Industrial Policies and Economic Development

Transcription

1 Industral Polces and Economc Development Ernest Lu* January 28, 2017 Abstract Many currently and prevously developng countres have adopted ndustral polces that push resources towards certan "strategc" sectors, and the economc reasonng behnd such polces s not well understood. In ths paper, I construct a model of a producton network where frms purchase ntermedate goods from each other n the presence of credt constrants. These credt constrants dstort nput choces, thereby reducng equlbrum demand for upstream goods and creatng a wedge between the potental sales nfluence and actual sales by upstream sectors. I analyze polcy nterventons and show that, under weak functonal form restrctons, the rato between a sector s nfluence and sales s a suffcent statstc that gudes the choce of producton and credt subsdes. Usng frmlevel producton data from Chna, I estmate my suffcent statstc for each sector and show that t correlates wth proxy measures of government nterventons nto the sector. Usng a panel of crosscountry nput-output tables and sectoral producton tax rates, I show that the tax rates for developng countres n Asa also correlate wth the model-mpled nterventon measure. *Department of Economcs, MIT. Emal: luer@mt.edu. I am ndebted to Daron Acemoglu and Abhjt Banerjee for ther gudance and support throughout ths project. I also thank Maros Angeletos, Davd Atkn, Vvek Bhattacharya, May Bunsupha, Esther Duflo, Sebastan Fanell, John Frth, Greg Howard, Yan J, Pooya Molav, Scott Nelson, Harry D Pe, Jeff Pcel, Frank Schlbach, Ludwg Straub, Tavneet Sur, Lnh Tô, Ivan Wernng, and especally Arnaud Costnot, Danel Green, Alp Smsek, Jesse Shapro, and Rob Townsend for conversatons and helpful comments. All errors are of course my own. 1

2 1 Introducton Industral polces are broadly defned as the selectve nterventons that attempt to alter the structure of producton towards certan sectors. Such polces are not only wdely adopted n developng countres today, but also played a promnent role n the developmental stage for many now-advanced economes. Prme hstorcal examples of ndustral polces nclude Japan n the 1950s and 1960s and South Korea and Tawan n the 1960s and 1970s. In all of these cases, the government heavly promoted strategc upstream sectors that supply to many others sectors. A wealth of polcy nstruments was adopted durng these perods, ncludng varous forms of tax ncentves and subsdzed credt, and n the case of Tawan, drect state nvolvement n producton. In Korea, the explct ndustral movement was termed the Heavy-Chemcal Industry drve, and for almost a decade frms n selected ndustres receved polcy loans wth sgnfcantly reduced nterest rates Amsden 1989, Woo-Cumngs Total polcy loans drected towards the targeted sectors accounted for 45% of the total domestc credt of the bankng system n 1977 Hernandez Many of the largest manufacturng conglomerates n Korea today orgnated durng ths era. By ther nature, these polces seek to affect the development of the aggregate economy through selectve nterventon n a few sectors. Understandng the effects of such nterventon therefore requres modelng the lnkages among sectors n the economy. Moreover, the frequent use of subsdzed or targeted loans suggests fnancng constrants play an mportant role n the desgn of these polces. Motvated by these facts, ths paper develops a framework for studyng optmal ndustral polcy n a general equlbrum settng wth fnancal frctons and network lnkages among sectors. In my model, producton requres factor nputs as well as ntermedate goods produced by other sectors, and frms face credt constrants when purchasng some of these nputs for producton. These credt constrants dstort nput choces and endogenously affect sectoral nput-output lnkages, thereby reducng demand for upstream goods that are subject to constrants. In equlbrum, the constrants generate a wedge between the total sales of the affected upstream sectors and the elastcty of aggregate output wth respect to sectoral Hcks-neutral productvty shocks. Ths elastcty, known as the sectoral nfluence n the producton networks lterature, can be nterpreted as the potental sectoral sales absent market mperfectons Hulten I analyze polcy nterventons and show that, under weak functonal form restrctons, the rato between a sector s nfluence and sales whch I refer to as the sectoral sales gap s a suffcent statstc that summarzes the neffcences n the nput-output network and could gude polcy nterventons that expand sectoral producton. Specfcally, I show that startng from a decentralzed equlbrum wthout dstortonary taxes, a sector s sales gap captures the rato between socal and prvate margnal return to spendng resources n the sector on producton nputs and on credt. Moreover, f producton functons are so-elastc, the same suffcent statstc captures the optmal sectoral subsdes to labor, whch s the value-added nput n the model. These results are potentally surprsng because sectors wth the hghest sales gaps are not necessarly the sectors n whch frms are most constraned; nstead, they are upstream sectors that drectly or ndrectly supply to many constraned downstream sectors. In fact, my results mply that even f the prvate returns to credt are equalzed across all frms n the economy, a benevolent planner mght stll want to drect credt to up- 2

