Introduction

Despite its role as the centerpiece of modern growth theory, the Solow model is decid­edly silent on some of its basic questions: Why is average growth in per capita income so much higher now than it was 200 years ago? Why is per capita income so much higher in the member countries of the OECD than in the less developed countries (LDC) of the world? The standard implementation of the Solow model provides no answers for these questions except, perhaps, for differences across time and across countries in the production possibility set.

This basic weakness in the Solow model (and its followers) was the driving force behind the development of the class of endogenous growth models. This literature has been wide and varied, with the models developed ranging from perfectly competitive, convex models to ones featuring a range of types of market failures (e.g., increasing returns, external effects, imperfectly competitive behavior by firms, etc.). A common feature that has been emphasized throughout is knowledge, or human capital, and its production and dissemination. In some cases, this has been directly treated in the mod­eling, in others it has been more tangential, an important consideration for quantitative development, but less so for qualitative work. That this focus is essential follows from the fact that the Solow model already accurately reflects the quantitative limits of using models with only physical capital.

In this paper we limit ourselves to studying neoclassical models. By this we mean models with convex production sets, well behaved preferences and a market structure that is consistent with competitive behavior. Therefore, we do not review the large litera­ture that addresses the role of externalities and non-competitive markets. As it turns out, most of the basic ideas behind this literature can be expressed in simple, convex models of aggregate variables without uncertainty. These are the models that are the first focus of this chapter. They have proved both highly flexible and easy to use. With them, we can give substance to statements like those above that property rights and other govern­mental institutions are key to long run growth rates in a society. Most of this branch of the literature is well known by now, and much of it appears on standard graduate macro reading lists. Accordingly, our discussion will be fairly brief.^[4] One important, and as of yet unresolved issue, is the size of the growth effects of cross-country differences in fiscal policy. Thus, our review of the standard convex model is complemented with a discussion of the more recent findings about the quantitative effects of taxes (and gov­ernment spending) on growth.

Much less is known about the answers to these questions at the present time and that knowledge that does exist is much less widespread. For this reason, we present a fairly detailed discussion of the properties of stochastic, convex models of endogenous growth. To this end, we study models in which technologies and policies are subject to random shocks. We characterize the effects of differential amounts of uncertainty on average growth. We show that increased uncertainty can increase or decrease average growth depending on both the parameters of the model and the source of the uncertainty. A separate, but related topic, is the business cycle frequency properties of these models. This is left to future work.

In Section 2, we lay out the basics of the class of neoclassical (i.e., convex) mod­els of endogenous growth. We show how differences in social institutions across time and across countries can give rise to different performance, even over the very long run. We also lay out some of the interpretations of the model, including human capi­tal investment and innovation and knowledge diffusion sectors, that lend richness to its interpretation. Section 3 discusses properties of the models when uncertainty is added, and shows how this can affect the long run growth rate of an economy.

2.