Four Centuries of British Economic Growth: The Roles of Technology and Population

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1 MPRA Munich Personal RePEc Archive Four Cenuries of Briish Economic Growh: The Roles of Technology and Populaion Jakob Madsen and James Ang and Rajabraa Banerjee Monash Univerisy, Monash Univerisy, Monash Univerisy 2010 Online a hps://mpra.ub.uni-muenchen.de/23510/ MPRA Paper No , posed 28. June :46 UTC

2 FOUR CENTURIES OF BRITISH ECONOMIC GROWTH: THE ROLES OF TECHNOLOGY AND POPULATION Jakob B. Madsen, James B. Ang * and Rajabraa Banerjee Deparmen of Economics, Monash Universiy Absrac: Using long hisorical daa for Briain over he period , his paper seeks o explain he imporance of innovaive aciviy, populaion growh and oher facors in inducing he ransiion from he Malhusian rap o he pos-malhusian growh regime. Furhermore, he paper ess he abiliy of wo compeing second-generaion endogenous growh models o accoun for he Briish growh experience. The resuls sugges ha innovaive aciviy was an imporan force in shaping he Indusrial Revoluion and ha he Briish growh experience is consisen wih Schumpeerian growh heory. Keywords: endogenous growh; Briish Indusrial Revoluion JEL classificaion: O30; O40 * Corresponding auhor: Deparmen of Economics, Monash Universiy, 900 Dandenong Road, Caulfield Eas, Vic 3145 Ausralia. Acknowledgmens: Helpful commens and suggesions received from paricipans a Monash Universiy seminar, he 14 h Ausralasian Macroeconomics Workshop, he Economeric Sociey Ausralasian Meeing, and paricularly, from hree referees, are graefully acknowledged. James B. Ang and Jakob B. Madsen acknowledge suppor from ARC Discovery Grans from he Ausralian Research Council. 1

3 1. Inroducion Before he lae 18 h cenury, per capia growh raes were eiher zero or miniscule and average per capia incomes in differen regions of he world were quie similar (Galor, 2005; Maddison, 2007). Galor and Weil (2000), Hansen and Presco (2002) and Galor (2005) argue ha his period of sagnaion can be described as he Malhusian epoch. Insead of resuling in improved sandards of living, echnological progress led o increased populaion. However, wih he onse of he Grea Divergence was around 1760, on he eve of he Firs Indusrial Revoluion in Briain, he Briish economy began he ransformaion from he Malhusian rap o he pos-malhusian epoch during which he rae of echnological progress oupaced he populaion growh drag, resuling in posiive per capia growh raes. Ye he ransformaion of he Briish economy is sill one of he grea myseries in he hisory of human evoluion. Economic growh lieraure conains exensive coverage of Briain due mainly o is preeminen posiion in he Firs Indusrial Revoluion and he availabiliy of well-documened hisorical facs and daa. However, despie being one of he mos significan evens in economic hisory, lile is known abou he role played by innovaion in freeing he Briish economy from is Malhusian sraighjacke. While he lieraure suggess differen roles played by echnology during he Indusrial Revoluion, echnological progress has also been deemphasized as being imporan for he Briish growh experience by some economic hisorians. Allen (2003, p. 405) noes ha recen research has downplayed he imporance of echnological progress and lieracy in explaining he Briish indusrial revoluion. Furhermore, Crafs (1995) suggess ha he augmened neoclassical growh model is he appropriae ool for modeling growh during he Indusrial Revoluion and ha he mos imporan innovaions were exogenous during ha period. Based on he saisical properies of produciviy daa, hisoriography and growh accouning exercises, Crafs (1995) concludes ha boh he AK model of Rebelo (1991) and he endogenous growh model of Grossman and Helpman (1990) are incapable of explaining he growh raes experienced by England during he Indusrial Revoluion. However, several sudies have sressed ha he Indusrial Revoluion was associaed wih high levels of innovaive aciviy (see Sullivan, 1989; Mokyr 1993, 2005; Crafs, 2005; Galor, 2005; Clark, 2007; Greasley and Oxley, 2007; Khan and Sokoloff, 2007; Crafs and Mills, 2009). Sullivan (1989, p. 424) describes he period as he Age of Invenion for England during which paenable invenions increased markedly. Greasley and Oxley (1997) demonsrae ha oupu flucuaions were very persisen during he period , and use his as evidence o argue ha endogenous growh models are more relevan in accouning for he glorious period of Briain s indusrializaion han he neoclassical growh model. In a similar vein, using coinegraion 2

4 and causaliy echniques, Oxley and Greasley (1998) sugges ha he Indusrial Revoluion was shaped mosly by echnological progress. Crafs (1995) and Oxley and Greasley (1998) focus on he validiy of he firs-generaion endogenous growh models of Grossman and Helpman (1990) and Rebelo (1991) in explaining he Indusrial Revoluion. However, following Jones (1995) famous criique, he firs-generaion endogenous growh models are no longer accepable o have any empirical validiy. In paricular, Jones (1995) noes ha he number of R&D workers increased subsanially during his period, while he US pos-wwii growh raes have remained relaively consan. This observaion is inconsisen wih he predicions of he firs-generaion endogenous growh models ha produciviy growh is proporional o he number of R&D workers. The second-generaion endogenous growh models overcome his unwarraned propery of he firs-generaion growh models by abandoning he assumpion of consan reurns o scale in ideas producion (semi-endogenous growh models) or by assuming ha he effeciveness of R&D is dilued due o he proliferaion of producs when an economy expands (see Schumpeerian growh models of Aghion and Howi 1998; Howi, 1999; Pereo and Smulders, 2002; Ha and Howi, 2007). Thus, given he shorcomings of firs-generaion endogenous growh models earlier findings based on hem, he second-generaion endogenous growh models may be more consisen wih he Briish growh experience since However, i remains o be seen wheher any of hose modern innovaion-based growh models, exended o allow for populaion growh drag, are capable of explaining he glorious period of Briain s indusrializaion. The objecives of his paper are o examine: 1) wheher he second-generaion endogenous growh heories, augmened o allow for he populaion growh pah, are useful in explaining Briish economic growh over he pas four cenuries including he wo Indusrial Revoluions; 2) he role played by populaion growh during he ransiional period, paricularly he reducions in he populaion growh rae afer 1813 and hen again afer 1907; and 3) he effecs on produciviy growh of foreign knowledge, governmen spending, financial developmen, reducion in rade barriers, availabiliy of coal, urbanizaion and secoral movemens. This paper is, o he bes of our knowledge, he firs ha aemps o formally es wheher here is a significan relaionship beween growh, innovaive aciviy and populaion growh during he firs and he second-phase of he indusrial revoluion in Briain by using a direc measure of innovaive aciviy and by allowing for land as a facor of producion. The paper proceeds as follows: he nex secion shows he empirical implicaions of various endogenous growh heories and exends he growh framework used by Ha and Howi (2007) and Madsen (2008b) o allow for land as a fixed facor of producion. Secion 3 discusses he consrucion of variables and provides some graphical analyses. Using long hisorical daa over he 3