3 stream sectors n order to mprove producton effcency. The sales gap s a suffcent statstc for network neffcences because whle sales capture the relatve sectoral sze under equlbrum producton n the presence of frctons, nfluence captures the relatve sectoral sze under optmal producton. The dstance between the two vectors thus reveals a drecton n whch producton effcency can be mproved. Ths fndng can be vewed as an ant-network result smlar to Hulten s: as long as we know the sales gap the dfference between a sector s potental and actual sales knowledge of the underlyng frctons n the nput-output system becomes rrelevant for welfare analyss. I conduct two dstnct emprcal exercses to estmate sales gap and examne ts correlatons wth proxy measures of government nterventons. The frst exercse focuses on Chna, whose socalst roots and strong legacy of state nterventon makes t a partcularly nterestng settng to apply my results. Relyng on frm-level manufacturng census, I estmate frm producton elastctes and the dstrbuton of credt dstortons for the manufacturng sectors, and I use these estmates to compute sectoral nfluence and sales gap based on the observed Chnese nput-output table. I fnd that prvate frms n sectors wth hgher sales gaps tend to receve more external loans and pay lower nterest rates, and that the sectoral presence of Chnese State-Owned Enterprses SOEs s heavly drected towards sectors wth hgher sales gaps. My theory suggests that these selectve nterventons can enhance welfare by effectvely subsdzng upstream producton and potentally ameloratng the network neffcences. My fndngs therefore allow for a postve reapprasal of the selectve state nterventons n Chna and provde a counterpont to the prevalng vew e.g. Song et al that SOEs are a sgn of sectoral neffcency. My second emprcal exercse compares across countres. Usng a panel of cross-country nput-output tables, I construct the sales gap measure for a set of developng countres based on the nput-output tables from a set of developed countres, adoptng a strategy that s smlar n sprt to Rajan and Zngales 1998 and Hseh and Klenow I show that, as a group, developng countres tend to have hgher sales gaps n tertary and heavy manufacturng sectors and lower sales gaps n prmary and lght ndustral sectors. Moreover, I show that the sectoral sales gaps of a set of developng countres n Asa strongly and postvely correlate wth a measure of sectoral subsdes adopted by these countres. The pattern s largely absent or even reversed n developng countres from the other contnents, whch on average have had worse economc performances n recent years than ther Asan counterparts. These results are consstent wth the hypothess that governments n countres wth strong economc performances are better at understandng the network dstortons and are adoptng polces to address them. Lterature Revew My paper s related to a large body of development macro lterature on the msallocaton of resources, ncludng Banerjee and Duflo 2005, Jeong and Townsend 2005, Restucca and Rogerson 2008, Hseh and Klenow 2009, Banerjee and Moll 2010, Song et al. 2011, Buera et al. 2011, and Rotemberg 2014, among many others. The broad purpose of ths lterature s to study the mplcatons of mcro-level fnancal frctons on aggregate productvty. My paper draws on ths lterature but provdes a dfferent focus. Rather than studyng how fnancal constrants dstort the effcent use of resources wthn a sector, I study how constrants endogenously affect nput-output lnkages and 3

4 dstort the relatve sze of sectors, generatng the msallocaton of resources across sectors n a producton network. The mportance of sectoral lnkages for economc development was frst ponted out by Hrschman 1958, who argues that ndustral polces should target and promote sectors wth the strongest lnkages. Hs work has nspred an early and substantal development economcs lterature that ams to measure the Hrschmanan lnkages and study ther relatonshps wth economc performance and ndustral polces, ncludng Chenery and Watanabe 1958, Rasmussen 1965, Yotopoulos and Nugent 1973, Chenery et al. 1986, Jones 1976, and Shultz 1982, among others. My paper revsts ths topc usng a model wth neoclasscal mcrofoundatons to formalze the mplcatons of lnkages for ndustral polces. My modelng approach embeds cross-sector nput-output lnkages nto a statc verson of the compettve entry model wth the convex-concave technologes of Hopenhayn 1992 and Hopenhayn and Rogerson The model sts squarely wthn the class of generalzed Leontef models as defned n Arrow and Hahn 1971, pp. 40, Leontef economy. Ths class of generalzed Leontef models has been extensvely studed n the early general equlbrum lterature, ncludng Hulten 1978, who shows that wthout market mperfectons and under aggregate constant returns to scale, sectoral nfluence s equal to sales, an equvalence that s broken n my model due to fnancal frctons. A modern revval of ths Leontef nput-output approach, often referred to as the producton networks lterature, mposes functonal forms on generalzed Leontef models and more explctly studes how productvty shocks transmt through nput-output lnkages. Key contrbutons to ths lterature nclude Long and Plosser 1983, Horvath 1998, 2000, Dupor 1999, Shea 2002, and Acemoglu et al Several papers n ths lterature embed fnancal frctons nto producton networks: Jones 2013 and Bartelme and Gorodnchenko 2015 model fnancal frctons through mplct wedges or dstortons n factor prces à la Hseh and Klenow 2009, and Altnoglu 2015 and Bgo and La O 2016 model frctons through workng captal constrants. These papers am to characterze how lnkages amplfy sectoral fnancal frctons and study ther mplcaton on aggregate output. Relatedly, Baqaee 2016 studes a producton network model wth monopolstc markups, whch also create wedges between margnal product and margnal cost of producton nputs. Market mperfectons n the models of these papers also break Hulten s equvalence theorem. My theoretcal analyss dffers substantvely from those offered by the current producton networks lterature. Frst, because the decouplng of nfluence and sales s at the heart of my analyss, I conduct a detaled characterzaton of how sectoral constrants and network structure affect the sales gap. Second, I show that under aggregate constant returns to scale, sectoral sze s proportonal to nfluence under optmal producton, even though t s proportonal to sales under equlbrum producton n the presence of constrants. I further show that ther rato, the sales gap, exactly captures the rato between socal and prvate margnal returns to spendng productve resources n a sector, thus provdng a drecton n whch producton can be mproved through polcy nterventon. These results do not rely on the Cobb-Douglas or the constant elastcty-of-substtuton assumptons mposed by the producton networks lterature. Baqaee 2015 and Acemoglu et al observe that n a producton network under Cobb-Douglas 4

