SHSU ECONOMICS WORKING PAPER

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1 Sam Houson Sae Unversy Deparmen of Economcs and Inernaonal Busness Workng Paper Seres Secoral Prce Changes and Oupu Growh: Supply and Demand n General Equlbrum Nahan S. Balke and Hranya K Nah SHSU Economcs & Inl. Busness Workng Paper No. SHSU_ECO_WP6-4 Sepember 26 Absrac: Prce changes and oupu growh, boh a he aggregae and he secoral level, appear o be negavely correlaed. A a basc level, hs suggess ha secoral supply shocks are more prevalen han secoral demand shocks. However, s no clear wha hese secoral prce-oupu correlaons mean once one hnks n erms of general equlbrum. To help us undersand he mplcaon of hese prce-oupu correlaons, hs paper examnes a mul-secor dynamc general equlbrum model ha ncludes secoral echnology shocks and secoral demand shocks, as well as aggregae money growh shocks. We show ha whle a model drven solely by secoral echnology shocks can generae plausble prce-oupu correlaons, demand shocks, parcularly secoral demand shocks, are needed for he model o generae he secoral prce-oupu correlaons observed n he daa. We also show ha echnology shocks do no always look lke supply shocks. Posve echnology shocks o secors producng goods ha are used for nvesmen frequenly resul n ncreases n oupu and prces n oher secors whle posve echnology shocks o secors producng goods ha are used prmarly as nermedae npus look lke supply shocks n oher secors SHSU ECONOMICS WORKING PAPER

2 Secoral Prce Changes and Oupu Growh: Supply and Demand n General Equlbrum Nahan S. Balke a and Hranya K. Nah b Absrac: Prce changes and oupu growh, boh a he aggregae and he secoral level, appear o be negavely correlaed. A a basc level, hs suggess ha secoral supply shocks are more prevalen han secoral demand shocks. However, s no clear wha hese secoral prce-oupu correlaons mean once one hnks n erms of general equlbrum. To help us undersand he mplcaon of hese prce-oupu correlaons, hs paper examnes a mul-secor dynamc general equlbrum model ha ncludes secoral echnology shocks and secoral demand shocks, as well as aggregae money growh shocks. We show ha whle a model drven solely by secoral echnology shocks can generae plausble prce-oupu correlaons, demand shocks, parcularly secoral demand shocks, are needed for he model o generae he secoral prce-oupu correlaons observed n he daa. We also show ha echnology shocks do no always look lke supply shocks. Posve echnology shocks o secors producng goods ha are used for nvesmen frequenly resul n ncreases n oupu and prces n oher secors whle posve echnology shocks o secors producng goods ha are used prmarly as nermedae npus look lke supply shocks n oher secors. a Deparmen of Economcs, Souhern Mehods Unversy, Dallas TX and Research Deparmen, Federal Reserve Bank of Dallas, Dallas TX 752, USA. E-mal: nbalke@mal.smu.edu; Phone: ; Fax b Deparmen of Economcs and Inernaonal Busness, Sam Houson Sae Unversy, Hunsvlle, TX , USA. E-mal: eco_hkn@shsu.edu; Phone: ; Fax: *The auhors would lke o hank Davd Black, Greg Huffman, M. Ayhan Kose, Tmo Terasvra, Mark Wynne, and members of he audence a he Growh and Busness Cycle n Theory and Pracce Conference held a he Unversy of Mancheser n uly 2, and he Souhern Economc Assocaon Meengs held a Arlngon (VA) n November 2, for her commens and suggesons. The vews expressed n hs paper do no reflec hose of he Federal Reserve Bank of Dallas or he Federal Reserve Sysem. 2

3 . Inroducon The relaonshp beween prce and oupu has been a cenral heme of he busness cycle research. Much of hs leraure has focused on he Phllps Curve, whch emphaszes a posve relaonshp beween nflaon and he level of economc acvy (see Kng and Wason 994, Gordon 997, Sock and Wason 999). Recenly, several sudes have quesoned wheher prces were ndeed procyclcal. Cooley and Ohanan (99) fnd lle evdence n over a hundred years of daa of a conssen relaonshp beween oupu and prce n he Uned Saes. Cross-counry sudes such as Backus and Kehoe (992), Foro and Kolnzas (994), and den Haan and Summer (2) sugges ha counercyclcal prce movemen s que common. Balke and Wynne (2) documen ha a negave relaonshp beween oupu and prces predomnaes a he secoral level as well. They examne NIPA measures of secoral prce and oupu as well as prces and oupu for four dg SIC level manufacurng ndusres. Thus, counercyclcal prce movemen appears o be he rule raher han he excepon. In hs paper, we examne furher he relaonshp beween prce and oupu a he secoral level. As n Balke and Wynne (2), we fnd a negave relaonshp beween secoral prces and oupu. In addon, we show ha he correlaon beween prce changes and secoral Solow resduals s also negave and s arguably sronger han he relaonshp beween secoral oupu growh and prce changes. A smple economc nerpreaon of he negave relaonshp beween secoral prce and oupu s ha A relaed leraure has examned he relaonshp beween nflaon and he dsrbuon of relave prce changes. In parcular, Vnng and Elwerowsk (976) have examned he relaonshp beween nflaon and he sandard devaon and skewness of he dsrbuon of relave prce changes for he U.S. whle Domberger (987) has done lkewse for he U.K. Ball and Mankw (995) and Balke and Wynne (2) provde alernave heorecal explanaons for he exsence of such relaonshps. 3

4 secoral supply shocks are mporan sources of secoral flucuaons. However, as we show below, he fac ha he prce-oupu relaonshp s weaker han he prce-solow resdual relaonshp suggess ha secoral demand shocks could play an mporan role n he behavor of secoral oupu and prces. The problem wh hnkng abou secoral prces and oupu n erms of secoral demands and supples s ha n a general equlbrum framework s hard o label wha s a demand shock and wha s a supply shock. As a resul, we buld a smple mulsecor dynamc general equlbrum model o help us evaluae wha facors mgh be mporan conrbuors o he prce-oupu correlaons ha we see n he daa. Whle several mulsecor models have appeared n he leraure recenly (see Huffman and Wynne 999, Horvah 2, Balke and Wynne 2), none has examned n deal he prceoupu relaonshp mpled by hose models. We fnd ha boh secoral echnology shocks and shocks o secoral auonomous spendng (for example, secoral governmen expendure shocks) are needed for our model o generae secoral prce-oupu correlaons close o hose observed. In addon, we show ha echnology shocks do no always look lke supply shocks. Tha s, posve echnology shocks n secors whose oupu s used prmarly for nvesmen and consumpon have effecs on oher secors ha are remnscen of demand shocks: prce and oupu rse. However, hey begn o look more lke supply shocks a longer horzons. On he oher hand, posve echnology shocks o secors whose oupu s used prmarly as nermedae npus do ndeed have effecs on oher secors ha look lke he effec of a radonal supply shock: prces fall and oupu rses. The paper s organzed as follows. In he nex secon, we revew he relaonshp beween secoral prce, secoral oupu, and secoral Solow resdual. In secon 3, we 4

