Wage and price Phillips curve

Transcription

1 Wage and price Phillips curve Miroslav Hloušek Faculy of Economics and Adminisraion of Masaryk Universiy in Brno Deparmen of Applied Mahemaic and Compuer Science Lipová 4a, 62 Brno Absrac This paper presens an opimizing-agen model in which boh labor and produc markes exhibi monopolisic compeiion. The wage and price equaions are derived from opimizing behavior and hus depend on he underlying srucure of preferences and echnology. All model equaions are log-linearised around seady sae. Two ypes of shocks occur: shock o household s preferences and echnology shock. The implicaions of hese shocks on adjusmen process of main variables are examined. Keywords Phillips curve, nominal rigidiies, wage and price sickiness, microfoundaions, opimizing-agen model Inroducion We formulae an opimizing-agen model in which boh labor and produc markes exhibi monopolisic compeiion. The model environmen includes four subjecs: households, firms and disribuors of goods and labor. The inegraion of disribuors is due o analyical simpliciy. For illusraion he produc marke is described as follows. The disribuors buy homogenous goods produced by firms a perfec compeiive produc marke. Each disribuor labels he goods and hen sells i as differeniaed good (ha is consumed by households) a monopolisically compeiive marke. The disribuor is a price-seer. The srucure of labor marke is similar o he srucure of produc marke. 2 Model All individuals have idenical preferences and consrains, herefore we can analyze he opimizaion problem of represenaive agen. This paper has been worked as a par of research aciviies a he gran projec of GA CR No. 42/2/393. I immensely hank Jaromír Beneš for useful commens and suggesions.

2 Households Typical household maximize he uiliy funcion ( ) max E β k Y ( σ) Y+k ϕ +k Z +k Y,Y +,L σ ϕ k= subjec o he budge consrain B ( + i ) + W L = Y P + B, + ( L +k ) e ɛ +k where E is expecaional operaor, Y is he real consumpion index, Z is habi in consumpion, L is labor supplied by household, ɛ is shock in ineremporal preferences, B is an asse yielding ineres, i is he nominal ineres rae, W is nominal wage and P is price index. 2 Firms Typical firm maximize he profi funcion subjec o he producion funcion max L Q y V L y = A L α, where Q is price of homogenous goods, y is quaniy of produced goods, L is he labor index and V is he wage index, 3 A is echnological progress and α is share of labor in he producion funcion. The echnology process is saionary and has form: A = A ν eϖ, where ϖ is echnology shock. Disribuor of goods The disribuor of goods maximize he profi funcion subjec o he demand funcion max (p Q )y p y = ( p P ) θ Y, where p is price of good se by disribuor, Q is price of homogenous good bough from firms, y is demand for good 4 and θ is he elasiciy of subsiuion beween differeniaed goods. From his opimizaion problem flexible price opimum is derived. The price p is Expecaion of a + formed upon informaion available in period. 2 The consumpion index Y and he price index P has he Dixi-Sigliz (977) form wih consan elasiciy of subsiuion. 3 The indexes L and V also follow he Dixi-Sigliz (977) form. 4 The demand for differeniaed good is equal o he demand for homogenous good. 2

3 se as he markup o he price of homogenous good: p = θ θ Q. However some fricions ener he disribuor s profi funcion. The disribuor faces he menu cos: fixed cos conneced wih adjusing of a nominal price. The profi is also influenced when he price is no se a opimal level. These rigidiies are minimized by quadraic form. max Ψ,+k p [ ( p p γ p ) 2 ( p p ) ] 2 p where γ is weigh o he menu cos, p is he opimal price and Ψ,+k is discoun facor. 5 Disribuor of labor The disribuor of labor behaves in similar manner o he disribuor of goods and maximize he profi funcion max(v W )l v subjec o he demand funcion l = ( v V ) ξ L. where v is wage se by disribuor, W is wage rae of homogenous labor service, l is demand for labor service and ξ is he elasiciy of subsiuion beween labor services. The flexible wage equilibrium is: v = ξ ξ W and again he menu cos and non-opimally se price influence he disribuor s profi. The opimizaion of his funcion by quadraic form is similar o he previous case. 3 Phillips curves From he opimizaion problem of he disribuor of goods a price-seing equaion (price Phillips curve) is derived. The log-linearised version of his equaion has form p = ω ω E p + + δ ω ( rmc ˆ ). Curren price inflaion p depends posiively on expeced price inflaion and on deviaion of he real marginal cos rmc ˆ from seady sae value. The key equaion concerning opimizaion problem of disribuor of labor is wageseing equaion (wage Phillips curve) ha has form: v = κ κ E v + + χ κ ( mrs ˆ ˆrv ). This equaion saes ha curren wage inflaion v depends posiively on expeced wage inflaion and on he gap beween he marginal rae of subiuion of consumpion for leisure mrs ˆ and he real wage ˆrv (boh expressed as deviaions from seady sae value). 5 Ψ,+k is defined as: Ψ, =, Ψ,+ = +r, Ψ,+2 = rae. (+r )(+r +,... where r is he real ineres ) 3

