February 2017 The Canadian Produciviy Sagnaion, 2002-2014* Juan Carlos Conesa Sony Brook Universiy Pau S. Pujolàs McMaser Universiy ABSTRACT Toal Facor Produciviy s (TFP) conribuion o GDP per working age populaion growh during 2002-2014 in Canada has been only 0.16%. This figure is subsanially smaller han for he U.S. during he same period (1.33%), and for Canada during 1970-2002 (1.45%). We perform muliple counerfacual exercises o show ha he lack of TFP growh canno be accouned for by measuremen issues in, nor misallocaion of, facors of producion. However, despie he lack of TFP growh Canada has experienced susained income growh because of a prolonged period of appreciaion of he erms of rade. *The auhors would like o hank Tasos Papanasasiou, Wya Brooks, Beina Brüggemann, Aranxa Crespo, Tim Kehoe, Zach Mahone, Jeff Racine, Alisa Tazhidinova and Mike Veall for helpful commens and suggesions, as well as he paricipans a he Third Annual Workshop in Inernaional Trade and Macroeconomics in Nore Dame, ITAM, Banco de Mexico and Calgary. All errors are our own.
1. Inroducion Canada s oal facor produciviy (TFP) growh beween 1970 and 2002 was 1.45% per year. This number is lower han, bu similar o, ha of he Unied Saes during he same period, 1.55%. During he 12 years ha followed, beween 2002 and 2014, Canada s TFP grew by 0.16% per year while ha of he Unied Saes grew by 1.33%. 1 More han a decade of negligible TFP growh makes Canada much poorer han i would be if TFP had grown as i did in he U.S. (GDP per wap would have been 9.4% larger in 2014 ha i acually was), or as i did in Canada beween 1970 and 2002 (GDP per wap would have been 10.42% larger by 2014 han i was). Lack of TFP growh consiues a puzzle: as documened in various sudies see Kehoe and Presco (2002) and Cosa e al. (2016a,b) in he long run, GDP per wap in developed economies grows a around 2% per year, and his growh is enirely driven by TFP growh. There are many examples of counries wih no TFP growh for more han a decade ha end up suffering severe recessions. 2 Afer esablishing ha Canada had negligible growh of TFP during 2002-2014, we analyze wheher his lack of produciviy growh can be accouned for by several issues regarding he measuremen of facors of producion or by how facors of producion are allocaed. We do no find any suppor for his hypohesis. However, we show ha during he Canadian Produciviy Sagnaion, Canadian erms of rade grealy appreciaed, while U.S. erms of rade slighly depreciaed and he erms of rade are no refleced in he measuremen of GDP (see Kehoe and Ruhl, 2008). Hence, real Canadian income grew more han real Canadian oupu (and he opposie is rue for he U.S.). Using real Gross Domesic Income (GDI) growh insead of real GDP growh capures he difference beween income and oupu. We perform he same growh accouning exercise using GDI insead of GDP and find ha during 2002-2014, Canadian TFP-GDI conribuion o GDI per wap growh is 0.95% per year, whereas his number is 1.13% in he U.S. Hence, using GDI insead of GDP grealy narrows he difference in performance beween he wo counries. Our growh accouning decomposiion exercise is based on he work of Cole and Ohanian (2002) and Kehoe and Presco (2002) o sudy Grea Depressions. I has been used o sudy Grea 1 Our findings are in line wih hose of he Groningen Growh and Developmen Cener. In heir analysis, hey conrol for labor qualiy and differen ypes of capial, and find ha TFP in Canada grows even less han wha we find. 2 During he 1980 s and 1990 s, here are he examples of Argenina (Kydland and Zarazaga, 2003), Brazil (Bugarin e al., 2002), and Mexico (Bergoeing e al., 2002), and 1990-2014 Spain (Conesa and Kehoe, 2016, Diaz and Franjo, 2016, and Moral-Benio e al., 2016). 1
