ECO 2 – Economic Growth

Business cycle analysis asks where an economy sits relative to its own trend. Growth analysis asks what that trend is and what moves it. The two questions have different time horizons and different tools, and for a global investor the second one is the more consequential. Equity prices discount a stream of future earnings, and over long horizons that stream is bounded by how fast the economy itself can expand. The expected long-run growth rate of real income also anchors the average level of real interest rates, and therefore the level of real returns across every asset class. In the shorter term, the gap between actual output and potential output, the degree of slack, is a principal driver of fixed-income returns.

The quantity that carries all of this is potential GDP, the maximum level of output an economy can sustain without pushing the inflation rate up. Over long periods actual real GDP growth must equal potential GDP growth, because producing above potential means employing labour and capital beyond their optimal levels, which cannot continue indefinitely. Potential GDP growth is therefore a ceiling on the sustainable rate of expansion, and raising it is the only durable way to lift the level of income, the level of profits and the standard of living.

Real GDP against real GDP per capita

Two measures do different jobs and are routinely confused. Growth in real GDP tells you how fast the total economy is expanding, which matters for the absolute size of the market and for aggregate corporate earnings. Growth in real GDP per capita, real GDP divided by population, tells you what is happening to average material well-being. Real GDP per capita rises only when real GDP grows faster than population. A country can post respectable headline growth and see no improvement in living standards at all if its population is expanding just as quickly.

Why cross-country comparisons use purchasing power parity

Each economy reports output in its own currency, so comparison requires conversion to a common unit, normally the US dollar. Two conversion routes exist: current market exchange rates, or the rates implied by purchasing power parity. Purchasing power parity is the proposition that exchange rates settle at levels where a representative basket of goods and services costs the same everywhere.

The market exchange rate route fails for two reasons. First, market rates are highly volatile, so measured GDP can swing sharply from one year to the next even when nothing at all has happened to real activity in the country. Second, market rates are set by financial flows and by flows of tradable goods and services, yet a large share of what households actually consume is non-tradable. Non-traded items are systematically cheaper in developing countries, because the labour that produces them is cheaper. A haircut or a taxi ride costs far less in Mexico City than in London, and ignoring that difference understates the real standard of living of the Mexican consumer. Cross-country comparisons of GDP should therefore be built on purchasing power parity rather than on spot exchange rates.

Two groups of economies, and wide dispersion inside each

Economies are conventionally split into developed (or advanced) and developing. Developed economies tend to have high per capita GDP, but there is no agreed set of criteria. The International Monetary Fund classifies 39 economies as advanced and 155 as developing, and states plainly that the classification rests on no strict economic test and has changed over time. The advanced group contains the United States, Canada, Australia, Japan and the major European economies, where growth has generally slowed over recent decades, with the United States outpacing Europe and Japan. It also contains Singapore, Ireland and Spain, which were poor in the 1950s and reached high per capita income through sustained fast growth over half a century.

The developing group covers Africa, Asia and Latin America. Per capita income is lower, aggregate growth is generally faster, and dispersion within the group is enormous. China and India have grown rapidly for decades, while Latin America, Africa and the Middle East have lagged Asia. In 1970 the Singaporean figure for GDP per head was under half the American one, and it now stands above it. Ethiopia and Kenya remained poor with little per capita progress. The growth literature explains part of this with capital, labour and technology, but the rest turns on institutions: whether a country has the legal, financial and political machinery that lets accumulation and innovation happen at all.

The single most visible difference between a poor economy and a rich one is the amount of capital standing behind each worker. Capital is accumulated out of saving, both private and public, and this is precisely where many developing economies are trapped. Low disposable income makes saving hard, low saving means low investment, low investment means slow growth in GDP, and slow growth keeps income and saving low. The loop is self-reinforcing, which is why domestic policy alone struggles to break it. The escape route is external: a country that can attract foreign capital is no longer limited to what its own residents can save.

Financial markets and intermediaries

The level of saving is only half the story. The other half is how well that saving is allocated. Banks and financial markets contribute to growth through three distinct channels.

• Selection and monitoring. Lenders and investors screen applicants before funding them and watch them afterwards, which pushes capital toward the projects offering the best risk-adjusted return rather than toward whoever happens to hold the cash.
• Risk transfer and liquidity. By creating instruments that let savers diversify, transfer risk and exit when they need to, the financial sector makes people willing to save and to accept risk in the first place.
• Relaxing credit constraints. Intermediaries pool many small deposits into amounts large enough to fund projects that can exploit economies of scale, which no individual saver could finance alone.

The empirical work supports this: economies with better functioning financial systems grow faster (Levine, 2005). The relationship is not unconditional, however. Financial deepening that works by loosening credit standards or by raising leverage adds risk without adding to long-run growth.

Political stability, rule of law and property rights

Property rights are the legal arrangements protecting private property, including intellectual property. When they are clearly defined and reliably enforced, households and companies have a reason to save and invest, because they can expect to keep the return. Establishing them requires a legal system with two components: substantive law, which sets out the rights and responsibilities of parties and the relationships between them, and procedural law, which provides the machinery to protect and enforce the substantive rules. Developed economies take both for granted. Many developing economies have one, neither, or laws that exist on paper only.

Political instability compounds the problem. Wars, coups and endemic corruption raise the perceived risk of any investment, deter foreign capital and depress growth directly. For much of Africa in particular, building a legal system that establishes, protects and enforces property rights ranks ahead of every other growth intervention.

Education and health

Weak education at every level is a major brake on growth. Illiteracy is widespread in some developing economies and few workers have the skills to operate current technology. The problem is often made worse by a brain drain, in which the best educated leave for advanced economies. Basic schooling raises the skill level of the workforce, and because human capital and physical capital are complements, it also raises the productivity of the physical capital already in place. China and India have invested heavily in education and graduated very large numbers of engineering and technology students, materially improving workforce quality.

