Measuring Consumer Inflation Expectations in Turkey

Size: px
Start display at page:

Download "Measuring Consumer Inflation Expectations in Turkey"

Transcription

1 Masuring Consumr Inflaion Expcaions in Turky Ec Oral Rsarch and Monary Policy Dparmn, Cnral Bank of h Rpublic of Turky, İsiklal Cad. 10 Ulus, Ankara Tl: Ec.Oral@cmb.gov.r. Rviwrs: Robr CZUDAJ, Univrsiy of Duisburg-Essn, Grmany; Miroslav MATEEV, Amrican Univrsiy in Bulgaria, Bulgaria; Olna SOKOLOVSKA, Insiu Of Indusrial Economics of Naional Acadmy of Scincs of Ukrain, Ukrain. Absrac Th abiliy o masur inflaion xpcaions is an ingral par of cnral bank policy spcially for cnral banks ha ar implmning inflaion-arging rgim. A forward-looking prspciv is ssnial o h succss of inflaion arging. Thrfor, a cnral bank having h primary objciv of pric sabiliy is inrsd in inflaion xpcaions. Th main aim of his papr is o consruc dirc masurs of h consumr inflaion xpcaions and o xamin h naur of consumr inflaion xpcaions in Turky. Qualiaiv daa on inflaion xpcaions obaind from survys can b quanifid ino numrical indicaors of h xpcd inflaion. This papr prsns h rsuls of diffrn quanificaion chniqus such as Carlson-Parkin, balanc and rgrssion mhods. Ths mhods ar compard wih ach ohr and h rgrssion mhod is found o b h closs on o ralizaions. In addiion, unbiasdnss assumpion is sd and rjcd. Afr rjcing a raional modl, hybrid modl of xpcaions formaion is considrd. Th pur backward and forward looking xpcaions hypohss ar rjcd. Thr xiss h srong backward looking naur of xpcaions in h long run. Kywords: Consumrs, Inflaion Expcaions, Survy Daa, Quanificaion Mhods JEL cods : C1, C83, D84, E31, N3 Inroducion Inflaion xpcaions hav spcial significanc for h Cnral Bank, as hy may play an imporan rol in conomic dcisions such as h sing of inrs ras, prics, wags, consumpion and invsmn dcisions. Th ffcs of monary policy ar also influncd by inflaion xpcaions. Many of h acions of conomic agns, housholds, corporas and financial scor, dpnd on hir xpcaions abou fuur conomy. As inflaion plays a crucial par in conomic dvlopmn, 43 Easrn Europan Businss and Economics Journal Vol.2, No. 1, (2016): 43-74

2 44 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn pric dvlopmns, susainabl conomic growh and invsmns in long run, h xpcd inflaion cras a ky rol for monary policy purposs (Tyagi, 2009). Inflaion xpcaions ar drmind in larg par by how popl bliv h cnral bank will conduc monary policy. Thrfor, cnral banks communica xplici or quasi-xplici inflaion args o hlp anchor h public s long-run xpcaions abou inflaion. Brk and Hbbink (2009) find hr possibl aims for inflaion xpcaions. Th firs on is o hink xpcaions as a facor o b akn ino accoun for drmining h monary policy sanc ha hlps o rach h arg. Th scond aim can b o ak xpcaions as a ool o coninuously monior h crdibiliy by comparing hm wih h inflaion arg; and h las aim can b as a valuabl inpu o h inflaion forcas procss carrid ou by cnral banks (Rodriguz and Uriz, 2013). Alhough inflaion xpcaions ar of ky imporanc o cnral banks, hir masurmn is no an asy ask. Th informaion of inflaion xpcaions formd by various conomic agns is obaind by xracing implici xpcaions conaind in financial insrumns or by conducing survys among profssional forcasrs or consumrs. In ordr o br undrsand h inflaion xpcaions of h gnral public, h xpcaions of Turkish consumrs ar analyzd in his documn. Cnral Bank of h Rpublic of Turky (CBRT) conducs monhly survy calld Survy of Expcaions which moniors h xpcaions of xprs and dcision makrs from financial scors mosly rlad o various conomic variabls. Th survy rsuls ar quaniaiv. I has bn conducd sinc Augus Th Businss Tndncy Survy (BTS) of CBRT is a monhly survy carrid ou o produc indicaors ha will rflc h shor-rm ndncis in h manufacuring indusry. Th survy compils h assssmns of h snior managrs, whos dcisions ar imporan for h conomy, on h rcn pas, currn siuaion and hir xpcaions rgarding h fuur cours of businss nvironmn. BTS has bn conducd sinc Dcmbr Th survy rsuls ar qualiaiv. A lo of rsarch has bn don on inflaion xpcaions gahrd from hs wo survys. A rcn sudy by Kara and Tugr (2005), which is basd on daa from hr diffrn survys (namly h SOE, h Businss Tndncy Survy of CBRT and h Manufacuring Indusry Monhly Tndncy Survy of Turkish Saisics Insiu) argus ha inflaion xpcaions, xcp for on-monh ahad forcass, ar biasd

3 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn 45 and infficin. Thy find ha agns ignor h laggd ffcs of xchang ras on inflaion whil forming hir xpcaions. Anohr sudy ha uss Turkish inflaion xpcaions daa is Karadas and Ögünç (2005). Thir sudy analyzs h inflaion xpcaions of h priva manufacuring scor by convring qualiaiv survy rsponss ino quaniaiv inflaion xpcaion daa. Thy valua h form of xpcaions (xrapolaiv vrsus adapiv xpcaions) using a squnial sing procdur. Thy find ha h raionaliy hypohsis canno b rjcd, a las for h 1989Q4-1998Q4 priod, and hr ar som forward-looking lmns in h formaion of xpcaions. Lar, Başkaya al (2008) analyz h bhavioral aspcs of inflaion xpcaions in Turky by uilizing daa from a panl of survy rspondns, and draws implicaions for h formulaion of monary policy and communicaion sragy. Thy sa ha h survy rspondns ak h inflaion args and h official forcass of h Cnral Bank of Turky ino accoun in forming hir xpcaions. Bsids, hy also show ha inflaion xpcaions during h rapid disinflaion pisod of wr firmly anchord by h announcd args. Thr is also significan hrogniy in h xpcaion formaion procss such as ral scor aachs a grar wigh o pas inflaion han h financial scor. Furhrmor, h financial scor sms o b comparaivly mor snsiiv o variaions in variabls such as xchang ras, risk prmium, suggsing ha communicaion o financial marks should kp mphasizing h mdium-rm policy prspciv of h monary policy. Oral al (2009) invsiga h raionaliy of financial and ral scors CPI inflaion xpcaions in Turky using h mulivaria panl coingraion mhod. Th us of panl chniqus srnghnd hir mpirical rsuls by no only incrasing sampl siz bu also allowing hrogniy across groups of rspondns. Having found h xpcaions irraional in h sricr sns, hy procd o analyz h significanc of boh pas and fuur inflaion ras as drminans of agns fuur inflaion forcass. Boh rcursiv and rolling simas show ha forcasrs wigh on fuur/arg inflaion ras vrsus pas acual and xpcd inflaion ras changs ovr im as unxpcd shocks drail inflaion from is disinflaionary pah. Lasly, hy find asymmry in xpcaions such ha h rspons of inflaion xpcaions o an incras in h inflaion ra is wic h siz of h rspons o a dcras in h inflaion ra. This may indica long dlays

4 46 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn in rsoring crdibiliy of cnral banks afr a posiiv shock on h inflaion ra. Başkaya al (2012) considr how inflaion xpcaions rspond o inflaion args, forcass, and ralizaions. Thy find ha forcass, args, and pas inflaion ar imporan drminans of inflaion xpcaions. Addiionally, xpcaions ar mor snsiiv o inflaion ralizaions a highr lvls of inflaion. Thy also discovr ha snsiiviy of xpcaions o inflaion has dcrasd ovr im, spcially sinc h nd of 2011 dspi a vry rapid and sizabl incras in CPI inflaion. Employing aggrgad im sris daa from h Survy of Expcaions for h priod bwn 2001 and 2007, Kara and Küçük- Tuğr (2010) rcnly show ha dspi h rjcion of h classical raionaliy ss, im-varying paramr simas indica ha man inflaion forcass of priva agns in Turky has improvd ovr im in rms of hir unbiasdnss and fficincy. Howvr, hr has bn no daild analysis on inflaion xpcaions of consumrs drivd from Consumr Tndncy Survy. Thrfor, unlik prvious sudis, his sudy focuss on h inflaion xpcaions of consumrs drivd from Consumr Tndncy Survy. This papr givs mphasis o inflaion xpcaions obaind from Consumr Tndncy Survy (CTS) of h CBRT and Turkish Saisical Insiu (TurkSa). Expcaions obaind from h Consumr Tndncy Survy ar no dircly obsrvabl du o qualiaiv survy daa. Qualiaiv survy can only provid a dircion of chang for a givn variabl insad of an xac figur. Thrfor, xpcaions collcd as qualiaiv survy daa ar convrd ino quaniaiv simas of h variabls undr considraion. Thr ar diffrn mhods o quanify h qualiaiv survy rsuls. Th main aim of his papr is o consruc dirc masurs of h consumr inflaion xpcaions via quanificaion mhods and o xamin h naur of consumr inflaion xpcaions in Turky. Th sudy is composd of four scions. Th aims of h sudy ar prsnd in h inroducion par. Th daild knowldg abou h survy and h xplanaion of h quanificaion mhods ar givn in h scond scion. Th quanifid inflaion xpcaions ar givn in h hird scion. Th fourh scion givs brif knowldg abou h formaion procss of consumr inflaion xpcaions. Finally, h conclusion par givs h final rsuls.

5 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn 47 Consumr Tndncy Survy and Quanificaion Mhods Consumr Tndncy Survy Consumr Tndncy Survy (CTS), has bn carrid ou wih h coopraion of Turkish Saisical Insiu and Cnral Bank of h Rpublic of Turky sinc Dcmbr CTS aims o masur prsn siuaion assssmns and fuur priod xpcaions of consumrs' on prsonal financial sanding and gnral conomic cours and o drmin consumrs' xpndiur and saving ndncis for nar fuur. Consumr Confidnc Indx is calculad by h following sub-ims: Financial siuaion xpcaion of houshold ovr h nx 12 monhs, Gnral conomic siuaion xpcaion ovr h nx 12 monhs, Numbr of popl unmployd xpcaion ovr h nx 12 monhs and Th probabiliy of saving ovr h nx 12 monhs. Indics ar compild in accordanc wih h balanc mhod of Europan Union. Th balanc is calculad as h diffrnc bwn h prcnags of posiiv and ngaiv rsponss and 100 is addd o his diffrnc, hus forming a spara diffusion indx for ach qusion. Thn, h gnral indx is calculad by aking arihmic mans of diffusion indics of h qusions includd in consumr confidnc indx. Th indx is valuad bwn 0 and 200. If i is abov 100, i mans consumr confidnc is opimisic, if i is blow 100, consumr confidnc is pssimisic. CTS sard o b applid in accordanc wih h Join Harmonizd Europan Union Programm of Businss and Consumr Survys in CTS and h Consumr Confidnc Indx hav bn buil-up according o h EU covrag in Nw harmonizd survy covrs housholds a h ag of 16 and abov in urban and rural aras of Turky. Th prson is slcd randomly by h daa nry programm and h arg ara is h whol counry. CTS is conducd on a monhly basis wih an indpndn survy. Th survy rsuls ar wighd by ag and gndr cagoris. Addrss Basd Populaion Rgisraion Sysm is usd as fram. A compur-basd, fac-o-fac inrviw mhod is applid. Th fildwork priod of h survy is h 1s-15h day of ach monh. Th survy rsuls concrning h rfrnc monh ar publishd on h las wk of h monh as is in h Naional Daa Rlas Calndar. Daild informaion and survy qusions can b found on h Turkish Saisical Insiu's (Turksa) wb si hp:// Th pric qusion in CTS can b givn as follows:

6 48 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn In comparison o h ralizaions, how do you xpc ha prics will dvlop ovr h nx 12 monhs? 1. Incras mor rapidly 2. Incras a h sam ra 3. Incras a a slowr ra 4. Say abou h sam 5. Fall 6. No ida Quanificaion Mhods Inflaion xpcaions hav an imporan rol in modrn macroconomic hory. Th imporanc of xpcaions has bn mphasizd by h rcn inflaion xprincs of mos counris. Dirc masurmn of xpcaions can b mad hrough h ndncy survy daa. Th quaniaiv xpcaions daa ar gahrd in som survys. Howvr, h rspondns indica whhr prics will fall, ris or rmain unchangd for som monhs ahad in h ohr survys. Th daa gahrd from hs survys do no hav a man valu bcaus hy ar qualiaiv. Thr ar svral chniqus o quanify h qualiaiv survy daa (Bachlor, 1982). Diffrn quanificaion mhods such as Carlson-Parkin mhod, balanc mhod, rgrssion mhod hav bn considrd wih h aim of quanifying survy daa on inflaion xpcaions. Carlson-Parkin mhod usd in h pnachoomous cas as in his sudy has wo advanags such ha i dos no impos unbiasdnss and rspons hrsholds ar prmid o vary ovr im. On disadvanag is ha h xpcaions via his mhod giv diffrn rsuls du o h choic of probabiliy disribuion. On h ohr hand, rgrssion mhod dosn rquir probabiliy disribuion. Howvr, hr ar wo shorcomings of h rgrssion mhod. On of hm is ha long im sris of survy daa is ndd in ordr o implmn his mhod. Th ohr shorcoming is ha simaing h rgrssion modl of prcpion wih h official currn inflaion on is lf sid and survy rsponss o h qusion on inflaion prcpion on is righ hand sid, rgrssion mhod imposs unbiasdnss of inflaion prcpions. Whn balanc mhod is considrd, alhough his mhod dosn masur xpcaions dircly, i is no influncd by h assumpions imposd in ohr wo mhods.

