Bankruptcy and Aggregate Productvty Julan Nera Unversty of Eeter May 27, 205 Abstract I develop a model of fnancal ntermedaton to study the lnk between bankruptcy effcency the amount a lender can recover from bankrupt borrowers and aggregate productvty. The theory mples that countres wth low bankruptcy effcency are characterzed by a low fracton of large (productve) frms, and low aggregate productvty. These mplcatons are supported by the emprcal evdence. I then use the model to evaluate the quanttatve mplcatons of the model. I fnd that dfferences n bankruptcy effcency generate large aggregate productvty dfferences, close to those observed n the data for European countres. J.E.L. Codes: E44, E23, E02, D24, O47 Keywords: Bankruptcy, Fnancal Frctons, Msallocaton, Aggregate Productvty Correspondence to: j.nera@eeter.ac.uk. A prevous verson of ths paper was crculated under the ttle Recovery Rate, Msallocaton of Talent and Cross-Country Productvty Dfferences. I am partcularly grateful to Juan Sanchez and Javer Brchenall for helpful early dscussons of ths paper. I am also grateful to Peter Rupert, Fnn Kydland, Javer Brchenall, Marek Kapcka, Rsh Snghana, partcpants at the UCSB Macro Semnar, CERGE-EI and other venues for helpful comments and dscusson. All errors are my own.
Introducton Income dfferences across countres are large. The current consensus s that dfferences n physcal captal, human captal and labor across countres can account at most for half of the dfferences n GDP per capta (Hseh and Klenow, 200). The remanng s accounted for by dfferences n Total Factor Productvty (TFP), whch s the effcency wth whch these nputs are converted nto output. Consequently, understandng why TFP levels vary so much across countres s crucal for understandng the drvers of ncome dfferences. Yet, our understandng of the determnants of aggregate TFP remans vague. In ths paper, I use evdence from frm-sze dstrbutons across European countres to propose a theory of aggregate TFP based on the effcency of bankruptcy procedures. The startng pont of ths paper s to note that aggregate TFP s an average of frmlevel productvtes. Therefore, aggregate TFP can be decomposed nto two components: frm-level productvtes (level component) and the measure of frms of each productvty type (composton component). Evdence from Europe suggests that the composton component s an mportant drver of TFP dfferences. I document fve observatons from four European countres: the Unted Kngdom, Germany, Span, and Italy. The frst observaton s that Germany and the Unted Kngdom have hgher aggregate productvty than Span and Italy. Second, n all these countres larger frms (n terms of employees) are more productve than smaller frms. Thrd, German and Brtsh frm-sze dstrbutons have a larger proporton of large frms than Span and Italy. Fourth, condtonal on frm sze, Brtsh and German frms are not more productve than Spansh and Italan frms. These observatons together suggest that the composton component s an mportant drver of TFP dfferences. To llustrate the mportance of the composton component, I perform an accountng eercse usng the above data that suggests that aggregate productvty n Span and Italy would be about 0% hgher f they had the frm composton of Germany and the UK but kept ts own frm productvtes. The last observaton s that the effcency of bankruptcy procedures, as measured by the percentage of a loan a lender can recover from a bankrupt borrower, s hgher n Germany and the UK than n Span and Italy. I use these observatons to propose a Aggregate bankruptcy effcency for a country s measured by the World Bank Dong Busness database usng a methodology developed by Djankov, Hart, McLesh and Shlefer (2008). I dscuss the bankruptcy effcency data n detal n Secton 2. 2
new source of cross-country productvty dfferences: bankruptcy effcency. Countres wth less effcent bankruptcy procedures (tend to) have lower aggregate productvty because t nduces lenders to allocate funds to smaller (less productve) frms. I formalze ths dea n a model of fnancal ntermedaton wth entrepreneurs of heterogenous productvtes. The model allows for a closed form epresson for TFP, whch makes transparent the contrbuton of bankruptcy effcency to TFP through the composton of frms. I then nvestgate whether dfferences n bankruptcy effcency can generate large dfferences n aggregate productvty. I consder a statc model that features a compettve lender and households wth ether hgh or low entrepreneural productvty. If households fal to secure fundng to become entrepreneurs and operate ther technology then they become workers and rent ther labor for a wage. The lender wants to allocate resources to hgh-productvty entrepreneurs, but s constraned by two frctons. Frst, entrepreneural productvty s prvate nformaton of the entrepreneurs at the tme when loans (resources) are allocated. However, productvty can be nferred by lenders after producton has taken place. Hence, the lender could acheve frst best allocatons f t could mpose unlmted penaltes to entrepreneurs who msrepresent ther type. The second frcton lmts the penalty the lender can mpose for false productvty reports. An eogenous lmt on the penalty for false reports can be mapped to bankruptcy effcency n equlbrum, as t dctates the percentage of the loan that can be recovered by lenders on borrowers who msrepresent