Anticipated Shocks in Continuous-time Optimization Models: Theoretical Investigation and Numerical Solution

We derive the well-known continuity principle for adjoint variables for preannounced or anticipated changes in parameters for continuous-time, infinite-horizon, perfect foresight optimization models. For easy and intuitive numerical computation of the resulting multi point boundary value problem we suggested to simulate the resulting differential algebraic system representing the first order conditions. By ensuring that the state variables and the adjoint variables are continuous, potential jumps in the control variables are calculated automatically. This can be easily conducted with the relaxation algorithm as proposed by Trimborn et al. (2007). We solve a Ramsey model extended by an elementary Government sector numerically. Simulations of a preannounced increase in the consumption tax show a qualitative different pattern depending on the intertemporal elasticity of substitution.