Verspagen, Bart

English

Research Papers in Economics

On Technological Convergence among
Countries. A Comment on Patel and Pavitt
BART VERSPAGEN
In a recent article, Patel and Pavitt (1994) presented statistical evidence
related to the hypothesis of 'striking differences—even divergences—in the
rate and direction of technological accumulation in the industrial countries'
(p. 770). Although the theoretical framework Patel and Pavitt presented to
explain their statistical findings is not without appeal, one might argue that it
tends to put a large degree of emphasis upon those factors in technological
development that have been identified as causing 'cumulativeness' and
persistent differences between countries, or, at a lower level of aggregation,
firms. In previous work with Luc Soete (Soete and Verspagen, 1993, 1994), I
stressed that the empirical facts tend to support a hypothesis which, contrary
to Patel and Pavitt, takes into account a mix of factors related to the
international diffusion of knowledge and convergence of national levels of
technology, investment and specialization structure on the one hand, and
cumulativeness of knowledge development and specialization patterns on the
other hand [see, for example, Dosi (1988) for an overview of these various
•o factors]. During recent decades (Soete and Verspagen, 1993, 1994) those
- factors related to convergence seem to have been slightly dominant in the
jj OECDarea.
I This conclusion is in obvious contrast with the one drawn in the work by
^ Patel and Pavitt (1994). In this note, I will argue that this contrast is due to
§ an interpretation of the empirical evidence by Patel and Pavitt which is at
5 least partly open to criticism. My comments will be focused on two of their
t
tables related to technological indicators at the country level.
Firstly, Patel and Pavitt, on the basis of their table 1, which gives the
1 standard deviation (SD) of industry-financed R&D to GDP ratios among 17
« advanced OECD countries, argued that 'there are no statistical signs of
i convergence in the industry-funded shares over time, since the standard
J deviation of the distribution has not decreased over time. On the contrary, it
3 © Oxford University Press 1996
897Technological Convergence among Countries: a Comment
has increased markedly in the 1980s, suggesting technological divergence
among countries' (p. 763).
The coefficient of variation (defined as the ratio of the mean of a
distribution to the SD) measures percentual deviations from the mean, rather
than the absolute deviations from the mean in the SD. In the convergence
debate, the coefficient of variation is therefore generally accepted as a more
useful indicator of convergence than the 'raw' SD (e.g. Dollar and Wolff,
1993). In the data by Patel and Pavitt, it is certainly true that the SD of
industry-financed R&D as a fraction of GDP has risen over time. However,
the same holds for the mean of the variable, so that we may expect the results
on convergence to differ between the coefficient of variation and the 'raw' SD.
This is documented in Table 1.
This table shows that the SD, compared with the mean, in fact fell
consistently over the 1967-1991 period. Although this result is not a robust
statistical test of convergence, it certainly shows that the conclusion of
divergence drawn by Patel and Pavitt is not supported when more appropriate
indicators are used.
The second point relates to their table 6, which documents correlations
between countries' technological specialization patterns as measured by the
so-called 'revealed technological advantage' index (RTA). It is worth recalling
that this index for country / and sector/ is defined as the share of/ in total
patenting from sector /, divided by the share of / in total patenting in all
sectors. A value of 1 indicates no particular specialization, whereas values
smaller (larger) than one indicate negative (positive) specialization of country
/ in sector/.
1 ,
Patel and Pavitt calculated RTA indices for 34 sectors and 19 countries, and
presented the correlation coefficients between the 171 meaningful pairs of
countrywise specialization patterns that arose. They found that 'only' 18% of
these 171 correlation coefficients were significantly positive, and on the basis
of this, they concluded that this 'confirms that countries tend to differ
markedly in their patterns of technological specialization' (p. 767).
Note that by definition, the weighted average of countries' RTA-indices in
a sector is 1, and the same holds for the weighted average of sectors'
RTA-indices in a particular country. Thus, if we set up a matrix of
RTA-indices for 34 sectors and 19 countries, as Patel and Pavitt did, we would
' This points to a well-known problem with RTA-Iike indices, namely that measures of negative
specialization are squeezed into the interval from 0 to 1, whereas positive specialization is measured on the
interval from 1 to infinity. In other words, the RTA index is asymmetric. This can be changed by taking
the log of the RTA, or by applying the transformation (RTA - 1)/(RTA + 1). Here I follow Patel and Pavitt
(1994) in not bothering to make any of these transformations, although the conclusions in this note are
not sensitive to that.
898Technological Convergence among Countries: a Comment
TABLE 1. Ratio of SD to Mean (Coefficient of Variation) of Industry-financed R&D to GDP
Ratios in 17 OECD Countries, 1967-1991
Ind. US Exd. US
1967 0.70 0.73
1971 0.60 0.62
1981 0.57 0.60
1991 0.52 0.54
Source: Calculations on che basis of Patel and Pavitt (1994, table 1).
expect that, on average, for each value > 1 in any particular row or column
of this matrix, there would be a value < 1 in the same row or column.
2 In
other words, the RTA index has been devised to express relative differences,
not similarities.
On average; therefore, one would expect that if one correlates two rows
from this RTA matrix, as Patel and Pavitt do, a negative correlation arises.
This only holds on average, though, because it is perfectly possible that, for
