4626233

7/28/2019 4626233

1/20

Human Capital and Overinvestment in R&DAuthor(s): Ana Balco Reis and Tiago Neves SequeiraSource: The Scandinavian Journal of Economics, Vol. 109, No. 3 (Sep., 2007), pp. 573-591Published by: Wiley on behalf of The Scandinavian Journal of EconomicsStable URL: http://www.jstor.org/stable/4626233 .

Accessed: 22/05/2013 22:24

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

of scholarship. For more information about JSTOR, please contact [email protected].

.

Wiley and The Scandinavian Journal of Economics are collaborating with JSTOR to digitize, preserve and

extend access to The Scandinavian Journal of Economics.

http://www.jstor.org

This content downloaded from 111.68.105.84 on Wed, 22 May 2013 22:24:03 PMAll use subject to JSTOR Terms and Conditions
http://www.jstor.org/action/showPublisher?publisherCode=blackhttp://www.jstor.org/action/showPublisher?publisherCode=sjehttp://www.jstor.org/stable/4626233?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/stable/4626233?origin=JSTOR-pdfhttp://www.jstor.org/action/showPublisher?publisherCode=sjehttp://www.jstor.org/action/showPublisher?publisherCode=black

7/28/2019 4626233

2/20

Scand. J of Economics 109(3), 573-591, 2007DOI: 10.1111/j.1467-9442.2007.00508.xHuman Capital and Overinvestmentin R&D*Ana Balcdo ReisUniversidadeNova de Lisboa,P-1099-032Lisboa,[email protected] SequeiraUniversidade a BeiraInterior,P-6200Covilhn,[email protected]

AbstractWe introduce negativeeffect of technologicaldevelopment n humancapitalaccumulationin a growthmodel with endogenous nnovationand accumulation f humancapital.Thisimplies a negativeexternalityof R&D in humancapitalaccumulation.Some calibrationexercisessuggestthat this distortionmaybe sufficientlystrongnot only to offset the usualeffects of spilloversand of returns o specializationbut also to induce overinvestmentnR&D.Keywords:Humancapital;optimalR&D;endogenousgrowthJELclassification: 15; 030; 031; 033; 041

I. IntroductionIn this paper we examine the interactionbetween technological change andhumancapitalaccumulation nd its implications or investment n R&D.A negativeeffect of technologicalchangeon humancapitalaccumulationhasbeen consideredn the literaturen both theoretical ndempirical tud-ies. In theirmodel,Galorand Moav(2002,p. 1148) introducean "erosioneffect":"thetimerequiredor learning he new technologydiminisheswiththe level of educationandincreaseswith the rateof technological hange".In Galor's(2005) model there is a positive association between humancapital accumulationand technologicalprogressbecause rising levels ofschoolinglessenthe adverseeffect of technological hangeon humancap-ital accumulation.Kumar 2003) and Tamura2006) found, n econometric*We aregrateful o JoseTavares,Ant6nioAntunes, wo anonymous efereesandparticipantsat the SATPEGSeminar, he Quantitative conomicsDoctoratemeeting,the Annual2003Spie Meetingand the 2005 EuropeanEconomicAssociationConferenceormanycommentsandusefulsuggestions.Theusualdisclaimer pplies.Weacknowledge upportromFundataoparaa Ciincia e Tecnologia, hroughPOCI/EGE/60845/2004.OThe editorsof the Scandinavianournal f Economics 007. Published y BlackwellPublishing,600Garsington oad,Oxford,OX42DQ,UK and 350 MainStreet,Malden,MA 02148,USA.

This content downloaded from 111.68.105.84 on Wed, 22 May 2013 22:24:03 PMAll use subject toJSTOR Terms and Conditions
http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp

7/28/2019 4626233

3/20

574 A. B. Reis and T N. Sequeiraestimations,a negative nfluenceof total factorproductivityTFP)growthin humancapitalaccumulation hat questionsthis result (also presentinTamura's wn model).1

