We analyse some practical aspects of implementing adaptive learning in the context of forward-looking linear models. In particular, we focus on how to set initial conditions for three popular algorithms, namely recursive least squares, stochastic gradient and constant gain learning. We propose...

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,...

We examine a two country model of the EU and the US. Each has a small sector of the labour and product markets in which there is wage/price rigidity, but otherwise enjoys flexible wages and prices with a one quarter information lag. Using a VAR to represent the data, we find the model as a whole...

Using Monte Carlo experiments, we examine the performance of indirect inference tests of DSGE models in small samples, using various models in widespread use. We compare these with tests based on direct inference (using the Likelihood Ratio). We find that both tests have power so that a...

We extend the method of indirect inference testing to data that is not filtered and so may be non-stationary. We apply the method to an open economy real businss cycle model on UK data. We review the method using a Monte Carlo experiment and find that it performs accurately and has good power.

Vector autoregressions (VARs) are flexible time series models that can capture complex dynamic interrelationships among macroeconomic variables. However, their dense parameterization leads to unstable inference and inaccurate out-of-sample forecasts, particularly for models with many variables....

This paper derives the asymptotic distribution for a number of rank-based and classical residual specification tests in AR-GARCH type models. We consider tests for the null hypotheses of no linear and quadratic serial residual autocorrelation, residual symmetry, and no structural breaks. For...

Using Monte Carlo experiments, we examine the performance of Indirect Inference tests of DSGE models, usually versions of the Smets-Wouters New Keynesian model of the US postwar period. We compare these with tests based on direct inference (using the Likelihood Ratio), and on the Del...

A researcher is interested in a set of variables that he wants to model with a vector autoregression and he has a dataset with more variables. Which variables from the dataset to include in the VAR, in addition to the variables of interest? This question arises in many applications of VARs, in...

Many users of structural VAR models are primarily interested in learning about the shape of structural impulse response functions. This requires joint inference about sets of structural impulse responses, allowing for dependencies across time as well as across response functions. Such joint...