A life-cycle overlapping-generations model of the small open economy: Mathematical appendix

In this paper we construct an overlapping generations model for the small open economy incorporating a realistic description of the mortality process. With age-dependent mortal-ity, the typical life-cycle pattern of consumption and saving results from the maximizing behaviour of individual households. Our “Blanchard-Yaari-Modigliani ” model is used to analytically study a number of typical shocks affecting the small open economy, namely a balanced-budget public spending shock, a temporary Ricardian tax cut, and an interest rate shock. The demographic details matter a lot—both the impulse-response functions and the welfare profiles (associated with the different shocks) are critically affected by them. These demographic details furthermore do not wash out in the aggregate. The model is flexible and can be applied to a wide variety of theoretical and policy issues