Using the Aggregate Demand-Aggregate Supply Model to Identify Structural. Demand-Side and Supply-Side Shocks: Results Using a Bivariate VAR

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1 Octobr 4, 3 Using th Aggrgat Dmand-Aggrgat Supply Modl to Idntify Structural Dmand-Sid and Supply-Sid Shocks: Rsults Using a Bivariat VAR Jams Pry Covr Univrsity of Alabama Waltr Endrs Univrsity of Alabama C. Jams Hung Wstrn Michigan Univrsity Abstract This papr uss th short-run rstrictions implid by th aggrgat dmand-aggrgat supply modl as an aid in idntifying structural shocks. Combind with th Blanchard-Quah rstriction, this allows us to stimat th slop of th aggrgat supply curv, th variancs of structural dmand and supply shocks, and th xtnt to which structural dmand and supply shocks ar corrlatd. An spcially important finding is that dmand and supply shocks ar highly corrlatd and that dmand shocks can account for as much as 8% of th long-run forcast rror varianc of ral U.S. GDP. Ky Words: Structural VAR, Supply and Dmand Shocks, Blanchard-Quah Dcomposition JEL Classifications: E3 - Prics, Businss Fluctuations, and Cycls C3 - Economtric Mthods: Multipl Tim Equation Tim Sris Modls Corrsponding author: Profssor Jams Pry Covr. Dpartmnt of Economics, Financ & Lgal Studis Univrsity of Alabama Tuscaloosa, AL jcovr@cba.ua.du

2 . Introduction Vctor autorgrssion (VAR analysis has bn a popular tool for analyzing th dynamic proprtis of conomic systms sinc Sims s (98 influntial work. Rsarch on th rlationship btwn VARs and structural conomtric modls has mad possibl th idntification of unobsrvabl structural shocks and an xamination of th dynamic ffcts of ths shocks on th obsrvabl data. For xampl, Blanchard and Quah (B-Q (989 us a bivariat VAR of ral output growth and th unmploymnt rat to dcompos ral output into its tmporary and prmannt componnts. Similarly, Spncr (996 applis th B-Q idntification stratgy to a bivariat VAR of output and th pric lvl. A critical idntifying assumption in th B-Q mthodology is that th shock with no long-run ffct on ral output is th dmand shock. Hnc, it is natural to assum that th shock with a prmannt ffct on output is th supply shock. Studis that us a largr dimnsion VAR oftn impos mor rstrictions on th long-run or short-run ffcts of slctd shocks. Th scond st of idntifying assumptions in th B-Q mthodology is that th varianccovarianc matrix of structural shocks is an idntity matrix. In a bivariat framwork guidd by th aggrgat dmand and aggrgat supply (AD-AS modl, this is quivalnt to assuming that th dmand and supply shocks hav idntical variancs and ar uncorrlatd. Our point of dpartur from th standard B-Q mthodology is to argu that ths normalizations ar implausibl in practic and can lad to a misintrprtation of th mpirical rsults. To avoid this, w propos to us th complt st of rstrictions from an AD-AS modl in ordr to achiv full idntification of th structural paramtrs of a VAR. Our altrnativ dcomposition allows us to prsnt an stimat of th slop of th AS curv (that is, a masur of th short-run outputinflation tradoff, stimats of th variancs of th structural supply and dmand shocks, and an

3 stimat of thir covarianc. W find that th aggrgat supply curv is flat nough for th structural dmand shock to hav important short-run ffcts on output. W also find that th corrlation btwn th structural dmand and supply shocks is positiv and high nough for most of th variation in ral output (54% in th long run and 7% in th short run to b attributd to simultanous shifts of th aggrgat dmand and aggrgat supply curvs. Th papr is organizd as follows. Sction rviws th standard Blanchard and Quah (989 mthodology and placs spcial mphasis on th conditions ncssary for th xact idntification of th structural aggrgat dmand and aggrgat supply shocks. Sction 3 prsnts a basic AD-AS modl and shows that it implis a st of idntification rstrictions that ar sufficint to rplac all th constraints normally placd on th covarianc matrix of structural shocks. Sctions 4 and 5 us Unitd Stats data for th 954Q-Q4 sampl priod and compar th rsults obtaind from a standard B-Q dcomposition to thos obtaind using th AD-AS modl. Sction 6 offrs a summary and som conclusions.. Structural VARs with th Blanchard-Quah Rstriction Lt y t and p t rspctivly rprsnt masurs of output and th pric lvl, which hav bn diffrncd sufficintly to achiv stationarity. Now considr th following bivariat VAR in which yt and pt rspctivly ar th random disturbancs in th output and pric lvl quations and th a ij (L ar polynomials of ordr n in th lag oprator, L, or a ij (L= n k al ij : k = yt y a( L a( L y t yt. p = t p a ( L a( L p t pt (

