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OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalCash in AdvanceDiscussing three examplesSharif University of TechnologyFebruary 23, 2016Special Topics in MacroeconomicsCash in Advance

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalSpecial Topics in MacroeconomicsCash in Advance

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalHousehold’s ProblemFirm’s Problem & Equilibrium ConditionsF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockSvenson ModelHousehold’s ProblemFirm’s Problem & Equilibrium ConditionsF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockEarly Financial Markets (Lucas Model)CIA with CapitalSpecial Topics in MacroeconomicsCash in Advance

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalHousehold’s ProblemFirm’s Problem & Equilibrium ConditionsF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockHousehold:max{ct ,mt ,nt ,bt }E0( X)tβ ((1 γ) ln(ct ) γ ln(1 nt ))t 0Subject to Budget Constraint: ct bt mt wt nt Cash in Advance:ct Special Topics in Macroeconomics1 it1 πt bt 1 mt 11 πtCash in Advancemt 1 τt1 πt(1)

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalHousehold’s ProblemFirm’s Problem & Equilibrium ConditionsF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockFirm:max (At nt wt nt ){nt }wt At(2)ct At nt(3)Goods market Clearing:Money Market Clearing:mt (1 µt )Mt 1 Pt 11 µtMt . mt 1PtPt 1Pt1 πt(4)Bonds Market Clearing:bt 0Special Topics in MacroeconomicsCash in Advance(5)

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalHousehold’s ProblemFirm’s Problem & Equilibrium ConditionsF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockFirst Order Conditions:1 γ λ1t λ2tctγ λ1t wt[nt ] :1 nt λ1t 1 λ2t 1[mt ] : λ1t βEt1 πt 1 1 it 1[bt ] : λ1t βEt λ1t 11 πt 1[ct ] :Special Topics in MacroeconomicsCash in Advance(6)(7)(8)(9)

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalSteady State equilibrium: 1 γn̄ (1 γ) γ(1 ρ)(1 µ̄)c̄ Ān̄m̄ c̄(1 µ̄)Special Topics in MacroeconomicsHousehold’s ProblemFirm’s Problem & Equilibrium ConditionsF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply Shockπ̄ µ̄ī (1 ρ)(1 µ̄) 1w̄ ĀCash in Advance

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalHousehold’s ProblemFirm’s Problem & Equilibrium ConditionsF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockAfter simplifying equations and omitting λ1t & λ2t :πbbtcbt m[t 1 1 π̄ ib dbtπdt 1Et {cd t 1 cbt } Et 1 ī 1 π̄ bibtct n̄ nbt A1 n̄1 īct nbtcbt Aµbbtπbbtm[ mctt 1 1 µ̄ 1 π̄cbt Special Topics in MacroeconomicsCash in Advance(1)(2)(3)(4)(5)

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalSpecial Topics in MacroeconomicsHousehold’s ProblemFirm’s Problem & Equilibrium ConditionsF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockCash in Advance

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalSpecial Topics in MacroeconomicsHousehold’s ProblemFirm’s Problem & Equilibrium ConditionsF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockCash in Advance

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalHousehold’s ProblemF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockSvenson ModelEarly Financial Markets (Lucas Model)Household’s ProblemF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockCIA with CapitalSpecial Topics in MacroeconomicsCash in Advance

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalHousehold’s ProblemF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockHousehold:max{ct ,mt ,lt ,bt ,kt 1 }E0( X)tβ ((1 γ) ln(ct ) γ ln(1 nt ))t 0Subject to Budget Constraint: ct bt mt wt nt Cash in Advance:ct 1 it1 πt bt 1 mt 1 bt1 πtSpecial Topics in MacroeconomicsCash in Advancemt 1 τt1 πt(1)

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalHousehold’s ProblemF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockFirst Order Conditions:1 γ λ1t λ2tctγ λ1t wt[nt ] :1 nt λ1t 1 λ2t 1[mt ] : λ1t βEt1 πt 1 1 it 1[bt ] : λ1t λ2t βEt λ1t 11 πt 1[ct ] :Special Topics in MacroeconomicsCash in Advance(6)(7)(8)(9)

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalHousehold’s ProblemF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockSteady State equilibrium: 1 γn̄ (1 γ) γ(1 ρ)(1 µ̄)c̄ Ān̄π̄ µ̄m̄ c̄(1 µ̄)w̄ ĀSpecial Topics in Macroeconomicsī (1 ρ)2 (1 µ̄)2 1Cash in Advance

