Ifo Institute for Economic Research at the University of Munich. Macroeconomics. Prof. Dr. Kai Carstensen LMU and Ifo Institute

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1 Macroeconomics Prof. Dr. Kai Carstensen LMU and Ifo Institute

2 Definition: Economic Growth and Business Cycles Economic Growth: Long term increase of real GDP, of the real potential 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. Business cycle theory (2. half of the semester). 2

3 Business Cycles and Growth Dynamics in China (Growth Rates in Percent) W ACHSTUM_CHINA KONJUNKTUR_CHINA Questions: Why did China experience such high growth rates over the last 30 years? What are the growth drivers of the Chinese economy? 3

4 Business Cycles and Growth Dynamics in the United States (Growth Rates in Percent) KONJUNKTUR_USA W ACHSTUM_USA Questions: Is monetary or fiscal policy able to smooth business cycles? Are smoother business cycles really desirable? 4

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6 Overview A. Growth Theory 1. Neoclassical Growth Model (Solow/Swan Model) 2. Ramsey Model 3. New Growth Theory B. Business Cycle Theory 4. Real Business Cycle Model 5. New Keynesian Model 6

7 A. Growth Theory Introduction 7

8 Growth Theory Introduction 1. Definitions 2. Stylized Facts 3. Aim and History of Economic Growth Theory 4. Basics: Mathematical Properties of the Growth Paths 5. Exercises 8

9 Growth Theory Definitions (1) Economic growth is the quantitative/qualtitative increase 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, where, PCI = GDP L with L as population number within the country. 9

10 Growth Theory Definitions (2) Change of the per capita income: PCI PCI PCI = GDP GDP GDP L L L 2 L GDP, with Growth rate of the per capita income: When g PCI =. g L PCI δ PCI = tδ t is defined as growth rate it follows that = g g.. GDP L. 10

11 Growth Theory Definitions (3) The macroeconomic productivity of labour y must be distinguished from the per capita income: y = g y GDP L = ggdp gl., where L is the number of employees. Germany US China 11 GDP per capita (2007) 31,306 $ 42,886 $ 7,868 $ GDP per worker (2007) 61,776 $ 84,341 $ 13,201 $ Source: Penn World Tables 6.3; Notes: GDP data in 2005 dollars. If every individual of the economy provides one unit of labour absolutely inelastic, both terms (productivity of labour and per capita income) are equivalent.

12 Growth Theory Introduction 1. Definitions 2. Stylized Facts 3. Aim and History of Economic Growth Theory 4. Basics: Mathematical Properties of the Growth Paths 5. Exercises 12

13 Growth Theory Stylized Facts (1) GDP per capita 100 United States Germany Greece GDP per Capita in the World Economy in Turkey China India Population 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. 13

14 Growth Theory Stylized Facts (2) Growth rate 8 Singapore South Korea Thailand Ireland United States Catching Up and Falling Behind ( ) Indonesia Italy India Germany UK Kenia Argentina Tanzania Côte d'ivoire Note: Average annual growth rate of real GDP per person (RGDPCH) in percent, 107 countries. Source: PWT 6.1. Zambia Nicaragua Niger

15 Growth Theory Stylized Facts (3) GDP per capita, 1970 GDP per capita, 2007 Average annual growth rate "Rich" countries USA 19,749 42, % Germany 15,364 31, % Japan 13,856 30, % France 14,818 29, % U.K. 13,990 32, % "Poor" countries 1,654 1, % Laos 714 2, % % Uganda 1,101 1, % Source: Penn World Tables 6.3; Note: GDP data in 2005 dollars. 15

16 Growth Theory Stylized Facts (4) GDP per capita, 1970 GDP per capita, 2007 Average annual growth rate "Growth miracles" China 796 7, % South Korea 3,058 23, % Taiwan 3,123 27, % Botswana 1,319 9, % "Growth desasters" Liberia 1, % Dem. Rep. Kongo 1, % Kuwait 97,813 42, % Nicaragua 3,775 2, % Iraq 5,683 4, % Source: Penn World Tables 6.3; Note: GDP data in 2005 dollars. 16