This motivatesus to introducea negativeinfluence of TFP growthonhumancapitalaccumulationn an endogenousgrowthmodel. We showthat this has implicationsfor the result of under- or overinvestmentnR&D. Jones and Williams(1998, 2000) have established hat in generalwe should expect to have too little R&D in equilibrium.However,thenew distortion mpliedby the negative impactof R&D on humancapitalaccumulation orks n theoppositedirection. nour theoreticalmodel,thereare the usualeffects such as knowledgespillovers,whichimplythatin thedecentralizedquilibriumhereshouldbe underinvestmentnd effects thatimply overinvestment. ollowing Stokey (1995) and Jones and Williams(2000) we calibrate he model to estimatethe empiricalrelevanceof thisnew distortion.We buildon Arnold(1998), who sets up a growthmodel with endogen-ous innovationand accumulation f humancapitalthatintegratesa Lucas(1988)-typemodel andan R&D model, similarto those in Romer(1990)or Grossmanand Helpman(1991). We extend his model by introducingthe negativeeffect of technologicaldevelopment n humancapitalaccumu-lation.2Romer(1990) indicated hat humancapitalis probably he maininputof R&D.Thispaper ntroduces notherink,in the oppositedirection,between humancapitaland R&D: a negativeimpactof R&D on humancapitalaccumulation.Humancapitaldealswithnewtechnology;hus,whenthere is an advanceon the knowledgefrontier,existing humancapitalbecomes less valuable.This effect can be seen as a type of "creativedestruction" f humancapital.3In anextension,we followBenassy (1998) and Alvarez-Palaeznd Groth(2005), in disentangling eturns o specialization rom the marketpowerparameter.This furthertests the strengthof the depreciationdistortionintroduced ereby taking nto account he consumer urplusappropriabilityproblemwhich Jones and Williams(2000) regardas the main force pro-motingunderinvestment.We nowbrieflyreviewthe evidence n Kumar 2003) and Tamura2006)which motivates our assumptionthat innovation mplies a cost on the1In his theoreticalmodel, Kumarexplainsthis featureof the datathrough he impactofthe real interestrate on the schoolingdecision;when the economybecomes more open,technologyadoption ncreases, mplyinga rise in the real interestrateand, thus,a decreasein humancapitalaccumulation.2Arnold(1998, 2000) and FunkeandStrulik 2000) have studied he convergence ropertiesof the decentralizedquilibriumn a similarmodel,withoutthe negativeeffect of TFP onhumancapitalaccumulationnd withoutspillovers.3We thanka refereefor callingthis effect an alternativeorm of creativedestruction.OThe editors of the Scandinavian Journal of Economics 2007.


7/28/2019 4626233

4/20

7/28/2019 4626233

5/20

576 A. B. Reisand T N. SequeiraThe Accumulation of Human CapitalThe existing stock of humancapitalis denotedby H. Accumulationofhumancapitaluses humancapitalwith a CRS technologyand the depre-ciationrate of humancapital s a positivefunctionof the rateof technolog-ical development.This formalizes he idea thattechnologicalprogresshasa negativeeffect on the existinghumancapitalstock.Thus,we have that:

IH= yHH 8gnH, y, > , (1)wheregn representshe rate of technologicaldevelopment iven by the rateof growthof the numberof varietiesof intermediate apital goods.4 Theparameter in equation(1) reflects the impactof technologicalprogresson the accumulation f H. This introducesa negativeexternality mposedby technologicaldevelopment n humancapitalaccumulation.

ProductionThe final good, Y, whichwe takeas numeraire,s producedwith a Cobb-Douglas technology:

Y=DDH1-, 8< 1, (2)whereHy is humancapitalallocated o final good production nd D is anindex of intermediate apital goods. We normalize he population o one,so that all variablescan be read as per capitavalues.D is given by theusualDixit-Stiglitzformulation:

D=[f xdi ,0

7/28/2019 4626233

6/20

Human apitalandoverinvestmentn R&D 577Productionof a new intermediategood requiresthe invention of anew blueprint.The productionof new ideas is determinedby humancapital employed in R&D labs and by the stock of disembodied

knowledgen:fri=EHnn, E>0, 0

7/28/2019 4626233

7/20

578 A. B. Reis and T N. Sequeira

flYPDD

(11)wherepD representshe price for the indexof intermediateapital goods.The demand or each intermediate ood results from the maximizationofprofitsin the final good sector.Eachfirm in the intermediate oods sectorowns an infinitely-lived atent orsellingits varietyxi. Producers ctundermonopolisticcompetitionandmaximizeoperatingprofits,

7ri= (Pi - r)xi, (12)wherepi denotes the price of intermediate ood i and,from (4), r is theunit cost of xi. Profit maximizationn this sector implies that each firmchargesa priceof

pi = p= r/a. (13)With identicaltechnologiesand symmetricdemand, he quantitysuppliedis the samefor all goods,xi= x. Hence,equation 3) can be writtenas

D=nl/ax. (14)FromPDD =pxn, togetherwith equations 11) and(13), we obtain

aofYxn=K-= (15)rAfter insertionof equations 13) and(15) into(12), profitscanbe rewrit-ten as:

r = (1 - a)pY/n. (16)Let v denote the valueof an innovation,definedby

t = e-[R(r)-R(t)]Jr(r)dr, whereR(r)= r(r)dr. (17)Taking nto accountthe cost of an innovationas determinedby (5), freeentryin R&D impliesthat

wl/(n) = v if i >0(Hn >0); (18)w/(EnO) > v ifri=O(Hn 0=). (19)

Finally,no arbitrage equires hatinvesting n patentshas the same returnas investing n bonds:- =r - r/v. (20)V3

? The editors of the Scandinavian Journal of Economics 2007.


