The paper establishes a quasi-Bayesian local likelihood (QBLL) estimation methodology for a multivariate model with time varying parameters. The asymptotic validity of the resulting quasiposterior distributions of the drifting parameters is proven in general and, in the special case of a Gaussian VAR model, a closed form time varying Normal-Wishart expression for the quasiposterior distribution of the parameters is provided. In addition, this paper develops several Gibbs algorithms, which can sample from a VAR model with a mixture of time varying and time invariant parameters. The proposed estimators di¤er from existing state space approaches to VAR models in that they estimate parameter time variation nonparametrically, without imposing parametric stochastic processes on the parameters. The QBLL estimators are robust to misspeci…cation of the state equation and exhibit good …nite sample performance, even when compared to correctly speci…ed parametric state space models, as illustrated by a Monte Carlo exercise. In addition, we demonstrate that the QBLL approach provides a remedy to the 'curse of dimensionality'by accommodating large dimensional VAR systems and delivers improvements in the out-of-sample forecasts of key macroeconomic variables. Finally, the paper makes an empirical contribution to the literature on changing in ‡ation dynamics in the U.S., presenting evidence of a fall in in ‡ation persistence and volatility during the Great Moderation period.

We build a time varying DSGE model with …nancial frictions in order to evaluate changes in the responses of the macroeconomy to …nancial friction shocks. Using US data, we …nd that the transmission of the …nancial friction shock to economic variables, such as output growth, has not changed in the last 30 years. The volatility of the …nancial friction shock, however, has changed, so that output responses to a one-standard deviation of the shock increase twofold in JEL codes: C11, C53, E27, E52

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We estimate a time-varying parameter structural macroeconomic model of the UK economy, using a Bayesian local likelihood methodology. This enables us to estimate a large open-economy DSGE model over a sample that comprises several di¤erent monetary policy regimes and an incomplete set of data. Our estimation identi…es a gradual shift to a monetary policy regime characterised by an increased responsiveness of policy towards in ‡ation alongside a decrease in the in ‡ation trend down to the two percent target level. The time-varying model also performs remarkably well in forecasting and delivers statistically signi…cant accuracy improvements for most variables and horizons for both point and density forecasts compared to the standard …xed-parameter version.