Sources of Inflaion Uncerain and Real Economic Acivi Jh-Lin Wu Deparmen of Economics Naional Chung Cheng Universi Chia-Yi 6, Taiwan and Show-Lin Chen Deparmen of Economics Fu-jen Caholic Universi Taipei 4, Taiwan and Hsiu-Yun Lee Deparmen of Economics Naional Chung Cheng Universi Chia-Yi 6, Taiwan Absrac This paper examines he effecs of inflaion uncerainies on real GDP. We argue ha differen sources of inflaion uncerain have differen impacs on real GDP. The empirical evidence poins ou ha uncerain arising from changing regression coefficiens has negaive impacs on real GDP. However, he effec of uncerain due o heeroscedasici in disurbances on real GDP is insignifican. Moreover, we find ha he surve-based measure of inflaion uncerain appears o be more associaed wih he uncerain ha arises from changing regression coefficiens. Corresponding auhor. Email address: ecdjlw@ccunix.ccu.edu.w.
. Inroducion In his Nobel Prize lecure, Milon Friedman (977) poins ou he poenial for increased inflaion o creae nominal uncerain ha hinders he efficien allocaion of resources and reduces real oupu. Ever since hen, here have been several heoreical and empirical discussions on he relaionship beween inflaion and inflaion uncerain (Ball, 99; Cukierman and Melzer, 986; Evans, 99 and Evans and Wachel, 993; Davis and Kanago, 000). In addiion, here are also several aricles ha empiricall examine he impacs of inflaion uncerain on real economic acivi, which can be caegorized ino wo differen approaches ha differ in heir prox for inflaion uncerain. The firs one is he surve-based approach, in which inflaion uncerain is proxied b he variabili across he individual forecass. In oher words, he sandard deviaion of inflaion forecass is used o measure inflaion uncerain. The inflaion uncerain obained from surve daa ends o negaivel correlae wih real economic aciviies (Hafer, 986 and Davis and Kanago, 996). The alernaive approach measures uncerain b esimaing he ime-varing condiional variance of a variable s unpredicable innovaion. In his approach he auoregressive condiional heeroscedasici (ARCH) model provided b Engle (98) or he generalized ARCH (GARCH) model provided b Bollerslev (986) is applied o esimae a ime-varing condiional residual variance. Based on an ARCH model, Coulson and Robins (985) find ha uncerain is posiivel correlaed wih real economic acivi, bu heir correlaion relaionship is no significan. Appling a sae-dependen condiional heeroscedasici model provided b Brunner and Hess (993), Lee and Ni (995) find ha inflaion uncerain is negaivel correlaed wih real economic aciviies. Adoping a bivariae GARCH model, Grier and Perr
(000) find ha inflaion uncerain significanl lowers real oupu growh. ARCH- or GARCH-pe models provide esimaes of how he condiional variance of inflaion varies over ime wihin a given srucure and herefore he ignore he possibili of srucural changes caused b changing regimes. Evans (99) poins ou ha here are man aspecs o inflaion uncerain and applies a ime-varing parameer model wih an ARCH specificaion for he shocks o inflaion in order o measure differen pes of uncerain. Evans and Wachel (993) accoun for he prospecs of changing inflaion regimes b appling a Markov-swiching model. The find ha uncerain abou he inflaion process conribues significanl o he overall degree of inflaion uncerain as measured b he condiional variance of fuure inflaion. Furhermore, he show ha heir measure of inflaion uncerain has a significan influence on unemplomen based on a vecor auoregressive esimaion. According o he previous discussion, we find ha here are wo pes of uncerain wihin a regression conex. These uncerainies arise due o heeroscedasici in he disurbance erms and he unknown or changing regression coefficiens, respecivel. However, he previousl-menioned lieraure fail o consider ha inflaion uncerain from differen sources ma have differen effecs on economic agens decision-making and hus on economic acivi. Mos of he previousl-menioned lieraures appl a convenional wo-sep approach in analzing he impacs of uncerainies on real economic acivi, excep for he paper b Grier and Perr (000). Pagan (984) criicizes he inappropriaeness of he wo-sep approach b showing ha he esimaes or sandard errors from he second sep are biased. The purpose of his paper is wo-fold. Firs, we examine he effecs of differen
3 sources of inflaion uncerain on real economic acivi measured b real GDP. Kim (993) firs applies a ime-varing parameer model wih Markov-swiching heeroscedasici o measure monear growh uncerain ha arises from heeroscedasici in disurbances and from changing regression coefficiens, respecivel. We herefore appl Kim s (993) model o calculae differen sources of inflaion uncerain and hen examine heir impacs on real GDP. To avoid Pagan s criicism of his approach, we joinl esimae he oupu equaion and he inflaion equaion wih he maximum likelihood esimaion mehod. Second, we examine he informaion conen embeded in he surve-based measure of inflaion uncerain b comparing he dnamic paern of he surve-based measure wih ha of model-based measures. Findings from our empirical invesigaion indicae ha uncerain due o changing regression coefficiens has a negaive impac on real GDP, bu he impac of uncerain arising from heeroscedasici in disurbances is negligible. Moreover, we discover ha he surve-based measure of inflaion uncerain appears more closel associaed wih he uncerain ha arises from changing regression coefficiens han wih he uncerain arising from heeroscedasici in disurbances. The remainder of he paper is organized as follows. Secion describes he inflaion s ime series model, in which parameers are ime varing and he condiional variance of disurbances is Markov-swiching. We hen discuss our measure of inflaion uncerainies based on he presened model. Secion 3 begins b discussing he daa before presening he model esimaes. The effecs of differen pes of inflaion uncerain on real GDP are hen examined empiricall. We hen decompose he oal inflaion uncerain ino wo differen sources of inflaion uncerain, and hen examine heir conribuion o oal uncerain. In addiion, we
4 also examine he linkage beween a surve-based measure of inflaion uncerain wih he model-based measures. Finall, conclusions are summarized in he las secion.. Measuring Inflaion Uncerainies There are wo differen pes of uncerain in convenional regression analsis. Over ime, i is highl likel ha changes in privae secor behavior, economic polic, and/or insiuions induce significan variaions in he srucure of he inflaion process. Under he assumpion of raional expecaion, i is no reasonable o assume ha coefficiens in inflaion regression are ime invarian since he econom s srucure ma change over ime. Economic agens will learn abou he polic regime changes and respond accordingl if here are frequen polic shifs (Lucas, 976). Talor (980) poins ou ha he dnamics of inflaion depend on he naure of wage conracs and he form of monear polic rules. Therefore, ime-varing coefficiens in an inflaion equaion is one source of inflaion uncerain. Second, mos exising lieraure esimae inflaion uncerain b assuming ha uncerain is due o shocks o he inflaion process, and hence he measure inflaion uncerain b using he condiional variance of inflaion. An ARCH specificaion on disurbances fails o ake ino accoun he influence on uncerain of possible fuure regime changes. Therefore, he second source of inflaion uncerain is measured b he condiional variance of inflaion ha will be affeced b he possibili of swiches in he inflaion process. To decompose he inflaion uncerain ino wo disinc sources menioned previousl, we appl a ime-varing-parameer model wih Markov-swiching heeroscedasici o describe he inflaion process:
5,,, T 0 X k i i, i ~ N(0, h ), h 0 ( 0 )S, () ~ iidn(0, ), (), wih Pr[S Pr[S S 0S ] p 0] p ; 00 ; Pr[S Pr[S 0S S ] p 0] p, 00, (3) where X (... ) is a (k+) vecor of explanaor variables; k is a (k+) vecor of ime-varing regression coefficiens; is a posiive definie marix; and h is he condiional variance of. The sae ( S ) is given b he wo-sae, firs-order Markov process wih he ransiion probabiliies described in (3). The ransiion probabili b sae i. p ii represens he probabili ha sae i will be followed Equaion () is he measuremen equaion, which describes he relaionship beween he unobserved sae and a T vecor of measuremen. Equaion () is he ransiion equaion, which describes he evoluion of coefficien. A random walk specificaion is used for he ime-varing coefficiens following he specificaion of Kim and Nelson (989) and Kim (993). Markov-swiching heeroscedasici is refleced b he equaion of h, which saes ha he uncondiional variance iself is subjec o shifs (srucural changes). B considering Markov-swiching heeroscedasici, he change in uncondiional variance is acuall regarded as resuling from endogenous regime changes in he variance srucure. However, if 0, hen he model degeneraes o he convenional ime-varing parameer model. Equaions () and () are easil recognized as sae-space models,
6 which can be recursivel esimaed b he Kalman filer. A deailed discussion of he esimaion mehod can be found in Kim (993) and hence is no described here. The wo uncerain erms of differen sources can be calculaed from he forecas error s condiional variance in equaion () as: where U ~ U ~ U ~, U ~ V ~ ' U ~ X X, (5) 0 ( 0 ) Pr[S ], (6) V ~ i Pr[S i ]{V ( ~ i )( ~ i )'}. (7) - i0 (4) Here, ~ i i Pr[S i ; is he esimae of based on ] i0 S i V informaion up o ime -, given i ; is he covariance marix of i and is he informaion available a ime. Terms U ~ and U ~ are he condiional variances due o changing regression coefficiens and he heeroscedisici of he disurbance erms, respecivel. 3. Inflaion Uncerainies and Real Economic Acivi: An Empirical Invesigaion The purpose of his secion is o empiricall examine he effecs of differen pes of uncerain on real GDP. 3. Daa Descripion Quarerl daa of real GDP and he consumer price index (CPI) for he Unied Saes (US) are obained from IMF s Inernaional Financial Saisics. Inflaion raes are compued from he CPI. The sample period sars from 957Q and ends in 000Q3. The one-quarer forecass of he GDP deflaor and CPI inflaion rae are
7 obained from he Surve of Professional Forecasers published b he Federal Reserve Bank of Philadelphia. The forecass of he GDP deflaor sar from he las quarer of 968, while he forecass of CPI inflaion raes begin from he hird quarer of 98. 3. Model Esimaion We follow Hamilon (989) and Kim (993) b assuming ha real GDP is composed of wo unobserved componens. The firs componen follows a random walk wih drif, which evolves according o a wo-sae Markov process, and he second componen follows an auoregressive process. Therefore, he specificaion for real GDP is given as follows: C, (8) s U ~ U ~, (9) C ~ C C 3, ~ iidn(0, ), (0) S, S 0,, () s Pr Pr 0 S S q and PrS 0 S q, S 0 S 0 q and PrS S 0 q, 00 where is he log of real GDP a ime ; and are he rend and cclical C 00 () componens of real GDP, respecivel; s is he drif erm, which changes according ~ o a wo-sae Markov process; and is he condiional forecas error of inflaion. If Friedman s argumen is correc, hen we expec ha and/or be negaive. in (9) should I is worh noing ha Equaion (0) is derived b using a Phillips curve which relaes cclical unemplomen o he forecas error of inflaion and Okun's law ha relaes cclical oupu o cclical unemplomen. A Phillips curve presened in is
8 empirical forma is: u u n p n ~ l (u l u l ) 0, 0 0, (3) l in which is he unemplomen rae, u is is naural rae, and u n is a seriall- uncorrelaed error erm. Noe ha 0 measures he rade-off beween he unemplomen gap and inflaion surprise. Okun's law relaion, on he oher hand, is n (u u ), 0. (4) Equaion (0) is obained b combining (3) and (4) ogeher. Thus, 3 0 in equaion (0) should be posiive. In oher words, he rade-off beween inflaion raes and unemplomen raes is suppored if 3 is significanl posiive. Equaions ()-(3) and (8)-() can be esimaed b a convenional wo-sep mehod. As such, we can esimae U ~ and U ~ from ()-(3) in he firs sep and hen use hem o esimae parameers of (9) and (0) in he second sep. However, as we saed before, Pagan (984) poins ou ha we ma ge biased parameer esimaes or biased sandard errors from he second sep esimaion procedure. To avoid Pagan s criique, we herefore esimae he inflaion equaion and he oupu equaion joinl b emploing a maximum likelihood esimaion mehod. The lag order of inflaion equaion () needs o be deermined, and i is seleced b choosing he maximum value of he log likelihood funcion from he join esimaion. The lag order in he inflaion equaion () is hen se o 3. To jusif he model in equaions ()-(3) and (8)-(), i would seem appropriae o show ha he esimaed disurbances from equaion () b he ordinar leas square (OLS) mehod are seriall correlaed and condiionall heeroscedasic. We herefore esimae () b OLS and hen examine he serial correlaion of residuals and squared
9 residuals b using he Q saisic of Ljung and Box (978). We also appl he ARCH es provided b Engle (98) o examine he null hpohesis of no auoregressive condiional heeroscedasici in he esimaed residuals. Findings from Table indicae no significan serial correlaion since he Q-saisics are no significan a he 5% level for he residuals from OLS. However, he Q-saisics are significan a he % level for he squared residuals. The ARCH es also rejecs he null of no ARCH effecs in he residuals. Table furher repors he diagnosic checks for residuals from a convenional ime-varing-parameer model. Again, Q-saisics are insignifican for sandardized residuals, bu significan a he % level for squared residuals. The ARCH es reveals a significan ARCH effec a he 5% level in he esimaed residuals. Therefore, findings from Table impl ha some of he dnamics of condiional variance are no full capured b a consan parameer model or a convenional ime-varing parameer model. To ake ino accoun he heeroscedasici in disurbances, we assume ha he condiional variance of disurbances is Markov-swiching. The join esimaions of he generalized model in equaions ()-(3) and (8)-() are repored in Table, which indicaes ha boh pes of uncerain have a negaive impac on real GDP. Uncerain arising from changing parameers has significanl negaive impacs on real GDP, bu he effec of uncerain from heeroscedasici in disurbances is negligible. Therefore, he hpohesis ha uncerain due o changing coefficiens discourages economic acivi is srongl suppored. 3.3 Robusness of he empirical esimaes The period saring from 970 in general has higher average inflaion uncerain han he period of pre-970. To check he robusness of our finding, we re-examine he effecs of inflaion uncerain on real GDP growh based on he
0 period 970Q 000Q3. The specificaion of he inflaion equaion over he sub-sample period is similar o ha over he full sample period. Findings from he las column of Table indicae ha he effec of uncerain arising from changing parameers is significan a he 0% level, bu he size of he esimae is /4h of ha in he whole period. Again, he impac of he uncerain from heeroscedasici of disurbances is insignifican a convenional levels. The rade-off beween inflaion raes and unemplomen raes is suppored since he esimaed coefficien of posiive. 3 is The previous wo findings are he same as hose in he whole period s esimaion. As for he diagnosic ess, here is no serial correlaion in he residuals and squared residuals, and no ARCH effec in he residuals. Overall, our finding ha uncerain arising from changing parameers has a negaive impac on real GDP is suppored, and his finding is robus for differen sample periods. We also find ha uncerain due o heeroscedasici in disurbances is negligible in affecing real GDP, and ha here is a rade-off beween inflaion and unemplomen raes. These wo findings are robus o he sample periods. One ma argue ha our finding of a significan negaive impac of he regime uncerain componen of inflaion uncerain ma be due o our failure of conrolling oil price shocks. Following Hamilon (996), we herefore include nominal oil price changes and ne oil price changes in equaion (0), respecivel, and hen re-esimae he model simulaneousl. Empirical findings indicae ha he impac of oil price changes on real oupu is no significan a he convenional significance level. Alhough our findings from Table are no significanl affeced when we include eiher nominal oil price changes or ne oil price changes, he residual diagnosic checks reveal he exisence of ARCH effecs in esimaed residuals.
(resuls are no repored here, bu are available upon reques). Therefore, his indicaes ha our findings from Table are no due o our failure of conrolling oil price shocks. 3.4 Decomposiion of Inflaion Uncerain Equaion (4) indicaes ha he condiional variance of disurbances consiss of wo disinc erms. The are he condiional variance arising from changing regression coefficiens and he condiional variance due o he heeroscedasici of he disurbance erms. These wo differen sources of uncerain can be calculaed based on equaion (5) and (6), respecivel. The plo of he oal uncerain, U ~, and he decomposed uncerain, U ~ and U ~, based on (5) and (6), respecivel, is given in Figure. From Figure we observe ha he overall inflaion uncerain is higher during he periods of 973 975, 978-983, and 985-99 han in oher periods, which reflecs basicall wo oil price shocks ha occurred in 973 and 979, financial deregulaion saring from 979, he swiching of he Fed s monear polic arge in 98, and he Plaza accord in 985. We also observe ha uncerain due o changing regression coefficiens is in general higher han ha arising from he heeroscedasici of disurbances during he period of 974-983. The average level of inflaion uncerain during he period of 974-983 is 0.46, approximael 58% of which is due o he uncerain arising from changing regression coefficiens. However, he average level of inflaion uncerain is 0.5 during he sample period of 984-000, approximael 65% of which is due o he heeroscedasici of residuals. Convenional lieraure consruc inflaion uncerain from surve forecass, in which he sandard deviaion of inflaion forecass is used o measure inflaion
