BEQM non-core equations

log(c)-log(c(-1))+ydotgap=0.197*(log(eagg/eagg(-1))+ndotgap)-1.125*(rg-rg(-1))+0.221*(log(ly/ly(-1))+ydotgap)+varrho*0.194*(log(phse*d(-1))-log(phse(-1)*d(-2))+ydotgap(-1))-0.125*(log(c(-1))-log(c_core(-1)))+0.006*(log(a(-1))-log(a_core(-1)))+c_res;

log(id)-log(id(-1))+ydotgap=-6.859*(rg(-1)-rg(-2))+1.667*(log(c(-2))-log(c(-3))+ydotgap(-2))-0.153*(log(id(-1))-log(id_core(-1)))+id_res;

log(ik)-log(ik(-1))+ydotgap=0.346*(log(y(-1))-log(y(-2))+ydotgap(-1)-(log(y(-2))-log(y(-3))+ydotgap(-2)))+0.067*(log(ik(-1))-log(ik(-2))+ydotgap(-1))-0.107*(log(ik(-1))-log(ik_core(-1)))-0.255*(log(k(-1))-log(k_ss(-1)))+ik_res;

io=io_core+io_res;

dels=s-s(-1)/(1+ydot)+dels_res;

s=s_core+s_res;

log(x)-log(x(-1))+ydotgap=0.73*(log(cf)-log(cf(-1))+ydotgap)-0.172*(log(x(-1))-log(x_core(-1)))+x_res;

mi=rhoch*ch+rhoikh*ikh+rhog*g+rhox*x+mi_res;

log(cm)-log(cm(-1))+ydotgap=1.134*(log(c/c(-1))+ydotgap)+0.221*(log(c(-1))-log(c(-2))+ydotgap(-1))-0.187*(log(pcm/pch)-log(pcm(-1)/pch(-1)))-0.08*(log(cm(-1)/c(-1))-log(cm_core(-1)/c_core(-1)))+cm_res;

log(ikm)-log(ikm(-1))+ydotgap=0.242*(log(ikm(-1)/ikm(-2))+ydotgap(-1))-0.526*(log(pkm/pkh)-log(pkm(-1)/pkh(-1)))-0.056*log(ikm(-1)/ikm_core(-1))+ikm_res;

ch=c-cm;

ikh=ik-ikm;

pdot-pdot(-1)=0.138*fu(-1)/100-0.421*(pdot(-1)-pdot(-2))+0.047*(pmindot(-1)-pmindot(-2))-0.35*(pdot(-2)-pdot(-3))+0.072*(log(eagg(-1))-log(e_ss(-1)+eg_ss(-1)))-0.332*(pdot(-1)-pdot_core(-1))+pdot_res;

fu=100*(y-ycap)/ycap;

ycap=tfp*((1-alpha)*((1-phi)*e*avhstar)^(1-1/sigmay)+alpha*(phi*z_ss*k(-1)/(1+ydot))^(1-1/sigmay))^(sigmay/(sigmay-1));

log(px)-log(px(-1))=0.373*log(px(-1)/px(-2))+0.119*log(px(-3)/px(-4))-0.046*log(px(-1)/px_core(-1))+px_res;

log(phse)-log(phse(-1))+lambdotgap=0.611*(log(phse(-1)/phse(-2))+lambdotgap(-1))-1.452*(rg(-2)-rg(-3))-0.019*(log(phse(-1))-log(pdv(-1))+2.02934408207531)+0.192*(log(phse(-2)/phse(-3))+lambdotgap(-2))+0.071*(log(phse(-3)/phse(-4))+lambdotgap(-3))+phse_res;

d4cpi=0.25*(pdot+pdot(-1)+pdot(-2)+pdot(-3)-(cpiwedge+cpiwedge(-1)+cpiwedge(-2)+cpiwedge(-3)));

pch=(pc*c-pcm*cm)/ch+pch_res;

pcm=pcm_core+pcm_res;

pmin=pmin_core+pmin_res;

pmindot=(1+pdot)*pmin/pmin(-1)-1;

pc=1;

