In this chapter we examine growth models in which the efficiency of labor is no longer entirely exogenous, but may be influenced either through positive externalities from the accumulation of physical capital, or through the accumulation of human capital, or even through the generation of new ideas and innovations. These models, under certain conditions, can lead to endogenous growth, unlike the models that we have analyzed so far.

Initially we present a growth model which is based on the assumption of positive externalities from aggregate capital accumulation on labor efficiency. The main idea that drives this model is learning by doing, an idea introduced to growth models by Arrow (1962). This assumption can, under certain conditions, lead to endogenous growth, as in Romer (1986).

In the learning by doing model, labor efficiency is a function of both exogenous technical progress, as well as aggregate capital per worker. Thus, the efficiency of labor, which is the same for all firms, depends on capital per worker in the rest of the economy. Because of learning by doing, as suggested by Arrow (1962), the accumulation of aggregate capital increases labor productivity both directly and indirectly, through “knowledge spillovers”, that have a direct effect on the efficiency of labor. It is assumed here that “knowledge” is like a public good, and that the accumulation of knowledge depends on the accumulation of aggregate capital.

An important consequence of this approach is that diminishing returns from capital accumulation set in more slowly, and that, under certain conditions, there may even be constant or increasing returns from capital accumulation. In these latter circumstances growth becomes endogenous and is determined by the rate of accumulation of aggregate physical capital.

To analyze the impact of the savings behavior of households in the process of endogenous growth, we combine this approach with the assumptions of the Solow model, for a fixed savings and investment rate, as well as with the savings assumptions of the Ramsey representative household model and the overlapping generations model of Blanchard and Weil.

We then present an alternative class of growth models, which emphasizes the dependence of labor efficiency on education and training, and the accumulation of human capital.

We start with a generalized Solow model, in which the accumulation of human capital is the result of spending on education and training. The model is due to Mankiw, Romer and Weil (1992), and generalizes the Solow model in two directions. First, labor efficiency depends in part on exogenous technical progress and in part on the accumulated human capital of workers. Second, the accumulation of human capital depends on spending on education and training, which is a fixed, exogenous share of total output. Thus, in this model, there is investment in both physical and human capital. Under certain conditions, this generalized Solow model can also lead to exogenous growth.

We also present an alternative model in which investment in human capital depends not on the share of income spent on education and training, but on the amount of time devoted to education and training. These models (Lucas 1988, Jones 2002) assume that workers spend part of their time in education and training, and that this investment of their time increases their human capital and the efficiency of labor. Under certain conditions, these models can also lead to endogenous growth.

Finally, we present a class of models in which technical progress is the result of investment in research and development. These models also emphasize the externalities associated with the production of new ideas and innovations that increase labor efficiency. Although models of research and development have existed since the late 1960s, their full economic implications for the functioning of markets were developed in the early 1990s, based on the work of Romer (1990). Under certain conditions, these models can also lead to endogenous growth.

It is worth noting that endogenous growth models do not necessarily imply convergence in per capita output, as the corresponding exogenous growth models. Initial conditions matter for the evolution of per capita output and income. However, the available empirical evidence from post-war international data (see Mankiw, Romer and Weil 1992 and Barro 1997) suggests that the issue of convergence of per capita incomes cannot be dismissed easily. The convergence observed can be explained by broader exogenous growth models, in which there is learning by doing, or accumulation of human capital and ideas and innovations, but not to an extent that completely neutralizes the diminishing returns from the accumulation of physical and human capital.

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