Download Long-Run Economic Growth

Long-Run Economic Growth
Prof Mike Kennedy
2013
2012
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1996
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1989
10
1988
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1985
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1982
1981
1980
Growth experiences:
Three large groups of countries
15
World
Emerging market and developing economies
Advanced economies
5
0
-5
-10
-15
Growth experiences:
The developing world
15
10
5
0
-5
-10
-15
Emerging market and developing economies
Central and eastern Europe
Commonwealth of Independent States
Developing Asia
Middle East, North Africa, Afghanistan, and Pakistan
Sub-Saharan Africa
Growth experiences:
Advanced economies seem to move together
15
10
5
0
-5
Canada
Japan
United States
Euro area
-10
-15
United Kingdom
Why growth matters:
Small changes make a big difference over a lifetime
135
High gorwth (3.5%)
$133,000
120
Moderate growth (3.0%)
105
$113,000
Low growth (2.5%)
90
75
60
$95,000
45
30
15
0
y-2015
y-2020
y-2025
y-2030
y-2035
y-2040
y-2045
y-2050
The Sources of Economic Growth
• The relationship between output and
inputs is described by the production
function:
Y = AF(K, N)
• For Y to grow, either quantities of K or N
must grow or productivity (A) must
improve, or both.
The Growth Accounting Equation
• The growth accounting equation:
ΔY ΔA
ΔK
ΔN

 αK
 αN
Y
A
K
N
∆Y/Y is the rate of output growth;
∆K/K is the rate of capital growth;
∆N/N is the rate of labour growth;
∆A/A is the rate of productivity growth.
The Growth Accounting Equation
(continued)
aK = elasticity of output with respect to
capital (about 0.3 in Canada);
aN = elasticity of output with respect to
labour (about 0.7 in Canada).1
• The elasticity of output with respect to capital/labour
is the percentage increase in output resulting from a
one per cent increase in the amount of capital
stock/labour.
1
Recall the table on income shares in lecture on the national
accounts (Chap 2).
The Growth Accounting Equation (continued)
• There is another way to derive the equation using logs. The
production function can be written as:
ln(Y) = ln(A) + αKln(K) + αNln(N)
• The term “ln” means the natural log of the variable in
question.
• Since the first derivative of the natural log of a variable is
approximately equal to the proportional change then:
dln(Y) = dln(A) + αKdln(K) + αNdln(N)
• This is approximately equal to growth accounting equation in
slide 7.
– Note that dln(X) is approximately ∆X/X for somewhat small changes
(around 5% or less).
Growth Accounting
• Growth accounting measures empirically the relative
importance of capital stock, labour and productivity for
economic growth.
• The impact of changes in capital and labour is estimated from
historical data.
• The impact of changes in total factor productivity is treated as
a residual; that is, not otherwise explained.
ΔA ΔY
ΔK
ΔN