5 technology assumpton, productvty shocks travel downstream through nput-output lnkages from supplers to buyers, whle demand shocks travel upstream. My paper shows that these results can be generalzed wthout the specfc functonal form assumptons, and I apply these ntutons to show how credt constrants affect allocatons and dstort the relatve sze of sectors. Frst, as an applcaton of the non-substtuton theorem by Samuelson 1951, demand shocks have no effect on equlbrum prces n a generalzed Leontef model and affect equlbrum quanttes only through backward lnkages or, n other words, by travelng upstream. Second, even wthout the Cobb-Douglas assumpton, productvty shocks n a sector travel through forward lnkages, affectng the unt cost of producton hence equlbrum prces of downstream buyers. Equlbrum prces of upstream sectors are unaffected, and output quanttes n upstream sectors change n response to downstream productvty shocks only through the changes n demand nduced by these shocks. Lastly, fnancal frctons n a generalzed Leontef model serve both as a productvty shock and a shock to ntermedate demand that emanates from the constraned sectors. The productvty shock aspect of fnancal frctons propagates downstream by lowerng aggregate output, whle the demand shock aspect propagates upstream and suppresses the relatve sze of upstream sectors. My model promnently features pecunary externaltes and thus relates to the lterature on the neffcency of general equlbrum wth prces n addtonal constrants, ncludng semnal work by Greenwald and Stgltz 1986 and Geanakoplos and Polemarchaks More broadly, my polcy analyss leverages the fact that n the presence of nput-output lnkages, polcy nstruments need not drectly target the source of dstortons n order to mprove welfare. My analyss therefore relates to the second-best lterature ntated by Lpsey and Lancaster 1956 and more recently contrbuted by Farh and Wernng 2013, Klenthong and Townsend 2016, and Kornek and Smsek 2016, among others. Whle I provde closed-form solutons for second-best polces under Cobb-Douglas assumptons, my man results study welfare changes n response to a margnal change n producton subsdes. Ths approach s related to a seres of papers n publc fnance lterature, ncludng Ahmad and Stern 1984, Deaton 1987, and Ahmad and Stern 1991, that study the welfare effect of margnal tax reforms. The emprcal settng of my analyss bulds on a broad emprcal and polcy lterature on state nterventon and ndustral polces, ncludng Pack and Westphal 1986, Chenery et al. 1986, Amsden 1989, Wade 1989, Wade 1990, Westphal 1990, Page 1994, Pack 2000, Noland 2004, and more recently, Rodrk 2004, 2008 among others. Compared to the Computable General Equlbrum approach adopted by some papers n the polcy lterature, such as Dervs et al and Robnson 1989, my work s mcrofounded as I explctly model frm-level ncentves and ther behavor under credt constrants. My frst emprcal exercse focuses on Chna and relates to a large lterature that studes the growth experence of the country, ncludng Brandt et al. 2008, Song et al. 2011, Zhu 2012, Ba et al. 2014, Storesletten and Zlbott 2014, Aghon et al. 2015, and Hseh and Song Most notably, I borrow from Song et al n modelng SOEs as unconstraned proft maxmzers, an assumpton that plays a central role n ths emprcal analyss. The observaton that Chnese SOEs are more present n upstream sectors has also been made by L et al. 2015, who adopt the upstreamness measure by Antras et al. 5

6 2012. My second emprcal exercse uses cross-country nput-output tables to test the relatonshp between the sales gap measure and a measure of sectoral tax rates n developng countres. I use observed nputoutput tables for developed countres to predct undstorted producton technologes for developng countres, an exercse that s smlar n sprt to Rajan and Zngales 1998 and Hseh and Klenow Bartelme and Gorodnchenko 2015 conduct a smlar exercse to nfer unconstraned nput-output producton technologes, though they examne a dfferent emprcal relatonshp, one that s between aggregate TFP and a measure of total lnkages across ndustres. The rest of the paper s organzed as follows: Secton 2 provdes the theoretcal results, Secton 3 conducts the emprcal exercse based on frm-level Chnese manufacturng data, Secton 4 conducts the cross-country analyss, and secton 5 concludes. 2 Theory 2.1 Model Setup Economc Envronment There s a representatve consumer who consumes a unque fnal good wth prce normalzed to 1 wth non-satated preferences and supples labor L nelastcally. There are S ntermedate producton sectors n the economy, each producng a dfferentated good that s used both for ntermedate producton and also the producton of the unque fnal good. I wll refer to the output of sector as good and refer to the S goods altogether as ntermedate goods. The fnal good s produced compettvely by combnng ntermedate goods under producton functon F Y 1,, Y S where Y s the unts of good used for fnal producton. I assume F s dfferentable, has constantreturns-to-scale, and s strctly ncreasng and jontly concave n ts arguments. Producton of ntermedate goods s modeled as a two-stage entry game. In the frst stage, a large measure of dentcal, rsk-neutral, and atomstc potental entrants freely choose whether to set up a frm n any sector, takng the expected proft and cost of entry as gven. In the second stage, frms that have entered n sector produce an dentcal and perfectly substtutable good. To buld a frm n sector, an entrant ν pays a fxed cost κ unts of the fnal good and acqures a producton technology q ν = h z ν f l ν, m 1 ν,, m S ν, where l ν s the amount of labor employed by frm ν n sector, m j ν s the amount of good j used as ntermedate nputs for producton of good by frm ν, and z ν captures frm-specfc Hcks-neutral productvty. Lastly, h s a sector-wde Hcks-neutral productvty shock common to all frms n sector, whch s ntroduced for notatonal purposes and s normalzed to h 1 unless explctly noted. 6

7 The model formulaton mplctly assumes no jont producton each ndustry produces only one good. We make the followng assumptons on f and F: Assumpton 1. Producton functons f and F are contnuously dfferentable and strctly concave. Furthermore, 1. F satsfes the Inada condtons: F Y 1,, Y,, Y S F Y lm = 1,, Y,, Y S, lm = 0. Y 0 Y Y Y 2. f 0, m 1, m S = 0 and f l,m 1, m S l > 0 at all nput levels. That s, every frm needs labor to produce and output s always strctly ncreasng n labor. Fnancal Constrants Fnancal frctons n ths network economy are modeled as pledgeablty constrants faced by frms n the ntermedate goods sectors. I assume the cost of a subset of producton nputs has to be pad before producton takes place, and each entrepreneur ν has an exogenous amount of expendable funds W ν. Formally, for each frm ν n ndustry, there s a subset of nputs K {1,, S} that s subject to constrants of the followng form: j K p j m j W ν 1 where p j s the prce of good j, and m j s the amount of good j used for producton. I use K to denote the set of constraned ntermedate nputs and X to denote the set of unconstraned nputs, wth K X = {1,, S}. In ths statc producton model, the left-hand sde of the fnancal constrant 1 can be nterpreted as an upfront payment requrement on certan nputs, before the frms make sales and are able to recover the nput expendtures. The rght-hand sde of the constrant captures the total avalable funds to cover such upfront costs, whch can be nterpreted as the sum of entrepreneural wealth and the total bank credt avalable to the entrepreneur to purchase the constraned nputs. Inputs n K that are subject to the constrant and can be thought of as captal goods e.g. machnery, equpments and computers or servces that can be subject to hold-up problems such as outsourced R&D servces, for whch trade credt s dffcult to obtan and costs must be ncurred upfront. The unconstraned nputs n X can be thought of as materal or commodty nputs such as ntermedate materals for the producton of consumer goods e.g. textles, commodtzed servces, and energy nputs for whch trade credt s more avalable Fsman 2001 such that the nput cost can be pad after producton s carred out. The fact that labor nput s unconstraned s not mportant for my theoretcal results: the same suffcent statstc wll capture the rato between socal and prvate margnal return to spendng addtonal resources on any producton nput, ncludng labor, whether or not the nput s constraned. On the other hand, when I apply my model to data n sectons 3 and 4, I take the emprcal stance that labor s unconstraned. Ths assumpton s motvated by the emprcal evdence that frms n developng countres do not seem to be constraned n labor choces Cohen 2016, De Mel et al Note also that that the 7

