The Mystery of Economic Growth First Draft

Attempts to answer the question "why some countries are so much richer than others" have been as numerous as they have been infructiferous.

Durlauf et al (2005) put it like this:

"Understanding the wealth of nations is one of the oldest and most important research agendas in the entire discipline. At the same time, it is also one of the areas in which genuine progress seems hardest to achieve. The contributions of individual papers can often appear slender. Even when the study of growth is viewed in terms of a collective endeavor, the various papers cannot easily be distilled into a consensus that would meet standards of evidence routinely applied in other fields of economics".

Among the biggest problems facing growth theorists are the comparatively small number of countries to work from, the comparatively limited time duration of the available data, and the wide variety of explanatory models which have been proposed in explanation of the phenomenon. Indeed, in the course of a long and arduous literature history, approximately as many growth determinants have been proposed as there are countries for which data are available.


However despite the not inconsiderable amount of research and energy dedicated by economists to the theme of economic growth and development (Nobel economist Robert Lucas, for example, informs us that not a day goes by without his spending at least some time thinking about the topic), collectively we have yet to discovered how to make poor countries rich.


Whatsmore the road to progress seems fraught with difficulty. If we take it as self-evidently true that technology is one of the primary determinants of a country’s growth and income, and if the know-how relating to modern production technologies is essentially free and there for the taking, then why, oh why is it that so many people still find it so difficult to get on the development track?


Simply posing the question is, of course, to already answer it, since even in the case of something so apparently 'neutral' as technology there are clearly self-reinforcing mechanisms, or 'traps' (or 'bad equilibria') that act either as barriers to adoption or impediments to effective use even when adopted. Development traps arise from a variety of circumstances, and again these have generated an extensive literature with much of the focus being centred on market imperfection and institutional failure.

Another explanation often advanced for the poor growth performance of the LDCs is the existence of poor institutions and bad domestic policy. And of course those who argue this do so not without justification. The LDCs as a group are not exactly short on examples of corruption and bad government. And clearly sound governance and healthy market influences are necessary to reap the benefits of economic growth. But isn't this story perhaps just a little too simple.

In a pathbreaking paper on Geography, Demography and Economic Growth in Africa, David Bloom and Jeffrey Sachs make the following plea:


"Our paper could well be misunderstood. Some will regard it as a new case of "geographic determinism," that Africa is fated to be poor because of its geography. Some will regard it as a distraction from the important truth that geographic difficulties or not, African governments seriously mismanaged economic policy in the past generation. Let us therefore be clear at the outset. We believe emphatically that economic policy matters, and our formal econometric results show that to be true, a point we have also made in related recent studies (especially Sachs and Warner, 1997) We nonetheless focus most of our attention on geography for three reasons. First, there is little to be gained from yet another recitation of the damage of statism, protectionism, and corruption on African economic performance. Amen. Second, most economists are woefully neglectful of the forces of nature in shaping economic performance, in general and in Africa in particular. They treat economies as blank slates, upon which another region's technologies and economic history may be grafted. Our profession's formal models tend to be like that; so do our profession's standard statistical analyses of cross-country growth....Third, and perhaps most importantly, good policies must be tailored to geographical realities.If agricultural productivity is very low in Africa for climatological reasons, perhaps the real lesson is that growth should be led much more by outward-oriented industry and services, rather than yet another attempt to blindly transplant "integrated rural development" strategies from other parts of the world that are not customized to Africa’s unique conditions."

If Bloom and Sachs are accused of geographical determinism, it is easy to imagine that I might here be accused of "demographic determinism", so let me just endorse the above argument: economic and political policy also matters. But what I would also like to stress is the importance of their second point, namely that "most economists are woefully neglectful of the forces of nature in shaping economic performance, in general and in Africa in particular. They treat economies as blank slates, upon which another region's technologies and economic history may be grafted." To ram this home: most economists' appreciation of the workings of evolutionary biology and its implications for demographic processes is rudimentary to say the least. And what outrageously many economists understand about demographic processes in and of themselves their relevance for growth and development would provide material for only the shortest of short papers. The fact is, with some emminent and notable exceptions, demography is simply not seen as an important part of the macro-economic panorama.

In this context I would simply single out two underlying prejudices which I think have had an enormous influence.