 αK
 αN
A
Y
K
N
Growth Accounting and the Productivity
Slowdown
• Output growth was rapid during 1962-1973 and
then slowed in 1974-2006.
• Much of the decline in output growth can be
accounted for by a decline in productivity
growth.
• The slowdown in productivity starting in 1974
was widespread, suggesting a global
phenomenon.
The Post-1973 Slowdown in Productivity
Growth
• Explanations of the reduced growth in
productivity are:
– Output measurement problem:
• Quality of output and inputs
• Shifts to lower productivity sectors
• Measurement problems have always been there
– Technological depletion and slow commercial
adaptation:
• The easy stuff has been used up
• Firms slow to take up new technologies
The Post-1973 Slowdown in
Productivity Growth (cont’d)
• The dramatic rise in oil prices:
– Old capital was energy intensive and thus inefficient
– Timing and the fact that the slowdown was international in scope
make this an attractive story
– But price of capital did not fall and energy was not that important for
several sectors
– As well, productivity should have picked up when oil prices fell in the
1980s – it did somewhat but later
• The beginning of a new industrial revolution:
–
–
–
–
The beginning of the computer age
Takes time to adopt new technologies
Have seen some pick up in productivity
The industrial revolution was like this
The More Recent Experience:
After a Pickup, Total Factor Productivity Has Slowed…
0.55
LnTFP
Trend TFP
0.50
0.45
0.40
0.35
0.30
… with Implications for Growth
4.5
Trend Labour
Trend Capital (adjusted)
4.0
Trend TFP
3.5
Potential output production function
Actual growth
3.0
1.2
2.5
1.1
2.0
0.9
0.9
1.5
0.7
1.1
0.6
0.9
1.0
1.1
0.8
1.1
1.1
0.5
1.0
0.8
0.5
0.0
0.4
0.1
1985-90
1990-95
1995-00
2000-05
Note the calculations are based on the growth accounting framework shown in slide 9
2005-10
0.1
2010-15
Contributions to potential growth since 1985
(based on growth accounting equation)
3.50
Trend Labour
3.00
Trend Capital (adjusted)
Trend TFP
2.50
2.00
1.50
1.00
0.50
0.00
Potential output production function
There have been many advances
over the past 40 years
Growth Dynamics:
The Neoclassical Growth Model
• Accounting approach is just that – it is not an explanation
of growth.
• The neoclassical growth model:
– clarifies how capital accumulation and economic growth are
interrelated;
– explains the factors affecting a nation’s long-run standard of
living;
– is suggestive of how a nation’s rate of economic growth evolves
over time; and
– can say something about convergence – do poor
countries/regions catch up?
Assumptions Underlying the Growth Model
• Assume that:
– population (Nt) is growing;
– at any point in time the share of the population
of working age is fixed;
– both the population and workforce grow at a
fixed rate n;
– the economy is closed and there are no
government purchases.
Setup of the Model of Economic
Growth
• Part of the output produced each year is
invested in new capital or in replacing worn-out
capital (It).
• The part of output not invested is consumed
(Ct).
Ct = Yt – It
The per-Worker Production
Function
• The production function in per worker terms is:
yt = Atf(kt)
(6.5)
yt = Yt/Nt is output per worker in year t
kt = Kt/Nt is capital stock per worker in year t
At = the level of total factor productivity in year t
• When the production is written like (6.5) it is
often called the “intensive form”.
Graph of the per-Worker Production
Function
• The production function slopes upward. As
we move rightward, K is rising faster than N
so that k increases.
• With more capital, each worker can produce
more output.
• The slope gets flatter at higher levels of
capital per worker due to diminishing MPK.
Steady States
• In a growth model, equilibrium is defined by
something called the steady state.
• A steady state is a situation in which the
economy’s output per worker (yt), consumption
per worker (ct), and capital stock per worker (kt)
are constant; these ratios do not change over
time.
• Remember that these variables are all ratios to
Nt so that for example both Yt and Nt are
growing but yt, the ratio of the two, is constant.
Steady States (continued)
• Holding productivity growth constant, the
economy reaches a steady state in the long run.
• Since yt, ct and kt are constant in a steady-state,
Yt, Ct and Kt all grow at rate “n”, the rate of
growth of the workforce.
• As noted above, this is the definition of the
steady state.
Characteristics of a Steady State
• Gross investment in year t is:
It = (n + d)Kt
• Kt grows by nKt in a steady state, which ensures
that K/N is constant.
• Kt depreciates by dKt where d is the capital
depreciation rate.
• Is this equation consistent with what we have
already studied about investment?
Characteristics of a
Steady State (continued)
• We can show that it is consistent with what we have already studied.
Start by differentiating (K/N) and setting that derivative to zero (i.e.,
fulfilling the condition that K/N does not change). Using “Δ” to represent
changes:
K  NK  KN K N K
 
N 
N2

N

N N
0
K  nK

(note ΔN/N = n, the growth rate of the labour force, and we have
multiplied the first expression by N)

• Using the gross investment identity (I = K* – K + dK) and remembering
that ΔK = K* – K = nK in the steady state we get:
I = (n + d)K
(See Addendum 2 for the discrete version)
Characteristics of a
Steady State (continued)
• Consumption is total output less the amount
used for investment.
Ct = Yt – (n + d)Kt
(6.7)
• Put Eq. (6.7) in per-worker terms.
• Replace yt with Atf(kt) (Eq. (6.5)).
ct = Atf(kt) – (n + d)kt
(6.8)
Steady-State Consumption per Worker
• An increase in the steady-state capitallabour ratio has two opposing effects on
consumption per worker:
1) it raises the amount of output a worker can
produce, Af(k); and
2) it increases the amount of output per worker
that must be devoted to investment, (n + d)k.
Steady-State Consumption per Worker
(continued)
• The Golden Rule level of the capital stock maximizes
consumption per worker in the steady state.
• At that point the slope of the production function (it’s
derivative wrt to k) equals (n + d), the slope of the
investment line.
• From this we can show that r = n, sometimes referred to as
the biological interest rate.
• The key here is to use the definition of the user cost of
capital assuming no taxes and a price of capital normalised
to equal one:
MPKG = (n + d) = (r + d) implying that r = n
Steady-State Consumption per Worker
(continued)
• The model shows that economic policy focused solely on
increasing capital per worker may do little to increase
consumption possibilities of the country citizens if we are
close to the Golden Rule level of k.
• Empirical evidence is that, given existing starting
conditions, a higher capital stock would not lead to less
consumption in the long run; i.e., economies are away
from kG.
• We will assume that an increase in the steady-state
capital-labour ratio raises steady-state consumption per
worker.
Reaching the Steady State
• We haven’t described how an economy would reach
a steady state.
• Why will the described economy reach a steady state?
• Which steady state will the economy reach?
• The piece of information we need is saving.
• Assume that saving in this economy is proportional
to current income:
St = sYt
(6.9)
where “s” is a number between 0 and 1.
• It represents the faction of current income saved.
Reaching the Steady State
(continued)
• National saving (in this case, private saving as
there is no government in the model) has to
equal investment.
• Here we set our simple saving function equal to
the amount of investment that is required to
maintain the capital-labour ratio constant:
sYt = (n + d)Kt
(6.10)
Reaching the Steady State
(continued)
• Put Eq. (6.10) in per-worker terms.
• Replace Yt with Atf(kt) (Eq. (6.5))
sAf(k) = (n + d)k
(6.11)
• Subscript t is dropped because the variables
are constant in the steady state.
Steady-State Capital-Output Ratio
• Equation 6.11 says that, in the steady state,
the capital-labour ratio must ensure that
saving per worker and investment per worker
are equal.
• k* is the value of k at which the saving curve
and the steady-state investment line cross.
• k* is the only possible steady-state capitaloutput ratio for this economy.
Equilibrium in the Solow-Swan growth model
(note that the position k* is stable)
The Steady-State Consumption per
Worker
• Steady-state output per worker is:
y* = Af(k*)
• Then the steady-state consumption per worker is:
c* = Af(k*) – (n + d)k*
• While steady-state investment per worker is:
i* = (n + d)k*
• Note that the steady-state investment curve slopes
upward because a higher k means more I is needed
to maintain it.
The Model’s Implications
• The economy’s capital-labour ratio will
converge to k*.
• It will remain there forever, unless something
changes.
• In this steady state the capital-labour ratio,
output per worker, investment per worker,
and consumption per worker all remain
constant over time.
• The model determines an equilibrium but not
growth – that is given by assumption.
The Model’s Implications
(continued)
• If the level of saving were greater than the amount of
investment needed to keep k constant, then that extra
saving gets converted into capital and k rises.
• If saving were less than the amount needed to keep k
constant, the reverse would happen – k would fall.
• Note that there is no reason to suppose that the
steady state is at a point of maximum consumption –
the “Golden Rule”.
The Model Implications
(continued)
• You could get a situation in a poor country where, at low
levels of income, saving is below (n + d)k – that is, it is not
high enough for the country to reach the level of income in
other countries,
• Here it is possible to have a low steady state, which is
unstable.
– A negative shock pushes the economy towards poverty
– A positive shock has the opposite effect
• Stability here requires that the saving function crosses
(n + d)k from above.
• Note that the unstable point is bounded by two stable
points.
s
The Determinants of Long-Run Living
Standards
• Long-run well-being is measured here by the
steady-state level of consumption per worker.
• Its determinants are:
1) the saving rate (s);
2) the population growth rate (n);
3) the rate of productivity growth (how fast A
grows).
Long-Run Living Standard and the
Saving Rate
• A higher saving rate implies a higher living
standard.
– The increased saving rate raises output at every
level of capital per worker.
• A steady-state with higher output and
consumption per worker is attained in the
long run.
The Saving Rate (continued)
• An increase in the saving rate has a cost – a
fall in current period consumption.
• As before, in the decision to consume,
there is a trade-off between current current
and future consumption.
• Beyond a certain point, the cost of lost
consumption today will outweigh the
future benefits.
The Saving Rate (continued)
• It is also the case that a policy that increases
saving will generate a temporary spurt in the
growth rate.
• Since y = Y/N and N is growing at a constant
rate (n), then as we move to a new and
higher k* output must grow faster than n at
least temporarily.
Long-Run Living Standard and Population
Growth
• Increased population growth tends to lower living
standards.
• When the workforce is growing rapidly, a larger part
of current output must be devoted to just providing
capital for the new workers to use.
• Absent here is any effect increased population may
have on output – increased immigration of highly
skilled workers would improve growth by raising
TFP.
Population Growth (continued)
• However, a reduction in population growth
means:
– lower population and lower total productive
capacity;
– lower ratio of working-age people to the
population and perhaps an unsustainable pension
system.
• In some countries, low population growth can be
raised by encouraging immigration and/or higher
