Stochastic Macro-equilibrium and Microfoundations for the Keynesian Economics

Transcription

1 Stochastc Macro-qulbrum and Mcrofoundatons for th Kynsan Economcs 26th Jun, 2012 Hrosh Yoshkawa Unvrsty of Tokyo

2 Stochastc Macro-qulbrum and Mcrofoundatons for th Kynsan Economcs Abstract Ths papr bgns wth pontng out lmtatons of th standard labor sarch thory. It thn prsnts an altrnatv concpt of stochastc macro-qulbrum basd on th prncpl of statstcal physcs. Ths concpt of qulbrum s motvatd by th prsnc of all knds of unspcfabl mcro shocks n th macroconomy. Thy mak th us of optmzaton xrcss on rprsntatv agnt assumptons dm. W prsnt a modl whch mmcs th mprcally obsrvd dstrbuton of labor productvty. Th dstrbuton of productvty dpnds crucally on aggrgat dmand. Whn aggrgat dmand rss, mor workrs ar mployd by frms wth hghr productvty. At th sam tm, th unmploymnt rat dclns. Th rsult provds a propr mcro-foundaton for Kyns prncpl of ffctv dmand. 1

3 Gnral Equlbrum GE Thory from Walras to Arrow and Dbrw 1954 Ss th Economy as a Systm of Smultanous Equatons. 2

4 GE Thory Is a Grand and Wll-stablshd Thory. But It Cannot b Mor Dffrnt from th Ral Economy. 3

5 GE Thory Spcfs Prfrncs and Tchnologs of All th Consumrs and Frms, and Dfns th Equlbrum In Whch Mcro-Bhavor of All th Economc Agnts ar Prcsly Dtrmnd. 4

6 It s Just as On Analyzs Obct such as Gas Comprsng Many Partcls by Dtrmnng th Equatons of Moton for All th Partcls. 5

7 Two Challngs to GE 1 Kyns Gnral Thory Damond-Mortnsn-Psards Sarch Thory 6

8 Th Hyday of Kynsan Economcs was th 1950 s and 60 s. Bgnnng th 1970 s, Macrocnomcs has turnd to th noclasscal doctrn. 7

9 Th most ntrstng rcnt dvlopmnts n macroconomc thory sm to m dscrbabl as th rncorporaton of aggrgatv problms such as nflaton and th busnss cycl wthn th gnral framwork of mcroconomc thory. If ths dvlopmnts succd, th trm macroconomc wll smply dsappar from us and th modfr mcro wll bcom suprfluous. Robrt Lucas

10 Macroconomcs was born as a dstnct fld n th 1940 s, as a part of th ntllctual rspons to th Grat Dprsson. Th trm thn rfrrd to th body of knowldg and xprts that conomc dsastr. My thss n ths lctur s that macroconomcs n ths orgnal sns has succdd: Its cntral problm of dprsson prvnton has bn solvd, for all practcal purposs, and has n fact bn solvd for many dcads. Robrt Lucas, Nobl Laurat Prsdntal Addrss to th 2003 Amrcan Economc Assocaton 9

11 Th Fnancal Crss n Japan Dmonstrats th Prncpl of Effctv Dmand Onc Agan! 2005= Exports Industral Producton Sourc: METI, Cabnt Offc 10

12 Th Turnng Pont of Macroconomcs? 11

13 Most macroconomcs of th past 30 yars was spctacularly uslss at bst, and postvly harmful at worst. Paul Krugman Jun 2009 at Lonl Robbns Lcturs n London School of Economcs 12

14 Kynsan Economcs Noclasscal Economcs Unmploymnt Full Employmnt 13

15 Mcroconomc Foundatons for Kynsan Economcs 14

16 Standard Mcro-Foundatons for Kynsan Economcs Inflxbl Prc / Wags Involuntary Unmploymnt 15

17 Nw Mcro-Foundatons for Kynsan Economcs Not basd on optmzaton of mcro agnts But on th mthods of statstcal physcs. 16

18 Nw Mcro-Foundatons for Kynsan Economcs W can not xplan macro troubls such as congstons on turnpks by way of optmzng bhavors of mcro agnts. 17