Depression episodes in many counries, including Canada beween 1929-1939 (Amaral and MacGee, 2002), business cycles (Chari, Kehoe and McGraan, 2007), fiscal policy (Conesa, Kehoe and Ruhl, 2007), and developmen (Bosworh and Collins, 2008). We are by no means he firs ones o perform a growh accouning exercise of he Canadian economy. On op of he aforemenioned Amaral and MacGee (2002) for he Grea Depression, Cociuba and Ueberfeld (2008) apply he mehodology of Chari, Kehoe and McGraan (2002) o he analysis of he Canadian business cycles. Our analysis differs from previous work along wo elemens: firs, we documen he Canadian sagnaion in produciviy growh during 2002-2014; second, we analyze he robusness of his resul o several measuremen and composiional issues. Our paper is also relaed o he lieraure ha analyses he relaionship beween TFP and changes in he erms of rade. We find ha he period of high appreciaion of erms of rade in Canada is unrelaed o increases in Canadian TFP, a resul ha is in line wih he findings of Kehoe and Ruhl (2008). In conras, De Soyres (2016) shows ha he wo can be conneced by he amoun of profis ha firms make. We leave he exploraion beween he wo for he case of Canada for fuure work. The baery of exercises we perform o undersand he impac of measuremen issues on TFP growh is spli ino four blocks: How capial is consruced, how labor is consruced, how he producion funcion is used, and wheher we should use oupu or income. Firs, we look a he consrucion of he series of capial. We begin by looking a how capial depreciaes in Canada. As Diewer (2005) poins ou, consumpion of fixed capial in he Naional Accouns of Canada (driven by he differen ypes of invesmens done) is larger han in he U.S., which implies ha he depreciaion of Canadian capial is larger. Diewer (2005) calculaes he depreciaion rae of he economy using micro daa on many differen indusries from Saisics Canada. In conras, we use aggregae daa on invesmen and consumpion of fixed capial. Sill, we reach he same conclusion: The depreciaion of Canadian capial (7.54%) is higher han in he U.S. (6.77%). Using he depreciaion rae of he U.S. o measure Canadian TFP has lile impac on solving he puzzle, hough: TFP grows by 0.18% per year during he 2002-2014 insead of 0.16%. We nex explore he implicaions for he measuremen of capial of is composiion beween consrucion and oher ypes of invesmen. Diaz and Franjo (2016) argue ha he lack of TFP growh in Spain is due o increased invesmen in consrucion. For he case of Canada, invesmen in consrucion represens 55.56% of oal invesmen in 2002, increasing o 69.22% in 2014. We 2
consruc a counerfacual series of GDP and capial leaving invesmen in consrucion ou of he series, and perform he growh accouning exercise again. We find ha under his scenario TFP falls by -0.10% per year during 2002-2014, wih mos of he fall happening beween 2002 and 2009, wih an average fall of 0.99% per year, and growh a 1.16% aferwards. Performing he same exercise for he period 1970-2002 implies a TFP growh of 1.34% in Canada, while he figures for he U.S. are 1.45% for he period 1970-2002 and 1.47% for 2002-2014. In he second block of counerfacual exercises we look a he consrucion of he series of labor. Beween 2002 and 2014, females paricipaion rae in he labor marke increases, hey earn less han males, and he difference in earnings narrows. Since females earn less han males and heir labor paricipaion increases, we ask wheher he lack of TFP growh is caused by a composiion effec in he labor force. We find ha his is no he case: If he paricipaion rae of females (relaive o ha of males) had sayed a is 2002 level, TFP growh would have been only 0.17%, insead of 0.16%. If he gender wage gap had remained consan a heir 2002 level (insead of shrinking) and hours worked by females evolved he way hey did, we would have had a TFP growh of -0.03% per year. A similar analysis can be done by looking a he indusry composiion of he labor marke. There is a lo of heerogeneiy across indusries in erms of he wage hey pay, how much labor hey employ, and he evoluion of hese variables beween 2002 and 2014. We find ha if relaive wages had sayed consan a heir 2002 levels, TFP would have fallen by -0.36% per year. If, insead, relaive employmen across secors had sayed