This thesis investigates monetary policy within the New Keynesian framework in dynamic macroeconomics. It includes three original research papers. The first paper examines the rules and transmission mechanisms of monetary policy in one of the fast growing economies in the 21st century, China, by extending a standard New Keynesian dynamic stochastic general equilibrium model with financial frictions and investment-specific shocks in order to capture some of the Chinese characteristics and applying a Bayesian estimation strategy to real-time data. It offers a new way of empirically examining the rule of China's monetary policy and indicates a structural break of the neutral technology development that may have caused the slowing down of GDP growth since 2010. The second paper revisits optimal monetary policy in open economies, in particular, focusing on the noncooperative policy game under local currency pricing in a theoretical two-country dynamic stochastic general equilibrium model. Quadratic loss functions of noncooperative policy makers and welfare gains from cooperation are obtained in the paper. The results show that noncooperative policy makers face extra trade-offs regarding stabilizing the real marginal costs induced by deviations from the law of one price under local currency pricing. As a result of the increased number of stabilizing objectives, welfare gains from cooperation emerge even when two countries face only technology shocks, which usually leads to equivalence between cooperation and noncooperation. Still, gains from cooperation are not large, implying that frictions other than nominal rigidities are necessary to strongly recommend cooperation as an important policy framework to increase global welfare. The third paper focuses on the noncooperative policy game specified by choice of policy instrument for implementing optimal monetary policy in a two-country open economy model similar to the one in the second paper. It examines four options of policy instruments including the producer price index inflation rate, the consumer price index inflation rate, the import price inflation rate and the nominal interest rate. It shows that choosing different policy instruments generally leads to different equilibria and, in particular, choosing the nominal interest rate results in equilibrium indeterminacy. In addition, the welfare ranking of these policy instruments depends on a country's degree of openness which is measured as the weight assigned to imported goods in the consumers' utility function. In less open countries, domestically produced goods carry a relatively higher weight in the consumers' utility function. For these less open countries, choosing the producer price index inflation rate induces a larger welfare cost from noncooperation than choosing the consumer price index inflation rate would. Choosing the consumer price index inflation rate in turn causes a larger welfare cost than choosing the import price inflation rate. Conversely, the reverse is true when countries are more open. This result sheds light on the important role that policy instrument choice plays in determining the equilibrium outcomes, to which policy makers should pay special attention when implementing optimal monetary policy under noncooperation.