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The `Pile-up Problem' in Trend-Cycle Decomposition of Real GDP: Classical and Bayesian Perspectives

  • Kim, Chang-Jin
  • Kim, Jaeho

In the case of a flat prior, a conventional wisdom is that Bayesian inference may not be very different from classical inference, as the likelihood dominates the posterior density. This paper shows that there are cases in which this conventional wisdom does not apply. An ARMA model of real GDP growth estimated by Perron and Wada (2009) is an example. While their maximum likelihood estimation of the model implies that real GDP may be a trend stationary process, Bayesian estimation of the same model implies that most of the variations in real GDP can be explained by the stochastic trend component, as in Nelson and Plosser (1982) and Morley et al. (2003). We show such dramatically different results stem from the differences in how the nuisance parameters are handled between the two approaches, especially when the parameter estimate of interest is dependent upon the estimates of the nuisance parameters for small samples. For the maximum likelihood approach, as the number of the nuisance parameters increases, we have higher probability that the moving-average root may be estimated to be one even when its true value is less than one, spuriously indicating that the data is `over-differenced.' However, the Bayesian approach is relatively free from this pile-up problem, as the posterior distribution is not dependent upon the nuisance parameters.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 51118.

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Date of creation: Oct 2013
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Handle: RePEc:pra:mprapa:51118
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  1. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
  2. DeJong, David N. & Whiteman, Charles H., 1991. "Reconsidering 'trends and random walks in macroeconomic time series'," Journal of Monetary Economics, Elsevier, vol. 28(2), pages 221-254, October.
  3. Charles Nelson & Christian Murray, 1997. "The Uncertain Trend in U.S. GDP," Computational Economics 9702001, EconWPA.
  4. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
  5. Diebold, Francis X & Senhadji, Abdelhak S, 1996. "The Uncertain Unit Root in Real GNP: Comment," American Economic Review, American Economic Association, vol. 86(5), pages 1291-98, December.
  6. Murray, Christian J & Nelson, Charles R, 2002. "The Great Depression and Output Persistence," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 34(4), pages 1090-98, November.
  7. Christopher A. Sims & Harald Uhlig, 1988. "Understanding unit rooters: a helicopter tour," Discussion Paper / Institute for Empirical Macroeconomics 4, Federal Reserve Bank of Minneapolis.
  8. Chib, Siddhartha & Greenberg, Edward, 1994. "Bayes inference in regression models with ARMA (p, q) errors," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 183-206.
  9. Harvey, A C, 1985. "Trends and Cycles in Macroeconomic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(3), pages 216-27, June.
  10. Kim, Chang-Jin & Kim, Jaeho, 2013. "Bayesian Inference in Regime-Switching ARMA Models with Absorbing States: The Dynamics of the Ex-Ante Real Interest Rate Under Structural Breaks," MPRA Paper 51117, University Library of Munich, Germany.
  11. Margaret M. McConnell & Gabriel Perez Quiros, 1997. "Output fluctuations in the United States: what has changed since the early 1980s?," Research Paper 9735, Federal Reserve Bank of New York.
  12. Newbold, Paul & Leybourne, Stephen & Wohar, Mark E., 2001. "Trend-stationarity, difference-stationarity, or neither: further diagnostic tests with an application to U.S. Real GNP, 1875-1993," Journal of Economics and Business, Elsevier, vol. 53(1), pages 85-102.
  13. Campbell, John Y & Mankiw, N Gregory, 1987. "Are Output Fluctuations Transitory?," The Quarterly Journal of Economics, MIT Press, vol. 102(4), pages 857-80, November.
  14. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
  15. Lawrence J. Christiano, 1988. "Searching For a Break in GNP," NBER Working Papers 2695, National Bureau of Economic Research, Inc.
  16. Sargan, J D & Bhargava, Alok, 1983. "Maximum Likelihood Estimation of Regression Models with First Order Moving Average Errors When the Root Lies on the Unit Circle," Econometrica, Econometric Society, vol. 51(3), pages 799-820, May.
  17. Davidson, James E. H., 1981. "Problems with the estimation of moving average processes," Journal of Econometrics, Elsevier, vol. 16(3), pages 295-310, August.
  18. Plosser, Charles I. & Schwert, G. William, 1977. "Estimation of a non-invertible moving average process : The case of overdifferencing," Journal of Econometrics, Elsevier, vol. 6(2), pages 199-224, September.
  19. Clark, Peter K, 1987. "The Cyclical Component of U.S. Economic Activity," The Quarterly Journal of Economics, MIT Press, vol. 102(4), pages 797-814, November.
  20. Chib, Siddhartha, 1998. "Estimation and comparison of multiple change-point models," Journal of Econometrics, Elsevier, vol. 86(2), pages 221-241, June.
  21. Gospodinov, Nikolay, 2002. "Bootstrap-Based Inference in Models with a Nearly Noninvertible Moving Average Component," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 254-68, April.
  22. DeJong, David N & Whiteman, Charles H, 1993. "Estimating Moving Average Parameters: Classical Pileups and Bayesian Posteriors," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 311-17, July.
  23. Pierre Perron† & Tatsuma Wada, 2005. "Let’s Take a Break: Trends and Cycles in US Real GDP?," Boston University - Department of Economics - Working Papers Series WP2005-031, Boston University - Department of Economics, revised Oct 2005.
  24. DeJong, David N, et al, 1992. "Integration versus Trend Stationarity in Time Series," Econometrica, Econometric Society, vol. 60(2), pages 423-33, March.
  25. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
  26. Ansley, Craig F. & Newbold, Paul, 1980. "Finite sample properties of estimators for autoregressive moving average models," Journal of Econometrics, Elsevier, vol. 13(2), pages 159-183, June.
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