consan o heir 2002 levels, TFP would have also fallen, in his case by -0.02% per year. This exercise poins ou ha he allocaion of labor across indusries, on average, wen from low paying jobs o high paying jobs, and ha indusries ha grew mos were he ones ha were paying higher wages. In he hird block we look a he specificaion of he producion funcion. We sar by looking a a crucial erm in he Cobb-Douglas producion funcion: The parameer ha governs he fracion of oal oupu ha is devoed o paying for labor, ypically called he labor share. Mos developed economies build he Naional Accouns dividing he economy in hree differen secors: The household secor, he governmen secor, and he corporae secor. In he laer wo, oal compensaion of employees accuraely reflecs paymens o he labor force. For he household secor, insead, mos of he income generaed by small unincorporaed businesses direcly goes o mixed income, even hough a large fracion migh be he compensaion of he labor services 3
provided by he business owner (and ofen family members). Hence, when compuing he labor share of an economy a common pracice suggess o exclude he household secor of boh GDP and compensaion of employees, and use he res of he economy o compue he labor share (see Conesa e al., 2007, for a deailed explanaion). Unforunaely, he Canadian Naional Accouns are buil wihou properly disinguishing hese hree secors. Due o his, he labor share we use in our benchmark exercise is he one for he U.S., which is 0.65. We show ha using alernaive labor shares around he values found in Gollin (2002) does no change he main resul: Wih a labor share of 0.6, TFP growh is 0.00% during 2002-2014 (1.21% in he U.S.), and wih a labor share of 0.75, TFP growh is 0.52% (1.60% in he U.S.). NEW: I is worh poining ou ha we do no explore alernaive specificaions of he producion funcion. In paricular, we absrac from he growing lieraure on changes in he labor share. See Karabarbounis and Neiman (2013), Koh e al (2016), or Auor e al (2017). We believe ha he ime period we analyze is shor enough so ha he long run rend in labor income shares should no maer much. Nex, we perform a growh accouning exercise a he secoral level. We find ha wo of he secors, manufacuring and mining and oil and gas exracion, are i) very large (a leas hey accoun for 25% of oal employmen and GDP in Canada), ii) have negaive TFP growh (-0.78% for manufacuring and -2.70% in mining and oil and gas exracion), iii) in he U.S. hey have a posiive TFP growh (3.74% and 6.33%), and iv) hey are secors heavily exposed o inernaional rade (a leas 71% of Canadian rade occurs in hese wo secors, and a leas 65% in he U.S.). This exercise shows ha he differences in TFP growh beween he wo economies are largely driven by a handful secors ha are highly exposed o inernaional rade. This las finding brings us o he fourh (and las) block of counerfacual exercises, where we are concerned wih wheher we should use a measure of oupu or a measure of income for our analysis. The sandard growh accouning pracice is done using real GDP per wap. The use of GDP reflecs he producive abiliy of an economy, which is ighly linked o is purchasing abiliy. However, in periods of large movemens in he erms of rade, real GDP can move differenly han real Gross Domesic Income (GDI). The erms of rade are no incorporaed in he measuremen of real GDP, bu hey are incorporaed in he measuremen of real GDI (see Kehoe and Ruhl, 2008). During he period of he Canadian Produciviy Sagnaion, Canada had a large appreciaion of he erms of rade (1.44% per year) while he U.S. had a mild depreciaion (0.16% per year). In 4
