $p_k,$ the user cost of capital. 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. Also, $\tau $ varies by
asset type, and $\rho $ is a function of the way of financing (equity versus
debt primarily). That is, there are, on the one hand, several shortcomings
in the construction of the cost-based factor shares due to unavailability of
more detailed data. The chapter by Fullerton and Karayannis (1993) presents
a sensitivity analysis in several dimensions. In addition, I have myself
experimented with different values for $\iota $, and found that the basic
results presented above do not depend on a particular choice for $\iota $.
On the other hand, this approach has the advantage of using all data on the
user cost of capital compiled in Jorgenson and Landau (1993) to arrive at a
TFP index which is robust to deviations from perfect competition.

Having obtained the series on the user cost of capital $p_k$ and $k$, all
what is left to obtain robust wage shares $\alpha $ is to deflate the
current price labor costs $wl$, available in the \textit{STAN} data base
(again using sectoral output deflators), and form 
\begin{equation}
\alpha =\frac{w\,l}{w\,l+p_k\,k}.  \label{ws}
\end{equation}
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. Calculating log
differences of year-to-year gross production, and taking the difference
between this and total input growth, I have constructed a TFP growth series.
A value of 100 in 1970 is chosen for each of the $8\,x\,6$ time series, for
all industries $j$ and countries $i.$

\section{Relation of Monte-Carlo Experiments and General R\&D Spillover
Regression}

Consider, for simplicity, the model above with only one regressor (with
industry and time subscripts are suppressed): $\frac{\Delta F_i}{F_i}=\alpha
_0+\beta _1\theta _v^i(b)\frac{\Delta S_i^d}{S_i^d}+\varepsilon _i.$ Let $%
\theta _v^i(b)=\sigma (\bar b)+\eta _v^i(b),\forall b,$ where $\eta _v^i(b)$
is the deviation of the trade share from its expected value--partner
country-by-partner country--of $1/7$. Then the OLS estimate of $\beta _1(b)$
equals 
\[
\beta _1\left( b\right) =\frac{\sum_i\left( \theta _v^i(b)\frac{\Delta S_i^d%
}{S_i^d}\frac{\Delta F_i}{F_i}\right) }{\sum_i\left( \theta _v^i(b)\frac{%
\Delta S_i^d}{S_i^d}\right) ^2}=\frac{\sum_i\left( \sigma (\bar b)\frac{%
\Delta S_i^d}{S_i^d}\frac{\Delta F_i}{F_i}+\eta _v^i(b)\frac{\Delta S_i^d}{%
S_i^d}\frac{\Delta F_i}{F_i}\right) }{\sum_i\left( \left[ \sigma (\bar
b)+\eta _v^i(b)\right] \frac{\Delta S_i^d}{S_i^d}\right) ^2},\forall b. 
\]
If the denominator is approximated by $\sum_i\left( \frac{\Delta S_i^d}{S_i^d%
}\right) ^2\left[ \sigma (\bar b)\right] ^2$,$\forall b,$ this means that
the average of the Monte-Carlo estimates, $\beta _1(\bar b)=\frac
1B\sum_b\beta _1(b)$ , equals 
\begin{equation}
\begin{array}{ccc}
\beta _1(\bar b) & \simeq & \frac{\sum_{b=1}^B\sum_i\left( \sigma (\bar b)%
\frac{\Delta S_i^d}{S_i^d}\frac{\Delta F_i}{F_i}+\eta _v^i(b)\frac{\Delta
S_i^d}{S_i^d}\frac{\Delta F_i}{F_i}\right) }{B\sum_i\left( \frac{\Delta S_i^d%
}{S_i^d}\right) ^2\left[ \sigma (\bar b)\right] ^2} \\ 
&  &  \\ 
& = & \frac{\sum_i\sigma (\bar b)\frac{\Delta S_i^d}{S_i^d}\frac{\Delta F_i}{%
F_i}}{\sum_i\left( \frac{\Delta S_i^d}{S_i^d}\right) ^2\left[ \sigma (\bar
b)\right] ^2}+\frac{\sum_i\frac{\Delta S_i^d}{S_i^d}\frac{\Delta F_i}{F_i}%
\sum_{b=1}^B\eta _v^i(b)}{B\sum_i\left( \frac{\Delta S_i^d}{S_i^d}\right)
^2\left[ \sigma (\bar b)\right] ^2}.