px=kapxv*pxv+rhox*pmin+(1-rhox-kapxv)*pbpa;

pch=kapchv*pchv+rhoch*pmin+(1-kapchv-rhoch)*pbpa;

pg=kapgv*pgv+rhog*pmin+(1-kapgv-rhog)*pbpa;

pkh=kapikhv*pkhv+rhoikh*pmin+(1-kapikhv-rhoikh)*pbpa;

pio=kapiov*piov+(1-kapiov)*pbpa;

log(pdv)=log(pdv_core)+pdv_res;

pg=pg_core+pg_res;

pkg=pg_core+pkg_res;

pkm=pkm_core+pkm_res;

pkh=pkh_core+pkh_res;

pio=pio_core+pio_res;

psv=psv_core+psv_res;

pgc=(pg*g-pkg*ig)/gc+pgc_res;

pbpa=tauc*py*y/(ym-y)+pbpa_res;

pym*ym=ch*pch+id*pdv+pkh*ikh+g*pg+x*px+io*pio+dels*psv-pmin*mi+sdexp;

py=(pym*ym-pbpa*(ym-y))/y+py_res;

cpixrdot=pdot-cpiwedge+cpixrdot_res;

cprdot=pdot-cpiwedge+cprdot_res;

cpidot=mucpr*cprdot+(1-mucpr)*cpixrdot+cpidot_res;

rpxchdot=cpidot+rpixwedge+rpxchdot_res;

rphdot=0.5*(phse/phse(-1)*(1+pdot)*(1+lambdot)-1)+0.25*(phse(-1)/phse(-2)*(1+pdot(-1))*(1+lambdot(-1))-1)+0.25*rphdot(-1)+rphdot_res;

rpccdot=dumq2*(taxd/taxd(-1)*(1+pdot)*(1+lambdot)*(1+ndot)-1-(d/d(-1)*(1+lambdot)*(1+ndot)-1))+rpccdot_res;

rpixdot=mucc/(1-mumip)*rpccdot+murph/(1-mumip)*rphdot+(1-(murph+mucc)/(1-mumip))*rpxchdot+rpixdot_res;

mipsdot=rg/rg(-1)-1+phse/phse(-1)*(1+pdot)*(1+lambdot)-1+d/d(-1)*(1+lambdot)*(1+ndot)-1+mipsdot_res;

rpidot=mumip*mipsdot+(1-mumip)*rpixdot+rpidot_res;

rpidotsa=rpidot+0.0017*dumq1-0.005*dumq2+0.0035*dumq3-0.0002*dumq4+rpidotsa_res;

cpixr=cpixr(-1)*(1+cpixrdot);

cpr=cpr(-1)*(1+cprdot);

cpi=(dumq1*cpi(-1)+dumq2*cpi(-2)+dumq3*cpi(-3)+dumq4*cpi(-4))*((1-mucpr)*cpixr/(dumq1*cpixr(-1)+dumq2*cpixr(-2)+dumq3*cpixr(-3)+dumq4*cpixr(-4))+mucpr*cpr/(dumq1*cpr(-1)+dumq2*cpr(-2)+dumq3*cpr(-3)+dumq4*cpr(-4)))*(1+cpi_res);

rph=rph(-1)*(1+rphdot);

rpcc=rpcc(-1)*(1+rpccdot);

mips=mips(-1)*(1+mipsdot);

rpxch=rpxch(-1)*(1+rpxchdot);

rpxc=(dumq1*rpxc(-4)+dumq2*rpxc(-1)+dumq3*rpxc(-2)+dumq4*rpxc(-3))*(murph/(1-mumip-mucc)*rph/(dumq1*rph(-4)+dumq2*rph(-1)+dumq3*rph(-2)+dumq4*rph(-3))+(1-murph/(1-mumip-mucc))*rpxch/(dumq1*rpxch(-4)+dumq2*rpxch(-1)+dumq3*rpxch(-2)+dumq4*rpxch(-3)))*(1+rpxc_res);

