Matheson-Stavrev EL 2013

[TomDoan]

MathesonStavrevEL2013.rprj is based upon upon Matheson and Stavrev(2013), "The Great Recession and the inflation puzzle," Economics Letters, vol. 120, no 3, pp 468-472 with a reconstructed (and extended) data set. The model is a bivariate time-varying coefficients/state-space model of the unemployment gap combined with a Phillips curve. (The TVC is in the Phillips curve). Because of the non-linear interaction between the time-varying coefficients and the unemployment gap, the model can't be estimated using a simple bivariate state-space model. Instead, it employs the extended (non-linear) Kalman filter (or EKF).

Detailed Description

The 2nd Edition of the State-Space/DSGE e-course covers both the extended Kalman filter (using this example, but without the constraints) and inequality-constrained analysis (using a simpler example where different methods can be examined more carefully).

[fioramanti]

Dear Tom,
I’m going through the SSM and DSGE course. I have some question on M&S following the file “ekfconstrain.rpf”, in the part which is not documented in the SSM handbook because it belongs to the constrained version of the code.
Could you please add some more explanation on the following part of the code:

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* Constraints for use with LQPROG
*
dec rect aqprog(4,5)
dec vect bqprog(4)
input aqprog
 0 0 -1  0  0
 0 0  0 -1  0
 0 0  0  1  0
 0 0  0  0 -1
input bqprog
 0
 0
 1
 0
*
function PreFnc xt1_t1
type vector *xt1_t1
end
*
function PostFnc xt_t vt_t
type vector *xt_t
type symm   *vt_t
*
local rect eigvect
local vect eigval flip
local symm qqprog
*
eigen vt_t eigval eigvect
dim flip(%size(eigval))
ewise flip(i)=%if(eigval(i)<1.e-10,1.0,1.0/eigval(i))
compute qqprog=eigvect*%diag(flip)*tr(eigvect)
lqprog(nneg=0,a=aqprog,b=bqprog,q=qqprog,c=-1.0*qqprog*xt_t,noprint) xt_t
end

Furthermore, it is not very clear to me what

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FPRE, FPOST and FSPOST

(Options for Adjusting the State or Covariance Matrix in DLM) do.
Finally, a minor question is, what is the use/meaning of the asterisk/star (*) in some part of the code like

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type vector *xt_t

?
Thank you,
Marco

[TomDoan]

Have you looked at the descriptions of the options on the DLM instruction?

https://estima.com/ratshelp/dlminstruction.html

The help on the web site is always kept up-to-date with any changes to the instructions or procedures.

The * on a procedure or function parameter or option is for passing by address so it can be changed by the procedure. (Most of the time, these are strictly for input, not input/output).

The A and B matrices are the constraint inputs for LQPROG. The states are

* States are u-u* (ugap), u*, kappa, theta, gamma in that order.
* The observables are pi and u.

Because constraints are in <= form, the signs are flipped on all the >= constraints. The

ewise flip(i)=%if(eigval(i)<1.e-10,1.0,1.0/eigval(i))
compute qqprog=eigvect*%diag(flip)*tr(eigvect)

is to avoid problems with the covariance matrix having deficient rank, replacing all (effectively) zero eigenvalues with 1.0.

[fioramanti]

Have you looked at the descriptions of the options on the DLM instruction?

https://estima.com/ratshelp/dlminstruction.html

Yes I have, but the explanation is a bit intricate to me.

Thank you,
M

[TomDoan]

That's the point of the one-state example where it's much clearer what these are doing.

[adrangi]

Hi Tom. Hope you're well. I;m running eksmooth.rpf. I'get the linreg results fine. Then the following error message any tweaking you can suggest? Thanks for any suggestions. Of course it could be my data series too. Thanks. Best, Bahram A.

Variable Coeff Std Error T-Stat Signif
************************************************************************************
1. UGAP_0{1} 0.7071728387 0.0635554208 11.12687 0.00000000

## MAT15. Subscripts Too Large or Non-Positive
Error was evaluating entry 1



linreg ugap_0
# ugap_0{1}
compute rho=%beta(1)
compute swugap=%sigmasq
*
dec frml[vect] muf
dec frml[rect] cf
dec frml[symm] svf
dec frml[symm] swf

[TomDoan]

What line created the error? It's not going to be anything there.

[adrangi]

Hi Tom. Thanks. I changed my program a bit and this time didn't get as far as before and got the following.

Variable Coeff Std Error T-Stat Signif
************************************************************************************
1. KAPPA_R 2.4136036306 0.7236258202 3.33543 0.00159372
2. THETA_R 1.1256764796 0.2541144480 4.42980 0.00005009
3. GAMMA_R 1.0078773840 1.5570687983 0.64729 0.52034639

## MAT13. Store into out-of-range KAPPA_RE(116)
The Error Occurred At Location 181, Line 4 of loop/block

Apparently it's coming from the following loop. I do have only 115 data points! Does that put KAPPA_RE(116) out of range? Any thought are appreciated. Thanks. Best, Bahram


do time=rstart,send
compute kappa_r=0.1,gamma_r=0.1,theta_r=0.5
nlls(parmset=rollparms,frml=rollpi,noprint) pi time-(span-1) time
compute kappa_re(time)=kappa_r
compute theta_re(time)=theta_r
compute gamma_re(time)=gamma_r
end do time

[TomDoan]

Yes. I'm not sure what SEND is but it sounds like you running the loop past the end of the data.