ACCOUNTING FOR CANADA S ECONOMIC GROWTH

Transcription

1 ACCOUNTING FOR CANADA S ECONOMIC GROWTH By Knnh Carlaw Univrsiy of Canrbury Sphn Kosmpl Univrsiy of Gulph Dparmn of Economics and Financ Univrsiy of Gulph Discussion Papr Accpd Journal of Economic Dvlopmn Th final publicaion of his aricl is availabl a hp://

2 Accouning for Canada's Economic Growh Sphn Kosmpl and Knnh Carlaw ϒ Absrac A dynamic sochasic gnral quilibrium modl is consrucd and calibrad o h Canadian conomy. Tchnology disurbancs from h Canadian conomy ar filrd hrough h modl and usd o gnra arificial im sris. Oupu growh in h modl is hn dcomposd ino h shar wighd growh ras of h facor inpus and produciviy. Th modl is hn usd o idnify h ndognous rsponss of h facor inpus o h chnology disurbancs. Th rsuls suggs ha much of h slowdown obsrvd in Canadian oupu growh sinc 1974 can b xplaind by flucuaions in h ras of invsmn-spcific and rsidual-nural chnological chang. JEL classificaion: E30; O43; O47 Kywords: Invsmn-spcific chnological chang; oal facor produciviy; conomic growh Corrsponding auhor. Dparmn of Economics, Univrsiy of Gulph, Gulph, Onario, N1G 2W1, Canada; Tl.: (519) Ex ; Fax: (519) ; addrss: kosmpl@uogulph.ca ϒ Sphn Kosmpl and Knnh Carlaw ar Assisan Profssors in h Dparmn of Economics a h Univrsiy of Gulph and h Univrsiy of Canrbury, rspcivly. 1

3 1 Inroducion Ral GDP pr capia in Canada grw by a facor of 1.9 from $15,751 in 1961 o $29,695 in 1996, all masurd in 1992 dollars. This incras corrsponds o an avrag growh ra of 1.9 prcn pr yar. Howvr, h avrag annual growh ra ovr h nir priod may provid a mislading sima of Canada's mor rcn conomic prformanc, bcaus Canada xprincd rlaivly rapid growh ovr h arlir yars in h sampl priod and slow growh ovr h lar yars. For xampl, GDP pr capia grw a an avrag annual ra of 3.3 prcn during h priod, bu hn slowd o 1.1 prcn during h priod. Th purpos of his papr is o idnify h sourcs of growh in Canadian ral GDP pr capia during h priod and o xplain diffrncs in growh ras bwn h wo sub-priods. Growh accouning sudis involv h dcomposiion of oupu growh ino h shar wighd growh ras of h labor and capial inpus and h ra of chnological chang. Typically, h producion funcion rsidual is usd o provid a masur of h ra of chnological chang. Howvr, h rsidual alon dos no provid an accura masur of h conribuion of chnology o oupu growh. This is bcaus i dos no accoun for h inducd xpansion of capial which is, a las in par, an ndognous rspons o chnological chang. In ordr o mak infrncs abou h conribuion of various chnologis o h ra of capial accumulaion, a dynamic sochasic gnral quilibrium modl of h conomy is mployd. Th rsuls show ha much of h slowdown obsrvd in Canada's GDP growh sinc 1974 can b xplaind by flucuaions in h ras of chnological chang. Tchnological advancmns ar sparad ino wo cagoris: rsidual-nural chnological chang (RNT) and invsmn-spcific chnological chang (IST). RNT capurs changs in produciviy associad wih h organizaion of capial and labor. I also capurs improvmns in h qualiy of labor, o h xn ha hos improvmns ar no accound for in h masur of h labor inpu. IST accouns for improvmns in h qualiy of capial, as i capurs chnological advancmns mbodid in nw machinry and quipmn. Sinc IST masurs improvmns o produc qualiy, i capurs h fac ha mor ffciv unis of oupu ar bing producd pr uni of capial and labor mployd. Th dcomposiion of chnological chang ino RNT and IST is 2

4 ncssary parly bcaus h growh ra of Canada's GDP is snsiiv o h yp of chnology dvlopd, and parly bcaus h wo forms of chnology diffr in hir im sris bhavior. A rcn IMF rpor on Canada rvald ha h avrag annual ra of IST was highr, and h ra of RNT lowr, afr h ra of GDP growh slowd, 1974 (s Dunaway al., 2000). Tabl 1 summarizs h masurs of IST and RNT rlaiv o h ra of GDP growh ovr slcd priods. Th avrag annual ra of IST incrasd from 1.29 prcn ovr h priod o 5.12 prcn ovr h priod. In comparison, h avrag annual ra of RNT dclind from 1.80 prcn ovr h priod o prcn ovr h priod. 1 Ths obsrvaions lad h radr o corrcly conclud ha h incras in h ra of IST was no sufficinly larg o compnsa for h rducion in h ra of RNT, and hrfor h ra of GDP growh slowd. Howvr, h daa displayd blow and in h IMF rpor do no provid answrs o a numbr of imporan qusions. Firs, hrough wha channls do RNT and IST affc h ra of GDP growh? Scond, how snsiiv is h ra of GDP growh o changs in h ras of chnological chang? Th currn papr provids answrs o hs qusions, and amps o improv our undrsanding of h various sourcs of growh, by quanifying h individual conribuions of IST and RNT o h growh ra of ral GDP pr capia in Canada for slcd priods. {Insr Tabl 1 hr} This analysis adds o h xising liraur on IST, RNT and hir conribuion o growh (.g., Carlaw and Kosmpl, 2000; Grnwood, Hrcowiz and Krusll, 2000, 1997). Our arlir sudy idnifid h channls hrough which RNT and IST affc oal facor produciviy (TFP) growh, whras h currn sudy amps h somwha mor difficul ask of isolaing h conribuion of h chnologis o h ra of GDP growh. Th ask is mor difficul bcaus GDP growh can occur if nw chnologis improv h produciviy of xising rsourcs, ha is if hy affc TFP, or if hy lad o incrass in h quaniy of rsourcs availabl for producion. Grnwood, Hrcowiz and Krusll (1997) hav sudid h ffcs of RNT and IST on U.S. labor produciviy growh. In hir sudy chnological chang was rsricd 3

