A model of endogenous growth that elucidates the complexity of South–North convergence

Abstract

This North–South model of Schumpeterian endogenous growth combines a market, productivity and knowledge effect. Depending upon the interaction of these effects, various convergent and divergent South–North growth paths occur: for example, full or partial convergence of the Southern technology level to the Northern one, conditional convergence or divergence depending upon the Southern initial technology level and absorptive capacity, higher or lower as well as decreasing or increasing growth rates during the phase of catching up, and equal or higher growth rates of the South compared to the North after catching up. This set of growth paths can better explain the diversity of the empirical observations for economies at different income and technology levels than those generated by existing models. In this new model, convergence based on North–South trade and associated flows of patents (innovations) is guaranteed if the knowledge effect dominates the productivity effect. A larger Southern market expands the area of convergence and can prevent divergence. Not only a larger Southern market, but also a higher Southern steady state growth rate benefit the North so that convergence is desirable for both, the South and the North.

Keywords:

• Schumpeter
• endogenous growth
• technology diffusion
• convergence

JEL Classifications:

• F17
• O11
• O33
• O41

Acknowledgements

I thank Johann Grüneweg, Michael Jakob, Marian Leimbach and the anonymous reviewers for their helpful comments.

Notes

1. For example, it is more difficult to raise the speed of a microprocessor once the speed has already come close to the technically possible limit at a later stage of development than at an early stage.

2. Different to an endogenous growth model with horizontal product differentiation, an innovation (a patent) holds only for a limited period of time in this model with vertical product differentiation through Schumpeterian creative destruction. Thus, profits are only gained within this period, not in form of a profit stream until infinity.

3. The derivative of a power function yields a marginal effect, which increases the original exponent, here β_X, no matter whether the basis is above or below unity, as long as the basis is positive. One can think of a constant-returns-to-scale Cobb–Douglas function, which generates reasonable outcomes, no matter the input values are above or below unity. In a dynamic set-up with knowledge accumulation, the marginal impact of trade and associated innovations creates a shadow price like the marginal product of a factor determines its price. This marginal impact matters for resource allocation and drives the results.

4. Intermediate goods also enter the Southern production function as a necessary input. Thus, production would cease if no intermediate goods were delivered because of a productivity too low. To prevent this effect, one may add a constant term to the intermediate goods input x_st in the production function. Such a constant term may represent any local substitutes for x_st. Without loss of generality, we leave this constant out in the calculations for the sake of mathematical simplicity.

5. Since the asymptotic behavior matters for divergence, it is not relevant whether the initial value of is above or below unity.

6. This can be verified by inserting in equations (29(29) ) and (30).