The first paper in this thesis deals with the issue of whether there are bubble components in stock prices. This is joint research with Wenjuan Chen (Free Universtiy Berlin). We investigate existing bivariate structural vector autoregressive (SVAR) models and test their identifying restriction by means of a Markov switching (MS) in heteroskedasticity model. We use data from six different countries and find that, for five of the country models, the structural restriction is supported at the 5% level. Accordingly, we label the two structural shocks as fundamental and non-fundamental. This paper illustrates the virtue of being able to test structural restrictions in order to justify the relevant shocks of interest. The second paper proceeds in the spirit if the first paper. In particular, five trivariate structural VAR or vector error correction (VEC) versions of the dividend discount model are considered, which are widely used in the literature. A common structural parameter identification scheme is used for all these models, which claims to be able to capture fundamental and non-fundamental shocks to stock prices. A MS-SVAR/SVEC model in heteroskedasticity is used to test this identification scheme. It is found that for two of the five models considered, the structural identification scheme appropriately classifies shocks as being either fundamental or non-fundamental. These are models which use real GDP and real dividends as proxies of real economic activity. The findings are supported by a series of robustness tests. Results of this paper serve as a good guideline when conducting future research in this field. The third thesis paper addresses the question of how sustainable a government's current debt path is by means of a Markov switching Augmented Dickey-Fuller (MS-ADF) model. This model is applied to the debt/GDP series of 16 different countries. Stationarity of this series implies that public debt is on a sustainable path and hence, the government's present value borrowing constraint holds. The MS specification also allows for unit root and explosive states of the debt/GDP process. Two different criteria are used to test the null hypothesis of a unit root in each state. The countries with a sustainable debt path are found to be Finland, Norway, Sweden, Switzerland and the UK. The model indicates that France, Greece, Ireland and Japan have unsustainable debt trajectories. The remaining seven countries, (Argentina, Germany, Iceland, Italy, Portugal, Spain and the US) are all found to have uncertain debt paths. The model is robust to the sample size and number of states used. It is shown that this model is an improvement to existing models investigating this subject.