Survey_Caroll_2005

Abstract

This paper’s key contribution is to introduce an alternative approach that does not require numerical rootfinding. The trick is to begin with end-of-period assets at and to use the end-of-period marginal value function vat , the first order condition, and the budget constraint to construct the unique values of middle-of-period mt generated by those at values. We now have a collection of {?i,?i} pairs in hand and can interpolate as before to generate an approximation to ct. This completes the recursion. The key distinction between this approach and the standard one is that the gridpoints for the policy functions are not predetermined, instead they are endogenously generated from a predetermined grid of values of end-of-period assets (hence the method’s name). One reason the method is efficient is that expectations are never computed for any grid- point not used in the final interpolating function, the standard method may compute expectations for many unused gridpoints. We first specialize to a macroeconomic stochastic growth model. Assuming aggregate production is Cobb-Douglas in capital and labor F(K,P) = K?P1??, after normalizing by productivity P (and assuming a constant value G for the labor productivity growth factor), under the usual assumptions of perfect competition etc. if there is no aggregate transitory shock. In the microeconomic literature, the usual approach is to take aggregate interest and wage rates as exogenous, and to focus on transitory (?) and permanent (?) shocks to idiosyncratic labor productivity. We again start the recursion with cT (m) = m, and the permanent shocks are retained exactly as specified for the macro problem.