kin1
' ' л* л mm л &.1Ы1 ■ Ava^aa л ьам #* a t ft. i r-
A4J
The population in all OECD countries is ageing.This is a great concern because it is putting pressure on the general social security system and national savings.
The age pension was introduced by the Commonwealth government of Australia soon after Federation at the beginning of the twentieth century. In 2007-08.41 per cent of all Commonwealth government spending went on transfers to individuals for social safety net reasons, representing almost 9 per cent of GDR Of these transfers, the age pension remains the biggest item at 3 per cent of GDP. The government provides other forms of support for those who are retired. Two examples are residential aged care (which now costs 0.7 per cent of GDP), and Commonwealth health spending (taking almost 4 per cent of GDP), which disproportionately benefits the aged due to their higher need. The total fiscal support for the aged is now about 5 per cent of GDP, a significant amount of social security expenditure, and this expenditure is projected to grow rapidly in the next forty years, putting immense pressure on government finances. All over the developed world, the social security system is in trouble.
The reason: demographic changes. Life expectancy has steadily increased to about eighty years, and with it, the average length of retirement. The large baby-boom generations (born between 1946 and 1965) are approaching retirement.The fertility rate has fallen from 3.5 babies per woman in 1965 to 1.8 in 2008. but it seems to have stabilised. As a result, the racio of retirees to workers (about 20 per cent in 1980 in Australia) has been steadily increasing and will continue to increase over the next fifty years. In 2007 there were 3.1 million people over forty-five years who were retired, a ratio of 30 per cent to employment—for every retiree there were about three workers in Australia.The Commonwealth Treasury predicts that this ratio will increase to 40 per cent by 2042. For the OECD countries in total, this dependency ratio will rise from about 20 per cent now to about 50 per cent. At given benefit and tax rates, the ageing population means a growing imbalance between benefits and contributions. If governments do nothing, future budget deficits are bound to deteriorate.This will reduce future national savings.This is an ongoing problem that goes a long way towards explaining why the saving rote declined in Australia from 27 per cent between 1960 and 1974 to about 20 per cent thereafter. The same occurred elsewhere and is particularly acute in Japan. How can we solve this problem?
Consider these two ways to set up and run a social security system to support retirees:
• Tax workers and distribute the tax contributions as benefits to retirees.This is called a pay-as-you-go system. The system pays benefits out'as it goes'—that is. as it collects them in contributions.
• Tax workers, invest the contributions in financial assets, and pay back the principal plus the interest to workers when they retire.This is called a fully funded system. At any time, the system has funds equal to the accumulated contributions of workers from which it will be able to pay out benefits when these workers retire.
From the point of view of retirees, the two systems feel quite similar, although not identical:
BOX
• What the retirees receive in a pay-as-you-go system depends on demographics—the ratio of retirees to workers—and on the evolution of tax rates and revenues.
SAVING. CAPITAL ACCUMULATION AND OUTPUT
chapter 11
• What the retirees receive in a fully funded system depends on the rate of return on the financial assets held by the fund.
But in both cases workers pay contributions when they work and receive benefits when they have retired.
From the point of view of the economy, the two systems are very different: in a pay-as-you-go system the contributions are redistributed, not invested: in a fully funded system they are invested, leading to a higher capital stock.
Most actual social security systems are somewhere between pay-as-you-go and fully funded systems.The UK national insurance system is pay-as-you-go. with relatively high dedicated national insurance contributions and earnings-related payouts on retirement.The US system is close to pay-as-you-go, and is partially funded with a low social security tax and earnings-related payouts.The Australian age pension is pay-as-you-go. but without a tax dedicated to the age pension. It is considered unusual among rich countries because it is unfunded and means-tested, with the maximum pension to single people paid at a flat rate equal to 25 per cent of the average male wage (or $547 a fortnight in 2008). The payout is reduced gradually as income and assets exceed various thresholds. About three-quarters of Australian retirees have the age pension as their main source of income.The average age pension in Australia is now about 25 per cent of the average worker's income, which is much lower than in most other rich countries (the United States is 38 per cent, Canada is 37 per cent, the United Kingdom is 26 per cent, Germany is 45 per cent, Italy is 72 per cent, Japan is 49 per cent and France is 79 per cent).This means that age pensioners are treated less generously in Australia. It also means that the ageing population problem will have a smaller impact on Australia than these other countries. In 2004 the Australian government introduced a 'Future Fund', which it plans to build up to finance the superannuation liabilities for its own civilian and military employees. But this will do nothing directly for the ageing problem in general.
Even though Australia will suffer less than other rich countries from ageing, the Commonwealth Treasury predicted in its Intergenerationol Report in 2002. which was updated in 2007. that the cost of the age pension will rise from 2.5 per cent of GDP in 2007 to 4.4 per cent in 2047.Treasury expects the percentage point increase of 1.9 to be similar to that in the United States, but much less than in New Zealand, at 6, with the OECD average being 3.1. In addition. Australian spending on aged care is expected to almost triple to 2 per cent of GDP. and Commonwealth health spending is expected to almost double to 7.3 per cent of GDP in 2047, particularly due to the Pharmaceutical Benefits Scheme. (You can read more on this issue in Chapter 27.)
It is clear that much will have to be done to balance the system over the twenty-first century. Measures can be implemented now. perhaps used to accumulate a large trust fund, or they can be implemented later. The longer the wait, the larger the needed adjustment.
Possible measures are:
• Introducing a contributory tax for pensions.Though new taxes are never popular, a dedicated age pension tax would improve intergenerational equity and alleviate the looming budget crisis. In 1996 the Australian government imposed a 15 per cent tax (or surcharge) on employer-funded superannuation contributions for those on higher incomes.This was a progressive measure that could have helped to ease the future budgetary crisis. However, it was unpopular and was abolished in 2005.
• Increasing the retirement age. In Australia, men become eligible for the age pension at age sixty-five, while women currently need to be only sixty-three, though by 2014 the eligibility age for women will also be sixty-five. Some people argue that the pension age should be raised, even to seventy.
It used to be mandatory that people retire at age sixty-five. In Australia, it is now illegal to discriminate against employees on the basis of age. Even though many people now work well beyond sixty-five, the participation rate of older Australians in the labour force is continuing to decline.
• Decreasing the benefit rate paid by the government. Although there is no plan to reduce the age pension benefit rate, successive governments have worked hard at encouraging people to save more for their own retirement, which should reduce the demands on the age pension system.
- In the 1980s, the Labor government negotiated Accords with the unions, granting wage increases provided they were paid into superannuation funds. These initiatives weren't very effective in increasing the superannuation coverage of workers because they were one-off events.
- In 1992. the government introduced the Superannuation Guarantee Charge, which made it com¬pulsory for all employers to contribute a percentage of a worker's wage or salary into approved superannuation funds.The percentage was initially 3 per cent, and had risen to 9 per cent by 2003.
- The Howard government introduced tax concessions on earnings of superannuation funds to encourage voluntary contributions by employees.
- Individuals were given the right to choose their superannuation fund.
- From 2006, the income tax system no longer discouraged lump sum payouts from superannuation on retirement.
- People can split their superannuation contributions with their spouse, and from 2008 taxes on retirees have been eliminated. These changes make superannuation savings much more attractive to households.
Although superannuation is far from mature as a part of the solution to the ageing population problem, it has led to a boom in the superannuation industry, and provided an important boost to national savings in the 1990s. More than 90 per cent of workers had superannuation in 2008. compared with 55 per cent in 1988, but for many of these workers their super savings will not be enough to support their retirement. The Treasury estimates that, when the superannuation solution matures, workers will retire (on average) with double the real income they would have received with an age pension alone. In turn, this means that the government will have a smaller pension burden. More than nineteen countries in the world have introduced similar superannuation schemes to help deal with the ageing problem. Though the superannuation solution has eased the Australian government's future burden, the worrying conclusion of the Intergenerational Report remains: the proportion of GDP devoted to supporting the aged population will rise by 1.7 percentage points in each of the next forty years. National savings will continue to be an issue.
In the next chapter, we will see in more detail the role of population and labour force growth in our growth model. |
To leom more about the issues confronting Australia's social security "i the future, go to The Intergenerational Report, Commonwealth Treasury. 2007.
For developing countries, there are other lorces at work that can drive up their low saving rate and improve their standard ol living. How can changes in a developing country's demography affect its standard of living? In two ways:
• As a less-developed country develops, much of its niral population which experiences high fertility and high mortality, drifts to the towns, where fertility (births per woman i and mortality (deaths per capita) are much lower, fertility falls lirst. and so, with lewer children to feed, lamilies have more to spend per individual. Thus the standard ol living improves. This is the first dividend, which can last up to fifty years.
• Eventually labour force growth converges on thc lower birth rates, and the first dividend evaporates. But at about this stage lower mortality becomes apparent. When people realise that they will live longer, they plan for their longer survival by saving more in their prime working years. Thus more capital is accumulated to support the ageing socicty. This is the second dividend, and if policy is set to encourage it, its effect is permanent.
11.3 GETTING A SENSE OF MAGNITUDES
How large is thc effect of a change in the saving rate on output in the long run? For how long and by how much does an increase in the saving rate affect growth? How far is Australia from thc golden-rule level of capital? To get a better sense ol the answers to these questions, let us now make more specific assumptions, plug in some numbers, and see what we get.
Assume the production function is given by
Y = VWN (11.6)
Output equals ihe product ol the square root ol capital and the square root of labour. This pro¬duction function isn't too different from what wc would gel Irom econometric estimates for Australian GDP it we included human capital as well as physical capital. Note that this production function exhibits both constant returns to scale and decreasing returns to either capital or labour. It is an example of a Cobb-Douglas production function, which we discuss more in the appendix to this chapter.
Dividing both sides by N (because we are interested in output per worker):
УК VN \ К
N
K,
" \N =
N
Output per worker equals the square root of capital per worker. Put another way, the production function, /, relating output per worker to capital per worker is given by
f
Now return to equation (11.3). repeated here for convenience:
^f-i ^f ( ^t i ^f "7Г - ~n = sf ¥ " 8~x
Replacc }(K,/N) by V(K,/N)-.