In the first place the 'state of nature' argument. Basically most economists seem to work from some variant of Cantillion's notion that: "Men multiply like mice in a barn if they have unlimited means of subsistence", ie that in the pre-modern (Mathusian regime epoch) women produced children at an extraordinarily high rate. This is certainly a counter-factual belief, not only because in most foraging societies fertility falls universally well short of the biological maximum, but also since there is often evidence in history for the idea that as subsistance rises fertility declines.

Secondly the homeostatic principle which normally lies behind modern conceptions of steady state growth. Basically - and this is a point which has been often made - most economists seem to see their discipline as much closer to physics than it is to biology. So the preferred yardstick for measuring the validity of our economic models is far more often the celestial motion of the planets than ever it is the Darwinian evolution of living organisms. So the essential idea is that 'modern' (or if you want market-driven) economies represent a break from an earlier high fertility regime to a new growth regime which has a steady state dynamic, or balanced growth path, and has an internalised homeostatic conditioner which produces a population fertility rate of on or around a 2.1 TFR. Whether by accident or design, the excellent Consise History of Population by Massimo Livvi Bacci is the most widely quoted population reference source in modern growth economics. I say whether by accident or design, because, Livvi-Bacci is, of course, the best know demographic exponent of the homeostatic population view.


To concretise, the story that the competitive neoclassical benchmark model of economic systems tells is the following one: Markets are complete, entry and exit is free, transaction costs are negligible, and technology is convex at an efficient scale relative to the size of the market. As a result, the private and social returns to production and investment are equal and a complete set of 'virtual prices' ensures that all projects with positive net social benefit are undertaken. Diminishing returns to the set of reproducible factor inputs implies that as an economy develops the rate of return on investment declines, whilst where capital is scarce the returns to investment (and of course the level of risk) will be concomitanly higher.

The dynamic implications of this benchmark were intitially summarized by Solow (1956), Cass (1965), and Koopmans (1965). Even for countries which start with different endowments, the main conclusion is that there ought to be an underlying convergence process.


Needless to say the influence on development policy of what might be called the neoclassical 'prejudice' has been enormous. One of the clearest examples is, of course, to be found in the series of structural adjustment programs implemented by the International Monetary Fund. The key components of the Enhanced Structural Adjustment Facility —the centerpiece of the IMF’s strategy to aid poor countries and promote long run growth in the years between 1987 and 1999 — were prudent macroeconomic policies and the liberalization of markets. Growth, it was hoped, would then follow automatically.

Yet the evidence on whether or not non-distortionary policies and diminishing returns to capital will soon carry the poor to opulence is mixed to say the least. In recent years even relatively well governed countries have experienced little or no growth. Mali, for example, although not exactly corruption-free, scores relatively well in comparative measures of governance and real resources (Radlet 2004; Sachs et al. 2004). Yet Mali is still desperately poor. According to a 2001 UNDP report, 70% of the population lives on less than $1 per day. The infant mortality rate is 230 per 1000 births, and household final consumption expenditure is down 5% from 1980. And of course Mali continues to have one of the highest TFR rates on the planet. And Mali is not exactly an isolated case.

So are we perhaps missing something here?


Well lets go back to where we started. Now apart from the existence of model uncertainty, another major set of growth issues revolves around the difficulty of identifying empirically salient determinants of growth when the range of potential factors is large relative to the number of observations.

Individual researchers, seeking to identify the extent of support for particular growth determinants, typically emphasize a single model (or small set of models) and then carry out an inference procedure as if that model had generated the data. Standard inference procedures based on a single model, and which are conditional on the truth of that model, can grossly overstate the precision of inferences about a given phenomenon. In particular such procedures often ignore the uncertainty that surrounds the validity of the model itself.

Given that there are usually other models that have strong claims to consideration, the standard errors which arise can significantly understate the true degree of uncertainty about the parameters, and the choice of model to can ultimately appear somewhat arbitrary. This need for a proper account of model uncertainty has lead naturally toward Bayesian or pseudo-Bayesian approaches to data analysis.


Despite the existence of these widely known problems attempts to develop a unified growth theory along the abovementioned lines have not been notably deterred. In particular we have seen a continuing effort to establish common 'covergent' characteristics to growth across countries. One such approach has centred around the attempt to establish a series of 'stylised facts' about growth.


Stylised Facts

As I have said, most neo-classical growth models start from the idea of steady state growth. One idea closely associated with the steady state one is that there exist a number of 'stylised facts' of growth which are waiting to be uncovered. The tradition of attempting to produce stylised facts in economic growth theory goes back at least to the work of Kuznets and Kaldor in the 1960s.

