Part Human Capital 3.8 Introduction

The discussion in Section 3.6 suggests that theories based on knowledge accumulation are unlikely to explain cross-country differences in incomes. This part of the chapter therefore investigates another strand of the new growth theory: models that emphasize the accumulation of human capital.

Although the acquisition of human capital by a worker involves learning, there is a clear conceptual distinction between human capital and abstract knowledge. Human capital consists of the abilities, skills, and knowledge of particular workers. Thus, like conventional economic goods, human capital is rival and excludable. If, for example, an engineers full effort is being devoted to one activity, that precludes the use of his or her skills in another. In contrast, if an algorithm is being used in one activity, that in no way makes its use in another more difficult or less productive.

The models of this section therefore resemble the Solow model (and the Ramsey and Diamond models) in assuming constant returns to scale. Thus they do not provide candidate explanations for worldwide economic growth. (An exception occurs in Section 3.10, where the case of increasing returns is discussed briefly.) But the models differ from the Solow model in implying that moderate changes in the resources devoted to physical and human capital accumulation may lead to large changes in output per worker. As a result, they have the potential to account for large differences across countries in incomes.

To see why introducing human capital has the potential to greatly increase our ability to account for cross-country differences, recall that in models with only physical capital, the effect of a change in the saving rate on output depends on capitals share. In the Solow model, the long-run elasticity of output with respect to the saving rate is a /(1 -a), where a is capitals share (see equation [1.22]). If capitals share is moderate, this elasticity is not large. In terms of our familiar Solow-model diagram, a moderate value of capitals share means that s/(k) is relatively curved, and thus that an in-

Kremer argues that, since Australia is largely desert, these figures understate Australias effective population density. He also argues that direct evidence suggests that Australia was more technologically advanced than Tasmania. Finally, he notes that there was in fact a fifth separate region. Flinders Island, a 680-square-kilometer island between Tasmania and Australia. Humans died out entirely on Flinders Island around 3000 . .

8 million for Australia, and 0.1 million for Tasmania. Population estimates for the four regions in 1500 imply densities of approximately 4.9 people per square kilometer for Eurasia-Africa, 0.4 for the Americas, and 0.03 for both Australia and Tasmania.

(n-i-g-hg)k

•OLDAk)

FIGURE 3.12 How capitals share affects the impact of a change in the saving rate in the Solow model

crease in s does not have a large impact on *. This is shown in Panel (a) of Figure 3.12. In addition, the moderate value of capitals share means that fik*) is not very responsive to *. The end result is that output is not greatly affected by changes in the saving rate.

If capitals share is close to 1, on the other hand, sf{k) is nearly linear; thus a small increase in s causes a large increase in k*. This is shown in Panel (b) of the figure. The increase in capitals share also increases the effect of * on f (k*). Thus in this case the long-run elasticity of output with respect to the saving rate is large. And in the extreme case where capitals share is 1 (such as in the linear growth models discussed in the first part of the chapter), a change in s has a permanent effect on the growth rate of output; thus its effect on the level of output grows without bound.

Assumptions

Output is given by

Y(t) = K{trH{tf[A(mt)V--, a>0, )8 > 0, a + )8 < 1, (3.43)

where H is the stock of human capital. I continues to denote the number of workers; thus a skilled worker supplies both 1 unit of I and some amount of Note that (3.43) implies that there are constant returns to K, H, and I together.

We make our usual assumptions about the dynamics of and I:

k{t) = sk Y(t), (3.44)

i(f) = ), (3.45)

where we now use Sk to denote the fraction of output devoted to physi-

The model follows Mankiw, D. Romer, and Weil (1992). For other models of human capital and growth, see Lucas (1988); Azariadis and Drazen (1990); Becker, Murphy, and Tamura (1990); Rebelo (1991); Kremer and Thomson (1994); and Problem 3.15.

-A way of writing (3.43) that may be more intuitive is = k"(h/ 1) (. 1 -. This formulation expresses output in terms of capital, labor, and human capital per worker.

Some of workers earnings reflect acquired skills rather than their inherent abilities. Thus recognizing the existence of human capital implies that we must raise our estimate of the share of income that is paid to capital of all kinds. In addition, the accumulation of human capital is broadly similar to the accumulation of physical capital: devoting more resources to the accumulation of either type of capital increases the amount of output that can be produced in the future. Thus, as the analysis that follows shows, adding human capital to our models increases the output effects of changes in the resources devoted to capital accumulation, just as raising physical capitals share in the Solow model increases the output effects of changes in the saving rate. It is this fact that makes the models able to account for large cross-country differences in incomes.

3.9 A Model of Human Capital and Growth

We now turn to a simple model of physical and human capital accumulation and growth. Aside from the inclusion of human capital, the model resembles the Solow model with Cobb-Douglas production.