The Choice of a Growth Path under a Linear Quadratic Approximation

There is a recent strand of literature which suggests that second order approximations of linear quadratic objective functions in the steady state vicinity, namely when assuming stochastic scenarios, lead to very interesting and useful results. For example, applications in monetary policy resort to such technique. In this paper we find that, for a specific optimal control problem under a purely deterministic setup, a second-order approximation of the objective function may lead to inaccurate results, particularly when one considers exogenous variables as arguments of the objective function. These results are related to the stability conditions, which in the present case can be written as constraints to a discount rate associated with future outcomes. We designate the proposed model as an ‘optimal growth control’ model, from which we compute general conditions about stability and analyse the application of such a framework to a fertility–human capital problem.