On the Adjustment Time in Neo-Classical Growth Models

Abstract

1. A typical neo-classical growth model is characterized by the economy's long-run convergence to the steady-state growth path. An important practical question is how long is this long run, i.e. how much time is required for the economy to arrive within a reasonable vicinity of the equilibrium growth path from any initial disturbance? Professor Ryuzo Sato ([7], [8]) has shown that it may take a hundred years to cover the preponderant portion, say 90 per cent, of the disturbance. He concludes from this finding that any policy prescriptions, e.g. those of fiscal policy, derived from neo-classical growth models have very little practical content and that the Harrod-Domar model with fixed coefficients may be a better approximation of reality. In a recent survey of growth literature ([3], p. 812), Hahn and Matthews state that " insofar as it [Sato's finding] is generally valid * . . it means that steady-solutions are likely to be of very limited value as an approximation to reality ", though they caution that " this conclusion will have to be tested for a variety of models before its significance can be properly judged ". 2. This note shows that the conclusion above is not generally valid. Indeed, the adjustment time responds very sensitively to realistic modifications of the neo-classical model. These modifications refer to explicit recognition of depreciation of capital and of technical improvements embodied in new investment and the saving behaviour underlying the model. Then, the adjustment time at issue may be reduced by as much as threequarters. (It may be noted that the model analyzed in [7] and [8] defines output and investment in net terms and excludes the embodied type of technical progress from consideration.) We, therefore, conclude that it is too premature to abandon neo-classical models for analytical purposes including policy diagnosis. 3. As the model is very familiar, we need few words on it. We examine a perfectly competitive economy producing output Y (gross of depreciation) from two inputs, capital and labour. Labour (L) is fully employed and grows at a constant percentage rate n, i.e.