Economic Growth: Where does it come from?

One of the fundamental questions of economics is why are some countries rich and others poor? Why do some countries experience heavy growth which allows them to catch-up with the economic giants of the world, whilst others are relegated to the bottom and are unable to jump on the growth train? Is it due to luck, geography, culture or institutional factors? This article explains some of the different theories of economic growth, beginning with the Solow growth model (neoclassical model), before criticising such a model and suggesting that endogenous growth models have more to tell us about the growth phenomenon. We highlights the pitfalls of each model, but conclude that the main reason that incomes are different between countries is due to institutional differences.

The Solow Model

According to the World Bank 50% of the world population have only 10% of the world income. Norway is 98 times as rich as the Democratic Republic of Congo and 24 times richer than Bangladesh (correcting for PPP). We begin to answer our question of what causes economic growth by using the Solow growth model. This model assumes that the capital stock depends on the level investment (which itself is determined by the amount of savings in the economy) minus the level of depreciation and that other neoclassical assumptions (such as profit maximising firms) are satisfied. The model then looks at what happens a long a balanced growth path, this is characterised as the situation in which capital, output, consumption, wages and return to capital are constant. After some mathematical derivations we find that capital grows at the rate n + g, where n is population growth and g is the growth rate of technology. Investment is used to replace depreciated capital, to equip new workers (population growth), and to upgrade capital (technological growth). Per capita growth must then be equal to g which tells us that any increases in the capital stock only originate due to increases in technological growth.  Further derivations tell us that the growth rate of output equals the growth rate of capital, and thus output per capita only grows at the rate g: any change in growth originates from new developments in technology.

Before we summarise the findings of this model we need to be careful to distinguish between level and growth effects. Imagine that the balanced growth path output of the economy is 5%, this is the level we are at. If there is a storm which temporarily reduces output then y may fall to 3% and so we have growth in output to return to our balanced growth path level of output. This growth is only temporary and when we return to the BGP, we have no more growth. Instead we may increase our savings rate so that more is invested, and this will lead to a level growth effect whereby the BGP level of output is now 7%, there will be growth whilst we reach this new level, but once obtained there will be no change in per capita growth.

The Solow growth model implies that a higher population growth means capital widening (giving capital to more people) rather than capital deepening, and thus a lower steady state level of both capital and output. Thus higher population growth should result in lower output per capita. It predicts that a higher savings rate will lead to higher growth rates, both predictions are empirically verified by looking at cross-country analyses.

In summary, according to this model, the only source of permanent growth is technological advances, but this is something which is left unexplained by the model! The neoclassical model tells us nothing about where technological growth comes from, instead taking it as exogenous!

Empirical Support for the Solow Model

Shortly we move on to looking at  how we can incorporate growth into our model to get a richer understanding of growth, but first we look at the empirical success of the Solow growth model. The model does not predict that poorer countries grow faster than richer countries (absolute convergence), but instead we see conditional convergence, whereby countries with similar parameters (and hence steady states) grow at similar rates and only poor countries with similar parameters to rich countries will grow fast. Empirically we see no absolute convergence whilst there is conditional convergence amongst OECD countries with similar parameters, thus supporting the model. Mankiw, Romer and Weil conduct a regression analysis to test whether the Solow growth model matches what we witness in reality. They find that about 59% of cross country income difference can be explained by differences in the investment rate and population growth. An increase in the investment rate (for non-oil countries) raises the GDP per working age person by about 1.42% whilst an increase in (n+g+δ) reduces GDP by about 1.97%. The paper predicts the correct signs for coefficients, as we would expect, but it implies an alpha (capital-labour ratio) of about 0.6, which is much higher than we observe, suggesting that the Solow growth model isn’t entirely consistent with what we observe. When we take alpha to be 1/3 then the neoclassical model predicts a relatively short transition (fast convergence) but this paper finds that the observed rate of convergence is about 2% per year to cover half of the distance between k(0) and k* which requires an alpha of 0.75, which is again too high and suggests problems with the Solow model. Noy and Nualsri find no statistical evidence supporting the neoclassical hypothesis that a natural disaster leads to high growth as a result of deviating from the steady state. Their estimated coefficient for physical capital is positive, but statistically insignificant whilst the coefficient for human capital is negative, suggesting that a negative shock to human capital lowers growth. The authors believe that endogenous growth theory seems to be more compatible with their findings with Romer’s emphasis on R+D activities as a major force behind economic growth appearing to be “especially relevant”. This is due to the emphasis on human capital and when natural disasters threaten human life then the expected return on human capital falls leading to lower investment in human capital and thus lower long-run growth. In a similar vein to Mankiw, Romer and Weil, Lucas finds that we would expect capital to flow from rich countries to poor countries given differences in marginal returns to capital, but that this is not the case and thus concludes that we should add the effects of human capital to our analysis, which greatly reduces the marginal return to capital and explains why we don’t see drastic transfers of capital from rich countries to poor countries.