K,
(11.7)
N N "V N "N
This equation describes the evolution ol capital per worker over time. Let's look at what it implies. The effects of the saving rate on steady-state output
How large is the effect of an increase in the saving rate on the steady-state level of output per worker?
4 A more geneml specification for the production would be Y= К 'N1 ' where a is a number between 0 and 1. In equation (11.6) we are assuming и is 0.5. giving equal weights to capital and labour. A more realistic productior function of К and N would give a smaller weight to capital, for example a = 0.3.We use 0.5 becausc we take a broader view of capital. In Section 11.4, we will explain how the accumulation of skills— say. through education or on-the-job training— generates human capital in addition to physical capital. Under this broader view, a coefficient of 0.5 for tool capital is reasonable.
4 The second equality follows from the following steps: v N/N =
VN l(yJN s/N) = 1/v'N.
SAVING. CAPITA I ACCUMULATION AND OUTPUT
chapter 11
Start with equation (117). In steady slate, the amount of capital per worker is constant, so the left side of the equation equals zero. This implies
= 8-
K*_ N
(We have dropped lime indexes, which are no longer needed because in steady state K/N is constant.' Square both sides:
ICY
= &
N
Divide both sides by (K*/Ni and reorganise:
(11.8)
K* N
Steady-state capital per worker equals the square of the ratio of the saving rate to the depreciation rate. From equations ( 1 1.6) and (I 1.8), steady-state output per worker is then given by
ii f*L lit]2 (i
N = V N = V U = U,
(П.9)
Steady-state output per worker equals the ratio of the saving rate to the depreciation rate. A higher saving rate and a lower depreciation rate both lead to higher steady-state capital per worker (equation 111.8]) and higher steady-siatc output per worker (equation 111.9]). To sec what this
implies, let s take a numerical example. Suppose lhat lhe depreciation rate is 0.1 (or 1(1 per cent per year and the saving rate is also 0.1 or 10 per cent . Then, from equations 1 I 1.8) and ( I 1.9). steady-state capital per worker and output per worker are both equal lo I Now suppose that thc saving rate doubles Irom 0.1 to 0.2. It follows from equation (11.8 that in the new steady state, capital per worker increases Irom 1 to 4. And Irom equation (I 1.9), output per worker doubles, from 1 to 2. Thus, doubling lhe saving rate leads, in the long run to doubling output per worker-, this is a large effect.
The dynamic effects of an increase in the saving rate
After ar increase in the saving rate, how long does it take tor output to reach its new steady-state level? Put another way. by how much and lor how long does an increase in the saving rate affect the growth rale?
To answer these questions, we must use equation (I 1.7 and solve il lor capital per worker in year 0 in year I, and so on.
Suppose that the saving rate, which had always been equal to 0.1, increases in year 0 from 0.1 to 0.2 and remains ai this higher value forever. In year 0, nothing happens lo ihe capital stock. 1 Recall thai il takes one year for higher saving and higher investment to show up in higher capital.) So, capital per worker remains equal to the steady-state value associated with a saving rate ol 0.1. From equation (I 1.8):
K„/N = (0.I/O.!)2 - l; - 1
In year I, equation (1 1.7) gives:
K.
N
With a depreciation rate equal to 0.1 and a saving rate now equal to 0.2, this equation implies that:
Ki г
— - I - 0.2\ I - 0.1(1) I.I N
In ihe same way, we can solve lor fG/.V and so on. Once we have the values ol capital per worker in year 0, in year I, and so on we can then use equation (1 1.6 to solve lor output per worker in year 0, in year I, and so on. Thc results ol this calculation are presented in Figure 11.7. Panel (a1 plots the level of output per worker against time. (V/\ increases over lime Irom its initial value of I in year 0 to iis steady-state value ot 2 in the long run. Panel b> gives the same information in a different way, plotting instead the growth rate ol output per worker against lime. As panel b i shows, growth ol output per worker is highest at the beginning and then decreases over lime. As the economy reaches iis new steady state, growth of output per worker returns to zero.
What Figure 11.7clearly shows is that the adjustment to lhe new. higher, long-run equilibrium takes a long time. It is only 40 per cent complete alter icn years, 63 per cent complete after twenty years. Put another way, the increase in the saving rate increases the growth rate ol output per worker tor a long time. The average annual growth rate is .3.1 per cent lor the lirsl ten years, 1.5 per cent lor the next ten. While changes in lhe saving rate have no effect on growth in thc long run. they do lead to higher growth for quite some time.
Effect on the level of output per worker 2.00
Years
SAVING, С Ail AL ACCUMULATION AND 01ЛРШ
chapter 11
Figure I 1.7 Dynamic effects of an increase in the saving rate from 10 to 20 per cent on the level and the growth rate of output per worker
0 5 10 15 20 25 30 35 40 45 50
Years
0
(b) Effect on output growth 5
To gt) back to the question raised at the beginning of the chapter: Can the low saving rate in Australia and the much lower US one) explain why the Australian and the US) growth rate has been low- -relative to many other OECD countries—since 1950? The answer would be yes' if Australia (and the United States) had had л higher saving rate in lhe past, and il this saving rate had decreased substantially in the last lilty years. II this were thc case, this could explain the period ol lower growth in Australia (and the United States) in the last lilty years along the lines of the mechanism in Figure I 1.7 iwiih the sign reversed, as we would be looking at a decrease—not an increase—in the saving rale). There is some truth in this. Focusing on Australia, the gross saving rate averaged .30 percent Irom 1959 /t takes a long time for output to adjust to its new higher level after an increase in the saving rate. Put another way. an increase in the saving rate leads to a long period of higher growth.
to 1975, and then dropped to 23 per cent by 2008. But this is only a partial explanation. Though the saving rate has been low in Australia for a long time, it is a small open economy, and so it docs not have to rely on domestic saving-, lor investment. Throughout the past 100 years, Australia has run current account deficits, and so real investment has been partly financed by foreign savings. This means that investment in Australia has not been constrained by low domestic savings. Therefore, the lower domestic saving rate can only be a partial explanation ol the modest Australian growth performance over the last fifty years.
chapter I I
The Australian saving rate and the golden rule
What is the saving rate that would maximise steady-state consumption per worker? Recall that, in steady state, consumption is equal to what is left alter enough is put aside to maintain a constant level of capital. More formally, in steady state, consumption per worker is equal to output per worker minus depreciation per worker:
C* Y* K* N = ~ 8 N
Check your understanding of the issues. Using the equations in this section, argue the pros and cons of policy measures aimed at increasing the Australian saving rate from its current value of about 20 per cent to. say. 30 per cent. ►
Using equations (I 1.8 and (11.9) for the steady-state values ol output per worker and capital per worker, consumption per worker is thus given by
Using this equation, together with equations I 18 and ( I 1.9), Table 11.1 gives the steady-state values of capital per worker, output per worker and consumption per worker for different values ol the saving rate (and lor depreciation rate equal to 10 per cent'.
Steady-state consumption per worker is largest when s equals a hall The golden-rule level ot capital is associated with a saving rate ol 50 per cent. Below that level increases in the saving rate lead to an increase in long-run consumption per worker. Above that level, they lead to a decrease. Few economies in the world today have saving rales above 40 per cent, and as we saw at the beginning of the chapter the Australian saving rate is actually about 23 per cent now. As rough as il is. our calculation suggests that, in most economies and especially in Australia, an increase in the saving rate would increase both output per worker and consumption per worker in the long run.
Table 1 I.I
worker The saving rate and the steady-state levels of capital, output and consumption per
Saving rate S Capital per worker K*IN Output per worker Y*IN Consumption per worker C*IN
0 0.0 0.0 0.00
0.1 1.0 1.0 0.90
0.2 4.0 2.0 1.60
0.3 9.0 3.0 2.10
0.4 16.0 4.0 2.40
0.5 25.0 5.0 2.50
0.6 36.0 6.0 2.40
1 100.0 10.0 0.00
1 1
I 1.4 PHYSICAL VERSUS HUMAN CAPITAL
We have concentrated so far on physical capital—on machines, plants, office buildings, and so on. But economics have another type of capital: the set of skills of the workers in the economy, what economists call human capital An economy with many highly skilled workers is likely to be much more productive than an economy in which most workers cannot read or write.
Thc increase in human capital has been as large as the increase in physical capital over the last two centuries. At the beginning ol the Industrial Revolution, only 30 per cent ol the population knew how to read. Today, the literacy rate in OECD countries is above 95 per cent. Schooling wasn't compulsory prior to the Industrial Revolution. Today it is compulsory usually until the age ol 16. Still, there are large differences across countries. In OECD countries, nearly 100 per cent of children gel a primary education, 90 per cent get a secondary education and 38 per cent gel a higher education. The corres¬ponding numbers in poor countries, countries with CDP per capita below $-100 in 1985, arc 95 per cent, 32 per cent and 4 per cent, respectively.
How should we think about the effect of human capital on output? How does the introduction of human capital change our earlier conclusions? These arc thc questions we take up in this last section.
Extending the production function
4 Even this comparison may be misleading.The quality of education may be quite different across countries.
SAVING. CAPI1AL ACCUMULATION AND ОШРЦТ
chapter 11
I he most natural way of extending our analysis to allow tor human capital is to modily the production Iunction relation ' I I. I) to read
— = —
(1 1.101
N1N (+ ,+)
N ' 1 w
The level of output per worker depends on both the level of physical capital per worker, K/N, and the level ol human capital per worker, H/N. As before, an increase in capital per worker (K/N) leads to an increase in output per worker. And an increase in the average level ol skill (H/N) also leads to more output per worker. More skilled workers can use more complex machines,- thev can deal more easily with unexpected complications,- they can adapt laster to new tasks. All ot these lead to higher output per worker.
