Is Schumpeterian "Creative Destruction" a Plausible Source of. Endogenous Real Business Cycle Shocks?

Transcription

1 s Schumpeteran "Creatve Destructon" a Plausble Source of Endogenous Real Busness Cycle Shocks? Kerk L. Phllps * Department of Economcs P.O. Box Brgham Young Unversty Provo, UT phone: (80) fax: (80) emal: kerk_phllps@byu.edu Jeff Wrase U.S. Senate Jont Economc Commttee G-0 Drksen Senate Offce Buldng Washngton, DC 2050 phone: (202) emal: jeff_wrase@jec.senate.gov January 2004 JEL Codes: E32, O30, O40 * We wsh to thank Val Lambson for helpful nput. Partcpants at the 999 Theores and Methods n Macroeconomcs Conference at the Unversty of Quebec at Montreal, the 2000 Conference on Growth and Busness Cycles n Theory and Practce at the Unversty of Manchester, the 2000 World Congress of the Econometrc Socety, and the 200 Far East Meetngs of the Econometrc Socety provded helpful comments on earler drafts. Fundng for travel and presentaton of ths research from the Federal Reserve Bank of Phladelpha and from the J. Fsh Smth Endowed Char n Free Markets s gratefully acknowledged.

2 Abstract Ths paper looks at the lnkages between growth and busness cycles by brngng together two strands of lterature. We ncorporate a qualty ladders engne of growth nto an otherwse standard real busness cycle model. Our fundamental queston s, can Schumpeter s creatve destructon process whch leads to lumpy technologcal mprovement over tme also generate realstc busness cycles? We use a standard real busness cycle approach to solve for rules of moton n our state varables and proceed to generate artfcal tme seres. We compare the statstcal propertes of these seres wth ther hstorcal counterparts to determne f the model mmcs the real world closely. One advantage our approach has over the standard approach s that the trend component s ncluded n our artfcal seres just as t s n the data. Hence, we are not ted to any partcular flterng method when we compare smulatons wth the real world data. We fnd that Schumpeteran fluctuatons alone cannot generate realstc busness cycles. We also fnd, however, that a model wth both Schumpeteran and standard RBC shocks performs better n many dmensons than a model relyng on standard RBC shocks alone.

3 . ntroducton Dynamc general equlbrum models have proved to be valuable tools for examnng both economc growth and fluctuatons. One class of these models the Schumpeteran or qualty ladders models focuses on explanng observed smooth growth trends. Segerstrom, Anant & Dnopoulos (990), Grossman & Helpman (99), and Aghon & Howtt (992) frst ntroduced ths lterature n ther semnal papers. n addton, there have been numerous extensons of the basc qualty ladders model, focusng on nnovaton versus mtaton, North-South trade patterns, and other related topcs. Schumpeteran models have the advantages that they are rgorously based n mcroeconomc theory and have a great deal of ntutve appeal. n ths lterature, growth s drven endogenously by attempts to nnovate and clmb up the qualty ladder to capture a stream of monopoly profts. Attenton s normally focused on the steady state, where growth s smooth over tme due to a large number of ndependent, but dentcal nnovators each targetng a unque good. Growth for any gven good, proceeds n a lumpy fashon wth dscrete jumps n qualty occurrng randomly over tme, but the law of large numbers leads to smooth aggregate growth. A second class of models focuses on explanng the behavor of economc aggregates over the course of the busness cycle. Usually referred to as real busness cycle (RBC) models, early work began wth semnal papers by Kydland & Prescott (982) and Long & Plosser (983). Agan, numerous papers have extended ths lterature to the examnaton of aggregate labor behavor, monopolstc competton, monetary aggregates, and varous other topcs. 2 The RBC methodology generally nvolves buldng a general equlbrum model, wth changes n productvty (and, more recently, other economc fundamentals) drvng aggregate behavor. These models are capable of generatng artfcal data that mmc observed busness cycles. Unlke For an extensve overvew of ths lterature see Grossman and Helpman (99) and Aghon and Howtt (998). 2 For an excellent overvew of the RBC lterature see Cooley (995). 2

4 the Schumpeteran lterature, attenton s focused on the off-steady-state hgh-frequency behavor of aggregate economc varables. n practce, RBC models are typcally transformed nto a statonary varant and solved numercally to yeld statonary laws of moton for endogenous varables as functons of endogenous states and exogenous drvng processes. A statonary model economy s then smulated and evaluated by comparng propertes of data drawn from the model wth data drawn from actual economes. Snce the focus of RBC models s on hgh-frequency fluctuatons and not on economc growth, the growth component s usually gnored. However, n order to compare the artfcal economy wth real world data t s necessary to remove the growth component from the real world data;.e. to detrend t. Whle many busness cycle stylzed facts are nvarant to the flter used, there are some mportant facts that are not 3. Generally n RBC models, the source of shocks s an exogenously mposed sequence of large and volatle productvty shocks. A common specfcaton of such shocks s a smple AR(), and there s lttle or no economc theory nvolved n the specfcaton of the drvng process. Moreover, there s ncreasng skeptcsm that technology shocks, measured by Solow resduals, are a major source of busness cycle fluctuatons. As Kng and Rebelo (998) pont out A key dffculty s that typcal estmates of Solow resduals mply a probablty of techncal regress on the order of 40%, whch seems mplausble to most economsts. Ths paper ntegrates the two branches of lterature dentfed above: the RBC lterature, whch focuses on detrended, hgh frequency fluctuatons; and the Schumpeteran lterature, whch focuses on low-frequency growth trends. The objectve s to construct a dynamc general equlbrum model wth an endogenous drvng process for busness cycles derved from mcroeconomc prmtves, and wth hgh- and low-frequency movements n economc aggregates that mmc those observed n the U.S. economy. 3 See Canova (998). 3

