Advanced Macroeconomics

Transcription

1 Advancd Macroconomcs Chaptr 18 INFLATION, UNEMPLOYMENT AND AGGREGATE SUPPLY

2 Thms of th chaptr Nomnal rgdts, xpctatonal rrors and mploymnt fluctuatons. Th short-run trad-off btwn nflaton and unmploymnt. Th rlatonshp btwn th thory of nflaton and th thory of structural unmploymnt. Supply shocks and th Nw Economy. Th aggrgat supply curv.

3 Th Phllps curv n th Untd Kngdom,

4 Th Phllps curv n th Untd Kngdom,

5 Inflaton (prcnt) Unmploymnt rat (prcnt) Th Phllps curv n th Untd Stats n th 1960s

6 Inflaton (prcnt) Unmploymnt rat (prcnt) Th brakdown of th smpl Phllps curv n th Untd Stats

7 Whrar w Hadng? Th thoryof nflaton and unmploymnt dvlopd n ths chaptr may b summarzd n: Th xpctatons-augmntd Phllps curv π=π +α α> ( u u ), 0 (1) p = actual rat of nflaton p = xpctd rat of nflaton u = actual rat of unmploymnt u = natural rat of unmploymnt In th followng w wll drv th xpctatons-augmntd Phllps curv from a thory of wag and prc sttng.

8 Prc Sttng Producton functon n sctor Y = BL, 0<α< 1 (3) 1 α Th margnal product of labour ( 1 ) MPL dy/dl= α BL α (4) Th dmand curv for th product of sctor σ P Y Y, = σ> P n 1 (5) Total rvnu s TR PY, so accordng to (5) margnal rvnu s

9 Prc Sttng Margnal rvnu n sctor dtr dp dp Y MR = P + Y = P 1 + dy dy dy P 1 MR = P 1 σ (6) MC Margnal cost n sctor W MPL = = W ( 1 α) BL α Maxmzaton of profts rqurs MR = MC, mplyng

10 Prc Sttng Mark-up prcng MC p W p σ P = m, m > 1 ( 1 ) BL α α σ 1 (7) From (7) w obtan an xprsson for P /P. Insrt ths along wth (3) nto (5) to gt P / P Y } p 1 m W / P α Y BL = ( 1 ) α α BL n σ

11 Labour Dmand n Sctor w, / ( 1 α) Y B ε L = w p, nb m W P ε σ ε σ 1 +α σ 1 ε ( ) (8) Thus labour dmand s a dclnng functon of th ral wag w, and th numrcal wag lastcty of labour dmand at th sctoral lvl s gvn by.

12 Wag sttng undr Prfct Informaton Workrs n sctor ar ducatd and trand to work n that partcular sctor, so thy cannot mov to anothr sctor to look for a job. Hnc thr outsd opton s smply qual to th ral rat of unmploymnt bnft, b. All workrs n sctor ar organzd n a monopoly trad unon whch sks to maxmz: Th total rnt accrung to workrs n sctor (trad unon objctv) ( ) ( ) ( ) Ω w = w b L w η (9) whr th labour dmand functon L (w ) s gvn by (8), and whr th paramtr? masurs th unon s prfrnc for hgh mploymnt rlatv to th goal of a hgh ral wag for mployd mmbrs. If th unon has prfct nformaton about th currnt prc lvl P, t wll choos th nomnal wag rat W so as to maxmz O(w ) wth rspct to w, mplyng th frst-ordr condton:

13 Wag sttng undr Prfct ( ) Informaton dω w η η 1 dl = L + ( w b) η L = 0 dw dw = ε η( w b) dl w 1+ = 0 w dw L w w ηε w = m b, m ηε 1 (10) Thus th unon sts th ral wag as a mark-up ovr th ral rat of unmploymnt bnft. Th mark-up s lowr th hghr th valus of? and.

14 Wag sttng undr mprfct nformaton Equaton (10) assums that th unon has prfct nformaton on th currnt prc lvl. In practc, th unon must st th nomnal wag rat at th start of th currnt prod, basd on th prc lvl xpctd to prval ovr that prod (P ), so as to achv an xpctd ral wag qual to th targt lvl m w b. Hnc w gt: Th optmal nomnal wag rat undr mprfct nformaton Not that: w W = P m b (11)? th nomnal wag rat s pr-st for on prod at a tm, so n th short ru w hav nomnal rgdty? P may dvat from P, so thr may b xpctatonal rrors

15 Th Expctatons-augmntd From (11) w gt: Phllps curv Th actual ral wag W P P = m P whch may b nsrtd nto (8) to gv: Labour dmand n sctor w b L ε / σ ε ( 1 α) Y B P = nb m m b P p w (12) In a symmtrc qulbrum aggrgat mploymnt s L=nL and total output s

16 Th Expctatons-augmntd Phllps curv Aggrgat output n symmtrc qulbrum 1 Y = ny = nbl α Substtutng ths nto (12) and usng th dfnton of, w gt Aggrgat mploymnt n symmtrc qulbrum B ( 1 α) L = nl = n m m b P P p w 1 / α Insrtng th long run qulbrum condton P =P nto (13), w fnd (13) Th natural lvl of mploymnt L B = n p w m m b ( 1 α) 1 / α (15)

17 Th Expctatons-augmntd Phllps curv Dvdng (13) by (15) and dnotng th labour forc by N, w gt ( 1 ) ( 1 ) L u N P = = L u N P 1 / α Takng logs on both sds of (16), and usng th approxmaton ln(1+x) x, w obtan p= p +α u u, p P, p P from whch w drv: ( ) ln ln (16) Th xpctatons-augmntd Phllps curv ( u u, ) p p, p p 1 1 π=π +α π π (17)

18 Explanng th brakdown of th smpl Phllps curv n th lat 1960s Up untl th 1960s th prc lvl was rasonably stabl n pactm. In such a stuaton t s rasonabl to assum that p = 0. From (17) w thn gt Th smpl Phllps curv π = α u u (18) ( ) Howvr, n th lat 1960s th nflaton rat had bn postv and rsng for svral yars, so popl startd to xpct a postv nflaton rat, p > 0. In accordanc wth (17), ths ld to a gradual rs n th rat of nflaton assocatd wth any gvn rat of unmploymnt. Thus th apparnt trad-off btwn unmploymnt and nflaton dscovrd by Phllps s only a short-run trad-off whch wll hold only as long as th xpctd rat of nflaton stays constant. Whn th xpctd nflaton rat ncrass, th short-run Phllps curv wll shft upwards, and vc vrsa.

19 π Long run Phllps curv Short run Phllps curv π>π 2 1 u π>π π 0=0 1 0 u Th xpctatons-augmntd Phllps curv

20 Th lnk btwn unmploymnt and th chang n nflaton Th natural rat ofunmploymnt u s th rat of unmploymnt prvalng n a long-run qulbrum whr xpctatons ar fulflld, p = p. Suppos w hav Statc xpctatons From (17) w thn gt π = (19) π 1 π π π ( ) 1 = α u u (20) whch shows that nflaton wll acclrat whn unmploymnt s blow th natural rat and dclrat whn unmploymnt s abov ts natural lvl. For ths rason th natural rat s somtms calld th Non-Acclratng-Inflaton- Rat-of-Unmploymnt (NAIRU).

