Harrod’s project

Harrod’s book The Trade Cycle. An Essay (1936) and his article “An essay on dynamic theory” (1939) set the agenda for research into formal business cycle and growth models in the 1950s.

This raised two major issues. The first concerned the stability properties of that steady growth path, and the adjustment mechanism between the actual and warranted growth rates. Harrod’s point was that forces will systematically drive the economy away from a steady growth path: any departure of the actual rate of growth from its warranted value will be self-aggravating rather than self-defeating so that cumulative growth at a constant warranted rate is unlikely. An illustration provided by Sen (1970) is of help here; it is a typically knife-edge interpretation which Harrod disliked (Harrod 1973). We treat the case of a saving rate of 20 per cent and a capital-output ratio of 2 so that the warranted growth rate is 10 per cent. Then let us suppose that current output is 90 so that a 10 per cent rate of growth will result in an output of 100, taking the growth rate as a proportion of the final output. How the actual rate behaves depends on the expecta­tions that rule the investment behaviour. If entrepreneurs expect an output of 100 they will invest 20 units in the effort to create capacity for an additional 10 units of demand. This investment of 20 units will generate through the multiplier of 5 (implicit in a savings coefficient of 20 per cent) a demand level of 100, so that the expectation will be fulfilled.

Harrod’s view of the trade cycle was based on the argument that an actual movement away from the “warranted growth path” could be checked because the warranted rate would “chase” the actual rate upwards or downwards: “If the former eventually over­takes the latter a new equilibrium is achieved and if the former goes beyond the latter forces are generated setting up a reverse movement” (Harrod 2003: 1198-9). The way that expectations and income distribution were supposed to change during the adjustment process was essential to explaining the behaviour of the warranted rate of growth, and ultimately proposing a cycle theory endogenously generated along an endogenous trend (see Assous et al. 2014; Bruno and Dal Pont Legrand 2014). Tinbergen and Marschak were among the first to point out the difficulties inherent in modelling Harrod’s theory of cyclical growth. In his review of The Trade Cycle, Tinbergen (1937) made it clear that Harrod’s mathematical formulation only applied to exponential growth.

The second issue concerned the adjustment process between the warranted rate (assumed to remain equal to the actual growth rate) and the natural rate. Harrod assumed that the natural rate of growth is given by the maximum rate permitted by the rate of growth of the population, technology, and labour force participation. Thus, in a model with no technical progress and with a constant participation rate, the “natural” rate of growth is the maximum sustainable rate of growth in the long run measured as the rate of growth of the labour force.

In focusing on the process of adjustment between the warranted (assumed to remain permanently equal to the actual growth rate) and the natural growth rates, neoclassical economists overlooked the issue of cyclical growth. This led to the out-of-equilibrium interpretation of observed growth being abandoned in favour of an equilibrium interpre­tation, and the widespread view that economic dynamics, rather than being essentially endogenously driven, was the response to continuous external forces. These develop­ments led to the employment of two critical assumptions: (1) the development of growth models based on the assumptions of permanent full employment and equality of savings and investment with the result that the possibility of fluctuations vanished, and (2) the possibility of a steady and continuous increase in productivity.

Solow was aware that the neoclassical growth model had shunted aside all the rigidi­ties and general (short-run) coordination problems likely to generate cyclical growth. In 1956, he expressed an interest in such questions, saying that “It is not my contention that these problems don’t exist, nor that they are of no significance in the long run” (Solow 1956: 91; see also Hagemann 2009: 85). Later, he repeatedly tried to find a way to deal with Harrod’s instability problem related to adjustment of the actual and war­ranted growth rates (Assous 2015). He concentrated mainly on finding a way to define a robust investment function capable of explaining the failed expectations of entrepre­neurs who deviated from the equilibrium path. With no adequate fact-based treatment of representing expectations, and no solution to the sensitive problem of valuing durable capital in the context of an uncertain future, Solow doubted that a satisfactory solution was possible (Solow 2012). In his opinion, the dichotomy between cycles and growth analysis was no more than the unsatisfactory outcome of the difficulties faced by econo­mists when dealing with growth and cycles simultaneously.