Several formal methods have been proposed to check local identification in linearized DSGE models using rank criteria. Recently there has been huge progress in the estimation of non-linear DSGE models, yet formal identification criteria are missing. The contribution of the paper is threefold: First, we extend the existent methods to higher-order approximations and establish rank criteria for local identification given the pruned state-space representation. It is shown that this may improve overall identification of a DSGE model via imposing additional restrictions on the moments and spectrum. Second, we derive analytical derivatives of the reduced-form matrices, unconditional moments and spectral density for the pruned state-space system. Third, using a second-order approximation, we are able to identify previously non-identifiable parameters: namely the parameters governing the investment adjustment costs in the Kim (2003) model and all parameters in the An and Schorfheide (2007) model, including the coefficients of the Taylor-rule.

This paper studies the pruned state-space system for higher-order approximations to the solutions of DSGE models. For second- and third-order approximations, we derive the statistical properties of this system and provide closed-form expressions for first and second unconditional moments and impulse response functions. Thus, our analysis introduces GMM estimation for DSGE models approximated up to third-order and provides the foundation for indirect inference and SMM when simulation is required. We illustrate the usefulness of our approach by estimating a New Keynesian model with habits and Epstein-Zin preferences by GMM when using first and second unconditional moments of macroeconomic and financial data and by SMM when using additional third and fourth unconditional moments and non-Gaussian innovations.

This paper develops a novel approach for estimating latent state variables of Dynamic Stochastic General Equilibrium (DSGE) models that are solved using a second-order accurate approximation. I apply the Kalman filter to a state-space representation of the second-order solution based on the 'pruning' scheme of Kim, Kim, Schaumburg and Sims (2008). By contrast to particle filters, no stochastic simulations are needed for the filter here -- the present method is thus much faster. In Monte Carlo experiments, the filter here generates more accurate estimates of latent state variables than the standard particle filter. The present filter is also more accurate than a conventional Kalman filter that treats the linearized model as the true data generating process. Due to its high speed, the filter presented here is suited for the estimation of model parameters; a quasimaximum likelihood procedure can be used for that purpose.

We study how structural parameter variations affect the decision rules and economic inference. We provide diagnostics to detect parameter variations and to ascertain whether they are exogenous or endogenous. A constant parameter model poorly approximates a time-varying data generating process (DGP), except in a handful of relevant cases. Linear approximations do not produce time-varying decision rules; higher-order approximations can do this only if parameter disturbances are treated as decision rule coefficients. Structural responses are time invariant regardless of order of approximation. Adding endogenous variations to the parameter controlling leverage in Gertler and Karadi's model substantially improves the fit of the model.

The book provides a comprehensive overview of the latest econometric methods for studying the dynamics of macroeconomic and financial time series. It examines alternative methodological approaches and concepts, including quantile spectra and co-spectra, and explores topics such as non-linear and non-stationary behavior, stochastic volatility models, and the econometrics of commodity markets and globalization. Furthermore, it demonstrates the application of recent techniques in various fields: in the frequency domain, in the analysis of persistent dynamics, in the estimation of state space models and new classes of volatility models. The book is divided into two parts: The first part applies econometrics to the field of macroeconomics, discussing trend/cycle decomposition, growth analysis, monetary policy and international trade. The second part applies econometrics to a wide range of topics in financial economics, including price dynamics in equity, commodity and foreign exchange markets and portfolio analysis. The book is essential reading for scholars, students, and practitioners in government and financial institutions interested in applying recent econometric time series methods to financial and economic data.

This text aims to provide a survey of the state of knowledge in the broad area that includes the theories and facts of economic growth and economic fluctuations, as well as the consequences of monetary and fiscal policies for general economic conditions.