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This is a replication file for Morley, Nelson & Zivot(2003), "Why Are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP So Different?," The Review of Economics and Statistics, vol. 85(2), 235-243. This examines the implications of allowing for correlation in the shocks in a standard unobserved components model. (UC models generally assume uncorrelated shocks). Related work is Perron and Wada(2009) (http://www.estima.com/forum/viewtopic.php?f=8&t=1504), which allows for a break in the trend rate in the UC model.

Dear Tom:

I always study winrats by replicating examples, so I encounter lots problem.

Morley Nelson Zivot (2003) considered that BN and UC are identical if relaxing the correlation between trend and cycle innovations for U.S. real GDP 1947Q1--1998Q2. Of course, the results of the UC-0(zero correlation) and UC-UR ( correlation ) are different.
Perron & Wada(2009) re-examined MNZ works, and argued that there is a break around 1973Q1 of GDP, once account for it, all methods yield the same results.

I still want to prove which is the best model among UC-0, UC-UR and BN models without break. For avoid break, I split that sample into two subsample 1947Q1-1973Q1 and 1973Q1-1998Q2. However, with first subsample, the series follows ARMA(2,2) process, but UC-0 and UC-UR cannot converge, BN is ok. With second subsample, the series follows AR(1), UC-0 and UC-UR can converge but both their sn and sne are zero.
Why do subsample go wrong due to smaller sample?


Best regard
Hardmann

Models don't always work. It is quite possible that even the Perron and Wada "fix" doesn't really adequately describe the difference between the data pre- and post-1973.

IF I use UC-0 and UC-UR models to estimate the U.S. GDP 1947Q1-1973Q1. How I can deal wuth disconverge problem. I had tried pmothod=simple or genetic.

Code: Select all

open data lgdp.txt
calendar(q) 1947
data(format=free,org=columns) 1947:01 1973:01 lgdp
*
* Everything is run on 100*log data
*
set lgdp = 100.0*lgdp
*
@NBERCycles(down=recession)
*
* UC-0 decomposition with AR(2) cycle, fixed trend rate.
*
nonlin mu sn ph1 ph2 se
*
dec frml[rect] af
dec frml[vect] zf
dec frml[symm] swf
*
frml af = ||1.0,0.0,0.0|$
            0.0,ph1,ph2|$
            0.0,1.0,0.0||
frml zf = ||mu,0.0,0.0||
frml swf = %diag(||sn^2,se^2||)
*
compute [vect] c=||1.0,1.0,0.0||
compute [rect] f=%identity(2)~~%zeros(1,2)
*
* Get initial guess values
*
filter(type=hp) lgdp / gdp_hp
set gap_hp = lgdp - gdp_hp
linreg gap_hp
# gap_hp{1 2}
compute ph1=%beta(1),ph2=%beta(2),se=sqrt(%seesq)
set trend = t
linreg gdp_hp
# constant trend
compute mu=%beta(2)
compute sn=sqrt(.1*%seesq)
*
* In order to be comparable with the BN decomposition (which is a
* "filtered" calculation), this uses filtered rather than smoothed
* estimates of the components.
*
dlm(presample=ergodic,a=af,z=zf,sw=swf,c=c,f=f,y=lgdp,pmethod=simplex,piter=5,method=bfgs,type=filter) / states0
*
set cycle0 = states0(t)(2)
set trend0 = states0(t)(1)
*
graph(footer="Figure 1 UC-0 Cycle, US Real GDP. Percent Deviation from Trend",$
  shaded=recession)
# cycle0
*
* Estimation of unrestricted ARIMA(2,1,2) model
*
boxjenk(maxl,ar=2,diffs=1,ma=2,const) lgdp
*
* Generation of BN trend implied by that. Compute the persistence
* measure of the ARMA model (sum of MAR coefficients).
*
summarize (1+%beta(4)+%beta(5))/(1-%beta(2)-%beta(3))
*
* Compute accumulation of psi(1)*residuals + trend rate
*
set incrbn = %sumlc*%resids+%beta(1)
acc incrbn / trendbn
*
* Normalize value of trend based upon starting value of data. Compute
* cycle as residual.
*
set trendbn = trendbn+lgdp(1947:1)
set cyclebn = lgdp-trendbn
graph(footer="Figure 2 Beveridge-Nelson Cycle, US Real GDP",$
  shaded=recession)
# cyclebn
*
* Unrestricted UC model, allowing for correlation between the shocks
*
compute rhone=0.0
nonlin(parmset=fullset) mu sn ph1 ph2 se rhone
*
frml zf = ||mu,0.0,0.0||
frml swf = ||sn^2|rhone*sn*se,se^2||
dlm(a=af,z=zf,sw=swf,c=c,f=f,y=lgdp,$
   presample=ergodic,parmset=fullset,method=bfgs,type=filter) / statesur
set cycleur = statesur(t)(2)
set trendur = statesur(t)(1)
*
* Save the log likelihood and estimated coefficients for future use
*
compute baselogl=%logl,baseparms=%parmspeek(fullset)
*
graph(footer="Figure 3 UC-UR Cycle, US Real GDP",$
  shaded=recession)
# cycleur


Add the option CONDITION=2 to the DLM instructions. The AR(2) cycle can be near unit root at which there is a discontinuity in the likelihood function. By conditioning on the first 2 data points (one comes with the forced unit root, the other for the possibility of the second one), you eliminate the term that causes the discontinuity.

problem resolved with added condition=2 option

Merged questions with post presenting original example code.