7/28/2019 4626233

8/20

Human apitaland overinvestmentn R&D 579This fully describesthe economy.In the following section we charac-terize the steady-statesolution of the decentralizedequilibriumof thiseconomy.6III. DecentralizedEquilibriumAt the steadystate,the shares of factors n each sectormustbe constant.Thus, from (5), to obtaina constant nnovationrate in the steady state,we must have gH= (1- O)gn. At the steadystate, the rate of growthofconsumption s constant, mplyingthat consumptionand outputgrow atconstantandequalrates.Thus,usingconditions 8), (9) and(10), we obtainthatgH= Y- 8gn - p. Fromthis andgH= (1 - q)gn, we reach:

(1- )(y- p)H= , (21)gn =-- ?(22)-0+8Taking nto account hatin the steadystate the sharesof factors n eachsectormustbe constant, 2) and(14) implythat

1-agr = (1 -/)gH + Pg+n fgK. (23)Again,at the steadystate,the rateof growthof consumptions constant,implyingthatconsumption, utputandcapitalgrow at constantandequalrates.Thus,the rateof growthof outputat the steadystateis

-gy +-(1 -0)- . (24)gr 1-f! o 1-b+8The growth rates of consumptionand production ncrease with themonopolisticmarkup 1/a) and the productivityn humancapitalaccu-mulation(y). The effect of the spilloverparameter0) is ambiguous.Anincreasein 0 increasesgn but decreasesgH. Thus,the level of spilloversincreases he outputgrowthrateif andonly if

6< (25)1-fl athatis, only if the "erosioneffect" is sufficiently ow in comparisonwiththe gain fromspecialization.76The model is well behavedregarding onvergence;ee Sequeira 2007) for details.7Werespect his condition n the calibration xercise.



7/28/2019 4626233

9/20

580 A. B. Reis and T N. SequeiraNote thatin the steadystateof this economy, he patent/R&D atiomaybe decreasing,n agreementwith whatwe observein the data.8As men-tionedby Alvarez-Palaez nd Groth(2005, p. 452) this is not verified in

Romer's 1990) originalmodel.We now determinehe sharesof H in eachsector,whichwe latercompareto the optimalsolutions.From the varietiesproduction unction,(5), andthe humancapitalaccumulationechnology,(1), takinginto accountthatgH=(1 - O)gn,we obtainY-P(26)HE= (26)Y

1uDE n ' (27)E Hwhere ufDEs the decentralized quilibrium DE) share of H in sector i.From(18) we obtaingw= go + qgn. Substitutingn equation 20) we get

gw - =gn r - E7r/(wn-f). (28)Inserting he equation or w that results from(10), (9) and(16) into (28),we obtainthe humancapitalshare n the final good sector:

DE 1- 1 n )(29)E

-I (Y g, ,n

(29)1- HIn the expressionsabove,the sharesu, and Uy dependon gn as well ason the ratioH/n'-1. Using (26), (29), and the conditionun + uH+ uy = 1,we obtainthe competitive quilibriumevel of this ratio:1-/ 1

(_ DE gn+ 1(Y-Sgn

+(30)n1-@ --ep/y

IV. Comparisonwith the Efficient SolutionWe now access the optimalityof growthrates and allocations of humancapitalacrosssectorsin the economy.Since the capital intermediate-goodsector is symmetric,the optimalsolution implies utilizationof the quantityxi = x = K/n of each capi-tal intermediategood, and is obtainedfrom the maximizationof Ut=8 Thepatent/R&D atiocan be writtenas ri/wHn.Toobtaina decreasing atio,we musthavegy - gn> 0, which occursfor

P 1-a1-3 a &Werespect his condition n the calibration xercise.



7/28/2019 4626233

10/20

Human apitaland overinvestmentn R&D 581

ft"log(Ct)e-P(r-)d, subject o K= Y- C, whereY is givenby (2),the human apital ccumulationechnology,1), and he R&D echnology,(5). The control ariables reC,H, andHy.Proposition1. All growth ates in the decentralizedquilibriumf thiseconomyreoptimal.Proof:See theAppendix.

Arnold1998)andFunke ndStrulik2000)alsoobtainedhisoptimalityresult.However,s stated n the followingproposition,he allocation fresources cross ectors s notoptimal.9Proposition . In thecompetitivequilibrium,heallocation fH to R&Dandtheproductionf the inalgoodis, ingeneral,notoptimal.The hareofH in the accumulationfH is optimal.Theoptimal uman apital haresare:

Y-PH- (31)Y1 n1* - (32)E H

* - 1(Y+anF

(33)ur--

(y-8g) + 8p/y , (33)3 1 -aeL HJwhere

1-fl aSn+ a (Y Sgn)(H 1-a y )(34)(Ep/y) 1- 8 i-a)

Proof: The derivationof the optimalshares is shown in the Appendix.Compare(29) with (33), (27) with (32) and (26) with (31), taking intoaccount(30) and(34). UComparison etweenoptimalandequilibriumharesshows thattheydif-fer dueto three differentdistortions:i) the spillover,measuredby 0, from

9This s similaro Funke ndStrulik2000).However,ince heydonotconsiderheeffectsof either echnological hangeon humancapitalaccumulationr of spillovers,he distortionpresent n theirmodelis only dueto differences n markups etweensectors.Arnold(1998)does not look at the allocationof H across sectors.? The editorsof the Scandinavianournalof Economics 007.