What the empirical work adds is that the allocation of education spending across levels matters as much as the total, and that the right allocation depends on where the country sits relative to the technological frontier. An economy at the frontier grows by innovating, so it needs post-secondary education, and incremental spending on primary and secondary schooling adds relatively little. An economy that grows mainly by adopting technology invented elsewhere needs primary and secondary education, because that is what raises the capacity to absorb imported technology and to organise existing work more efficiently. Spending the developed-country way in a developing country wastes the money.

Health is the parallel constraint. Life expectancy is substantially lower across much of the developing world, tropical disease is widespread in Africa and the AIDS epidemic has been devastating. Botswana grew impressively through the 1970s and 1980s and then slowed dramatically over the following two decades, with the epidemic among the causes.

Tax and regulatory systems

Tax and regulatory policy bear on growth mainly through their effect on company formation. Lighter regulation encourages entrepreneurial activity and the entry of new firms, and firm entry correlates strongly with average productivity. Work by the Organisation for Economic Co-Operation and Development identifies low administrative start-up cost as a key factor encouraging entrepreneurship (OECD 2003).

Free trade and unrestricted capital flows

Opening an economy to trade and capital changes what is possible. With an open capital account, world saving can fund domestic investment, which breaks the low income, low saving, low investment loop directly. Foreign investment arrives in two forms:

• Foreign direct investment, where a foreign company builds or buys property, plant and equipment in the domestic economy.
• Indirect or portfolio investment, where foreign companies and individuals buy equity and fixed-income securities issued by domestic companies.

Both raise the physical capital stock, and with it productivity, employment and wages, and possibly domestic saving as well. The policy implication is to remove the obstacles: high tariffs on imports, especially of capital goods, and restrictions on direct and indirect foreign investment. Brazil and India illustrate the payoff. Foreign companies invested $48.5 billion directly in Brazil in 2010, a material share of Brazilian investment spending. India liberalised direct and indirect foreign investment in 1999, giving foreign institutional and venture capital investors far more freedom to invest in Indian entities and in Indian capital markets and making it easier for foreign companies to build plant and equipment; the acceleration in Indian growth over the following decade followed from that. Foreign direct investment also carries technology with it, giving the recipient access to production methods developed in advanced economies.

Trade is the second channel. Free trade delivers more goods at lower cost. Domestic companies lose some pricing discretion because they face more competition, but they gain access to a much larger market.

The limiting factors, collected

Pulling the institutional argument together, growth in developing economies is held back by low rates of saving and investment; underdeveloped financial markets; weak or corrupt legal systems and failure to enforce the law; absent property rights and political instability; poor public education and health provision; tax and regulatory policy that discourages enterprise; and restrictions on international trade and capital flows. None of these is unique to developing economies, but all are more prevalent there. Beyond the institutional list, growth may also be limited by simple shortages of physical, human and public capital, and by the absence of innovation.

Anticipated growth in aggregate earnings is the fundamental driver of an equity market, and potential GDP places a limit on how fast the economy that generates those earnings can expand. The question that follows is whether earnings growth is bounded by the same limit.

It is. For aggregate real earnings to grow faster than real GDP indefinitely, the ratio of corporate profits to GDP would have to trend upward without end. That cannot happen. At some point stagnant labour income would make people unwilling to work and would undercut the demand that the profits depend on. Over long horizons, then, real earnings cannot expand faster than potential GDP does.

From economic growth to equity return: the Grinold–Kroner decomposition

The bound on earnings growth does not translate mechanically into a bound on equity returns, because several other terms sit between the two. The Grinold–Kroner (2002) decomposition sets them out.

Take the terms one at a time. The dividend yield dy has historically been fairly stable and a significant contributor to total return. The repricing term Δ(P/E) captures movement in the market multiple; there is some evidence that faster GDP growth lifts P/E ratios as investors judge the economy less risky, but the dominant characteristic of this term is its volatility across market cycles rather than any reliable trend. Inflation i plus real growth g gives nominal economic growth, and this is the channel through which the real economy actually reaches equity returns.

The term that breaks the simple story is ΔS, the change in shares outstanding, known as the dilution effect. If shares outstanding were constant, real economic growth would pass straight through into expected equity returns. Empirically it does not, and dilution is why. It has two components:

• Net buybacks (nbb) capture the net of share repurchases and new issuance at the level of the whole national market. Repurchases raise returns to continuing holders; issuance dilutes them.
• Relative dynamism (rd) captures the part of economic growth generated by small and medium-sized entrepreneurial companies that are not listed. The larger that share, the wider the wedge between the growth of the economy and the earnings growth of the companies an index investor actually owns.

Derived from L’Her, Masmoudi and Krishnamoorthy, Financial Analysts Journal 74, no. 4 (2018). Causes vary: privatisation of large state-owned enterprises in China and Poland, index membership falling from 19 companies to 4 in the Czech Republic and from 13 to 3 in Egypt, bank recapitalisations and reclassification in Greece, and the privatisation of a telecom operator plus secondary offerings in Ireland.

Read the two extreme rows together. China posted the fastest real per capita growth in the table at 8.2% and delivered a real equity return of only 0.7%, because net buybacks of −26.5% swamped everything else as state-owned enterprises were privatised and the index expanded from 28 companies in 1997 to 152 in 2017. Egypt grew at 2.3% and returned 9.4%, largely because the number of listed companies in the index collapsed. The dispersion in these two columns is the reason the observed correlation between economic growth and equity returns is so much weaker than intuition suggests.

The honest conclusion is that all else equal, faster economic growth should be associated with higher equity returns, but all else is rarely equal. Returns are heavily affected by dilution arising from the need to raise new capital to fund the growth, from large-scale privatisations, from merger waves and from buybacks. Listed companies are only one slice of the economy, and growth also creates new companies, attracts new investors and reprices the market. Economic growth does not by itself guarantee that existing shareholders capture the wealth it creates.

