Adv. Time Series and Panel Data

Transcription

1 Overview and Objectives PART 1 (by Marek Jarocinski) Bayesian Vector autoregressions (VARs) are becoming a standard tool both in the academia and in policy institutions. They are useful for forecasting and for structural analysis. This module starts with an introduction to the Bayesian approach to econometrics and then familiarizes students with the theory and practice of Bayesian VARs. Examples from central banking practice are given throughout the course. We explain the standard priors for VARs introduced by Sims, Litterman and their coauthors. We run examples implemented in matlab and in Dynare and discuss applications of Bayesian VARs to forecasting. We discuss density forecasts and define the Marginal Likelihood - the basic ingredient in Bayesian model choice. We interpret the Marginal Likelihood and discuss its relation with out-of-sample density forecasting. We finish with applications of conditional forecasting in policy institutions and, time permitting, optional topics such as other priors for VARs, choice of variables and non-gaussian errors. PART 2 (by Gabriel Pérez-Quirós) Economists from central bankers, large firms, universities, international organizations or government agencies use sophisticated techniques to obtain information about the state of the business cycle from financial and economic data. This course presents the economic motivation, the statistical principles and the practical use of different type of models to analyze the cyclical position of an economy. Understanding this cyclical position is a necessary condition for private agents and policymakers to take optimal decisions and to forecast future developments of the macroeconomic variables. The orientation of this section is mainly applied. We will cover theoretical econometric issues but the main objective of the course is to provide the student with the tools to solve economic questions with the data. Each session starts with the presentation of one or several models, followed by the careful study of some specific applications and the detailed explanation of the computer programs to obtain the results. The typical session implies 1-2 hours of presentation of the techniques, 1-2 hours of presentation of papers and 1-2 hours of the analysis of the computer programs. The papers presented will be replicated in class with the original data, just to make sure that the student understands all the calculations made to obtain the final results. Advanced Time Series and Panel Data 1

2 PART 3 (by Joan Llull) This course provides the basic coverage of the main methods and models used in the econometric analysis of panel and duration data, with empirical applications for macroeconomic policy. We review the main set of tools used for the analysis of panel data, including static and dynamic models, using fixed and random effects approaches. The particular focus of this course is in the context of large cross-sections and short time periods. We also review duration analysis, providing an overview for proportional hazard models both for discrete and continuous time durations. The course is designed for students with an interest in empirical macroeconomic analysis. Course Outline PART 1 1 (by Marek Jarocinski) 1. Introduction to / refreshment of Bayesian econometrics Likelihood, prior, posterior, posterior simulation Linear regression, prior as additional observations Koop (2003, Ch.1), Sims (2002) 2. Bayesian VARs Motivation for the standard priors for VARs Minnesota prior, one-unit-root prior, no-cointegration prior Forecasting examples: Medium size VAR, Large VAR, ECB short-term projections Litterman (1986), Sims and Zha (1998), Sims (2006) Banbura et al. (2010), Giannone et al. (2010) 3. Density forecasts and Bayesian model choice Koop (2003, Ch.1), Geweke (2005) 4. Unconditional vs conditional forecasting. Example: missing disinflation and missing inflation during the Great Recession Waggoner and Zha (1999), Bobeica and Jarocinski (2016) Advanced Time Series and Panel Data 2

3 PART 2 (by Gabriel Pérez-Quirós) Session 0: Review Introduction to programming. Univariate and multivariate standard linear models. ARIMA, VAR, Cointegration and ECM Session 1: Kalman Filter General introduction to unobserved components models. Kalman filter as a linear filter to capture unobserved components. Derivation of the Kalman filter. Estimation of the parameters. Smoothing. Kalman filter with time varying parameters. HP original algorithm. HP as a particular case of the Kalman Filter. HP as a moving average. HP from a frequency domain point of view. Permanent and transitory components of economic time series. Coincident indicators. Output gap. NAIRU estimation Session 2: Nowcasting and real time forecasting Real time analysis as the only option for useful forecasting. Analyzing big and small information sets. Out of sample analysis. GDP forecast, inflation forecast. Session 3: Markov switching models. Intuition and motivation. Derivation of Hamilton filter. Estimation of the parameters. Smoothing. Extensions. Linearity tests. Statistical definitions of economic recessions. Predictability of recessions. Analysis of the New Economy. Financial effects of macroeconomic variables. Session 4. Combinations of Markov Switching and Kalman filter Models. Motivation. Why do we need to combine different techniques? Technical complications. Advanced Time Series and Panel Data 3