our las exercise we redo he growh accouning exercise for he Canadian and he U.S. economy using real GDI insead of real GDP. The measure ha we obain, which we call GDI-TFP, experiences growh of 0.95% per year in Canada during he 2002-2014 period (subsanially higher han he 0.16%) and by 1.13% in he U.S. (slighly smaller han 1.33%). These findings imply ha even hough he U.S. had a much larger growh in is abiliy o produce oupu han Canada during ha period, differences in purchasing power did no change by nearly as much. 2. Measuring oal facor produciviy In his secion we show how o measure TFP, closely following Conesa e al. (2007) and repor he resuls of he growh accouning exercise for Canada and he Unied Saes. The exercise consiss of aribuing all he growh in GDP per wap o a capial, a labor, and a TFP componen. Firs, suppose he producion funcion of he economy is given by he following Cobb-Douglas producion funcion Y A K L, (1) 1 where Y is a measure of income/oupu (GDP in our benchmark measuremen), sock, L is he oal amoun of labor in he economy, K is he capial A is he oal facor produciviy, and is he capial share in he economy. Then, GDP per working age populaion, as N, can be expressed 1 1 1 A Y K L N Y N, (2) which implies ha he series of oupu per working age populaion is accouned for by he combinaion of he evoluion of he TFP facor, he capial inensiy facor, and he labor inensiy facor. Noice ha in a balanced growh pah he inensiy in he use of capial and labor should be consan, and he TFP facor drives enirely he evoluion of oupu. In wha follows, we show how o consruc a series for all he objecs in (2) using he Naional Accouns and labor survey daa. 5
2.1. Consrucion of he series In order o measure TFP for Canada and he Unied Saes we need measures on GDP, labor, working age populaion, and capial. We sar wih GDP. We use series on gross domesic produc a curren and a consan prices for GDP, from he OECD for boh Canada and he Unied Saes. Then, we compue he GDP deflaor aking he raio beween he wo, wih base year prices in he year 1970. The series of GDP a 1970 prices is our series of Y. We compue he amoun of labor, L, muliplying he series of he number of workers in each period by he average hours worked. The series of working age populaion, series on working age populaion 15-65. N, is given he We compue he series for capial using daa on gross capial formaion and consumpion of fixed capial a curren prices. We deflae boh series by he GDP deflaor. The series on deflaed gross capial formaion is our measure of invesmen, I. Then, we assume ha capial is formed using he perpeual invenory mehod, K 1 (1 ) K I, (3) where is he depreciaion rae of capial. We choose he value for his parameer o mach he average value of he raio of consumpion of fixed capial o GDP in he daa, Cons of fixed capial GDP K 2014 1980, (4) 1970 1971 Y and assume ha he firs capial sock is such ha he capial-oupu raio is he same as he average for he firs 10 years of he series K Y 1970 1970 1980. (5) 1971 K Y We find ha he depreciaion rae for Canada is 7.54% and he depreciaion rae in he U.S. is 6.77%. Finally, we are lef wih he compuaion of he capial share parameer,. The naional accouns divide all he economy in hree secors: households, corporae and governmen. While i 6
is clear ha salaries paid by he corporae and he governmen secor o employees is labor compensaion, i is less clear ha he same objec in he household secor coincides wih labor compensaion. The household secor includes small firms operaed by he business owners and may no include all paymens o labor in compensaion of employees. To avoid his problem and o ge a proper esimae of he capial share, we would like o compue he following objec 1 2014 Compensaion Employees HH C.E., (6) GDP HH C.E. HH Mixed Income Ind Tax 1970 where he series of Compensaion Employees consiss of all paymens o employees in he economy, HH C.E. is he paymens o employees done by he household secor, HH Mixed Income is he paymen from he household secor o oher facors including capial, bu also labor and Ind Tax consiss of Indirec Taxes. This number can easily be compued for he Unied Saes: 0.35. However, Canadian Naional Accouns feaure he following curiosiy: all paymens o employees are aribued o he household secor. This would imply ha he numeraor in he righ erm of equaion (6) expression is always 0. Given ha, we use he same parameer for he capial share in Canada as in he Unied Saes. We perform robusness exercises and he resuls do no change. 2.2. Resuls As is well-known, from he series for he Unied Saes, in Figure 1, he paern ha emerges consiss of a growh rae of GDP per working age populaion mosly driven by he growh rae of TFP, wih he labor per working age populaion and he capial-oupu raio componens being very sable. The picure ha emerges for Canada, in Figure 2, is similar, bu i has a key difference: beween 2002 and 2014, he series for TFP is (almos) fla. 7