5 presen a smple mulsecor dynamc general equlbrum model wh a cash-n-advance consran. We wll use hs model o help us undersand he economc sgnfcance of he negave secoral prce/oupu correlaon apparen n he daa. In secon 4, we dscuss how we calbrae he parameer values and varous ypes of shocks for he model. In secon 5, we examne whch feaures of he model, he ype of shocks and he naure of secoral neracons, have mporan effecs on secoral prce-oupu correlaons whle n secon 6, we examne how secoral oupu and prces respond o varous ypes of secoral shocks. Secon 7 concludes. 2. The Relaonshp beween Secoral Prce, Oupu, and Solow Resdual Cooley and Ohanan (99) show ha conrary o he wdely held vew, procyclcal behavor of prces s an excepon raher han a rule. Only durng he ner-war perod was he prce level unequvocally procyclcal. Usng quarerly daa for he enre pos-war perod from 948 o 987, hey fnd a negave correlaon beween logdfferenced oupu and prces, ha vares beween.5 and.38. Esmaes for he subsample 966:-987:2 show he sronges negave relaonshp. Oher mehods of derendng he daa, such as lnear derendng or Hodrck-Presco flerng, yeld even sronger resuls. Balke and Wynne (2) show ha a negave correlaon beween prces and oupu s wdespread a he secoral level as well, usng 2 dg SIC level NIPA daa and 4 dg SIC level daa for manufacurng. Here, we examne he relaonshp beween prce and oupu a he secoral level usng a dfferen daa se for he pos-war U.S. economy. The prmary source of daa for our analyss s an exended verson of he KLEM daa se ha consss of annual 5

6 observaons on gross oupu, prce and varous npus for 35 secors of he US economy, orgnally compled by orgenson, Gollop and Fraumen (987). Ths daa se covers he perod from 947 o 989 and hese hry-fve secors roughly mach he 2-dg SIC of he U.S. ndusres. Ths daa se forms he bass for he calbraon of secoral echnology shocks used n our dynamc general equlbrum model below. Table presens summary sascs of correlaon of secoral prce changes (log frs dfferences) wh secoral oupu growh, beween prce changes and secoral Solow resdual growh 2, and of oupu growh wh Solow resdual growh. The frs column presens average correlaons beween hese varables, averaged over hry- fve secors. Medan and sandard devaon of hese secoral correlaons are shown n he second and he hrd column. The fourh and he ffh column presen he mnmum and he maxmum of hese correlaons across secors. As we can see, on average prce changes and oupu growh are negavely correlaed. However, prce-oupu correlaon vares across secors, rangng from.6 for elecrc uly servces o.33 for lumber and wood producs. For mos of hese hry-fve secors he correlaon s negave and only for four secors s posve. Furhermore, he correlaon beween prce changes and Solow resdual growh s negave, and larger n magnude han he ones ha exs beween prces and oupu, and beween oupu and Solow resduals. 2 Usng he KLEM daa se, we calculae he growh of sandard Solow resduals for each secor,.e. log(a, ) log(a,- ) = [log(y, )- log(y,- )] α K [log(k, )-log(k,- )]-α H [log(h, )-log(h,- )] α N [log(n, )- log(n,- )]where A, s a measure of producvy (echnology) n secor n perod, Y, s gross oupu n secor a perod, K, s he ne sock of capal, H, s he labor npu and N, s he maeral npus. α K, α H, and α N are ncome shares of capal, labor, and maeral npus respecvely. In recen years, researchers have come up wh several modfcaons of he sandard Solow resdual. These modfcaons nclude adjusmens for ncreasng reurns o scale or for cyclcal varaons n npu uses (for example, see Hall 99 and Basu and Kmball 997). However, he sgns of he correlaons consdered here are robus o all hese alernave measures of Solow resdual. 6

7 To help undersand he observed relaonshp, and o explan he movaon behnd our analyss le us consder a paral equlbrum model n whch demand and supply nerac o se equlbrum prce and quany for each secor. Under he assumpon of consan reurns o scale echnology and a fxed vecor of npu prces, we have horzonal supply curve for secor (S n Fgure (a) and (b)). Noe ha hs supply funcon, q s (P), s homogenous of degree zero n npu and oupu prce vecor, P. Demand for good s gven by a downward slopng curve, D. The demand funcon, q d (P,NY) s homogenous of degree zero n he prce vecor, P, and nomnal ncome, NY. Now suppose secor experences a posve echnology shock. As n Fgure (a), he supply curve shfs downward: prce falls and oupu rses. In hs paral equlbrum seng, hs echnology shock does no have any effec on demand. Thus, f here were only echnology shocks, one would expec changes n prce and changes n oupu o be perfecly negavely correlaed. Smlarly, changes n prce and changes n echnology would be perfecly negavely correlaed. However, a purely nomnal shock, on he oher hand, would shf boh supply and demand curves upward by he same amoun resulng only n an ncrease n prce (see Fgure (b)). Thus, purely nomnal shocks would end o lower boh he correlaon of prce changes wh oupu growh, and he correlaon of prce changes wh Solow resdual growh. However, f here were an ncrease n secoral demand, secoral oupu could rse (bu no secoral prce) weakenng he correlaon beween secoral oupu and prces bu no beween secoral prces and secoral Solow resduals. In oher words, he correlaon beween secoral oupu and secoral Solow resduals falls n he presence of secoral demand shocks. The fac ha we observe a smaller correlaon beween oupu and Solow resdual growh han beween prce and 7

