Discussion of State Space and Dynamic Stochastic General Equilibrium Models
hardmann
Posts: 182
Joined: Sat Feb 26, 2011 9:49 pm

Dear Tom:
Recently, I read Fernandes et al.(2003), “Modelling output gaps in the Euro Area with structural breaks: The COVID-19 recession”. I read again the several papers about UC model with structural break, including, Morley et al. (2003), Perron & Wada(2009), Luo & Startz(2014), Grant & Chan(2017).
I have two questions for your help.
1. In tradition UC decomposition, the log GDP, y is sum of trend component tau and cyclical component c, not including irregular component e. However, Morley et al. (2003) said “sometimes an additional irregular term is added, although these changes have little influence on the estimated cycle component for U.S. GDP”. These papers all wrote before Covid-19 pandemic. When sample including the 2020Q2, the estimates is different while UC model with or without irregular component. On the other hand, Harvey always incorporates the irregular component in his series papers.
My question is whether or not standard UC model includes the irregular component?

2. Perron & Wada (2009) used exogenous break date, whereas Luo & Startz (2014) used endogenous break date. They did not allow the trend growth rate drift as random walk, i.e, local linear trend. Allowing for a break significantly reduces estimates of trend variance. I guess the multi breaks reduce much. Further, local linear trend allowing time-varying the drift is ideal.
Perron & Wada (2009) said “The reason is that any positive variance [of irregular] would imply changes in the slope occurring at every period, though of different magnitudes each time, and the real GDP series would then be I(2), a feature not supported by the data”. However, in measuring the natural rate of interest (working paper), Laubach and Williams (2001) use the local linear trend, and argued in p5 “The hypothesis that log real GDP is I(2) is typically rejected by an ADF test. However, as Stock and Watson (1998) point out, when the disturbance to the growth rate component has small variance, such a test statistic has a high false-rejection rate”
My question is, should trend component be local linear trend or local lever with multi-breaks?

Best Regard
Hardmann

Reference
Morley, J.C., Nelson, C.R., Zivot, E., 2003. Why are the Beveridge-Nelson and unobserved-components decompositions of GDP so different? Rev. Econ. Stat. 85 (2), 235–243.
Perron, P., Wada, T., 2009. Let’s take a break: Trends and cycles in US real GDP. J. Monetary Econ. 56 (6), 749–765.
Luo, S., Startz, R., 2014. Is it one break or ongoing permanent shocks that explains U.S. real GDP? J. Monetary Econ. 66, 155–163.
Grant, A.L., Chan, J.C.C., 2017. Reconciling output gaps: Unobserved components model and Hodrick–Prescott filter. J. Econom. Dynam. Control 75, 114–121.
Harvey,A.C., 1985. Trends and cycles in macroeconomic time series. J. Bus. Econ. Stat. 3(3), 216–227.
Harvey, A.C., Jaeger,A., 1993. Detrending, stylized facts and the business cycle. J. Appl. Econom. 8(3), 231.
Harvey, A.C., Trimbur, T.M., VanDijk, H.K., 2007. Trends and cycles in economic time series: a Bayesian approach. J. Econom. 140, 618–649.
TomDoan
Posts: 7534
Joined: Wed Nov 01, 2006 4:36 pm