7/28/2019 4626233

11/20

582 A. B. Reis and T N. Sequeirawhich we tend to have higherH/n1-- thanthe optimal;(ii) the markupdistortion,measuredby 1/la, from which we again tend to have higherH/n'-0 than the optimal;and (iii) the depreciation xternality,measuredby 3, that worksin the oppositedirection. f the first two distortionsdom-inate, in the decentralized quilibriumhere is underinvestmentn R&D,UDE< U*, and the share in the productionof the final good is too high,uDE> U*. This occursbecause privateagents do not take into accountthepositiveexternaleffects (spillovers)of their ownresearchandbecausetheyact in monopolisticcompetition,which the social plannereliminates.If,however, he third distortiondominates, here is overinvestmentn R&Din the decentralized quilibrium, fE > un. This occursbecause individualresearchersdo not take into accountthe negativeeffect theiractivityhasin humancapitalaccumulation.Thus,the depreciation xternalitys a newreasonto obtainoverproductionf ideas.The shareof humancapital n itsown accumulations alwaysoptimal(u* = uHE).10Thisproposition mpliesthatthe existenceof too much or too little R&Ddependson the relativestrengthof the threedistortions.Below, followingJones and Williams 2000),we calibratehemodelto gainsomeknowledgeabout the quantitative imensionof this new distortion.

V. CalibrationWe calibrate he model in Section II and an extension that disentanglesreturns o specializationromthe marketpowerparameter.Followingthe literature,we assume a value of 0.36 for the share ofphysical capital, 8, a valueof 0.1 for R&Dproductivity, , and a valueof0.02 for p.11Regardinghe elasticityof substitution etweenvarieties,weassumea valueof 0.55 for a. Thisimpliesa markup f 1.82,consistentwithvalues used by Funke and Strulik 2000). As this parameter as influencein the results, we also consider a higher value of the markupof 3.33(a = 0.3) and a lower value of 1.37 (a = 0.73), in the range of valuesused in Jones and Williams(2000).12 For the spillover,we considertwovalues for b:0.8, which is in the upperend of the intervalused by Jones10Whencomparing30) and(34), notethat,besidesthe effectthroughhe marketpowerdis-tortion see (ii)), the substitutabilityetweendifferentiatedoodsalso influences he strengthof boththe spilloversandthe depreciationffect. Thus the higher he markup,he lowertheeffect of spilloversandthe lowerthe effectof depreciation f humancapital.11Weperformed ome sensivityanalysison p. However,as it did not affectthe resultsandfor simplicity,we chose to base the exerciseon just one value.12A markup f 3.33 seems to be muchhigher han the values basedon empirical vidence;see Norrbin 1993).However, s remarked y a referee, f one calculates heaveragemarkupratio for all intermediate ndfinal good producers,henac= 0.3 wouldimplya much moremoderateeconomy-wide/grossmarkupratio, comparableo the empiricalreferencesmen-tionedabove.OTheeditorsof the Scandinavianournalof Economics 007.


7/28/2019 4626233

12/20

Humancapital and overinvestment n R&D 583Table2. CalibrationParameters a E pBenchmark 0.55 0.4 0.36 0.1 0.02Alternative 0.30/0.73 0.8 - - -Targetgy 0.0185

Somesteady-statetatisticsMarkups

Spillovers 1/a = 3.33 1/a = 1.82 1/a = 1.37= 0.4 gTFP 0.813% 0.514% 0.305%= 0.4 gH 0.580% 1.050% 1.370%= 0.8 gTFP 1.030% 0.825% 0.604%= 0.8 gH 0.245% 0.560% 0.907%

(1995) and Jones and Williams(2000), and 0.4, half of the first value.In fact, recent empiricalwork that includeshumancapitalreveals lowervalues for national and international pilloversthan previouslyreported.Accordingto resultsin Barrio-Castro, 6pez-Bazoand Serrano-Domingo(2002),domesticspilloversn thepresenceof humancapitaldecreasenearly55%whencomparedo the model withouthumancapital.Forthe GDPgrowthrate(gy), we assumea valueof 1.85%,equalto thatin Funke and Strulik(2000) and in the intervalof availableestimatesforthis ratein thepost-WorldWarIIperiod n the USA.13 Table2 summarizesthe values used in the calibration. n addition,in order to evaluatethefitness of this exercise,we calculatevalues for the growthrateof humancapitaland TFP.Below we compare his with the knownevidence. Notethat,for gy = 1.85%,(24) and (22) implythat each combination f a, Pand 0 implies a given value for gn, and consequentlya given value forgTFP. According o (23),