5 period , he empirical analysis is performed and subsequen resuls are presened and discussed in Secion 4. Secion 5 provides an anaomy of he Briish Indusrial Revoluion. The las secion concludes. 2. Innovaion-Based Growh wih Land as a Fixed Facor of Producion When land is a significan facor of producion, labor produciviy growh is a race beween populaion growh and echnological progress. Technological progress is deermined by innovaive aciviy. This secion incorporaes he implicaions of populaion growh ino he second-generaion endogenous growh models and shows he funcional relaionship beween innovaions and growh. Consider he following homogenous Cobb-Douglas producion funcion: Y A K T L (1 ) (1 )(1 ) (1) where Y is real oupu, A is he knowledge sock, K is he capial sock, T is land, L is labor, αis he share of income going o capial and β is he share of income going o land under he mainained assumpion of perfec compeiion. The producion funcion exhibis consan reurns o scale in K, T and L and increasing reurns o scale in A, K, T and L ogeher. Eq. (1) can be wrien as per worker oupu so ha: Y L (1 ) 1 1 (1 ) K A T L 1 (1 ) Y, (2) where /[1 (1 )]. Labor produciviy is cas in erms of he K-Y raio o filer ou echnology-induced capial deepening (Klenow and Rodriguez-Clare, 1997). The reason why produciviy growh riggers capial deepening is ha echnological progress increases expeced earnings per uni of capial and causes Tobin s q o exceed is seady-sae value hrough he channel of he equiy marke. This iniiaes a capial deepening process ha erminaes when Tobin s q reaches is seady-sae equilibrium, which may no be one in he presence of axes, echnological progress and populaion growh (see Madsen and Davis, 2006). The K-Y raio can change ransiionally due o changes in ime-preferences and axes. Taking logs and differeniaing Eq. (2) under he assumpion ha land is a fixed facor of producion, yields labor produciviy growh along he balanced growh pah: 4

6 g g g y A L (3) where g y is labor produciviy growh, g A is growh in TFP and g L is growh in he labor force. The role of capial for growh is suppressed in Eq. (3) under he assumpion ha he economy is on is balanced growh pah in which he K-Y raio is consan. Capial deepening canno ac as an independen growh facor since i is driven enirely by echnological progress along he balanced growh pah. Transiional dynamics is allowed for in he empirical esimaion. In he case where land is omied as a facor of producion (β= 0), Eq. (3) reduces o a sandard neoclassical growh model in which labor produciviy growh is driven enirely by echnological progress, independen of populaion growh, along he balanced growh pah. Growh is independen of populaion growh along he balanced growh pah in hese models because capial sock endogenously adjuss unil he K-Y raio reurns o is iniial level following a populaion shock. When land is an essenial facor of producion, populaion growh reduces labor produciviy. Populaion growh slows growh in Eq. (3) because of diminishing reurns inroduced by land as a fixed facor of producion. The greaer he imporance of agriculural producion in oal oupu, he more populaion growh acs as a growh-drag on he economy. The populaion growh drag was poenially imporan for labor produciviy growh during he firs par of he period considered in his paper. Agriculure was a dominan producion secor in Briain up o he Second Indusrial Revoluion. In 1600 almos 75% of he English working populaion was employed in he agriculural secor (Allen, 2001). Agriculure remained he dominan mode of producion over he nex wo cenuries. The fracion of he working populaion in agriculure was 35% in 1800 (Allen, 2001), 28% in 1851 and 12% in 1901 (Michell, 1988). Thus, populaion growh raes lowered per capia income growh raes almos on a one-o-one basis around 1600 and were sill very influenial for per capia growh over he nex wo cenuries. While populaion affecs growh direcly, innovaive aciviy influences growh indirecly hrough he channel of ideas producion. There are hree esablished heories of ideas producion funcions and hey have quie differen implicaions for how innovaive aciviy is ransformed ino echnological progress and, consequenly, growh. In he firs-generaion endogenous growh models of Romer (1990), Grossman and Helpman (1991) and Aghion and Howi (1992), ideas producion is associaed wih he number of researchers. In he semi-endogenous growh models of Jones (1995), Korum (1997) and Segersrom (1998), R&D inpus are required o grow permanenly o mainain susained ideas producion following he assumpion of diminishing reurns o knowledge. According o he Schumpeerian models of Aghion and Howi (1998), Dinopoulos and Thompson (1998), Pereo (1998), Howi (1999) and Pereo and Smulders (2002), a posiive 5

