The Dynamic Inflationary Effects of Permanent and Transitory Energy Price Shocks

Transcription

1 The Dynamic Inflaionary Effecs of Permanen and Transiory Energy Price Shocks By Rober J. Myers, Sanley R. Johnson, Michael Helmar and Harry Baumes * Augus 4, 2015 Absrac: We provide new economeric evidence on he inflaionary effecs of energy price shocks. A novel aspec of our approach is ha we use a permanen-ransiory (P-T) decomposiion o separae shocks ino permanen effecs due o long-run changes in underlying economic fundamenals, versus ransiory effecs ha represen only shor-run emporary disurbances o long-run equilibrium relaionships. We find ha he P-T decomposiion provides some ineresing new insighs ino he inflaionary effecs of energy price shocks. In paricular, only permanen shocks are inflaionary while ransiory shocks have very lile effec on he CPI or PPI. We explain his phenomenon in erms of he follow hrough effec of energy price shocks on oher prices. If energy price changes are perceived as permanen hen oher consumer and producer prices respond which leads o permanen changes in he underlying price indexes. Bu if a shock is perceived o be ransiory oher consumer and producer prices do no respond and here is lile impac on he underlying price indexes. Keywords: energy prices, inflaion, permanen-ransiory decomposiion JEL Codes: Q02, Q11, O13 * Respecively, Universiy Disinguished Professor, Michigan Sae Universiy, Eas Lansing MI 48824; Board Chair, Naional Cener for Food and Agriculural Policy, Washingon, DC 20036; Research Scienis, Universiy of Nevada, Reno, Reno Nevada 89557; and Direcor, Office of Energy Policy and New Uses/Office of he Chief Economis/USDA, Washingon DC Research suppored by USDA Cooperaive Agreemen.

2 The Dynamic Inflaionary Effecs of Permanen and Transiory Energy Price Shocks 1. Inroducion Energy prices have an imporan dynamic relaionship wih inflaion for wo main reasons. Firs, energy price changes affec consumer and producer price indexes direcly because energy prices have a significan weigh in he consrucion of broader price indexes. Second, in addiion o his direc relaionship here is also an indirec effec as energy price changes feed hrough ino changes in oher prices ha make up he indexes. Boh of hese pahways may be dynamic as fuure prices of many differen goods and services each respond o curren and pas energy price changes, and energy prices may respond o curren and pas changes in price indexes. Therefore, i can be difficul disenangle he rue dynamic relaionship beween energy price changes and curren and fuure changes in aggregae price indexes, such as he consumer price index (CPI) and producer price index (PPI). The naure of he relaionship beween energy prices and general measures of inflaion is imporan because i characerizes he inflaionary effecs of energy price shocks, as well as he effec ha inflaion in he general price level can have on energy prices. Since managing inflaion is an imporan macroeconomic policy goal, knowledge of he relaionship beween energy prices and he CPI and PPI can inform sraegies for responding o he inflaionary effecs of energy price shocks. An undersanding of he role of energy price shocks may also be used o forecas he effecs ha paricular ypes of shocks, such as hose brough abou by an expansion of U.S. biofuel producion, or he expansion and conracion of U.S. shale oil producion, will have on movemens in he general price level. The mos common heoreical explanaion for a posiive relaionship beween energy prices and inflaion is a classic supply-side effec. Rising energy prices indicae an increase in energy 1

3 scarciy and, because energy is a basic inpu ino producion, aggregae oupu falls puing upward pressure on he general price level. Early empirical sudies found srong evidence of a negaive relaionship beween energy prices and oupu growh (see Hamilon, 1983 for a seminal conribuion and summary of earlier lieraure; and Brown and Yücel 2002 for a more recen summary and review). More recenly, aenion has urned o invesigaing he relaionship beween energy prices and inflaion more direcly, in mos cases finding srong evidence of a significan posiive relaionship (e.g., Hooker, 2002; Cunadoa, and Perez de Gracia, 2005; Ewing and Thompson, 2007 and Cologni and Manera, 2008). Asymmeries in he dynamic relaionship beween energy prices and economic aciviy have also been invesigaed, wih some evidence suggesing ha he inensiy of he relaionship has declined over ime (e.g., Lardic and Mignon, 2008). In his paper we provide new economeric evidence on he inflaionary effecs of energy price shocks. A novel aspec of our approach is ha we use a permanen-ransiory (P-T) decomposiion o separae shocks ino permanen effecs due o long-run changes in underlying economic fundamenals, versus ransiory effecs ha represen only shor-run emporary disurbances o long-run equilibrium relaionships. We find ha he P-T decomposiion provides some ineresing new insighs ino he inflaionary effecs of energy price shocks. In paricular, only permanen shocks are inflaionary while ransiory shocks have very lile effec on he CPI or PPI. We explain his phenomenon in erms of he follow hrough effec of energy price shocks on oher prices. If energy price changes are perceived as permanen hen oher consumer and producer prices respond which leads o permanen changes in he underlying price indexes. Bu if a shock is perceived o be ransiory oher consumer and producer prices do no respond and here is lile impac on he underlying price indexes. Therefore, disinguishing beween permanen and 2

