2. Solow model with Human capital.

Consider the following Solow growth model with human capital a la Mankiw, Romer

and Weil (1992). "A Contribution to the Empirics of Economic Growth," Quar-

terly Journal of Economics 107, 407-437. They treated physical and human capital

symmetrically

Production function: Y(t) = (A(t)L(t))¹-a-³H(t)³K(t)ª, a, 3 € (0, 1), a + ß < 1.

Capital accumulation: K(t) = 8kY(t) — 5K(t), 6, 8k € (0,1).

Technical progress: A(t) = est A(0).

Population growth: L(t) = entL(0).

Human capital accumulation: Ĥ(t) = 8HY(t) - 5H(t), 6, 8H € (0,1).

Society invests SH and SK percent of its total income Y in human capital and physical

capital, respectively.

a. What is the long run (Balanced Growth Path) growth rate of output per capita.

Does it depend on sh?

1

b. Write down the stationary system and find out the steady-state level of output,

physical and human capital per unit of efficiency labor. Show the dynamics of

this system.

c. This model augmented with human capital can be tested empirically with cross-

country data if we assume that all countries are in the steady-state. Derive a

log-linear regression equation for output per worker in the long run.

d. Discuss the empirical findings of Mankiw, Romer and Weil (1992). Also, what

are the main concerns with their empirical strategy?