7 consan rae of ideas producion can be mainained provided ha R&D per worker remains consan. In oher words, R&D has o increase over ime o counerac he increasing range of producs ha lowers he produciviy effecs of R&D aciviy in order o ensure susained ideas producion. I is no clear which of he second-generaion endogenous growh heories can bes accoun for he Briish growh experience and wheher any of hese heories can explain innovaion-induced growh hroughou he four cenuries considered in his paper. Alhough Ha and Howi (2007) and Madsen (2008b) have found ha Schumpeerian growh heory is mos consisen wih he experience of modern growh regimes, here is no assurance ha he heory will work during he Malhusian and he pos-malhusian growh regimes, as highlighed by Howi and Mayer-Foulkes (2005). Parene and Presco (2005) argue ha he knowledge erm in he producion funcion should be decomposed ino wo componens: 1) he echnological knowledge ha is available domesically and on a worldwide scale, and 2) effecive uilizaion of echnology. The laer depends on how effecively echnology is used and he exen of efficiency of operaions wihin organizaions. If innovaions in he firs par of he period were no used effecively, posiive growh raes would no have ranspired. Based on hisorical evidence, Moneiro and Pereira (2006) argue ha many growh spurs in hisory failed o become susained growh regimes because insufficien human capial was provided o deal wih he increasing complexiy of innovaions. The following general ideas producion funcion can be used o discriminae beween differen endogenous growh models (Ha and Howi, 2007; Madsen, 2008b): g A A X A Q A 1, 0 1, 1, (4) Q L in seady sae 0 1, 1, where is he duplicaion parameer (zero if all innovaions are duplicaions and 1 if here are no duplicaing innovaions), proliferaion, is reurns o scale in knowledge, is he coefficien of produc is he research produciviy parameer, Q is a measure of produc variey, L is employmen or populaion and X is R&D inpus for semi-endogenous growh models or he produciviy-adjused R&D inpus for Schumpeerian growh models. The produciviy adjusmen in Schumpeerian models recognizes ha here is a endency for decreasing reurns o R&D due o increasing complexiy of innovaions (Ha and Howi, 2007). Semi-endogenous growh heory assumes ha 1, 0 and 0 while Schumpeerian models assume ha 1, 0 1. The firs-generaion endogenous growh heory assumes ha 1, 0 and 0. and 6

8 Schumpeerian growh models mainain he assumpion from he firs-generaion endogenous growh models of consan reurns o he sock of R&D knowledge. However, hey assume ha he effeciveness of R&D is dilued due o he proliferaion of producs as he economy expands. Thus, growh can sill be susained if R&D is kep a a fixed proporion of he number of produc lines, which is in urn proporional o he size of he populaion in he seady sae. As such, o ensure susained ideas producion, R&D has o increase over ime o counerac he increasing range and complexiy of producs ha lower he produciviy effecs of R&D aciviy. 2.1 Empirical Models of Economic Growh Coinegraion analysis and growh regressions are carried ou o examine he facors ha have been responsible for he Briish economic growh over he pas four cenuries. While he coinegraion analysis is guided by he analyical framework oulined above, he growh models will be exended o allow for facors explaining growh oher han populaion and innovaions, which have been sressed by economic hisorians in explaining he ransiion of he Briish economy from he Malhusian regime o he pos-malhusian growh regime. Firs consider he coinegraion analysis. Assuming ha shocks, e, are idenically and normally disribued wih a mean of zero, Eq. (4) forms he following model (see Ha and Howi, 2007): ln A 1 ln ln X ln Q ln A e, (5) Given ha ln A is saionary, i follows ha variables in he square brackes are coinegraed. Following he parameer resricions discussed above, semi-endogenous growh heory requires ha: (i) boh ln X and ln A be non-saionary and inegraed a he same order; and (ii) boh variables are coinegraed wih he coinegraed vecor of 1 1,, in which he second elemen is expeced o be negaive. Schumpeerian growh heory predics: (i) ln( X / Q) is saionary; and (ii) ln X ln Q are coinegraed wih he coinegraed vecor of 1, 1. Imposing he resricions suggesed by he wo second-generaion endogenous growh models implies ha he erms and in he following equaions are saionary: and 1 ln X ln A Semi-endogenous growh heory (6) ln X ln Q. Schumpeerian growh heory (7) 7

9 Taking logs of Eq. (2) and combining i wih Eq. (6) yields: Y (1 ) K ln ln X ln L [1 (1 )](1 ) 1 (1 ) Y lnt ln L [1 (1 )](1 ). (8) Using coinegraion echnique, Eqs. (7) and (8) can be used o es wheher he wo secondgeneraion models are consisen wih Briish hisorical daa. Noe ha he oupu elasiciy of land,, is allowed o vary over ime in Eq. (8), and is compued as he share of agriculure in oal GDP. Annual daa in he period are used in he coinegraion analysis. However, coinegraion ess are necessary, bu no sufficien, condiions for secondgeneraion growh models o be consisen wih he growh process (Madsen, 2008b). A sufficien condiion is ha hese models can explain long-run growh. Furhermore, an imporan par of his paper is o examine he exen o which produciviy growh in Briain has been driven by innovaions and oher facors ha have been highlighed in he economic hisory lieraure such as reducions of rade barriers, financial developmen, echnology spillovers from oher counries, secoral movemens, availabiliy of coal, and public invesmen projecs. Anoher aim is o explain he role played by innovaions in he ransformaion of he Briish economy from he Malhusian rap o he pos-malhusian and modern growh regimes (see Goodfriend and McDermo, 1995; Galor and Weil, 2000; Hansen and Presco, 2002; Galor, 2005). Consequenly, he following growh model is regressed o: 1) examine he imporance on growh of innovaions and oher forces highlighed by economic hisorians, during he differen growh epochs in Briain; 2) discriminae beween semi-endogenous and Schumpeerian growh models; and 3) evaluae he imporance of demographic ransiions on growh during he differen phases of he Briish economic growh experience: ln y b b ln X b ln( X / Q) b ln L b ln b ln g b FD b I K b S b S u W IM 6 ln 7 ln( / ) 8 ln 9 ln (9) where y is labor produciviy, Y/L; τ is rade barriers and is measured as he raio of cusom duies o impors; g is he raio of governmen expendiure o GDP; FD is financial deepening; I is invesmen; K is capial sock; W S is he world sock of knowledge, IM S is inernaional knowledge spillovers hrough he channel of impors, and u is a sochasic error erm. Here, X is measured by 8