5 The endogenous growth component of the model s ncluded n smulatons, whch create artfcal data. Propertes of the artfcal data are then compared to lke propertes of ther real data counterparts to evaluate the model s performance. 4 An mportant feature of the model s that growth and cyclcal propertes of data stem from a common source endogenous nnovatons to technology. Techncal regress s not necessary for busness cycle fluctuatons n the model. Rather, the endogenous movements of resources between goods producton and technologcal advancement gves rse to cyclcal fluctuatons, as well as lower frequency movements n key macroeconomc varables. n prncple, the model does not requre large and varable technology shocks that mply hgh lkelhoods of techncal regress to explan busness cycles. Rather, endogenous mprovements n technology and the dffuson of the mprovements nto producton of fnal goods can help explan both growth and cycles. Methodology Our methodology s as follows. We ncorporate features of the Schumpeteran growth lterature nto a real busness cycle model of the macroeconomy. We nterpret what are usually called ncreases n qualty n the Schumpeteran lterature as ncreases n productvty, and we keep the qualty of goods constant over tme. f a small number of ndustres are assumed, ths gves rse to aggregate growth n technology that s "lumpy" and can therefore serve as a drvng process for busness cycles. The model s evaluated by: lnearzng agents Euler equatons, wth market clearng condtons mposed; numercally solvng the model for endogenous varables as functons of endogenous states and exogenous shocks; smulatng the model to generate sequences of macroeconomc aggregates; comparng propertes of data generated by the model wth propertes of data drawn from the U.S. economy at both hgh- and low- frequences. 4 Note that snce growth s endogenous n the model, the choce of whch partcular detrendng method to use s less crtcal than n a protoypcal RBC model. 4

6 There are two sources of shocks n the model. One (denoted A) s a sequence of random draws to determne success or falure of potental nnovators who nvest resources n basc research and development (R&D) to nfluence ther success probabltes. n aggregate the sze of ths shock goes to zero as the number of ndependent ndustres assumed s ncreased. A second source of shocks (denoted z) s nnovatons to labor productvty governed by a process typcally used n RBC models. Ths set-up has the advantage of nestng both the pure RBC model and the Schumpeteran model as specal cases. To examne the dynamcs of the RBC model we can set the number of ntermedate goods to a very large number (lke,000,000) and vrtually all fluctuatons wll come from the exogenous shocks. Smlarly, we can set the varance of the exogenous shocks to zero and the number of ndustres to a small number to examne the dynamcs of the pure Schumpeteran case. A Comparson wth Other Dynamc Schumpeteran Models Our approach s related to recent papers by Andolfatto & MacDonald (998), Collard (999), Freeman, Hong & Peled (999), and Ozlu (996) whch also focus on dynamc mplcatons of endogenous growth models. There s also an expandng lterature on Schumpeteran waves, whch looks at the behavor of the economy n response to large but nfrequent movements n basc technology. Early work by Cheng & Dnopoulos (992 & 996) looked at these longer-run fluctuatons. Aghon & Howtt (998) devote a porton of ther book to ths phenomenon as well 5. Wälde (2002) examnes the mplcatons of Schumpeteran growth n a contnuous tme framework, but does not calbrate or compare model generated data wth real world data. Collard and Ozlu each consder extensons of a standard RBC model to nclude endogenous growth through human captal accumulaton effects of learnng-by-dong. Ozlu consders labor market mplcatons of allowng learnng-by-dong effects on human captal, whle Collard consders mplcatons for the autocorrelaton of output growth and mpulse response functons n the trendrevertng component n output. These authors fnd mprovements n quanttatve mplcatons of 5 Chapter 8, especally secton

7 RBC models augmented to nclude learnng-by-dong effects over standard RBC models wthout human captal features. Our analyss s smlar to those performed by Collard and Ozlu n two respects. Frst, we also consder busness cycle mplcatons of an RBC model augmented to nclude an endogenous growth mechansm. Second, as n Collard s analyss, we consder mplcatons of our model for fluctuatons n key varables at varous frequences ncludng, but not lmted to, busness cycle frequences. Our model dffers from thers, however, n an mportant way. Whle Collard and Ozlu essentally provde a model of an endogenous mechansm for the propagaton of exogenous technology shocks, we model both propagaton of shocks and the shocks themselves. That s, we present a model that accounts for how shocks to technology arse, as well as how they may be propagated and dffused through tme. Closer to the sprt of our analyss s the work by Andolfatto & MacDonald, and by Freeman, Hong & Peled. The latter set of authors construct a model of large and costly technologcal changes whch gve rse to determnstc cycles and long run growth. Ther economy requres a suffcently large amount of captal, dverted from consumpton and physcal nvestment, for brth of a technologcal nnovaton. Then, when an nnovaton occurs, captal s more hghly valued n physcal nvestment than n R&D nvestment. Consequently, resources flow away from R&D and toward fnal goods producton. As the margnal product of captal usng exstng technology fades through tme, resources subsequently flow back toward consumpton and the producton of R&D nnovatons. These flows of captal gve rse to endogenous movements n consumpton and nvestment patterns wthn each fxed-length nnovaton cycle. Our analyss smlarly accounts for endogenous movements n key macroeconomc varables wthn nnovaton cycles, but also explctly models nnovaton cycles of random duratons. 6 n addton, when explorng quanttatve predctons of our model relatve to quanttatve propertes of actual data, we explctly consder movements n key 6 Another dfference between our model and the one constructed by Freeman, Hong, and Peled s that our model consders labor, rather than captal, as the nput to the R&D process. We nclude only labor to smplfy the analyss but are free to enter captal nto the R&D process as well. 6

8 macroeconomc varables at well-defned frequences. n contrast, Freeman, Hong, and Peled are agnostc about the frequency one should look at n actual data for the nnovaton-drven cyclcal patterns of movements that ther model predcts. The analyss of Andolfatto & MacDonald s close to that n ths paper n that they consder fluctuatons and growth n key macroeconomc aggregates arsng from the dscovery and dffuson of technologcal nnovatons. As n our model, Andolfatto & MacDonald have growth arsng from technologcal dscovery and use, and fluctuatons arsng from dffuson of appled, or fronter, research. Some type of dffuson mechansm s requred n each model to smooth out what would otherwse be unrealstc spkes n economc aggregates from nfrequent, possbly large, technologcal nnovatons sprngng up from appled research. Andolfatto & MacDonald consder a dffuson mechansm nvolvng mtaton and learnng how to use new technology, whch dverts resources from producton. Agents choose the amount of resources to devote to varous mtaton and learnng possbltes avalable to them, the outcomes of whch are random. Wth such a mechansm, the authors compare Hodrck-Prescott fltered seres (n levels, not devatons from fltered seres) from actual data wth lke seres drawn from ther model. The model n ths paper has no such mechansm for nnovaton and dffuson, though prevous work has focused on a smlar dffuson process. Our analyss dffers from Andolfatto & MacDonald s n the frequences of movements n macroeconomc varables consdered. Our model s an attempt at smultaneously accountng for growth and busness cycle fluctuatons. Consequently, we consder movements n macroeconomc varables at varous frequences, ncludng those that arse at busness cycle frequences. We do not restrct attenton to data movements at frequences at or below those at whch major nnovatons dffuse, as do Andolfatto & MacDonald. 2. A Dynamc General Equlbrum Schumpeteran Model n ths secton, nsghts of the Schumpeteran or qualty ladders growth models are ncorporated nto a dscrete-tme stochastc general equlbrum model of the real busness cycle tradton. Snce t s well known that the equlbrum from Schumpeteran growth models s socally suboptmal, we proceed to examne the compettve equlbrum. Frst, we examne the behavor of 7

9 households, then that of producton frms, and fnally the behavor of research frms. mposng aggregate resource constrants and market clearng condtons closes the model. 7 The model contans households, producton frms, and research frms. Each nfntely lved household s endowed wth one unt of labor each perod suppled to frms at wage wt. Households also accumulate physcal captal, K, over tme, whch they rent to frms each perod at rental rate rt. n addton to physcal captal, households buy and sell equty shares n two types of exstng frmsproducton and research frms-n dfferent ntermedate ndustres. These shares nfluence the household s budget by generatng dvdends and captal gans or losses. There s also a fnal goods sector, whch we assume s perfectly compettve and generates no profts. For smplcty, we abstract from buyng and sellng of these frms' equtes 8. n each perod there s a sngle producton frm n each ntermedate ndustry wth an exclusve rght to a partcular level of producton technology, A, that s some factor θ > better than the closest compettor. Ths producton frm enjoys monopoly power and earns monopoly rents durng the current perod, and possbly many future perods, untl a frm wth even better technology replaces t. The producton frms hre labor and rent captal to produce ntermedate goods, and pay out profts as dvdends to shareholders each perod. Fnal goods are produced by combnng ntermedate goods. There also exsts a sngle new research frm for each ntermedate ndustry, whch ncorporates wth the ntent of dsplacng the current producton frm n ts role of monopolst. The research frm ssues equty shares and uses the proceeds to hre unts of labor to attempt an nnovaton. f successful, the research frm dscovers a technology that s a factor θ better than the current producton frm and begns producton as the monopolst next perod. f unsuccessful, the frm ceases to exst and ts equty shares become worthless. We account for successes and falures 7 A lstng of notaton and varables used n the model s contaned n Table. 8 The assumpton s nnocuous because these equtes would have zero prces. 8

10 across the ndustres wth an -dmensonal vector S', wth element S f a research frm succeeds n the current perod and S 0 f not. f S, then today s research frm n ndustry becomes the producton frm tomorrow wth technology A that s a factor θ better than ts predecessor. 9 There s also an aggregate random shock to productvty n the model, unrelated to any of the A's whch we denoted z. Ths exogenous shock s to the productvty of labor n the ntermedate goods producng frms producton functons. We nclude such shocks to allow for shocks to productvty unrelated to actual movements n technology, such as ol prce shocks, changes n margnal tax rates, changes n government regulaton of producton processes, or smlar nontechnology shocks. Ths shock to productvty, assumed to be common to all ntermedate good producers, s of the form used n standard RBC models. One of our nterests wll be the extent to whch, by allowng for random nnovatons n R&D, the model does not requre productvty shocks that are as persstent and volatle as those typcally employed n RBC models to explan busness cycle fluctuatons. The tmng of nformaton, shocks, and actvtes n the economy s as follows. Agents begn a perod wth captal stock K knowng research and shock realzatons A 0, and z. At the begnnng of the perod, factor and equty markets open and clear. Frms rent captal from households, and real rental rate r s determned. Frms also hre labor from households, and a real wage w s determned. Research frms ssue shares, and prces of those shares, q R (also a vector), are determned, and producton frms ssue shares, and ther prces, q P, are determned. Followng nput and fundng acqustons, producton of goods and research occurs and the research results and random shocks A', 9 We adopt the notaton conventon that varables wthout a prme denote current perod values and varables wth a prme denote next-perod values. Addtonally, bold letters are used to denote -dmensonal vectors of varables. 0 Ths s a vector contanng all the A shocks 9

