Piecewise-linear approximations and filtering for DSGE models with occasionally-binding constraints

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