We assumed earlier that increases in physical capital per worker increased output per worker but that the effect became smaller as the level ol capital per worker increased. The same assumption is likely to apply to human capital per worker. Think of increases in H/N as coming from increases in the number of years of education. Thc evidence is that the returns to increasing the proportion ol children acquiring a primary education are very large. At thc very least, the ability to read and write allows people to use equipment that is more complicated but more productive, for rich countries, however, primary education and. tor that matter, secondary education are no longer the relevant margins- most children now get both, lhe relevant margin is higher education. The evidence here—and we arc sure this will come as good news to most of you—is that higher education increases skills, at least as measured by the increase in wages for those who acquire it. But, to take an extreme example, it isn't clear lhat forcing everybody to acquire a university degree would increase aggregate output very much. Many people would end up ovcrqualitied and probably more frustrated rather than more productive.
How should we construct the measure for human capital. H? The answer is: Very much in the same way we construct the measure for physical capital, fs. In constructing K, we just add the values of the dillerent pieces of capital, so lhat a machine that costs $2,000 gets twice thc weight of a machine thai costs $1,000. Similarly, we construct the measure ol II such that workers who are paid twice as much get twice thc weight. Take, for example, an economy with 100 workers, hall ol them unskilled and hall ol them skilled. Suppose the relative wage ot skilled workers is twice that ol unskilled workers. We can .hen construct // as [(50 X 1 ■ + 150 x 2)] - 150. Human capital per worker, H/N, is equal to 150/100 = 1.5.
Human capital, physical capital and output
How does the introduction of human capital change the analysis of the previous sections?
Note that we are using the same symbol. H. to denote the monetary base in Chapter 4 and human capital in this chapter. Both uses are traditional. Don't be confused.
4 We look at this evidence in Chapter 13.
The rationale for using relative wages as weights is that they reflect relative marginal products. A worker who is paid three times more than another is assumed to have a marginal product equal to three times that of the other worker.
An issue is whetner relative wages accurately
4 reflect marginal products. To take a controversial example: in the same job. with the same seniority, women still often earn less than men. Is it because their marginal product is lower? Should they be given a lower weight than men in the construction of human capital?
Our conclusions about physical capital accumulation remain valid: an increase in the saving rate increases steady-state physical capital per worker, and therefore increases output per worker. But our conclusions now extend to human capital accumulation as well. An increase in how much society saves
in the form of human capital—through education and on-the-job training—increases steady-state human capital per worker, which leads to an increase in output per worker.
Our extended model therefore gives us a richer picture of the determination of output per worker. In the long mn. it tells us. output per worker depends on both how much society saves and how much it spends on education.
What is the relative importance of human capital and physical capital in the determination of output per worker? A place to start is to compare how much is spent on formal education with how much is invested in physical capital. An OFCD report shows that Australia spent about 6 per cent of GDP on formal education in 2(105, which is just above the OECD average of 5.6 per cent. This number includes both government expenditures on education and private expenditures by people on education. This number is about a quarter of the gross investment rate for physical capital (which is around 2.3 per cent of G.DP . But this comparison is only a lirst pass. Consider the following complications:
• Education, especially higher education, is partly consumption—done lor its own sake—and partly investment. We should include only the investment part for our purposes. However, the 6 percent number in the preceding paragraph includes both.
• At least lor post-secondary education, the opportunity cost of a person's education is also forgone wages while acquiring the education. Spending on education should include not only the actual cost of education but also the opportunity cost The 6 per cent number doesn't include this opportunity cost.
• Formal education is only part ol education. Much of what we learn comes Irom on-the-job trainirg. tormal or inlormal. Both the actual costs and the opportunity costs of on-the-job training should also be included. The 6 per cent number doesn't includc the costs associated with on-the-job training.
• We should compare investment rates net of depreciation. Depreciation ol physical capital, especially ol machines is about 0 per cent of GDP in Australia, and is likely to be higher than depreciation of human capital. Skills deteriorate, but do so slowly. Unlike physical capital, skills deteriorate more slowly the more they are used.
For all these reasons, it is dilficult lo come up with reliable numbers lor investment in human capital. A recent LIS study concludes thai investment in physical capital and in education play roughly similar roles in the determination ol output. This conclusion implies thai output per worker depends roughly equally on the amount ol physical capital and the amount ol human capital in the economy. Countries that save more, or spend more on education, can achieve substantially higher steady-state levels of output per worker.
Endogenous growth
Note what the conclusion we just reached did say and didn t say. Il did say thai a country that saves more or spends more on education will achieve a higher level ol output per worker in steady state. It didn't say that by saving or spending more on education, a country can sustain permanently higher growth of output per worker.
We have mentioned ► This conclusion, however, has been challenged in the past two decades. Following the lead ol Lucas once already, in Robert Lucas and Paul Romer researchers have explored ihe possibility that the combination of connection with the physical capital and human capital accumulation may actually be enough to sustain growth. Given Lucas critique in human capital, increases in physical capital will mn into decreasing returns. And given physical capital, Chapter 9. increases in human capital w ill also run into decreasing returns. But, these researchers have asked, what il both physical and human capital increase in tandem? Can't an economy grow lorever just by having steadily more capital and more skilled workers?
Nobel Prize winner ► James Heckman has concluded that investment in early childhood development has far greater returns than at any other stage in life.
How large is your ► opportunity cost relative to your degree cost?
See N. Gregory Mankiw. David Romer and David Weil. A contribution to the empirics of ^ economic growth', Quarterly Journal of Economics, 1992. pp. 407-37.
Models lhat generate steady growth even without technological progress are called models of endogenous growth to reflcct the lact that in those models—in contrast to the model we saw in earlier sections ol this chapter growth depends even in the long mn, on variables such as the saving rate and the rate of spending on education. The jury on this class ol models is siill out, but the indications so far are that the conclusions wc drew earlier need to be qualified, not abandoned. The current consensus is as follows:
• Output per worker depends on the level ot both physical capital per worker and human capital per worker. Roth forms of capital can be accumulated, one through physical investment, the other through education and training. Increasing either thc saving rate or the fraction of output spent on education and training can lead to much higher levels of output per worker in the long run. However, given the rate of technological progress such measures don't lead to a permanently higher growth rate.
• Note the qualifier in the last proposition: given the rate of technological progress. But is technological progress unrelated to the level ol human capital in the economy? Can't a better educated labour force lead to a higher rate ol technological progress? These questions take us to the topic ol the next chapter, thc sources and the implications ol technological progress.
SUMMARY
• In the long run, the evolution ol output is determined by two relations. (To make the reading ol this summary easier, we will omit per worker in what follows, l irst. thc level ol output depends on the amount ol capital. Second, capital accumulation depends on the level ol output, which determines saving and investment.
• These interactions between capital and output imply that, starting Irom any level of capital (and ignoring technological progress, the topic ot Chapter 12 1 an economy converges in the long run to a steady-state (constant i level of capital. Associated with this level of capital is a steady-state level of output.
• Thc steady-state level of capital, and thus the steady-state level of output, depends positively on thc saving rate. A higher saving rate leads to a higher steady-state level of output during the transition to the new steady state, a higher saving rate leads to positive output growth. But in the long run (again ignoring technological progress), thc growth rate of output is equal to zero, and is thus independent of the saving rate.
• An increase in the saving rate requires an initial decrease in consumption In the long run, the increase ir the saving rale may lead to an increase or a decrease in consumption, depending on whether the economy is below or above the golden-rule level ol capital, the level of capital at which steady-state consumption is highest.
SAVING. CAPITAL ACCUMULATION AND OUTPUT
chapter 11
• Most countries have a level ol capital below the golden-rule level. Thus, an increase in the saving rate will lead to an initial decrease in consumption, followed by an increase in the long mn. In thinking about whether to take policy measures aimed at changing the saving rate, policy-makers must decide how much weight to put on the welfare ot current generations versus the wellare ol future generations.
• While most of the analysis of this chapter focuses on the effects of physical capital accumulation output depends on the levels ol both physical and human capital. Both forms of capital can be accumulated, one through investment, the other through education and training. Increasing the saving rate or thc fraction ol output spent on education and training can lead to large increases in output in the long run.
KEY TERMS
• killv funded social security system, 262
• superannuation, 263
• Cobb- Douglas production function, 265
• human capital, 26S
• models of endogenous growth 270
QUESTIONS AND PROBLEMS
Quick check
1. Using the information in this chapter, label each of the following statements 'true', 'false' or 'uncertain'. Explain briefly.
a. The saving rate is always equal to the investment rate.
h. A higher investment rate can sustain higher growth ol output forever.
c. It capital never depreciated growth could go on forever.
d. The higher the saving rate the higher the consumption in steady slate.
e. We should introduce an age pension tax. This would increase consumption, now and in ihe future.
I. The Australian capital stock is tar below the golden-rule level. The government should give tax breaks tor saving.
g. Education increases human capital, and so output. It follows that governments should subsidise education.
2. Consider the following statement: 'The Solow model shows that the saving rate does not affect the growth rate in the long run, so we should slop worrying about the low Australian saving rate. Increasing the saving rate wouldn't have any important effects on the economy.'
Do you agree or disagree?
3. In Chapter Я we saw that an increase in the saving rate can lead to a recession in the short run (the paradox of saving!. We can now examine the effects beyond the short run.
Using the model presented in the chapter, what is the effect ol an increase in the saving rate on output per worker likely lo be alter one decade? After five decades?
Dig deeper
4. Discuss the likely impact of the following changes on the level of output per worker in the long run:
a. The righi lo exclude saving from income when paying income tax
b. A higher rate ot female participation (but constant population
5. Suppose that the production function is given by
Y 0.5 V fCVN
a. Derive the steady-state levels of capital per worker and output per worker in terms ot the saving rate (s) and the depreciation rale 5).
b. Derive the equation for steady-state consumption per worker in terms of s and <5.
c. Suppose that 5 = 5 per cent (0.05). With your lavourile spreadsheet software, calculate steady- state output per worker and steady-state consumption per worker lor > 0, 0 1, 0.2 . I. Explain.
d. Use your software lo graph the steady-state level ot output per worker and the steady-state level of consumption per worker as a function ol the saving rate 'that is, measure the saving rate on the horizontal axis of your graph and the corresponding values ol output per worker and consumption per worker on the vertical axis).
e. Does the graph show that there is a value ot s that maximises output per worker? Does the graph show that there is a value of > that maximises consumption per worker? II so what is this value?