11 and z are revealed. Subsequently, at the end of the perod, factor payments w and rk are made, producton-frm profts π are dstrbuted to shareholders, next perod s captal stock K' s chosen, and consumpton occurs. We now turn to decsons made by the household, producton frms, and research frms. The Household's Problem A representatve household enters a perod wth captal K carred over from the prevous perod and a normalzed unt labor endowment. The household also owns stocks of equty shares n last perod's producton and research frms, denoted by share vectors P and R. The household knows the followng: the current levels of technology, A, to be employed by ths perod's producton frms, the current random productvty shock, z, and whether last perod's research frms succeeded or faled, the vector S. Takng prces r, w, q P, q R, and the probabltes of success by the current research frms, ρ, as gven, the household chooses new stocks of equtes P' and R' to carry over to next perod. After producton s completed and next perod's values for technology, A', and z', are revealed, the household chooses a level of captal, K', to carry nto next perod. Consumpton then occurs accordng to the household s choces and budget constrant. The value functon for the household s thus: V ( K, P, R; Ω) Max E{ Max u( C) + βv ( K', P', R'; Ω' )} P', R' K ' P P R where: C w + ( δ + r) K K' + { [ π + q ][( S ) P + S R ] q P ' q R '}, u(c) s the R P momentary utlty functon, β s the dscount factor, Ω { w, r, q, q, ρ, S, A, z} s an nformaton set, and E s the expectaton operator gven nformaton avalable at the begnnng of the perod. ρ n the nformaton set represents the vector of ndustry R&D success probabltes. S represents the The household supples ts endowment nelastcally and therefore receves wages w*. The labor endowment s dvded between research and producton frms actvtes. 0

12 vector of ndustry R&D success ndcator varables, takng values of f a success occurs, and 0 f falure occurs. For ndustry, ρ s the probablty of an appled research frm successfully nnovatng n the current perod to become next perod s ntermedate goods producer wth an mproved technology. We explctly model the nnovaton probabltes below n the dscusson of the research frms problems. What s relevant for the household s decson s that wth probablty ρ a share n today s ndustry research frm wll pay off next perod. f today s research frm pays off next perod, then a share n that ndustry s current ntermedate goods producng frm wll not pay off next perod because t s replaced by the current perod s successful nnovator. Correspondngly, wth probablty ρ, ndustry s current research frm s unsuccessful and won t pay off next perod. n that case, the current ntermedate goods producer remans as next perod s producer provdng payoffs on ts shares. shares P and The envelope condtons from the household s problem consst of condtons each for the V R, and a condton for captal stock K gven, respectvely, by: P ( C P K, P, R; Ω) E{ u ( C)}( π + q )( S ),2,, V ( K, P, R; Ω) E{ u ( C)}( π + q ) S,2,, V R C P ( K, P, R; Ω) E{ u ( C)}( δ r) K C + The Euler equatons correspondng to the household s choces consst of condtons each for next perod shares P and R, and a condton for next perod s captal stock K gven by: P E{ uc ( C)}( q ) + β E{ VP ( K', P', R'; Ω' )} 0 for,2,, R E{ uc ( C)}( q ) + β E{ VR ( K', P', R'; Ω' )} 0 for,2,, u ( C)( ) + V ( K', P', R'; Ω' ) 0 C β K Combnng envelope and Euler equatons gves the followng 2+ system of equatons: P P E { u ( C)} q β ( ρ ) E{ u ( C')( π ' + q ') A θ},2,, (2.) C C

13 R P E{ u ( C)} q βρ E{ u ( C')( π ' + q ') A },2,, (2.2) u C C C ( C) β E{ u ( C' )( δ + r' ) A', z'} (2.3) C where expectaton operator E {x y } denotes the expectaton of x gven all the nformaton avalable at the begnnng of the perod, plus addtonal nformaton revealed after the begnnng of the perod that s contaned n y. The laws of moton governng each ndustry s appled technology level A, appled research success ndex S, exogenous technology shock z, and basc technology level B, known to the household, are: θa, A ', S ' A,0 wth probablty ρ wth probablty ρ (2.4) z ' ψ z + η' ; where η' s dstrbuted Normal (0,σ 2 ) (2.5) The endogenous choces and random shocks governng the appled R&D success probabltes ρ are dscussed n detal below when the R&D frms choce problems are dscussed. The z shocks are the productvty shocks dscussed earler. Producton of Fnal Goods Fnal goods producton s an Armngton aggregator of all ntermedate goods, and uses no captal or labor. 2 Y / Y (2.6) Frms vew the prces of ntermedate goods as fxed, and a typcal frm maxmzes profts: 2 We could take the usual approach and use ths aggregator as a utlty functon expressng a preference for varety across the ntermedate goods. nterpretng t as a fnal good, however, has the advantage of yeldng a natural numerare good for the calculaton of real values. 2

14 3 Π F Y p Y / (2.7) Frst-order condtons for the frm s problem yeld: Y Y p, (2.8) Ths shows that all ntermedate frms earn the same amount of real revenue. Alternatvely stated, regardless of the amount produced, expendtures on each ntermedate good are equal. Producton of ntermedate Goods The producton frm produces output usng a Cobb-Douglas producton functon wth two sources of productvty varaton, both of whch are assumed to be labor augmentng: ] [ z N A e K Y (2.9) Productvty varatons come from productvty shocks, z, along wth the endogenous growth shocks A. The monopolstc producton frm faces a downward slopng demand curve defned by (2.8). However, there s a potental compettor that places lmts on the prce the monopolst wll charge. The prevous producer of the good has access to a technology that s /θ as productve as the current frm's. The current frm wll never charge a prce that exceeds ts margnal cost by more than a factor of θ. To do so would be to surrender producton to the prevous producer. t can easly be shown that the margnal cost for the current frm s: r w A e z +, Smlarly, the margnal cost for ts closest compettor s: θ r w A e z + Hence, the optmal prce for the frm s to charge a multplcatve markup of θ over margnal cost.