1-agTFP= -g,. (35)aBefore comparing he decentralized quilibriumwith the optimalsolu-tions, it is useful to evaluate he fitness of the steady-state redictions.Thegrowthrates of TFPand humancapitalarein line withvaluesin Jorgenson

13Estimatesorthegrowth ateof outputoscillateaccordingo the variable onsideredoutputper capitaor outputperworker),o the sourceof information, nd to the periodconsidered.In generalfor the post-warperiod, hese ratesoscillate betweenaround1.20%and 2.20%.Thus,we are consideringan intermediate-upperalue. The higherthe rate,the higherthedepreciation eededto obtainoverinvestment.? The editors of the Scandinavian Journal of Economics 2007.


7/28/2019 4626233

13/20

584 A. B. Reis and T N. Sequeiraand Fraumeni1993) for the USA, thatrangefrom0.425%,for the period1973-1986-the valueusedby Funkeand Strulik 2000)--to 1.02%, or thewhole period 1948-1986 for TFPand from 1.41%(1973-1986) to 2.55%(1948-1986), for humancapital.14Finally,solving(24) with respectto y, we obtainthat,

ac(1 )(1 -q + 8)gr[(1 - (1 -)( -)]+ p. (36)a )P a ( , 0 ) ( I M l1The expressionabove allowsus to determinepairsof y and3 according oour calibration f the model.First,we calculateyo with 8 = 0 to fulfill the1.85%growthrate.Then,we successively ncrease8 and, for each 8, wecalculate he y for whichthe economygrowsat 1.85%.Thus,we considera rangeof pairs(y, 8) that fulfill gy.CalibrationResults or the Basic ModelWe now reportthe decentralized quilibriumand the optimal sharesofhumancapital n R&D for differentpairsof parameters and8, obtainedas describedabove.We also obtain hreshold alues for the "erosioneffect"parameter, +, andfor the depreciation ate8+gn abovewhich overinvest-ment in R&D occurs.Figure 1 shows the decentralized quilibriumandthe optimalsharesof humancapital n R&D for differentcombinations fparameters. or each case it depictsthe thresholdvaluesmentionedabove.For 8 < 6+, there is underinvestmentn R&D; for 8 > 8+, there is over-investmentn R&D.Fromthe empirical iteraturewe judge the scenariowith low spilloverandlow markupo be reliable; ee Norrbin 1993) and Barrio-Castrot al.(2002). In this case, for 8 > 0.082 and a depreciation ate 8gn > 0.19%,the economyoverinvestsn R&D. The higherthe spilloversand the higherthe markup,he higherthe thresholdvalues for the depreciation arameterabove which there is overinvestmentn R&D.Returns o SpecializationBenassy (1998) disentangledreturns to specializationfrom the marketpower parametero show that overinvestmentmay occur in an increas-ing varietymodel. Alvarez-Pelaezand Groth(2005, p. 437) took a stepfurtherby disentanglinghe marketpowerparameterromthe capitalsharein final output,which allowedthem to improve he empiricalperformanceof the model and show that"in view of the empirically ealistic orderof14Values orhuman apitalweretakenusingtheoutputof the education ector; ee Jorgensonand Fraumeni1993, p. 19).? The editorsof the Scandinavianournalof Economics 007.


7/28/2019 4626233

14/20

Human capital and overinvestmentn R&D 585

LowSjillowrs (0.4), High Markup(3.33) High Spillovers (0.8) High Markup(3.33)0.3- 0.3-3 *=0.860;b*g,=0.83% 0.3*=0.903;*g,=1.10%0.25- 0.25

c 0.2*

0.2-

S0.1-01o.o5 -= 0.050.00-Coefficient of growth rate of n in Eq.(1) - 6 66 6 6 6 6 6 6 6d"5" Coefficient of growth rate of n in Eq.(1)- "5"

LowSpilloers (0.4), Intermediate Markup(1.82) High Spillovers (0.8), Intermediate Markup(1.82)0.16- 0.145=0.227;6'g,=0.440% 14=0.283;00g,=0.79%0.14 0.12

".. " 00

0 0-ddddddddd dddddddddCoefficient of growth rate of n in Eq.(1) - "5" Coefficient of growth rate of n in Eq.(1) - "6"

Low Spillovers (0.4) oweMarkup(1.37) High Spillovers (0.8), Low Markup (1.37)