ther type and do not have resources to pay back the full amount of the loan. I show that, as the level of bankruptcy effcency decreases, two forces decrease aggregate productvty. Frst, the average frm qualty decreases. Ths effect s due to the tghtenng of the ncentve compatblty constrant of low-productvty entrepreneurs. As low-productvty agents face lower punshments for msrepresentng ther type, the lender deters them from lyng by mprovng ther relatve chances of obtanng a loan. In the aggregate, the composton of frms nvolves a hgher proporton of low-productvty frms than before. Second, the total number of frms decreases. Ths effect comes from the lender s feasblty constrant. Wth lnear utlty, the level of bankruptcy effcency also caps the amount the lender can etract from proftable projects to fnance other proftable projects. Hence, wth lower bankruptcy effcency, a lower number of projects 3
are funded. In equlbrum, the lender does not dstort the frm-sze margn so that frms produce at ther effcent level. Ths mples that there s a one-to-one mappng between frm productvty and frm sze (measured n number of employees). Hence, large frms are more productve than small ones. By constructon, frm TFP levels are eogenous and therefore nvarant wth bankruptcy effcency. Aggregate TFP then vares wth bankruptcy effcency solely through the composton of the frm-sze dstrbuton. I then proceed to endogenze wages. Endogenous wages renforce the dfferences n TFP. Lower bankruptcy effcency decreases total producton and wages. Wth a worsenng outsde opton of workng for a wage, prvate nformaton frctons are renforced by ncreasng the ncentves of low-productvty agents to msreport n order to mprove ther chances of operatng ther technology. I calbrate the model to the frm-sze dstrbuton and bankruptcy effcency of the Unted States. I then vary the level of bankruptcy effcency to levels of bankruptcy effcency observed for other countres. I fnd that dfferences n bankruptcy effcency are able to generate large dfferences n TFP among hgh-ncome countres, smlar to those observed for European countres. Emprcal support for the mechansm proposed n my paper comes from Pontcell (203), whch eplores the mpact of a reform n Brazlan bankruptcy law whch ncreased Brazl s aggregate recovery rate by 2 ponts. The author eplots varaton n the applcaton of the bankruptcy reform across Brazlan judcal dstrcts due to congeston of local courts. Crucally, Brazlan laws do not allow credtors or frms to choose the dstrct n whch to fle a bankruptcy case. The author fnds that bankruptcy reform led to hgher probablty of et by small frms and hgher frm growth, whch would lead to the type of shft n the frm-sze dstrbuton proposed n my paper. Ths paper s related to the estng lterature on msallocaton. Much of the lterature has focused on the msallocaton of captal across estng frms (Banerjee and Moll (200), Buera, Kabosk and Shn (20), Amaral and Quntn (200), Mdrgan and Xu (204), Moll (204), Stenberg (203), Greenwood, Sanchez and Wang (203)). I nstead focus on the etensve margn of captal msallocaton: not all hgh-productvty entrepreneurs are able to operate ther technology, but once they do, they obtan suffcent captal and labor to operate at ther effcent level. I abstract from captal msallocaton 4
at the ntensve margn because I am nterested n capturng the observaton that the largest frms are also the most productve. Wth captal msallocaton the relatonshp between sze and productvty mght be nverted (captal and labor could be mostly held by the unproductve frms). 2 European Productvty and Frm-Sze Dstrbutons Ths secton presents evdence motvatng the theoretcal approach of the artcle. The frst observaton s that Germany and the UK are more productve than Span and Italy. Aggregate Productvty, 2004-2009 Germany U.K. Labor Productvty 46.6 47.7 Total Factor Productvty, US n 2005= 89.3 97.7 Span 38.8 75.2 Italy 38.9 83. 36 38 40 42 44 46 48 50 70 75 80 85 90 95 00 Labor Productvty: PWT 7.0. TFP: GGDC PLD and EU KLEMS. Fgure : Germany and UK are more productve than Span and Italy Fgure plots GDP per hour worked (labor productvty) for the years 2000-2009. 2 The story s smlar f one nstead looks at TFP measurements n Fgure??, whch account for dfferences n captal ntensty. 3 Accordng to both fgures, the UK and Germany are more productve than Span and Italy (Italy snce the year 200). A more dsaggregated vew of these economes reveals that an mportant drver of 2 From Penn World Tables 7.0, varable rgdpl2th: PPP Converted GDP Laspeyres per hour worked by employees at 2005 constant prces. 3 I construct the TFP seres by combnng cross-country TFP level rankngs n the year 2005 from the GGDC PLD wth TFP growth rates from EU KLEMS. TFP levels n GGDC PLD are TFP Value Added, Sngle Dscounted. TFP growth rates n EU KLEMS come from sectoral data. 5