10 he number of paen applicaions by domesic residens; Q is measured by he labor force; FD is measured as he raio of money sock, M1, over GDP; (I/K) is measured as he raio of nonresidenial real gross invesmen o capial sock. The invesmen o capial raio is included in he model o allow for ransiional dynamics. The measuremen of W S and IM S are discussed in he nex secion. The funcional relaionship beween he innovaion variables and growh is derived in Madsen (2008b). Eq. (9) is esimaed in 5-year non-overlapping inervals o overcome cyclical influences and he erraic movemens in he daa on annual frequencies. To address he issue of possible reverse causaliy, lagged populaion growh, deah raes and changes in life expecancy are used as insrumens for ln L. Furhermore, he growh in X and L and he level of research inensiy are lagged one period. I canno be ruled ou ha innovaive aciviy is driven parly by growh o he exen ha aciviies leading o innovaions are more affordable during upurns han downurns. Furhermore, Malhusian heory predics ha populaion growh is posiively relaed o income growh hrough he channels of feriliy and moraliy. During he Malhusian period birh raes were poenially posiively relaed o per capia income growh as feriliy was increasing when per capia income exceeded subsisence levels and deah raes were negaively relaed o per capia income because hygiene sandards, housing qualiy and nuriion are posiively relaed o income. The esimaion resuls are similar if he growh in X and L and he level of research inensiy are unlagged, which suggess ha endogeneiy is no a serious problem. Tariff raes are included in he regressions as a proxy for rade barriers. The sum of expors and impors over GDP was also included as a proxy for openness o inernaional rade in he iniial regressions bu i was found o be insignifican, which may reflec ha i is a poor proxy for rade openness. Several heoreical and empirical sudies sugges ha rade barriers inhibi produciviy (see Vamvakidis, 2002; Lucas, 2007; Madsen, 2009). Since ariffs were reduced subsanially afer he Napoleonic wars hey may have played an imporan role for Briish economic growh during he 19 h cenury. Exraordinarily high ariff raes on impors of agriculural producs before 1820 rendered Briish agriculural producion quie profiable and Briain was a ne exporer of agriculural producs during he Firs Indusrial Revoluion (Deane, 1969, Ch 12). The sharp reducion in impor ariffs afer he Napoleonic Wars reduced he influence of agriculure in oal producion (Deane, 1969, Ch 12). Since manufacuring was more producive han agriculure he secoral ransiions induced by lower ariff raes would have led o more produciviy gains. Furhermore, Briain impored a large volume of commodiies which were used as inpus for manufacuring during indusrializaion. Since changes in he prices of commodiies can have large oupu effecs, as shown by Bruno and Sachs (1985), i follows ha variaions in impor ariff raes can also have poenially imporan oupu effecs. 9

11 Williamson and his collaboraors have long argued ha globalizaion was an imporan facor behind he Indusrial Revoluion in he UK and oher counries (see, e.g., O Rourke and Williamson, 2005). This view suppors he findings of Allen (2003). The key poin is ha a large world marke was essenial for Briish manufacuring expansion because of he sheer size of he global marke. The hypohesis is consisen wih he evidence of Clark (1987), which shows ha several invesmen goods used around he world a cenury ago were manufacured in he UK. Thus, overall, we would expec he reducions in ariff raes o have had imporan impeuses for he Briish indusrializaion. Furhermore, Pomeranz (2001) argues ha accessibiliy o he commodiies in Norh America was pivoal for Briish indusrializaion. Governmen spending is included in he model o allow for posiive exernaliies of governmen spending and public invesmen as prediced by he model of Barro (1990). Governmen spending on educaion, a good jusice sysem ha enforces propery righs, a medical sysem ha keeps he labor force healhy, and infrasrucure invesmen are likely o be growh enhancing whereas spending on miliary and income ransfers are no. The presence of a good legal sysem and enforcemen of propery righs have been sressed o have played key roles for he Firs Briish Indusrial Revoluion (Deane, 1969; Galor, 2005). Furhermore, governmen provision of healh and educaion was considered by Cour (1965, pp ) as being imporan for he Briish Indusrial Revoluion. Financial developmen is considered as being poenially influenial for Briish indusrializaion by rendering access o credi easier and by he creaion of a moneary sysem ha eased he paymen of manufacuring workers and commercial ransacions (Deane, 1969, Ch 11; Cour, 1965, pp ). The esablishmen of he Bank of England in 1694, and he inroducion of a money marke, checks and an acive sock exchange in he lae 17 h cenury have been described as a financial revoluion (Deane, 1969, Ch 11; Rousseau and Sylla, 2005). Furhermore, noes issued by he Bank of England and by privae banks in he 17 h and 18 h cenuries, were essenial for he developmen of a modern financial sysem (Deane, 1969, Ch 11). The raio of broad money o GDP is used here as a proxy for financial developmen, which is sandard in he lieraure on financial developmen and growh (see, e.g., Rousseau and Sylla, 2005; Ang and McKibbin, 2007; Ang, 2010). Knowledge spillovers are assumed o be ransmied o Briain hrough he channel of impors, S IM, and hrough channels ha are independen of impors, S W. Several empirical sudies have esablished ha growh in impors of knowledge hrough he channel of impors play imporan roles for growh (see, e.g., Madsen, 2007b). The imporance of foreign knowledge for he Briish Indusrial Revoluion has been highlighed by several economic hisorians. Mokyr (1994) argues ha ideas flowed from he Coninen o Briain. He mainains ha he ideas creaed on he Coninen 10