17 Growth Theory Stylized Facts (5) 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 countries can become rich (compared to other countries) and vice versa. 17

18 Growth Theory Introduction 1. Definitions 2. Stylized Facts 3. Aim and History of Economic Growth Theory 4. Basics: Mathematical Properties of the Growth Paths 5. Exercises 18

19 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 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 stage of development we have in West-Germany? 19

20 What is the Aim of Growth Theory? (2) Why did West-Germany experience a growth miracle 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? 20

21 The History of Growth Theory Growth Theory (GT) Neoclassical GT (Solow/Swan (1956) Ramsey-Model, Cass/Koopmans (1965)) Endogenous GT With constant technology parameter (e.g. constant productivity of capital, Rebelo (1991)) With flexible technology parameter (e.g. horizontal/ vertical innovation, Grossman/Helpman (1991)) 21

22 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? 22

23 Growth Theory Introduction 1. Definitions 2. Stylized Facts 3. Aim and History of Economic Growth Theory 4. Basics: Mathematical Properties of the Growth Paths 5. Exercises 23

24 Basics: Growth Paths and the Logarithm 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: X t = X 0 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(x t ) = ln(x 0 ) + g t The slope of the time series in logs can be interpreted as a growth rate: ln(x t ) - ln(x t-1 ) = g t g (t-1) = g This is approximately the same as a discrete growth rate: ln( X t ) ln( X t ) X t X t X t + 1 X t = = t X t t X t X t. 24

25 Real GDP of China Base Year 1987, Bn Renminbi (Yuan) 8,000 BIP_CHINA GDP_China 7,000 6,000 5,000 4,000 3,000 2,000 1, The development of the GDP in China seems to follow an exponential path!

26 Regression of the log of Chinese real GDP on a linear trend 26

27 Log of Chinese real GDP and linear trend Base year 1987, Bn Renminbi (Yuan) 9.0 LOG_GDP_China Slope: LOG_BIP_CHINA LOG_BIP_CHINA_SIM 27

28 Comparison of discrete and continuous (logbased) growth rates of Chinese real GDP in percent LOG_W ACHSTUMSRATE W ACHSTUMSRATE Calculation: LOG_GROWTH_RATE = LOG_GDP_CHINA(t)-LOG_GDP_CHINA(t-1), 28 GROWTH_RATE=GDP_CHINA(t)/GDP_CHINA(t-1)-1.

29 Solving Growth Equations Assume the change of GDP follows the equation: GDPt = g GDP. GDP t Assume we know the average growth rate want to know the level of GDP in 10 years. g GDP and we We need a function consisting of the following arguments: GDP = f ( GDP,g,t ). t 0 GDP. Homogenous differential equation. 29

30 Deterministic Differential Equation of Order 1 (1) A linear homogenous differential equation of order 1 has the following form: x t = ax t Example: GDPt, where a is a fixed coefficient. = GDPt, with GDP 0 = 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

31 Deterministic Differential Equation of Order 1 (2) To solve the problem, the following steps are necessary: xt x x t 0 = = = ax t Ce C at K K K homogene Differentialgleichung homogenous differential equation, Allgemeine general Lösung, solution, C ist a eine constant, Konstante Anfangsbedingung initial condition (remember e a 0 =1 ). Solution of the homogenous differential equation: xt at = x0e. 31

32 Deterministic Differential Equation of Order 1 (3) For our example we get: GDP t = GDP t 0. 05t GDP = C e t GDP = C 0 homogenous differential equation, general solution, C is a constant, initial condition. Solution of the homogenous differential equation: GDP t 0. 05t = GDP0 e. t = 10 GDP = For and we get: GDP t = = 0. 05t GDP0 e = 100 e 164, 9. 32

33 Growth Theory Introduction 1. Definitions 2. Stylized Facts 3. Aim and History of Economic Growth 4. Basics: Mathematical Properties of the Growth Paths 5. Exercises 33

34 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? 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 $ 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? 34