Computing Transitional Cycles for a Deterministic Time-to-Build Growth Model

Capital investment requires a gestation lag for being productive. This time-to-build feature can lead to an autonomous system of mixed-type functional differential equations (FDEs), causing aggregate fluctuations for a deterministic economy. We present a continuation method to solve a system of mixed FDEs by solving a sequence of boundary value problems for systems of ordinary differential equations (ODEs). Unlike other iteration techniques, this method can avoid the need to predetermine both forward-looking and backward-looking difference terms. The strategy is to form a homotopy that can deform a simpler ODE system into a target FDE system, while treating the deformation process as a sequence of ODEs. We can thereby compute oscillatory cycles for a time-to-build economy while it is in transition to the steady state.