female participation.
An increase in N, the stock of labour, with the
growth rate, n, constant: The case of China
• We can think of China’s growth as due, in part, to an
increase in the total stock of labour, N.
• Imagine a great migration from the country side to the
manufacturing sector, raising the level of N but with n
unchanged.
• The initial effect would be a drop in the capital-labour
ratio, shifting it leftward.
• At the now lower k, investment is larger than what is
required to maintain it constant. The K/N ratio now
moves rightward and growth increases during this
adjustment period.
Implications of a rise in N, with n constant
Long-Run Living Standard and
Productivity Growth
• The model accounts for the sustained growth by
incorporating productivity growth.
• Increased productivity will improve living standards:
– it raises y at every k;
– then saving per worker increases;
– and a higher k* is attained.
• This is important:
– without productivity improvements, living standards would
remain unchanged once the economy achieves a steady state.
Productivity Growth (continued)
• A one-time productivity improvement shifts
the economy only from one steady state to a
higher one.
• Only continuing increases in productivity can
perpetually improve living standards.
• Remember again, productivity growth is
exogenous in this model.
Total Factor Productivity (TFP) in Canada has
slowed recently …
0.55
0.53
LnTFP
0.51
0.49
0.47
0.45
0.43
0.41
0.39
0.37
0.35
Trend(TFP)
… this has affected the growth of output per
worker
The growth of output per worker
1.80
Trend Capital (adjusted)/labour ratio
Trend TFP
1.60
Potential output per unit of labour
1.40
1.20
1.00
0.80
0.60
0.40
0.20
0.00
Do Economies Converge to Each Other?
• Unconditional convergence is a situation when the poor
countries eventually catch up to the rich countries so that in the
long run, living standards around the world become more or
less the same. Certain conditions apply:
– For example, if the only difference is K/N but all else is the same (s,
n, A) then the model predicts that living standards in countries will
converge to that of other countries.
– Note that the further away a country is from the lead country, the
faster it will grow, given the above conditions.
– Some evidence suggests yes – poorer countries have tended to
grow faster than richer ones.
– Trade and capital flows may be routes that facilitate unconditional
convergence (Fischer’s results).
Do Economies Converge?
(continued)
• Conditional convergence is a situation in which
living standards will converge only within a group
of countries with similar characteristics.
– OECD and developing economies could be considered
two such groups but even here the effect is not clear
cut.
– This result occurs if there are differences in s, n and A,
all else the same.
– The further away an economy is from the steady state,
the faster it will grow.
What Convergence Would Look Like
in an Idealized World
7
Required growth rate to catch up within 50 years
6
Required growth rate = – 0.02 – 2.06 ln(Initial position)
5
4
3
2
1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Initial position vis-à-vis US economy
0.7
0.8
0.9
1
Unconditional Convergence:
Some evidence from 20 advanced economies
7
KOR
Actual growth = 1.79 – 1.62ln(Initial position)
(3.43)
R² = 0.83
6
Growth rate from 1960 to 2011
SGP
5
HKG
4
JAP
PRT
3
FIN
ESP
ITA
AUT
BEL DEU
FRA
NED
SWE
GBR
2
NOR
ISL
CAN
AUS
DEN
1
0
0.1
0.2
0.3
0.4
0.5
0.6
Initial position vis-à-vis US in 1960
0.7
0.8
0.9
1
A different perspective on convergence
Australia
GDP as % of US GDP
1.6
1
Austria
Belgium
End of convergence
1.4
0.9 Canada
Denmark
0.8
1.2
0.7
France
Finland
Germany
1
0.6 Hong Kong
Iceland
0.8
0.5 Italy
Japan
0.6
0.4 Korea
Netherlands
0.3
0.4
0.2
Norway
Portugal
Singapore
0.2
0.1 Spain
Sweden
0
0
United Kingdom
United States
Another look at unconditional convergence
for 15 OECD Economies (1960-2013)
Japan
GDP as % of US GDP
1
Germany
UK
0.9
France
Italy
0.8
Canada
Spain
0.7
Australia
Belgium
0.6
Netherlands
0.5
End of convergence
Sweden
Denmark
0.4
Austria
Finland
0.3
USA
Do Economies Converge?
(continued)
• Most studies find support for the idea of conditional
convergence.
• Studies show that low saving (including human capital,
often measured as spending on education) in developing
countries are important in explaining growth differences.
• Capital flows are again important.
• Other studies highlight the importance of competition,
well-functioning labour markets and macroeconomic
policy.
Unconditional convergence does not exist among
emerging markets economies (1960-2011)
Average growth rate 1960-2011
7
CHN
KOR
6
SPR
5
HUN
4
MAL IDA
IND
KEN BLZ
EGY
3
CHL PAN
LES
PAK MOR
BRA
MEX
2PAR COL
CRA
PHLGTA
BGD
ECU
NIG
SAF
KEN
1
ALG
-0.1
GNA
BUR CAM NIC
0
CDI
0.1
GRC
0.3
0.5
0.7
0.9
1.1
Position vis-à-vis US in 1960
-1
LIB
-2
ISR
There is no real convergence among emerging market
economies (1960-2011)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
USA
Bangladesh
Belize
Bolivia
Brazil
Chad
CAR
China
Costa Rica
Dominican Republic
Egypt
Gabon
Greece
Guyana
Hungary
Indonesia
Kenya
Liberia
Malawi
Mauritania
Morocco
Nicaragua
Pakistan
Papua NG
Philippines
Seychelles
Sri Lanka
Sudan
Togo
Tunisia
Uruguay
Zambia
Algeria
Barbados
Benin
Botswana
Burundi
Camaroon
Chile
Colombia
Côte d'Ivoire
Ecuador
Fiji
Ghana
Guatemala
Honduras
India
Isreal
Lesotho
Madagascar
Malaysia
Mexico
Nepal
Nigeria
Panama
Paraguay
Senegal
Sierra Leone
South Africa
The Bahamas
Trinidad-Tobago
Turkey
Venezuela
Required Growth Rate for Emerging Market
Economies to close the “Gap” over 30 Years
11
10.5%
10
9
Required growth (shown on top of bars)
to close the gap in 30 years for initial
position (shown on horizontal axis)
Average growth rate from 1960-2012
8
7
6.5%
6
5
4.7%
4
3.6%
3
2
1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
-1
-2
-3
Initial position vis-à-vis US in 1960
1
Implication of the Neoclassical Growth Theory
• The neoclassical model highlights the role and
importance of productivity.
• However, it assumes, rather than explains,
productivity – the crucial determinant of living
standards (see first part of Chapter 6).
• In other words, the model does not explain
growth in output per capita which is of great
interest.
Endogenous Growth Theory
• In part, because of the failure or difficulties of the
unconditional convergence hypothesis, economist
started to look for other explanations, focussing in
particular on the role of productivity.
• Endogenous growth theory tries to explain productivity
growth within the model (endogenously).
• An implication of endogenous growth theory is that a
country’s growth rate depends on its rate of saving and
investment, not only on exogenous productivity growth.
Setup of the Endogenous Growth Model
