Introduction
In a short paper in 1966 Nelson and Phelps offered a new hypothesis to explain economic growth. Their explanation had two distinct components. The first component postulated that while the growth of the technology frontier reflects the rate at which new discoveries are made, the growth of total factor productivity depends on the implementation of these discoveries, and varies positively with the distance between the technology frontier and the level of current productivity.
Applied to the diffusion of technology between countries, with the country leading in total factor productivity representing the technology frontier, this is a formalization of the catch-up hypothesis that was originally proposed by Gerschenkron (1962). The second component of the Nelson-Phelps hypothesis suggested that the rate at which the gap between the technology frontier and the current level of productivity is closed depends on the level of human capital. This was a break with the view that human capital is an input into the production process. Nelson and Phelps make this point starkly in the concluding sentence of their paper: “Our view suggests that the usual, straightforward insertion of some index of educational attainment in the production function may constitute a gross mis-specification of the relation between education and the dynamics of production.”The catch-up or technology diffusion component of the Nelson-Phelps hypothesis raises a basic question. If a country, or a firm within an industry, has to incur costs in order to innovate, then why should it not sit back and wait for technology diffusion to flow costlessly? Modern theories of economic growth have paid a great deal of attention to the incentives for innovation and to the market structures that are necessary to sustain R&D. Inventions are typically assumed to give rise to new (often intermediate) products which generate monopoly rents over their lifetime.
These rents provide the financial incentives to innovate and to cover the costs of innovation. The costs of invention typically reflect the wages or the patent incomes of researchers. The labor markets allocate workers between research and production, and in certain cases the allocation of workers across different occupations can involve decisions to acquire costly human capital. When a vintage structure is present, newer and technologically more efficient intermediate goods or production processes may coexist with older ones that remain inside the technology frontier. A critical by-product of an innovation, not captured by the monopoly rents that it generates, is the expansion of the stock of basic knowledge. This basic knowledge, freely available to all, enhances the productivity of future research, facilitates future innovations and is the source of scale effects.In the Nelson-Phelps framework, disembodied technical know-how flows from the technology leader to its followers and augments their total factor productivity. Patent protection or blueprint ownership is not explicitly postulated, and therefore an alternative mechanism must be in operation to sustain inventive activity and to prevent free-riding. A number of models have directly addressed the impact of imitation that dissipates rents on innovative activity by explicitly introducing costs of imitation. In an early investigation by Grossman and Helpman (1991, Chapter 11) [see also Helpman (1993), Segerstrom (1991)], the North, where patent protection is in effect, innovates, and the South, where labor costs are lower, imitates at a cost. Aghion, Christopher and Vickers (1997), building on Grossman and Helpman (1991), suggest a leapfrogging model where firms can, by incurring an appropriate cost, catch-up and overtake their rivals to capture a larger share of the profits. Eaton and Kortum (1996a, 1996b) construct a model with patenting costs where patents decrease but do not eliminate the hazard of imitation.
To construct an equilibrium with technology diffusion, Barro and Sala-i-Martin (1995, 1997) introduce a model where in the leading country the costs of innovation are low relative to the costs of imitation, while in the follower country the reverse is true. Basu and Weil (1998) propose a model where technological barriers to imitation in the South arise from significant differences in factor proportions between North and South, with the possible emergence of “convergence clubs”. Such differences in endowments may not provide the most “appropriate” opportunities for imitation, and fail to direct technical change towards efficient cost savings [see Acemoglu (2003)]. Technology may nevertheless flow between convergence clubs, with imitation costs rather than patent protection sustaining innovative activity within the clubs. Eeckhout and Jovanovic (2000) construct a model where imitators can implement technology only with a lag, and this implicit imitation cost means that innovators find it optimal to maintain their lead. It seems clear then that some costs of imitation and certain advantages to innovation must be present if technology diffusion is to play a role in economic growth. Therefore, underlying the Nelson-Phelps model there must be an appropriate market structure with an economic equilibrium that sustains innovative activity in the face of technology diffusion.The empirical literature on technology diffusion has been growing, despite difficulties in measurements. The survey of Griliches (1992) lends support to the view that there are significant R&D spillovers. Coe and Helpman (1995) find that R&D abroad benefits domestic productivity, possibly through the transfer of technological know-how via trade. Branstetter (2001), looking at disaggregated data, finds research spillovers across firms that are close in “technology space”. Nadiri and Kim (1996) suggest that the importance of research spillovers across countries varies with the country: domestic research seems important in explaining productivity in the US but the contribution of foreign research is more important for countries like Italy or Canada.