7 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn 49 Probabiliy Mhod Th probabiliy mhod which is wll known as Carlson-Parkin mhod (Carlson and Parkin, 1975) was firs mployd by Thil (1952). Th original mhod has bn drivd for a richoomous survy, i.. h survy paricipans hav hr possibl answr cagoris. In his conx, h pric xpcaions having hr cagoris such as pric will incras, pric will dcras and no chang in pric (Bachlor and Orr, 1988) ar usd. Howvr, in his sudy, h pric qusion ha is usd from CTS has fiv possibl answr opions. Thrfor h pnachoomous cas will b considrd (Brk, 1999). Th CP mhod assums ha rspondns sanding a im (monh) hav formd an xpcaion π + 1 abou inflaion in h +1 monhs whn answring h survy. Th individual subjciv probabiliy disribuions can b aggrgad o giv h join probabiliy disribuion f(x+1 Ω), whr x+1 is h fuur prcnag chang of prics a im for h priod + 1 and Ω h informaion s a im. I is assumd ha his disribuion has fini firs and scond ordr momns and ha E[x+1 Ω] = π + 1, whr π + 1is h xpcd valu of x a im for h priod +1. Anohr assumpion on h pnachoomous cas can b givn as follows: Thr xiss an inrval ( L U L U δ, δ ) around 0, wih δ, δ > 0, such ha h paricipans rpor no chang in prics if h pric chang xpcd by hm lis wihin his inrval. Thr xiss also an inrval ( p L p π -ε, π + U p ε ) around h subjciv man prcivd inflaion ra π L U, wih ε and ε > 0, such ha h individuals rpor ha prics incras a h sam ra if h xpcd pric chang is covrd by his inrval. Th paricipans answr hrfor in h following mannr: Prics will fall, if x+1 - L δ L say abou h sam, if - δ < x+1 incras a slowr ra, if U δ U δ < x+1 π -ε incras a sam ra, if π -ε < x+1 < p incras mor rapidly, if π + ε U x+1. p L p L p π + ε U

8 50 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn Th proporions of h oal rspons, dnod as A+1 fall, B+1 say abou h sam, C+1 incras a slowr ra, D+1 incras a sam ra and E+1 incras mor rapidly ar wrin in rms of h aggrgad probabiliy disribuion. A sandardizd variabl is usd wih a spcifid disribuion funcion. I is assumd ha h indiffrnc inrvals ar symmric, i.. δ = L =δ and ε = ε U = ε. Howvr, im-variaion is allowd for h inrvals. Th quaions abov giv soluion o h unknown paramrs: π + = 1 p π (a+1+ b+1) q+1 σ+1 = - 2π p q+1 p δ = π (a+1- b+1) q+1 p ε = π (c+1- d+1) q+1 1 whr q = a + b c d. Th paramrs dpnd on h p choic of h disribuion and h prcivd inflaion ra, π. Th disribuion funcion can b chosn as Normal (Carlson and Parkin, 1975). Howvr, h normal disribuion may no b appropria for h pric xpcaions. Som mpirical sudis, basd on financial mark daa or quaniaiv daa on xpcaions, rcommnd ha h acual disribuion of xpcaions can b posiivly skwd in ims of high inflaion and havir ails compard o normal. Thus, alrnaivly ohr yps of disribuions ar applid in h liraur, such as h uniform disribuion (Psaran(1987)), h logisic disribuion (Bachlor and Orr (1988), Nilsn (2003)), h cnral and non-cnral disribuions (Brk (1999), Nilsn (2003)). To capur h dviaion from normaliy; logisic, uniform, cnral- which ar mor pakd han h normal disribuion and chi-squar disribuion which is posiivly skwd ar mployd (Nilsn, 2003). In addiion o hs wll-known disribuions, Sabl disribuion is also applid in ordr o quanify qualiaiv daa. Thr ar svral rasons for using a sabl disribuion o dscrib a sysm. Th mos imporan rason is h Gnralizd Cnral Limi Thorm which sas ha h only possibl non-rivial limi of normalizd sums of indpndn idnically disribud rms is sabl. This horm sas ha rgardlss of h xisnc of h varianc, h limiing disribuion of a sum of indpndn and idnically disribud random variabls is sabl (Borak, Härdl and Wron, 2005). In addiion o his inriguing saisical propry, sabl disribuions ar prfrrd L U δ

9 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn 51 wih rspc o h Sudn s- or h GED sinc hy ar a rich class of probabiliy disribuions ha also allow skwnss. Thrfor, alhough h lack of closd formulas for mos sabl dnsiis and disribuion funcions has bn a major drawback o hir us, hy hav bn widly mployd in modling non-normal conomic & financial daa bcaus of hir flxibiliy. Sabl disribuions, also calld Lvy-Paro disribuions, ar usd o dscrib complx sysms in physics, biology, sociology and conomics as wll (Zoloarv, 1986). In gnral, h uppr and lowr ails of sabl disribuions dcras lik a powr funcion which gnras h havy ails. Sabl disribuions ar a rich class of probabiliy disribuions ha allow skwnss and havy ails and hav many inriguing mahmaical propris. Sinc dnsiis and disribuions ar no known in closd form for mos sabl disribuions (xcpions bing h normal, Cauchy and Lvy disribuions), hy ar usually dfind by hir characrisic funcions (Michll, 2002): α ( [ ]) φ() = E( ix ) = xp iδ c 1+ iβsgn() w (, α) (1) x whr πα an, α 1 w (, α) = 2 (2/ π)ln, α = 1 - < <, 0< α 2, β min(α, 1- α), c> 0, - < δ <. A sabl disribuion has four paramrs; α, β, δ and γ (γ = c α ). α is calld characrisic xponn and inrprd as a shap paramr. Th Normal disribuion is sabl wih α=2 and is h only sabl disribuion which scond and highr absolu momns xis. Whn α<2, absolu momns of ordr qual o and grar han α do no xis whil hos of ordr lss han α do. Th disribuion bcoms havy aild. Th ail hicknss incrass as α dcrass. δ and c ar h locaion and scal paramrs rspcivly. Whn β (skwnss paramr) is posiiv (ngaiv), h disribuion is skwd o h righ (lf). If β is zro, h disribuion bcoms symmric abou δ (locaion paramr). As α

10 52 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn approachs o 2, h disribuion approachs o a Normal disribuion rgardlss of β (Fama and Roll, 1968). p A variy of masurs for h scaling paramr, π, hav bn usd in h liraur. As i should rflc h obsrvd inflaion ra, h mos rcn ra availabl o h survy paricipans, i.. π 1, whr π is h officially publishd inflaion ra, can b usd for h scaling paramr. Du o h dlay in publicaion h laggd inflaion is considrd rahr han π. A scond possibiliy is h man of h acual inflaion ra ovr h whol obsrvd priod, bu his would imply ha h paricipans bas hir dcisions in par on informaion ha is no availabl a h im h dcision is mad. Thrfor no h man ovr h whol sampl can b usd, bu insad h man ovr h priod ha prcds h im of h dcision. This is h running man of inflaion from h bginning of h sampl o h poin whr xpcaions ar survyd. Anohr choic can b h linar inrpolaion bwn h avrag valu of inflaion ovr h firs half of h sampl and ha ovr h scond half of h sampl afr hos valus ar assignd o h firs and las monhs in h sampl, rspcivly (Mill, 2006). In conras o original Carlson-Parkin approach, whr h scaling paramr is simad by imposing unbiasd xpcaions, an imporan advanag is ha i dos no impos unbiasdnss. Scond advanag is ha h rspons hrsholds ar prmid o vary ovr im (Forslls and Knny, 2002). Rgrssion Mhod Psaran (1984, 1987) dvlopd h rgrssion approach ha originas in Andrson (1952). Th quanifid xpcaions ar a funcion of a spcific rgrssion modl rahr han a funcion of a spcific probabiliy disribuion. This mhod is basd on h simaion of h rlaionship bwn currn inflaion as masurd by official saisics and is survy prcpion by rspondns. I is assumd hn ha h sam rlaionship holds bwn qualiaiv opinions of rspondns concrning fuur pric changs and xpcd inflaion, so i srvs as a yardsick for quanificaion of rspondns xpcaions (Lyziak, 2010). If h prcnag chang in prics, π, is composd of a wighd combinaion of rspondns having xprincd incrasing or falling prics, hn

11 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn 53 π = αr βf + ε Psaran (1987) assums ha during inflaionary priods, hr xiss an asymmrical rlaionship bwn h ra of chang of individually xprincd prics and ovrall inflaion, dpnding on h dircion of chang rpord. Asymmric bhaviour mans ha all rspondns rporing an incras giv addiionally mor incras up o a random disanc whras hs rporing a dcras giv h sam dcras up o a random disanc. Afr subsiuing hs rlaions, w g αr βf π = + ε (1 λr) (2) whr R and F dno h prcnags of rspondns rporing pric riss or falls in hir answr o h prcpions qusion, rspcivly. Onc h cofficins from quaion (2) hav bn rcovrd, i is possibl o apply hm o h survy proporions rlaing o xpcaions his im, hrby driving a masur of inflaion xpcaions: π + 1 ˆ αr ˆ βf = (1 ˆ λr ) (3) Th assumpion is ha h simad rlaionship bwn survy daa and inflaion holds no only for ralizaions, bu also for xpcaions. This can b hough o b a srong assumpion. Psaran (1987) poins ou ha a rgrssion lik (2) is no a causal xplanaion of pric changs bu simply idnifis h rlaionship bwn wo diffrn sourcs of informaion (namly official saisics and survy rsuls), and srvs as a yardsick by mans of which cagorical rsponss concrning h dircion of fuur changs in prics can b convrd ino quaniaiv masurs. Psaran (1984) furhr rcommndd corrcing for h rsidual auocorrlaion in quaion (2) by imposing an AR srucur on h rror rm: αr βf + ρ((1 λr ) π αr βf ) + ρ((1 λr ) π αr βf ) = + (1 λr) π ε (4)

12 54 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn Balanc Mhod Balanc mhod is h asis chniqu o quanify qualiaiv daa. Th calculaion of h balanc saisic is compild in accordanc wih h balanc mhod of Europan Union (Usr Guid, 2003). Th possibl oucoms ar -1,-0.5, 0, 0.5 and 1 for a pnachoomous survy. Ths oucoms ar associad wih h sampl proporions A+1, B+1, C+1, D+1, E+1 rspcivly. b Th xpcd man of his random variabl, dnod as π + 1 is hn for a pnachoomous survy dfind as: b π + 1 = 1* A+1 0.5* B+1 + 0* C * D+1 + 1* E+1 = E * D+1 0.5* B+1 A+1 Quanifid Expcaions Th xpcd inflaion qusion of CTS is quanifid in ordr o g quaniaiv inflaion xpcaions of h consumrs. Th mhods dscribd abov ar usd o obain h quanifid xpcaions sris (Oral, 2013). Th las officially publishd inflaion ra blongs o March 2011, so h survy priod usd in h sudy covrs h priod from Dcmbr 2003 o April Thn inflaion xpcaions can b calculad for h priod from Novmbr 2004 o March 2011 and compard wih h ralizaions. Th probabiliy mhod is mployd o h inflaion xpcaions gahrd from CTS by using diffrn disribuion funcions. Normal disribuion is usd in many sudis sinc i is asy o handl. Howvr, normal disribuion may no b suiabl wih h mpirical findings. Thrfor, chi-squar disribuion, cnral -disribuion and Sabl disribuion ar also applid in addiion o normal, logisic and uniform disribuions. To accoun for h pakdnss of h acual pric changs, logisic and cnral- disribuions ar usd. To modl h asymmric bhaviour of pric changs, chi-squar disribuion is usd. To capur no only h asymmric bhaviour bu also h havy aild parn, Sabl disribuion is applid. A grid sarch is usd in ordr o driv quanifid xpcaions sris via diffrn Sabl disribuion across diffrn α and β valus (α in h rang 0.1 o 2 and β in h rang -1 o 1 a inrvals of

