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Kaldor’s model of economic growth

Nicholas Kaldor, Baron Kaldor was one of the foremost Cambridge economists in the post-war period. He developed the famous “compensation” criteria called Kaldor-Hicks efficiency for welfare comparisons, derived the famous cobweb model and argued that there were certain regularities that are observable as far as economic growth is concerned.

Nicholas Kaldor summarised the statistical properties of long-term economic growth in an influential 1957 paper. He pointed out the 6 following ‘remarkable historical constancies revealed by recent empirical investigations’:

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The shares of national income received by labour and capital are roughly constant over long periods of time

The rate of growth of the capital stock is roughly constant over long periods of time

The rate of growth of output per worker is roughly constant over long periods of time

The capital/output ratio is roughly constant over long periods of time

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The rate of return on investment is roughly constant over long periods of time

The real wage grows over time

Kaldor did not claim that any of these quantities would be constant at all times; on the contrary, growth rates and income shares fluctuate strongly over the business cycle. Instead, his claim was that these quantities tend to be constant when averaging the data over long periods of time.

His broad generalisations, which were initially derived from U.S. and U.K. data, but were later found to be true for many other countries as well, came to be known as ‘stylised facts’. These may be summarised and related as follows: Output per worker grows at a roughly constant rate that does not diminish over time.

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Capital per worker grows over time.

The capital/output ratio is roughly constant.

The rate of return to capital is constant.

The share of capital and labour in net income are nearly constant.

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Real wage grows over time

Nicholas Kaldor argued that, under the assumption that workers have a negligible propensity to save; the profit rate in a capitalist economy is governed by the natural rate of growth and the capitalists’ propensity to save.

The most important refinement of Kaldor’s result was provided by Pasinetti who corrects a ‘logical slip’ in Kaldor’s paper: since workers save, they must receive profits, and hence Kaldor’s result regarding the irrelevance of workers’ saving behaviour in determining the profit rate can still be established even if their propensity to save is greater than zero.

Assuming long-run full employment, exogenous investment, a constant rate of growth, a constant distribution of income and the equality of the interest rate and the profit rate in the long run, Pasinetti decomposes total profits into capitalists’ profits and workers’ profits. The equilibrium condition becomes:

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where I is investment and sw and sc are the workers’ and capitalists’ propensities to save respectively, Pw and Pc their respective shares of profits, W is workers’ wages and Y is national income. Another source of difficulty in the literature on the Kaldor-Pasinetti model is the tremendous confusion between interest and profit.

This confusion, which Pasinetti introduces the interest rate only about halfway into his discussion of the model; we shall see that this modification has significant implications.

Perhaps stems in part from the fact that both are property incomes, may explain why many variations of these models adopt the very strong assumption of the long-run equality of the interest rate and the profit rate.

Pasinetti has been criticised for this assumption, and models that relax the assumption have been used to challenge his results But Pasinetti and other

defenders of his results have themselves relaxed that assumption, and claim to have shown that the Cambridge Equation still holds.

Pasinetti’s claim that the interest rate has no effect on the distribution of income is, to say the least, open to question. To permit relatively easy comparisons with Pasinetti’s own formulation, the interest-based model retains his assumptions.

However, the interest-based model in the present paper distinguishes between interest and profit by treating the first as a strictly contractual income, and the second as a residual income.

The second objective of the paper is to show that the treatment just outlined makes a tremendous difference as to the influence of the interest rate on the distribution of income and in particular on the profit rate.

Another extension was provided by Luigi Pasinetti. Originally, Kaldor proposed that workers did save out of wages, but less than capitalists-in which case, profits would be more sensitive to the investment decision than we have allowed.

However, Pasinetti called this “a logical slip”. If workers can save, we should conceive of two different “types” of capital falling under different ownership: “workers’ capital” and “capitalists’ capital”. Let us call the former K’ and the latter K. Thus total savings are S = sP + s'(P’ + W), workers save out of both profits and wages.

It is necessary that workers be paid a rate of interest on their capital just in the same manner as capitalists receive a rate of profit on theirs. By competition and arbitrage, Pasinetti argued that the rate of profit/ interest for both capitalist and workers on their capital is equalised.

Where P’ is workers’ profits. For savings, let S be capitalist savings and S’ worker savings out of profits. Therefore, for steady state growth:

In the long-run, for steady-state, it must be that the rate of accumulation must be equal for both capitalists and workers, i.e.

Otherwise, if the rate of wealth accumulation is faster for either of the classes, then there will be a change in distribution and, as a result, a change in the composition of aggregate demand. In long-run equilibrium, aggregate demand must be stable therefore this is a necessary assumption.

However, as a consequence of this assumption, we can note that:

Where s and s’ are the marginal propensity to save of capitalists and workers. Note again that workers also save out of wages, W, as well as profits, P’, whereas capitalists only receive and save out of profits. Cross- multiplying:

i.e., for long run Golden Rule steady-state growth, only the capitalist’s propensity to save needs to be considered-workers’ saving propensities can be dropped by the wayside. Thus, even with worker savings, the “Cambridge rule” is iron-clad. Only capitalists’ savings propensity matters.