• Assume that the number of workers remains constant.
• This implies that the growth rate of output per worker is simply
equal to the growth rate of output.
• The aggregate production function is:
Y = AK
(6.12)
where A is a positive constant capturing productivity.
• The marginal product of capital (MPK) is equal to A and does
not depend on the capital stock (K).
• The MPK is not diminishing, it is constant.
• This is a major departure from the previous growth model.
Constant MPK and Human Capital
• One explanation of constant MPK is human capital –
the knowledge, skills and training of individuals.
• As an economy’s physical capital increases, its human
capital stock tends to increase in the same proportion.
• Workers get better at using capital – there is learningby-doing – an idea due to Kenneth Arrow.
• An example of learning-by-doing is computers. Over
time the efficiency of computing has increased 43
million times. While increased computing power has
played a role, most is due to improved algorithms; i.e.,
humans got better at using computers.
Constant MPK and
Research and Development
• Another explanation of constant MPK is
research and development (R&D) activities.
• The resulting productivity gains offset any
tendency for the MPK to decrease.
• As the economy grows, firms have an
incentive to invest in R&D.
The Model of Endogenous Growth
• The implications of the model in equilibrium.
– Assume that national saving, S, is a constant
fraction s of aggregate output, AK, so that
S = sAK.
– In a closed economy I = S.
– As we know, total gross investment equals net
investment plus depreciation
I = ∆K + dK
The Model of Endogenous Growth
(continued)
• Therefore:
(6.13)
ΔK  dK  sAK
ΔK
or
 sA  d
(6.14)
K
ΔY
and
 sA  d
(6.15)
Y
• Since the growth rate of output is proportional to
the growth rate of capital stock.
• Increases in s will raise growth since it leads to a
higher capital stock.
Implication of the Endogenous Growth
Model
• The endogenous growth model places greater
emphasis on saving, human capital formation and
R&D as sources of long-run growth.
• Higher saving and capital formation generate
investment in human capital and R&D raising A.
• Remember, in the neoclassical (or Solow-Swan)
growth model, over time, the saving rate affects
only the level of output, not growth.
Economic Growth and the Environment
• So far we have assumed that there are no natural
limits to growth, like declining non-renewable
resources or the environment.
• The empirical facts:
– Levels of many pollutants rise and then fall as economy
grows.
– The costs of controlling pollution are rising but remain
relatively constant as a fraction of GDP.
– Pollution emissions per unit of GDP have been falling since
the late 1940s.
Economic Growth and the Environment
(continued)
• During the rapid initial economic growth phase, the
impact of output growth overwhelms the
improvements in pollution-abatement technology.
• Near the steady state economic growth slows down
and technological progress in pollution control
overwhelms the impact of economic growth.
• These results are often due to policy choices.
CO2 Emissions per capita are Levelling off …
25
CO2 emissions (metric tons per capita)
20
15
EUR
AUS
10
CAN
GBR
USA
5
0
JPN
… and Falling as a Fraction of GDP
0.9
CO2 emissions (kg per 2005 PPP $ of GDP)
0.8
0.7
0.6
0.5
0.4
0.3
0.2
CAN
GBR
USA
EUR
Time to act?
Government Policies and Long-Run Living
Standards
• Government policies that are useful in raising
a country’s long-run standard of living are:
– polices to raise the saving rate;
– policies to raise the rate of productivity.
Policies to Affect the Saving Rate
• One view is to let individuals decide for
themselves.
• The other view is that government actions are
needed:
– They can try to affect the return on saving, but the effect
is small.
– By taxing consumption a government can exempt from
taxation income that is saved.
– A government can increase the amount that it saves by
reducing its deficit – this seems to have some positive
benefits.
National saving rates have been declining
35
30
25
20
15
10
AUS
CAN
FRA
JPN
GBR
USA
DEU
Affecting Productivity Growth:
Improving Infrastructure
• Some research finds a link between productivity and
the quality of nation’s infrastructure.
• Other research finds that public investments cannot
explain cross-country differences.
• There is a political dimension here: powerful members
of parliament/legislatures funnel funds into their
ridings – Japan had lots of infrastructure investment
but not much growth.
• Higher growth in productivity may lead to more
infrastructure, and not vice versa; that is, richer
countries may want better infrastructure, like roads,
schools, hospitals and communications networks.
Affecting Productivity Growth:
Building Human Capital
• Recent research finds a strong connection
between productivity growth and human
capital.
• Governments affect human capital through
education policies, training programs, health
programs, etc.
• Productivity growth may increase if barriers
to entrepreneurial activity are removed
(cutting red tape) and competition increased.
Spending on Education is Declining in Some Countries
8
Education expenditure (% of GNI)
7
6
AUS
CAN
5
FRA
DEU
JPN
4
GBR
USA
3
2
Affecting Productivity Growth:
Research and Development
• Direct government support of basic research is
a good investment for raising productivity –
the resulting knowledge spreads through the
economy.
• Some economists believe that even
commercially-oriented research deserves
government aid.
• Here public-private partnerships may help.
Affecting Productivity Growth:
Industrial Policy
• Industrial policy is a growth strategy in which the
government attempts to influence the country’s
pattern of industrial development.
• The arguments for the industrial policy are
borrowing constraints, spillovers, and nationalism.
The danger is favouritism.
• “Government’s are not very good at finding
winners, but losers are good at finding
governments.” Sylvia Ostry
Affecting productivity Growth:
Market Policy
• Market policy is government restriction on free
markets.
• Economists favour respect for property rights and
a reliance on free markets to allocate resources
efficiently.
• The reasons for government to interfere are:
market failures and efficiency vs. equity trade-off.
• A social safety net may encourage workers to be
more in favour technical change, which can be
disruptive
Addendum 1: Solving the Model
for Key Variables
• We can use the neo-classical growth model to solve for
various key variables.
• To determine the steady-state capital-labour ratio (k*), start
with the equilibrium condition that S = I in per capita terms.
Thus:
(n + d)k* = sAk*α
• This implies that k* is:
1
(1 )
 sA 
k  

