EXPORT GROWTH, CAPACITY UTILIZATION, AND PRODUCTIVITY GROWTH: EVIDENCE FROM THE CANADIAN MANUFACTURING PLANTS

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1 bs_bs_banner Revew of Income and Wealth Seres 59, Number 4, December 2013 DOI: /row EXPORT GROWTH, CAPACITY UTILIZATION, AND PRODUCTIVITY GROWTH: EVIDENCE FROM THE CANADIAN MANUFACTURING PLANTS by John R. Baldwn, Wulong Gu* and Belng Yan Statstcs Canada Aggregate labor and multfactor productvty growth slowed substantally post-2000 n the Canadan manufacturng sector. To examne the source of the declne, ths paper proposes a decomposton method that delves deeper nto the two mcro-components of aggregate productvty growth: a wthnplant component and a between-plant component. The decomposton bulds on earler work by Jorgenson and hs collaborators that decomposes aggregate productvty growth nto ts ndustry components, but apples t to the plant level and ntroduces non-neoclasscal features of the plant-level economc envronment. It fnds that the preponderance of the aggregate labor and multfactor productvty growth slowdown s due to the pro-cyclcal nature of productvty growth arsng from capacty utlzaton. Almost all of the aggregate productvty growth slowdown s drven by exporters, as exporters experenced large declnes n labor productvty growth n the post-2000 perod as a result of large declnes n ther capacty utlzaton. JEL Codes: D24, O47 Keywords: excess capacty, export growth, productvty 1. Introducton Growth n labor and multfactor productvty n the Canadan manufacturng sector declned sharply after Ths post-2000 declne accounted for most of the slower productvty growth of the busness sector n Canada (Baldwn and Gu, 2009). The economc envronment post-2000 dffered markedly from the prevous decade. Durng the perod from 1990 to 1996, average tarff reductons between Canada and the U.S. were large, wth an annual average rate of declne of 0.60 percentage ponts (Baldwn and Yan, 2012). In addton, the Canada/U.S. exchange rate deprecated at an average annual rate of 2.0 percentage ponts from 1990 to As a result, total merchandse exports (mostly gong to the U.S. market) as a proporton of gross domestc product (GDP) n Canada ncreased. The tradng envronment post-2000 was very dfferent. Most of the tarff reductons pursuant to the Canada U.S. free trade treates had already been mplemented. At the same tme, trade costs rose due to post-9/11 border frctons. Note: We would lke to thank Isabelle Amano, Claude Lavoe, Alla Lleeva, Annette Ryan, Janmn Tang, Ben Tomln, and semnar partcpants at Industry Canada and Statstcs Canada for comments, and Danny Leung for hs help wth GMM estmaton. We would also lke to thank two anonymous referees and an edtor for ther helpful comments. *Correspondence to: Wulong Gu, Economc Analyss Dvson, Statstcs Canada, Ottawa, Ontaro, Canada, K1A 0T6 (Wulong.Gu@statcan.gc.ca) Internatonal Assocaton for Research n Income and Wealth 665

2 Revew of Income and Wealth, Seres 59, Number 4, December 2013 Moreover, the Canadan dollar apprecated steeply from US$0.67 n 2000 to US$0.88 n 2006, an average annual apprecaton of 3.5 percentage ponts, powered by the worldwde resource boom that led to a dramatc expanson of the resource-based Western Canadan economy. Durng that perod, total merchandse exports as a proporton of gross domestc product n Canada declned. The post-2000 perod was also characterzed by the development of excess capacty n the Canadan manufacturng sector. Capacty utlzaton declned n 16 out of the 20 manufacturng ndustres n that perod. The emergence of excess capacty post-2000 manly orgnated from the large declne n exports as a result of the change n the trade envronment durng that perod. 1 Ths paper examnes how changes n the envronment post-2000 are related to slower productvty growth n the Canadan manufacturng sector. It examnes how ths slowdown n productvty growth post-2000 was assocated wth the ncrease n excess capacty. To understand how changes n the economc envronment are related to slower productvty growth, we decompose changes n aggregate productvty growth nto underlyng mcro-components to examne whether dfferences n these components suggest causes that relate to changes n the economc envronment. Prevous emprcal studes have decomposed aggregate productvty growth nto the effect of reallocaton and the effect of wthn-plant growth (Grlches and Regev, 1995; Bartelsman and Doms, 2000; Foster et al., 2001; Bartelsman et al., 2005). The orgnal decomposton methods used n those studes focused only on the extent to whch growth takng place at ndvdual frms contrbuted to overall productvty growth (wthn-plant component) and the extent to whch shfts n output and nputs across frms enhanced productvty growth (between-plant component or the effect of reallocaton). Ths paper proposes a decomposton method that delves deeper nto these two mcro-components of aggregate labor and multfactor productvty (MFP) growth. The wthn-plant component for aggregate MFP growth s further decomposed nto the effect of technologcal progress, scale economes, and varable nput utlzaton at the plant level; for aggregate labor productvty growth, the wthn-plant component s decomposed nto those effects plus the effect of captal deepenng. The between-plant component for aggregate MFP growth captures the effect of reallocaton across plants on aggregate MFP growth; for aggregate labor productvty growth, the between-plant component s further decomposed nto the effect of reallocaton on aggregate MFP growth plus the effect of reallocaton on aggregate captal deepenng. The queston of nterest s the extent to whch most of the declne n productvty growth came from a declne n capacty utlzaton or whether t came from other sources a declne n producton effcency (MFP growth) or a declne n the mpact of the reallocaton of resources that generally tends to contrbute to productvty growth. The decomposton bulds on earler work (Jorgenson, 1966; Jorgenson et al., 2005) that decomposes aggregate productvty growth nto ts ndustry components but apples t n ths nstance to the plant level. It also ntroduces 1 Excess capacty also developed n several ndustres as they experenced dramatc declnes n demand after 2000 that were related to structural adjustments. For example, the large declne n producton n the electronc product manufacturng sector after 2000 was related to the burst of the dot-com bubble n that perod Internatonal Assocaton for Research n Income and Wealth 666