these TFP dfferences s the composton of each country s frm-sze dstrbuton. 4 Gross Value Added per employee, 2007-9 0-9 20-49 50-249 >250 employees employees employees employees employees Germany 34 42 46 57 82 U.K. 46 47 49 57 84 Span 29 35 43 54 85 Italy 28 43 50 62 73 34 42 47 58 8 Calculaton: Value added (at factor costs) dvded by total employment (number engaged); Thousands of EUR. Source: OECD.Stat SDBS ISIC Rev.3; Manufacturng Sector. Fgure 2: Large frms are more productve and frms of the same sze are smlarly productve across countres Dstrbuton of employees by sze of company, 2007 Germany 7% 8% 7% 25% 53% U.K. % 7% 2% 26% 44% Span 8% % 20% 24% 27% Italy 26% 5% 6% 2% 22% -9 employees 0-9 20-49 50-249 >250 employees employees employees employees Calculaton: Share of total employees (engaged) by sze class. Source: OECD.Stat SDBS ISIC Rev.3; Manufacturng Sector. Fgure 3: Germany and the UK have a hgher proporton of workers n large productve frms Fgure 2 llustrates two observatons. Frst, larger frms are more productve than 4 Others have notced ths before. For eample, see Mackenze... 6
smaller frms across all four countres (observaton 2). Second, there are no strkng dfferences between the productvty of frms of smlar sze across all four countres (observaton 3). Italy, for eample, s less productve than Germany and the UK n large and small frms, but Italy s medum szed frms are more productve than German and Brtsh frms. Spansh large frms are slghtly more productve than German and Brtsh large frms. Fgure 3 llustrates observaton 4. It shows that the frm composton s qute dfferent across Northern and Southern European countres. In Germany and the UK, 57% and 44% of workers are employed by the largest frms 5. In contrast, n Span and Italy only 24% and 2% of employees work for the largest frms. Productvty Levels vs Composton In ths secton I use an accountng eercse to assess the relatve mportance of frm productvty levels versus the composton of the frm-sze dstrbuton for TFP. The GDP dentty from natonal accounts s, Y = AK α N γ where Y s output, K s captal wth share α, N s labor wth share γ, and A s TFP. Suppose frm produces ouput y usng captal k, labor n, and productvty a wth a Cobb-Douglas technology, 6 y = a k α nγ. We can connect frm productvty levels and composton of the frm-sze dstrbuton to aggregate productvty by the followng dentty, A = ( π a α γ ) α γ () 5 The sze brackets are those reported by the Eurostat Structural and Demographc Busness Statstcs. 6 In order to sustan a non-degenerate dstrbuton of frm szes n an equlbrum model one needs to assume ether a sngle good and decreasng returns to scale producton technologes, or dfferentated products and constant returns to scale technologes. Hseh and Klenow (2009) (Append ) show that both formulatons are somorphc. 7
where π s the measure of frms of productvty a. Hence, π s control the composton of frms whereas a s control frm productvty levels. Epresson () s the man result of Proposton 2. Frm labor productvty s a good proy of frm total factor productvty f captal deepenng s roughly smlar across frms and across countres. Gven the lack of avalablty of cross-country frm-level captal data, 7 I assume n ths accountng eercse that captal-labor ratos, k α /n γ, are constant and equal to one for all frms. Table shows how aggregate productvty would change n each country f t had other countres set of frm level productvtes and frm composton (a s and π s n equaton ). 8 For eample, keepng Span s frm-sze productvtes constant and movng to Germany s composton would yeld hgher productvty (78.3) than Germany tself (75.75). On the other hand keepng Germany s frm-sze productvtes constant and movng to Span s composton would yeld lower productvty (67.8) than Span tself (69.2). The same s true for Span and the UK; e.g. the change n composton by tself generates larger productvty gans and losses than those seen n the data. The mpact of composton on aggregate productvty s not as stark for the combnatons of Italy wth Germany and the UK, but t s stll substantal. Italy s productvty would ncrease from 59.75 to 67.83 f t had the German frm composton, and to 65.69 f t had the Brtsh frm composton. Table : Impled aggregate labor productvty from combnatons of frm productvty levels and frm composton Germany Composton UK Composton Span Composton Italy Composton Germany Productvtes 75.75 73.09 67.8 65.90 UK Productvtes 77.58 74.87 68.92 67.68 Span Productvtes 78.3 75.46 69.2 67.76 Italy Productvtes 67.83 65.69 60.87 59.75 7 The best known cross-country frm-level datasets, Amadeus and Orbs (publshed by Bureau van Djk), do not typcally nclude the smallest frms and the qualty of data (percentage of frms covered) vares wdely from country to country. 8 The level of decreasng returns to scale s set to α + γ = 0.85, a standard value n the lterature, as n Basu and Fernald (995). 8
Bankruptcy effcency A strand of lterature argues that an mportant factor affectng the frm sze dstrbuton s the fnancng constrants faced by startups (for eample Evans and Jovanovc (989), Cabral and Mata (2003), and Kerr and Nanda (2009)). Ths paper proposes that one partcular factor affectng lender s fundng decsons the ablty to recover the loan n case of busness falure can by tself generate frm-sze dstrbutons consstent wth those of Europe. Fgure 4 shows that UK and Germany have hgher recovery rates the World Bank s measure of bankruptcy effcency than Span and Italy. In Germany and the UK a bank can recover more than 80 cents on each dollar loaned to a bankrupt company, whereas ths same fgure s n the low 70 s for Span and n the low 60 s for Italy. Recovery Rate, 2004-2009 8.7 Germany 85. U.K. Span 72.5 Italy 57. 40 50 60 70 80 90 Source: WB Dong Busness Fgure 4: Germany and UK have better bankruptcy effcency than Span and Italy The methodology used to collect the statstc was developed by Djankov, Hart, McLesh and Shlefer (2008) and adopted by the World Bank. The way the statstc s collected s the followng. The World Bank contacts bankruptcy lawyers n the country of nterest and sends them a case scenaro of a busness that s facng nsolvency. The scenaro s made as specfc as possble, detalng type of company, sze, locaton, and other factors to allow for cross-country comparablty. The company has a 0-year loan agreement wth a domestc bank, and due to nsolvency, s forced to default on ts loan. The com- 9