8 fxed cost of entry κ does not appear n constrant 1, but ths s wthout loss of generalty: I can always relabel the amount of exogenous expendable funds as W and defne W W κ. Smlarly, we can also renterpret the constrant 1 as requrng only a fracton of the cost of captal nputs to be pad upfront by relabelng W wth a multplcatve constant. In Appendx C I consder several dfferent formulatons of fnancal frctons. Appendx C.1 reformulates the model wth fnancal frctons n the form of a montorng cost that s lnear n the amount of credt delvered. The lnear montorng cost creates an exogenous wedge between margnal product and margnal cost of nputs, smlar to the mplct wedges n Hseh and Klenow 2009, Jones 2013, and Bartelme and Gorodnchenko 2015, and our results survve n that envronment. I relax the constrant formulaton 1 n Appendces C.2 and C.3 by successvely ntroducng nput-specfc requrement for upfront payment wth the left-hand-sde of constrants takng the form of j S η j ν p j m j for η j ν [0, 1] and partal pledgeablty of revenue by ntroducng δ ν p q ν to the rght-hand-sde of constrants. I show that all of my theoretcal results survve when producton nputs have varyng degrees of upfront-payment requrement η j ν. When revenue pledgeablty s also ntroduced, the constrant formulaton nests the pledgeablty constrants n Bgo and La O 2016 and my results stll hold f wthn-sector frm heterogenety s removed, an assumpton mantaned by other papers n ths lterature. My theory focuses on ntermedate producton, and I assume the fnal good producer operates wthout any credt constrants. Frm s Proft Maxmzaton Problem credt constrant n 1: Frms choose nputs n order to maxmze proft subject to the { } S P frm max p q ν, l, mj p j m j wl subject to 1. {m j} S,l j=1 j=1 Free Entry Before producton takes place, there s a large unbounded pool of prospectve entrants nto any ndustry, and all potental entrants are dentcal ex-ante. After ncurrng the fxed cost of entry κ unts of the fnal good, frms ndependently draw Hcks-neutral productvtes z ν and expendable funds W ν from a sector-specfc dstrbuton wth a compact, non-negatve support and cumulatve dstrbuton functon Φ. Because all same-sector frms wth dentcal productvty and wedges make the same allocaton choce, I abuse the notaton and use ν as the ndex for both the random draws of z ν, W ν and also for the frm wth these draws. To make entry decsons, prospectve entrepreneurs form ratonal expectatons on the varable profts π ν 0, the maxmand of P frm. The expected proft net of fxed cost n sector s E ν [π ν] κ. If ths value were negatve, no frm would want to enter. In any equlbrum where entry s unrestrcted, an assumpton I mantan, ths value cannot be strctly postve, hence κ = E ν [π ν]. 2 8

9 Equlbrum Defnton 1. A decentralzed equlbrum s a collecton of prces {p } S =1, wage rate w, measure of frms {N } S =1, frm-level allocatons {l ν, m 1 ν,, m S, q ν} =1, S, producton nputs for the fnal good {Y } S =1, aggregate consumpton C, net aggregate output Y, and aggregate labor supply L such that 1. The representatve consumer maxmzes utlty subject to hs budget constrant, such that: wl = C. 2. A frm ν n each sector solves the constraned proft maxmzaton problem P frm, takng wage rate w, prces {p } S =1, ts own productvty z ν, and expendable funds W ν as gven. 3. Free-entry drves ex-ante profts to zero n all sectors such that equaton 2 holds. 4. Producton nputs for the fnal good solve the proft maxmzaton problem of the fnal producer Y 1,, Y S = arg max {Ỹ} F Ỹ 1,, Ỹ S p Ỹ All markets clear: labor nterm. good j for all j fnal good L = L 4 Q j = Y j + M j 5 Y = F Y 1,, Y S κ N, 6 where captal case letters L, M j, Q j denote total sectoral quanttes: L N M j N Q = N 6. The net aggregate output equals consumpton: Y = C. ν ν ν l ν dφ ν m j ν dφ ν q ν dφ ν. 9

10 Before I ntroduce government expendture n secton 2.4, net aggregate output Y always equals aggregate consumpton C, and I use the two terms nterchangeably. Example E There s no closed-form soluton for equlbrum allocatons wthout addtonal functonal form assumptons. To make the dscusson concrete, I sometmes refer to a specfc three-sector example that s nested under my model. I refer to the example as E and the setup s as follows. There are S = 3 ntermedate producton sectors n the economy, and these sectors form a vertcally connected producton network: good 1 s produced upstream usng labor only, good 2 s produced by combnng good 1 and labor, and good 3 s produced downstream by combnng good 2 and labor. I assume the fnal good s produced lnearly from the downstream good 3: F = Y 3. I remove heterogenety across frms wthn a sector, and I drop the frm ndex ν to smplfy notaton. The frm-level producton functons take the so-elastc form: q 1 = l 1 α 1, q 2 = l 2 α 2 m 21 σ 2, q 3 = l 3 α 3 m 32 σ 3, where q s the frm-level output, l s the labor nput for producton, and m, 1 s the amount of good 1 used by a frm n the producton of good. I normalze α 1 α + σ for sectors = 2, 3 so that the concavty of producton s constant across all three sectors to avod carryng addtonal constants and obfuscatng notaton for ths example. I normalze frm-level productvty to z 1. All ntermedate goods are subject to credt constrants. I also assume W s constant for all frms n sector : p 1 m 21 W 2, p 2 m 32 W 3. 7 The flow of nputs and outputs n the network s represented n fgure 1. Fgure 1: Illustraton of the Vertcal Producton Economy 10

