MODEL > RPZ_PLT

ENDOG>   

                    R        _NOTD
                    Rnot     _NOTD
                    y        _NOTD
                    c        _NOTD
                    inv      _NOTD
                    q        _NOTD
                    kbar     _NOTD
                    rk       _NOTD
                    k        _NOTD
                    u        _NOTD
                    w        _NOTD
                    L        _NOTD
                    Rk       _NOTD
                    n        _NOTD
                    mc       _NOTD
                    pit      _NOTD
                    mrs      _NOTD
                    gdp      _NOTD
                    g        _NOTD
                    sigma_w  _NOTD
                    ztild    _NOTD
                    z        _NOTD
                    b        _NOTD
                    mu       _NOTD
                    rm       _NOTD
                    asw      _NOTD
                    omegabar      _NOTD
                    Welf      _NOTD
                    Util      _NOTD
                    ptilde      _NOTD
                    epsilon_z            _NOTD
                    epsilon_b            _NOTD
                    epsilon_sigma_w      _NOTD
                    epsilon_g            _NOTD
                    epsilon_rm           _NOTD
                    epsilon_asw         _NOTD
                    epsilon_mu           _NOTD
                    one              _DTRM



EQUATION> Notational rule (1)
EQTYPE> IMPOSED
EQ>     Rnot=rho_r*(LAG(Rnot,1))+(1-rho_r)*(phi1*ptilde+phi2*y)+phi3*(y-LAG(y,1))+rm

EQUATION> Nom interest rate (2)
EQTYPE> IMPOSED
EQ>     R =  Rnot

EQUATION> Euler Equation (3)
EQTYPE> IMPOSED
EQ>     c*(1+hab*emzstar)=(hab*emzstar-1)*(R+(iota_b-1)*LEAD(pit,1))
+ hab*emzstar*(LAG(c,1)-z)
+LEAD(c,1)+(rho_z-1)/(1-alpha_p)*ztild - b


EQUATION> Tobin's q law of motion (4)
EQTYPE> IMPOSED
EQ>     q = (S2*e2zstar) * (1+beta)*(inv - mu -(LAG(inv,1)-z)/(1+beta)
 -beta /(1+beta)*(LEAD(inv,1)+(rho_z-1)/(1-alpha_p)*ztild))


EQUATION> Raw Capital law of motion (5)
EQTYPE> IMPOSED
EQ>     kbar=(1-delta)*emzstar*(LAG(kbar,1)-z)+IKbar*(inv + S2*e2zstar*(1+beta)*mu)

EQUATION> Spread (6)
EQTYPE> IMPOSED
EQ>     LEAD(Rk,1)-R = zeta_spb*(q+kbar-n)+sigma_w + iota_b*LEAD(pit,1)

EQUATION> Entrepreneurs' return (7)
EQTYPE> IMPOSED
EQ>    Rk-pit=(rk_st*rk+(1-delta)*q)/(rk_st+1-delta)-LAG(q,1)

EQUATION> Services of capital (8)
EQTYPE> IMPOSED
EQ>    k=u-z+LAG(kbar,1)

EQUATION> Rental rate of capital (9)
EQTYPE> IMPOSED
EQ>     (1-phi)/phi*rk=u


EQUATION> Firms capital / labor ratio (10)
EQTYPE> IMPOSED
EQ>    k=w-rk+L


EQUATION> Real marginal cost (11)
EQTYPE> IMPOSED
EQ>    mc=w+alpha*(L-k)

EQUATION> Aggregate Production function (12)
EQTYPE> IMPOSED
EQ>    y=PHI_p*(alpha*k+(1-alpha)*L)+(PHI_p-1)*ztild/(1-alpha)


EQUATION> Aggregate Resource constraint (13)
EQTYPE> IMPOSED
EQ>    y = gst*g + CY*c + IY*inv + rk_st*KY*u + bigtheta*((1-varrho)/varrho)*nkstar*KbarY*n
          +muestar*Gstar*Rk_st*KY * (zeta_Gw * omegabar + Rk + LAG(q,1) + LAG(kbar,1) )

EQUATION> Definition of GDP (14)
EQTYPE> IMPOSED
EQ>    gdp = YGDP*( gst*g + CY*c + IY*inv + bigtheta*((1-varrho)/varrho)*nkstar*KbarY*n )

