ECONOMICS 916 WINTER 2007
ADVANCED TOPICS IN APPLIED MACROECONOMICS II
C. FERRALL

Assignment 2.0
Integration, Simulation and Approximation

Introduction

Reference: Consumption over the Life Cycle, by Pierre-Olivier Gourinchas and Jonathan A. Parker Econometrica, Vol. 70, No. 1. (Jan., 2002), pp. 47-89, available from JSTOR. See also Adda and Cooper (6.3.6, pp 160-4) for a summary. Your job is to develop code to solve the Euler equation in GP. Namely, given period t+1 consumption and current cash x, solve the following for current consumption:


See equation (6) for the terminal conditions on cash at the end of the lifecycle.

Preparation

Develop an Ox program to solve this problem. Try to practice modular programming, but only to the extent that you are comfortable with Ox syntax. The outer program should initialize parameters of the problem and then call routine to solve the problem. At first this routine might do nothing. Eventually it has to loop backwards in t computing consumption conditional on state x and future values. This is done by solving the equation above. Again, at first this routine might compute the right hand side of (16) as if there was no uncertainty (CEQ-LCH in the paper). Then introduce uncertainty in one variable and then another.

Analysis

1. Integration
   1. Following the authors, use Gauss-Hermite Quadratures. Replicate the basic patterns reported in the paper for a particular problem (a particular set of parameters from Tables I and II).
   2. Next, use Monte Carlo integration to do the same thing.
   3. Finally, use quasi-Monte Carlo to do the same thing.
   Write your code so that you can choose the method of integration and vary the parameters that determine precision (at least for the last two techniques).
2. Simulation
   Simulate your model following the method in the paper. (detailed instructions to follow.)
3. Approximation
   Would like to suggest exploration of an approach to solving the model not using Euler equations. But have to think about this more.