6. The Cobb-Douglas production function and the steady slate
This problem is based on the material in the appendix. Suppose thai the economy's production is given by
SAVING. CAP' AL ACCUMULATION AND OUTPUT
chapter 11
У - К" N'-".
Assume that a - 1/3.
a. Is this production function characterised hy constant returns to scale? Explain, h. Are there decreasing returns to capital?
c. Are there decreasing returns to labour?
d. Translorni the production function into a relationship between output per worker and capital per worker.
e. for a given saving rate (s and a depreciation rate (6), give an expression lor capital per worker in the steady state.
1. C.ive an expression for output per worker in the steady state.
g. Solve (or the steady-state level ol output per worker when 8 0.08 and s 0.32.
h. Suppose lhat the depreciation rate remains constant at 8 - 0.08 while the saving rale is reduced by hall lo s = 0.16. What is the new steady-state output per worker?
7. Suppose that the economy's production function is given hy V = K' 3N; and that both the saving rate (s) and the depreciation rate lb) are equal to 0.10.
a. What is the steady-state level ol capital per worker?
b. What is the steady-state level ol output per worker?
Suppose that the economy is in steady slate, and that, in period t, the depreciation rate increases permanently from 0.10 to 0.20.
c. What will he the new steady-stale levels of capital per worker and output per worker?
d. Calculate the path ol capital per worker and output per worker over the lirst three periods after the change in the depreciation rate.
в. Deficits and the capital stock
For the production function, Y = К 'N" \ equation 111.8) gives the solution for the steady-state capital stock per worker.
a. Retrace the steps in lhe text that derive equation (1 1.8).
b. Suppose that the saving rale, s, is initially 15 per cent per year, and the depreciation rale, 8, is 7.5 per cent. What is the steady-state capital stock per worker? What is steady-state output per worker?
c. Suppose lhat there is a government deficit of 5 per cent of GDI' and thai the government eliminates this deficit. Assume that private saving is unchanged so that national saving increases lo 20 per cenl. What is the new steady-state capital slock per worker? What is the new steady- state output per worker? How docs this compare with your answer to part i b)?
Explore further
9. Funding age pensions with a fully funded system
The current age pension system in .Australia is best described as a pay-as-you-go system where current benefits are largely paid by current taxes. An alternative system is a fully funded system where workers' contributions arc saved and repaid with interest upon retirement.
I low would a shili to a fully funded system affect output per worker and the growth of output per worker in the long run?
10. The Empirics of Saving and Growth. Go to the OECD website (www.oecd.org), click on 'Statistics', do a search on 'E083' and select and download the spreadsheets containing historical saving rates and real GDP growth rates for OF.CD countries. Choose Australia, Japan and the United States.
a. Plot the saving rate and growth rate in one graph for Australia and then one lor Japan.
b. Do the dillerent saving rates for the two countries explain their different growth rates relative to LIS growth rates?
We invite you to visit the Blanchard-Sheen page on the Pearson Australia
website at
www.pearson.com.au/highered/blanchardsheen3e
for many World Wide Web exercises relating to issues similar to those in this
chapter.
FURTHER READINGS
• The classic treatment ol the relation between the saving rate and output is by Robert Solow, Growth Theory: An Exposition (New York: Oxford University Press 1970 .
• A useful survey ol the problems and policies related to inadequate savings in Australia is provided by Malcolm F.dey and Luke Cower National savings: Trends and policies', in David Gruen and Sona Shrestha (cds> The Australian Economy in the 1990s, Reserve Hank of Australia Conference 2000,
• An easy-to-read discussion of whether and how to increase saving and improve education in the United States is given in Memoranda 23 to 27 in Memos to the President: A Guide Through Macroeconomics for the Busy Policymaker, by Charles Schultze (the chairman of the Council of Economic Advisers during the Carter administration Washington DC: Brookings Institution, 1992).
(IIA.I)
APPENDIX: THE COBB-DOUGLAS PRODUCTION FUNCTION AND THE STEADY STATE
SAVING. CAPITAL ACCUMULATION AND OUTPUT
chapter 11
Output per worker Y/N is equal to the ratio of capital per worker KIN raised to the power a. Saving per worker is equal to the saving rate times output per worker, which using the previous equation becomes
s(K/N)"
• Depreciation per worker is equal to the depreciation rate times capital per worker:
,%KIN)
• The steady-state level of capital. K . is determined by the condition that saving per worker equals depreciation per worker:
s(K*/N)" = 8{K*IN)
To solve this expression for the steady-state level of capital per worker K*IN, divide both sides by (K*IN)":
s = fi(K*/N)1a
Divide both sides by 8. and change the order of the equality:
(K*/N) 1-" = si 8 Finally, raise both sides to the power 1/(1 - «):
(K*/N) = (s/5)1''1 ->
This gives the steady-state level of capital per worker.
• From the production function, the steady-state level of output per worker is then equal to
(Y*!N) = (KIN)" = (s/<5)"'(1-tt>
Let's see what this last equation implies.
• First, note that, in the text, we worked with a special case of equation (I I A. I), the case where « = 0.5. (Taking a variable to the power 0.5 is the same as taking the square root of the variable.) If о = 0.5. the preceding equation implies that
У* _ £ N ~ 8
Output per worker is equal to the ratio of the saving rate to the depreciation rate. This is the equation discussed in the text. A doubling of the saving rate leads to a doubling in steady-state output per worker.
• The empirical evidence suggests, however, that, if we think of К as physical capital.
This implies smaller effects of the saving rate on output per worker than was suggested by the calculations in the text. A doubling of the saving rate, for example, implies an increase in output per worker by a factor of V2 or about 1.4 (or, put another way. a 40 per cent increase in output per worker).
• There is an interpretation of our model for which the appropriate value of a is close to 1/2, in which case the calculations in the text are applicable.This is when we allow for a broader definition of capital to include both physical and human capital along the lines of Section 11.4.Thus, one interpretation of the numerical results in Section I 1.3 is that they g ve the effects of a given saving rate, but with saving interpreted to include saving in both physical capital and human capital (more machines and more education).
CHAPTER ф
Technological Progress and Growth
O
ur conclusion in Chapter 11 that capital accumulation cannot by itself sustain growth has a straightforward implication: sustained growth requires technological progress.This chapter looks at the role of technological progress in growth.
• Section 12.1 looks at the respective role of technological progress and capital accumulation in growth. It shows how, in steady state, the rate of growth of output per capita is simply equal to the rate of tech¬nological progress.This doesn't mean, however, that the saving rate is irrelevant: the saving rate affects the level of output per capita—but not its rate of growth.
• Section 12.2 turns to the determinants of technological progress, focusing in particular on the role of research and development (R&D).
• Section 12.3 returns to the facts of growth presented in Chapter 10, and interprets them in the light of what we have learned in this chapter and in Chapter I I.
12.1 TECHNOLOGICAL PROGRESS AND THE RATE OF GROWTH
II we think ol output as the set of underlying services provided by the goods produced in the economy, we can think ol technological progress as leading to increases in output for given amounts of capital and labour. We can then think ol the state of technology as a variable that tells us how much output can be produced from given amounts ol capital and labour at any time. Let's denote the stale ol technology by A and rewrite the production function as
У = F(K,N,A) [ ,*,*)
This is our extended production function. Output depends on both capital and labour, К and N, and on the state of technology, A: given capital and labour, an improvement in the stale ol technology, A, leads to an increase in output.
(12.1)
4 AN is also sometimes called labour in efficiency units.Tne
use of 'efficiency' for efficiency units' here and for 'efficiency wages' in Chapter 6 is a coincidence: the two notions are unrelated.
Il will be convenient to use a more restrictive lorm of the preceding equation, namely,
У = F(K,AN)
This equation slates lhat production depends on capital and on labour multiplied by the state ol technology. This way of introducing the state of technology makes it easier to think about the effect of technological progress on the relation between output, capital and labour. liquation (12.1 implies that we can think of technological progress in two equivalent ways:
• Technological progress reduces the number ot workers needed to achieve a given amount of output. Doubling A produces the same quantity of output with only halt the original number of workers N.
• Technological progress increases AN. which we can think of as the amount ol effective labour in lhe economy. If the state ol technology, A doubles, it is as il the economy had twice as many workers. In other words, we can think ol output being produced by two factors: capital, K, and effective labour, AN.
What restrictions should we impose on the extended production Iunction I 12.1)? We can build directly here on our discussion in Chapter 10.
4 As you saw in the focus box 'Real GDR technological progress and the price of computers' in Chapter 2. thinking of products as providing a number of underlying services is the method used to construct the price index for computers.
4 For simplicity, we will ignore human capital here. We return to it later in the chapter
I ГО INOLOOCAL PROGRESS AND GROWTH chapter 12
Il is again reasonable to assume constant returns to scale for a given state ot technology (A), doubling both the amount ol capital (K i and the amount ol laboui \ is likely lo lead to a doubling ot
OUtpUt:
2У - F(2K,2AN)
More generally, for any number .r
xY = F(xK.xAN)
It is also reasonable to assume decreasing returns to each ol the two factors, capital and effective labour. Given ellective labour, an increase in capital is likely lo increase output, but at a decreasing rate. Symmetrically, given capital, an increase in effective labour is likely lo increase output, but at a decreas¬ing rate.
It was convenient in Chapter I I lo think in terms ot output per worker and capital per worker. That was because the steady state ot the economy was a state where output per worker and capital per worker were constant. It is convenient here lo look ai output per effective worker and capital per effective ivorker. Thc reason is the same: as we will soon see, in steady state, output per effective worker and capital per effective worker .ire constant.
Y
AN
= F
To gel a relation between output per ellective worker and capital per ellective worker, take т - 1/Л,\т in the preceding equation. This gives
К
Per worker: divided by the number of workers
<(N>.
Per effective worke": divided by the number of effective worker» (AN)—the number of workers, N. times the state of technology, A.
AN'
Or, it we define the function f so that f(K/AN) = F(K/AN, I):
ЛЛ' r\ /IN
In words: Output per effective worker (the left side is a function of capital per effective worker (the expression in the function on the right side).