8 Solow resdual growh (n absolue erms) suggess ha secoral demand shocks could be mporan source of relave movemens of secoral prce and oupu. However, once we move away from a paral equlbrum framework, s much more dffcul o hnk n erms of supply or demand shocks. For example, f secors nerac wh one anoher hrough npu-oupu srucures, a echnology shock n one secor would change demand and supply condons n oher secors. For example, f good s used as an npu, hen posve echnology shock n secor would cause he average cos o fall n oher secors and hus her supply curves would shf downward. Alernavely, a echnology shock n a gven secor could change demand n oher secors as frms and consumers respond o changes n relave prces. As a resul, s no clear wha wll be he fnal effecs on prces and oupu across secors of a posve echnology shock n a gven secor. In order o undersand he behavor of secoral prces and oupu n a general equlbrum seng wh varous forces of demand and supply workng a andem, we need a general equlbrum model, o whch we now urn. 3. A Smple Mulsecor General Equlbrum Model In hs secon we presen a mulsecor dynamc model wh capal accumulaon and a cash-n-advance consran. Whle here have been recen aemps o buld secoral general equlbrum models (Long and Plosser 983, Huffman and Wynne 999, Horvah 2, Balke and Wynne 2), wh he excepon of Balke and Wynne (2), hese models have no examned he behavor of secoral prces. The curren model dffers from ha n Balke and Wynne (2) by ncludng capal accumulaon and a cash-n- 8

9 advance consran for consumpon goods. In Balke and Wynne, money only affecs he aggregae prce level. In he model presened below, wh a cash-n-advance consran, money growh shocks wll now have relave prce mplcaons as well as aggregae prce level mplcaons. 3.. Economc Envronmen There are dfferen secors n he economy, each producng a dfferen good. Each secor consss of a large number of dencal frms. Each frm has consan reurns o scale echnology ha uses capal, labor and maeral npus. There are poenally four dfferen uses for he oupu of each secor: prvae consumpon, nvesmen npu, nermedae npus n oher secors, and governmen (or more generally, auonomous) purchases. A. Consumers and Preferences We assume ha he economy s populaed by a large number of dencal nfnely-lved consumers. The represenave consumer has me-separable preferences summarzed by he followng uly funcon: ( ) = = = = U θ + θ j log c j, log h β j, () j j where < β < s he dscoun facor and θ j for j =,2,. c j, s he consumpon of he jh commody n perod, whle h j, s he hours suppled o he jh producon acvy n perod. We normalze he me endowmen o uny. 9

10 The consumer earns wage ncome by supplyng labor o varous producon acves and renal ncome by renng ou capal goods. She also receves a nomnal lump-sum ransfer T from he governmen n each perod. Besdes consumpon, she purchases nvesmen goods for dfferen secors o augmen her sock of capal goods. Thus he budge consran for he represenave consumer s gven by j, j, j, j, W h + R k + π + T + m P c + Q z + τ + m j, j, j, j, j, (2) where W j, s he nomnal wage n secor j n perod ; R j, s he nomnal ren pad by secor j n perod and k j, s he capal rened ou o secor j. m s he nomnal money balance wh he consumer a he end of he perod. P j, s he prce of commody j n perod. Q j, s he prce of capal n secor j and z j, s he gross nvesmen of he represenave consumer n secor j n perod. τ s he lump-sum ax pad by he consumer whle T s a lump-sum money ransfer n perod. π j, s redsrbued profs of (he represenave) frm n secor j. We assume ha labor s perfecly moble across secors. Ths wll mply ha n equlbrum W j, = W. The represenave consumer also faces a cash-n-advance consran gven by m + T P c (3) j, j, The prmary purpose of nroducng a cash-n-advance consran s o enable our model o produce nomnal prces. Because no all goods are subjec o he cash-n-advance consran, moneary shocks wll have mplcaons for relave prces. The sock of capal n secor j evolves accordng o k + j,+ = ( δ j )k j, z j, (4)

11 where z j, s he gross nvesmen n secor j durng perod and δ j s he rae of s deprecaon. Subsung (4) and W j, = W no (2), we oban W h Q j, j, + R ( δ j j, )k k j, j, + τ + π j, + m + T + m P j, c j, + Q j, k j,+ (5) The problem faced by he represenave consumer s o maxmze her dscouned uly sream gven by () subjec o he budge consran (5) and he cash-n-advance consran (3). B. Frms and Producon The echnology avalable o a represenave frm n secor s gven by a consan reurns o scale, Cobb-Douglas producon funcon: b α, y = A (μ h ) k n (6),,,, a, j, j,, j = where b >, α > and b + α + a. y, s he gross oupu of secor n perod ; A, denoes oal facor producvy n secor n perod ; μ, denoes labor augmenng echncal change n secor n perod ; h, and k, are respecvely he labor npu and he capal sock n secor n perod ; and n,j, s he quany of commody j used as an npu n secor n perod. The frm maxmzes s profs subjec o a consran mposed by he echnology as gven by (6) n each perod. The prof funcon for frm n perod s gven by Π, = P y W h R k P n (7),,,,, j,, j,

12 where P, s he prce of oupu n secor (or good ). C. Invesmen Good Producer There s an nvesmen good producer who combnes goods (bu uses no addonal capal or labor) o produce nvesmen goods accordng o he followng echnology: z =, x j, (8) = j = d j where x j, s he quany of commody j used o assemble nvesmen good. The problem faced by hs producer s o maxmze profs subjec o he consran (8) n each perod. Prof of he nvesmen good producer s gven by Q z P x (9) =,, =,, Noe ha he specfcaons of (8) and (9) mply ha s cosless o move capal from one secor o anoher. The reason for havng an nvesmen or capal good producer s ha he npuoupu ables are specfc abou he commodes used as nermedae npus, bu do no provde any breakdown of dfferen ypes of capal used by a parcular ndusry (secor). The npu-oupu able, however, does ell he amoun of a commody used for nvesmen, denoed by x j, n our model. Thus, n he npu-oupu ables here s jus one ype of nvesmen good, bu many commodes are used o form ha nvesmen good. By nroducng nvesmen good producer, we rean ha srucure n our model. 2

13 D. Governmen Secoral governmen expendures are assumed o be exogenous. However, governmen faces he followng budge consran: T + P, g, = τ + M M () = We assume ha lump-sum ransfer T s equal o change n sock of money, M - M -, where M s he per capa money supply n perod. The money sock follows a law of moon M = ν M -, () where ν s he gross growh rae of he money supply n perod. E. Secoral Resource Consrans Fnally, for each secor, =,2,, oal uses of he commody mus no exceed oupu. Tha s, y = c + x + g + n (2),,,, j,, Snce we canno oban me seres daa on secor specfc governmen spendng, we use me seres on secoral governmen spendng plus secoral ne expors n our calbraon and smulaon. Thus, g, wll acually correspond o secoral auonomous expendures Seady Sae Growh Followng Kng, Plosser and Rebelo (987, 988), we have resrced preferences and echnologes so ha he sysem exhbs balanced growh. In parcular, we assume 3

