We develop an algorithm to construct approximate decision rules that are piecewise-linear and continuous for DSGE models with an occasionally-binding constraint. The functional form of the decision rules allows us to derive a conditionally optimal particle filter (COPF) for the evaluation of the likelihood function that exploits the structure of the solution. We document the accuracy of the likelihood approximation and embed it into a particle Markov chain Monte Carlo algorithm to conduct Bayesian estimation. Compared with a standard bootstrap particle filter, the COPF significantly reduces the persistence of the Markov chain, improves the accuracy of Monte Carlo approximations of posterior moments, and drastically speeds up computations. We use the techniques to estimate a small-scale DSGE model to assess the effects of the government spending portion of the American Recovery and Reinvestment Act in 2009 when interest rates reached the zero lower bound.

我们开发了一种算法来构建近似决策规则，这些规则对于具有偶尔绑定约束的 DSGE 模型是分段线性和连续的。决策规则的函数形式允许我们推导出条件最优粒子滤波器 (COPF)，用于评估利用解决方案结构的似然函数。我们记录了似然近似的准确性，并将其嵌入到粒子马尔可夫链蒙特卡罗算法中以进行贝叶斯估计。与标准自举粒子滤波器相比，COPF 显着降低了马尔可夫链的持久性，提高了后验蒙特卡罗近似的准确性，并大大加快了计算速度。