Endogenous Growth: An Alternative Measuring Device? I. Introduction

Transcription

1 Endogenous Growh: An Alernaive Measuring Device? I. Inroducion Facs are essenial in economics as hey allow us o es heory. However, hey are also useful in he calibraion procedure for he purpose of choosing a good measuring device. In Chaper 3, we presened he Solow Growh model, an example of exogenous growh model on accoun ha he driver of economic growh, echnological change, is deermined ouside he model. Exogenous growh is only one ype model ha researchers have developed. Anoher branch of growh heory comes under he heading of Endogenous Growh. Endogenous Growh began wih he Ph.D. hesis of Paul Romer a he Universiy of Chicago in 1986, and has flourished ever since. The heading, endogenous growh refers o he resul ha economic growh does no rely on some exogenous increase in some parameer or variable in his class of models. Alhough his seems like a huge advanage of endogenous growh relaive o exogenous growh, his does no mean ha endogenous growh is a beer measuring device for he quesion we have in hand, namely, why are some counries so much poorer han ohers? The ypes of models ha fall in his caegory are varied. There are really wo branches of endogenous growh models. Boh share he feaure ha economic growh is he resul of decisions made by firms and households in he model. The wo branches are disinguished by wheher hey assume perfecly compeiive markes or imperfecly 1

2 compeiive markes. The imperfec compeiion based models focus on he decisions of firms o creae new ideas hrough research and developmen. Paul Romer was one of he founders of his sub-branch of models, publishing a 1990 paper. His 1986 paper esablished he oher sub-branch of his lieraure. To undersand he inuiion behind he endogenous growh, a leas he variey ha mainains he perfec compeiion assumpion, i is insrucive o review he reason for he failure for he Solow model o generae susained growh in he absence of echnological change. Recall, ha he growh canno be susained in he Solow model because he marginal produc of capial decreases and in he limi approaches zero. Thus, o break his resul we need for he marginal produc of capial o no go o zero as he capial sock is increased. This is effecively wha is done in he AK model, as he marginal produc of capial is consan and equal o A. There are oher imporan differences beween Exogenous and Endogenous growh. Recall he Solow growh model is a model of relaive income levels. Counry facors such as TFP, savings raes, or populaion do no affec he economy s growh rae along he balanced growh pah. They do, however, deermine a counry s income level relaive o oher counries; a counry wih a higher savings rae will have a higher level of per capia oupu a each dae along he balanced growh pah. For his reason, exogenous growh is ofen referred o as a level effec model. This is no he case wih endogenous growh models of he AK variey. Here any difference beween counries resul in permanen differences in growh raes along he balanced growh pah. Moreover, as we 2

3 shall see here is no convergence of per capia GDP for counries ha are idenical in every way excep for heir iniial per capia capial sock. We begin by sudying he endogenous growh models ha assume perfec compeiion. As we shall see, he analysis for he simples of hese models, he Ak model, is acually less involved hen he analysis for he Solow model. II. Perfecly Compeiive Models: The AK Growh Model The model s srucure is he same as he Solow growh model wih he excepion of he producion funcion. The aggregae producion funcion is now (Y) Y AK. The corresponding per capia producion funcion is (y) y Ak. Consequenly, he aggregae capial sock evolves according o he following equaion (K) K 1 (1 ) K sak. The per capia producion funcion hen is (k) ( 1 n) k 1 (1 ) k sak. Balanced Growh Pah The easies way o deermine if here is a seady sae equilibrium or a balanced growh pah equilibrium is o use he above equaion (k) and solve for he growh rae of he per capia capial sock. This is done by firs dividing each side of he above equaion by k k 1 (1 n) (1 ) sa. k 3

4 The growh rae is hus, (gr-rae) k 1 sa1. k 1 n Since (y) is linear in k, i follows ha per capia oupu increases a his rae as well. Now for here o be posiive growh in mus be he case ha sa n This requires ha sa n. In effec, he produciviy of capial and savings rae mus be large enough relaive o he depreciaion rae and populaion growh rae. Noice ha he growh rae is affeced by he economy s savings rae, s, TFP, A, and populaion growh rae, n, as well as he depreciaion rae. Here hen is he resul ha counry specific variables affec he is growh rae he so called growh rae effec. No Transiional Dynamics Having solved for he growh rae along he balanced growh pah, we can ask wheher here is any convergence ype propery associaed wih he AK model. In conras o he Solow growh model, here is no convergence in his model; iniial differences in per capia capial socks beween oherwise idenical counries will be forever mainained. Income gaps will never be eliminaed beween oherwise idenical counries. This resul should no be surprising in ligh of he algebra used o solve for he balanced growh pah. A no sep in he analysis did we invoke he balanced growh condiion ha 4

