Salient features of the Solow model of economic growth
One of the earliest models of economic growth was developed in Solow. Economic growth is measured by a steady positive increase total output produced by a country, and at the theoretical level it is approximated by an aggregate production function.
Solow’s model is set in a neoclassical framework where it is assumed that all prices have adjusted to clear all the markets (i.e., supply is equal to demand) and incentives have generated efficient outcomes.
The model is consistent with long-term adjustments having fully taken place. In the simplest form, three factors determine aggregate output: labour, capital and technology.
Growth models concentrate on explaining the behaviour of potential output, which is output achieved with a given technology and the full employment use of other factors.
Naturally, they focus on the effects, over time, of changes in labour, capital and technology. Changes in labour can be induced by changes in the population or in the proportion of the people available for work, namely the participation rate.
Changes in existing productive capital depend on net investment that is gross investment minus depreciation of existing capital. As long as net investment is positive, capital grows and production growth follows.
However, the size of investment matters. It can be so small that the induced change in capital is marginal and so is the effect on production. Finally, technology combines the other inputs, labour and capital, to produce output. Hence, in the absence of changes in one of the two.
The production function for aggregate output (Y) is then represented as Y = F (A, K, L) with A for technology, K for capital and L for labour. The rate of growth is defined as the per cent change in output? Y
Note that full employment of factor does not mean capital is used at 100% capacity and there is no unemployed person. Full employment is achieved when measured unemployment is equal to the natural rate and capital utilisation rate is around 90-95%.
A “better” technology is one that increases total factor productivity that is increases production with a constant amount of inputs used. Technological changes can take several forms: existing technologies are improved or new technologies appear; the organisation of work changes; the quality and or composition of inputs and/or outputs changes (increased education level in workforce, move from production of clothing to computers).
Concretely, the Solow growth model is based on an aggregate production function, which exhibits constant returns to scale and diminishing marginal returns. As a consequence, output per worker depends only on capital per worker.
For output growth in such framework per worker to change, the ratio of capital per worker must change. This will happen if capital accumulation is larger than labour force growth that is if capital grows faster than labour and k increases.
In other words, if the accumulation of capital is larger than what is necessary to provide each new worker with the quantity of capital existing workers have, the ratio will increase. In this model, financial markets do not explicitly enter the picture.
Nevertheless, in the macroeconomic framework, gross capital accumulation is equal to investment and, in a closed economy; investment is equal to domestic saving.
Hence, savings in the economy feeds into investment and net capital accumulation (k), or the change in capital that will contribute to production growth, is defined as total saving (s) minus compensation for labour force growth (nk). As a result, growth in capital (gk) and growth and where n is the rate of growth of population.
The main feature of Solow’s model is that in the long run, after all adjustments have taken place, total saving is used to make capital grow exactly at the same rate as population.
Each new worker gets the same capital as existing workers and capital per worker is constant (gk = 0). Alternatively, it can be said that the rate of growth of capital and labour converge to the same value (sAk a – 1 = n) and there is a steady-state value of the capital labour ratio.
In Solow’s model, in the long run, once the level of capital per worker is stabilised, output per worker is stabilised and both, capital and output grow at the same rate. This is known as the balanced growth argument.
From the viewpoint of the role of the financial sector, the surprising implication of this model is that in the long run, the rate of growth of output per worker is equal to that of the labour force, regardless of the savings rate.
Hence, improvements in the collection of savings or financial innovations that stimulate savings have no effect on economic growth.
There is a transition period during which- the difference between capital growth and labour growth is positive and thus, capital per worker and output per worker rise. But, the phenomenon is temporary and eventually, the steady state prevails as k and y reach a new constant level.
Therefore, the savings rate affects permanently the level of output, not its growth rate.
Finally, in the case of an open economy, some of the increase in capital can be financed by foreign saving through capital inflow and current account deficit. The opening up of the economy will put it on a temporary adjustment path if the domestic interest rate is not equal to the world interest rate and investment (or dis-investment) will take place.
Once the capital per worker ratio is such that interest rates are equalised, the economy will resume its growth at the labour force rate, n, with current account disequilibrium and a level of capital flows just necessary to maintain the new capital-labour ratio.
The Solow growth model has been used extensively as a basis for empirical investigations on the sources of growth. Many studies focus on the role of technological changes, the so-called TFP calculation (Total Factor Productivity calculation). The following formula can be derived from Solow’s model,
Total output growth rate is a weighted average of the growth rates of the three factors: capital (gK), labour ( L) and technology ( A). This equality is known as the growth accounting framework or the source of growth methodology.
Even if an economy has not reached the steady state (i.e., is not in balanced growth), it is possible to determine the contribution of labour, capital and technical changes to economic growth. In industrial countries 70% of growth is attributed to labour (aL = 0.7), 30% to capital (aK = 0.3). The residual growth is due to technology.
Hence, for given values of the capital and labour growth rates, it is possible to evaluate the non- measurable contribution of technology. It must be noted that this methodology has been used for developing countries with mixed results.