Solow–Swan model
The Solow–Swan model or exogenous growth model is an economic model of long-run economic growth. It attempts to explain long-run economic growth by looking at capital accumulation, labor or population growth, and increases in productivity largely driven by technological progress. At its core, it is an aggregate production function, often specified to be of Cobb–Douglas type, which enables the model "to make contact with microeconomics".[1]: 26 The model was developed independently by Robert Solow and Trevor Swan in 1956,[2][3][note 1] and superseded the Keynesian Harrod–Domar model.
Mathematically, the Solow–Swan model is a nonlinear system consisting of a single ordinary differential equation that models the evolution of the per capita stock of capital. Due to its particularly attractive mathematical characteristics, Solow–Swan proved to be a convenient starting point for various extensions. For instance, in 1965, David Cass and Tjalling Koopmans integrated Frank Ramsey's analysis of consumer optimization,[4] thereby endogenizing[5] the saving rate, to create what is now known as the Ramsey–Cass–Koopmans model.
Mankiw–Romer–Weil version of model[edit]
Addition of human capital[edit]
In 1992, N. Gregory Mankiw, David Romer, and David N. Weil theorised a version of the Solow-Swan model, augmented to include a role for human capital, that can explain the failure of international investment to flow to poor countries.[20] In this model output and the marginal product of capital (K) are lower in poor countries because they have less human capital than rich countries.
Similar to the textbook Solow–Swan model, the production function is of Cobb–Douglas type:
The Solow–Swan model augmented with human capital predicts that the income levels of poor countries will tend to catch up with or converge towards the income levels of rich countries if the poor countries have similar savings rates for both physical capital and human capital as a share of output, a process known as conditional convergence. However, savings rates vary widely across countries. In particular, since considerable financing constraints exist for investment in schooling, savings rates for human capital are likely to vary as a function of cultural and ideological characteristics in each country.[23]
Since the 1950s, output/worker in rich and poor countries generally has not converged, but those poor countries that have greatly raised their savings rates have experienced the income convergence predicted by the Solow–Swan model. As an example, output/worker in Japan, a country which was once relatively poor, has converged to the level of the rich countries. Japan experienced high growth rates after it raised its savings rates in the 1950s and 1960s, and it has experienced slowing growth of output/worker since its savings rates stabilized around 1970, as predicted by the model.
The per-capita income levels of the southern states of the United States have tended to converge to the levels in the Northern states. The observed convergence in these states is also consistent with the conditional convergence concept. Whether absolute convergence between countries or regions occurs depends on whether they have similar characteristics, such as:
Additional evidence for conditional convergence comes from multivariate, cross-country regressions.[25]
Econometric analysis on Singapore and the other "East Asian Tigers" has produced the surprising result that although output per worker has been rising, almost none of their rapid growth had been due to rising per-capita productivity (they have a low "Solow residual").[7]