1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012 190 190 170 Y / N 170 Y / N 150 A 1/(1 α ) 150 A 1/(1 α ) 130 130 110 L / N α /(1 K α ) / Y 110 L / N 90 90 α /(1 K α ) / Y Figure 1 (lef): Growh Accouning Decomposiion for he Unied Saes, 1970-2014 Figure 2 (righ): Growh Accouning Decomposiion for Canada, 1970-2014 An alernaive way o see he difference beween he series consiss of compuing he annualized growh rae for he periods of 1970-2002 for he four series and he wo economies, and repeaing he compuaion for he period 2002-2014. We show he resuls in Table 1. Y N 1 1 A 1 Unied Saes Canada 1970-2002 2002-2014 1970-2002 2002-2014 1.81% 1.00% 1.56% 0.94% 1.55% 1.33% 1.45% 0.16% K Y 0.03% 0.12% -0.10% 0.74% L N 0.22% -0.44% 0.21% 0.04% Table 1: Annualized growh raes During he period 2002-2014 GDP growh is very similar in he Unied Saes and in Canada, bu TFP growh differs dramaically. US TFP grew a an annualized rae of 1.33%, while Canadian TFP grew much less, a only 0.16%. In conras, facor inensiy grew more in Canada han in he Unied Saes, and ha is why GDP growh is similar across he wo economies. This difference is no presen in he period 1970-2002, and ha is why we will look a composiional and measuremen issues ha migh have arificially generae his differen paerns in 2002-2014. 8
If he lack of TFP growh were robus, i migh poin o poenial concerns for fuure growh in Canada, since growh hrough facor accumulaion is by definiion very limied. 3. Aggregae measuremen of capial The increase in GDP per wap in Canada is mosly driven by he capial per oupu erm. In his secion we perform a robusness check on he measuremen of capial, and find ha he resuls on produciviy sagnaion remain. 3.1. Depreciaion of capial A common concern abou how o measure capial in he Canadian economy is posed by Diewer (2005), since Canada depreciaes a larger sock of is capial han he Unied Saes. Indeed, in our baseline case, he depreciaion rae for Canada is 7.54%, while he depreciaion rae for he Unied Saes is 6.77%. This concern is very imporan since i affecs he measuremen of capial and hence he measuremen of TFP. Furhermore, he calibraed dela has an impac on he calibraed capial level of he iniial period; in he benchmark case his raio is only 2.08 in Canada, while in he Unied Saes i is 2.25. However, from he perspecive of his paper we can solve he problem posed by a large depreciaion rae by simply impuing he same depreciaion rae o he wo economies. When we compue he change in TFP of he Canadian economy for he period 2002-2014 using he depreciaion rae of he Unied Saes, we ge ha he raio of iniial capial sock o GDP is 2.20, very similar o he one in he Unied Saes. Sill, under his alernaive scenario we measure ha he TFP componen grows a 0.18%, insead of 0.16% in he baseline case. 3.2.Invesmen in buildings and dwellings According o Diaz and Franjo (2016) he lack of TFP growh in Spain during he 1990-2014 period can be accouned for by he rise in he share of invesmen in buildings and dwellings. The Canadian economy is similar o he Spanish economy in ha i also had a remendous increase in he fracion of oal invesmen devoed o buildings and dwellings during he period 2002-2014: i wen from 55.56% of oal invesmen a he beginning of he period o 69.22% a he end of i. In order o deermine he impac of his feaure of invesmen daa for our measuremen of TFP we subrac all invesmen in buildings and dwellings from he series of invesmen and GDP, and repea he growh accouning exercise. 9
