Chapters 7 and 8 (Part II)

Objective of this lecture

• Learn about how to explain the differences in growth performance of different countries using the Solow model

• Learn about TFP growth and the Solow residuals

Graphical view

sk

k*

Investment, break-even investment

Capital per effective labor, k

(n +g +) k

k = s k (n +g+)k

k>0

k<0

Graphical view(not in textbook)

k = k /k = s k (n +g+)

n+g+

sk

k*

Rate of inflow, rate of outflow

Capital per effective labor, k

k>0

k<0

Steady-State Growth Rates in the Solow Model (to be derived in class)

n + gY = y E L Total output

g(Y/ L ) = y E Output per capita

0y = Y/ (L E )Output per effective labor

0k = K/ (L E )Capital per effective labor

Steady-state growth rate

SymbolVariable

Explaining the variety of growth experiences If all the countries were in their respective

steady states, we could explain their differences in growth rate of real GDP per capita only in terms of differences in technological growth rates g.

But surely, a lot of developing countries are still below their steady states. In this case, we could explain their differences in growth performance by looking at other differences.

Growth Rates below or beyond the steady state (to be derived in class)

n + g + kY = y E L Total output

g + k(Y/ L ) = y E Output per capita

ky = Y/ (L E )Output per effective labor

kk = K/ (L E )Capital per effective labor

Growth rate below or beyond the steady state

SymbolVariable

Explaining the variety of growth experiences In what follows, we make use of the

graphical analysis of the dynamic equation

k = k /k = s k (n +g +)

to explain the variety of growth experiences

We focus on the differences in the distance from the steady state, the savings rate s, population growth rate n and the technological growth rate g as explanatory variables.

Savings rates and growth performance (not in textbook)

k = k /k = s k (n +g+)

n+g+

s1 k

k1*

Rate of inflow, rate of outflow

Capital per effective labor, k

k 1

k1=k2

k 2

s2 k

k2*

Savings rates and growth performances

• Growth rate of real GDP per capita is given by

Y/L = g + k

• From the above analysis, other things equal (so g and are treated as the same), the higher the savings rate, the higher k is. Hence, the higher

the current growth rate of real GDP per capita Y/L.

Population growth and economic growth performance (not in textbook)

k = k /k = s k (n +g+)

n1+g+

s k

k1*

Rate of inflow, rate of outflow

Capital per effective labor, k

k 1

k1=k2

k 2

k2*

n2+g+

Population growth and economic growth performances

• Growth rate of real GDP per capita is given by

Y/L = g + k

• From the above analysis, other things equal (so g and are treated as the same) the higher the population growth rate, the lower k is. Hence,

the lower the current growth rate of real GDP per capita Y/L.

Convergence(not in textbook)

k = k /k = s k (n +g+)

n+g+

sk

k*

Rate of inflow, rate of outflow

Capital per effective labor, k

k poor

kpoor krich

k rich

Convergence

• Growth rate of real GDP per capita (Y/L) is given by

Y/L = g +k

• From the above analysis, other things equal, the farther a country is from the steady state, the higher the growth rate of real GDP per capita.

• Therefore, Solow model predicts that, other things equal, “poor” countries (with lower Y/L and K/L ) should grow faster than “rich” ones.

Absolute Convergence If absolute (or unconditional) convergence

truly happens, then the income gap between rich & poor countries would shrink over time, and living standards “converge.”

In real world, many poor countries do NOT grow faster than rich ones. That is, absolute (or unconditional) convergence is not generally observed. Does this mean the Solow model fails?

Conditional Convergence• No, because “other things” aren’t equal.

In samples of countries with similar savings & pop. growth rates, income gaps shrink about 2%/year.

In larger samples, if one controls for differences in saving, population growth, and human capital, incomes converge by about 2%/year.

• What the Solow model really predicts is conditional convergence - countries converge to their own steady states, which are determined by saving, population growth, and education. And this prediction comes true in the real world.

Long-run and transitional growth

From the above analyses, the savings rate, the population growth rate and the convergence effect only affect the term k in

Real GDP per capita growth rate = g + k

Eventually, as economies reach their respective steady states, k=0. Real GDP per capita growth rate in the long run is only affected by g. Higher savings rate, lower population growth rate and lower initial real GDP per capita only lead to higher real GDP per capita growth rate in the meantime but not in the eventual steady states.

Technological growth rates and growth performances Though savings rate and population growth

rate only affect real GDP per capita growth rate in the transition, technological growth rate affects real GDP per capita growth rate both in the transition and in the long run.

Obviously, in the long run the growth rate of real GDP per capita is given by g. So higher g means higher real GDP per capita growth rate. How does different g affect transitional growth?

Technological growth and economic growth performance (not in textbook)

k = k /k = s k (n +g+)

n+g1+

s k

k1*

Rate of inflow, rate of outflow

Capital per effective labor, k

k 1

k1=k2

k 2

k2*

n+g2+k=k2-k1 =g1-g2

Technological growth and economic growth performance (not in textbook) Although country with a higher technological

growth g1 has a lower k, it turns out that such a country commands a higher Y/L. From the graph,

k2-k1 =g1-g2

Now, Y/L=g+k. So,

Y/L1-Y/L2 =(g1+k1) – (g2+k2)

=(g1–g2)+(k1-k2)

=(g1–g2)- (g1–g2)

=(1-)(g1–g2)>0

Case Study: the East Asian Miracles

• East Asian miraculous performance: is it purely catch-up effect or can such miraculous growth of 6% be sustained?

• Surely, East Asia might have done everything right: high savings, attraction of foreign investment through secure property rights, promotion of education, outward-oriented trade policy, control of population growth.

The East Asian Miracles

• Such good policies will lead to growth increase for a while, but eventually diminishing returns will set in. For sustained growth performance, one needs technological improvement.

• In practice, technological improvement is measured by something called total factor productivity (TFP) growth rate.

TFP Think about the Cobb-Douglas

production function Y=KEL). We could rewrite it as

Y=A KL

where A=E. We call A the total factor productivity (TFP).

The Solow ResidualFrom Y=A KL

We use the rules 1-3 in mathematical digression to obtain

Y =A+ K + L

To obtain the TFP growth rate A) we rearrange the above equation to get

A= Y - K - L

The TFP growth rate obtained this way is called the Solow residual

TFP growth rates across countries

Country TFP growth per year 60-90

Country TFP growth per year 66-90

Canada 0.46% Hong Kong 2.2%

France 1.45% Singapore -0.4%

Germany 1.58% South Korea

1.2%

Italy 1.97% Taiwan 1.8%

Japan 1.96%

U.K. 1.3%

U.S. 0.41%

Implications of TFP growth findings The results from Young (1995) and later

on popularized by Krugman imply that the East Asian “miraculous” growth is nothing “mysterious”. TFP growth of these E. Asian countries is similar to TFP growth of the more advanced countries.

The prediction is that DMR will eventually set in and growth of these countries will diminish as time passes. (Many see the E. Asian debacle in 1998 as a sign of DMR setting in.)