Chapter 13 A Perfectly Competitive New Classical Model

Transcription

1 George Alogoskoufis, Dynamic Macroeconomics, 2016 Chaper 13 A Perfecly Compeiive New Classical Model In his chaper we inroduce a perfecly compeiive new classical model of aggregae flucuaions in which here is no capial accumulaion. This is a dynamic sochasic general equilibrium models (DSGE), based on opimizing households and firms, flexible wages and prices, and fully compeiive markes. Flucuaions are caused by real shocks o produciviy, bu we absrac from capial accumulaion which propagaes he dynamic effecs of such shocks in he sochasic growh model of Chaper 11. The reason for inroducing his simplified model, is o have a new classical model which is comparable o he new keynesian models ha we shall analyze in subsequen chapers, so ha we can beer undersand he similariies and differences beween he new classical and he new keynesian approaches o aggregae flucuaions. The main impulses ha generae aggregae flucuaions are real, i.e shocks o produciviy. However, we also analyze he role of moneary shocks and moneary policy in his class of new classical models. Moneary shocks have no real effecs on oupu, employmen and oher real variables in his model, and only affec real money balances, and nominal variables such as he price level, inflaion and nominal wages and ineres raes. Thus, he role of moneary policy in his model is simply o sabilize inflaion in he presence of moneary and real shocks A Perfecly Compeiive New Classical Model wihou Capial In wha follows we shall focus on a perfecly compeiive new classical model of aggregae flucuaions, in which he only variable facor of producion is labor. We shall hus absrac from capial accumulaion, which is a imporan propagaion mechanism in he sochasic growh model ha we analyzed in Chaper 11. In his analyically simpler model we allow for a more general approach o he preferences of he represenaive household, and also disinguish beween nominal and real variables, in order o consider he deerminaion of he level of prices and wages, inflaion and nominal ineres raes, and he role of moneary facors in new classical models The Represenaive Household The represenaive household is assumed o maximize,

2 s 1! E (13.1) 1+ ρ u(c +s, L +s ) s0 where C is consumpion and L is labor supply. We assume ha,! u C u > 0,! u C C,!,!. (13.2) C 2 u C 0 u 2 L u 0 u L L L 2 u C 0 2 The consrains under which he maximizaion akes place are given by, P C i B B 1 + W L T lim E B 0 T T (13.3) (13.4) where P is he price level, W he nominal wage, i he nominal ineres rae, B a nominal one period bond, and T an exogenous ransfer of nominal income o he household (dividends, governmen ransfers of axes). From he firs order condiions i follows ha,! u L W (13.5) u C P 1! 1 (13.6) 1+ i 1+ ρ E u C+1 P u C P +1 We assume ha he per period uiliy funcion is given by, 1 θ 1+λ! U(C, L ) C, where θ>0 and λ>0 (13.7) 1 θ L 1+ λ The firs order condiions for he problem of he represenaive household in his case ake he form, W P! C θ λ L (13.8) 1! 1 θ (13.9) 1+ i 1+ ρ E C +1 P C P +1 (13.8) and (13.9) can be wrien in log-linear form, as,! w p θc + λl (13.10)!2

3 ( )! c E (c +1 ) 1 (13.11) θ i E (π ) ρ +1 where wlnw, plnp, clnc, llnl and! π p p 1 is he inflaion rae The Represenaive Firm Producion of he represenaive firm is a posiive funcion of employmen, and is described by an aggregae producion funcion of he form, 1 α! Y A L (13.12) where Α>0 and 0<α<1 are exogenous echnological parameers. α is a consan, while A follows an exogenous sochasic process. The represenaive firm chooses employmen in order o maximize profis, for given nominal wages and prices. Profis are deermined by,! P Y W L (13.13) Profi maximizaion implies ha employmen will be deermined so as o equae he marginal produc of labor o he real wage. Thus, W P α! (1 α )A L (13.14) One can solve he marginal produciviy condiion for he price level. The inerpreaion is ha he produc price is equal o marginal cos. W! P (13.15) α (1 α )A L Log-linearizing he firs order condiion (13.14) we ge,! w p a αl + ln(1 α ) (13.16) where alna. Log-linearizing he producion funcion (13.12) we ge,! y a + (1 α )l (13.17) Having deermined he behavior of households and firms, we can now analyze he equilibrium in his model General Equilibrium!3