3 Revew of Income and Wealth, Seres 59, Number 4, December 2013 non-neoclasscal features of the plant-level economc envronment such as mperfect competton and economes of scale, whereas the orgnal Jorgenson decomposton was developed under the assumpton of perfect competton and constant returns to scale. 2 Labor and multfactor productvty measures are both examned here. Labor productvty s used to tell us how effcently labor s transformed n the producton process. It s of nterest because of ts close connecton wth the growth n real wage rates. Multfactor productvty s a more comprehensve weghted average of both labor and captal productvty. It s calculated as the dfference between the growth of output and the growth n expected output from the applcaton of labor and captal nputs usng assumptons about producton technology that s, how much output addtonal unts of labor and captal mght be expected to have produced. It s of nterest because of ts nterpretaton as capturng all unmeasured factors ncludng dsemboded techncal progress. But more mportantly for our purposes, labor productvty growth can be decomposed nto multfactor productvty growth and a term nvolvng the growth n captal/labor ntensty. Thus, underlyng changes n the economy that affect labor productvty wll be found both n those that affect multfactor productvty growth and n those that affect changes n captal ntensty. 2. Methodology A number of emprcal studes have decomposed aggregate productvty growth nto the effect of reallocaton and the effect of wthn-plant growth (Grlches and Regev, 1995; Foster et al., 2001; Bartelsman et al., 2005; Baldwn and Gu, 2006). The decomposton methods used n these studes focused on aggregate labor productvty or aggregate multfactor productvty and the extent to whch shfts n output and nputs across frms enhanced productvty growth. However, prevous emprcal studes dd not focus on the underlyng causes of changes n labor and multfactor productvty at the plant level arsng from factors such as nvestment, technologcal progress, scale economes, or varable nput utlzaton only on whether changes were nternal to the plant or were caused by reallocaton of outputs across plants that arse from the dynamc compettve process. In order to proceed further, t s necessary to ntroduce producton functons at the plant level to mprove our understandng of the sources of the wthn-plant growth effect and the between-plant reallocaton effect on overall productvty growth. Ths paper extends the prevous work that just examned the sze of wthnand between-plant components to allow us to delve deeper nto these components usng the methodologes of Jorgenson and hs collaborators. 3 The methodologes of Jorgenson and hs collaborators were developed under the assumpton of 2 A number of recent papers have presented a decomposton of aggregate multfactor productvty growth (Basu and Fernald, 2002; Petrn and Levnsohn, 2012). Smlar to ths paper, these papers can be seen as an extenson of the Jorgenson decomposton to a non-neoclasscal framework. 3 Prevous work also extends that analyss by not just examnng the effects of the reallocaton of labor or other nputs (as s done here) to nvestgatng the mpact of shftng market share n order to quantfy the mpact of competton on productvty growth Internatonal Assocaton for Research n Income and Wealth 667

4 Revew of Income and Wealth, Seres 59, Number 4, December 2013 perfect competton and constant returns to scale. Ths paper ntroduces nonneoclasscal features of the plant-level economc envronment such as mperfect competton and ncreased returns to scale, as n Hall (1988, 1990), Basu and Fernald (2002), and Petrn and Levnsohn (2012). It also takes nto account the effect of changes n capacty utlzaton. Jorgenson (1966) and Jorgenson et al. (2005) developed two alternatve approaches for constructng the aggregate estmates of labor and multfactor productvty growth a producton possblty fronter approach and the drect aggregaton across mcro-producers (frms or plants). 4 The former s the tradtonal approach used to estmate productvty when only aggregate data are avalable. The latter allows for a decomposton of the wthn- and between-plant components. For the emprcal analyss below, value-added wll be used to measure output at both aggregate ndustry level and plant level. As such, the decomposton n ths paper wll be presented usng the value-added output concept. Alternatvely, gross output can be used to measure output at aggregate ndustry and plant levels. The gross output of an aggregate ndustry s defned as the sum of gross output of ndvdual plants. The gross output approach s presented and appled n Gu and Lafrance (2012) n ther study on the dynamcs of productvty growth n the broadcastng and telecommuncaton ndustry n Canada. 5 The value-added approach used n ths paper mposes a separablty assumpton necessary for the exstence of value-added producton at the plant level; the gross output approach, whle t captures more of the producton process by takng nto account the role of ntermedate nputs at the plant level, may suffer from the double countng of ntermedate nputs transactons among plants wthn an ndustry. 6 In addton, as shown by Basu and Fernald (2001), the chaned-torqvst aggregaton method used n statstcal agences for calculatng valued added as the dfference between gross output and ntermedate nputs mples that value-added growth s not, n general, a functon of captal and labor nputs alone. It s also affected by ntermedate nput growth when there s mperfect competton. Wth mperfect competton, value-added growth s a functon of captal and labor alone when the rato of ntermedate nputs to gross output s constant. Basu and Fernald (2001) also show that the value-added approach s expected to yeld a hgher MFP growth and larger effect of capacty utlzaton on MFP growth. But the value-added approach and gross output approach often yeld smlar trends n aggregate labor and multfactor productvty growth. In addton to the value-added and gross output approaches, the thrd alternatve s to use the gross output concept at the plant level and the value-added concept at the aggregate level. That framework wll be approprate to examne the 4 Those two approaches are sometmes called top-down and bottom-up approaches. 5 The decomposton methodology based on gross output concept s a straghtforward extenson of the methodology based on the value-added concept used n ths paper from two nputs (captal and labor) to three nputs (captal, labor, and ntermedate nputs). 6 As a result of the double countng of ntermedate nputs, a reorganzaton of producton that resulted n ncreased use of ntermedate nputs would count as an ncrease n productvty even though the amount of producton for use outsde of the ndustry would not be ncreased by ths reorganzaton. We thank an anonymous referee for makng ths pont Internatonal Assocaton for Research n Income and Wealth 668