We find ha insead of 12 years of roughly fla TFP, he series splis ino 7 years of pronounced negaive growh (-0.99%) followed by 5 years of posiive growh (1.16%) for a combined effec of a fall of 0.10% per year during 2002-2014. Hence, invesmen in buildings and dwellings canno accoun for he lack of TFP growh in Canada, bu i changes he overall picure: insead of a Produciviy Sagnaion ha lased welve years, we find a severe fall in TFP for a shorer ime period. Repeaing he same exercise for previous periods does no have major effecs on he growh raes we repor in Secion 2. In he case of he U.S. during 2002-2014, he growh rae would have been 1.34% (insead of 1.33%). During 1970-2002, Canada would have grown a 1.45% (exacly he same we go including buildings and dwellings) and he U.S. would have been 1.47% (insead of 1.55%). 4. Measuremen of labor When we measure labor, he exercise consiss of couning how many bodies are working, and muliply ha number by he average amoun of hours worked. One concern ha we may have, hough, is ha differen bodies are differen levels of produciviy. If he composiion of labor changes over ime, wih some ypes of labor growing a he expense of ohers, hen he resuling aggregae TFP growh may be affeced. Consider he following producion funcion, insead of he one in (1) 1 Y K E L (7) where now, insead of A (TFP), we have E as efficiency unis of labor, which is wha we have been referring o as he TFP facor since A 1 E. Suppose ha differen labor unis have differen efficiencies, namely ha working wih hose efficiencies, and hen equaion (2) becomes E is a vecor of efficiencies, and E L e i i in L is a vecor of bodies/hours. Then, he decomposiion equivalen o e Y K L N L Y N i i 1 in (8) 10
which is equivalen since 1 TFP ei i L. in In wha follows, we experimen wih his alernaive specificaion analyzing he role of he increased female paricipaion in he labor force, as well as differen secoral composiion of labor in he economy. 4.1. Gender wage gap and female labor force paricipaion An imporan difference beween differen ypes of workers is ha of gender. Canadian females have been earning beween 72% and 87% of wha heir male counerpars earned during he 1981-2014 period, females acive in he labor force represened beween 68% and 90% of males acive in he labor force, and females have worked beween 79% and 84% of he hours worked by heir male counerpars. See Figure 3 for he evoluion of hese hree gaps. Wih his informaion, we consruc he series for ei i MAv.H.Worked-Male F Av.H.Worked-Female GAP (9) in where he firs erm consiss of he number of males working imes he amoun of hours worked by hem on average, and he second is he female counerpar, where GAP is he relaive wage of females wih respec o males. By consrucion, measured TFP of his series coincides wih measured TFP in he baseline case. However, we can perform wo ineresing counerfacual exercises: wha would have been he evoluion of Canadian TFP if he gender wage gap remained consan o heir 2002 level hroughou he period analyzed, and wha would have been he evoluion of Canadian TFP if female s paricipaion rae and hours worked sayed consan o heir 2002 level hroughou he period. 11
0.95 0.9 Bodies Gap 0.85 Hours Worked Gap 0.8 0.75 Gender Wage Gap 0.7 0.65 Figure 3: Gender gaps in Canada, 1981-2014. If he gender wage gap remained ha of 2002, bu female paricipaion rae was he one observed, TFP would have been he series from equaion (9) would have been e i2002 i in TFP ' TFP e i i in 1. (10) The series of TFP ' from equaion (10) has negaive growh, equal o -0.02% per year during he 2002-2014, compared o he growh of 0.10% in he baseline case. The fall of hese series has a clear explanaion: he gender wage gap narrowing beween 2002 and 2014, in our framework, is equivalen o having females increasing heir produciviy. If hey were as producive as in 2002, overall produciviy would have been smaller han i acually was. Similarly, we can compue wha would have been TFP, had he labor paricipaion decisions remained consan o hose of 2002, bu he gender wage gap changed as i did. In his case, 12
