A two-stroke growth cycle model for a small open economy

The Hicksian multiplier–accelerator model with a floor and/or a ceiling stands as one of the most successful representations of the economy capable of generating endogenous business cycles. In the present paper, we take some of the main insights of this literature as starting points to develop a continuous-time growth-cycle model for a small open economy. Our main innovation lies in assuming that capital accumulation is constrained only from above by the growth rate compatible with equilibrium in the balance-of-payments, i.e. the dynamic Harrod trade multiplier. It is shown that the obtained piecewise second order differential equation is a so-called two-stroke oscillator. Conditions under which the model produces periodic or aperiodic trajectories are studied analytically and through numerical simulations. An initial assessment of the statistical properties of the time-series indicates that they exhibit high kurtosis and negative skewness.