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

Multicriteria Analysis of Neural Network Forecasting Models: An Application to German Regional Labour Markets

This paper develops a flexible multi-dimensional assessment method for the comparison of different statistical-econometric techniques based on learning mechanisms with a view to analysing and forecasting regional labour markets. The aim of this paper is twofold. A first major objective is to explore the use of a standard choice tool, namely Multicriteria Analysis (MCA), in order to cope with the intrinsic methodological uncertainty on the choice of a suitable statistical-econometric learning technique for regional labour market analysis. MCA is applied here to support choices on the performance of various models -based on classes of Neural Network (NN) techniques-that serve to generate employment forecasts in West Germany at a regional/district level. A second objective of the paper is to analyse the methodological potential of a blend of approaches (NN-MCA) in order to extend the analysis framework to other economic research domains, where formal models are not available, but where a variety of statistical data is present. The paper offers a basis for a more balanced judgement of the performance of rival statistical tests

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

An Evolutionary Algorithm for the Estimation of Threshold Vector Error Correction Models

We develop an evolutionary algorithm to estimate Threshold Vector Error Correction models (TVECM) with more than two cointegrated variables. Since disregarding a threshold in cointegration models renders standard approaches to the estimation of the cointegration vectors inefficient, TVECM necessitate a simultaneous estimation of the cointegration vector(s) and the threshold. As far as two cointegrated variables are considered this is commonly achieved by a grid search. However, grid search quickly becomes computationally unfeasible if more than two variables are cointegrated. Therefore, the likelihood function has to be maximized using heuristic approaches. Depending on the precise problem structure the evolutionary approach developed in the present paper for this purpose saves 90 to 99 per cent of the computation time of a grid search.evolutionary strategy, genetic algorithm, TVECM

Simulation based Bayesian econometric inference: principles and some recent computational advances

In this paper we discuss several aspects of simulation based Bayesian econometric inference. We start at an elementary level on basic concepts of Bayesian analysis; evaluating integrals by simulation methods is a crucial ingredient in Bayesian inference. Next, the most popular and well-known simulation techniques are discussed, the MetropolisHastings algorithm and Gibbs sampling (being the most popular Markov chain Monte Carlo methods) and importance sampling. After that, we discuss two recently developed sampling methods: adaptive radial based direction sampling [ARDS], which makes use of a transformation to radial coordinates, and neural network sampling, which makes use of a neural network approximation to the posterior distribution of interest. Both methods are especially useful in cases where the posterior distribution is not well-behaved, in the sense of having highly non-elliptical shapes. The simulation techniques are illustrated in several example models, such as a model for the real US GNP and models for binary data of a US recession indicator.