Figure 1.1 Output of the U.S. economy, 1869–2002–Watch TV –Play video games Unequal Standards of Living Across Time John D. Rockefeller, oil entrepreneur who lived from 1839

Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 1-2

Figure 1.1 Output of the U.S. economy, 1869–2002

The Long View: Economic Growth


� Important distinction between BUSINESS CYCLES (cyclicalfluctuations) and LONG-RUN GROWTH (secular trend).



� The most striking feature of U.S. economic history since 1870is the sustained growth in real GDP per capita.



� The most striking feature of U.S. economic history since 1870is the sustained growth in real GDP per capita.

� Central question: What determines the long-run growth rateof an economy?

Unequal Standards of Living Across Countries


Fraction of Fraction of Probabilitypopulation high-school age of surviving

GDP in extreme children to age 65per capita poverty in school Men Women




U.K. $27,650 Almost zero 95% 0.83 0.89




U.K. $27,650 Almost zero 95% 0.83 0.89Mexico $8,950 25% 60% 0.71 0.82




U.K. $27,650 Almost zero 95% 0.83 0.89Mexico $8,950 25% 60% 0.71 0.82Mali $960 > 50% < 10% 0.37 0.41

Unequal Standards of Living Across Time


John D. Rockefeller, oil entrepreneur who lived from 1839 to 1937,had a net worth of $200 billion (in today’s dollars), twice that ofBill Gates (today’s richest American).



But he could not:



But he could not:

–Watch TV



But he could not:

–Watch TV–Play video games



But he could not:

–Watch TV–Play video games–Surf the Internet



But he could not:

–Watch TV–Play video games–Surf the Internet–Send an e-mail (let alone a text message)



But he could not:

–Watch TV–Play video games–Surf the Internet–Send an e-mail (let alone a text message)–Cool his home with air conditioning



But he could not:

–Watch TV–Play video games–Surf the Internet–Send an e-mail (let alone a text message)–Cool his home with air conditioning–Use antibiotics



But he could not:

–Watch TV–Play video games–Surf the Internet–Send an e-mail (let alone a text message)–Cool his home with air conditioning–Use antibiotics–Use a telephone to call his family (for much of his life)



But he could not:

–Watch TV–Play video games–Surf the Internet–Send an e-mail (let alone a text message)–Cool his home with air conditioning–Use antibiotics–Use a telephone to call his family (for much of his life)–Travel by car or plane (for much of his life)



But he could not:

–Watch TV–Play video games–Surf the Internet–Send an e-mail (let alone a text message)–Cool his home with air conditioning–Use antibiotics–Use a telephone to call his family (for much of his life)–Travel by car or plane (for much of his life)–Play golf with a hybrid 5-iron



But he could not:

–Watch TV–Play video games–Surf the Internet–Send an e-mail (let alone a text message)–Cool his home with air conditioning–Use antibiotics–Use a telephone to call his family (for much of his life)–Travel by car or plane (for much of his life)–Play golf with a hybrid 5-iron

ARE YOU RICHER THAN JOHN D. ROCKEFELLER?

Growth in per capita income (average, percent per year)

0.00.20.40.60.81.01.21.41.6

Gro

wth

in p

er c

apita

inco

me

up to 1700

1700-1830

1830 to present

Data for Western Europe from Angus Maddison

© 2007 Thomson South-Western

Table 1 The Variety of Growth Experiences

United States per capita GDP Country at this

Year Level (2004 $) level in 20041800 1,195 Kenya1850 1,700 Bangladesh1900 4,391 Morocco1910 5,408 China1916 6,189 Algeria1920 6,180 Ukraine1930 7,002 Namibia1940 8,539 Romania1950 12,783 Argentina1960 15,099 Hungary1970 20,065 South Korea1980 24,729 Spain1990 31,016 UK2000 37,814 Ireland (almost)2005 40,718 US, Norway

1960

19802000

0.0

0005

.000

1.0

0015

.000

2.0

0025

Den

sity

of c

outr

ies

0 10000 20000 30000 40000 50000gdp per capita

Figure 1.1. Estimates of the distribution of countries according to PPP-adjusted GDP per capita in 1960, 1980 and 2000.

