NOMINAL RIGIDITIES IN A DSGE MODEL: THE PERSISTENCE PUZZLE OCTOBER 4, 200 Empirical Moivaion EMPIRICAL EFFECTS OF MONETARY SHOCKS Hump-shaped responses o moneary shocks (Chrisiano, Eichenbaum, and Evans (2005 JPE)) GDP in paricular PERSISTENT AND DELAYED Model predicions? Yun (996) model did no deliver his Fuhrer (2000 AER): hab persisence in consumpion Chrisiano, Eichenbaum, and Evans (2005 JPE): big model Chari, Kehoe, and McGraan (2000 EC): simple Taylor-saggeredconracs model Ocober 4, 200 2
Taylor Saggered Conracs TAYLOR CONTRACTS MODEL Original (Taylor 980) model no based on opimizing framework Nominal price can only be (re-)se every N periods (simples: N = 2) Original formulaion: nominal wage (no price) conracs Basic idea: saggering of (sicky!) conracs causes period- conrac price (in equilibrium) o be boh backward-looking and forward-looking Some conracs wren yeserday, some wren oday, some wren omorrow, ec.), bu all wren for a fixed number of periods Hence real erms of conrac are relaive o boh lagged and fuure conracs shocks ge passed from conrac o conrac Embed in DSGE model familiar basic srucure Final goods assembled via Dix-Siglz echnology Monopolisically-compeive differeniaed goods producers choose opimal nominal P subjec o pricing fricion (can only (re-)se price every N periods) Res of model sandard Ocober 4, 200 3 Taylor Saggering in DSGE Model DIFFERENTIATED-GOODS FIRMS Dynamic prof-maximizaion problem + N max E Ξ+ s { P yis Pmc s syi s } P s= Noe disincion beween and s subscrips!!! Nominal price in effec for N periods Discoun facor beween and s because dynamic firm problem; in equilibrium, = household sochasic discoun facor Subsue in demand funcion + N P max E Ξ+ s Pi ys Pmc s s ys P s= Ps P s Rewre + N ε ε + ε max E Ξ + s { Pi Ps P Ps mcs} ys P s= Ocober 4, 200 4 2
DIFFERENTIATED-GOODS FIRMS Firs-order condion wh respec o P + N P P P E Ξ+ s ( ε) ys+ ε ys mcs = 0 s= Ps Ps Ps SAME EXACT MANIPULATIONS AS IN CALVO-YUN MODEL! The pricing fricion explored by CKM (2000) wh focus on explaining he persisence puzzle + N ε P E Ξ+ s ys mcs = 0 s= Ps ε P s If prices are compleely flexible (i.e., if N = ) P ε = mc P ε Sandard saic Dix- Siglz pricing condion Ocober 4, 200 5 OTHER MODEL DETAILS MIU o moivae money demand Exogenous AR() money growh process No indexaion of prices o average or lagged inflaion Indexaion largely undoes effecs of price sickiness Varians Aggregaor wh non-consan elasicy of demand (Kimball (995 JMCB)) Kinked (concave) demand funcion makes price less sensive o mc Upward-sloping mc funcion (wh respec o quany) Through specific-facors model Numerical implemenaion: linearizaion Simply a label o mean DRS in k and n joinly Main Meric: conrac muliplier Ocober 4, 200 6 3
CONTRACT MULTIPLIER A measure of amplificaion of exogenous price sickiness o endogenous price sickiness ITSELF is only equal o half he lengh of price sickiness muliplier half-life of oupu wh saggered price-seing half-life of oupu wh synchronized price-seing Half-life of oupu: # of periods afer moneary shock before oupu deviaion shrinks o half s impac-period deviaion BOTH under STICKY prices IMPORTANT: Prices are exogenously sicky no maer wheher hey are se in saggered fashion or synchronized fashion No simply a es of wheher nominal sickiness explains oupu persisence following a moneary shock a es of wheher saggering of price-seing amplifies he effecs of nominal sickiness on oupu persisence following a moneary shock Ocober 4, 200 7 PRICE DISPERSION For firm i, Inegraing over i Idenical o Calvo-Yun model y = y = z f( k, n ) P = (, ) P 0 0 Symmeric choices of k/n raio across all firms i y di z f k n di k =, P 0 n 0 y di z f n di s A measure of dispersion: relaive price dispersion leads o dispersion of facor usage across differeniaed firms, hence dispersion of quany across differeniaed firms zf ( k, n) Oupu available for final demand is y = (CKM eqn. (20)) s Some producion is a pure deadweigh loss Ocober 4, 200 8 4
