A Mathematical Approach to Harrod's Open Economy Dynamics

Abstract

This paper investigates an open economy dynamic model in the Harrod tradition. Its goal is to check if in accordance with Harrod's thought, opening to foreign trade is able to reduce the cyclical instability the economic system exhibits when it is closed to the international trade. We show that the system's dynamic behavior depends on changes in the saving rate, the competitiveness of home products in the foreign markets and the initial sign of the balance of trade. We demonstrate that stable cycles are possible only under particular conditions. Otherwise, the economy may experience chaotic motions in the long period.

An Empirical Test on Harrod’s Open Economy Dynamics

“…However, with calibrations 2 and 3, we displayed sub-optimal results to provide a context for our results. In fact, qualitatively, we obtain similar values to the ones in [34]. Moreover we concur with this conclusion "when the value of is large enough, the long period dynamics of the saving rate is such that it can generate an irregular cycle in the system only if the net export rate is very low.…”

“…Since the problem is not convex, the optimization algorithm may converge to a local optimal solution. To better explore the space of the optimal solutions, we introduce a multi-start algorithm: the optimization is then run several times starting from a randomly perturbed sample draft from a distribution centred in the parameter setting provided in [34]. Original data as provided in [34] and calibrations.Ḡ = max G n .…”

“…However for Yoshida the instability derives from a putty-clay technology in conjunction with flexibility of prices, while for Sportelli the instability derives from the gaps between Harrod's rates of growth: actual, warranted and natural. Further, it has been shown that in that framework [34] opening to foreign trade can lead to reducing cyclical instability of the economy as Harrod suggested.…”

“…Finally Yoshida (1999) [32] and Sportelli (2001) [33,34], from the 1990s Harrod's Dynamics offered a theoretical framework to explain jointly economic growth and business cycles through the Harrod's "instability principle". However for Yoshida the instability derives from a putty-clay technology in conjunction with flexibility of prices, while for Sportelli the instability derives from the gaps between Harrod's rates of growth: actual, warranted and natural.…”

“…In those specific conditions regular cycles in the long period can be achieved. From now onwards the notation we are going to use is: As in [34] we assume that:…”