Solow's 1956-7 model (cited above) implies that capital should exhibit diminishing returns, that is, that either savings and investment as a fraction of output must increase or the growth-rate must slow down as capital stock increases. For the same reason it also implies that less developed economies will grow faster than more mature economies. As mentioned above, neither slowdown nor convergence has been observed as a general characteristic of the real world (Barro and Sala-I-Martin 1995). This fact, among others, stimulated interest in the late 1980s in new models capable of explaining continuous steady-state growth. They attempt to overcome the limitations of Solow's production function approach by modifying the traditional feature of diminishing returns to capital.
In response to this problem, neoclassical development economists began thinking about other possible ways to endogenize the standard theory without making drastic changes. Although not emphasized in neoclassical growth theory, there is an endogenous mechanism that can explain a part of this residual, that is, beyond that which is accounted for by labor and capital accumulation. The part that can be explained without radical (structure-changing) technological innovations is due to learning, economies of scale and the accumulation of general knowledge (for example, computer literacy) that leads to cost savings and product improvements.
As explained in Chapter 2, the mechanism in question is a simple positive feedback between increasing consumption, investment, increasing scale and 'learning by doing' or 'learning by using' at the societal level (Figure 1.1). This feedback cycle, first suggested by Arrow, results in declining costs leading to declining prices, stimulating increases in demand, increased production and new investment to increase capacity (Arrow et al. 1961; Kaldor 1966, 1971; McCombie 1982).14 Increasing production generates learning by doing and increasing capacity gives rise to further economies of scale, both of which drive costs down. Lower costs result in lower prices (in a competitive equilibrium), greater demand, more production and so forth.
However, the dominant neoclassical endogenous growth theories now in the literature do not explicitly depend upon feedback. On the contrary, they are all 'linear' in the sense that they assume a simple uni-directional causal mechanism. The endogenous theory literature can be subdivided into three branches. The first is the so-called AK approach, harking back to the older Harrod-Domar 'AK' formalism mentioned above. In the newer version, capital K is taken to include human capital (hence population and labor force). The growth of human capital is not subject to declining returns -as in the Solow model - because of the supposed (exactly) compensating influence of factor augmentation and technology spillovers. Spillovers are, of course, externalities, which - surprisingly - enables increasing returns to remain compatible with general equilibrium and thus with computable general equilibrium (CGE) models.
Neo-AK models began with Paul Romer (1986, 1987b, 1990). Romer postulated a tradeoff between current consumption and investment in undifferentiated 'knowledge'. He assumed that knowledge can be monopolized long enough to be profitable to the discoverer, but yet that it almost immediately becomes available as a free good (spillover) accessible to others.15 The original Romer theory also postulated positive returns to scale - because knowledge begets knowledge - as an explanation for economic growth. A closely related approach by Lucas, based on some ideas of Uzawa, focused instead on 'social learning' and the tradeoff between consumption and the development of 'human capital' (Lucas 1988; Uzawa 1962). In the Lucas version the spillover is indirect: the more human capital the society possesses, the more productive its individual members will be.
This externality is embedded in the production function itself, rather than in the knowledge variable.
Other contributors to this literature divide capital explicitly into two components, 'real' and human (King and Rebelo 1990). An alternative version assumes one kind of capital but two sectors, one of which produces only capital from itself. Another approach was to allow increasing returns by preserving the distinction between cumulable and non-cumulable factors (for example, labor, land) and modifying the production function to prevent capital productivity from vanishing even with an infinite capital/labor ratio (for example, Jones and Manuelli 1990).
The second approach to endogenous growth theory emphasizes active and deliberate knowledge creation. This is presumed to occur as a result of maximizing behavior (for example, R&D). Knowledge is assumed to be inherently subject to spillovers and dependent on the extent to which benefits of innovation can be appropriated by rent-seeking Schumpeterian innovators. Most models assume that inventors and innovators have negligible success at appropriating the benefits of their efforts. A recent empirical study suggests that this assumption is quite realistic (Nordhaus 2001).