The key to understanding the > results in this chapter: the results derived for output per worker in Chapter 11 still hold in this chapter, but now for output per effective worker. For example, in Chapter 11 we saw that output per worker was constant in steady state. In this chapter we will see that output per effective worker is constant in steady state.
And so on.
The relation between output per effective worker and capital per effective worker is drawn in Figure 12.1. Il looks very much the same as the relation drawn in Figure 1 1.2 between output per worker and capital per worker in the absence ol technological progress. There, increases in KfN led to increases in Y/.Y, but at a decreasing rate. Here, increases in K/AN lead lo increases in Y/AN. but at a decreasing rate.
Interactions between output and capital
We now have the elements we need to think about the determinants of growth. Our analysis will parallel the analysis ol Chapter 11. There we looked at the dynamics ol output per worker and capital per worker. Here we look at the dynamics of output per effective worker and capital per effective worker.
In Chapter I I, we characterised the dynamics ol output and capital per worker using Figure I 1.2. In that figure, we drew three relations:
• The relation between output per worker and capital per worker.
• The relation between investment per worker and capital per worker.
• The relation between depreciation per worker—equivalently, ihe investment per worker needed to maintain a constant level ot capital per worker—and capital per worker.
The dynamics ol capital per worker, and by implication of output per worker, were determined by the relation between investment per worker and depreciation per worker. Depending on whether investment per worker was greater or smaller than depreciation per worker, capital per worker increased or decreased over time, as did output per worker.
Suppose that F has the ► 'double square root' form: V = F(KAN) = vKV(AN).Then, Y/(AN) = \K\'(AN)I(AN) = V K/v'(AN) = V[K/(AN)].
So the function fis simply the square root function: flK/AN) = \'[K/(AN)].
(12 2)
Wc follow exactly the same approach in building Figure 12.2. The dilfercnce is that wc focus on output, capital and investment per effective worker, rather than per worker.
Figure 12.1
z
Capital per effective worker, K/AN
I
Output per effective worker versus capital per effective worker
Because of decreasing returns to capital, increases in capital per effective worker lead to smaller and smaller increases in output per effective worker.
TSCHNOI OGiCAl PROGRtSS AND GROWTH chapter 12
Figure 12.2 Dynamic effects of capital per effective worker and output per effective worker
Required investment
Production f(KIAN) Investment sf(KIAN)
(K/AN) о (KIAN)*
Capital per effective worker, KIAN
2
g
>■
(AN)
|
01 Q.
u
Э a.
3
О
technological progress is 2 per cent per year then the growth rate of effective labour is equal to 3 per cent per year.
These assumptions imply that the level ol investment needed to maintain a given level ol capital per effective worker is given bv:
Я К + (gA + gN)K
or, equivalently,
(в + Л'л + g»)K
An amount SK is needed just to keep the capital stock constant. II the depreciation rate is 10 per cent, then investment must be equal to 10 per cent of the capital stock just to maintain the same leve! ol capital. And an additional amount (gA + g\)K is needed to ensure that the capital stock increases at the same rate as effective labour. If effective labour increases at 3 per cent per year, then capital must increase by 3 per cent per year to maintain the same level til capital per effective worker. Putting SK and + g\)K together in this example: if the depreciation rate is 10 per cent and thc growth rate of eflective labour is 3 per cent, then investment must equal 13 per ccnt of the capital stock to maintain a constant level of capital per effective worker.
Dividing the preceding expression by the number of effective workers to get the amount ol investment per effective worker required to maintain a constant level of capital per effective worker gives
К
(S + 8л
If the number of effective workers is constant then constant output per effective worker implies constant output.This was the case in Chapter 11, where we assumed that
there was neither ^ population growth nor technological progress. But this is not the case here.
If WAN is constant, Y ► must grow at the same rate as AN. So it must grow at the rate gA + gv
The level of investment per effective worker needed to maintain a given level ol capital per effective worker is represented by the upward-sloping line. Required investment', in figure 12.2. The slope of the line equals 8 * g\ + gN.
Dynamics of capital and output
We can now give a graphical description ol the dynamics ot capital per ellective worker and output per effective worker. Consider in Figure 12.2 a given level ot capital per elfective worker, say, (K/AN\At that level, output per elfective worker equals the vertical distance AB. Investment per effective worker is equal to AC. The amount of investment required to maintain lhat level ol capital per eflective worker is equal lo AD. Because actual investment exceeds thc investment level required to maintain lhe existing level of capital per effective worker, K/AS increases.
• Hence, starting from (KMN)n, the economy moves to the right, with the level of capital per effective worker increasing over time. This goes on until investment per ellective worker is just sufficient to maintain the existing level of capital per effective worker, until capital per effective worker reaches (K/AN)*.
• In the long run, capital per ellective worker reaches a constant level, and so docs output per effective worker. Put another way, the steady stale ol this economy is such that capital per effective worker and output per effective worker are constant, and equal to IK/AN)* and IY/AN)* respective!}/.
Note what this conclusion implies: in stead}/ state, in this economy, what is constant is not output but rather output per effective worker. This implies lhat, in steady state, output, Y, is growing at the same rate as eflective labour, AS (so thai thc ratio of the two is constant). Because effective labour grows at rate (#л + gy), output growth in steady state must also equal (gA + gs). The same reasoning applies to capital. Because capital per effective worker is constant in steady state, capital is also growing at rate (gA + gN).
The growth rate of the ► product of two variables is the sum of the growth rates of the two variables. See Proposition 7 in Appendix 2 at the end of the book.
T hese conclusions give us our first important result. In stead}/ state, the growth rate of output equals the rate of population growth lg\l plus the rate of technological progress, lg,\). By implication, the growth rate of output is independent of the saving rate.
To strengthen your intuition, go back to the argument used in Chapter I I to show that, without technological progress and population growth, the economy couldn t sustain positive growth lorever.
• The argument went as lollows: Suppose the economy tried to achieve positive output growth. Because of decreasing returns to capital, capital would have to grow faster than output. The economy would have to devote a larger and larger proportion ol output to capital accumulation. At some point, there would be no more output to devote to capital accumulation. Growth would come lo an end.
• Exactly the same logic is at work here. Effective labour grows at rate (g..\ + g\). Suppose the economy tried to sustain output growth in excess ol + h Because of decreasing returns to capital, capital would have to increase laster than output. The economy would have to devote a larger and larger proportion ol output lo capital accumulation. At some point, this would prove impossible. Thus, the economy cannot permanently grow laster than (gA + g\).
We have focused on the behaviour of aggregate output. To get a sense of what happens not to aggregate output but lo ihe standard of living over time, we must look instead at the behaviour of output per worker (not output per effective worker). Because output grows at rate (g,\ - g^) and the number ol workers grows at rate g.v output per worker grows at rate gA. In other words, in steady state, output per worker grows at the rate of technological progress.
Because output, capital and cttcciivc labour all grow at the same rate, (g^ + g\) in steady state, the steady slate ol this economy is also called a stale ol balanced growth. In steady stale, output and the two inputs, capital and effective labour, grow in balance (at the same rate). The characteristics of balanced growth will be helpful later in the chapter and are summarised in Table 12.1.
On ihe balanced growth path (equivalcntly, in steady slater equivalentlv, in the long run):
• Capital per effective worker and output per effective worker are constant; this is the result derived in Figure 12.2.
• Equivalcntly, capital per worker and output per worker are growing at the rate of technological progress, gA.
• Or, in terms ol labour, capital and output: labour is growing ai the rate ol population growth, g\; capital and output are growing ai a rate equal to the sum of population growth and the rate ol technological progress, (gA + gN).
The effects of the saving rate
The standard of living is given by output per
4 worker (or. more accurately, output per capita), not output per effective worker.
i The growth rate of Y/N is equal to the growth rate of Y minus the growth rate of N (see Proposition 8 in Appendix 2 at the end of the book). So the growth rate of Y/N is given by (gy - gN) =
(g* + gJ ~ gN =
TCCIINOIOGICAL PROGRESS AND GROWTH
chapter 12
In steady state, the growth rate of output depends only on the rate ol population growth and the rate of technological progress. Changes in the saving rate don't affect the steadv-siaie growth rate. But changes in the saving rale do increase the steady-stale level ol output per effective worker.
This result is best seen in Figure 12.3, which shows the ellect ol an increase in ihe saving rale Irom Si, to s,. The increase in the saving rale shilts the investment relation from st)f(K/AN^ to sJiK/AN).
Table I 2.1 The characteristics of balanced growth
Rate of growth
1. Capital per effective worker 0
2. Output per effective worker 0
3. Capital per worker gA
4. Output per worker gA
5. Labour gN
6. Capital gA + gN
7. Output gA + gN
Figure 12.3
The effects of an ^
increase in the :>-
с
saving rate:I JJ
L.
0
1
0> >
'C
1 » > >
(KMN)0 (KMN),
Capital per effective worker, K/AN
f(KIAN)
+ BA + Sn)«'/5N s,f(KIAN)
s0 f(KIAN)
b. «
a
и 3
a з О
An increase in the saving rate leads to an increase in the steady-state levels of output per effective worker and capital per effective worker.
Il follows thai thc steady-slate level of capital per effective worker increases from 1 K/AS)„ to (K/AN)t, with a corresponding increase in thc level of output per effective worker from i Y/AN)0 lo (Y//1,VI,.
Following the increase in the saving rate, capital per effective worker and output per ellective worker increase for some time as they converge to their new higher level. Figure 12.4 plots capital against time (upper graph) and output against time (lower graph1. Both capital and output arc measured on logarithmic scales. The economy is initially on the balanced growth path AA: capital and output arc growing ai rate [g \ r gx)—the slope ol AA is equal lo (£л + gN). Alter the increase in the saving rale at time I. output and capital grow taster for some period ol lime. Eventually, capital and output end up at higher levels than they would have been without thc increase in saving. But their growth rate returns lo (gA + gN). In the new steady state, the economy grows at the same rate but on a higher growth path. BE—thc line BE, which is parallel to AA, also has a slope equal to (gA + gN0.
