Essays in dynamic stochastic general equilibrium models

The first chapter develops a two-country DSGE model with heterogeneous firms and endogenous export participation, consistent with firm-level facts on international trade documented in various studies. The endogenous tradeability feature of the model provides a new additional channel for the transmission of monetary shocks. The model predicts that under financial autarky and balanced trade, endogenous export participation magnifies the real exchange rate volatility when producer-currency pricing is assumed. Under local-currency pricing, the volatility is dampened. The contrasting responses of the change in relative availability of varieties across countries (extensive margin) following monetary shocks provide the exhibited results. These variations in the relative set of available varieties serve to modify the extent of expenditure switching, which importantly affects the real exchange rate fluctuations.;The second chapter presents a new approach to computing approximate equilibria for nonlinear Rational Expectations models. Unlike the standard approach in the literature, we deduce restrictions directly on the stochastic differentials of the approximate equilibrium stochastic processes. We illustrate the approach using second- and third-order approximations. Solutions are shown to be in state-space form, which makes for a direct impulse-response computation. The approach also extends existing methods to accommodate state-dependent responses and endogenous time-varying uncertainty. Extensions to any order of approximation are direct.;The third chapter concerns the analysis of optimal monetary policy in a state-dependent pricing (SDP) environment. As is common from the public finance literature, monetary policy in the model operates through its influence on the variations in the distortions in the economy. In terms of the solution methodology, the chapter also characterizes the optimal monetary policy solution using the second-order approximation technique presented in the second chapter, in addition to the standard linear approximate solution. We find that the optimal policy under SDP is to closely replicate the optimal dynamics under TDP assumption. This conclusion holds for both under the 1st- and 2nd-order approximate solutions. In terms of the start-up problem, despite of the still existence of the incentive to generate surprise inflation, the ability of the monetary authority to erode average markup is more limited under SDP.