TY - JOUR
AU - Benigno, Pierpaolo
AU - Woodford, Michael
TI - Linear-Quadratic Approximation of Optimal Policy Problems
JF - National Bureau of Economic Research Working Paper Series
VL - No. 12672
PY - 2006
Y2 - November 2006
DO - 10.3386/w12672
UR - http://www.nber.org/papers/w12672
L1 - http://www.nber.org/papers/w12672.pdf
N1 - Author contact info:
Pierpaolo Benigno
Dipartimento di Economia e Finanza
Luiss Guido Carli
Viale Romania 32
00197 Rome
ITALY
Tel: 39-0685225-552
E-Mail: pbenigno@luiss.it
Michael Woodford
Department of Economics
Columbia University
420 W. 118th Street
New York, NY 10027
Tel: 212/854-1094
Fax: 212-854-8059
E-Mail: mw2230@columbia.edu
AB - We consider a general class of nonlinear optimal policy problems involving forward-looking constraints (such as the Euler equations that are typically present as structural equations in DSGE models), and show that it is possible, under regularity conditions that are straightforward to check, to derive a problem with linear constraints and a quadratic objective that approximates the exact problem. The LQ approximate problem is computationally simple to solve, even in the case of moderately large state spaces and flexibly parameterized disturbance processes, and its solution represents a local linear approximation to the optimal policy for the exact model in the case that stochastic disturbances are small enough. We derive the second-order conditions that must be satisfied in order for the LQ problem to have a solution, and show that these are stronger, in general, than those required for LQ problems without forward-looking constraints. We also show how the same linear approximations to the model structural equations and quadratic approximation to the exact welfare measure can be used to correctly rank alternative simple policy rules, again in the case of small enough shocks.
ER -