PED401. Applications and Cases in International Development Teaching Notes 1 Are SubSaharan African countries in a Malthusian trap? The case of Mali In this case we look at interactions between growth and population. This takes us to the central questions of unified growth how to explain in a consistent framework the last few millennia of economic experience, including the recent period of modern growth. It also takes us to a different angle over debates on the contemporary problems of SubSaharan Africa. Is stagnation in much of the region due to a Malthusian problem of too much population for available resources? What does this mean? And what does this imply for policy choices? Take Mali. Mali is an extraordinarily beautiful country, with rich cultural traditions and some of the best contemporary music in the world. (Or in terms of our recent discussions, in music Mali is at the frontier.) It is also landlocked and is mainly desert see the map. Things are only likely to get worse for agriculture if global warming leads to less and more uncertain water availability. It has been growing in recent years, owing in part to a gold boom, but has a population growth rate of some 3 percent per annum, a total fertility rate that has only recently dropped just below 7 expected births per woman, and a contraceptive prevalence of 8 percent amongst women of childbearing age. Surely population dynamics matter here? Long-run history, the Great Divergence and the condition of Sub-Saharan Africa The essence of the story to be explained is given in Figure 1, taken from Galor (2004). For most of history there was essentially no growth in income per capita. But after around 1800 something starts happening, and by the end of the 20 th Century there had been a historically unprecedented transformation of income per capita in parts of the world, with an associated enormous expansion of well-being. But the expansion has been extraordinarily uneven, in what has become known as the Great Divergence. In particular, some countries including many in SubSaharan Africa have sustained a growth path that doesn t look much different from the history of stagnation in previous centuries. 1 These were prepared by Alexander Culiuc and Michael Walton and are solely for teaching purposes.
2 Figure 1 Long-run patterns of regional income per capita Source: Galor (2004) Underlying the stylized facts in Figure 1 is another: in the long period before the transition, total output was not stagnant. But population adjusted. This is why this period is termed the Malthusian phase. Malthus is most remembered for population expansion being a source of problems: growing population would put pressure on resources, income per capita would decline and eventually so would population. But the core idea of their being an equilibrating mechanism between population and income applies on the upside too. Expansion in aggregate income induced by technological change or increased efficiency largely translated into growing populations, leaving income per capita broadly unchanged (and vice versa in periods of decline). Figure 2 Two patterns of relationship between output and population: Western Offshoots and Africa Source: Galor (2004) based on work by Maddison.
3 This pattern raises two types of question: What theory of growth can both explain the long period of near-stagnation and the (staggered) takeoff? This is the quest for unified theory, that extends the primary preoccupation of growth theory of the past few decades in in explaining the recent period. Do the mechanisms that historically explain long-run stagnation and the transition to modern growth help in interpreting the growth malaise of poor countries today? And does this have implications for policy? This will get us into another debate: if population dynamics make a difference to income per capita and well-being, is there a case for focusing policy on the determinants of population change and especially fertility? And if so, what is likely to be most efficacious in the conditions prevailing in poor countries today? Analytical context We start with the simplest possible representation of the Malthusian trap in the framework of the Solow model which we have already introduced in the Big Push discussion. Figure 3 Malthusian trap in the Solow model The problem with the representation is that it gives us no intuition behind this strangely shaped population growth line. It only provides us with a mechanical picture of the trap. Galor (2004) reviews a number of theories that attempt an explanation of the very long-term historical trends in income levels. For most of human history, until the early 18 th century, the notion of economic growth belonged squarely in the realm of fiction (we can t use science fiction because in those days there was neither science fiction, nor science in the present meaning of the word), with income per capita increasing at less than 0.05% per year. Any increases in output were offset by increased population, a property which defines a Malthusian
