How Would Monetary Policy Look Like if John Rawls Had Been Hired as a Chairman of the Fed?

Transcription

1 How Would Moneary Policy Look Like if John Rawls Had Been Hired as a Chairman of he Fed? Mara B. M. Areosa, Waldyr D. Areosa and Pierre Monnin February 217 CEP Working Paper Draf

2 ABOUT THE AUTHORS Mara Areosa is a researcher a he Research Deparmen of he Cenral Bank of Brazil. Her work focuses on moneary policy and he formaion of expecaions. Regarding he former heme, her main ineres is on he ineracion beween moneary policy and inequaliy, while informaional fricions is he focal poin of he laer. Mara is responsible for one of he analyses ha give suppor o he Moneary Policy Commiee s decisions. She has also aced as a lecurer a he Deparmen of Economics of he Ponifical Universiy of Rio de Janeiro (PUC-Rio). Mara graduaed in Elecronic Engineer from he Federal Universiy of Rio de Janeiro. She also holds a Maser degree in Mahemaical Economics from he Naional Insiue for Pure and Applied Mahemaics (IMPA) and a PhD in Economics from PUC-Rio. Waldyr Dura Areosa is a eam leader of he Research Deparmen a he Cenral Bank of Brazil where he oversees a eam generaing proposals and policy-oriened research on moneary policy and financial sabiliy. Prior o ha, he has been wih he Cenral Bank of Brazil in various roles for a oal of seveneen years in he Deparmen of Bank Operaions and Paymen Sysems, he Execuive Secrearia and he Deparmen of Foreign Reserves. He was also a Visiing Cenral Bank Research Fellow a he Bank for Inernaional Selemens in Basel. Dr. Areosa s research spans economerics and macroeconomics, wih paricular emphasis on moneary and exchange rae policy and informaional fricions. He holds a PhD and a MSc in Economics from Ponifical Caholic Universiy of Rio de Janeiro, where he is a lecurer a he Economics Deparmen, as well as a MSc and a BSc in Indusrial Engineering from he Federal Universiy of Rio de Janeiro. Pierre Monnin is a fellow wih he Council on Economic Policies (CEP) where he is focusing on he disribuive effecs of moneary policy and on he role ha cenral banks can play in he ransiion oward an environmenally susainable economy. Prior o ha he has been wih he Swiss Naional Bank (SNB) in various roles for a oal of en years - counselling SNB s Board Members on issues concerning financial markes and moneary policy as well as developing measures of financial sabiliy and inegraing hem ino he bank s moneary policy framework. He also worked a Man Invesmens as a Quaniaive Analys, developing asse allocaion sraegies for alernaive invesmens. Dr. Monnin holds a PhD in Economics from he Universiy of Zurich, a MSc in Economics from Queen Mary, Universiy of London, as well as a MSc in Saisics and a BA in Economics from he Universiy of Neuchael.

3 The CEP Working Paper Series is published by he Council on Economic Policies (CEP) an inernaional economic policy hink ank for susainabiliy focused on fiscal, moneary, and rade policy. Publicaions in his series are subjec o a prepublicaion peer review o ensure analyical qualiy. The views expressed in he papers are hose of he auhors and do no necessarily represen hose of CEP or is board. Working papers describe research in progress by he auhors and are published o elici commens and furher debae. For addiional informaion abou his series or o submi a paper please conac Council on Economic Policies, Seefeldsrasse 6, 88 Zurich, Swizerland, Phone: , info@cepweb.org

4 ABSTRACT Using a exbook New Keynesian model exended wih an inequaliy channel, we examine opimal moneary policy deparing from he radiional uiliarian social welfare funcion, o consider alernaive funcions, including he Rawlsian approach of puing only weigh o he agen wih he lowes welfare level. Our main resuls show he opimal responses from a Rawlsian moneary auhoriy are: (i) a less aggressive moneary ighening, bu inducing a more pronounced drop in inflaion afer a moneary shock; (ii) a moneary policy easing afer an increase in governmen spending and (iii) a more pronounced drop in he ineres rae afer a posiive oal facor produciviy shock. ACKNOWLEDGEMENTS AND DISCLAIMER The views expressed in he paper are hose of he auhors and do no necessarily reflec hose of he Banco Cenral do Brasil.

