On a Generalization of Tinbergen's Condition in the Theory of Policy to Dynamic Models

[5]. Recently, a problem of achieving designated target values in dynamic context has been analysed by Preston as a dynamic generalization of Tinbergen's conditions. He pointed out among other things, using the controllability condition of dynamic systems, that the number of instruments could be less than the number of target variables in achieving target variables at a point in time [4]. In practice, policy makers would be interested in not only achieving desired target values but also keeping them on some desired time trajectories once achieved.3 For example, they would be interested not only in achieving a certain inflation rate or level of foreign reserves but also in keeping them at some designated levels or changing them with time in some prescribed manner. This type of target variable manipulation requires more than the condition that dynamic systems are controllable. Since it is important that instruments have this added capability and since this aspect has not been covered in [4], it is the purpose of this note to describe the conditions for policy makers to be able to make the target variables follow desired time trajectories (including stationary values). This turns out to contain the original Tinbergen condition. Thus it may be considered to be a more proper dynamic generalization of Tinbergen's theory of policy. We consider economic models described by differential equations and give conditions for constant (time-invariant) linear economic models in Section 2.4 Under suitable conditions the local behaviour of non-linear economic models can be deduced from the corresponding linear ones. This is described in Section 3.