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 Fbruary, 4 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 a simpl aggrgat dmandaggrgat supply modl as an aid in idntifying structural shocks. Combind with th Blanchard-Quah rstriction, it allows stimation of 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. This papr finds that dmand and supply shocks ar highly corrlatd and that dmand shocks possibly 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 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. On critical idntifying assumption in th B-Q mthodology is that on shock has no long-run ffct on ral output. In a bivariat systm it is natural to assum that this shock is an aggrgat dmand (AD shock, whil th othr shock is an aggrgat supply (AS shock. Th othr critical idntifying assumption in th B-Q mthodology is that th varianccovarianc matrix of structural shocks is diagonal. In a bivariat framwork guidd by an aggrgat dmand and aggrgat supply (AD-AS modl, this is quivalnt to assuming that th AD and AS shocks ar uncorrlatd. This papr dparts from th standard B-Q mthodology by pointing out that thr ar sound conomic rasons for prsuming that structural AD and AS shocks ar corrlatd. As such, an altrnativ st of idntification rstrictions is rquird. W propos to us th complt st of rstrictions from a simpl 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 stimat of thir covarianc. W find that th AS curv is flat nough for th structural dmand

3 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 AD and AS curvs. Th papr is organizd as follows. Sction rviws th standard B-Q mthodology and placs spcial mphasis on th conditions ncssary for th xact idntification of th structural AD and AS 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 from our dcomposition. 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 k quations and th a ij (L ar polynomials of ordr n in th lag oprator, L, or a ij (L= al: n k = ij yt y a( L a ( L y t yt. p = t p a( L a( L p t pt ( Assum that th rsiduals yt and pt ar composd of th two undrlying structural shocks rsponsibl for variations in y t and p t, or yt c c εt = pt c c η, ( t

4 3 whr ε t is th AS shock and η t is th AD shock. Equation ( implis var( yt cov( ytpt cov( ytpt c = var( pt c c c ε εη εη c η c c c. (3 If it is assumd that =, η =, εη = and ε c [ - a (] c a ( =, (4 thn th valus of th c ij and th tim paths of th structural shocks {ε t } and {η t } can b dtrmind from stimation of th VAR. Blanchard and Quah (989 show that (4 is a longrun nutrality rstriction guaranting that th AD shock, η t, has no prmannt ffct on output. Thr ar at last two rasons to b concrnd about th abov rstrictions. Th first is that th AD shock is assumd to hav no long-run ffct on output and to b orthogonal to all past valus of itslf and to currnt and past valus of th AS shock. Hnc, it is not surprising that paprs using th B-Q mthodology oftn find that AD shocks play only a small rol in xplaining fluctuations in ral conomic activity. Th shocks idntifid in this way may not bar any rasonabl rlationship to actual shifts in AD and AS curvs bcaus such shifts ar likly to b corrlatd. Clarly, th assumption that AD and AS 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 AS may rsult from AD 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 AD and AS shocks ar corrlatd as som firms incras output (rathr than pric in rspons to a positiv dmand shock. 3 Th dcomposition prsntd blow allows for th two shocks to b corrlatd and for th ffcts of th pur AD and AS innovations to b stimatd.

5 4 Th scond rason to b concrnd about th B-Q rstrictions is a statistical issu argud by Waggonr and Zha (3. In th bivariat VAR rprsntd 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. Thrfor, additional rstrictions on th signs of th c ij ar ndd. As a rsult of th additional rstrictions, Waggonr and Zha (3 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 function and thus confidnc intrvals for th impuls rsponss. Our dcomposition is dsignd to addrss ths problms. In particular, w do not nd to rstrict th valu of εη in ordr to obtain th idntifid dmand and supply shocks. As w show blow, th stimatd valu of εη for th Unitd Stats is qual to.576. Morovr, instad of normalizing th varianc-covarianc matrix of th structural shocks to an idntity matrix, w us th normalizations usually suggstd by an AD-AS modl: a on-unit dmand shock shifts AD by on unit and a on-unit supply shock shifts AS by on unit. Th impuls rsponss and varianc dcompositions attaind by using our dcomposition can b 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. Allowing for 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 finding is consistnt with th argumnt by Wst (988 that dmand shocks may account for a larg shar of output fluctuations at long horizons. It is, howvr, in stark contrast to th findings of thos