(n  d) 
*
Addendum 1: Solving the Model
for Key Variables (continued)
• Suppose we want to know the Golden Rule
level of the capital-labour ratio, kG.
• When the marginal productivity of k equal
n + d, we know that consumption is
maximised and the capital-labour ratio = kG.
Addendum 1: Solving the Model
for Key Variables (continued)
• Assuming that the production function, in intensive
form, is Cobb-Douglas (y = Akα), then the marginal
product of k is αAkα–1. Substituting kG into this
relationship and setting it equal to n + d, we get:
αAkGα-1 = n + d
• It then follows that:
1
(1 )
 A 
kG  

(n  d) 
• Once we know kG we can now solve for y, investment
and c.
Addendum 1: Solving the Model
for Key Variables (continued)
• If we wanted to know what saving rate (s) would get us to kG,
(whose value we now know) we go back to our old friend
saving = investment and assume that we were at the point kG.
sAkGα = (n + d)kG
• Then s is given by:
n  d  1
s  
kG

 A 
– The strategy is to go to the point kG and ask the question: what must
have been s to get us to this point.
– Once we know kG we can solve for y and investment, which of course
gives us c.
Addendum 1: Solving the Model
for Key Variables (continued)
• Using the saving = investment identity we can solve for
the effects of other changes.
• Suppose we want to know what is the effect of higher
labour for growth (n’). From the S-I identity we have:
sAkα = (n’ + d)k
• Which yields a new k equal to:
1
(1 )
 sA 
kn'  