ALB ARG

ARM

AUSAUT

AZE

BDI

BEL

BEN

BFA

BGD

BGR

BLR

BLZ

BOL

BRA

BRB

CANCHE

CHL

CHN

CIVCMR

COG

COL

COM

CPV

CRI

CZEDNK

DOM

DZA

ECU

EGY

ESP

EST

FINFRA

GAB

GBR

GEO

GHA

GINGMB

GNBGNQ

GRC

GTM

HKG

HND

HRV

HUN

IDN

IND

IRL

IRN

ISLISR ITA

JAMJOR

JPN

KAZ

KEN

KGZ

KOR

LBNLCA

LKA

LSO

LTU

LUX

LVA

MAC

MARMDA

MDG

MEXMKD

MLI

MOZ

MUS

MWI

MYS

NERNGA

NIC

NLDNOR

NPL

NZL

PAK

PAN

PERPHL

POL

PRT

PRYROM

RUS

RWA

SEN

SLV

SVK

SVN

SWE

SWZ

SYR

TCD

TGO

THA

TJK

TTOTUN

TUR

TZA

UGA

UKR

URY

USA

VCTVEN

YEM ZAF

ZMB

ZWE

ETH

4050

6070

8090

life

expe

ctan

cy 2

000

6 7 8 9 10 11log gdp per capita 2000

Figure 1.6. The association between income per capita and life expectancyat birth in 2000.

SpainSouth Korea

India

Brazil

USA

Singapore

Nigeria

Guatemala

UK

Botswana

67

89

10lo

g gd

p pe

r ca

pita

1960 1970 1980 1990 2000year

Figure 1.8. The evolution of income per capita in the United States, UnitedKingdom, Spain, Singapore, Brazil, Guatemala, South Korea, Botswana,Nigeria and India, 1960-2000.

USA

Britain

Spain

Ghana

Brazil

China

India

67

89

10lo

g gd

p pe

r ca

pita

1800 1850 1900 1950 2000year

Figure 1.12. The evolution of income per capita in the United States,Britain, Spain, Brazil, China, India and Ghana, 1820-2000.

Growth and Human Welfare


Is there some action a government of India could take that wouldlead the Indian economy to grow like Indonesia’s or Egypt’s?


Is there some action a government of India could take that wouldlead the Indian economy to grow like Indonesia’s or Egypt’s? If so,what exactly? If not, what is it about the “nature of India” thatmakes it so?


Is there some action a government of India could take that wouldlead the Indian economy to grow like Indonesia’s or Egypt’s? If so,what exactly? If not, what is it about the “nature of India” thatmakes it so? The consequences for human welfare involved inquestions like these are simply staggering: Once one starts to thinkabout them, it is hard to think of anything else.


Is there some action a government of India could take that wouldlead the Indian economy to grow like Indonesia’s or Egypt’s? If so,what exactly? If not, what is it about the “nature of India” thatmakes it so? The consequences for human welfare involved inquestions like these are simply staggering: Once one starts to thinkabout them, it is hard to think of anything else.

R.E. Lucas, Jr. (1988), “On the Mechanics of EconomicDevelopment,” Journal of Monetary Economics.

Making a Miracle

Making a Miracle

How does one acquire knowledge about reality by working in one’soffice with pen and paper?

Making a Miracle

How does one acquire knowledge about reality by working in one’soffice with pen and paper? (...) [I] think this inventive,model-building process we are engaged in is an essential one . . . .

Making a Miracle

How does one acquire knowledge about reality by working in one’soffice with pen and paper? (...) [I] think this inventive,model-building process we are engaged in is an essential one . . . . Ifwe understand the process of economic growth—or anythingelse—we ought to be capable of demonstrating this knowledge bycreating it in these pen and paper (and computer-equipped)laboratories of ours.

