Economic Growth

1. Economic Growth • Core hypothesis: Economic growth doesn’t just happen; rather, it is endogenous, and depends on the choices society makes about political and economic organization, policies, and history. • In this module, we look at • History of thought on growth • Stylized facts of growth • Early models of growth, from Malthus to Solow • Current models of endogenous growth

2. History:The first revolution: Adam Smith (1723-1790) • Theory of wealth creation, public policy, and economic growth Saving and investment are by-products and precursors of domestic and foreign trade size of the market division of labour efficiency

3. The first revolution:Adam Smith • Saving and investment stimulate growth • direct effects through accumulationof capital • indirect effects through labour productivity • further indirect effects through interaction with exchange and trade, through foreign investment • domestic market can take the place of foreign markets

4. The first revolution:Adam Smith • Smith’s reference to ‘private misconduct’ and the ‘publick extravagance of government’ • Problem of public corruption and what economists now call “regulatory capture” • Distinction between quantity and quality • Quality enhances the productivity of workers and other technological inputs to production, and permits further technical innovation to occur • Mutual advantages of trade and growth, links to geography • First recognition of the concept of comparative advantage

5. The first revolution:Adam Smith Benefits from division of labour • If specialization increases efficiency • and wealth and, thereby, economic • growth, then ... ... just about anything that increases efficiency by the same amount, other things being equal, should be expected to have the same effect on growth.

6. The first revolution:Adam Smith • Implications for growth If foreign trade enlarges themarket and thus facilitates further division of labour à la Smith, thereby increasing wealth and growth, then ... • ... all other equivalent means of • increasing the efficiency or quality • of labour, capital, and land should be • expected to affect economic growth in the same way.

7. The first revolution:Adam Smith • Smith on education, efficiency, and growth • Distinction between the quantity and quality of labour  education, by increasing labour productivity, also increases efficiency and growth • Smith feared the economic, political, and social consequences of inferior education among the masses • He favoured public support for education • First recognition of the external economic benefit to society of mandatory universal education

8. The first revolution:Adam Smith - Summing up • Economic growth = increase in the quantity and quality of the three main factors of production: labor, capital, and land • Growth accounting is based on this classification • Two shortcomings: • Fixed quantity of land – diminishing returns • Increase in the labour force does not reallycount as a source of economic growth

9. Adam Smith’s followers Thomas Malthus Question of population growth and its effect on economic growth David Ricardo Impact of the distribution of wealth and of foreign trade

10. Malthus: A Formal Model Ld=labor demand Labor (Pop.) Ls=labor supply Real Wage CBR CBR, CDR NRI=0 CDR Real Wage w*

11. Effects of CharityA Malthusian Perspective Growth shifts Ls curve up thus reducing the effective wage. Labor (Pop.) Ls2 3 Ls The effective wage falls until CBR=CDR, leaving the level of living as was prior to charity. Ld Real Wage CBR CBR, CDR CBR>CDR => Growth 2 Worker receives w*-c from labor and c in charity. CDR Real Wage (w*-c) w* (w*+c) 1

12. Malthus: The Plague Ld Labor (Pop.) Ls 2 Ls2 Real Wage CBR CBR, CDR 1 CDR2 CDR Real Wage w* w2*

13. Technological Advances Ld Ld2 Labor (Pop.) 1 Ls2 4 Ls Real Wage CBR CBR, CDR 3 population grows NRI=0 CDR Real Wage w* w2 5: wage returns to w* 2

14. Adam Smith’s followers • John Stuart Mill • rejected Malthus’s prediction that population would outgrow productive capacity • more and better education would restrain population growth • distribution a different matter than production but can be changed through policy

15. Adam Smith’s followers • Karl Marx • Economic mechanisms driving production and distribution are closely related • Anticipates Henry Ford’s comment on the importance of income as a determinant of aggregate demand • General equilibrium effects are important • The limits to growth observed by Malthus are inescapable  ‘technological unemployment’

16. Adam Smith’s followers • Alfred Marshall • organization as a fourth factor of production • made explicit the connection between education and growth • distribution of income and wealth matters for efficiency and growth ‘Knowledge is our most powerful engine of production ... Organization aids knowledge’

17. Adam Smith’s followers • Joseph Schumpeter • technology through invention, innovation, and entrepreneurship • rent-seekers motivated by monopoly profits • perfectly competitive markets may not be very conducive to economic growth • no rent to capture under perfect competition

18. Adam Smith’s followers • John Maynard Keynes Accumulation of capital ‘Science and technical inventions’ ‘I draw the conclusion that, assuming no important wars and no important increase in population, the economic problem may be solved, or be at least within sight of solution, within a hundred years.’