4 In he basic form of his model we shall assume ha here is no invesmen or public consumpion. Accordingly, in produc marke equilibrium, consumpion will be equal o oal oupu.! y c (13.18) The equilibrium condiion (13.18) will deermine he real ineres rae. The condiion for equilibrium in he labor marke will require ha labor demand, as implied by (13.16), should be equal o labor supply, as implied by (13.10). This will deermine he real wage. The model consiss of equaions (13.10), (13.11), (13.16) and (13.17) and he equilibrium condiion (13.18), and deermines employmen, oupu, consumpion, real wages and he real ineres rae, as funcions of he exogenous labor produciviy process a. The real ineres rae is defined by he Fisher equaion, as, 1! r i E (π +1 ) (13.19) Solving he model for he five endogenous variables, we ge,! l η LA a + l _ (13.20) 1 θ where,! η LA and,! l _ ln(1 α ). θ(1 α ) + α + λ θ(1 α ) + α + λ! y c η YA a + y _ (13.21) 1+ λ where,! η YA 1+ (1 α )η LA and,! y _ (1 α )l _. θ(1 α ) + α + λ! w p η WA a + ω _ (13.22) θ + λ where,! η WA 1 αη LA and,! ω _ ( θ(1 α ) + λ)l _. θ(1 α ) + α + λ! r ρ +θη YA E (Δa +1 ) (13.23) (13.20), (13.21), (13.22) and (13.23), along wih he produc marke equilibrium condiion (13.18), deermine he five endogenous variables, as a funcion of he exogenous labor produciviy process a. To quoe from Fisher (1896), When prices are rising or falling, money is depreciaing or appreciaing relaive o 1 commodiies. Our heory would herefore require high or low ineres according as prices are rising or falling, provided we assume ha he rae of ineres in he commodiy sandard should no vary. (p. 58). The rae of ineres in he commodiy sandard is he real ineres rae, and rising or falling prices are expeced inflaion.the Fisher equaion was furher elaboraed in Fisher (1930), where i was made even clearer ha Fisher referred o expeced inflaion.!4

5 ! George Alogoskoufis, Dynamic Macroeconomics, 2016 Chaper 13 I worh noing ha flucuaions in employmen, oupu, consumpion and real wages are a funcion only of flucuaions in labor produciviy and flucuaions in he real ineres rae depend on flucuaions in he expeced rae of change of produciviy. Oupu, consumpion and real wages are posiive funcions of produciviy, while employmen is a posiive funcion of produciviy only if θ<1, i.e. if he ineremporal elasiciy of subsiuion of consumpion is greaer han one. If θ>1, employmen is a negaive funcion of produciviy, while if θ1, employmen is independen of produciviy. This is because if θ<1 he subsiuion effec dominaes over he income effec, afer a change in produciviy and real wages, and employmen rises. If θ>1 he income effec dominaes over he subsiuion effec, while in he case θ1 he wo effecs cancel each oher ou, and employmen is no affeced. Only real facors, such as real produciviy, affec flucuaions in real variables. As in he sochasic growh model, moneary facors such as money supply and nominal ineres raes have no impac on he evoluion of real variables Moneary Facors in he New Classical Model In order o examine he impac of moneary facors in he new classical model, we shall assume he exisence of a money demand funcion by households and firms, which, in logarihms, akes he form, m p y ηi (13.24) where η is he semi-elasiciy of money demand wih respec o he nominal ineres rae. From he definiion of he real ineres rae hrough he Fisher equaion (13.19), he nominal ineres rae is equal o,! i r + E (π +1 ) (13.25) where he real ineres rae r is deermined by (13.23) and is independen of moneary facors. We will show ha, like in he case of he models analyzed in Chaper 10, when he cenral bank follows a rule for he money supply, hen he model deermines he price level and he level of inflaion and nominal ineres raes. If he cenral bank pegs he nominal ineres rae, he price level and he level of he nominal money supply canno be deermined, unless he nominal ineres rae reacs sufficienly srongly o changes in he price level An Exogenous Pah for he Money Supply If he cenral bank deermines an exogenous pah for he money supply, hen, from (13.24) and (13.25) i follows ha,! p η (13.26) 1+ η E (p ) η m 1 ( 1+ η y ηr ) Under he assumpion ha η>0, he soluion of (13.26) implies ha,!5