We have thus far seen that the neo-classical growth model works qualitatively but not quantitatively, with the estimated capital share being too high, the estimated rate of convergence being half the rate predicted by the model and observed interest rate differentials and international capital flows much lower than model predictions.Mankiw, Romer and Weil add to this further by complementing the neoclassical model by incorporating human capital. Increasing savings now increases both the long run stock of capital and human capital, and is therefore complementary.

The authors estimate this equation and find that R2 equals around 80%, which is an improvement on the previous 59%. Now a percentage increase (in non-oil countries) in investment increases GDP per working age person by 6.9% whilst a percentage increase in (n+g+δ) would lead to a fall in GDP by 17.3%. The estimated parameters are now α=0.31 and γ=0.28 which is consistent with the empirical evidence.

Augmented Solow Growth Model

Unfortunately the story does not end here with us congratulating ourselves on the success of the augmented Solow model (which includes human capital), as there are a number of issues with this study. Firstly, they use OLS which could suffer from endogeneity bias (savings rates and n could depend on Y/L); secondly A(0) is systematically larger in rich countries which if omitted and correlated with y0 means we have omitted variables bias; thirdly Klenow and Rodriguez-Clare show the mismeasurement of investment in human capital. There are further more general issues with this augmented Solow model in that growth in technology is still exogenous and the assumption of perfect competition means there can be no profits (Euler’s exhaustion theorem) which means there’s no income to spend for research and development which can lead to increases in growth (Schumpeter) leaving us to question where growth is coming from. The results of Mankiw, Romer and Weil boil down to their definition of human capital: Caselli runs a similar regression but finds that only 20-40% of income differences are explained by factors, with the rest being left to TFP (unexplained residual). Weil uses slightly different data and finds that factor accumulation is responsible for at most 47% of the difference in per capita GDP between countries.

Klenow and Rodriguez-Clare update the MRW data and add primary and tertiary schooling, where primary schooling varies less between countries than secondary education and thus estimates of human capital vary much less across countries than MRW find. Hall and Jones adopt a different methodology to the authors above but find similar conclusions that productivity differences are important in explaining international income variation.

Endogenous Growth Theories

We have so far seen that the augmented Solow growth model has its limitations but is not terrible as an approximation for growth. However, it attributes growth to technology, without telling us where this comes from. Endogenous growth models include technology in their description and thus try to find where this comes from.

There are two basic ways to deal with the increasing returns to scale that area required to endogenise the accumulation of knowledge: imperfect competition or externalities.

The first generation of endogenous growth models had technological progress being an accidental by-product of investment (learning by doing, externalities or spill over); whilst the second generation had technology and knowledge consciously developed in the research and development industry by both the public and private sector.

Technology is knowledge and ideas that improve production; they are usually non-rivalrous whereas many private goods (such as capital goods) are rival. Note also that human capital is rivalrous: if a scientist (or educated person) is working on one project then he cannot be working on another. Technology is usually given as A in our production functions and is an index of the level of technology. It is improved by new ideas improving the technology of production, allowing a given bundle of inputs to produce more or better output.  This means that ideas can exhibit increasing returns to scale as their use is not restricted by a finite physical stock. There may be a high fixed cost to discovering a new idea, but the marginal cost of replicating the idea is zero (the only cost is associated with embodying this idea into a rivalrous good). Increasing returns to scale implies that our market will be characterised by imperfect competition. Ideas can be partially excludable, for example intellectual property introduces a monopoly situation over technology but there are also knowledge spillovers.

Arrow and Romer treat these knowledge spillovers as accidental by-products of economic activity, leading to learning by doing models. They separate the production function of individual firms from the aggregate production function and allow for positive externalities from actions of individual firms/agents to all other firms/agents, but do not internalise this externality. Depending on the parameters of this model we can either have increasing returns to scale with mutliple equilibrium (multiple steady states) and no growth paths, which makes any analysis difficult; we can return to the Solow model; or we can return to the AK model. The AK model is the simplest form of endogenous growth theory where Y=AK and graphically we would have an upward sloping sY curve and an upward sloping δK curve which only intersect at 0, suggesting that this is the first equilibrium but otherwise we have explosive growth.: the capital stock is always growing and growth never stops. The reason for this explosive growth is that capital accumulation is characterised by constant marginal return as opposed to the usual situation of diminishing returns. In a simple AK model policymaker should encourage a higher investment schedule (greater savings) to achieve higher, perpetual growth.  In reality such a model is not very likely because it requires that alpha is 1, whereas we know that for capital it is 1/3 and incorporating human capital might possibly make it 2/3.

Perhaps the most established endogenous growth model is Romer’s R+D model which works by incorporating multiple sectors into the analysis.