5 o occur a consan ras. In ohr words, hir sudy focusd only on h U.S. conomy's long run growh pah. Howvr, in h Canadian conomy h ras of chnological chang and h growh ra of ral GDP pr capia wr found o dpnd on h priod sudid (s Tabl 1). As such, in h currn papr h ras of chnological chang ar allowd o flucua. Th currn sudy is also h firs o b basd on Canadian rahr han U.S. ras of chnological chang and growh. Grnwood, Hrcowiz and Krusll (2000) hav also sudid h ffcs ha invsmn-spcific chnology shocks hav on h businss cycl. In hir modl, a posiiv invsmn-spcific chnology shock lowrs h pric of nw quipmn rlaiv o h pric of nondurabl consumpion goods and srvics, and hrfor simulas invsmn and incrass oupu. Thus, h qualiy of nw quipmn and oupu ar posiivly rlad in hir modl. Howvr, w hav obsrvd a ngaiv corrlaion bwn h drndd qualiy of nw quipmn goods and GDP in h Canadian conomy during h priod. In Canada advancs in invsmn-spcific chnology appar o b associad wih conomic slowdowns. In ordr o xplain his puzzl, w build on h Grnwood al. modl. In ordr o xplain h ngaiv corrlaion obsrvd bwn qualiy and oupu in h Canadian daa, i is ncssary o incorpora rsidual-nural chnology shocks ino h Grnwood al. modl and o accoun for h spcific iming of h chnology disurbancs. Grnwood al. do no considr h iming of h chnology disurbancs o b an imporan facor in hir modl. Th common procdur applid in h liraur, and h procdur usd by Grnwood al., is o obain chnology disurbancs from a random numbr gnraor on a compur. Howvr, his procdur canno guaran ha IST will grow fasr, and RNT slowr, afr In ordr o accoun for h iming of chnology shocks, h acual chnology disurbancs from h Canadian conomy will b filrd hrough h modl and usd o gnra flucuaions in h modl's simulad im sris. In our modl, IST is high whn RNT is low, as i is in h daa. Furhrmor, sinc RNT was low during h pos-1974 priod, oupu was low. This is ru dspi h fac ha IST was high and had a posiiv ffc on oupu during h lar priod. As a rsul, in h modl conomy h qualiy of nw capial is high whn oupu is low, as i is in h daa. 4

6 Th papr is organizd as follows: Th modl o b sudid is consrucd in Scion 2. Th rsuls ar prsnd and discussd in Scion 3. Concluding rmarks ar providd in Scion 4. 2 Th modl Th modl is a vrsion of h ral businss cycl (RBC) modl consrucd by Grnwood al. (2000) which allows for nw quipmn o bcom incrasingly mor fficin wih h passag of im. 2.1 Housholds Th rprsnaiv houshold maximizs h xpcd valu of a discound sram of uiliy givn by 0 U ( c, l ) =0 E β, 0 < β < 1, (1) whr c and l dno h da lvls of consumpion and lisur. Th houshold's im ndowmn is normalizd o on, and hrfor l n = 1, whr n dnos h + fracion of im dvod o work. Th momnary uiliy funcion has h following form: ω 1 ω 1 γ ( c l ) 1 if 0 < γ < 1 or γ > 1, U( c, l ) = 1 γ (2) ω lnc + (1 ω) lnl if γ = 1. Th houshold budg consrain is givn by, c + i ( τ + τ a p a. (3) s, + pqi, 1 n ) w n + (1 τ k ) ( rs, s + r, ) This sas ha h houshold's xpndiurs on consumpion and invsmn ar boundd by afr ax oal incom lss adjusmn coss. Th ral wag ra is dnod by w, h s,, ral rnal ra of srucurs by r, and h ral rnal ra of quipmn by r,. Labor s incom is axd a a ra of τ n, and capial incom a a ra of τ k. Th houshold rcivs a lump-sum ransfr of τ from govrnmn. Th capial sock compriss srucurs, s, and quipmn,. Invsmn xpndiurs for srucurs ar i, and s p qi, for 5

