SIMPLE DSGE MODELS OF MONEY DEMAND: PART I OCTOBER 4, 204
Inroducion BASIC ISSUES Money/moneary policy issues an enduring fascinaion in macroeconomics How can/should cenral bank conrol he economy? Should i/can i a all? Roles of money Medium of exchange (ransacions role) Uni of accoun (numeraire role) Sore of value (asse role) Ocober 4, 204 2
Inroducion BASIC ISSUES Money/moneary policy issues an enduring fascinaion in macroeconomics How can/should cenral bank conrol he economy? Should i/can i a all? Roles of money Medium of exchange (ransacions role) Uni of accoun (numeraire role) Sore of value (asse role) Highlighed in CIA, MIU, and New Monearis approaches Highlighed in New Keynesian approach How o model money demand in DSGE environmen? Which role o model? Which role is racable o model? Which role is mos relevan for conduc of moneary policy? Ocober 4, 204 3
HOUSEHOLDS Household opimizaion max E u( c, n ) c, n, M, B 0 0 Lump-sum moneary injecion/conracion s.. P he nominal price of c equivalenly, he nominal price level Pc M B Pw n M ( i ) B T Flow budge consrain Nominal consumpion spending Nominal money holdings Nominal bond holdings Pc M Nominal labor income Nominal ineres rae (on previously-accumulaed nominal bonds) Cash-in-advance (CIA) consrain - forces consumers o hold money Ocober 4, 204 4
HOUSEHOLDS Household opimizaion max E u( c, n ) c, n, M, B 0 0 Lump-sum moneary injecion/conracion s.. P he nominal price of c equivalenly, he nominal price level Pc M B Pw n M ( i ) B T Flow budge consrain Nominal consumpion spending Nominal money holdings Nominal bond holdings Pc M CIA consrain a fricion on economy Nominal labor income Nominal ineres rae (on previously-accumulaed nominal bonds) Cash-in-advance (CIA) consrain Pareo-opimal allocaions do no require i Money no essenial as in models of Kiyoaki and Wrigh (993), Lagos and Wrigh (2005) New Monearis Lieraure - forces consumers o hold money Does no ENDOGENOUSLY EXPAND consumers se of feasible rades. Because underlying DSGE model feaures full se (including over all sae-dae pairs) of Arrow securiies complee markes! Trade does no require money Ocober 4, 204 5
SIMPLE POLICY ANALYSIS Removing moneary fricion.requires an allocaion ha feaures a zero muliplier on CIA consrain implies zero nominal ineres rae Friedman Rule Benchmark resul in moneary heory Compleely relaxing moneary fricion requires eliminaing any (opporuniy) cos of holding money Ocober 4, 204 6
SIMPLE POLICY ANALYSIS Removing moneary fricion.requires an allocaion ha feaures a zero muliplier on CIA consrain implies zero nominal ineres rae Friedman Rule Really he same hing Benchmark resul in moneary heory Compleely relaxing moneary fricion requires eliminaing any (opporuniy) cos of holding money Oher Inerpreaions Eliminae he wedge beween alernaive nominal asses: i = 0 makes money and nominal bonds equivalen asses (in erms of heir cos and benefi properies) Eliminae he wedge in he consumpion-leisure opimaliy condiion Are moneary fricions empirically imporan?...and hus, is he Friedman Rule of pracical use for advising moneary policy? Ocober 4, 204 7
SIMPLE POLICY ANALYSIS Household opimaliy condiions hh muliplier on CIA consrain hh muliplier on budge consrain Noe disuiliy of labor appears in ineremporal MRS If moneary fricion were shu down, would have u c here as usual. i i un( c, n ) i w u ( c, n ) i c No-arbirage beween money and nominal bonds (Assumpion: i in he informaion se of ime ) Consumpion-leisure opimaliy condiion - relaive price depends on w AND i Efficiency requires C-L opimaliy depends on real wage. bu no on moneary aspecs of economy (nonechnology) u ( c, n ) ( i ) u ( c E, n ) P n n w w P Friedman Rule achieves efficiency along his margin Ocober 4, 204 8 Consumpion-savings opimaliy condiion (aka bond Euler equaion) (aka Fisher equaion!)
SIMPLE POLICY ANALYSIS Household opimaliy condiions hh muliplier on CIA consrain hh muliplier on budge consrain Noe disuiliy of labor appears in ineremporal MRS If moneary fricion were shu down, would have u c here as usual. i i un( c, n ) i w u ( c, n ) i c Eiher hrough Friedman Rule or hrough cashless New Keynesian environmen No-arbirage beween money and nominal bonds (Assumpion: i in he informaion se of ime ) Consumpion-leisure opimaliy condiion - relaive price depends on w AND i Efficiency requires C-L opimaliy depends on real wage. bu no on moneary aspecs of economy (nonechnology) u ( c, n ) ( i ) u ( c E, n ) P n n w w P Friedman Rule achieves efficiency along his margin Ocober 4, 204 9 Consumpion-savings opimaliy condiion (aka bond Euler equaion) (aka Fisher equaion!)
