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# Appendix 2 Equations for the steady state model

The model equations are reported using TROLL syntax. Each equation begins with a label, which indicates the endogenous variable in the system. All the variables with a suffix _eq are steady state values and all the nominal variables are deflated by PYD.

## PRODUCTION BLOCK

RPTSR: RPTSR=((RPTEX/(A5))**(THETA/(THETA-1)) +(RPYD/A6A)**(THETA/(THETA-1)))**((THETA-1)/THETA),

RPYSR: RPYSR=A4A*(RPTSR**(DELTA/(DELTA-1)) -(RPM/(A3))**(DELTA/(DELTA-1)))**((DELTA-1)/DELTA),

RWA: RWA=(A1)*(RPYLR**(RHO/(RHO-1)) -(RPKLR/A2A)**(RHO/(RHO-1)))**((RHO-1)/RHO),

YSR: YSR=1000000*(((A1)*NSR/1000000)**RHO +(A2A*KBF/1000000)**RHO)**(1/RHO),

KBF: KBF=1/A2A*(A1)*NSR*((RPYSR/(RWA/(A1))) **(RHO/(RHO-1))-1)**(1/RHO),

YD: YD=TSR/A6A*(RPYD/(A6A*RPTSR))**(-1/(1-THETA)),

TSR: TSR=((A4A*YSR)**DELTA+((A3)*IMSR)**DELTA)**(1/DELTA),

EXRSR: EXRSR=TSR/(A5)*(RPTEX/((A5)*RPTSR))**(1/(THETA-1)),

IMSR: RPM=(A3)*RPTSR*((IMSR*(A3)/(YSR*A4A))**(-DELTA)+1) **((1-DELTA)/DELTA),

RPTLR: RPTLR=RPTSR,

RPYLR: RPYLR=RPYSR,

RPKLR: RPKLR=RPKLR_EQ,

AR: AR=RPKLR,

PNA10: PNA10=TEXPS+YD-IM,

A1: A1=A1(-1)*EXP((BETA)*0.25),

A3: A3=A3(-1)*EXP(π1*0.25),

A5: A5=A5(-1)*EXP(π2*0.25),

GR: GR=EXP((BETA)*0.25)*EXP(POPGR_EQ),

GR_1: GR_1=(GR-1),

## LABOUR MARKET

NTS: PARTT=100*NTS/(RPOP3*(POP3_EQ+POP4_EQ)),

NSR: URT=100*(1-(NSR+NGG_EQ)/NTS),

NT: NT=NSR+NGG_EQ,

PARTT: PARTT=PARTT_EQ,

URT: URT= NAIRU,

POPGR_EQ: POPGR_EQ=LOG(POP3_EQ+POP4_EQ)-

LOG(POP3_EQ(-1)+POP4_EQ(-1)),

## CONSUMPTION SECTOR

COND: LOG(COND)=C0101+C0102*LOG((1-POL1)*RWA*NT+RTRPUPR +RTROSPR+RMTRANSFER)

+(1-C0102)*LOG((RB-RZPA-ZP/RE)+KH+KBF) -RLPCON,

RLPCON: RLPCON=LOG((CONO*(1+POL4_EQ)+CONH*RPCONH)/CON),

RPCONH: LOG(RPCONH/(1+POL4_EQ))=C0200+C0202*LOG(CONH/CONO)+

C0201*TREND,

CONH: CONH=CON-CONO,

SHARE: CONH=(SHARE/(1+SHARE))*(COND*EXP(RLPCON))/RPCONH,

CON: CON=COND,

RINCOME: RINCOME=(1-POL1)*RWA*NT+RTRPUPR +RTROSPR+RMTRANSFER,

RWEALTH: RWEALTH= (RB-RZPA-ZP/RE)+KH+KBF,

## STOCK and INVESTMENT

DEM: IINR=YD-DEM,

CONO: DEM=CONO+(IH+IBF+GGCO_EQ+GGIF_EQ),

KINR1: KINR1=KINR+IINR,

IINR: IINR=SSRATIO_EQ*YD,

KINR: KINR=KINR1(-1),

KH: KH=CONH/(KSRATIO),

IH: IH=(DRRB_EQ+GR_1)*KH,

KH1: KH1=KH*(1-DRRB_EQ)+IH,

IBF: IBF=KBF1-KBF*(1-DR_EQ),

KBF1: KBF1=KBF*GR,

IIE: IIE=CESRATIO_EQ*CEXPS,

KIE: KIE =KIE1(-1),

KIE1: KIE1=KIE+IIE,

RP1: RP1=AR-(DR_EQ+RI),

RP : RP= KSRATIO*(RPCONH-POL7_EQ)-(DRRB_EQ+RI),

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