0.08 -3+=0.082; gn,=0.19% 0.018 5=0.127; 6+gn=0.58%

S0.05 ? 0.014*0.03- 0.0120 42 0.10 3 0.006z 0.02 0.0040.01 - 0.002

0. 0 or-w0. d02 o wo dw o d d d ow

0Coefic of g. - "0"Coefficient of growth rate of n in Eq.(1) - "6" Coefficient of growth rate of n in Eq. (1) - "6"

Fig. 1. Comparisonbetweenunandu* forhigh and low spilloversandmarkups

magnitudebetween he parameters...[this]tends to diminish he scope forexcessiveR&D".So far,ourmodeldisentangleshe marketpowerparameterfrom the capitalsharein final outputbut not from returns o specializa-tion. This implies that, as in Romer(1990) and Grossmanand Helpman(1991, p.82), the surplusappropriabilityroblem hat leads to underinvest-ment compensates he creativedestruction ffect that leads to overinvest-ment in R&D.In Jonesand Williams(2000, p.76) the consumersurplusappropriabilityroblem s the main force promotingunderinvestment.Wethereforeregard t as importanto look at an extensionof the model thatisolates this distortion, thereby allowing a better calibrationof itsquantitativeffect.



7/28/2019 4626233

15/20

586 A. B. Reis and T N. SequeiraThus, followingAlvarez-Pelaezand Groth(2005), we changethe pro-ductionfunction 2) to:

Y= D HI-in", < 1,r> 0, (37)wherenowD=n L nxi di (38)n o

and r measures he returns o specialization.Following he same steps asabove,we determinehe growthrate of the economy,which is againequalin the decentralized quilibrium ndin the optimalsolution:gy =

+(1-p]- (39)g-1-/ 1-b+8"

gH andgn are the same as in the benchmarkmodel as we did not usethe productionunction or the final good to obtain hem.Moreover, s thereturns o specializationare not taken into accountby privateagents,thesharesof H in the decentralizedquilibrium reexactlythe same as before.In the optimalsolution, he shareof humancapital n the final good sectorbecomes:=1- 1 nH

-4uY [(ysg"n) +SEp/y. (40)

p e

All other equations, except the one for (H/n' - )*, which derives fromu* + u* = 1- uH, are maintained. Comparing (29) and (40) and taking(Hn' - )DE and (H/n' - )* into account, we may see that for 6= =0,P(1 - a)

7/28/2019 4626233

16/20

Humancapital and overinvestmentn R&D 587Table3. Threshold erosionffects"

1/a = 3.33 1/ac= 1.82 1/ca= 1.373+ S+gn 8+ 8+gn 3+ 8+gn0.4 1.64 2.02 1.18% 2.21 1.30% 2.34 1.37%0.8 1.64 2.05 1.37% 2.22 1.49% 2.35 1.57%

0.4 0.64 0.50 0.67% 0.72 0.82% 0.82 0.95%0.8 0.64 0.63 0.98% 0.75 1.16% 0.85 1.30%

parameter, bove which the economyoverinvestsn R&D,that are higherthan in the earlierpartof our analysis.16However, hese threshold evelsstill seem to be low.17 Our next step is to try andcompare hemwith theempiricalestimatesavailablen the literature.

Does theEconomyOverinvest n R&D?We have calculated hresholdvalues for the "erosioneffect",above whichthe economyoverinvestsn R&D. We wouldnow like to get some notionof how high these thresholdvalues are in empirical erms.An empiricalvalue for the depreciation oefficient 8 couldbe givenbythe effect of the rate of technological hangeon the valueof "old"humancapital.To obtain this we would need dataon the value of humancapitalthatdistinguishesbetween "new"and "old"humancapital.As these dataare not availablewe consider he mostappropriatemacroeconomic ata onhumancapitalat ourdisposal: hehumancapitalstocksbuiltby KlenowandRodriguez-Clare1997), that were calculatedusing a Mincerianapproach,where returnsfrom schooling, experienceand humancapitalqualityaretaken into account.18Using these data,Kumar(2003) sheds some lighton the empiricallyplausiblevalues for 8. He uses instrumental ariablesmethodsto estimatea system of two equationson a cross-sectionsam-ple. The first regresseshumancapitalusing TFP growth,life expectancyand government ducationexpenditureso GDP as explanatory ariables,andthe secondregressesTFPgrowthon humancapitalandopenness;seeKumar 2003, p. 601). Coefficients from the regressionof the log of the16Inthis case,due to the functionalormof the differentiatedoodssector, he lowermarkupdoes not increase he tendency owardoverinvestment,ut acts in the oppositedirection: sit decreases he privategain (i(1 - a)), the tendency owardunderinvestmentncreases.17Thethreshold aluesseem to be low,in particularwhencomparinghesedepreciationateswith the typicalvalue of 5% used for physicalcapitaldepreciation.8Thus,this measureof humancapital akesinto account he value of schoolingandexpe-rience.