11 2.2 Equlbrum Characterzaton Frm-level Allocatons Under Assumpton 1, the soluton to frm ν s proft maxmzaton problem post-entry P frm s characterzed by the frst-order condtons wth respect to nputs, whch can be re-arranged nto the followng set of expendture share equatons: wl ν p q ν = ln f ν ln l 8 p j m j ν p q ν = ln f ν ln m j for all j X 9 p j m j ν p q ν = ϕk ν ln f ν ln m j for all j K 10 The frst two equatons are standard: because labor and ntermedate goods j X are unconstraned, ther expendture shares wl ν p q ν and p jm j ν are equal to the respectve output elastcty of the frm producton functons evaluated at equlbrum quanttes of nputs. On the other hand, ths equvalence p q ν breaks down for ntermedate goods j K that are subject to credt constrants, reflected by frm-specfc wedge ϕ K ν 1, whch shows up n the expendture share equaton for the constraned nputs. When the credt constrant bnds, ϕ K ν < 1, and t dstorts nput expendture downwards relatve to the effcent level. For each frm, the wedge ϕ K ν s pnned down by equlbrum prces and frm-specfc random draws. The nverse wedge ϕ K ν 1 can be nterpreted as the frm s prvate return to spendng on constraned nputs, whle ϕ K ν 1 1 captures the margnal gans of havng addtonal workng captal and s the nterest rate the frm s wllng to pay to obtan credt. Defnton 2. The prvate return to spendng on nput j for frm ν n sector s the rato between the margnal product and margnal cost of nput j: PR j ν p Smlarly, the prvate return to spendng on labor s / q ν p j. m j / PR l q ν ν p w. l Lemma 1. Consder the nverse of the wedge on ntermedate nput n sector, ϕ K ν Let η ν 0 be the Lagrange multpler on the fnancal constrant 1 for the frm ν s proft maxmzaton problem P frm. We have ϕ K ν 1 = 1 + η ν. 11

12 2. ϕ K ν 1 captures the prvate return to spendng on constraned nputs: 1 ϕ K j ν = PR ν for all j K. 3. ϕ K ν 1 1 captures the frm s margnal gans from havng access to addtonal workng captal W : 1 ϕ K dπ ν 1 = ν dw ν. The varable proft earned by frm ν can be found by subtractng varable costs from revenue: π ν = p q ν wl ν S p j m j ν. j=1 For labor and unconstraned ntermedate nputs, the lack of a wedge that dffers from one n 8 and 9 mples that the prvate return to spendng on these nputs s 1 and the margnal product of these nputs s equal to ther margnal costs: PR l ν = PR j ν = 1 for j / K. 11 To smplfy notatons, n what follows I let α ν denote frm ν s equlbrum output elastcty wth respect to labor, whch s also equal to the labor expendture share because labor s not subject to the credt constrant. Let σ j ν and ω j ν respectvely denote the output elastcty and potentally dstorted expendture share of ntermedate nput j: α ν ln f ν ln l = wl ν p q ν, σ j ν ln f ν ln m j, ω j ν p jm j ν p q ν. Sectoral Allocatons total output and nputs are defned as Let N be the number of frms that enter sector n equlbrum. Recall sectoral Q = N E ν [q ν], M j = N E ν [ mj ν ], L = N E ν [l ν], where I use E ν [ ] to replace ν dφ ν n Defnton 1. The sectoral total expendture on labor as a share of sectoral revenue, whch I denote as α wl p Q wthout the ndex for frms, ν, can be expressed as a weghted average of frm-level labor share, wth weghts beng each frm s output: α wl = E ν [wl ν] p Q E ν [p q ν] [ ] wl ν q = ν E ν p q ν E ν [q ν] ] q = E ν [α ν ν E ν [q ν] 12

13 The sectoral expendture share of ntermedate nputs, whch I denote as ω j p j M j p Q, can be smlarly expressed as ω j p jm j p Q = E ν [ ω j ν ] q ν E ν [q ν] The number of frms N s pnned down by the free-entry condton 2, whch can be expressed as 12 S κn = 1 α p Q ω j. 13 j=1 Equlbrum To characterze the equlbrum, I take note that despte frm s producton functons beng convex-concave, the economy features sectoral and aggregate constant returns to scale. Ths s because I allow for the entry of ex-ante dentcal entrepreneurs nto sectors that produce homogeneous goods: any frm-level profts nduced by concavty wll be drven down to zero n net of fxed cost, and as a result the number of frms can be vewed as a flexble nput at the sector level. Takng out nput-output lnkages, my sectoral producton model s ndeed a statc verson of the dynamc compettve model wth entry studed by Hopenhayn 1992, Hopenhayn and Rogerson 1993, and more recently, by Restucca and Rogerson 2008 and Buera et al. 2011, Gven nput prces w, { p j }, the cost of producng q unts of output can be captured by the sectoral cost functon, whch s the soluton to the dual of the entry and proft maxmzaton problem: T C q; w, { pj } mn } n {l ν,{m j ν} j n, ν κ + ν wl ν + s.t. n z ν q ν dφ ν q ν j K p j m j W ν q ν = f l ν, m 1 ν,..., m S ν S p j m j ν dφ ν j=1 A drect mplcaton of the constant returns to scale property s that the sectoral cost functon s lnear n the level of output q. In other words, the sectoral unt cost of producton, whch I wrte as C w, { pj } T C q; w, { pj } q 14, 15 s a functon of only nput prces but not output levels. Moreover, because the producton functon F of the fnal good also features constant returns to scale, I can wrte ts unt cost functon as C F { p j } mn {Ỹj} j p j Ỹ j s.t. F Ỹ j 1 13

