Insider/Outsider Theory

Transcription

1 Insde/Outsde Theoy Developped y Lndeck-Snowe Fms maxmze pofts, takng as gven nume of nsdes, expected wage of nsdes, wage dffeental etween nsdes and outsdes and choosng level of outsde employment and wage levels gven poductvty level. Ψ [ [ ] ( ) ] A F L I L w L I w L λ p U ( w ) U p O I I O I 0

2 Insde/Outsde Theoy II What s w O? FOCs Ψ L O 0 A F' ( L L ) w C I O I Ψ w I p ( L L ) λp U '( w ) 0 U '( w ) I O I I L I L λ O

3 Insde/Outsde III If we assume that outsde lao supply s completely nelastc and suffcently lage, we have equlum unemployment as a consequence.

4 Hysteess Sometmes shocks so lage that some nsdes ae lad off. Then, new goup of nsdes eagans wage contacts, choosng hghe wages ove employment snce thee ae less nsdes now. Ths means that a negatve shock to poductvty leads to low employment ths peod and low employment the peod afte: postve seal coelaton n unemployment levels o hysteess.

5 Seach Unemployment I: Boad Ovevew People have dffeentated etween dffeent types of unemployment: seach (o fctonal unemployment) and stuctual unemployment (.e. due to aggegate demand falues). Chcago-Vew: Fctonal unemployment exsts ut govenment can not nfluence ts level Stuctual employment fluctuatons occu ut thee s no stuctual unemployment MIT/Havad/Pnceton/Bekeley Vew: Fctonal unemployment can e neffcently hgh due to maket falues n lack of centalzed maket fo employment (lack of Walasan Auctonee) Stuctual unemployment exsts and can e neffcently hgh due to aggegate demand falues

6 Seach Unemployment II: Model Setup I Wokes choose whethe to e n the lao maket (f they ae unemployed, ths means they seach fo a jo; f they ae employed, t means they eman at the jo) Fms choose whethe o not to post a poston (f they aleady employ someone, ths means they etan the poston; f they do not aleady employ someone, they post a vacancy) Matches (fm/woke pas) fnd eachothe wth ate M(U,V) dependng upon the unemployment ate and vacancy ate. An equlum, (a level of employment: E and a set of decsons y fms and wokes to post vacances and seach fo wok) s a steady state level of employment such that no fms have ncentves to change the vacancy postng decson and no wokes have the ncentve to change the decsons to look fo wok.

7 Seach Unemployment III: Solvng the Model I We wll desce how to solve fo the level of employment, E, and ts popetes (how t changes wth paametes). Fst, compute the value of postng a vacancy, postng a flled poston, eng employed, and eng unemployed. Then, equate the dffeence n values etween a vacancy and flled poston wth an unemployed and employed poston and solve fo the wage as a functon of employment. Havng calculated the wage, we can solve fo the value of postng a vacancy. Equlum wll occu when the value of postng a vacancy s zeo. Ths value of postng a vacancy functon wll e a functon of the employment level and wll defne equlum employment and unemployment.

8 Seach Unemployment IV: Model Setup II Fms choose They choose V v V F o 0 f vacant o 0 f flled Wokes choose Wokes choose V E V U o 0 f employed o 0 f unemployed

9 Seach Unemployment V: Model Setup III Solve fo Steady State Level of Emp./Unemp. E M ( U, V ) KU β V γ M(U,V) s called the matchng functon Rate at Whch Wokes Fnd Jos M ( U, V ) a U Rate at Whch Jos Fnd Wokes α M ( U, V ) V

10 Seach Unemployment II: Constuctng Value Functons Value of Beng Employed: V E Value of Beng Unemployed: Value of A Flled Poston: V F A w C V F V V Value of A Vacant Poston: V v V U w ( ) V E V U ( ) a V V E U ( ) C α V F V V ( )

11 Seach Unemployment: Solvng the Model II Splt the suplus Sutact Equatons fom Pevous Slde Smlaly U E V V V V V F ( ) ( ) V F V F V V C V V C w A α - V V V F w A V V V F α a w V V U E

12 Seach Unemployment VIII: Solvng the Model III So But a w w A α ( ) a A a w α A a a A C w A C V V α α α α α

13 Seach Unemployment IX: Computng Equlum Emp. Inflow nto Unemployment Equals Outflow Fom Unemployment a L E [ ] E Inflow Into Vacances Equals Outflow fom Vacances E M ( U, V ) α E KU α K E E β V ( ) γ L E γ V E KU M ( U, V ) V β γ K E ( L E) β γ

14 Seach Unemployment X: Computng Equlum Emp. II Model Closue: Fms ae ndffeent etween postng a vacancy and not (lke lao demand): V V α( E) ( E) α( E) C A a 0 Equlum Employment s whateve E solves the aove equaton; unemployment s then. L E

15 Seach Unemployment XI: Unqueness of Equla Want to show that ( E) da de d E L E de L E E ( L E) dv V de > 0 < 0 Rememe that γ dα de ( E) d γ ( E) γ K ( L E) de β γ γ γ [ ] β γ β γ β K ( L E) γ < 0 ( E) γ K ( L E)