Kaldor (1961) described what he considered to be a number of stylized facts about economic growth:


1. Per capita output grows over time, and its growth rate does not tend to diminish.
2. Physical capital per worker grows over time.
3. The rate of return to capital is nearly constant.
4. The ratio of physical capital to output is nearly constant.
5. The shares of labor and physical capital in national income are nearly constant.
6. The growth rate of output per worker differs substantially across countries.


When Simon Kuznets delivered his Nobel Address back in 1971 he also singled out six stylised 'characteristics' of modern economic growth:

1/. The high rates of growth of per capita product and of population in the developed countries.

2/. The high rate of rise in productivity, i.e. of output per unit of all inputs in comparison with earlier epochs.

3/. The rate of structural transformation of the economy is also high by historical standards.

4/. Structures which are extremely important in general societal terms - eg levels of urbanization and secularization - have also changed rapidly, leading sociologists to use the term modernization process.


5/. The economically developed countries have the propensity to reach out to the rest of the world (we would now call this globalisation).



6/. Despite the spread of modern economic growth, wide inequality in growth rates and income levels persists.



These early efforts (and in particular those of Kaldor) have not worn especially well with time. As Sala i Martin (2002) points out one important innovation of the new generation of growth literature that took off in the late 80s was that it attempted to tie economic theory much closer to empirical studies of growth. The neoclassical literature of the 1960s seem to link theory and evidence by simply 'mentioning' a list of stylized facts (such the Kaldor 'facts' above) and then attempting to show that the theory proposed was consistent with one, two or perhaps several of
these 'facts'. Indeed as Sala i Martin notes, some of these 'stylised facts' were never really derived from careful empirical analysis, but that did not stop them being quoted and used as if they had been. (Kuznets himself, of course, had carried out significant empirical research on economic growth).


Today’s research, on the other hand, tends to be characterised by a drive to derive more precise econometric specifications through direct recourse to the data. The best examples of this kind of work can be found in the convergence literature. Barro and Sala-i-Martin (1992) use the Ramsey-Cass-Koopmans (Ramsey (1928), Cass (1975) and Koopmans (1965)) growth model to derive an econometric equation that relates growth of GDP per capita to initial levels of GDP. Mankiw, Romer and Weil (1992) derive a similar equation from the Solow-Swan model ((Solow (1956) and Swan (1956)). These researchers derived a relationship where the growth rate of per capita GDP is given by the difference between a constant (beta) and the product of that same beta and the natural log of per capita GDP for country and the steady-state value of per capita GDP for country i plus an error term.

The coefficient is positive in the case that the production function is neoclassical, and is zero if the production function is linear in capital (which was usually the case in the first generation one-sector models of endogenous growth, also known as AK models). The central point is that the modern literature took this equation and used it to 'test' competing the models, namely the endogenous growth ones (the so called AK models) which should predict beta = 0 and the neoclassical models (which should predict beta>0.)


Early findings seemd to indicate that there was no positive association between growth and the initial level of income. The possibility existed however that this finding could be a statistical artifact resulting from the misspecification of the original equation. Basically, the problem is that, if researchers make the assumption that countries converge to the same steady state and the finding is that they don’t, then the original equation is, in turn, misspecified. If the steady state is correlated with the initial level of income, then the error term is correlated with the explanatory variable, so the estimated coefficient is biased towards zero.



One proposed solution to the problem was to continue using cross-country data but, instead of estimating the univariate regression, estimate a multivariate regression where, on top of the initial level of income, the researcher would also hold constant proxies for the steady state. This approach came to be known as conditional convergence. Subsequent research has shown that the idea of conditional convergence describes one of the strongest and most robust empirical regularities to be found in the data. The consequence of all this was the exact opposite of the original conclusion: the neoclassical model was not rejected by the data. The AK model was.

Sala i Martin draws a number of lessons from all this:

(i) There is no simple determinant of growth.
(ii) The initial level of income is the most important and robust variable (so conditional convergence is the most robust empirical fact in the data).
(iii) The size of the government does not appear to matter much. What is important is the 'quality of government'.
(iv) The relation between most measures of human capital and growth is weak. Some
measures of health, however, (such as life expectancy) are robustly correlated with growth.
(v) Institutions (such as free markets, property rights and the rule of law) are important for growth.
(vi) More open economies tend to grow faster.