14 ha he uses of secor s oupu gven n equaon (2) exhb balanced growh. The model also assumes he growh rae of work effor o be zero,.e., η, =,2, h = where h,+ η h = for all, s he seady sae gross growh rae of work effor. h, Le η ω be he seady sae gross growh rae of varable ω n secor, hen balanced growh of he uses of secoral oupu requres ha η = η = η = η = η (3) y c x g n j, Le η μ be he growh facor assocaed wh labor augmenng echnologcal progress for producon n secor. Noe ha he uses of oupu n secor (see Equaon 2) need no be he growh facor for oupu n secor. Also, balanced growh n he allocaon of nvesmen goods across secors mples η z = η z. Thus, he growh facor for he nvesmen good producer s ηz = η (4) d j x j The capal accumulaon echnology, however, mples η = η (5) k j z j whch along wh (3) and (4) mples ηk j = ηk = η d j y j (6) Combnng equaons (3) and (6) and he secoral producon funcons (Equaon 6), we oban log( η Y ) = (I αd a) b log( η μ ) (7) 4

15 where log( η Y ) s a vecor of logarhm of he growh facor of secoral oupu, I s a deny marx, α s a vecor of α s, d s a vecor of d s, a s he npu-oupu marx, b s a dagonal marx of b s and log( η μ ) s a vecor of logarhm of he growh facors of labor augmenng echnologcal progress n secors. From (6) follows ha log( η ) = d log(η ) (8) k Y where log( ηk ) s he logarhm of he growh raes of secoral capal socks. In our analyss below, we normalze real secoral oupu and secoral demand componens by her respecve secoral growh componens D, ( ηy ) =.Secoral capal s normalzed by he growh facor for capal D k, where D k, = ( η k ) = D d j j,. So ha nomnal expendures are consan n he seady sae, we normalze nomnal secoral expendures by M. Thus, he normalzed prce of secoral oupu s p, = P, D, /M ; he normalzed prce of secoral capal s q, = Q, D k, / M ; he normalzed wage rae s w = W / M ; and he renal rae on secoral capal s r, = R, D k, / M. Fnally, boh money holdngs and lump sum axes are normalzed by M Decenralzed Opmzaon A. Frs-order Condons for he Represenave Agen s Uly Maxmzaon Recall ha he represenave agen s uly funcon s gven by equaon (), her budge consran s gven by equaon (5) and he cash-n-advance consran s gven by equaon (3). Dervng and normalzng he frs order condons for he consumer s 5

16 uly maxmzaon yelds 3 : c θ, = p, * ( λ + γ * ) (9) θ h j, = λ * w (2) * r, + q, + E βλ + ( δ ) q, + q, * = λ η k + (2) * β * * λ = E ( λ + + γ + ) (22) ν + w h j, + rj, k j, p j, c j, q j, k j, + η k + E = ν ( δ j)q j, k j, + m + τ m ν ν (23) m ν (ν ) + p ν j, c j, = (24) * * Fnally, lmβ λ q,k,+ =, =,2,. and lmβ λ m = are he ransversaly condons for secoral capal and money, respecvely. The varables λ and γ are he Lagrange mulplers for he budge consran and he cash-n-advance consran n he consumer s problem, respecvely. For convenence, we make he followng ransformaons: λ * = λ / β and γ * = γ / β. 3 Noe ha he varables are normalzed; for parsmony we are no usng dfferen noaon. 6

17 B. Frs-order Condons for Secoral Oupu and Invesmen Good Producers Secoral oupu producers maxmze profs (Equaon 7) gven producon echnology (Equaon 6) and oupu and npu prces yeldng: b p y = w h (25),,, α p y = r k (26),,,, a p y = p n (27), j,, j,, j, Noe ha gven he Cobb-Douglas producon echnology, he npu cos shares are equal o her respecve oupu elasces. The frs- order condons for prof maxmzaon by he producer of nvesmen (capal) good (whch, recall, s freely moble across secors) are gven by: q, = ξ (28) p x = ξ d x (29),, d j j, z x (3) =, = d j j, where ξ s he Lagrange mulpler for he echnology consran n he nvesmen good producer s problem. Noe ha perfec capal mobly across secors mples ha he prce of he capal across secors s equal (Equaon 28). C. Marke Clearng Condons Marke clearng n he secoral good markes mples 7

18 y = c + x + g + n (3),,,, j,, and for money mples m = (32) Furhermore, supply and demand of secoral npus of labor and capal (h, and k, respecvely) wll be equal n equlbrum Saonary Equlbrum A saonary equlbrum for hs economy s defned as he prce vecors p, r =, prces q, w =, quany vecors c,h,k, x, z, y and shadow = prces { λ γ ξ },, such ha for a gven vecor { } = = = A of echnology shfs, gven money supply growh ν, and gven secoral governmen (auonomous) expendures denoed by a vecor { g } =, he followng condons hold: () he consumer s problem s solved; ha s, condons (9) - (24) are sasfed; (2) he necessary and suffcen condons for he frm s prof maxmzaon, (25) - (27) are sasfed; (3) he nvesmen good producer maxmzes her profs; ha s, condons (28) - (3) are sasfed; (4) all markes clear. 8

19 3.5. Seady Sae and Near Seady Sae Dynamcs We solve for some key seady-sae raos ha wll be useful for calbrang he model. The share of real consumpon expendures of ndusry s oupu s gven by c y θ = (33) φ where φ s he h elemen of he vecor Φ = ( I dρ α a g) θ, d s he vecor of he secors shares of aggregae gross fxed nvesmen expendures, g s he vecor of secoral governmen expendure shares n secoral oupu (whch s aken o be exogenous), ρ s a vecor of ρ s where ρ = k j ηk ( δ ) β β( η + δ ), α s a dagonal marx of oupu elasces of capal n secors, and θ s he vecor of secoral shares of aggregae nomnal consumpon expendures. The erm φ also represens secor s share of oal nomnal expendures. The fracon of secor s oupu ha s used as maeral npu n ndusry j s gven by: n y j, φ j = a j, (34) φ whle he fracon of secor s oupu ha s used for nvesmen s gven by: x y = d φ j ρ jα j φ (35) In our analyss below, we analyze he local dynamcs around he seady sae when he economy faces alernave shocks, boh secoral and aggregae. Secoral echnology (represened by A, s n he model), secoral governmen expendures (denoed by g, s), and aggregae money growh (denoed by ν ) are all modeled as frs 9

