NONLINEAR BUSINESS CYCLE MODELLING

Abstract. Literature which employs nonlinearities to explain economic fluctuations, commonly called business cycles, is surveyed. Relaxation of the linearity assumption significantly increases the range of possible dynamic solution paths and introduces the possibility that business cycles are endogenously determined. The dominant post‐war modelling strategy has been the Frisch (1933) (and Slutsky, 1937) inspired one of developing essentially (log) linear economic models which produce damped cycles (or monotonic damping) to propagate the energy provided by repeated random (or autocorrelated) shocks. The cycle is exogenously driven, since it would die out in the absence of shocks. Deterministic (nonstochastic) nonlinear models can produce a wide range of endogenous fluctuations, including: stable limit cycles; growth cycles; and chaotic output, which have the appearance of random fluctuations. Further, the same model can produce qualitatively different outputs according to starting and parameter values. If the possibility of shocks to parameters is admitted, then behaviour can change abruptly following shocks. Evidence on the existence of nonlinearities and chaos in macroeconomic time series is assessed and alternative approaches to modelling dynamic economic development, related to the work of Keynes, Marx, Schumpeter and Shackle, are discussed. Their ideas have not proved readily amenable to mathematical modelling, but attempts to encapsulate some of them are reviewed.