5 Revew of Income and Wealth, Seres 59, Number 4, December 2013 dynamcs of productvty growth at the total economy level where the approprate output concept s value-added (Basu and Fernald 2001; Jorgenson et al., 2005) Producton Possblty Fronter The producton possblty fronter approach assumes that captal and labor nputs receve the same prce n all plants, but plants have dfferent producton functons that relate value-added output (V) to captal, and labor nputs at the plant level and the prce of output dffers across plants. 8 Under these assumptons, aggregate value-added can be expressed as a functon of aggregate captal, aggregate labor, and a tme varable that proxes technology (T). The aggregate value added s defned as a Tornqvst ndex of plant value-added: (1) V = F( K, L, T), and ΔlnV = wδln V, where Dln denotes the change between perods t - 1 and t n logarthm, and w s the share of plant n aggregate nomnal value-added, averaged over the two perods. Aggregate labor productvty growth, defned as the dfference between growth n aggregate value added and growth n aggregate labor nput, can be wrtten as: (2) Δln P = ΔlnV Δln L = wδln P + wδln L Δln L, where DlnP =DlnV -DlnL s labor productvty growth at plant defned as dfference between value-added growth DlnV and labor nput growth DlnL. The growth on aggregate labor productvty n equaton (2) s decomposed nto two components: the wthn-plant effect and between-plant reallocaton effect. The wthn-plant effect measures the contrbuton to overall productvty growth of growth wthn ndvdual plants, holdng ther shares of output constant. The second term s the between-plant effect that represents the effect of reallocaton of labor nput on aggregate labor productvty growth. The reallocaton effect s postve f plants wth hgher average labor productvty level have faster growth n labor nput. 9 To see that, aggregate growth n labor nput can be approxmated as the weghted average of labor nput growth across plants usng labor nput shares of plants as weghts,.e. Δln L = sδln L. Aggregate labor productvty 7 The framework requres Domar aggregaton (Domar, 1961). 8 The exstence of value-added producton functon at the plant level requres the assumpton that ntermedate nputs are separable from captal, labor, and technology varables (Jorgenson et al., 2005). 9 The equaton has been appled to ndustry level data by Jorgenson et al. (2005). The economc nterpretaton of the reallocaton effect s vald when average labor productvty s equal to margnal labor productvty n the plants that are characterzed by constant returns to scale. When there are ncreasng returns to scale and plants operate at dfferent scales, average labor productvty s not proportonal to margnal productvty across plants. In that case, a porton of the reallocaton effect s ncluded n the wthn-plant effect Internatonal Assocaton for Research n Income and Wealth 669

6 Revew of Income and Wealth, Seres 59, Number 4, December 2013 rses and the reallocaton effect s postve f plants whose value-added shares exceed ther employment shares (w > s) (or plants wth hgher average labor productvty levels) experence faster growth n labor nput (Jorgenson et al., 2005). The decomposton n equaton (2) dffers from the decomposton used n most emprcal studes (Grlches and Regev, 1995; Foster et al., 2001; Baldwn and Gu, 2006, 2011). Those studes start wth the equaton that aggregate labor productvty level s a weghted sum of labor productvty level across plants usng employment shares s as weghts: P = sp. Frst-dfferencng the equaton provdes a decomposton of aggregate labor productvty changes nto a wthn-plant component and a between-plant component: ΔP = sδp + ΔsP, where a bar over a varable denotes average values over two perods. The decomposton n those prevous emprcal studes s vald when the prce of output s the same across all plants. When that s true, aggregate output can be expressed as the sum of output across plants and aggregate labor productvty level s equal to a weghted sum of plant labor productvty usng plant employment share as weghts. However, when the prce of output dffers across plants as s the case for the producton possblty fronter approach, the decomposton n those prevous studes only provdes an approxmaton to the correct decomposton n equaton (2). When the product and factor markets are compettve and the aggregate producton functon s characterzed by constant returns to scale, aggregate multfactor productvty growth can be expressed as the dfference between aggregate labor productvty growth and the effect of captal deepenng: (3) v = Δln P α Δln ( K L), T where v T s multfactor productvty growth, and α K s the share of captal cost n nomnal output, averaged over the two perods Drect Aggregaton Across Plants The alternatve approach for estmatng aggregate labor and multfactor productvty s drect aggregaton across plants (Jorgenson et al., 1987, 2005). The approach relaxes the assumpton adopted n the producton possblty fronter approach that all nputs receve the same prce among all plants. Instead, t assumes that the prces of captal and labor nputs dffer across plants. For the purpose of ths paper, the drect aggregaton approach s extended to take nto account non-neoclasscal features of the economc envronment facng plants. More specfcally, t s assumed that the plant producton functon s characterzed by ncreasng returns to scale and there s mperfect competton n the product market. Plant s assumed to have a producton functon that expresses output (V )as a functon of captal (K ), labor (L ), and technology (T ): (4) V = F ( e K, e L, T), K K L 2013 Internatonal Assocaton for Research n Income and Wealth 670