20 order auoregressve processes. Appendx descrbes he lnear sysem used o approxmae he dynamcs of he model. 4. Calbraon The Inpu-Oupu (I-O) Tables provde a well-defned srucure a varous levels of dsaggregaon ha s represenave of he way he secors nerac among hemselves. In 987 benchmark I-O ables, 95 ndusres are covered a he wo-dg level, whle deals are provded for 48 ndusres a he sx-dg level. Unforunaely, we do no have me seres daa on prces, oupu, and npus for hs classfcaon of ndusres. However, as we use an exended verson of KLEM daa se o calculae secoral Solow resduals (whch represen producvy n he seup of our model), we consoldae he 987 I-O able o hry-fve secors o conform o he classfcaon of secors n he KLEM daa se. From he consoldaed I-O able, we calbrae he marx, a, whch descrbes he npu-oupu relaonshps beween he secors. The share of compensaon of employees n (nomnal) oupu s compued for each of he hry fve secors from he 987 I-O able, and used o calbrae he vecor of oupu elasces of labor, b. Then he vecor of capal share coeffcens, α, s recovered from he assumpon of consan reurns o scale,.e. α = a b. The vecor d, whch descrbes he secors shares of, j aggregae gross fxed nvesmen expendures, and he share of each secor s oupu (φ ) n aggregae oupu are also calculaed from he 987 I-O able. The fracon of each secor s oupu purchased by governmen, g, s aken o be mnus he shares of consumpon, nvesmen, and maeral npu usage of ha secor s oupu. Average 2

21 growh n he secoral Solow resduals over our sample and labor shares are n urn used o calbrae he vecor of labor-augmenng echnologcal growh facor, η μ. The secoral deprecaon raes, δ s, are aken from Horvah (2). These, n urn, are used o calculae he vecor of secoral shares of aggregae consumpon expendures, θ. Fnally, we se he dscoun facor, β =.95, whch s comparable o hose used n oher sudes. In order o esmae a sochasc process for secoral governmen expendures, we need me seres daa on secoral governmen purchases. Unforunaely, annual me seres for secoral governmen expendures alone s no avalable. Therefore, o oban annual me seres daa on secoral governmen expendures (as opposed o seady sae values) we ake he resdual of secoral real GDP (value added) afer subracng off secoral consumpon and gross fxed nvesmen. Snce here s no way ha we can decompose hese resduals no governmen expendures and ne expors hese daa are subjec o he volaly ha s presen n ne expors. Thus, hese mgh be more accuraely descrbed as secoral auonomous expendure. A dealed dscusson on our mehodology o consruc hs varable s presened n Appendx 2. Daa on aggregae money base for he perod from 947 o 989 are obaned from he DRI-Pro daabase. We se ν = exp (.486), whch mples an approxmae growh rae of 5 percen for money supply. In order o calbrae shocks o secoral echnology and secoral auonomous expendures, we frs derend hese varables by subracng he respecve rend componens obaned from lnear regressons of hese varables on a consan and me. We hen esmae AR() models for he derended varables and save he resduals from hese regressons. For money growh raes, we smply esmae an AR() model for he 2

22 growh raes of money sock and save he resduals. In mos of he expermens below, shocks wll be se o resampled resduals. By usng he emprcal dsrbuon of shocks, we can manan n our smulaons he covarance srucure of shocks seen n he daa, whou havng o specfy a parcular jon dsrbuon for hese shocks. Table 2 lss he hry-fve secors and presens he fracons of each secor s oupu ha goes for nermedae uses or for varous fnal uses such as consumpon, nvesmen, governmen purchases and ne expors n 987. As we can see from column of he able, for weny-one secors more han half of her oupu s used as maeral npus n oher secors. Among hem, meallc ores mnng, crude peroleum and naural gas, nonmeallc mnerals mnng, sone and prmary meal secors supply almos all of her oupu for nermedae uses. For en secors, more han half of her oupu s used for consumpon. Food and kndred producs, obacco producs, apparel, foowear and leaher producs and mscellaneous manufacurng producs are predomnanly consumpon good producng secors. On he oher hand, consrucon and machnery manufacurng are predomnanly nvesmen good producng secors. Noe ha he governmen purchases nearly half of he oal oupu of he ransporaon equpmen secor. In he foowear and leaher producs secor, more han s domesc oupu s mpored no he U.S. Furhermore, more han 4 percen of he domesc producon of crude peroleum and naural gas and mscellaneous manufacurng producs s mpored. Snce crude ol s manly used as nermedae npus, one would expec ha exernal dsurbances n hs secor would have sgnfcan mpac on he U.S. domesc producon of peroleum producs. As we can see, none of 22

23 hese secors s a major ne exporer n erms of he fracon of s oupu ha s beng expored. 5. Smulaon Resuls 5.. Average Secoral Correlaons beween Prce, Oupu and Solow Resdual Table 3 dsplays average prce-oupu growh correlaons across he hry-fve secors for four separae expermens. For each of hese expermens, we smulae he model, mes for 4 perods (he lengh of our sample perod), wh an nal sarup of 5 perods o elmnae any poenal effec of nal condons. For each smulaon, we calculae average correlaons along wh he neror 9 percen nerval of he dsrbuon of smulaed correlaons. Table 3 also ncludes he average secoral prce- Solow resdual correlaon and he average oupu-solow resdual correlaon. Examnng column (2) n Table 3, we observe ha he model wh he full complemen of secoral echnology, secoral demand, and money growh shocks yelds average (across secors) secoral prce-oupu and secoral prce-solow resdual correlaons ha are que close o hose found n he daa. For boh hese correlaons, he neror 9 percen of he smulaed correlaons nclude he acual secoral prceoupu and prce-solow resdual correlaons. On he oher hand, he average secoral oupu-solow resdual correlaon generaed by he model s oo hgh relave o ha n he daa. To see how he dfferen feaures of he model affec he average prce-oupu correlaon, we consder hree addonal expermens. Frs, we examne a model n whch here s no secoral npu-oupu neracon, secoral echnology shocks are 23