To summarise: In an economy with technological progress and population growth output grows over time. In steady state, output per effective worker and capital per effective worker are constant. Put another way, output per worker and capital per worker grow at the rate ol technological progress. Put yet another way, output and capital grow at the same rate as effective labour, thus ai a rale equal to the growth rate ot lhe number of workers plus the rate of technological progress. When thc economy is in steady state, it is said to be on a balanced growth path
Thc rate of output growth in steady state is independent ot the saving rate. The saving rate affects thc steady-state level of output per effective worker, however. And increases in the saving rate lead, lor some time, to an increase in thc growth rate above the steady-state growth rate.
12.2 THE DETERMINANTS OF TECHNOLOGICAL PROGRESS
We have iust seen that thc growth rate of output per worker is ultimately determined by the rate of technological progress. But what determines the rate ol technological progress? This is the question we take up in this section.
The second panel in Figure 12.4 is the same as Figure 11.5. which anticisaced thc derivation presented here. ►
For a description of ► logarithmic scales, see Appendix 2 at the end of the book.
When a logarithmic t scale is used, a variable growing at a constant rate moves along a straight line.The slope of the line is equal to the rate of growth of the variable.
Technological progress brings to mind images of major discoveries: the invention ol thc microchip, the discovery of the structure ol DNA, and so on. These discoveries suggest a process driven largely by scientific research and chance, rather than by economic forces. But the truth is that most technological progress in modern economies is the result ol a humdrum process—the outcome ol lirms research and development R&D activities. The OECD reported that R&D expenditures account for an average ol 2.5 per cent ot GDP tor the latest year available to 2007 for thc six major rich countries we looked at
1ECHNOLOGJCAL PROGRESS AND GROWTH chapter 12
Figure 12.4 The effects of an increase in the saving rate: II
slope (gA + gN)
Time
и
Associated with sn > s0
slope (gA + gN)
Associated with s0
JL
Time
An increase in the saving rate leads to higher growth until the economy reaches its new, higher, balanced growth path.
in Chapter 10 (Australia, the United States, France, Germany, lapan and the United Kingdom* and 2.2 per tent lor the OFCD. Australia is the lowest ot the group of six countries with 1.8 per cent, and lapan is the highest with 3.3 per cent. Firms in Australia accounted lor just 53 per cent of all R&D one ol the lowest of the group ol six, which averaged 61 per cent. About 70 per cent of the roughly 1.4 million US scientists and researchers working in R&D are employed by firms. In contrast, only 54 per ccnt of the 81,000 Australian R&D personnel are employed by firms. These statistics suggest that Australian lirms have some way to go in R&D expenditures il they are to catch up to their competitors in other countries.
Firms spend on R&D for the same reason they buy new machines or build new plants—to increase profits. By increasing spending on R&l) a firm increases the probability that it will discover and develop a new product. (We will use the word product as a generic term to denote new goods or new techniques ol production.) If the new product is successful, the firm's profits will increase. There is, however, an important difference between purchasing a machine and spending more on R&D. The difference is that the outcome of R&D is fundamentally ideas. And, unlike a machine, an idea can potentially be used by
many firms at the same time. A firm that has just acquired a new machine doesn't have to worry that another firm will use that particular machine. A firm that has discovered and developed a new product can make no such assumption.
In Chapter I I we ► looked at the role of human capital as an inpuc in production— more educated people can use more complex machines or handle more complex tasks. Here, we see a second role of human capital better researchers and scientists and, by implication, a higher rate of technological progress.
FOCUS 'BOX
This last point implies that the level ot R&D spending depends not only on the fertility ol the research process—how spending on R&D translates into new ideas and new products—hut also on the appropriability ol research results—the extent to which firms benefit from the results ol their own R&D. Lets look at each aspect.
The fertility of the research process
II research is very lertile—ii R&l) spending leads to many new products—then, other things being equal, lirms will have more incentives to spend on R&D; R&D and technological progress will be higher. The determinants ol the fertility ol research lie largely outside the realm ol economics. Many factors interact here.
The fertility of research depends on the successful interaction between basic research (the search tor general principles and results and applied research and development (the application ot these results to specific uses, and the development ol new products). Basic research doesn't lead, by itself, to technological progress. But the success ol applied research and development depends ultimately on basic research. Much ol the computer industry's development can be traced to a few breakthroughs, Irom the invention ol the transistor to the invention of the microchip. Indeed, the recent increase in productivity growth in rich countries, discussed in Chapter I is widely attributed to the diffusion across the economies ol the breakthroughs in information technology, iThis is explored further in the locus box 'Information technology, the New Economy and productivity growth .)
Some countries appear more successful at basic research; others are more successful at applied research and development. Studies point to the relevance of the education system. For example, it is often argued that the French higher education system, with its strong emphasis on abstract thinking, produces researchers who are better at basic research than at applied research and development. Studies also point to the importance of a culture of entrepreneurship, in which a big part of technological progress comes from entrepreneurs' ability to organise the successful development and marketing ol new products.
It takes many years, and often many decades, tor the lull potential of major discoveries to he realised. Thc usual sequence is one in which a major discovery leads to the exploration of potential applications, then to the development of new products, then to the adoption of these new products. The focus box The diffusion ol new technology: Hybrid corn , shows the results of one of the first studies of this process ol the diffusion ot ideas. Closer to us is the example of personal computers. Twenty years alter the commercial introduction of personal computers, it olten leels as if we have just started discovering their uses.
An age-old worry is that research will become less and less lertile, that most major discoveries have already taken place, and that technological progress will now slow down. This tear may come from what happened to thc mining industry, where higher-grade mines were exploited lirst, and where the industry has had to exploit increasingly lower-grade mines. But this is only an analogy, and so far there is no evidence that it is correct.
THE NEW ECONOMY AND PRODUCTIVITY GROWTH
Average annual productivity growth in the United States from 1996 to 2006 reached 2.8 per cent (while in Australia it reached 1.5 per cent)—a high number relative to the anaemic 1.8 per cent average (1.0 per cent in Australia) achieved from 1970 to 1995. This 50 per cent improvement has led some to proclaim an information technology revolution, to announce the dawn of a New Economy, and to forecast a long period of high productivity growth in the future.
What should we make of these claims? Research to date gives reasons both for optimism and for caution. It suggests that the recent high productivity growth is indeed linked to the development of information technologies. It also suggests that a sharp distinction must be drawn between what is happening in the information technology (IT) sector (the sector that produces computers, computer software and software services, and communications equipment) and the rest of the economy (which uses these products). • In the IT sector, technological progress has been proceeding at an extraordinary pace. In 1965, researcher Gordon Moore, who later became the founder of Intel Corporation, predicted that the number of transistors in a chip would double every eighteen to twenty-four months, allowing for steadily more powerful computers. As shown in Figure I. this relation—now known as Moore's law—has held extremely well over time. The first logic chip produced in 1971 had 2,300 transistors; the Pentium 4. released in 2000 had 42 million. (The Intel Core 2, released in 2006 and not included in the figure, has 291 million. In 2008, Intel announced the first 2 billion processor, codenamed Tukwila.)
While proceeding at a less extreme pace, technological progress in the rest of the IT sector has also been very high. And the share of the IT sector in GDP is steadily increasing, from 3 per cent of US GDP in 1980, to 4.5 per cent in 1990, and to 7 per cent today; in Australia, IT grew to 4.7 per cent of GDP in 2007. The combination of high technological progress in the IT sector and an increasing IT share implies a steady increase in the economy-wide rate of technological progress.This is one of the factors behind the higher productivity growth since the mid-1990s in the United States and Australia.
TECHNOLOGICAL PROGRISS AND GROWTI!
chapter 12
In the non-IT sector—the Old Economy, which still accounts for more than 90 per cent of the US economy and 95 per cent of the Australian one—however, there is little evidence of a parallel technological revolution.
Figure I Moore's law: number of transistors per chip. 1970-2000
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о I07
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1980
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1996 2000
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1988
1992
1984
1972 1976
SOURCE Adapted from Vernon W. Rutton. Technology. Grawt/i and Development (Oxford University Press. 20001 by Dale jorgenson.
• On the one hand, the steady decrease in the price of IT equipment (reflecting technological progress in the IT sector) has led firms in the non-IT sector to increase their stock of IT capital. This has led to an increase both in the ratio of capital per worker and in productivity growth in the non-IT sector.
Let's go through this argument a bit more formally. Go back to equation (12.2), which gives the relation of output per effective worker to the ratio of capital per effective worker: YIAN = f[KIAN).
Think of this equation as giving us the relation between output per effective worker and capital per effective worker in the non-IT sector. The evidence is that the decrease in the price of IT capital has led firms to increase their stock of IT capital and, by implication, their overall capital stock. In other words. KIAN has increased in the non-IT sector, leading to an increase in YIAN.
• On the other hand, the IT revolution doesn't appear to have had a direct effect on the pace of technological progress in the non-IT sector. You have surely heard claims that the IT revolution was forcing firms to drastically reorganise, leading to large gains in productivity. Firms may be reorganising, but so far there is no evidence that this is leading to large gains in productivity. Measures of technological progress show only a small rise in the rate of technological progress in the non-IT sector relative to the post-1970 average.This rise is evident in Australia, which has a very small IT-producing sector.
In terms of the production function relation just discussed, there is only a little evidence that the technological revolution has led to a higher rate of growth of A in the non-IT sector.
Are there reasons to expect productivity growth to be higher in the future than in the last twenty-five years? The answer is 'yes'.The factors we have just discussed are here to stay.Technological progress in the IT sector is ikely to remain high.The share of IT will continue to increase. Firms in the non-IT sector are likely to further increase their stock of IT capital, leading to further increases in productivity.
How high can we expect productivity growth to be in the future? Probably not as high as it was from 1996 to 2006, but, according to some estimates, we can expect it to be perhaps 0.5 percentage points higher than its post-1970 average.This may not be the miracle some have claimed, but if sustained it is an increase that will make a substantial difference to our standard of living in the future.