6 j ( )! p 1 η (13.27) j0 1+ η 1+ η E m + j y + j + ηr + j From (13.27), he price level and inflaion are deermined as funcions of he exogenous pah of he money supply, and he pahs of real oupu and he real ineres rae, which, as we have seen, are independen of moneary facors in he new classical model. The nominal ineres rae is deermined endogenously from (13.27) and (13.25) An Exogenous Pah for he Nominal Ineres Rae If we assume ha he cenral bank follows an exogenous pah for he nominal ineres rae, hen, from he Fisher equaion (13.25), i follows ha,! E (π +1 ) i r (13.28) (13.28) does no deermine inflaion, bu expeced inflaion, given he exogenous pah of nominal ineres raes. (13.28) is consisen wih any price level pah ha saisfies,! p +1 p + i r + ξ +1 (13.29) ( ) 0 where ξ is any shock ha saisfies! E ξ +1. (13.29) suggess ha here are muliple equilibria for he price level and inflaion, depending on ξ. This price level indeerminacy when he cenral bank follows an exogenous pah for he nominal ineres rae is also ransferred o he money supply, hrough he money demand funcion (13.24). Consequenly neiher he money supply nor he price level can be deermined uniquely when he cenral bank follows an exogenous pah for he nominal ineres rae. 2 However, no all ineres rae rules resul in price level indeerminacy. As suggesed more han a cenury ago by Wicksell (1898), and we demonsraed in Chaper 10, if he cenral bank condiions is nominal ineres rae on he price level, or inflaion, hen price level and inflaion indeerminacy do no necessarily follow An Inflaion Based Nominal Ineres Rae Rule Cenral banks predominanly use he nominal ineres rae as heir preferred moneary insrumen. However, hey follow policies according o which he pah of nominal ineres raes is no exogenous, bu depends on pas, curren and expeced fuure economic developmens, mainly The classic analysis of he appropriae choice of moneary insrumens in a simple sochasic macro model was Poole 2 (1970). As we argued in Chaper 10, Sargen and Wallace (1975) demonsraed ha under raional expecaions, a nonconingen ineres rae arge leads o price level indeerminacy and insabiliy in such a model. However, i is now acceped ha his problem does no arise in he case of coningen ineres rae rules ha make he nominal ineres rae depend on he price level (McCallum 1981), or a sufficienly sensiive posiive funcion of inflaion. See Woodford (2003) Ch.1 for he relevan argumens. In addiion, cenral banks, have been consisenly using ineres raes and no moneary aggregaes as heir main moneary policy insrumen, especially in he las hiry years. As noed by Bernanke (2006), In pracice, he difficuly has been ha, deregulaion, financial innovaion, and oher facors have led o recurren insabiliy in he relaionships beween various moneary aggregaes and oher nominal variables..!6