7 Revew of Income and Wealth, Seres 59, Number 4, December 2013 where e K, e L denote the unobserved utlzaton of captal, labor, and T ndexes technology. The producton functon exhbts ncreasng return to scale g. Followng Hall (1990) and Basu and Fernald (2001, 2002), output growth can be wrtten as: 10 (5) ΔlnV = μ ΔlnX + aδln e + v, T, where DlnX s a weghted sum of nput growth usng the share of nput costs n nomnal output as weghts (6) ΔlnX = ( α Δln K + α Δln L ), K L And Dlne s a weghted sum of the changes n nput utlzaton: (7) Δlne = α Δlne + α Δln e. α K K K L L and α L, are the average shares of captal and labor n nomnal output. The sum of those nput cost shares n nomnal output s less than one f there s economc proft. v T,I s multfactor productvty growth. m s the mark-up over margnal cost. The mark-up s related to the returns to scale g and the rato of economc profts to nomnal output s p by the followng equaton: P AC P (8) μ = = = γ ( 1 sπ). MC MC AC The frst equalty n equaton (8) follows from the defnton of mark-up as the rato of output prce (P ) to margnal cost (MC ). The last equalty follows from an mplcaton of cost mnmzaton that the rato of average cost (AC ) to margnal cost equals returns to scale g. In the emprcal analyss that follows, economc profts wll be assumed to be zero. Ths wll be the case f the ndustry s characterzed by monopolstc competton. When economc profts are zero, mark-up s equal to returns to scale and the sum of nput costs share n nomnal output s equal to one. Subtractng labor nput growth from both sdes of equaton (5) yelds the followng equaton that shows the source of growth n labor productvty at plant : (9) Δln P = ( μ 1) ΔlnX + α Δln( K L )+ aδln e + v. K T, The equaton decomposes the growth n plant labor productvty nto ts varous components ncludng scale economes, captal deepenng, varable nput utlzaton, and technologcal progress. The growth n plant labor productvty can be aggregated to derve aggregate labor productvty growth usng equaton (2), whch s then substtuted n equaton (3) to obtan a decomposton of aggregate multfactor productvty growth: 10 It s assumed that mark-ups do not change over a perod. When they do change, the average mark-up over the perod should be used n the equaton Internatonal Assocaton for Research n Income and Wealth 671

8 Revew of Income and Wealth, Seres 59, Number 4, December 2013 (10) vt = w( μ 1) Δ ln X + waδ ln e + wvt + REALL, J J REALLJ = αj w Δ J J J Δ PJ ln ln J, wj, PJ J K, L, = = where w J s the share of plant n the cost of nput J averaged over two perods, P J s the prce that nput J receves at a plant, and P J s the prce of nput J n the producton possblty fronter approach. 11 Aggregate multfactor productvty growth s decomposed nto a wthn-plant component and a between-plant component. The wthn-plant component captures the effect of changes takng place at ndvdual plants holdng ther output share constant, and t s further decomposed nto the effect of scale economes, the effect of varable nput utlzaton, and the effect of techncal progress. The last term of the decomposton s the between-plant component that measures the effect of reallocaton of captal and labor on aggregate multfactor productvty growth. The reallocaton of an nput contrbutes postvely to aggregate MFP growth f the nput s shfted toward those plants wth hgher nput prce and hgher margnal product. The MFP decomposton (10) smplfes to the decomposton (8.34) n Jorgenson et al. (2005) under the assumpton of constant returns to scale, perfect composton, and no excess capacty. Prevous emprcal studes also decomposed aggregate MFP growth nto wthn-plant and between-plant components. The wthn-plant component was estmated as a weghted sum of MFP growth across plants usng ther output shares as weghts. The between-plant component was calculated as the change n the output share of a plant tmes the average MFP level of the plant, summed over all plants. Our contrbuton here s to delve deeper nto those two components and provde a rcher understandng of the sources of wthn-plant growth effect and between-plant reallocaton effect. 12 Aggregaton of plant labor productvty growth gven n equaton (9) usng equaton (2) yelds a decomposton of aggregate labor productvty growth: (11) Δln P = wδln P + wδln L Δln L, wδln P = w ( μ 1 ) ΔlnX + wα JΔ ln( J L) J= K + waδln e + wv, T, wδln L Δln L REALLJ K ln K L wk ln K L. = + ( ) ( ) α Δ Δ J= K, L J 11 When plant output s based on gross output and aggregate output s a value-added concept, the correct weghts for aggregatng MFP growth across plants are Domar weghts whch are equal to the rato of plants gross output to aggregate nomnal value-added (Domar, 1961). 12 A number of recent studes have proposed a smlar decomposton of aggregate multfactor productvty growth (Basu and Fernald, 2002; Petrn and Levnsohn, 2012). These papers, lke ths one, can be seen as extenson of the Jorgenson decomposton to a non-neoclasscal framework. For example, the MFP decomposton n Basu and Fernald (2002) (equaton 28) and Petrn and Levnsohn (2012) (equaton 9) are varants of the decomposton (12) n ths paper Internatonal Assocaton for Research n Income and Wealth 672

