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The Choice of a Growth Path under a Linear Quadratic Approximation


  • Orlando Gomes

    (Instituto Politécnico de Lisboa)


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.

Suggested Citation

  • Orlando Gomes, 2005. "The Choice of a Growth Path under a Linear Quadratic Approximation," Notas Económicas, Faculty of Economics, University of Coimbra, issue 22, pages 68-81, December.
  • Handle: RePEc:gmf:journl:y:2005:i:22:p:68-81

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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • J13 - Labor and Demographic Economics - - Demographic Economics - - - Fertility; Family Planning; Child Care; Children; Youth
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models


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