What to make of the Kaldor-Verdoorn law?

The Kaldor-Verdoorn law refers to a positive but less than one-for-one relationship between the growth rates of output and labor productivity, with causality running from the former to the latter. Empirical research has affirmed such a relationship and have found that the Kaldor-Verdoorn coefficient lies between 0 and 1. But the interpretation of this finding remains unclear. In this paper, we present a model to derive the Kaldor-Verdoorn law. Our results show that the Kaldor-Verdoorn coefficient is jointly determined by the elasticity of factor substitution, labor supply elasticity, the profit share and the increasing returns to scale (or demand-induced technical change) parameter. Hence, estimated Kaldor-Verdoorn coefficients cannot be used, on their own, to infer the presence of aggregate increasing returns to scale - other than in very special cases. We also show that, perhaps surprisingly, an economy without aggregate increasing returns to scale (or without any demand-induced technical progress) can generate a Kaldor-Verdoorn coefficient that lies between 0 and 1.