9 Revew of Income and Wealth, Seres 59, Number 4, December 2013 Aggregate labor productvty growth s decomposed nto a between-plant and a wthn-plant component. The wthn-plant effect n equaton (11) s the sum of the followng components: scale effect, captal deepenng effect, varable nput utlzaton effect, and techncal progress. The between-plant reallocaton effect s traced to the effect of the reallocaton of labor and captal nputs on aggregate MFP growth REALL J J= K L and the effect of reallocaton on captal deepenng., To complete the decomposton, t can be shown that the aggregate captal deepenng effect can be decomposed nto the effect of captal deepenng at the plant level and the effect of nput reallocaton across plants on aggregate captal deepenng. (12) αkδln( K L)= wαkδln( K L)+ αk Δln( K L) wkδln ( K L). The between-plant reallocaton effect s postve f labor moves toward those plants wth hgher captal costs and hgher margnal products of captal. The decomposton of aggregate MFP growth, aggregate labor productvty growth, and aggregate captal deepenng effects can be extended to estmate the effect of entrants and exters. For entrants, nputs and outputs are only observed at the end of the perod, whle for exters, nputs and outputs are only observed at the start of the perod. As such, the growth rates of nputs, outputs, and productvty over a perod cannot be calculated for entrants and exters. For ths reason, recent emprcal studes often focused on contnung plants and gnored the effect of entry and ext (Basu and Fernald, 2002; Petrn and Levnsohn, 2012). In order to estmate the effect of entry and ext, t s assumed that a hypothetcal plant exsts whose nputs and outputs at the start of the perod s set equal to those of exters, and whose nputs and outputs at the end of the perod s set equal to those of entrants at the end of the perod. The contrbuton of entry and ext to aggregate MFP growth, labor productvty growth, and captal deepenng effect can be measured as the contrbuton of the hypothetcal plant to the wthnplant component n the decomposton. For example, the contrbuton of entry and ext to aggregate labor productvty s estmated as the dfference between the average labor productvty of the entry cohort at the end of a perod and that of the ext cohort at the start of the perod, multpled by ther average shares n aggregate output. Ths approach for estmatng the effect of entry and ext s consstent wth the approach proposed by Baldwn (1995) to estmate the effect of entry and ext. Baldwn argues that f the entrants essentally dsplace the exters, the effect of entry and ext should be evaluated by comparng entrants and exters Alternatvely, the effect of entry and ext s estmated separately (e.g., Grlches and Regev, 1995; Foster et al., 2001). The effect of entry on productvty s estmated from a comparson of an entry cohort wth average contnung plants or plants at the end of a perod and the effect of ext s obtaned from a comparson of an ext cohort wth average contnuers or plants at the start of a perod. The methods are equvalent to a method suggested by a referee that the effect of entry and ext can be derved by comparng aggregate productvty growth wth and wthout entry and ext. Baldwn and Gu (2011) show that the combned effects of entry and ext from those dfferent approaches are smlar for Canadan manufacturng, snce the sze of entry cohort s often smlar to the sze of ext cohort Internatonal Assocaton for Research n Income and Wealth 673

10 Revew of Income and Wealth, Seres 59, Number 4, December Data Ths paper examnes productvty growth n the Canadan manufacturng sector over two perods: and , and the causes of the slowdown that occurred. The plant-level data used n ths study come from Statstcs Canada s Annual Survey of Manufacturers (ASM) longtudnal fle, a database that covers the entre Canadan manufacturng sector usng both survey and admnstratve data, and permts plants to be tracked over tme. The ASM database has nformaton on shpments, value-added, employment, labor cost, heat and power costs, materal costs, exports, ownershp, and ndustry afflaton. Industry afflaton s at the dgt Canadan Standard Industral Classfcaton (SIC) from 1979 to 1999, and at the 6-dgt North Amercan Industry Classfcaton System (NAICS) from 1997 onwards. The two ndustry classfcatons are mapped to the 3- and 4-dgt NAICS ndustry classfcaton. For the emprcal analyss, we use value-added as a measure of output. 14 Ths value-added approach requres the assumpton that tme (used to proxy technology) and captal and labor nputs are separable from ntermedate nputs. 15 The real value-added at a plant s derved by deflatng the nomnal value-added by a value-added deflator at ndustry level taken from the Productvty Accounts of Statstcs Canada (Baldwn and Gu, 2009). The value-added deflator n the Productvty Accounts of Statstcs Canada s n turn constructed from a double deflaton of output and ntermedate nputs usng the chaned-tornqvst ndex. 16 Labor nput n the ASM fle s calculated as the sum of producton and non-producton workers. Captal nput s not avalable from the ASM fle, and t s estmated usng the assumpton that energy cost s proportonal to captal nput. Specfcally, t s estmated by allocatng captal nput of an ndustry at the 4-dgt NAICS ndustry classfcaton among the plants accordng to ther shares of heat and power costs. 17,18 Fgure 1 shows the number of plants, captal, labor, and real value-added n the total manufacturng sector from the ASM longtudnal plant fle. There were about 30,000 plants a year n the ASM fle before The number of plants n the ASM fle ncreased after 2000, as a result of the redesgn of the Annual Survey of 14 The value-added estmate constructed from the ASM fle used here ncludes the costs of purchased servces. Ths may generate an upward bas n the estmated labor productvty growth as purchased servces are ncreasngly substtuted for labor. But as shown n Table 1, the value added and labor productvty estmates from the ASM fle and the Productvty Program of Statstcs Canada show smlar trends over tme, and therefore the bas s lkely to be small and wll not affect our results on the sources of the declne n productvty growth after Whle the assumpton s restrctve, decomposton results based on gross output and value-added are smlar. 16 The data are avalable from Statstcs Canada CANSIM table Tomln (2010) used a smlar procedure to estmate captal stock of ndvdual plants. Estevadeordal and Taylor (2002) constructed a proxy for captal stock based on energy consumpton n ther emprcal test of factor abundance theory of trade. Energy costs are found to be hghly correlated wth captal costs across the manufacturng plants n the ASM mcro-fle, whch provdes emprcal support for the assumpton that energy costs are proportonal to captal stock. 18 Prevous studes assumed that energy costs are related to capacty utlzaton and used energy costs to proxy capacty utlzaton. Accordng to that assumpton, the varaton of captal stock estmated here may nclude the varaton of capacty utlzaton resultng n based parameter estmates. But as shown n the paper, energy costs are not related to capacty utlzaton and therefore the potental bas should be small Internatonal Assocaton for Research n Income and Wealth 674