24 ndependen of each oher, and here are no money growh or secoral demand shocks. Of he specfcaons of he model we examne, hs s he closes o he smple paral equlbrum example dscussed n secon 2. As expeced he average secoral prceoupu, secoral prce-solow resdual correlaons are close o (see column 3 of Table 3). Tha he average correlaon s no equal o mnus one s due o he fac ha oupu of some secors s used as capal goods. Posve echnology shocks, n any secor, end o ncrease he demand for capal. Ths, n urn, acs o ncrease demand n secors ha produce capal goods. As we add secoral npu-oupu neracon (column 4), we see ha secoral prceoupu and prce-solow resdual correlaons drop (n absolue value). 4 In hs case, a secoral echnology shock wll also affec he demand for goods ha are used as nermedae npus. Addng secoral demand shocks (column 5), nroduces shocks ha have drec effecs on secoral demands lowerng prce-oupu and prce-solow resdual correlaons furher. For hs expermen, we oban smulaed prce-oupu correlaons ha are geng close o ha observed n he daa. Fnally, by comparng column (5) wh column (2), we see he ncremenal effec of money growh shocks. No surprsngly, money growh shocks end o lower average secoral prce-oupu and prce-solow resdual correlaons. In sum, no sngle feaure s responsble for generang secoral prce-oupu correlaon smlar o ha n he daa: secoral npu-oupu relaonshps, secoral demand shocks, and money growh shocks all have mplcaons for secoral prce-oupu correlaons. 4 We also allow secoral echnology shocks o be correlaed. Ths s accomplshed by resamplng he vecor of resduals from a AR() fed o acual Solow Resduals. 24

25 How well does our secoral model replcae some of he sandard aggregae busness cycle sascs? Table 4 presens varances, relave varances, crosscorrelaons wh aggregae value-added (GDP). Even hough he focus of our analyss s no on hese aggregae real relaonshps, hey provde a benchmark wh whch we can compare he aggregae flucuaons mpled by our model wh hose n he busness cycle leraure. 5 Whle our model does well for many of hese aggregae sascs, fals dramacally n wo crucal respecs - he relave volaly of nvesmen s oo hgh and he correlaon beween oupu and consumpon s oo low. Ths appears o be rue regardless of wheher we nclude secoral neracons, secoral demand shocks, or money growh shocks Indvdual Secoral Prce-Oupu Correlaons To ge a beer sense of wha s happenng a he secoral level, we presen n Table 5 prce-oupu correlaons for each secor ndvdually. Comparng he prceoupu correlaon from he daa (column ) wh ha mpled by he baselne model (column 2), we observe ha, even hough he averages (across secors) are smlar, here are several secors n whch he daa and model are dramacally dfferen. These nsances mos ofen occur n secors ha are mporan nvesmen good producers - consrucon, furnure, machnery, elecrc machnery, and nsrumens - or are mporan nermedae npus o hese secors - sone, prmary meals, and fabrcaed meals. Here he model generally mples a posve prce-oupu correlaon whle he acual correlaons are generally negave. 5 As we examne annual daa, we lnearly derend he naonal ncome and produc accoun daa n order o solae he cyclcal behavor raher han employ Hodrck-Presco fler. 25

26 For hese secors, as we suggesed above, any echnology shock ha ncreases demand for capal wll ncrease demand n hese capal good producng secors. Ths s clear from he model n whch here are ndependen echnology shocks, no npu-oupu srucure, and no demand shocks (column 3). Wh log uly, no npu-oupu srucure, and no auonomous expendures, nomnal expendures (p, y, ) n secors whose oupu s no used as an nvesmen good s proporonal o he money sock. Thus, unless a secor s oupu s used for nvesmen (see Table 2), prce-oupu correlaons are mnus one. As we add secoral npu-oupu neracon (column 4), prce-oupu correlaons for all secors fall. In fac, as we add secoral npu-oupu relaonshps and secoral demand shocks (column 5) o he model, he prce-oupu correlaons for many of he nvesmen good secors and secors ha produce mporan maeral npus o nvesmen goods become posve. Tha our model generaes posve prce-oupu correlaons for nvesmen goods and mporan nvesmen good npus may be relaed o he very hgh nvesmen volaly mpled by he model. In he baselne model, whle he curren (me ) secoral capal sock s fxed, s cosless o move capal n and ou of a secor a me +. Because of he secoral capal mobly, he model mples counerfacually large changes n nvesmen demand. Ths leads o hgh aggregae nvesmen volaly, as well as large changes n he demand for capal good producng secors and n he demand for npus of hose secors. 6. Responses of Secoral Oupu and Prces o Aggregae and Secoral Shocks In hs secon we ry o undersand more deeply how dfferen secors respond o boh aggregae and secoral shocks. In parcular, we are neresed n knowng o wha 26

27 exen a secor s role as an npu or fnal good producer deermnes how responds o alernave ypes of shocks, and how shocks n ha secor are ransmed o oher secors. Fgure 2 llusraes he dsrbuon of responses of oupu and prce across secors o a money supply growh shock a varous me horzons:,, 5 and. From Fgure 2, we observe ha prces ncrease n all secors a all me horzons. Moneary shocks whle generally ncreasng all prces do, however, have consequences for curren relave prce changes. A shorer horzon, secors producng goods for nvesmen or nermedae uses experence relave prce ncreases. A longer horzons, prce changes are abou one percen approxmaely equal o he magnude of he change n he money sock n almos all secors. On he oher hand, money growh shocks resul n oupu ncreases n some secors and declnes n ohers. Noe ha he secors experencng a rse n oupu a shorer horzons (.e. a perod and ) produce goods ha are used eher for nvesmen or for nermedae uses whle he secors producng consumpon goods experence some of he hghes oupu declnes. I appears ha a shor me horzon, a money growh shock causes household o subsue away from consumpon goods and no nvesmen goods. Because money growh shocks are perssen (bu no permanen), ancpaon of nflaon wll lead people o subsue away from consumpon goods ha requre cash. The ne resul s ha demand for nvesmen goods and for some maeral npus rse. Fgures 3 and 4 plo he cross-secon responses of oupu and prces o a echnology shock o maeral npu producng secors. In parcular, we are consderng shocks o he crude ol and naural gas secor, and he rubber secor. Noe ha almos he enre oupu of he crude ol secor and 9 percen of he oal oupu of he rubber secor s used as maeral npus (see column of Table 2). A posve echnology shock o he 27