7/28/2019 4626233

17/20

588 A. B. Reis and T N. SequeiraTable 4. Empirical "erosioneffects"

Benchmark model1/c 83+ Empirical3.33 0.860-0.903 0.514-1.0371.82 0.227-0.283 0.181-0.3641.37 0.082-0.127 0.082-0.164

Returns to Specialization ModelSr 6+ Empirical

1.64 2.02-2.35 1.01-2.030.64 0.50-0.85 0.39-0.79

humancapitalstockon the percentagegrowthrateof TFP(conditionalonlife expectancyand totalgovernment ducationexpenditureso GDPratio)oscillate from -0.160 to -0.321.19Assumingthat the initial value of humancapitalstock is not affectedby the growth rate of TFP, we can use these values as estimates of

(agH/agTFP(%))t. The model counterpart f this expressionmay be ob-tainedbyrewriting1) asgH= yuH - 8gTFP(%)/(C*1l 0), wheregTFP(%) =Cl*00gn and C1=(1l - a)/a in the benchmarkmodel (see (23)) andC1= ri in the extension(see (36)). Thus,we obtainthat

agH _ 20agTFP(%) C1*100

Noting that the period length (t) in Kumar(2003) is 26 years, we getapproximateestimates for 8 accordingto the different values for theparametersndto the versionof the model considered.These areshownandcomparedwith the threshold aluesobtained o farin Table4.These values show that, according o availabledata,overinvestmentsa plausiblepossibility.The case for which the whole intervalfor empiri-cal estimates s almost below the thresholdvalues for interval s the onewith the highergains of specialization.Even in the highest markupcase,the model intervalfor thresholdvalues is consistentwith the empiricallyobtained nterval.Anotherpossibly important ffect of technologicalprogresson humancapitalis that when the rate of technologicalprogressincreases,it may

19Thesecoefficientsarecontrolledorcausalityas theyarebasedon a systemof simultaneousequationsusing two-stage east-squaresstimates.20This is a partialderivative f the precedingequationwith uH held fixed. We can regardtotal government ducationexpenditures s a reasonable roxyfor UH,which is held fixedwhencalculatinghe TFPgrowthcoefficients.? Theeditorsof theScandinavianournalof Economics 007.


7/28/2019 4626233

18/20

Human apitaland overinvestmentn R&D 589be more difficult to learn, i.e., to build new human capital. To cap-ture this effect we could write the accumulationof human capital asH= HHy(l - 8gn), y, 3 > 0. If we consider his formulationnsteadof (1),the resultsarevery similar o thosereported bove.21Of course, f we useda formulation hat combinesboth effects, the tendencytowardoverinvest-ment would increase.

Accordingto these arguments,our results suggest that the "erosioneffect"presentedhere can be sufficientlystrong o lead to overinvestment.Note also that we have assumed hat there are no duplication xternalitiesin R&D,whichin Jones andWilliams(2000) is the main forcepromotingoverinvestmentn R&D.The inclusionof this distortionwould strengthenour result in favor of overinvestment.

VI. ConclusionWe introducea negativeeffect of technologicaldevelopmenton humancapitalaccumulationn a growthmodel with endogenous nnovationandaccumulationof humancapital. Consideration f this effect, previouslydescribedby Galor and Moav (2002), is justified by empiricalevidencein Kumar 2003).This new featureintroducesa distortion hat favors overinvestmentnR&D: a negative externality mposed by technological developmentonhumancapitalaccumulation.na comparison f thecompetitive quilibriumand the optimalsolution,we conclude hatall growthrates areoptimal,butthe allocationsof humancapitalbetweensectorsare not. These differencesare due to a numberof distortions,such as spilloversand specializationgains usually foundin the literature, s well as an "erosioneffect".Thislast effect is a new theoreticalpossibilityfor obtainingoverinvestmentnideas.In a calibrationexercise, we obtain threshold evels for the "erosioneffect" above which the economy overinvests n R&D, for various andplausible values of the other effects in the model. Results from thisexercisesuggest that the new distortionmay be quite strongwhen com-paredto spillovers,markupand specialization ains.Whencomparingheresults from calibrationwith the availableempiricalevidence, we con-clude that overinvestmenteems to be empiricallyplausible,contrary othe finding in Jones and Williams (2000). Exceptionsto this conclu-sion occur mainly when social returnsto specializationare particularlyhigh.21These results are available from the authors on request.



