MONOPOLISTIC COMPETITION IN A DSGE MODEL: PART II OCTOBER 4, 2011 BUILDING THE EQUILIBRIUM. p = 1. Dixit-Stiglitz Model

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1 MONOPOLISTIC COMPETITION IN A DSGE MODEL: PART II OCTOBER 4, 211 Dixi-Sigliz Model BUILDING THE EQUILIBRIUM DS MODEL I or II Puing hings ogeher impose symmery across all i 1 pzf k( k, n) = r & 1 pzf n( k, n) = w implies w r mc = = z f ( k, n ) z f ( k, n ) n k & p = mc 1 Symmeric equilibrium relaive price of an inermediae good? Subsiue demand funcions ino DS aggregaor and compue p = 1 1 mc = Wih measure one of inermediae firms, can hink of as a normalizaion bu wha if measure [,N] of firms? < 1 wih > 1 and < infiniy Monopoly power causes facor prices o fall below marginal producs hence inefficienly low equilibrium facor use hence inefficienly low oal oupu Ocober 4,

2 Canonical Dixi-Sigliz Model MONOPOLISTICALLY-COMPETITIVE EQUILIBRIUM Equilibrium Condiions (symmeric across all differeniaed goods) Consumpion-leisure opimaliy condiion Consumpion-savings opimaliy condiion Aggregae resource consrain c + k+ 1 (1 δ ) k = z f( k, n) (possibly also include g ) (Marke clearing in labor, capial, and goods markes) 1 mc = ( < 1 wih > 1) Facor prices a markdown of marginal producs 1 1 w = z fn( k, n), k = z fk( k, n) Ocober 4, Dixi-Sigliz Model THE LABOR WEDGE D S markdown of real wage from marginal produc of labor Labor Wedge MP N w Monopoly disorion in goods marke refleced in disorion in labor (and oher facor) markes L M L F Labor Ocober 4,

3 DSGE Dixi-Sigliz Model Embed D-S framework in sandard RBC model Can approximae and simulae using usual mehods Roemberg and Woodford use King, Plosser, Rebelo (1988) linear approximaion mehod (One ) predecessor o SGU algorihm Empirical Issues Are oupu flucuaions associaed wih labor demand shifs or labor supply shifs? For example, hose induced by g shocks? Empirical evidence on goods-marke markups? Variaions in markups? Exogenous or Endogenous? Theoreical Issue: endogenous/self-fulfilling/sunspo flucuaions? i.e., flucuaions no due o changes in primiives (echnology, preferences, endowmen, ec.) of economy Canno occur in RBC economy (unique equilibrium) Ocober 4, DSGE Dixi-Sigliz Model Effecs of TFP shocks in RBC model and wih monopolisic compeiion (μ = 1.2) SD % Relaive SD: SD(x)/SD(GDP) Effec of TFP shocks on hours are dampened by imperfec compeiion RBC Model Imperfec Compeiion RBC Model Imperfec Compeiion GDP Consumpion Gross Invesmen Hours Real Wage Marginal Produc of Labor Ocober 4,

4 DSGE Dixi-Sigliz Model Effecs of TFP shocks in RBC model and wih monopolisic compeiion (μ = 1.4) SD % Relaive SD: SD(x)/SD(GDP) Effec of TFP shocks on hours are dampened by imperfec compeiion RBC Model Imperfec Compeiion RBC Model Imperfec Compeiion GDP Consumpion Gross Invesmen Hours Real Wage Marginal Produc of Labor Ocober 4, DSGE Dixi-Sigliz Model Effecs of governmen purchase shocks in RBC model and wih monopolisic compeiion (can depend on oher deails of model ) Relaive SD: SD(x)/SD(GDP) RBC Model μ = 1.2 μ = 1.4 μ = 1.6 GDP Consumpion Gross Invesmen Hours Real Wage Marginal Produc of Labor Ocober 4,