4 ransiory shocks has imporan implicaions for how we perceive and undersand he inflaionary effecs of energy price changes. 2. Empirical Approach A price index I (e.g., he CPI) will depend on he m prices ha make up he index, which we represen generally as: (1) I f P,P,..., P ). ( 1 2 m The indexes are calculaed based on weighed changes in he underlying prices from a base period in which he index is normalized o The prices included in he calculaion are based on a represenaive baske of he underlying consumer or producer goods and services. To consruc he change in he index, price changes for componen goods and services are weighed according o heir imporance (expendiure or cos share) for he underlying represenaive populaion. 2 Energy prices ypically play a prominen role in boh CPI and PPI consrucion because hey have significan expendiure and cos share weighs in he underlying represenaive baske of goods and services. Because of he way he indexes are consruced, he funcional relaionship represened in (1) will depend implicily on price levels in he base year as well as he expendiure weighs used o consruc he index. I is imporan o remember, however, ha because CPI and PPI indexes are consruced using price changes of specific producs, here is no way o direcly ascerain he 1 A deailed mehodological descripion is available in he Bureau of Labor Saisics Handbook of Mehods, a hp:// 2 For he CPI underlying prices are colleced each monh in 87 urban areas across he U.S. from abou 4,000 housing unis and approximaely 26,000 reail esablishmens-deparmen sores, supermarkes, hospials, filling saions, and oher ypes of sores and service esablishmens. For he PPI price daa are provided by firms on a volunary basis. The Bureau of Labor Saisics srongly encourages cooperaing companies o supply acual ransacion prices a he ime of shipmen o minimize he use of lis prices. Prices submied by survey respondens are effecive on he Tuesday of he week conaining he 13h day of he monh. 3

5 impac of a paricular price change (say for energy producs) on he prices of oher goods or services ha make up he index. Furhermore, expendiure and coss weighs are recalculaed annually making i difficul o isolae he effecs of energy price changes direcly from he formula used o calculae he index. Given hese problems we ake a reduced form ime series approach o invesigaing he dynamic relaionship beween energy price changes and changes in he general price level. The dimensionaliy of m in he index formulas (1) is usually large making full dynamic analysis involving he index and all of he relevan prices impracical. The approach we ake is o consider a reduced dimension log-linear approximae relaionship beween he index and a subse of prices: 3 n 1 j 1 (2) ln I 0 j ln Pj e where e is a random error and n is considerably smaller han m. Because here are many relevan prices missing from (2) we inerpre he relaionship a reduced form whose ' s encompass he indirec effec of changes in he P j ' s on all of he oher prices no included in he reduced dimension sysem. Similarly, since e will include he random effecs of missing prices all of he variables in (2) should be reaed as endogenous. For economeric modeling each of he variables in (2) could be inegraed of order zero, denoed I(0), or inegraed of order one, denoed I(1). However, previous sudies and he evidence presened below sugges ha boh he indexes and prices we include in our analysis can be modeled as I(1). In his case i follows ha here could be coinegraing (i.e., long-run equilibrium) relaionships among he variables in he reduced dimension sysem (2). If all variables are I(1) a 3 Log ransformaions are commonly used in price modeling because hey are consisen wih he saisical properies of mos price daa and faciliae inerpreaion of coefficiens in erms of proporional relaionships beween prices. 4

6 maximum of n-1 coinegraing relaionships are possible among he n variables in he sysem (n-1 log prices plus he log index). Because he sysem is reduced dimension i is also possible ha (2) iself is no a coinegraing relaionship, in which case he error erm e would be I(1). To complee he sysem we add equaions for each of he log prices included in (2). In specifying hese equaions we wan o allow for he possibiliy of long-run coinegraing relaionships among variables in he sysem, as well as for rich dynamics in he ineracions beween he prices and he index. A convenien way of accomplishing hese goals is o represen he sysem as a vecor error correcion (VEC) model. In marix form he VEC models he n-vecor y ln P,ln P,...,ln P,ln I ) as: ( 1 2 n 1, q 1 i ε i 1 (3) y μ α z Γi y where z 1 β' y 1 is he (r x 1) vecor of lagged equilibrium errors from he r coinegraing relaionships; β conains he coinegraing vecors represening long-run equilibrium relaionships beween he variables; he μ, α, and Γi' s are unknown parameers o be esimaed, q is he lag order for he dynamics; and he VEC errors ε are serially uncorrelaed bu may be conemporaneously correlaed. The advanages of he VEC represenaion for our applicaion are ha i is sraighforward o esimae using Johansen s maximum likelihood mehods, i reas all variables as endogenous, i allows for I(1) and coinegraed variables, and i also allows for rich dynamics in he way ha he prices and he index inerac wih one anoher over ime. The VEC errors ε represen unpredicable shocks o he variables in he sysem bu analyzing and inerpreing he effecs of hese shocks is hampered because hey are conemporaneously correlaed and represen he join effecs of many differen fundamenal influences on he prices and price index. To provide a srucural inerpreaion of he effecs of 5

7 differen shocks we need o impose addiional idenificaion assumpions. The convenional way of solving his problem is o orhogonalize he shocks and impose a recursive ordering, leaving he dynamics of he sysem unresriced. This approach o idenificaion in VEC models is now sandard and will no be discussed furher here (see, for example, Hamilon 1994). A disadvanage of he convenional recursive approach o idenificaion for our purposes is ha i produces orhogonalized srucural shocks ha remain mixures of permanen and ransiory effecs. I is herefore incapable of decomposing shocks ino hose ha have permanen effecs and hose ha have ransiory effecs, and herefore incapable of idenifying separae long-run and shor-run dynamic relaionships beween he prices and he index. To overcome his problem we follow Gonzalo and Ng (2001) and impose an alernaive idenificaion scheme ha decomposes ε ino orhogonal permanen and ransiory shocks. The dynamic effecs of he resuling permanen and ransiory shocks can hen be simulaed o evaluae he effecs of boh ypes of shocks on he pah of prices and he index. To moivae he alernaive idenificaion approach consider he marix G ' [ α, β] where ' α (defined by α α 0 ) is he orhogonal complemen of he speed of adjusmen parameers α ' from he VEC; and using G gives: ' β is he marix of coinegraing vecors. Transforming he VEC model (3) (4) G y Gμ Gα z 1 G Γi y i Gε. q i 1 By consrucion, he firs n r rows of G eliminae he lagged equilibrium errors z 1 from he firs n r equaions, causing hese equaions o be specified in erms of differences only. Also by consrucion, he remaining r rows of G form I(0) linear combinaions of he 6 y vecor a all lags which causes he remaining r equaions o depend on saionary linear combinaions only. The

8 resul is ha he ransformed errors u Gε form a P-T decomposiion wih he firs n - r rows being permanen shocks and he remaining r rows being ransiory shocks. We can inerpre he permanen shocks as unpredicable shocks o he n r fundamenal common facors (or common rends ) driving he long-run equilibrium values of variables in a coinegraed sysem (see Sock and Wason, 1988; Gonzalo and Granger, 1995; Proiei, 1997; and Hecq, Palm, and Urbain, 2000). The ransiory shocks can be inerpreed as emporary deviaions from he r long-run equilibrium relaionships ha correc hemselves over ime (i.e., shocks o he equilibrium errors z ). To faciliae analyzing he effecs of shocks we wrie he VEC model (4) explicily in erms of he permanen and ransiory shocks: 1 (5) y μ α z 1 Γi y i G u. q i 1 In principle we could use (5) o race ou he dynamic effecs of permanen and ransiory shocks o he sysem. However, his ask is complicaed by he fac ha alhough he elemens of u is a P-T decomposiion u will generally be conemporaneously correlaed. Gonzalo and Ng (2001) sugges solving his problem by imposing a recursive ordering on he permanen and ransiory shocks. To accomplish his consider a marix H such ha u Hv where v is a vecor of orhogonal srucural permanen and ransiory shocks wih uni variance. Coinegraion requires ha H be lower block riangular (ransiory shocks canno conemporaneously influence permanen shocks, oherwise hey would no be ransiory; see Gonzalo and Ng, 2001). If we furher impose a recursive ordering among he permanen shocks (permanen componens of permanen 7 v only influence u shocks ordered equal or lower in he sysem) and a recursive ordering among he ransiory shocks (ransiory componens of v only influence ransiory u shocks ordered equal

9 or lower in he sysem), hen H is lower riangular and saisfies HH ) ' ' Cov( u ) G Cov( ε G. The marix H can be esimaed by compuing he Cholesky decomposiion of G Cov G and Cov( ε ) are esimaed using he VEC model (3). given by: ' ( ε ) G where The complee P-T decomposiion defined on orhogonalized shocks wih uni variance is 1 (6) y μ α z 1 Γi y i G Hv q i 1 where, as before, z 1 β' y 1. All componens of his model can be esimaed from he VEC esimaion form (3). Afer esimaion, (6) can hen be used o simulae he dynamic effecs of he differen permanen and ransiory shocks on each of he y variables. Resuls can be displayed as impulse response funcions (IRFs). For some purposes i will also be useful o decompose he forecas error variance of he y variables ino componens due o permanen versus ransiory shocks (FEVD). By consrucion, he firs n r elemens of v will be orhogonal permanen shocks and he las r elemens will be orhogonal ransiory shocks. IRF and FEVD resuls may be sensiive o he ordering of shocks wihin each caegory (permanen and ransiory), bu he applicaion can ofen provide guidelines on wha ordering makes sense (essenially a jusidenifying assumpion). In he applicaion below we show how a paricular recursive ordering can be inerpreed in erms of srucural permanen and ransiory shocks. I is also imporan o noe ha orhogonalizaion of he permanen and ransiory shocks via Cholesky decomposiion does no preclude cerain shocks from influencing some variables in y conemporaneously (unlike in convenional recursive VECs). This is because in convenional Cholesky decomposiion 1 G is an ideniy marix bu under he P-T decomposiion his marix can ransmi orhogonal permanen and ransiory shocks conemporaneously o all variables in he 8

10 sysem. In his sense he P-T recursive srucure is no as rigid as he convenional recursive srucure ypically applied in srucural VEC analysis. 3. Variables and Daa In his paper we consider several rivariae VEC models, each including wo energy prices and one index. The wo energy prices are he price of gasoline and he price of ehanol. Gasoline is included because i is arguably he mos imporan energy price in he deerminaion of boh consumer and producer prices, and because i is highly correlaed wih oher imporan energy prices, such as he price of crude oil and diesel. Ehanol is included because one of he goals of his sudy is o invesigae he effecs of permanen and ransiory shocks o ehanol prices, such as hose ha may be associaed wih expansion of he role of biofuels in he U.S. economy. The applicaion is o U.S. daa. Three differen price indexes are sudied wih separae rivariae models esimaed for each index. 4 The firs index is opline CPI which is he mos inclusive measure of he general level of consumer prices. The second index is he energy CPI which is invesigaed o see if resuls differ when he price index is more direcly dependen on he gasoline and ehanol prices included in he analysis. The hird and final index used is he opline PPI which is invesigaed o see if resuls differ markedly for producer price indexes versus consumer price indexes. We also invesigaed models using he energy componen of he PPI bu resuls are similar o hose using he energy componen of he CPI and so are no repored here. Furhermore, we invesigaed models using CPI and PPI excluding energy bu resuls were virually idenical o hose for opline CPI and PPI 4 Higher dimensional models wih muliple indices (and addiional energy prices) included could have been invesigaed bu he high correlaion beween indices, and beween many energy prices, makes esimaion and inerpreaion of higher order models more difficul. We find useful insighs can be obained even when limiing ourselves o rivariae models. 9

11 and so are no repored here eiher. All models are esimaed using monhly daa from January 1990 o June Gasoline prices are regular gasoline spo price, FOB New York Harbor $/gallon. Ehanol prices are he average ehanol rack price, FOB Omaha, Nebraska in $/gallon. Boh prices are ploed monhly in Figure 1. There is clearly a close connecion beween he wo prices suggesing a long-run equilibrium relaionship exiss beween hem. However, gasoline prices appear o have risen relaive o ehanol prices over ime, paricularly since Topline CPI is he U.S. ciy average CPI for all iems wih = 100 and he energy CPI is he U.S. ciy average CPI for all energy prices, again wih = 100. Year over year monhly changes in each of hese indexes are ploed monhly in Figure 2. For compleeness we also show year over year changes in he CPI for all iems less energy. The CPI for all iems less energy follows opline CPI closely and P-T decomposiion resuls are very similar using eiher of hese indexes. Therefore only P-T decomposiion resuls for opline CPI are repored here. As expeced, he energy CPI is much more volaile han opline CPI. Topline PPI is he PPI for all indusrial commodiy iems wih 1982 = 100. Year over year monhly changes are ploed in Figure 3. For compleeness we also include year over year changes in he energy PPI (PPI for fuels and relaed producs and power, 1982=100) and he PPI for all iems less energy (PPI, for all indusrial commodiies less fuels, 1982=100). Topline PPI is clearly more volaile han opline CPI because producer goods depend relaively more on maerial goods in he supply chain which end o vary more han consumer good prices. The PPI for all iems less energy follows opline PPI closely and P-T decomposiion resuls are very similar using eiher index, so only resuls for opline PPI are repored here. The energy PPI is much more variable han opline PPI, as expeced. However, P-T decomposiion resuls using he energy PPI were very similar o hose using he energy CPI as he price index, so only he laer resuls are repored here. 10

12 All of he variables included in he analysis were ransformed using logarihms and esed for uni roos using he augmened Dickey-Fuller, Phillips-Perron, and Dickey-Fuller GLS es wih rend. Resuls are repored in Table 1 and provide suppor for he hypohesis ha all series are I(1), possibly wih drif. These findings are consisen wih considerable exising evidence. We also esed for coinegraion among variables in each of he rivariae models esimaed using Johansen race ess. Resuls are repored in Table 2 and suppor wo coinegraing relaionships (one single common facor is driving he permanen componen of all series) in each model. Hence, VECs wih wo coinegraing vecors are esimaed for each rivariae model. 4. Resuls for Energy Prices and he CPI We begin wih a rivariae model ha includes gasoline price (PGAS), ehanol price (PETH), and opline CPI (CPI). Lag lengh selecion crieria (FPE and AIC) suppor wo lagged differences in he VEC (i.e., q = 2) and a join LM es for no auocorrelaion in he residuals of he 2 lag model canno be rejeced (p-value = agains firs order auocorrelaion and agains second order auocorrelaion). Full VEC resuls are of lile inrinsic ineres by hemselves and so are no repored. However, resuls for he wo coinegraing vecors ( β marix) esimaed using Johansen s maximum likelihood mehod are: (7a) (7b) ln( CPI ) ln( PGAS (9. 91) ln( PETH ) ln( PGAS ) (17.32) ) where numbers in parenheses are consisen -saisics. Two coinegraing vecors imply a single I(1) common facor, so here is a single permanen shock driving he long run equilibrium values of all hree series. We inerpre his facor as a common economic fundamenal ha drives 11

13 permanen changes in energy prices and he CPI. When a shock o he common facor increases long-run equilibrium (permanen) gasoline price by 1% he coinegraion resuls sugges a corresponding long-run equilibrium CPI increase of 0.23% and a long-run equilibrium ehanol price increase of 0.49%. Hence, a permanen 1% increase in gasoline prices will evenually be associaed wih permanen increases in boh ehanol prices and he CPI, alhough he proporional CPI (ehanol price) increase is only abou one quarer (one half) of he proporional gasoline price increase. This long-run CPI change is much higher han would be suggesed by simply looking a he expendiure weigh on gasoline price in he CPI, which for was around 5% (i.e., would sugges a 1% gasoline price increase would be associaed wih jus a.05% increase in he CPI, holding oher prices consan). The difference is because he VEC model allows oher prices (and fuure gasoline prices) o respond dynamically o any curren gasoline price shocks (i.e., is a long-run relaionship ha allows oher prices o change and respond). Because here are wo coinegraing vecors and one permanen shock here are wo ransiory shocks, one represening shocks o he firs long-run equilibrium relaionship (7a) beween gasoline price and he CPI and one represening shocks o he second long-run equilibrium relaionship (7b) beween gasoline and ehanol prices. I will be shown below ha neiher ransiory shock influences he CPI significanly so a ransiory shock o he firs long-run equilibrium relaionship (7a) is anamoun o a ransiory gasoline price shock. Because he gasoline marke is much larger han and dominaes he ehanol marke, we order his ransiory gasoline price shock firs in he recursive order. Therefore, ransiory gasoline price shocks are allowed o spill over conemporaneously ino he ehanol marke. This leaves he orhogonal shock o he ehanol-gasoline price relaionship (7b) ordered second, which excludes i from conemporaneously influencing he gasoline price-cpi relaionship. This provides a naural inerpreaion for he second ransiory shock as an ehanol price shock. 12

14 We used hese idenificaion assumpions, along wih esimaes from he VEC, o compue IRFs for each of he hree shocks by simulaing he decomposiion (6) saring from an iniial poin of long-run equilibrium. The sysem is hen perurbed wih a one-ime change o one of he orhogonal shocks and he resuling dynamic ime pah for all variables is compued. Then he simulaion is repeaed sequenially for each of he orhogonal permanen and ransiory shocks. Graphs of he resuling IRFs are provided in Figures 4-6. The size of he permanen shock (Figure 4) is normalized so ha i evenually increases gasoline price by 1% (see he convergence poin for he gasoline price response in he figure). To be consisen wih he coinegraion esimaion resuls he long-run effec on ehanol price and he CPI should hen be a 0.49% and 0.23% increase, which is eviden in he figure (see he respecive convergence poins for ehanol price and he CPI). Noice, however, ha he dynamic response paern of energy prices o he permanen shock is quie differen o ha of he CPI. The iniial energy price responses overshoo heir long-run equilibrium value and hen converge slowly back o i. In conras, he CPI adjuss almos immediaely o is new long-run equilibrium value and hen says here. Hence, he inflaionary impac of a permanen shock is almos immediae. The effec of he ransiory gasoline price shock (Figure 5) is normalized so he immediae conemporaneous impac of he shock is o increase gasoline price by 1%. Gasoline prices hen remain above heir long-run equilibrium relaionship wih he CPI for many monhs. Indeed, i akes abou monhs before half of he adjusmen back o long-run equilibrium levels occurs. Evenually, however, he effec of he ransiory shock does dissipae. The posiive ransiory gasoline price shock also increases ehanol prices emporarily bu by proporionaely less han gasoline prices. The dynamic adjusmen of ehanol prices back o heir long-run equilibrium relaionship hen follows a similar paern o gasoline prices (see Figure 5). However, he ransiory gasoline price shock has virually no effec on he CPI. Hence, while ransiory gasoline price 13

15 shocks spill over ino ehanol prices hey have virually no effec on he CPI. Indeed, FEVD resuls show ha 93% of he unpredicable variaion in CPI is due o he permanen shock wih only 7% due o ransiory shocks. In conras, 35% of he unpredicable variaion in gasoline prices is due o emporary gasoline price shocks. The effec of he ransiory ehanol price shock (Figure 6) is normalized so he immediae conemporaneous impac of he shock is o increase ehanol price by 1%. Remembering his shock is a shock o he long-run equilibrium relaionship beween ehanol and gasoline prices, he laer respond immediaely wih a small proporional decline. However, he effecs of he ransiory ehanol price shock on boh ehanol and gasoline prices dissipaes much more rapidly han he effecs of a ransiory gasoline price shock on hese same energy prices. Furhermore, he ransiory ehanol shock has virually no effec on he CPI and lile effec on gasoline prices (see Figure 6). Consisen wih his resul, FEVD resuls sugges ha 84% of he unpredicable variaion in ehanol price is due o ransiory ehanol price shocks. Overall, he IRF resuls sugges shocks ha permanenly increase gasoline prices also permanenly increase ehanol prices and he CPI, bu by smaller proporions (abou one half and one fourh, respecively). On he oher hand, he CPI responds minimally o emporary gasoline or ehanol price increases. A possible explanaion for hese resuls is ha permanen energy price increases permeae hrough he economy and affec all of he prices ha make up he CPI, herefore having a significan bu subdued effec on he CPI. On he oher hand, energy price shocks which are viewed as ransiory do no ransmi o oher prices in he economy and herefore have lile effec on he CPI, even in he shor run. 14