5 he growh rae of he capial sock equals 1+g k. This is in conras o he derivaion of he balanced growh pah growh rae for he Solow model. Inuiively, he failure of economies ha differ only in heir iniial capial socks o converge is relaed o he fac ha here are no diminishing reurns o capial in he Ak economy. As such here is no advanage wih saring ou wih a lower capial sock. The marginal produc of capial in he poorer economy is he same as he marginal produc of capial in he richer counry. Adding a new machine resuls in he same increase in oupu, A, in each counry. This is in conras o he Solow model where he new machine in he poor counry brings abou a much larger increase in per capia oupu han he new machine in he rich counry. III. Monopolisic Endogenous Growh The second ype of endogenous growh model has markes ha are characerized by imperfec compeiion. The need for deviaing from he assumpion of perfec compeiion is relaed o he special properies of echnology or ideas. Paul Romer (1990) poined ou ha alhough echnology can be viewed as an inpu in he producion process, i has very differen properies han oher inpus such as labor and machines. The bes way o hink of a echnology is a recipe for combining inpus o produce oupu. (I is useful o hink abou cooking or baking some ype of food, such as chocolae chip cookies) Wha makes he recipe unique from oher inpus such a labor or capial, is ha is use by one person does no preclude is use by anoher. I can be using he recipe for 5

6 making chocolae chip cookies in my house and anoher 10 people The Case Agains Paens David Levine and Michele Boldrin have recenly challenged he Schumperian Growh Lieraure s view ha paens are necessary for innovaion. They argue ha he lag beween when an innovaion is made and when i is copied by a compeior is sufficienly long ha he innovaor can earn enough rens on his innovaion o more han compensae for R&D expendiures. In effec, copying is no a cosless and insananeous aciviy. They poin o empirical evidence ha shows ha despie he large increase in he number of paens and he increase in paen proecion, here has been no noable increase in he rae of echnological change. They also review hisorical evidence ha shows ha he creaion of mos indusries is he resul of a burs of discoveries ha are done wihin highly compeiive condiions. could be doing so a he same ime. When one person s use of an inpu does no preven someone else from using i a he same ime, we say ha i is non-rival in naure. Technology is hus a non-rival inpu. This is in conras o labor or machines, which are rival inpus. The non-rival propery implies ha no one would ever underake cosly R&D unless here is a paen sysem, as someone could jus copy wha you expensively creaed, and because hey did no have o spend any resources on R&D, could undercu your price, effecively puing you ou of business. A paen of course creaes a monopoly, which means ha markes are no perfecly compeiive. This is he source of imperfec compeiion in his second caegory of Endogenous Growh models. Anoher propery of echnology idenified by Paul Romer is ha i is hard for is creaor o exrac paymens from everyone in a sociey ha uses his or her idea. For sure, paens preven someone from direcly copying your idea, bu hey do no preven someone from using your idea o creae a new idea. The abiliy o collec paymen for he use of a good or resource you own goes under he heading of excludabiliy. The abiliy o collec fees for he use of somehing you own is a funcion of boh he physical qualiies of he asse as well as he legal sysem. 6

7 Because he paen sysem does no preven someone from using your idea o creae a new one, echnology is only parially excludible. The implicaion here is ha here are likely o be imporan exernaliies ha imply ha marke is no doing enough R&D from a social perspecive. A he same ime, a line of research under he endogenous growh lieraure wih monopolisic elemens known as Schumpeerian Growh argues ha as new ideas replace old ideas, hey desroy he value of he resources used o discover hose old ideas. There is, hus, a desrucive elemen associaed wih he creaion of an idea, somehing which he famous Ausrian American economis, Joseph Schumpeer referred o as Creaive Desrucion. This desrucion of he value of pas invesmens suggess ha an economy may be doing oo much raher han oo lile from he sandpoin of maximizing social welfare. To show how hese properies affec he modeling and analysis, we provide an ouline of Paul Romer s 1990 aricle iled Endogenous Technological Change. In doing so, we do no aemp o solve ou he general equilibrium. Again, our aim is o show how he special properies of knowledge/ideas are refleced in he model, or beer said, how hey change he model s srucure. Ineresingly enough, he model we skech ou has become he building block of business cycle analysis associaed wih New Keynesian analysis. Reviewing he monopolisic srucure here will prove useful when we sudy he New Keynesian model in our las chaper. For Romer s (1990) model we shall coninue o assume he same consumpion equaion and capial sock equaion 7