SIMPLE POLICY ANALYSIS Household opimaliy condiions (coninued) i i un( c, n) i w uc( c, n) i Res of he environmen u ( c, n ) ( i ) u ( c E, n ) P M c P n n w w P w = marginal produc of labor (linear producion + compeiive facor marke) Gov budge: Resource consrain: c zn T M M M No-arbirage beween money and nominal bonds Consumpion-leisure opimaliy condiion Consumpion-savings opimaliy condiion (aka bond Euler equaion) (aka Fisher equaion) Binding CIA consrain Obvious if i > 0 (why hold excess money?) Also assume i even in saes where i = 0: pins down a moneary equilibrium level of M, hence is an equilibrium selecion device Ocober 4, 204 0
SIMPLE POLICY ANALYSIS Define π + = P + / P μ + = M + / M - Household opimaliy condiions (coninued) i i un( c, n) i w uc( c, n) i Combine and - (binding) CIA consrains No-arbirage beween money and nominal bonds Consumpion-leisure opimaliy condiion un( c, n ) un( c, n ) ( i) E w w c c inflaion Ariculaes a quaniy-heoreic channel Consumpion-savings opimaliy condiion (aka bond Euler equaion) (aka Fisher equaion) Equilibrium link beween money growh and Res of he environmen w = marginal produc of labor (linear producion + compeiive facor marke) Gov budge: Resource consrain: c zn T M M M Examine seady-sae equilibrium Ocober 4, 204
SIMPLE POLICY ANALYSIS Household opimaliy condiions in deerminisic seady sae un(, c n) i w u (, c n) i c i i No-arbirage beween money and nominal bonds Consumpion-leisure opimaliy condiion Friedman Rule: i = 0 π = β - BUT ONLY IN STEADY STATE! NOT (necessarily) dynamically. and opimal policy calls for μ = β - (i.e., SHRINK nominal money supply!) Res of he environmen ( i) Consumpion-savings opimaliy condiion (aka bond Euler equaion) (aka Fisher equaion) Ariculaes a quaniy-heoreic channel Equilibrium link beween money growh and inflaion w = marginal produc of labor (linear producion + compeiive facor marke) Gov budge: Resource consrain: T / P ( )( M / P)(/( )) c n Ocober 4, 204 2
OTHER ANALYSIS Imply φ < 0, i.e., money NOT valued for exchange Oher aspecs of equilibrium μ < β - (in seady-sae!) inconsisen wih moneary equilibrium Dynamic analog: i < 0 inconsisen wih moneary equilibrium Zero-lower-bound consrain Model s policy rae ypically idenified wih a (shor-run Euler equaion) marke ineres rae Wheher CIA models, MIU models, New Keynesian models, money search models Model mechanism: change in policy rae (poenially) affecs ineremporal incenives (i.e., he real ineres rae) A valid empirical idenificaion? Term-srucure issues? Oher issues? See Canzoneri, Cumby, and Diba (2007 JME) Ocober 4, 204 3
CIA Models OTHER VARIANTS OF CIA Cash good/credi good model Lucas and Sokey (983) Foundaion for Ramsey models of opimal fiscal and moneary policy see Chari and Kehoe (999 Macro Handbook chaper) Subse of goods (c ) require cash in advance Subse of goods (c 2 ) do no require cash in advance u c i u MRS cash/credi = gross nominal ineres rae c2 Moneary policy creaes a STATIC wedge!... Invesmen in CIA consrain Sockman (98): long-run inflaion lowers long-run capial sock M c k ( ) k P Basic Idea: Posiive nominal ineres rae axes whaever is in he CIA consrain Ocober 4, 204 4
Oher Approaches ALTERNATIVE MONETARY MODELS Alernaives o CIA Money in he uiliy funcion (MIU) models E 0 0 Shopping-ime & ransacions coss models Nominal money holdings reduce cos of acquiring goods M uc, P Feensra (986 JME) shows condiions under which CIA, MIU, shopping-ime are equivalen Can hink of as Friedman Rule running in he background Go cashless New Keynesian models don model money demand a all (or, a bes, as an appendage separae from he main equilibrium) Go for New Monearis models Kiyoaki and Wrigh (989, 993) Lagos and Wrigh (2005), Aruoba, Waller, and Wrigh (20 JME) Ocober 4, 204 5