15 Standard optmalty condtons for the frm reveal that t dvdes revenues between payments to labor, captal, and dvdends accordng to: wn rk py θ θ p Y Y θ Y θ π θ θ p Y θ θ Y These dstrbuton equatons show that captal, labor, and profts are dentcal for all ntermedate frms regardless of the level of technology they use. The aggregate values are, then, K K, N N and π π. Substtutng these values nto (2.9) and (2.6), the producton of fnal goods can be wrtten as an aggregate producton functon of the form: Y z / z [ K ( e A N ) ] K ( e AN ) (2.0) where A / A (2.) Ths shows how we can collapse the producton of ntermedate and fnal goods nto a sngle aggregate producton functon. Gven the manner n whch the A evolve n (2.4), and the aggregaton n (2.), aggregate technology, A, evolves accordng to the followng Bnomal law of moton: A' J / Aθ ; wth J dstrbuted as Bnomal (,ρ) (2.2) The Research Frm s Problem 4

16 Each perod, a sngle research frm sprngs nto exstence n each ndustry. 3 t sells equty shares, normalzed to a quantty of one, to the household at prce labor. Takng prces w and Max L Π R E S' s. t. P R q and uses the proceeds to hre R q as fxed, the frm chooses the amount of labor to hre by solvng: V ' R ρ wl q (2.3) + r where V ' π ' + q ' s the reward for a successful nnovaton, and ρ ι s the probablty of success. The reward for success conssts of the expected present value of the stream of profts gven that a success occurs, whch happens wth probablty ρ. Appendx shows that ths reward can be wrtten as: θ V ' θ ( ) ( ) s t+ Ysd s (2.4) where d s s a dscount factor defned n the appendx. The rght sde of equaton (2.4) s smply the dscounted sum of all future profts n the ndustry, wth dscountng nclusve of tme and probabltes of loss of the proft stream n future perods. We model the research frm as hrng labor nputs that are used to produce research tres. n the lmt, wth a contnuous measure for the tres, the probablty of success comes from a Posson dstrbuton. As shown n Lambson and Phllps (999), ths gves the followng functonal form for an ndustry s appled R&D success probablty: ρ exp{ κl } (2.5) where κ s the "ease" of dong research. For the sake of tractablty we are assumng that all ndustres have the same level of ease of R&D,.e. that there s no advantage or dsadvantage to dong R&D n an ndustry that s hgher or lower on the qualty ladder than the average. 3 For s dscusson of the ssues nvolved wth assumng more that one R&D frm n such a dscrete tme framework see Lambson & Phllps (2003). 5

17 n a symmetrc equlbrum, arsng when all frms have the same probablty functon for ρ, the reward for success n (2.4) wll be the same for all frms. All frms then face an dentcal problem. The soluton to the problem s for the frm to hre the amount of labor t can afford, gven the constrant from equty sales. Consequently, q wl for each ndustry and aggregate R employment by all research frms s L L. n addton, snce the expected revenue streams for all ntermedate goods producers are the same, the prces of equtes for all research and producton frms are equal. Market-Clearng Condtons n addton to the Euler equatons from the household and frms' problems, market clearng condtons must be satsfed. Clearng of the labor and captal markets requres: [ L + N ] L + N (2.6) K K (2.7) and clearng of equty markets requres: P P' (2.8) R R' (2.9) Wth these condtons, Walras' law ensures goods market clearng. 3. The Transformed Model The model economy experences growth n consumpton and output per household due to the ncreases n A over tme. t wll be convenent to work wth a transformed model where the endogenous varables are all statonary. Snce transformatons to nduce statonarty are commonly used, we delegate detals to Appendx 2 and hereafter consder a transformed verson of the model. Varables growng at the same rate as A are transformed wth dvson by A, and the transformed varables wll be denoted wth a caret so that, for example, K ˆ K / A. The transformed law of moton for A s: 6

18 g A ' A' / A ρ ( θ ) + + ε ' (3.) where ε ' [( J / ) ρ]( θ ), J s dstrbuted Bnomal (,ρ), E { ε'} 0, and ρ( ρ) { ε '} ( θ ) 2 Var. The law of moton for z remans: z ' ψ z + η' (3.2) wth η' dstrbuted N(0,σ 2 ). We use a standard CES momentary utlty functon of the form, γ C u( C) γ. Substtutng for margnal utlty and transformng household optmalty condtons (2.) - (2.3) gves: { ˆ γ P γ γ E C }ˆ q β ( ρ) E{[ + ( ρ + )( θ ) + ε ' ] Cˆ' ( ˆ' π + qˆ P { ˆ γ R γ γ E C }ˆ q βρe{[ + ρ ( θ ) + ε ' ] Cˆ' ( ˆ' π + qˆ P ˆ γ γ γ C βe{[ + ρ( θ ) + ε ' ] Cˆ' ( δ + r' )} ' )} ' )} (3.3) (3.4) (3.5) Substtutng (2.6), (2.8) and (2.9) nto the household's budget constrant and takng expectatons gves: Cˆ wˆ + ( + ) ˆ + ˆ π ˆ ' ' ˆ R δ r K K g A q (3.6) The addtonal transformed equatons from frms decsons are: Yˆ Kˆ [ e ( L)] z (3.7) wˆ ( L) Yˆ (3.8) θ rkˆ Yˆ θ (3.9) θ ˆ π Yˆ (3.0) θ ρ exp{ κl} (3.) 7

