Time-Consistent Control in Non-Linear Models

This paper shows how to use optimal control theory to derive time-consistent optimal government policies in nonlinear dynamic general equilibrium models. It extends the insight of Cohen and Michel (1988), who showed that in linear models time-consistent policies can be found by imposing a linear relationship between predetermined state variables and the costate variables from private agents’ maximization problems. We use an analogous procedure based on the Den Haan and Marcet (1990) technique of parameterized expectations, which replaces nonlinear functions of expected future costates by flexible functions of current states. This leads to a nonlinear relationship between current state and costate variables, which is verified in equilibrium to an arbitrarily close degree of approximation. The optimal control problem of the government is recursive, unlike the Ramsey (1927) problem which is common in the optimal taxation literature. We use a model of public investment to illustrate the technique.