5 CONTENTS 1 Inroducion Brief lieraure review The model IS curve Inequaliy evoluion New Keynesian Phillips curve Opimal moneary policy Implicaions for welfare and ransiion dynamics Calibraion Opimal response o policy disurbances Conclusions References

6 1 INTRODUCTION Cenral banks are key players in shaping economic policies. Indeed, hey have an immense privilege: hey are he only insiuions allowed o creae cenral bank money. This gives hem he power o influence a cenral price in he economy: he ineres rae. Ineres raes are criical in many long erm decisions by economic agens. Thus, by guiding hese raes, cenral banks can significanly influence he economic choices made every day. To help craf opimal moneary policy, cenral banks rely on economic models. In paricular, hey use models o deermine he policy ha would maximize social welfare. Presenly, mos models used by cenral banks, like dynamic sochasic general equilibrium (DSGE) models, rely on he assumpion of a represenaive agen or household. In such a framework, he quesion of he maximizaion of social welfare is sraighforward: since here is only one agen in he economy, maximizing social welfare is equivalen o maximizing individual welfare. Recen economic research, hough, abandons he represenaive agen hypohesis, because many macro quesions of grea relevance simply canno be addressed wihou allowing for a leas some heerogeneiy (Heahcoe e al., 29). A model wih heerogeneous agens appears o be more aligned wih realiy. However, moving o models wih heerogeneous agens raises he quesion of which social welfare funcion o use, i.e., now ha we have muliple agens, how do we aggregae heir individual welfare levels ino overall social welfare? The classic answer is o use a uiliarian social welfare funcion, in which social welfare is jus he sum of individual welfare levels. This choice is raher arbirary and several oher social welfare funcions could be used, ranging from a uiliarian funcion (same weigh o all agens) o a Rawlsian funcion (weigh o he agen wih he lowes welfare level only), derived from he philosophical work of John Rawls. The objecive of his paper is o idenify and compare opimal moneary policy under differen social welfare funcions. We base our analysis on he research by Areosa and Areosa (216). Their framework is similar o a exbook New Keynesian model wih he addiion of heerogeneous agens. Concreely, households are separaed ino wo groups, which differ in hree dimensions: produciviy, wage and financial marke access. While one group has higher produciviy, higher 1

7 wages and beer access o financial markes (henceforh, financially included or FI households), he oher group has lower produciviy, lower wages and no access o financial markes (financially excluded or FE households). The auhors show ha when agens differ no only in wheher hey have access o he financial marke, bu also in heir labor produciviy, an inequaliy channel from moneary policy o inflaion emerges. 1 This channel appears because he ineres rae affecs inflaion no only hrough changes in he level of aggregae consumpion, bu also hrough changes in is disribuion. The raionale behind his effec is he following: changes in ineres rae direcly affec FI households demand (and hus heir labor supply) hrough ineremporal subsiuion. Since FE households canno use financial markes o smooh heir consumpion over ime, heir demand (and consequenly heir labor supply) is only indirecly affeced by a change in ineres raes, hough is impac on FE households demand. 2 The consequence of ha is ha incenives o work and consume for FI and FE households are differenly impaced by ineres rae changes. Firms incorporae hese heerogeneous labor supply responses when opimizing heir producion coss. Under hese condiions, firmsâăź marginal cos is no only a funcion of aggregae labor supply, bu also of is composiion. Since, as in any New Keynesian model, inflaion reflecs expecaions abou marginal coss hrough he Phillips curve, Areosa and Areosa (216) show ha, in heir framework, inflaion is no only a funcion of he aggregae oupu gap bu also of is disribuion, generaing an inequaliy channel of moneary policy ransmission o inflaion. 3 Areosa and Areosa (216) sudy he case of a uiliarian cenral bank and show ha inroducing heerogeneous agens wih limied access o financial markes and heerogeneous produciviy ransforms he cenral bank s objecive funcion. In addiion o he oupu gap and inflaion, as in he represenaive agen case, cenral banks now also include inequaliy in heir objecive funcion. Under his "inequaliy-expanded" objecive, an opimal moneary policy can no longer simulaneously sabilize he oupu gap and inflaion, since i has o ake he effecs of inequaliy ino consideraion. We exend heir analysis o incorporae he fac ha he cenral bank migh no use a uiliarian social welfare funcion, bu pu any oher weighs on he wo groups of agens. We focus paricularly on he case in 1 Areosa and Areosa (216) choose a consumpion-based inequaliy index, moving beyond income as an indicaor of well-being and being in line wih Krueger and Perri (26). 2 Moll e al. (216) highligh he decomposiion beween he direc and he indirec effec of moneary policy on households consumpion. 3 The inequaliy channel of moneary policy ransmission is absen from similar New Keynesian models like Bilbiie (28) and Galí e al. (24) because hese models do no include heerogeneiy on he labor marke. 2

