Theories of Growth. Vani Borooah University of Ulster September 2007

Transcription

1 Theories of Growth Vani Borooah University of Ulster September 2007

2 The Power of Compound Interest Suppose growth in GDP is 3% per year Then after T years, an initial output of y 0 will become: y T =y 0 (1.03) T How long will it be before y doubles? For what value of T, will y T =2y 0? Answer: T=log(2)/log(1.03)=(0.69/0.03)=23 years or 1 generation Another country s economy is growing at 7%: in 20 years (1 generation) its output will quadruple

3 Catching Up The Tiger economies (y 1 ) are growing at 7% per year, while mature economies (y 2 ) are growing at 3% per year. Currently: y 1 = 0.5y 2. How long will it be before the Tiger economies catch up? In T years, income in both sets of countries will grow so that: y 2 (1.03) T =0.5y 2 (1.07) T Tlog(1.03)=Tlog(1.07) + log(0.5) T=log(0.5)/(log(1.03)-log(1.07)) T=18 years

4 The Harrod-Domar Model: I No theory of growth has had as much influence as the Harrod-Domar (H-D) model of growth all foreign aid to LDCs is based upon this model The central idea is as follows: Output (Y) is proportional to physical capital (K) Y = K/, where =K/Y is the capital-output ratio The basic relation for the change in capital between two time periods is: K t = (1- )K t-1 + I t, where is the depreciation rate

5 The Harrod-Domar model: II In a closed economy, S=I or s=(s/y)=i=(i/y) Y t = (1- ) Y t-1 + sy t-1 [(Y t -Y t-1 )/Y t-1 ]=s/ - This yields the basic H-D equation: g+ = s/ or g+ = i/ The growth rate is proportionate to the (saving) investment rate (share of saving or investment in national income)

6 The Financing Gap Approach to Growth Suppose =4. So, an investment rate of 4% (share of investment in GDP = 4%) will generate 1% growth per year If a country wants to raise its growth rate to 4% per year, it needs an investment rate of 16% But, its savings rate is only 4%: so there is a financing gap of 12 points between required investment and current investment This financing gap can be filled by foreign aid This is known as the financing gap approach to aid and underpins the logic of foreign aid

7 Role of Population Suppose population is growing at 2% per year. Then under a 1% growth rate, per capita income will fall over time Under a 4% growth rate, per capita income will increase at 2% per year or double every 36 years. Under population growth, the basic H-D equation is: g * + n + s/ where g * is growth in per-capita income and n is population growth

8 Role of Population: formal analysis Y t = (1- ) Y t-1 + sy t-1 Divide by P t-1 (population) to get: (Y t /P t )(P t /P t-1 )=(1- ) (Y t-1 /P t-1 )+s (Y t-1 /P t-1 ) y t =Y t /P t is per-capita income y t (1+n) = (1- ) (y t-1 ) + sy t-1 Divide by y t-1 to get: (1+g * )(1+n) = (1- ) + s/, g * is growth in y t g * + n + + ng * = s/ Since ng * is small: g * + n + s/

9 How to generate growth? Reduce population growth Increase domestic savings Seek foreign assistance

10 Stages of Growth The next step in the financing gap approach was to persuade rich countries to fill the gap This was provided by W.W. Rostow in his book, The Stages of Economic Growth. The last stage was take-off into sustained growth if investment could be increased to 10% of national income, growth would be self-sustaining This needed the financing gap to be plugged and, in turn, this needed foreign assistance.