7 quipmn, whr p masurs h purchas pric of nw quipmn rlaiv o h pric of h consumpion good and q indicas h qualiy (or rlaiv fficincy) of h nws vinag of quipmn. Insalling nw capial may rquir adjusmn coss - a s, for srucurs and p a hav h following form, 2 a x, θ x ( x ψ x ) = x, for quipmn. Th adjusmn cos funcions ar assumd o x, ( s, ) x. (4) All variabls in h houshold's budg consrain ar masurd in consumpion unis. Thus, ach uni of invsmn in srucurs coss on uni of consumpion, and ach uni of quipmn coss p unis of consumpion. In h daa, h rlaiv pric sris displays a downward rnd - indicaing ha invsmn in quipmn is bcoming rlaivly lss xpnsiv as im passs. Efficincy gains also lad o cos savings for invsors. For his rason, h rciprocal of h rlaiv pric provids a masur of h fficincy, or h qualiy ( q ), of h nws vinag of quipmn. 3 Th houshold's capial socks volv according o: i = + ) s, and (5) s, s 1 (1 δ s i, 1 (1 δ q = + ). (6) Hr δ s and δ dno h ras of dprciaion of srucurs and quipmn, rspcivly. 2.2 Firms max { N, S, E } Firms ar compiiv and sk o maximiz profis, π = F( N, S, E ; A ) w N r S r E. (7) s, Th producion chnology is Cobb-Douglas, F α n α s α ( N, S, E ; A ) = A N S E, wih α + α = 1 whr, n + s α, (8) A dnos h sa of rsidual-nural chnology. Sinc rsidual-nural chnological advancmns improv h conomy's abiliy o produc all yps of goods, 6

8 hy do no alr rlaiv prics. Th oupu producd via (8) is sold o housholds, who hn alloca i for consumpion or invsmn purposs. 2.3 Tchnological procsss Th chnologis follow h laws of moion givn by: A = z g, whr (9) A, A 2 ln z ρ + ε, wih 0 ρ < 1, ε ~ iidn (0, ) ; (10) A, = A ln z A, 1 q zq, q < A = g, whr (11) 2 ln z ρ + ν, wih 0 ρ < 1, ν ~ iidn (0, ). (12) Hr q, = q ln zq, 1 g and A < q g q dno h gross long run ras of RNT and IST, rspcivly. Th σ ε σ ν variabls z A, and z q, ar chnology shocks - z A, capurs h dviaions of h rsidual-nural chnology sris from is drminisic rnd and z q, dviaions of h invsmn-spcific chnology sris from is drminisic rnd. 2.4 Govrnmn Th govrnmn axs labor and capial incom and hn rbas h procds o housholds subjc o h following budg consrain: τ = τ w n + τ r s + r ). (13) n k ( s,, 2.5 Compiiv quilibrium c, i for,, q i, n, s, A compiiv quilibrium consis of an allocaion { } s, =0 h ypical houshold, an allocaion { }, S, E =0 { p }, w, rs,, r, =0, such ha: N for h ypical firm and a s of prics 1. h houshold's allocaion solvs h houshold's problm of maximizing (1) subjc o (2)-(6), aking prics as givn; 7

9 2. h firm's allocaion solvs h firm's problm of maximizing (7), aking prics as givn; 3. h govrnmn's budg consrain (13) is saisfid; and 4. all marks clar: n = N, s = S, = E, a, c + is, + i, + as, + = F( N, S, E ; A ). (14) q Combind, h accumulaion quaion for quipmn (6) and h rsourc consrain (14) indica ha a houshold can acquir qi unis of nw quipmn a a cos of i unis of currn consumpion. Dspi is apparanc, h qualiy componn mbodid in nw quipmn is no fr. Housholds pay a pric for ach fficincy uni of quipmn ( qi ) ha hy purchas. Howvr, whn oupu is masurd in unis of h consumpion good, qualiy improvmns lowr h uni pric ( p = 1/ q ) of nw quipmn. A lowr uni pric offss h charg for highr qualiy. As a rsul, qualiy improvmns do no appar in h oal cos of an invsmn in quipmn. Whn all yps xpndiur and sourcs of incom hav bn dividd by h pric of h consumpion good, so ha ach im has a consan uni of masurmn, h masur of oupu is as shown by quaion (14). In h daa, howvr, invsmn xpndiurs ar no masurd in rms of forgon consumpion. Insad a spara dflaor is applid o ach cagory of xpndiur, so ha ach im is masurd in consan dollars, bu no ncssarily in a common uni. In h daa, nominal oupu ( is givn by p y, y pc, c + pi is pi q i pi as pi a s,, +,, + s,, +,,, (15) and ral oupu ( y ) by y c + is, + qi, + as, + a, Hr. (16) x p y y ) p dnos h implici pric dflaor for im x y, c, i s, i ). Noic h sima ( of oupu obaind from h daa (16) dos no coincid wih h sima obaind via 8