8 which he cenral bank pu give more imporance o he leas well-off group in he economy. Our main resuls highligh how differen weighing schemes in he social welfare funcion affec he opimal response o moneary, fiscal and produciviy shocks. The opimal response o a posiive moneary shock does no depend significanly on how he cenral bank weighs he welfare of each ype of agen. In all cases, afer a moneary shock, he ineres rae rises, causing inflaion and oupu gap o drop. Alhough his dynamic is observable for all weighs, under a Rawlsian welfare funcion, he ineres rae rises less and he oupu gap fall slighly less. In urn, inflaion falls slighly more while inequaliy rises less. Even wih less aggressive moneary policy, inflaion drops more under a Rawlsian moneary policy. This finding is in line wih he empirical evidence ha poins o inflaion as a major concern for low-income people. In his conex, an opimal moneary policy wih focus on he low-income group would figh inflaion insofar as i erodes real wages. A compleely differen siuaion arises afer a fiscal shock, represened by an increase in governmen spending. While opimal moneary policy pushes he ineres rae up when he cenral bank overlooks he financially excluded households, i comes down when he bank implemens a Rawlsian moneary policy. This difference in he opimal policy appears in inflaion: i drops in he former case and climbs in he laer. The idea ha under a Rawlsian moneary policy, he cenral bank allows inflaion o go up migh seem puzzling. Neverheless, despie a possible increase in inflaion, a fiscal shock always benefis households wih no access o he financial markes insofar as an increase in economic aciviy raises boh real wages and working hours, increasing heir consumpion. An increase in he ineres rae would parially offse his benefi. This dynamics suggess ha when he cenral bank looks exclusively o he low-income group, i is prone o accep increases in he price index ha are lower han he nominal wage growh. Finally, our resuls sugges ha a posiive oal facor produciviy shock amplifies he difference in he producion of he wo groups of workers - skilled and unskilled. For his reason, he real wage grows more inensively for he qualified workers. When he cenral bank implemens he moneary policy o benefi he less qualified workers, his difference diminishes, bu does no disappear. The increase in real wages generaes an increase in labor income, which in urn induces an increase in consumpion. Compared o he unskilled workers, he skilled workers increase heir consumpion proporionally more. This difference in he response of he wo 3

9 groups appears as an increase in inequaliy, which becomes less inense when he cenral bank maximizes he welfare of he low-income group. The nex secion briefly describes he lieraure ha links moneary policy, inflaion and inequaliy. We summarize he log-linear version of he model of Areosa and Areosa (216) in Secion 3. We hen derive he opimal moneary policy in Secion 4, calibrae he model o evaluae is quaniaive implicaions in Secion 5, and provide concluding remarks in Secion 6. Deails of all he derivaions are available from us. 2 BRIEF LITERATURE REVIEW EMPIRICAL EVIDENCE. Considering he empirical lieraure abou he influence of inflaion and moneary policy on inequaliy, Romer and Romer (1999) find a srong posiive relaionship beween inflaion and inequaliy while Easerly and Fischer (21) find ha direc measures of improvemen in he well-being of he poor and inflaion are negaively correlaed. In opposiion o hese findings, Doepke and Schneider (26) assess he effecs of inflaion hrough changes in he value of nominal asses o show ha he main losers from inflaion are rich, old households, he major bondholders in he economy. Recenly, Coibion e al. (212) documen ha in he U.S. moneary policy conracions have subsanial and persisen redisribuive effecs, increasing income and consumpion inequaliy. Few empirical sudies focus on he influence of inequaliy on inflaion. For insance, Al-Marhubi (1997) finds ha counries wih greaer inequaliy have higher mean inflaion, even afer accouning for he level of openness, poliical insabiliy and cenral bank independence, while Dolmas e al. (2) documen a posiive correlaion beween income inequaliy and inflaion in democracies. THEORETICAL LITERATURE. The analysis of moneary policy in much of he recen lieraure is based on a framework ha assumes he exisence of a represenaive household, which is 4

10 clearly inadequae o evaluae inequaliy. 4 Recenly, a growing lieraure incorporaes heerogeneous agens ino his framework in order o sudy he disribuional effecs of moneary policy. 5 This aricle relies heavily on he works of Galí e al. (24) and Bilbiie (28). Galí e al. (24) inroduce rule-of-humb consumers in a convenional New Keynesian model wih invesmen o show how heir presence can dramaically change he properies of widely used ineres rae rules. Bilbiie (28) and Navik (212) modify his framework o answer a differen se of quesions. While he former auhor neglecs capial accumulaion o sudy how he presence of non-asse holders alers he slope of he IS curve and he deerminacy properies of ineres rae rules, he laer shows ha he abiliy o explain he posiive consumpion response as a consequence of rule-of-humb behavior hinges on he arbirary assumpion ha wealh is redisribued across households in seady sae. Wihin his lieraure, Muscaelli e al. (25) and Landon-Lane and Occhino (25) use U.S. daa o esimae models wih liquidiy-consrained consumers and find a significan role for rule-of-humb consumer behavior, while Moa and Tirelli (214) repor ha moneary conracions have redisribuive effecs in favor of asse holders, broadly confirming he findings in Coibion e al. (212). 6 More recenly, Ascari e al. (211) and Ko (215) inroduce sicky wages ino a model similar o Bilbiie (28). While he former sudy neglecs heerogeneous labor and concludes ha he limied asse marke paricipaion is no relevan for moneary policy, he laer incorporaes segmened labor markes and, similar o us, obains ha inequaliy poses a radeoff wih radiional moneary policy objecives. We, however, consider ha our modeling choice, wihou sicky wages and simply considering differen ypes of labor in he producion funcion, keeps he mos relevan insighs of he relaion beween inflaion, inequaliy and moneary policy wih greaer simpliciy of exposiion. 4 See Goodfriend and King (1997), Clarida e al. (1999) and Woodford (23). 5 For a broader view of he disribuional consequences of moneary policy and inflaion, see Doepke e al. (215), Aucler (215), Brunnermeier and Sannikov (212), Williamson (28) and Albanesi (27). Nakajima (215) presens a recen overview. 6 Oher sudies modeling several ypes of marke segmenaion are Occhino (24), Vissing-Jorgensen (22), Alvarez e al. (22) and Alvarez e al. (21). 5

11 3 THE MODEL We use he model presened in Areosa and Areosa (216) o accoun for inequaliy effecs while keeping he model as close as possible o he sandard New Keynesian framework. There is a coninuum of infiniely-lived households indexed in he uni inerval and monopolisically compeiive firms seing prices as in he sicky price model of Calvo (1983). There are, however, wo main deparures from he sandard model: (i) an exogenous fracion λ (, 1) of households - henceforh called financially excluded (FE) agens - offer unskilled labor, do no own any asses, and do no pay axes, while he remaining fracion 1 λ of households - he financially included (FI) agens - offer skilled labor, pay axes, and have access o financial markes and (ii) each firm uses a Cobb-Douglas echnology o combine he wo ypes of labor o produce a differeniaed good. 6

12 Wih a sligh abuse of erminology, we refer o financially included (FI) and financially excluded (FE) agens as "skilled" and "unskilled". This erminology comes from he fac ha under he baseline calibraion, FI agens are more producive and have a higher hourly wage and payroll han FE agens in seady sae. The leers e and i refer o variables associaed wih FE and FI consumers. The following equaions summarize he log-linear version of he model, being ẑ (z z) / z he percen deviaion of a given variable z from is seady-sae level z, excep for governmen spending Ĝ ( G Ḡ) /Ȳ, and he Gini index ĝ ĝ ḡ. In order o make fuure references easier, we describe he srucural parameers of he model in Table IS CURVE The demand side of he model is represened by an ineremporal IS equaion: [ ] x = E {x +1 } ϑ î E {π +1 } r f, (1) where x is he oupu gap measure, π is he inflaion rae, and î is he nominal ineres rae. The real ineres rae ha sabilizes he oupu gap, r f, called he naural rae of ineres, evolves according o: } }] r f ϑ [ νe 1 {Ĝ+1 Ĝ + ( q ν) E {Â+1 Â, where  represens he produciviy facor, Ĝ is governmen spending and where ν (1 ν)λσ νqω, q q and ν 1 qσ. qω+λσ qω+λσ 1 qσ q(1+ω) This equaion combines wo differen behaviors: while FI agens use changes in he real ineres rae o smooh heir consumpion in ime, FE households do no reac o hose changes and simply consume heir curren labor income. As no all agens respond o ineres rae changes, he slope of he IS curve ( ( )) λ 1, ϑ η σ q being η 1 qσ λ(1 σ), is differen from wha is obained in he 1 qσ q(1+ω) sandard New Keynesian model, which depends only on he ineremporal elasiciy of subsiuion σ >. This resul is in line wih Bilbiie (28), since boh models assume he exisence of Limied Asse Marke Paricipaion (LAMP) agens. However, as Areosa and Areosa (216) assume ha he wo ypes of agens offer differen ypes of labor, he slope ϑ also depends on he elasiciies associaed wih 7

13 each ype of labor, q and (1 q), on he inverse of elasiciy of labor supply ω and on he fracion of FE agens. 3.2 INEQUALITY EVOLUTION Areosa and Areosa (216) show how ha i is possible o decompose he effec of each exogenous shock of he model ino wo differen componens: changes in he oupu gap, relaed o he level of aggregae consumpion, and changes in he disribuion of consumpion, expressed hrough he Gini index, ĝ. This decomposiion is expressed in he following equaion: ( ) ( ) λ 1 + γ Φ = (1 σ) (1 + ω) x ĝ, (2) q λ where γ σ ( λ q 1 λ), and Φ is a funcion of he fiscal and produciviy shocks: Φ λ (ω + σ) q ( )Ĝ ω + σ λ q ( λ ) 1 (1 + ω) q ( ) Â. ω + σ λ q The evoluion of he Gini index, obained from subsiuing (2) in he IS curve, gives us an inuiive way of seeing how moneary policy affecs inequaliy: ĝ = E {ĝ +1 } + ϑ δ [ î E {π +1 } r δ ], (3) where ϑ δ η δ σ 1, η δ (1 λ) (η 1), and r δ, he real ineres rae ha sabilizes ĝ, is defined as: } }] r δ ϑ 1 ν [E δ {Ĝ+1 Ĝ E {Â+1 Â, where ν δ ν λ(ω+σ) q q(1+ω) λ(1 σ). If η > 1, inequaliy rises wih he ineres rae. The difference beween he real ineres raes ha sabilize he oupu gap and he Gini index is based on he evoluion of governmen spending and produciviy. 3.3 NEW KEYNESIAN PHILLIPS CURVE The log-linear version of an aggregae supply relaion akes he form: π = ξ MC + βe {π +1 }, (4) 8

14 where ξ (1 α) (1 αβ) /α > and MC, he percen variaion of real marginal coss, akes he form: MC = ( ω + σ ( )) λ x + γ q λĝ. The firs componen of marginal cos is sandard, bu now has a differen inerpreaion. Marginal coss are proporional o he oupu gap ha would occur if consumpion of boh agens was equal. The second erm correcs his measure hrough he inequaliy effec. We can use his equaion and (4) o obain our New Keynesian Phillips curve (NKPC): where κ ξ ( ω + σ ( λ q π = κx + βe {π +1 } + κ δ ĝ, (5) )) and κ δ ξγ/λ. From (2) and (5), he NKPC can be wrien in a more familiar forma π = κ x + βe {π +1 } + u, (6) where he slope of he NKPC is ( ) [ ( )] 1 λ κ κ + κ δ λ 1 + γ q 1. and he shock u is where Φ is he same as in (2). u ξ ( ) γ Φ, 1 + γ 4 OPTIMAL MONETARY POLICY Areosa and Areosa (216) assume ha, following Erceg e al. (2) and Woodford (23), he policymaker maximizes he average expeced uiliy of households by aking a second-order approximaion of he aggregae uiliy of all agens. We depar from his approach by assuming he moneary auhoriy may pu differen weighs s on agens uiliy funcions. In his conex, he cenral bank maximizes W s = su e + (1 s) U. i When s = λ, we have again he uiliarian case. When s = 1, he cenral bank implemens a Rawlsian moneary policy, while when s =, he moneary auhoriy simply overlooks he exisence of FE agens. 9

15 In a echnical appendix, available on reques, we show ha he second-order approximaion of he uiliy funcion for a ype-k {e, i} agen resuls in: { W k = 1 2 Y ( ) (C) σ E β {λ k x x x k 2 ) + λ k g (ĝ ĝ k 2 } } + λ k π π 2 + ip (7) = where λ k x, λ k g and λ k π are consans ha depend on he srucural parameers of he model, while x k and ĝ k are variables ha depend on he shocks. From his expression, i becomes clear ha for boh FE and FI households: (i) i is no opimal o mainain zero inflaion and a zero oupu gap in he face of inequaliy variaions, (ii) he oupu gap he cenral bank should pursue is differen from he sandard New Keynesian gap measure, and (iii) here is an inequaliy gap. The maximizaion of (7) subjec o he consrains represened by he NKPC in (5) and equaion (2), relaing x and ĝ, generaes he following crierion under commimen: π = 1 [ κ (x κ x 1 ) Ψ θ ( ϑ δ ϑ ) ] (ĝ ĝ 1 ). (8) This so-called opimal arge crierion represens a policy rule ha is opimal from a imeless perspecive, following Giannoni and Woodford (25). Inflaion should be acceped as long as i is negaively proporional o oupu gap variaions correced for inequaliy variaions over he same period. To implemen he arge rule, we obain an opimal insrumen rule by subsiuing equaions (1), (3), and (5) in he opimal crierion (8): î = φ s πe {π +1 } + φ s xe {x +1 } + φ s δe {ĝ +1 } + φ s x 1x 1 + φ s δ 1ĝ 1 + ɛ s, (9) where he φ js are funcions of he srucural parameers of he model and of he weigh s while composie shock ɛ s depends on he naural rae of ineres, on he real ineres rae ha sabilizes ĝ, and on boh he oupu gap and he inequaliy gap. 7 We call equaion (9) our expecaions-based reacion funcion, following Evans and Honkapohja (26). If he moneary auhoriy commis iself o seing ineres raes in accordance wih his reacion funcion a all imes, hen he raional-expecaions equilibrium is necessarily deerminae. 7 See he appendix for deails. 1

