This thesis contains three chapters, each addressing a highly relevant area of interest in modern macroeconomics. The first chapter tests the presence of state-dependent pricing frictions by analysing the effects of monetary policy during high inflation and after large monetary shocks. The second chapter focuses on the interaction of heterogeneity in firm potential with financial frictions and its effect on macroeconomic outcomes. The final chapter presents a global solution method for heterogeneous agent models that can handle interesting and relevent extensions to the standard setting.