11 Revew of Income and Wealth, Seres 59, Number 4, December 2013 Number of Plants 70,000 60,000 50,000 40,000 30,000 20,000 10,000 K, L A Sample sze Value-added (A) Labour (L) Captal (K) Fgure 1. Captal, Labor, Value-Added, and Number of Plants n Manufacturng Manufacturers over that perod. For the perod after 2000, there were between 50,000 and 60,000 plants a year n the ASM fle. The ASM survey now captures more small plants, whose data are derved from tax forms. The addtonal plants that the ASM captured after 2000 had a neglgble effect on the estmate of output and nputs, as shown n Fgure 1. To remove any potental bas that the ASM redesgn may have on the results, the decomposton of aggregate productvty growth nto wthn- and between-plant components and the effect of net entry s carred out separately for the two perods and Each perod s consstent wth regard to sample coverage. The growth rates of output, nputs, and productvty derved from the ASM mcro-fle are compared wth the aggregate statstcs from the KLEMS productvty database of Statstc Canada n Table 1. The ASM data and the KLEMS data exhbt smlar output and labor productvty growth rates durng the 1990s, and slghtly dfferent growth rates durng the post-2000 perod. They both show the same declne n labor productvty growth after The data from the ASM show that labor productvty growth declned from 3.7 percent per year to 1.7 percent per year from the perod to the perod. 19 The data from the KLEMS database show that labor productvty growth declned from 3.3 percent per year to 1.0 percent per year between those two perods Measures of Capacty Utlzaton To examne the extent to whch the declne n productvty growth came from a declne n capacty utlzaton, a measure of capacty utlzaton needs to be 19 The part of the dfference n the growth of value-added s due to the dfference n treatment of purchased servces. The value-added estmate from the ASM fle ncludes purchased servces, whle that form the Productvty Program of Statstcs Canada does not Internatonal Assocaton for Research n Income and Wealth 675

12 Revew of Income and Wealth, Seres 59, Number 4, December 2013 TABLE 1 Annual Growth Rates of Output, Captal, and Labor n Total Manufacturng ASM KLEMS Labor productvty Real value added Captal nput Labor nput Nomnal value added Captal ncome Labor ncome Source: The authors tabulaton from the Annual Survey of Manufacturers and CANSIM table constructed. As drect measures of capacty utlzaton are often not observable, prevous emprcal studes have used a number of proxes. Solow (1957) used unemployment rates for adjustng the changes n the utlzaton of both captal and labor. Jorgenson and Grlches (1967) used an ndex of electrc motor utlzaton n U.S. manufacturng to adjust captal utlzaton n the U.S. prvate economy. Other measures used nclude growth of materals (Basu, 1996), hours worked per worker (Basu and Fernald, 2001), the rato of energy costs to captal stock (Burnsde et al., 1995), and proft shares (Denson, 1979). As noted n Berndt and Fuss (1986), the use of ad-hoc proxes s unsatsfactory snce t lacks adequate theoretcal framework. An alternate measure has been developed by Berndt and Fuss (1986) and Hulten (1986) who show that the ex-post captal ncome compared wth ex-ante captal cost provdes a good measure of the utlzaton of captal. 20 They argue that an adjustment should be made to the prce of captal nput n the tradtonal growth accountng framework to take nto account the changes n capacty utlzaton. They show that the ex-post return on captal captures the effect of changes n capacty utlzaton. When the ex-post return on captal s used to measure the contrbuton of captal to output growth, MFP growth calculated as the dfference between output growth and the contrbutons of captal and other nputs s adjusted for changes n capacty utlzaton. As noted n a number of prevous studes, the procedure by Berndt and Fuss does not completely remove the cyclcal fluctuatons n the MFP growth assocated wth varable capacty utlzaton (e.g., Basu and Fernald, 2001). Gu and Wang (2012) buld upon the dea n Berndt and Fuss (1986) that the varaton n ex-post return to captal reflects the varaton n capacty utlzaton and argue that the ex-post return to captal should be used to adjust the quantty of captal nput rather than the prce of captal nput as n Berndt and Fuss (1986). They show that when the rato of ex-post to ex-ante return to captal s used to adjust the quantty of captal nput, the estmated MFP growth takes nto account the rate of captal utlzaton. 20 In rapdly growng ndustres, the value of margnal product of captal can be hgher than the ex-ante captal costs (Hulten, 1986) Internatonal Assocaton for Research n Income and Wealth 676