pany also has real estate property valued at eactly the same amount outstandng under the loan agreement. Gven that the bank wants to recover as much as possble of ts loan, the bankruptcy lawyers are asked for ther opnon on the fracton of the outstandng loan that can be recovered by the bank through reorganzaton, lqudaton, or foreclosure. The recovery rate accounts for the cost and tme of proceedngs. If a country has not eperenced more than one bankruptcy case go through ts courts n the last four years no data s collected. The followng secton sets up a model where frm composton s endogenously generated by dfferences n bankruptcy effcency. 3 Model I consder a standard verson of the Lucas (978) span of control model, augmented along the lnes of Erosa and Hdalgo-Cabrllana (2008) to ntroduce fnancal ntermedaton. The economy s populated by a contnuum of fnancal ntermedares and a contnuum of households of mass one. Preferences and Endowments Households are endowed wth ntal resources ˆf, one unt of labor and a producton technology. Some households become entrepreneurs and operate ther technology. Entrepreneurs employ captal and labor, produce a fnal good, and consume the profts. The remanng households become workers and rent ther labor to entrepreneurs. Households have lnear utlty over consumpton, u(c) = c. 9 Technology Households are heterogeneous n entrepreneural productvty a, where {low, hgh}, and have a producton functon of the form, y = a k α n γ, α, γ (0, ), 0 < α + γ <, (2) 9 The assumpton of lnear utlty s helpful n obtanng a closed-form soluton to the contract. Wth lnear utlty, entrepreneurs can be thought of as frms who are mamzng profts rather than utlty. 0
wth captal k and labor n. A fracton ν of households are endowed wth low entrepreneural productvty a l and a fracton ν are endowed wth hgh entrepreneural productvty a h. The costs of operatng the technology nclude a fed cost f. The need for fnancng arses because entrepreneurs cannot self-fnance the fed cost of producton, f > ˆf. Frctons In the frst-best scenaro all agents pool ther resources. Fundng goes to the hghproductvty agents frst and any remanng fundng goes to the low-productvty agents, gven that they are proftable (ther profts are hgher than the outsde opton of workng). There are two frctons that make the frst-best allocaton unachevable. Frst, entrepreneural productvty s prvate nformaton of the agents. Hence, low-productvty agents have an ncentve to pretend to be hgh-productvty so as to mprove ther chances of obtanng fundng. Producton occurs at the end of the perod and s observable. Therefore, productvty levels can be nferred by common knowledge of the producton functon and observable nputs. Agents could stll obtan the frst best allocatons f they wrte contracts that nclude nfnte punshments for false reports. However, there s a second frcton that lmts repayments to a fracton φ of the loan. Bankruptcy n ths model s the scenaro where entrepreneurs are unable to repay ther epected amount because they msrepresent ther type. I label, φ, the level of bankruptcy effcency. Fnancal Intermedares Fnancal ntermedares operate n a perfectly compettve market and lend to a set of homogeneous households (agents do not learn ther type untl after they have entered the contract). Compettve markets mply that ntermedares offer contracts that mamze the epected welfare of ther pool of borrowers. 0 that there ests a representatve fnancal ntermedary. E-ante homogenous agents mply 0 The assumpton of perfect competton mght seem strong n ths settng, but t could be replaced by an assumpton of a few lenders engagng n Bertrand competton n contracts. If agents are heterogenous before they enter the contract, then a poolng Nash equlbrum - where no lender can devate from the representatve fnancal ntermedary and offer a better contract n order to attract a better pool of agents - mght not est (see Prescott and Townsend (984)).
The tmng of events - see Fgure 5 - s as follows: Fgure 5: Tmng Intermedary posts contracts Enter contract Yes Household learns type and reports Intermedary chooses who operates technology by randomzng Chosen Become entrepreneur: Produce True Report No Not Chosen False Report Pay Loan Work for wage Work for wage Pay Penalty. Fnancal ntermedares post contracts. A contract s a 6-tuple {(e l, L l, Ll F), (e h, L h, Lh F)}. For each productvty type, the contract specfes the fracton of entrepreneurs who wll operate ther technology, e. The rest (fracton e ) work for a wage. For entrepreneurs who are chosen to operate ther technology, the contract specfes the repayment schedule for true reports, L L(a a ), and for false reports, L F L(a a ). 2. Households decde whether to enter the contract wth the fnancal ntermedary. Households who do not enter the contract work for a wage, rent out ther captal, and consume w + η at the end of the perod, where η = ( + r) ˆf s the household s ntal endowment after earnng nterest. 3. Households learn ther type and report t to the fnancal ntermedary. 4. The fnancal ntermedary chooses the households who operate ther technology for each type (through a randomzaton devce). 5. Households who are chosen to operate ther technology become entrepreneurs. They are allocated captal k, labor n, and fed cost f. The households who are not chosen to operate ther producton technology supply labor, earn the market wage rate and consume w. 2