6 5 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 an AD-AS Modl Considr th following simpl AD-AS modl: y = y ( p - p εt, >, (5 s t t- t t t- t d yt pt t- yt p d t t ( = ( η, (6 y = d t y t s, (7 whr y t and p t rspctivly ar th logarithms of output and th pric lvl during priod t; t- y t and t- p t ar thir xpctd valus givn information availabl at th nd of priod t-; th suprscripts s and d rprsnt supply and dmand; whil ε t and η t rspctivly dnot th srially uncorrlatd structural AS and AD shocks. Equation (5 is a Lucas (97 AS curv in which output incrass in rspons to unxpctd incrass in th pric lvl and positiv ralizations of th AS shock ε t. Equation (6 is th AD 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 on rqust, w rport similar findings within a nw-kynsian framwork. It is instructiv to compar th four idntifying rstrictions mbddd within our AD-AS modl to thos of Blanchard and Quah. Our normalization rstrictions ar that an ε t shock has a

7 6 on-unit ffct on y s t and an η t shock has a on-unit ffct on. Finally, (6 implis that th slop of th AD curv is unity. To show how ths rstrictions xactly idntify th systm, solv quations (5 (7 for output and th pric lvl. If it is assumd that t-y t and t- p t ar qual to linar combinations of thir past obsrvd valus, th rsult can b writtn in a form similar to quation (, which yilds: d y t yt εt = pt η t (8 so that var( y cov( y, p cov( y, p = var( - p ε εη εη η -. (9 Th assumption that th structural AD hock, η t, has no long-run ffct on output now implis that = -a (/[ - a (], ( which yilds an stimat of, th slop of th AS curv. Onc th stimat of is obtaind, quation (9 can b usd to solv for ε, η, and εη. Thus, th systm is xactly idntifid. Du to th additional constraints introducd by mploying an AD-AS modl, it is not ncssary to assum that structural shocks ar mutually uncorrlatd in ordr to idntify th structural dmand and supply shocks. Howvr, in ordr to obtain th varianc dcompositions and impuls rsponss, it is ncssary to idntify orthogonal structural shocks. In Sction 5, this is don by implmnting th two possibl rcursiv ordrings traditionally usd in a Cholski

8 7 dcomposition. Th first ordring assums that supply shocks ar causally prior to dmand shocks and th scond ordring assums that dmand shocks ar causally prior to supply shocks. Th assumption that causality runs from th supply shock to th dmand shock can b implmntd by assuming that unxpctd AD quals a pur AD shock, ν t, plus an unxpctd chang in AD that is inducd by th AS shock, ρε t, or η t = ρε t ν t. Thr ar at last two motivations for such an assumption. Th first coms from th lif-cycl/prmannt incom hypothsis (LC/PIH. According to th LC/PIH, if a particular shock to AS 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 AD. Howvr, if a particular shock to AS 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. 4 Th scond motivation for allowing causality to run from th supply shock to th dmand shock is th possibility that th montary authority is attmpting to stabiliz th pric lvl or th rat of inflation. If thr is a positiv AS shock, thn in ordr to prvnt th pric lvl from dclining, th montary authority must incras AD. This causs unxpctd changs in AD to b positivly corrlatd with unxpctd changs in AS. Th assumption that causality runs from th dmand shock to th supply shock can b implmntd by assuming that unxpctd AS quals a pur AS shock, δ t, plus an unxpctd chang in AS that is inducd by th AD shock, γη t, or ε t = γη t δ t. All 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

9 8 additional output dmandd. Th valu of γ dpnds upon th shar of firms in th conomy that do not chang thir currnt pric in rspons to an unxpctd chang in AD. 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. Th solid lins in Figurs and ar th impuls rspons functions for th structural AS and AD shocks as idntifid by th standard B-Q st of idntifying rstrictions. 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 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. What might on conclud from ths 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 this conclusion

10 9 may b sound, it hings on th assumption that th structural shocks ar contmporanously uncorrlatd. If th structural shocks ar corrlatd, both th rspons of output to th supply shock and th importanc of supply shocks in xplaining th varianc of output could b th rsult of AD shifting at th sam tim as AS. In particular, th nxt sction shows that th varianc dcomposition obtaind from this modl is idntical to that obtaind from an AD-AS modl in which dmand and supply shocks ar corrlatd such that supply shocks ar causally prior to dmand shocks. If instad it is assumd that supply shocks do not affct AD, thn most of th variation in output (in both th short and long runs will b th rsult of th structural dmand shocks. 5. Estimation and Idntification of Our AD-AS modl Th first row of Tabl prsnts th stimats of th structural paramtrs (along with thir bootstrappd 95% confidnc intrvals obtaind by using th rstrictions of our AD-AS modl. Th point stimat of, th slop of th AS 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 output-inflation tradoff paramtr implis that th immdiat ffct on output of a structural dmand shock is largr than that of an qual-sizd structural supply shock. Th varianc of ach structural shock is lss than unity (i.., ε =.9 and η =.7. Mor importantly, th covarianc btwn th shocks is.58; thus, th AD and AS curvs tnd to shift togthr. In ordr to obtain impuls rspons functions and varianc dcompositions, it is ncssary to us orthogonal shocks to avoid any ambiguity rgarding th typ of shock undr xamination. Sinc Eε t η t, it is ncssary to mak an assumption concrning th sourc of th corrlation btwn th shocks. Although thr ar an infinit numbr of possibilitis, ach on

11 can b rprsntd by a combination of two xtrm possibilitis th two rcursiv ordrings discussd in Sction 3, abov. Th first rcursiv ordring is that th supply shock is causally prior to dmand. It is straightforward to show that this yilds an AD-AS modl idntical to th standard B-Q modl discussd in Sction 4. This rcursiv ordring is rprsntd by: η t = ρε t ν t. ( If ( is substitutd into (8 and (9, th rsult is: = ρ ρ ν ε - var(, cov(, cov( var( - p p y p y y, ( whr: ε 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 this orthogonalization and is still givn by (. It can b shown that quation ( implis = ν ε ν ε ν ε ν ε ρ ρ ρ ρ ( ( var(, cov(, cov( var( - - p p y p y y. (3 This xprssion is idntical to quation (3 undr th idntifying assumptions of th standard modl if w assum that = ( c c c c - ν ε ν ε ρ ρ. (4 In addition, substituting (4 into th long-run nutrality rstriction (4 in th standard B- Q modl yilds xactly (--th long-run nutrality rstriction in our AD-AS modl with th supply shock causally prior to th dmand shock. Thrfor, th two modls ar idntical. As a

12 rsult, th standard B-Q modl forcs all th variations in output rsulting from common shifts in th AD and AS curvs to b attributd to th structural supply shock. Th paramtr stimats obtaind from mploying ( ar prsntd in th scond row of Tabl. Th valus of and ε 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 AD is th rsult of shifts in th AD curv inducd by structural shocks to AS. 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 bcaus thy ar simply proportional to thos shown in Figurs and. Th shaps ar idntical sinc a dcomposition using ( 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 ( ar idntical to thos rportd in Tabl. Th othr rcursiv ordring assums that th dmand shock is causally prior to th supply shock. This cas is rprsntd by ε t = γη t δ t. (5 If (5 is substitutd into (8 and (9, th rsult is var( y cov( y, p cov( y, p = var( - p γ δ η γ -, (8 whr: η continus to b th varianc of th total structural dmand shock and δ is th varianc of th indpndnt structural supply shock.

13 Th third row of Tabl prsnts th rsults obtaind using (6. Th valus of and η ar th sam as thos in th basic modl bcaus hr th long-run nutrality condition is th assumption that any shift in th AD curv, givn no shift in AS, 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, ε, rportd in th first row. Thrfor, with this orthogonalization, slightly mor than on-half of th variation in unxpctd AS is th rsult of shifts in th curv inducd by structural shocks to AD. 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 3 and 4 prsnt th impuls rspons functions obtaind from this orthogonalization. Comparing ths rsponss to thos shown in Figurs and, a % dmand shock hr inducs a rlativly largr rspons of output and a rlativly smallr rspons of inflation. This rsult is obtaind bcaus a % structural dmand shock shifts th AD curv by % and th AS 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, 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. About 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.

14 3 6. Summary and Conclusions. This papr uss an AD-AS modl to idntify a structural VAR and compars this idntification to that obtaind from th standard Blanchard-Quah dcomposition. Our dcomposition imposs th natural normalizations that a dmand shock has a on-unit ffct on AD and a supply shock has a on-unit ffct on AS. 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 th corrlation btwn unxpctd shifts in th AD and AS curvs as wll as obtain a point stimat of th slop of th short-run AS curv. W find that th AS curv is flat nough for dmand shocks to hav an important shortrun ffct on output. 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% only slightly lowr than th.78% incras in output causd by a % supply shock (including its inducd shift of AD. Prhaps, th most important finding is th high corrlation btwn dmand and supply shocks. This papr shows that assumptions about th sourc of this corrlation affct varianc dcompositions and impuls-rspons functions. For xampl, w prov that a causal ordring in which structural supply shocks shift th dmand curv is mathmatically quivalnt to th standard B-Q modl (up to a scalar. In this cas, th structural dmand shock accounts for 8% of th long-run variation in output. 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 only 8% of th variation in output. Thrfor, dmand shocks ar capabl of accounting for a larg shar of th long-run variation in output, as suggstd by th modl in Wst (988.

15 4 This papr xplicitly considrs only th two simplst xplanations for th contmporanous corrlation btwn th structural AD and AS shocks. Evn though ach of ths two possibilitis is rathr xtrm it is most likly that causality is bidirctional, that is dmand shocks affct supply shocks and vic vrsa thy dmonstrat that assumptions about th corrlation btwn structural shocks hav important ffcts on VAR rsults. Sinc it is not possibl to dtrmin th rason why th curvs shift togthr without placing additional rstrictions on th data, without furthr vidnc it is not possibl to claim that dmand shocks play a limitd rol in ral output variability.

16 5 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 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 (3, Optimal Montary Policy and th Corrlation btwn Prics and Output. Contributions to Macroconomics, Issu. Gali, Jordi (99, "How Wll Dos th IS-LM Modl Fit Postwar U.S. Data?" Th Quartrly Journal of Economics 7, pp 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. and Edward Nlson (999, "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. 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

17 6 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 Wst, Knnth D. (988, On Th Intrprtation of Nar Random-Walk Bhavior in GNP. Amrican Economic Rviw 78, pp. -9.

18 7 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

19 8 ( ( (3 Tabl Point Estimats of Structural Paramtrs of AD-AS Modl 956:3-:4 Modl Nam ε εη η ν Basic AD-AS 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 γ _.84 (.66,.948 Th numbrs in parnthsis ar 95% confidnc intrvals from bootstrapping. = snsitivity of AS to an unxpctd chang in inflation. ε = varianc of total structural shock to AS. εη =covarianc btwn total structural shocks to AS and AD. η = varianc of total structural shock to AD. ν = varianc of indpndnt structural shock to AD. ρ = ffct of shock to AS on total shock to AD if causality runs from supply shock to dmand shock. δ = varianc of indpndnt structural shock to AS. γ = ffct of shock to AS on total shock to AD if causality runs from supply shock to dmand shock.

20 9 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

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

22 Figur 3: Output Rspons in our AD-AS Modl Panl A: Rspons of Output to a % Supply Shock Panl B: Rspons of Output to a % Dmand Shock % of Ral GDP % of Ral GDP Lag Lag Figur 4: Inflation Rspons in our AD-AS Modl Panl A: Rspons of Inflation to a % Supply Shock Panl B: Rspons of Inflation to a % Dmand Shock % of Inflation % of Inflation Lag Lag

23 Endnots Studis that us a largr dimnsion VAR oftn impos mor rstrictions on th long-run or short-run ffcts of slctd shocks. For xampl, using an IS-LM-Phillips Curv framwork, Gali (99 distinguishs th supply shock from IS-curv shocks and from LM-curv shocks by assuming that ach of ths lattr shocks has no long-run ffct on output. S, for xampl, Clarida, Galí, and Grtlr (999: p. 674 and Covr and Pcorino (3 3 S, for xampl, Romr (, pp and Ball, Mankiw and Romr (988, pp. 3-9 who prsnt modls in which firms chang output rathr than pric in rspons to dmand shocks bcaus of ral rigidity. 4 S, for xampl, McCallum (989 and McCallum and Nlson (999 for drivations that show that currnt AD dpnds upon xpctd futur output. Gali (99 taks this possibility into account by including th AS shock in both th IS curv and th AS curv. 5 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.