4 economy. Then something happened in Western Europe around the border of the 18 th and 19 th centuries, and growth took off around the globe. Some take-offs (Japan in the end of the 19 th and then again the middle of 20 th century, Korea in the second half of the 20 th ) were more impressive than others (Latin America in early 20 th century), some are uncertain or yet to happen (Africa). However, the general pattern of the take-off is roughly the same everywhere: Decreased mortality rates (esp. infant and child mortality) were offset by even sharper decreases in fertility rates, resulting in lower population growth rates. Rapid increase in education attainment levels. Urbanization and industrialization with a decreased role of agriculture in overall output Since then, economic growth got a new meaning. The world economy grows today nearly 100 times faster than two centuries ago. The change is so dramatic, that it s hard to imagine that the two types of economies could be driven by the same underlying economic forces. And that has been exactly the way most economists reacted: it is hard to envision a growth theory that would explain both worlds. Malthus s theory explains why economies didn t grow for most of history. New growth theories explain why modern economies grow today. But each approach fails to explain the other historical epoch. This matters for theory. It also matters for contemporary interpretations. Unified Growth Theory Galor to the rescue. Together with Weil, he developed a complicated model that can explain both periods (Malthusian and modern), as well as the transition phase between the two. The general story goes as follows (this is a slightly abridged quote from Galor s paper). In early stages of development the economy was in a stable Malthusian steady state equilibrium. Technology advanced [ ] slowly, and generated proportional increases in output and population. The inherent positive interaction between population and technology in this epoch, however, gradually increased the pace of technological progress and the delayed adjustment of population permitted output per capita to creep forward at a miniscule rate. The slow pace of technological progress in the Malthusian epoch provided a limited scope for human capital in the production process and parents therefore had no incentive to reallocate resources towards child quality during this era. The Malthusian interaction between technology and population accelerated the pace of technological progress permitting a take-off. [ ] The expansion of resources was partially counterbalanced by the enlargement of population and the economy was characterized by rapid growth rates of income per capita and population. The acceleration in technological progress increased the demand for human capital, while having two opposing effects on population growth. On the one hand, it eased households budget constraints, allowing the allocation of more resources for raising children. On the other hand, it induced a reallocation of these additional resources toward child quality. In the Post-Malthusian regime, due to the limited demand for human capital, the first effect dominated and the rise in
5 real income permitted households to increase their family size as well the quality of each child. [ ] The interaction between investment in human capital and technological progress generated a virtuous circle: human capital generated faster technological progress, which in turn further raised the demand for human capital, inducing further investment in child quality, and ultimately initiating a demographic transition. The offsetting effect of population growth on the growth rate of income per capita was eliminated and the interaction between human capital accumulation and technological progress permitted a transition to a state of sustained economic growth. The building blocks The story above is based on the dynamics of an overlapping generations model (OLG) developed by Galor and Weil. You ll learn OLG later in the semester (in Macro), so we ll only explain the basics. Instead of having infinitely living individuals, like in the Ramsey model, we are dealing with mortals, whose life is composed of two periods. In this case the periods are child and adult. The adult generation is indexed by t (so children of generation t are considered generation t+1). The only decision maker is the Adult, who derives utility from consumption c and a combination of children quantity (n) and quality (h, measured by human capital): There exists a minimum subsistence level of consumption, so the adult will not allocate any time to making/raising children as long as this minimum consumption is not satisfied. Notice that the adult decides how much time to allocate to work (which provides income for consumption), the rest being dedicated to either to making or educating children. The output (and hence consumption) generated from work depends on two factors of production: land X and human capital H. 2 Land is fixed, but its marginal product depends on the level of technology used: In per-capita terms, this becomes adult). (where x t =A t X/L t is the effective resources per The human capital embodied in people is determined by their quality (education) as well as by the technological environment. Technological progress reduces the adaptability of existing human capital for the new technological environment (the erosion effect ). Education, however, lessens the adverse effects of technological progress. That is, skilled individuals have a comparative advantage in adapting to the new technological environment. In particular, the time required for learning the new technology diminishes with the level of education and increases 2 The authors don t model include physical capital in their model, since that would complicate things by adding a savings decision.