6. Entrepreneurs produce and all nformaton s revealed. If an entrepreneur reported her productvty truthfully she consumes y L. If an entrepreneur msreported her productvty she consumes y F L F. Fnancal ntermedares mamze households epected consumpton subject to ncentve compatblty, enforcement, partcpaton, and resource feasblty constrants, as descrbed below. The Intermedary s Problem The revelaton prncple allows us to focus, wthout loss of generalty, on allocatons n whch households report ther type truthfully. The objectve of the fnancal ntermedary s to choose allocatons (k l, n l, k h, l l ) and terms of contract (e l, L l, Ll F, e h, L h, Lh F ), gven prces w and r, such that. Entrepreneur s epected consumpton s mamzed (before they learn ther type), ma E[c] = νc l + ( ν)c h (3) where c = e (y L ) + ( e )w. 2. Incentve Compatblty: e (y L ) + ( e )w e (y F L F ) + ( e )w, {l, h} (4) A type entrepreneur who falsely clams to be type wll operate hs productve technology wth probablty e and be assgned captal k, labor n, and fed cost f. Wth these nputs, type entrepreneur wll produce y F n B). = a a y (dervaton 3. Imperfect Enforcement: L φy (5) L F φy F (6) 3
4. Partcpaton Constrant: If a household declnes to enter a contract, he gets wage w, and consumes hs wage plus hs net worth for a total consumpton of w + η. The partcpaton constrant s therefore νc l + ( ν)c h w + η (7) Snce ntermedares can acheve any allocaton that households can acheve on ther own, and snce the ntermedary mamzes household s epected utlty, households are weakly better off contractng wth the ntermedary. 2 5. Feasblty: The fnancal ntermedary faces a known fracton ν of low-productvty entrepreneurs and a fracton ( ν) of hgh-productvty entrepreneurs. Let κ = rk + wn + f stand for the cost of producng output y. The feasblty constrant requres that the resources dsbursed by the fnancal ntermedary to entrepreneurs (left hand sde) cannot eceed collectons plus ntal resources (rght hand sde). νe l κ l + ( ν)e h κ h νe l L l + ( ν)e h L h + η (8) Notce that n the drect mechansm the ntermedary allocates captal and labor contngent on the productvty report, and hence contngent output y and y F, drectly to the entrepreneurs. 3. Partal Equlbrum: Optmal Contract Allocatons The ntermedary allocates the proft-mamzng levels of captal and labor to each operatng enterprse, gven prces r and w. To see why ths s so, notce that the objectve of the ntermedary s equvalent to a socal planner problem, and as such, the ntermedary wll try to dstort as few margnal decsons as possble. Any ncentve compatblty benefts from devatng from proft-mamzng output can be replcated by changes n 2 The ntermedary can match the outsde opton by settng e h = e l = 0 and returnng the ntal endowment to households. 4
the terms of the contract that do not dstort the ntensve margn of producton. Thus, k = k and n = n. To smplfy notaton from here on, (y, k, n ) stand for ther proft mamzng levels (y, k, n ). It follows that there s no captal msallocaton on the ntensve margn. I say there s msallocaton of talent f there ests a hgh-productvty entrepreneur who s not operatng her technology whle a low-productvty entrepreneur operates hers. Terms of the contract The followng propostons state some partal equlbrum propertes of the contract. Proposton Suppose wages are low enough so that the no-prvate-nformaton allocaton s not ncentve compatble, w < a l a h y h φκ l.. Average Qualty: The rato of hgh to low-productvty projects funded s gven by the epresson e h e l = y l L l w ( φ) a l a y h h w. (9). Quantty of Hgh-Productvty Projects: The quantty of hgh-productvty projects funded s gven by the epresson e h = ( a ( φ) l ν(κ l L l ) a h y h w y l L l w η ) ) (0) + ( ν) (κ h φy h. Furthermore, suppose wages are hgh enough so that low-productvty projects are not proftable, w > y l κ l. Then L l = 0, and average qualty of projects (9) and the quantty of hgh-productvty projects (0) are strctly ncreasng n the recovery rate φ. Proof. For. and. see Append C. For., f L l = 0 then (e h/e l ) φ (0), respectvely. > 0 and e h φ > 0 n (9) and Epresson (9) s obtaned by combnng the bndng ncentve compatblty constrant for low-productvty wth mamum punshment for false reports, L F l = φy F l, and replacng y F l = a l a h y h. Epresson (0) s obtaned by combnng epresson (9) wth the feasblty constrant and mamum collecton from hgh-type proftable projects, 5