some technological or economic logic, certain countries are specialized in the
same fields as certain other countries. On average, however, not every country
can be specialized in the same area, so there must be a fairly large number of
negative correlations.
In order to get a more intuitive feeling of how many of the 171 correlation
coefficients could be expected to be positive or negative, I undertook a simple
Monte Carlo experiment. In this experiment, a 19 X 34 matrix of random
numbers was drawn from a uniform distribution on the interval [0,l).
} This
matrix was used to calculate the RTA indices, which were then correlated
in the 'country' dimension. The experiment was repeated 100 times with
different random seeds. The mean value of the fraction of (significantly)
positive and negative correlations is reported in Table 2.
The table confrrms the expectation that the majority of correlation
coefficients is negative. The number of significantly negative correlations is
also proportionally larger than the significantly positive ones. The standard
errors of the fractions are fairly small in comparison with the fractions
themselves, with the exception of the fraction of significantly positive
correlations. This shows that if countries' patenting were purely distributed
randomly over activities, one would on average expect a little less than
' Actually, this holds only if the country sizes are not extremely different.
' The random number generator in Borland Pascal 7.0 was used to set up the experiment.
899Technological Convergence among Countries: a Comment
TABLE 2. The Mean Value of the Fraction of Positive and Negative Correlations in the
Monte Carlo Experiment for a 19 X 34 Matrix of RTA Indices
Mean Standard error
Negative correlations 0.622 0.022
Significantly negative correlations 0.035 0.022
Positive correlations 0.378 0.008
Significantly positive correlations 0.013 0.016
Significant values are taken as values with P < 0.05, as in Patel and Pavitt.
two-thirds of the entries in the Patel and Pavitt correlation matrix to be
negative, with only a small proportion of them being significant (either
positive or negative).
4
It is obvious that the Patel and Pavitt matrix is not based upon random
numbers. For example, they found that 25.7% of all their correlation
coefficients were significant. The majority of those (18.1 percentage-points)
were significantly positive. Overall, they found that 60.8% of their correlation
coefficients were positive. Thus, compared with the results from the random
distribution, they found a relatively large number of (significantly) positive
correlations, whereas they based the above-cited conclusion with regard to the
'marked differences' between countries upon the supposed finding that there
were 'too few' significantly positive coefficients.
It is not obvious what their results, when interpreted correctly, imply
exactly. Whether the large number of positive correlations is due to an uneven
distribution in country size (as measured, for example, by the number of
patents taken out) or to some systematic factors behind the technological
development reflected in the patent statistics is not clear. There is, however,
a clear danger of getting stuck in tautologies when correlating RTA indices
across different dimensions, because the index itself has been divised to
measure 'relative' differences and not similarities. But above all, it is clear that
the • specific pattern of correlations observed by Patel and Pavitt is not an
indication of 'marked differences' between countries.
Overall, the conclusion must therefore be that, at least in these two cases,
which are the bulk of the 'macro' evidence in their paper, Patel and Pavitt's
conclusions with regard to cumulativeness and divergence of technological
levels cannot withstand closer inspection. It is beyond the scope of this note
* I also undertook experiments in which the distribution from which numbers were drawn was
(approximately) normal. This yields results which are almost exactly equal to those reported in Table 2.
900Technological Convergence among Countries: a Comment
to present more elaborate evidence supporting the opposite case of
convergence. To 'conclude that technological gaps among the OECD
countries are here to stay' (p. 759), seems, however, a bit too premature.
Acknowledgements
My research was made possible by a fellowship of the Royal Netherlands
Academy of Arts and Sciences. This note was written during my stay as a
visiting fellow at the University of Aalborg, Denmark. I have benefited from
discussions with Bent Dalum, Keld Laursen, Keith Smith and Gert
Villumsen.
References
Dollar, D. and E. N. Wolff (1993), Competitiveness, Convergence and Internationalization. MIT Press: Cambridge,
MA.
Dosi, G. (1988), 'Sources, Procedures and Microeconomic Effects o{\Daavavan,'Journal of Economic Literature,
26,1120-1171.
Patel, E and K. Pavitt (1994), 'Uneven (and Divergent) Technological Accumulation among Advanced
Countries: Evidence and a Framework for Explanation', Industrial and Corporate Change, 3, 739—787.
Soete, L. and B. \fcrspagen (1993), Technology and Growth: The Complex Dynamics of Catching Up,
Falling Behind and Taking Over,' in E. Szirmai, B. van Ark and D. Pilat (eds), Explaining Economic Growth.
Elsevier Amsterdam.
Soete, L. and B. Verspagen (1994), 'Competing for Growth: The Dynamics of Technology Gaps,' in L.
Pasinetti and R. Solow (eds), Economic Growth and the Structure of Long-Term Development. St Martin's Press:
London.
901

Competing for Growth: The Dynamics of Technology Gaps,'

Competitiveness, Convergence and Internationalization.

Technology and Growth: The Complex Dynamics of Catching Up, Falling Behind and Taking Over,'

Uneven (and Divergent) Technological Accumulation among Advanced Countries: Evidence and a Framework for Explanation',

On Technological Convergence among Countries. A Comment on Patel and Pavitt.

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On Technological Convergence among Countries. A Comment on Patel and Pavitt.

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