rpix=(dumq1*rpix(-4)+dumq2*rpix(-1)+dumq3*rpix(-2)+dumq4*rpix(-3))*(mucc/(1-mumip)*rpcc/(dumq1*rpcc(-4)+dumq2*rpcc(-1)+dumq3*rpcc(-2)+dumq4*rpcc(-3))+(1-mucc/(1-mumip))*rpxc/(dumq1*rpxc(-4)+dumq2*rpxc(-1)+dumq3*rpxc(-2)+dumq4*rpxc(-3)))*(1+rpix_res);

rpi=(dumq1*rpi(-4)+dumq2*rpi(-1)+dumq3*rpi(-2)+dumq4*rpi(-3))*(mumip*mips/(dumq1*mips(-4)+dumq2*mips(-1)+dumq3*mips(-2)+dumq4*mips(-3))+(1-mumip)*rpix/(dumq1*rpix(-4)+dumq2*rpix(-1)+dumq3*rpix(-2)+dumq4*rpix(-3)))*(1+rpi_res);

q=q_core+q_res;

v=v_core+v_res;

rk=rk_core+rk_res;

bk=mubkv*v+bk_res;

log(w)-log(w(-1))+lambdotgap=-pdot+rpidotsa+0.508*(log(w(-1)/w(-2))+lambdotgap(-1)+pdot(-1)-rpidotsa(-1))-0.488*(rpidotsa-rpidotsa(-1))-0.599*(rpidotsa(-1)-rpidotsa(-2))-0.519*(rpidotsa(-2)-rpidotsa(-3))-0.12*(u-u_ss)-0.42*log(w(-1)/w_core(-1))+w_res;

log(wg)-log(wg(-1))+lambdotgap=0.348*(log(w(-1))-log(w(-2))+lambdotgap(-1))-0.166*(log(wg(-1))-log(w(-1)*muwg(-1)))+wg_res;

log(e)-log(e(-1))+ndotgap=0.649*(log(e(-1)/e(-2))+ndotgap(-1))+0.094*(log(y/y(-1))+ydotgap)-0.031*log(e(-1)/e_core(-1))+0.053*fu(-1)/100+e_res;

log(avh)-log(avh(-1))=0.56*log(avh(-1)/avh(-2))+0.037*(log(y/y(-1))+ydotgap)+0.055*(log(y(-1)/y(-2))+ydotgap(-1))-0.048*log(avh(-1)/avh_core(-1))+avh_res;

log(l)-log(l(-1))+ndotgap=0.499*(log(l(-1)/l(-2))+ndotgap(-1))+0.249*(log(l(-2)/l(-3))+ndotgap(-2))+0.044*(log((w(-2)*e(-2)+wg(-2)*eg(-2))/eagg(-2))-log((w(-3)*e(-3)+wg(-3)*eg(-3))/eagg(-3))+lambdotgap(-2))-0.099*log(l(-1)/l_core(-1))+l_res;

log(eh)=log(e)+log(avh)+eh_res;

bg*pg=(1+rg(-1))*bg(-1)*pg(-1)/((1+pdot)*(1+ydot))+pc(-1)*mon(-1)/((1+pdot)*(1+ydot))+pg*g+(1+ecostg)*wg*eg+gosgexp+trans-tax-pc*mon+bg_res;

taulumpc=taulumpc(-1)+thetabg*(bg-bgtar)/(py*y)+thetadbg*(bg/(py*y)-bg(-1)/(py(-1)*y(-1)))+taulumpc_res;

bgtar=mubgy*py*y/pg+bgtar_res;