12 were urned ino pracical applicaions by Briish engineers and oher skilled individuals. More generally, he reducion of raveling ime during he 19 h cenury increased he inernaional ransmission of echnology (Clark, 2007, Ch 15). Before ha echnologies were predominanly ransmied inernaionally hrough journeymen and arisans (Clark, 2007, Ch 15). The growh model is esimaed using daa covering he period Differen daa periods are considered in he esimaion o check: 1) he validiy of he model during differen periods in Briish hisory; 2) wheher he coefficiens are srucurally sable; and 3) he exen o which second-generaion endogenous growh models can explain differen eras of Briish hisory and wheher hese models are consisen wih he growh experience since he Scienific Enlighenmen or only recenly. The following sample periods are considered in he analyses: , , , , , , , and These conain he benchmark periods ofen highlighed in he lieraure. The period marks he Firs Indusrial Revoluion (Sullivan, 1989), includes he preindusrial period and he Firs Indusrial Revoluion, includes preindusrial and indusrial periods (boh 1 s and 2 nd ), includes boh indusrial revoluions, and akes ino accoun he pos indusrial revoluion period which also includes he wenieh cenury. The period covers he Malhusian era during which echnology-induced produciviy growh raes were counerbalanced by he populaion growh drag (Galor, 2005) and he period covers he pos-malhusian and modern growh regimes wih innovaion-driven growh and a gradual reducion in feriliy raes (Galor, 2005). Esimaion covering he Second Indusrial Revoluion over he period and he pos-malhusian growh regime over he period canno be underaken wih confidence since i would resul in only a few degrees of freedom in he regressions where all variables in Eq. (9) are included. 3. Daa Tesing he role played by innovaions in Briish growh over he period /2006 is no an easy ask because of he difficulies associaed wih he measuremen of labor produciviy, innovaive aciviy, and he inernaional ransmission of echnology. Labor produciviy is difficul o measure because he measuremen of oupu is conroversial. Harley (1982) and Crafs (1985) argue ha he aggregae oupu daa compiled by Deane and Cole (1962), which are available from 1700, end o overesimae growh during he period The GDP daa from Feinsein (1972) are available firs from 1855 whereas daa from Linder and Williamson (1982) are available only for he years 1688, 1759 and 1801/03. In view of hese consideraions, we use hree differen 11

13 measures of labor produciviy ha are all spliced wih per capia GDP from Maddison (2008) afer The firs measure is GDP per capia using he income daa for England and Wales compiled by Clark (2001), henceforh referred o as YC. These daa are available in decadal frequencies from 1620 and are consruced as he sum of compensaion o employees, axes and ren and deflaed by prices on a baske of goods ha is considered represenaive of GDP. The second measure is per capia indusrial producion compiled by Crafs and Harley (1992) and is available on an annual basis from 1700, henceforh referred o as IP. The hird measure, which is our preferred measure, is consruced as a weighed average of facor paymens: YA A B (1 ) W W R T, (10) P P P L where W A is daily wages for agriculural workers from Clark (2007), which are available on an annual basis since 1301, W B is he unweighed averages of skilled and unskilled labor wages for London and Oxford from Allen (2001), which are available annually from 1264 onwards, R is land ren per acre from Clark (2001), and are available on decadal frequencies, is he share of agriculure in oal GDP, and P is he consumer price level. Facor shares are adjused o mach he decadal facor share daa esimaed by Clark (2001). Like he GDP esimaes of Clark (2001) his measure has he advanage of covering all facor paymens in he economy; however, in conras o Clark s daa he YA daa are available in annual frequencies. Since annual daa are used in he coinegraion analysis in he nex secion and he VARs esimaion of he growh equaion, he annual daa are clearly preferable o Clark s decadal daa. The main advanage of using economywide daa as opposed o real wages as a measure of labor produciviy is ha variaions in land ren are accouned for. This is paricularly imporan in medium-erm frequencies where real wages may deviae from labor s marginal produciviy because of rigid wages and prices (Bruno and Sachs, 1985). Alhough he pos-1830 per capia GDP daa from Maddison (2008), which are mainly based on Feinsein s (1972) esimaes, are probably he mosly widely used and acceped daa, hey do have pifalls. Income and populaion daa cover he Republic of Ireland up o is independence in Daa covering Briain only during he period are no ye available. 1 The inclusion of Ireland in his period gives rise o wo poenial problems. Firs, he Grea Irish Famine in he mid 19 h cenury resuled in a emporary bu marked decline in he Irish populaion. Since he 1 While he Unied Kingdom includes he Republic of Ireland during he Briish rule over he period , we use he erm Briain hroughou he manuscrip because he Republic of Ireland is no included in he daa in mos of he esimaion periods. 12

14 Malhusian mechanism is caered for in he model his dip in he populaion size should no consiue a problem; however, such a large shock may affec he dynamic adjusmen and, as such, inerfere wih he esimaes. To overcome his problem an impulse dummy was included in Second, when Ireland gained independence, he size of he populaion in Maddison s daa shrunk by hree million. Since GDP is reduced by almos he same proporion, per capia GDP is no oo severely affeced by he ransiion. However, he populaion growh rae shrinks arificially and, herefore, gives rise o a measuremen error in populaion growh in Anoher impulse dummy variable is included in he esimaion o address his problem. The number of paen applicaions by domesic residens as opposed o paens graned is used as he measure of innovaive aciviy (X ) since he processing periods vary subsanially over ime (Griliches, 1990). Paen daa are available back o They are measured direcly from paen couns wihou errors, and are he only currenly available hisorical daa on innovaive aciviy. The main criicisms of using paens as measures of innovaive aciviy are ha he qualiy of paens varies over ime, no all innovaions are paened, he propensiy o paen may change over ime, and he high coss of paening give invenors srong incenives o keep heir invenions secre (see Boehm and Silberson, 1967). While he law of large numbers ends o render he average qualiy of paens relaively consan in recen years (Griliches, 1990), his law is unlikely o hold in he early par of he sample period when he number of paens was quie modes. A major concern is wheher he propensiy o paen has changed over four cenuries considered in his sudy. In probably he mos deailed examinaion of he qualiy of Briish paens over he pas four cenuries, Sullivan (1989) does no find any evidence of shifs in he propensiy o paen in individual indusries nor changes in he indusrial disribuion of paens. Regarding he expense of paens, heir high coss of acquisiion should a leas, in principle, have led o paens of higher qualiy and, as such, weeded ou low-qualiy ones ha are unimporan for growh. Thus, high coss of paens may improve heir average qualiy as a measure of innovaive aciviy. This line of reasoning is suppored by he findings of Khan and Sokoloff (2007). They find ha 87 percen of he grea invenors in Briain over he period from 1750 o 1930 were paenees, indicaing ha mos of he imporan innovaions have been capured by paen couns. Anoher concern is ha major innovaions such as he seam engine, he Spinning Jenny, Crompon s mule and he flying shule are hardly visible in he paen saisics. In his conex i is imporan o noe ha i was a large series of subsequen paenable innovaions ha rendered mega innovaions commercially viable. The Newcomen seam engine of 1769 consumed coal a he cos of GBP 3000 per annum, whereas 500 horses wih he same power cos only GBP 900 per annum (Greenwood, 1999). However, several innovaions over he course of he Firs Indusrial Revoluion gradually rendered he seam engine much more cos effecive. The cos per uni of horse power 13