13 Revew of Income and Wealth, Seres 59, Number 4, December 2013 The approach developed by Berndt and Fuss (1986), Hulten (1986), and Gu and Wang (2012) requres an estmate of ex-ante return to captal at the plant level whch s not easy to construct. Therefore, the share of captal ncome n total value added wll be used here nstead. The alternatve used here should bear a close relatonshp to the Berndt Fuss measure snce the share of captal ncome wll be hghly correlated wth the rato of ex-post captal to ex-ante captal ncome. It s also related to Denson (1979) who used an ndex of corporate proft share n corporate natonal ncome to adjust captal nput for fluctuatons n ntensty of use. The log changes n capacty utlzaton rates as measured by the share of captal ncome n value added from the ASM are found to be postvely correlated wth the log changes n capacty utlzaton rates as measured by the rato of actual output to potental output from a survey of manufacturng frms across ndustres. 21 The correlaton s large and statstcally sgnfcant. The two capacty utlzaton rates also showed a smlar trend for the total manufacturng sector. It ncreased n the 1990s as manufacturng frms ncreased output to meet the ncreasng demand for ther outputs arsng from the mplementaton of the North Amercan Free Trade Agreement. It then declned after 2000 and the declne concded wth the apprecaton of the Canadan dollar relatve to the U.S. dollar, whch made Canadan products more expensve n the U.S. markets, and wth the U.S. recesson, whch resulted n lower demand for mported goods. As noted above, prevous studes used alternatve proxes for capacty utlzaton such as the rato of energy costs to captal stock and hours worked per worker. However, those proxes are found to be a poor measure of capacty utlzaton for the Canadan manufacturng plants over the last 20 years. The rato of energy costs to captal stock n the manufacturng sector ncreased durng the early 1990s when there was a deep recesson and declnes n capacty utlzaton. The hours worked per worker showed lttle fluctuatons over tme n the Canadan data. Whle not perfect, the rato of captal ncome to value-added proposed n ths paper provdes a good measure of capacty utlzaton based on the emprcal evdence presented here, and the theoretcal development of Berndt and Fuss (1986), Hulten (1986), and Gu and Wang (2012). 4. Emprcal Results Ths secton reports the results from the decomposton of aggregate labor and multfactor productvty growth for the total manufacturng sector. In the frst step, the parameters of the producton functon are estmated usng plant-level data to obtan estmates of the economes of scale and the effect of varable capacty utlzaton on labor productvty growth. In the second step, these parameter estmates are used n the decomposton formulae to break down aggregate productvty growth nto ts components. Alternatve econometrc technques are used to estmate the parameters to assess the senstvty of the results to alternatve estmaton technques. Fnally, the relatve contrbutons of exporters and non-exporters, and foregn- and domestc-controlled plants to aggregate labor productvty growth are measured n 21 The rato of actual output to potental output s taken from CANSIM table Internatonal Assocaton for Research n Income and Wealth 677

14 Revew of Income and Wealth, Seres 59, Number 4, December 2013 order to see whether the mpact of capacty utlzaton was greater n those producers most affected by the apprecaton of the Canadan dollar Producton Functon Estmaton Ths secton reports parameter estmates of scale economes and capacty utlzaton that wll be used to decompose aggregate productvty growth. The estmaton equaton s obtaned from rewrtng the frst-dfference equaton (5) n a level form: (13) lnv = α ln K + α ln L + aln e + δ + ( η + ν + m ), t K t L t t t t t where d t s a year effect. The equaton ncludes three error terms. h s an unobserved plant effect, n t s a possbly autoregressve productvty shock, and m t reflects serally uncorrelated measurement errors. The estmate of returns to scale s derved as the sum of the coeffcents on captal and labor nputs, a K and a L.As output s measured by value-added, only captal, labor, and capacty utlzaton are ncluded as ndependent varables. The equaton s estmated for each of 20 manufacturng ndustres usng the 3-dgt NAICS ndustry classfcaton. The SYS-GMM and Dfference-GMM estmaton methods are used to address the effect of the possble endogenety of the ndependent varables n the producton functon (Arellano and Bond, 1991; Blundell and Bond, 1998). For example, the endogenety of the capacty utlzaton varable arses when a negatve productvty shock leads to a loss n market shares of Canadan frms n nternatonal markets, whch n turn leads to the declne n nput utlzaton. Dfference-GMM transforms all varables by dfferencng, and uses lagged levels of the ndependent varables (captal, labor, and capacty utlzaton varables) as nstruments for frst-dfferenced varables. SYS-GMM makes an addtonal assumpton on the ntal condton process that s desgned to allow the ntroducton of more nstruments and mproves the propertes of the Dfference-GMM estmator. The dscusson n Secton 3.1 suggests that t s the change n the share of captal ncome n value added over tme that captures the change n capacty utlzaton. The cross-sectonal dfferences n the share of captal ncome n value added may not necessarly reflect the dfferences n capacty utlzaton. The capacty utlzaton varable and all other varables are therefore demeaned at the ndvdual plants before the estmaton. The sample used for estmaton conssts of all plants n the ASM longtudnal fle that exsted for at least fve years n the perod The sample of plants that exsted for at least 2 years, 10 years, or n all years durng the sample perod s also employed; the resultng estmates are smlar. The estmates of the degree of returns to scale and the effect of capacty utlzaton are presented n Table 2. The estmates are derved usng SYS-GMM and Dfference-GMM allowng for AR(1) error n the level equaton. 22 The 22 SYS-GMM and Dfference-GMM wth AR(1) error were employed. The Arellano Bond test does not reject the second-order and thrd-order seral correlaton n the dfferenced equaton. The Levnsohn Petrn estmaton technque (Levnsohn and Petrn, 2003) was also employed. But the estmated degree of returns to scale was unreasonably low n the latter. Ths may be due to the collnearty problem assocated wth Levnsohn Petrn estmaton as shown by Ackerberg et al. (2006) Internatonal Assocaton for Research n Income and Wealth 678