10 (14). Qualiy improvmns add o oal oupu ( y ), bu hy do no add o oal xpndiurs ( F ). 2.6 Balancd growh This scion dscribs h balancd growh pah of h modl conomy. Th growh ras of h variabls along h balancd growh pah ar drmind as follows. Firs, im dvod o work is consan in balancd growh. Scond, from h rsourc consrain (14) and h accumulaion quaion for srucurs (5) i follows ha F( ), c, i, i, a, a / q, and s all hav o grow in h long run a h sam gross ra - s s say g. This rsricion combind wih h accumulaion quaion for quipmn (6) implis ha qi, and a all grow in h long run a a gross ra of g = g g. Nx, q α s α h producion funcion implis ha g = g g. Finally, by combining hs rsricions i can b shown ha: g = 1 α n n g α α A g q A g, and (17) g = g 1 α n A g α + α n αn q (18) Th modl and h Canadian conomy shar many common avrag growh propris. For xampl, hours workd pr capia dos no grow in h sady sa, h ral inrs ra (or h ra of rurn on a capial invsmn) follows a horizonal rnd, h ra of invsmn in quipmn ( qi / y) displays a posiiv rnd, and oupu ( y or GDP) dos no hav a balancd growh pah - is avrag growh ra convrgs o g. 2.7 Calibraion Bfor h dcision ruls can b compud and an arificial im sris can b gnrad, i is ncssary o assign valus o h modl's paramrs. Paramr valus ar s using vidnc from h rlvan mpirical liraur, o achiv crain long run avrags obsrvd in h Canadian conomy and o saisfy h rsricions imposd by h srucur of h modl. 9

11 Tchnology Paramrs. Valus for h paramrs in h chnological procsss ar s so ha h im sris propris of h chnologis in h modl and h daa ar h sam. Th long run ra of IST ( g 1) is s o 3.81 prcn, and machs h q avrag annual ra of dclin in h rlaiv pric of quipmn. Th long run ra of RNT ( g 1) is s o 0.64 prcn. For his valu, h long run growh ra of oal A xpndiurs ( g 1) in h modl is 1.72 prcn (as calculad from quaion 17), which machs h avrag annual growh ra of oal xpndiurs in h Canadian conomy. Th long run growh ra of h quipmn sock ( g 1) is qual o 5.60 prcn, and was s o saisfy (18). Th im sris for boh chnologis wr drndd via linar rgrssion lins. Auxiliary rgrssions wr hn prformd o obain simas of h paramrs in quaions (10) and (12). Th rsuls of hs rgrssions suggs h following valus: ρ = (14.91), σ = , ρ = (16.31), and σ = Valus in A ε q parnhsis ar -saisics. Th auocorrlaion cofficins in boh procsss ar saisically significan a a 1 prcn lvl. Labor's shar paramr ( α ) is s o , and machs h raio of labor n incom o oal incom in Canada. Capial's shar paramrs ar s so ha in h sady sa h purchass of srucurs accouns for 5.90 prcn of oal xpndiurs and h i purchass of quipmn 7.49 prcn: s i = and = Ths valus F( ) F( ) wr obaind from h daa, and imply a = and a = s Dprciaion Ras. Th ras of capial dprciaion ar consisn wih common pracic in h rlvan liraur (s Grnwood al., 2000, 1997; or Dunaway al., 2000): δ = and δ = s Tax Ras. Th ax ra on labor incom ( τ n ) is s o 40 prcn. This is h valu lisd in h IMF rpor on Canada (s Dunaway al., 2000). Th ax ra on capial incom ( τ k ) is s o prcn, so ha in h sady sa h afr ax ra of rurn o capial is 4 prcn pr yar. ν 10

12 Prfrnc Paramrs. A survy of h micro vidnc on h cofficin of rlaiv risk avrsion (γ ) was conducd by Mhra and Prsco (1985). Thir survy suggss ha γ is bwn 1 and 2. As a compromis a valu of 1.5 was slcd. Th shar paramr in h uiliy (ω ) funcion is s o , so ha housholds spnd on avrag 1/3 of hir im a work. This valu is consisn wih vidnc on houshold im us. Th discoun facor ( β ) is qual o , and was s o saisfy h Capial Accumulaion Eulr quaions. Adjusmn Cos Paramrs. Unforunaly, long run vidnc dos no provid informaion ha will hlp in drmining appropria valus for h paramrs in h adjusmn cos funcions. Insad, hir valus ar s following h procdur oulin by Grnwood al. (2000). For a jusificaion of his procdur, w rfr radrs o hir papr. Firs, ψ is s qual o g and s ψ o g, so ha no adjusmns coss ar incurrd along h balancd growh pah. Scond, h symmry condiion θ s = g 2 qθ θ is imposd, afr which only on adjusmn cos paramr rmains o b drmind, θ. Adjusmn coss hav bn includd o modra h variabiliy of capial accumulaion. By sing θ o 0.733, quipmn invsmn in h modl ( qi ) has h sam sandard dviaion as ral pr capia non-rsidnial fixd invsmn in machinry and quipmn in Canada. 3 Th rsuls Th rsidual-nural and invsmn-spcific chnology sris wr filrd hrough h modl, and arificial im sris wr gnrad for h ohr variabls in h modl. Various saisics ha summariz h im sris bhavior of h Canadian and arificial conomy ar displayd in h abls and figurs blow. 3.1 Businss cycls Annual businss cycl saisics for Canada ar displayd in Tabl 2 and for h modl in Tabl 3. Th modl's abiliy o mimic ky aspcs of Canadian businss cycl bhavior is imporan, ohrwis i will no do a good job xplaining flucuaions in h 11