As a result of this re-evaluation it is now possible to outine a rather different group of stylised facts:



1. Over the second half of the 20th century most countries have grown richer, but at varying rates, and vast income disparities remain. For all but the richest group, growth rates have differed to an unprecedented extent, regardless of the initial level of development. Indeed far from a clear convergence process reality has rather conformed to what Lance Pritchett once famously termed 'divergence bigtime'.

2. Past growth has turned out to be a surprisingly weak predictor of future growth. In the developing world distinct 'winners' and 'losers' have begun to emerge. The strongest performers are located in East and Southeast Asia, which have sustained growth rates at unprecedented levels. The weakest performers are predominantly located in sub-Saharan Africa, where some countries have barely grown at all, or even become poorer. The record in South and Central America is also distinctly mixed. In these regions, output volatility is high, and dramatic output collapses are not uncommon.

3. For many countries, growth rates were lower in 1980-2000 than in 1960-1980, and this growth slowdown has been observed throughout most of the income distribution. Moreover, the dispersion of growth rates has increased. A more optimistic reading would also emphasize the growth take-off that has taken place in China and India, home to two-fifths of the world’s population and a greater proportion of the world’s poor.


But despite all the research two oustanding questions still seem to remain.

Firstly, the issue of convergence: are contemporary differences in aggregate economies transient over sufficiently long time horizons?

And secondly, what are the key growth determinants: which factors are better able to explain observed differences in growth?

Two separate approaches have continued to dominate the extensive literature on economic growth modeling: simple correlations, and production functions.


Simple-correlations

Simple-correlations studies hypothesize that per capita output growth is influenced by various dimensions.



Production Functions

Production-function studies are based on estimating variants of a model along the following lines:

Y = g(K, L, H, R, T),

where output (Y) is produced by the stocks of various factors: physical capital (K), labor (L), human capital (H: education and health), resources (R: land, minerals, and environment), and technology (T).


In the neoclassical model, if each country has access to the same aggregate production function the steady-state is independent of an economy's initial capital and labor stocks and hence initial income. In this model, long-run differences in output reflect differences in the determinants of accumulation, not differences in the technology used to combine inputs to produce output. Mankiw (1995, p. 301), for example, argues that for “understanding international experience, the best assumption may be that all countries have access to the same pool of knowledge, but differ by the degree to which they take advantage of this knowledge by investing in physical and human capital.”

Even if one relaxes the assumption that countries have access to the same production function, convergence in growth rates can still occur so long as each country’s production function is concave in capital per efficiency unit of labor and each country experiences the same rate of labor-augmenting technical change.

Klenow and Rodríguez-Clare (1997a) challenge this “neoclassical revival” with
results suggesting that differences in factor accumulation are, at best, no more important than differences in productivity in explaining the cross-country distribution of output per capita. They find that only about half of the cross-country variation in the 1985 level of output per worker is due to variation in human and physical capital inputs while a mere 10% or so of the variation in growth rates from 1960 to 1985 reflects differences in the growth of these inputs. The differences between the results of Mankiw, Romer, and Weil (1992) and the findings of Klenow and Rodríguez-Clare (1997a) in their reexamination of Mankiw, Romer and Weil have two principal origins. MRW found support for the Solow model’s predictions that, in the long-run steady state, the level of real output per worker by country should be positively correlated with the saving rate and negatively correlated with the rate of labor-force growth. However, their estimates of the textbook Solow model also implied a capital share of factor income of about 0.60, high compared to the conventional value (based on U.S. data) of about one-third.

To address this possible inconsistency, MRW considered an “augmented” version of the Solow model, in which human capital enters as a factor of production in symmetrical fashion with physical capital and raw labor. They found that the augmented Solow model fits the data relatively better and yields an estimated capital share more in line with conventional wisdom. They concluded (abstract, p. 407) that “an augmented Solow model that includes accumulation of human as well as physical capital provides an excellent description of the cross-country data.”


[Bernanke and Gürkaynak model]: Assume that in a given country at time t, output Y depends on inputs of raw labor L and three types of accumulated factors: K , H , and Z . The factors K and H are accumulated through the sacrifice of current output (think of physical capital and human capital, or structures and equipment). The factor Z , which could be an index of technology, or of human capital acquired through learning-by-doing, is assumed to be accumulated as a byproduct of economic activity and does not require the sacrifice of current output.]

