Error in State Space estimation

[matheus_silva92]

Hello,

I'm having trouble to estimate the first stage of Laubach and Williams' (2003) model. This model goes as follows:

100*(y - y_star) = a1 * (y(-1) - y_star(-1)) + a2 * (y(-2) - y_star(-2)) + e1
y_star = c1 + y_star(-1) + e2

Where y is the GDP and y_star is the (unobserved) potential GDP, e1 and e2 are errors.

My code is the following:

Code: Select all

param c(3) -0.3236 c(1) 116.7985 c(2) -38.83865 c(4) 0.008786 c(5) 0 @ename e1 @ename e2 @evar var(e1) = exp(c(3)) @evar var(e2) = exp(c(5)) @signal gdp = gdp_+ c(1)/100 * (gdp(-1) - gdp_m1) + c(2)/100*(gdp(-2)-gdp_m2) + e1/100 @state gdp_ = gdp_(-1) + c(4) + e2 @state gdp_m1 = gdp_(-1) @state gdp_m2 = gdp_m1(-1) @mprior media_1est @vprior var_1est

Please note I changed the notation (from y to gdp, and y_star to gdp_). I obtained the param part by OLS estimation of the "equivalent" equations using the HP filtered values for GDP. Also, my mean and covariance matrix priors are also obtained from the HP filtered values (just like they do in their original paper).

When I run this code, it says...

Failure to improve Likelihood after 2 iterations

I have also tried to play with the c(3) and c(5) starting values, without success (even though it may converge with VERY low values for these, gdp_ and gdp are equal).

Can anyone figure out what is going on?

For the data, I use the one provided by the authors themselves available in this link:

www.frbsf.org/economic-research/files/L ... mates.xlsx

Many thanks in advance,
Matheus