Economics

The SEM approach - basic elements - Building a SEM The role of theory and statistics: VARDL form - Identification issues Order and rank conditions for identification - Estimation and model evaluation Limited information methods and full information methods Measures of fit, within and out-of-sample - Forecasting and policy simulation Static v. dynamic simulation - Applications Setting-up, estimating and simulating a small-scale open economy SEM - Discussion The SEM approach and its main drawbacks: the Lucas critique and the Sims critique. Two directions in quantitative macroeconometric methods: structural VARs and DSGE models Structural VARs - Vector Moving Average (VMA) representation of a VAR Impulse Response Function (IRF) Forecast Error Variance Decomposition (FEVD) - Identification strategies for stationary VARs Cholesky decomposition A-B model (Amisano and Giannini, 1992) Long-run exclusion restrictions approach (Blanchard and Quah, 1989) - Identification strategies for nonstationary CI-VARs: The structural VEC representation (SVEC) and its MA representation Common Trends approach (CTs): (King, Plosser, Stock and Watson, 1991) - Further issues VAR identification and instrumental variables (Shapiro and Watson, 1989) Sign restrictions Time-varying coefficients SVARs - basic elements Markov-switching SVARs - basic elements - Applications Identifying fiscal policy shocks using contemporaneous restrictions (Blanchard and Perotti, 2002) Identifying technology shocks using long-run restrictions (Blanchard and Quah, 1989) Identifying technology shocks using long-run and contemporaneous restrictions (CT approach) - Discussion SEMs and SVARs: how big are the differences? DSGE modelling, solution and estimation - Solving and simulating DSGE models Decision rules and behavioral equations for baseline RBC and monetary models The nonlinear system of expectational difference equations Equilibrium characterization Linearization: Taylor series expansions and logaritmic approximations Solution methods for the linearized system: Blanchard and Kahn's method; Sims' method; Klein's method Solution of nonlinear systems with REs: the deterministic case and the stacked Newton's method Calibration and simulation - Estimation: limited information methods The Generalized Method of Moments (GMM) The Simulated Method of Moments (SMM) estimator, Impulse Response Matching (IRM) Indirect inference - Estimation: full information methods Maximum-Likelihood estimation and the Kalman filter (unconstrained and constrained FIML) Bayesian Monte Carlo Markov Chain (MCMC) estimation: Gibbs sampler and the Metropolis-Hastings (MH) algorithm - Applications GMM estimation Calibrating a DSGE model via SMM and IRM Full system Estimation: constrained FIML and Bayesian MCMC estimation (MH) - Discussion SEMs, SVARs and DSGEs: again on the role of theory in macroeconomic modelling

Students participating to the classes should be familiar with post-grad level topics in macroeconomics, statistics and matematics. Knowledge of the following topics in univariate and multivariate time series analysis can speed-up the learning process: - Univariate time series Stationary and non-stationary univariate stochastic processes: finite sample properties Identifying the stochastic process: autocorrelation, partial autocorrelation functions (ACF, PACF) and spectral density; testing the order of integration of a series: DF-ADF, Phillips-Perron and KPSS tests ARMA and ARIMA models Structural breaks, near nonstationarity and estimation biases - Multivariate stochastic processes: VARs for stationary time series Vector generalisation of the AR representation: the unrestricted VAR Deterministic components and lag structure of the VAR: exclusion tests, residual analysis, and Bayesian Information Criteria Granger Causality and the VAR - Models for non-stationary time series: Cointegration (CI) and Error-Correction (EC) representation CI as a long-term statistical equilibrium: Granger Representation Theorem and EC The bivariate case: the Engle-Granger (1987) two-stage approach and the Pesaran et al. (1995) ARDL-based approach Vector-EC (VEC) representation and multiple CI: Johansen's max eigenvalue and trace tests Observational equivalence and the "Statistical" vs. "theoretical" identification of the CI space

SEM - Johnston and Di Nardo (1996). Econometric Methods IV edition. McGraw-Hill. ch. 9.4, 9.5 and 9.6. SVAR - Lutkepohl, H. and Kratzig, M., (2004). Applied Time Series Econometrics, Cambridge, Cambridge University Press. ch. 4. TV/MS-SVAR - Canova, F. (2005). Methods for Applied Macroeconomic Research. Princeton University Press. ch. 10.4 and 11.3. DSGE - DeJong, D. and Dave, C. (2007). Structural Macroeconometrics. Princeton University Press. ch. 2, ch. 4.3, ch. 5, ch. 6, ch. 7, ch. 8, ch. 9. DSGE - Mancini Griffoli, T. Dynare User Guide (2007) - Dynare v4, 2013. Further readings and material will be distributed during the lessons. Econometric/math packages E-views JMulTi SVAR, Malcolm for RATS Dynare-Matlab.

Attendance is recommended but not mandatory. However, it is strongly advised to attend classes to fully grasp the course content and adequately prepare for the exam.

The evaluation is based on a written exam and two small research projects, in which students are required to set up original analyses or replicate those found in relevant literature. The two research projects will address topics in SEM (small team-work project), VAR, and DSGE modeling (individual project). The specific topics are chosen under the supervision of the course coordinator.

The classes are held for two hours, two days a week. Approximately 30% of the class time is dedicated to applications using specialized software and the development of specific codes in Matlab.