13 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn ). Th accuracy of ach simad sris is calculad by comparing agains h ralizaion. Four diffrn choics for h scaling paramr ar applid. Firs on is h mos rcn officially publishd inflaion ra availabl o h survy paricipans. Th scond choic usd is h linar inrpolaion. Th hird opion is h running man of inflaion. Th final choic is h man of h acual inflaion ra ovr h whol obsrvd priod. Th forcasing prformancs of diffrn modls can b sn in Tabl 1. Four masurs of scaling paramr ar analyzd for ach disribuion and running man of inflaion has h las rror valus for all disribuions xcp for chi-squar disribuion. Whn h prformancs ar compard wih ach ohr for h probabiliy mhod, Sabl disribuion having paramr valus 0.30 for α and for β wih h linar inrpolaion as hrshold paramr shows h bs prformanc du o low man absolu rror (MAE), man squar rror (MSE) and hil U (TU1) saisics. Quanificaion Mhods MAE* MSE** TU1*** Probabiliy Mhod Thrshold Paramr Normal Disribuion Mos rcn inflaion ra Linar inrpolaion Running man of inflaion Man of h acual inflaion ra Uniform Disribuion Mos rcn inflaion ra Linar inrpolaion Running man of inflaion Man of h acual inflaion ra Logisic Disribuion Mos rcn inflaion ra Linar inrpolaion Running man of inflaion Man of h acual inflaion ra Cnral- disribuion Mos rcn inflaion ra Linar inrpolaion Running man of inflaion Man of h acual inflaion ra Chi-squar disribuion Mos rcn inflaion ra

14 56 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn Linar inrpolaion Running man of inflaion Man of h acual inflaion ra Sabl Disribuion Balanc Mhod Rgrssion Mhod Tabl 1. Thr Saisical Criria o compar h Quanificaion Mhods n * MAE = P P / n = 1 n ( ) 2 ** MSE = P P / n, = 1 n n 2 2 ** TU1 = ( P P ) ( P) = 1 = 1 P P, whr and dno acual inflaion and inflaion xpcaions rspcivly. 1/2, Figur 1 illusras h xpcaions drivd via diffrn disribuions. I can b concludd ha h bs fi o acual valus of inflaion can b aaind by h xpcaions drivd from Sabl disribuion. Tabl 1 suppors his claim. Th qusion of pric xpcaions in CTS has fiv cagoris. Th proporions ar addd in ordr o g hr-cagory opions. Fall opion is qual o A+1, Sam opion is qual o B+1 and Ris opion is qual o C+1+ D+1+ E+1. Afr having hr-opion cagoris, h modl givn in quaion (4) is applid. Th qusion of inflaion prcpions dos no xis in CTS, so h rgrssion modl is consrucd for h xpcd inflaion qusion. Th rsuls ar givn in Tabl 2 and Figur 2.

15 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn 57 Fig. 1. Quanifid Expcaions by Carlson-Parkin Mhod Nov-04 Mar-05 Jul-05 CPI % Normal disribuion Nov-05 Mar-06 Jul-06 Nov-06 Mar-07 Jul-07 Nov-07 Mar-08 Jul-08 Nov-08 Sabl disribuion Logisic disribuion Mar-09 Jul-09 Nov-09 Mar-10 Jul-10 Nov-10 Mar-11 Tabl 2. Rgrssion Modl Cofficin * Significan a 5 % lvl. Psaran AR(12) Corrcion α * β * λ 2.033* ρ * R monh laggd inflaion ra is usd in ordr o avoid ovrlapping of priods for h rror rm. All h paramrs in h modl ar found o b significan.

16 58 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn Fig. 2. Quanifid Expcaions by Rgrssion Mhod CPI % Psaran 3.0 Nov-04 Mar-05 Jul-05 Nov-05 Mar-06 Jul-06 Nov-06 Mar-07 Jul-07 Nov-07 Mar-08 Jul-08 Nov-08 Mar-09 Jul-09 Nov-09 Mar-10 Jul-10 Nov-10 Mar-11 Th balanc mhod can b sn in Figur 3. Th figur indicas ha hr is no similar parn wih ralizaions in ndncy. Howvr, i should b mniond ha his saisic can only giv informaion abou ndncy insad of quaniy of inflaion xpcaions. Fig. 3. Quanifid Expcaions by Balanc Mhod 13.0 CPI % Balanc Mhod (righ axis) Nov-04 Apr-05 Sp-05 Fb-06 Jul-06 Dc-06 May-07 Oc-07 Mar-08 Aug-08 Jan-09 Jun-09 Nov-09 Apr-10 Sp-10 Fb

17 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn 59 Th comparisons of h modls can b sn in Figur 4. Th bs modl for quanifid pric xpcaions can b said o b h rgrssion modl. Fig. 4. Comparisons of Expcaions obaind by Diffrn Mhods CPI % Sabl disribuion Nov-04 Apr-05 Sp-05 Fb-06 Jul-06 Dc-06 May-07 Oc-07 Mar-08 Aug-08 Jan-09 Jun-09 Nov-09 Apr-10 Sp-10 Fb Th official inflaion ra for h priod bwn Novmbr 2004 and March 2011 is considrd wih h aim of invsigaing h prformancs of h quanificaion mhods a diffrn im priods. I divid h daa ino wo pars such as h firs 20 obsrvaions and h rmaining ons. I calcula h sandard dviaions of ach porion and ak h diffrncs of h sandard dviaions. Thn I roll h sampl and kp calculaing h diffrncs for h ohr following sampls. Afr calculaing for nir sampl, I choos h spli da as April 2008 according o h comparison of h diffrncs. This monh has h maximum valu for diffrnc. Th 1s priod o b analyzd now bcoms Novmbr April 2008 and h 2nd priod is May 2008-March I compar ach mhod du o hs wo priods sparaly.

18 60 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn Tabl 3a. Comparisons of Quanificaion Mhods for h 1 s Priod Quanificaion MAE MSE TU1 Mhods Probabiliy Thrshold Paramr Mhod Normal Mos rcn inflaion ra Disribuion Linar inrpolaion Running man of inflaion Uniform Disribuion Logisic Disribuion Cnral- disribuion Chi-squar disribuion Man of h acual inflaion ra Mos rcn inflaion ra Linar inrpolaion Running man of inflaion Man of h acual inflaion ra Mos rcn inflaion ra Linar inrpolaion Running man of inflaion Man of h acual inflaion ra Mos rcn inflaion ra Linar inrpolaion Running man of inflaion Man of h acual inflaion ra Mos rcn inflaion ra Linar inrpolaion Running man of inflaion Man of h acual inflaion ra Balanc Mhod Rgrssion Mhod Sabl Disribuion

19 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn 61 Tabl 3b. Comparisons of Quanificaion Mhods for h 2 nd Priod Quanificaion MAE MSE TU1 Mhods Probabiliy Thrshold Paramr Mhod Normal Mos rcn inflaion ra Disribuion Linar inrpolaion Running man of inflaion Uniform Disribuion Logisic Disribuion Cnral- disribuion Chi-squar disribuion Man of h acual inflaion ra Mos rcn inflaion ra Linar inrpolaion Running man of inflaion Man of h acual inflaion ra Mos rcn inflaion ra Linar inrpolaion Running man of inflaion Man of h acual inflaion ra Mos rcn inflaion ra Linar inrpolaion Running man of inflaion Man of h acual inflaion ra Mos rcn inflaion ra Linar inrpolaion Running man of inflaion Man of h acual inflaion ra Balanc Mhod Rgrssion Mhod Sabl Disribuion Th comparison rsuls givn in Tabls 3a and 3b mak us rly on ha rgrssion mhod ouprforms h rmaining mhods for ach priod.

20 62 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn Thrfor, i can b concludd ha for diffrn priods, w can sill choos rgrssion mhod as bs for quanificaion purposs. I also calcula 1-sp ahad (saic) forcass for h xpcaions drivd by rgrssion mhod. I compar hs forcass wih forcass of Naiv Expcaions which ar h xpcd inflaion sris qual o h currn ra of inflaion. I masur 1-sp ahad forcass in boh ways such as rolling and rcursiv windows for h rgrssion mhod. Th comparisons of diffrn mhods ar givn in Tabl 4. In lin wih h rsuls, rcursiv window forcass via rgrssion mhod prforms br han naiv xpcaions for 1-sp ahad forcas. Tabl 4. Comparisons of 1- sp ahad forcass Mhods MAE MSE TU1 Rgrssion Mhod (rolling window forcas) Rgrssion Mhod (rcursiv window forcass) Naiv Expcaions Formaion of Turkish Consumr Inflaion Expcaions Th xpcaions hav bn imporan issu in macroconomics for many yars. Sinc h way in which xpcaions ar formd has imporan implicaions for conomic bhaviour, many conomiss hav usd survy daa o s hypohss abou xpcaion formaion (Kan & Runkl, 1990). Wha is of concrn for monary policy makrs ar signs ha xpcaions hav bcom d-anchord, which w can inrpr as bing h cas if h public racs o a shor priod of highr-hanxpcd inflaion by incrasing hir long-run xpcaions. Masuring whn inflaion xpcaions hav bcom d-anchord is undoubdly no asy. On of h problms is ha how individuals form xpcaions is no known. Indd, i is probably impossibl o gnraliz, as individuals ar likly o form hir xpcaions using diffrn informaion ss, rlying on diffrn modls. Drivr and Windram (2007) found ha som housholds may form hir xpcaions basd on a srucural rlaionship, such as h rad-off bwn inflaion and unmploymn or dmand; ohrs may us an mpirical approach, such as hir rcn mmoris of inflaion daa. Furhrmor, popl may b nirly forward looking or nirly backward looking, or a combinaion of boh.

21 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn 63 Th xpcaion formaion modls in h liraur rang from simpl, purly backward-looking o xplicily modling larning procsss o h hypohsis of prfcly raional xpcaions (Psaran, 1989). Backwardlooking modls assum ha agns us only pas pric dvlopmns and arlir forcas rrors o form xpcaions whil ohr influncs ar disrgardd. Muh (1961) assums ha h subjciv xpcaions of conomic agns mach h prdicions of h rlvan conomic hory in his raional xpcaions hypohsis. Thus, a crucial faur of his dfiniion of raional xpcaions is ha conomic agns do no mak sysmaic rrors. Many criics hav poind o h imporanc of informaion problms and hav srssd h nd o ak ino accoun h coss of making opimal forcass and also o xplicily modl larning procsss. Howvr, sinc is adopion by Lucas (1972, 1975), Sargn (1973), Barro (1977) and ohrs, h raional xpcaions hypohsis has bcom on of h broadly accpd paradigms of macroconomic analysis. Th non-linar rgrssion modl is found o b h bs modl o masur inflaion xpcaions; hnc h analyss in his scion will b basd on h xpcaions aaind via his modl. As an iniial poin bfor h conomric analyss, daild informaion abou inflaion xpcaions and official inflaion can b givn as follows: CBRT followd an implici inflaion arging rgim saring from 2002 unil h nd of 2005 and announcd a yar-nd uppr limi for h inflaion arg. Ths applicaions mad h crdibiliy and ransparncy of h nw rgim incras and h acual yarly inflaion was abl o b kp blow h lvl of h args for h yars 2004 and 2005 (Figur 5). Th bank sard o hav fully-fldgd inflaion arging in 2006 and announcd is 3-yar inflaion arg. Th announcd inflaion args ar on annual basis. Thus, linar inrpolaion is usd for calculaing crdibiliy gap on monhly basis which is h diffrnc bwn inflaion xpcaions and inflaion args. According o h graph of h crdibiliy gap, i can b sn ha h inflaion xpcaions was clos o h arg valus during his priod (Figur 6). Howvr, hy sard o driora du o supply shocks and unfavorabl inrnaional and domsic condiions afr Inrnaional financial urmoil a h priod May-Jun 2006 had h mos noicabl influnc on xpcaions. Consumrs smd o bliv in h arg inflaion unil 2006, bu afr ha im, hir xpcaions driorad. Th crdibiliy gap sard o incras and aaind h