Forecasting potential growth, and why extrapolation fails

Estimates of potential GDP and its growth rate are published by both the OECD and the IMF as part of their intermediate and long-term country forecasts. Simply projecting past GDP growth forward is unreliable, because trend growth changes. The wave of economic transformation, privatisation and liberalisation across several Latin American and European economies in the late 1990s produced brisk growth and large equity returns, and for many of those countries it was followed by markedly slower long-run growth. Because small changes in potential growth compound into large differences in living standards and activity, recognising a change in the underlying economic factors and policies is one of the higher-value tasks a global equity investor performs.

What potential GDP does for the fixed-income analyst

For bonds the relevant quantity is usually the difference between actual and potential growth. Actual GDP growth above the potential rate puts upward pressure on inflation, and therefore on nominal interest rates and against bond prices; growth below potential does the reverse. The growth rate of potential GDP also sets the level of real interest rates, because faster potential growth requires higher real rates to call forth the saving that funds capital accumulation, and higher real rates in turn mean higher expected real returns across assets generally.

Three further uses arise in fixed-income work:

1. Credit quality. A higher rate of potential GDP growth improves the general credit standing of fixed-income issuers, and rating agencies use potential growth in assessing sovereign credit risk. All else equal, a downgrade to the potential growth estimate raises the perceived risk of the bonds.
2. Monetary policy. Central bank decisions respond to the gap between potential and actual output, the output gap, and to actual growth relative to the sustainable rate. Monitoring both is how an investor anticipates a policy turn.
3. Fiscal position. Deficits widen in recessions and narrow in expansions, so actual fiscal balances are judged against the structural or cyclically adjusted deficit, the theoretical balance that would prevail with the economy operating at potential GDP.

Diminishing marginal returns dictate how much capital and how much technology can each contribute to growth, and the distinction between the two is the most heavily examined idea in the reading. Growth in output per capita comes from exactly two sources: capital deepening, which is an increase in the capital-to-labour ratio, and technological progress, which is an improvement in TFP.

Capital deepening and where it stops

Capital deepening is a movement along a given production function, from A toward B in the figure. The capital-to-labour ratio rises whenever the growth rate of capital, meaning net investment, exceeds the growth rate of labour. Early on, when capital per worker is low, this is powerful. Once the ratio is already high, as at B, adding more capital barely moves output per worker at all, which is the move from B to D.

The stopping point is defined economically, not arbitrarily. Profit-maximising producers stop adding capital at the point where the marginal product of capital equals its marginal cost. In the neoclassical model this point matters enormously, because per capita growth in the economy comes to a halt there. After the economy settles at that steady state, no lasting growth can come out of deepening. Only when the economy operates below the steady state, with the marginal product of capital above its marginal cost, can deepening raise per capita growth.

One refinement. Once technological progress is in the picture, the capital-to-labour ratio must keep rising simply to hold the marginal product of capital equal to its marginal cost. But the substance of the point survives: companies will not raise the capital-to-labour ratio any faster than is required to maintain that equality.

The neoclassical conclusion, that faster capital accumulation cannot permanently raise per capita growth, is deflating. Endogenous growth theory offers a way round it, discussed later: if the additional capital embodies new and more efficient production methods, or products that did not exist before, rather than being pure replication of what is already installed, then faster accumulation can raise the permanent growth rate of per capita output.

Technological progress

An improvement in TFP does something different in kind. It shifts the entire production function upward proportionately, so the economy produces more output per worker at every level of capital per worker. That is the move from B to C. Technological progress also raises the marginal product of capital relative to its marginal cost, which makes further capital investment profitable and pushes back the limit that diminishing returns would otherwise impose. Continued growth in output per capita is possible even in the steady state, provided TFP keeps improving. Stated as a single sentence: sustained growth in per capita output requires progress in TFP.

Growth needs raw materials, and the category runs from land through oil to water. They divide into two categories. Renewable resources can be replenished: cut a tree, plant a seedling, harvest a new forest later. Non-renewable resources are finite and are gone once consumed, oil and coal being the obvious cases.

Intuition says resource-rich countries should be wealthy countries, and sometimes they are. Middle Eastern economies have high per capita incomes built on large oil reserves. Brazil has an abundance of land suited to large-scale agriculture, which makes it a major exporter of coffee, soybeans and beef. But the relationship between resource endowment and growth is far weaker than intuition predicts.

The key distinction is between access to resources and ownership of them. Access is essential; ownership is not. South Korea and other East Asian economies have grown rapidly with almost no natural resources, acquiring what they need through trade. Venezuela and Saudi Arabia hold large oil reserves, produce heavily and have grown less impressively than resource-poor Singapore and South Korea. As Example 1 showed, Venezuelan growth over the past six decades was far below that of Singapore, Japan and South Korea.

Why resources can actually hurt

In some countries resources appear to restrain growth outright, a pattern named the resource curse. Venezuela and Nigeria are the standard examples: well endowed, slow growing. Two mechanisms are proposed.

• Institutional failure. A country that can fund itself from resource rents may never build the economic and legal institutions that growth requires, because the immediate pressure to do so is absent.
• Dutch disease. Strong export demand for the resource drives the currency up, and the appreciation makes the rest of the tradable sector, manufacturing in particular, uncompetitive internationally. The label comes from the Netherlands, where the discovery of large natural gas fields was followed by an appreciation of the Dutch guilder and a contraction of manufacturing. The lasting damage is not the lost output itself but the lost TFP progress: a country without a vigorous manufacturing sector does not participate in the productivity gains that sector generates.

Will finite resources eventually cap growth

The opposing worry is long standing: rapid growth against a fixed stock of resources must eventually exhaust the stock and stop the growth. Three arguments suggest the concern is probably overstated.

1. Technological progress, from every source, lets the economy use fewer resources per unit of output and develop substitutes for what is scarce.
2. Growing scarcity in any specific resource raises its price, and the higher price itself drives the shift toward more plentiful alternatives. The adjustment is automatic and does not require anyone to plan it.
3. The share of national income accruing to land and resources has been falling in most countries, particularly as the composition of global output shifts toward services.

