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 mod-els. 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 proce-dure 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 prob-lem 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