Making a Miracle

How does one acquire knowledge about reality by working in one’soffice with pen and paper? (...) [I] think this inventive,model-building process we are engaged in is an essential one . . . . Ifwe understand the process of economic growth—or anythingelse—we ought to be capable of demonstrating this knowledge bycreating it in these pen and paper (and computer-equipped)laboratories of ours. If we know what an economic miracle is, weought to be able to make one.

Making a Miracle

How does one acquire knowledge about reality by working in one’soffice with pen and paper? (...) [I] think this inventive,model-building process we are engaged in is an essential one . . . . Ifwe understand the process of economic growth—or anythingelse—we ought to be capable of demonstrating this knowledge bycreating it in these pen and paper (and computer-equipped)laboratories of ours. If we know what an economic miracle is, weought to be able to make one.

R.E. Lucas, Jr. (1993), “Making a Miracle,” Econometrica.

Simple Mathematics of Growth Rates


� Define: Yt = U.S. GDP in year t.



� Suppose the growth rate of GDP is g : Yt+1 = (1 + g)Yt .




� In the U.S., g (on average) is about 0.03, or 3%.





� Let log(x) denote the natural logarithm, or the log to the basee, of x (log(x) is sometimes also denoted ln(x)).






� A useful fact: log(ax) = log(a) + log(x).






� A useful fact: log(ax) = log(a) + log(x).

� A useful approximation: log(1 + g) ≈ g if g is close to 0.

Simple Mathematics of Growth Rates (cont’d)


� A simple derivation...



log(Yt+1) = log((1 + g)Yt)




= log(1 + g) + log(Yt)





≈ g + log(Yt)





≈ g + log(Yt)

⇒ log(Yt+1) − log(Yt) ≈ g





≈ g + log(Yt)


� ...yields a useful approximation:





≈ g + log(Yt)


� ...yields a useful approximation: The difference in the logs is(approximately) equal to the growth rate.

Compounding

Compounding

� Let the base year be year 0 and suppose that GDP grows at aconstant rate g . Then:

Compounding


Y1 = (1 + g)Y0

Compounding


Y1 = (1 + g)Y0

Y2 = (1 + g)Y1 = (1 + g)2Y0

Compounding


Y1 = (1 + g)Y0

Y2 = (1 + g)Y1 = (1 + g)2Y0

Y3 = (1 + g)Y2 = (1 + g)2Y1 = (1 + g)3Y0

Compounding


Y1 = (1 + g)Y0

Y2 = (1 + g)Y1 = (1 + g)2Y0

Y3 = (1 + g)Y2 = (1 + g)2Y1 = (1 + g)3Y0

� The general formula is: Yt = (1 + g)tY0.

Compounding


Y1 = (1 + g)Y0

Y2 = (1 + g)Y1 = (1 + g)2Y0

Y3 = (1 + g)Y2 = (1 + g)2Y1 = (1 + g)3Y0

� The general formula is: Yt = (1 + g)tY0.

� Given the values of GDP in two years 0 and t, a value of gsatisfying this formula is called the (geometric) averagegrowth rate of GDP between year 0 and year t.

Logarithmic Graphs

Logarithmic Graphs

� Another useful fact: log(xa) = a log(x).

Logarithmic Graphs


� Recall that Yt = (1 + g)tY0 if U.S. GDP grows at a constantrate g .

Logarithmic Graphs



� Take logs of both sides:

Logarithmic Graphs




log(Yt) = log((1 + g)tY0

)

Logarithmic Graphs





)= log

((1 + g)t

)+ log(Y0)

Logarithmic Graphs





)= log

((1 + g)t

)+ log(Y0)

= t log(1 + g) + log(Y0)

Logarithmic Graphs





)= log

((1 + g)t

)+ log(Y0)

= t log(1 + g) + log(Y0)

≈ log(Y0) + gt

Logarithmic Graphs





)= log

((1 + g)t

)+ log(Y0)

= t log(1 + g) + log(Y0)

≈ log(Y0) + gt

If GDP grows at a constant rate, then the log of GDP,graphed against time t, is a straight line with slope equal tothe growth rate g.