Quantity of labour is only one half of the labour input. Quality is the other, and it is captured by human capital.

Human capital

Human capital is the accumulated knowledge and skill that workers acquire through education, training or experience. Better educated and more skilled workers are more productive, and they are also more adaptable when technology or market conditions change, which matters as much over a working life as raw productivity does.

Schooling and training on the job are the two ways a country builds it. The outlay is real, just as it is for a machine, and so is the payoff: more years of education show up in higher pay. What makes education different from a machine is the spillover. Raising the education level of one person raises the output of that person and also the output of the people around them, because education is linked to the generation and diffusion of technology. Education therefore improves the quality of the labour force and encourages growth through innovation at the same time. The consequence is important for the theory later in this reading: increased education, whether formal or on the job, can produce a permanent increase in the growth rate of an economy, if the better educated workforce delivers more innovation and faster technological progress. Investment in population health belongs in the same category and is especially significant in developing economies.

Physical capital and the investment record

So long as gross investment exceeds depreciation, leaving net investment positive, the stock of physical capital grows each year. Economies with a higher investment rate should therefore have a faster-growing capital stock and faster GDP growth. One qualification applies immediately: if population is growing, part of net investment is absorbed simply in equipping the new workers and maintaining the capital-to-labour ratio, so the effect on per capita GDP growth is smaller than the effect on aggregate GDP growth.

Source: IMF. Rows are ordered by the 2018 investment share. The United States share is low relative to other developed economies.

The correlation between investment and growth across these economies is high. China, India and South Korea devote a large share of GDP to investment and have grown fast; Brazil and Mexico devote less and have grown more slowly. Ireland and Spain, among the faster-growing European economies of the 1990s and for long stretches after 2000, carry some of the highest investment-to-GDP ratios. The Chinese record is the extreme case: annual GDP growth above 10% over long periods, funded by investment in factories, equipment and infrastructure running at more than 40% of GDP, the highest share in the world.

Reconciling the correlation with the limits of capital deepening

This sits awkwardly beside the earlier conclusion that sustainable growth cannot rest on pure capital deepening. Three explanations resolve the tension.

First, the transition can be very long. Diminishing marginal productivity will eventually limit the contribution of capital deepening, but “eventually” can mean decades in an economy starting from a low level of capital per worker.

Second, the effect of a given amount of investment depends on the stock it is added to. The dispersion in capital per worker is extreme. In 2000 the average US worker had $148,091 of capital behind them, against $42,991 in Mexico and $6,270 in India. A Mexican worker has relatively little machinery, so adding a small amount makes a large percentage difference. In the United States, Japan, Germany, France or the United Kingdom the accumulated stock is so large that a year of positive net investment moves it only slightly in percentage terms, even though the absolute increase is bigger than in a developing economy. Developed economies need a sustained high level of investment over many years to make a meaningful relative difference to the capital stock.

Third, physical capital is not homogeneous, so composition matters. Work from endogenous growth theory and from attempts to measure TFP more accurately both point the same way, and both suggest splitting capital spending into two categories.

ICT capital and non-ICT capital

ICT investment covers information, computers and telecommunications equipment, and measures the effect of the information technology sector on growth. The IT sector has been one of the key drivers of growth in developed economies, driven by innovation that pushed the cost of central technologies, semiconductors above all, sharply downward. As high-technology capital goods became cheaper, investment moved toward IT and away from other assets.

The reason ICT is treated separately is network externalities. Computers connect people through the internet and email and let them work more productively, and the productivity gain grows with the number of people connected. These effects are largely captured inside TFP rather than showing up as a distinct, directly observable effect, which is one reason ICT investment and TFP growth are hard to disentangle. The share of ICT investment in GDP tends to run in the 3% to 5% range for most developed economies. The sector remains relatively small in most countries, and spending on IT lost ground as a proportion of GDP across 2000 to 2008, since the recession early in that decade fell especially heavily on high-technology outlays.

Non-ICT capital spending takes in machinery, transport equipment and construction other than housing. Heavy spending under this heading should in the end amount to capital deepening and therefore have less effect on potential GDP growth. A growing share of ICT investment, through its externalities, may genuinely raise the growth rate of potential GDP.

Public infrastructure

The final extension of the capital input is public infrastructure investment: roads, bridges, municipal water, dams and, in some countries, electricity grids. Public capital has few substitutes and is largely complementary to private sector production rather than competing with it. Ashauer (1990) concluded that spending on infrastructure drives productivity gains substantially enough to earn a place in the production function as a separate input. As with research and development spending, the full effect reaches beyond the direct benefit of the individual project, because better infrastructure raises the productivity of private investment generally.

Technology is the most important factor affecting growth in per capita GDP, and it is decisively so in developed economies. It allows an economy to escape part of the limit imposed by diminishing marginal returns by shifting the production function upward. Technological progress makes it possible to produce more goods and services, or better ones, from the same inputs; it creates goods and services that did not previously exist; and it improves how efficiently businesses are organised and managed.

Technological change can be embodied in human capital, meaning knowledge, organisation, information and experience, or in new machinery, equipment and software. That is why high rates of investment matter, and ICT investment particularly. Countries also innovate through public and private spending on research and development.

Research and development spending

Spending on research and development and counts of patents issued do not measure innovation directly, but they give useful insight into innovative performance. The pattern in the data is systematic: developed economies spend the highest percentage of GDP on research and development, because they sit at the technological frontier and must innovate to grow. Developing economies spend less, because they can acquire technology by imitating or copying what was developed elsewhere. Technology embodied in imported capital goods is one of the main channels through which a relatively poor country narrows the gap on the technology leaders.

Source: OECD. Rows are ordered by the 2016 share.