L h = φy h. 3 The assumpton of an upper threshold for wages s smply a formalzaton of the ntal premse that prvate nformaton s a constrant on lender s fundng decsons. If wages are too hgh, low-productvty entrepreneurs are better off rentng ther labor than they are operatng ther technology. In that scenaro they have no ncentve to msreport ther type as they prefer a lower probablty of operatng ther technology, and nformaton constrants do not bnd. The frst part of Proposton epresses the rato of hgh to low productvty projects. If low-productvty projects are unproftable, then ths rato decreases as the level of contract enforceablty decreases. The ntuton s that as the ablty of punshment for false reports shrnks, the lender has to ncrease the relatve probablty of acceptance of low-type n order to prevent low-types from reportng falsely. Notce ths average qualty effect goes solely through the ncentve compatblty of low-type. The second part of Proposton shows the epresson for the total quantty of hghproductvty projects. If low-type projects are unproftable, the epresson ncreases wth the recovery rate. Ths effect comes from the feasblty constrant. As recovery rates ncrease, the lender s able to etract hgher rents from proftable projects n order to fund other proftable projects. The assumpton of unproftablty of low type s a suffcent, but not necessary, condton to obtan clean predctons for the change n average qualty and total quantty wth recovery rates. If low types are proftable, the average qualty and quantty of hgh type projects could stll ncrease, dependng on model parameters. However, n the quanttatve eercse n Secton 5, I do not mpose any restrctons on parameters and verfy that all condtons and assumptons hold. Notce that ntal resources, η, s an mportant parameter. If agents are born wth zero wealth then η = 0 and there are no resources to allocate among entrepreneurs, hence e l = e h = 0. Hgher ntal wealth wll ncrease the number of projects funded and wll play an mportant role n nterpretng the results for low-ncome countres n Secton 5. For these countres, dfferences n recovery rates seem to be of secondary mportance for eplanng cross-country dfferences n TFP. Of prmary mportance s the ntal resources they have to dstrbute among entrepreneurs, η. 3 Incentve compatblty for hgh-type mght bnd, and then L h s set by the bndng ncentve compatblty constrant for hgh-type. Ths s n contrast to Erosa and Hdalgo-Cabrllana (2008); see C for detals. 6
3.2 Total Factor Productvty Defne π l νe l and π h ( ν)e h as the measure of low and hgh-productvty projects operated n the economy, respectvely. Let Y π y, K π k, and N π n be the aggregate ouput, captal and labor n the economy. The followng proposton states that the aggregate producton functon and TFP have a closed-form soluton. Proposton 2. The aggregate producton functon has a closed-form soluton gven by Y = AK α N γ () where total factor productvty s ( A νe l a α γ l + ( ν)e h a α γ h ) α γ (2) Measured TFP n the compettve equlbrum s Y K α N γ = Y A (3). TFP s strctly ncreasng n quantty of hgh-productvty projects e h. In addton, f ( ν)a α γ h > νa α γ l, TFP s strctly ncreasng n the average qualty of projects e h /e l, as long as e l + e h s smultaneously non-decreasng. Proof. For., see Append A. For., t follows from (2). Notce A s not the same as measured TFP. In level accountng eercses the aggregate producton functon s assumed to dsplay constant returns to scale wth captal share equal to /3. Snce frms n the model have decreasng returns to scale, equaton (3) s the correct epresson to compare to the data, wth α set to /3. For a non-decreasng total quantty of projects as the recovery rate ncreases, all that s needed s that the quantty of low-productvty projects does not decrease faster than hgh-productvty projects ncrease. In the quanttatve eercse, both hgh-type projects and low-type projects ncrease wth the recovery rate. 7
3.3 Compettve Equlbrum Wth the household and ntermedary s problem specfed, the compettve equlbrum n ths economy can now be defned. Aggregate labor supply s determned by the measure of households who dd not become entrepreneurs, ν( e l ) + ( ν)( e h ). Aggregate labor demand s gven by the total amount of labor demanded by frms of both types, νe l n l + ( ν)e h n h. Smlarly aggregate captal demand and aggregate fnal good supply are determned by νe l k l + ( ν)e h k h and νe l y l + ( ν)e h y h, respectvely. Fnally, aggregate fnal good demanded s determned by the resdual consumpton from the household s problem, c e = ν[e l (y l L l ) + ( e l )w] + ( ν)[e h (y h L h ) + ( e h )w]. Defnton A compettve equlbrum conssts of a fnancal contract {e, L, L F}, allocatons {y, k, n } and prces w and r such that. Allocatons k, n and y mamze frms profts, gven prces w and r for all 2. The fnancal contract solves the fnancal ntermedary s problem 3. Markets Clear: w clears the labor market: νe l n l + ( ν)e h n h = ν( e l ) + ( ν)( e h ) Gven r, the captal market clears: νe l k l + ( ν)e h k h = K The fnal goods market clears: E[c] + f (νe l + ( ν)e h ) = νe l y l + ( ν)e h y h Notce that the general equlbrum effects renforce the msallocaton of resource at low levels of enforceablty. Wth better contract enforceablty, there s hgher labor demand whch drves up wages. Ths relaes ncentve compatblty constrant of low types by makng the outsde opton of entrepreneurs more attractve (hgher wages rela (4) snce ( e l ) > ( e h )). 4 Takng the Model to the Data: Mult-Sector Model As the prevous secton showed, an mportant parameter n the calculatons of TFP s the levels of frm productvtes, a l and a h. The frst order condtons for the frm problem 8