15 was reduced from GBP 30 o 2.5 over less han a cenury (Greenwood, 1999). The imporan lesson is ha, alhough he Indusrial Revoluion produced only a handful of miracles, he subsequen array of small innovaions following he grand innovaions was an imporan facor behind he success of he Briish economy. Griliches (1990) concludes ha in spie of all he difficulies, paen saisics remain a unique resource for he analysis of he process of echnical change. Furhermore, Madsen (2007a) finds ha he null hypohesis of consan reurns o R&D canno be rejeced, which implies ha here is a proporionaliy beween R&D and paen applicaions. However going back as far as four cenuries, one canno deny ha here are flaws in paens as indicaors of innovaive aciviy. Wha his essenially means is ha he number of paens is poenially a noisy measure in mos pars of he esimaion period and, as such, may bias he parameer esimaes owards zero. Thus, our esimaes are likely o undersae he imporance of innovaive aciviy for growh during he pas four cenuries of Briish hisory. Anoher benefi of using paens as he measure of innovaive aciviy is ha i is consisen wih he hypohesis ha he insiuionalizaion of a paen sysem in Briain long before oher counries may have helped Briain o indusrialize earlier han he res of he world. The wo knowledge spillover variables, S W and S IM, are measured as follows. The world sock of knowledge, S W, is measured as he sum of paen sock in he US, France and he Neherlands over he period from 1791 o 1870 and, hereafer, spliced wih he sum of paen couns for he 21 OECD counries lised in he Daa Appendix. 2 Following he approach of Coe and Helpman (1995) knowledge spillovers hrough he channel of impors is consruced as: S IM M N IM IM j ln S N j Y IM, j 1 j = 1,2,...N. where IM M is he Briish manufacured impors, Y N is Briish nominal GDP, IM j is impors of goods from counry j o Briain, IM is oal impors of goods o Briain, and Sj is he paen sock in counry j. The counries included in he esimaion of Sj are he sample of hose used o consruc S W. The share of manufacured impors in oal income and no he oal impor share as in Coe and Helpman (1995) is used o consruc S IM. This is because a high share of Briish impors during he 17 h and 18 h and mos of he 19 h cenury consised of raw maerials and agriculural producs and hence echnology is highly unlikely o be ransmied inernaionally hrough impors of commodiies. 2 We also included he number of imporan scieniss in he world excluding Briain in he iniial regressions. However, he coefficien was insignifican in he regressions. 14

16 The inernaional echnology variables sar from a very low base in 1791, when he daa become available, and inernaional echnology spillovers firs sar gaining momenum in he mid 19 h cenury. Coupled wih he fac ha Briish manufacured impors relaive o GDP were miniscule a he beginning of he 19 h cenury, echnology ransmission hrough he channel of impors could no have played much of a role around As such inernaional knowledge ransmission hrough channels independen of impors, was poenially more imporan. Alhough he echnologies used in Briain were invened elsewhere, i is no enirely clear how foreign invenions reached Briain and he exen o which hey had a significan impac on Briish produciviy growh. The empirical applicaion of he Mokyr (1994) hypohesis ha Briain applied he ideas creaed on he Coninen is rendered difficul by he long and ime-varying lag beween he creaion and he applicaion of an idea. Probably he mos direc roue hrough which echnologies were ransmied was hrough journeymen; however, no such daa are currenly available. 3.1 Graphical Analysis The pahs of he hree produciviy series are displayed in Figure 1. Clark s produciviy daa (YC) follow he rend of he daa based on Eq. (10), (YA), which is no surprising since hey are consruced based on he same mehod and, o a large exen, he same daa. The decline in produciviy in he period is likely o be a resul of a series of crop failures (Deane, 1969, Ch 11) and ha major innovaions are iniially counerproducive because he iniial incarnaions of he new ideas are slow and waseful (Greenwood, 1999). The seam engine and Cor s puddling and rolling process were commercially unsuccessful because hey were inefficien, required raining and educaion of skilled operaors, and he qualiy of he seam engine and he puddling and rolling process varied. Noe ha he argumen ha mega innovaions are iniially couner-producive seems o be inconsisen wih he increasing indusrial producion per worker (IP series) during he period However, since IP is measured as indusrial producion as a proporion of he oal labor force and no in proporion o he manufacuring labor force, one canno be cerain wheher indusrial labor produciviy increased, remained unchanged or fell during he period Looking a he long-run pah, labor produciviy remained prey fla up o around 1825 and, his herefore, can be considered as he Malhusian period in which per capia oupu is kep down by populaion growh. Indusrial produciviy increased slowly during he 18 h cenury and gained momenum in he 19 h cenury. Common o all indicaors of produciviy is a seep increase during he laer par of he Firs Indusrial Revoluion in he period , indicaing he compleion of he learning period and he appearance of supporive innovaions ha were required o render he mega-innovaions efficien and economically viable. A similar delay in produciviy gains can be raced back o afer he Second Indusrial Revoluion, during which ime he mos significan 15