The link from research spending to growth is not clean, and it is worth being precise about why. Technological innovation from high research spending raises output and productivity in the long run, but in the shorter run it can slow growth cyclically as companies and workers are displaced by the new technology. This is Schumpeter’s creative destruction, and it captures the double-edged character of innovation: the same process that raises the level of productivity destroys the businesses and the jobs attached to the older way of doing things.

Reading a productivity table correctly

Because TFP is measured as a residual, TFP estimates are very sensitive to how the labour and capital inputs are measured. Empirical work at the Conference Board and the OECD adjusts for changes in the composition and quality of both inputs, so the resulting TFP measure should capture genuine technological and organisational improvement rather than measurement noise.

The decomposition that follows is the one to memorise. Labour productivity growth depends on capital deepening and on technological progress. Therefore:

Source: Conference Board Total Economy Database. The productivity level column reports GDP per hour worked in 2018 dollars and is shown once per economy. Rounding causes minor discrepancies within rows.

Work one row to fix the method. From 2005 to 2018, South Korean labour productivity grew 3.3% per year, of which 3.3% − 0.8% = 2.5% came from capital deepening and the remainder from TFP. Now read the level column, which reports GDP per hour worked. It reflects how much human and physical capital has been built up, and it is far higher in developed economies: 73 dollars per hour in the United States against 15 in China. China has a population above 1.3 billion, against slightly more than 300 million in the United States, and yet real US GDP is much larger, because US workers have historically produced far more per hour. The growth rate of productivity runs the other way, and typically favours developing economies, where human and physical capital are scarce but expanding fast and diminishing returns are still weak.

The investment conclusion follows directly. A permanent increase in the growth rate of labour productivity raises the sustainable growth rate of the economy, lifts the ceiling on earnings growth and therefore raises the potential return on equities. A persistently low rate of labour productivity growth does the reverse: it lowers both long-run potential growth and the upper limit on earnings growth, which implies slow profit growth and correspondingly poor equity returns.

Source: Conference Board Total Economy Database. An expanded version of Equation 4 is used, with each input weighted by its share in national income and TFP capturing everything the labour and capital inputs leave unexplained. Rounding is used throughout.

With the steady state defined, the next question is what each parameter does to it. Take an economy already on its steady-state growth path, so that the exogenous factors, labour supply and TFP, are fixed, and ask how the steady-state capital-to-labour ratio and output per worker respond. Equivalently: if two economies differ in exactly one parameter, what does that imply about their per capita incomes?

• Saving rate (s). A higher saving rate raises the capital-to-labour ratio k and output per worker y, because it generates more saving and investment at every level of output. Graphically the saving curve shifts upward and meets the unchanged required investment line further to the right. The crucial qualification is that although both k and y reach higher levels, the steady-state growth rates of output per capita and of output are unchanged, exactly as Equation 8 says.
• Labour force growth (n). Faster labour force growth reduces the equilibrium capital-to-labour ratio, because a correspondingly faster rate of capital growth is now required and, with the saving rate given, that can only be achieved at a lower capital-to-labour ratio. Output per worker is lower as well. Graphically the required investment line becomes steeper and cuts the saving curve at a lower point.
• Depreciation rate (δ). A higher depreciation rate reduces both the equilibrium capital-to-labour ratio and output per worker, because a given rate of gross saving now yields less net capital accumulation. Graphically it steepens the required investment line in exactly the same way as faster labour force growth.
• TFP growth (θ). Faster TFP growth also reduces the steady-state capital-to-labour ratio and output per worker, for a given labour supply and a given level of TFP. This result has to be read carefully. Faster TFP growth means output per worker will grow more quickly in future, which is unambiguously good. Yet fix the date, fix the supply of labour and fix the level of TFP, and output per worker comes out beneath what a slower TFP trend would have produced, because the economy is climbing a steeper path that starts lower down. Graphically, faster TFP growth steepens the required investment line, just as n and δ do.

The summary sentence is worth memorising in this form: saving behaviour, demographic expansion and the wear rate on capital all reset the level at which output per worker sits, and none of them resets the rate at which it climbs. Shifting that rate permanently takes a shift in how fast TFP improves.

Off the steady state: transition dynamics

Everything so far describes an economy already on its balanced path. Away from it, growth can run faster or slower than the steady-state rate. Combining Equations 6, 7 and 9 gives the growth rates during the transition.

Read the figure from the right-hand side first. When the output-to-capital ratio stands above where equilibrium would put it, the deviation term in Equations 10 and 11 turns positive and each growth rate runs beyond the balanced rate θ/(1 − α). This is the case where actual saving and investment exceed required investment, so above-trend growth in per capita output is being driven by above-trend capital deepening. It usually reflects a relatively low capital-to-labour ratio, though in principle it could arise from high TFP. Because α is less than one, capital grows faster than output, the output-to-capital ratio falls, and over time both growth rates decline back to the steady-state rate.

The mirror image holds on the left. With the output-to-capital ratio below its steady-state level, actual investment is insufficient to sustain the trend rate of increase in the capital-to-labour ratio, so both output per capita and the capital-to-labour ratio grow more slowly than trend. This usually corresponds to a high and unsustainable capital-to-labour ratio, though it could reflect low TFP and hence low output. Output then grows faster than capital, the output-to-capital ratio rises, and growth converges upward to trend.

The four groups of conclusions

The neoclassical model delivers four clusters of results, and examination questions are drawn from all four.

1. Capital accumulation. Capital accumulation affects the level of output but not the long-run growth rate. Whatever its initial capital-to-labour ratio or initial productivity level, a growing economy moves toward steady-state growth. In the steady state, output grows at the rate of labour force growth plus the rate of TFP growth scaled by labour’s share of income, n + θ/(1 − α), and does not depend on the accumulation of capital or on the rate of business investment.