19 qˆ R wl ˆ (3.2) Equatons (3.) (3.2) defne the dynamc model that we solve, parameterze, and smulate. Because the hghly nonlnear nature of the system makes closed form solutons ntractable, we consder a lnear approxmaton of the system about ts steady state. 4. Calbraton and Smulaton We solve the system usng the method of undetermned coeffcents developed n Chrstano (990). Because we approxmate about the model s steady state, we frst need to solve for the steady state. The parameters and ther values are lsted n table 2. There are sx parameters whch defne the steady state:, β, γ, δ, κ, and θ. For consstency wth exstng RBC-model parameterzatons, we set captal s share n output,, to.3, the quarterly dscount factor, β, to.995, and the quarterly deprecaton rate, δ, to.02. We also set the autocorrelaton coeffcent on the z shocks, ψ, to.95. θ, the jump up the technology ladder, s set to.04877, a value whch sets the varance of A nnovatons to the varance of z nnovatons needed to drve a pure RBC verson of our model. κ and γ are chosen to exactly fx two steady state values, the average quarterly growth rate of real output, and the user cost of captal, r-δ. We set average quarterly real growth equal to.00834, and r-δ to.0062, or 2.5% per annum, by settng κ and γ equal the approprate values. 4 Gven the parameter values we have assgned, the steady state probablty of success n appled R&D s ρ.056, whch we take to be an emprcally plausble and conservatve value. The standard devaton of technology shocks s set at.084, smlar to the value used n most RBC analyses. For example, usng data from the U.S. economy n the post Bretton Woods era, Schlagenhauf and Wrase (995) use a value of.04. Our objectve s to see how the model, wth substantally less relance on auto-correlated productvty shocks than standard RBC models, 4 To see how γ s chosen, consder the steady state verson of equaton (3.6): γ β( g A ' ) ( δ + r ). Note that t s necessary to pck a value of β suffcently large f we are to generate postve values for γ. 8

20 performs n accountng for busness cycle fluctuatons observed n key macroeconomc varables. Gven the parameter values we use the standard devaton of the nnovatons to R&D n (3.) s.084 when. We are not, however, smply assumng the varablty of the R&D nnovatons. The varablty of nnovatons to the evoluton of A n (3.) depends on the probablty of success n R&D. n turn, the success probablty depends endogenously on labor choces made by R&D frms and households n the model. We cannot smply choose the standard devaton of nnovatons n appled R&D wthout restrcton. One restrcton s that the probablty of success n the model must be an emprcally plausble value. Note that the model generates a seres of growth rates. We can use these to construct a seres for the level of technology, the A s, and then convert all the statonary, caret-bearng, varables to ther non-statonary counterparts. Hence, smulaton of the model generates data wth both cyclcal and growth components. The model was smulated 000 tmes usng a sample of 200 observatons, correspondng to 50 years of data. We flter both actual data drawn from the U.S. economy and model-generated data usng two flters: the Hodrck-Prescott (HP) flter; and, to consder movements of varables at other than smply busness cycle frequences, a band-pass flter. We then compute statstcal propertes of the data, and compare propertes of model-generated data wth lke propertes of actual data. We focus on standard RBC measures of varablty, cyclcalty, and persstence, but consder more than the busness cycle frequences that are the sole focus of RBC analyses. 5. Quanttatve Results Table 3 presents busness cycle moments summarzng behavors of key macroeconomc aggregates for the U.S. economy over a sample perod 947: to 2002:V. 5 We defne output as real GDP, consumpton as real consumpton of servces and non-durables, and nvestment as real nvestment n non-resdental structures and equpment. As s well known, and as revealed n the 5 The data are real GDP, real consumpton of servces and nondurables, and real gross fxed nvestment n nonresdental structures and equpment. 9

21 table, nvestment s close much more varable than output, wth varablty measured by standard devatons. Consumpton has only three-quarters the varablty of output. n addton, output s hghly serally correlated, consumpton s hghly correlated wth output contemporaneously and at one to two perod leads and lags, and nvestment s not strongly correlated wth output contemporaneously or at leads and lags. The purpose of ths paper s not necessarly to match all of these busness cycle facts. Whle t would certanly be desrable to do so, our prmary queston s how well a model wth endogenzed shocks from a Schumpeteran framework performs relatve to standard exogenous shock models. t s well-known that smple versons of such models cannot replcate all busness cycle facts and requre addtonal modelng detals. Wth the excepton of the endogenous R&D process, our model s qute basc and lacks many features needed to conform to measured movements. To answer our fundamental queston, therefore, we proceed to solve and smulate several dfferent versons of our model and compare them. The frst model we smulate s a smple RBC model wth no R&D process and a fxed supply of labor. Here there s only one source of shocks. n all other respects we treat the model exactly as the one outlned above. We assume a fxed rate of growth for A, rather than a stochastc one, for example, and add ths trend nto the smulated model when creatng artfcal data seres. These seres are then detrended usng the same flters as table 3. The results of 000 smulatons of ths model wth 224 observatons are reported n table 4. The table shows the usual sorts of problems wth such smple models. The volatlty of consumpton s too hgh, and the volatlty of nvestment s too low. The auto-correlatons of output over tme are not too dfferent from the US data, but the correlatons of consumpton and nvestment wth leads and lags of output are very poor matches regardless of the flterng method used. We also report measures of busness cycle asymmetry, snce the shocks from the A process have the potental of beng hghly skewed, especally n our parameterzaton of the model. We use Schel s (993) measures of deepness and steepness, whch are the skewness of the seres and the skewness of ts frst-dfference, respectvely. n ths case, of course, the shocks are not skewed, snce the nnovatons to z are normally dstrbuted, and wth a 20