13 ra of GDP growh bwn priods. A comparison of Tabls 2 and 3 rvals ha h modl shars many of h sam srnghs and waknsss wih ohr spcificaions of h RBC modl. For a dscripion and valuaion of ohr RBC modls radrs ar rfrrd o Kydland (1995), Chrisiano and Eichnbaum (1992) or Hansn and Wrigh (1992). Th modl's srnghs: 1. Invsmn is hr ims mor volail han oupu and consumpion is lss volail han oupu. 2. Invsmn, consumpion, and hours workd ar all procyclical as hy ar in h daa. 3. Thr is a posiiv rlaionship bwn oupu and h rlaiv pric in boh h modl and h daa. Th srngh of his rlaionship is also similar. Th modl's waknsss: 1. In h arificial conomy oupu flucuas lss han in h Canadian conomy, suggsing ha much, bu no all, of h variaion in oupu can b xplaind by chnology disurbancs. 2. Som of h labor mark prdicions ar counrfacual. For xampl, in h arificial conomy hours workd is considrably lss volail han i is in h daa and labor produciviy is oo highly corrlad wih oupu. Judgd on h dimnsion of h composiion of oupu and is co-movmns, h mach bwn h modl and h daa is pry good bu crainly no prfc. Th modl dos display a businss cycl. {Insr Tabls 2 and 3 hr} Th dynamic bhavior of h modl can b dscribd by h impuls rsponss ha i gnras. For xampl, a posiiv rsidual-nural chnology shock incrass h marginal produc of ach inpu. In urn, his inducs a grar han normal dmand for ach inpu. Furhrmor, his incras in h dmand raiss h ral wag ra and h ral 12

14 rnal ras of capial, and hrfor provids an addiional incniv o work and o undrak capial invsmns. Oupu also rsponds posiivly o his shock. Th posiiv rspons of oupu is parially a rsul of h fac ha produciviy is highr for a givn amoun of labor and capial, and parially du o h incras in mploymn. In comparison, a posiiv invsmn-spcific chnology shock lowrs h purchas pric of nw quipmn rlaiv o h pric of consumpion goods and srucurs. As a rsul, housholds ralloca hir xpndiurs, so ha hy purchas rlaivly mor quipmn goods. Howvr, h posiiv walh ffc producd by his shock is sufficinly larg o offs h subsiuion ou of consumpion, and hrfor consumpion riss. Th ris in quipmn invsmn and consumpion xcd h fall in h producion of srucurs, and hrfor oupu incrass. Furhrmor, oupu, consumpion and invsmn in srucurs rspond posiivly in fuur priods, whn nw quipmn goods bcom availabl for producion. Sinc boh yps of shocks mov hours workd, consumpion and invsmn in h sam dircion as oupu; hs variabls ar all procyclical, as hy ar in h daa. Howvr, givn h dynamics jus dscribd, i was surprising o find ha oupu and h rlaiv pric hav a posiiv corrlaion in boh h modl and h daa. Sinc lowr prics lad o highr oupu lvls, a posiiv corrlaion bwn h rlaiv pric and h lvl of oupu prsns a puzzl. In ordr o xplain his corrlaion, i is ncssary o accoun for h iming of h chnology disurbancs. Rcall, oupu flucuaions in h modl wr gnrad using h acual chnology disurbancs from h Canadian conomy. Thus, in boh h daa and h modl, h ra of RNT slowd in 1974, whras h ra of IST incrasd. Furhrmor, sinc RNT was low during h pos-1974 priod, oupu was low. As a rsul, in our modl oupu was low whn h qualiy of nw capial was high and whn rlaiv prics whr low, as i was in h daa. This is ru dspi h fac ha rapid advancmns in invsmn-spcific chnology had ngaiv ffcs on prics and posiiv ffcs on oupu during h lar priod. 13

15 3.2 Economic growh Th avrag annual ras of oupu growh in Canada and h modl ar displayd in Figur 1 and Tabl 4. Th modl appars o rack h growh ra of ral GDP pr capia in Canada fairly closly. Th saisics displayd in Tabl 4 indica ha hr is a growh slowdown in h modl, howvr, i is lss svr compard o wha was acually xprincd in Canada. In h daa, h ra of oupu growh fll by 2.24 prcnag poins - from 3.34% o 1.09%. Whras in h modl i dclind by only 1.60 prcnag poins - from 2.76% o 1.16%. Th modl canno fully accoun for h vry rapid growh xprincd in Canada bwn 1961 and This is an implicaion of h fac ha oupu in h modl flucuas lss han i dos in h Canadian daa. {Insr Figur 1 and Tabl 4 hr} To hlp undrsand why oupu growh slowd in 1974, i is usful o dcompos h growh ra of oupu ino various componns. Convnional growh accouning involvs h dcomposiion of h growh ra of oupu ino h growh ras of facor inpus and produciviy, as follows: Δy y Δn Δs Δ = ΔTFP + α n + αs + α, (19) n s whr ΔTFP dnos h ra of oal facor produciviy growh. Radrs mus no inrpr h ra of TFP growh as quivaln o h ra of RNT growh. Th formr is calculad from oupu as masurd by quaion (16); whr as h lar is calculad from xpndiurs as masurd by quaion (14), so ha ΔRNT ΔF = F Δn Δs Δ α n + α s + α. (20) n s In boh quaions (19) and (20) h masur of inpus o producion ar idnical. I is only h masur of oupu ha diffrs wih quaion (20) having h invsmn-spcific improvmns in qualiy rmovd. 4 Tabl 5 prsns h rsuls of a convnional growh accouning xrcis. {Insr Tabl 5 hr} Th convnional growh accouning xrcis has idnifid hr facors ha conribud o h slow down in Canadian oupu growh: (i) a fall in h growh ra of h labor inpu (i.. a dclin in hours workd pr capia), (ii) a rducion in h ra of 14

