Joint smoothing of GDP and unemployment with a bivariate HP filter
The problem of jointly estimating unobserved trends and cycles of a bivariate time series considered here appears within the macroeconomic context of Okuns Law when relating output gaps and the unemployment rate. Joint estimation of the output and unemployment trends is carried out by applying a bivariate time series filter that allows for simultaneous estimation of the correlation between cycles. The estimation procedure employed is based on an extension of the univariate Hodrick-Prescott filter and its application in practice is relatively easy. The main contribution of our approach is that we can control the amount of smoothness in the trends by fixing the smoothing parameter. The empirical application uses data on U.S. real gross domestic product and the unemployment rate.
Adams, C. and D.T. Coe. 1990. A systems approach to estimating the natural rate of unemployment and potential output for the United States, IMF Staff Papers, 37: 232-293.
Blanchard, O.J. and D. Quah, 1989. The dynamic effects of aggregate demand and supply disturbances, The American Economic Review, 79(4): 655-673.
Boone, L. 2000. Comparing semi-structural methods to estimate unobserved variables: The HPMV and Kalman filters approaches, OECD Economics Department Working Papers, no. 240.
Chagny, O. and M. Lemoine, 2002. The impact of the macroeconomic hypothesison the estimation of the output gap using a multivariate Hodrick-Prescott filter: The case of the Euro area, Eurostat Colloquium on Modern Tools for Business Cycle Analysis.
Clark, P. K. 1987. The cyclical component of U.S. economic activity, The Quarterly Journal of Economics, 102: 797-814.
Clark, P. K. 1989. Trend reversion in real output and unemployment, Journal of Econometrics , 40: 15-32, DOI: 10.1016/0304-4076(89)90027-4.
Dermoune, A., B. Djehiche, and N. Rahmania. 2009. Multivariate extension of the Hodrick-Prescott Filter-Optimality and characterization, Studies in Nonlinear Dynamics & Econometrics, 13(3): 1-33.
Dupasquier, C., A. Guay, and P. St-Amant. 1999. A survey of alternative methodologies for estimating potential output and the output gap, Journal of Macroeconomics, 21(3): 577-595.
Evans, G.W. 1989. Output and unemployment dynamics in the United States: 1950-1985, Journal of Applied Econometrics, 4(3): 213-237, DOI:10.1002/jae.3950040302.
Federal Reserve Bank of St. Louis. 2006. FRED II (Federal Reserve Economic Data), <https://fred.stlouisfed.org/>;.
Ford, R. and D.E. Rose. 1989. Estimates of the NAIRU using an extended Okun’s Law, Working Paper, no. 89-3, Bank of Canada.
Gómez, V. 1999. Three equivalent methods for filtering finite nonstationary time series, Journal of Business and Economic Statistics, 17: 109-166.
Grant, A.P. 2002. Time-varying estimates of the natural rate of unemployment: A revisitation of Okun’s Law, The Quarterly Review of Economics and Finance, 42(1): 95-113, DOI: 10.1016/S106297-69(01)00109-0.
Guerrero, V. M. 2007. Time series smoothing by penalized least squares, Statistics and Probability Letters, 77: 1225-1234, DOI: 10.1016/j.spl.2007.03.006.
Guerrero, V. M. 2008. Estimating trends with percentage of smoothness chosen by the user, International Statistical Review, 76(2): 187-202, DOI: 10.1111/j.1751-5823.2008.00047.x.
Guerrero, V. M., C.A. Islas, and R.L. Ramirez. 2017. Trend estimation of multivariate time series with controlled smoothness, Communications in Statistics-Theory and Methods, 46(13): 6704-6726, DOI: 10.1080/03610926.2015.1133826.
Hodrick, R.J. and E.C. Prescott. 1997. Postwar U.S. business cycles: An empirical investigation, Journal of Money Credit and Banking, 29: 1-16.
Kydland, F.E. and E.C. Prescott. 1982. Time to build and aggregate fluctuations, Econometrica, 50(6): 1345-1370.
Laxton, D. and R. Tetlow. 1992. A simple multivariate filter for the measurement of potential output, Technical Report no. 59, Bank of Canada.
Morley, J.C., C.R. Nelson, and E. Zivot. 2003. Why are the Beveridge-Nelson and unobserved components decompositions of GDP so different? The Review of Economics and Statistics, 85(2): 235-243.
Nelson, C. R. 1988. Spurious trend and cycle in the state decomposition of a time series with a unit root, Journal of Economic Dynamics and Control, 12(2/3): 475-488.
Nelson, C. R., and C.I. Plosser. 1982. Trends and random walks in macroeconomic time series: Some evidence and implications, Journal of Monetary Economics, 10: 139-162.
Okun, A.M. 1962. Potential GNP: Its measurement and significance, American Statistical Association, Proceedings of the Business and Economic Statistics Section, 98-104.
Prachowny, M.F.J. 1993. Okun’s law: Theoretical foundations and revised estimates, Review of Economics and Statistics, 75: 331-336, DOI: 10.2307/2109440.
Prescott, E.C. 1987. Theory ahead of business cycle measurement, Carnegie Rochester Conference Series on Public Policy, 25: 11-44.
Sinclair, T.M. 2009. The relationship between permanent and transitory movements in U.S. output and the unemployment rate, Journal of Money, Credit and Banking, 41(2-3): 529-542.
Stock, J.H. and M.W. Watson. 1988. Variable trends in economic time series, Journal of Economic Perspectives, 2: 147-174.
Theil, H. 1963. On the use of incomplete prior information in regression analysis, Journal of the American Statistical Association, 58: 401-414, DOI:10.2307/2283275.
US Department of Commerce. 2004. Bureau of Economic Analysis (BEA).<http://www.bea.doc.gov/bea/dn/home/gdp.htm.>;
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