Review of Economic Dynamics

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1 Revew of Economc Dynamcs 16 (2013) Contents lsts avalable at ScVerse ScenceDrect Revew of Economc Dynamcs wwwelsevercom/locate/red Factor market dstortons across tme, space and sectors n Chna Loren Brandt a,trevortombe b, Xaodong Zhu a, a Unversty of Toronto, Canada b Unversty of Calgary, Canada artcle nfo abstract Artcle hstory: Receved 16 March 2011 Revsed 3 October 2012 Avalable onlne 12 October 2012 JEL classfcaton: O11 O47 O53 Keywords: Factor markets Dstortons Total factor productvty Chna In ths paper, we measure TFP losses n Chna s non-agrcultural economy assocated wth labour and captal msallocaton across provnces and sectors between 1985 and 2007 We also decompose the overall loss nto factor market dstortons wthn provnces (between state and non-state sectors) and dstortons between provnces (wthn sectors) Over the entre perod, msallocaton lowers aggregate non-agrcultural TFP by an average of twenty percent However, after ntally declnng, these losses ncreased apprecably begnnng n the md-1990s Ths reversal can be attrbuted almost exclusvely to ncreasng msallocaton of captal between state and non-state sectors wthn provnces, whle losses from between provnce msallocaton remaned farly constant We argue that the recent ncrease n captal market dstortons s related to government polces that encourage nvestments n the state sector at the expense of nvestments n the more productve nonstate sector 2012 Elsever Inc All rghts reserved 1 Introducton Some of the rapd growth that Chna has enjoyed the last three and a half decades has lkely come from reductons n dstortons as a result of economc reform An mportant feature of Chna s pre-reform economy was a hgh degree of local autarky At the provncal level, self-suffcency n both agrculture and ndustry were aggressvely pursued, and renforced through lmted nvestment n transportaton nfrastructure (Donnthorne, 1972) These polces were coupled wth tght restrctons on labour moblty both wthn and between provnces through the household regstraton or hukou system and strct control over the allocaton of captal through the use of admnstratve credt plans Wth the onset of economc reform n the late 1970s, some of the restrants on resource moblty perssted In addton to restrctons on the moblty of labour out of the countrysde (Chan et al, 2008), local protectonsm and trade barrers arose to mpede the nter-regonal flow of goods (Young, 2000; Poncet, 2003) A credt plan contnued to be used to ensure access to new loans by stateowned frms (Brandt and Zhu, 2000), the effects of whch were renforced by barrers to the flow of captal across regons (Boyreau-Debray and We, 2005; Dollar and We, 2007) We thank the guest edtors for the ssue, Dego Restucca and Rchard Rogerson, and two anonymous referees for very valuable comments and suggestons We also thank Abhjt Banerjee, Steve Davs, Martn Echenbaum, Dong He, Aloysus Sow, Mchael Zheng Song, Kjetl Storeslettern, Danel Y Xu, Denns Yang and Shang-Jn We for helpful dscussons We have also benefted from comments by semnar partcpants at Chnese Unversty of Hong Kong, Federal Reserve Banks at Mnneapols and San Francsco, Hong Kong Insttute for Monetary Research, Ryerson Unversty, Shangha Unversty of Fnance and Economcs, Southwest Unversty of Fnance and Economcs, Unversty of Mchgan, Unversty of Toronto, Unversty of Vrgna, Wlfrd Laurer Unversty, and by partcpants at the 2010 Chna Economc Summer Insttute, 2010 NBER Chna Workng Group Meetng, 2011 European Economc Assocaton Meetngs n Oslo, 2011 SED Mn-conference on Msallocaton n Ghent, and 2011 Tsnghua Workshop n Macroeconomcs Part of ths paper s research was done whle Xaodong Zhu was a research fellow at the Hong Kong Insttute for Monetary Research and he s grateful to the nsttute s generous fnancal support * Correspondng author E-mal addresses: brandt@chassutorontoca (L Brandt), ttombe@ucalgaryca (T Tombe), xzhu@chassutorontoca (X Zhu) /$ see front matter 2012 Elsever Inc All rghts reserved