6 with the rate of technological change. 3 Therefore the level of human capital is increasing in their parental time investment in education, e t+1, and decreasing in the rate of technological progress, g t+1 (where g t+1 (A t+1 A t )/A t ): h t+1 = h(e t+1, g t+1 ) The last building block that needs to be endogenized is the rate of technological progress g. In Galor and Weil (2000), g depends positively on the size of the population (as in the Kremer model revenues from a fixed cost technology investment depends on the size of the market, i.e. there is a scale effect) and the level of education: g(e, L). Finally, we have to state the starting conditions of the economy. We assume that the world comes into existence with (i) a small population, for whom (ii) the subsistence consumption constraint is binding, which is due to (iii) low technological level. The maximization problem Members of generation t choose the number and quality of their children, and therefore their own consumption, so as to maximize their intertemporal utility function subject to the subsistence consumption constraint. The maths is messy, so we won t present it here. The results are as follows (you can check them on pages 60-61 of the Galor paper): a. An increase in the rate of technological progress reduces the number of children and increases their quality. b. If the subsistence consumption constraint is binding, an increase in parental potential income raises the number of children, but has no effect on their quality. This is the essence of the Malthusian trap all additional input is eaten away by increased population. c. If the subsistence consumption constraint is not binding, an increase in parental potential income does not affect the number of children or their quality (i.e. past a certain level of income, the Malthusian effect disappears). The dynamics of the system The key component of the model is the circular relation between education and technological growth. Notice that in order to provide a given level of human capital to their children, the adult must invest more in education for higher rates of technological growth. On the other hand, the higher the education level, the higher the technological progress. So technology is a concave function of education and population g t+1 (e t, L t ), and education is a concave function of technological growth, e t+1 = e(g t+1 ) We can put these two functions in a single e-g graph. There are several potential scenarios: e(g) and g(e, L) don t intersect at all, or intersect one or more times. The Malthusian epoch corresponds to the first scenario. 3 Yes, this assumption of the model is debatable.
7 Figure 4. The Malthusian trap How do we interpret such a graph? Let s say that the adult is pondering whether to give their child a certain level of education e 0. The desired level of technology would then be g 0. However, if that will be the actual technological progress in the next period, the adult would actually prefer to provide children only with e 1, since that s what his utility maximization solution tells him to do (determined by the e(g) function). But for this new e, the technological growth will be even smaller (g 1 ). Continuing this logical sequence, we quickly conclude that there is only one possible outcome the child will receive zero education. The arrows that go between the two curves take us towards this equilibrium. You can think of this graph as being the mathematical representation of the vicious circle. However, there will be still some technological progress due to the population effect (remember, population affects technological progress). As technology slowly creeps ahead, population slowly increases, which is due to result (b) from the maximization problem. This in turn increases technological progress for any given level of education, which gradually shift the g(e, L) curve up. So the vicious circle between e and g is gradually being eroded by the effect of the virtuous circle between g and L. At some point in time, the two curves will intersect, as depicted in figure 3. We now have three equilibria: (0, g l ), (e h, g h ) and (e u, g u ). The second one is unstable notice that the arrows go away from it (you can see how this graph is similar in spirit to the Solow representation of the Malthusian trap and our big push discussion). So, depending on expectations, policies and luck, the economy can go to either the high modern (e h, g h ) or the low Malthusian equilibrium (0, g l ).
8 Figure 5. Multiple equilibrium scenario However, even if the country is inhabited by unlucky pessimists ruled by the worst government and the economy gets stuck at the bad equilibrium, the situation is not hopeless. The reinforcing effects of population and technology growths will continue to slowly push the g(e, L) curve up until the bad equilibrium disappears, in which the economy progresses to the modern equilibrium, as depicted in figure 4. Figure 6. A modern economy equilibrium A final note on the model. In the original paper, these graphs are supplemented by complex phase diagrams that link education with effective resources x (pages 67-68). You may want to test your understanding of phase diagrams by trying to interpret them (good luck!).
