MACROECONOMICSMACROECONOMICS

Chapter 8Chapter 8

Economic Growth II: Economic Growth II: Technology, Empirics, and Technology, Empirics, and

PolicyPolicy

22

Outline of the ChapterOutline of the Chapter

1.1. Including technological change into Including technological change into Solow Model.Solow Model.

2.2. Testing the model with data.Testing the model with data.

3.3. Discussing policy options to improve the Discussing policy options to improve the standard of living.standard of living.

4.4. New growth theories.New growth theories.

33

Including Technological ProgressIncluding Technological Progress

Suppose technology is labor-augmenting.Suppose technology is labor-augmenting. It increases efficiency of labor.It increases efficiency of labor. It increases the “effective” number of workers.It increases the “effective” number of workers.Y = F(K,LE)Y = F(K,LE)

ExampleExampleY = KY = Kαα(LE)(LE)1-1-αα

y = ky = kαα where y = Y/LE and k = K/LE where y = Y/LE and k = K/LE

44

What Does E Include?What Does E Include?

KnowledgeKnowledgeHealthHealthEducationEducation Institutions that promote growth of Institutions that promote growth of

productionproduction

55

Long Term Growth of ELong Term Growth of E

If efficiency of labor (E) doubles in 35 If efficiency of labor (E) doubles in 35 years, E must be growing at annual rates years, E must be growing at annual rates of 2%.of 2%.

If E doubles in 10 years, annual growth If E doubles in 10 years, annual growth rate is 7%.rate is 7%.

The growth rate of E, labeled g, will be The growth rate of E, labeled g, will be given outside of the system (exogenous) given outside of the system (exogenous) in our analysis.in our analysis.

66

Long Term Growth of LELong Term Growth of LE

If E grows at rate g and population grows If E grows at rate g and population grows at rate n, then LE must grow at rate g+n.at rate n, then LE must grow at rate g+n.%%ΔΔ(LE) = %(LE) = %ΔΔL + %L + %ΔΔEE

If LE grows by n+g, then, once the If LE grows by n+g, then, once the economy reaches the steady state (k*), K economy reaches the steady state (k*), K must also grow by n+g to keep it at that must also grow by n+g to keep it at that level.level.

77

Steady StateSteady State

Steady State k was the level of k, once reached, Steady State k was the level of k, once reached, remained there.remained there. No increase or decrease of k takes place once that No increase or decrease of k takes place once that

equilibrium (k=k*) is reached.equilibrium (k=k*) is reached.

Accumulation of k depends on investments Accumulation of k depends on investments being larger than the depreciation plus n+g.being larger than the depreciation plus n+g.

sf(k*) = (sf(k*) = (δδ+n+g)k*+n+g)k* If savings (=investments) are larger than If savings (=investments) are larger than

((δδ+n+g)k, k will increase; smaller: decrease.+n+g)k, k will increase; smaller: decrease.

88

Steady State and Golden RuleSteady State and Golden Rule

k = (K/LE)

y= (Y/LE)y

sy

(δ+n+g)k

k*k k

99

Steady State and Golden RuleSteady State and Golden Rule

k = (K/LE)

y= (Y/LE)y

sy

(δ+n+g)k

c*

s*y

k*

1010

Growth Rates in Steady StateGrowth Rates in Steady State

In steady state, k=k* and y=y*.In steady state, k=k* and y=y*.k=K/LE implies that at steady state, in k=K/LE implies that at steady state, in

order to keep k constant, K must increase order to keep k constant, K must increase at rate n+g while k (capital per effective at rate n+g while k (capital per effective worker) remains constant.worker) remains constant.

y=Y/LE implies that to keep y=y*, Y must y=Y/LE implies that to keep y=y*, Y must grow at rate n+g.grow at rate n+g.

Per capita income must grow at g; capital-Per capita income must grow at g; capital-output ratio constant.output ratio constant.

1111

Steady State and Golden RuleSteady State and Golden Rule

Steady State: Steady State: sf(k*)=(sf(k*)=(δδ+n+g)k*+n+g)k* f(k*)-c*=sf(k*)f(k*)-c*=sf(k*)c*=f(k*)-c*=f(k*)-((δδ+n+g)k*+n+g)k*

But, the slope of f(k) at Golden Rule is But, the slope of f(k) at Golden Rule is ((δδ+n+g) which is the definition of MPK.+n+g) which is the definition of MPK.