CKM RESULTS Conrac muliplier = in benchmark model (T =, N = 3) Saggered price-seing provides no amplificaion of exogenous price sickiness Removing endogenous capal accumulaion and/or explic money demand Conrac muliplier = sill ROBUSTNESS TO OTHER FEATURES Convex ( kinked ) demand curve makes demand more elasic he higher is price Final-goods aggregaor wh nonconsan elasicy of demand (see Kimball (995 JMCB)) Generaes decreasing reurns in labor hence upward-sloping mc funcion (wh respec o quany) Makes coss less sensive o wages Ocober 4, 200 9 CKM CONCLUSION The [Taylor (980)] idea is ha saggered price-seing leads o ineracions among price-seers ha generae longer movemens in oupu han does a similar model wh synchronized priceseing. (p. 52) Daa and reasonable lengh of exogenous price sickiness would require conrac muliplier > 5 (or >> 5 ) For our benchmark [and oher] specificaion[s], he saggered price-seing mechanism does no generae persisence. (p. 53) mechanisms o solve he persisence problem mus be found elsewhere. (p. 77) A very negaive view of he promise of nominal rigidies in DSGE models Ocober 4, 200 0 5
THE BASIC MECHANISM Srip ou capal accumulaion and explic money demand Append a saic money demand formulaion (based on quany heory) Suppose N = 2 Pricing relaions, expressed in logdeviaions (see CKM p. 63-665) Basically he (parial equilibrium) model of Taylor (980) excep Taylor s was in erms of saggered wages Aggregae price level * * P = P + P 2 P = P +γ y FLEX P = P + E P + 2 * FLEX FLEX Opimal P chosen in subjec o pricing fricion Opimal P chosen in if no pricing fricion Opimal sicky P can be represened recursively in erms of opimal flexible P The crical parameer for he persisence puzzle: in Taylor, was a free parameer, in CKM, is a parameer pinned down by model primives and general equilibrium effecs! THE SMALLER IS γ, THE LONGER-LASTING IS RESPONSE OF OUTPUT Ocober 4, 200 THE BASIC MECHANISM Simple (no capal, no explic money demand) model γ =.35 given model (preference and echnology) parameers Would need γ = 0.0003 o mach a reasonable conrac muliplier Underlying problem: wages are oo responsive o consumpion (p. 64) Broader read of resuls: need o model labor markes more finely Sicky (nominal) wages? Deeper (i.e., maching) fricions in labor markes? Worker immobily? Alvarez and Shimer (2007): res unemploymen, an alernaive heory o search and maching heory of labor marke Labor wedges (CKM 2007) he key o undersanding a lo in macro Ocober 4, 200 2 6
Wha Nex? FOLLOWING UP ON CKM Taylor (999 Macro Handbook) conjecure: saggered priceseing does no deliver persisence in oupu because he underlying sandard consan-elasicy marke srucure is oo simple CKM p. 63: in order o ge persisence, he equilibrium wage rae mus change lle Huang and Liu (2002 JME): saggered (Taylor) wage-seing is capable of generaing persisence in oupu following moneary shock Basic idea: saggering of nominal wages spills over ino saggering of nominal prices Because P depends on MC, which in urn depends on W Quesion: Sickiness in which P or W is more imporan? Today: resurgen ineres in sicky-nominal-wage models Chrisiano, Eichenbaum, and Evans (2005 JPE) Wage-sickiness (and oher hings ) much more imporan han price-sickiness Ocober 4, 200 3 Conclusion TAYLOR VERSUS CALVO? Probably no he righ quesion Calvo formulaion PRO: Exremely racable inroduces very few (only one ) new sae variable (dispersion) PRO: In equilibrium, differen firms have fixed prices for differen lenghs of ime (due o random adjusmen) CON: In equilibrium, a few firms will have fixed price for very long lengh of ime.realisic? Taylor formulaion PRO: All firms will adjus price in fine ime wh probabily one PRO: Accords wh (casual?) empirical evidence ha firms have a regular schedule a which hey re-price (i.e., every January, ec.) CON: No as racable (especially as N ges large ) bu wh modern compuaional power, maybe no such a big deal Which formulaion o choose likely bes guided by problem a hand Ocober 4, 200 4 7