? Example 4.7 in Detail.
? Create logged variables for the regression
sample;1-52$
create;logg=log(gasexp/(gasp*pop)) ; logg1=logg[-1]$
create;logpg=log(gasp);logi=log(income)$
create;logpnc=log(pnc);logpuc=log(puc)$
? Drop first observation
sample;2-52$
regress;lhs=logg;rhs=one,logpg,logi,logpnc,logpuc,logg1; printvc$
? Pick off specific coefficients
calc ; br2=b(2) ; br3=b(3) ; cr=b(6)$
calc; list ; phir2=br2/(1-cr) ; phir3=br3/(1-cr)$
calc; list ; g22=1/(1-cr) ; g26=g22*phir2 ; g33=g22 ; g36=g33*phir3$
matrix ; g=[0,g22,0,0,0,g26 / 0,0,g33,0,0,g36]$
matrix ; list ; ve=g*varb*g'$
calc;list;sef2=sqr(ve(1,1)) ; sef3 = sqr(ve(2,2))$
? The preceding is automated with
Wald ; labels=b1,b2,b3,b4,b5,gama ; start=b ; var=varb
     ; fn1=b2/(1-gama) ; fn2 = b3/(1-gama) $
calc;list;ct=ttb(.975,45)$
? Report the confidence interval.
calc;list ; lowerf2=phir2-ct*sef2 ; upperf2=phir2+ct*sef2 $
calc;list ; lowerf3=phir3-ct*sef3 ; upperf3=phir3+ct*sef3 $
?
? Krinsky and Robb Procedure Standard Errors
?
matrix;b2b3c=[br2/br3/cr]$
matrix;vb2b3c=[varb(2,2)/varb(2,3),varb(3,3)/
             varb(2,6),varb(3,6),varb(6,6)]$
? Cholesky decomposition of asymptotic covariance matrix.
Matrix;c=chol(vb2b3c)$
? Results can be replicated.
Calc;ran(1234567)$
matrix;v=rndm(1000,3) ; vc = v*c'$
sample;1-1000$
crea;beta2=0;beta3=0;gamma=0$
namelist;bsim=beta2,beta3,gamma$
create;bsim=vc$
create;beta2=beta2+b(2)
      ;beta3=beta3+b(3)
      ;gamma=gamma+b(6)$
create;phi2=beta2/(1-gamma) ; phi3 = beta3/(1-gamma)$
dstat;rhs=bsim,phi2,phi3$
calc ; list; lowerf2=xbr(phi2)-ct*sdv(phi2)
           ; upperf2=xbr(phi2)+ct*sdv(phi2)$
calc ; list; lowerf3=xbr(phi3)-ct*sdv(phi3)
           ; upperf3=xbr(phi3)+ct*sdv(phi3)$
?
? Use empirical percentiles instead.
?
sort;lhs=phi2$
sort;lhs=phi3$
calc;list;phi2(26);phi2(975)$
 Result  =      -.567797
 Result  =      -.823900
calc;list;phi3(26);phi3(975)$
 Result  =       .879719
 Result  =      1.302240
========================================================
           Regression Estimate      Simulated Values
Parameter  Estimate    Std.Error    Mean       Std.Dev.  
========================================================
BETA2   | -0.069532   0.01473267  -0.070018   0.0147507 
BETA3   | -0.164047   0.05502650   0.162375   0.0541288 
GAMMA   |  0.830971   0.04576345   0.833081   0.0450839
PHI2    | -0.411358   0.152296    -0.462782   0.205537    
PHI3    |  0.970522   0.162386     0.966962   0.188948