2. Capital deepening against technology. Rapid, above-trend growth occurs when countries first begin to accumulate capital, and slows as accumulation continues. Long-term sustainable growth cannot rely solely on capital deepening: if the capital-to-labour ratio grows faster than labour productivity, capital becomes less productive and growth is slower rather than faster. Stated broadly, pushing any one input up too quickly against the others meets falling marginal returns and will not carry sustainable growth. Without improvement in TFP, growth in labour productivity and per capita output would eventually slow. Because of diminishing marginal returns to capital, the only way to sustain growth in potential GDP per capita is through technological change, which shifts the production function upward so that the economy produces more from any given mix of inputs.

3. Convergence. Capital is scarce in developing economies and its marginal productivity is correspondingly high, and saving rates there may also be higher, so growth in those economies ought to run ahead of growth in developed ones, and per capita incomes should therefore converge over time.

4. The effect of saving on growth. A higher saving rate temporarily raises the growth rate. The mechanics are visible in the equations: Equation 9 says a higher s lowers the steady-state output-to-capital ratio Ψ, which makes the last term in Equations 10 and 11 positive and pushes both growth rates above the steady-state rate. Growth exceeds the steady-state rate through a transition period, and over that stretch the economy climbs to a richer position in both output per head and productivity, after which it rejoins the balanced path. Back on the balanced path, what fraction of income is put aside no longer affects how fast the economy expands. Thrift buys no permanent addition to the rate of expansion. It does buy a permanently richer economy: more output per head, more capital behind each worker, and higher productivity of labour.

Where the neoclassical model runs out

Solow (1957) used the growth accounting equation on United States data for 1909 to 1949 and reached a surprising conclusion: more than 80% of per capita growth came from TFP. Denison (1985) repeated the exercise for 1929 to 1982 within the same framework and found TFP explaining nearly 70%. That is the problem. The neoclassical model offers no explanation whatsoever of what determines technological progress or how TFP evolves. Technology is exogenous, which means the model attributes most of growth to a factor it does not model. Critics reasonably observe that this amounts to ignoring the very thing driving growth.

A second line of criticism attacks the prediction that the steady-state growth rate is unrelated to saving and investment. In the Solow model, long-run output growth depends only on labour force growth and technology, so raising investment from 10% to 15% of GDP lifts near-term growth and leaves the ultimate sustainable rate untouched. Many economists find that uncomfortable, and Mankiw (1995) presented evidence that saving rates and growth rates are positively correlated across countries. A third objection is empirical: the model predicts that in an economy where the capital stock is rising faster than labour productivity, the return on investment should fall over time, and for the advanced economies returns have not fallen.

The augmented Solow response

These criticisms produced two lines of research. The first, originated by Jorgenson (1966, 2000), is the augmented Solow approach. It stays inside the neoclassical tradition: diminishing marginal returns remain central and technological progress is still unexplained. What it tries to do is shrink the residual empirically, by measuring the inputs better and by broadening the definition of investment to include human capital, research and development, and public infrastructure. The composition of capital spending matters too, with high-technology investment expected to lift productivity more than machine tools or structures.

Adding inputs such as human capital lets the augmented model measure the contribution of technological progress more accurately. The economy still moves toward a steady-state growth path, because even broadly defined capital is assumed to run into diminishing marginal returns eventually. In essence this line of work applies the growth accounting method with more inputs in order to get a cleaner reading of technological progress. The second response was more radical, and is the subject of the next section.

Endogenous growth theory is a family of models that set out to explain technological progress rather than assume it. Growth that feeds itself drops out of the model as an ordinary result rather than being assumed, and nothing forces the economy toward any balanced rate at all. What sets these models apart is the absence of any decline in the marginal return to capital taken at the level of the whole economy. Increasing the saving rate therefore raises the rate of economic growth permanently, and increasing returns to scale become possible.

Romer and the argument against diminishing returns

Romer (1986) supplied both a model of technological progress and a reason why capital need not run into diminishing returns. His argument is that capital accumulation is the main factor behind long-run growth once the definition of capital is widened to include human or knowledge capital and research and development. Research and development means putting money into fresh knowledge that makes the production process better. In this framework knowledge, human capital and research spending are factors of production in the same sense as capital and labour, and must be paid for out of saving.

Companies spend on research for the same reason they build factories: to make a profit. Research succeeds when it yields a new product or production method that works in the market. But there is a fundamental difference between a new factory and a research programme. The output of research is ideas, and ideas can be copied and used by other companies. Research spending therefore carries potentially large positive externalities. Spending by one company raises the productivity of others and enlarges the pool of knowledge available to everyone. The benefit to the economy as a whole exceeds the private benefit to the company that paid for it, because no company can fully capture everything it creates. The gap between the two is the difference between private returns and social returns.

That distinction does more work than it first appears. Once diminishing returns to capital are dropped, returns to capital become constant and returns to every factor taken jointly become increasing. Were one company able to capture those scale economies for itself, each industry would collapse into a single dominant firm, and nothing in the data looks like that. Separating private from social returns resolves the contradiction: individual companies face constant returns to scale over their own private factors, so there is no inherent advantage to being large, while the externality delivers increasing returns to scale across the whole economy as each company benefits from the spending of the others.

The endogenous production function

Since the externalities stop returns to capital from ever tailing off, this model draws its production function as a straight line.

The significance of a constant marginal product is that the output-to-capital ratio is fixed at c, so output per worker always grows at exactly the same rate as capital per worker. Any change in the pace of accumulation shows up one for one in the pace at which output per head rises. Putting Equation 12 inside Equation 7 yields:

A higher saving rate s therefore implies a permanently higher growth rate. That single sentence is the key result of the endogenous growth model, and it is precisely what the neoclassical model denies.

Why this is an argument for public support of research

If private companies capture only part of the return their research generates, they will spend less on it than is best for society. This is a textbook market failure: private under-investment in the production of a good with positive externalities. The corrective is government intervention, either through direct public spending on research and development, or through tax breaks and subsidies for private production of knowledge capital. Because the endogenous model has no diminishing returns, higher spending on knowledge capital can translate into faster economic growth even in the very long run, not merely for a transition period.