22 64 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn highs valu in March, Tha indicas ha h consumrs wr affcd by h acual inflaion which was 9.7 prcn qui abov h arg valu of 5 for h yar Th financial crisis of , also known as h global financial crisis hi hardr Turky s conomy. Th crdibiliy gap was fairly larg during ha priod du o his financial crisis. Thn i dclind saring from Spmbr Th rason for his dclin was h dcras in acual inflaion for h yars I can b sn ha h inflaion was kp blow h args again for hs yars. As a rsul, i can b said ha whn h args wr hi, consumrs had a ndncy o bliv in h args. On h ohr hand, hos priods whn h args could no b achivd, consumrs bcam pssimisic and xpcd high ras of inflaion. I can b concludd ha incras in inflaion ra has impac on no only h crdibiliy of CBRT bu also h inflaion xpcaions. An incras in h inflaion ra drioras h crdibiliy of h bank and h diminishd crdibiliy worsns h inflaion xpcaions. Fig. 5. Acual Inflaion and Inflaion Targs Targ CPI %

23 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn 65 Fig. 6. Crdibiliy Gap Nov-05 Mar-06 Jul-06 Nov-06 Mar-07 Jul-07 Nov-07 Mar-08 Jul-08 Nov-08 Mar-09 Jul-09 Nov-09 Mar-10 Jul-10 Nov-10 Mar-11 To bgin wih h conomric analyss, h im sris hav o b sd for a uni roo bfor furhr analysis. Sandard Augmnd-Dicky- Fullr (ADF) ss ar applid. Lag lnghs ar chosn according o Schwarz Informaion cririon (SIC). Th rsuls of hs ss ar prsnd in Tabl 5. I can b concludd ha acual yar on yar inflaion and xpcd inflaion hav uni roo (hy ar boh I(1)). Tabl 5. Uni roo ss for analyzd im sris Variabl lags Ts-saisic Probabiliy* Rsul π I(1) π I(1) π I(0) π I(0) * MacKinnon on-sidd p-valus. Sinc boh acual inflaion and consumr inflaion xpcaions ar nonsaionary, h coingraion bwn hs variabls is sd. Bfor h coingraion s is applid, I obain h opimal lag-lnghs for h VAR procss via VAR lag ordr slcion criria. Lags 1, 2 and 11 can b chosn du o diffrn criria such as Liklihood-Raio Ts (LR), Final Prdicion Error (FPE), Hannan-Quinn (HQ), Akaik (AIC) and

24 66 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn Schwarz informaion (SC). Th rsuls of h Johansn s ar givn in Tabl 6: Tabl 6. Rsuls of h Johansn s Lag lngh Cririon Null hypohsis Trac-saisic Prob.* SC, HQ r= r= LR, FPE r= r= AIC r= r= * MacKinnon-Haug-Michlis p-valus. Th null hypohsis ha h coingraion rank r is zro. Th null hypohsis ha h coingraion rank r is zro can b rjcd a lag 11 showing ha hr is on coingraing quaion a 5% significanc lvl. In an ffor o drmin h shor run causaliy among h wo variabls, Grangr Causaliy/Block Exogniy Wald Tss basd upon VEC modl is applid. Th rsuls of Tabl 7 show ha shor run causaliy is from h inflaion o inflaion xpcaions. Tabl 7. VEC Grangr Causaliy/Block Exogniy Wald Tss π Dpndn Variabl Excludd π Chi squar saisic Dgrs of frdom Prob. π π I also prform Grangr causaliy ss bwn chang in inflaion xpcaions and unobsrvd fuur chang in h inflaion ra (Tabl 8). Th rsuls show ha h changs in fuur inflaion ra Grangr caus inflaion xpcaions bu no h ohr way. In ohr words, xpcaions ar acually somwha forward looking. Howvr, pas changs in inflaion xpcaions do no hav any significan ffc on changs in h inflaion ra.

25 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn 67 Tabl 8. Grangr Causaliy Tss* Expcaion Vrsus Fuur Inflaion Chang in inflaion xpcaions formd a im - 11 ( ) dos no Grangr Caus chang in h π inflaion ra a im ( π) Chang in h inflaion ra a im ( π) dos no Grangr Caus chang in inflaion xpcaions formd a im -11 ( ) π * Lag lngh is chosn as 12. F-saisic Probab iliy Addiionally, h variabls ar sd for wak xogniy in ordr o s whhr h coingraion rlaion is significan for boh ndognous variabls or no. Th rsuls can b sn in Tabl 9. Tabl 9. Wak Exogniy Ts Analyzd Variabl Lag lngh Chi squar saisic Prob. π π Th s-saisics poin ou ha h hypohsis of wak xogniy can b rjcd for h xpcd inflaion ra, bu no for h acual inflaion ra. Consqunially, rror corrcion modl can b simad for h xpcd inflaion ra as dpndn variabl. Th long-run rlaionship bwn consumr inflaion xpcaions and acual inflaion (sandard rrors in parnhss) can b givn as: π = π + ε (Sampl: 2006: :03) (3.773) (0.429) Trac s indicas 1 coingraing quaion(s) a 5% lvl Max-ignvalu s indicas 1 coingraing quaion(s) 5% lvl Th coingraing vcor should hav a null consan rm and opposi cofficins for xpcd and acual inflaion undr h raional xpcaions hypohsis (unbiasdnss assumpion). Th join rsricion of a uni cofficin and zro consan wihin VECM is rjcd wih Chi- Squar saisic and probabiliy valu qual o and

26 68 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn rspcivly. I can b concludd ha h xpcaions ar no unbiasd. Consqunly, h xpcaions ar said o b no raional. Afr rjcing a raional modl of h formaion of inflaion xpcaions, hybrid modl of xpcaions formaion is considrd for h purpos of masuring h formaion, whr xpcaions ar comprisd of no only forward-looking bu also backward-looking porions (Lyziak, 2012). Following h inflaion xpcaion quaion prsnd in Hinmann and Ullrich (2006), which is an xndd vrsion of Carlson and Valv (2002) and Grbrding (2001), h inflaion xpcaions modl can b rprsnd in such a way as o conain boh forward (raional) and backward-looking lmns as in quaion blow: π 1 (1 1) 12 2( 12 12) 3( 12 23) 4( = βπ + β π + β π π + β π π + β π 1 π 12) + ε (5) In his formulaion, xpcaion formaion can b parially characrizd as raional, whil h backward looking prspciv sill plays a rol. Th rlaiv imporanc of h raional vrsus adapiv componns of xpcaions is masurd by β 1, whr xpcaions ar considrd fully raional if β 1=1. This quaion is rahr flxibl in incorporaing adapiv naur of xpcaions such ha β 2 masurs agns spd of adjusmn o hir pas forcas rrors, whil β 3 and β4masur h wighs of h rgrssiv par of xpcaions formaion. Equaion (5) which was prsnd in consraind form is r-simad in unconsraind form in quaion blow by allowing h sum of h raional and adapiv rms o b diffrn from on. π = β π + β π + β ( π π ) + β ( π π ) + β ( π π ) + ε I is sn in Tabl 10 ha h simad cofficin for h fuur inflaion is 0.11 in h 1s column. Th hypohsis of pur backward-looking xpcaions is hrfor rjcd. Th cofficin of h pas inflaion xpcaion howvr is much biggr (0.89) rprsning h srong backward looking naur of xpcaions in h long run. Thrfor, h pur forward-looking xpcaions hypohsis is also rjcd. In addiion, xpcaions ar found o b highly rgrssiv wih h (6)

27 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn 69 cofficin Th impac of h chang in pas inflaion on h formaion of xpcaions is, howvr, unxpcdly small and has a ngaiv sign. Th srucur of h xpcaions dos no chang whn w consrain h sum of h cofficins of forward and backward looking lmns o b qual o on (Tabl 11). Tabl 10. Srucur of Expcaions (Unconsraind Modl) Tabl 11. Srucur of Expcaions (Consraind Modl) Cofficins π π 12 ( π π ) ( π π ) ( π π ) ** (1.824) 0.89* (16.526) 0.07 (0.712) (-1.423) 0.73* (8.682) 0.12** (1.944) 0.87* (16.078) ** (-1.837) 0.72* (9.337) R * Significan a 5 % lvl. ** Significan a 10 % lvl. Cofficins 0.11** 0.13* π (1.984) (2.322) 0.10 ( π 12 π 12) - (1.074) ** ( π 12 π 23) (-1.609) (-1.978) 0.83* 0.83* ( π 1 π 12) (8.285) (8.270) R * Significan a 5 % lvl. ** Significan a 10 % lvl. Conclusion A nw ra bgan in Turky in rms of fiscal and monary policis following h financial and currncy crisis in On h fiscal fron,

28 70 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn Turky iniiad a s of policis aiming o rduc h public dfici o accpabl lvls. On h monary fron, policy swichd from a fixd xchang ra o an inflaion arging rgim. In his nw rgim, inflaion xpcaions play a valuabl dual rol. On h on hand, h nw monary policy mphasizs h nd o manag public xpcaions o curail inria in inflaion dynamics by swiching conomic agns inflaion xpcaions from a backward o a forward-looking prspciv, in ordr o rduc h inflaion ra rapidly. By monioring h crdibiliy gap of h monary policy, h gap bwn h inflaion arg and inflaion xpcaions, h cnral bank may s how succssful i is in anchoring inflaion xpcaions ha wr damagd by a pas hisory of high inflaion ras. On h ohr hand, agns inflaion xpcaions may conain som informaion rgarding a fuur pah of inflaion ha is unknown o h cnral bank. Th succss of h inflaion-arging rgim crucially dpnds on a cnral bank s abiliy o fors changs in inflaion ras du o long lags in h monary ransmission channl. Thus, inflaion xpcaion survys may b a valuabl sourc for cnral banks o collc informaion rgarding h prospc of inflaion ras (Oral al., 2011). This papr has ampd o analyz h qualiaiv inflaion xpcaions gahrd from h Consumr Tndncy Survy daa. Th survy rsuls ar xamind and h qualiaiv inflaion xpcaions ar quanifid by using diffrn mhods such as Carlson-Parkin mhod, balanc mhod, rgrssion mhod. Ths mhods ar compard by using svral saisical criria, lik man squar rror, man absolu rror and Thil s inqualiy cofficin. Carlson-Parkin mhod is applid for h pnachoomous survy qusion. In his approach, on advanag is ha h scaling paramr is no simad by imposing unbiasd xpcaions. Anohr advanag is ha h hrsholds ar prmid o vary ovr im. Diffrn disribuions ar applid and xpcaions obaind by Sabl disribuion show h bs prformanc du o saisical criria. Th balanc mhod is applid and i is found ha consumrs ar backward-looking. Thirdly, nonlinar rgrssion modl is consrucd o g h inflaion xpcaions sris. Finally, h xpcaions drivd from hr diffrn chniqus ar analyzd and h nonlinar rgrssion modl is found o b h closs on o ralizaions. Th inflaion xpcaions drivd from h nonlinar rgrssion modl is usd in ordr o analyz h formaion of inflaion

29 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn 71 xpcaions. Acual inflaion and inflaion xpcaions ar found o hav a coingraion rlaion. Unbiasdnss assumpion undr Raional Expcaions Hypohsis is rjcd wihin VECM. Hnc, hybrid modl of xpcaions formaion is consrucd. On imporan rsul aaind from h modl is ha h hypohsis of pur backward-looking xpcaions is rjcd. Th cofficin of h pas inflaion xpcaion howvr is much biggr ha indicas h srong backward looking naur of xpcaions in h long run. Thrfor, h pur forwardlooking xpcaions hypohsis is also rjcd. In addiion, xpcaions ar found o b highly rgrssiv. As a rmark, h impac of h chang in pas inflaion on h formaion of xpcaions is qui small. Howvr, i can b concludd ha an incras in inflaion ra has dirc ffc on h crdibiliy of CBRT and indirc ffc on h inflaion xpcaions. An incras in h inflaion ra drioras h crdibiliy of h bank and h waknd crdibiliy worsns h inflaion xpcaions. Nos 1. All h viws xprssd in h sudy ar hos of h auhor and should no b aribud o h Cnral Bank of h Rpublic of Turky. 2. Targ inflaion ra is also usd insad of fuur inflaion ra in Equaions (5) and (6). In h unconsraind form, h arg inflaion ra is found o b saisically significan wih a cofficin I is availabl upon rqus from h auhor. Rfrncs Andrson, O. (1952). Th businss s of h IFO-Insiu for Economic Rsarch Munich, and is horical modl. Rvu d l Insiu Inrnaional d Saisiqu, 20, Barro, R. J. (1977). Unanicipad Mony Growh and Unmploymn in h Unid Sas. Amrican Economic Rviw, 67, Başkaya, S., Kara, H., & Mulur, D. (2008). Expcaions, Communicaion and Monary Policy in Turky. Th Cnral Bank of h Rpublic of Turky, Rsarch and Monary Policy Dparmn, Working Papr No:08/01. Başkaya, S., Gülşn, E., & Kara, H. (2012). Inflaion Expcaions and Cnral Bank Communicaion in Turky. Cnral Bank Rviw, Vol. 12 (July 2012), 1-10.

