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An Introduction to the New Zealand Treasury Model

Appendix 2:  Dynamic equations

Please note that the definitions of variable names are available in Appendix 4 and all the endogenous variables are in bold.

Production block

Profit maximising conditions.

a1 =a1(-1)*exp(beta*0.25)

a3 =a3(-1)*exp(beta2*0.25)

a5 =a5(-1)*exp(beta1*0.25)

Labour market

log(nthpr1)=(pa1_1*log((nthsr(-1))*exp(popgr_eq))+(1-pa1_1)*log((nthpr1(-1))*exp (popgr_eq)))+pa1_2*log(rpydmr(-2))

nthpr1=nsr*prhr_eq*13/1000

nt =nsr+ngg_eq

partt = pa2_1*partt(-1)+pa2_2*(partt_eq)+pa2_3*(nairu-urt)+pa2_4*(nairu(-1)-urt(-1))

log(nts)=log(partt/100*(rpop3_eq*(pop3_eq+pop4_eq)))

urt =100*(1-nt/nts)

Real exchange rates

re =0.25*ere+0.25*ere(-1)*exp(eregr)+0.25*ere(-2)*exp(eregr+eregr(-1))

+0.25*ere(-3)*exp(eregr+eregr(-1)+eregr(-2))+pa3_1* ldgdpr(+7)+pa3_2*ldgdpr(+8)

log(e)=pa4_1*log(e(-1))+(1-pa4_1)*log(e(+1))+log((1+rcs/400)/(1+(rcsf+srp)/400))

+pa4_2*log(rer(-1)/re(-1))

rer =e*pydo

Export sector

log(cexps)=pa5_1*log((exp((gr-1)+(-1*beta1*0.25)))**3*exrsr(-3))

+(1-pa5_1)*log(exp((gr-1)+(-1*beta1*0.25))*cexps(-1))

log(ncexps)= pa6_1*log((exp((gr-1)))**2*encexps(-2))+ (1-pa6_1)*log(exp((gr-1))*ncexps(-1))+ pa6_2*log(rpexncs(-2)/erpexncs(-2)) +pa6_3*log(rpexncs(-3)/erpexncs(-3))+pa6_4*log(rpexncs(-4)/erpexncs(-4)) +pa6_5*log(rpexncs(-5)/erpexncs(-5))+pa6_6*log(rpexncs(-6)/erpexncs(-6))

log(ncexpg)= pa7_1*log((exp((gr-1)))**2*encexpg(-2))+ (1-pa7_1)*log(exp((gr-1))*ncexpg(-1)) +pa7_2*log(rpexncg(-3)/erpexncg(-3))

ncexp =ncexps+ncexpg

log(cexp)=log((1-cesratio_eq)*cexps)+0.3*log(kie(-1)/ekie(-1))

iie =cexps-cexp

texp =ncexp+cexp

Import sector

log(imo)=pa8_1*log(exp((gr-1)+(-1*beta2*0.25))*imsr(-1))+(1-pa8_1)*log(exp((gr-1)+(-1*beta2*0.25))*imo(-1))

log(imca/(ibfr+ggifr_eq))-log(imca(-1)/(ibfr(-1)+ggifr_eq(-1)))=pa9_1*(log(imca(-1)/(ibfr(-1)+ggifr_eq(-1))) -(pa401+pa402*log(rpmca(-1))))

log(imc/(conor))-log(imc(-1)/(conor(-1)))=pa10_1*(log(imc(-1)/(conor(-1))) -(pa404+pa405*log(rpmc(-2))+pa406*TF(-2))) +pa10_2*log(etwit(-2)/etwit(-3))

log(imcs/(conor))-log(imcs(-1)/(conor(-1)))=pa11_1*(log(imcs(-1)/(conor(-1))) -(pa407+pa408*log(rpmcs(-3)))) +pa11_2*log(etwit(-2)/etwit(-3))

im =imo+imc+imcs+imca

External sector

rdos =-1*(tbal+ibal+tfbal+rmtransfer_eq)

tbal =rpexc*cexp+rpexnc*ncexp-im*rpm/(1+pol5_eq)

ibal =ryospr+ryospu

tfbal =rtrospr-rtrpuos

rfdebt1 =rfdebt+rdos

rfdebt =rfdebt1(-1)

dgdpr =rfdebt/rgdp

rtnziaa =tnziar_eq*rgdp

rapa =rtnziaa*0.2

rap =0.8*rtnziaa-0.7*rnzsal

rfdebt=rtfinza-rtnziaa

rtfinza=rzpa+rzp+rzga+rzg

rzp =fpdratio_eq*(rzp+rzpa)

rtrospr = pol14_eq*rgdp

ryospr =-((rif_eq+ereturn)*(rzp)+(ri_eq+ereturn)*rzpa)+(rif_eq+ereturn)*(rap)

+(ri_eq+ereturn)*rapa

ryospu =-((rif_eq)*(rzg)+(ri_eq)*rzga)+(rif_eq)*(0.7*(rnzsal))

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