The role of human capital in facilitating technology adoption is documented by Welch (1975), Bartel and Lichtenberg (1987) and Foster and Rosenzweig (1995). Benhabib and Spiegel (1994), using crosscountry data, investigate the Nelson-Phelps hypothesis and conclude that technology spills over from leaders to followers, and that the rate of the flow depends on levels of education. In fact a good deal of the recent empirical literature has focused on whether the level of education speeds technology diffusion and leads to growth, as suggested by Nelson and Phelps, or whether education acts as a factor of production, either directly or through facilitating technology use. [See for example, Islam (1995), Eaton and Kortum (1996a, 1996b), Temple (1998), Krueger and Lindahl (2001), Klenow and Rodriguez- Clare (1997), Hall and Jones (1999), Bils and Klenow (2000), Duffy and Papageorgiou (2000), and Hanushek and Kimko (2000).]The policy implications of distinguishing between the role of education as a factor of production and a factor that facilitates technology diffusion are significant. In the former, the benefit of an increase in education is its marginal product. In the latter, because the level of education affects the growth rate of total factor productivity and technology diffusion, its benefit will be measured in terms of the sum of its impact on all output levels in the future. Following Nelson and Phelps (1966), in Benhabib and Spiegel (1994) we characterize the latter relationship through a specification that includes a term interacting the stock of human capital with backwardness, measured as a country’s distance from the technology leader.
There are potentially important implications of distinguishing between different functional forms for the technology diffusion process.[550] The technology diffusion process specified by Nelson and Phelps and widely used in the literature is known as the confined exponential diffusion [Banks (1994)].
An alternative diffusion process is the logistic model of technology diffusion. A priori, there appears to be no reason to favor one of these specifications over the other, and they appear to differ by very little. Nevertheless, as we demonstrate below, these specifications can have very different implications for a nation’s growth path: For the exponential diffusion process, the steady state is, for all parameterizations, a balanced growth path, with all followers growing at the pace determined by the leader nation acting as the locomotive. In contrast, the logistic model allows for a dampening of the diffusion process so that the gap between the leader and a follower can keep growing. Indeed, we demonstrate that if the human capital stock of a follower is sufficiently low, the logistic diffusion model implies divergence in total factor productivity growth rates, not catch-up. On this point, also see Howitt and Mayer-Foulkes (2002).Below we derive an empirical specification that nests these two forms of technology diffusion in a model where total factor productivity growth depends on initial backwardness relative to the stock of potential world knowledge, proxied in our model as the total factor productivity level of the leader country. We then test this specification for a cross-section of total factor productivity growth of 84 countries from 1960 through 1995. We obtain robust results supporting a positive role for human capital as an engine of innovation, as well as a facilitator of catch-up in total factor productivity.
As our results favor a logistic form of technology diffusion, some countries may indeed experience divergence in total factor productivity growth. To investigate this result, we derive a point estimate for the minimum initial human capital level necessary to exhibit catch-up in total factor productivity relative to the leader nation, which is the United States in our sample. The point estimate in our favored specification indicates that an average of 1.78 years of schooling was required in 1960 to allow convergence in total factor productivity growth with the United States.
Under this criterion, we identify 27 countries in our sample that our point estimates predict will exhibit slower total factor productivity growth than the United States. Our data shows that over the next 35 years, 22 of these 27 countries did indeed fall farther behind the United States in total factor productivity, while the remaining bulk of the nations in our sample exhibited positive catch-up in total factor productivity. While this result is not a formal test of our model, its ability to correctly identify countries that would subsequently exhibit slower total factor productivity growth than the United States is reassuring.
We then repeat our exercise using 1995 figures to identify the set of nations that are still falling behind in total factor productivity growth. Because the United States had higher education levels in 1995, we estimate a higher threshold level for total factor productivity growth convergence with the United States. Our estimate is that 1.95 average years of schooling in the population over the age of 25 is necessary for faster total factor productivity growth than the leader nation. Fortunately, the higher overall education levels achieved by most countries over the past 35 years left few countries falling the threshold levels in education to achieve catch-up in growth rates. We identified only four countries that were still below the threshold in 1995: Mali, Mozambique, Nepal, and Niger. With the exception of these four nations, our results indicate that most of the world is not in a permanent development trap, at least in terms of total factor productivity growth. Nevertheless, it should be pointed out that catch-up in total factor productivity and in growth rates is not a guarantee of convergence in per capita income, as nations must also be successful in attracting physical capital to achieve the latter goal.
The remainder of the paper is divided into five sections. Section 2 introduces the exponential and logistic specifications of the Nelson-Phelps model and examines their steady-state implications. Section 3 compares the diffusion models with that of Barro and Sala-i-Martin (1997). Section 4 derives a non-linear growth specification that nests the exponential and logistic technology diffusion functional forms. Section 5 estimates this model using maximum likelihood for a cross-section of countries. Section 6 uses the point estimates from our estimation to identify nations that are predicted to fail to exhibit divergence in total factor productivity growth in 1960 and 1995. Lastly, Section 7 concludes.
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