21 What dtrmns th natural rat of unmploymnt? Rcall that aggrgat mploymnt s L = nl. W may choos unts such that Th rat of mploymnt th labour forc n ach L sctor (N ) s 1 so = L that th total labour N forc (N) s qual to n. Thus w hav: Aggrgat output Y = ny = nbl = nb 1 α 1 α Insrtng ths rlatonshps along wth th symmtry condton W =W nto th labour dmand curv (8) and solvng for (usng th dfnton of ), w gt: Aggrgat labour dmand ( ) 1/ α 1/ 1 α W B m P = p α (14)

22 What dtrmns th natural rat of unmploymnt? By rarrangng (14), w obtan th ral wag mplctly offrd by frms, also trmd Th prc sttng curv W P MPL α = B( 1 α p ) m In a symmtrc qulbrum (W =W) whr xpctatons ar corrct (P =P), quaton (11) gvs th ral wag clamd by workrs, also trmd Th wag sttng curv (PS) W w m P = b (WS)

23 What dtrmns th natural rat of unmploymnt? Th natural rat of mploymnt s th valu of whch maks th ral wag clamd by workrs consstnt wth th ral wag mplctly offrd by frms. Equatng th rght-hand sds of (PS) and (WS) and solvng for, w thus gt Th natural rat of mploymnt B = p w m m b ( 1 α ) 1/ It s rasonabl to assum that unmploymnt bnfts ar lnkd to ral ncom pr capta whch s proportonal to total factor productvty n th long run. Hnc w assum that b=cb. Insrtng n th xprsson abov, w thn obtan Th natural rat of unmploymnt α u 1 α 1 = 1 p w mmc 1/ α (22)

24 What dtrmns th natural rat Implcatons of (22): of unmploymnt? Th natural rat of unmploymnt s hghr? th lowr th dgr of comptton n product markts (a lowr valu of s ncrass m p and m w )? th wakr th unon prfrnc for hgh mploymnt rlatv to a hgh ral wag (a lowr valu of? ncrass m w )? th mor gnrous th lvl of unmploymnt bnfts (th hghr th valu of c ) Not that th natural unmploymnt rat s ndpndnt of th lvl of productvty (B). Ths s consstnt wth mprcal vdnc.

25 Altrnatv Mcro foundatons for th xpctatons-augmntd Phllps curv? th trad unon modl wthout ntrsctoral labour moblty (s abov) or wth labour moblty (s xrcs 18.1)? th ffcncy wag modl (s Chaptr 23, scton 4)? th workr-msprcpton modl of a compttv labour markt (s Chaptr 18, scton 3) Th workr-msprcpton modl dos not nclud nomnal rgdts, so to obtan an xpctatons-augmntd Phllps curv t s only ncssary to assum xpctatonal rrors. Howvr, as shown n scton 18.3, th xstnc of nomnal rgdts wll amplfy th mploymnt fluctuatons gnratd by nomnal rgdts. Our modl abstracts from nomnal prc rgdts, but n practc such rgdts may hlp to xplan th sluggsh adjustmnt of nflaton and unmploymnt to thr long run qulbrum lvls.

26 Supply Shocks In practc, th lvl of productvty and th wag and prc mark-ups wll fluctuat around thr long-run trnd lvls (whch w dnot by bar supr-scrpts). It s plausbl to assum that th rat of unmploymnt bnft s lnkd to th trnd lvl of productvty. In that cas w may rwrt (13) as: Actual mploymnt 1/ α ( 1 ) B α P L ( 1 u) N = n mmcb P p w (31) Th long-run qulbrum lvl of mploymnt s th mploymnt lvl prvalng whn xpctatons ar fulflld and whn productvty as wll as th mark-ups ar at thr trnd lvls. Hnc w hav: Natural mploymnt 1 α L ( 1 u ) N = n p w m m c 1 / α (32)

27 Th xpctatons-augmntd Phllps curv wth supply shocks Dvdng (31) by (32), w gt: p w 1 u Bm m P = p w 1 u Bm m P 1/ α (33) Takng logs n (33) and usng th approxmaton ln(1+x) x plus th Dfntons of p and p, w nd up wth: u u s, % ( ) π=π +α + s% p w m m B ln ln ln p w m + m B (34)