9 Additions to the model In the model presented above, the rise in the demand for human is an outcome of the acceleration in technological progress, underlying the role of educated individuals in coping with a rapidly changing technological environment. The mechanism is founded on the premise that the introduction of new technologies increases the demand for skilled labor in the short-run. In his review study, Galor (2004) briefly discusses other possible mechanisms for the rise of human capital, that he argues are complementary influences: A technology-life expectancy interaction. Improvements in medical technology lower mortality rates and increases life expectancy, which can increase the utility that parents derive from better educated children. The lower mortality means that the education will not go to waste, whereas long life expectancy means that the life-long return on this education will be larger. (This interaction will be an important part of our discussion on HIV-AIDS next week) Capital-skill complementarities. The accumulation of physical capital in the early stages of industrialization enhanced the importance of human capital in the production process and generated an incentive for the capitalists to support the provision of public education for the masses. [ ] The accumulation of physical capital by the capitalists in the first phase of the Industrial Revolution increased the importance of human capital in sustaining the rate of return to physical capital inducing capitalists to support the provision of public education for the masses. (p. 72) You have seen this model in your macroeconomics class, in the opening lecture on endogenous growth, where the production function exhibited CRS to the combination of human and physical capital: y=ak α h 1-α. Policy on education. While the demand side is interpreted as central to the transition, supply-side interventions can play a complementary role in changing the incentives for households to send their kids to school, in particular pushes to lower the cost of schooling or change the household demand for education through socialization processes. Historically two aspects of this were the support for education policy from industry, just noted, and for present purposes religious or nationalist drives for education. Decline in the gender gap. Extending the discussion to account for gender differences can provide an additional explanation of the human capital accumulation and demographic transition. technological progress and capital accumulation complemented mental-intensive tasks and substituted for physical-intensive tasks in the industrial production process. In light of the comparative physiological advantage of men in physical-intensive tasks and women in mentalintensive tasks, the demand for women s labor input gradually increased in the industrial sector, decreasing monotonically the wage deferential between men and women. In early stages of industrialization, wages of men and women increased, but the rise in female s relative wages was insufficient to induce a significant increase in women s labor force participation. Fertility,
10 therefore increased due to the income effect that was generated by the rise in men s absolute wages. Ultimately, however, the rise in women s relative wages was sufficient to induce a significant increase in labor force participation, increasing the cost of child rearing proportionally more that households income and triggering a demographic transition and a shift from stagnation to growth. (p. 75) This argument can be strengthened further by the fact that work and the number of children are (traditionally) substitutes for women. However, in the presence of an educational system, work and quality of children no longer need to be substitutes, since education can be [partially] outsourced. In fact, greater female labor participation can further increase education of children, by providing additional financing for educational expenditures. The particularly strong influence of female labor participation on the demographic transition and education points towards an important policy implication: female education is, in some sense, more important than male education. The graph below 4 puts some of these links together, though note that this starts from the contemporary focus on more education for women, rather than this being a product of shifts in demand for female labor. Figure 7. The decline in the gender gap, the demographic transition and growth Contemporary patterns and policy choices We set up the discussion of contemporary issues with some illustrative data from Africa and Asia, and a brief sketch of the policy options. The assessment of these alternatives will be discussed further in class. Patterns of growth and fertility change in Africa and Asia Let s start with an overview at a regional level, comparing East Asia, South Asia and SubSaharan Africa. In the 30-year period between 1975 and 2005, SubSaharan Africa essentially stagnated in terms of income per capita (though with growth of both output and population, as seen in Figure 2), while East Asia and South Asia, both initially poorer, grew at rapid and modest rates, respectively(figure 8). This was associated with a very slow fall in fertility rates in SubSaharan Africa, both absolutely and in comparison with East and South Asia. 4 Borrowed from Ricardo Hausmann s PED-309 lecture slides.
11 Figure 8. GDP per capita in East Asia, South Asia and SubSaharan Africa 5 (in PPP at 2000 prices) Figure 9. Fertility rates in East Asia, South Asia and SubSaharan Africa As a consequence of this fertility transition, East Asia and South Asia have been experiencing a fall in the dependency ratio (the ratio of young and old to the working age population), and fall that will eventually be reversed as the old age population rises (Figure 10). And while schooling has risen in all periods, it remains significantly lower in SubSaharan Africa. 5 All data from World Bank, World Development Indicators.