2 40 L Brandt et al / Revew of Economc Dynamcs 16 (2013) The general presumpton s that many of these barrers have now been sgnfcantly relaxed For example, the stock of non-hukou mgrants s currently n upwards of 150 mllon, half of whch have crossed a provncal boundary In addton, annual hukou mgraton averages 20 mllon per year There have also been sgnfcant ncreases n nter-regonal trade accompanyng a reducton n barrers (Holz, 2009; Holz, n press) Reform n the bankng system datng from the late 1990s, ncludng the development of an nter-bank market, may be allowng a more effcent regonal allocaton of captal through the nter-bank market and other channels Possbly offsettng these tendences s the fact that the state contnues to exercse consderable nfluence on the allocaton of factors of producton land, labour and captal (World Bank, 2012) that s reflected n dfferences n productvty across regons and forms of ownershp A majorty of nvestment resources contnues to be drected by Chna s hghly regulated fnancal system to state-owned frms and actvtes n whch the local governments are often a benefcary (Walter and Howe, 2011) Snce the late 1990s, there have also been efforts through such polces as Xbu Kafa (Develop the Great West) to redress perceved polcy bases n favour of coastal provnces by reallocatng nvestment resources towards the nteror regons Persstent dfferences n returns to captal and labour between the state and the non-state sectors have recently been documented by Brandt and Zhu (2010) and Kamal and Lovely (2012) Gven these opposng developments, t s mportant to measure the overall mpact of factor market dstortons n Chna and examne ther evoluton over tme In a recent paper, Hseh and Klenow (2009) nvestgate the mpact of factor msallocaton across frms wthn four-dgt manufacturng ndustres on aggregate total factor productvty (TFP) n Chna and Inda, usng an approach proposed by Restucca and Rogerson (2008) They found that a more effcent factor allocaton contrbuted to around 2 percent a year aggregate TFP growth n Chna s manufacturng sector between 1998 and 2005 In ths paper, we follow ths approach, but examne factor msallocaton and ts mpact on TFP at a more aggregate level, between provnces and between the state and the non-state sectors n Chna s non-agrcultural economy, whch ncludes both manufacturng and servces We focus on factor msallocaton at ths level of aggregaton because, as we dscussed above, there are sgnfcant barrers to factor moblty across regons and forms of ownershp n Chna Our analyss also covers a longer perod, from 1985 to 2007, so that we can examne the evoluton of factor msallocaton over tme Fnally, we decompose the overall TFP loss nto the losses due to between-provnce and wthn-provnce nter-sectoral dstortons Our man results are the followng: On average, the msallocaton of factors across provnces and sectors resulted n a reducton of non-agrcultural TFP of at least 20%, wth the wthn-provnce dstortons accountng for more than half of the total loss TFP losses from between-provnce dstortons were relatvely constant over the entre perod Despte sgnfcant nter-provncal labour flows, the TFP loss from between-provnce labour market dstortons remans hgh due to an ncrease n the cross-provnce dsperson n TFP The measure of wthn-provnce dstortons declned sharply between 1985 and 1997, contrbutng to 052% nonagrcultural TFP growth per year, but then ncreased sgnfcantly n the last ten years, reducng the non-agrcultural TFP growth rate by 05% a year Almost all of the wthn-provnce dstortons was due to the msallocaton of captal between the state and the non-state sectors, whch ncreased sharply n recent years The magntude of average TFP loss due to factor msallocaton that we estmate (20%) for the non-agrcultural economy s slghtly lower than the estmate of Hseh and Klenow (30%) for the manufacturng sector A more mportant dfference between our estmate and Hseh and Klenow s s the trend after 1997 They found that the mpact of dstortons declned for the manufacturng sector, whle we fnd the mpact of dstortons ncreased for the non-agrcultural sector as a whole Hseh and Klenow only measure the mpact of wthn-ndustry msallocaton for the manufacturng sector alone, suggestng two potental reasons for the dfference n results: (1) ncreased between-ndustry dstortons for the manufacturng sector; and (2) ncreased dstortons wthn the servce sector and between the manufacturng and servce sectors We do not have data that would allow us to separate servces from manufacturng actvtes Also note that Hseh and Klenow study mcro-dstortons between ndvdual producers whle we focus on sectoral and geographc aggregates Our result of the ncreasng mpact of factor market dstortons (especally the msallocaton of captal between the state and the non-state sector) snce 1997 s robust to alternatve specfcatons of the model and alternatve parameter values that we use to measure the dstortons It provdes quanttatve evdence for the vew that Chna s captal markets have become more dstorted n recent years Gven the rapd growth of the Chnese economy snce 1997, ths result may come as a surprse However, the problem has been wdely recognzed wthn Chna, wth ongong debate over Guojn Mntu (the state advances, the prvate sector retreats), and dscussed outsde by poltcal scentsts and fnancal practtoners (see, for example, Huang, 2008, and Walter and Howe, 2011) Ths paper s part of a recent lterature that nvestgates the mpact of msallocaton of factors, ether across sectors or across frms wthn sectors or ndustres, on aggregate productvty Among many others, Golln et al (2004), Restucca et al (2008), Vollrath (2009) and Song et al (2011) analyze the sectoral dmenson whle Alfaro et al (2008), Banerjee and Duflo (2008), Guner et al (2008), Restucca and Rogerson (2008), Bartelsman et al (2009) and Hseh and Klenow (2009) focus on the msallocaton across frms wthn a sector Adamopoulos and Restucca (2011) examne the mpact of msallocaton across producton unts wthn agrculture on msallocaton between the agrcultural and non-agrcultural sector Lke us, Song et al (2011) also emphasze the wedges n the returns to captal between the state and the non-state sectors However,

3 L Brandt et al / Revew of Economc Dynamcs 16 (2013) they do not consder factor allocaton across provnces nor quantfy the TFP loss assocated wth dstortons, whch s the focus of our paper Several exstng studes have used separate measures of dsperson n the ndvdual returns to labour and captal to study Chna s factor market dstortons Boyreau-Debray and We (2004), Dollar and We (2007), and Ba et al (2006), for example, examne the dsperson n returns to captal Gong and Xe (2006) and Zhang and Tan (2007) look at the dspersons n returns to labour as well as n returns to captal, but separately Whle these measures are nformatve about factor market dstortons, there s no clear lnk between them and aggregate TFP The rest of the paper s organzed as follows In Secton 2, we present the theoretcal framework for measurng factor market dstortons and n Secton 3, dscuss data used for emprcal analyss We present the emprcal results n Secton 4 and provde dscussons on the man results n Secton 5 Fnally we extend our analyss by ncorporatng nfrastructure and human captal n Secton 6 and Secton 7 concludes 2 A framework for measurng factor market dstortons In ths paper, we consder a statc allocaton problem For each year, we take total employment and total captal stock as gven and examne the allocaton of the two factors across provnces and between the state and non-state sectors Consder an economy wth m provnces, ndexed by = 1,,m, and two sectors, state and non-state, ndexed by j = s,n, respectvely We assume Cobb Douglas producton technologes wth the same factor elastctes n all provnces and sectors 1 : Y j = A j L a j K 1 a, 0 < a < 1 (1) j Here Y j, L j, K j and A j are the real GDP, employment, captal stock and TFP n provnce and sector j It s mportant to note that Y j s the real GDP and A j s the quantty TFP To measure them we need provncal and sectoral deflators n addton to measures of nomnal GDP, employment and captal stock Whle we have estmates of provncal deflators, no data on sectoral deflators are avalable To deal wth ths problem, we follow Hseh and Klenow (2009) s approach and nfer the sectoral prce nformaton from nomnal value-added shares by usng a product market equlbrum condton that we wll dscuss n Secton 23 below The exact procedure wll be dscussed n Secton 42 We assume that provncal GDP s a CES aggregate of goods produced n the two sectors and the aggregate GDP s a CES aggregate of provncal GDPs: and Y = ( Y n ( Y = + Y s ) 1 ) 1 1 ω Y 1 (3) =1 Here 1 and 1 are the elastctes of substtuton among sectors and provnces, respectvely, and ω s provnce s weght n aggregate GDP Note that the state and non-state sectors output appear symmetrcally n the provncal GDP functon wthout weghts We make ths assumpton manly because both the state and non-state frms are present n most ndustres and produce smlar (but possbly dfferentated) products To avod the result that absent dstortons all factors flow to the provnce and sector wth the hghest TFP level, we assume that the goods across sectors and regons are mperfect substtutes, e, postve and 2 21 Factor allocaton and aggregate TFP Let L = L n + L s and K = K n + K s be the employment and captal stock n provnce and L = =1 L and K = =1 K be the total employment and total captal stock Let l j = L j /L, k j = K j /K, l = L /L, and k = K /L be the shares of employment and captal Factor allocaton across provnces and sectors s determned by a set of these shares, {l, k,l j, k j } =1,,m; j=n,s, whch we smply call an allocaton For a gven set of provnce-sector specfc TFPs, A j, = 1,,m, j = n, s, the followng two equatons show how we can calculate the provncal and aggregate TFP for any gven allocaton: + Y ] 1 /( ) [( ) L a n K 1 a = As l a ( ) s k1 a s + An l a ] 1 n k1 a, n A = [ Y s [ A = =1 ω Y 1 ] 1 1 /( L a K 1 a) = [ m =1 ] 1 1 ( ) ω A l a 1 k1 a (2) 1 Usng factor shares of US ndustres and the ndustry composton of each Chnese provnce and sector, we calculated the weghted average factor shares of Chnese provnces and sectors Average labour shares are very smlar across provnces, and slghtly hgher n the state sector than n the non-state sector Detals on the calculaton are provded n the supplementary materal We wll dscuss the mplcaton of relaxng the equal factor elastcty assumpton n Secton 6 2 Alternatvely, we could have assumed these goods are perfect substtutes but there are dmnshng returns

