This thesis extends the framework developed by Psaradakis et al. (2005) for the analysis of Markov switching Granger causality in three different ways. In the first chapter, the bivariate VAR setting is extended to a trivariate one to provide a comprehensive account of the evolution of macroeconomic causal relationships of the monetary rules and map the direction of causality associated with Federal Reserve chairs’ tenures since 1965. While the Federal Funds rate (FFR) or Domestic Money (DM) have causal predictive content to explain variations in real output and inflation in most periods, this chapter demonstrates that these are often substitutes in their role as lead or feedback variables. Estimated shifts in smoothed regime probabilities align remarkably well with monetary policy shock dates as identified by Romer and Romer (1989, 1994, 2004). In the second chapter, flexible likelihood functions suitable in the analysis of financial time series are considered. The chapter contributes to the analysis of the causal relationship between sovereign bond and stock markets in three ways. First, the exact dates when there are shifts in the causality are found. Second, although the markets are very integrated, the chapter provides evidence that a global (or regional) crisis affects the countries asymmetrically. Finally, the results indicate that economic events, whether they are global or country specific, can trigger reversals in the causality between these two variables. The third chapter incorporates time-varying volatility into the analysis of Markov switching causality. The extended model is applied to a monetary aggregate and Federal Funds rate, in the search of the so called Liquidity Effect. The impulse responses functions are computed and conditional on a particular regime. Based on these impulse responses, it is possible to conclude that the Liquidity Effect is present in domestic money but not in the currency component of M1, even if the vector autoregression is conditioned on inflation.