(1+ecostg)*wg*eg-(1+ecostg)*wg_core*eg_core=eg_res;

pg*g-pg_core*g_core=g_res;

ig-ig_core=ig_res;

gc=g-ig+gc_res;

gosgexp-gosgexp_core=gosgexp_res;

tax=taxw+taxee+taxd+taxef+taxk+taxlumpc+taxlumpk+taxf+taxind+gosgexp+tax_res;

taxw=tauw*(w*e+wg*eg)+taxw_res;

taxee=tauee*(w*e+wg*eg)+taxee_res;

taxd=taud*pdv*d+taxd_res;

taxef=tauef*(w*e+wg*eg)+taxef_res;

taxk=tauknd*py*y+taxk_res;

taxlumpc=taulumpc*y*py+taxlumpc_res;

taxlumpk=taulumpk*y*py+taxlumpk_res;

taxf=tauf*y*py+taxf_res;

taxind=pbpa*(ym-y)+transksubs-taxeu+taxind_res;

ecost=tauef+trkp+ecost_res;

ecostg=tauef+trec;

taxeu=taueu*py*y+taxeu_res;

trans=transc+transu+transk+transf+transksubs+rgprem+trans_res;

transc=trc*y*py+transc_res;

transfp=trfp*y*py+transfp_res;

transu=ben*u*l+transu_res;

transk=trk*y*py+transk_res;

transf=trf*y*py+transf_res;

transksubs=trksubs*y*py+transksubs_res;

transec=trec*wg*eg+transec_res;

rg=(1-thetarg)*(rg_core+thetapdot*(d4cpi-pdotss)+thetay*log((y+gl)/ystar))+thetarg*rg(-1)+rg_res;

ystar=tfp*((1-alpha)*((1-phi)*(1-u_ss)*l_ss*avhstar)^(1-1/sigmay)+alpha*(phi*k(-1)/(1+ydot))^(1-1/sigmay))^(sigmay/(sigmay-1));

gl=tfp*((1-alpha)*((1-phi)*eagg*avhstar)^(1-1/sigmay)+alpha*(phi*k(-1)/(1+ydot))^(1-1/sigmay))^(sigmay/(sigmay-1))-tfp*((1-alpha)*((1-phi)*e*avhstar)^(1-1/sigmay)+alpha*(phi*k(-1)/(1+ydot))^(1-1/sigmay))^(sigmay/(sigmay-1));

chv=ch*kapchv;

ikhv=ikh*kapikhv;

iov=kapiov*io;

gv=g*kapgv;

xv=kapxv*x;

y=c+id+ik+io+dels+g+x-cm-ikm-mi+sd-bpa+y_res;

yd=chv+id+ikhv+iov+gv+xv;

ym=y+bpa+ym_res;

bpa=(1-kapchv-rhoch)*ch+(1-kapikhv-rhoikh)*ikh+(1-kapgv-rhog)*g+(1-kapxv-rhox)*x+(1-kapiov)*io+bpa_res;

ioexp=pio*io+ioexp_res;

cir=cir_core+cir_res;

cirexp=psicir*pdv*d+cirexp_res;

bf*pc/q+bg*pg+v+bk=pc(-1)*mon(-1)/((1+ydot)*(1+pdot))-pc*mon+(1+rf(-1))*bf(-1)*pc/((1+ydot)*(1+pdotf)*q)+(1+rg(-1))*bg(-1)*pg(-1)/((1+ydot)*(1+pdot))+v+dv+(1+rk(-1))*bk(-1)/((1+ydot)*(1+pdot))+wl*l-pc*c+transc+transkc+transkp+transfp+rfprem+rgprem-taxlumpc+transec-pdv*(d-(1-deltad)*d(-1)/(1+ydot))-taud*pdv*d+bf_res;

mon=mon_core/c_core*c+mon_res;

dv=chv*pchv+ikhv*pkhv+iov*piov+pxv*xv+pdv*id+gv*pgv+psv*dels-(1+ecost)*w*e-ikh*pkh-psv*dels-transkc-ikm*pkm-io*pio-rk(-1)*bk(-1)/((1+ydot)*(1+pdot))+bk-bk(-1)/((1+ydot)*(1+pdot))-taxk-taxlumpk-transkf+transk;

transkp=trkp*w*e+transkp_res;

transkf=trkf*py*y+transkf_res;

transkc=psisnp*py*y;

a=v+bk+bg*pg+mon*pc+nfa;

d=(1-deltad)*d(-1)/(1+ydot)+id+d_res;

kh=(1-deltakh)*kh(-1)/(1+ydot)+ikh+kh_res;

km=(1-deltakm)*km(-1)/(1+ydot)+ikm+km_res;