4 42 L Brandt et al / Revew of Economc Dynamcs 16 (2013) We call the allocaton that maxmzes the aggregate TFP (or, equvalently, the aggregate output) the effcent allocaton and the correspondng aggregate TFP the effcent TFP If there are factor market dstortons, the actual allocaton may devate from the effcent allocaton and the actual aggregate TFP may be lower than the effcent TFP We use the resultng TFP loss as a measure of the cost of factor market dstortons In the rest of ths secton, we wll dscuss the effcent allocaton, the compettve allocaton under factor market dstortons, and the dentfcaton and measurement of the dstortons 22 Effcent allocaton and TFP losses from dstortons The effcent allocaton s the soluton to the followng socal planner s problem: max Y L j,k j subject to (1), (2), (3) and L j = L,, j K j = K, j (4) (5) Proposton 1 For any gven L and K, the allocaton that maxmzes the aggregate GDP s gven by: L j L = K j K = π j, L L = K K = π, where and π j = π = ( ) Aj A = ω 1 (A ) 1 =1 ω 1 (A ) 1 As Aj, + An, A = [ As + A n ] Proof All proofs of propostons n ths paper are gven n the supplementary materal 3 Proposton 1 says that to maxmze output, the share of captal and labour allocated to a sector and provnce should equal the TFP share n the sector and provnce, as defned by π j and π Under the effcent allocaton, t can be shown that A s the provncal TFP and aggregate TFP s [ m ] A = ω 1 1 ( ) 1 A =1 For any gven allocaton and the assocated aggregate and provncal TFP A and A, we can then measure proportonal TFP losses due to dstortons n the aggregate and n a provnce as follows: D = ( ln A ) /A and D = ( ln A ) /A 3 Also avalable onlne at:

5 L Brandt et al / Revew of Economc Dynamcs 16 (2013) Factor allocaton n a compettve market wth dstortons We consder three dstortons: provnce-specfc output wedges and sector-provnce specfc captal and labour wedges Whle there are other equvalent ways of ntroducng dstortons, our choce s motvated by the emprcal evdence on provnce-sector dfferences n returns to labour and captal and geographcal dfferences n prces that have been documented by the references we dscussed n the ntroducton 231 Frms problem The proft maxmzaton problem for producng the aggregate GDP, Y, s { ( P ) 1 1 max ω Y 1 Y, =1,,m =1 =1 whch mples the followng frst order condtons: ( Y τ y P = ω P Y m ), = 1,,m τ y P Y } Here τ y s a wedge between margnal cost and margnal revenue of usng Y n aggregate producton We wll smply call t the output wedge of provnce The proft maxmzaton problem of producng Y s { ( max P Y s Y s, Y n + Y ) 1 } n P s Y s P n Y n and the correspondng frst-order condtons are (6) ( ) Yj P j = P, j = s,n; = 1,,m (7) Y Note that we have assumed that there are no sector-specfc output wedges We make ths assumpton because we do not have data to dentfy them separately However, the allocaton of factors across sectors may stll be dstorted because of wedges n factor markets Usng the defnton of Y and Y, t can be shown that and Here, P = ( 1 P s ( P = =1 P = τ y P ω 1 + P P 1 n 1 ) 1 (8) ) 1 The stand-n frm s proft maxmzaton problem n provnce and sector j s { max P j A j L a j K 1 a j K j, L j τ l j wl j τ k j rk j} Here, w s the wage, r s the rental prce of captal, and τ l j and τ k j are labour and captal wedges, respectvely The standard frst-order condtons of the problem are: (9) (10) ap j A j L a 1 K 1 a = τ l j j j w, (1 a)p j A j L a j K a j = τ k j r (11) (12) Defnton 1 For any gven set of wedges {τ y, τ l j, τ k j } =1,,m; j=n,s, the compettve equlbrum s a set of prces {P, P, P j } =1,,m; j=n,s, output {Y, Y, Y j } =1,,m; j=n,s, employments and captal stocks {L j, K j } =1,,m; j=n,s such that Eqs (1) to(12) hold The correspondng set of shares of employment and captal stock {l, k,l j, k j } =1,,m; j=n,s s called the compettve allocaton mplemented by the set of wedges {τ y, τ l j, τ k j } =1,,m; j=n,s