12 Figure 10. Dependency ratios in East Asia, South Asia and SubSaharan Africa Figure 11. Primary and secondary school enrollment East Asia, South Asia and SubSaharan Africa The following figures provide selected numbers for Mali, in comparison with two Asian countries, Bangladesh and Indonesia, both highly populous that some 30-40 years ago pessimists would undoubtedly have characterized as being caught in a Malthusian trap. First, in terms of GDP per capita trends broadly reflect the regional patterns shown above. Though when we look at growth rates, we see a slight acceleration in growth in population in Mali in the 1990s. Fertility rates in Mali remain extraordinarily high, while there have been dramatic declines in both Bandladesh and Indonesia (Figure 14)
13 Figure 12. GDP per capita in Bangladesh, Indonesia and Mali (at 2000 PPP) Figure 13. GDP and population growth in Bangladesh and Mali Figure 14. Fertility rate in Bangladesh, Indonesia and Mali
14 Figure 15 compares education enrollment in the three countries, while Figure 16 shows the stark differences in contraceptive prevalence with Mali still way below 10 percent of adult women. Figure 15. Secondary education enrollment in Bangladesh, Indonesia and Mali Figure 16. Contraceptive prevalance Bangladesh, Indonesia and Mali (%, women aged 15-49) Policy options Do population dynamics matter to the expansion of welfare? Let s put aside some deep ethical issues for now, at least for these notes. Or more specifically, we could follow the position of one of the founders of the Enlightenment, the Marquis Marie-Jean-Antoine-Nicolas Caritat Condorcet who looked forward to a time in which people will know that, if they have a duty towards those who are not yet born, that duty is not to give them existence but to give them happiness (cited in Sen, 1999 p. 214). Given this position, we are interested in the interaction between population and human well-being of those who are born. Then there are (at least) four interesting policy positions for a country in Mali s position.
15 Population push. The contemporary world has the benefit of contraceptive technologies unavailable in the 19 th century, that opens up a whole new control variable (though one that Malthus would undoubtedly have favored): proactive policy to directly reduce fertility at low levels of income. Education and women s empowerment push. Fertility choices are fundamentally driven by the decisions of young women, so what really drives a demographic transition is the variety of determinants of their power, with girl s education and outside work key drivers of change. Growth and technological change pull. The (desirable) shifts in education and women s position will only occur if, as in 19 th Century Europe and Western Offshoots, there is a major change in the economic demand for skills. The question is how to get Mali on to such a growth path. Malthus redux: migration. Mali simply can t get rich given its geographic endowment, and the only way to transform living standards of Malians is through substantial outmigration. This would not even be controversial if Africa s national boundaries weren t created by 19 th Century European interests. Note that the second, and then the third, position don t deny a role for the first (and then the second). Take the third position, that is closest to Galor s interpretation of history. This can surely be helped by government action on provisioning of schooling and social mobilization for women. And access to contraceptives can make it easier for women to implement their preferences on family size. But the central question is what the primary driver of change is. Since these notes are already long, we sketch the arguments, in order to frame the discussion we will have on Mali s option, rather than discuss the evidence in detail. On population push there are two big issues, whether it is ever likely to be significant, and over coercion. In the development literature of the early 1970s, some economists argued that family planning had just terrific cost-benefit ratios. Condoms and pills were cheap, they had a big impact on the denominator of income per capita (and released resources for public provisioning), with minor, or even positive effects on the numerator 6, so could have large impacts on welfare. The key assumption in this line of reasoning is that families had more kids then they wanted that there was unmet demand for contraception. Pritchett (1994) directly attacks this, arguing that, to first order, all the variation in actual fertility is driven by differences in desired fertility. This is, of course, entirely consistent with Galor s interpretation of history: the fertility transition was an endogenous consequence of shifts in the economy-wide factors that in turn influenced both household preferences and government policy as discussed above. Yes, contraceptive prevalence rose dramatically in countries such as Bangladesh and Indonesia (Figure 16), and this was welfare-improving, but to attribute causation from the family planning programs to the fertility decline is like attributing to tonic the inebriating effects of gin and tonic. (Or to put it a less colourfully, there s an identification problem). Not all family planning specialists agree 6 We postpone to a future session discussion of whether or not there is a demographic bonus.