16 accumulaion of srucurs and (iii) a lowr ra of produciviy growh. Th im sris gnrad for h arificial conomy also displays a slow down in h growh ra of srucurs and produciviy afr Noic, howvr, ha in h arificial conomy h produciviy slowdown is slighly mor svr han i is in h Canadian conomy. In par, h TFP sris in h modl is compnsaing for h fac ha hours workd is rlaivly sabl. Th convnional growh accouning analysis fails o provid answrs o a numbr of imporan qusions. Firs, why did h growh ras of h facor inpus and h ra of produciviy growh dclin? Scond, how snsiiv is h ra of GDP growh o changs in RNT and IST? Th rmaindr of his scion is dvod o answring hs qusions. Rcalling h impuls rsponss o h chnology shocks ha wr dscribd in Scion 4.1 can solv h firs qusion. Rcall, a ngaiv RNT shock producd a dclin in facor produciviy, and his in urn lowrd h ra of rurn o a capial invsmn. As such, a slow down in h ra of RNT growh afr 1974 would hav producd a dclin in TFP growh and a fall in h ra of accumulaion of capial. In comparison, in h modl a posiiv IST shock allowd mor quipmn o b producd pr uni of capial and labor mployd, and lowrd h rlaiv pric of quipmn. As such, a ris in h ra of IST growh afr 1974 would hav producd a ris in h produciviy of h facors mployd in h manufacuring of quipmn goods, and a ris in h ra of accumulaion of quipmn. No ha changs o h im sris bhavior of h wo yps of chnology afr 1974 had opposi ffcs on h incnivs o accumula quipmn and TFP. This may xplain why h accumulaion of quipmn did no slow down as much as srucurs afr Th prdicions of h modl also indica ha h ris in h ra of IST growh was no sufficinly srong nough o offs h dclin h ra of RNT growh, and hrfor TFP growh slowd afr Th fac ha TFP is mor snsiiv o RNT han i is o IST should no sm oo surprising, afr all improvmns in IST only affc h capial good scor, whras improvmns in RNT affc all scors. In boh Canada and h modl, growh in h facor inpus and TFP rprsn inducd rsponss o RNT and IST. Sinc h wo chnologis affc h ra of capial accumulaion and h ra of produciviy growh, hy will also affc h ra of oupu 15

17 growh. In fac, wihou chnological chang a modrn indusrial conomy, such as Canada, would xprinc no oupu growh. In ordr o isola h conribuion of a paricular chnology o oupu growh, ach chnology sris was filrd hrough h modl sparaly. Th rsuls ar summarizd in Tabl 6. {Insr Tabl 6 hr} Th modl prdics ha ovr h nir priod IST accound for 50 prcn of Canada's oupu growh. Th rmaining 50 prcn is aribud o RNT. I is vidn ha hr has bn a considrabl shif in h sourcs of growh. Bwn 1961 and 1973, only 9 prcn of growh could b xplaind by improvmns in invsmnspcific chnology. Howvr, sinc h mid-1970s h conribuion of IST o h ra of oupu growh incrasd significanly. Today, IST accouns for virually all of Canada's conomic gains. Th rsuls also indica ha h incras in h ra of IST ovr h pos-1974 priod producd an incras in h ra of oupu growh of 0.93 prcnag poins, cris paribus. Howvr, his gain was mor han offs by h rducion in h ra of RNT, which producd a dclin in h ra of oupu growh of 2.61 prcnag poins, cris paribus. Th n ffc was a fall in h ra of oupu growh by 1.60 prcnag poins. 4 Conclusion This papr quanifid h conribuions of RNT and IST o h growh ra of Canadian GDP pr capia ovr slcd priods. Th rsuls ar as follows: IST was found o accoun for approximaly 50 prcn of h growh in GDP ovr h nir priod, 9 prcn ovr h pr-1974 priod and 100 prcn ovr h pos-1974 priod. RNT accound for h rmaindr in ach priod. Th incras obsrvd in h ra of IST ovr h pos-1974 priod producd an incras in h ra of oupu growh of 0.93 prcnag poins, cris paribus. Howvr, his gain was mor han offs by h rducion in h ra of RNT, which producd a dclin in h ra of oupu growh of 2.61 prcnag poins, cris paribus. Th n ffc was a fall in h ra of oupu growh by 1.60 prcnag poins. 16