28 maeral npu producng secor looks very much lke a ypcal supply sde shock n ha secor - prce declnes and oupu rses. Furhermore, he effecs n oher secors look very much lke supply shocks. For crude ol, wo oher secors, namely peroleum refnng and gas ules whch receve he bulk of her maeral npus from he crude ol secor, experence large changes n her oupu and prces. The effecs n oher secors are neglgble. We see smlar paern of oupu and prce responses a longer horzons as well; however, he magnudes of oupu and prce responses decrease over me. The effecs on prces and oupu n oher secors of a shock o he Rubber secor also look lke hose of a radonal supply shock. Fgures 5 and 6 llusrae he responses of secoral oupu and prces o a echnology shock o consumpon good producng secors. We chose he moor vehcle secor and he wholesale and real rade secor as he former sells abou 52 percen of s oupu and he laer sells abou 62 percen of s oupu for consumpon (see column 2 of Table 2). Fgures 5 and 6 llusrae he resuls of hs expermen. As evden from hese fgures, a echnology shock n a consumpon good secor acs as a supply shock n ha secor: oupu ncreases and prce decreases a all horzons. On he oher hand, he responses of prce and oupu n oher secors a shor horzons are suggesve of demand shocks; hose secors prces and oupus rse. Immedaely afer a consumpon good secor experences a posve echnology, demand for oher goods ha are eher nermedae npus or nvesmen goods appears o ncrease. However, over me hese emporary demand dsurbances dsappear. A longer horzons, he responses n hese secors are more lke supply shocks hough he magnudes of he responses of oupu and prces are relavely small. 28

29 Fgures 7 and 8 presen he responses of secoral oupu and prces o a echnology shock o nvesmen good producng secors. We choose consrucon and machnery secors for hs expermen. As we see from column 3 of Table 2, 6 percen of he oupu of he consrucon secor and 5 percen of he machnery secor oupu s used for nvesmen. As a resul of a posve echnology shock, whle oupu rses and prce declnes n he consrucon secor (and n he machnery secor) mos of he oher secors experence oupu ncreases and prce ncreases a shor me horzons. Thus he effecs of a echnology shock n an nvesmen good producng secor on oher secors oupus and prces a shor horzons are more remnscen of demand shocks. Agan, a posve echnology shock o an nvesmen good producng secor ncreases demand for he goods manly used as maeral npus or nvesmen goods n ha secor. However, as he prces n he nvesmen good producng secors connue o decrease, he producon coss n oher secors decrease, and consequenly a longer horzons (me horzon ) he oupu and prce responses are suggesve more of supply shocks. Tha secoral echnology shocks can look lke demand shocks n oher secors may hold a he aggregae level as well. Fgure 9 presens he response of aggregae value added (GDP) and he valued added deflaor o echnology shocks n he rubber secor and o machnery secors. GDP rses and he deflaor falls n response o a echnology n nermedae good producng secor (rubber). On he oher hand, he deflaor may rse a leas nally n response o a shock o a capal good producng secor (machnery). One mplcaon s ha f aggregae echnology shocks are akn o a lnear combnaon of secoral echnology shocks, hen posve echnology shocks may no have large nal aggregae prce effecs as he posve and negave secoral prce effecs end o cancel 29

30 each oher ou. Thus, even hough prces are perfecly flexble, he aggregae prce level may appear o respond sluggshly o a echnology shock. 7. Summary and Conclusons In hs paper, we examned he relaonshp beween secoral oupu growh and prce changes. We fnd ha prce changes and oupu growh, boh a he aggregae and he secoral level, are on average negavely correlaed. We also fnd ha a flexble prce, mulsecor, dynamc general equlbrum model s capable of reproducng he average secoral prce-oupu correlaon. Boh secoral echnology and secoral auonomous expendure shocks play mporan roles n generang he negave prce-oupu correlaon. We show ha echnology shocks o secors producng goods ha are used prmarly as npus o oher secors look lke radonal supply shocks, prces fall and oupus rse. On he oher hand, echnology shocks o nvesmen or consumpon goods secors can, a leas n he shor-erm horzons, look lke demand shocks n oher secors, prces and oupus rse whle a longer horzons hey ake he appearance of supply shocks. 3

31 Appendx Lnear Approxmaon and Sae Space Soluon of he Mulsecor Flexble Prce Model In hs appendx we show how we approxmae he opmzng condons (9) - (32) lnearly around a seady sae and solve he resulng lnear dynamc sysem. Noe ha he percenage devaons of he varables from seady sae levels are denoed by a crcumflex (^). Combnng equaons (9), (22), (24) and (32) and akng lnear approxmaon we oban, ĉ, + pˆ, = (A.) We subsue for y, from he producon funcon no (25) and solve for w. Then subsung for w no (2) and lnearzng, we oban ( b ) ĥ, + sh ĥ, a, j nˆ, j, pˆ, = Â, + α kˆ, E νˆ + = (A.2) where sh s he rao of labor npu n secor o lesure. Subsuon for y, from he producon funcon no (28) and lnear approxmaon yelds b ĥ, + a, j nˆ, j, nˆ, j, + pˆ, pˆ j, = α kˆ, Â, (A.3) Subsung for ξ no (29) from (28) and hen lnearzng we oban,, d j xˆ j, + pˆ, qˆ, xˆ = (A.4) Lnear approxmaon of he marke clearng condon (3) yelds 3

32 sc ĉ, + b g + ( + ~ g ) y ĥ, + ĝ + a, j g ĝ, y nˆ, j, sn j, nˆ j,, sx xˆ, = α kˆ, Â, (A.5) where sc s he fracon of secor s oupu allocaed o consumpon. Smlarly, sn j, s he fracon of good oupu used as maeral npus n secor j, and sx s s fracon used for nvesmen. Noe ha n order o lnearze he marke clearng condon (3), we frs re-wre he equaon as follows: g, g y, = c, + x, + g + g + n j,, (A.6) g We defne ~ g, g =, where g, s he governmen (auonomous) expendure on g, g good n perod and g s he aggregae governmen expendures. Therefore, ~ g, can be nerpreed as percenage devaon of secoral governmen expendures from he mean. We subsue for y, from he producon funcon no (26) and solve for r,. Then subsung for r, no (2) and lnearzng, we oban ( δ ) E b ĥ, + + β η k (α a, j nˆ ) kˆ, j,+,+ + pˆ + ( δ,+ + Â,+ ) β η k qˆ + ( δ ) qˆ νˆ νˆ + β η k = (A.7) We subsue for z, n (3) from he capal accumulaon echnology and lnearze around seady sae o oban, = k = η k sz( δ ) sz kˆ = kˆ + d xˆ (A.8) =, + { η ( δ )} { η ( δ )} k where sz s he share of nvesmen n secor o aggregae nvesmens n he economy., 32