16 Table 1: Baseline calibraion Parameer Descripion Value α Fracion of firms ha leave heir prices unchanged.66 β Time discoun facor.99 θ Elasiciy of subsiuion among differeniaed goods 11 λ Proporion of unskilled agens wih no access o he financial sysem.4 σ Risk aversion parameer.9 ω Inverse of elasiciy of labor supply.33 q Elasiciy associaed wih unskilled labor.1 φ g (φ a ) Fiscal (produciviy) shock ineria.9 5 IMPLICATIONS FOR WELFARE AND TRANSITION DYNAMICS To illusrae no only he impac on welfare, bu also he response o moneary and fiscal shocks under opimal commimen, we calibrae he model represened by equaions (1), (3), (5), and (9) and solve i numerically. 5.1 CALIBRATION We use he same calibraion saed in Areosa and Areosa (216).The baseline values of he parameers, described in Table 1, are sandard and based on Giannoni and Woodford (25). 5.2 OPTIMAL RESPONSE TO POLICY DISTURBANCES Moneary shocks Figure 1 shows he impulse responses of he four endogenous variables o a moneary shock. The differen lines are indexed by s. Clearly he opimal response o a moneary shock does no depend significanly on how he cenral bank weighs he welfare of each ype of agen. In all cases, afer a moneary shock he ineres 11

17 Figure 1: Impulse responses o a moneary shock under opimal commimen under alernaive values of s - aggregae variables 3.5 (A) Ineres rae, annualized (B) Oupu Gap (C) Inflaion, annualized (D) Gini Index for consumpion s= or FI s=.4 or Benham s=.7 s=1 or Rawls Figure 2: Impulse responses o a moneary shock under opimal commimen under alernaive values of s - FE versus FI agens.5 (A) Ce Consumpion of FE agens (B) Ci Consumpion of FI agens (C) We/P Real wage of FE agens (D) He Working hours of FE agens (D) Wi/P Real wage of FI agens (E) Hi Working Hours of FI agens.1.1 s= or FI.2 s=.4 or Benham.3 s=.7 s=1 or Rawls rae rises, causing inflaion and oupu gap o drop. Figure 2 shows he impulse responses of consumpion, real wages and hours worked of each group o a moneary shock. Because FE households canno smooh heir consumpion in ime, under a conracion heir consumpion falls more han FI s (beween 1% and 1.5% 12

18 afer less han 1%), leading o an increase in inequaliy. Alhough his dynamic is observable for all weighs, when s is closer o one, he ineres rae rises less, he oupu gap fall slighly less and inflaion falls slighly more, while inequaliy rises less. The difference in he inensiy of he responses suggess ha when he cenral bank is more concerned wih no huring he low-income group, i becomes less aggressive in implemening he moneary policy, avoiding oupu from falling more seeply. For boh groups, a smaller drop in economic aciviy makes consumpion, real wages and working hours fall less. Neverheless, here is a subsanial difference beween he wo groups of agens: in comparison o FE agens, he working hours drop abou hree imes more han for FI agens (.3% afer.1%). This difference comes from he fac ha FE agens are less willing o diminish heir working hours, since hey depend exclusively on heir labor income o consume. Even wih a less aggressive moneary policy, inflaion drops more under a Rawlsian moneary policy. This finding is in line wih he empirical evidence ha poins o inflaion as a major concern for low-income people. In his conex, an opimal moneary policy wih focus on he low-income group would figh inflaion insofar as i erodes real wages. Fiscal shocks According o Figure 3, he impulse responses of he endogenous variables afer a fiscal shock depend grealy on he weigh he cenral bank pus on agens welfare funcion. While opimal moneary policy pushes ineres rae up when he cenral bank overlooks he FE households, i comes down when he bank implemens a Rawlsian moneary policy. This difference in he opimal policy appears in inflaion: i drops when s = and rises when s = 1. The idea ha under a Rawlsian moneary policy, he cenral bank allows inflaion o go up migh seem puzzling. Neverheless, despie a possible increase in inflaion, a fiscal shock always benefis households wih no access o he financial markes insofar as an increase in economic aciviy raises boh real wages and working hours, increasing heir consumpion, as shown in Figure 4. An increase in he ineres rae would parially offse his benefi. This dynamics suggess ha when he cenral bank looks exclusively a he low-income group, i is prone o accep increases in he price index ha are lower han he nominal wage growh. 13