Y = K, H (Z, L).

Bernanke and Gürkaynak also use the MRW framework to consider some alternative models of economic growth, such as the Uzawa-Lucas model and the AK model. These models are rejected as literal descriptions of the data.

However, the implications of these models, that country growth rates depend on behavioral variables such as the rate of human capital formation and the saving rate, seem more consistent with the data than the Solow model’s assumption that growth is exogenous. Future research should consider variants of endogenous growth models to see which if any provide a more complete and consistent description of the
cross-country data. We believe that the generalized MRW-type framework we have developed here could prove very helpful in assessing the alternative possibilities.


Indeed both Prescott (1998) and Hall and Jones (1999) confirm the view that differences in inputs are unable to explain observed differences in output and Easterly and Levine (2001, p. 177) state that "the 'residual' (total factor productivity, TFP) rather than factor accumulation accounts for most of the income and growth differences across countries."

Despite these concerns and the differences in the precise estimates found by different researchers, it is clear that cross-country variation in inputs falls short of explaining the observed cross-country variation in output. The result that the TFP
residual, a “measure of our ignorance” computed as the ratio of output to some index of inputs, is an important (perhaps the dominant) source of cross-country differences in long-run economic performance is useful but hardly satisfying and the need for a theory of TFP expressed by Prescott (1998) is well founded. Research such as Acemoglu and Zilibotti (2001) and Caselli and Coleman (2003) are promising contributions to that agenda.


Convergence Patterns

Convergence-patterns studies, rooted in neoclassical growth theory, explore the relationships between economic growth and the *level* of economic development. They focus on the pace at which countries move from their current level of labor productivity (Y/L) to their long-run, or steady-state equilibrium level of labor productivity.

The effect of initial conditions on long-run outcomes arguably represents the primary empirical question that has been explored by growth economists. The claim that the effects of initial conditions eventually disappear is the heuristic basis for what is
known as the convergence hypothesis.


The goal of this literature is to answer two questions concerning per capita income differences across countries (or other economic units, such as regions). First, are the observed cross-country differences in per capita incomes temporary or permanent? Second, if they are permanent, does that permanence reflect structural heterogeneity or the role of initial conditions in determining long-run outcomes?


If the differences in per capita incomes are temporary, unconditional convergence (to a common long-run level) may occur. If the differences are permanent solely because of cross-country structural heterogeneity, only conditional convergence may occur. If initial conditions determine, in part at least, long-run outcomes, and countries with similar initial conditions exhibit similar long-run outcomes, then one can speak of convergence clubs.

In practice, the distinction between initial conditions and structural heterogeneity generally amounts to treating stocks of initial human and physical capital as the former and other variables as the latter. As such, both the Solow variables X and the control variables Z that appear in garden variety cross-country growth regression are usually interpreted as capturing structural heteogeneity. This practice may be criticized if these variables are themselves endogenously determined by initial conditions, a point that will arise below.

Here the rate of labour productivity growth is taken to be proportional to the gap between the logs of the long-run, steady state and the current level of labor productivity. The greater this gap, the greater are the gaps of physical capital, human capital, and technical efficiency from their long run levels. Large gaps allow for significant "catching up" through (physical and human) capital accumulation, and through technology creation and diffusion across, and within countries.

Under restrictive assumptions, this type of model predicts "unconditional convergence" by all countries to the same long-run level of labor productivity. Were the steady state rate of growth of labor productivity to be the same for all countries, then low-income countries would be father away from their state determined income level and hence - following the standard equation - their productivity would grow faster as a result. In fact, however, positive rather than negative correlations have been observed between the level and growth rate of labor productivity. The model has not unsurprisingly been modified as a consequence.

As indicated above, models now tend to hypothesize "conditional convergence", whereby long-run labor productivity differs across countries depending on country-specific characteristics following the following equation:

ln(rate of change of labour productivity) = a + bZ.



The actual specification of the determinants of long-run labor productivity (the Z's) varies notably, but the basic model is the same across scores of empirical studies.

X contains a composite - log (n+g+delta) - where delta denotes the depreciation rate. The variables spanned by log income and X thus represent those growth determinants that are suggested by the Solow growth model whereas Z represents those growth determinants that lie outside Solow’s original theory. The distinction between the Solow variables and Z is important in understanding the empirical literature. While the standard Solow variables usually appear across a wide variety of different empirical studies - a situation which reflects the treatment of the Solow model as a baseline for growth analysis - choices concerning which Z variables to include vary greatly.