\end{array}
\label{mess}
\end{equation}
Because $\sum_{b=1}^B\eta _v^i(b)=0,$ however, the second term in (\ref{mess}%
) will drop out, so that $\beta _1(\bar b)$ is approximately equal to the
OLS estimate of projecting $\frac{\Delta F_i}{F_i}$ on $\sigma (\bar b)\frac{%
\Delta S_i^d}{S_i^d}.$ Clearly, how good the approximation above is depends
on how large $\left[ \frac{\Delta S_i^d}{S_i^d}\right] ^2\left( \left[ \eta
_v^i(b)\right] ^2+2\eta _v^i(b)\sigma (\bar b)\right) $ is, or, more
generally, $\lambda _i^2\left( \left[ \eta _v^i(b)\right] ^2+2\eta
_v^i(b)\sigma (\bar b)\right) $. In particular, if $\lambda _i=\log S_i^d,$
then the average Monte-Carlo estimate will differ more from the general
spillover regression than if $\lambda _i=\frac{\Delta S_i^d}{S_i^d},$ as
presented in Table 4.\newpage

{\footnotesize 
\[
{\small \fbox{%
\begin{tabular}[b]{l|c|c}
\multicolumn{3}{l}{TABLE 1} \\ \hline\hline
\multicolumn{3}{l}{} \\ 
\multicolumn{3}{l}{TFP Level Specification; 1056 observations} \\ 
\multicolumn{3}{l}{} \\ \hline
\multicolumn{1}{c|}{Country} & $
\begin{array}{c}
\text{Model} \\ 
(\ref{l8})
\end{array}
$ & $
\begin{array}{c}
\text{Model} \\ 
(\ref{l8i})
\end{array}
$ \\ \hline
CAN & \multicolumn{1}{c|}{$
\begin{array}{c}
0.101^{**} \\ 
(0.027))
\end{array}
$} & \multicolumn{1}{c}{$
\begin{array}{c}
0.201^{**} \\ 
(0.043)
\end{array}
$} \\ \hline
FRA & \multicolumn{1}{c|}{$
\begin{array}{c}
0.209^{**} \\ 
(0.019)
\end{array}
$} & \multicolumn{1}{c}{$
\begin{array}{c}
0.236^{**} \\ 
(0.024)
\end{array}
$} \\ \hline
GER & \multicolumn{1}{c|}{$
\begin{array}{c}
0.071^{**} \\ 
(0.009)
\end{array}
$} & \multicolumn{1}{c}{$
\begin{array}{c}
0.019^{**} \\ 
(0.009)
\end{array}
$} \\ \hline
IT & \multicolumn{1}{c|}{$
\begin{array}{c}
0.066^{**} \\ 
(0.014)
\end{array}
$} & \multicolumn{1}{c}{$
\begin{array}{c}
0.083^{**} \\ 
(0.015)
\end{array}
$} \\ \hline
JAP & \multicolumn{1}{c|}{$
\begin{array}{c}
0.068^{**} \\ 
(0.014)
\end{array}
$} & \multicolumn{1}{c}{$
\begin{array}{c}
0.127^{**} \\ 
(0.020)
\end{array}
$} \\ \hline
SWE & \multicolumn{1}{c|}{$
\begin{array}{c}
0.206^{**} \\ 
(0.022)
\end{array}
$} & \multicolumn{1}{c}{$
\begin{array}{c}
0.276^{**} \\ 
(0.025)
\end{array}
$} \\ \hline
UK & \multicolumn{1}{c|}{$
\begin{array}{c}
0.188^{**} \\ 
(0.022)
\end{array}
$} & \multicolumn{1}{c}{$
\begin{array}{c}
0.150^{**} \\ 
(0.027)
\end{array}
$} \\ \hline
USA & \multicolumn{1}{c|}{$
\begin{array}{c}
0.111^{**} \\ 
(0.007)
\end{array}
$} & \multicolumn{1}{c}{$
\begin{array}{c}
0.080^{**} \\ 
(0.011)
\end{array}
$} \\ \hline
R$^2$ & \multicolumn{1}{c|}{$0.472$} & \multicolumn{1}{c}{0.357}
\end{tabular}
}} 
\]
}\setlength{\oddsidemargin}{-0.6in} \setlength{\evensidemargin}{-0.4in} %
\setlength{\textwidth}{7.5in}

{\scriptsize 
\[
{\small \fbox{%
\begin{tabular}[b]{lccc||ccc}
\multicolumn{7}{l}{TABLE 2} \\ \hline\hline
\multicolumn{7}{l}{} \\ 
\multicolumn{7}{l}{Total Factor Productivity Levels Regressions; 1056
observations} \\ 
\multicolumn{7}{l}{} \\ 
& \multicolumn{3}{c}{NIS Specifications} & \multicolumn{3}{c}{IS
Specifications} \\ \hline
\multicolumn{1}{c|}{} & \multicolumn{1}{c|}{$
\begin{array}{c}
\text{Observed} \\ 
\text{Shares} \\ 
\text{Eq. (\ref{l8})}
\end{array}
$} & \multicolumn{1}{c|}{$