2000

U.S. GDP

GD

P in

bill

ion

s o

f 19

92 d

olla

rs

6,400

3,200

1,600

800

400

200

1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990

Figure 10-1U.S. GDP Since 1890

Aggregate U.S. output has increased by a factor of 43 since 1890.Source: 1890–1929: Historical Statistics of the United States; 1929–2000: National Income and Product Accounts.

Oliver BlanchardMacroeconomics, 3E

© 2003 Prentice Hall, IncUpper Saddle River, NJ 07458

Log of US Real GDP (with trend line)

7.359

8.052

8.745

9.438

1947

1948

1950

1952

1954

1955

1957

1959

1961

1962

1964

1966

1968

1969

1971

1973

1975

1976

1978

1980

1982

1983

1985

1987

1989

1990

1992

1994

1996

1997

1999

2001

2003

US Real GDP: Percentage Deviations from Trend

-12

-8

-4

0

4

8

12

1947

1948

1950

1952

1954

1955

1957

1959

1961

1962

1964

1966

1968

1969

1971

1973

1975

1976

1978

1980

1982

1983

1985

1987

1989

1990

1992

1994

1996

1997

1999

2001

2003

Perc

enta

ge d

evia

tion

The Rule of 70

The Rule of 70

� Question: If U.S. GDP grows at a constant rate g , how longdoes it take for U.S. GDP to double?

The Rule of 70


� Suppose that GDP doubles in exactly T years: YT = 2Y0.

The Rule of 70


� Suppose that GDP doubles in exactly T years: YT = 2Y0.We want to solve for T in the equation: (1 + g)T = 2.

The Rule of 70



� Take logs of both sides: log((1 + g)T

)= log(2) ≈ 0.693.

The Rule of 70




)= log(2) ≈ 0.693.

� Also: log((1 + g)T

)= T log(1 + g) ≈ Tg .

The Rule of 70




)= log(2) ≈ 0.693.

� Also: log((1 + g)T

)= T log(1 + g) ≈ Tg .

� Result:

T ≈ 0.693

g

(or: T ≈ 70

100g

).

The Rule of 70 (cont’d)


Annual growth rate of GDP Doubling time



1% 70 years



1% 70 years2% 35 years



1% 70 years2% 35 years3% 23 years



1% 70 years2% 35 years3% 23 years5% 14 years



1% 70 years2% 35 years3% 23 years5% 14 years

� Lesson: Small changes in growth rates have dramatic long-runeffects!

U.S. Growth History

U.S. Growth History

� U.S. GDP doubled between 1947 and 1965: 18 years.

U.S. Growth History


� Average growth rate during this period: 70/18 ≈ 3.9%.

U.S. Growth History



� U.S. GDP doubled again between 1965 and 1987: 22 years.

U.S. Growth History



� U.S. GDP doubled again between 1965 and 1987: 22 years.


Population Growth

Population Growth

� What we really care about is GDP per capita (or GDP perperson).

Population Growth


� Define: Nt = U.S. population in year t.

Population Growth



� Suppose the population growth rate is n: Nt+1 = (1 + n)Nt .

Population Growth




� The U.S. population roughly doubled between 1950 and 2006(from 150,000,000 to 300,000,000).

Population Growth




� The U.S. population roughly doubled between 1950 and 2006(from 150,000,000 to 300,000,000).

� Average annual growth rate n = 70/56 ≈ 1.3% (or 0.013).

Growth in GDP per Capita


� GDP per capita in year t is: Yt/Nt .



� Final useful fact: log(x/y) = log(x) − log(y).




� Growth in GDP per capita is (approximately):





log

(Yt+1

Nt+1

)− log

(Yt

Nt

)





log

(Yt+1

Nt+1

)− log

(Yt

Nt

)= log(Yt+1) − log(Yt) −

(log(Nt+1) − log(Nt))





log

(Yt+1

Nt+1

)− log

(Yt

Nt



≈ g − n.





log

(Yt+1

Nt+1

)− log

(Yt

Nt



≈ g − n.