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20 Solow s commnt Thoughtful macroconomsts ar uncomfortably awar that consumrs, frms, and workrs vary wdly n thr local nvronmnts, prcptons, and blfs. Ignorng ths htrognty, as modrn macro dos, s a lkly sourc of systmatc rror. Aok and Yoshkawa propos to rpar ths falur by modlng th macroconomy xplctly as a cloud of ntractng partcls. Th goal s to dduc th dstrbutons of conomc charactrstcs that dscrb th systm as a whol. Ths puts mor mphass on statstcal proprts and lss on th ntrnal dcson makng of ach agnt. Thr ar alrady som surprsng bgnnng rsults, ncludng a novl tratmnt of aggrgat dmand, and on can xpct mor whn thr approach s combnd wth standard conomc rasonng. Ths s th start, not th fnsh, of a potntally far-rachng rsarch program. It should xct th curosty of all thos thoughtful macroconomsts. Robrt M. Solow

21 Typcal Obcton to th Mthod Ths mthod has bn tm and agan succssful n natural scncs whn w analyz obct comprsng many mcro lmnts. Economsts mght b stll skptcal of th valdty of th mthod n conomcs sayng that norganc atoms and molculs comprsng gas ar ssntally dffrnt from optmzng conomc agnts. Evry studnt of conomcs knows that bhavor of dynamcally optmzng conomc agnt such as th Ramy consumr s dscrbd by th Eulr quaton for a problm of calculus of varaton. On th surfac, such a sophstcatd conomc bhavor must look rmot from mchancal movmnts of an norganc partcl whch only satsfy th law of moton. 20

22 Obcton Unfoundd Howvr, vry studnt of physcs knows that th Nwtonan law of moton s actually nothng but th Eulr quaton for a crtan varatonal problm. It s calld th prncpl of last acton: s Chaptr 19 of Fynmann 1964 s Lcturs on Physcs, Vol. II. Thrfor, bhavor of dynamcally optmatzng conomc agnt and motons of norganc partcl ar on a par to th xtnt that thy both satsfy th Eulr quatons for rspctv varatonal problms. Th mthod of statstcal physcs can b usfully appld not bcaus motons of mcro unts ar mchancal, but bcaus obct undr nvstgaton comprss many mcro unts ndvdual movmnts of whch w ar unabl to know. 21

23 What Mattrs Is Not Employmnt or Unmploymnt 0 or 1 But Many Lvls of Productvty namly Dstrbuton of Productvty 22

24 Th Prncpl of Statstcal Physcs Boltzmann or Exponntal Dstrbuton n statonary stat Yoshkawa, H Th Rol of Dmand n Macroconomcs, Japans Economc Rvw, Vol.54, No.1,

25 Th Basc Modl Suppos that n k workrs blong to frms whos productvty s c k. Thr ar K lvls of productvty n th conomy. Th total numbr of workrs s N. K k=1 n k = N 24

26 Th probablty that a partcular allocaton n=n 1, n 2,, n k s obtand s P n = W 1 N! n = K N K N K n k= 1 k! 25

27 Th maxmzaton of p n s quvalnt to that of th followng ntropy S. K S = p k = 1 k = p lnp k n k N k 26

28 Macro Constrants K k=1 c n = k k D 27

29 Th Stat to b Ralzd n k N = K k= 1 Nc D k Nc D k 28

30 Dstrbuton Changs as Aggrgat Dmand Changs Sourc : Aok M. and H. Yoshkawa, 2007 Rconstructng Macroconomcs: A Prspctv from Statstcal Physcs and Combnatoral Stochastc Procsss, Cambrdg Unvrsty Prss 29