8 (C) (K) N c ( 1 s) Y K 1 (1 ) K sy The model differs from he ones we have sudied on he producion side. Here here are hree levels of producion: he Final Goods Secor, he Inermediae Goods Secor, and he R&D Secor. We discuss each in urn. Final Goods Secor The Final Goods secor is perfecly compeiive. I combines inermediae goods, x z, o produce he final good, Y, according o he following producion funcion (Y) Z Y x z z1 1/ The above producion funcion is generally referred o as a Spence-Dixi-Sigliz funcion or aggregaor for is originaors: Michael Spence, Avenish Dixi and Joseph Sigliz. I is characerized by consan reurns o scale. The variable, Z, denoes he number of inermediae goods. The parameer, σ, is resriced o be less han one, and deermines how subsiuable he inermediae goods are in he producion funcion. If σ=1, hen inermediae goods are perfec subsiues making he elasiciy of subsaion infinie. This specificaion of he producion funcion acually capures he idea of increasing reurns o specializaion, an idea ha harkens back o Adam Smih and he Wealh of Naions. To see his, le us assume ha all inermediae goods are equal in quaniies. Then (Y) reduces o Y z Z 1/ x. Thus, he more inermediae goods produced by a counry, he larger is TFP is. 8

9 Being perfecly compeiive, he final goods producers are price akers and maximize profis (Y-Prof) max Z z1 x z 1/ Z z1 p z x z This leads o he following profi maximizaion problem (Y-FONC) Z z1 x z 1 1 x 1 z p z Using he definiion of (Y), he lef hand side can be rewrien as 1 1 (x z -Demand) Y x z pz This is he Final Good Secor s demand for inermediae good z. Deriving his demand is necessary for he problem of a monopolis inermediae good producer. Inermediae Goods Secor The inermediae Goods Secor is monopolisically compeiive. Each inermediae good z is produced by a unique monopolis. This monopoly posiion is he resul of he firm buying a paen ha lass forever from he R&D secor. I is compeiive in he sense ha in equilibrium a monopolis effecively makes enough o cover is fixed coss. As new ideas can be creaed, and hence new inermediae goods, here is effecively free enry ino he inermediae good secor. Even hough each producer fixes is own price, his enry drives he price of inermediae goods and paens up so ha firms are only making enough profis o cover he cos of buying a paen. 9

10 An inermediae good producer hires workers o produce he inermediae good. I pays a compeiively deermined wage rae. w. However, being a monopolis i ses he price for is own produc, p z, based on he demand for is produc given by (x z Demand). For simpliciy, we shall assume ha one uni of labor produces one uni of he inermediae good. Using (x z Demand), he profi of he monopolis are (x z Profi) Y xz xz w xz Y xz w xz We can differeniae wih respec o x z and se he derivaive o zero. This yields he following profi maximizaion condiion 1 1 (x z - FONC) Y xz w If we use (x z - FONC) wih (x z -Demand), we obain he imporan resul in hese models of monopolisic compeiion ha he price is a consan mark up over he marginal cos, w. Namely, (Price Mark Up) w pz. If each worker produced A unis of he inermediae good, hen he Price mark up equaion would include A in he denominaor. Effecively, we have se A=1. The R&D Secor Ideas are produced by he R&D secor. To produce new ideas, he R&D secor rens capial from he households. Le Z be he sock of ideas ha exis a dae. Then new ideas are (Z +1 -Z ). The amoun of new ideas depends on he capial used in he R&D 10

11 secor. Following Romer s poin ha ideas are parially excludible, he exising sock of ideas is assumed o impac he number of new discoveries. A simple formulaion of his producion funcion is (R&D) Z 1 Z K Z The imporan poin here is ha alhough he R&D Secor pays for he capial inpu, i does no pay for he Z inpu. This is on accoun ha old ideas can be used o produce new ideas, and need no be compensaed for his use- he noion of parial excludabiliy. The profis of he R&D secor are hus (R&D Profi) p P ( Z 1 Z ) r K where p p is he price of he paen. This is a one-ime cos ha is incurred by he buyer of he paen, an inermediae good producer. Indeed, he exisence of his one-ime cos, means ha we mus have a monopolisic srucure o he inermediae good secor. If a producer were a price aker and if here are consan reurns o producion in labor as here is in he inermediae good secor, hen a firm ha paid is inpus heir marginal produc would earn zero profis. However, he monopoly srucure guaranees enough profis o pay for he paen. Indeed, in hese models he monopolis mus make profis each period over heir infinie lifeimes so as o jus pay for he one-ime cos of he paen. This is a necessary condiion of he general equilibrium, which we do no develop any furher in his chaper as i akes oo much ime and knowledge han we have a his poin. 11

12 III. Choice of Measuring Device How useful is Endogenous Growh heory for undersanding he curren huge dispariy in inernaional incomes? Can eiher branch of his lieraure accoun for he lae sars of some counries? Le us sar wih he endogenous growh models wih monopolisic elemens. Recall, ha his lieraure emphasized he decisions of firms o expend resources o generae new ideas. The problem wih his ype of heory for undersanding he growh and developmen facs is ha lae sarers are no in he business of creaing new ideas. They need no reinven he wheel. Insead, hey can use ideas ha have been discovered in he rich counries. Indeed, imiaion raher han innovaion is he criical elemen in he early cach-up of many counry. Japan did no begin is growh miracle in he 1950s producing auomobiles or oher high ech goods. Texiles and assembly of oys and elecronic equipmen were large pars of is early miracle days. Nahan Rosenberg in his 1983 book, Inside he Black Box, documens ha he exile indusry in Japan sared by using obsolee machines discarded from he UK. They hen modified hese machines o realize produciviy gains. Evenually, hey sared o produce heir own exile machines. More recenly, he specacular growh of China has mimicked his ype of process, wih perhaps a greaer reliance on mulinaional firms for seing up manufacuring sies in special expor zones. Mulinaionals have been exremely imporan in ransferring knowledge from he rich o he poor counries. 12

13 For his reason, his ype of endogenous growh model does no seem paricularly relevan for he purpose of undersanding he evoluion of inernaional income differences. This is no o say ha hese ypes of models have no value. Indeed, if we were rying o undersand growh in he sock of knowledge over ime, or why he US growh rae of per capia oupu has been roughly 2 percen per year for he las cenury, his is exacly he ype of model ha we should use as a measuring device. However, we are no sudying hese quesions in his course. This leaves us wih he firs ype of endogenous growh model o consider. Is his a beer measuring device han he exogenous growh model we have developed ha combines Solow wih Malhus? Your iniial reacion probably is ha he AK model is a more reasonable choice of measuring device precisely for he reason ha i does no require echnology o fall from he sky. Addiionally, you migh hink ha is predicion ha counry specific facors have a permanen effec of a counry s growh raes is a virue of he model. I is cerainly he case ha over he las hree cenuries, growh raes of per capia GDP have differed dramaically across counries. The Ak model, hus, can easily explain his difference in growh raes, and by doing so, can accoun for he widening of inernaional income differences o heir curren size. However, he increase in income dispariies since 1700 is only one propery of he daa. Before we conclude ha he AK model is a good measuring device, i is insrucive o examine wheher he model is qualiaively consisen wih he remaining se of facs. As i urns ou, i is no. In paricular, he Ak model canno accoun very well for he fac 13

14 ha growh models are a very recen phenomenon limied o counries ha were poor a he ime heir miracles began. Indeed, as we shall see, he model predics ha growh miracles are every bi as likely o occur in rich counries, and were every bi as likely hree cenuries ago. How would one explain he growh miracle of Japan wihin he conex of he AK model? Recall, ha an increase in eiher he counry s savings rae or TFP or a decrease in is populaion growh rae leads o a permanen increase in a counry s growh rae. One could hen explain he large surge in Japan s growh rae saring in 1950 o a change in any of hese facors. Japan s savings rae did in fac show a large increase in he pos war period. A change in 1950 along hese lines would change he pah of (log) per capia GDP as shown below. Figure 1: AK Model and Japanese Growh Miracle 1950 ime 14

15 Now Japan has no managed o mainain an average annual growh rae equal o is average over he 1950 o 1960 or he 1960 o 1970 period. In fac, as Japan s income gap wih he Unied Saes has decreased, is growh rae has fallen. In he 1960s, his growh rae was close o 10 percen; in he 1970s, i was approximaely 5 percen on average; and in he 1980s, 4 percen. The 1990s, referred o as he Los Decade, was disasrous wih a growh rae close o 0 percen. How could we explain his decline in Japan s growh rae wihin he Ak model? One way is o argue ha Japan s savings rae or is TFP fell coninuously afer he big increase experienced in Savings raes and TFP are in he end deermined by a counry s policies, and so his really is a sory abou a coninual deerioraion of Japanese policies afer This is a raher complicaed sory, bu no an implausible one. We canno dismiss he AK model for his reason alone. However, we can dismiss i for he reason ha i predics ha growh miracles are as likely in rich counries as in poor ones. Le us ask wha would he AK model predic if he Unied Saes were o now adop Japanese policies ha were in place during he 1950 s? The following diagram shows he pah prediced by he Ak model if he Unied Saes adoped Japanese policies in Since policies have growh rae effecs, and hese policies led o 6 percen growh in Japan over he period, hen he 15

16 Unied Saes according o he Ak model would grow a 6 percen per year saring in The Unied Saes would herefore experience a growh model. We could also ask he quesion of wha would happen o he US economy if i had in year 1800 adoped Japan s 1950 policies. The effec would be idenical as o when he Unied Saes adops he policy in 2000: he Unied Saes would hereafer grow a 6 percen per year. The Ak model hus predics ha growh miracles are every bi as likely o happen in he leader and are every bi as likely o have happened wo cenuries ago. This is compleely a odds wih he paern of growh and developmen. For hese reasons, we conclude ha he Ak model is no a good measuring device for undersanding oday s huge differences in incomes across counries. Figure 2: Growh Miracles are Jus as Likely in he US US Japan 1950 Before concluding he chaper, i is worhwhile o ask wha he Solow Model predics for he pah of he Unied Saes if i were o adop Japan s 1950 policies. In he Solow 16

17 model, a change in he savings rae or TFP resuls in a change in a counry s income level along he balanced growh pah. Following he change, he model predics a ransiion from one balanced growh pah o anoher. In he case ha he Unied Saes adoped Japanese policies, he new balanced growh pah of he Unied Saes would probably lie somewha lower han is curren pah. We say his because Japan even before he 1990s appeared o be converging o a level of income around 90 percen of he US level. Thus, if he Unied Saes becomes like Japan, he Solow model predics ha he Unied Saes would be worse off and would experience lower growh unil i converges o is new balanced growh pah. This is a very differen conclusion han he Ak model. IV. Conclusion Endogenous growh is a raher recen developmen in macroeconomics. Righfully so, i has araced a lo of aenion. Alhough i has raher limied value in undersanding why some counries sared he growh process so much laer, here are many oher imporan quesions for which i is ideally suied o address. For example, a curren area of research ries o undersand why he Indusrial Revoluion was primarily a Norhern European phenomenon. This lieraure has found ha saring daes seem o be deermined by wha happened o counries much earlier in hisory. For example, counries ha underwen a Neolihic Revoluion earlier in ime (i.e., swiched from huner/gaherer o agriculure) were far more likely o indusrialize earlier. We will come back o his issue and some similarly relaed ones in our las chaper on economic growh and developmen, Chaper 8. 17

18 References: Romer, Paul M, "Increasing Reurns and Long-run Growh," Journal of Poliical Economy, Universiy of Chicago Press, vol. 94(5), pages , Ocober. Romer, Paul M, "Endogenous Technological Change," Journal of Poliical Economy, Universiy of Chicago Press, vol. 98(5), pages S71-102, Ocober. Rosenberg, Nahan Inside he Black Box: Technology and Economics. Cambridge, London, New York, New Rochelle, Melbourne, Sydney Cambridge Universiy Press. Problems 1. In he Ak model explain why a growh miracle is every bi as likely o occur in a rich counry such as he Unied Saes as i is in a poor counry. In oher words, wha would happen in he model if he U.S. adoped Japanese policies? Compare his predicion wih ha of he Solow Model. 2. Compare he pah of an economy s per capia oupu in boh he Solow Model wih exogenous echnological change and he Ak model before and afer he following changes. Assume ha he prior o he change, he economy is on is balanced growh pah. (Noe: your answer should consis of a graph of he ln(y ) on he verical axis, and ime on he horizonal. a. An increase in he populaion growh rae. b. A decrease in he economy s savings rae c. An increase in TFP d. A earhquake ha desroys half of he naion s capial sock bu no is populaion e. A disease ha kills off half of he populaion. 3. Consider he AK model. Suppose you were o assign parameer values so ha he model maches he US long run growh experience. Lis he Kaldor Growh facs ha you would use in Sep 4 of he calibraion exercise. Use hese facs wih he model equilibrium resuls o assign he parameer values. 18

19 4. Suppose we asked he quesion: Do differences in Savings Raes accoun for he difference in average annual growh raes observed across counries over he period? Furher suppose ha we chose he AK model as our measuring device and ha we calibraed he model parameers in Sep 4 o he US experience as in Quesion 3 above. a. Explain how you would es he heory being careful o lis he variables in he Penn World Tables ha you would use. b. Execue he es you have oulined above. Hand in a plo of acual average annual growh raes or he period versus growh raes prediced by he model 19