19. Modern Models of Growth

20. Stylized Facts of Growth Per capita growth rate

21. Stylized Facts of Growth Return to Capital

22. Stylized Facts of Growth Why is the rate of depreciation increasing?

23. Stylized Facts of Growth Capital-Output Ratio

24. Stylized Facts of Growth Investment rates

25. Stylized Facts of Growth Consumption and income Time-series data 1929-82, in 1982 $$

26. Enter mathematics: Harrod and Domar • Paul Samuelson’s • Foundations of Economic Analysis(1948) • laid the basis for mathematical economics, including the modelling of dynamic interactions among macroeconomic variables

27. Enter mathematics: Harrod and Domar Net investment equals the increase in the capital stock … net of depreciation due to physical or economic wear and tear High level of investment entails an increasing level of the capital stock High levels of saving and investment are good for growth even if they are stationary, that is, not increasing By continuously augmenting the capital stock ... • … even stationary levels of saving and investment relative to output drive output higher and higher, thus generating economic growth • Flows of investment add to the stock of capital

28. Enter mathematics: Harrod and Domar Efficiency is crucial for growth High level of efficiency stimulates growth by ... … amplifying the effects of a given level of saving and investment on the rate of growth of output All that is required is a steady accumulation of capital through saving and investment A given level of efficiency, including the state of technology will, then translate the capital accumulation into economic growth

29. Enter mathematics: Harrod and Domar • Harrod and Domar expressed the dynamic relationship between saving, efficiency, and growth in a simple equation So, Samuelson’s work neatly formalized, simplified, and summarized the essence of almost 200 years’ theorizing about economic growth The Harrod-Domar model 

30. The Harrod-Domar model • Economic growth depends on three factors: • A. the saving rate • B. the capital/output ratio • C. the depreciation rate

31. The Harrod-Domar model:Mathematics • Notation: • Y denotes national income • K denotes capital stock • S denotes saving • Y denotes national income

32. The Harrod-Domar model:Mathematics • Assumptions: • Saving is proportional to income: S=sY • Capital-output ratio is constant: K=vY • Investment (newly produced capital goods) must be allocated between increasing the stock of capital and replacing depreciated capital: I=K+K • At equilibrium S=I (desired saving =desired investment)

33. The Harrod-Domar model:Mathematics • Harrod-Domar equation • From the capital-output ratio assumption, we can write K=v Y. • Substituting into the expression for investment, we have I=v Y+vY • Using the equilibrium condition, we then have sY= v Y+vY or D Y/Y=s/v-d • Example: s=0.2, v=3, d=0.04 yields a growth rate of roughly 3%.

34. The Harrod-Domar model • Shortcomings: • Neither theory nor empirical evidence seemed to provide much support for the capital/output ratio as an exogenous behavioural parameter in the model • a more elaborate formulation of the link between capital and output was called for • The model did not leave much room for the other crucial factor of production, labor • population or labor-force growth is absent from the formula, which explains output growth solely by saving and efficiency

35. The second revolution: The neoclassical model Since population growth is basically a demographic phenomenon and, hence, exogenous from an economic point of view, it must follow that economic growth is also exogenous According to Solow, saving behaviour was no longer relevant for long-run growth, nor was efficiency in a broad sense, except insofar as it mattered for technology Economic growth was considered immune to economic policy, good or bad Even so, saving and efficiency play an important role for growth over long periods, that is, the medium term

36. The second revolution:The neoclassical model Solow showed how the capital/output ratio, rather than being exogenously fixed as in the Harrod-Domar model, • … is better viewed as an endogenous variable, which moves over time and ultimately reaches long-run equilibrium Once attained, the long-run equilibrium is consistent with not only a constant capital/output ratio • … but also with a constant rate of growth of output per capita, a constant rate of interest, and a constant distribution of national income between labour and capital, all of which seemed to apply to the real world

37. The Neoclassical ModelMathematics • Output is produced via a production function which uses capital and labor as inputs where the parameter a is between 0 and 1. • Taking logs on both sides and differentiating yields • Here, g is the rate of growth of output in percentage terms, n is the exogenously given rate of growth of the labor force (or equivalently, of population), and is the rate of growth of the capital stock.