show a drect relatonshp between the employment dstrbuton and the dstrbuton of productvty. In partcular, n h n l = ( ah a l ) α γ (4) In order to calbrate the dstrbuton of productvtes one could arbtrarly dvde the U.S. frm sze dstrbuton nto a representatve large frm and a representatve small frm and use equaton (4). Alternatvely, one can etend the model n some drecton to obtan a dstrbuton of frm szes. Ths s the approach I pursue here. In partcular ths secton etends the model to the case of multple sectors and shows that the man results hold n ths more general framework. Preferences, producton functons, and frctons are the same as n the one-sector economy. A sector s defned as a group of frms who produce an dentcal product. There s a unt mass of agents born nto each sector. Agents are born wth a sectorspecfc technology but they can work n any sector for wage w, same across sectors. Sectors dffer n the level of the fed cost to operate a technology. There s one ntermedary per sector (no cross-subsdzaton across sectors), so that the contract of the one-sector economy can be vewed as the contract of a specfc sector. Let subscrpt j be the sector subscrpt and be the productvty level subscrpt. To redefne the problem wth dfferent sectors, one can rewrte ndvdual producton functons as y j = a k α j nγ j (5) An entrepreneur s problem s ma k j,n j p j y j rk j wn j f j (6) where p j are sector-specfc output prces. Let π lj νe lj and π hj = ( ν)e hj stand for the measure of low and hgh-productvty projects n sector j, respectvely. Usng the aggregaton n A, each sector has a representatve frm wth producton functon of the form y j = A j k α j nγ j (7) 9
( where, y j = π j y j, k j = π j k j, n j = π j n j, and A j π j a representatve sector frm solves the followng problem α γ ) α γ. The ma k j,n j p j y j rk j wn j (8) Notce the fed cost shows up as a cost n the frm problem but not n the representatve sector frm problem. Fnally, I ntroduce a new parameter, θ, whch determnes the complementartes between sectors. In partcular, assume a perfectly compettve representatve frm produces a sngle fnal good by combnng sector outputs wth a CES technology, so that t solves the followng problem ma {y j } ( j y θ j ) /θ j p j y j (9) where θ s the elastcty of substtuton between sectors. The man dfference wth the prevous compettve equlbrum s that there are now J new markets and prces, one for each sector. Defnton 2 A compettve equlbrum wth sectors conssts of fnancal contracts {c j, e j, L j, L F j } j, allocatons {n j, k j, y j } j and prces w, r, and {p j } j such that. k j and n j, and y j solve the frm s problem,, j 2. The fnancal contract solves the fnancal ntermedares problem, j 3. Markets Clear: p j clears the sector market, y Supply j (p j, r, w) = y Demand j (p j, {c e }) j w clears the labor market, j π n j = j [ν( e lj ) + ( ν)( e hj )] Gven r, the captal market clears: j π k j = K The fnal goods market clears, j E[c j ] + j f j (ν( e lj ) + ( ν)e hj ) = ( ) /θ j y θ j where y Supply j s output by sector j, y Demand j s demand by the fnal good producer. Proposton 3 TFP n the mult-sector economy wth sectors s analogous to the sngle sector economy. In partcular, 20
Y K α N γ = ( j ( y j A j ) θ ) θ θ θ (20) where ( A j νe lj a α γ l + ( ν)e hj a α γ h ) α γ (2) Proof. See Append D. 5 Quanttatve Analyss In ths secton I calbrate the model to data for the Unted States. In my calbraton I treat the Unted States as an economy wth prvate nformaton and mperfect enforcement frctons, and wth a recovery rate of 80%. Wth the calbrated economy n place, I vary the recovery rate as n the data to eplore what fracton of TFP dfferences that can be attrbuted to bankruptcy effcency. 5. Calbraton and Measurement Several of the model parameters are those of the growth model and I follow standard procedures for choosng those values. Relatve to the growth model, what s new are the parameters that determne the dstrbuton of frms n equlbrum. Tables 2 and 3 summarze the calbraton. Table 2: Benchmark Calbraton to U.S. Data: Parameters Set Before Equlbrum Symbol Defnton Value Target/Source φ Recovery Rate 80% Data α Frm Captal Share 28.3% Agg. Captal Share, Dec. Returns γ Frm Labor Share 56.7% Agg. Captal Share, Dec. Returns θ Complementarty between Sectors 0.9 Markup of % J Number of Sectors 36 Rajan and Zngales (998) [ f, f 36 ] Range of Fed Costs [, 4.3] Rajan and Zngales (998) a l Productvty of Low Type Normalzaton 2
Table 3: Benchmark Calbraton to U.S. data: Parameters Calbrated to Equlbrum Outcomes Symbol Defnton Value Target Moments U.S. Data Model r Interest Rate 0% Captal Output Rato 3 3.2 a h Productvty of Hgh Type.695 Top 0% employment share 65% 65% ν Fracton of Low Type 63% Skew of frm-sze dstrbuton 5.05 4.99 η Intal endowment 0.376 Mean frm sze 50.5 50.5 Frst I dscuss the choce of parameters for whch drect estmates are avalable and then I dscuss the ones that are chosen to match equlbrum moments. The data on recovery rate s collected by World Bank Dong Busness database. I use the average from 2004 (the earlest avalable data) to 2009 (to eclude the fnancal crss). The recovery rate s φ = 80% for the Unted States. The etent of decreasng returns n the producton functon s an mportant parameter n my analyss. Drect estmates of frm-level producton functons and dfferent calbraton procedures pont to a value for α + γ = 0.85. 