18 Thr is on final poin of inrs ha h modl has no addrssd. Thr is a ngaiv corrlaion bwn ras of IST and RNT of -0.53, which suggss h possibiliy ha h procss of mbodying nw chnologis has implicaions for gnral produciviy. Thr is a larg liraur on h issu of growh drivn by chnological chang, which argus ha h procss of invsmn in nw chnology rquirs subsqun invsmn in complmnary nw skills and human capial, as wll as in ohr complmnary capial goods (.g., Lipsy, Bkar and Carlaw, 1998; David, 1991; Rosnbrg, 1982). Our calculaions may b vidnc of his ffc. RNT is a las parially a masur of labor produciviy, and h fac ha w occasionally obsrv ngaiv RNT a h sam im w obsrv posiiv IST may b a rflcion of a skill s mbodid in labor which is no compaibl wih h chnology bing mbodid in nw capial goods. Is h ngaiv rlaionship bwn IST and RNT vidnc of a mor fundamnal rlaionship? Nohing in h analysis conducd hr lls us h answr o his qusion, bu i is a lin of rsarch ha w wish o pursu. W bliv ha hr is sufficin circumsanial vidnc o warran rsarch ino h rlaionships bwn IST and RNT and IST and TFP. Paricularly sinc his has policy implicaions for long-rm conomic growh in Canada. If i is possibl o vrify h xisnc of a complmnary rlaionship bwn chnological mbodimn in human as wll as physical capial, hn hr is mor advic for policy han h sandard noclassical prscripion ha invsmn and saving ar good for growh. In paricular, whil capial invsmn is ncssary, i may no b sufficin. Invsmn in physical and human capial mus b complimnary o ach ohr. A Appndix: Daa dfiniions and sourcs A dscripion of h daa and macroconomic variabls usd in his sudy is providd blow. All xpndiurs and facor inpus wr dflad by h 16+ populaion. All dollar valus ar basd on 1992 prics. Daa is from h Canadian Socio-conomic Informaion and Managmn Sysm Daabas (CANSIM). 17

19 Oupu ( y ): ral gross domsic produc (D22467) n of gross housing produc (masurd by gross impud rns D22923 and gross paid rns D22924). Consumpion ( c ): ral xpndiurs on consumr smi-durabls (D22439), non-durabls (D22440) and srvics (D22441) n of gross housing produc. Invsmn in Srucurs ( i s ): ral businss gross fixd capial formaion in srucurs (D22449). Invsmn in Equipmn ( qi ): ral businss gross fixd capial formaion in machinry and quipmn (D22450). Toal Expndiurs ( F ): calculad as oupu ( y ) lss invsmn in quipmn ( qi ) plus xpndiurs on quipmn ( i ). Hr xpndiurs on quipmn ar masurd in rms of forgon consumpion, ha is, hy hav bn dflad by h implici pric dflaor for consumr non-durabls, smi-durabls and srvics. Hours Workd ( n ): oal hours a work in non-agriculural indusris. Calculad from oal hours a work (I190301) lss hours workd in agriculur (I190302). Capial Inpus ( s and ): Tim sris for h capial socks wr simad by iraing on hir rspciv laws of moion. Th iniial valus wr s a hir balancd growh lvls. Rlaiv Pric ( p ): h raio of h implici pric dflaor for ral businss gross fixd capial formaion in machinry and quipmn o h implici pric dflaor for consumr smi-durabls, non-durabls and srvics. Invsmn-Spcific Tchnology ( q ): h rciprocal of h rlaiv pric (bas = 1992). 18

20 Th Ra of Rsidual-Nural Tchnological Chang: calculad as h growh ra of oal xpndiurs ( F ) lss h shar wighd growh ras of h labor and capial inpus. Th Ra of Toal Facor Produciviy Growh: calculad as h growh ra of oupu ( y ) lss h shar wighd growh ras of h labor and capial inpus. Rcall, oupu is masurd in ffciv unis, and hrfor i includs qualiy componns. Expndiurs ar masurd in consumpion quivalns, and hrfor hy xclud qualiy componns. Hnc, hr is a diffrnc bwn RNT and TFP. 16+ Populaion: Toal populaion (D for pr-1971 and C for pos-1971) lss populaion undr ag 15 (D for pr-1971 and C for pos-1971) 19

21 REFERENCES Baxr, M. and R.G. King (1995), "Masuring Businss Cycls: Approxima Band-Pass Filrs for Economic Tim Sris," Naional Burau of Economic Rsarch Working Papr No Carlaw, K. and S. Kosmpl (2000), "Th Sourcs of Produciviy Growh in Canada," Univrsiy of Gulph Discussion Papr No Chrisiano, L.J. and M. Eichnbaum (1992), "Currn Ral-Businss-Cycl Thoris and Aggrga Labor Mark Flucuaions," Amrican Economic Rviw 82(3), David, P. (1991), "Compur and Dynamo: Th Modrn Produciviy Paradox in a No Too Disan Mirror," in Tchnology and Produciviy: Th Challng for Economic Policy, d. by OECD, Paris: OECD. Dunaway, S., al. (2000), "Canada: Slcd Issus," IMF Saff Counry Rpor No. 00/34, Grnwood, J., Z. Hrcowiz and P. Krusll (2000), "Th Rol of Invsmn-Spcific Tchnological Chang in h Businss Cycl," Europan Economic Rviw 44(1), (1997), "Long-Run Implicaions of Invsmn Spcific Tchnological Chang," Amrican Economic Rviw 87(3), Hansn, G. D. and R. Wrigh (1992), "Th Labor Mark in Ral Businss Cycl Thory," Fdral Rsrv Bank of Minnapolis Quarrly Rviw 16(2),