16 Seach Unemployment XII: Unqueness of Equla II Dffeentatng, we get: dα( E) dv V ( ) de α E A de α( E) a( E) [ α( E) a( E) ] dα A de ( E) da( E) de dv V de ( E) dα( E) a( E) α A < 0 A D de D Whee D α ( E) a( E) Fom ths we know that equla ae unque f they exst

17 Seach Unemplomyent: Exstence of Equla Note that E anges fom zeo to L We now take the lmts of the value of a vacancy as employment vaes fom zeo to full employment: lmα ( E), lma( E) 0 lmv A C E 0 E 0 E 0 lmα ( E) 0, lma( E) lmv C E L E 0 E 0 Gven contnuty of the value of postng a vacancy n the ange of zeo to full employment, we have exstence of an equlum! V V

18 Seach Unemployment: Compaatve Statcs I How do we look at Cyclcal Changes n ths model? How do we look at long-tem changes n ths model (.e. the effect of gowth)?

19 Seach Unemployment: Compaatve Statcs II A moves fo cyclcal fluctuatons; the ato of A and C fo gowth. Impact of Gowth: None an ncease n A and C leavng the ato unchanged has no mpact on lao demand: ( E) α V V a α C ( E) ( E) A

20 Seach Unemployment: Compaatve Statcs III Equlum Vacances ae gven y: γ γ β γ E ( L U ) M ( U, V ) KU V E V β β KU KU Negatve Relatonshp etween vacances and unemployment: Bevedge Cuve Shot tem changes lead to smalle employment effects and lage wage adjustment: thnk aout nfntessmally shot educton n A: comes out of wages entely ecause thee ae no changes n value of vacances and value of unemployment whch means no change n M(U,V) o E. Pocyclcal Wage: How do we fgue ths out?

21 Seach Unemployment: Compaatve Statcs IV Wage expesson: Total dffeentate: Solve: ( ) a A a w α ( ) ( ) ( ) ( ) ( ) ( ) ( ) a de E E a A de E E a A a de E E a A a dw α α α ( ) ( ) ( ) ( ) 0 > a E E a E E a A de dw α α

22 Seach Unemployment: Recent Empcal Results US manufactung: 3% of wokes leave jos n a typcal month and 0% of jos dsappea n a typcal yea. Volatlty n unemployment mostly deved fom nceased jo destucton not deceased jo ceaton.

23 Othe Models of Unemployment Why assume supply equals demand? Wetzman: Contnuum of Equla Out of Equlum Dynamcs Models: Assume pce adjustment mechansm (.e. pce adjusts to educe net excess demand ut ths feeds ack nto demand)

24 Phllps Cuve I: Ognally studed y Phllps, A. W. (958), The Relatonshp etween Unemployment and the Rate of Change of Money Wages n the Unted Kngdom, , Economca 5, pp ISLM ntepetaton: Monetay Expanson: dy dm * > 0

25 Phllps Cuve II: Phllps Cuve US Inflaton,0 0,0 8,0 6,0 4,0,0 Sees 0,0 0 0,05 0, 0,5 Unemployment

26 Phllps Cuve III: New Classcal Vew: Lucas Supply Cuve; monetay confuson when fms notce hgh nomnal demand, they mstake t fo fm-specfc demand and expand output. Howeve, monetay expansons that ae expected have no effect on employment just on pces.

27 Lucas Supply Cuve I: Soluton Concept I (.) Satsfes ndvdual supply equals ndvdual demand (.e. fo each good) (.) Satsfes aggegate demand (output equals eal money supply) Equlum s a set of pces, p, and quanttes, q, such that (.) and (.) ae satsfed.

28 Lucas Supply Cuve II: Soluton Concept II Two vesons of the model: Complete Infomaton Incomplete Infomaton Complete Infomaton: Take money supply as gven (commonly known) and pce level... Money has no effects. Incomplete Infomaton: Pces used to fgue out state of demand. Agents use tue elatve vaances of aggegate (nomnal) vesus ndvdual (eal) shocks to fgue out level of demand. Fst pape to use pces as evealng nfomaton.

29 Lucas Supply Cuve III: Soluton Concept III Thee types of shocks: Shocks to elatve demand Expected shocks to money supply (Monetay polcy) Unexpected shocks to money supply

30 Lucas Supply Cuve III: Complete Infomaton I Poducton: Q L Consumpton: U γ L C, γ γ Budget Constant: Value of ndvdual consumpton equals value of ndvdual poducton P Q PC Pluggng Poducton nto Budget Constant and Budget Constant nto Consumpton: γ PL L U P γ

31 Lucas Supply Cuve IV: Complete Infomaton II FOC: Tanslate nto Logs: Add ndvdual demand (can we deve ths fom utlty functons?): * 0 γ γ P P L L P P dl du ( ) p p * λ l ( ) ( ), 0 ~ z ; z N p p z y q σ η

32 Lucas Supply Cuve V: Complete Infomaton III Means of dstutons: ( ) z f z 0 D ( p ) p f D ( q ) q f D p y

33 Lucas Supply Cuve VI: Complete Infomaton IV Add aggegate demand (eal money equals output) y m p Fom Q, we get: q L l η γ p Solvng fo, we get: γ p y z ηγ η ( p p) y z ( p p) ( ) p

