Re: trend plus stationary cycle model
Posted: Wed Feb 25, 2015 10:52 am
Hi there!
This time the question is related to time-varying parameter specification. I included some restrictions to the last model above and things are working much better. Nevertheless, I realised that the assumption of “beta” being constant is not plausible. In fact, the catalan labour productivity was boosting in the 60s, whereas in the 70s and the 80s labour productivity increased but at a slower pace. And from then on, labour productivity behaves countercyclically.
I would like “beta” to be time-varying (in equation 7). So, I thought in two possible strategies:
The first one does not seem plausible to me. It consists on interacting two state variables and including a state variable in the F matrix (the loadings from the W’s to the X’s). I guess that this is not possible by construction.
(7) Employment cycle (t) = delta* Employment cycle (t-1)+beta(t)*GDP cycle(t) +e_ec (t)
(8) beta(t)=beta(t-1)+e_beta(t)
The second one consists on changing the structure of my model and estimating sth like:
Observation equations
(1) GDP (t)=GDPtrend(t)+GDPcycle(t)
(2) ∆Employment (t)=delta*∆Employment(t-1)+beta(t)* ∆GDP(t)+e_e(t)
State equations
(3) GDPtrend(t)=GDPtrend(t-1)+alfa(t)+e_yp(t)
(4) alfa(t)= alfa(t-1)+e_alfa(t)
(5) GDPcycle(t)=ph1*GDPcycle(t-1)+ph2*GDPcycle(t-2)+e_yc(t)
(6) beta(t)=beta(t-1)+e_beta(t)
But, in this case I am dubious about the gains of adding equation (2) and (6) to the Clark model, as there is no modeled relation between GDP and Employment (as the employment equation is specified in first differences). I would appreciate your opinion and some ideas to introduce the productivity dynamics in the Clark model.
This time the question is related to time-varying parameter specification. I included some restrictions to the last model above and things are working much better. Nevertheless, I realised that the assumption of “beta” being constant is not plausible. In fact, the catalan labour productivity was boosting in the 60s, whereas in the 70s and the 80s labour productivity increased but at a slower pace. And from then on, labour productivity behaves countercyclically.
I would like “beta” to be time-varying (in equation 7). So, I thought in two possible strategies:
The first one does not seem plausible to me. It consists on interacting two state variables and including a state variable in the F matrix (the loadings from the W’s to the X’s). I guess that this is not possible by construction.
(7) Employment cycle (t) = delta* Employment cycle (t-1)+beta(t)*GDP cycle(t) +e_ec (t)
(8) beta(t)=beta(t-1)+e_beta(t)
The second one consists on changing the structure of my model and estimating sth like:
Observation equations
(1) GDP (t)=GDPtrend(t)+GDPcycle(t)
(2) ∆Employment (t)=delta*∆Employment(t-1)+beta(t)* ∆GDP(t)+e_e(t)
State equations
(3) GDPtrend(t)=GDPtrend(t-1)+alfa(t)+e_yp(t)
(4) alfa(t)= alfa(t-1)+e_alfa(t)
(5) GDPcycle(t)=ph1*GDPcycle(t-1)+ph2*GDPcycle(t-2)+e_yc(t)
(6) beta(t)=beta(t-1)+e_beta(t)
But, in this case I am dubious about the gains of adding equation (2) and (6) to the Clark model, as there is no modeled relation between GDP and Employment (as the employment equation is specified in first differences). I would appreciate your opinion and some ideas to introduce the productivity dynamics in the Clark model.