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Concepts of ‘golden rule’ in neoclassical growth model

The neoclassical model was an extension to the 1946 Harrod-Domar model that included a new term: productivity growth. Important contributions to the model came from the work done by Robert Solow; in 1956, Solow and T.W. Swan developed a relatively simple growth model which fit available data on US economic growth with some success.

In 1987, Solow received the Nobel Prize in Economics for his work. Solow was also the first economist to develop a growth model which distinguished between vintages of capital.

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In Solow’s model, new capital is more valuable than old (vintage) capital because-since capital is produced based on known technology, and technology improves with time-new capital will be more productive than old capital.

Both Paul Romer and Robert Lucas’, Jr. subsequently developed alternatives to Solow’s neoclassical growth model. Today, economists use Solow’s sources-of-growth accounting to estimate the separate effects on economic growth of technological change, capital, and labour.

The key assumption of the neoclassical growth model is that capital is subject to diminishing returns. Given a fixed stock of labour, the impact on output of the last unit of capital accumulated will always be less than the one before.

Assuming for simplicity no technological progress or labour force growth, diminishing returns implies that at some point the amount of new capital produced is only just enough to make up for the amount of existing capital lost due to depreciation.

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At this point, because of the assumptions of no technological progress or labour force growth, the economy ceases to grow. Assuming non-zero rates of labour growth complicates matters somewhat, but the basic logic still applies-in the short-run the rate of growth slows as diminishing returns take effect and the economy converges to a constant “steady-state” rate of growth (that is, no economic growth per-capita).

Including non-zero technological progress is very similar to the assumption of non-zero workforce growth, in terms of “effective labour”: a new steady state is reached with constant output per worker-hour required for a unit of output. However, in this case, per-capita output is growing at the rate of technological progress in the “steady-state” (that is, the rate of productivity growth).

In neoclassical growth models, the long-run rate of growth is exogenously determined-in other words, it is determined outside of the model. A common prediction of these models is that an economy will always converge towards a steady state rate of growth, which depends only on the rate of technological progress and the rate of labor force growth.

A country with a higher saving rate will experience faster growth, e.g. Singapore had a 40% saving rate in the period 1960 to 1996 and annual GDP growth of 5t6%, compared with Kenya in the same time period which had a 15% saving rate and annual GDP growth of just 1 %.

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This relationship was anticipated in the earlier models, and is retained in the Solow model; however, in the very long- run capital accumulation appears to be less significant than technological innovation in the Solow model.

A key prediction of neoclassical growth models is that the income levels of poor countries will tend to catch up with or converge towards the income levels of rich countries as long as they have similar characteristics- like for instance saving rates.

Since the 1950s, the ยง opposite empirical result has been observed on average. If the average growth rate of countries since, say, 1960 is plotted against initial GDP per capita (i.e. GDP per capita in 1960), one observes a positive relationship.

However, a few formerly poor countries, notably Japan, do appear to have converged with rich countries, and in the case of Japan actually exceeded other countries’ productivity, some theories that this is what has caused Japan’s poor growth recently convergent growth rates are still expected, even after convergence has occurred; leading to over-optimistic investment, and actual recession.

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The evidence is stronger for convergence within countries. For instance the per-capita income levels of the southern states of the United States have tended to converge to the levels in the Northern states.

These observations have led to the adoption of the conditional convergence concept. Whether convergence occurs or not depends on the characteristics of the country or region in question, such as:

Institutional arrangements

Free markets internally, and trade policy with other countries.

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Education policy

Evidence for conditional convergence comes from multivariate, cross-country regressions.

If productivity were associated with high technology then the introduction of information technology should have led to noticeable productivity acceleration over the past twenty years; but it has not:

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”).