uncerain. Based on his approach, Hafer (986) and Davis and Kanago (996) suppor Friedman s hpohesis. I is herefore quie ineresing o examine he dnamic paerns of our esimaed inflaion uncerain wih ha from a surve measure b ploing hem ogeher. Firs of all, we consruc he surve-based measure of inflaion uncerain from he GDP deflaor and CPI inflaion rae, respecivel. According o Figure, we find ha he size of he model-based measure of oal inflaion uncerain is in general higher han (wih several excepions) ha of surve-based measures, bu he flucuaion of he laer is much larger han ha of he former. The swiching of he Fed s monear polic arge in 98, he Plaza Accord in 985, and Iraq s invasion of Kuwai in 990 are he periods wih high uncerain according o he CPI surve-based measure of inflaion uncerain. 3 The wo oil price shocks in he 970s, he onse of he Iran-Iraq war in 980, he swiching of he Fed s monear polic arge in 98, and he Iraq s invasion of Kuwai in 990 are he periods wih high inflaion uncerain according o he surve-based measure from he GDP deflaor. The previousl-menioned periods wih high inflaion uncerain are also consisen wih hose from he model based measure of oal inflaion uncerain. In Figure 3, we compare he surve-based measure of inflaion uncerain from he GDP deflaor wih differen sources of model-based measures. We find ha he movemen of he surve-based measure of inflaion uncerain is more associaed wih he uncerain arising from changing regression coefficiens. The correlaion coefficien beween he surve-based measure of inflaion uncerain and he measure of uncerain arising from changing regression coefficiens is 0.45. This is higher han he correlaion coefficien beween he surve-based measure of inflaion uncerain and he uncerain arising from he heeroscedasici of
3 disurbances which is 0.33. Figure 4 plos he model-based measure of inflaion uncerain and he surve-based measure from he forecas of he CPI inflaion rae. Again, we find ha he surve-based measure of inflaion uncerain is more associaed wih ha arising from changing regression coefficiens. The correlaion coefficien beween he surve-based measure of inflaion uncerain and he uncerain arising from changing regression coefficiens is 0.69. This is higher han he correlaion coefficien beween he surve-based measure of inflaion uncerain and he uncerain arising from he heeroscedasici of disurbances which is 0.559. Findings from Figures o 4 are ineresing since he indicae ha he surve-based measure of inflaion uncerain is more associaed wih he uncerain from changing regression coefficiens which can be characerized b a model wih ime-varing-parameers in coefficiens and Markov-swiching in disurbances. 4. Conclusions Inflaion uncerain is convenionall measured as he condiional variance of inflaion in mos exising lieraure. The effecs of inflaion uncerain on real economic acivi are hen examined b he convenional wo-sep approach. In his paper we appl a ime-varing-parameer model wih Markov-Swiching variance o measure wo differen pes of uncerain. The effecs of uncerainies on real GDP are hen examined b a join esimaion of he maximum likelihood. Empiricall, our join esimaion mehod sideseps Pagan s criique on he convenional wo-sep approach. The empirical findings poin ou ha uncerain due o changing regression coefficiens has a significan influence on real GDP, bu he effecs of uncerain arising from heeroscedasici of disurbances are negligible. Moreover,
4 we also find ha he surve-based measure of inflaion uncerain appears more associaed wih he uncerain arising from changing regression coefficiens.
5 Endnoes d The surve-based inflaion uncerain is given b γ [ (π π) ]/n, where i π i is he forecas of he ih forecaser and π is he average forecas across n forecasers. The series of ne oil price increases is he difference beween he level of oil prices for quarer and he maximum price observed during he preceding four quarers, if his difference is posiive. Oherwise, he series of ne oil prices is defined o be zero. 3 The daa for he surve forecass of he CPI inflaion rae sar from he hird quarer of 98, and hence heir uncerain is available from he same ime.