As outlined above, statistical analyses of convergence have largely focused on the properties of β in regressions. β convergence, defined as β<0 is easy to evaluate because it relies on the properties of a linear regression coefficient. It is also easy to interpret in the context of the Solow growth model, since the finding is consistent with the dynamics of the model. The economic intuition for this is simple.

If two countries have common steady-state determinants and are converging to a common balanced growth path, the country that begins with a relatively low level of initial income per capita has a lower capital-labor ratio and hence a higher marginal product of capital; a given rate of investment then translates into relatively fast growth for the poorer country.

This is why β convergence is commonly interpreted as evidence against endogenous growth models of the type studied by Romer and Lucas, since a number of these models specifically predict that high initial-income countries will grow faster than low initial-income countries, once differences in saving rates and population growth rates have been accounted for. However, not all endogenous growth models imply an absence of β convergence and therefore caution needs to be exercised in drawing inferences about the nature of the growth process from the results of β convergence tests.


In moving from unconditional to conditional β convergence, complexities arise in terms of the specification of steady-state income. The reason for this is the dependence of the steady-state on Z . Theory is not always a good guide in the choice of elements of Z; differences in formulations of the standard equation have led to a “growth regression industry” as researchers have added one plausibly relevant variable after another to the baseline Solow specification. As a result, there are variants of the equation where convergence appears to occur and there are variants where divergence has a consistent interpretation.

Abramowitz (1986), Baumol (1986), DeLong (1988) among many others view convergence as the process of follower countries 'catching up' to leader countries by adopting their technologies. On the other hand some more recent contributors, starting with Barro (1991) and Mankiw, Romer, and Weil (1992), have emphasised the view that convergence is driven by diminishing returns to factors of production.

One hypothesis is that differences in capital accumulation, productivity, and therefore output per worker are fundamentally related to differences in social infrastructure across countries. By social infrastructure is normally meant the institutions and government policies that determine the economic environment within which individuals accumulate skills, and firms accumulate capital and produce output. A social infrastructure favorable to high levels of output per worker provides an environment that supports productive activities and encourages capital accumulation, skill acquisition, invention, and technology transfer. Such a social infrastructure
gets the prices right so that, in the language of North and Thomas [1973], individuals capture the social returns to their actions as private returns.

Some evidence for this can be found in Hall and Jones (1999) who - in a study running across 127 countries - find a powerful and close association between output per worker and measures of social infrastructure. Countries with long-standing policies which they characterise as favorable to productive activities produce much more output per worker. In one example, they find that the observed difference in social infrastructure between Niger and the United States is more than enough to explain the 35-fold difference in output per worker which is to be found between the two countries.

One influential line of research born from neo-classical growth research and which uses cross-country regressions to find the empirical determinants of the growth rate originates in the work of Robert Barro (1991). The basic Barro equation postulates that the growth rate of per capita GDP for a given country country equals a constant (beta) multiplied by a vector of variables that are thought to reflect determinants of long-term growth (the Zs) plus an error term.

Regressions which have this form are sometimes known as Barro regressions, given Barro’s extensive use of such regressions to study alternative growth determinants starting with Barro (1991). This regression model has been subsequantly become the workhorse of empirical growth research. In modern empirical analyses, the equation has been generalized in a number of dimensions. Some of these extensions reflect the application of the vasic equation to time series and panel data settings, while others have introduced nonlinearities and parameter heterogeneity.

The Economic Zs. In particular work in the Barro tradition has attempted to show growth in output per capita as being positively related to:

(1) A lower initial level of productivity. On this account convergence is posited to be more rapid in countries with higher levels of schooling attainment.

(2) Higher male secondary and tertiary schooling attainment, which facilitates the absorption of new technologies.

(3) Higher life expectancy, a proxy for better health and human capital in general.

(4) Improvement in terms of trade, posited to generate added employment and income.

(5) A lower rate of inflation, leading to better decisions with predictable price
expectations.

(6) A lower government consumption share netted of education and defense spending, which is posited to release resources for more productive private investment.