In the learning by doing models technological progress is an unintended by-product of economic activity and knowledge creation is unrewarded. Euler’s exhaustion theorem suggests – with a CRS assumption – that there is no profit left to pay for knowledge creation and technological progress, suggesting that there is no room for a research and development sector in the economy. In Romer’s model we have 3 sectors: a final goods sector, an intermediate goods sector and an R+D sector. The final goods sector employs currently available technology and labour input to produce a homogenous output good. It is characterised by perfectly competitive markets. The intermediate goods sector buys monopoly rights for the ideas generated from scientists in the R+D sector. They produce an intermediate good that is sold for production in the final goods sector. The research and development sector generates new ideas with technology and labour.

So this endogenous growth model tells us that the growth rate of the economy is determined within the model and the long-run growth rate is increasing in the population growth rate. Hence more people means more ideas, although given that technology crosses borders one country can increase its growth rate by reducing its countries population growth and benefit from externalities of other countries having high population growth rates. Growth is predicted as an increasing function of research effort, which is problematic as research has grown tremendously over time whilst growth is slowing down. The model also tells us that we need positive population growth to sustain growth of Y/L because of diminishing returns to knowledge production, and a change in the labour share in R+D has a level effect but no growth effect.

These are some good (but not perfect) observations from the model, and the model is effectively a micro-founded version of the Solow growth model which allows the introduction of a monopolistic sector and rewards knowledge creation. There are some problems in that the rewards to the research sector reflect only monopoly profits and not consumer surplus. Additionally, it assumed that research workers do not take into account the effect of their behaviour on the rate of discoveries.

This model assumes no conditional convergence, scale effects and the long-run effects of policies; all of which have been refuted by the empirical evidence. The model also focuses on growth rates instead of levels, and explaining levels is the key problem in economic development.

So what causes growth?

Thus far we have seen that the neoclassical growth model tells us that technology causes growth, but doesn’t tell us where technology comes from. The endogenous growht models tell us that technology – and therefore growth – come from having larger populations (more ideas), greater savings rate and fundamentally strong property rights so that patents are protected. This implicitly requires that we have strong institutions to promote patents and protect the property rights of investors.

North places particular emphasis on institutions as an important determinant of growth; “Institutions are the underlying determinant of the long run performance of economies”. He defines institutions quite broadly to include laws, constitutions, customs, tradition, religion, constraints and government policies which “shape the interactions of economic actors”.

We can use different measures of institutions to see their effect on income but we are unable to use a simple regression such as Y = αIns + βX’ + u because there will be the issue of reverse causality and omitted variables (endogeneity), so that OLS wouldn’t find a consistent estimator. A solution to this would be to find an instrumental variable that is correlated with institutions but uncorrelated with the error term (the unobserved component of Y).

Acemoglu, Johnson and Robinson do this using the mortality rates of soldiers, bishops and sailors stationed in colonies as an instrument. They see this as valid because the mortality rates of these people will have no effect on current GDP except through their impact on institutional development. This will be a relevant instrument so long as it is correlated with measures of current institutions.

They use risk of expropriation (how likely it is that private foreign investments are expropriated by government) as their indicator of current institutions and control for variables such as latitude, continental dummies, legal origin, geographical variables and different languages. They believe that settler mortality led to settlement strategy which affected early institutions which have effects on current institutions and thus on current levels of development.

They find that their IV estimate of 0.94 is greater than their OLS estimate of 0.52 which suggests downward bias and thus that the measurement error in the institutions variable is more important than reverse causality or omitted variable bias. Overall Acemoglu et al conclude that the results show a “large effect of institutions on economic performance” with the instrument explaining 25% of variation in today’s income.

Hall and Jones believe it is social infrastructure which affects growth. They define social infrastructure as the institutions and policies that determine the economic environment in which individuals accumulate skills and firms accumulate capital and produce. Olson shows that economic growth can’t be fundamentally different due to culture because countries such as North and South Korea have fundamentally the same culture but different growth rates. The social infrastructure argument gains support from Acemoglu et al as well as Dell on the persistence of institutions and their effects. They discuss the business environment (i.e. the amount of bribes and the length of time to set up a business) as being embedded within this social infrastructure which affects the level of growth.

Conclusion

We started by noting the large differences in incomes between countries and then used the neoclassical growth model (Solow) to try and account for such differences. It provided qualitative support but was not particularly successful quantitatively. We introduced human capital which led to higher quantitative predictions but still didn’t solve the issue on interest rate differentials and still assumed that growth was driven by exogenous technological progress, there were also issues in how we measured human capital which affected our empirical outcomes. Then we turned to spill-over effects and externalities to explain where this endogenous growth was coming from. This created problems in that we expect to see scale effects which are not empirically observed, the R+D model of Romer similarly was not particularly good at explaining cross-country differences in income levels and did not explain the issue of convergence. Finally, we looked at the limits to growth and incorporated land and non-renewable resources into our neoclassical model to show that growth may not persist forever.

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