A second implication runs the other way from the neoclassical prediction. Endogenous growth theory gives no reason for the incomes of developed and developing countries to converge. Constant, or even increasing, returns to investment in knowledge capital allow developed economies to keep growing as fast as or faster than developing ones indefinitely.

A wide gap separates living standards in developed and developing economies. The question is whether it persists forever or whether per capita income in the developing world catches up. Convergence means that countries with low per capita income should grow faster than countries with high per capita income, so that the gap narrows over time. The answer matters for growth prospects and directly for asset allocation.

Three kinds of convergence

Absolute convergence means developing economies, whatever their particular characteristics, eventually catch up with developed economies and match them in per capita output. It is worth being precise about what the neoclassical model does and does not say here. Every country is assumed to be able to reach the same technology, from which it follows that income per head everywhere ends up expanding at one common rate. It therefore implies convergence of growth rates. It does not imply that the level of per capita income ends up the same everywhere regardless of underlying characteristics, so it does not imply absolute convergence.

Conditional convergence makes the conditions explicit: convergence occurs conditional on countries sharing the same saving rate, population growth rate and production function. Given those conditions, the neoclassical framework has the economies ending up with a common output per head and a common balanced growth rate, since they share one steady-state capital-to-labour ratio. If they start from different capital-to-labour ratios their growth rates differ during the transition, with the economy starting lower experiencing faster productivity and income growth, and the differential shrinking until they meet. Countries with different saving rates or population growth rates have different steady-state capital-to-labour ratios and therefore different steady-state levels of per capita income, but their per capita growth rates still converge.

Club convergence is the response to the data, which show some poorer countries diverging from rather than converging to developed-country income levels. Under club convergence convergence on the income of the very richest economies is confined to club members, which are the rich and the middle-income countries, and within the club the poorest members grow quickest. Everyone outside keeps slipping further back. Membership is earned: a poor country can join by making the institutional changes discussed earlier in this reading.

The corollary is the non-convergence trap, which catches countries that do not implement the necessary reforms. Failure to reform labour markets undermined growth in several European economies that saw weak employment growth and high unemployment over two decades. Arrangements that initially promote growth can become traps if kept too long: import substitution policies let Latin American economies grow rapidly in the 1950s and 1960s and then left them stagnating through the 1970s and 1980s.

What convergence implies for a portfolio

If convergence, and club convergence in particular, does occur, then investing in lower per capita income countries that are members of the club should deliver a higher rate of return over long horizons than investing in higher-income countries. The logic runs through potential GDP: convergence means potential growth is higher in developing economies that have made the institutional changes required for club membership; faster long-term growth should produce faster growth in corporate profits; and faster earnings growth should support faster appreciation in share prices. Risk is also higher in those markets. What follows sensibly is a weighting toward club-member developing economies sized to the investor tolerance for risk, and not a concentrated bet on them.

The two channels through which convergence happens

The first channel is capital accumulation and capital deepening. On the per capita production function, developed economies operate at a point where adding capital does almost nothing to productivity, while developing economies operate at a point where adding capital raises labour productivity substantially. That difference alone generates faster growth in the poorer economy.

The second channel is technology transfer. Developing economies can imitate or adopt technology already in wide use in advanced economies, learning from them as scientific and management practice spreads with globalisation. Importing technology lets a developing economy grow faster and converge on advanced-economy income. There is a condition attached, and it is the condition that separates the club from everyone else: technology transfer narrows the gap only if the poor country invests the resources needed to master the technology and apply it. That spending is analogous to research and development spending, and it is what buys club membership. Without it the country is left out and continues to fall behind. For members of the club, the steady-state growth rate is set by the global rate of technological progress.

Set against this, the endogenous growth model makes no prediction of convergence at all. An economy that begins richer, and better equipped with capital, is free under this model to keep growing at least as quickly and never be overhauled. Where knowledge and human capital throw off large externalities, the rich economy holds its lead indefinitely by investing heavily in exactly those inputs.

What the evidence shows

If convergence holds, there should be an inverse relationship between the initial level of per capita real GDP and subsequent growth in per capita GDP. Ranking economies by 1950 income and looking at growth from 1950 to 2018 tests exactly that.

Source: IMF. GDP per capita in constant 2011 US dollars adjusted for purchasing power parity. Rows are ordered by growth over 1950 to 2018. Other economies in the full sample include the United Kingdom, Mexico, Peru, Turkey, the Philippines and Pakistan.

The verdict is mixed, and both halves of it matter. In favour of convergence: Canada, Australia, New Zealand and the United States occupied the four richest positions in 1950, whereas the quickest growth from 1950 to 2018 came from Korea and China, both above 5% per year and both starting far beneath the United States. Japan, Singapore, Spain and Korea all converged on advanced-economy income levels. In total, 17 of the 26 economies in the sample grew faster than the United States over the period.

Against it: New Zealand, Venezuela, Argentina and South Africa all lost ground relative to the United States over the same span. Since 2000 convergence has been relatively strong overall, with 16 of the sample economies, 60% of them, outpacing the United States. That group includes Australia and New Zealand alongside Peru, Turkey, Ethiopia, South Africa and the Philippines. Among the most advanced economies the pattern broke down: Italy, Japan and France each trailed Canada, Australia and the United States. The overall reading is that poorer countries may converge if they build the appropriate legal, political and economic institutions, and that trade policy is the other decisive variable.

The Solow model as developed above assumes a closed economy, where domestic investment equals domestic saving and there is neither international trade nor cross-border capital flow. Relaxing that assumption changes the growth outlook through five distinct routes.

