Monthly Archives: August 2014

Malthusian regime: Introduction

This paper examines the evolution of the relationship between population growth, technological change, and the standard of living. It develops a unified model that enconv passes three distinct regimes that have characterized the process of economic development. We call these regimes “Malthusian,” “Post-Malthusian,” and “Modern Growth.” The analysis focuses on two differences between these regimes: first, in the behavior of income per capita, and second, in the relationship between the level of income per capita and the growth rate of population.

The modern growth regime is characterized by steady growth in both income per capita and the level of technology. In this regime there is a negative relationship between the level of output and the growth rate of population: the highest rates of population growth are found in the poorest countries, and many rich countries have population growth rates near zero.


Patent citations offer a rich repository of information about the locus of technological activity, and the relationships among activities in different places. Systematic use of these data requires, however, careful attention to the need to control for time and technology field effects that otherwise have an impact on simple comparisons across countries or other units of observation. Fortunately, the patent data are sufficiently numerous that detailed controls can, in fact, be implemented. Though any model obviously imposes structure on the data, one can allow for complex patterns of interactions among effects. Indeed, readers of this paper have no doubt already thought of additional interactions that we could have estimated with our data but did not. We hope that, as these data become more widely available, other researchers will pursue questions that we have not considered read.


An issue that remains for further study is the extent to which the results may be tainted by systematic biases in the patent approval process that generates citations. Our maintained hypothesis is that the citation process itself does not differ depending on the domicile of the inventor. One possible bias is introduced by the fact that we are examining citations within the U.S. patent system. If a given invention is covered by patents issued in more than one country, then the obligation to cite this invention can be discharged by a citation to any of the members of the patent “family” around the world that cover the same invention in different countries. Further, U.S. inventions are often patented in the U.S. but not in Japan, while Japanese inventions patented in the U.S. are usually also patented in Japan.

As a result, localization of citations to U.S. patents might be explained by a tendency of Japanese inventors to cite the Japanese patent covering prior art rather than the U.S. patent on the same invention, combined with the fact that such a patent will often be unavailable for U.S.-invented patents. This would not, however, explain why U.S. patents issued to Japanese inventors are more likely to cite other U.S. patents issued to Japanese inventors than they are to cite U.S. patents issued to German inventors; if anything, the bias introduced by patent families would suggest that our estimates of localization for citations to countries other than the U.S. are understated.


In our view, the results in this paper demonstrate that there is much to be learned about international knowledge diffusion from patents and their citations. Despite the fact that we focus on patents granted by the U.S. patent office, rich patterns of interaction are revealed, including interesting findings about the diffusion of citations within and between countries other than the U.S. Some widely-held notions about differences in the inventive processes across countries were confirmed, such as the reliance of the Japanese on a relatively recent technological base. Others are less obvious, such as the strong symmetry between citing and cited intensities, and the greater proximity of Japan to the U.S. relative to Europe.


All of the results discussed so far derive from estimation of the “full” model of Eq. 3. For comparison to our earlier paper, as well as for the light it sheds on the interaction of different effects, it is useful to consider briefly how the results differ in less complete or different models. In particular, our earlier research did not exclude self-citations, and did not include the “technological proximity” effect. These effects are interesting in their own right, and may also be expected to interact in important ways with geographic localization. Table 5 summarizes the results with and without these non-geographic effects. Generally, excluding self-cites significantly reduces the apparent geographic localization, as well as reducing the extent to which that localization “fades.”

That is, the citation intensity from other countries, relative to the domestic citation rate, is lower in columns 1 and 2 than in columns 3 and 4 in the first year, but is higher in columns 1 and 2 than in columns 3 and 4 after 20 years. What this means is that self-cites are highly geographically localized (which should not be a surprise) and generally come at shorter lags (Trajtenberg, Henderson and Jaffe, 1997). Thus including them creates strong localization particularly in early years; excluding them dilutes localization; this weaker initial localization then also fades less.


Comparing Figure 2 to Figure 1 shows some of the effects of controlling for nongeographic effects. First, as suggested above, the “tails” in the estimated functions in Figure 2 are much thinner. Second, while geographic localization is clearly present in Figure 2, its magnitude is noticeably diminished, with the citation frequency for other countries at the modal lag being roughly 55-75% of U.S.-U.S. as compared to 40-60%.

In terms of the effects seen numerically in Table 3, the Figures show the “speed” of Japan, as its line typically peaks early and then fades, and the “slowness” of the U.S., whose predicted frequency of citation is the highest after long lags in all of the pictures. The graphs also show that the differences among non-domestic citing countries are always smaller than the localization effect that separates domestic citations from foreign ones.

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