e i i2002 in L TFP '' TFP ei i L 2002 in 1. (11) The series for TFP '' from equaion (11) increases, bu only a 0.11% per year. Since hroughou he period females are less producive han males, and here is an increase in he female paricipaion rae, ha means ha here was a relaive increase of less efficien workers (a leas as measured by wage daa). However, his effec is very small and i canno accoun for he lack of TFP growh for he enire period. 4.2 Secoral composiion of labor Nex, we invesigae he relaionship beween he secoral composiion of labor and he lack of TFP growh. The analysis ha follows is similar o he one in he secion before, bu using daa on he 19 differen secors of he economy. There is heerogeneiy in he volume of employmen per indusry Trade is he larges secor, wih over 2.000.000 workers, and Foresry, Logging and Suppor is he smalles, wih less han 100.000 as well as in wages Accommodaion and food services pay 22.6% of wha Uiliies pay in 2002. Using informaion by secor, we compue effecive hours worked, e in i i, where N is he se of indusries, e i is compued using he wage of secor i, deflaed using he GDP deflaor, and i is he number of workers in secor i Canadian daa does no include hours worked in each secor, only he body coun of workers. In he firs exercise we make use of he formulaion of equaion (10), keeping relaive wages consan and changing he relaive employmen in each secor. In his counerfacual case, TFP would have had a negaive growh rae of -0.23% per year. The reason for his fall compared o he growh of 0.10% in he baseline case is he same as in he case of lower growh when he gender wage gap says consan: he sum of efficiency increases, weighed by he employmen level in each secor, is posiive, i.e. ei 2000 i2014 ei 2000 i2000 TFP2014 ' TFP2014 in in ei 2014 ei 2000 i2014 0. (12) TFP ' TFP e e 2001 2001 i2014 i2014 i2000 i2000 in in in 13
Similarly, in he second exercise we make use of he formulaion of equaion (11), keeping relaive employmen in each secor consan and changing he relaive wages in each secor. In his counerfacual exercise, he series for TFP falls by -0.01% per year. Noice ha his resul is exacly he opposie of wha we found in he case of he gender wage gap. In fac, and similar o he case where wages are fixed, his number being smaller han 0.10% implies ha he sum of labor increases, weighed by he efficiency level in each secor, is posiive, i.e. TFP2014 '' TFP 2014 i2014 i2000 ei 2014 0 TFP2000 '' TFP2000 in L 2014 L. (13) 2000 These wo resuls imply ha he reallocaion of labor and he relaive increases in efficiency during he las 14 years in Canada have been in he direcion of increasing produciviy, referred o as produciviy-enhancing srucural ransformaion by McMillan & Rodrik (2011). 5. Measuremen of he producion funcion When we measure TFP, we need o assume a cerain specificaion of he producion funcion. The mos common pracice in growh accouning exercises sugges he use of Cobb-Douglas, even hough here are many sudies regarding he long run decrease of he labor share. The simpliciy of he Cobb-Douglas specificaion is ha i relies on obaining one calibraed parameer, he capial share. The firs exercise consiss of invesigaing he role ha his parameer plays furher. The second exercise consiss of obaining a separae series for TFP for each differen indusry in he economy. 5.1 Capial share When we compued he capial share in he economy, equaion (6), we saed ha due o he srange compilaion of he household secor in Naional Accouns daa in Canada, he capial share was borrowed from he Unied Saes. The number we have used in our baseline analysis is 0.35, slighly larger han he 1/3 measured in Gollin (2002). To perform he robusness check, we compue he increase in TFP during he 2002-2014 period in Canada if he capial share was differen. If he capial share were equal o 0.25, TFP would have grown a 0.52% (in he U.S. his figure would be 1.60%); if he capial share were 0.40, TFP would have experience 0.00% growh (in he U.S. his figure would be 1.21%). 14