k=(psik*(phik*kh)^(1-1/sigmak)+(1-psik)*((1-phik)*km)^(1-1/sigmak))^(sigmak/(sigmak-1));

ly=wl*l+transc;

u=(l-en-eg)/l;

eagg=en+eg;

wagg=eg/eagg*wg+(1-eg/eagg)*w;

en=e;

wl=(1-u-mueg)*(1-tauw-tauee)*w+u*ben+mueg*(1-tauw-tauee)*wg;

ben=mubenw*w;

mueg=eg/l;

nfa=bf*pc/q+nfa_res;

xm=px*x-pcm*cm-pkm*ikm-pmin*mi;

xmca=px*x-pcm*cm-pkm*ikm-pmin*mi+taxf-transf-transkf+transfp-taxeu+rfprem+rf(-1)*nfa(-1)/((1+pdot)*(1+ydot))+xmca_res;

ydotgap=log(1+ydot)-log(1+ydotss);

lambdotgap=log(1+lambdot)-log(1+lambdotss);

ndotgap=log(1+ndot)-log(1+ndotss);

1+wdot=(1+pdot)*(1+lambdot)*w/w(-1);

pchvdot=(1+pdot)*pchv/pchv(-1)-1;

pcmdot=(1+pdot)*pcm/pcm(-1)-1;

pchdot=(1+pdot)*pch/pch(-1)-1;

eer=eer(-1)*q/q(-1)*(1+pdotf)/(pcdef/pcdef(-1));

pcdef=pcdef(-1)*(1+pdot);

aakp=(dels-(s-s(-1)/(1+ydot)))*lambda*nhds;

gdpexp=pym*ym+cirexp+(1+ecostg)*wg*eg+gosgexp+gdpexp_res;

gdpbpexp=py*y+cirexp+(1+ecostg)*wg*eg+gosgexp+gdpexp_res;

gonsexp=pg*g+(1+ecostg)*wg*eg+gosgexp;

gons=gonsexp/pgons;

gdp=ym+cir+gons-g+gdp_res;

gdpbp=y+cir+gons-g+gdp_res;

pgdp=gdpexp/gdp;

pgdpbp=gdpbpexp/gdpbp;

avhrs=avhrs(-1)*avh/avh(-1);

avhrsg=avhrsg(-1)*avh_ss/avh_ss(-1)+avhrsg_res;

avhrsagg=avhrs*e/eagg+avhrsg*eg/eagg;

compcp=(1+ecost)*w*e*lambda*nhds*pcdef;

compgcp=(1+ecostg)*wg*eg*lambda*nhds*pcdef;

ipdgcp=rgpremcp+rg(-1)*bgcp(-1)+ipdgcp_res;

ipdfcp=rfpremcp+rf(-1)*nfacp(-1)+ipdfcp_res;

dvcp=dv*lambda*nhds*pcdef+dvcp_res;

ipdpcp=ipdgcp+ipdfcp+dvcp+rk(-1)*bkcp(-1)-transkccp+ipdpcp_res;

gospcp=gospcp(-1)*circp/circp(-1)+gospcp_res;

transbencp=transccp+transucp;

transctcp=transbencp+transkpcp+transeccp+transfpcp;

taxpcp=taxwcp+taxeecp+taxlumpccp+taxdcp;

cnacp=ccp+circp;

cnakp=ckp+cirkp;

pcnadef=cnacp/cnakp;

rhpikp=(1+rhpikp_res)*(wscp+wsgcp+gospcp+transctcp+ipdpcp-taxpcp)/pcnadef;

savr=(pcnadef*rhpikp-cnacp)/(pcnadef*rhpikp);

nlp=pcnadef*rhpikp-cnacp-idcp+nlp_res;

tmecp=gcp+transccp+transucp+transfcp+transkcp+transksubscp+ipdgcp+compgcp+gosgcp+tmecp_res;

nlgg=taxcp-tmecp+nlgg_res;

ggnbcp=tmecp-taxcp+ggnbcp_res;

nlf=-xmcacp+nlf_res;