This paper shows that the trimmed Whittle estimation of the SVAR is superior to filtering (or differencing) undesired, low-frequency fluctuations that may arise in macroeconomic data. Pre-filtering destroys the low-frequency range of the spectrum, thus biasing the estimated parameters and the responses of the variables to shocks. The proposed method, by contrast, accounts for the undesired fluctuations while overcoming these drawbacks. Furthermore, the method remains reliable even when the observed low-frequency variability has been incorrectly considered as external to the SVAR. An empirical application that examines the effect of technology shocks on hours worked is provided to illustrate the results. We find the response of hours positive and similar using both long and short-run identification restrictions, thus providing a solution to a wide debate in the business cycle literature.
Baxter, M., and R. G. King. 1999. “Measuring Business Cycles: Approximate Band-Pass Filters for Economic Time Series.” The Review of Economics and Statistics 81: 575–593.
Canova, F., D. Lopez-Salido, and C. Michelacci. 2010. “The Effects of Technology Shocks on Hours and Output: A Robustness Analysis.” Journal of Applied Econometrics 25: 755–773.
Christiano, L. J., M. Eichenbaum, and R Vigfusson. 2003. “What Happens After a Technology Shock?” NBER Working Papers 9819, National Bureau of Economic Research, Inc.
Cogley, T., and J. M. Nason. 1995. “Effects of the Hodrick-Prescott Filter on Trend and Difference Stationary Time Series: Implications for Business Cycle Research.” Journal of Economic Dynamics and Control 19: 253–278.
Dahlhaus, R. 1988. “Small Sample Effects in Time Series Analysis: A New Asymptotic Theory and a New Estimate.” The Annals of Statistics 16: 808–841.
Engle, R. F. 1974. “Band Spectrum Regression.” International Economic Review 1–11.
Fernald, J. G. 2007. “Trend Breaks, Long-Run Restrictions, and Contractionary Technology Improvements.” Journal of Monetary Economics 54: 2467–2485.
Francis, N., and V. A. Ramey. 2009. “Measures of Per Capita Hours and their Implications for the Technology-Hours Debate.” Journal of Money, Credit, and Banking 41: 1071–1097.
Gospodinov, N. 2010. “Inference in Nearly Nonstationary SVAR Models with Long-Run Identifying Restrictions.” Journal of Business and Economic Statistics 28: 1–12.
Gospodinov, N., A. Maynard, and E. Pesavento. 2011. “Sensitivity of Impulse Responses to Small Low-Frequency Comovements: Reconciling the Evidence on the Effects of Technology Shocks.” Journal of Business and Economic Statistics 29: 455–467.
Hamilton, J. D. 2018. “Why you should Never Use the Hodrick-Prescott Filter.” The Review of Economics and Statistics 100: 831–834.
Hansen, L. P., and T. J. Sargent. 1993. “Seasonality and Approximation Errors in Rational Expectations Models.” Journal of Econometrics 55: 21–55.
Harvey, A. C. 1989. Forecasting, structural time series models and the Kalman Filter. Cambridge, UK: Cambridge University Press.
Harvey, A., and A. Jaeger. 1993. “Detrending, Stylized Facts and the Business Cycle.” Journal of Applied Econometrics 8: 231–247.
Hodrick, R. J., and E. C. Prescott. 1997. “Postwar U.S. Business Cycles: An Empirical Investigation.” Journal of Money, Credit and Banking 2: 1–16.
Hou, J., and P. Perron. 2014. “Modified Local Whittle Estimator for Long Memory Processes in the Presence of Low Frequency (and other) Contaminations.” Journal of Econometrics 182: 309–328.
King, R. G., and S. T. Rebelo. 1993. “Low-Frequency Filtering and Real Business Cycles.” Journal of Economic Dynamics and Control 17: 207–231.
Lovcha, Y., and A. Perez-Laborda. 2015. “Hours Worked – Productivity Puzzle: Identification in Fractional Integration Settings.” Macroeconomic Dynamics 19: 1593–1621.
McCloskey, A. 2013. “Estimation of the Long-Memory Stochastic Volatility Model Parameters that is Robust to Level Shifts and Deterministic Trends.” Journal of Time Series Analysis 4: 285–301.
McCloskey, A., and J. B. Hill. 2014. “Heavy Tail Robust Frequency Domain Estimation.” Typescript, September 2014.
McCloskey, A., and J. B. Hill. 2017. “Parameter Estimation Robust to Low-Frequency Contamination,” Journal of Business and Economic Statistics 35: 598–610.
Qu, Z., and D. Tkachenko. 2012. “Identification, and Frequency Domain Quasi-Maximum Likelihood Estimation of Linearized Dynamic Stochastic General Equilibrium Models.” Quantitative Economics 3: 95–132.
Ramey, V. A. 2016. “Macroeconomic Shocks and their Propagation.” In Handbook of Macroeconomics, edited by J. B. Taylor, and H. Uhlig, Vol. 2, pp. 271–162, North Holland, Amsterdam: Elsevier.
Sala, L. 2015. “DSGE Models in the Frequency Domain.” Journal of Applied Econometrics 30: 219–240.
Tukey, J. W. 1967. “An Introduction to the Calculations of Numerical Spectrum Analysis.” In Advanced Seminar on Spectral Analysis of Time Series, edited by B. Harris, New York: Wiley.
Velasco, C. 1999. “Gaussian Semiparametric Estimation of Non-Stationary Time Series.” Journal of Time Series Analysis 20: 87–127.
Whittle, P. 1963. “On the Fitting of Multivariate Autoregressions, and the Approximate Canonical Factorization of a Spectral Density Matrix.” Biometrika 50: 129–134.
Zhang, H. C. 1991. “Reduction of the Asymptotic Bias of Autoregressive and Spectral Estimators by Tapering.” Journal of Time Series Analysis 13: 451–469.
SNDE recognizes that advances in statistics and dynamical systems theory can increase our understanding of economic and financial markets. The journal seeks both theoretical and applied papers that characterize and motivate nonlinear phenomena. Researchers are required to assist replication of empirical results by providing copies of data and programs online. Algorithms and rapid communications are also published.