An Overview of Long-Run Economic Growth

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1 An Overview of Long-Run Economic Growth Week 3 Vivaldo Mendes Dep. of Economics Instituto Universitário de Lisboa 1 October 2018 (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

2 Summary 1 Growth over the Very Long Run 2 Modern Economic Growth 3 Modern Growth around the World 4 Some Useful Properties of Growth Rates 5 The Costs of Economic Growth 6 Required reading (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

3 I Growth over the Very Long Run (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

4 Growth over the Very Long Run The Great Divergence 1 Sustained increases in standards of living are a recent phenomenon. 2 The Great Divergence 1 The recent era of increased di erence in standards of living across countries. 3 Before Today 1 Per capita GPD in nations di ered only by a factor of two or three. 1 Per capita GPD di ers by a factor of 50 for several countries. (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

5 Growth over the Very Long Run Graph of the Great Divergence (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

6 Growth over the Very Long Run II Modern Economic Growth (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

7 Modern Economic Growth The amazing improvement in living standards 1 From 1870 to 2000, United States per capita GDP rose by nearly 15-fold. 2 Implications for you? 1 A typical college student today will earn a lifetime income about twice his or her parents. 3 See next gure. (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

8 Modern Economic Growth Per capita GDP in the United States (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

9 Modern Economic Growth The De nition of Economic Growth 1 Growth of per capita GDP 2 Percentage change in GDP between period t and and t 1 3 Or g = y t y t 1 y t 1 y 1 = y 0 (1 + g) 1... y t = y 0 (1 + g) t (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

10 Modern Economic Growth The Rule of 70 and the Ratio Scale 1 If y grows at a rate of g percent per year, then the number of years it takes y to double is approximately equal to 2 Small di erences in growth rates result in large di erences over time. 3 The time it takes to double only depends on the growth rate and not the initial value. 4 A ratio scale 1 Its like a logarithm scale 70 g 2 When plotted on a ratio scale, a variable that grows at a constant rate will be a straight line (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

11 Modern Economic Growth The absolute vsersus ratio scale (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

12 Modern Economic Growth GDP has been rising since the 1880 s (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

Modern Economic Growth Calculating Growth Rates 1 The rule for computing growth rates 2 This formula can be applied even if the data does not exhibit

13 Modern Economic Growth Calculating Growth Rates 1 The rule for computing growth rates 2 This formula can be applied even if the data does not exhibit constant growth. 1 In this case we get an average annual growth rate solve for growth rate (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

14 Modern Economic Growth III Modern Growth around the World (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

15 Modern Growth around the World Real Economic Convergence 1 After World War II, growth in Germany and Japan accelerated. 2 Convergence (real): 1 Poorer countries will grow faster to catch up to the level of income in richer countries. 3 Brazil had accelerated growth until 1980 and then stagnated. 4 China and India have had the reverse pattern. (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

16 Modern Growth around the World Real convergence in a ratio scale (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

17 Modern Growth around the World Convergence: A Broad Sample of Countries 1 Over the period Some countries have exhibited a negative growth rate. 2 Other countries have sustained nearly 6 percent growth 3 Most countries have sustained about 2 percent growth. 2 Small di erences in growth rates result in large di erences in standards of living. (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

18 Modern Growth around the World The lack of convergence (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

19 Modern Growth around the World IV Some Useful Properties of Growth Rates (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

20 Some Useful Properties of Growth Rates Real Economic Convergence 1 Growth rates of ratios, products, and powers follow several simple rules. 2 Growth rates obey mathematical operations that are a level simpler than the operation on the original variable. 1 Variables divided growth rates subtracted 2 Variables multiplied growth rates added 3 Variable taken to a power number growth rate multiplied by that number (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

21 Some Useful Properties of Growth Rates Transforming functions into log-di erences: summary Variables in levels Variables in logs y t = 2x t, g y = g x y t = 2x t z t, g y = g x + g z y t = 2x t zt 3, g y = g x 3g z xt zt y t+1 = x t+1 + z t+1, g y = g x + g z y t y t xt y t+1 = x t+1 + a, g y = g x y t (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

22 Some Useful Properties of Growth Rates An example (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

23 Some Useful Properties of Growth Rates Growth Rules in a Famous Example 1 Original output equation 2 In terms of growth rates we have Y t = A t Kt 1/3 L 2/3 t g Y = g A + (1/3)g K + (2/3)g L (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

24 Some Useful Properties of Growth Rates Growth Rules in a Famous Example (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

25 Some Useful Properties of Growth Rates V The Costs of Economic Growth (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

