macroeconomics - lmu

Ifo Institute for Economic Research at the University of Munich

Macroeconomics

Prof. Dr. Kai Carstensen

LMU and Ifo Institute


Definition: Economic Growth and Business Cycles

Economic Growth:

• Long term increase of real GDP, of the real potential

output (1. half of the semester).output (1. half of the semester).

Business Cycles:

• Multi-year fluctuations in the degree of utilization of the

potential output, which show certain similarities.

• Indicators: growth rate of the (real) GDP, degree of

utilization of the potential output.

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utilization of the potential output.

• Business cycle theory (2. half of the semester).


Business Cycles and Growth Dynamics in China (Growth Rates in Percent)

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16

4

6

8

10

12

3

Questions: Why did China experience such high growth rates over the last 30 years?

What are the „growth drivers“ of the Chinese economy?

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1980 1985 1990 1995 2000 2005

WACHSTUM_CHINA KONJUNKTUR_CHINANqpi"Vgto"Itqyvj"Tcvg Ujqtv"Vgto"Itqyvj"Tcvg


Business Cycles and Growth Dynamics in the United States (Growth Rates in Percent)

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8

-2

0

2

4

6

4

-4

1980 1985 1990 1995 2000 2005

KONJUNKTUR_USA WACHSTUM_USA

Questions: Is monetary or fiscal policy able to smooth business cycles?

Are smoother business cycles really desirable?

Nqpi"Vgto"Itqyvj"Tcvg Ujqtv"Vgto"Itqyvj"Tcvg

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Overview

A. Growth TheoryA. Growth Theory

1. Neoclassical Growth Model (Solow/Swan Model)

2. Ramsey Model

3. New Growth Theory

B. Business Cycle Theory

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4. Real Business Cycle Model

5. New Keynesian Model


A. Growth Theory – Introduction

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Growth Theory – Introduction

1. Definitions1. Definitions

2. Stylized Facts

3. Aim and History of Economic Growth Theory

4. Basics: Mathematical Properties of the Growth Paths

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5. Exercises


Growth Theory – Definitions (1)

• Economic growth is the quantitative/qualtitative increase in the availability/production of goods and services in an in the availability/production of goods and services in an economy. The typical reference value is the GDP.

• One can distinguish extensive growth, which only refers to the absolute growth of GDP,

• and intensive growth, which refers to the per capita income (PCI) growth of GDP,

GDP

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where ,

with L as population number within the country.

L

GDPPCI =


• Change of the per capita income:


••

δ∂, with

• Growth rate of the per capita income:

L

L

GDP

GDP

PCI

PCI•••

−= .

2L

GDPLLGDPPCI

⋅−⋅=

•

t

PCIPCI

δ

δ=

•

.t

PCIPCI

∂

∂=

•

10

• When is defined as growth rate it follows that

LGDPPCI

g

LGDPPCI ggg −= . .



• The macroeconomic productivity of labour y must be distinguished from the per capita income:

, where L is the number of employees.GDP

y = , where L is the number of employees.L

y =

LGDPy ggg −= .

Germany US China

GDP per capita (2007) 31,306 $ 42,886 $ 7,868 $

GDP per worker (2007) 61,776 $ 84,341 $ 13,201 $

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• If every individual of the economy provides one unit of labour absolutely inelastic, both terms (productivity of labour and per capita income) are equivalent.

GDP per worker (2007) 61,776 $ 84,341 $ 13,201 $

Source: Penn World Tables 6.3; Notes: GDP data in 2005 dollars.




2. Stylized Facts



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5. Exercises


90

100United States

GDP per capita

Growth Theory – Stylized Facts (1)

30

40

50

60

70

80Germany

Turkey

Greece

GDP per Capita in the World Economy in 2000

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0

10

20

0 10 20 30 40 50 60 70 80 90 100

ChinaIndia

Turkey

Note: Real GDP per Person, current purchasing power parity; 162 countries; United States = 100; total population of 162 countries = 100. Source: World Bank, World Development Indicators, CDROM.

