This dissertation explores modeling existing nonlinear dynamics in exchange rates and economic growth. Particularly, the three essays, herein, investigate the stability of the International Monetary Fund's Special Drawing Rights (SDR) and synchronicity of economic growth across provinces in China. The first essay empirically assesses the degree of fluctuations in the SDRs attributable to U.S monetary policy. In this vein, I contribute to the financial asset/exchange rate literature by identifying structural shocks to real-time U.S. output growth, inflation, and short-term interest rates. Moreover, I exploit the time-varying heteroskedasticity of the data without imposing a priori exclusion restrictions. Over the period 1981.Q1-2018.Q1, a contractionary U.S. monetary policy shock results in an immediate depreciation of the U.S. dollar value of the euro, Yen, and pound in the SDR basket. After the introduction of French and German Euros in 1999.Q1, all the currencies appreciated against the USD. Also, U.S. monetary policy contributes about 4% of the variations in the SDR basket's return. Chapter 2, explores the effects of U.S. monetary policy shocks on the value of SDRs during the 1981.M1 – 1998.M12 and 1999.M1 – 2016.M9 vintages. Unlike the first chapter, we test the data against different monetary policy indicators presented in the macroeconomics literature. To this end, we use a structural vector autoregression with identification through heteroskedasticity to identify the appropriate instruments of monetary policy. We find that the nominal exchange rates are insulated from U.S. policy shocks— the contribution does not exceed 15%. In both subsamples, policy easing induces an appreciation in the dollar. In the third chapter, we use a dynamic factor model with time-varying loading parameters and stochastic volatility to document significant evidence of time-varying synchronization of the regional growth dynamics in China. The correlation in cross-region economic growth performance increased during the recent global recession and declined post-recession, albeit still at a higher level than before 2008. While the large degree of synchronization of regional growth dynamics permits the central government (bank) to implement a uniform fiscal (monetary) policy, this also reduces China's ability to stymie the propagation of external shocks and instead increases systemic risks across regions.