30 72 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn Bachlor, R. A. (1982). Expcaions, Oupu and Inflaion, Th Europan Exprinc. Europan Economic Rviw, 17, Bachlor, R. A., & Orr, A. B. (1988). Inflaion xpcaions rvisid. Economica, 55, Brk, J. M. (1999). Masuring inflaion xpcaions: a survy daa approach. Applid Economics, 31, Brk, J.M., & Hbbink, G. (2009). Th Europan consumr and monary policy. Chapr 9 in: P.J.N. Sinclair, (d.). Inflaion Expcaions. London and Nw York: Rouldg. Borak, S., Hardl, W., & Wron, R. (2005). Sabl Disribuions. SFB 649 Discussion Papr , Humbold-Univrsiä zu Brlin. Carlson, J. A., & Parkin, M. (1975). Inflaion Expcaions. Economica, Vol: 42, Carlson, J.A., & Valv, N.T. (2002). A Disinflaion Tradoff: Spd Vrsus Final Dsinaion. Economic Inquiry, 40, Drivr, R., & Windram, R. (2007). Public aiuds o inflaion and inrs ras. Bank of England Quarrly Bullin, Vol. 47, No. 2, Fama, E.F., & Roll, R. (1968). Som Propris of Symmric Sabl Disribuions. Journal of h Amrican Saisical Associaion, 63, Forslls, M., & Knny, G. (2002). Survy xpcaions, raionaliy and h dynamics of uro ara inflaion. Papr prsnd o 26h CIRET Confrnc. Grbrding, C. (2001). Th Informaion conn of Survy Daa on Expcd Pric Dvlopmns. Economic Rsarch Cnr of h Dusch Bundsbank, Discussion Paprs 9. Hinmann, F., & Ullrich, K. (2006). Th Impac of EMU on Inflaion Expcaions. Opn Economis Rviw, 17 (2), Kara, H., & Küçük Tuğr, H. (2005). Som Evidnc on h (Ir)raionaliy of Inflaion Expcaions in Turky. Th Cnral Bank of h Rpublic of Turky, Working Papr 50/12. Kara, H., & Küçük-Tuğr, H. (2010). Inflaion Expcaions in Turky: Larning o b Raional. Applid Economics, 42(21), Karadaş, E., & Öğünç, F. (2005). An Analysis of Inflaion Expcaions of h Turkish Priva Manufacuring Indusry. Cnral Bank Rviw, 2,

31 Oral E Masuring Consumr Inflaion Expcaions in Turky. Easrn 73 Kan, M. P., & Runkl, D. E. (1990). Tsing h Raionaliy of Pric Forcass: Nw vidnc from Panl daa. Th Amrican Economic Rviw, 80 (4), Krshoff, G. (2000). Masuring Businss and Consumr Confidnc in Souh Africa. Burau for Economic Rsarch, Sllnbosh, Dcmbr. Lucas, R. E. (1972). Economric sing of h naural ra hypohsis, in Ecksin, O. (d.), Th Economrics of Pric Drminaion, Confrnc, Washingon DC. Lucas, R. E. (1975). An Equilibrium Modl of h Businss Cycl. Journal of Poliical Economy, 83, Lyziak, T. (2010). Masurmn of prcivd and xpcd inflaion on h basis of consumr survy daa. IFC Working Paprs, No 5. Lyziak, T. (2012). Inflaion xpcaions in Poland. Naional Bank of Poland Working Paprs, 115. Michll, J. (2002). Th us of non-normal disribuions in quanifying qualiaiv survy daa on xpcaions. Economics Lrs, 76, Mill, F.C. (2006). Finding h opimal mhod of quanifying inflaion xpcaions on h basis of qualiaiv survy daa. Manuscrip, Balliol Collg, Univrsiy of Oxford. Muh, J. F. (1961). Raional Expcaions and h Thory of Pric Movmns. Economrica, 29, Nilsn, H. (2003). Inflaion Expcaions in h EU Rsuls from Survy Daa. Discussion Papr, FU and HU Brlin. Oral, E, Saygılı, H., Saygılı M., & Tuncl, S. O. (2009). An Asssmn of h CBRT s Survy of Expcaions. Journal of Economics Businss and Financ, 24(276), 23-51, March. Oral, E, Saygılı, H, Saygılı M., & Tuncl, S. O. (2011). Inflaion Expcaions in Turky: Evidnc from Panl Daa. OECD Journal: Journal of Businss Cycl Masurmn and Analysis, 1, Oral, E. (2013). Consumr Inflaion Expcaions in Turky. IFC Working Paprs, Bank for Inrnaional Slmns, No. 10, May. Psaran, M. (1984). Expcaions formaion and macroconomic modlling. In P. Magrang, & Mu, P., Conmporary Macroconomic Modlling (pp ). Oxford: Blackwll Psaran, M. H. (1987). Th Limis o Raional Expcaions. Oxford: Basil Blackwll.

I) Title: Rational Expectations and Adaptive Learning. II) Contents: Introduction to Adaptive Learning

I) Title: Rational Expectations and Adaptive Learning. II) Contents: Introduction to Adaptive Learning I) Til: Raional Expcaions and Adapiv Larning II) Conns: Inroducion o Adapiv Larning III) Documnaion: - Basdvan, Olivir. (2003). Larning procss and raional xpcaions: an analysis using a small macroconomic

More information

CHAPTER CHAPTER14. Expectations: The Basic Tools. Prepared by: Fernando Quijano and Yvonn Quijano

CHAPTER CHAPTER14. Expectations: The Basic Tools. Prepared by: Fernando Quijano and Yvonn Quijano Expcaions: Th Basic Prpard by: Frnando Quijano and Yvonn Quijano CHAPTER CHAPTER14 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 14-1 Today s Lcur Chapr 14:Expcaions: Th Basic Th

More information

Spring 2006 Process Dynamics, Operations, and Control Lesson 2: Mathematics Review

Spring 2006 Process Dynamics, Operations, and Control Lesson 2: Mathematics Review Spring 6 Procss Dynamics, Opraions, and Conrol.45 Lsson : Mahmaics Rviw. conx and dircion Imagin a sysm ha varis in im; w migh plo is oupu vs. im. A plo migh imply an quaion, and h quaion is usually an

More information

Institute of Actuaries of India

Institute of Actuaries of India Insiu of Acuaris of India ubjc CT3 Probabiliy and Mahmaical aisics Novmbr Examinaions INDICATIVE OLUTION Pag of IAI CT3 Novmbr ol. a sampl man = 35 sampl sandard dviaion = 36.6 b for = uppr bound = 35+*36.6

More information

INFLATION EXPECTATIONS DERIVED FROM BUSINESS TENDENCY SURVEY OF THE CENTRAL BANK

INFLATION EXPECTATIONS DERIVED FROM BUSINESS TENDENCY SURVEY OF THE CENTRAL BANK INFLATION EXPECTATIONS DERIVED FROM BUSINESS TENDENCY SURVEY OF THE CENTRAL BANK Ec Oral Saisics Dparmn Cnral Bank of Th Rpublic of Turky Ec.Oral@cmb.gov.r ABSTRACT Th xpcaions obaind from survys play

More information

1. Inverse Matrix 4[(3 7) (02)] 1[(0 7) (3 2)] Recall that the inverse of A is equal to:

1. Inverse Matrix 4[(3 7) (02)] 1[(0 7) (3 2)] Recall that the inverse of A is equal to: Rfrncs Brnank, B. and I. Mihov (1998). Masuring monary policy, Quarrly Journal of Economics CXIII, 315-34. Blanchard, O. R. Proi (00). An mpirical characrizaion of h dynamic ffcs of changs in govrnmn spnding

More information

Economics 302 (Sec. 001) Intermediate Macroeconomic Theory and Policy (Spring 2011) 4/25/2011. UW Madison

Economics 302 (Sec. 001) Intermediate Macroeconomic Theory and Policy (Spring 2011) 4/25/2011. UW Madison conomics 302 (Sc. 001) Inrmdia Macroconomic Thory and Policy (Spring 2011) 4/25/2011 Insrucor: Prof. Mnzi Chinn Insrucor: Prof. Mnzi Chinn UW Madison 21 1 Th Mdium Run ε = P * P Thr ar wo ways in which

More information

4.1 The Uniform Distribution Def n: A c.r.v. X has a continuous uniform distribution on [a, b] when its pdf is = 1 a x b

4.1 The Uniform Distribution Def n: A c.r.v. X has a continuous uniform distribution on [a, b] when its pdf is = 1 a x b 4. Th Uniform Disribuion Df n: A c.r.v. has a coninuous uniform disribuion on [a, b] whn is pdf is f x a x b b a Also, b + a b a µ E and V Ex4. Suppos, h lvl of unblivabiliy a any poin in a Transformrs

More information

AR(1) Process. The first-order autoregressive process, AR(1) is. where e t is WN(0, σ 2 )

AR(1) Process. The first-order autoregressive process, AR(1) is. where e t is WN(0, σ 2 ) AR() Procss Th firs-ordr auorgrssiv procss, AR() is whr is WN(0, σ ) Condiional Man and Varianc of AR() Condiional man: Condiional varianc: ) ( ) ( Ω Ω E E ) var( ) ) ( var( ) var( σ Ω Ω Ω Ω E Auocovarianc

More information

Economics 302 (Sec. 001) Intermediate Macroeconomic Theory and Policy (Spring 2011) 3/28/2012. UW Madison

Economics 302 (Sec. 001) Intermediate Macroeconomic Theory and Policy (Spring 2011) 3/28/2012. UW Madison Economics 302 (Sc. 001) Inrmdia Macroconomic Thory and Policy (Spring 2011) 3/28/2012 Insrucor: Prof. Mnzi Chinn Insrucor: Prof. Mnzi Chinn UW Madison 16 1 Consumpion Th Vry Forsighd dconsumr A vry forsighd

More information

UNIT #5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS

UNIT #5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS Answr Ky Nam: Da: UNIT # EXPONENTIAL AND LOGARITHMIC FUNCTIONS Par I Qusions. Th prssion is quivaln o () () 6 6 6. Th ponnial funcion y 6 could rwrin as y () y y 6 () y y (). Th prssion a is quivaln o

More information

14.02 Principles of Macroeconomics Problem Set 5 Fall 2005

14.02 Principles of Macroeconomics Problem Set 5 Fall 2005 40 Principls of Macroconomics Problm S 5 Fall 005 Posd: Wdnsday, Novmbr 6, 005 Du: Wdnsday, Novmbr 3, 005 Plas wri your nam AND your TA s nam on your problm s Thanks! Exrcis I Tru/Fals? Explain Dpnding

More information

Themes. Flexible exchange rates with inflation targeting. Expectations formation under flexible exchange rates

Themes. Flexible exchange rates with inflation targeting. Expectations formation under flexible exchange rates CHAPTER 25 THE OPEN ECONOMY WITH FLEXIBLE EXCHANGE RATES Thms Flxibl xchang ras wih inlaion arging Expcaions ormaion undr lxibl xchang ras Th AS-AD modl wih lxibl xchang ras Macroconomic adjusmn undr lxibl

More information

The Science of Monetary Policy

The Science of Monetary Policy Th Scinc of Monary Policy. Inroducion o Topics of Sminar. Rviw: IS-LM, AD-AS wih an applicaion o currn monary policy in Japan 3. Monary Policy Sragy: Inrs Ra Ruls and Inflaion Targing (Svnsson EER) 4.