(n'd) 
• We can use kn’ (the capital/labour ratio resulting from n’)
to calculate the new y, investment and c.
Addendum 1: Solving the Model
for Key Variables (continued)
• A productivity improvement (call it A’) can be handled in a
similar fashion; i.e., through the saving-investment identity.
sA’kα = (n + d)k
• Then as before, we solve for a new k,
1
(1 )
 sA' 
kA '  

(n  d) 
• Once we have kA’ we proceed as before and get the other
variables of interest.
• Remember, when re-calculating y, adjust it for the now larger
productivity, A’.
Addendum 2: Solving the Model
for Key Variables in Discrete Time
• Start with the following
Kt+1 – Kt = It – dKt, which is the capital accumulation identity and
can be written as:
Kt+1 = (1 – d)Kt + It
• The labour force (or population) evolves as:
Nt+1 = (1 + n)Nt, where n is the growth rate of labour.
• Divide both sides by Nt+1 bearing in mind the growth of labour
equation and that St = It:

K t 1
Kt
sAKt N1
dK t
t



N t 1 (1 n)N t
(1 n)N t (1 n)N t
Addendum 2: Solving the Model for Key
Variables in Discrete Time (con’t)
• Remembering that k = K/N, the equation on the previous slide can
be written as:
 s  
(1  d)
kt 1 
kt  
Akt
(1 n)
(1 n) 
• This expression shows what is called the law of motion of capital.
Simply stated, it shows how the capital stock per worker (kt+1)

evolves over time if the term in square brackets were to change.
• As can be seen, kt+1 depends on the amount of capital already in
place [kt, times (1-d)/(1+n)] as well as the amount of new capital
being added, sAktα, divided by (1+n).
• Next we show that the implied steady state capital labour ratio is
the same as already derived.

Addendum 2: Solving the Model for Key
Variables in Discrete Time (con’t)
• Multiplying both sides by 1+n we get:
(1+n) kt+1 – (1–d) kt = sAktα
• In the steady kt+1 = kt = k the equation becomes:
(n+d)k = sAkα
• The steady state level of capital per worker (k*) is then:
1
(1 )
 sA 
k*  

(n  d) 
• This is identical to the expression shown in Addendum 1.
Raising Growth Can Be a Slow Process:
Patience is required to see the results