(7) Stronger democratic institutions at low levels of democracy, which promote market activity by loosening autocratic controls. However, stronger democracies at high
levels can dampen growth by the government exerting an increasingly active role in
redistributing income. Democrcy is thus entered in quadratic form, posited to rise and then fall.

(8) A stronger rule of law which stimulates investment by promoting sanctity of contracts, security of property rights, etc.


One revealing feature of the convergence-patterns models can be gleaned by considering variables omitted by Barro and those who have normally worked in this tradition. Here authors tend to emphasize variables that determine longrun, or “potential” steady state labor productivity, and downplay variables that bring about the “adjustment” or “transition” to long-run equilibrium.

An example of one such omitted variable would be investment shares. Putting aside the problem of endogeneity, investment can be viewed as an adjustment variable. The gap between current and long-run labor force productivity largely dictates the return to investment. Investment will flow to those countries with highest returns. Rather than investment accounting for growth per se, it can be argued that the “structural” features of countries that impede or facilitate investment should be highlighted in the modeling of Z (e.g., measures of the risk of expropriation, restrictive licensing, political conditions, etc.). Such features modify long-run potential labor productivity because they impede or encourage investment.



From Mathus to Solow

Another approach to the growth problem has been the attempt to develop a unified growth theory which accounts for the transition from the earlier Malthus regime to the modern growth one. Typical of that approach is the work of Hansen and Prescott (2002). They presnt the problem in the following way:

"Prior to 1800, living standards in world economies were roughly constant over the very long run: per capita wage income, output, and consumption did not grow.Modern industrial economies, on the other hand, enjoy unprecedented and seemingly endless growth in living standards."

The existing theoretical literature on the transition from stagnation to growth has focused mostly on the role played by endogenous technological progress and/or human capital accumulation rather than the role of land in production.4 For example, human capital accumulation and fertility choices play a central role in Lucas (1998), who builds on work by Becker, Murphy, and Tamura (1990). Depending on the value of a parameter governing the private return to human capital accumulation, Lucas’s model can exhibit either Malthusian or modern features. Hence, a transition from an economy with stable to growing living standards requires an exogenous change in the return to human capital accumulation.

Like Hansen and Prescott, Galor and Weil (2000) and Jones (1999) study models where the transition from Malthusian stagnation to modern growth is a feature of the equilibrium growth path, although their approaches differs by incorporating endogenous technological progress and fertility choice. Living standards are initially constant in these models due to the presence of a fixed factor in production and because population growth is increasing in living standards at this stage of development. In Galor and Weil (2000), growing population, through its assumed effect on the growth rate of skill-biased technological progress, causes the rate of return to human capital accumulation to increase. This ultimately leads to sustained growth in per capita income.

In Jones (1999), increasing returns to accumulatable factors (useable knowledge and labor) causes growth rates of population and technological progress to accelerate over time and, eventually, this permits an escape from Malthusian stagnation.

A transition from Malthus to Solow implies that land has become less important as a
factor of production. Indeed, the value of farmland relative to the value of gross national product (GNP) has declined dramatically in past two centuries. The value of farmland relative to annual GNP in the US fell from 88 percent in 1870 to less than 5 percent in 1990.


Steady State Growth in the USA

All of this leads naturally on to another question, can exponential growth be sustained forever?

How do we understand the exponential increase in per capita income observed over the last 150 years? The growth literature provides a large number of candidate theories to address these questions, with the evident characteristic that such theories are nearly always constructed so as to generate a steady state, or balanced growth path, in the long term.

That is to say that the growth rate of per capita income settles down eventually to a constant. In part, this choice reflects modeling convenience. However, it is also a desirable feature of any model that is going to fit some of the 'stylised facts' of growth.

Barro and Sala-i-Martin (1995) for example argue that one good reason to stick with the simpler framework with a steady state is that the long-term experiences of the United States and some other developed countries indicate that per capita growth rates can be positive and trendless over long periods of time... This empirical phenomenon suggests that a useful theory would predict that per capita growth rates approach constants in the long run; that is, the model would possess a steady state.

Clearly there are many examples of countries that display growth rates that are rising or falling for decades at a time, and thus it is a pertinent question to ask just how 'typical' is the US in this case?

As Kaldor of course recognised, the United States has for the last 125 years exhibited positive growth for long periods with no noticeable trend. However while it seems reasonable that a successful candidate for a generalised growth theory should at least admit the possibility of steady-state growth, it is not clear that this steady state generation need be a model property.




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