This paper shows how particle filtering facilitates likelihood-based inference in dynamic macroeconomic models. The economies can be non-linear and/or non-normal. We describe how to use the output from the particle filter to estimate the structural parameters of the model, those characterizing preferences and technology, and to compare different economies. Both tasks can be implemented from either a classical or a Bayesian perspective. We illustrate the technique by estimating a business cycle model with investment-specific technological change, preference shocks, and stochastic volatility.

We document five novel facts about the role of search effort in forming trading relationships among firms by combining a variety of micro and macro datasets. These facts strongly suggest the presence of search complementarities. To study the implications of these facts for aggregate fluctuations, we build a dynamic general equilibrium model, disciplined by our new firm-level evidence on search effort. The model matches key aspects of the macro and micro data that have remained unaccounted for by standard models, including the time-varying bimodal distribution of output and the strong, nonlinear propagation of shocks. Also, changes to the volatility of shocks have nonlinear effects on macroeconomic fluctuations that advance a novel interpretation of the Great Moderation. Finally, we provide a new account of the state-dependent effects of fiscal policy.

This article studies the pruned state-space system for higher-order perturbation approximations to dynamic stochastic general equilibrium (DSGE) models. We show the stability of the pruned approximation up to third order and provide closed-form expressions for first and second unconditional moments and impulse response functions. Our results introduce generalized method of moments (GMM) estimation and impulse-response matching for DSGE models approximated up to third order and provide a foundation for indirect inference and simulated method of moments (SMM). As an application,we consider a New Keynesian model with Epstein–Zin preferences and two novel feedback effects from long-term bonds to the real economy, allowing us to match the level and variability of the 10-year term premium in the U.S. with a low relative risk aversion of 5.