5 DSGE Dixi-Sigliz Model Main Message: model flucuaions can (qualiaively and quaniaively) depend on naure of seady sae Disored or efficien long-run equilibrium? Can be imporan for cyclical properies of a model Analogy: welfare coss of bad moneary policy depend on presence/magniude of oher disorions (Cooley and Hansen 1991) Monopoly power a saic disorion on he equilibrium Akin o a labor income ax Inroduces a wedge beween u n /u c and marginal produc of labor Bu a consan wedge so far Ocober 4, DSGE Dixi-Sigliz Model Main Message: model flucuaions can (qualiaively and quaniaively) depend on naure of seady sae Disored or efficien long-run equilibrium? Can be imporan for cyclical properies of a model Analogy: welfare coss of bad moneary policy depend on presence/magniude of oher disorions (Cooley and Hansen 1991) Monopoly power a saic disorion on he equilibrium Akin o a labor income ax Inroduces a wedge beween u n /u c and marginal produc of labor Bu a consan wedge so far Cyclical behavior of labor wedge perhaps he mos imporan challenge for business cycle modeling Chari, Kehoe, McGraan (27 Economerica), Shimer (29 AEJ:Macro) Variable markups may be imporan for cyclical flucuaions An acive area of research: enry and exi of firms and produc varieies over he business cycle Ocober 4,

6 Beyond Basic Dixi-Sigliz Model PRODUCT VARIETIES { N+ 1, NE, } = FOCs N Ξ ρ ) ( i ρi di E, E, = max E ( mc q ) mc f N s.. N = 1 (1 δ )( N + Law of moion for number of + NE, ) produc varieies, which urn over a rae δ f E he produc developmen cos, in erms of labor unis N +1 : N E, : Ocober 4, Beyond Basic Dixi-Sigliz Model PRODUCT VARIETIES max E Ξ ( ρ mc ) q( ρ ) di mc f N { N+ 1, NE, } = FOCs N i i E, E, = s.. N = 1 (1 δ )( N + Law of moion for number of + NE, ) produc varieies, which urn over a rae δ f E he produc developmen cos, in erms of labor unis N +1 : N E, : Produc creaion condiion Characerizes opimal invesmen in R&D/produc developmen { Ξ } mc f = (1 δ) E ( ρ mc ) q( ρ ) + mc f E, E, 1 δ = 1?... so ry insead N +1 = (1-δ)N + N E, Ocober 4,

7 Beyond Basic Dixi-Sigliz Model PRODUCT VARIETIES Differen forms of final goods aggregaors Dixi-Sigliz (1977) N 1 1 y = yi di Benassy (1996) N 1 κ = i y N y di Translog No closed-form aggregaor exiss Primiive is expendiure funcion See Feensra (23 Economics Leers) for good overview ² measures elasiciy of subsiuion across any wo differeniaed varieies κ + 1 = ²/(²-1) recovers Dixi- Sigliz κ measures love of variey effec Ocober 4, DSGE Dixi-Sigliz Model Main Message: model flucuaions can (qualiaively and quaniaively) depend on naure of seady sae Disored or efficien long-run equilibrium? Can be imporan for cyclical properies of a model Analogy: welfare coss of bad moneary policy depend on presence/magniude of oher disorions (Cooley and Hansen 1991) Monopoly power a saic disorion on he equilibrium Akin o a labor income ax Inroduces a wedge beween u n /u c and marginal produc of labor Bu a consan wedge so far Cyclical behavior of labor wedge perhaps he mos imporan challenge for business cycle modeling Chari, Kehoe, McGraan (27 Economerica), Shimer (29 AEJ:Macro) More generally, variable labor wedges imporan for cyclical flucuaions Variable markups may be imporan for cyclical flucuaions An acive area of research: enry and exi of firms and produc varieies over he business cycle Ocober 4,

8 Labor Wedges LABOR MARKET DYNAMICS D S MP N μ = markup of marginal produc of labor over real wage Monopoly disorion in goods marke refleced in disorion in labor (and oher facor) markes w L M L F Labor Ocober 4, Labor Wedges LABOR MARKET DYNAMICS Described by firm opimaliy: MP N = wμ Described by household opimaliy: -u n /u c = w D S MP N μ = markup of marginal produc of labor over real wage In general, disorion in eiher or boh goods and labor markes refleced as wedge in labor marke w Labor Labor wedge measuremen and heory an acive area of research Shimer (29 AEJ:Macro), Ohanian (21 JEP), many ohers Ocober 4,

9 Recen Research THE LABOR WEDGE Shimer (29 AEJ:Macroeconomics) Ocober 4, Recen Research THE LABOR WEDGE Ohanian (21 Journal of Economic Perspecives) Ocober 4,