17 innovaions were he generaion of elecriciy (he dynamo), he elecric globe, elecommunicaion and he combusion engine. The sronges produciviy gains were no during he Second Indusrial Revoluion , bu hereafer. Figure 1: GDP series, (on log scale, 1700=100) Ln YC IP YA Noes: IP = per capia indusrial producion, YC = Clark s (2001) per capia GDP, which are boh available on decadal frequencies, and YA = annual GDP esimaes based on real wages and land ren (Eq. (10)). % Figure 2: Annual growh raes of labor produciviy, Figure 3: Number of paen applicaions by domesic residens, Ln Noes: Daa in Fig. 2 are measured in 5-year differences. The growh raes, which are based on he YA measure, are annualized Based on he YA measure, annualized produciviy growh raes in 5-year inervals are displayed in Figure 2. Produciviy growh can naurally be subdivided ino he Malhusian epoch wih average annual growh raes of 0.07% ( ), he pos-malhusian growh regime wih average growh raes of 1.28% ( ) and he modern growh regime wih average growh raes of 1.49% ( ) (Galor, 2005). Alhough he Firs Indusrial Revoluion sared around 1760, labor produciviy growh raes remained miniscule up o circa This may seem 16

18 paradoxical, given he high and increasing level of innovaive aciviy. However, Briain was sill rapped in he Malhusian regime in which he improved living sandards derived from echnological progress were ranslaed ino increasing populaion growh raes. Populaion growh raes increased gradually from zero a he beginning of he 18 h cenury o 1.5% a he beginning of he 19 h cenury, as shown in Secion 5 below. Wih populaion growh raes of 1.5%, significan echnological progress was required jus o mainain living sandards a consan levels during he firs phase of he Indusrial Revoluion. Figure 3 shows he ime-pah of he log of he number of paens. The Firs and Second Indusrial Revoluions are easily idenifiable from he surge in paening aciviy afer circa The increase in paening aciviy was brough o an end a he peak of he Second Indusrial Revoluion around The surge in paening aciviy during he Indusrial Revoluions is sill visible from he daa when paens are normalized by he labor force (Figure 4). Figure 4 shows ha research inensiy (X/Q) increased over he firs hree cenuries and sabilized afer Apar from he period , he rends in per capia income growh raes and research inensiy approximaely coincide, as prediced by Schumpeerian growh heories. The gap beween research inensiy and produciviy growh during his period is due o an exraordinarily high populaion growh rae during ha period. Figure 4: The raio of domesic paen applicaions o he labor force Ln Figure 5: Annual growh raes of paen applicaions % Noes: he daa are in 5-year averages Finally, Figure 5 displays he growh raes of paen applicaions. The daa are annualized growh raes in five-year inervals. Semi-endogenous growh heory predics a posiive relaionship beween per capia income growh and growh in innovaive aciviy. Comparing Figures 2 and 5, here is no clear-cu relaionship beween growh in paens and labor produciviy growh, paricularly afer Thus, hese diagrams give no clear evidence in favor of semi-endogenous growh heory. 17

19 4. Regression resuls Inegraion and coinegraion ess are underaken o es he long-run relaionships prediced by semi-endogenous and Schumpeerian growh heories (Eqs. (8) and (7), respecively). The growh equaion (Eq. (9)) is esimaed in he second par of his secion. Labor produciviy is measured by YA (Eq. (10)) hroughou his secion. The esimaes in which per capia indusrial producion (IP) and Clark s per capia income daa (YC) are used o measure labor produciviy are repored in Appendix 1. However, he main resuls from hese esimaes are briefly discussed in Secion Inegraion and coinegraion analyses Table 1: Uni roo ess ( ) ADF Zivo-Andrews Levels 1 s differenced Levels 1 s differenced Conclusion Labor produciviy [ ln( Y / L ) ] (0.98) # (0.00) # (BP = 1800) #. (BP = 1814) I(0) / I(1) Paen applicaions ( ln X ) (0.21) # (0.00) (BP = 1853) # (BP = 1706) I(1) Capial deepening [ ln( K / Y ) ] (0.54) # (0.00) # (BP = 1762) # (BP = 1802) I(0) / I(1) Land [ lnt ] (0.79) # (0.00) (BP = 1945) # (BP = 1679) Populaion growh drag # # I(1) [ ln L (0.96) (0.00) (BP = 1877) (BP = 1853) ] Paen applicaions / labor force # # # I(0) [ ln( X / Q ) (0.00) (0.00) (BP = 1884) (BP = 1706) ] Noes: p-values for he ADF ess are indicaed in parenhesis. For he Zivo-Andrews ess in levels, he 1% and 5% criical values are and -5.08, respecively. In firs-differenced form, he values are and , respecively. The endogenously deermined break poin (BP) for each series is indicaed in parenheses. + and # indicae 5% and 1% significance, respecively. The labor produciviy daa are based on YA. I(1) Firs, inegraion and coinegraion ess are applied o Eqs. (7) and (8). Annual daa are used in all esimaions in his sub-secion. Uni roo ess for he enire sample period are performed using he convenional Augmened Dickey-Fuller (ADF) and he Zivo and Andrews (1992) ess, where 18

20 he laer accouns for he possible presence of an endogenous srucural break. I ess he null of a uni roo agains he alernaive of rend saionariy wih an unknown break in he series. The resuls of he uni roo ess presened in Table 1 show ha ln X, lnt, and ln L are inegraed a order one, regardless of which es is applied. However, ln( Y / L) and ln( K / Y ) are found o conain a uni roo according o he convenional ADF ess bu he Zivo-Andrews ess sugges saionariy once a srucural break is allowed for. The resuls underscore he imporance of esimaing he models for differen sub-sample periods. When he YC and IP series are used as alernaive measures of labor produciviy, boh ess sugges ha labor produciviy conains a uni roo (see Appendix 1). Research inensiy (ln( X / Q ) ) is found o be saionary, as prediced by Schumpeerian growh heory under he mainained assumpion ha produciviy growh is saionary. The null hypohesis of saionariy is rejeced a he 1% level and he es resuls are insensiive o he choice of uni roo ess. Table 2: Johansen coinegraion ess for semi-endogenous growh heory (Eq. (8)) (1) Period (2) No. of CEs based on Trace es (3) No. of CEs based on Maxeigenvalue es [-1.24] # [-6.71] # [-4.66] (4) Coinegraing vecor [lny/l, lnx, ln K/Y, lnt, lnl] 0.11 [0.44] # [-3.29] [2.24] [-2.27] 0.85 # [21.25] [-2.11] [-1.43] # [-4.14] [-2.52] [-0.33] [-0.60] * [-1.85] [-0.41] # [-3.43] 1.44 [0.97] 0.58 [0.78] # [-5.51] [-0.45] [-0.38] # [3.79] # [-3.32] (5) ECT # [-6.36] [-1.08] # [-4.94] [-2.01] [-0.89] [-0.83] Noes: he resuls show he number of coinegraed equaion(s) found based on he race and maximumeigenvalue ess using he 5% decision rule. An inercep bu no rend is included in he esimaion. The opimal lag lengh is pinned down using he SBC. Criical values are aken from Mackinnon e al. (1999). ECT is he error-correcion erm associaed wih he ln(y/l) equaion. Figures in parenhesis indicae - saisics. *, + and # indicae 10%, 5% and 1% levels of significance, respecively. Y/L is measures using he YA series. Turning o he coinegraion analysis, i is esed wheher ln( Y / L ), ln X, ln( K / Y ) ), lnt and ln L are coinegraed (semi-endogenous growh) and wheher ln X is coinegraed wih ln Q (Schumpeerian growh). Tables 2 and 3 display he resuls of hese coinegraion ess. 19

