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".
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.
Today, economists use Solow's sources-of-growth accounting to estimate the separate effects on economic growth of technological change, capital, and labor.
[8] Basically, it asserts that outcomes on the "total factor productivity (TFP) can lead to limitless increases in the standard of living in a country.
Solow sees the fixed proportions production function as a "crucial assumption" to the instability results in the Harrod-Domar model.
His own work expands upon this by exploring the implications of alternative specifications, namely the Cobb–Douglas and the more general constant elasticity of substitution (CES).
One central criticism is that Harrod's original piece[11] was neither mainly concerned with economic growth nor did he explicitly use a fixed proportions production function.
Both shifts in saving and in population growth cause only level effects in the long-run (i.e. in the absolute value of real income per capita).
This convergence could be explained by:[13] Baumol attempted to verify this empirically and found a very strong correlation between a countries' output growth over a long period of time (1870 to 1979) and its initial wealth.
The key assumption of the Solow–Swan growth model is that capital is subject to diminishing returns in a closed economy.
In the Solow–Swan model the unexplained change in the growth of output after accounting for the effect of capital accumulation is called the Solow residual.
This residual measures the exogenous increase in total factor productivity (TFP) during a particular time period.
The increase in TFP is often attributed entirely to technological progress, but it also includes any permanent improvement in the efficiency with which factors of production are combined over time.
The model can be reformulated in slightly different ways using different productivity assumptions, or different measurement metrics: In a growing economy, capital is accumulated faster than people are born, so the denominator in the growth function under the MFP calculation is growing faster than in the ALP calculation.
(Therefore, measuring in ALP terms increases the apparent capital deepening effect.)
The textbook Solow–Swan model is set in continuous-time world with no government or international trade.
) in an aggregate production function that satisfies the Inada conditions, which imply that the elasticity of substitution must be asymptotically equal to one.
The number of workers, i.e. labor, as well as the level of technology grow exogenously at rates
, which is a measure for wealth creation:[note 2] The main interest of the model is the dynamics of capital intensity
In essence, the Solow–Swan model predicts that an economy will converge to a balanced-growth equilibrium, regardless of its starting point.
In this situation, the growth of output per worker is determined solely by the rate of technological progress.
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.
Therefore, there are two fundamental dynamic equations in this model: The balanced (or steady-state) equilibrium growth path is determined by
Klenow and Rodriguez-Clare cast doubt on the validity of the augmented model because Mankiw, Romer, and Weil's estimates of
This insight significantly strengthens the case for the Mankiw, Romer, and Weil version of the Solow–Swan model.
[22] The exogenous rate of TFP (total factor productivity) growth in the Solow–Swan model is the residual after accounting for capital accumulation.
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.
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.
[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").