4 3 Structural VARs rcogniz that th rsiduals yt and pt ar composd of th undrlying structural shocks that ar rsponsibl for variations in y t and p t. Assum that on of ths structural shocks is a supply shock, t, whil th othr is a dmand shock, η t, so that yt c c t = pt c c η t ( whr: c ij rprsnts th contmporanous ffct of shock j on variabl i. Th problm is to idntify th four valus of c ij from th rsiduals of (. It turns out that th solution to th problm is straightforward. From ( it follows that var( yt cov( yt pt cov( ytpt c = var( pt c c c η η η c c c c. (3 Estimation of th VAR yilds var( yt, var( pt and cov( yt pt. Hnc, thr ar thr indpndnt quations that can b usd to dtrmin th four valus of th c ij along with th valus of, and η. Thus, xact idntification of th structural modl rquirs that four η rstrictions b imposd on th VAR. Th B-Q dcomposition assums that =, =, η η = and that c [ - a (] c a ( =. (4 Th assumptions that = and η = ncssarily rstrict th variability of th dmand and supply shocks to b qual. Morovr, th assumption η = rquirs that th shocks to aggrgat dmand and supply b uncorrlatd with ach othr. Blanchard and Quah (989 show that (4 is a long-run nutrality rstriction in that it guarants that th dmand shock, η t, has no prmannt ffct on output. Ths four rstrictions ar sufficint to idntify th c ij and th tim paths of th structural shocks { t } and {η t }.

5 4 On th surfac, th four rstrictions sm to b innocuous. Howvr, th mor rcnt tim-sris litratur has shown that thr ar thr important rasons to b concrnd about th Blanchard-Quah rstrictions:. Uncorrlatd dmand and supply shocks: Th B-Q mthodology forcs th so-calld dmand shock to hav no long-run ffct on output and to b orthogonal to all past valus of dmand and to currnt and past valus of supply. Paprs that us th B-Q mthodology oftn find that such dmand shocks play a small rol in th fluctuations of ral conomic activity. Howvr, it is mor appropriat to claim that th shock that has a tmporary ffct on GDP and that is orthogonal all supply and dmand shocks at all lads and lags plays a small rol in fluctuations in conomic activity. Th point is that dmand and supply shocks idntifid in this way may not bar any rasonabl rlationship to known conomic variabls sinc shifts in aggrgat dmand and supply ar likly to b corrlatd. Clarly, th assumption that dmand and supply shocks ar uncorrlatd is implausibl if th montary or fiscal authority acts in rgard to th currnt or past stat of conomic activity. Similarly, shifts in aggrgat supply may rsult from aggrgat dmand shocks. In an intrtmporal optimizing modl, a tmporary incras in dmand will lad to a positiv supply rspons as agnts ract to a tmporary incras in ral wags. Nw- Kynsian modls also suggst rasons to bliv that dmand and supply shocks ar corrlatd as som firms incras output (rathr than pric in rspons to a positiv dmand shock. Our dcomposition allows for th two shocks to b corrlatd and for th ffcts of th pur dmand and supply innovations to b stimatd.. ad hoc normalizations: Waggonr and Zha (997 show that th normalizations usd to idntify th shocks ar not innocuous for two rasons. First, in th two-variabl VAR rprsntd

6 5 by (3, thr ar actually four solutions for th valus of th c ij. Th B-Q rstrictions produc a systm of quadratic quations so that th signs of th c ij ar not idntifid. In ths circumstancs, Taylor (3 rcommnds th us of ovridntifying rstrictions or thos normalizations that ar consistnt with an undrlying conomic modl. Scondly, bcaus of th rstrictions on th signs of th c ij, Waggonr and Zha (997 argu that a normalization can hav important ffcts on statistical infrnc. In particular, th choic of th c ij can hav profound ffcts on th shap of th liklihood and thus confidnc intrvals for th impuls rsponss. In th words of Hamilton, Waggonr and Zha (, th standard RATS procdurs that hav bn usd by applid rsarchrs for twnty yars to calculat confidnc intrvals for impuls rspons functions can produc sriously mislading rsults as a consqunc of mishandling th normalization problm. 3. Nonrobust impuls rsponss: Th impuls rspons functions of structural VARs ar not spcially robust to altrnativ dcompositions. Britung (, for xampl, provids a numbr of instancs in th litratur showing that th output rsponss to various shocks ar havily dpndnt on th form of th structural VAR. Part of th ambiguity can b attributd to th fact that th dimnsion of th VAR is smallr than th actual numbr of shocks in th conomy. On th dmand sid, changs in montary policy, govrnmnt spnding, tax rats and import dmand will all hav diffrnt influncs on th dynamic procss rprsntd by (. Similarly, supply shocks includ th ffcts of tchnological innovation, changs in labor forc participation, and changs in th capacity utilization rat. Th ky qustion is whthr th singl aggrgatd dmand and supply shocks hav th sam proprtis as th myriad of structural shocks. In thir original papr, Blanchard and Quah mntion th conditions that nd to b assumd to idntify n orthogonal shocks in an m < n dimnsional VAR. Mor formally, Faust

7 6 and Lpr (997 driv th conditions that allow th various shocks to b aggrgatd. Although ths conditions ar not dirctly tstabl, Faust and Lpr provid indirct vidnc that th ncssary conditions ar violatd for th st of variabls typically usd in a structural VAR. Our dcomposition is dsignd to addrss th first two problms. In particular, w do not nd to rstrict th valu of η in ordr to obtain th idntifid dmand and supply shocks. As w show blow, th stimatd valu of η for th Unitd Stats is qual to.576. Morovr, instad of imposing ad hoc normalizations on th varianc of th supply and dmand shocks, w us th normalizations suggstd by th AD-AS modl: a on-unit dmand shock shifts aggrgat dmand by on unit and a on-unit supply shock shifts aggrgat supply by on unit. Th impuls rsponss and confidnc intrvals attaind by using ths normalizations ar quit diffrnt from thos of th B-Q dcomposition. Howvr, our main rsult only adds to th notion that structural dcompositions ar not robust to structural idntifying assumptions. W dm it important that th rsults of our dcomposition ar contrary to th prvailing viw that supply shocks account for th prpondranc of th long-run forcast rror varianc of ral output. Unlik most structural dcompositions of ral GDP, allowing for natural normalizations and a nonzro corrlation btwn shifts in supply and dmand, w show that dmand shocks can account for mor than 8% of th long-run forcast rror varianc of output. This is in stark contrast to th findings of thos who forc th corrlations of shocks to b zro. Gali (99, for xampl, finds that mor thn 8% of output variability can b attributd to supply shocks. 3. Idntification of th AD-AS Modl Considr th following simpl AD-AS modl: y = y ( p - p, >. (5 s t t- t t t- t t

8 7 ( y p = ( y p η (6 d d t t t- t t t d t s t y = y (7 In th abov modl, y t is th logarithm of output during priod t, whil t- y t is th lvl of output xpctd givn information availabl at th nd of priod t-. Similarly, p t is th logarithm of th pric lvl during priod t, whil t- p t is th pric lvl xpctd givn information availabl at th nd of priod t-. Th suprscripts s and d rprsnt supply and dmand, rspctivly. W lt t and η t dnot th srially uncorrlatd structural aggrgat supply and aggrgat dmand shocks, rspctivly. Equation (5 is a Lucas (97 aggrgat supply curv in which output incrass in rspons to unxpctd incrass in th pric lvl and positiv ralizations of th pur aggrgat supply shock t. Equation (6 is th aggrgat dmand rlationship; nominal aggrgat dmand quals its xpctd valu plus a random dmand disturbanc, η t. Although quations (5 through (7 rprsnt an ovrly simplifid modl of th aggrgat conomy, our goal is to suggst that a plausibl macroconomic modl is consistnt with th notion that dmand shocks can play a prdominant rol in ral GDP fluctuations. Th ssntial fatur of th modl is th absnc of a rstriction forcing th dmand and supply shocks to b contmporanously uncorrlatd. In an unpublishd appndix (availabl from us on rqust, w rport similar findings within a nw-kynsian framwork. Howvr, w bliv that th vidnc supporting a ky rol for dmand shocks is mor complling in a non-kynsian nvironmnt. It is instructiv to compar th four idntifying rstrictions mbddd within th AD-AS modl to thos of Blanchard and Quah. Obviously, both modls mploy th long-run nutrality rstriction that dmand shocks hav no long-run ffct on output. Our normalization rstrictions

9 8 ar that an t shock has a on-unit impact ffct on y and an η t shock has a on-unit impact s t ffct on d y t. Finally, (6 implis that th slop of th aggrgat dmand curv is unity. To show how ths rstrictions xactly idntify th systm, not that quations (5 (7 can b solvd for output and th pric lvl: yt t- yt t p = t t- p t η. (8 t Finally, if it is assumd that t- y t and t- p t ar qual to linar combinations of thir past obsrvd valus, thn th systm can b rprsntd by quation (. Hnc, th rlationship btwn th VAR rsiduals and th structural innovations of th AS-AD modl is: yt t = pt η t (9 so that var( y cov( y, p cov( y, p = var( - p η η η -. ( Again, stimation of th VAR yilds var( y, var( p and var( y, p. Thr ar four paramtrs to b stimatd--,, η η and --so that only on idntification rstriction is rquird. Th assumption that th structural aggrgat dmand shock, η t, has no long-run ffct on output now implis that [ - a (] a ( =, or: = -a (/[ - a (]. (

10 9 Thus, th systm is xactly idntifid, and w hav not rstrictd th valus of,, or η η. As such, any additional rstriction on ths paramtrs, such as η =, rsults in an ovridntifid systm. Anothr way to mak th sam point is to combin (3 and (: - c c ηc c η c c η η c c =. ( - η η Rcall that Blanchard and Quah (989 impos th four rstrictions: =, η =, η = and c [ - a (] c a ( =. In contrast, our AS-AD modl imposs thr indpndnt rstrictions among th c ij ; in particular, c = c, c = -c and c = c. Ths thr rstrictions, along with th long-run nutrality rstriction, ar sufficint to fully idntify th modl. As should b clar from (, imposing th Blanchard-Quah rstriction yilds an stimat of th slop of th aggrgat supply curv. Bcaus of th additional constraints introducd by mploying th AD-AS modl, it is not ncssary to assum that th structural shocks ar mutually uncorrlatd. Hnc, th modl allows for th possibility that E( t η t = η. In sction 5, this possibility is implmntd using two distinct causal ordrings. Th first ordring assums that th corrlation btwn t and η t is th rsult of causality that runs ntirly from supply to dmand. Th scond ordring assums that a dmand shock has a contmporanous ffct on supply but that supply shocks hav no contmporanous ffct on dmand. Th assumption that causality runs from th supply shock to th dmand shock can b implmntd by assuming that unxpctd aggrgat dmand quals a pur aggrgat dmand shock, ν t, plus an unxpctd chang in aggrgat dmand that is inducd by th aggrgat supply shock, ρ t, or η t = ρ t ν t. Thr ar at last two motivations for such an assumption.

11 Th first coms from th lif-cycl/prmannt incom hypothsis (LC/PIH. According to th LC/PIH, if a particular shock to aggrgat supply has only a tmporary ffct on output, it has vry littl ffct on th prsnt valu of xpctd futur incom and thrfor has only a littl, if any, ffct on currnt aggrgat dmand. Howvr, if a particular shock to aggrgat supply has a prmannt ffct on output, thn th prsnt valu of futur incom incrass by nough for currnt dmand to incras by an amount approximatly qual to th incras in output supplid. Th valu of ρ thrfor dpnds upon how th tim sris of structural supply shocks is dividd btwn prmannt and tmporary shocks. Th scond motivation for a positiv corrlation btwn dmand and supply shocks is th possibility that th montary authority is attmpting to stabiliz th pric lvl or th rat of inflation. If thr is a positiv aggrgat supply shock, thn in ordr to prvnt th pric lvl from dclining, th montary authority must incras aggrgat dmand. This would caus unxpctd aggrgat dmand to b positivly corrlatd with unxpctd aggrgat supply. 3 Th assumption that causality runs from th dmand shock to th supply shock can b implmntd by assuming that th aggrgat supply shock consists of two distinct componnts: a pur supply shock, δ t, and a chang in output that rsults ntirly from th dcision of som firms to rspond to an unxpctd chang in dmand by passivly changing output, γη t, or t = γη t δ t. All of th motivations for this assumption ar Kynsian. For xampl, if thr is ral rigidity in th conomy, thn som firms do not adjust pric in rspons to unxpctd changs in dmand; rathr, thy simply supply th additional output dmandd. 4 Th valu of γ thrfor dpnds upon th shar of firms in th conomy that do not chang thir currnt pric in rspons to an unxpctd chang in aggrgat dmand.

12 4. Estimation Rsults for th Standard B-Q Modl Data on ral GDP and th GDP dflator for th priod 954Q-Q4 wr obtaind from th Unitd Stats Dpartmnt of Commrc. Standard Dicky-Fullr tsts of th logarithms of ral GDP and th GDP dflator indicatd that ral GDP was diffrnc stationary, whil th GDP dflator had to b diffrncd twic to bcom stationary. Hnc, th variabls mployd in th VAR ar th log-first diffrnc of ral GDP and th log-scond diffrnc of th GDP dflator. Th log liklihood ratio tst, modifid for small sampls, usd in Sims (98 indicatd that th optimal lag lngth is lags. Th solid lins in Figurs and ar th impuls rspons functions for th structural aggrgat supply and aggrgat dmand shocks as idntifid by th standard B-Q st of idntifying rstrictions discussd abov. 5 Th dashd lins dnot uppr and lowr on-standard dviation bands. From Figur -A, notic that a % supply shock causs output to incras by about.75%, whil in Figur -B a % dmand shock causs output to incras by only about.35%. Th ffcts of both shocks dclin vry rapidly. Th ffct of th supply shock is about zro by th fourth quartr and th ffct of th dmand shock bcoms ngativ by th third quartr aftr th shock. Th rspons of output to th dmand shock rmains blow -. for thr quartrs, so that aftr six quartrs th cumulativ ffct on output of a % shock to dmand is approximatly zro. Th varianc dcompositions prsntd in Tabl show that about 8% of th short-run variation in output and 7% of th long-run variation in output in th Unitd Stats has bn th rsult of th structural supply shock. Th prcntags ar approximatly rvrsd for th variation in inflation, with th dmand shock accounting for 75% of th short-run variation and narly 7% of th long-run variation in inflation.

13 What might on conclud from th rsults for th standard B-Q modl? On possibl conclusion is that dmand shocks hav bn th primary sourc of variations in inflation, whil supply shocks hav bn th primary sourc of variations in output. Although it is possibl that this conclusion is sound, it hings on th assumption that th dmand and supply shocks ar contmporanously uncorrlatd. In particular, th nxt sction shows that th varianc dcomposition obtaind from this modl is idntical to that obtaind from th dmand-supply modl using causal ordring such that th causality runs xclusivly from th structural supply shock to th structural dmand shock. If it is assumd that th causality runs in th opposit dirction, thn most of th variation in output (in both th short and long-runs will b th rsult of th structural dmand shock. Anothr conclusion that on might draw from th standard modl is that dmand shocks do not hav narly th sam ffct on output in th short run as do supply shocks. Howvr, this conclusion rsts on th assumption that th structural shocks ar uncorrlatd and hav unit variancs. If th assumption of unit variancs is rlaxd, th rsults of th standard modl do not support this conclusion. Th rason is that th rsponss to th % shocks prsntd in Figurs and ar actually th rsponss to on standard dviation shocks. If th standard dviation of th structural dmand shock is lss than %, thn th ffct of a % dmand shock is largr than th rspons prsntd in th figurs. Furthrmor, as shown in th nxt sction, if th structural shocks ar actually corrlatd, th rspons of output to a supply shock prsntd in Figur -A could b th rsult of th dmand curv shifting at th sam tim as th supply curv. Similarly, Tabl shows that th structural dmand shock has accountd for only % to 3% of th variation in output. This rlativly small contribution of dmand shocks to th historical variation in output, howvr, could b th rsult of two vry diffrnt undrlying

14 3 causs. On possibility is that th aggrgat supply curv is rlativly stp, so that any givn dmand shock has a much smallr ffct on output than dos an qual-sizd supply shock. Th othr possibility is that historical dmand shocks hav had only a rlativly small varianc. Bcaus th standard procdur rsts on th assumption that both structural shocks hav unit variancs, th procdur cannot dtrmin th xact rason dmand shocks hav had a rlativly small ffct on output. 5. Estimation and Idntification of th AD-AS modl Th first row of Tabl prsnts th stimats, along with thir bootstrappd 95% confidnc intrvals, of th structural paramtrs obtaind by using th rstrictions of th AD-AS modl. Th point stimat of, th slop of th aggrgat supply curv, is.56. From quation (8, th immdiat ffct of a % supply shock on output is /( =.39. Th ffct of th structural dmand shock on output is /( =.6. Hnc, th point stimat of th outputinflation tradoff paramtr, which is th slop of th short-run aggrgat supply curv in th AD-AS modl, implis that th immdiat ffct on output of a structural dmand shock is largr than that of an qual-sizd structural supply shock. Notic that th varianc of ach structural shock is lss than unity (i.., =.9 and η =.7. Mor importantly, th covarianc btwn th two shocks is.58; thus, th aggrgat dmand and supply curvs tnd to shift togthr. Using th rstrictions implid by th basic AD-AS modl, w can obtain th {η t } and { t } squncs. On attractiv fatur of our dcomposition is that it yilds a straightforward masur of xcss dmand, or inflationary prssur, as th sum η t - t. Inflationary prssur and th actual inflation rat ar shown in Figur 3. In ordr to dpict a rasonably smooth sris, th figur masurs inflationary prssur as th annual avrag 3.5 ( η. Figur 3 clarly i= t i t i

15 4 shows a prpondranc of shocks gnrating inflationary prssur bginning in th lat 96s and lasting through 975. Aftr a dclin in inflation in th mid-97s, inflationary prssur rsums until th contractions of th lat-97 s and arly 98s. Figur 4 shows th annualizd valus of th output gap as th four-month moving avrag 3.5 ( η. Larg valus of i= t i t i η t t should b associatd with incrass in output. An spcially intrsting fatur of th figur is that sharply positiv movmnts ar associatd with an conomic turn around. Th NBER dats th troughs of th businss cycl occurring in our sampl priod ar 958Q, 96Q, 97Q4, 975Q, 98Q3, 99Q and Q. Clarly, sharp upward movmnts in th figur ar associatd with ths dats. Impuls Rsponss In ordr to obtain impuls rspons functions, it is ncssary to us orthogonal shocks to avoid any ambiguity rgarding th typ of shock undr xamination. Sinc E t η t, it is ncssary to mak an assumption concrning th sourc of th corrlation btwn th shocks. Although thr is an infinit numbr of possibilitis, ach on can b rprsntd by a combination of two xtrm possibilitis. Th first ordring is that th supply shock is causally prior to dmand, whil th scond assums that causality runs in th opposit dirction. It is straightforward to show that th cas in which causality runs ntirly from th supply shock to th dmand shock yilds an AD-AS modl idntical to th standard B-Q modl discussd in sction 4. Assum that th dmand shock is a linar combination of an indpndnt structural dmand shock, ν t, and th aggrgat supply shock: η t = ρ t ν t. (3

16 5 Hnc, v t is th indpndnt portion of th dmand shock and ρ capturs th corrlation btwn η t and t. If (3 is substitutd into (, th rsult is: = ρ ρ ν - var(, cov(, cov( var( - p p y p y y, (4 whr: continus to b th varianc of th total structural supply shock and ν is th varianc of th indpndnt structural dmand shock. Th B-Q constraint is not affctd by th orthogonalization and is still givn by (. Not that quation (4 is quivalnt to = ρ ρ ν ν - var(, cov(, cov( var( - p p y p y y, (5 which implis that = ν ν ν ν ρ ρ ρ ρ ( ( var(, cov(, cov( var( - - p p y p y y. (6 This xprssion is idntical to quation (3 undr th idntifying assumptions of th standard modl if w assum that = ( c c c c - ν ν ρ ρ. (7 In addition, substituting (7 into (4, th B-Q constraint of th standard modl, yilds xactly (, th B-Q constraint of th AD-AS modl with causality running ntirly from th supply shock to th dmand shock. Thrfor, th standard modl is idntical to th AD-AS modl with causality running ntirly from th supply shock to th dmand shock. That is, all th

17 6 variations in output rsulting from common shifts of th AD and AS curvs ar attributd to th structural supply shock in th standard modl. Th paramtr stimats obtaind from mploying (4 ar prsntd in th scond row of Tabl. Th valus of and ar th sam as thos in th basic modl. Th stimat of th varianc of th indpndnt dmand shock, ν =.35, is slightly lss than on-half of th varianc of th total dmand shock, η, rportd in th first row. Hnc, if w us this ordring, slightly mor than on-half of th variation in unxpctd aggrgat dmand is th rsult of shifts in th AD curv inducd by structural shocks to aggrgat supply. Th stimat of ρ is.64, implying that a % structural supply shock not only shifts th AS curv % to th right but also shifts th AD curv.64% to th right. W do not dpict th impuls rspons functions for this cas. If causality runs from supply shocks to dmand shocks, th impuls rspons functions ar simply proportional to thos shown in Figurs and. Th shaps ar idntical sinc a dcomposition using (4 is idntical to that using th standard B-Q rstrictions. Th scal changs sinc th standard dviations of th shocks ar blow unity. Morovr, th varianc dcompositions obtaind from (4 ar idntical to thos rportd in Tabl. Th othr way to obtain orthogonal shocks is to assum that th dmand shock is causally prior to th supply shock. This cas is implmntd by assuming that th supply shock is a linar combination of an indpndnt structural supply shock, δ t, and a chang in aggrgat supply inducd by th aggrgat dmand shock, γη t, or t = γη t δ t. (9 If (9 is substitutd into (, th rsult is

18 7 var( y cov( y, p cov( y, p = var( - p γ δ η γ -, ( whr: η continus to b th varianc of th total structural dmand shock and δ is th varianc of th indpndnt structural supply shock. Th rsults obtaind using quation ( ar prsntd in th third row of Tabl. Th valus of and η ar th sam as thos in th basic modl bcaus th Blanchard-Quah rstriction is dfind as th assumption that any shift in th aggrgat dmand curv, givn no shift in aggrgat supply, has no long-run ffct on output. Th stimat of th varianc of th indpndnt supply shock, δ =.43, is slightly lss than on-half of th varianc of th total supply shock,, rportd in th first row. Thrfor, with this orthogonalization, slightly mor than on-half of th variation in unxpctd aggrgat supply is th rsult of shifts in th curv inducd by structural shocks to aggrgat dmand. Th stimatd valu of γ is.8, implying that a % dmand shock not only causs th AD curv to shift by % of GDP, but also causs th AS curv to shift by.8% of GDP. Figurs 5 and 6 prsnt th impuls rspons functions obtaind from this orthogonalization. A comparison of ths rsponss to thos shown in Figurs and indicats that th orthogonalization has important implications for th rol of supply and dmand shocks. Whn causality runs from dmand to supply, a % dmand shock inducs a rlativly larg rspons of output and a rlativly small rspons of inflation. This rsult is obtaind bcaus a % structural dmand shock shifts th aggrgat dmand curv % and th aggrgat supply curv by γ%. Hnc, th immdiat ffct of a % structural dmand shock is to caus output to incras by slightly mor than.9%, whil thr is almost no ffct on inflation. In contrast,

19 8 supply shocks hav rlativly small ffcts on output sinc thy hav no contmporanous ffct on dmand. Th varianc dcompositions with this orthogonalization ar rportd in Tabl 3. In th AD-AS modl with causality from dmand to supply, 9% of th short-run variation in output and narly 83% of th long-run variation in output is th rsult of th structural dmand shock. Ovr 9% of th variation in inflation is th rsult of th structural supply shock. 6. Summary and Conclusions. This papr dmonstrats how it is possibl to us th AD-AS modl to idntify a structural VAR and compars th idntification with that obtaind using th standard Blanchard- Quah dcomposition. Our dcomposition imposs th natural normalizations that a dmand shock has a on-unit ffct on dmand and a supply shock has a on-unit ffct on supply. Morovr, th procdur has th advantag that it dos not forc th corrlation btwn dmand and supply shocks to b zro. As such, w ar abl to stimat of th corrlation btwn unxpctd shifts in th AD and AS curvs as wll as a point stimat of th slop of th shortrun aggrgat supply curv. W find that th aggrgat supply curv is flat nough so that dmand shocks ar just as capabl as supply shocks of having an important ffct on output in th short run. Evn if it is assumd that all th corrlation btwn th structural dmand and supply shocks is th rsult of on-way causality from supply to dmand, a % dmand shock continus to caus output to incras by.6%, but a % supply shock (including its inducd shift of AD causs output to incras by.78%. Prhaps, th most important finding is th high corrlation btwn dmand and supply shocks. If it is assumd that causality runs from th structural supply shock to th structural

20 9 dmand shock, th structural dmand shock accounts for 8% of th long-run variation in output. W prov that a causal ordring such that structural supply shocks shift th dmand curv is mathmatically quivalnt to th standard B-Q modl (up to a scalar. On th othr hand, if th ordring is such that causality runs from dmand to supply, thn th structural supply shock (which in this cas is an indpndnt structural supply shock accounts for 8% of th variation in output. Our own viw is that ach of ths causal ordrings is xtrm; rathr, it is likly that dmand shocks can contmporanously affct supply and visa vrsa. Bcaus this papr uss a bivariat modl, it is not possibl to dtrmin th rason why th curvs ar shifting togthr unlss additional rstrictions ar imposd on th data. Sinc th standard B-Q dcomposition is just on of th two xtrm ordrings, without furthr vidnc, it is not possibl to claim that dmand shocks play a limitd rol in ral output variability.

21 Rfrncs Ball, Laurnc, Grgory N. Mankiw, and David Romr (988, "Th Nw Kynsian Economics and th Output-Inflation Tradoff." Brookings Paprs on Economic Activity I, pp Blanchard, Olivir J. and Danny Quah (989, Th Dynamic Effcts of Aggrgat Dmand and Supply Disturbancs. Amrican Economic Rviw 79, pp Britung, J. ( Structural Infrnc in Cointgratd Vctor Autorgrssiv Modls Clarida, Richard, Jordi Galí, and Mark Grtlr (999, "Th Scinc of Montary Policy: A Nw Kynsian Prspctiv." Journal of Economic Litratur XXXVII, pp Covr, Jams P. and Paul Pcorino, Optimal Montary Policy and th Corrlation btwn Prics and Output. Contrinutions to Macroconomics, Issu, 3. Faust, J. and E. M. Lpr (997, Whn do Long-Run Idntifying Rstrictions Giv Rliabl Rsults? Journal of Businss and Economic Statistics 5, Gali, Jordi (99, "How Wll Dos th IS-LM Modl Fit Postwar U.S. Data?" Th Quartrly Journal of Economics 7, pp Hamilton, Jams, Waggonr, Danil and Tao Zha. (. Normalization in Economtrics. mimo. Lucas, Robrt E. Jr. (97, "Expctations and th Nutrality of Mony." Journal of Economic Thory 4, pp McCallum, Bnntt T (989. Montary Economics: Thory and Practic. (Nw York: McMillan. McCallum, Bnntt T. (999, and Edward Nlson, "An Optimizing IS-LM Spcification for Montary Policy and Businss Cycl Analysis." Journal of Mony, Crdit and Banking, pp Romr, David, (, Advancd Macroconomics, Scond Edition. (Nw York: McGraw-Hill.

22 Sims, Christophr (98, "Macroconomics and Rality." Economtrica 48, pp Spncr, David E. (996, "Intrprting th Cyclical Bhavior of th Pric lvl in th U.S." Southrn Economic Journal 63, pp Taylor, Mark P. (3, Estimating Structural Macroconomic Shocks Through Long-Run Rcursiv Rstrictions on Vctor Autorgrssiv Modls: Th Problm of Idntification. Dpartmnt of Economics Working Papr, Univrsity of Warwick. Waggonr, Danil and Tao Zha (3, Liklihood Prsrving Normalization in Multipl Equation Modls. Journal of Economtrics 4. pp

23 Tabl Varianc Dcomposition for Standard Modl (and AD-AS Modl with causality from Supply to Dmand Variation in Output Variation in Inflation du to du to Supply Dmand Supply Dmand Shock Shock Shock Shock Horizon (Quartrs

24 3 Tabl Point Estimats of Structural Paramtrs of AD-AS Modl 956:3-:4 Modl Nam η η ν ( Basic AD-AS ( (3 Causality from Supply to Dmand Causality from Dmand to Supply.559 (.449, (.449, (.449, (.546, (.546,.36 _.576 (.35, (.47, (.47,.88 ρ δ.346 (.8,.54 _.643 (.334, (.6,.95 Th numbrs in parnthsis ar 95% confidnc intrvals from bootstrapping. = snsitivity of aggrgat supply to an unxpctd chang in inflation. = varianc of total structural shock to aggrgat supply. η =covarianc btwn total structural shocks to aggrgat supply and dmand. η = varianc of total structural shock to aggrgat dmand. ν = varianc of indpndnt structural shock to aggrgat dmand. ρ = ffct of shock to aggrgat supply on total shock to aggrgat dmand if causality runs from supply shock to dmand shock. δ = varianc of indpndnt structural shock to aggrgat supply. γ = ffct of shock to aggrgat supply on total shock to aggrgat dmand if causality runs from supply shock to dmand shock. γ _.84 (.66,.948

25 4 Horizon (Quartrs Tabl 3 Varianc Dcomposition for AD-AS Modl with Causality from Dmand to Supply Shock Variation in Output Variation in Inflation du to du to Supply Dmand Supply Dmand Shock Shock Shock Shock

26 5 Endnots For xampl, using th IS-LM-Phillips Curv framwork, Gali (99 distinguishs th supply shock from IS, mony-dmand, and mony-supply shocks by assuming that ach of ths lattr shocks has no long-run ffct on output. To idntify th IS shock, h assums that monydmand and mony-supply shocks hav no contmporanous ffct on output. S, for xampl, McCallum (989 and McCallum and Nlson (999 for drivations that show that currnt aggrgat dmand dpnds upon xpctd futur output. Gali (99 taks this possibility into account by including th aggrgat supply shock in both th IS curv and th aggrgat supply curv. 3 S, for xampl, Clarida, Galí, and Grtlr (999: p. 674 and Covr and Pcorino (3. 4 For a discussion of th importanc of ral rigidity for Kynsians modls s Romr (, pp and Ball, Mankiw and Romr (988, pp Thr ar four ral solutions with diffrnt signs for th c ij solvd from quations (3 and (4. As discussd in Taylor (3, w pick th on that implis a positiv long-run ffct of dmand shocks on pric and a positiv long-run ffct of supply shocks on output.

27 Figur : Output Rsponss with th B-Q Rstrictions Panl A: Rspons of Output to a % Supply Shock Panl B: Rspons of Output to a % Dmand Shock % of Ral GDP Lag Figur : Inflation Rsponss with th B-Q Rstrictions % of Ral GDP Lag Panl A: Rspons of Inflation to a % Supply Shock Panl B: Rspons of Inflation to a % Dmand Shock % of Inflation % of Inflation Lag Lag

28 Figur 3: Actual Inflation and Inflationary Prssur (Inflationary Prssur (Actual Inflation % pr yar Rcssion Inflationary Prssur Actual Inflation

29 Figur 4: Output Gap (-yar moving avrag

30 Figur 5: Output Rspons in th AD-AS Modl Panl A: Rspons of Output to a % Supply Shock Panl B: Rspons of Output to a % Dmand Shock % of Ral GDP Lag Lag Figur 6: Inflation Rspons in th AD-AS Modl % of Ral GDP Panl A: Rspons of Inflation to a % Supply Shock Panl B: Rspons of Inflation to a % Dmand Shock % of Inflation Lag % of Inflation Lag Not: In Figurs 5 and 6, dmand shocks ar causally prior to supply shocks