34 Lucas Supply Cuve VII: Complete Infomaton V Takng the aveage of oth sdes of: p γ ηγ η ( y z ) p We get: γ p y p y ηγ η 0 Ths mples that: p m

35 Lucas Supply Cuve VIII: Complete Infomaton Intepetaton An ncease n the money supply s eflected one fo one n hghe pces. Thee s no effect of an ncease n money supply on output: money s neutal. y0: output s uncoelated wth nflaton

36 Lucas Supply Cuve IX: Incomplete Infomaton I Same as complete nfomaton model except that thee ae two souces of nfomaton whch s not oseved: shocks to money supply, m, and shocks to poductvty, z; Why do we need two shocks to e unoseved? The dstuton of each of the shocks s known: z ~, ( 0 ) N σ ( m ~ N 0 σ ) z, We wll know deve a coelaton etween the aggegate pce level, m, and aggegate output, y m

37 Lucas Supply Cuve X: Incomplete Infomaton II Poduces maxmze: γ PL L EU E p P γ Appoxmate actual soluton wth cetanequvalence: l [ ] E p p p γ Denote elatve pce y: p p

38 Lucas Supply Cuve XI: Incomplete Infomaton III Assume atonal expectons: the expectatons of the elatve pce gven the oseved maket-specfc pce s the tue dstuton of the elatve pce gven the oseved maket-specfc pce.

39 Lucas Supply Cuve XII: Incomplete Infomaton IV Need to calculate E [ p ] E[ p p p ( p p) ] Fo now, assume that p and ae nomally dstuted and ndependent of eachothe. Ths wll e vefed late once we have calculated the equlum p and (ths s called the guess and check method).

40 Lucas Supply Cuve XIII: Incomplete Infomaton V Lnea Condtonal Expectatons gven two sgnals: ndvdual pce and aveage pce level: E [ p ] αp βp The coeffcents ae just the pecsons of the estmates n the nomal dstuton model (ememe vaances of p and ae endogenous): α β σ p σ σ p

41 Lucas Supply Cuve XIV: Incomplete Infomaton VI Multplyng top and ottom y σ σ p, gves us α β σ σ σ Thus ou expesson fo the condtonal expectaton s: E[ p ] σ ( p Ep) σ σ p Pluggng ths nto lao supply, we get: σ l ( p Ep) γ σ σ p p

42 Lucas Supply Cuve XV: Incomplete Infomaton VII Aveagng lao nput acoss wokes gves us aggegate output y σ γ σ p σ ( p Ep) Defnng a constant to e equal to γ σ, we p σ otan the Lucas Supply Cuve (how do we know t s a supply cuve and not a demand cuve?) y ( p Ep) σ

43 Lucas Supply Cuve XVI: Incomplete Infomaton VIII Comne Lucas supply cuve wth aggegate demand cuve: Solve fo p and y p m y ( ) Ep p y Ep m y p Ep m y p

44 Lucas Supply Cuve XVII: Incomplete Infomaton IX Thus: p y m m Ep Ep What s stll endogenous?

45 Lucas Supply Cuve XVIII: Incomplete Infomaton X Solvng fo Ep: Ep Em EEp Fom the law of teated expectatons, we get: EEp Ep Thus: Ep Em Ep Em

46 Lucas Supply Cuve XIX: Incomplete Infomaton XI Rewtng the solutons to y and p, we get: p y m Em ( m Em) Em ( m Em) Ae we fnshed yet? How do we ntepet these equatons? How ae they dffeent fom the complete nfomaton model? What s the ole of monetay polcy? Supses n money supply? How do we ntepet m? Em? m-em?

47 Lucas Supply Cuve XX: Incomplete Infomaton XII Rememe that σ γ σ σ The vaances ae endogenous ut we ae now n a poston to solve fo them. Fst, takng vaances of the equaton fo p, we get: σ σ p ( ) To solve fo the vaance of, we susttute the lucas supply cuve nto the ndvdual demand equaton: q ( p Ep) z η m p

48 Lucas Supply Cuve XXI: Incomplete Infomaton XIII We do the same fo ndvdual lao supply: l ( p Ep) Equaton ndvdual lao supply and ndvdual lao demand, we get: ( p Ep) ( p Ep z η ) Thus we can solve fo as a functon of exogenous vaales: z η

49 Lucas Supply Cuve XXII: Incomplete Infomaton XIV Thus the vaance of s: σ σ z ( η) Fnally, pluggng ou expessons fo vaances of endogenous vaales nto the expesson fo, we get: γ σ z σ z ( η ) ( ) σ m

50 Lucas Supply Cuve XXIII: Incomplete Infomaton XV In geneal we can not solve fo paametcally only mplctly. Howeve, f η, then we can solve explctly fo : σ z γ σ σ z In ths case, we can expess ou solutons fo p and y: y σ z ( m Em) γσ γ σ z ( ) σ z p Em ( ) γ σ m σ z m m ( m Em)