21 The resuls are based on he Johansen (1988) procedures. Firs, consider he resuls for semiendogenous growh heory in Table 2. Excep for one case, he resuls in columns (2) and (3) show ha he variables in Eq. (8) are eiher no coinegraed or have more han one coinegraing vecor. These resuls are inconsisen wih he predicion of only one coinegraed relaionship among he variables by semi-endogenous growh heory (see he derivaion in Eq. (8)). Moreover, alhough innovaive aciviy (ln X ) eners he equaion significanly in some cases, in half of he cases he coefficiens are eiher insignifican or significan bu have he wrong sign. The coefficiens of ln L are eiher saisically insignifican or of he wrong sign when significan. Finally, he coefficiens are highly sensiive o he esimaion periods. Overall he resuls in Table 2 provide no suppor for semi-endogenous growh heory. The same conclusion is reached when he Malhusian era ( ) and he modern growh regimes period ( ) are considered (as shown in Appendix 2). The resuls are also consisen when he oher wo labor produciviy measures, YC and IP, are used (see Appendix 1). Table 3: Johansen coinegraion ess for Schumpeerian growh heory (Eq. (7)) Period Hypohesis Trace saisic Max-eigenvalue saisic Coinegraing Vecor [ln X, ln Q] ECT r # # 1.00, # # r [-5.89] [-5.93] r # , # r [-6.46] [-1.97] r # # 1.00, # # r [-12.53] [-2.86] r , # # r [-28.36] [-4.23] r # # 1.00, # # r [-26.63] [-3.93] r , # # r [-7.60] [-3.02] Noes: he null hypohesis is ha here is r coinegraed relaionships beween he variables. An inercep bu no rend is included in he esimaion. The opimal lag lengh is deermined by SBC. Criical values are aken from Mackinnon e al. (1999). ECT is he error-correcion erm associaed wih he lnx equaion. Figures in parenheses are -saisics. + and # indicae 5% and 1% levels of significance, respecively. On he oher hand, he coinegraion resuls in Table 3 provide srong suppor for Schumpeerian growh heory. The null hypohesis of no coinegraion beween innovaive aciviy ( ln X ) and produc variey (ln Q ) is rejeced in all cases. Furhermore, he coefficiens of ln Q are saisically and economically significan a he 1% level in all cases and are quie sable across 20

22 periods. The saisical and economic significance of he coefficiens of he error-correcion erm provides furher evidence in favor of he presence of a long-run relaionship beween he variables. On average, he economy akes abou six years o adjus owards equilibrium following a shock o he seady sae (he inverse of he average coefficiens of he ECT erms). Finally, he coefficiens of produc variey are quie consisen across ime periods, suggesing ha a sable funcional relaionship exiss beween produc varieies and innovaive aciviy, as prediced by Schumpeerian growh heory. 4.2 Esimaes of labor produciviy growh The resuls of regressing Eq. (9) are presened in Table 4. 3 Four ses of resuls are presened: hree ses of regressions wihou conrol variables and wih differen combinaions of he innovaive aciviy variables and one regression including all variables conained in Eq. (9). The coefficiens of populaion growh are consisenly negaive and significan in he regressions covering he earlier cenuries of he sample. Similar resuls are obained when Clark s income daa (YC) are used, as shown in Appendix 1. The resuls are reasonably consisen wih he finding in he lieraure ha real wages respond negaively o populaion growh in Briain (Anderson and Lee, 2002; Nicolini, 2007; Crafs and Mills, 2009). The principal difference beween his sudy and hose of Anderson and Lee (2002), Nicolini (2007) and Crafs and Mills (2009) is ha hey regress real wages on populaion and le he consan erm varies over ime o allow for he upward drif in labor demand, which is driven enirely by echnological progress along he balanced growh pah. They do no allow he coefficiens of he populaion drag o change over ime o accoun for he reducions in his variable as land s imporance as a facor of producion diminishes. Ineresingly, he populaion growh drag loses some of is significance when labor produciviy growh is measured by per capia indusrial producion, IP, as shown in Appendix 1, or when i is based on Clark s (2005) daa on growh in urban real wages (resuls are no shown). These resuls give furher suppor o he Malhusian heory where populaion growh is a drag on he economy hrough allowing for land as a non-reproducible facor of producion ha inroduces diminishing reurns as he populaion grows. Since he Malhusian mechanism is no direcly operaive in he urban secor, where land is no an imporan facor of producion, hese resuls underscore he poin ha populaion growh influences growh predominanly hrough land, raher han hrough oher channels ha have been highlighed in he lieraure. 3 The following five dummy variables were iniially included in he regressions, however, hey were subsequenly omied from he regressions since he esimaes were unaffeced by heir inclusion. The firs dummy capures he abrup changes in per capia GDP growh during he period The second dummy capures he sudden increases in per capia growh in he years The hird dummy capures he severe negaive growh in per capia GDP in he years The fourh dummy capures he Grea Irish Famine during he period The fifh dummy is in 1925, spanning he priod , as he Irish Republic becomes independen from Briain in

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