38. The Neoclassical ModelMathematics • From empirical work by Kuznets, it is plausible to assume that the long-run capital-output ratio is constant, which implies that • Plugging into the growth equation, then, we have

39. The Neoclassical ModelMathematics • Thus, in the Solow model, the long-run rate of growth is determined entirely by the exogenously given rate of population growth. • It also follows that in the long-run, there can be no growth in per capita output • Since we obviously have seen significant increases in standard of living since the onset of industrialization in the early 1800’s, the model must be modified if it is to explain this.

40. The Neoclassical ModelMathematics • We can explain the observed growth in per capita output by assuming that technological change makes the labor input more productive over time, due to factors such as better technology or better education of the workforce. With this assumption, the production function becomes • B represents some initial state of technology • e is the base of the natural logarithm • Labor productivity grows at the rate q • We refer to as the efficiency unit equivalent of the labor input

41. The Neoclassical ModelMathematics • Log differentiating the production function now gives • As before, taking the long-run capital-output ratio as constant yields • So, we now have that growth is exogenous, being driven by productivity improvements, but per capital growth is now positive and equal to q.

42. The Neoclassical ModelMathematics • Comparing the growth equation for the Solow model with that of the Harrod-Domar model, we see that we must now have • If all the parameters n,q,s,v, and d are exogenously given, then we would generally not expect the equality above to hold. • Mathematically, the Harrod-Domar model is now over-identified. • Solow resolved this over-identification by assuming that the capital-output ratio, rather than being exogenously specified, was a function of the other parameters of the model:

43. The Neoclassical ModelMathematics • How do we know the capital-output ratio is the right parameter to make endogenous? • Consider the original definition of investment: • This can be re-written as • Since saving must equal investment in the long-run, I/Y=s, and we may then solve the equation above for the capital-output ratio as • Hence, changes in any of the right-hand parameters will affect the value of the capital-output ratio.

44. The Neoclassical ModelMathematics • We can also use this result to solve for the rate of growth of capital in terms of other parameters of the model: • Substituting for the rate of growth of capital in the Solow growth equation yields • This equation tells us that if we increase saving, then the economy will grow as long as the capital-output ratio remains constant. • We turn next to the question of whether this ratio will in fact remain constant.

45. The Neoclassical ModelMathematics • Dynamics of the capital-output ratio • Define the following ratios of capital and output per efficiency unit at time t: • The percentage rate of change of the first ratio is where we use the relationship between the rate of change of capital to the capital-output ratio to arrive at the right-hand side of the equation.

46. The Neoclassical ModelMathematics • We can also write the production function in terms of the two ratios as • Now, since substituting into the expression for the rate of growth of capital, we get a key equation:

47. The Neoclassical ModelMathematics • The Solow differential equation • If k is small, so that is large, the the rate of change of k will be positive, so the capital stock will increase. On the other hand, if k is large, will be small, so that the rate of change will be negative. • This means that if we start at a low level of capital, the economy will accumulate capital, while if we somehow started with a large amount of capital, we will decumulate it. • Hence, independently of where the economy starts, it will evolve toward a steady-state at which

48. The Neoclassical ModelMathematics • Steady-state • Set the time derivative of k to zero and solve for k • Using the definition of k, we can find the steady-state values of capital and output:

49. The Neoclassical ModelMathematics • Note that the steady-state capital stock and flow of output are actually growing, but in a balanced way, at the same rate, so that the capital output ratio remains constant at • Income distribution in the Solow model • Standard results from producer theory tell us that at the competitive equilibrium, inputs are paid their marginal products. For the simple model with only capital and labor inputs, these are given by

50. The Neoclassical ModelMathematics The Neoclassical ModelMathematics • Hence, for the Cobb-Douglas specification of technology, each factor of production is paid a constant share (a for labor, 1-a for capital) of output. This is consistent with data for modern industrial economies, where labor receives 2/3 of total output, while capital receives 1/3. • This also gives us a way to calibrate the model, since it says we should set a=2/3. • Since the capital-output ratio is constant, it also follows that along a balanced growth path, interest rates will remain constant. • For labor, the real wage will grow at the rate g-n=q, since labor productivity is growing over time. • Calibration spreadsheet