16 5. Resuls for Energy Prices and he Energy CPI Nex we analyze a second rivariae model ha includes he same energy prices--gasoline and ehanol--bu uses he energy componen of he CPI (CPIEN). We wan o invesigae if resuls and conclusions are differen if we use a price index ha is more dependen on he underlying energy prices. Lag lengh selecion crieria again suppor wo lagged differences in he VEC (i.e., q = 2) and here is no evidence of residual auocorrelaion from his model. Resuls from esimaing he wo coinegraing vecors are: (8a) (8b) ln( CPIEN ) ln( PGAS (21. 29) ln( PETH ) ln( PGAS ) (14.19) ) where numbers in parenheses are again consisen -saisics. Two coinegraing vecors implies a single I(1) common facor, so here is a single permanen shock driving he long run equilibrium values of all hree series. A shock o he common facor which permanenly increases long-run gasoline price by 1% will also increase long-run equilibrium ehanol price by 0.47% and long-run equilibrium energy CPI by 0.53%. The long-run equilibrium beween gasoline and ehanol prices is virually idenical o ha esimaed wih he model using opline CPI (compare Equaions 7b and 8b). However, gasoline prices are conneced more srongly o he energy CPI han o he opline CPI, as expeced (long-run elasiciy of 0.53% versus 0.23%). IRF graphs are for he P-T decomposiion using he same procedures and idenificaion assumpions as for he opline CPI model are provided in Figures 7-9. Responses o a permanen shock (Figure 7) are again normalized so he long-run permanen increase in gasoline price is 1% and he associaed long-run increases in ehanol prices and CPIEN are consisen wih he coinegraion resuls. Furhermore, energy prices do no iniially overshoo heir long-run 15

17 equilibrium values and adjus o hem much more quickly han in he model wih opline CPI. Togeher hese resuls show ha long-run equilibrium values of energy prices have a much closer relaionship wih long-run equilibrium values of he energy CPI compared o opline CPI (as expeced). Furhermore, ransiory shocks o gasoline prices (Figure 8) and ehanol prices (Figure 9) now induce shor-run adjusmen in he energy CPI, wih ransiory gasoline price shocks being more persisen han ransiory ehanol price shocks. Hence here is boh a shor-run connecion and a more significan long run connecion beween energy prices and he energy CPI compared o energy prices and opline CPI. 6. Resuls for Energy Prices and he PPI The final rivariae model esimaion resuls we repor are for gasoline prices, ehanol prices, and he opline PPI. Lag lengh selecion crieria again suppor wo lagged differences in he VEC (i.e., q = 2) and here is no evidence of residual auocorrelaion from his model. Resuls from esimaing he wo coinegraing vecors are: (9a) (9b) ln( PPI ) ln( PGAS (15. 11) ln( PETH ) ln( PGAS ) (13.78) ) where again numbers in parenheses are consisen -saisics. The wo coinegraing vecors are almos idenical o hose esimaed wih opline CPI, he only difference being ha he long run elasiciy beween gasoline prices and he PPI is slighly higher han for he opline CPI (0.33% versus 0.23%). This suggess ha IRF analysis under he P-T decomposiion will be very similar o ha for opline CPI, which indeed urns ou o be he case. IRF graphs for his model (no shown) show ha permanen shocks overshoo long-run gasoline and ehanol prices bu ha he PPI 16

18 adjuss o is new long-run equilibrium level almos immediaely. Similarly, ransiory shocks o gasoline and ehanol prices have virually no effec on he PPI. Therefore, similar o he relaionship beween energy prices and opline CPI, only permanen increases in energy prices are associaed wih increases in he PPI, wih he proporional increase in he laer being considerably smaller han proporional increases in he former (abou one hird). Transiory energy prices have virually no effec on he PPI, even in he shor run. Evidenly, oher producer prices only respond o increases in energy prices ha are perceived as being permanen, wih lile effec when price increases are perceived as ransiory. 7. Deviaions from Long-Run Equilibrium Relaionships We also analyze he ime pah of equilibrium errors from he VEC model and idenify periods where variables are in long-run equilibrium versus periods of divergence. We do his insample as well as make ou of sample forecass. The goal is o idenify periods where long-run equilibrium relaionships fail o hold and analyze how hese periods ge resolved. To conserve space we do his for he CPI model only bu PPI resuls are similar. To analyze deviaions from he long-run gasoline price-cpi relaionship we use he coinegraion equaion (7a) o forecas long-run equilibrium gasoline prices condiional on observed CPI boh in-sample and over he Augus 2014-February 2015 ou-of-sample period. 5 The resuling esimaes of long-run equilibrium gasoline prices are hen graphed agains acual gasoline prices over he same period (see Figure 10). The difference beween he wo lines in he graph represens deviaions from long-run gasoline price-cpi equilibrium. The graph shows ha gasoline prices can say ou long-run equilibrium wih he CPI for exended periods of ime (years a a 5 CPI daa for February 2015 is no ye available so we used he January value o consruc he condiional forecass for February (i.e., we assumed no change in he CPI beween January and February 2015). 17