31 Dstrbuton of Labor Productvty n Japan a Manufacturng Sctor n 2004 Manufacturng Sctor n Dstrbuton of Employs N_mpl c kloyn Sourc: Iytom

32 Dstrbuton of Labor Productvty n Japan b Non-manufacturng Sctor n Nonmanufacturng Sctor n 2004 Dstrbuton of Employs N_mpl c kloyn Sourc: Iytom

33 Th Purpos of th Prsnt Study Is to Explan ths Emprcal Dstrbuton of Productvty And To Provd a Mcro-Foundaton for Kyns Prncpl of Effctv Dmand 32

34 To xplan th lft-hand sd upward slopng dstrbuton, Iytom 2012 ntroducd th Ngatv Tmpratur. 33

35 Th Natur of Mcro Shocks Slf-Avragng Non Slf-Avragng S : Sorntt, D 2000, Crtcal Phnomna n Natural Scncs, Sprngr. 34

36 Th Natur of Mcro Shocks In Standard Modls, Mcro Shocks ar Assumd to Wash Out W Can Undrstand Macro by th Avrag Slf-Avragng 35

37 Non Slf-Avragng W Cannot Undrstand Macro by th Avrag Standard Mcroconomc Foundatons Basd on Rprsntatv Agnt Do not Mak sns S : Aok M. and H. Yoshkawa, 2011 "Non-Slf-Avragng n Macroconomc Modls: A Crtcsm of Modrn Mcro-foundd Macroconomcs", Journal of Economc Intracton and Coordnaton, Vol.7, 1, pp

38 Damond-Mortnsn-Pssards Equlbrum Sarch Thory Th Thory s a curous hybrd. 1 Htrognous agnts du to varous markt frctons and matchng costs. 2 Optmzaton xrcss on th rprsntatv agnt assumpton. 37

39 To gt closr to th actual markts, t was ncssary to ntroduc th Matchng Functon --- a macro black box NOT xplctly drvd from mcro optmzaton xrcss. 38

40 For th mthod to mak sns, th dffrnc btwn norganc partcls and brany conomc agnts s nssntal. Th pont s that th systm conssts of a larg numbr of mcro unts. Th numbr of houshold ~10 7 Th numbr of frms ~

41 Modl of Stochastc Macro-qulbrum a Dynamcs of Craton and dstructon of Potntal Jobs Th numbr of potntal ob sts n log Productvty n log 40

42 Modl of Stochastc Macro-qulbrum b Stochastc Macro-qulbrum Th Numbr of Employd Workrs Aggrgat Dmand D or Pool of Unmploymnt Rsrvaton wags μ Th Lvl of Productvty 41

43 Th Modl K N = n = 1 Y = c n U = L N n { 0, 1, L, f } = 1, 2, LK 42

44 43 Partton Functon = Y Y Y g = Y Z = = Y Y Y Y d d d Z d log log Y Y Y E Y Yg Y = = =

45 Grand Canoncal Partton Functon 1 Y g Y = Z = Z N = Y Y N = { n } xp K = 1 Y c n Φ= N= 0 z N Z N whr z = µ 44

46 45 Grand Canoncal Partton Functon 2 } xp{ 0 Φ= = n N N c n z whr µ z = ] xp[ } xp{ K n n N n n n c c n K = = Φ = = + + µ µ L = + = = + + Φ= K c c f c f c K ] 1 1 [ ] 1 [ µ µ µ µ L > =< = = Φ = = N Z Z N Z N N N N N N N N N ] [ 1 ] log [ 1 ] log [ µ µ µ µ µ

47 46 Dstrbuton of Productvty ] log [ 1 Φ = µ N } log1 {log c c f K + = = µ µ µ = = K c c c f c f f ] [ µ µ µ µ = + + c c c f c f f n µ µ µ µ

48 Smulatd Dstrbuton of Labor Productvty Hgh D = 38362, u = 2.2% Low D = 35063, u = 9.9% 47

49 Prcntag of Potntal Job Sts Occupd by Employd Workrs 48