Population


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8

Growth rate

South Korea

Singapore

Catching Up and Falling Behind


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3

4

5

6

7

United States

South Korea

Thailand

Indonesia

Ireland

UK

Italy

TanzaniaArgentina

Kenia

IndiaGermany

Catching Up and Falling Behind (1960 – 2000)

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-2

-1

0

1

NicaraguaZambia

Côte d'Ivoire

Niger

Note: Average annual growth rate of real GDP per person (RGDPCH) in percent, 107 countries.Source: PWT 6.1.



GDP per

capita, 1970

GDP per

capita, 2007

Average annual

growth rate 1970-2007

"Rich" countries

USA 19,749 42,886 2.12%

Germany 15,364 31,306 1.94%

Japan 13,856 30,585 2.16%

France 14,818 29,633 1.89%

U.K. 13,990 32,181 2.28%"Poor" countries

""Jckvk 1,654 1,581 -0.12%

Laos 714 2,282 3.19%

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Laos 714 2,282 3.19%

""Iwkpgc/Dkuucw 340 623 3.11%

Uganda 1,101 1,171 0.17%

Source: Penn World Tables 6.3; Note: GDP data in 2005 dollars.



GDP per

capita, 1970

GDP per

capita, 2007

Average annual

growth rate 1970-2007

"Growth miracles"

China 796 7,868 6.39%

South Korea 3,058 23,850 5.71%

Taiwan 3,123 27,005 6.00%

Botswana 1,319 9,404 5.45%"Growth desasters"

Liberia 1,874 386 -4.18%

Dem. Rep. Kongo 1,786 390 -4.03%

Kuwait 97,813 42,074 -2.25%

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Kuwait 97,813 42,074 -2.25%

Nicaragua 3,775 2,176 -1.48%

Iraq 5,683 4,868 -0.42%

Source: Penn World Tables 6.3; Note: GDP data in 2005 dollars.


Upshot:


• There exist big differences between the per capita incomes of the particular countries.

• The growth rates differ significantly.

• The growth rates are not necessarily constant over time.

• The ordering of the counries can change over time. Poor

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countries can become rich (compared to other countries) and vice versa.




2. Stylized Facts



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5. Exercises


What is the Aim of Growth Theory? (1)

It wants to provide answers to questions like:

• Why do countries like East- and West-Germany, Taiwan • Why do countries like East- and West-Germany, Taiwan and China, South- and North-Korea develop so differently, although they have comparable starting situations? Why are we so rich and other countries so poor?

• Is China able to draw level with the biggest industrialized countries of the world?

• How much time does East-Germany need to reach the

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• How much time does East-Germany need to reach the stage of development we have in West-Germany?


• Why did West-Germany experience a „growth miracle“ after WW II and why did the winning countries France

What is the Aim of Growth Theory? (2)

after WW II and why did the winning countries France and England only have average growth rates at the same time?

• Why did economic output increase so much over the last centuries?

• What is the driver of economic growth?

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The History of Growth Theory

Growth Theory (GT)

Neoclassical GT(Solow/Swan (1956)Ramsey-Model,Cass/Koopmans (1965))

Endogenous GT

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With constant technology parameter (e.g. constant

productivity of capital, Rebelo (1991))

With flexible technology parameter (e.g. horizontal/ vertical innovation, Gross-

man/Helpman (1991))


Central Questions during this Course!

How do the models discussed in this course contribute to

the questions outlined on the previous slides?

We want to focus on two main aspects/dimensions:

• Time dimension: Why are we so much richer today

than we were in the past?

• Cross-country dimension: Why are some countries

so much richer than others?

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so much richer than others?




2. Stylized Facts



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5. Exercises


• The time series of real GDP typically follows a growth process and therefore exhibits an exponential shape.

• Intuition: In the long run, all time series grow exponentially:

Basics: Growth Paths and the Logarithm

• Intuition: In the long run, all time series grow exponentially: Xt = X0 exp(g t), where g is the long run growth rate.