19 ime). Therefore, deviaions from his equilibrium relaionship can be quie persisen. In paricular, gasoline prices were considerably higher han heir long-run equilibrium value during he commodiy price boom run up o he financial crisis of 2008 and considerably lower in he afermah of he crisis. We also see ha he recen decline in gasoline price a he end of 2014 and beginning of 2015 has lef prices considerably below heir long-run equilibrium levels wih he CPI. Indeed, he only period when gasoline prices have been as low relaive o heir equilibrium relaionship wih he CPI as hey are oday was during he financial crisis of This suggess we can expec one (or boh) of wo hings o happen o bring gasoline prices back ino long-run equilibrium wih he CPI eiher gasoline prices have o rise or significan deflaion has o occur. Previous episodes of relaively low gasoline prices would sugges gasoline prices will experience much of he (upward) adjusmen. However, he adjusmen can be slow so i is no obvious when realignmen will ake place. To analyze deviaions from he long-run ehanol-gasoline price relaionship we use he coinegraion equaion (7b) o forecas long-run equilibrium ehanol prices condiional on observed gasoline prices boh in-sample and over he Augus 2014-February 2015 ou-of-sample period. 6 The resuling esimaes of long-run equilibrium ehanol prices are graphed agains acual ehanol prices over he same period (see Figure 11). The graph shows ha ehanol prices say close o heir long-run equilibrium wih gasoline price much of he ime, wih deviaions being resolved much more rapidly han was he case for he gasoline price-cpi relaionship. Therefore, deviaions from his equilibrium relaionship are less persisen. Ehanol prices were considerably higher han would be indicaed by heir long-run equilibrium wih gasoline prices during he commodiy price boom, a period when gasoline prices have already been shown o be high relaive 6 Ehanol price daa for February of 2015 is no ye available so we used he January 2015 value o consruc he condiional forecass for ha monh (i.e., we assumed no change in ehanol prices from January o February 2015). 18

20 o heir long-run equilibrium wih he CPI. We also see ha ehanol prices have mainained heir long-run equilibrium relaionship wih gasoline prices during he recen decline in he price of gasoline a he end of 2014 and beginning of 2015 (i.e., ehanol prices have fallen along wih gasoline prices). Therefore, as gasoline prices re-esablish heir long-run equilibrium relaionship wih he CPI by rising over ime we can expec ehanol prices o also rise accordingly. 8. Conclusion This paper uses he Gonzalo and Ng (2001) P-T decomposiion o analyze he dynamic effecs of permanen and ransiory energy price shocks on alernaive measures of he general price level. We find ha only permanen shocks influence opline CPI and PPI wih ransiory shocks having virually no effec. We explain his phenomenon in erms of he response of oher consumer and producer prices o energy price shocks. If he change is viewed as permanen oher prices respond and he CPI and PPI adjus, hough by only a fracion of he proporional increase in gasoline and ehanol prices. If he change is viewed as emporary hen oher prices do no adjus and he effec on opline CPI and PPI is minimal, even in he shor run. These conclusions are moderaed somewha if we do he analysis on energy componens of he indexes. As we migh expec, he proporional response of he energy CPI (and PPI) o a permanen shock is closer o he associaed proporional increase in gasoline and ehanol prices. There is also more of a shor run response in he energy CPI (and PPI) o ransiory shocks compared o he opline CPI and PPI. Therefore, energy price changes are more conneced o increases in he energy componens of indexes han o he opline indexes, in boh he shor run and he long run (as expeced). We also examine he naure of deviaions from esimaed long-run equilibrium relaionships. Resuls sugges ha, despie he recen decline in gasoline prices, gasoline and 19

21 ehanol prices have remained close o heir long-run equilibrium relaionship as ehanol prices have fallen along wih gasoline prices. However, boh gasoline and ehanol prices are currenly quie low relaive o heir long-run equilibrium relaionship wih he CPI, suggesing ha considerable adjusmen will need o ake place moving forward. 20

22 References Brown, S. P.A. and M.K. Yücel (2002). Energy prices and aggregae economic aciviy: an inerpreaive survey. The Quarerly Review of Economics and Finance 42: Ciaian, P., and d A. Kancs (2011). Inerdependencies in he energy-bioenergy-food price sysems: A coinegraion analysis. Resource and Energy Economics 33(1): Cologni, A. and M. Manera (2008). Oil prices, inflaion and ineres raes in a srucural coinegraed VAR model for he G-7 counries. Energy Economics 30: Cunadoa, J. and F. Perez de Gracia (2005). Oil prices, economic aciviy and inflaion: evidence for some Asian counries. The Quarerly Review of Economics and Finance 45: Ewing, B.T. and M.A. Thompson (2007). Dynamic cyclical comovemens of oil prices wih indusrial Producion, consumer prices, unemploymen, and sock prices. Energy Policy 35: Gonzalo, J. and C. Granger (1995). Esimaion of common long-memory componens of coinegraed sysems. Journal of Business and Economic Saisics 13(1): Gonzalo, J. and S. Ng (2001). A sysemaic framework for analyzing he dynamic effecs of permanen and ransiory shocks. Journal of Economic Dynamic and Conrol 25: Hamilon, J. D. (1983). Oil and he macroeconomy since World War II. Journal of Poliical Economy 91: Hamilon, J. D. (1994). Time Series Analysis. Princeon Universiy Press, Princeon NJ. Hecq, A., F.C. Palm, and J-P Urbain (2000). Permanen-ransiory decomposiion in VAR Models wih coinegraion and common cycles. Oxford Bullein of Economics and Saisics 62(4): Hooker, M. (2002). Are oil shocks inflaionary? Asymmeric and nonlinear specificaion versus changes in he regime. Journal of Money, Credi, and Banking 34: Lardic, S. and V. Mignon (2008). Oil prices and economic aciviy: An asymmeric coinegraion approach. Energy Economics 30: Proiei, T. (1997). Shor-run dynamics in coinegraed sysems. Oxford Bullein of Economics and Saisics 59(3): Sock, J.H., and M.W. Wason (1988). Tesing for common rends. Journal of he American Saisical Associaion 83(404):

23 Figure 1. Gasoline and Ehanol Prices, January 1990 o June

24 Figure 2. Year over Year Changes in monhly CPI componens, January 1990-June

25 Figure 3. Year over Year Changes in monhly PPI componens, January 1990-June

26 % Change Monhs afer Shock Gas Price CPI Ehanol Price Figure 4. Impulse Response o a Permanen Shock 25

27 0 % Change Monhs afer Shock Gas Price CPI Ehanol Price Figure 5. Impulse Response o a Transiory Gasoline Price Shock 26

28 0 % Change Monhs afer Shock Gas Price CPI Ehanol Price Figure 6. Impulse Response o a Transiory Ehanol Price Shock 27

29 0.25 % Change Monhs afer Shock Gas Price CPIEN Ehanol Price Figure 7. Impulse Response o a Permanen Shock 28

30 0 % Change Monhs afer Shock Gas Price CPIEN Ehanol Price Figure 8. Impulse Responses o a Transiory Gasoline Shock 29

31 0 % Change Monhs afer Shock Gas Price CPIEN Ehanol Price Figure 9. Impulse Responses o a Transiory Ehanol Shock 30

32 $/Gallon m1 1995m1 2000m1 2005m1 2010m1 2015m1 Dae Gas Price Equilibrium Gas Price Figure 10. Deviaions from Long-Run Equilibrium Gasoline Price-CPI Relaionship 31

33 1 1.5 $/Gallon m1 1995m1 2000m1 2005m1 2010m1 2015m1 Dae Ehanol Price Equilibrium Ehanol Price Figure 11. Deviaions from Long-Run Equilibrium Gasoline-Ehanol Price Relaionship 32

34 Table 1. Uni Roo Tes Resuls Variable Tes Saisic p-value Gasoline Price Dickey-Fuller Phillips-Perron GLS Dickey-Fuller Ehanol Price Dickey-Fuller Phillips-Perron GLS Dickey-Fuller CPI Dickey-Fuller Phillips-Perron GLS Dickey-Fuller Energy CPI Dickey-Fuller Phillips-Perron GLS Dickey-Fuller PPI Dickey-Fuller Phillips-Perron GLS Dickey-Fuller Noes: All variables are in logarihms. Dickey-Fuller ess are augmened wih 3 lagged differences included in he esimaion equaions (suggesed by lag lengh selecion ess) and he number of 2 / 9 Newey-Wes lags in he Phillips-Perron ess is he suggesed defaul of in{4( N /100) } where N is he number of observaions. The number of lags for he Dickey-Fuller GLS es (wih rend) is chosen by he Schwarz crierion. 33

35 Table 2. Coinegraion Tes Resuls Coinegraing Relaionship Maximum No. of Coinegraing Relaionships Trace Saisic 5% Criical Value CPI and Energy Prices * Energy CPI and Energy Prices * PPI and Energy Prices * Noes: All variables are in logarihms. Trace saisics based on VEC esimaion wih wo lagged differences included in each model (as suggesed by lag selecion crieria). * indicaes he number of coinegraing vecors suppored by he saisics. 34