14 Equlbrum prces w, { p j } solve the set of equatons C w, { pj } C F { p j } = p for all 16 = 1, 17 where 17 reflects the normalzaton that the prce of the fnal good s 1. Proposton 1. There exsts a unque decentralzed equlbrum. The ntuton for the result s as follows. In ths economy, the set of prces w, { } p j completely pns down equlbrum allocatons. Frst, frm-level allocatons are drectly pnned down by prces, and solvng for equlbrum bols down to dervng total sectoral level of output and nputs. Second, because labor supply s exogenous, the wage rate pns down aggregate consumpton as C = wl. Thrd, gven that sectoral producton features constant returns to scale, when holdng nput prces constant, the expendture share on nputs s constant for both ntermedate producers and the fnal producer. Gven the level of aggregate consumpton, we know the quanttes of ntermedate goods that go nto the producton of aggregate consumpton. Next, gven ntermedate expendture shares, we know the second round quanttes of ntermedate goods as well as the number of frms n each sector that go nto the producton of the ntermedate goods that are used drectly for the producton of aggregate consumpton. Iteratng ths logc ad nfntum and sum over quanttes of goods at each teraton, we can derve the total nput and output levels n each sector. The nfnte sum s well defned because labor share s postve n every ndustry by Assumpton 1, and as a result, ntermedate shares sum to less than one. The unqueness of the decentralzed equlbrum therefore depends on the unqueness of the prce vector that satsfes the unt cost equatons 16 and 17. My model s nested under the class of generalzed Leontef models, and the standard argument of unqueness for ths class of models also apples to ths settng e.g., see Stgltz 1970, Arrow and Hahn 1971, n whch the Jacoban matrx of the mappng that represents the system of unt cost equatons has the domnant dagonal property, whch ensures the global unqueness of soluton by the classc results of Gale and Nkado Influence and Sales We now proceed to better understand how credt constrants affect equlbrum allocatons and sectoral sales. Recall ω j denotes sector s expendture share on ntermedate good j and, as shown n equaton 12, can be re-wrtten as a weghted average of frm-level expendture shares wth weghts beng each frm s output. I defne a smlar object based on frm-level elastctes: σ j E ν [σ j ν ] q ν. E ν [q ν] That s, σ j captures the proportonal change n total output of sector f every frm n sector expands ts use of ntermedate nput j by 1%. I refer to σ j as the sectoral output elastcty wth respect to nput j, and ndeed t s the elastcty of sectoral unt cost wth respect to the prce of nputs: 14

15 Proposton 2. In equlbrum, σ j = ln C { } w, pj for all, j. ln p j Absent credt constrants, σ j ν = ω j ν for all frms, and as a result, sectoral expendture shares are also equal to sectoral elastctes. On the other hand, when the constrants bnd for a postve measure of frms, the sectoral expendture shares of constraned nputs are dstorted downwards relatve to the equlbrum elastctes, wth ω j < σ j for j K. Furthermore, the presence of addtonal constrants n the cost mnmzaton problem 14 mples that f nput prces are held fxed, the unt cost of output s hgher when frms n a sector are subject to constrants. I defne the sectoral wedge on nput j as the rato between sectoral expendture share and average sectoral elastcty: ϕ j ω j σ j 1. If every frm n sector expands ts use of constraned nput j by 1%, the total ncrease n sectoral sales would be σ j % whle the cost of usng these addtonal nputs s ω j % of the sectoral sales. The nverse sectoral wedge on nput j, ϕ j 1, can therefore be nterpreted as the average prvate return to expendture on nput j as t captures the rato between the margnal product and margnal cost of an unform expanson n the use of nput j across all frms n the sector. It can also be wrtten as the average frmlevel prvate returns to expendture on constraned nputs, ϕ K ν c.f. Lemma 1, weghted by the level of good j used by each frm: PR j [ ] 1 1 ϕ j = E ν ϕ K m j ν ν [ E ν mj ν ] for j K. Relatedly, I denote the sectoral average prvate return to captal nputs as a whole by PR K ϕ K 1 = j K σ j j K ω j = E ν 1 ϕ K j K p j m j ν ν ]. 18 E ν [ j K p j m j ν When the producton functon f s homothetc, ϕ j = ϕ K for all j K. The sectoral average prvate return of unconstraned nputs, ncludng labor and ntermedate nputs j / K, s equal to one, just as the frm-level counterparts n equaton 11: PR l = PR j = 1 for j / K. Because a smaller fracton of revenue s spent on nputs, a larger fracton must accrue to varable profts and attract frm entry. Indeed, equaton 13 reveals that, holdng nput prces fxed, when frms 15

16 n a sector are constraned, more frms enter per unt of sectoral output relatve to when there are no constrants n the sector. Intutvely, fnancal constrants manfest themselves at the sector level by creatng wedges between the margnal product and margnal cost for both the constraned ntermedate nputs and the number of frms that are establshed. When a sector s constraned, resources are msallocated wthn the sector, wth too many frms n equlbrum, each usng too lttle of the constraned nputs. Whle the result may seem counterntutve, t s merely a statement about a local property of the equlbrum and does not mply that dscrete changes to the envronment, such as removng credt constrants altogether from a sector, would nduce fewer frms to be n the new equlbrum. Furthermore, the result s not necessarly at odds wth emprcal observatons: Hseh and Olken 2014 fnd that the dstrbutons of manufacturng frm sze n Inda, Indonesa, and Mexco are skewed to the left relatve to that n the U.S., wth the developng countres havng many more small frms relatve to medum and large frms. I now defne three mportant objects that are central to the analyss. Recall that h denotes the Hcksneutral sectoral productvty that s common to all frms n sector, whch s normalzed to 1 throughout the exposton. The notaton s ntroduced solely for the purpose of the followng defnton: Defnton 3. The nfluence vector µ respect to sector productvty, µ 1,, µ S s the elastcty of net aggregate output Y wth µ d ln Y d ln h. Defnton 4. The sales vector γ γ 1,, γ S s the rato between total sectoral sales and net aggregate output, γ p Q Y. Defnton 5. The sales gap vector ξ ξ 1,, ξ S s the element-wse rato between nfluence and sales: ξ µ γ. The nfluence vector µ s a noton of sectoral mportance, whereas the sales vector γ represents the equlbrum sze of sectors. The sales gap ξ captures the the wedge between sectoral mportance and sze and s a key object n the polcy analyss. To better understand these objects and how credt constrants endogenously affect them, I frst go to the specfc example E. Influence and Sales n Example E The expendture shares on ntermedate goods n sectors 2 and 3 are: p 1 M 21 p 2 Q 2 = σ 2 ϕ K 2, p 2 M 32 p 3 Q 3 = σ 3 ϕ K 3, 19 where σ s the output elastcty n sector wth respect to ntermedate nput and σ ϕ s sector s expendture share on the constraned ntermedate nput, wth ϕ < 1 ff the constrant n sector bnds. 16