6 44 L Brandt et al / Revew of Economc Dynamcs 16 (2013) Proposton 2 Gven any set of postve wedges {τ y, τ l j, τ k j } =1,,m; j=n,s,let and τ l j = τ y τ l j, à j = τ la j A j k1 a τ j ( à τ l s = τ l 1 s Ãs ( τ l =1 = ω 1 =1 ω 1 τ k j = τ y τ k j,, à = [ Ãs + à + à 1 à à n n τ l 1 n τ l à n ], ) 1, τ k = ( à ) 1, τ k = ( =1 ω 1 s τ k 1 s Ãs =1 ω 1 1 à à + à + à n n τ k 1 1 Then, the compettve allocaton mplemented by the set of wedges s unquely determned by the followng equatons: and l j = Ãs ω 1 Ãj τ l 1 j τ l 1 s 1 à l = ω 1 =1 à + à n τ l 1 1, k j = τ l 1 n τ l 1, k = ω 1 Ãs =1 ω 1 1 à Ãj τ k 1 j τ k 1 s à τ k à n τ k 1, τ k 1 n τ k 1 n ) 1 ) 1, Furthermore, the correspondng provncal and aggregate TFP are gven by the next two equatons: and A = à τ la τ k1 a, A = [ m =1 ω 1 à 1 ] 1 τ la τ k1 a Proposton 2 shows how one can calculate the compettve allocaton and correspondng provncal and aggregate TFP for any gven set of wedges The proposton also shows that the compettve allocaton s a functon of the product of output wedges and factor market wedges, whch mples that the output wedges cannot be separately dentfed by usng the factor allocaton alone Wth nformaton on provncal prce levels, however, both output wedges and factor market wedges can be dentfed up to a scalar 24 Identfcaton of wedges Proposton 3 Let (P 1,,P m ) be an arbtrary vector of postve numbers For any allocaton {l, k,l j, k j } =1,,m; j=n,s,there exsts a set of wedges such that the allocaton s the compettve allocaton mplemented by the set of wedges and that P /P j s the equlbrum relatve prce between provnce and provnce j for any, j = 1,,m Two sets of wedges {τ y, τ l j, τ k j } =1,,m; j=n,s and {θ y,θ l j,θk j } =1,,m; j=n,s mplement the same compettve allocaton and the same relatve prces across provnces f and only f there exsts some postve constants, α, β and γ such that θ y = ατ y, θ l j = βτ l j and θk j = γ θk j Proposton 3 shows that we can dentfy the wedges (up to a scalar) from the actual allocaton of labour and captal and the provncal prce levels More specfcally, from Eqs (11) and(12), we have τ l j P jy j, L j τ k j P jy j, K j and from (6), τ y P 1 ( ) P ω Y P (13) (14) (15)

7 L Brandt et al / Revew of Economc Dynamcs 16 (2013) From Proposton 2 we know that factor allocaton s not affected by any proportonal change n wedges that s common across all provnce and sectors So we can smply set the labour and captal wedges as average value products of labour and captal, respectvely Smlarly, we can set the output wedge to be the term on the rght-hand sde of Eq (15) 3 Data In order to generate measures for the Chnese economy of dstortons n factor allocaton derved above, data at the provnce-level for both the state and non-state sectors are requred We consder only non-agrcultural sectors of Chna s economy and, therefore, all aggregate varables n the model correspond only to non-agrcultural data Unfortunately, the NBS (Natonal Bureau of Statstcs) does not provde nformaton for all the key varables we need, and for others there are measurement ssues Consequently, we construct our own unque panel data set that spans the perod between 1985 and 2007 and covers 27 out of 31 provnces n manland Chna 4 Ths secton hghlghts key procedures and sources 5 31 Employment The NBS reports employment totals at the provnce level, wth breakdowns provded between agrculture (prmary) and non-agrculture (non-prmary) and state and non-state 6 There are several mportant shortcomngs wth the offcal data Frst, the provncal employment estmates do not aggregate to reported natonal employment Second, provncal employment estmates often nclude mgrants n ther provnce of resdence (or hukou) rather than n the provnce n whch they work By 2005, the mgrant populaton exceeded 150 mllon, half of whch was out of provnce Thrd, employed persons nclude those unemployed Fourth, employment n the prmary (non-prmary) sector s lkely overstated (understated) And ffth, employment n the state sector s often not reported drectly as state employment We use census mcro-data records from 1982, 1990, 1995, 2000, and 2005 to deal wth the frst three problems 7 Dfferences between total provncal employment and reported natonal employment are dstrbuted amongst provnces n a manner consstent wth the dstrbuton of employment found n the census Next, we utlze alternatve estmates of the share of the labour force n the prmary sector made by Brandt and Zhu (2010) to adjust offcal provncal prmary employment 8 Fnally, from 1993 onwards, some of the former state-owned frms have been reclassfed as shareholdng corporatons We nclude employment n these corporatons as state employment Note that all adjustments to provncal employment data, wth the excepton of that to provncal state sector employment, are effectvely adjustments to employment n the non-state sector In other words, we take state sector (and shareholdng) employment as offcally reported, and calculate non-state sector employment as the resdual from our revsed estmates of employment n the non-agrcultural sectors after subtractng off the broadly defned state employment It s wdely agreed that the NBS does a much better job of collectng data n the state sector than t does outsde 9 32 Captal stocks We construct captal stock estmates wth a perpetual nventory method usng annual fxed nvestment data reported by the NBS These data are reported by provnce, and wth breakdowns between prmary and non-prmary, and state and non-state After 1993, fxed nvestment by shareholdng companes s reported separately, and after 2005, fxed nvestment by lmted lablty corporatons s also reported separately Investments by these corporatons are added to that by the state sector 10 Investment data are deflated usng offcal provnce-level prce ndexes of nvestment goods for the perod Pror to 1993, however, such provncal data are not avalable Instead, we construct an out-of-sample forecast of prncpal asset deflators based on a regresson of provncal asset prce deflators on GDP deflators, the natonal asset prce ndex, and year and provnce fxed effects Assumng a deprecaton rate of 7%, nvestment growth rates over the lfe of a provnce are used to generate ntal captal values for Our estmates of annual real fxed nvestment are then used to calculate captal stock n subsequent years These totals are rescaled proportonately across provnces so that the total state and non-state captal stocks equal the total natonal levels as determned by Brandt and Zhu (2010) We perform ths re-scalng snce, begnnng n the md-to-late 4 Chongqng, whch was part of Schuan untl 1997, s merged wth Schuan; Tbet, Hanan, and Hunan are excluded for mssng data; for a number of provnces (Tanjn and Inner Mongola, manly) we are mssng selectve nformaton between 1978 and 1984, and so results are only reported for the perod 5 Tables of raw data are provded n an appendx to ths paper that wll be made avalable upon request 6 Employed persons s dstnct from staff and workers, whch only cover part of the urban workers 7 Data are nterpolated between census years Rates of growth for 1982 to 1990 are used to project estmates back to 1978, whle data between 2000 and 2005 are used to forecast totals for 2006 and Specfcally, the correcton factor appled to each provnce s based on the rato of reported natonal reported prmary sector employment share relatve to the share n Brandt and Zhu (2010) arrved at through household-level surveys Provnce-specfc adjustment factors would be deal but we lack approprate data 9 On data ssues, see Holz (2009), Holz (n press) and Ortk (2011) 10 These subcategores of nvestment are found n the Fxed Asset Investment Yearbooks of Chna 11 All provnces have an ntal year of 1978, except for Tbet and Chongqng, whch begn n 1992 and 1996, respectvely