22 few exceptons, the deepness and steepness measures are not sgnfcantly dfferent from the US measures. There are two sources of aggregate fluctuatons n our model: an aggregate effect workng through technology n each sector that wll be non-zero f there are a small number of sectors, A, and other shocks to productvty whch could proxy for a varety of thngs, z. Our next attempt s to see how well a model drven only by the Schumpeteran source of shocks does n fttng the US moments. The results of ths model, where we set to the extreme value of one, and σ equal to zero, are presented n table 5. As that table shows, the ft s consderably worse than the smple exogenous shock model. The volatlty of consumpton s rdculously hgh for all flterng methods. n addton, the model matches the busness cycle asymmetres only for very low frequency movements. n terms of other moments t does no better than the exogenous shock case. We conclude that our model as presently setup s not any an mprovement n terms of ts ablty to match busness cycle moments. We next consder a verson of our model drven entrely by exogenous shocks. Ths s not the same as the model n table 4, however, snce our model allows for these exogenous shocks to nfluence the allocaton of labor or producton and R&D. There s an addtonal transmsson mechansm that s mssng n the frst case. The results of settng equal to mllon and σ to the same value as table 4, are reported n table 6. The only substantve dfference ths model yelds s a drop n the volatlty of nvestment at all frequences. Snce nvestment volatlty s already too small, ths s not an encouragng development. Fnally, we consder a verson of the model where shocks come from both sources. We set to ten and σ to.075. n terms of the volatlty, the exogenous shocks are by far the most mportant source of varaton., but the contrbuton of endogenous shocks s stll nontrval. These results are n table 7. Consumpton volatlty s stll too hgh, and hgher than the frst model. nvestment volatlty s too low and lower than the frst model. Ths model does just as well n terms of asymmetres, and slghtly better n terms of matchng correlatons wth leads and lags of output. But the overall ft s not overwhelmngly better or worse. 2

23 n order to formalze our comparson of moments across we compute measures of the percentage devatons of the models moments from the US data moments. We report both the root mean squared devaton (RMSD), and the mean absolute devatons (MAD) for two sets of moments. The frst set of moments s the volatlty of output, the relatve volatlty of consumpton, the relatve volatlty of nvestment, and the contemporaneous correlatons of consumpton and nvestment wth output. These are reported n the top panel of table 8. As can be seen the smple exogenous shock model wth no R&D s clearly the best fttng model. The verson of our model wth only exogenous shocks fts almost as well. The two shock model s a bt worse and the model wth only Schumpeteran shocks has a very bad ft. f we use all the reported moments we get the values n the bottom panel. Here the results are dentcal to the frst table when the HP-flter s used. Surprsngly, the results are dfferent f one uses the band pass flter. n ths case the two-shock verson fts best, the exogenous shock verson wth R&D s generally second best, and the no-r&d model s thrd best. The Schumpeteran shocks only model s fourth, though t s not bad n relatve terms as n the top panel. 6. Conclusons n ths paper, we are tryng to dscover f the process of creatve destructon used n Schumpeteran models of growth s a reasonable source for the technology shocks used to drve busness cycles, partcularly n the context of RBC models. We conclude that the process alone s not approprate. n our smple model wth no labor-lesure choce and no dffuson mechansm for these technology shocks, we fnd that n order to generate realstc volatltes for output we also generate hghly counterfactual volatltes of consumpton and nvestment, and that we fal to match observed busness cycle asymmetres. We also show that versons of our model whch rely heavly on exogenous symmetrc shocks fal to match consumpton and nvestment movements any better than an equvalent RBC model wth no Schumpeteran mechansm. 22

24 On the other hand, we do fnd that when we consder correlatons of consumpton and nvestment wth output leads and lags, our model matches moments better than the smple RBC model, at least when a band pass flterng method s used. As a result we conclude that further exploraton of the potental contrbuton of Schumpeteran shocks to busness cycle and other aggregate fluctuatons s worth consderng. Whle ths model cannot ft the US moments as well as many RBC models, t s lkely that ths falure can be attrbuted n large part, to the lack of sophstcaton n modelng the non- Schumpeteran aspects of the model. n partcular, we do not have any sort of labor-lesure decson n our model. Allowng for ths type of substtuton would go a long way n dampenng the volatlty of consumpton our model generates. n addton, our model does not ncorporate any sort of R&D spllovers or technologcal dffuson of nnovatons across sectors. These may well be mportant and wll undoubtedly change the aggregate behavor of output, nvestment & consumpton. Because of ths lack of dffuson we are forced to drve changes n aggregate output by assumng a small number of ntermedate goods sectors. t may be more proftable to buld a model wth a large number of ntermedate sectors generatng approxmately smooth growth, and consder nnovatons whch affect all ndustres equally as comng from some other source. n earler related work, we were able to generate more realstc models when we allowed for movements n basc research to be dstnct from movements n appled research, for example. 23

25 Table Defnton of Varables Endogenous varables that change over tme: A level of appled knowledge n ntermedate ndustry A aggregate level of appled knowledge z aggregate RBC-style productvty shock K captal stock owned by household K captal employed n ndustry P shares of producton frm owned by household ( n equlbrum) R shares of research frm owned by household ( n equlbrum) S state of research success for ndustry ; s success, 0 s falure w real wage r real nterest rate L labor hred by research frm (same for all n equlbrum) L aggregate labor hred by all R&D frms N labor hred by producton frm (same for all n equlbrum) N aggregate labor hred by all producton frms Y output of ntermedate good Y output of fnal goods p prce of ntermedate good π profts earned by current producton frm (same for all n equlbrum) P q prce of one share n the current producton frm (same for all n equlbrum) R q prce of one share n the current research frm (same for all n equlbrum) ρ probablty that S' (same for all n equlbrum) number of ndustres n the economy J number of ndustres that successfully nnovate; J η random nnovatons to z Parameters: captal share n output from a Cobb-Douglas producton functon; 0<<. β tme dscount factor; β<. γ CES parameter from momentary utlty functon; γ>0. δ rate of deprecaton; δ>0. θ growth factor for A when S; θ>. κ senstvty of ρ to R&D nputs; κ>0. ψ autocorrelaton parameter for z. σ 2 varance of nnovatons n z. 24