17 In ths example, the nfluence, sales, and sales gap are respectvely: γ ξ µ σ 3 σ 2, σ 3, 1, σ 3 ϕ3 K σ 2 ϕ2 K, σ 3 ϕ3 K, 1, 1 1 ϕ3 K ϕ2 K, ϕ3 K, 1. I hghlght three observatons. Frst, the nfluence of downstream sector 3 s larger than that of mdstream sector 2, whch n turn has larger nfluence than upstream sector 1. Ths s because the fnal good s produced drectly from the downstream good, and any productvty shock n sector 3 wll drectly affect the effectve aggregate productvty, whereas postve productvty shocks n up- and mdstream sectors wll affect the effectve aggregate productvty only through ther ndrect effect on the relatve prce of good 3. A smlar ntuton apples to more general network structures: the sectors wth hgh nfluence wll be those that heavly supply to the fnal good ether drectly or ndrectly through other sectors. The second observaton relates to how credt wedges ϕ K affect sales and the sales gap. In ths economy, the entre output of sector 2 s used as nputs by sector 3, hence the total sales of sector 2 relatve to those of sector 3 s captured by σ 3 ϕ3 K, the ntermedate expendture share of sector 3. Smlarly, sales of sector 1 relatve to sector 2 s smply σ 2 ϕ2 K. Note that sector 2 s relatve sales are affected by ϕk 3 but not ϕk 2 : n other words, t s the credt constrants faced by downstream buyers, not wthn the sector tself, that affect the relatve sze of sector 2. Furthermore, sales s most suppressed n upstream sector 1, despte the fact that sector 1 tself s unconstraned. Ths s because sector 1 s sze s affected by constrants n both mdstream and downstream sectors an effect that s multplcatve n the sectoral wedges. The further upstream we go, and as we travel through an ncreasng number of constraned sectors, the hgher sales gap we would fnd of a sector. In equlbrum, the upstream sectors are too small n sales relatve to ther nfluence, whle the downstream ones are too large. Lastly, absent credt constrants, ϕ2 K = ϕk 3 = 1 and nfluence equals sales. Ths property holds under my general model and s orgnally formalzed by Hulten Influence and Sales n the General Model I now proceed to derve nfluence and sales n the general model and extend the ntutons to ths envronment. To fnd nfluence and sales n equlbrum, t s convenent to stack the sectoral elastctes and expendture shares nto matrces Σ and Ω: σ 11 σ 12 σ 1M σ Σ 21 σ 22 σ 2M..... ω 11 ω 12 ω 1M, Ω ω 21 ω 22 ω 2M σ M1 σ M2 σ MM ω M1 ω M2 ω MM 17

18 Each row n the matrces represents an output sector, whle each column represents an nput sector. That s, σ j, or the entres on the -th row and j-th column of the matrx Σ, represents the sectoral output elastcty n sector of nput j. Smlarly, ω j s the share of expendture on nput j as a fracton of the total sales n sector. For ths reason, Ω represents the nput-output table of the economy and s drectly observable from natonal accounts. In an economy wthout any dstortons or tax nterventons, the output elastcty matrx concdes wth the nput-output table: Ω Σ. The entres σ j and ω j dffer precsely because of sectoral dstortons such as fnancal constrants and tax nterventons. Let β denote the equlbrum vector of expendture share of the fnal good producer, β p 1 Y 1 F Y 1,, Y S,, p S Y S, F Y 1,, Y S whch s referred to as the vector of fnal shares. Because the fnal producer s unconstraned, β also represents the equlbrum vector of fnal good s output elastctes wth respect to nputs,.e. β = ln FY 1,,Y S ln Y. Proposton 3. In the decentralzed equlbrum, 1. The nfluence vector µ equals µ = β I Σ 1 β I Σ 1 α, where α s the vector of sectoral output elastcty wth respect to labor. 2. The sales vector γ equals γ = β I Ω 1 β I Ω 1 α. Corollary 1. Hulten 1978 Absent credt constrants, ω j = σ j for all, j, and nfluence equals to sales. The fact that nfluence s equal to sales absent market mperfectons s frst shown by Hulten 1978 on the class of generalzed Leontef models wth aggregate constant returns to scale, and t s the bass for usng sales to measure sectoral mportance n the growth accountng lterature. Ths equvalence holds n my model when there are no credt constrants but s otherwse broken. I now provde the ntuton for why ths s the case through the lens of the general model. The object I Σ 1 = I + Σ + Σ 2 + s the Leontef nverse of the sectoral output-elastcty matrx Σ. Ths object, mportant n the nput-output lterature, summarzes how sectoral productvty shocks propagate downstream to other sectors through the nfnte herarchy of cross-sectoral lnkages. To understand why nfluence takes the form n the proposton, consder normalzng all prces by wage rate and hold constant the fxed cost of entry relatve to the wage rate at κ/w. An one-percent ncrease n Hcks-neutral productvty h j n sector j has the drect effect of lowerng output prces n ts downstream sector by σ j percent, represented by the j-th entry of the output elastcty matrx Σ. The shock also has a second order effect that lowers output prces for all goods k that use j s output as nputs, whch n turn further lowers the prces n sector. Ths second order effect s[ captured by the j-th entry of the matrx Σ 2, and so on. The j-th entry n the Leontef nverse matrx I Σ 1] therefore captures the total j 18