EQUATION> New Keynesian Phillips curve (15)
EQTYPE> IMPOSED
EQ>    pit=((1-zeta_p*beta)*(1-zeta_p)/zeta_p)/(1+ita_p*beta)*mc
+ita_p*LAG(pit,1)/(1+ita_p*beta) + beta*LEAD(pit,1)/(1+ita_p*beta)

EQUATION> Wage Phillips curve (16)
EQTYPE> IMPOSED
EQ>     w-LAG(w,1) + z = beta*ezstar * ( LEAD(w,1) - w )+ (1-zeta_w*beta)*(1-zeta_w*emzstar)/(zeta_w*emzstar) * (mrs - w) + asw
            +beta*emzstar*(rho_z-1)/(1-alpha_p)*ztild



EQUATION> Law of motion for net worth (17)
EQTYPE> IMPOSED
EQ>    n = zeta_nRk*(Rk-pit) - zeta_nR*(LAG(R,1)+(iota_b-1)*pit) + zeta_nqk*(LAG(q,1)+LAG(kbar,1)) + zeta_nn*LAG(n,1)
          -zeta_nsig*LAG(sigma_w,1) - varrho*VN*z 


EQUATION> Threshold for omegabar (18)
EQTYPE> IMPOSED
EQ>     omegabar = ( (LAG(q,1)+LAG(kbar,1)-LAG(n,1))/xstar - Rk + LAG(R,1)+iota_b*pit - zeta_zsigw/zeta_spsigw*LAG(sigma_w,1) ) / zeta_zw


EQUATION> Inflation Definition (19)
EQTYPE> IMPOSED
EQ>     pit = ptilde-LAG(ptilde,1)



EQUATION> Technology shock (20)
EQTYPE> IMPOSED
EQ>     ztild=rho_z*LAG(ztild,1)+epsilon_z

EQUATION> Technology shock 2(21)
EQTYPE> IMPOSED
EQ>     z=((rho_z-1)*LAG(ztild,1)+epsilon_z)/(1-alpha)


EQUATION> Government spending (22)
EQTYPE> IMPOSED
EQ>     g=rho_g*LAG(g,1)+epsilon_g

EQUATION> Preference shock (23)
EQTYPE> IMPOSED
EQ>     b=rho_b*LAG(b,1)+epsilon_b


EQUATION> Investment specific technology shock (24)
EQTYPE> IMPOSED
EQ>     mu=rho_mu*LAG(mu,1)+epsilon_mu



EQUATION> Monetary Policy shock (24)
EQTYPE> IMPOSED
EQ>     rm=rho_rm*LAG(rm,1)+epsilon_rm



EQUATION> Reservation wage shock (25)
EQTYPE> IMPOSED
EQ>  asw=rho_asw*LAG(asw,1)+epsilon_asw


EQUATION> Risk shock (26)
EQTYPE> IMPOSED
EQ> sigma_w=rho_sigma_w*LAG(sigma_w,1)+epsilon_sigma_w


EQUATION> MRS (27)
EQTYPE> IMPOSED
EQ>    (1-hab*emzstar)*mrs = varphi*(1-hab*emzstar)*L+c-hab*emzstar*(LAG(c,1)-z)

EQUATION> Welfare (28)
EQTYPE> IMPOSED
EQ>    Welf = (1-beta)* Util + beta*LEAD(Welf,1) 


EQUATION> Utility (29)
EQTYPE> IMPOSED
EQ>    Util = (1/( 1 - hab*emzstar ))*(c-hab * (LAG(c,1) - z) )


EQUATION> Innovation
EQTYPE> IMPOSED
EQ>     epsilon_z = 0*one

EQUATION> Innovation
EQTYPE> IMPOSED
EQ>     epsilon_b = 0*one

EQUATION> Innovation
EQTYPE> IMPOSED
EQ>     epsilon_sigma_w = 0*one

EQUATION> Innovation
EQTYPE> IMPOSED
EQ>     epsilon_g = 0*one


EQUATION> Innovation
EQTYPE> IMPOSED
EQ>     epsilon_rm = 0*one


EQUATION> Innovation
EQTYPE> IMPOSED
EQ>     epsilon_asw = 0*one


EQUATION> Innovation
EQTYPE> IMPOSED
EQ>     epsilon_mu = 0*one




EQUATION > one
EQTYPE > IMPOSED
EQ >    one = LAG(one,1)		

END