FOCUS
4Г \
Гвох
For more on Jiese issues, read Dak lorgenscn, 'Information technology and the US economy'. American Economic Review, vol. 9l.no. I. March 2001. pp. I 32.
THE DIFFUSION OF NEW TECHNOLOGY: HYBRID CORN
New technologies are not developed or adopted overnight. One of the first studies of the diffusion of new technologies was carried out in 1957 by Zvi Griliches, who looked at the diffusion of hybrid corn in different states in the United States.
Hybrid corn is. in the words of Griliches,'the invention of a method of inventing'. Producing hybrid com entails crossing different strains of corn to develop a type adapted to local conditions. Introduction of hybrid corn can increase yield by up to 20 per cent.
While the idea of hybridisation was first developed at the beginning of the twentieth century, the first commercial application didn't take place until the 1930s in the United States. Figure I shows the rate at which hybrid corn was adopted in a number of US states from 1932 to 1956.
The figure shows two dynamic processes at work. One is the process through which hybrid corns appropriate to each state were discovered. Hybrid corn became available in southern states (Texas. Alabama) more than ten years after it had become available in northern states (lowa.Wisconsin, Kentucky). The other is the speed at which hybrid corn was adopted within each state. Within eight years of hybrid corn's introduction, practically all corn in Iowa was hybrid corn.The process was much slower in the south. More than ten years after its introduction, hybrid corn accounted for only 60 per cent of total acreage in Alabama.
ТГС1INOI OGIC AI PROGRESS AND GROWTH chapter 12
Figure 1
100 -| ^ Percentage of
/ Wisconsin total corn
80 - acreage planted
/ Kentucky Iowa / sT with hybrid
/ / / Texas seed—selected
60 - / / / US states.
/ / / 1932-56
40 - If / / Alabama /
/ / /
20- J / / У
10-
0 - 1 1 1 1 1 1 1 I I l l 1 l
1932 1934 1936 1938 1940 1942 1944 1946 1948 1950 1952 1954 1956
Why was the speed of adoption higher in Iowa than in the South? Griliches's article showed that the reason was economic: the speed of adoption in each state was a function of the profitability of introducing hybrid corn. And profitabi ity was higher in Iowa than in the southern states.
SOURCE: Zvr Griliches. 'Hybrid corn: an exploration in the economics of technological change". Econometrico. vol. 24. no. 4. October 1957. pp. 501 22. Reproduced with kind permission of the Econometric Society.
The appropriability of research results
The second determinant of the level ol R&D and of technological progress is the degree of appropriability of research results. II firms cannot appropriate the profits from the development ol new products, they won't engage in R&D and technological progress will be slow. Many lactors are also at work here.
The nature of the research process itself is important. For example, il it is widely believed that the discovery of a new product will quickly lead to the discovery of an even better product, there may be little payoff to being first. A highly fertile field of research may not generate high levels ol R&D. This example is extreme, but revealing.
Even more important is the degree of protection given to new products by the law. Without legal protection, profits from developing a new product are likely to be small. Except in rare cases where the product is based on a trade secret (such as Coca-Cola), it generally won't take long tor other firms to produce the same product, eliminating any advantage the innovating lirm may initially have had. This is why countries have patent laws. Patents give a lirm that has discovered a new product—usually a new technique or device—the right to exclude anyone else from the production or use ol the new product for a period ol lime.
Australia tripled its patent applications over the last twenty years to 0.4 patents per 1.000 employees in 2005. but is still well below that in the United States (1.7), Japan (1.5). Germany 4 (I.I) and France (0.6).
This type of dilemma is known as 'time inconsistency'.We will see other examples and discuss it at length in 4 Chapter 25.
The issues go beyond patent laws.To ask two controversial questions: Should Microsoft be kept in one piece or broken up to stimulate R&D? Should the government impose caps on the prices of AIDS 4 drugs?
How should governments design patent laws? On the one hand, protection is needed to provide lirms with the incentives to spend on R&D. On the other once firms have discovered new products, it would be best lor society it the knowledge embodied in those new products was made available without restrictions to other firms and to people. Take, lor example, biogenetic research. Only the prospect ot large profits is leading biocngineering lirms to embark on expensive research projects. Once a firm has found a new product, and this product can save many lives, it would clearly be best to make it available at cost to all potential users. Hut il such a policy was systematically followed, it would eliminate incentives tor lirms to do research in the lirst place. Patent law must strike a difficult balance. Too little protection will lead to little R&D. Too much protection will make it difficult lor new R&D to build on the results ot past R&D, and may also lead to little R&l ).
Countries that are less technologically advanced often have poorer patent protection. China, for example, is a country with poor enlorcement ol patent rights. Our discussion helps to explain why. Those countries are typically users rather than producers, of new technologies. Much of their improve¬ment in productivity comes not from inventions within the country but Irani the adaptation ol foreign technologies. In this case, the costs ol weak patent protection are small, because there would be few domestic inventions anyway. But the benefits of low patent protection are clear: they allow domestic lirms to use and adapt foreign technology without having to pay royalties to the foreign firms that developed the technology.
12.3 THE FACTS OF GROWTH REVISITED
In Australia, for example. ► che ratio of employment to population increased from 42 per cent in 1950 to 50 per cent in 2008. This represents an increase of 0.3 per cent per year. Thus, in Australia, output per capita has increased 0.3 per cent more per year than output per worker—a small difference, relative to the numbers in die table.
We can now use the theory developed in this chapter and Chapter 11 to interpret some of the lacts we saw in Chapter 10.
Capital accumulation versus technological progress in rich countries since 1950
Suppose we observe an economy with a high growth rate of output per worker over some period ol time. Our theory implies that this fast growth may come from two sources.-
• It may be due to a higher rate of technological progress.
• Ii may reflect thc adjustment of capital per effective worker, K/AN, to a higher level. As we saw in Figure 12.4, such an adjustment leads to a period ol higher growth even if the rate of technological progress hasn't increased.
Can we tell how much ol the growth comes from one source and how much comes trom the other? Yes. It high growth reflects high balanced growth output per worker should he growing at a rate equal lo the rale ol technological progress (see Table 12.1, line 4). II high growth reflects instead the adjustment to a higher level of capital per effective worker, this adjustment should be reflected in a growth rate of output per worker that cxceeds the rate of technological progress.
Iter's apply this approach to interpret thc tacts about growth in rich countries iexcluding Germany! seen in Table К).I. This is done in Table 12.2, which gives, in column I. the average rate ol growth ol output per worker and, in column 2, the average rate ot technological progress, £.], since 1950, lor each ot the five countries. (Note one dilterence between Tables 10.1 and 12,2: As suggested by the theory, Table 12.2 looks at the growth rate ol outpul per worker, while Table 10.1, which focuses on the standard of living, looks at the growth rale of output per person. The diflerences are small. Thc rate ot
Table 12.2 Average annual growth per worker and technological progress in five rich countries, 1950-2004
Rate of growth of output per worker (%) 1950-2004 Rate of technological progress (%) 1950-2004
Australia 1.8 1.0
France 3.2 3.1
Japan 4.2 3.8
United Kingdom 2.4 2.6
United States 1.8 2.0
Average 2.4 2.5
1
'Average' is a GDP( PPP)-weighted average of the growth rates in each column.'Rate of technological progress' is weighted growth rates of labour and capital subtracted from output growth, divided by a fixed labour share of 0.7.
SOURCES: 1950 to 1970: Angus Maddison. Dynamic Forces in Capitalist Development (New York: Oxford University Press. 1991). 1970 со 2004: OECD Economic Outlook database: for Australia: ABS. cat no. 1364. and M. Butlin. RBA Discussion Paper. 1977. RBA Table GIO.
-ECHNOLOGICAl PROGRESS AND GROWTH chapter 12
technological progress, is constructed using a method introduced hy Robert Solow; the method and the details of construction are given in the appendix to this chapter.
The table leads to two conclusions. l irst, growth since 1950 has been a result ol rapid technological progress, not unusually high capital accumulation. This conclusion follows Irom the tact that, in ail live countries except Australia, the growth rate of output per worker (column 1 has been roughly equal to the rale ol technological progress column 2). This is what we would expect when countries are growing along their balanced growth path.
Note what this conclusion docs not say. It does not say that capital accumulation was irrelevant. Capital accumulation was such as to allow these countries to maintain a roughly constant ratio of output to capital and achieve balanced growth. What it says is that, over the period, growth did not come from an unusual increase in capital accumulation- it came from an increase in the ratio of capital to output.
In the case ol Australia only half ot the growth was attributable to technological progress, and so capital accumulation did raise the capital to output ratio. I Iowevcr, by the 2000s, Australia was likely to be close to balanced growth.
Second, convergence of output per worker across countries has come from higher technological progress, rather than from faster capital accumulation, in the countries that started behind. This conclusion follows from the ranking ol the rates ol technological progress across the countries in the second column with lapan at the top and the United States and Australia at the bottom.
This is an important conclusion. One can think, in general, of two sources of convergence between countries. First, poorer countries are poorer because they have less capital to start with. Over time, they accumulate capital faster than the others, generating convergence. Second, poorer countries are poorer because they arc less technologically advanced than the others. Over time, they bccome more sophisticated, either by importing technology from advanced countries or by developing their own. As technological levels converge so does output per worker. The conclusion we can draw from Table 12.2 is that in the ease of rich countries, the more important source ot convergence in this case is clcarly the second one.
It would seem that the best way of uncovering the secrets ot growth is to look at the poor countries in 1950 that have grown rapidly in the last twenty years (such as the lour tigers: I long Kong, Taiwan, Singapore and South Korea) or the even more recent last growers such as China, Indonesia, Malaysia and Thailand1 But here again the lessons aren t proving simple. In all these countries, growth has come with the rapid accumulation ol both physical capital and human capital. It has also come with an increase in the importance ol toreign trade—an increase in exports and imports. But beyond these two factors, clear differences emerge. Some economies, such as Hong Kong, have relied mostly on tree markets and limited government intervention. Others such as Korea and Singapore, have relied instead on government intervention and an industrial policy aimed at fostering the growth of specific industries.