8 46 L Brandt et al / Revew of Economc Dynamcs 16 (2013) s, Chna prvatzed many of ts small and medum-szed SOEs We utlze nformaton on the total number of SOEs, and the number of frms that were prvatzed each year to adjust the natonal captal stock n the state and non-state sectors Lackng frm-level nformaton on the captal stock, we assume that the prvatzed frm s share of the total state sector captal stock s proportonal to ther share of the total number of SOEs Snce these frms were typcally small to medum n sze, ths procedure lkely over-estmates the change n assets assocated wth the prvatzaton Informaton on prvatzaton of SOEs s not avalable by provnce Our rescalng of provncal captal stocks to match aggregate fgures effectvely assumes that prvatzaton of state sector assets n a provnce s proportonal to the provnce s share of total state sector assets 33 GDP and GDP deflators Chna s NBS annually reports nomnal GDP levels and real GDP growth for each provnce but not real GDP levels These are reported separately for agrculture, manufacturng, and servce sectors To construct real non-agrcultural GDP for each of Chna s provnces between 1978 and 2007, we use nformaton on nomnal non-agrcultural GDP, real non-agrcultural GDP growth rates, and prce level dfferences n 1990 We frst proportonately re-scale reported nomnal non-agrcultural GDP values n every year such that the sum across provnces equals the natonal total Reported year-over-year real growth rates for each provnce are used to construct the growth rate of each provnce s GDP deflator Specfcally, ths s gven by the rato of the gross nomnal growth to the real growth rates To capture level dfferences n our base year (1990), the 1990 GDP deflator s set equal to each provnces cost of a common basket of goods relatve to the natonal average The costs of these baskets are taken from Brandt and Holz (2006) Wthn non-agrculture however, the NBS does not provde a complete breakdown for GDP between the state and nonstate sectors Followng the methodology of Brandt and Zhu (2010), we approxmate the relatve GDP-per-worker by relatve wages Ths mples that each sector s share of non-prmary GDP s dentcal to ther share of the total wage bll Detaled wage data for state and non-state sectors, ncludng townshp and vllage enterprses, are used to construct estmates for relatve wages 12 We test our estmaton method by applyng t to Chna s manufacturng sector for the perod between 1998 and 2007, durng whch we have detaled frm level data and therefore can calculate value-added by ownershp drectly For the whole perod, the average state sector s share of value added s 053 and the average share mpled by our estmaton s Emprcal analyss In ths secton, we use the model of Secton 2 wth data descrbed n Secton 3 to estmate the magntude of, and TFP losses assocated wth, factor market dstortons n Chna To be clear, we are nvestgatng only non-agrcultural actvtes n Chna References to sectors should also be understood as state and non-state sectors, not partcular ndustres 41 Parameter choces In addton to the provncal weghts ω, = 1,,m, there are three parameters n the model: the output elastcty a, and the nverse of elastcty of substtuton of output across provnces and between sectors, and Brandt and Zhu (2010) report that the labour share n Chna s around 05 Due to factor market dstortons, however, the labour share s generally not equal to the output elastcty of labour We follow Hseh and Klenow (2009) by assumng that the technology parameter s the same as that n the US and set the output elastcty of labour a to 067 There are no avalable estmates of and n the lterature We choose 067 as the value for both parameters Ths mples that the elastctes of substtuton across provnces and between sectors are both 15, whch s the value commonly used n the nternatonal real busness cycle lterature and s much lower than the values that are used n the trade lterature (see, eg, Ruhl, 2008) We choose ths low value of elastcty to be on the conservatve sde n our estmate of the TFP loss from msallocaton Wth hgher values for these elastctes (and therefore lower values for and ), the estmated TFP loss n Chna would be larger For the provncal weghts, we choose ω such that Eq (6) holds on average over the entre perod of f there were no product market dstortons Specfcally, we set ω as follows: ω = t=1985 ( P (t)y ) (t) =1 P (t)y (t) We wll also report results when we use alternatve values of a, and and provncal weghts As t turns out, our man results are robust to the choces of parameter values (16) 12 Total and state-sector employment and wages, by provnce, for years pror to 1995 are taken from Chna Regonal Economy Statstcs For later years, we utlze the Labour Statstcs Yearbook of Chna and the Statstcal Yearbook of Chna