16 with this, and for those interested there is a comment and response in the Population and Development Review a year later. See also Caldwell et al (1999) who argues the relevance of social change in affecting household choices over children. The second issue concerns coercion. Here China is the reference case. It is argued that China, with its one-child policy, did successfully make population policy a control variable, and while this had unattractive elements, it could be justified in the grander (Malthusian) scheme of things. Sen (1999) argues against this perspective (and against continued, if less pervasive, examples of coercion that he cites in India in the 1990s), both on ethical grounds, and more immediately relevant for these notes on practical grounds. He in particular suggests that the experience of Kerala and Tamil Nadu shows an alternative path is feasible, that is based on expanding the freedoms ( capabilities in his technical terminology) of young women in particular through education and outside earnings opportunities. To illustrate, he points out that in 1979, when the one-child policy was introduced in China, Kerala had a higher fertility rate than China: 3.0 as opposed to China s 2.8. By 1991 its fertility rate of 1.8 is as much below china s 2.0 as it had been above in 1979. Despite the added advantage of the one-child policy and other coercive measures, the fertility rate seems to have fallen much more slowly in China then in Kerala. (Sen, 1999 p. 222.) This takes us already deeply into whether the second or third position is a better description of contemporary processes. Sen also has a view on this. He adduces cross-sectional evidence from India (Murthi et al. 1995) that finds that the substantial inter-district variation in fertility across India is only significantly associated with female literacy and female labor force participation. Income has no statistically significant influence. If this interpretation is correct, it would suggest there are different causal dynamics at work across India than in the historical transitions. But there is still room for debate over this. And it would still leave us with the question of what mix of developments would sustain a fertility transition in the very different conditions of Mali. Finally, let s go to Malthus redux the view that, whatever your interpretation of causal dynamics of change in the past, some countries simply don t have the natural resources and geographic location to effect a major increase in GDP per capita at least in a reasonable space of time. An advocate of this position is Lant Pritchett again (see Pritchett, 2006), who argues that outmigratoin was precisely how historically many ghost towns, or unproductive countries (Ireland in the 19 th Century?) did adjust, with positive welfare consequences both for those who moved and those who stayed. This is a controversial position, but one that is important to discuss. Note that it has two alternative visions. The first (that Pritchett argues) is of much greater mobility to rich countries. The second is a vision of Africa in which urbanization and industrialization takes off in coastal areas or areas with either major resource potential or lowcost access to the global economy and that within Africa migration will be an important mechanism whereby all Africans can participate in this process.
17 The policy question You are a Malian economist, just returned from graduate training, and you have joined the planning office. There is a debate on Mali s growth process. By Mali s own historical standards, and by the standards of most countries in SubSaharan Africa, Mali s growth has been quite good over the past decade or so six percent per annum for 1995-2005. But it comes from an extraordinarily low level, is at least in part driven by gold, and expansion in income per capita is only about half this, owing to continued rapid population growth. Fertility rates remain very high, and there is concern that as the currently very high mortality falls, population growth will remain high for some time. What should be done? Is there a case for action to reduce population growth? If so, how? Or should the whole focus be on determinants of growth? Or, is the transformation of Mali s economy impossible at current and projected population levels, so that migration has to be a major part of any solution? The President has asked the planning office to come up with an answer. You have been asked to give a briefing to the team responsible for this to frame the discussion, making use of your learning on growth, history and international experiences. Notes: (i) you may pick another country if you prefer; (ii) for this question, the focus is not on HIV/AIDS, that will be at the center of a future case. References Caldwell, John, Barkat-e-Khuda, Bruce Caldwell, Indrani Pieris and Pat Caldwell. 1999. The Bangladesh Fertility Decline: An Interpretation. Population and Development Review, 25(1) Galor, Oded. 2004. From Stagnation to Growth: Unified Growth Theory. In Philippe Aghion and steven Dulauf eds. The Handbook of Economic Growth. Murthi,Mamta, Anne-Catherine Guio and Jean Drèze. 1995. Mortality, Fertility, and Gender Bias in India: A District-Level Analysis. Population and Development Review 21. Pritchett, Lant. 1994. Desired Fertility and the Impact of Population Policies. Population and Development Review, 20(1). Pritchette, Lant. 2006. Let Their People Come: Breaking the Gridlock on Global Labor Mobility. Washington DC: Brookings Institution Press. Sen, Amartya. 1999. Development as Freedom. New York: Alfred A. Knopf. Sturzenegger, Federico. 2007. Teaching notes API119
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