This thesis makes three main contributions to the literature on Dynamic Stochastic General Equilibrium (DSGE) models. The first contribution is to bridge the gap between a theoretical small open DSGE model provided by Gali and Monacelli and an empirical model developed by Lubik and Schorfheide, as no previous studies have shown their relationship explicitly. Since all the models suffer from the misspecification problem to some extent, the second contribution is to apply two methodologies including DSGE-VAR approach and indirect inference to study the effect of the possibly misspecified equation of the change rate of terms of trade. The third contribution is to search for the model with the best data fitting in two stages of model comparisons. The thesis assumes that the parameters of the simplified DSGE model are constant at the first stage, and based on the constant parameter models with the best performance on data fitting, it assumes a subset of the parameters including exogenous shock variances and policy parameters follow two independent Markov-switching Markov chains at the second stage.

The empirical results are quite different for the UK and Canada within the sample
period covering 1992: Q4 – 2008: Q4. The UK data supports that the movement
of the nominal exchange rate should not enter into the monetary policy reaction
function. Also, the data supports that it is possible for the UK to experience
the two kinds of structural changes, including the economic environment and the behaviours of policymakers simultaneously. Comparatively, Canadian data is in favour of the movement of the nominal exchange rate in the policy function. Moreover, the data supports that it is less likely for Canada to experience two kinds of structural changes simultaneously.