15 Revew of Income and Wealth, Seres 59, Number 4, December 2013 Industry TABLE 2 GMM Estmates of Returns to Scale and the Effect of Capacty Utlzaton on Output Growth Returns to Scale SYS-GMM Effect of Utlzaton Returns to Scale DIFF-GMM Effect of Utlzaton Food manufacturng Beverage and tobacco Textle and textle products Clothng manufacturng Leather and alled products Wood products Paper manufacturng Prntng and related actvtes Petroleum and coal products Chemcal manufacturng Plastcs and rubber products Non-metallc mneral products Prmary metal manufacturng Fabrcated metal products Machnery manufacturng Computer and electronc products Electrcal equpment Transportaton equpment Furnture and related products Mscellaneous manufacturng Average Arellano and Bond test of second-order and thrd-order seral correlaton both reject seral correlaton n the dfferenced equaton n most ndustres. But the Sargan test rejects the null hypothess that the overdentfyng restrctons are vald. As the Sargan test s prone to weakness, the results from the Sargan test may not necessarly mean that the nstruments n the GMM estmator are nvald. The average returns to scale s about 0.98 n the 20 manufacturng ndustres, ndcatng that, on average, constant returns to scale are present. Our estmates of returns to scale are smlar to the evdence from prevous studes (Basu et al., 2009; Dewert et al., 2011). The coeffcents on the nput utlzaton varable are all postve and statstcally sgnfcant at the 5% level. A hgher utlzaton of captal and labor nputs results n hgher output. 23 Equaton (13) s also estmated usng OLS. The OLS estmates are reported n Baldwn et al. (2012). 24 The estmated coeffcent on the capacty utlzaton varable s lower than the GMM estmate presented n Table 2. That s, the OLS estmator underestmates the coeffcent on the capacty utlzaton varable. As shown n Levnsohn and Petrn (2003), the drecton of bas n the estmated coeffcent on a varable (capacty utlzaton) from the OLS depends on the 23 When the unobserved productvty shocks are correlated wth capacty utlzaton, scale economes, and other ndependent varables, t s dffcult to separately ndentfy those effects. The GMM estmate provdes an dentfcaton of those effects by mposng approprate moment restrctons. 24 The OLS estmates n Baldwn et al. (2012) are obtaned usng a slghtly dfferent sample. When the same sample as the one used for the GMM estmaton s used, the results are smlar Internatonal Assocaton for Research n Income and Wealth 679

16 Revew of Income and Wealth, Seres 59, Number 4, December 2013 TABLE 3 Sources of Aggregate Labor Productvty Growth, Producton Possblty Fronter Approach less Annual average labor productvty growth Contrbuton from: Captal deepenng MFP growth Reallocaton of labor across ndustres Source: Authors tabulaton from the ASM fle. relatve strength of correlaton between productvty shocks and the capacty utlzaton varable and other varables ncludng captal and labor nput. The downward bas for the capacty utlzaton varable generated by OLS occurs when the correlaton between productvty shocks and the capacty utlzaton s lower than the correlaton between the productvty shocks and the other varables. For the rest of the paper, we wll present decomposton results usng the parameter estmates from the SYS-GMM estmaton technque. The decomposton results based on alternatve parameter estmates are very smlar Decomposton Results for Total Manufacturng Ths secton reports the decomposton estmates for aggregate labor and multfactor productvty growth and examnes the sources of the declne n aggregate productvty growth n the total manufacturng sector. Table 3 presents a decomposton of the aggregate labor productvty growth from the producton possblty fronter approach nto two man sources: the effect of aggregate captal deepenng, and the effect of aggregate multfactor productvty growth. Aggregate labor productvty growth n manufacturng declned from 3.7 percent per year durng the perod to 1.7 percent per year durng the perod The deceleraton n labor productvty growth can be attrbuted to the declne n MFP growth. The contrbuton of captal deepenng ncreased slghtly between the two perods. Table 4 presents the decomposton results for aggregate MFP growth and aggregate captal deepenng effect, whle Table 5 presents decomposton results for aggregate labor productvty growth. They are each decomposed nto the wthn-plant effect, the between-plant reallocaton effect, and the effect of entry and ext. The decomposton s carred out for the 20 ndustres at 3-dgt NAICS ndustry classfcaton, and then aggregated to the total manufacturng sector, usng ther shares of total nomnal value-added as weghts. Prevous emprcal studes have decomposed aggregate labor and multfactor productvty growth nto the effect of wthn-plant growth, between-plant reallocaton, and net entry. The decomposton results n Tables 4 and 5 extend those emprcal studes to provde a rcher understandng of the between- and wthnplant components. 25 Those results are presented n Baldwn et al. (2012) Internatonal Assocaton for Research n Income and Wealth 680

17 Revew of Income and Wealth, Seres 59, Number 4, December 2013 TABLE 4 Decomposton of Aggregate MFP Growth and Aggregate Captal Deepenng Effect less Decomposton of aggregate MFP growth Aggregate MFP growth Contrbuton of: Wthn-plant effect Wthn-plant MFP growth Scale economes Input utlzaton Between-plant effect Reallocaton of captal Reallocaton of labor Net entry Decomposton of aggregate captal deepenng effect Aggregate captal deepenng effect Contrbuton of: Wthn-plant effect Between-plant effect Net entry Notes: Aggregate MFP growth s the sum of drect effect and reallocaton effect where the drect effect s the sum of wthn-plant MFP growth, the effect of scale economes and nput utlzatons at ndvdual plants, and the reallocaton effect ncludes the effect of reallocaton of labor and the effect of reallocaton of captal. Source: Authors tabulaton from the ASM fle. TABLE 5 Decomposton of Aggregate Labor Productvty Growth less Aggregate labor productvty growth Wthn-plant effect MFP growth Scale economes Input utlzaton Captal deepenng Between-plant effect Reallocaton of captal on MFP Reallocaton of labor on MFP Reallocaton effect on captal deepenng Net entry Notes: Aggregate labor productvty growth s the sum of wthn-plant effect, between-plant effect, and the effect of net entry. The aggregate labor productvty growth may dffer from the sum of those three components. The dfference reflects the effect of reallocaton of labor across ndustres on aggregate labor productvty growth. Source: Authors tabulaton from the ASM fle. Consstent wth the emprcal evdence from the prevous studes, the results n Tables 4 and 5 show that the aggregate labor and multfactor productvty growth can manly be attrbuted to the growth occurrng wthn ndvdual plants, but reallocaton s mportant. The between-plant reallocaton s especally mportant for the aggregate MFP growth n the perod , accountng for more than half of the 0.5 percent growth n the aggregate MFP growth for that perod. The 2013 Internatonal Assocaton for Research n Income and Wealth 681