\begin{array}{c}
\text{Shares (8)} \\ 
\text{Exchanged} \\ 
\text{Eq. (\ref{l8r})}
\end{array}
$} & $
\begin{array}{c}
\text{Imp. Shares} \\ 
\text{Exchanged} \\ 
\text{Eq. (\ref{l7r})}
\end{array}
$ & \multicolumn{1}{||c|}{$
\begin{array}{c}
\text{Observed } \\ 
\text{Shares} \\ 
\text{Eq. (\ref{l8i})}
\end{array}
$} & \multicolumn{1}{c|}{$
\begin{array}{c}
\text{Shares (8)} \\ 
\text{Exchanged} \\ 
\text{Eq. (\ref{l8ir})}
\end{array}
$} & $
\begin{array}{c}
\text{Import Shares} \\ 
\text{Exchanged} \\ 
\text{Model (\ref{l7ir})}
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{CAN} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.101^{**} \\ 
(0.027))
\end{array}
$} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.191 \\ 
(0.097)
\end{array}
$} & $
\begin{array}{c}
0.159 \\ 
(0.081)
\end{array}
$ & \multicolumn{1}{||c|}{$
\begin{array}{c}
0.201^{**} \\ 
(0.043)
\end{array}
$} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.026 \\ 
(0.253)
\end{array}
$} & $
\begin{array}{c}
0.104 \\ 
(0.085)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{FRA} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.209^{**} \\ 
(0.019)
\end{array}
$} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.132 \\ 
(0.068)
\end{array}
$} & $
\begin{array}{c}
0.161^{**} \\ 
(0.063)
\end{array}
$ & \multicolumn{1}{||c|}{$
\begin{array}{c}
0.236^{**} \\ 
(0.024)
\end{array}
$} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.028 \\ 
(0.156)
\end{array}
$} & $
\begin{array}{c}
0.180^{**} \\ 
(0.081)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{GER} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.071^{**} \\ 
(0.009)
\end{array}
$} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.115^{**} \\ 
(0.052)
\end{array}
$} & $
\begin{array}{c}
0.118^{**} \\ 
(0.042)
\end{array}
$ & \multicolumn{1}{||c|}{$
\begin{array}{c}
0.019^{**} \\ 
(0.009)
\end{array}
$} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.107 \\ 
(0.132)
\end{array}
$} & $
\begin{array}{c}
0.128^{**} \\ 
(0.049)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{IT} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.066^{**} \\ 
(0.014)
\end{array}
$} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.134 \\ 
(0.080)
\end{array}
$} & $
\begin{array}{c}
0.087^{**} \\ 
(0.028)
\end{array}
$ & \multicolumn{1}{||c|}{$
\begin{array}{c}
0.083^{**} \\ 
(0.015)
\end{array}
$} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.243 \\ 
(0.308)
\end{array}
$} & $
\begin{array}{c}
0.083^{**} \\ 
(0.028)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{JAP} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.068^{**} \\ 
(0.014)
\end{array}
$} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.123^{**} \\ 
(0.053)
\end{array}
$} & $
\begin{array}{c}
0.103^{**} \\ 
(0.043)
\end{array}
$ & \multicolumn{1}{||c|}{$
\begin{array}{c}
0.127^{**} \\ 
(0.020)
\end{array}
$} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.034 \\ 
(0.136)
\end{array}
$} & $
\begin{array}{c}
0.097^{**} \\ 
(0.046)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{SWE} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.206^{**} \\ 
(0.022)
\end{array}
$} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.147^{**} \\ 
(0.072)
\end{array}
