*
* CAGAN.RPF
* RATS Version 8, User's Guide, Example 10.4.
*
open data cagan_data.prn
data(format=prn,org=cols) 1 34 mu x
*
declare series a1 a2 eps eta
declare real   alpha lambda sig_eta sig_eps
*
frml(identity) f1 = x -(x{1}+a1-lambda*a1{1})
frml(identity) f2 = mu-$
    ((1-lambda)*x{1}+lambda*mu{1}+a2-lambda*a2{1})
frml(identity) f3 = a1-1.0/(lambda+(1-lambda)*alpha)*(eps-eta)
frml(identity) f4 = a2-(1.0/(lambda+(1-lambda)*alpha)*$
                      ((1+alpha*(1-lambda))*eps-(1-lambda)*eta))
frml           d1 = eps
frml           d2 = eta
*
group cagan f1 f2 f3 f4 d1 d2
*
* lambda+(1-lambda)*alpha needs to stay clear of its zero point. It
* appears that it needs to be negative, so alpha must be less than
* -lambda/(1-lambda) on the guess values.
*
compute alpha=-3.00,lambda=.7,sig_eta=.001,sig_eps=.001
*****
function EvalModel
dsge(model=cagan,a=adlm,f=fdlm) x mu a1 a2 eps eta
end EvalModel
*****
compute EvalModel()
compute cdlm=%identity(2)~~%zeros(%rows(adlm)-2,2)
*
* Because we really have no idea what the scale is on the variances, we
* first estimate the model with the alpha and lambda fixed. This uses
* only a small number of simplex iterations to get the sigmas into the
* right zone.
*
nonlin sig_eta sig_eps
dlm(start=%(EvalModel(),sw=%diag(||sig_eps^2,sig_eta^2||)),$
  a=adlm,f=fdlm,y=||x,mu||,c=cdlm,sw=sw,presample=ergodic,$
  method=simplex,iters=5,noprint)
*
nonlin alpha lambda sig_eta sig_eps
dlm(start=%(EvalModel(),sw=%diag(||sig_eps^2,sig_eta^2||)),$
  a=adlm,f=fdlm,y=||x,mu||,c=cdlm,sw=sw,presample=ergodic,$
  pmethod=simplex,piters=5,method=bfgs)