4 Third-phase in US GDP cycle. Friedman s plucking model, turning point detection. Multivariate MS models Session 5: Smooth transition regression models. Intuition and motivation. TAR, STAR, LSTAR models. OLS and Maximum likelihood estimations. Linearity tests. Unemployment in the US. STAR models for the US GDP. STAR models in finance. PART 3 (by Joan Llull) Part I. Panel Data 1. Introduction to Panel Data 2. Static Models a) The fixed effects model. Within-groups estimation. b) The random effects model. Error components. c) Applications. 3. Dynamic Models a) Autoregressive models with individual effects. b) Differenced GMM estimation. c) System GMM estimation. d) Applications. Part II. Duration Analysis 1. Introduction 1. Motivation 2. Duration data 2. The Hazard Function 1. Hazard function for a discrete variable 2. Hazard function for a continuous variable 3. Some frequently used hazard functions 3. Conditional Hazard Functions 1. The proportional hazard model 2. Discrete durations 4. Likelihood functions 1. Complete continuous durations 2. Censored continuous durations Advanced Time Series and Panel Data 4

5 3. Discrete durations 5. Unobserved Heterogeneity 1. Unobserved heterogeneity vs spurious state dependence 2. Dealing with heterogeneity in continuous hazard models 6. Multiple-Exit Discrete Duration Models 1. Discrete competing risks models 2. Full information ML 3. Competing risks models Required Activities & Evaluation This course will be evaluated by means of 35% home assignments and 65% final Exam. Materials PART 1 1 (by Marek Jarocinski) Bánbura, M., Giannone, D., and Reichlin, L. (2010). Large Bayesian vector auto regressions. Journal of Applied Econometrics, 25(1):71{92. Geweke, J. (2005). Contemporary Bayesian Econometrics and Statistics. John Wiley and Sons, Hoboken, New Jersey. Giannone, D., Lenza, M., Momferatou, D., and Onorante, L. (2010). Short-term ination projections: A Bayesian vector autoregression approach. CEPR Discussion Paper No Jarocinski, M. and Smets, F. (2008). House prices and the stance of monetary policy. Saint Louis Fed Economic Review, 90(4):339{365. Koop, G. (2003). Bayesian Econometrics. John Wiley and Sons. Litterman, R. B. (1986). Forecasting with Bayesian vector autoregressions- five years of experience. Journal of Business and Economic Statistics,(4):25{38. Sims, C. A. (2002). The role of models and probabilities in the monetary policy process. Brookings Papers on Economic Activity, 2002(2):1{40. Sims, C. A. (2006). Conjugate dummy observation priors for VAR's. lecture notes, df. Sims, C. A. and Zha, T. (1998). Bayesian methods for dynamic multivariate models. International Economic Review, 39(4):949{68. Waggoner, D. F. and Zha, T. (1999). Conditional forecasts in dynamic multivariate models. The Review of Economics and Statistics, 81(4):639{651. PART 2 (by Gabriel Pérez-Quirós) Session 0 Review James Hamilton. Time Series Analysis Princeton. (1994). Chapter 4, 11, 18, 19, Diebold, Francis. Elements of forecasting. Thomson Chapter 8 Clements, Michael and Hendry, David. Forecasting Economic Time Series Cambridge Kaiser, R. y A. Maravall (2000), "Notes on Time Series Analysis, ARIMA Models and Signal Extraction", Banco de España, Servicio de Estudios, Documento de Trabajo Maravall, A. (2003), Notes on Programs TRAMO and SEATS. Brief version: Part 1 Part 2 Part 3. Long version: Part 1 Part 2 Part 3. Advanced Time Series and Panel Data 5