The development of endogenous growth theory along neoclassical lines seems to have culminated, for the present, with the work of Aghion and Howitt (1992, 1998) and Barro and Sala-I-Martin (1995). The former have pioneered a 'neo-Schumpeterian approach' emphasizing the research-driven displacement of older sectors by newer ones. This is essentially equivalent to the process of creative destruction originally described by Schumpeter (1912, 1934). These authors (like Romer) focus on investment in knowledge itself (education, R&D) as a core concept. In fact, the idea that the investment in education might be the key to long-term economic growth has political resonance and has been taken up rather enthusiastically by, for example, the British 'New Labor' party.
The neoclassical endogenous theory has interesting features, some of which are shared by our semi-empirical approach, discussed hereafter. However, all of the so-called endogenous growth models based on 'human capital' or 'knowledge' share a fundamental drawback: they are and are likely to remain essentially qualitative and theoretical because none of the proposed choices of core variables (knowledge, human capital, etc.) is readily quantified. At best, the obvious proxies (like education expenditure, years of schooling, and R&D spending) exhibit significant multinational cross-sectional correlation with economic growth. In other words, countries with good school systems are likely to grow faster than countries with poor schools, ceteris paribus.
Before leaving the topic, it is worth pointing out where we differ substan-tively from Romer's theory. His article on economic growth in the on-line
Concise Encyclopedia of Economics contains the following explanation of the growth process, as he sees it:
Economic growth occurs whenever people take resources and rearrange them in ways that are more valuable. A useful metaphor for production in an economy comes from the kitchen. To create valuable final products, we mix inexpensive ingredients together according to a recipe . . . Human history teaches us . . . that economic growth springs from better recipes, not just from more cooking. New recipes generally produce fewer unpleasant side effects and generate more economic value per unit of raw material.
Every generation has perceived the limits to growth that finite resources and undesirable side effects would pose if no new recipes or ideas were discovered. And every generation has underestimated the potential for finding new recipes and ideas. We consistently fail to grasp how many ideas remain to be discovered. The difficulty is the same one we have with compounding. Possibilities do not add up. They multiply . . . The periodic table contains about a hundred different types of atoms, so the number of combinations made up of four different elements is about 100 x 99 x 98 x 97 = 94,000,000. A list of numbers like 1, 2, 3, 7 can represent the proportions for using the four elements in a recipe. To keep things simple, assume that the numbers in the list must lie between 1 and 10, that no fractions are allowed, and that the smallest number must always be 1. Then there are about 3,500 different sets of proportions for each choice of four elements, and 3,500 94,000,000 (or 330 billion) different recipes in total . . . (Romer 2006)
We don't suppose that Romer really thinks that growth is simply a matter of finding new 'recipes' for combining the elements. However his illustrations make it very clear that he thinks that the magnitude of knowledge capital (and the rate of growth) depends on the number of new recipes - in the broader sense - discovered, and not on their quality or (more important) sector of application.
For us, as we have pointed out already in Chapter 2, knowledge capital is emphatically not a homogeneous entity, consisting of a collection of recipes, to use Romer's analogy. Nor is knowledge in every field equally productive. On the contrary, some ideas are far more productive than others.16 An innovation that cuts the cost of electricity by a fraction of a cent is far more productive than an idea for a golf ball that flies further, an improved corkscrew, a better mosquito repellant, a longer-lived razor blade, a stronger stiletto heel, or a new computer game. Hundreds or thousands of such innovations may not have the impact of a more efficient power transformer design or an improved tertiary recovery process for oil. We differ with the theorists cited above, and Romer in particular, on this issue. In the Romer theory, all ideas are equally productive and it's just the number of ideas that counts. In our theory it is mainly innovations that increase the quantity and reduce the cost of 'useful work' that have caused the economy to grow in the past. Future economic growth may depend on innovations in another area, of course: probably information technology and/or biotechnology.
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