More information

Lecture 1: Numerical Integration The Trapezoidal and Simpson s Rule

Lecture 1: Numerical Integration The Trapezoidal and Simpson s Rule Lcur : Numrical ngraion Th Trapzoidal and Simpson s Rul A problm Th probabiliy of a normally disribud (man µ and sandard dviaion σ ) vn occurring bwn h valus a and b is B A P( a x b) d () π whr a µ b -

More information

Microscopic Flow Characteristics Time Headway - Distribution

Microscopic Flow Characteristics Time Headway - Distribution CE57: Traffic Flow Thory Spring 20 Wk 2 Modling Hadway Disribuion Microscopic Flow Characrisics Tim Hadway - Disribuion Tim Hadway Dfiniion Tim Hadway vrsus Gap Ahmd Abdl-Rahim Civil Enginring Dparmn,

More information

On the Derivatives of Bessel and Modified Bessel Functions with Respect to the Order and the Argument

On the Derivatives of Bessel and Modified Bessel Functions with Respect to the Order and the Argument Inrnaional Rsarch Journal of Applid Basic Scincs 03 Aailabl onlin a wwwirjabscom ISSN 5-838X / Vol 4 (): 47-433 Scinc Eplorr Publicaions On h Driais of Bssl Modifid Bssl Funcions wih Rspc o h Ordr h Argumn

More information

THE SHORT-RUN AGGREGATE SUPPLY CURVE WITH A POSITIVE SLOPE. Based on EXPECTATIONS: Lecture. t t t t

THE SHORT-RUN AGGREGATE SUPPLY CURVE WITH A POSITIVE SLOPE. Based on EXPECTATIONS: Lecture. t t t t THE SHORT-RUN AGGREGATE SUL CURVE WITH A OSITIVE SLOE. Basd on EXECTATIONS: Lcur., 0. In Mankiw:, 0 Ths quaions sa ha oupu dvias from is naural ra whn h pric lvl dvias from h xpcd pric lvl. Th paramr a

More information

Irving Fisher Committee on Central Bank Statistics. IFC Working Papers. No 10. Consumer Inflation Expectations in Turkey.

Irving Fisher Committee on Central Bank Statistics. IFC Working Papers. No 10. Consumer Inflation Expectations in Turkey. Irving Fishr Commi on Cnral Bank Saisics IFC Working Pars No 0 Consumr Inflaion Excaions in Turky by Ec Oral May 203 IFC Working Pars ar wrin by h saff of mmbr insiuions of h Irving Fishr Commi on Cnral

More information

Applied Statistics and Probability for Engineers, 6 th edition October 17, 2016

Applied Statistics and Probability for Engineers, 6 th edition October 17, 2016 Applid Saisics and robabiliy for Enginrs, 6 h diion Ocobr 7, 6 CHATER Scion - -. a d. 679.. b. d. 88 c d d d. 987 d. 98 f d.. Thn, = ln. =. g d.. Thn, = ln.9 =.. -7. a., by symmry. b.. d...6. 7.. c...

More information

Midterm Examination (100 pts)

Midterm Examination (100 pts) Econ 509 Spring 2012 S.L. Parn Midrm Examinaion (100 ps) Par I. 30 poins 1. Dfin h Law of Diminishing Rurns (5 ps.) Incrasing on inpu, call i inpu x, holding all ohr inpus fixd, on vnuall runs ino h siuaion

More information

Mundell-Fleming I: Setup

Mundell-Fleming I: Setup Mundll-Flming I: Sup In ISLM, w had: E ( ) T I( i π G T C Y ) To his, w now add n xpors, which is a funcion of h xchang ra: ε E P* P ( T ) I( i π ) G T NX ( ) C Y Whr NX is assumd (Marshall Lrnr condiion)

More information

Chapter 17 Handout: Autocorrelation (Serial Correlation)

Chapter 17 Handout: Autocorrelation (Serial Correlation) Chapr 7 Handou: Auocorrlaion (Srial Corrlaion Prviw Rviw o Rgrssion Modl o Sandard Ordinary Las Squars Prmiss o Esimaion Procdurs Embddd wihin h Ordinary Las Squars (OLS Esimaion Procdur o Covarianc and

More information

Survey Expectations, Rationality and the Dynamics of Euro Area Inflation

Survey Expectations, Rationality and the Dynamics of Euro Area Inflation Survy Expcaions, Raionaliy and h Dynamics of Euro Ara Inflaion M. Forslls* and G. Knny Rvisd: Dcmbr 2005 Absrac This papr uss survy daa in ordr o analys and assss h mpirical propris of consumrs inflaion

More information

Contents. Abstract 4. Non-technical summary Introduction 7

Contents. Abstract 4. Non-technical summary Introduction 7 EUROPEAN CENTRAL BANK WORKING PAPER SERIES WORKING PAPER NO 163 THE RATIONALITY OF CONSUMERS INFLATION EXPECTATIONS: SURVEY-BASED EVIDENCE FOR THE EURO AREA BY M FORSELLS AND G KENNY Augus 2002 EUROPEAN

More information

A MATHEMATICAL MODEL FOR NATURAL COOLING OF A CUP OF TEA

A MATHEMATICAL MODEL FOR NATURAL COOLING OF A CUP OF TEA MTHEMTICL MODEL FOR NTURL COOLING OF CUP OF TE 1 Mrs.D.Kalpana, 2 Mr.S.Dhvarajan 1 Snior Lcurr, Dparmn of Chmisry, PSB Polychnic Collg, Chnnai, India. 2 ssisan Profssor, Dparmn of Mahmaics, Dr.M.G.R Educaional

More information

University of Kansas, Department of Economics Economics 911: Applied Macroeconomics. Problem Set 2: Multivariate Time Series Analysis

University of Kansas, Department of Economics Economics 911: Applied Macroeconomics. Problem Set 2: Multivariate Time Series Analysis Univrsiy of Kansas, Dparmn of Economics Economics 9: Applid Macroconomics Problm S : Mulivaria Tim Sris Analysis Unlss sad ohrwis, assum ha shocks (.g. g and µ) ar whi nois in h following qusions.. Considr

More information

CPSC 211 Data Structures & Implementations (c) Texas A&M University [ 259] B-Trees

CPSC 211 Data Structures & Implementations (c) Texas A&M University [ 259] B-Trees CPSC 211 Daa Srucurs & Implmnaions (c) Txas A&M Univrsiy [ 259] B-Trs Th AVL r and rd-black r allowd som variaion in h lnghs of h diffrn roo-o-laf pahs. An alrnaiv ida is o mak sur ha all roo-o-laf pahs

More information

Elementary Differential Equations and Boundary Value Problems

Elementary Differential Equations and Boundary Value Problems Elmnar Diffrnial Equaions and Boundar Valu Problms Boc. & DiPrima 9 h Ediion Chapr : Firs Ordr Diffrnial Equaions 00600 คณ ตศาสตร ว ศวกรรม สาขาว ชาว ศวกรรมคอมพ วเตอร ป การศ กษา /55 ผศ.ดร.อร ญญา ผศ.ดร.สมศ

More information

The Optimal Timing of Transition to New Environmental Technology in Economic Growth

The Optimal Timing of Transition to New Environmental Technology in Economic Growth h Opimal iming of ransiion o Nw Environmnal chnology in Economic Growh h IAEE Europan Confrnc 7- Spmbr, 29 Vinna, Ausria Akira AEDA and akiko NAGAYA yoo Univrsiy Background: Growh and h Environmn Naural

More information

Boyce/DiPrima 9 th ed, Ch 2.1: Linear Equations; Method of Integrating Factors

Boyce/DiPrima 9 th ed, Ch 2.1: Linear Equations; Method of Integrating Factors Boc/DiPrima 9 h d, Ch.: Linar Equaions; Mhod of Ingraing Facors Elmnar Diffrnial Equaions and Boundar Valu Problms, 9 h diion, b William E. Boc and Richard C. DiPrima, 009 b John Wil & Sons, Inc. A linar

More information

Midterm exam 2, April 7, 2009 (solutions)

Midterm exam 2, April 7, 2009 (solutions) Univrsiy of Pnnsylvania Dparmn of Mahmaics Mah 26 Honors Calculus II Spring Smsr 29 Prof Grassi, TA Ashr Aul Midrm xam 2, April 7, 29 (soluions) 1 Wri a basis for h spac of pairs (u, v) of smooh funcions

More information

The transition:transversion rate ratio vs. the T-ratio.

The transition:transversion rate ratio vs. the T-ratio. PhyloMah Lcur 8 by Dan Vandrpool March, 00 opics of Discussion ransiion:ransvrsion ra raio Kappa vs. ransiion:ransvrsion raio raio alculaing h xpcd numbr of subsiuions using marix algbra Why h nral im

More information

A Condition for Stability in an SIR Age Structured Disease Model with Decreasing Survival Rate

A Condition for Stability in an SIR Age Structured Disease Model with Decreasing Survival Rate A Condiion for abiliy in an I Ag rucurd Disas Modl wih Dcrasing urvival a A.K. upriana, Edy owono Dparmn of Mahmaics, Univrsias Padjadjaran, km Bandung-umng 45363, Indonsia fax: 6--7794696, mail: asupria@yahoo.com.au;

More information

Let s look again at the first order linear differential equation we are attempting to solve, in its standard form:

Let s look again at the first order linear differential equation we are attempting to solve, in its standard form: Th Ingraing Facor Mhod In h prvious xampls of simpl firs ordr ODEs, w found h soluions by algbraically spara h dpndn variabl- and h indpndn variabl- rms, and wri h wo sids of a givn quaion as drivaivs,

More information

An Indian Journal FULL PAPER. Trade Science Inc. A stage-structured model of a single-species with density-dependent and birth pulses ABSTRACT

An Indian Journal FULL PAPER. Trade Science Inc. A stage-structured model of a single-species with density-dependent and birth pulses ABSTRACT [Typ x] [Typ x] [Typ x] ISSN : 974-7435 Volum 1 Issu 24 BioTchnology 214 An Indian Journal FULL PAPE BTAIJ, 1(24), 214 [15197-1521] A sag-srucurd modl of a singl-spcis wih dnsiy-dpndn and birh pulss LI

More information

Measuring the NAIRU: Evidence from the European Union, USA and Japan

Measuring the NAIRU: Evidence from the European Union, USA and Japan Inrnaional Rsarch Journal of Financ and Economics ISSN 10- Issu 1 (00) EuroJournals Publishing, Inc. 00 hp://www.urojournals.com/financ.hm Masuring h : Evidnc from h Europan Union, USA and Japan Gorg Sphanids

More information

14.02 Principles of Macroeconomics Fall 2005 Quiz 3 Solutions

14.02 Principles of Macroeconomics Fall 2005 Quiz 3 Solutions 4.0 rincipl of Macroconomic Fall 005 Quiz 3 Soluion Shor Quion (30/00 poin la a whhr h following amn ar TRUE or FALSE wih a hor xplanaion (3 or 4 lin. Each quion coun 5/00 poin.. An incra in ax oday alway

More information

3(8 ) (8 x x ) 3x x (8 )

3(8 ) (8 x x ) 3x x (8 ) Scion - CHATER -. a d.. b. d.86 c d 8 d d.9997 f g 6. d. d. Thn, = ln. =. =.. d Thn, = ln.9 =.7 8 -. a d.6 6 6 6 6 8 8 8 b 9 d 6 6 6 8 c d.8 6 6 6 6 8 8 7 7 d 6 d.6 6 6 6 6 6 6 8 u u u u du.9 6 6 6 6 6

More information

DEPARTMENT OF ELECTRICAL &ELECTRONICS ENGINEERING SIGNALS AND SYSTEMS. Assoc. Prof. Dr. Burak Kelleci. Spring 2018

DEPARTMENT OF ELECTRICAL &ELECTRONICS ENGINEERING SIGNALS AND SYSTEMS. Assoc. Prof. Dr. Burak Kelleci. Spring 2018 DEPARTMENT OF ELECTRICAL &ELECTRONICS ENGINEERING SIGNALS AND SYSTEMS Aoc. Prof. Dr. Burak Kllci Spring 08 OUTLINE Th Laplac Tranform Rgion of convrgnc for Laplac ranform Invr Laplac ranform Gomric valuaion

More information

General Article Application of differential equation in L-R and C-R circuit analysis by classical method. Abstract

General Article Application of differential equation in L-R and C-R circuit analysis by classical method. Abstract Applicaion of Diffrnial... Gnral Aricl Applicaion of diffrnial uaion in - and C- circui analysis by classical mhod. ajndra Prasad gmi curr, Dparmn of Mahmaics, P.N. Campus, Pokhara Email: rajndraprasadrgmi@yahoo.com

More information

ERROR ANALYSIS A.J. Pintar and D. Caspary Department of Chemical Engineering Michigan Technological University Houghton, MI September, 2012