19 Figure 3: Impulse responses o a fiscal shock under opimal commimen under alernaive values of s - aggregae variables 1 (A) Ineres rae, annualized.25 (B) Oupu Gap (C) Inflaion, annualized.5 (D) Gini Index for consumpion s= or FI.35 s=.4 or Benham.4 s=.7 s=1 or Rawls Figure 4: Impulse responses o a fiscal shock under opimal commimen under alernaive values of s - FE versus FI agens 2 (A) Ce Consumpion of FE agens (B) Ci Consumpion of FI agens (C) We/P Real wage of FE agens (D) He Working hours of FE agens (D) Wi/P Real wage of FI agens (E) Hi Working Hours of FI agens 1.5 s= or FI s=.4 or Benham 1 s=.7 s=1 or Rawls In conras o he low-income group, FI households decrease heir consumpion for all policies he cenral bank may implemen, including an ineres rae cu. The raionale for his behavior is simple: alhough he FI households also benefi from he increase in real wages and working hours, heir consumpion does no depend 14

20 exclusively on heir labor income. When he cenral bank hikes he ineres rae, hey have an incenive o pospone heir consumpion. Moreover, as he only group o pay axes, FI agens carry he burden of an increase in governmenal spending. When he cenral bank cus he ineres rae o accommodae he demand shock, hose agens face an increase in heir labor income. Bu his increase is insufficien o offse he decrease in heir income ha comes from axes. These opposie movemens in he consumpion of he wo ypes of agens cause inequaliy o drop. Clearly, he responses of real wages and working hours differ hugely beween he wo groups of agens. While working hours rise beween.5% and.15% for FE households, hey rise abou 1 imes more for FI households. This resul is no surprising, considering ha here is a major difference in he oupu elasiciy associaed wih each ype of agen. In his conex, an increase in producion depends grealy on he work supplied by FI agens. Concerning real wages, he opposie occurs: while i varies from -.2 o.4 for FI agens, i increases beween.5% and 1.5% for FE agens. This resul suggess ha when he cenral bank overlooks he FE households, he burden creaed by an increase in axes makes FI agens prone o accep a decrease in real wages, even wih an increase in working hours. Produciviy shocks There is no consensus abou wha would be a ypical response afer a posiive echnological shock. Galí (1999) addresses his imporan quesion considering boh he influence of nominal rigidiies and of real explanaions. The auhor shows ha he sylized facs presened by he empirical lieraure depend on he idenifying assumpions relaing srucural shocks. Despie some empirical evidence poining in he same direcion, here are muliple ways o explain hese sylized facs ha depend on he srucure of he model and on he parameers. As can be seen in Figure 5, our resuls show ha afer a oal facor produciviy shock, oupu increases. From he demand side, his increase in economic aciviy becomes eviden hrough he consumpion growh of boh agens, presened in Figure 6. Neverheless, he oupu gap becomes negaive, as poenial oupu increases more han acual oupu. Moneary policy responds o his siuaion by pushing ineres rae down. I is clear ha when he cenral bank focuses on maximizing he welfare of he low-income group, i eases moneary policy more 15

21 inensively (cuing approximaely.5% when s = afer 1.5% when s = 1), making he oupu gap less negaive and allowing inflaion o climb (almos.3%, when s = 1, afer no significan impac, when s = ). Figure 5: Impulse responses o a produciviy shock under opimal commimen under alernaive values of s - aggregae variables (A) Ineres rae, annualized.2 (B) Oupu Gap (C) Inflaion, annualized (D) Gini Index for consumpion s= or FI s=.4 or Benham s=.7 s=1 or Rawls An increase in oal facor produciviy is usually associaed wih a decrease in working hours. This sylized fac is also presen in he model, bu jus for FI agens (varying from slighly below.8%, when s =, o slighly above.8%, when s = 1). Concerning he FE agens, he model shows ha, since hey depend on heir labor income o consume, hey keep heir working hours almos unchanged (wih a small increase ha ranges from near.2%, when s =, o barely.5%, when s = 1). As his slighly posiive response is a leas 15 imes smaller han he drop of he FI agens working hours, he aggregae impac is clearly negaive. The difference in inensiy across he wo ypes of agens is also presen in wo oher variables - real wages and consumpion. In boh cases, variaions occur in he same direcion. Neverheless, while FE agens real wage increases beween.2% (when s = ) and.6% (when s = 1), FI agens varies a leas 2 imes more (from near 1%, when s =, o abou 1.5%, when s = 1). These figures sugges ha a posiive oal facor produciviy shock amplifies he difference in he producion of he wo groups of workers - skilled and unskilled. For his reason, 16