� Annual growth rate of U.S. GDP per capita since 1950:3.5% − 1.3% = 2.3%.





log

(Yt+1

Nt+1

)− log

(Yt

Nt



≈ g − n.

� Annual growth rate of U.S. GDP per capita since 1950:3.5% − 1.3% = 2.3%.

� Doubling time = 70/2.3 ≈ 35 years.

Determinants of Growth


� Physical capital:


� Physical capital:Machines, buildings, infrastructure.



� Human resources:



� Human resources:Labor supply, education, motivation, human capital.




� Technology:




� Technology:Science, engineering, management techniques.

Determinants of Growth (cont’d)

� Natural resources:


� Natural resources:Land, oil, minerals, quality of the environment.



� Institutions:



� Institutions:Property rights, enforceable contracts (legal system), patentand copyright law.




� Culture:




� Culture:Social capital, entrepreneurial energy, the Protestant workethic and the spirit of capitalism (Max Weber).

The Aggregate Production Function


� Basic economic models of growth set aside natural resources,institutions, and culture and focus instead on:


� Basic economic models of growth set aside natural resources,institutions, and culture and focus instead on: K (stock ofphysical capital),


� Basic economic models of growth set aside natural resources,institutions, and culture and focus instead on: K (stock ofphysical capital), L (labor supply),


� Basic economic models of growth set aside natural resources,institutions, and culture and focus instead on: K (stock ofphysical capital), L (labor supply), and A (technology).



� How much can an entire economy produce?



� How much can an entire economy produce? Economists usethe abstraction of an aggregate (or economywide) productionfunction F :




Y = F (K , L, A).




Y = F (K , L, A).

� A simple yet empirically plausible choice for F is theCobb-Douglas production function:




Y = F (K , L, A).


Y = AKαL1−α,




Y = F (K , L, A).


Y = AKαL1−α,

where α (pronounced “alpha”) is roughly 1/4.

Constant Returns to Scale


� The production function Y = AKαL1−α exhibits constantreturns to scale.



� For any constant s > 0,

sY = A(sK )α(sL)1−α.





� Rewrite the production function in per capita terms:






Y

L= A

(K

L

)α






Y

L= A

(K

L

)α

� GDP per worker (Y /L) depends on technology (A) and on theamount of capital per worker (K/L).

What are the Sources of Growth?


� Fundamental Question:


� Fundamental Question: What accounts for the observedgrowth of U.S. GDP?



� How much of the growth in GDP can be attributed to:



� How much of the growth in GDP can be attributed to:� Capital formation (changes in K )?



� How much of the growth in GDP can be attributed to:� Capital formation (changes in K )?� Growth in the supply of labor (changes in L)?



� How much of the growth in GDP can be attributed to:� Capital formation (changes in K )?� Growth in the supply of labor (changes in L)?� Growth in technology (changes in A)?




� Another useful approximation:




� Another useful approximation: Suppose Yt = (1 + gt)Yt−1,where the growth rate, gt , is allowed to change over time.Then:




� Another useful approximation: Suppose Yt = (1 + gt)Yt−1,where the growth rate, gt , is allowed to change over time.Then:

log(Yt) − log(Yt−1) = log(1 + gt) ≈ gt .

Growth Accounting

Growth Accounting

� Take logs of both sides of the aggregate production function:

Growth Accounting


log(Yt) = log(At) + α log(Kt) + (1 − α) log(Lt)

Growth Accounting



log(Yt−1) = log(At−1) + α log(Kt−1) + (1 − α) log(Lt−1)

Growth Accounting




� Subtract the second equation from the first:

log(Yt) − log(Yt−1) =

Growth Accounting





log(Yt) − log(Yt−1) = log(At) − log(At−1) +

Growth Accounting






α(log(Kt) − log(Kt−1)) +

Growth Accounting







(1 − α)(log(Lt) − log(Lt−1))

Growth Accounting







(1 − α)(log(Lt) − log(Lt−1))

� This delivers the growth accounting equation:

Growth Accounting







(1 − α)(log(Lt) − log(Lt−1))


gYt = gA

t + αgKt + (1 − α)gL

t .

