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Linear-quadratic approximation, external habit and targeting rules. (English) Zbl 1181.91143
Summary: We examine the linear-quadratic approximation of nonlinear dynamic stochastic optimization problems. A discrete-time version of M. J. P. Magill [J. Econ. Theory 15, 211–219 (1977; Zbl 0382.90028)] is generalized to models with forward-looking variables paying special attention to second-order conditions. This is the “large distortions” case in the literature. We apply the approach to monetary policy in a DSGE model with external habit in consumption. We then develop a condition for “target-implementability”, a concept related to “targeting rules”. Finally, we extend the approach to a comparison between cooperative and non-cooperative equilibria in a two-country model and show that the “small distortions” approximation is inappropriate for this exercise.

MSC:
91B51 Dynamic stochastic general equilibrium theory
91A10 Noncooperative games
91A12 Cooperative games
91B66 Multisectoral models in economics
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