MACROECONOMICS. Solow Growth Model Applications and Extensions. Zongye Huang ISEM, CUEB

Transcription

1 MACROECONOMICS Solow Growth Model Applications and Extensions Zongye Huang ISEM, CUEB

2 Kaldor Stylized Facts Kaldor (1957) proposed six statements about economic growth as "a stylized view of the facts". 1.The shares of national income received by labor and capital are roughly constant over long periods of time. 2.The rate of growth of the capital stock per worker is roughly constant over long periods of time. 3.The rate of growth of output per worker is roughly constant over long periods of time. 4.The capital/output ratio is roughly constant over long periods of time. 5.The rate of return on investment is roughly constant over long periods of time. 6.The real wage grows over time.

3 Kaldor Stylized Facts Shares of national income received by labor and capital are roughly constant over long periods of time. This is a feature of neoclassical production function. Capital stock (output) per worker grows at a roughly constant rate that does not diminish over time. Once we allow for exogenous technological change, output per capita grows permanently at a constant and positive rate that coincides with the exogenous rate of technological change. The capital-output ratio is roughly constant. In steady state output and capital grow at the exogenous rate of technological change and therefore the capital-output ratio is constant. The return to physical capital shows no trend. The marginal product capital, αy/k, is constant in steady state. Real wage grows over time. ( 1- α )Y/L increases at an exogenous rate g.

4 Cross Country Income Difference

5 Cross Country Income Difference

6 Quantify Income Differences

7 Quantify Income Differences

8 Quantify Income Differences Solow model implies huge differences in the returns to capital required to explain the observed variability across time or across countries in income per capita. In a world with some capital mobility the suggested differences in rates of return will lead to huge capital flows from rich to poor countries. Allocation puzzle of capital flows In 1990, the richest 20% of the world received 92% of the portfolio capital inflow; the poorest 20% only received 0.1%. Explanation: A and H.

9 Solow Model on Growth Rates The transitional dynamics: Change of growth rate over time. Loss of capital stock A higher saving rate Growth rates across countries. Economic convergence

10 The Transitional Dynamics k>0 k = 0 δ k < 0 s f(k) k k k t

11 A Example on Transitional Dynamics We can use the transitional dynamics of Solow model to consider the following example. West Europe after WWII. If there is a significant loss of capital stock, the Solow model predicts that relative low capital level leads to a period of high and decreasing growth.

12 Europe WWII There were significant reductions in capital stock.

13 Europe WWII

14 Change Saving Rate East Asian Growth Miracle A large increase in the saving rate, like the one experienced by some East-Asian economies in the 60 s, will be followed by a period of high (but decreasing) growth. Recall: how change investment/saving rate affect steady state?

15 An Increase of Saving Rate δ s f(k) k s f(k) k k k k t

16 East Asia

17 Convergence

18 Convergence

19 Convergence

20 Convergence This result is severely suffer from the sample selection problem. Only successful countries, the ones that meet the requirements to become part of the OECD, were included. Therefore, it is not surprising to find convergence, since those countries are rich nowadays wherever they began in Once the same prediction is checked against a broader data-set that includes not only high income countries but also middle and low income ones, the evidence of convergence disappears.

21 Convergence

22 Conditional Convergence When we look at economies that have similar underlying parameters and therefore similar steady states, we find that the initial level of income plays an important role in explaining the subsequent growth performance: areas with low initial incomes tend to grow faster reducing their distance to the leaders. US states, Japanese Prefectures and European regions,

23 Conditional Convergence

24 Conditional Convergence Once we control for the determinants of the steady state (specifically, investment in physical capital and human capital, and population growth) we recover some signs of convergence, what the literature calls conditional convergence. Economies that are further from their respective steady states tend to move towards those steady states taking larger steps.

25 Conditional Convergence

26 Conditional Convergence

27 Conditional Convergence In general the estimates of the speed of convergence are low, in the range of 1%- 2%. It implies that in one year the economy reduces by 1%~2% the distance to its own steady state, and it takes between 35 and 50 years to eliminate half of the initial gap. Overall the reported evidence on convergence tends to lean (weakly) towards models that stress the role diminishing returns to capital.

28 Development Accounting Decompose the income level of a country into contributions from inputs: Physical capital, Human capital, Labor And productivity (TFP). Goal: Highlight the relative importance of each of these factors in explaining income differences across countries.

29 Physical Capital Physical capital stock data are not available. But we have data on investment. Perpetual Inventory Method: use the data on investment (flow) to estimate capital stock (stock). Intuition: to interpret an economy s capital stock as an inventory.

30 Physical Capital

31 Physical Capital

32 Physical Capital

33 Hodrick Prescott Filter Hodrick and Prescott suggest 1600 for quarterly data. Ravn and Uhlig (2002) state that it should equal 6.25 for annual data and 129,600 for monthly data.

34 Physical Capital

35 Physical Capital

36 Human Capital

37 Development Accounting

38 Alternative Development Accounting

39 Alternative Development Accounting

40 Example: US vs China Data Sources: GDP and physical capital: Penn World Table 8.0. Output-side real GDP at current PPPs (in mil. 2005US$) Capital stock at current PPPs (in mil. 2005US$) Human capital: Barro and Lee database.

41 Example: US vs China Development Accounting

42 Results There is a broad consensus (Hsieh, and Klenow 2010): Differences in human capital account for percent of country income differences, Physical capital accounts for 20 percent of country income differences, Residual TFP may be the biggest part of the story ( accounting for percent of country income differences ). There are important positive feedback effects between human capital, physical capital, and TFP. In particular, the level of TFP of different sectors can influence the incentive to accumulate physical and human capital. Physical capital and human capital by lowering the price of capital Schooling by lowering the price relative to the price of output.

43 Traditional Growth Accounting

44 Traditional Growth Accounting

45 Traditional Growth Accounting What is the Solow residual? Conservative version: the part of growth that is not explained by (measurable) capital accumulation and labor force expansion. Solow s quote: a measure of our ignorance. Ambitious version: the part of growth that is explained by technological progress. There also an alternative way to do growth accounting.

46 Traditional Growth Accounting Industrialized countries over the period

47 Traditional Growth Accounting Source: Alwyn Young (1995 QJE)

48 Alternative Growth Accounting

49 Alternative Growth Accounting

50 Example:

51 Example: