# Optimal Time-Consistent Fiscal Policy with Finite Lifetimes

I am reading Optimal Time-Consistent Fiscal Policy with Finite Lifetimes by Calvo and Obstfeld.

Here is the paper :

Calvo and Obstfeld (1988)

In fact, their model consists of two stages. In the first part, there is an OLG model with individuals who have an individual discount factor (the same individual discount rate for all individuals). After, once the OLG is solved (consumption distributed optimally in a static way), the model reduces to a standard agent model.

There is a sentence that I can not understand on the page 418 of the paper

Notice that the optimal aggregate accumulation path is entirely independent of private time preference

How is this possible? The utility function depends on a parameter $\Phi$ which contains the private time preference (i.e individual discount rate). Then, the steady-state levels will be different with respect to different individual discount rates. It follows that the dynamics of the consumption and capital will depend on the individual discount rate.

• Just a thought. Didn't read the paper. Don't you think that what is independant is the optimality of the path, not the path as such? Something like, the "sum" of optima is not the optimal sum? – keepAlive Jul 17 '18 at 14:50
• Not sure they mean it. – optimal control Jul 17 '18 at 17:36