02559cam a22003137 4500001000700000003000500007005001700012006001900029007001500048008004100063100002400104245010200128260006600230300005700296490004200353500001900395520119700414530006001611538007201671538003601743588002501779690012301804690010101927700002302028710004202051830007702093856003802170856003702208w12672NBER20200119035506.0m o d cr cnu||||||||200119s2006 mau fo 000 0 eng d1 aBenigno, Pierpaolo.10aLinear-Quadratic Approximation of Optimal Policy Problems /cPierpaolo Benigno, Michael Woodford. aCambridge, Mass.bNational Bureau of Economic Researchc2006. a1 online resource:billustrations (black and white);1 aNBER working paper seriesvno. w12672 aNovember 2006.3 aWe 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. aHardcopy version available to institutional subscribers aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web.0 aPrint version record 7aC61 - Optimization Techniques • Programming Models • Dynamic Analysis2Journal of Economic Literature class. 7aC63 - Computational Techniques • Simulation Modeling2Journal of Economic Literature class.1 aWoodford, Michael.2 aNational Bureau of Economic Research. 0aWorking Paper Series (National Bureau of Economic Research)vno. w12672.40uhttp://www.nber.org/papers/w1267240uhttp://dx.doi.org/10.3386/w12672