$} & $
\begin{array}{c}
0.172^{**} \\ 
(0.053)
\end{array}
$ & \multicolumn{1}{||c|}{$
\begin{array}{c}
0.276^{**} \\ 
(0.025)
\end{array}
$} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.200 \\ 
(0.244)
\end{array}
$} & $
\begin{array}{c}
0.253^{**} \\ 
(0.042)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{UK} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.188^{**} \\ 
(0.022)
\end{array}
$} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.134 \\ 
(0.067)
\end{array}
$} & $
\begin{array}{c}
0.134^{**} \\ 
(0.064)
\end{array}
$ & \multicolumn{1}{||c|}{$
\begin{array}{c}
0.150^{**} \\ 
(0.027)
\end{array}
$} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.028 \\ 
(0.129)
\end{array}
$} & $
\begin{array}{c}
0.165 \\ 
(0.086)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{USA} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.111^{**} \\ 
(0.007)
\end{array}
$} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.108^{**} \\ 
(0.043)
\end{array}
$} & $
\begin{array}{c}
0.082^{**} \\ 
(0.039)
\end{array}
$ & \multicolumn{1}{||c|}{$
\begin{array}{c}
0.080^{**} \\ 
(0.011)
\end{array}
$} & \multicolumn{1}{c|}{$
\begin{array}{c}
0.035 \\ 
(0.092)
\end{array}
$} & $
\begin{array}{c}
0.081 \\ 
(0.044)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{R$^2$} & \multicolumn{1}{c|}{$0.472$} & 
\multicolumn{1}{c|}{0.522} & 0.490 & \multicolumn{1}{||c|}{0.357} & 
\multicolumn{1}{c|}{0.260} & 0.379
\end{tabular}
}} 
\]
}

{\scriptsize \newpage\ {\footnotesize $\fbox{%
\begin{tabular}[b]{lccc|c}
\multicolumn{5}{l}{TABLE 3} \\ \hline\hline
\multicolumn{5}{l}{} \\ 
\multicolumn{5}{l}{TFP Growth Specification; 240 observations} \\ 
\multicolumn{5}{l}{} \\ 
& \multicolumn{2}{c}{NIS} & \multicolumn{2}{c}{IS} \\ \hline
\multicolumn{1}{c|}{Country} & \multicolumn{1}{c|}{$%
\begin{array}{c}
\text{Observed} \\ 
\text{Shares} \\ 
\text{Eq. (\ref{g8})}
\end{array}
$} & \multicolumn{1}{c||}{$%
\begin{array}{c}
\text{Imp. Shares} \\ 
\text{Exchanged} \\ 
\text{Eq. (\ref{g8r})}
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
\text{Observed } \\ 
\text{Shares} \\ 
\text{Eq. (\ref{g8i})}
\end{array}
$} & $%
\begin{array}{c}
\text{Imp. Shares } \\ 
\text{Exchanged} \\ 
\text{Eq. (\ref{g8ir})}
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{CAN} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.351^{*} \\ 
(0.178)
\end{array}
$} & \multicolumn{1}{c||}{$%
\begin{array}{c}
0.383^{**} \\ 
(0.122)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.415^{**} \\ 
(0.158)
\end{array}
$} & $%
\begin{array}{c}
0.427^{**} \\ 
(0.022)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{FRA} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.437^{**} \\ 
(0.139)
\end{array}
$} & \multicolumn{1}{c||}{$%
\begin{array}{c}
0.431^{**} \\ 
(0.078)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.503^{**} \\ 
(0.141)
\end{array}
$} & $%
\begin{array}{c}
0.512^{**} \\ 
(0.018)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{GER} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.198^{**} \\ 
(0.067)
\end{array}
$} & \multicolumn{1}{c||}{$%
\begin{array}{c}
0.210^{**} \\ 
(0.027)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.235^{**} \\ 
(0.060)
\end{array}
$} & $%
\begin{array}{c}
0.252^{**} \\ 
(0.009)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{IT} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.093^{*} \\ 
(0.054)
\end{array}
$} & \multicolumn{1}{c||}{$%
\begin{array}{c}
0.126^{**} \\ 
(0.030)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.151^{**} \\ 
(0.053)
\end{array}
$} & $%
\begin{array}{c}
0.157^{**} \\ 
(0.007)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{JAP} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.068 \\ 
(0.076)
\end{array}
$} & \multicolumn{1}{c||}{$%
\begin{array}{c}
0.077^{**} \\ 
(0.037)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.166^{**} \\ 
(0.080)
\end{array}
$} & $%
\begin{array}{c}
0.169^{**} \\ 
(0.010)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{SWE} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.153^{**} \\ 
(0.072)
\end{array}
$} & \multicolumn{1}{c||}{$%
\begin{array}{c}
0.155^{**} \\ 
(0.037)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.172^{**} \\ 
(0.070)
\end{array}
$} & $%
\begin{array}{c}
0.189^{**} \\ 
(0.008)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{UK} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.380^{**} \\ 
(0.153)
\end{array}
$} & \multicolumn{1}{c||}{$%
\begin{array}{c}
0.358^{**} \\ 
(0.077)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.493^{**} \\ 
(0.158)
\end{array}
$} & $%
\begin{array}{c}
0.508^{**} \\ 
(0.018)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{USA} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.137^{**} \\ 
(0.062)
\end{array}
$} & \multicolumn{1}{c||}{$%
\begin{array}{c}
0.108^{**} \\ 
(0.024)
\end{array}
$} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.173^{**} \\ 
(0.061)
\end{array}
$} & $%
\begin{array}{c}
0.173^{**} \\ 
(0.009)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{R$^2$} & \multicolumn{1}{c|}{0.127} & 
\multicolumn{1}{c||}{0.134} & \multicolumn{1}{c|}{0.105} & 0.109
\end{tabular}
}$}\newpage\ }

{\scriptsize {\footnotesize 
\[
{\small \fbox{%
\begin{tabular}[b]{l|c|c}
\multicolumn{3}{l}{TABLE 4} \\ \hline\hline
\multicolumn{3}{l}{} \\ 
\multicolumn{3}{l}{TFP Growth Estimation; 240 observations} \\ 
\multicolumn{3}{l}{} \\ \hline
\multicolumn{1}{c|}{Country} & $
\begin{array}{c}
\text{General R\&D} \\ 
\text{Spillover} \\ 
\text{Eq. (\ref{g1i})}
\end{array}
$ & $
\begin{array}{c}
\text{Imp. Shares } \\ 
\text{Exchanged} \\ 
\text{Eq. (\ref{g8ir})}
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{CAN} & $
\begin{array}{c}
0.426^{**} \\ 
(0.156)
\end{array}
$ & $
\begin{array}{c}
0.427^{**} \\ 
(0.022)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{FRA} & $
\begin{array}{c}
0.513^{**} \\ 
(0.139)
\end{array}
$ & $
\begin{array}{c}
0.512^{**} \\ 
(0.018)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{GER} & $
\begin{array}{c}
0.252^{**} \\ 
(0.062)
\end{array}
$ & $
\begin{array}{c}
0.252^{**} \\ 
(0.009)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{IT} & $
\begin{array}{c}
0.156^{**} \\ 
(0.052)
\end{array}
$ & $
\begin{array}{c}
0.157^{**} \\ 
(0.007)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{JAP} & $
\begin{array}{c}
0.167^{**} \\ 
(0.080)
\end{array}
$ & $
\begin{array}{c}
0.169^{**} \\ 
(0.010)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{SWE} & $