7/28/2019 4626233

19/20

590 A. B. Reisand T N. SequeiraAppendix. Proofs of PropositionsProof (Proposition1)Thecurrent-valueamiltonianor hisproblems

1- = logCt+X1((n K)H (1-)- Ct)+ X2[y(H - Hy - H) - 8HEHn- 1] + 3(EHnfnl). (Al)C,Hn andHy arethecontrolvariables ndwe haveusedHH= H - Hy - Hn. Thefirst-order onditions re

1/Ct =).; (A2)X2[y + 8EHH/n'-] = X3EnO; (A3)

(1 - P)Yhi =yy~2; (A4)HyBY-K= ph -~1; (A5)K

X2(Y- 3gn) = pX2- -2; (A6)

f1(1- a)Y 2(1 -q)HgnX3gn =P)3 -3. (A7)an n

From A4) and(A6)we obtaingH = , (A8)1-0+8

which s equal o thedecentralizedolutiongivenby (21) and,again,gn= gH/(1 - )by the R&Dtechnology.Taking ntoaccount hat,at the steadystate,consumption,outputandcapitalgrowat constantandequalratesandthatthe sharesof factors neachsectorareconstant,we obtain he rateof growthof outputattheoptimum,gy = (1 -) (A9)gr 1-/ c 1-4+8'whichwe comparewith(24).

Proof (Proposition2)Insertion f 2 from(A4) in (A7) andconsiderationf (A3) provides ondition 33).Fromthe varietiesproductionunctionand the high-techhumancapitalaccumula-tiontechnology,we obtainconditions 31) and(32).As u*+ u*H u* = 1,we obtain(H/n'-a)*a. oC The editors of the Scandinavian Journal of Economics 2007.


7/28/2019 4626233

20/20

Humancapital and overinvestmentn R&D 591ReferencesAlvarez-Palaez,M. andGroth,C. (2005), "TooLittleor Too MuchR&D?",EuropeanEco-nomic Review49, 437-456.Arnold,L. (1998), "Growth,Welfareand Trade n an IntegratedModel of Human-capitalAccumulation ndResearch",ournalof Macroeconomics0, 81-105.Arnold,L. (2000), "EndogenousGrowthwith PhysicalCapital,HumanCapitaland ProductVariety:A Comment", uropeanEconomicReview44, 1599-1605.Barrio-Castro, ., L6pez-Bazo,E. and Serrano-Domingo, . (2002), "New Evidenceon In-ternationalR&D Spillovers,HumanCapitaland Productivityn the OECD",EconomicsLetters77, 41-45.Benassy,J.-P.(1998), "Is ThereAlwaysToo Little Research n EndogenousGrowthwithExpandingProductVariety?", uropeanEconomicReview42, 61-69.Funke,M. and Strulik,H. (2000), "OnEndogenousGrowthwith Physical Capital,HumanCapitaland ProductVariety",EuropeanEconomicReview44, 491-515.Galor,0. (2005), "FromStagnationo Growth:Unified GrowthTheory",n P.AghionandS. Durlauf eds.),Handbook f EconomicGrowth,North-Holland, msterdam, 71-293.Galor,0. and Moav,0. (2002), "NaturalSelection and the Originof EconomicGrowth",Quarterly ournalof Economics117, 1133-1191.Grossman,G. andHelpman,E. (1991),Innovation nd Growth n the GlobalEconomy,MITPress,Cambridge,MA.Jones,C. (1995),"R&D-basedModelsof EndogenousGrowth",ournalof PoliticalEconomy103, 759-784.Jones,C. andWilliams,J.(1998), "Measuringhe Social Return o R&D",Quarterlyournalof Economics113, 1119-1135.Jones,C. andWilliams,J.(2000),"TooMuchof a GoodThing?The Economics f Investmentin R&D",Journalof EconomicGrowth , 65-85.Jorgenson,D. and Fraumeni,B. (1993), "Education nd ProductivityGrowth n a MarketEconomy",AtlanticEconomicJournal21, 1-25.Klenow,P.andRodriguez-Clare,. (1997),"TheNeoclassicalRevival n GrowthEconomics:Has it GoneTooFar?",n B. S. Bernanke ndJ. J.Rotembergeds.),NBERMacroeconomicAnnual1997, MITPress,Cambridge,MA, 73-103.Kumar,K. (2003), "Education ndTechnologyAdoption n a SmallOpen Economy:TheoryandEvidence",Macroeconomic ynamics7, 586-617.Lucas, R. (1988), "On the Mechanicsof EconomicDevelopment", ournalof MonetaryEconomics22, 3-42.Norrbin,S. (1993), "The Relationbetween Price and MarginalCost in U.S. Industry:AContradiction",ournalof PoliticalEconomy101, 1149-1164.Romer,P. (1990), "EndogenousTechnologicalChange",Journalof PoliticalEconomy98,71-102.Sequeira,T. N. (2007), Working-Paperumber508, Faculdadede Economia,UniversidadeNova de Lisboa.Stokey,N. (1995), "R&Dand EconomicGrowth",Reviewof EconomicStudies62, 469-489.Tamura,R. (2006), "HumanCapitaland EconomicDevelopment",ournalof DevelopmentEconomics79, 26-72.FirstversionsubmittedApril2006;final versionreceivedJanuary 007.

OThe editors of the Scandinavian Journal of Economics 2007.

4626233

Documents

Transcript of 4626233