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, 211 2 1
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, 211 3 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, 211 4 2
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, 211 5 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 1.75 1.71 1 1 Consumpion 1.31 1.41.745.826 Gross Invesmen 5.77 6.28 3.283 3.668 Hours.68.62.386.363 Real Wage 1.38 1.44.785.841 Marginal Produc of Labor 1.38 1.44.785.841 Ocober 4, 211 6 3
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 1.75 1.65 1 1 Consumpion 1.31 1.49.745.898 Gross Invesmen 5.77 6.64 3.283 4.15 Hours.68.56.386.341 Real Wage 1.38 1.49.785.92 Marginal Produc of Labor 1.38 1.49.785.92 Ocober 4, 211 7 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 1 1 1 1 Consumpion.998.925.882.857 Gross Invesmen 8.27 9.277 1.494 11.679 Hours 1.435 1.435 1.436 1.437 Real Wage.477.49.54.519 Marginal Produc of Labor.477.49.54.519 Ocober 4, 211 8 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 Ocober 4, 211 9 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, 211 1 5
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, 211 11 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, 1 1 1 1 1 E, 1 δ = 1?... so ry insead N +1 = (1-δ)N + N E, Ocober 4, 211 12 6
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 + 1 1 1 = 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, 211 13 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, 211 14 7
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, 211 15 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, 211 16 8
Recen Research THE LABOR WEDGE Shimer (29 AEJ:Macroeconomics) Ocober 4, 211 17 Recen Research THE LABOR WEDGE Ohanian (21 Journal of Economic Perspecives) Ocober 4, 211 18 9