6 Table. Diagnosic Checks of Residuals CPM TVPM Q().883 [0.46] 3.85 [0.3] Q(4) 8.76 [0.5] 30.57 [0.8] Q () 4.3 [0.00] 38.606 [0.00] Q (4) 63.43 [0.00] 56.075 [0.00] ARCH() 0.998 [0.3].39 [0.4] ARCH(4) 3.79 [0.0].758 [0.00] Noes:. CPM and TVPM indicae he consan parameer model and he ime-varing parameer model, respecivel. The CPM is esimaed b he ordinar leas square mehod and he TVPM is esimaed b a Kalman filer.. Numbers in brackes are p-values. 3. Terms Q(p) and Q (p) are he Ljung-Box auocorrelaion es saisiics for residuals and residuals squared, respecivel, for up o ph-order auocorrelaions, which have a chi-square disribuion wih p degrees of freedom. ARCH(q) is he Lagrange muliplier es of Engle (99) for up o qh-order auoregressive condiional heeroscedasici, which has a chi-square disribuion wih q degrees of freedom.
7 Table. Join Esimaion Resuls wih Oupu and Inflaion Equaions C, s U ~ U ~ C ~, C C 3, ~ iidn(0, ), s 0 S, PrS 0 S 0 q 00, PrS S q, Pr S S 0 q 00, PrS 0 S q. 57Q~000Q3 70Q~000Q3-6.070* -.5# (.7) (0.84) -.09 -.739 (.960) (.39).037*.46* (0.04) (0.085) -0.096-0.47* (0.0) (0.084) 0. 543* 0.437* 3 (0.46) (0.45) 0.608* 0.638* (0.050) (0.045).596* 3.43* 0 (0.35) (0.45) -.409* -.47* (0.4) (0.43) q 0.97* 0.970* 00 (0.04) (0.07) q 0.57* 0.37* (0.7) (0.8) Q() 0.774 [0.548] 0.90 [0.537] Q(4) 3.936 [0.05].70 [0.537 ] Q () 0.647 [0.559] 9.97 [0.63] Q (4) 5.69 [0.39] 7.580 [0.83] ARCH() 0.880 [0.97] 0.305 [0.58] ARCH(4) 0.054 [0.87] 4.070 [0.400] Noe:. The oupu equaion is esimaed using 00 imes he log-difference in quarerl real GDP. Sandard errors are in parenhesis and numbers in he brackes are p-values.. * and # indicae significance a he 5% and 0% level, respecivel. 3. Terms Q(p) and Q (p) are he Ljung-Box auocorrelaion es saisiics for residuals and residuals squared, respecivel, for up o ph-order auocorrelaions, which have a chi-square disribuion wih p degrees of freedom. ARCH(q) is he Lagrange muliplier es of Engle (99) for up o qh-order auoregressive condiional heeroscedasici, which has a chi-square disribuion wih q degrees of freedom.
8.4..0 0.8 0.6 0.4 0. 0.0 59 6 63 65 67 69 7 73 75 77 79 8 83 85 87 89 9 93 95 97 99 TOT MKV TVP Figure. Model-based Measures of Inflaion Uncerain. TOT: model-based oal uncerain. MKV: uncerain arising from heeroscedasici of disurbances. TVP: uncerain arising from changing regression coefficiens..4..0 0.8 0.6 0.4 0. 0.0 59 6 63 65 67 69 7 73 75 77 79 8 83 85 87 89 9 93 95 97 99 TOT SVY(GDP) SVY(CPI) Figure. Model-based vs. Surve-based Measures of Inflaion Uncerain. TOT: model-based oal uncerain. SVY(GDP): surve-based measure of inflaion uncerain from a GDP deflaor. SVY(CPI): surve-based measure of inflaion uncerain from CPI inflaion raes.
9.4..0 0.8 0.6 0.4 0. 0.0 59 6 63 65 67 69 7 73 75 77 79 8 83 85 87 89 9 93 95 97 99 SVY(GDP) MKV TVP Figure 3. Surve-based vs. Model-based Measures of Inflaion Uncerain wih a GDP deflaor in he Surve. SVY(GDP): surve-based measure of inflaion uncerain from GDP deflaor. MKV: uncerain arising from heeroscedasici of disurbances. TVP: uncerain arising from changing regression coefficiens..4..0 0.8 0.6 0.4 0. 0.0 59 6 63 65 67 69 7 73 75 77 79 8 83 85 87 89 9 93 95 97 99 SVY(CPI) MKV TVP Figure 4. Model-based vs. Surve-based Inflaion Uncerain wih CPI Inflaion Rae in he Surve. SVY(CPI): surve-based measure of inflaion uncerain from CPI inflaion raes. MKV: uncerain arising from heeroscedasici of disurbances. TVP: uncerain arising from changing regression coefficiens.
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