Metropolis-Hastings prefetching algorithms

Prefetching is a simple and general method for single-chain parallelisation of the Metropolis-Hastings algorithm based on the idea of evaluating the posterior in parallel and ahead of time. In this paper improved Metropolis-Hastings prefetching algorithms are presented and evaluated. It is shown how to use available information to make better predictions of the future states of the chain and increase the efficiency of prefetching considerably. The optimal acceptance rate for the prefetching random walk Metropolis-Hastings algorithm is obtained for a special case and it is shown to decrease in the number of processors employed. The performance of the algorithms is illustrated using a well-known macroeconomic model. Bayesian estimation of DSGE models, linearly or nonlinearly approximated, is identified as a potential area of application for prefetching methods. The generality of the proposed method, however, suggests that it could be applied in many other contexts as well.Prefetching; Metropolis-Hastings; Parallel Computing; DSGE models; Optimal acceptance rate

Adaptive hybrid Metropolis-Hastings samplers for DSGE models

Bayesian inference for DSGE models is typically carried out by single block random walk Metropolis, involving very high computing costs. This paper combines two features, adaptive independent Metropolis-Hastings and parallelisation, to achieve large computational gains in DSGE model estimation. The history of the draws is used to continuously improve a t-copula proposal distribution, and an adaptive random walk step is inserted at predetermined intervals to escape difficult points. In linear estimation applications to a medium scale (23 parameters) and a large scale (51 parameters) DSGE model, the computing time per independent draw is reduced by 85% and 65-75% respectively. In a stylised nonlinear estimation example (13 parameters) the reduction is 80%. The sampler is also better suited to parallelisation than random walk Metropolis or blocking strategies, so that the effective computational gains, i.e. the reduction in wall-clock time per independent equivalent draw, can potentially be much larger.Markov Chain Monte Carlo (MCMC); Adaptive Metropolis-Hastings; Parallel algorithm; DSGE model; Copula

Optimal Opportunistic Monetary Policy in A New-Keynesian Model

The present paper compares the performance in terms of second order accurate welfare of opportunistic non-linear Taylor rules and with respect to traditional linear Taylor rules. The macroeconomic model representing the benchmark for the analysis includes capital accumulation (with quadratic costs of adjustment), price rigidities (quadratic approach), along the standard New-Keynesian approach. The model is solved up to second order approximation and welfare is evaluated according to several criteria (conditional to the non-stochastic steady state, unconditional, and according to a linear ad hoc function). The results show that: (i) the opportunistic rule is a Pareto improvement with respect to other monetary policy rules traditionally considered in the literature; (ii) the computation of welfare costs reveals that the burden of adjustment is almost entirely on labor supply fluctuations;(iii) increasing the degree of price rigidities and the degree of competition in the final goods markets, makes the opportunistic rule even more preferable with respect to the alternatives. Business Cycle statistics for the model with opportunistic rule show a large volatility in labor supply, with a limited volatility for the nominal interest rate

Block Kalman filtering for large-scale DSGE models

In this paper block Kalman filters for Dynamic Stochastic General Equilibrium models are presented and evaluated. Our approach is based on the simple idea of writing down the Kalman filter recursions on block form and appropriately sequencing the operations of the prediction step of the algorithm. It is argued that block filtering is the only viable serial algorithmic approach to significantly reduce Kalman filtering time in the context of large DSGE models. For the largest model we evaluate the block filter reduces the computation time by roughly a factor 2. Block filtering compares favourably with the more general method for faster Kalman filtering outlined by Koopman and Durbin (2000) and, furthermore, the two approaches are largely complementaryKalman filter; DSGE model; Bayesian estimation; Computational speed; Algorithm; Fortran; Matlab

Nonlinearity in monetary policy: A reconsideration of the opportunistic approach to disinflation

The proponents of the 'opportunistic' approach to disinflation suggest that, when inflation is close to the target, the central bank should not counteract inflationary pressures. Orphanides and Wilcox (2002) formalize this idea through a simple policy rule that prescribes a nonlinear adjustment to a history-dependent target for inflation. This embodies a regime change in monetary policy, which reacts to inflation only when this is far from the inflation target. Here we study the opportunistic approach in a New-Keynesian model with sizeable nominal and real rigidites in the form of a positive money demand and adjustment costs for investment. We find that the welfare gains delivered by the opportunistic rule arise from the time-varying inflation target, when welfare is measured by a quadratic approximation of household utility. The nonlinear zone of inaction on inflation improves welfare outcomes only when a central bank loss function with the absolute value of the output gap is used, as proposed by Orphanides and Wilcox (2002).Disinflation Monetary policy Dynamic models Regime change