• Before analysing the GDP time series it is standard to convert it into natural logarithms: ln(Xt) = ln(X0) + g t

• The slope of the time series in logs can be interpreted as a growth rate: ln(Xt) - ln(Xt-1) = g t – g (t-1) = g

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• This is approximately the same as a discrete growth rate:

1ln( ) ln( )t t t t t t

t t t

X X X X X X

t X t X X

•

+∂ ∂ ∂ −

= = ≈∂ ∂ ∂

.


8,000

BIP_CHINAGDP_China

Real GDP of China Base Year 1987, Bn Renminbi (Yuan)

2,000

3,000

4,000

5,000

6,000

7,000

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0

1,000

2,000

1980 1985 1990 1995 2000 2005

The development of the GDP in China seems to follow an exponential path!


Regression of the log of Chinese real GDP on a linear trend

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Log of Chinese real GDP and linear trendBase year 1987, Bn Renminbi (Yuan)

9.0

LOG_GDP_China

7.0

7.5

8.0

8.5

9.0

Slope: 0.094.

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6.0

6.5

1980 1985 1990 1995 2000 2005

LOG_BIP_CHINA LOG_BIP_CHINA_SIMNQIaIFRaEjkpc NQIaIFRaEjkpcaUKO


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Comparison of discrete and continuous (log-based) growth rates of Chinese real GDP

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6

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10

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in p

erc

en

t

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2

1980 1985 1990 1995 2000 2005

LOG_WACHSTUMSRATE WACHSTUMSRATE

Calculation: LOG_GROWTH_RATE = LOG_GDP_CHINA(t)-LOG_GDP_CHINA(t-1),

GROWTH_RATE=GDP_CHINA(t)/GDP_CHINA(t-1)-1.


Solving Growth Equations

• Assume the change of GDP follows the equation:

GDPgGDP ⋅=•

• Assume we know the average growth rate and we want to know the level of GDP in 10 years.

• We need a function consisting of the following arguments:

GDPg

tGDPt GDPgGDP ⋅= .

)t,g,GDP(fGDP GDPt 0= .

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Homogenous differential equation.

)t,g,GDP(fGDP GDPt 0= .


Deterministic Differential Equation of Order 1 (1)

• A linear homogenous differential equation of order 1 has the following form:

, where a is a fixed coefficient.

• Example:

, with .

tt axx =•

tt GDP.GDP ⋅=•

050 1000 =GDP

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This means that in each point in time, the change in GDP is 5 percent of the current level. The starting value in t=0 was 100.

.


•

• To solve the problem, the following steps are necessary:


0

homogene Differentialgleichung

Allgemeine Lösung, C ist eine Konstante

Anfangsbedingung

t t

at

t

x ax

x Ce

x C

•

=

=

=

K

K

K

• Solution of the homogenous differential equation:

…homogenous differential equation,

…general solution, C is a constant,

…initial condition (remember ).10=

⋅ae

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0

at

tx x e= .



• For our example we get:•


…homogenous differential equation,

…general solution, C is a constant,

…initial condition.

tt GDP.GDP ⋅=•

050t.

t eCGDP050

⋅=

CGDP =0

t.eGDPGDP

050⋅= .

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• For and we get:10t = 1000 =GDP

t eGDPGDP 0 ⋅= .

9164100 10050050

0 ,eeGDPGDP.t.

t =⋅=⋅=⋅

.




2. Stylized Facts

3. Aim and History of Economic Growth


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5. Exercises


Exercises

Exercise 1: The per capita income was equal to € 1,000. Within 10 years, the per capita income increased to € 2,594. What was the average growth rate over this period?growth rate over this period?

Exercise 2: After how many years would the income double, if the average growth rate is 2%, 3%, 5 %?

Exercise 3: Assume good growth policies increase average growth in Germany from 1.5% to 1.8%. Current income per capita is € 30,000. What is the reward after 5, 10, 50 years?

Exercise 4: In 2007 the per capita GDP was $ 42,886 in the US and $

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Exercise 4: In 2007 the per capita GDP was $ 42,886 in the US and $ 7,868 in China. Assume that both countries continue to grow with the average growth rates of the previous 20 years, which were 2.7% in the US and 8.8% in China. When will China overtake the US? Do you believe in this calculation?

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