Growth Accounting







(1 − α)(log(Lt) − log(Lt−1))


gYt = gA

t + αgKt + (1 − α)gL

t .

� Rearrange to get: gAt = gY

t − αgKt − (1 − α)gL

t .

What is the Rate of Technological Change?


� In the U.S. for the time period 1948–2001:


� In the U.S. for the time period 1948–2001:Average annual growth rate of GDP, gY , is 3.6%.


� In the U.S. for the time period 1948–2001:Average annual growth rate of GDP, gY , is 3.6%.Average annual growth rate of capital, gK , is 4.4%.


� In the U.S. for the time period 1948–2001:Average annual growth rate of GDP, gY , is 3.6%.Average annual growth rate of capital, gK , is 4.4%.Average annual growth rate of employment, gL, is 1.4%.


� In the U.S. for the time period 1948–2001:Average annual growth rate of GDP, gY , is 3.6%.Average annual growth rate of capital, gK , is 4.4%.Average annual growth rate of employment, gL, is 1.4%.Set α = 1/4 and “back out” the rate of technological change:

gA = gY − αgK − (1 − α)gL




= 3.6% − (1/4)(4.4%) − (3/4)(1.4)%




= 3.6% − (1/4)(4.4%) − (3/4)(1.4)%

= 3.6% − 1.1% − 1.1%




= 3.6% − (1/4)(4.4%) − (3/4)(1.4)%

= 3.6% − 1.1% − 1.1%

= 1.4%




= 3.6% − (1/4)(4.4%) − (3/4)(1.4)%

= 3.6% − 1.1% − 1.1%

= 1.4%

� Increases in inputs (K and L) account for (1.1+1.1)/3.6 =61% of the growth in GDP.




= 3.6% − (1/4)(4.4%) − (3/4)(1.4)%

= 3.6% − 1.1% − 1.1%

= 1.4%

� Increases in inputs (K and L) account for (1.1+1.1)/3.6 =61% of the growth in GDP.

� Technological change (or total factor productivity growth)accounts for 1.4/3.6 = 39% of the growth of GDP.

Growth Rate of GDP per Worker


� Rearrange the growth accounting equation:

gYt − gL

t = gAt + α(gK

t − gLt )



gYt − gL

t = gAt + α(gK

t − gLt )

� gYt − gL

t is the growth rate of GDP per worker (Y /L),sometimes called labor productivity.



gYt − gL

t = gAt + α(gK

t − gLt )

� gYt − gL


� gKt − gL

t is the growth rate of the capital-labor ratio (K/L).



gYt − gL

t = gAt + α(gK

t − gLt )

� gYt − gL


� gKt − gL


� Increases in K/L are called “capital deepening”: each workerhas more capital to work with.



gYt − gL

t = gAt + α(gK

t − gLt )

� gYt − gL


� gKt − gL



� In U.S. data:



gYt − gL

t = gAt + α(gK

t − gLt )

� gYt − gL


� gKt − gL



� In U.S. data:� gY − gL ≈ 2.2%



gYt − gL

t = gAt + α(gK

t − gLt )

� gYt − gL


� gKt − gL



� In U.S. data:� gY − gL ≈ 2.2%� gA ≈ 1.4%



gYt − gL

t = gAt + α(gK

t − gLt )

� gYt − gL


� gKt − gL



� In U.S. data:� gY − gL ≈ 2.2%� gA ≈ 1.4%� gK − gL ≈ 3.0%

U.S. Productivity Growth in the 20th Century

0

0.5

1

1.5

2

2.5

3

3.5

1899-2005 1899-1948 1948-1973 1973-1995 1995-2005

Gro

wth

in o

utpu

t per

hou

r (%

per

yea

r)

Figure 1.1 Output of the U.S. economy, 1869–2002–Watch TV –Play video games Unequal Standards of Living Across Time John D. Rockefeller, oil entrepreneur who lived from 1839

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