6 Advance Time Series and Panel Data Session 1: Kalman Filter James Hamilton. Time Series Analysis Princeton. (1994). Chapter 13. Chang-Jin Kim, Charles R. Nelson. State-Space Models With Regime Switching: Classical and Gibbs- Sampling Approaches With Applications. MIT Press (1999). Chapter 2. Clark, Peter K. (1987) The Cyclical Component of US Economic Activity Quarterly Journal of Economics, 102, Clark, Peter K. (1989) Trend Reversion in Real Output and unemployment Journal of Econometrics, 40, Kuttner, Ken (1996) Estimating Potential Output as a Latent Variable Journal of Business and Economics Statistics, Vol 12, Num Stock, James and Mark Watson (1991) A probability model of the Coincident Economic Indicators In Leading Economic Indicators: New Approaches and Forecasting Records, ed. K. Lahiri and G.H. Moore. Cambridge. Cambridge University Press, Harvey, A.C. and A. Jaeger (1993). Detrending, stylized facts and the Business Cycle. Journal of Applied Econometrics, 8, King, R.G. and S.T. Rebelo (1993). Low frequency filtering and real business cycle Journal of Economic Dynamic and Control, 17, Hodrick, R. and E.C. Prescott (1997). Postwar U.S. Business Cycles: An Empirical Investigation Journal of Money, Credit and Banking, Vol 29, Num 1. Cogley, T. and J. Nason (1995). Effects of the Hodrick-Prescott filter on trend and difference stationary time series. Implications for Business Cycle Research Journal of Economic Dynamic and Control, 19, Kaiser, R. and Maravall, A. Measuring Business Cycle in Economic Time Series Springer 2001 Session 2: Nowcasting and real time forecasting Maximo Camacho and Perez Quiros, Gabriel (2002) This is What the Leading Indicators Lead Journal of Applied Econometrics, 17, Stock, J., Watson, M. (2002) Macroeconomic Forecasting Using Difusion Indexes. Journal of Business and Economic Statistics 20: Giannone, D. Reichlin, L and Small, D. Nowcasting GDP and Inflation, the real time informational content of macroeconomic releases. ECB Working Paper Series, May 2006 Aruoba, B., F. Diebold and C. Scotti (2008). Real-time measurement of business conditions, PIER Working Paper No , Department of Economics, University of Pennsylvania Barhoumi, K, Benk, S., Cristadoro, R. Ard Den, Jakaitiene, A. Jelonek, P. Rua, A. Runstler, G. Ruth, K. Van Nieuwenhuyze, C. Short Term Forecasting og GDP using large monthly datasets: A Pseudo Real Time Forecast Evaluation Exercise. ECB Occasional Paper Series, N 84, April Angelini, E., Camba-Mendez, G., Giannone, D., Reichlin, L., and Runstler, G Shortterm forecasts of Euro area GDP growth. CEPR discussion paper No Boivin, J., and Ng, S Are more data always better for factor analysis? Journal of Econometrics 132: Bai, J., and Ng, S Forecasting economic time series using targeted predictors. Journal of Econometrics 148: Alvarez. Camacho y Perez Quiros (2011) Finite sample performance of small versus large scale dynamic factor models Banbura, Marta and Michelle Modugno (2010) Maximum Likelihood estimation of factor models on data sets with arbitrary pattern of missing data. ECB Working paper series Camacho, del Bianco and Perez Quiros Short-Run Forecasting of the Euro-Dollar Exchange Rate with Economic Fundamentals. Journal of International Money and Finance Vol 31 Issue 2 March 2012 pp Session 3: Markov switching models. James Hamilton. Time Series Analysis Princeton. (1994). Chapter 22 Chang-Jin Kim, Charles R. Nelson. State-Space Advance Time Series and Panel Data 2

