Conclusion

Externalities are not theoretically necessary to sustain growth. But they appear essential for understanding why many countries grow at similar rates despite differing investment rates.

Because diffusion is not costless, however, differences in knowledge investments may explain a significant portion of income differences across countries. We show that mod­est barriers to technology adoption could account for differences in TFP of a factor of four or more, as observed in the data. But we have not documented such barriers to knowledge diffusion in practice. We consider this a priority for future research. A related issue is that the high power of the model in explaining large productivity differences from small barriers to technology adoption comes at a cost, namely that the transition from one steady state to another after a discrete change in barriers takes a long time. This is what allows small changes in barriers to have large steady-state effects without implying huge social rates of return to research in poor countries. But it implies that the model is not very useful in understanding miracles. Perhaps a different formulation of the “benefits of backwardness” in Equation (4.2) would allow for a more attractive balancing of steady state and transition properties.

We have also left for future research the identification of the primary channels of international knowledge spillovers. Trade, joint ventures, FDI, migration of key person­nel, and imitation may all play important roles. See Keller (2004) for a survey of recent empirical work on this topic. A model with trade would lead naturally to some countries having a comparative advantage in doing innovative R&D and other countries focusing on adoption and imitation R&D. The evidence on international patenting supports the notion that innovative R&D is concentrated in rich countries. Of course, countries can imitate other imitators as well as the original innovators. We hope to see future research documenting not only the vehicles for knowledge diffusion, but their specific routes.

Acknowledgements

For helpful comments we are grateful to Bob Hall, Chad Jones, Robert Lucas, Ben Malin, Romans Pancs, and Paul Romer.