Economic Growth

Growth Accounting

Economic growth is an increase in output.

Y = A x F(K,N)

(change in Y)/Y = (change in A)/A + alphaK(change in K)/K + alphaN(change in N)/N

This equation can be used to measure empirically the contributions of the three sources of growth.

For the U.S from 1929-1982, the average annual growth rate of output was 2.92%.

contribution of labor growth: 1.34%

contribution of capital growth: 0.56%

contribution of productivity growth: 1.02%

Productivity Slowdown

Productivity growth averaged -0.67% a year between 1973 and 1979.

• 1. decline in the quality of the labor force

  2. excessive government regulation

  3. oil price shocks

Neoclassical Growth Model

let

Nt = size of the labor force in year t

n = growth rate of the labor force

Kt = capital stock in year t

Yt = output produced in year t

It = gross investment in year t

Ct = consumption in year t

Assume a closed economy with no government so that Ct = Yt - It.

We want to understand how these variables change over time:

• • yt = Yt/Nt = output per worker

  • ct = Ct/Nt = consumption per worker

  • kt = Kt/Nt = capital stock per worker = capital-labor ratio

The steady state is a situation in which output per worker, consumption per worker, and capital per worker are constant. In the absence of productivity growth, an economy reaches a steady state in the long run with output growing at the population growth rate.

Kt/Nt is constant in the steady state. Therefore, Kt must grow at the same rate as Nt.

Let d = rate of depreciation

(1) It = (n + d)Kt in the steady state

(2) Ct = Yt - (n + d)Kt in the steady state

divide equation (2) by Nt

(3) c = f(k) - (n + d)k

(assume that an increase in k causes c to increase)

Let saving = St = sYt.

Goods market equilibrium requires St = It. This means that sYt = (n + d)Kt in a steady state. Dividing both sides by Nt gives

(4) sf(k) = (n + d)k in the steady state.

Equation (4) says that saving per worker equals investment per worker in the steady state. The value of k given by equation (4), k*, is the steady state capital-labor ratio.

Once the economy capital-labor ratio reaches k*, it will stay there forever.

What Determines Long-Run Living Standards and Growth Rates

1. saving rate (s)

2. population growth (n)

3. Productivity growth

Convergence

Neoclassical growth theory predicts that poor countries will grow more rapidly than rich countries. The theory assumes that technological advances can spread easily and that capital and labor have diminishing returns. The idea is that poor regions will adopt advanced technology to improve productivity. Poor countries tend to have low capital per worker and output per worker. So, diminishing returns have not yet set in and the returns to capital are high. Therefore, poor countries will attract lots of investment so that capital per worker grows rapidly, giving rapid growth in output per worker.

Rich areas have a high capital-worker ratio so there are diminishing returns to capital. Therefore, there are low returns to capital and little investment. So, there is a low growth of output.

There is strong evidence for convergence within the U.S. and among advanced industrial countries. But, there has been little tendency for poor countries to grow more rapidly than rich countries. Differences in human capital may explain its absence.

Endogenous Growth Theory

criticisms of neoclassical model:

• 1. assumes that output growth rate is exogenous

  2. absence of convergence across nations

Endogenous growth theory makes the output growth rate endogenous, that is, determined by the theory. There are two ways to make growth endogenous:

• 1. can make productivity growth endogenous by assuming, say, that it is affected by the proportion of income devoted to R&D spending

  2. can assume that there are constant or increasing returns to labor or capital

For example,

Let Y = aK and n=d=0,

then change in K = sY = saK.

So, growth rate of the capital stock = growth rate of output = sa. The steady state growth rate is affected by the rate of savings. Countries with different saving and investment rates will have persistent differences in growth rates. Endogenous growth theory predicts the absence of convergence, but studies have found conditional convergence. The impact on growth of different saving rates is transitory.