11 Surplus Labour Theory Sir Arthur Lewis in his paper, Economic development with unlimited supplies of labour, Manchester School, 1954 provided more support He suggested a surplus labour model developing countries had excess labour but scarce capital With a fixed capital-output ratio, scarce capital set a ceiling to output However, increased investment would increase the capital stock which would absorb this surplus labour while agricultural production would not suffer

12 The Case for Aid Jefferey Sachs in his book The End of Poverty outlines the case for more aid to Africa 8,000 people die daily from Aids 27,000 children die daily from disease The number of poor in sub-saharan Africa has doubled in the last 20 years it is now 300 million Sachs calls for a doubling of aid from $65 billion to $135 billion

13 The Effectiveness of Aid Unfortunately, the history of aid is one of major failure In a study of 96 countries, countries which received large aid flows between fared no better than countries which received little aid (Peter Boone, Burnside and Dollar (AER, 2000) and Easterly et.al. (AER, 2004) came to he same conclusion large aid flows do not raise growth What works are very specific projects eradication of small pox, river blindness, vaccination programmes, famine relief etc. But, only 4% of aid goes to health the largest (23%) goes to economic infrastructure and that s where it is ineffective

14 Did it Work? The financing gap approach makes two assumptions Aid leads to investment Investment leads to growth Are these assumptions borne out by the facts?

15 Zambia In 1960, per-capita income in Zambia was $500 Between , Zambia received $2billion in aid If all this had gone 1-1 into investment and if investment had led to growth, Zambia s percapita income in 1993 should have been $20,000 In fact, it was $600

16 The Facts About the Financing Gap: Aid and Investment We have data on 88 countries between (see William Easterly, The Elusive Quest for Growth, MIT Press, 2001) Only 17 of the 88 countries showed a positive relationship between aid and investment In only 6 countries did investment increase one-toone with aid an additional 1% of GDP in aid lead to an extra 1% GDP in investment. Of these 6, only 4 Tunisia, Morocco, Malta, and Sri Lanka received non-trivial amounts of aid

17 The Facts About the Financing Gap: Investment and Growth Is there a positive relationship between investment and growth which is also reasonable? Only four of 138 countries pass this test so, investment is not sufficient for growth Is it necessary for growth? Look at four-year long high growth episodes and check how many were preceded by high investment Only 6% of high growth episodes were preceded by high investment i.e. investment was necessary for growth in only 6% of cases

18 Why Doesn t Aid Work? Aid goes into consumption not investment Aid goes into unproductive projects military hardware, presidential palaces Even when projects are prima facie useful, they are poorly chosen with little accountability It all boils down to the quality of governance in the aid receiving countries

19 Is Investment the Key to Growth? The Solow Model The big drawback of the H-D model was that the capital-output ratio ( ) was fixed only one technology was available In the Solow model, is endogenous because capital and labour combine via a production function to produce output: Y = F(L, K) where CRS implies Y/L = f(k/l) So, per-capita output will rise as per-capita capital increases

20 Diminishing Returns But as we apply more and more capital to a fixed amount of labour, diminishing returns to capital will set in each additional unit of capital will result in progressively smaller additions to output How severe these diminishing returns will be will depend upon how important capital is in production If capital is very important, diminishing returns will be slow But, if capital is relatively unimportant, diminishing returns will be rapid Capital accounts for only 1/3 of total income in the USA while labour accounts for 2/3

21 Implications If an economy tried to grow by increasing capital, then, initially, when capital was scarce, per-capita output (Y/L) would increase rapidly But, after a while, increases in per-capita output would slow down for given increases in capital Eventually, when the marginal product of capital was zero, per-capita income growth would be zero In the absence of technical progress, a country cannot sustain a growth in per-capita income, based on increasing its capital stock, indefinitely

22 Innovation is the Answer Technology refers to the amount of output a given quantity of labour and capital can produce Innovation means that over time larger outputs are obtained with the same quantities of inputs We write the production function as: Y=F(L,K,t) for a time variable, t Innovation means ( Y/ t)>0

23 Sources of Growth There are three sources of growth: Growth in Labour Growth in Capital Technological Progress (TFP)

24 TFP growth and the East Asian Miracle East Asian countries showed spectacular rates of growth between However, most of growth came from accumulation of capital through very high savings rates - and very little came from technological improvements (TFP growth)