4 Figure : Shock o households preferences ɛ y Real Consumpion l Labor mrs Marginal Rae of Subsiuion rmc Real Marginal Cos v Wage Inflaion 5 5 p Price Inflaion mpl Marginal Produc of Labor rv Real Wage r Real Ineres Rae Theoreic example and resuls The whole economic framework includes nex imporan equaions: he consumpion Euler equaion, he producion funcion, he definiions of he marginal produc of labor, he marginal cos and he marginal rae of subsiion and he ideniy for he real ineres rae and he real wage. Finally, a moneary policy rule, is required o close he model. The objecion of moneary auhoriy is minimizaion of he deviaions of oupu and inflaion from equilibrium. All equaions are log-linearised around symmeric seady sae. The real variables are expressed as deviaions from seady sae value. The parameers are appropriaely calibraed following sandard business cycle lieraure. 6 The model conains forward looking variables and herefore is solved as raional expecaions model. The process of solving is based on Blanchard-Kahn (98) and can be also found e.g. in Hloušek (23). We examine implicaions of srucural shocks o adjusmen process of imporan variables. Two ypes of shocks may occur: shock o households preferences ɛ (ineremporal shif in preferences) and shock o he producion funcion ϖ (echnology shock). The shock is unexpeced and has magniude of. We pay our aenion o he real variables and nominal varibles on monopolisically compeiive markes. The ime in periods is measured on x-axis, he deviaion from equlibrium is measured on y-axis in he graphs. 6 For more deails see Appendix. 4

5 Figure 2: Technology shock ϖ.2.5. y Real Consumpion.5 l Labor mpl Marginal Produc of Labor mrs Marginal Rae of Subsiuion rmc Real Marginal Cos 2 rv Real Wage v Wage Inflaion p Price Inflaion r Real Ineres Rae Figure shows he impac of shock ɛ on he real consumpion y, labor l, he marginal produc of labor mpl, he real marginal cos mc, he marginal rae of subsiuion mrs, he real wage rv, wage inflaion v, price inflaion p and he real ineres rae r. Real consumpion increases and also work effor mus increase because of budge consrain. Rise in real consumpion decrease he marginal uiliy from consumpion (no shown here) ha resuls in jump of he marginal rae of subsiuion of consumpion for leisure in he firs period because leisure in he uiliy funcion is linear. Rise in work effor reduce he marginal produc of labor. This implies increase of he marginal coss of he firms (hey are defined as proporion of he real wage and he marginal produc of labor). The real marginal cos is he driving force in he price Phillips curve and herefore induces increase of price inflaion. The difference beween he marginal rae of subsiuion and he real wage causes rise of wage inflaion bu only in he firs period afer shock. Then wage inflaion jumps ino negaive values and reurns o he equlibrium. Increase of he real ineres rae is caused by reacion of he nominal ineres rae (moneary insrumen) o he deviaions of consumpion and price inflaion from equilibrium values. The reurn of all relevan variables o he baseline is no longer han eigh periods. Figure 2 shows implicaions of echnology shock ϖ. The shock lile increases real consumpion and very reduces work effor (labor is replaced by echnological uilizaion). The marginal produc of labor rapidly increases. The real marginal cos decreases even 5

6 if he real wage rises. The price inflaion decreases and smoohly reurns o he baseline. The wage inflaion also decreases bu follows hump-shaped paern wih boom in he hird period. The real ineres rae decreases because he nominal ineres rae reacs more o decrease of price inflaion han o increase of consumpion. 5 Conclusion This paper inroduced model wih feaures of monopolisically compeiive markes. We believe ha boh prices and wages are sicky in acual economies and i is also characerisic of presened model. All equaions are derived from microeconomic foundaions and hus depend on he underlying srucure of preferences and echnology. The presence of shocks allowed us o examine reacion of main variables wihin he cycle and provided us useful insigh how economic agens behave. However he model is only heoreic. The furher research will be devoed o he comparison of he heoreic resuls wih behavior of real daa and o he esimaion of parameers. 6 Appendix The parameers of he model are se wih reference o Romer (2) and Erceg (2). For simulaion we use hese values of srucural parameers: β =, 95, σ = 2, ϕ = 4, α =, 7, ν =, 8, ω =, 6, δ =, 2, κ =, 6 and χ =,. Parameers in moneary policy rule ha has form: i = ςŷ + ζ p are se as follows: ς =, 5 and ζ =, 5. References [] BLANCHARD, O.; KAHN, C. The Soluion of Linear Difference Models under Raional Expecaions, Economerica, Volume 48, Issue 5 (Jul., 98), [2] DIXIT, A.; STIGLITZ, J.: Monopolisic Compeiion and Opimum Produc Diversiy. American Economic Review, Vol. 67, No. 3. (Jun., 977), pp [3] ERCEG, J. C.; HENDERSON, D. W.; LEVIN, A. T.: Opimal moneary policy wih saggered wage and price conracs. Journal of Moneary Economics, Vol. 46, No. 2, (Oc. 2), pp [4] HLOUŠEK, M.: Model of closed economy wih raional expecaions. Mahemaical Mehods in Economics 23. Prague: Czech Universiy of Agriculure in Prague, 23, Faculy of Economics and Managemen, pp [5] OBSFELD, M.; ROGOFF, K.: Foundaions of inernaional macroeconomics, Cambridge (Massachuses): MIT Press 996, ISBN: [6] ROMER, D. Advanced Macroeconomics. Boson: MacGraw-Hill, 2. Chaper 4, 5 & 6. ISBN: