Urgent help please: Smooth Transition VAR...
Posted: Sun Feb 05, 2012 8:33 am
I am using EViews 7. I am trying to estimate a smooth transition model (STVAR or STAR) proposed by Auerbach & Gorodnichenko that is:
Where X is a three dimensional vector including G (government spending), T(taxes) and Y(gdp, output). Pi_r and Pi_e are multipliers for expansions and recessions respectively. I am trying to translate this model using system in EViews however I have problems with introducing shocks into the model. Namely, I want to add a tax shock and observe the effect. And the code so far I wrote is:
After I run this program and try to estimate the system, it gives me an error that is "Near singular matrix". As I know, if I have a Structural VAR I can introduce shock with multiplying the shock with a matrix where I can obtain through structural factorization (for instance matrix MAT_A=var_p.@svaramat matrix MAT_B=var_p.@svarbmat and matrix mat_c=@inverse(mat_a)*mat_b, as I know one should multiply a shock with mat_c and then add to the model). However, i don't know exactly how should I introduce a tax shock into this model. If I omit the variable tax_shock then there is no problem so for the solution, I am considering maybe I should multiply tax_shock with a matrix obtained from structural factorization but I don't know how I can obtain A and B matrices from a system. Is there a way to transform this system into an SVAR or any other way that you can suggest?
Thank you and your help would be highly appreciated!
Where X is a three dimensional vector including G (government spending), T(taxes) and Y(gdp, output). Pi_r and Pi_e are multipliers for expansions and recessions respectively. I am trying to translate this model using system in EViews however I have problems with introducing shocks into the model. Namely, I want to add a tax shock and observe the effect. And the code so far I wrote is:
Code: Select all
smpl @all
!gamma = 1.5
!hrz = 10 'periods
genr z = (gr_gdp(-3)+gr_gdp(-2)+gr_gdp(-1)+gr_gdp+gr_gdp(1)+gr_gdp(2)+gr_gdp(3))/7 ' 7-period Moving average for gdp growth
genr z_normalized = (z-@mean(z))/0.006553 ' std dev of z = 0.006553
genr f = exp(-!gamma*z_normalized) / (1+exp(-!gamma*z_normalized))
delete sys_auerbach*
system sys_auerbach
series tax_shock = 0
coef (42) cf ' Defining different multipliers for recessions
sys_auerbach.append L_GG = C(1)*L_GG(-1)*(1-f(-1)) + CF(1)*L_GG(-1)*f(-1) + C(2)*L_GG(-2)*(1-f(-2)) + CF(2)*L_GG(-2)*f(-2) + C(3)*L_GG(-3)*(1-f(-3)) + CF(3)*L_GG(-3)*f(-3) + C(4)*L_GG(-4)*(1-f(-4)) + CF(4)*L_GG(-4)*f(-4) + C(5)*L_TT(-1)*(1-f(-1)) + CF(5)*L_TT(-1)*f(-1) + C(6)*L_TT(-2)*(1-f(-2)) + CF(6)*L_TT(-2)*f(-2) + C(7)*L_TT(-3)*(1-f(-3)) + CF(7)*L_TT(-3)*f(-3) + C(8)*L_TT(-4)*(1-f(-4)) + CF(8)*L_TT(-4)*f(-4) + C(9)*L_YY(-1)*(1-f(-1)) + CF(9)*L_YY(-1)*f(-1) + C(10)*L_YY(-2)*(1-f(-2)) + CF(10)*L_YY(-2)*f(-2) + C(11)*L_YY(-3)*(1-f(-3)) + CF(11)*L_YY(-3)*f(-3) + C(12)*L_YY(-4)*(1-f(-4)) + CF(12)*L_YY(-4)*f(-4) + C(13) +c(14)*tax_shock
sys_auerbach.append L_TT = C(15)*L_GG(-1)*(1-f(-1)) + CF(15)*L_GG(-1)*f(-1) + C(16)*L_GG(-2)*(1-f(-2)) + CF(16)*L_GG(-2)*f(-2) + C(17)*L_GG(-3)*(1-f(-3)) + CF(17)*L_GG(-3)*f(-3) + C(18)*L_GG(-4)*(1-f(-4)) + CF(18)*L_GG(-4)*f(-4) + C(19)*L_TT(-1)*(1-f(-1)) + CF(19)*L_TT(-1)*f(-1) + C(20)*L_TT(-2)*(1-f(-2)) + CF(20)*L_TT(-2)*f(-2) + C(21)*L_TT(-3)*(1-f(-3)) + CF(21)*L_TT(-3)*f(-3) + C(22)*L_TT(-4)*(1-f(-4)) + CF(22)*L_TT(-4)*f(-4) + C(23)*L_YY(-1)*(1-f(-1)) + CF(23)*L_YY(-1)*f(-1) + C(24)*L_YY(-2)*(1-f(-2)) + CF(24)*L_YY(-2)*f(-2) + C(25)*L_YY(-3)*(1-f(-3)) + CF(25)*L_YY(-3)*f(-3) + C(26)*L_YY(-4)*(1-f(-4)) + CF(26)*L_YY(-4)*f(-4) + C(27) +c(28)*tax_shock
sys_auerbach.append L_YY = C(29)*L_GG(-1)*(1-f(-1)) + CF(29)*L_GG(-1)*f(-1) + C(30)*L_GG(-2)*(1-f(-2)) + CF(30)*L_GG(-2)*f(-2) + C(31)*L_GG(-3)*(1-f(-3)) + CF(31)*L_GG(-3)*f(-3) + C(32)*L_GG(-4)*(1-f(-4)) + CF(32)*L_GG(-4)*f(-4) + C(33)*L_TT(-1)*(1-f(-1)) + CF(33)*L_TT(-1)*f(-1) + C(34)*L_TT(-2)*(1-f(-2)) + CF(34)*L_TT(-2)*f(-2) + C(35)*L_TT(-3)*(1-f(-3)) + CF(35)*L_TT(-3)*f(-3) + C(36)*L_TT(-4)*(1-f(-4)) + CF(36)*L_TT(-4)*f(-4) + C(37)*L_YY(-1)*(1-f(-1)) + CF(37)*L_YY(-1)*f(-1) + C(38)*L_YY(-2)*(1-f(-2)) + CF(38)*L_YY(-2)*f(-2) + C(39)*L_YY(-3)*(1-f(-3)) + CF(39)*L_YY(-3)*f(-3) + C(40)*L_YY(-4)*(1-f(-4)) + CF(40)*L_YY(-4)*f(-4) + C(41) +c(42)*tax_shock
' CF(13) CF(14) CF(27) CF(28) CF(41) AND CF(42) ARE ZERO, NOT ASSIGNED!
Thank you and your help would be highly appreciated!