ERROR ANALYSIS A.J. Pintar and D. Caspary Department of Chemical Engineering Michigan Technological University Houghton, MI September, 2012 ERROR AALYSIS AJ Pinar and D Caspary Dparmn of Chmical Enginring Michigan Tchnological Univrsiy Houghon, MI 4993 Spmbr, 0 OVERVIEW Exprimnaion involvs h masurmn of raw daa in h laboraory or fild I is assumd

More information

Predicting Growth Components Unemployment, Housing Prices and Consumption Using Both Government and Corporate Yield Curves

Predicting Growth Components Unemployment, Housing Prices and Consumption Using Both Government and Corporate Yield Curves Inrnaional Journal of Economics and Financ; Vol. 10, No. 6; 2018 ISSN 1916-971X E-ISSN 1916-9728 Publishd by Canadian Cnr of Scinc and Educaion Prdicing Growh Componns Unmploymn, Housing Prics and Consumpion

More information

Discussion 06 Solutions

Discussion 06 Solutions STAT Discussion Soluions Spring 8. Th wigh of fish in La Paradis follows a normal disribuion wih man of 8. lbs and sandard dviaion of. lbs. a) Wha proporion of fish ar bwn 9 lbs and lbs? æ 9-8. - 8. P

More information

CSE 245: Computer Aided Circuit Simulation and Verification

CSE 245: Computer Aided Circuit Simulation and Verification CSE 45: Compur Aidd Circui Simulaion and Vrificaion Fall 4, Sp 8 Lcur : Dynamic Linar Sysm Oulin Tim Domain Analysis Sa Equaions RLC Nwork Analysis by Taylor Expansion Impuls Rspons in im domain Frquncy

More information

7.4 QUANTUM MECHANICAL TREATMENT OF FLUCTUATIONS *

7.4 QUANTUM MECHANICAL TREATMENT OF FLUCTUATIONS * Andri Tokmakoff, MIT Dparmn of Chmisry, 5/19/5 7-11 7.4 QUANTUM MECANICAL TREATMENT OF FLUCTUATIONS * Inroducion and Prviw Now h origin of frquncy flucuaions is inracions of our molcul (or mor approprialy

More information

UNSTEADY FLOW OF A FLUID PARTICLE SUSPENSION BETWEEN TWO PARALLEL PLATES SUDDENLY SET IN MOTION WITH SAME SPEED

UNSTEADY FLOW OF A FLUID PARTICLE SUSPENSION BETWEEN TWO PARALLEL PLATES SUDDENLY SET IN MOTION WITH SAME SPEED 006-0 Asian Rsarch Publishing work (ARP). All righs rsrvd. USTEADY FLOW OF A FLUID PARTICLE SUSPESIO BETWEE TWO PARALLEL PLATES SUDDELY SET I MOTIO WITH SAME SPEED M. suniha, B. Shankr and G. Shanha 3

More information

A THREE COMPARTMENT MATHEMATICAL MODEL OF LIVER

A THREE COMPARTMENT MATHEMATICAL MODEL OF LIVER A THREE COPARTENT ATHEATICAL ODEL OF LIVER V. An N. Ch. Paabhi Ramacharyulu Faculy of ahmaics, R D collgs, Hanamonda, Warangal, India Dparmn of ahmaics, Naional Insiu of Tchnology, Warangal, India E-ail:

More information

Solutions to End-of-Chapter Problems for Chapters 26 & 27 in Textbook

Solutions to End-of-Chapter Problems for Chapters 26 & 27 in Textbook Soluions o End-of-Chapr Problms for Chaprs 26 & 27 in Txbook Chapr 26. Answrs o hs Tru/Fals/Uncrain can b found in h wrin x of Chapr 26. I is lf o h sudn o drmin h soluions. 2. For his qusion kp in mind

More information

5. An object moving along an x-coordinate axis with its scale measured in meters has a velocity of 6t

5. An object moving along an x-coordinate axis with its scale measured in meters has a velocity of 6t AP CALCULUS FINAL UNIT WORKSHEETS ACCELERATION, VELOCTIY AND POSITION In problms -, drmin h posiion funcion, (), from h givn informaion.. v (), () = 5. v ()5, () = b g. a (), v() =, () = -. a (), v() =

More information

Chapter 3: Fourier Representation of Signals and LTI Systems. Chih-Wei Liu

Chapter 3: Fourier Representation of Signals and LTI Systems. Chih-Wei Liu Chapr 3: Fourir Rprsnaion of Signals and LTI Sysms Chih-Wi Liu Oulin Inroducion Complx Sinusoids and Frquncy Rspons Fourir Rprsnaions for Four Classs of Signals Discr-im Priodic Signals Fourir Sris Coninuous-im

More information

Available online at ScienceDirect

Available online at   ScienceDirect Availabl onlin a www.scincdirc.com ScincDirc Procdia Economics and Financ 8 ( 204 ) 67 677 s Inrnaional Confrnc 'Economic Scinific Rsarch - Thorical, Empirical and Pracical Approachs', ESPERA 203 Th accuracy

More information

2.1. Differential Equations and Solutions #3, 4, 17, 20, 24, 35

2.1. Differential Equations and Solutions #3, 4, 17, 20, 24, 35 MATH 5 PS # Summr 00.. Diffrnial Equaions and Soluions PS.# Show ha ()C #, 4, 7, 0, 4, 5 ( / ) is a gnral soluion of h diffrnial quaion. Us a compur or calculaor o skch h soluions for h givn valus of h

More information

Chapter 9 Review Questions

Chapter 9 Review Questions Chapr 9 Rviw Qusions. Using h - modl, show ha if marks clar and agns hav raional xpcaions hn mporary shocks canno hav prsisn ffcs on oupu. If marks clar and agns hav raional xpcaions hn mporary produciviy

More information

Voltage v(z) ~ E(z)D. We can actually get to this wave behavior by using circuit theory, w/o going into details of the EM fields!

Voltage v(z) ~ E(z)D. We can actually get to this wave behavior by using circuit theory, w/o going into details of the EM fields! Considr a pair of wirs idal wirs ngh >, say, infinily long olag along a cabl can vary! D olag v( E(D W can acually g o his wav bhavior by using circui hory, w/o going ino dails of h EM filds! Thr

More information

Real time estimation of traffic flow and travel time Based on time series analysis

Real time estimation of traffic flow and travel time Based on time series analysis TNK084 Traffic Thory sris Vol.4, numbr.1 May 008 Ral im simaion of raffic flow and ravl im Basd on im sris analysis Wi Bao Absrac In his papr, h auhor sudy h raffic parn and im sris. Afr ha, a im sris

More information

H is equal to the surface current J S

H is equal to the surface current J S Chapr 6 Rflcion and Transmission of Wavs 6.1 Boundary Condiions A h boundary of wo diffrn mdium, lcromagnic fild hav o saisfy physical condiion, which is drmind by Maxwll s quaion. This is h boundary condiion

More information

B) 25y e. 5. Find the second partial f. 6. Find the second partials (including the mixed partials) of

B) 25y e. 5. Find the second partial f. 6. Find the second partials (including the mixed partials) of Sampl Final 00 1. Suppos z = (, y), ( a, b ) = 0, y ( a, b ) = 0, ( a, b ) = 1, ( a, b ) = 1, and y ( a, b ) =. Thn (a, b) is h s is inconclusiv a saddl poin a rlaiv minimum a rlaiv maimum. * (Classiy

More information

Control System Engineering (EE301T) Assignment: 2

Control System Engineering (EE301T) Assignment: 2 Conrol Sysm Enginring (EE0T) Assignmn: PART-A (Tim Domain Analysis: Transin Rspons Analysis). Oain h rspons of a uniy fdack sysm whos opn-loop ransfr funcion is (s) s ( s 4) for a uni sp inpu and also

More information

Lecture 2: Current in RC circuit D.K.Pandey

Lecture 2: Current in RC circuit D.K.Pandey Lcur 2: urrn in circui harging of apacior hrough Rsisr L us considr a capacior of capacianc is conncd o a D sourc of.m.f. E hrough a rsisr of rsisanc R and a ky K in sris. Whn h ky K is swichd on, h charging

More information

Copyright(c) Shoko Nakano 2007 All Rights Reserved. FORWARD DISCOUNT BIAS: IS IT A RISK PREMIUM ON CRUDE OIL? August 10, 2007

Copyright(c) Shoko Nakano 2007 All Rights Reserved. FORWARD DISCOUNT BIAS: IS IT A RISK PREMIUM ON CRUDE OIL? August 10, 2007 Copyrigh(c) Shoo Naano 2007 All Righs Rsrvd. FORWARD DISCOUNT BIAS: IS IT A RISK PREMIUM ON CRUDE OIL? Augus 10, 2007 SHOKO NAKANO Gradua School of Economics, Hiosubashi Univrsiy, 2-1 Naa, Kuniachi, Toyo

More information

On the Speed of Heat Wave. Mihály Makai

On the Speed of Heat Wave. Mihály Makai On h Spd of Ha Wa Mihály Maai maai@ra.bm.hu Conns Formulaion of h problm: infini spd? Local hrmal qulibrium (LTE hypohsis Balanc quaion Phnomnological balanc Spd of ha wa Applicaion in plasma ranspor 1.

More information

Foreign Exchange Reserves and Inflation: An Empirical Study of Five East Asian Economies

Foreign Exchange Reserves and Inflation: An Empirical Study of Five East Asian Economies Th Empirical Economics Lrs, 8(5): (May 009) ISSN 68 8997 Forign Exchang Rsrvs and Inlaion: An Empirical Sudy o Fiv Eas Asian Economis Mi-Yin Lin * Dparmn o Economics, Shih Hsin Univrsiy, Taiwan Ju-Shyan

More information

Monetary Policy and Exchange Rate Overshooting in Iran

Monetary Policy and Exchange Rate Overshooting in Iran Inrnaional Economic Sudis Vol. 44, No. 1, Spring & Summr 2014 pp. 67-74 Rcivd: 15-10-2013 Accpd: 12-05-2014 Monary Policy and Exchang Ra Ovrshooing in Iran Hosin Sharifi-Rnani * Dparmn of Economics, Khorasgan

More information

CHAPTER CHAPTER15. Financial Markets and Expectations. Prepared by: Fernando Quijano and Yvonn Quijano

CHAPTER CHAPTER15. Financial Markets and Expectations. Prepared by: Fernando Quijano and Yvonn Quijano Financial Marks and Prpard by: Frnando Quijano and Yvonn Quijano CHAPTER CHAPTER15 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard Bond Prics and Bond Yilds Figur 15-1 U.S. Yild Curvs:

More information

Charging of capacitor through inductor and resistor

Charging of capacitor through inductor and resistor cur 4&: R circui harging of capacior hrough inducor and rsisor us considr a capacior of capacianc is conncd o a D sourc of.m.f. E hrough a rsisr of rsisanc R, an inducor of inducanc and a y K in sris.