33 Usng noaon n Kng, Plosser, and Rebelo (987), equaons (A.) - (A.5) can be wren as: Mcc cl = Mcs s + Mce e (A.9) where Mcc s a ( 2 +4) ( 2 +4) marx of he coeffcens; cl s a ( 2 +4) vecor of conrol varables, namely c, h, x, n,j and p, and,j =,2,3,.; Mcs s a ( 2 +4) (+) marx of coeffcens; s s a (+) vecor of predeermned varables, k, =,2,., and one non-predeermned varable, q; Mce s a ( 2 +4) (2+) marx of coeffcens and e s a (2+) vecor of exogenous varables. Gven hs sysem of equaons, (A.9) can be solved for he conrol varables as funcons of predeermned, non-predeermned and exogenous varables. Gven hese opmal soluons, equaons: (A.7) and (A.8) mply a frs-order dynamc sysem n s,.e. n k s and q, E s + + = Ws + R E e + Qe (A.) where W s a (+) (+) marx and R and Q are (+) (2+) marces. To oban he soluon o hs sysem of dfference equaons we decompose W as PμP -, where P s he marx of egenvecors of W and μ s a dagonal marx wh he egenvalues on he dagonal. For our sysem snce here s only one non-predeermned varable (q ), n order for hs sysem o have a unque soluon here should be jus one egenvalue of W ousde he un crcle. Afer algebrac manpulaon, he opmal me pah for capal accumulaon may be wren as follows: kˆ + = π kk + π ke ê (A.2) kˆ 33

34 where π kk and π ke are respecvely and (2+) marces of coeffcens. These coeffcens are complcaed funcons of he underlyng parameers of preferences and echnology. The dynamcs of capal accumulaon depend on he prevous perod s capal sock, curren exogenous facors and on he enre fuure me pah of hese facors. Appendx 2 Consrucon of Daa on Secoral Auonomous Expendures For he smulaon of he model, we need o calbrae shocks o he secoral governmen expendures, whch are assumed o be exogenous. Daa on governmen expendures by secors are, however, no readly avalable. Therefore, we decompose secoral real GDP no hree fnal expendure componens, namely, consumpon, nvesmen and governmen expendures. Ths decomposon scheme exacly maches he marke clearng condons of our model. The mehod we use for decomposon nvolves he followng seps: ) We oban daa on personal consumpon expendures and gross fxed nvesmens by major ype of producs from unpublshed ables of he Naonal Income and Produc Accouns (NIPA) for a perod from 947 o 997. Noe ha consumpon daa are avalable for 83 produc caegores and nvesmen daa are avalable for 26 produc caegores. 2) These consumpon and nvesmens by producs are hen mapped no consumpon and nvesmens by wo-dg npu-oupu (I-O) ndusres usng a mappng scheme 34

35 oulned n Survey of Curren Busness (Aprl, 994) for 987 Benchmark Inpu- Oupu Tables. Noe ha here are nney-fve wo-dg I-O ndusres. 3) These consumpon and nvesmens daa are hen consoldaed o mach hry-fve secors of he KLEM daa se. 4) We oban daa on GDP by 2-dg SIC ndusres from he Naonal Income and Produc Accouns (NIPA) Income, Employmen and Produc by Indusry unpublshed deal ables and consoldae, wherever necessary, for hry-fve secors. 5) Daa on governmen expendures by secors are hen obaned as resduals by subracng consumpon and nvesmens from secoral GDP. Noe ha all hese values are n curren dollars. In order o conver hem no 987 consan dollar we deflae he governmen expendures by he prce ndces obaned from he KLEM daa se. Noe ha secoral GDP also ncludes a ne expors componen and s mpossble o separae ou hs componen from he resduals we oban n he fnal sep. Therefore, we prefer he nomenclaure secoral auonomous expendures o secoral governmen expendures. Secors ha have relavely hgher shares of ne expors n her respecve oal GDP wll be subjec o volaly ha arses from changes n nernaonal marke condons. 35

36 Table. Summary Sascs of Correlaons across Secors Mean Medan Sandard Devaon Mnmum Maxmum Corr(Δp,Δy ) Corr(Δp,ΔA ) Corr(Δy,ΔA ) () (2) (3) (4) (5) -.27 (.4) (.33) (.45) Noe: Sample perod Esmaed sandard errors are n parenheses. 36

37 Table 2. Inermedae and Fnal Uses of Secoral Oupu n 987 Secor Fracons of oupu n dfferen uses Inermed Consum Inves Gov.pur Ne exp () (2) (3) (4) (5) Agrculure Meallc ores mnng Coal mnng Crude ol and naural gas Nonmeallc mnerals mnng Consrucon Food and kndred producs Tobacco producs Texle Apparel Lumber and wood producs Furnure and fxures Paper Prnng Chemcals Peroleum refnng and relaed prod Rubber Foowear, leaher, and leaher Sone Prmary meal Fabrcaed meal Machnery Elecrcal machnery Moor vehcle Transporaon equpmen Insrumens Mscellaneous manufacurng Transpor Communcaons Elecrc uly servce Gas uly servce Wholesale and real rade FIRE Servces Governmen enerprses Noe: These raos have been calculaed from BEA s 987 Benchmark I-O Use Table 37

38 Table 3. Smulaon Resuls: Average Secoral Correlaons Daa Corr(Δp,Δy ) -.27 Baselne Model No I-O srucure and ndependen echnology shocks I-O srucure and correlaed echnology shocks Add secoral demand shocks () (2) (3) (4) (5) -.27 (-.4, -.4) -.84 (-.87, -.8) -.6 (-.67, -.55) -.39 (-.49, -.29) Corr(Δp,ΔA ) (-.67, -.45) -.92 (-.95, -.89) -.79 (-.84, -.74) -.68 (-.75, -.6) Corr(Δy,ΔA ).45.7 (.67,.75).84 (.8,.87).83 (.8,.84).75 (.7,.78) Noe: The fve and nney-fve percenles for he smulaons are n parenheses. 38

39 Table 4. Smulaon Resuls: Aggregae Volaly and Aggregae Correlaons Daa Baselne Model No I-O srucure and ndependen echnology shocks I-O srucure and correlaed echnology shocks Add secoral demand shocks () (2) (3) (4) (5) SD (Y) SD(C) / SD(Y) SD(X) / SD(Y) SD(H) / SD(Y) Corr (Y, C) Corr (Y, X) Corr (Y, H) Noe: The sascs for he U.S. economy n column are calculaed by aggregang he daa for 35 secors from he KLEM daa se. Sample perod