9 L Brandt et al / Revew of Economc Dynamcs 16 (2013) Table 1 Total factor productvty for selected years by provnce and sector Provnce Aggregate State Non-state Anhu Bejng Fujan Gansu Guangdong Guangx Guzhou Hebe Helongjang Henan Hube Inner Mongola Jangsu Jangx Jln Laonng Nngxa Qngha Shaanx Shandong Shangha Shanx Schuan Tanjn Xnjang Yunnan Zhejang By regon East Mddle Northeast West Measurng TFP by provnce and sector To measure dstortons, we need to have measures of provnce- and sector-specfc TFP, A j, for all provnces and sectors To measure ths drectly, we need provnce- and sector-specfc deflators However, we only have deflators by provnce Thus, we need to adjust for the sectoral prce dfferences n each year Usng a method smlar to Hseh and Klenow (2009), we nfer the prce nformaton from nomnal value-added shares Wth the CES aggregate producton functons, t can be shown that the prces satsfy the followng equatons: ( P j (t)/p (t) = Y nomnal s Y nomnal (t) j (t) + Y nomnal n (t) ) Thus, we can calculate the real value-added for each sector and provnce n the followng way 13 : Y j (t) = Y nomnal j (t) = Y nomnal ( j (t) Y nomnal ) j (t) P j (t) P (t) Y nomnal (t) + Y nomnal (t) s n We use ths measure of real value-added by sector and provnce, along wth employment and captal data, to estmate TFP from Eq (1) Table 1 lsts the TFP of the non-state and state sectors for each of the 27 provnces n 1985, 1997 and 2007 Fg 1 also shows box plots of non-agrcultural TFP of the state and the non-state sectors across the 27 provnces for all years between 1985 and 2007 In general, the TFP levels n the non-state sector are hgher than those n the state sector and the gaps have ncreased over tme There are also sgnfcant dfferences n TFP across provnces especally n the state sector These TFP dfferences mply that the effcent allocaton should have more captal and labour be allocated to the non-state sector and to provnces wth hgher TFP levels Devatons from the effcent allocaton wll lead to lower TFP 13 Note that when = = 0, the case of perfect substtuton, the actual GDP s smply the measured GDP and therefore, the measured TFP s also the actual TFP In the case of mperfect substtuton, however, the two are not the same

10 48 L Brandt et al / Revew of Economc Dynamcs 16 (2013) Fg 1 Box plot of total factor productvty Note: Ths box plot llustrates, for each year and sector, the log provncal TFP All values are rescaled relatve to the lowest observed value The dark boxes gve the nter-quartle range across provnces for a gven year The medan s the whte lne wthn each dark box The bottom and top ends of the thn whsker mark the 5th and 95th percentles, respectvely The fgure llustrates the generally constant TFP n the state sector n all provnces In the non-state sector, TFP s contnuously ncreasng and the cross-provnce dsperson s generally declnng Fg 2 Productvty over tme Note: Ths plots the observed aggregate non-agrcultural TFP n Chna over tme wth the model-mpled effcent TFP The ncreasng gap between the two lnes llustrates the aggregate effect of the dstortons 43 The evoluton of factor market dstortons over tme We now examne the mpact of msallocaton of factors on aggregate non-agrcultural TFP Fg 2 plots the actual and effcent aggregate TFP, A and A, respectvely Throughout the perod between 1985 and 2007, there s a persstent and sgnfcant gap between the actual and effcent TFP, suggestng that there has been persstent msallocaton of factors n Chna Usng our measure of dstortons, D = ln(a /A), the average level of factor market dstortons for the entre perod s 020 In other words, on average the actual TFP s around 20% lower than the effcent TFP The gap between the actual and effcent TFP narrowed n the frst decade or so, but wdened afterwards Correspondngly, the measured level of factor market dstortons was 024 n 1985, 018 n 1997 and 023 n 2007

11 L Brandt et al / Revew of Economc Dynamcs 16 (2013) Table 2 Dstortons and TFP growth over tme, aggregate Perod Average dstorton Average effcent TFP growth 646% 644% 649% Average actual TFP growth 652% 695% 599% Impact of dstortons: actual effcent 006% 052% 050% Table 3 Dstortons and TFP growth over tme, by regon Regon Average wthn provnce dstorton Average actual TFP growth TFP growth dfferental: actual effcent East % 003% 036% 051% Mddle % 024% 089% 054% Northeast % 007% 056% 052% West % 017% 041% 085% Table 4 Robustness: Impact of dstortons Scenaro Average dstorton TFP growth dfferental: actual effcent Baselne % 052% 050% 1 = % 039% 060% 1 = % 063% 046% a = % 096% 069% Equal w % 037% 058% Table 2 shows the average level of dstortons and the growth rates of the effcent and actual TFP for the entre perod and two sub-perods, and Between 1985 and 1997, the actual annual TFP growth rate was 052% hgher than the growth rate of the effcent TFP In other words, mprovements n factor allocaton n the frst sub-perod contrbuted about half a percent to annual aggregate TFP growth In the last decade, however, the trend was reversed: The average annual growth rate of the actual TFP was 050% lower than that of the effcent TFP Ths mples that overall factor market dstortons ncreased durng the second sub-perod, offsettng almost all of the effcency gans from reduced dstortons n the frst sub-perod The level of wthn-provnce dstortons, as measured by D = ln(a /A ), vares sgnfcantly across provnces Table 3 shows the average level of wthn-provnce dstortons, average actual TFP growth and the mpact of the dstortons on TFP growth for the four regons n Chna: East, Mddle, Northeast and West For the entre perod, the Eastern provnces have the hghest average TFP growth rate (66%) and the lowest average level of dstortons (0087) In contrast, the Western provnces have the lowest TFP growth rate (497%) and the hghest level of dstortons (0158) However, the mpacts of the change n dstortons on TFP growth at the regonal level are smlar to that at the natonal level All four regons experenced a reducton n dstortons n the frst sub-perod followed by an ncrease n the second sub-perod The provnces that have hgher average level of dstortons are also the provnces that experenced larger ncreases n dstortons n the second sub-perod To see f our results above are robust to choces of parameter values, Table 4 reports both the average level of dstortons and the mpact of the change n dstortons on the dfference between the effcent and actual TFP growth rates for the benchmark case reported above (e, 1 = 15, 1 = 15, a = 067 and provnce weghts calbrated accordng to Eq (16)) and four other cases: (1) 1 = 3, (2) 1 = 3, (3) a = 05 and (4) equal provncal weght, respectvely Our benchmark parameter values are chosen conservatvely so that we do not overestmate the TFP losses assocated wth dstortons As expected, the measured effect on TFP of dstortons ncreases when we ncrease ether the elastcty of substtuton across provnces or the elastcty of substtuton between the two sectors When the labour elastcty s lowered or captal elastcty s ncreased, the msallocaton of captal between the state and non-state sectors becomes more mportant for the aggregate dstortons and the assocated TFP loss also ncreases Fnally, the provncal weghts that we calbrated assume that the average output wedge s zero and therefore mples TFP falls only slghtly due to product market dstortons Constant provncal weghts result n hgher TFP losses from product market dstortons In all cases, however, the growth rate of actual TFP s hgher than that of effcent TFP for the perod between 1985 and 1997, but lower than that of effcent TFP for the perod between 1997 and 2007 So, the trend n our measure of dstortons s robust to the alternatve parameter values 44 Evaluatng the mpacts of wthn- and between-provnce dstortons Next, we nvestgate the mpact of dfferent types of dstortons on the aggregate TFP by conductng a seres of counterfactual experments usng the model presented n Secton 3 To evaluate the mpact of wthn-provnce dstortons n captal allocaton, for example, we set the captal wedges of both the state and non-state to the average wedge of the two