More information

British Journal of Economics, Finance and Management Sciences 64 October 2011, Vol. 2 (1)

British Journal of Economics, Finance and Management Sciences 64 October 2011, Vol. 2 (1) riish Journal of conomics, Financ and Managmn Scincs 64 Ocobr 2011, ol. 2 (1 An mpirical valuaion of Using h Rsidual Incom Modl for rdicion of Sock ric Mhdi Sarikhani Dparmn of Accouning, Safashahr ranch,

More information

Phys463.nb Conductivity. Another equivalent definition of the Fermi velocity is

Phys463.nb Conductivity. Another equivalent definition of the Fermi velocity is 39 Anohr quival dfiniion of h Fri vlociy is pf vf (6.4) If h rgy is a quadraic funcion of k H k L, hs wo dfiniions ar idical. If is NOT a quadraic funcion of k (which could happ as will b discussd in h

More information

Transfer function and the Laplace transformation

Transfer function and the Laplace transformation Lab No PH-35 Porland Sa Univriy A. La Roa Tranfr funcion and h Laplac ranformaion. INTRODUTION. THE LAPLAE TRANSFORMATION L 3. TRANSFER FUNTIONS 4. ELETRIAL SYSTEMS Analyi of h hr baic paiv lmn R, and

More information

Routing in Delay Tolerant Networks

Routing in Delay Tolerant Networks Rouing in Dlay Tolran Nworks Primary Rfrnc: S. Jain K. Fall and R. Para Rouing in a Dlay Tolran Nwork SIGCOMM 04 Aug. 30-Sp. 3 2004 Porland Orgon USA Sudn lcur by: Soshan Bali (748214) mail : sbali@ic.ku.du

More information

Decomposing G7 Business Cycle

Decomposing G7 Business Cycle Dcomposing G7 Businss Cycl Sungjin Cho Jangryoul Kim In his papr, w hav simad a modl ha incorporas wo ky faurs of businss cycls, co-movmn among conomic variabls and swiching bwn rgims of xpansion and rcssion,

More information

Wave Equation (2 Week)

Wave Equation (2 Week) Rfrnc Wav quaion ( Wk 6.5 Tim-armonic filds 7. Ovrviw 7. Plan Wavs in Losslss Mdia 7.3 Plan Wavs in Loss Mdia 7.5 Flow of lcromagnic Powr and h Poning Vcor 7.6 Normal Incidnc of Plan Wavs a Plan Boundaris

More information

Testing the Real Interest Parity Hypothesis in Six Developed Countries

Testing the Real Interest Parity Hypothesis in Six Developed Countries Tsing h Ral Inrs Pariy Hypohsis in Six Dvlopd Counris Auhor Shi, Jami, Li, Bin, Alxiadis, Sam Publishd Journal Til Inrnaional Rsarch Journal of Financ and Economics Copyrigh Samn EuroJournals Publishing,

More information

Methodology for Analyzing State Tax Policy By Orphe Pierre Divounguy, PhD, Revised by Andrew J. Kidd, PhD (May 2018)

Methodology for Analyzing State Tax Policy By Orphe Pierre Divounguy, PhD, Revised by Andrew J. Kidd, PhD (May 2018) Mhodology for Analyzing Sa Tax Policy By Orph Pirr Divounguy, PhD, Rvisd by Andrw J. Kidd, PhD (May 2018) Inroducion To analyz how changs o ax policy impacs no only govrnmn rvnus bu also conomic aciviy

More information

3.9 Carbon Contamination & Fractionation

3.9 Carbon Contamination & Fractionation 3.9 arbon onaminaion & Fracionaion Bcaus h raio / in a sampl dcrass wih incrasing ag - du o h coninuous dcay of - a small addd impuriy of modrn naural carbon causs a disproporionaly larg shif in ag. (

More information

Lecture 1: Growth and decay of current in RL circuit. Growth of current in LR Circuit. D.K.Pandey

Lecture 1: Growth and decay of current in RL circuit. Growth of current in LR Circuit. D.K.Pandey cur : Growh and dcay of currn in circui Growh of currn in Circui us considr an inducor of slf inducanc is conncd o a DC sourc of.m.f. E hrough a rsisr of rsisanc and a ky K in sris. Whn h ky K is swichd

More information

Logistic equation of Human population growth (generalization to the case of reactive environment).

Logistic equation of Human population growth (generalization to the case of reactive environment). Logisic quaion of Human populaion growh gnralizaion o h cas of raciv nvironmn. Srg V. Ershkov Insiu for Tim aur Exploraions M.V. Lomonosov's Moscow Sa Univrsi Lninski gor - Moscow 999 ussia -mail: srgj-rshkov@andx.ru

More information

Investigating Neutrality and Lack of Neutrality of Money in Iranian Economy

Investigating Neutrality and Lack of Neutrality of Money in Iranian Economy AENSI Journals Advancs in Environmnal Biology Journal hom pag: hp://www.ansiwb.com/ab.hml Invsigaing Nuraliy and Lack of Nuraliy of Mony in Iranian Economy Abolghasm Esnaashari Amiri Dparmn of Economics,

More information

MEM 355 Performance Enhancement of Dynamical Systems A First Control Problem - Cruise Control

MEM 355 Performance Enhancement of Dynamical Systems A First Control Problem - Cruise Control MEM 355 Prformanc Enhancmn of Dynamical Sysms A Firs Conrol Problm - Cruis Conrol Harry G. Kwany Darmn of Mchanical Enginring & Mchanics Drxl Univrsiy Cruis Conrol ( ) mv = F mg sinθ cv v +.2v= u 9.8θ

More information

Taylor Principle Supplements the Fisher Effect: Empirical Investigation under the US Context

Taylor Principle Supplements the Fisher Effect: Empirical Investigation under the US Context Taylor Principl Supplmns h Fishr Effc: Empirical Invsigaion undr h US Conx Mohammd Saiful ISLAM Mohammad Hasma ALI 2 ABSTRACT This papr rviws h shor- and long-run dynamics of inrs ra and inflaion of h

More information

Modeling Inflation Expectations: The Case of Iran

Modeling Inflation Expectations: The Case of Iran Modling Inflaion Expcaions: Th Cas of Iran Dissraion zur Erlangung ds Grads Dokor dr Wirschafswissnschaf (Dr. rr. pol.) dr Jurisischn und Wirschafswissnschaflichn Fakulä dr Marin-Luhr-Univrsiä Hall-Winbrg

More information

Estimation of Metal Recovery Using Exponential Distribution

Estimation of Metal Recovery Using Exponential Distribution Inrnaional rd Journal o Sinii sarh in Enginring (IJSE).irjsr.om Volum 1 Issu 1 ǁ D. 216 ǁ PP. 7-11 Esimaion o Mal ovry Using Exponnial Disribuion Hüsyin Ankara Dparmn o Mining Enginring, Eskishir Osmangazi

More information

Chapter 12 Introduction To The Laplace Transform

Chapter 12 Introduction To The Laplace Transform Chapr Inroducion To Th aplac Tranorm Diniion o h aplac Tranorm - Th Sp & Impul uncion aplac Tranorm o pciic uncion 5 Opraional Tranorm Applying h aplac Tranorm 7 Invr Tranorm o Raional uncion 8 Pol and

More information

Journal of Applied Science and Agriculture

Journal of Applied Science and Agriculture Journal of Applid Scinc and Agriculur, 93 March 2014, Pags: 1066-1070 AENS Journals Journal of Applid Scinc and Agriculur SSN 1816-9112 Journal hom pag: www.ansiwb.com/jasa/indx.hml h Opimal ax Ra in Middl

More information

Section. Problem Representation. Substation. Protection Device. protection equipments. Substation. Client. EPDS divided in blocks connected by

Section. Problem Representation. Substation. Protection Device. protection equipments. Substation. Client. EPDS divided in blocks connected by HIERARCHICAL MULTIPLE CRITERIA OPTIMIZATION OF MAINTENANCE ACTIVITIES ON POWER DISTRIBUTION NETWORKS Problm Rprsaion EPDS comprising: Subsaions, primary nworks, scondary, nworks; Fdrs (cabls, lins, pols,

More information

Decomposing the relationship between international bond markets

Decomposing the relationship between international bond markets Dcomposing h rlaionship bwn inrnaional bond marks Andrw Clar and Ilias Lkkos 1 1. Inroducion Th corrlaions bwn major ass classs ar of concrn and inrs o monary auhoriis and financial rgulaors alik h ponial

More information

The Contemporaneous Correlation of Structural Shocks and Inflation-Output Variability in Pakistan

The Contemporaneous Correlation of Structural Shocks and Inflation-Output Variability in Pakistan Th Pakisan Dvlopmn Rviw 50: (Summr 011) pp. 145 16 Th Conmporanous Corrlaion of Srucural Shocks and Inflaion-Oupu Variabiliy in Pakisan MUHAMMAD NASIR AND WASIM SHAHID MALIK * Monary policy has changd

More information

EXCHANGE RATE REGIME AND HOUSEHOLD S CHOICE OF DEBT

EXCHANGE RATE REGIME AND HOUSEHOLD S CHOICE OF DEBT EXCHANGE RATE REGIME AND HOUSEHOLD S CHOICE OF DEBT Summary This papr looks a h impac of h xchang ra rgim and h houshold s choic of db. On of h characrisics of conomic ransiion in asrn Europan counris

More information

The data: Unemployment, CPI inflation, and CPI inflation expectations (Prospera)

The data: Unemployment, CPI inflation, and CPI inflation expectations (Prospera) Th Possibl Unmploymn Cos of Avrag Inflaion blow a Crdibl Targ Lars E.O. Svnsson Sockholm School of Economics www.larsosvnsson.n Ocobr, Th daa: Unmploymn, CPI inflaion, and CPI inflaion xpcaions (Prospra)

More information

Impulsive Differential Equations. by using the Euler Method

Impulsive Differential Equations. by using the Euler Method Applid Mahmaical Scincs Vol. 4 1 no. 65 19 - Impulsiv Diffrnial Equaions by using h Eulr Mhod Nor Shamsidah B Amir Hamzah 1 Musafa bin Mama J. Kaviumar L Siaw Chong 4 and Noor ani B Ahmad 5 1 5 Dparmn

More information

A Simple Procedure to Calculate the Control Limit of Z Chart

A Simple Procedure to Calculate the Control Limit of Z Chart Inrnaional Journal of Saisics and Applicaions 214, 4(6): 276-282 DOI: 1.5923/j.saisics.21446.4 A Simpl Procdur o Calcula h Conrol Limi of Z Char R. C. Loni 1, N. A. S. Sampaio 2, J. W. J. Silva 2,3,*,

More information

Ratio-Product Type Exponential Estimator For Estimating Finite Population Mean Using Information On Auxiliary Attribute

Ratio-Product Type Exponential Estimator For Estimating Finite Population Mean Using Information On Auxiliary Attribute Raio-Produc T Exonnial Esimaor For Esimaing Fini Poulaion Man Using Informaion On Auxiliar Aribu Rajsh Singh, Pankaj hauhan, and Nirmala Sawan, School of Saisics, DAVV, Indor (M.P., India (rsinghsa@ahoo.com

More information

Final Exam : Solutions

Final Exam : Solutions Comp : Algorihm and Daa Srucur Final Exam : Soluion. Rcuriv Algorihm. (a) To bgin ind h mdian o {x, x,... x n }. Sinc vry numbr xcp on in h inrval [0, n] appar xacly onc in h li, w hav ha h mdian mu b

More information

Demand Shocks, Credibility and Macroeconomic Dynamics

Demand Shocks, Credibility and Macroeconomic Dynamics Dmand Shocks, Crdibiliy and Macroconomic Dynamics José García-Solans* and Carmn Marín-Marínz** Univrsidad d Murcia Jun 2013 Absrac: In his papr w build and simula an opn macroconomic modl o invsiga h dynamic

More information

Decline Curves. Exponential decline (constant fractional decline) Harmonic decline, and Hyperbolic decline.

Decline Curves. Exponential decline (constant fractional decline) Harmonic decline, and Hyperbolic decline. Dlin Curvs Dlin Curvs ha lo flow ra vs. im ar h mos ommon ools for forasing roduion and monioring wll rforman in h fild. Ths urvs uikly show by grahi mans whih wlls or filds ar roduing as xd or undr roduing.

More information

Poisson process Markov process

Poisson process Markov process E2200 Quuing hory and lraffic 2nd lcur oion proc Markov proc Vikoria Fodor KTH Laboraory for Communicaion nwork, School of Elcrical Enginring 1 Cour oulin Sochaic proc bhind quuing hory L2-L3 oion proc

More information

An Analysis of the Jonsei and Purchase Prices in the Korean Housing Market

An Analysis of the Jonsei and Purchase Prices in the Korean Housing Market Modrn Economy, 205, 6, 8-89 ublishd Onlin January 205 in SciRs. hp://www.scirp.org/journal/m hp://dx.doi.org/0.4236/m.205.6007 An Analysis of h Jonsi and urchas rics in h Koran Housing Mark Giyoung Lim

More information

fiziks Institute for NET/JRF, GATE, IIT JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES MATEMATICAL PHYSICS SOLUTIONS are

fiziks Institute for NET/JRF, GATE, IIT JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES MATEMATICAL PHYSICS SOLUTIONS are MTEMTICL PHYSICS SOLUTIONS GTE- Q. Considr an ani-symmric nsor P ij wih indics i and j running from o 5. Th numbr of indpndn componns of h nsor is 9 6 ns: Soluion: Th numbr of indpndn componns of h nsor

More information

Smoking Tobacco Experiencing with Induced Death

Smoking Tobacco Experiencing with Induced Death Europan Journal of Biological Scincs 9 (1): 52-57, 2017 ISSN 2079-2085 IDOSI Publicaions, 2017 DOI: 10.5829/idosi.jbs.2017.52.57 Smoking Tobacco Exprincing wih Inducd Dah Gachw Abiy Salilw Dparmn of Mahmaics,

More information

EXERCISE - 01 CHECK YOUR GRASP

EXERCISE - 01 CHECK YOUR GRASP DIFFERENTIAL EQUATION EXERCISE - CHECK YOUR GRASP 7. m hn D() m m, D () m m. hn givn D () m m D D D + m m m m m m + m m m m + ( m ) (m ) (m ) (m + ) m,, Hnc numbr of valus of mn will b. n ( ) + c sinc

More information