26 The Costs of Economic Growth The bene ts of economic growth 1 Improvements in health 2 Higher incomes 3 Increase in the variety of goods and services (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

27 The Costs of Economic Growth The Costs of economic growth 1 Environmental problems 2 Income inequality across and within countries 3 Loss of certain types of jobs 4 Economists generally have a consensus that the bene ts of economic growth outweigh the costs. (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

28 The Costs of Economic Growth VI Required readings (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

29 The Costs of Economic Growth Required reading For this week you are required to read Read Chapter 3 of our adopted textbook. Charles I. Jones (2014). Macroeconomics, Third Edition, W. W. Norton & Company. (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

30 The Costs of Economic Growth Appendix How to transform functions in levels into log di erences The knowledge of this appendix is not compulsory. This is just used as a proof of the results above. (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

31 The Costs of Economic Growth Transforming functions into log-di erences: rst case 1 A linear function: Y t = 2X t. Apply logs to two consecutive periods: ln Y t = ln 2 + ln X t ln Y t+1 = ln 2 + ln X t+1 2 Therefore, the rst di erence of logs is ln Y t+1 ln Y {z } t = (ln 2 + ln X t+1 ) (ln 2 + ln X t ) = ln X t+1 ln X {z } t growth rate of Y: g Y growth rate of X: g X 3 In this kind of function, the growth rate of Y, let s call it ( g Y ), is equal to the growth rate of X, (g X ) g Y = g X (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

32 The Costs of Economic Growth Transforming functions into log-di erences: second case 1 A linear function of two independent variables: Y t = 2X t Z t. 2 Apply logs to two consecutive periods, and you will get g Y = g X + g Z 3 Prove this result yourself. (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

33 The Costs of Economic Growth Transforming functions into log-di erences: third case 1 A power function: Y t = 2X t Z 3 t. 2 Apply logs ln Y t = ln 2 + ln X t 3 ln Z t ln Y t+1 = ln 2 + ln X t+1 3 ln Z t+1 3 Therefore, the rst di erence of logs is ln Y t+1 ln Y {z } t = (ln 2 + ln X t+1 3 ln Z t+1 ) (ln 2 + ln X t 3 ln Z growth rate: g Y = ln X t+1 ln X {z } t 3(ln Z t+1 ln Z t ) {z } growth rate: g X 4 So this power function can be written in log as growth rate: g Z g Y = g X 3g Z (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

34 The Costs of Economic Growth Transforming functions into log-di erences: fourth case 1 The last function we need to consider is an additive function like Y t+1 = X t+1 + Z t+1 2 Here we can t apply logs. But there is another way 3 Firstly, multiply and divide through as follows Y t+1 Y t Y t = X t+1 X t X t + Z t+1 Z t Z t. 4 Now apply the following: Y t+1 Y t = 1 + g Y, X t+1 X t = 1 + g X, = 1 + g Z, and the previous eq. can be written as Z t+1 Z t 5 Divide through by Y t and get (1 + g Y ) Y t = (1 + g X ) X t + (1 + g Z ) Z t 1 + g Y = (1 + g X ) X t + (1 + g Z ) Z t Y t Y t (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

35 The Costs of Economic Growth Transforming functions into log-di erences: fourth case (cont.) 1 Notice that the previous equation can be written as Xt 1 + g Y = + Z t Xt Zt + g X + g Z Y t Y t Y t Y t {z } =(X t +Z t )/Y t =1 2 Therefore, an additive function like Y t+1 = X t+1 + Z t+1 can be expressed as Xt Zt g Y = g X + g Z Y t Y t 3 Notice that if Z = 2, its growth rate were z = 0, and we would get Xt g Y = g X Y t (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

36 The Costs of Economic Growth Transforming functions into log-di erences: summary 1 Let s summarize our results Variables in levels Variables in logs Y t = 2X t, g Y = g X Y t = 2X t Z t, g Y = g X + g Z Y t = 2X t Zt 3, g Y = g X 3g Z Y t+1 = X t+1 + Z t+1, g Y = g Xt X Y t + g Zt Z Y t Y t+1 = X t+1 + a, g Y = g X Xt Y t (Vivaldo Mendes ISCTE-IUL ) Macroeconomics I (L0271) 1 October / 36

Solow Growth Model. Michael Bar. February 28, Introduction Some facts about modern growth Questions... 4

Solow Growth Model. Michael Bar. February 28, Introduction Some facts about modern growth Questions... 4 Solow Growth Model Michael Bar February 28, 208 Contents Introduction 2. Some facts about modern growth........................ 3.2 Questions..................................... 4 2 The Solow Model 5