An Open-Economy Ramsey-Cass-Koopmans Model in Reduced Form

What is a good reduced-form representation of Ramsey-Cass-Koopmans. (RCK) model? Solow’s model (despite non-optimizing agents) provides predictions largely consistent with a closed-economy RCK but fundamentally differs regarding open-economy income convergence. Where RCK predicts partial income and consumption convergence between open economies Solow predicts full convergence. This paper presents, by a small modification of the savings behavior in the Solow model, a framework that matches RCK’s properties in closed and open economies. The model, labeled rSolow, is analytically tractable, allowing closed-form solutions of all variables, thus makes several explicit and novel predictions. This includes how income and inequality depend on country size; that income growth will be a U-shaped function of initial income thus creating differentiated convergence; and that poor countries bene.t from higher saving but rich countries may not.