Endogenous Growth Theory

The traditional Solow model of economic growth has proved quite useful, but it enαogeno^us nevertheless has at least one serious shortcoming as a model of economic growth.

According to the Solow model, productivity growth is the only source of long-run

growth of output per capita, so a full explanation of long-run economic growth requires an explanation of productivity growth. The model, however, simply takes the rate of productivity growth as given, rather than trying to explain how it is determined. That is, the Solow model assumes, rather than explains, the behavior of the crucial determinant of the long-run growth rate of output per capita. In other words, in the Solow model, productivity is an exogenous variable.

In response to this shortcoming of the Solow model, a newer branch of growth theory, endogenous growth theory, has been developed to try to explain produc­tivity growth—and hence the growth rate of output—endogenously, or within the model.²⁵ As we will see, an important implication of endogenous growth theory is that a country's long-run growth rate depends on its rate of saving and investment, not only on exogenous productivity growth (as implied by the Solow model).

Here we present a simple endogenous growth model in which the number of workers remains constant, a condition implying that the growth rate of output per worker is simply equal to the growth rate of output. Our simple endogenous growth model is based on the aggregate production function

Y = AK, (6.12)

where Y is aggregate output and K is the aggregate capital stock. The parameter A in Eq. (6.12) is a positive constant. According to the production function in Eq. (6.12), each additional unit of capital increases output by A units, regardless of how many units of capital are used in production. Because the marginal product

²⁵Two important early articles in endogenous growth theory are Paul Romer, “Increasing Returns and Long-Run Growth,” Journal of Political Economy, October 1986, pp.

Endogenous growth theorists have provided a number of reasons to explain why, for the economy as a whole, the marginal productivity of capital may not be diminishing. One explanation emphasizes the role of human capital, the econo­mists' term for the knowledge, skills, and training of individuals. As economies accumulate capital and become richer, they devote more resources to "investing in people," through improved nutrition, schooling, health care, and on-the-job train­ing. This investment in people increases the country's human capital, which in turn raises productivity. If the physical capital stock increases while the stock of human capital remains fixed, there will be diminishing marginal productivity of physical capital, as each unit of physical capital effectively works with a smaller amount of human capital. Endogenous growth theory argues that, as an econo­my's physical capital stock increases, its human capital stock tends to increase in the same proportion. Thus, when the physical capital stock increases, each unit of physical capital effectively works with the same amount of human capital, so the marginal productivity of capital need not decrease.

A second rationalization of a constant marginal productivity of capital is based on the observation that, in a growing economy, firms have incentives to undertake research and development (R&D) activities.

Having examined why a production function like Eq. (6.12) might be a reason­able description of the economy as a whole, once factors such as increased human capital and research and development are taken into account, let's work out the implications of this equation. As in the Solow model, let's assume that national saving, S, is a constant fraction s of aggregate output, AK, so that S = sAK. In a closed economy, investment must equal saving. Recall that total investment equals net investment (the net increase in the capital stock) plus depreciation, or I = ΔK + dK. Therefore, setting investment equal to saving, we have

∆K + dK = sAK. (6.13)

Next, we divide both sides of Eq. (6.13) by K and then subtract d from both sides of the resulting equation to obtain the growth rate of the capital stock.

Because output is proportional to the capital stock, the growth rate of output, equals the growth rate of the capital stock,. Therefore, Eq. (6.14) implies

Equation (6.15) shows that, in the endogenous growth model, the growth rate of output depends on the saving rate s. As we are assuming that the number of workers remains constant over time, the growth rate of output per worker equals

the growth rate of output given in Eq.

The endogenous growth theory approach appears promising in at least two dimensions. First, this theory attempts to explain, rather than assumes, the econo­my's rate of productivity growth. Second, it shows how the long-run growth rate of output may depend on factors, such as the country's saving rate, that can be affected by government policies. Many economists working in this area are opti­mistic that endogenous growth theory will yield further insights into the creative processes underlying productivity growth, while providing lessons that might be applied to help the poorest nations of the world achieve substantially higher stan­dards of living.

6.4