Transcript ch7&8 (Part II)

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
Investment,
break-even
investment
k = s ka  (n +g+)k
(n +g +) k
k<0
ska
k>0
k*
Capital per
effective
labor, k
Graphical view
(not in textbook)
gk = k /k = s ka1  (n +g+)
Rate of inflow,
rate of outflow
gk>0
n+g+
gk<0
k*
ska1
Capital per
effective
labor, k
Steady-State Growth Rates in the
Solow Model (to be derived in class)
Variable
Symbol
Steady-state
growth rate
Capital per
effective labor
Output per
effective labor
k = K/ (L E )
0
y = Y/ (L E )
0
Output per capita (Y/ L ) = y E
g
Total output
Y = y E L
n+g
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)
Variable
Symbol
Growth rate below
or beyond the
steady state
Capital per
effective labor
Output per
effective labor
k = K/ (L E )
gk
y = Y/ (L E )
agk
Output per capita
(Y/ L ) = y E
g + agk
Total output
Y = y E L
n + g + agk
Explaining the variety of
growth experiences

In what follows, we make use of the
graphical analysis of the dynamic
equation
gk = k /k = s ka1  (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)
Rate of inflow,
rate of outflow
gk = k /k = s ka1  (n +g+)
gk 1
gk 2
n+g+
s2 ka1
s1 ka1
k1=k2 k1*
k2*
Capital per
effective
labor, k
Savings rates and growth
performances
• Growth rate of real GDP per capita is given by
gY/L = g + a gk
• From the above analysis, other things equal (so g
and a are treated as the same), the higher the
savings rate, the higher gk is. Hence, the higher
the current growth rate of real GDP per capita
gY/L.
Population growth and economic
growth performance (not in textbook)
Rate of inflow,
rate of outflow
gk = k /k = s ka1  (n +g+)
gk 1
n1+g+
gk 2
n2+g+
s ka1
k1=k2 k1*
k2*
Capital per
effective
labor, k
Population growth and
economic growth performances
• Growth rate of real GDP per capita is given by
gY/L = g + a gk
• From the above analysis, other things equal (so g
and a are treated as the same) the higher the
population growth rate, the lower gk is. Hence,
the lower the current growth rate of real GDP per
capita gY/L.
Convergence
(not in textbook)
gk = k /k = s ka1  (n +g+)
Rate of inflow,
rate of outflow
gk poor
gk rich
n+g+
ska1
kpoor krich
k*
Capital per
effective
labor, k
Convergence
• Growth rate of real GDP per capita (Y/L) is
given by
gY/L = g +a gk
• 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 gk in
Real GDP per capita growth rate = g + a gk
Eventually, as economies reach their respective
steady states, gk=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)
Rate of inflow,
rate of outflow
gk = k /k = s ka1  (n +g+)
gk 1
gk=gk2-gk1 =g1-g2
n+g1+
gk 2
n+g2+
s ka1
k1=k2 k1*
k2*
Capital per
effective
labor, k
Technological growth and economic
growth performance (not in textbook)


Although country with a higher technological
growth g1 has a lower gk, it turns out that
such a country commands a higher gY/L. From
the graph,
gk2-gk1 =g1-g2
Now, gY/L=g+agk. So,
gY/L1-gY/L2 =(g1+agk1) – (g2+agk2)
=(g1–g2)+a(gk1-gk2)
=(g1–g2)-a (g1–g2)
=(1-a)(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=Ka(EL)1a. We
could rewrite it as
Y=A KaL1a
where A=E1a. We call A the total factor
productivity (TFP).
The Solow Residual
From
Y=A KaL1a
We use the rules 1-3 in mathematical
digression to obtain
gY =gA+a gK + (1a) gL
To obtain the TFP growth rate (gA), we
rearrange the above equation to get
gA = gY - a gK - (1a) gL
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
Japan
1.96%
U.K.
1.3%
U.S.
0.41%
1.8%
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.)