26 Table 2 Values of Parameters Used n Smulatons Parameter Descrpton Value Captal share n GDP 0.30 β Tme dscount factor for utlty δ Deprecaton rate 0.02 θ Sze of rungs on the appled technology ladder γ Elastcty of substtuton κ Ease of R&D ψ Autocorrelaton for z shocks 0.95 Ι Number of ntermedate Goods Sectors to,000,000 σ Standard devaton of z nnovatons 0 to

27 Table 3 Moments from U.S. Data (947:-2002:V) * HP Flter (λ600) Y C Band Pass (6,32) Y C Standard devaton Standard devaton Relatve to Y Relatve to Y Steepness Steepness Deepness Deepness Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Band Pass (2,6) Band Pass (20,80) Standard devaton Standard devaton Relatve to Y Relatve to Y Steepness Steepness Deepness Deepness Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y Correlaton wth Y * Source: Bureau of Economc Analyss. 26

28 Table 4 Moments from a pure exogenous shock verson of our model (Model ). 3, β.995, γ.397, δ.02, ψ.95, σ HP Flter (λ600) Y C Band Pass (6,32) Y C Standard devaton *** *** Standard devaton ** 0.056*** Relatve to Y.4457*** *** Relatve to Y.0854*** *** Steepness 0.000*** Steepness * Deepness Deepness *** *** Correlaton wth Y *** 0.363*** Correlaton wth Y *** 0.464*** Correlaton wth Y *** *** Correlaton wth Y *** *** Correlaton wth Y * *** *** Correlaton wth Y *** 0.988*** Correlaton wth Y *** *** *** Correlaton wth Y *** *** Correlaton wth Y *** Correlaton wth Y 0.603*** *** Correlaton wth Y *** Correlaton wth Y *** *** Correlaton wth Y * *** Correlaton wth Y *** * Correlaton wth Y *** *** Correlaton wth Y *** * Correlaton wth Y *** *** Correlaton wth Y *** ** Band Pass (2,6) Band Pass (20,80) Standard devaton *** 0.074*** *** Standard devaton ** Relatve to Y *** 3.86*** Relatve to Y *** 3.866*** Steepness Steepness Deepness Deepness *** *** Correlaton wth Y Correlaton wth Y *** 0.889*** Correlaton wth Y *** *** Correlaton wth Y *** *** Correlaton wth Y Correlaton wth Y *** *** Correlaton wth Y * *** *** Correlaton wth Y *** *** Correlaton wth Y *** *** Correlaton wth Y *** *** Correlaton wth Y * 0.640* *** Correlaton wth Y ** *** Correlaton wth Y Correlaton wth Y *** *** Correlaton wth Y ** 0.879*** Correlaton wth Y *** 0.34*** Correlaton wth Y *** 0.860*** Correlaton wth Y *** 0.24*** * sgnfcantly dfferent from the correspondng US data moment at 90% confdence ** sgnfcantly dfferent from the correspondng US data moment at 95% confdence *** sgnfcantly dfferent from the correspondng US data moment at 99% confdence 27

29 Table 5 Moments from our model drven only by A shocks (Model 2). 3, β.995, γ.397, δ.02, θ.04877,, ψ.95, σ 0 HP Flter (λ600) Y C Band Pass (6,32) Y C Standard devaton *** 0.063*** Standard devaton *** *** Relatve to Y *** *** Relatve to Y *** 2.66*** Steepness *** ***.6070*** Steepness Deepness.6699*** *** *** Deepness ** *** Correlaton wth Y *** *** Correlaton wth Y *** *** Correlaton wth Y *** ** Correlaton wth Y *** *** Correlaton wth Y * *** Correlaton wth Y *** *** Correlaton wth Y *** *** Correlaton wth Y *** *** Correlaton wth Y 0.454*** *** Correlaton wth Y *** 0.007*** Correlaton wth Y *** Correlaton wth Y *** *** Correlaton wth Y * *** *** Correlaton wth Y *** *** Correlaton wth Y *** * Correlaton wth Y *** *** Correlaton wth Y *** *** Correlaton wth Y *** Band Pass (2,6) Band Pass (20,80) Standard devaton *** 0.082*** *** Standard devaton *** 0.078*** Relatve to Y.4759*** *** Relatve to Y.947***.2008*** Steepness *** *** *** Steepness Deepness *** *** 0.09*** Deepness Correlaton wth Y Correlaton wth Y *** *** Correlaton wth Y *** *** Correlaton wth Y *** ** Correlaton wth Y *** Correlaton wth Y *** Correlaton wth Y ** *** 0.800*** Correlaton wth Y *** *** Correlaton wth Y *** *** Correlaton wth Y *** *** Correlaton wth Y ** Correlaton wth Y * *** Correlaton wth Y * 0.677*** Correlaton wth Y *** *** Correlaton wth Y ** 0.745*** Correlaton wth Y *** *** Correlaton wth Y *** *** Correlaton wth Y *** *** * sgnfcantly dfferent from the correspondng US data moment at 90% confdence ** sgnfcantly dfferent from the correspondng US data moment at 95% confdence *** sgnfcantly dfferent from the correspondng US data moment at 99% confdence 28