12 50 L Brandt et al / Revew of Economc Dynamcs 16 (2013) sectors wthn each provnce We then compare the resultng measure of the aggregate dstorton to the orgnal measure The dfference can be nterpreted as the contrbuton of the wthn-provnce msallocaton of captal on aggregate TFP The counterfactual experments that we conduct are lsted below: Wthn-provnce: No wthn-provnce dstorton n captal allocaton: Elmnatng the wthn-provnce dfference n captal returns by equalzng the wedges between the state and the non-state sector for captal only No wthn-provnce dstorton n labour allocaton: Elmnatng the wthn-provnce dfference n labour returns by equalzng the wedges between the state and the non-state sector for labour only No wthn-provnce dstorton: The combnaton of the two above Between-provnce: No between-provnce product market dstorton: Elmnatng the cross-provnce dfferences n output wedges No between-provnce dstorton n captal allocaton: Elmnatng the cross-provnce dfferences n captal wedges No between-provnce dstorton n labour allocaton: Elmnatng the cross-provnce dfferences n labour wedges No between-provnce dstorton: The combnaton of all three above Let A nw and A nb be the aggregate TFP when there s no wthn- and no between-provnce dstorton, respectvely We can defne our measure of between-provnce dstortons and wthn-provnce dstortons, respectvely, as D b = ln ( A /A nw ) and D w = ln ( A /A nb ) The former measures the aggregate dstorton when all wthn-provnce dstortons are elmnated and the later measures the aggregate dstorton when there s no between-provnce dstorton Fg 3(a) plots D b (no wthn) and D w (no between) over tme Elmnatng wthn-provnce dstortons or between provnce dstortons results n a sgnfcant reducton n the measure of dstortons However, elmnatng the between provnce dstortons does not change the tme pattern of the aggregate dstorton In contrast, elmnatng wthn-provnce dstortons leaves the aggregate dstorton relatvely constant over tme, suggestng that the changes n overall dstorton over tme were manly due to changes n wthn-provnce dstortons 441 Comparson wth the Unted States To put our measures of dstortons n perspectve, we compare the magntude of Chna s TFP losses from betweenprovnce dstortons wth what a smlar method fnds for the Unted States Whle we have no data suffcent to estmate wthn-state dstortons between varous sectors (and no comparable state-owned/non-state dstncton), we can estmate the magntude of the between-state factor market dstortons Specfcally, we follow the man model structure presented earler and use [ A = =1 ω 1 ( A ) 1 ] 1 as the effcent level of US productvty We presume for ths exercse there s no wthn-state dstorton; that s, A = A Our measure for the between-state dstorton s as before: D = ln(a/a ), where the actual aggregate TFP, A, s the aggregate GDP of Y =[ ω =1 (Y ) 1 ] 1 1 relatve to the aggregate nput bundle ( =1 L ) α ( =1 K ) 1 α We use data on state-level employment and GDP from the Bureau of Economc Analyss For the real value of state captalstock, weusethestate-by-statedataofgarofalo and Yamark (2002) Assumng a labour share (α) of067, state-level TFP can be calculated n the standard way: A = Y /L α K 1 α For comparson wth our analyss for Chna, we assume the same substtuton parameter value of 1 = 15 In order to measure the state-specfc output weghts, we presume product markets n the Unted States face no dstortons In that case, state-specfc prce levels for whch we have one year of data for 2005 from Aten (2008) 14 can be used to back-out the weghts wth the followng formula: ω = ( Y nomnal ) P P =1 ( P Y nomnal ) P We report the results of ths exercse n Fg 4, whch clearly fnds that between-state dstortons n the Unted States are small US productvty s approxmately 2% lower than the effcent level, moreover, t s relatvely stable over tme 14 The offcal state-level real GDP seres from the BEA uses a natonal prce ndex to deflate each state s nomnal GDP Aten (2008), wththeregonal Economcs Drectorate of the BEA, nfers and reports prces and real GDP data usng state-specfc prces

13 L Brandt et al / Revew of Economc Dynamcs 16 (2013) Fg 3 Dstortons wthn and between provnces of Chna, Note: Panel (a) llustrates the aggregate non-agrcultural TFP loss from overall dstortons, the TFP loss from wthn-provnce dstortons, and the TFP loss from between-provnce dstortons Panel (b) decomposes the wthn-provnce dstortons nto captal and labour market dstortons Panel (c) decomposes the between-provnce dstortons nto captal, labour, and product market dstortons (varyng between 15% and 35%) The correspondng loss n TFP from between-provnce dstortons n Chna (nearly 10%) s sgnfcantly larger than n the Unted States 442 Wthn-provnce dstortons To quantfy the contrbuton of wthn-provnce dstortons to aggregate dstorton, we use the followng measure: d w = D D b = ln(a nw /A) Dstortons wthn a provnce take the form of labour or captal market dstortons between the state and non-state sectors Let A nwl and A nwk be the aggregate TFP when there s no wthn-provnce labour and captal market dstorton, respectvely We also use d wl = ln(a nwl /A) and d wk = ln(a nwk /A) as measures of the contrbuton to aggregate dstorton of wthn-provnce labour and captal market dstortons, respectvely Fg 3(b) dsplays these measures along wth the measure d w over tme Clearly, most of the contrbuton of wthn-provnce dstortons comes from the msallocaton of captal between the state and the non-state sector Furthermore, the tme