7 inflaion. For example, if inflaion rises, cenral banks usually raise nominal ineres raes in order o reduce i, and vice versa. This was afer all he essence of he Wicksell rule. Le us herefore assume he following rule for deermining nominal ineres raes, 3! i ρ + φπ (13.30) where φ>0 is he reacion of he cenral bank nominal ineres rae o inflaion. From (13.25) και (13.30) we herefore have ha, ( ) + 1 ( φ r ρ)! π 1 (13.31) φ E π +1 where he real ineres r depends only on real facors, as is he implicaion of new classical models. 4 Solving (13.31) under raional expecaions, s+1 1! π, if φ>1 (13.32) s0 φ E ( r +s ρ) ( ) + ξ +1! π +1 φπ r ρ, if φ 1 (13.33) Thus, if he reacion of he cenral bank nominal ineres raes o inflaion is sufficienly pronounced (φ>1), here is no indeerminacy problem for inflaion. The fundamenal soluion is given by (13.33). If he reacion of he nominal ineres raes o inflaion is no sufficienly pronounced (φ 1), hen he problem of inflaion indeerminacy and he possibiliy of price bubbles remains. In any case, as we have already shown, in he new classical model of aggregae flucuaions only real facors affec flucuaions in real variables. Moneary facors and moneary policy only affec real money balances and nominal variables such as he price level and inflaion, nominal ineres raes and he nominal money sock Non-Neuraliy of Money in New Classical Models The shor run neuraliy of money implied by new classical models was iniially roublesome for some of heir proponens, as hese models were no compaible wih he evidence suggesing he exisence of a posiive shor run relaion beween inflaion and employmen, i.e an expecaions augmened Phillips curve. 3 Wicksell (1898) was probably he earlies advocae of a such a sabilizing ineres rae rule. We have shown how Wicksell's rule resuls in price level deerminacy in he models of Chaper 10. Here, we use a version of Wicksell s rule for inflaion raher han he price level. 4 See for example, equaion (13.57). We shall furher assume ha he process deermining he real ineres rae is saionary.!7

8 Lucas (1972), responded by developing a new classical model which was consisen wih a posiive shor run relaion beween inflaion and employmen. This model, which was subsequenly implemened empirically by Lucas (1973) and Sargen (1973, 1976), was based on he assumpion ha firms did no have full informaion abou he price level a he ime hey made heir producion decisions, and hey aribued par of any change in he price level o a change in he relaive price of heir produc. Thus, when inflaion was unexpecedly high, all producers hough he relaive price of heir produc had gone up, and hus increased producion and employmen. The opposie happened when inflaion was unexpecedly low. 5 However, his new classical explanaion of he shor run relaion beween inflaion and oupu and employmen was sill no compaible wih involunary unemploymen, and could only accoun for emporary deviaions of oupu and employmen from heir naural levels, due o ineremporal subsiuion in labor supply and unanicipaed inflaion Conclusions New classical models of aggregae flucuaions imply ha aggregae flucuaions are caused by real facors. This is why such models are ofen called real business cycle models. New classical models are dynamic sochasic general equilibrium models (DSGE) based on opimizing behavior by boh households and firms, flexible prices, and fully compeiive markes. Households maximize heir ineremporal uiliy, firms maximize he presen value of heir profis, and markes funcion efficienly. If he compeiive general equilibrium models of his kind could explain all he feaures of aggregae flucuaions, hen here would be no need for models ha sress disorions in produc and labor markes, and oher marke inefficiencies. However, new classical models have a number of weaknesses as models of aggregae flucuaions. Firs, hese models canno accoun for he real effecs of nominal and moneary shocks. For example, i is widely acceped ha he Grea Depression of he 1930s was caused by moneary and no real shocks. Similar views are prevalen regarding he recession of , which was one of he deepes pos World War II recessions. The sicky informaion assumpion of Lucas (1972, 1973) can be used for accouning for he real effecs of nominal shocks, bu he effecs of nominal shocks in such a model would be shor lived and no persisen. Second, even hough new classical models can accoun for employmen flucuaions, hey only do so on he basis of ineremporal subsiuion in labor supply. This explanaion, however, is no sufficien o explain he exisence and he persisence of unemploymen and he widely held view ha unemploymen is an involunary condiion for hose who experience i, and no he resul of a volunary raional choice. A log linear version of he Lucas (1972) model was analyzed by Barro (1976), and was exended o incorporae he 5 labor marke and ineremporal subsiuion in labor supply by Alogoskoufis (1983). In he exended model, as workers could no observe he price level immediaely, hey sysemaically aribued par of unexpeced inflaion o relaive price changes, and a emporary increase in heir real wage. Thus, hey increase labor supply in response o he increased labor demand of firms, and employmen and oupu rise in response o unanicipaed inflaion. However, here is no unemploymen in his model, and flucuaions in employmen are based on ineremporal subsiuion in labor supply.!8