7 Advance Time Series and Panel Data Models With Regime Switching: Classical and Gibbs- Sampling Approaches With Applications. MIT Press (1999). Chapter 4. Perez Quiros, Gabriel and Allan Timmermann (2000) Firm Size and Cyclical Variations in Stock Returns The Journal of Finance, Vol 55, Number 3. June Hamilton, James (1989) A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle Econometrica, 57: Hamilton, James and Perez Quiros, Gabriel (1996) What do the Leading Indicators Lead? Journal of Business, Vol 69, Number 1. McConnell Margaret, and Perez Quiros, Gabriel. (2000) Output Volatility in the US: What has Changed Since the Early 80s?.American Economic Review Vol 90, Num 5 December Perez Quiros, Gabriel and Allan Timmermann (2001) Business Cycle Asymmetries in Stock Returns: Evidence from Higher Order Moments and Conditional Densities Journal of Econometrics. Vol July 2001 Harding, D., and A. Pagan (2002). A comparison of two business cycle dating methods. Journal of Economic Dynamics and Control 27: Camacho, M., Pérez-Quirós, G. (2004) Jump and Rest Effects in the US Business Cycle. CEPR Working Paper. Bengoechea, P., Camacho M. y Pérez Quirós, G. International Journal of Forecasting, 22, 2006, pp Session 4. Combinations of Markov Switching and Kalman filter Models. Kim, Chang-Jin and Charles Nelson. (1998). Friedman s Plucking Models of Business Fluctuations: Tests and Estimates of Permanent and Transitory Components. Journal of Money Credit and Banking. Sichel, Daniel E. "Inventories and the Three Phases of the Business Cycle." Journal of Business and Economic Statistics, July 1994, 12(3), pp High-growth Recoveries, Inventories and the Great Moderation. (with Maximo Camacho and Hugo Rodriguez). Journal of Economic Dynamics and Control, Elsevier, vol. 35(8), pages , August 2011 James H. Stock & Mark W. Watson, "Estimating Turning Points Using Large Data Sets," NBER Working Papers 16532, National Bureau of Economic Research. Camacho, Perez Quiros and Poncela. Green Shoots and Double dips in the Euro Area, a real time approach, CEPR Working paper 2012 Session 5: Smooth transition regression models. Philip Hans Franses, Dick Van Dijk. Non-Linear Time Series Models in Empirical Finance. Cambridge (2000) Potter, Simon (1995) A Nonlinear Approach to US GNP Journal of Applied Econometrics, Vol 10. Pesaran, Hashem and Simon Potter (1997) A Floor and Ceiling Model of US Output, Journal of Economic Dynamics and Control. Num 21. Maximo Camacho and Perez Quiros, Gabriel (2002) This is What the Leading Indicators Lead Journal of Applied Econometrics, 17, Teräsvirta, T. (1994). Specification, estimation and evaluation of smooth transition autoregressive models. Journal of the American Statistical Association 89: Advance Time Series and Panel Data 3

8 Advance Time Series and Panel Data PART 3 (by Joan Llull) Panel data. Arellano, M. (2003) Panel Data Econometrics. Oxford University Press. Arellano, M. and Bond, S. (1991) Some tests of specification for panel data: Monte Carlo Evidence and an application to employment equations, Review of Economic Studies, 58, Arellano, M. and Bover, O. (1995) Another look at the instrumental variable estimation of error-components models, Journal of Econometrics, 68, Blundell, R. W. and Bond, S.R. (2000) GMM estimation with persistent panel data: an application to production functions, Econometric Reviews, 19, Caselli, F., G. Esquivel, and F. Lefort (1996): Reopening the convergence debate: a new look at cross-country growth empirics, Journal of Economic Growth, 18, 5-46 Zeldes, S.P. (1989): Consumption and liquidity constraints: an empirical investigation Journal of Political Economy, 97, Duration analysis. Cameron, A. Colin and Pravin K. Triverdi (2005), Microeconometrics: Methods and Applications, Cambridge University Press. Cox, David R. (1972), Regression Models and Life Tables (with Discussion)", Journal of the Royal Statistical Society, B, 34, Lancaster, Tony (1979), Econometric Models for the Duration of Unemployment", Econometrica, 47, Lancaster, Tony (1990), Econometric Analysis of Transition Data, Cambridge. Van den Berg, Gerard (2001), Duration Models: Speci cation, Identification and Multiple Durations", in J.J. Heckman and E. Leamer (eds.), Handbook of Econometrics, Vol. 5, Ch. 55. Advance Time Series and Panel Data 4