This paper is concerned with the Bayesian estimation of non-linear stochastic differential equations when only discrete observations are available. The estimation is carried out using a tuned MCMC method, in particular a blocked Metropolis-Hastings algorithm, by introducing auxiliary points and using the Euler-Maruyama discretisation scheme. Techniques for computing the likelihood function, the marginal likelihood and diagnostic measures (all based on the MCMC output) are presented. Examples using simulated and real data are presented and discussed in detail.

In this paper we estimate a small model of the euro area to be used as a laboratory for evaluating the performance of alternative monetary policy strategies. We start with the relationship between output and inflation and investigate the fit of the nominal wage contracting model due to Taylor (1980)and three different versions of the relative real wage contracting model proposed by Buiter and Jewitt (1981)and estimated by Fuhrer and Moore (1995a) for the United States. While Fuhrer and Moore reject the nominal contracting model in favor of the relative contracting model which induces more inflation persistence, we find that both models fit euro area data reasonably well. When considering France, Germany and Italy separately, however, we find that the nominal contracting model fits German data better, while the relative contracting model does quite well in countries which transitioned out of a high inflation regime such as France and Italy. We close the model by estimating an aggregate demand relationship and investigate the consequences of the different wage contracting specifications for the inflation-output variability tradeoff, when interest rates are set according to Taylor’s rule.

Abstract: This paper uses a simple New Keynesian monetary DSGE model as a prior for a vector autoregression and shows that the resulting model is competitive with standard benchmarks in terms of forecasting and can be used for policy analysis. JEL classification: C11, C32, C53

This paper studies the nature of capital adjustment at the plant-level. We use an indirect inference procedure to estimate the structural parameters of a rich specification of capital adjustment costs. In effect, the parameters are optimally chosen to reproduce

In this paper we will rigourously study some of the properties of continuous time stochastic volatility models. We have five main results: (i) the stochastic volatility class can be linked to Cox process based models of tick-by-tick financial data; (ii) we characterise the moments, autocorrelation function and spectrum of squared returns; (iii) based only on discrete time returns, we give a simple consistent and asymptotically normally distributed estimator of continuous time volatility models without any simulation or discretisation error. Furthermore, we review a new class of Ornstein-Uhlenbeck processes of volatility, introduced in a companion paper, which allows (iv) the discrete time returns to be simulated without any form of discretisation error, (v) explicit modelling of correlation structures and allow analytic calculations of the properties of returns. 1 Contents 1

This paper reviews Bayesian methods that have been developed in recent years to estimate and evaluate dynamic stochastic general equilibrium (DSGE) models. We consider the estimation of linearized DSGE models, the evaluation of models based on Bayesian model checking, posterior odds comparisons, and comparisons to vector autoregressions, as well as the nonlinear estimation based on a second-order accurate model solution. These methods are applied to data generated from correctly specified and misspecified linearized DSGE models, and a DSGE model that was solved with a second-order perturbation method. (JEL C11, C32, C51, C52)

This Guide shows how to use the computer package EMM, which implements the estimator described in "Which Moments to Match," (Gallant and Tauchen, 1996a). The term EMM refers to Efficient Method of Moments. The Guide provides an overview of the estimator, instructions on how to acquire the software, and a description of the package. It also walks the reader through two worked examples, one of which is estimation of a simple stochastic volatility model and the other is estimation of a stochastic differential equation for the short term interest rate. Contents 1 Introduction 1 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 GARCH-SNP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Availability-UNIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.5 Availability-PC . . . . . . . . . . . . . . . . . . . . ...

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This paper provides methods for carrying out likelihood based inference for diffusion driven models, for example discretely observed multivariate diffusions, continuous time stochastic volatility models and counting process models. The diffusions can potentially be nonstationary. Although our methods are sampling based, making use of Markov chain Monte Carlo methods to sample the posterior distribution of the relevant unknowns, our general strategies and details are different from previous work along these lines. The methods we develop are simple to implement and simulation efficient. Importantly, unlike previous methods, the performance of our technique is not worsened, in fact it improves, as the degree of latent augmentation is increased to reduce the bias of the Euler approximation. In addition, our method is not subject to a degeneracy that afflicts previous techniques when the degree of latent augmentation is increased. We also discuss issues of model choice, model checking and filtering. The techniques and ideas are applied to both simulated and real data.

In this paper we propose a Bayesian econometric procedure for the evaluation and comparison of DSGE models. Unlike in many previous econometric approaches we explicitly take into account the possibility that the DSGE mod-els are misspecified and introduce a reference model to complete the model space. Three loss functions are proposed to assess the discrepancy between DSGE model predictions and an overall posterior distribution of population characteristics that the researcher is trying to match. The evaluation proce-dure is applied to the comparison of a standard cash-in-advance (CIA) and a portfolio adjustment cost (PAC) model. We find that the CIA model has higher posterior probability than the PAC model and achieves a better in-sample time series fit. Both models overpredict the magnitude of the negative correlation between output growth and inflation. However, unlike the PAC model, the CIA model is not able to generate a positive real effect of money growth shocks on aggregate output. Overall, the impulse response dynamics of the PAC model resemble the posterior mean impulse response functions more closely than the responses of the CIA model.