19 effect of a productvty shock n sector j on the output prce of sector. These effects then translate nto hgher aggregate output or equvalently, lower relatve prce of the fnal good to wage rate, reflected by the dot product between the output elastcty of the fnal good β and the Leontef nverse I Σ 1. In sum, the sectors wth hgh nfluence n an economy are those wth hgh network-adjusted fnal shares. The scalar term 1 β I Σ 1 α, whch s not present n formulatons lke Acemoglu et al. 2012, arses from the endogenous entry of frms n my model. As the fnal good becomes cheaper relatve to the wage rate, entry becomes less costly. Ths attracts to more frms to enter all ndustres, creatng an amplfcaton effect. The sales vector takes the same form as the nfluence vector, replacng the elastcty matrx Σ wth the expendture share matrx Ω. To see why sales are constructed wth the expendture share matrx, note that sectoral sales can be wrtten as the nfnte sum that conssts of 1 ts output suppled to produce the fnal good; 2 ts output used by other sectors to produce the fnal good; 3 ts output used by other sectors, whch supply to other sectors to produce the fnal good, and so on: p j Q j = p j C j + S =1 p C ω j + S =1 p C [ Ω 2 ] j + 20 The common denomnator n the sales vector reflects the fact that only a fracton of the fnal good accrues to net aggregate output whle the remanng fracton s used to ncur the overhead fxed cost of entry. There are two ways n whch fnancal frctons affect equlbrum allocatons. Frst, as dscussed earler, constrants wthn a sector lower the effectve sectoral productvty by ncreasng the prce of sectoral output when nput prces are held constant. Ths effect travels downstream, servng as a negatve productvty shock that ncreases the prce of all downstream goods and eventually the fnal good. Second and more central to my analyss, fnancal frctons also affect the relatve sectoral sze and dstort sales away from nfluence. Credt constrants suppress equlbrum demand of constraned ntermedate nputs, endogenously affectng the equlbrum nput-output lnkages by reducng the sales of upstream goods that are subject to constrants. Contrary to the downstream travel of productvty shocks, ths effect nstead travels upstream, as can be seen from equaton 20. Credt constrants n sector reduce the equlbrum sales of good j to sector. Even f sector j s not constraned, the sector stll uses fewer nputs from ts own upstream supplers because t faces less demand for ts output, and n turn these upstream supplers end up wth lower sales. In equlbrum, t s the sectors that supply to many constraned sectors, whch n turn supply to many constraned sectors, ad nfntum, that have the least equlbrum sales relatve to nfluence. Baqaee 2015 and Acemoglu et al observe that n a producton network under Cobb-Douglas technology assumpton, productvty shocks travel downstream through nput-output lnkages from supplers to buyers, whle demand shocks travel upstream. My analyss so far makes two addtonal contrbutons to understandng how shocks propagate. Frst, fnancal frctons serve both as a productvty shock and a shock to ntermedate demand that emanates from the constraned sectors. The productvty shock aspect of fnancal frctons propagates downstream by lowerng aggregate output, 19

20 whle the demand shock aspect propagates upstream and suppresses the relatve sze of upstream sectors. Second, my analyss shows that these results do not rely on specfc functonal form assumptons. Demand shocks have no effect on the prces of output or the unt costs of producton n a generalzed Leontef model wth sectoral constant-returns-to-scale 1 and affect equlbrum quanttes only through backward lnkages or, n other words, by travelng upstream. On the other hand, productvty shocks travel only through forward lnkages, affectng the unt cost of producton and equlbrum prces of downstream buyers. Equlbrum prces of upstream sectors are unaffected, and output quanttes n upstream sectors change n response to productvty shocks from downstream only through the changes n demand nduced by these shocks. 2.4 Industral Polces I now proceed to show that the sales gap,.e. the rato between sectoral nfluence and sales, s a suffcent statstc that could gude polcy. There s clearly room for polcy nterventon n ths economy. Even wthout relaxng credt constrants, f a planner could mpose frm-level subsdes and taxes on producton nputs and profts, frst-best allocatons can be restored. Specfcally, the planner would tax frm profts to reduce entry n constraned sectors whle mposng frm-specfc subsdes to constraned nputs and undo the wedges mposed by credt constrants. The level of frm-specfc subsdes that restore frst-best would be such that the Lagrange multpler on credt constrants s precsely zero. However, to mplement such polces successfully n any real-world economes, a benevolent government has to grapple wth two dffcultes. Frst, the planner needs to have the fscal flexblty to talor subsdes to ndvdual frms wthn sectors. Second, the planner has to know the exact nature of credt constrants for each frm, whch requres not only nformaton on each frm s amount of workng captal and trade credt but also knowledge of frm-level productvtes. The requred nformaton and fscal flexblty n frst-best mplementaton are luxures that most polcymakers do not have. For ths reason, I consder tax nstruments that apply to all frms equally wthn a gven sector. To make progress, I leverage one crucal feature of generalzed Leontef models: not only do dstortons generated by credt constrants propagate through nput-output lnkages, but so does the effect of polcy nterventons. Due to pecunary externaltes from the nput-output lnkages, subsdzng producton upstream lowers the prces of upstream goods, whch ndrectly relaxes credt constrants downstream and amelorates cross-sector resource msallocaton. Ths property of producton networks leaves room for welfare-mprovng polcy nterventons, even when the planner only has access to a lmted set of nstruments. My man results show that the sales gap exactly captures the rato between the socal and prvate margnal return of spendng resources on sectoral producton, startng wth the decentralzed no-tax equlbrum. Rather than makng assumptons about the set of nstruments at the planner s dsposal and prescrbng optmal polces under these assumptons, an exercse I conduct under Cobb- Douglas assumptons, these results nstead provde answers to the followng queston: startng from the decentralzed equlbrum wthout any government nterventon, where should the fscal authorty spend the frst dollar of ts tax budget, among a gven set of lnear nstruments that nduce frms to use 1 Ths result can be vewed as an applcaton of the famous non-substtuton theorem by Samuelson