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalHousehold’s ProblemF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockAfter simplifying equations and omitting λ1t & λ2t :πbbtcbt m[t 1 1 π̄ id dddπdt 1t 1 πdt 2Et {cd t 2 cbt } Et 1 ī1 π̄ dn̄idπddt 1t 1c[nbt nd At 1 t 1 At 1 n̄1 π̄1 īct nbtcbt Aµbbtπbbtm[ mctt 1 1 µ̄ 1 π̄Special Topics in MacroeconomicsCash in Advance(1)(2)(3)(4)(5)

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalSpecial Topics in MacroeconomicsHousehold’s ProblemF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockCash in Advance

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalSpecial Topics in MacroeconomicsHousehold’s ProblemF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockCash in Advance

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalHousehold’s ProblemFirm’s Problem & Equilibrium ConditionsF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalHousehold’s ProblemFirm’s Problem & Equilibrium ConditionsF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockSpecial Topics in MacroeconomicsCash in Advance

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalHousehold:max{ct ,mt ,bt ,kt 1 }E0Household’s ProblemFirm’s Problem & Equilibrium ConditionsF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply Shock( X)β t ln(ct )t 0Subject to Budget Constraint: ct bt mt kt 11 it wt (1 δ vt )kt 1 πt bt 1 mt 1 τt1 πtCash in Advance:ct kt 1 (1 δ)kt Special Topics in Macroeconomicsmt 11 πtCash in Advance(1)

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalHousehold’s ProblemFirm’s Problem & Equilibrium ConditionsF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockFirm:max At ktα n1 α wt nt vt ktt {nt ,kt }wt (1 α)At ktαvt αAt ktα 1(2)(3)Goods market Clearing:ct kt 1 (1 δ)kt At ktα(4)Money Market Clearing:mt (1 µt )Mt 1 Pt 11 µtMt . mt 1PtPt 1Pt1 πt(5)Bonds Market Clearing:bt 0Special Topics in MacroeconomicsCash in Advance(6)

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalHousehold’s ProblemFirm’s Problem & Equilibrium ConditionsF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockFirst Order Conditions:1 λ1t λ2t(7)ct[kt 1 ] : λ1t λ2t Et {(1 δ)(λ1t 1 λ2t 1 ) λ1t 1 vt 1 } (8) λ1t 1 λ2t 1[mt ] : λ1t βEt(9)1 πt 1 1 it 1(10)[bt ] : λ1t βEt λ1t 11 πt 1[ct ] :Special Topics in MacroeconomicsCash in Advance

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalHousehold’s ProblemFirm’s Problem & Equilibrium ConditionsF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockSteady State equilibrium: αĀk̄ (1 ρ)(1 µ̄)(ρ δ)c̄ Āk̄ α δ k̄1 1 αm̄ (1 µ̄)(c̄ δ k̄)Special Topics in Macroeconomicsπ̄ µ̄ī (1 ρ)(1 µ̄) 1v̄ (1 ρ)(1 µ̄)(ρ δ)Cash in Advance

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalHousehold’s ProblemFirm’s Problem & Equilibrium ConditionsF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockAfter simplifying Equations:bibtπddt 1 (1)1 ī 1 π̄ dbvddid1 īibtπddt 1t 1t 1 (2)v̄1 ī (1 ī (1 δ)(1 π̄) 1 ī 1 π̄cdt 1 cbt bπbbtc̄cbt k̄ kdt 1 (1 δ)k̄ kt m[t 1 1 π̄c̄ δ k̄Special Topics in MacroeconomicsCash in Advance(3)

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalHousehold’s ProblemFirm’s Problem & Equilibrium ConditionsF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply Shockvbbtct (1 α)kbt Av̄bc̄cbt k̄ kdt 1 (1 δ)k̄ ktct αkbt Ac̄ δ k̄µbbtπbbtm[ mctt 1 1 µ̄ 1 π̄Special Topics in MacroeconomicsCash in Advance(4)(5)(6)

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalSpecial Topics in MacroeconomicsHousehold’s ProblemFirm’s Problem & Equilibrium ConditionsF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockCash in Advance

OutlineSvenson ModelEarly Financial Markets (Lucas Model)CIA with CapitalSpecial Topics in MacroeconomicsHousehold’s ProblemFirm’s Problem & Equilibrium ConditionsF.O.CsSteady State EquilibriumLog LinearizeTechnology ShockMoney Supply ShockCash in Advance

Cash in Advance Discussing three examples Sharif University of Technology February 23, 2016 Special Topics in Macroeconomics Cash in Advance. Outline Svenson Model Early Financial Markets (Lucas Model) CIA with Capital . Title: Cash in Advance - Discussing three examples Created Date: