Abstract:
Dynamic models with inequality constraints pose a challenging prob-
lem for two major reasons: Dynamic Programming techniques often necessitate a
non established differentiability of the value function, while Euler equation based
techniques have problematic or unknown convergence properties. This paper aims
to resolve these two concerns: An \envelope theorem" is presented that establishes
the differentiability of any element in the convergent sequence of approximate value
functions when inequality constraints may bind. As a corollary, convergence of an
iterative procedure on the Euler equation, usually referred to as time iteration, is
ascertained. This procedure turns out to be very convenient from a computational
perspective; dynamic economic problems with inequality constraints can be solved
reliably and extremely e±ciently by exploiting the theoretical insights provided by
the paper.