FOCUS
'box
The cases ol Hong Kong and Singapore are discussed in detail in the focus box Fast Asian growth. Their performances are compared with those of their cultural and ethnic neighbours, China and Taiwan The bottom line is that wc haven't yet unravelled the secrets of growth.
EAST ASIAN GROWTH
Most, but not all. East Asian countries over the last twenty years have done well to raise the standard of living of their citizens. Here, we examine a few successful East Asian countries, finding some similarities in how they achieved their growth and some glaring contrasts. First we look at Hong Kong and Singapore, then at Taiwan and China.
Between 1960 and 1985. the average growth rate of output in both Hong Kong and Singapore was 6.1 per cent per year. How did these two countries grow so fast? Looking closely, one is struck both by the similarities and by the differences in their economic evolutions.
A tale of two city states—the similarities
Hong Kong and Singapore have several things in common. Both are former British colonies. Both are essentially cities that served initially as trading ports with little manufacturing activity.The postwar population of both countries was composed primarily of immigrant Chinese from southern China. During the course of their rapid growth, the two countries have gone through a similar sequence of industries, with Singapore starting ater than Hong Kong by ten to fifteen years.The respective sequences are summarised in Table I.
The differences
A closer look, however, shows major differences in the way the two countries have grown.
Hong Kong grew under a policy of minimal government intervention. For the most part, the government had limited its intervention to providing infrastructure and selling land as it became required for further growth. In contrast, growth in Singapore was dominated by government intervention. Through budget surpluses, as well as forced saving through pension contributions, the government achieved a very high national saving rate. Singapore's share of gross investment in GDP increased from 9 per cent in I960 со 43 per cent in 1984. one of the highest investment rates in the world.The development of specific industries was the result of systematic government targeting, implemented through large tax incentives for mostly foreign investors.
These differences in strategies are reflected in the relative roles of capital accumulation and technological progress. In Hong Kong, the annual growth rate of output per worker from 1970 to 1990 was 2.4 per cent; the growth rate of technological progress over the same period was 2.3 per cent. Using the interpretation provided by the model developed in this chapter, growth in Hong Kong was roughly balanced. In Singapore, the growth rate of output per worker from 1971 to 1990 was 1.5 per cent. In the article on which this box is based. Alwyn Young, an economist at the University of Chicago, concludes that the rate of technological progress during that period was a surprisingly low 0.1 per cent. If his calculation is right (and, after an intense controversy triggered by his article, it appears to be largely right), this implies that Singapore grew nearly entirely through unusually high capital accumulation, not technological progress. Singapore's growth was very much unbalanced.
Why did Singapore achieve so litde technological progress up until the 1990s? Alwyn Young argues that, in effect, Singapore moved too fast from one industry to the next. By moving so fast, it didn't have time to learn how to produce any of them very efficiently. And, by relying largely on foreign investment, it allowed a class of domestic entrepreneurs to learn from and replace foreign investment in the future.
If Alwyn Young is right, what lies in store for Singapore? The model developed in this chapter suggests that a slowdown in growth after 1985 was inevitable (as seen in Figure I). High investment rates can lead to high growth only for a while. The numbers would have appeared brighter for Hong Kong, which seemed to be growing on a balanced growth path. But major changes have occurred in Hong Kong. In 1997, Hong Kong again became part of China; whether this will help or hinder its long-run growth remains to be seen, but since 1997 it has stumbled. On the other hand, it would appear that Singapore might have taken heed of Alwyn Young's warning, since its high growth reappeared from the 1990s.
Table 1 The sequence of activities in Hong Kong and Singapore since the early 1950s
Hong Kong Singapore
Early 1950s Textiles Early 1960s Textiles
Early 1960s Clothing, plastics Late 1960s Electronics, petroleum refining
Early 1970s Electronics Early 1970s Electronics, petroleum refining, textiles, clothing
1980s Trade, banking 1980s Banking, electronics
1 1
A comparison with China and Taiwan
TFCHNOI.OGICAL PROGRESS AND GROWTH chapter 12
Now let's see how our two cities performed in comparison with their cultural and ethnic neighbours. China and Taiwan.The comparison is very informative about the role of culture versus institutions, an issue we will discuss in more detail in Chapter 13. While China chose to adopt state planning and communist political institutions (and only marginally liberalised these in recent years). Hong Kong, Singapore and Taiwan chose the capitalist path with relatively well-enforced property rights.
Figure I
GDP per capita (PPP-adjusted). 1950-2001
25,000 -i
20,000 -
5.000
1950
2000
SOURCE. Ang.j-, Maddnon. The World Economy. Historical Slot/sues (OECD. 2004).
= 15,000 - o
-a Э
t 10,000 -
Figure I shows PPP-adjusted GDP per capita for the four economies since 1950. Hong Kong. Singapore and Taiwan prospered, but China stagnated. After Mao Tse Tung's death and the 1978 reforms, which introduced some basic property rights and gradual improvements in economic incentives, China is now experiencing a healthy growth rate. But it has a long way to go to catch up with Hong Kong, Singapore and Taiwan.
SOURCE: Alwyn Young. A tale of two cities: factor accumulation and technical change in Hong Kong and Singapore'. NRER Macroeconomics Annual. 1992. pp. 13-63.
Capital accumulation versus technological progress in China since 1980
Going beyond growth in OI.CD countries, one of the striking lacts in Chapter 10 was the high growth rates achieved by a number of Asian countries. This raises again the same questions: Do these high growth rates reflect fast technological progress, or do they reflect unusually high capital accumulation? To answer these questions, we will focus on China because of its size and because of the astonishingly high output growth rate, nearly 10 per cent, that it has achieved since the early 1980s.
Table 12.3 gives the average rate ol growth, gy , the average rate ol growth ol output per worker, gy~ Snr a,1cf ^e average rate of technological progress, for the period 1983 to 2003. The lact that the last two numbers arc nearly equal yields a very clear conclusion: growth in China since the early 1980s has been nearly balanced, and the high growth of output per worker reflects a high rate ol technological progress, 8.4 percent per year on average. This is an important conclusion, showing the crucial role ol technological progress in explaining China's growth. But, just as in our discussion of OF.CD countries, it would be wrong to conclude that capital accumulation is irrelevant. To sustain balanced growth at such a high growth rate, the Chinese capital slock has had to increase at the same
Table 12.3 Average annual growth per worker and technological progress in China. 1983-2003
Rate of growth of output (%) Rate of growth of Rate of technological output per worker (%) progress (%)
9.7 8.0 8.4
SOURCE OECD Economic Survey of China 2005.
rate as output. This in turn has required a very high investment rate. To see what investment rate was
required, go hack to equation 1 12.3) and divide both sides hy output, Y, to get
J_
у = + 8A + 8s) у
I et's plug in numbers lor China tor the period 1983 to 2003 The estimate of fi. the depreciation rate of capital in China, is 5 per cent a year. As we iust saw, the average value of Хд lor the period was 8.4 per cent. Thc average value of gy, the rate of growth ot employment, was 1.7 per cent The average value of the ratio of capital to output was 2.6. This implies a ratio of investment to output of (5 + 8.4 + 1.7) X 2.6 = 39 per cent. Thus, lo sustain balanced growth, China has had to invest 39 per cent ol its output a very high investment rate compared with, say, thc LIS investment rale. So capital accumulation plays an important role in explaining Chinese growth but it is still the case lhat sustained growth has come Irom a high rate of technological progress.
How has China been able to achieve such technological progress? A closer look ai ihe daia suggests two main channels. First, China has transferred labour from the countryside, where productivity is very low, lo industry and services in the cities, where productivity is much higher Second, China has imported the technology ot more technologically advanced countries. It has, for example, encouraged the development ot joint ventures between Chinese firms and foreign firms. Foreign firms have come up with better technologies, and over lime Chinese firms have learned how to use them.
This leads to a general point. The nature ol technological progress in more advanced economies is likely to be dilfcrcnt Irom that of less advanced economies, lhe more advanced economies, being by definition at the technological frontier need to develop new ideas, new processes and new products. They need lo innovate. The countries lhat arc behind can instead improve their level of technology by copying and adapting the new processes and products developed in the more advanced economies. They need to imitate. The further behind a country is, the larger the role of imitation relative to innovation. As imitation is likely to be easier than innovation, this can explain why convergence, both within the OF.CI) and in the case of China and other countries, typically lakes the lorm ol technological catch-up к raises, however, yet another question: If imitating is so easy, why is il lhat so many other countries do not seem lo be able lo do the same and grow? This points to the broader aspccts of technology discussed earlier in the chapter.
Technology is more than iust a set of blueprints. How efficiently the blueprints can be used and how productive an economy is depend on its institutions, on the quality of its government, and so on. We will return lo this issue in the next chapter.
SUMMARY
• When we think about the implications of technological progress for growth, it is useful to think of technological progress as increasing the amount ol ellective labour available in the economy (lhat is, labour multiplied by the stale ol technology i. We can then think of output as being produced with capital and effective labour.
1 ECHNOLOGICAL PROGRESS AND GROWTH chapter 12
• In steady state, output per effective worker and capital per effective worker arc constant. Put another way, output per worker and capital per worker grow at the rate ol technological progress. Put yet another way, output and capital grow at the same rate as effective labour, thus at a rate equal to the growth rate of the number ol workers plus the rate ol technological progress.
• When the economy is in steady state, it is said to be on a balanced growth path. Output, capital and effective labour are all growing 'in balance—that is, at the same rale.
• The rale ol output growth in steady state is independent of the saving rate. However, the saving rate affects the steady-state level of output per effective worker. And increases in the saving rate lead, for some time, to an increase in the growth rate above the steady-state growth raic.
• Technological progress depends on i I the Icrtilitv ol research and development—how spending on R&D translates into new ideas and new products, and 2 the appropriability of the results ol R&l)— the extent to which firms benefit from the results of their R&D.
• When designing patent laws, governments must balance their desire to protect future discoveries with a desire to make existing discoveries available to potential users without restrictions.
• France, Japan the United Kingdom and the United States have had roughly balanced growth since 1950. Convergence ol output appears to have come primarily trom a convergence in technology levels.
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