28 Tstng th Phllps curv thory Wth statc xpctatons, p = p -1, w may wrt (34) as: π = α β u+ s%, E s% = 0 (35) [ ] A rgrsson analyss basd on U.S. data for ylds: Th xpctatons-augmntd Phllps curv n th USA π = u, R = s..=1.081 s..= (26) Estmat of th natural unmploymnt rat n th USA u = α /β = 4.467/0.723 = 6.2%

29 Chang n nflaton (prcnt) Chang n nflaton (prcnt) Unmploymnt rat (prcnt) Unmploymnt rat (prcnt) Rlaton btwn unmploymnt and th chang n nflaton n th Untd Stats,

30 In Dnmark th rlatonshp btwn unmploymnt and th chang n domstc nflaton s lss clar, n part bcaus mport prcs play an mportant rol n th small opn Dansh conomy: Chang n nflaton (prcnt) Unmploymnt rat Rlatonshp btwn unmploymnt and th chang n nflaton n Dnmark,

31 Inflaton (prcnt) Unmploymnt rat (prcnt) Th shftng short-run Phllps curv n th Untd Stats

32 Inflaton (prcnt) 14 Actual Prdctd Yar Actual and prdctd nflaton n th Untd Stats

33 Productvty growth, th Phllps curv and th Nw Economy Th combnaton of low unmploymnt and nflaton n th U.S. snc 1995 may b xpland by a postv productvty shock, rflctd n an acclratng rat of productvty growth (s nxt sld). Whn productvty growth acclrats, w hav: lnb lnb > 0 s% < 0 Rcall that th targt ral wag of workrs s: w * = m w cb so n a prod of acclratng productvty growth, th targt ral wag lags bhnd th growth n actual productvty growth, thrby rducng nflatonary prssur.

34 Prcnt Prcnt Yar Yar Annual growth rat of labour productvty n th Untd Stats

35 Snc: Th Aggrgat Supply Curv Y = ny, L 1 u N = nl ( ) t follows from th producton functon (3) that: 1 α L α Y = nb = n B ( 1 u) N n 1 α (38) Takng logs on both sds of (33) and usng ln(1-u) -u, w gt: α y lny = lnn + lnb+ ( 1 α) ln ( 1 u) N α lnn + lnb+ 1 α lnn 1 α u ( ) ( ) lnn α + lnb y u = lnn + 1 α (39)

36 Th Aggrgat Supply Curv In paralll to (38), w may spcfy natural output as: and tak logs to gt: u α 1 Y = n B 1 u N α = lnn + ( ) lnn α + lnb y 1 α Substtutng (39) and (41) nto th xpctatons-augmntd Phllps curv (17), w gt: Th Short-Run Aggrgat Supply (SRAS) curv ( ) π=π+γ + y y s, p w α m m ln( B/B) γ, s ln + ln p w 1 α m m 1 α (41) (42)

37 Proprts of th Aggrgat Supply Curv? th SRAS curv slops upwards, bcaus hghr output? hghr mploymnt? lowr MPL? hghr MC? hghr prcs va th mark-up prcng bhavour of frms? th SRAS curv shfts upwards n cas of a rs n th xpctd nflaton rat or n cas of an unfavourabl supply shock (hghr mark-ups or a ngatv productvty shock)? th Long-Run Aggrgat Supply (LRAS) curv s obtand whn xpctatons ar fulflld (p = p) and mark-ups and productvty ar at thr trnd lvls. Th LRAS curv s vrtcal n (y,p)-spac, that s, n th long run thr s no trad-off btwn nflaton and output (mploymnt) Not that n a modl wth ntrsctoral labour moblty a rs n actvty lads to ncrasd wag prssur whch contrbuts to th postv slop of th SRAS curv.

38 π LRAS SRAS ( ) π 2 SRAS ( ) π 1 SRAS ( ) π 0 π 2 > π >π 1 0 y y Aggrgat supply n th short run (SRAS) and n th long run (LRAS)