Linear-Quadratic Approximation, Efficiency and Target-Implementability
Linear-Quadratic Approximation, Efficiency and Target-Implementability
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线性二次近似、效率和目标可实现性
DOI：
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发表时间：
2006
期刊：
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通讯作者：
R. Pierse
中科院分区：
文献类型：
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作者：
P. Levine;J. Pearlman;R. Pierse
我们研究线性二次（LQ）近似的随机动态优化问题在宏观经济学（和其他地方），特别是在政策分析中使用动态随机一般均衡（DSGE）模型。我们首先定义由社会规划者解决的问题，因为后者的目标是最大化平均福利;这产生了有效的解决方案。然后，我们评论的LQ近似的税收或补贴时，可以实施零通货膨胀的竞争性稳态输出水平等于有效水平。然后，我们检查正确的程序，取代随机非线性动态优化问题的线性二次近似。我们发现，Benigno和Woodford（2004）提出的一个程序，在经济中的大的潜在扭曲，可以更容易地实现通过一个二阶近似的汉密尔顿用于计算事先最优政策的承诺（拉姆齐问题）。然后，我们定义了目标可实现性的概念，这也是Ramsey问题的特定稳态最大值的充分条件，并解释了在稳定政策的背景下这一点的有用性
We examine linear-quadratic (LQ) approximation of stochastic dynamic optimization problems in macroeconomics (and elsewhere), in particular in policy analysis using Dynamic Stochastic General Equilibrium (DSGE) models. We first define the problem that is solved by a social planner, given that the objective of the latter is to maximize average welfare; this yields the efficient solution. We then comment on the LQ approximation when a tax or subsidy can be imposed such that the zero-inflation competitive steady state output level is equal to the efficient level. We then examine the correct procedure for replacing a stochastic non-linear dynamic optimization problem with a linear-quadratic approximation. We show that a procedure proposed by Benigno and Woodford (2004) for large underlying distortions in the economy can be more easily implemented through a second-order approximation of the Hamiltonian used to compute the ex ante optimal policy with commitment (the Ramsey problem). We then define the notion of Target-Implementability, which is also a sufficient condition for a particular steady-state maximum of the Ramsey problem, and explain the usefulness of this in the context of stabilization policy