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### State Space modelling

Posted: Mon May 27, 2019 6:01 am
Hi All
I want to estimate nairu with a state space model. The model is specified as
sspace ssnairu
ssnairu.append cpi = c(11)*cpie+c(12)*cpi(-1)+c(13)*cpi(-2)+c(14)*cpi(-3)+c(15)*ulc(-1)+c(16)*((rue-nairu)/rue)+c(17)*d(rue(-1))/rue+c(18)*(pm(-1)-pm(-2))+[var=exp(c(110))]
ssnairu.append ulc = c(21)*cpie+c(22)*cpi(-1)+c(23)*cpi(-2)+c(24)*((rue-nairu)/rue)+c(25)*d(rue(-1))/rue+[var=exp(c(26))]
ssnairu.append @state nairu =nairu(-1) +[var=exp(c(31))]

nairu is specified as a random walk. cpi is inflation, cpie is expected inflation, ulc is unit of labour cost, rue is the unemployment rate and pm is the import price.
No matter how hard I tried, the results don't converge. I tried to change initial values and optimisation methods, but no luck. A typical output is like:
Sspace: SSNAIRU
Method: Maximum likelihood (BFGS / Marquardt steps)
Date: 05/27/19 Time: 16:44
Sample: 12/01/1989 12/01/2018
Included observations: 117
Valid observations: 111
Partial observations: 1
Failure to improve likelihood (singular hessian) after 53 iterations
Coefficient covariance computed using outer product of gradients

Coefficient Std. Error z-Statistic Prob.

C(11) 0.195415 0.069796 2.799818 0.0051
C(12) 0.915364 0.077235 11.85171 0.0000
C(13) 0.110645 0.084827 1.304353 0.1921
C(14) -0.221659 0.073781 -3.004306 0.0027
C(15) -0.059256 0.037787 -1.568167 0.1168
C(16) -3.67E-09 0.212305 -1.73E-08 1.0000
C(17) -3.087926 2.558954 -1.206714 0.2275
C(18) 5.82E-05 0.016426 0.003542 0.9972
C(21) 0.416121 0.226537 1.836880 0.0662
C(22) -0.664531 0.298286 -2.227835 0.0259
C(23) 1.005604 0.377144 2.666368 0.0077
C(24) 3.56E-07 0.446858 7.97E-07 1.0000
C(25) 8.743475 7.308450 1.196352 0.2316
C(26) 1.410590 0.185800 7.591991 0.0000
C(31) 0.469357 6.42E+10 7.31E-12 1.0000
C(110) -1.289094 0.124707 -10.33697 0.0000

Final State Root MSE z-Statistic Prob.

NAIRU 0.057820 2024.489 2.86E-05 1.0000

Log likelihood -320.9730 Akaike info criterion 6.071585
Parameters 16 Schwarz criterion 6.462148
Diffuse priors 1 Hannan-Quinn criter. 6.230025