1. A country can borrow or lend in global markets, so domestic investment can be funded from world saving and is no longer constrained by domestic saving.
2. Resources can shift into industries where the country has a comparative advantage and out of industries where it is relatively inefficient, which raises overall productivity.
3. Companies gain access to a larger, global market, which lets them exploit economies of scale and raises the reward for successful innovation.
4. Technology can be imported, which raises the rate of technological progress.
5. Competition in the domestic market increases, which forces companies to make better products, raise productivity and hold costs down.

The neoclassical account of an open economy

Inside the neoclassical framework, openness speeds convergence up, because trade and cross-border lending together raise the rate at which capital-to-labour ratios are pulled toward one another. The adjustment path runs as follows.

1. Developing economies have less capital per worker and therefore a higher marginal product of capital, so returns on investment should be higher where the capital-to-labour ratio is low and lower where it is high.
2. Global savers chase those returns, so capital flows from countries with high capital-to-labour ratios to countries that are capital poor.
3. Because of the inflows, the physical capital stock in the developing economy grows faster than in rich countries even if the domestic saving rate is low. Faster capital growth raises productivity growth and per capita incomes converge.
4. Capital flows must be matched by offsetting trade flows, so capital-poor countries tend to run trade deficits as they borrow abroad to fund domestic investment, while the developed economies, exporting capital, tend to show surpluses on trade.
5. During the transition, the inflows temporarily push growth in the capital-poor country above its steady-state rate, while growth in the capital-exporting countries runs below theirs.
6. Over time the capital stock in the poor country rises and the return on investment falls, so the rate of investment and the size of the trade deficit both decline. Growth slows toward the steady-state rate. If investment eventually falls below domestic saving, the country switches from trade deficit to trade surplus and becomes a capital exporter itself.
7. After world saving has been reallocated, there is no permanent increase in the growth rate anywhere. Both developed and developing economies grow at the steady-state rate.

The endogenous account, and why it predicts more

Endogenous growth models predict that a more open trade policy raises the rate of economic growth permanently. International trade raises global output through three effects:

• A selection effect: pressure from foreign rivals drives the weaker domestic producers out and obliges the stronger ones to innovate, which lifts efficiency across the national economy.
• A scale effect: producers exploit economies of scale more fully by selling into a larger market.
• A backwardness effect: less advanced countries, or less advanced sectors within a country, catch up with the more advanced through knowledge spillovers.

Open trade also acts on the innovation process itself, encouraging higher spending on research and development and on human capital as companies invest to exploit access to larger markets and the greater flow of ideas across borders. The return on new investment rises, and so does the growth rate. Most countries gain, with the scale effect benefiting smaller countries most and the backwardness effect benefiting poorer, less developed ones.

There is one counter-case, and it is worth knowing because it is the exception examiners like. Trade can retard growth in small countries that lag well behind the technology leaders. Opening such a country may discourage domestic innovation, because companies recognise that even if they innovate they may still lose to more efficient foreign competitors, so they do not try.

Inward-oriented against outward-oriented strategies

Over the past 50 years developing economies have pursued two contrasting development strategies.

• Inward-oriented policies try to build domestic industry by restricting imports, encouraging the production of domestic substitutes even where doing so is more costly. These are also called import substitution policies.
• Outward-oriented policies try to integrate domestic industry with the global economy through trade, making exports a central driver of growth.

The historical record is unusually clear. Across much of Africa and Latin America the inward-oriented route was taken between the 1950s and the 1980s, and it delivered weak GDP growth together with sheltered industries turning out poor goods. Many East Asian countries, Singapore and South Korea among them, pursued outward-oriented policies over the same period and achieved high GDP growth and convergence with developed economies, benefiting also from foreign direct investment. Returning to Example 1, the divergence between Argentina and Venezuela on one side and Japan, South Korea and Singapore on the other is explained largely by openness: the Latin American economies were relatively closed, while the Asian economies relied on foreign investment and open markets.

Many African and Latin American countries have since removed trade barriers and moved toward outward-oriented policies, with better growth as a result. Brazil is a good illustration: the value of goods and services sold abroad went from $64.6 billion in 2000 to $218 billion in 2018, a rise of more than 237%, while the export share of GDP moved from 10.2% to 14.8%.

Source: OECD (2019).

What happened when China and India joined

The 1980s were when China and India joined the world economy in practice, turning toward market-based policy and opening themselves to trade. By 2018, on IMF figures based on purchasing power parity, China accounted for 20% and India 8% of world GDP, against a combined 4.2% of global output in 1980. Their entry sharply increased the global supply of skilled and unskilled labour at relatively low wages, which raised global potential GDP. Theory predicts that a supply-side increase in global productive capacity raises global output and puts downward pressure on prices, and that is what happened.

The neoclassical model adds a sharper prediction and one instructive failure. With lower wages and less capital than the United States and Europe, both countries should have offered a higher return on capital, capital should have flowed toward them, and both should therefore have run trade deficits. India did. China did not: it has run trade surpluses, which stem mainly from its very high domestic saving rate. China nonetheless received large foreign direct investment inflows, reinforcing an already high private investment rate. As both economies accumulate capital, their capital-to-labour ratios, real wages and per capita incomes should converge toward advanced-economy levels. Depending on global demand conditions, wages might even have to fall in developed economies as wealth and income shift toward the developing ones, and the global share of income going to labour should decline relative to capital because of the surge in labour supply. As the Chinese and Indian shares of world output climb, world productivity should climb with them.

Everything in this reading comes together in a single exercise: take published national accounts data, build a capital stock, apply both potential growth methods, compute the steady-state rate, and read the result for equities. The worked example below does exactly that, and it is the template for the item set style question this reading generates.

Before working it, fix the sequence in your mind. Build the capital stock from gross investment less depreciation. Compute the growth rates of capital, labour and TFP. Take the labour share from labour cost as a percentage of total factor cost, and set α to one minus that share. Apply Equation 4 for the growth accounting estimate, Equation 5 for the labour productivity estimate, and Equation 8 for the steady state. Then compare the three numbers, because the differences between them carry the analysis.