14 52 L Brandt et al / Revew of Economc Dynamcs 16 (2013) Fg 4 Between-state dstortons through tme for the Unted States Note: Ths fgure uses state-level data from the US to nfer the TFP loss from betweenprovnce (or state n ths case) dstortons n labour and captal markets For comparson wth Chna, see the dashed lne n Fg 3(a) varaton n the contrbuton of wthn-provnce dstortons to the aggregate dstorton also comes from the tme varaton n the contrbuton of the wthn-provnce captal market dstortons The contrbuton of wthn-provnce labour market dstortons has been modest and relatvely stable over tme 443 Between-provnce dstortons Smlarly, we can also measure the contrbuton of between-provnce dstortons by d b = D D w = ln(a nb /A) and decompose the between-provnce dstortons nto labour, captal and product market dstortons Let A nbl, A nbk, and A nby be the aggregate TFP when there s no between-provnce labour, captal and product market dstorton, respectvely We use d bl = ln(a nbl /A), d bk = ln(a nbk /A), d by = ln(a nby /A) as measures of the contrbuton to aggregate dstorton of between-provnce labour, captal and product market dstortons, respectvely Fg 3(c) plots these measures over tme along wth the measure d b In contrast to the wthn-provnce results, the contrbuton of between-provnce captal market dstortons has been very small and declnng over tme The contrbuton of between-provnce product market dstortons has also been small and declnng over tme The most mportant source of between-provnce dstortons s the labour market frcton Furthermore, Fg 3(c) shows that the TFP losses from between-provnce labour market dstortons has not declned over tme 45 Summary of emprcal results For the perod , we fnd that factor market dstortons reduced the aggregate non-agrcultural TFP conservatvely by about 20% TFP losses from msallocaton declned untl md-1990s, then rose afterwards Contrbutons of between-provnce and wthn-provnce dstortons are of comparable magntude Between-provnce dstortons lowered TFP by a roughly constant amount for the entre perod and mostly comes from wedges n labour markets In contrast, wthnprovnce dstortons results n TFP losses that vared over tme, declnng between 1985 and 1997, then rsng sharply after 1997 Nearly all of the wthn-provnce dstortons are due to wedges n captal markets Perhaps the most mportant result from our emprcal analyss above s regardng the msallocaton of captal between the state and non-state sectors Ths dstorton accounts for most of the wthn-provnce dstortons and, more mportant, almost all the tme varaton n the mpact of dstortons Also noteworthy s that, despte a large amount of cross-provnce labour reallocaton over the years, the TFP losses from between-provnce labour market dstortons has remaned remarkably constant over tme Why has the effect of labour market dstortons not declned? What drves the changes n captal market dstortons? We address these questons n the next secton

15 L Brandt et al / Revew of Economc Dynamcs 16 (2013) Fg 5 Cross-provnce dsperson n TFP Note: Ths fgure plots the varance n log TFP across provnces over tme 5 Dscussons 51 Why no declne n between-provnce labour market dstortons? Snce the md-1990s, Chna has experenced a massve labour mgraton across provnces, most of whch s gong from low TFP (mddle and western) provnces to hgh TFP (coastal) provnces Ths knd of reallocaton should help to reduce the dfferences n returns to labour across provnces and therefore the between-provnce labour market dstortons Yet, between-provnce labour market dstortons stll have a sgnfcant negatve effect on TFP One explanaton for ths fndng s the rsng dsperson n TFP across provnces As the dfferences n TFP between provnces wden, more labour should be reallocated to the more productve provnces n order to reduce the dfferences n labour returns Fg 5 plots the crossprovnce varance of ln(tfp) over tme In recent years, as the cross-provnce labour reallocaton ncreased, the cross-provnce dsperson n TFP has also ncreased How the dsperson n returns to labour behaves depends on the relatve speed of the two changes Our emprcal result suggests that the reallocaton of labour was not fast enough to offset the rsng dsperson n TFP Consequently, the effect of labour market dstortons remaned hgh despte huge flows of labour crossng provncal boundares 52 What drves the changes n captal market dstortons? Fg 3(c) shows that the TFP losses from between-provnce captal dstortons has declned over tme The wthn-provnce dstortons n the allocaton of captal between the state and non-state sectors, however, has n recent years lowered TFP by more Why? Here we provde evdence showng that t may be partly due to the Chnese government s regonal polces Fg 6(a) shows the average output per worker for Chna s four geographcal regons: East, Mddle, Northeast and West In 1997, among the four regons, the Eastern regon, whch ncludes all of the coastal provnces, had the hghest labour productvty whle the Western regon s labour productvty was the lowest Around that tme, many economsts and polcy makers argued that ths gap n performance was a product of the central government s preferental polces towards the Eastern provnces whch allowed them to attract more nvestment To reduce the dsparty, t was argued that the central government should adopt polces to drect more nvestment to the Western provnces Thus, a new polcy ntatve, Develop the Great West, was ntroduced n the late 1990s by the central government Was the lower level of development n the Western regon a result of captal scarcty? The answer s no Fg 6(b) shows that the Western regon actually had the hghest captal output rato among the four regons Fg 6(c) shows that low TFP s the man reason for the low output per worker n the West The Develop the Great West polcy worked n one aspect: The Western regon experenced sgnfcant ncreases n the captal output rato between 1997 and 2007 However, t faled to accomplsh ts stated objectve of reducng regonal ncome dsparty: Between 1997 and 2007, the dsparty n labour productvty between the Western and Eastern regons ncreased, not decreased The reason for ths polcy falure s clear: Most of the ncreased nvestment was drected to the regon s state sector, whch had much lower TFP than that of the non-state sector (see Fgs 6(e) and 6(f) for TFP and the captal output rato by sector and regon) Thus, msallocaton of captal between the state and the non-state sector worsened as a result of the regonal development polcy and the wthn-provnce dstortons ncreased sgnfcantly between 1997 and 2007 (see