5.2 Muliple secors We nex urn o measuring a series for TFP for each secor in he economy for boh, he U.S. and Canada, o highligh where he difference in oal TFP comes from. We use invesmen by each secor, and spli i beween invesmen and repair. Then, we compue a secor-specific depreciaion rae in order o i) capure he significan differences in repair invesmen across secors, and ii) mach he aggregae depreciaion rae from he benchmark exercise. Furhermore, we use informaion on paymens o labor by secor in order o ge a secor-specific capial share. Wih hese wo, we compue he series for TFP by each secor. There are wo secors ha sand ou: mining and oil and gas exracion and manufacuring. The firs consiss of 8 o 9% of Canadian GDP, i has 17 o 20% of Canadian capial, and i employs 10 o 15% of Canadian labor; he second one has 10 o 15% of GDP, 16 o 19% of capial and 10 o 14% of labor. The firs secor s TFP falls a -2.70% per year during he 2002-2014, and manufacuring TFP falls a -0.78% per year. By comparison, in he U.S. hese figures are posiive growh of 6.33% and 3.74% respecively. Given heir size and he subsanially differen evoluions of TFP in hese wo secors beween Canada and he U.S., i is clear ha a big par of he difference in he overall evoluion is ighly linked o hese wo secors. SHOULD WE REPORT SECTORAL TFPs? There is one dimension in which hese wo secors are very similar: hey are very imporan in he foreign secor. In Canada, he combined share of expors in hese wo caegories as a percenage of overall expors is 71%. In he U.S. his number is 65%. Hence, his exercise poins oward he direcion ha, perhaps, he foreign secor conains an answer o he Canadian Produciviy Sagnaion puzzle. We dig furher ino his quesion in he nex secion. 6. Income, Oupu, and he erms of rade In his secion we wan o emphasize a big difference beween Canada and he U.S. during he 2002-2014 period: heir erms of rade had a subsanially differen evoluion. Figure 4 shows ha Canada s relaive price of impors over expors falls by 1.44% per year beween 2002 and 2014, whereas he number in he U.S. increases by 0.16% per year. 15
1.25 1.2 1.15 Canada 1.1 1.05 1 0.95 Unied Saes 0.9 Figure 4: Terms of rade in Canada and U.S. 1990-2014. A fall in he price of impors implies ha domesic goods become relaively more expensive and foreign goods become relaively cheaper. Tha means ha he counry does no need o produce as much in order o enjoy a larger amoun of goods. Hence, wih less producion Canada can enjoy more purchasing power. This poin is key o differeniae oupu from income. When he erms of rade are sable, he wo objecs are he same. However, in periods of a prolonged appreciaion or depreciaion of he erms of rade, real measures of oupu differ from real measures of income. Take, for insance, Canada in he picure. For he period 2002-2014, if Canadian oupu was kep consan, Canadian ciizens could have enjoyed an addiional 1.44% of foreign goods every year. Hence, even hough he abiliy o produce goods would no change (oupu), he abiliy o purchase goods would have been growing (income). In he naional accouns, he firs objec is referred o as real GDP, whereas he second objec is real Gross Domesic Income (GDI). The exercise we perform consiss of reproducing he growh accouning exercise bu using GDI insead of GDP, in order o ge how differenly he incomes of boh counries changed during he period. We refer o he TFP equivalen measure as GDI-TFP, in his case. 16
We find ha he growh in GDI-TFP is 0.95% per year in Canada. This number is larger han he 0.16% per year ha we obained when we measured TFP using GDP. Similarly, we find ha he growh in GDI-TFP during 2002-2014 is 1.13% per year in he Unied Saes. This number is smaller han he 1.33% per year ha we obained when we measured TFP using GDP. Moreover, he difference beween he wo numbers is now largely reduced. 7. Conclusion [TBD] 17
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