\begin{array}{c}
0.185^{**} \\ 
(0.069)
\end{array}
$ & $
\begin{array}{c}
0.189^{**} \\ 
(0.008)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{UK} & $
\begin{array}{c}
0.508^{**} \\ 
(0.157)
\end{array}
$ & $
\begin{array}{c}
0.508^{**} \\ 
(0.018)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{USA} & $
\begin{array}{c}
0.173^{**} \\ 
(0.061)
\end{array}
$ & $
\begin{array}{c}
0.173^{**} \\ 
(0.009)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{R$^2$} & 0.109 & 0.109
\end{tabular}
}} 
\]
}}\newpage\ 

$\fbox{%
\begin{tabular}[b]{lc|cc}
\multicolumn{4}{l}{TABLE 5} \\ \hline\hline
\multicolumn{4}{l}{} \\ 
\multicolumn{4}{l}{TFP Growth Estimations; 240 Observations} \\ 
\multicolumn{4}{l}{} \\ \hline
\multicolumn{1}{l|}{} & \multicolumn{1}{c|}{$%
\begin{array}{c}
\text{General} \\ 
\text{Spillover}
\end{array}
$} & \multicolumn{2}{|c}{$%
\begin{array}{c}
\text{General and Trade-} \\ 
\text{Spillover}
\end{array}
$} \\ \hline
\multicolumn{1}{c|}{} & \multicolumn{1}{c|}{$\beta _v$} & \multicolumn{1}{c}{
$\beta ^I$} & $\beta ^{II}$ \\ \hline
\multicolumn{1}{l|}{CAN} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.426^{**} \\ 
(0.156)
\end{array}
$} & \multicolumn{1}{c}{$%
\begin{array}{c}
0.389^{*} \\ 
(0.231)
\end{array}
$} & $%
\begin{array}{c}
-13.61^{**} \\ 
(4.30)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{FRA} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.513^{**} \\ 
(0.139)
\end{array}
$} & \multicolumn{1}{c}{$%
\begin{array}{c}
0.398^{**} \\ 
(0.181)
\end{array}
$} & $%
\begin{array}{c}
4.11 \\ 
(3.39)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{GER} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.252^{**} \\ 
(0.062)
\end{array}
$} & \multicolumn{1}{c}{$%
\begin{array}{c}
0.126 \\ 
(0.083)
\end{array}
$} & $%
\begin{array}{c}
-1.24 \\ 
(0.82)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{IT} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.156^{**} \\ 
(0.052)
\end{array}
$} & \multicolumn{1}{c}{$%
\begin{array}{c}
0.102^{*} \\ 
(0.061)
\end{array}
$} & $%
\begin{array}{c}
-2.10 \\ 
(1.43)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{JAP} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.167^{**} \\ 
(0.080)
\end{array}
$} & \multicolumn{1}{c}{$%
\begin{array}{c}
0.129 \\ 
(0.086)
\end{array}
$} & $%
\begin{array}{c}
1.44 \\ 
(2.28)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{SWE} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.185^{**} \\ 
(0.069)
\end{array}
$} & \multicolumn{1}{c}{$%
\begin{array}{c}
0.165^{*} \\ 
(0.090)
\end{array}
$} & $%
\begin{array}{c}
-1.22 \\ 
(2.19)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{UK} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.508^{**} \\ 
(0.157)
\end{array}
$} & $%
\begin{array}{c}
0.310 \\ 
(0.189)
\end{array}
$ & $%
\begin{array}{c}
-5.12 \\ 
(6.19)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{USA} & \multicolumn{1}{c|}{$%
\begin{array}{c}
0.173^{**} \\ 
(0.061)
\end{array}
$} & $%
\begin{array}{c}
0.157^{**} \\ 
(0.067)
\end{array}
$ & $%
\begin{array}{c}
-0.39 \\ 
(0.84)
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{\=R$^2$} & 7.8 & \multicolumn{2}{|c}{9.6}
\end{tabular}
}${\scriptsize \ }

\end{document}