22 Figure 6: Impulse responses o a produciviy shock under opimal commimen under alernaive values of s - FE versus FI agens.8 (A) Ce Consumpion of FE agens 2 (B) Ci Consumpion of FI agens (C) We/P Real wage of FE agens (D) He Working hours of FE agens (D) Wi/P Real wage of FI agens (E) Hi Working Hours of FI agens.2.4 s= or FI.6 s=.4 or Benham.8 s=.7 s=1 or Rawls he real wage grows more inensively for he qualified workers. When he cenral bank implemens he moneary policy o benefi he less qualified workers, his difference diminishes, bu does no disappear. The increase in real wages generaes an increase in labor income, which in urn induces an increase in consumpion. Compared o he unskilled workers, he skilled workers increase proporionally more heir consumpion (near.2% afer 1.5%, when s =, and,.6% afer abou 1.7%, when s = 1). The raionale behind his observaion ress on he fac ha his group is also benefied by a greaer increase heir real wages, since as already menioned, a oal facor produciviy shock amplifies he difference in he producion of he wo groups of workers. This difference in he response of he wo groups appears as an increase in inequaliy, which becomes less inense when he cenral bank maximizes he welfare of he low-income group (.3%, when s =, afer.27%, when s = 1). 6 CONCLUSIONS In his work, we idenify and compare opimal moneary policy under differen social welfare funcions. We base our analysis on he research by Areosa and Areosa (216), which examines opimal moneary policy in he presence of inequaliy 17

23 by inroducing unskilled agens wih no access o he financial sysem ino an oherwise exbook New Keynesian model. We exend heir analysis o incorporae he fac ha he cenral bank migh no use a uiliarian welfare based funcion, bu pu any oher weighs on he wo groups of agens. The opimal response o a moneary shock does no depend significanly on how cenral bank weighs he welfare of each ype of agen. In all cases, afer a moneary shock, he ineres rae rises, causing inflaion and oupu gap o drop. Alhough his dynamics is observable for all weighs, when s is closer o one, he ineres rae rises less, he oupu gap fall slighly less, inflaion falls slighly more, while inequaliy rises less. Even wih a less aggressive moneary policy, inflaion drops more under a Rawlsian moneary policy. This finding is in line wih he empirical evidence ha poins o inflaion as a major concern for low-income people. In his conex, an opimal moneary policy wih focus on he low-income group would figh inflaion insofar as i erodes real wages. A compleely differen siuaion arises afer a fiscal shock. While opimal moneary policy pushes he ineres rae up when he cenral bank overlooks he FE households, i comes down when cenral bank implemens a Rawlsian moneary policy. This difference in he opimal policy appears in inflaion: i drops in he former case and rises in he laer. The idea ha, under a Rawlsian moneary policy, he cenral bank allows inflaion o go up migh seem puzzling. Neverheless, despie a possible increase in inflaion, a fiscal shock always benefis households wih no access o he financial markes insofar as an increase in he economic aciviy raises boh real wages and working hours, increasing heir consumpion. An increase in he ineres rae would parially offse his benefi. This dynamics suggess ha when he cenral bank looks exclusively o he low-income group, i is prone o accep increases in he price index ha are lower han he nominal wage growh. Our resuls also sugges ha a posiive oal facor produciviy shock amplifies he difference in he producion of he wo groups of workers - skilled and unskilled. For his reason, he real wage grows more inensively for he qualified workers. When he cenral bank implemens he moneary policy o benefi he less qualified workers, his difference diminishes, bu does no disappear. The increase in real wages generaes an increase in he labor income, which in urn induces an increase in consumpion. Compared o he unskilled workers, he skilled workers increase heir consumpion proporionally more. This difference in he response of 18

24 he wo groups appears as an increase in inequaliy, which becomes less inense when he cenral bank maximizes he welfare of he low income group. 19

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