9 For hese reasons, and despie he fac ha new classical models are heoreically consisen, many economiss consider hem as an unsaisfacory explanaion of aggregae flucuaions. The alernaive class of models are new keynesian models, which assume ha nominal wages and/or prices canno adjus immediaely in order o equilibrae labor and produc markes. Thus, following nominal shocks, quaniies have o adjus oo, resuling in flucuaions in real variables, deviaions of oupu and oher real variables from heir seady sae values and involunary unemploymen. I is o such models ha we now urn.!9

10 References Alogoskoufis G. (1983), The Labour Marke in an Equilibrium Business Cycle Model, Journal of Moneary Economics, 11, pp Alogoskoufis G. (1987a), On Ineremporal Subsiuion and Aggregae Labor Supply, Journal of Poliical Economy, 95, pp Alogoskoufis G. (1987b), Aggregae Employmen and Ineremporal Subsiuion in he UK, The Economic Journal, 97, pp Barro R.J. (1976), Raional Expecaions and he Role of Moneary Policy, Journal of Moneary Economics, 2, pp Bernanke B.S. (2006), Moneary Aggregaes and Moneary Policy a he Federal Reserve: A Hisorical Perspecive, Speech a he 4h ECB Cenral Banking Conference, Frankfur, Board of Governors of he Federal Reserve Sysem. Campbell John Y. (1994), Inspecing he Mechanism: An Analyical Approach o he Sochasic Growh Model, Journal of Moneary Economics, 33, pp Fisher I. (1896), Appreciaion and Ineres, Publicaions of he American Economic Associaion, 11, pp Fisher I. (1930), The Theory of Ineres, New York, Macmillan. Gali J. (2008), Moneary Policy, Inflaion and he Business Cycle, Princeon N.J., Princeon Universiy Press. King R.G. and Rebelo S.T. (1999), Resusciaing Real Business Cycles, in Taylor J.B. and Woodford M. (1999), Handbook of Macroeconomics, Vol. 1B, Amserdam, Elsevier. Kydland F.E. and Presco E.C. (1982), Time o Build and Aggregae Flucuaions, Economerica, 50, pp Long J.B. and Plosser C.I. (1983), Real Business Cycles, Journal of Poliical Economy, 91, pp Lucas R.E. Jr (1972), Expecaions and he Neuraliy of Money, Journal of Economic Theory, 4, pp Lucas R.E. Jr (1973), Some Inernaional Evidence on Oupu-Inflaion Tradeoffs, American Economic Review, 63, pp Lucas R.E. Jr (1976), Economeric Policy Evaluaion: A Criique, Carnegie Rocheser Conference Series on Public Policy, 1, pp Lucas R.E. Jr (1977), Undersanding Business Cycles, Carnegie Rocheser Conference Series on Public Policy, 5, pp Lucas R.E. Jr and Rapping L. (1969), Real Wages, Employmen and Inflaion, Journal of Poliical Economy, 77, pp McCallum B.T. Price Level Deerminacy wih an Ineres Rae Policy Rule and Raional Expecaions, Journal of Moneary Economics, 8, pp Poole W. (1970), Opimal Choice of Moneary Policy Insrumens in a Simple Sochasic Macro Model, The Quarerly Journal of Economics, 84, pp Presco E.C. (1986), Theory Ahead of Business Cycle Measuremen, Carnegie-Rocheser Conference Series on Public Policy, 25, pp Ramsey F. (1928), A Mahemaical Theory of Saving, Economic Journal, 38, pp Sargen T.J. (1976), A Classical Macro-economeric Model for he Unied Saes, Journal of Poliical Economy, 84, pp Sargen T.J. and Wallace N. (1975), Raional Expecaions, he Opimal Moneary Insrumen and he Opimal Money Supply Rule, Journal of Poliical Economy, 83, pp !10

11 Wicksell K. (1898), Ineres and Prices, (English ranslaion, Kahn R.F. 1936), London, Macmillan. Woodford M. (2003), Ineres and Prices: Foundaions of a Theory of Moneary Policy, Princeon N.J., Princeon Universiy Press.!11