22 Kydland, F.E. (1995), "Businss Cycls and Aggrga Labor Mark Flucuaion," in Fronirs of Businss Cycl Rsarch, d. by T.F. Cooly, Nw Jrsy: Princon Univrsiy Prss, Lipsy, R.G., C. Bkar and K. Carlaw (1998), "Wha Rquirs Explanaion," in Gnral Purpos Tchnologis and Economic Growh," d. by E. Hlpman, Cambridg: MIT Prss, Mhra, R. and E.C. Prsco (1985), "Th Equiy Prmium: A Puzzl," Journal of Monary Economics 15, Mndoza, E.G. (1991), "Ral Businss Cycls in a Small Opn Economy," Amrican Economic Rviw 81(4), Rosnbrg, N. (1982), Insid h Black Box: Tchnology and Economics, Cambridg: Cambridg Univrsiy Prss. Nos 1. On h surfac i appars ha w hav xprincd ngaiv chnology growh, somhing ha is implausibl in a maximizing framwork. Our indx of inpu nural fficincy improvmn has changd ngaivly, bu his could rflc a rad off bwn nw mbodid chnology oday and inpu nural fficincy growh in h fuur. 2. This configuraion of adjusmn coss is convnin parly bcaus i allows for balancd growh, and parly bcaus h adjusmn cos paramrs can b s o conrol h volailiy of h invsmn sris. Wih quadraic adjusmn coss, h cos of incrasing h capial sock by a fixd amoun incrass wih h spd of h dsird adjusmn. Adjusmn cos funcions wih h sam paramrizaion hav bn usd in ohr sudis (s Grnwood al., 2000; or Mndoza, 1991). 21

23 3. In his analysis all movmns in h rlaiv pric ar prcivd as IST. W fl ha IST is h mos likly xplanaion for h downward rnd obsrvd in his im sris. Howvr, i is no inconcivabl ha ohr conomic forcs hav som baring on rlaiv pric movmns. For xampl, sinc Canada is a n imporr of capial goods and n xporr of raw marials, movmns in h rms of rad may also affc h rlaiv pric. 4. For a discussion of h componns of oupu usd in hs calculaions radrs ar rfrrd back o scion 2.5. For a daild discussion of h conribuions of RNT and IST o TFP growh radrs ar rfrrd o Carlaw and Kosmpl (2000). Thy idnify wo channls hrough which IST affcs oal facor produciviy (TFP). Firs, IST improvs h qualiy of capial goods, and hrfor nabls mor ffciv unis of oupu o b producd pr uni of capial and labor mployd. Scond, IST rducs h pric of nw quipmn rlaiv o h pric of ohr goods, and hrfor i provids an incniv for conomic agns o ralloca hir xpndiurs away from consumpion goods and srucurs and owards quipmn goods. In ohr words, produciviy incrass parly bcaus of br producion chnologis in h capial goods producing scor and parly bcaus mor rsourcs g allocad o h mor produciv scor. 22

24 Tabl1 Avrag annual growh ras: Ral GDP pr capia and chnology Ral GDP Pr Capia Invsmn-Spcific Tchnology a Rsidual-Nural Tchnology 3.34% 1.09% 1.86% 1.29% 5.12% 3.81% 1.80% -0.07% 0.57% a Th im pah of IST was rackd using movmns in h rlaiv pric of quipmn. Bwn 1961 and 1996 h pric of nw quipmn rlaiv o h pric of consumr non-durabls and srvics dclind by approximaly 4.0 prcn pr yar, whil h ra of invsmn in quipmn ros by 4.0 prcn pr yar. This ngaiv co-movmn has bn inrprd in h liraur as vidnc of IST (s Grnwood al., 2000, 1997; Dunaway al., 2000). Tabl 2 Annual Canadian Businss Cycl Saisics, a Variabl Sandard Dviaion Corrlaion wih Oupu Oupu Consumpion Invsmn Rlaiv Pric Hours Workd Labor Produciviy a Bfor saisics wr rpord all sris wr convrd o 1992 dollars, dflad by h 16+ populaion, loggd and hn drndd via h Hodrick-Prsco (HP) filr. Th smoohing paramr in h HP filr was s o 10. Baxr and King (1995) suggs ha a valu of 10 is appropria for annual daa. Th daa is dscribd in dail in h appndix. 23

25 Tabl 3 Arificial conomy businss cycl saisics a Variabl Sandard Dviaion Corrlaion wih Oupu Oupu (y) Consumpion Invsmn Rlaiv Pric Hours Workd Labor Produciviy a Each simulad im sris was loggd and drndd using h sam procdurs applid o h Canadian sampl. Tabl 4 Annual growh ras: Ral GDP pr capia Canadian Economy 3.34% 1.09% 1.86% Modl Economy 2.76% 1.16% 1.71% Tabl 5 Convnional growh accouning Shar Wighd Growh Ras Economy Hours (n) Srucurs (s)equipmn () TFP Toal (y) Canada Modl

26 Tabl 6 Conribuion of chnologis o h ra of GDP growh Amoun Conribud (prcnag poins): (A) Invsmn-Spcific (g A =0) (B) Rsidual-Nural (g q =0) (C) Combind a Prcnag of Toal (D) Invsmn-Spcific (A/C)* (E) Rsidual-Nural (B/C)* a No ha adding up h conribuions of h wo chnologis yilds a growh ra ha diffrs slighly from h simas in his row. Ths diffrncs ar an implicaion of h fac ha whn boh chnologis opra oghr hy hav som offsing ffcs on h ra of oupu growh. 25

27 Valu Canada Th Modl Yar Figur 1. Annual Growh Ras: Ral GDP Pr Capia 26