If the economy is at Golden Rule Steady If the economy is at Golden Rule Steady State, then MPK (=real rental price of State, then MPK (=real rental price of capital) must be equal to capital) must be equal to δδ+n+g.+n+g.

1212

Steady StateSteady State

If long run growth of real GDP is 4% with If long run growth of real GDP is 4% with population growth of 1% and technology population growth of 1% and technology growth of 3%, then we fulfill the growth of 3%, then we fulfill the requirements of steady state.requirements of steady state.

If Y grows at 8% with 2% population If Y grows at 8% with 2% population growth and 3% technology growth we are growth and 3% technology growth we are not at steady state. (See slide #8)not at steady state. (See slide #8)

1313

Further ImplicationsFurther Implications

Constant returns to scale yields:Constant returns to scale yields: L(MPL)+K(MPK)=YL(MPL)+K(MPK)=Y Y growth is n+gY growth is n+g L growth is nL growth is n K growth is n+gK growth is n+g MPL growth must be g and MPK growth must be MPL growth must be g and MPK growth must be

zero.zero. US data show g=2% with MPL growth 2% and US data show g=2% with MPL growth 2% and

MPK constant!MPK constant!

1414

Is U.S. at Golden Rule?Is U.S. at Golden Rule?Givenn = 0.01g = 0.02δk = 0.1yk = 2.5yMPK(k) = 0.3y

12.05.2

3.0

5.2

3.0))((

MPK

MPK

y

y

k

kMPK

04.0

5.2

1.0

y

y

k

k

02.001.004.012.0

gnMPK

MPK will become smaller as k increases. In order for k* to be a higher number, s has to increase.

1515

Endogenous Growth ModelsEndogenous Growth Models

Knowledge does not have diminishing Knowledge does not have diminishing returns, and it has positive externalities.returns, and it has positive externalities.

Once included in the production function, it Once included in the production function, it eliminates the k* steady-state property.eliminates the k* steady-state property.

Production function can be straight line Production function can be straight line (Y=AK) or increasing slope (as E grows (Y=AK) or increasing slope (as E grows fast in Y=F[K,(1-u)LE]).fast in Y=F[K,(1-u)LE]).

1616

Endogenous Growth ModelsEndogenous Growth Models

As long as capital accumulation takes place, there is no end to growth of income.

1717

Convergence or DivergenceConvergence or Divergence

Same production function, same s, g, n, Same production function, same s, g, n, δδ..Convergence, even if they start at different k.Convergence, even if they start at different k.Production function might be connected to Production function might be connected to

urbanization.urbanization.Same production function, different s, g, n, Same production function, different s, g, n,

δδ..DivergenceDivergence

Different production functions: divergenceDifferent production functions: divergence

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SimilaritiesSimilaritiesProduction efficiency (E) and factor Production efficiency (E) and factor

accumulation (LE) and K seem to correlate accumulation (LE) and K seem to correlate (go hand in hand).(go hand in hand).Maybe an efficient economy promotes capital Maybe an efficient economy promotes capital

accumulation.accumulation.Maybe there are positive externalities to Maybe there are positive externalities to

capital: more savings, better production capital: more savings, better production function.function.

Maybe better institutions and policies affect Maybe better institutions and policies affect both.both.

1919

The economy can grow faster than normal for a period until it reaches the point where it would have been without the crisis, when it reaches its full potential again. (Friedman)

If the shortfall in demand persists it can do lasting damage to supply, reducing the level of potential output (scenario 2) or even its rate of growth (scenario 3). If so, the economy will never recoup its losses, even after spending picks up again.

In a recession firms shed labor and mothball capital. If workers are left on the shelf too long, their skills will atrophy and their ties to the world of work will weaken. When spending revives, the recovery will leave them behind. Output per worker may get back to normal, but the rate of employment will not.

World Economic Outlook: cost of 88 banking crises over the past four decades. On average, seven years after a bust an economy’s level of output was almost 10% below where it would have been without the crisis.

http://www.economist.com/specialreports/displayStory.cfm?story_id=14530093

2020

Does Free Trade Promote Growth?Does Free Trade Promote Growth?

Compare countries ranked according to Compare countries ranked according to openness with growth.openness with growth.

Study the impact of openness on growth.Study the impact of openness on growth. Instead of trade, look at geography. It is Instead of trade, look at geography. It is

an instrumental variable that correlates an instrumental variable that correlates with trade but does not correlate with other with trade but does not correlate with other variables that enhance growth.variables that enhance growth.