4 The splt between α and γ s done accordng to the ncome share of captal and labor, so I assgn /3 to captal and 2/3 to labor, mplyng α = 0.283 and γ = 0.567. 5 Sector outputs are aggregated wth a CES functon wth elastcty parameter θ. TFP dfferences are magnfed by the degree of complementarty between sectors, so I am conservatve n the choce of ths parameter and choose θ = 0.9. In a model of monopolstc competton ths would delver a markup of %, a lower bound among the emprcal estmates of markup costs. 6 The number of sectors and the sector-specfc fed cost are based on values provded by Rajan and Zngales (998). Usng Compustat data, Rajan and Zngales calculate the need for eternal fnance (defned as the fracton of captal ependtures not fnanced wth cash flow from operatons) for 36 sectors n the Unted States durng the 980s. The sector wth lowest need for eternal fnance s Tobacco, wth a measure of -0.45 and the one wth the hghest need s Drugs at.49. I set J = 36 and normalze the lowest 4 See for eample Basu and Fernald (995), Atkeson and Kehoe (2005), and Amaral and Quntn (200), among others. 5 Usng labor shares, Golln (2002) shows that captal shares are close to /3 for dfferent countres and do not systematcally vary wth development levels. 6 Ths value s n lne wth the choce n Atkeson and Kehoe (2005), and the evdence n Basu and Fernald (995), Basu (996) and Basu and Kmball (997). 22
level of sector fed cost to. Sector fed costs are chosen to range unformly from to (0.45 +.49)/0.45 = 4.3. To place the magntude of fed costs n perspectve, consder that the wage n the compettve equlbrum s around.05. Therefore, fed costs of startng a frm are about to 4.3 tmes the average annual salary. Now I dscuss the parameters calbrated to equlbrum moments. The nterest rate determnes the captal output rato and t s set to 0% to match a captal output rato of 3. Ths s consstent wth evdence n Gomme and Rupert (2007). I am left wth four parameters to match to equlbrum targets, a l, a h, ν and η. Any choce of a l can be undone by rescalng a h. Thus, I set a l = as a normalzaton. The other parameters are calbrated to moments of the U.S. frm-sze dstrbuton. The data for the U.S. frm-sze dstrbuton s from the US Census Bureau. 7 The U.S. Census reports the number of establshments for certan employment ranges for all sectors at the three-dgt level. I restrct the observatons to manufacturng to make t compatble wth Rajan and Zngales (998) fed cost data. I set a h to match the share of employment by the top 0% largest frms. ν controls the skewness of the dstrbuton, and I set t to match a skewness of 5.05 (defned here as mean dvded by medan). The endowment η shfts the frm-sze dstrbuton, so t s set to match the average frm sze n U.S. manufacturng of 50.5. 8 6 Fndngs 6. Varaton n the recovery rate, φ Fgures 6 and 7 llustrate the change n average qualty and total quantty of projects brought about by an eogenous change n the recovery rate. The fgures dsplay the results for the medan fed-cost sector, but the pattern s smlar n all sectors. Fgure 6 shows that the average qualty s not only ncreasng n the recovery rate, but the ncrease s happenng at an ncreasng rate. Two thngs are worth notng. Frst, low-productvty projects are not proftable, so Proposton () apples drectly: the partal equlbrum 7 I am grateful to Mark Wrght for provdng a specally tabulated dataset of the US frm sze dstrbuton for the year 2000. 8 From U.S. Census data I only observe the number of establshment for certan employment ranges. The mean employment sze for each range s used to compute the mean frm sze. 23
effect on the optmal contract leads the average qualty to ncrease as the recovery rate ncreases. Second, the general equlbrum effect on mprovng wages wth the recovery rate leads to a further ncrease n the average qualty. Fgure 7 shows that the overall quantty of projects ncreases as well. What s worth notng here s that the ncrease s not only happenng n the hgh-productvty projects, as epressed n Proposton (), but also n low-productvty projects. e h /e l e h +e l 0.4 0.24 0.22 0.35 0.2 0.3 0.8 0.6 0.25 0.4 0.2 0.2 0. 0.5 0.08 0. 0.06 0.05 0.04 0.02 0 0 0 20 30 40 50 60 70 80 90 00 0 0 0 20 30 40 50 60 70 80 90 00 Recovery Rate, ϕ Recovery Rate, ϕ Fgure 6: Average qualty of projects Fgure 7: Quantty of projects Recovery Rate 90 8% 9% 80 87% 3% 70 9% 9% 60 93% 7% Small frms Large frms Fgure 8: Frm sze dstrbuton. Small frms: π l /(π l + π h ). Large frms: π h /(π l + π h ) Fgure 8 shows the overall effect n the frm-sze dstrbuton for four values of the 24
recovery rate. As average qualty and total quantty of projects ncrease, the frm-sze dstrbuton contans a lower percentage of small frms (low-productvty). The percentage of small frms s calculated as π l /(π l + π h ) and the percentage of large frms as π h /(π l + π h ). 9 Ths fgure confrms that dfferences n bankruptcy effcency can ratonalze the observaton that dfferences n bankruptcy effcency alone generate varaton of the frm-sze dstrbuton consstent wth the European data n Fgure 3 n Secton??..4.2 TFP Relatve to U.S. 0.8 Model 0.6 0.4 0.2 0 0 0 20 30 40 50 60 70 80 90 Recovery Rate (Cents per Dollar, 2004-2009) Fgure 9: Model s calbrated to the Unted States at a recovery rate of 80% and TFP=. The lne traces the TFP predcted by the model from varyng the recovery rate from 0 to 90%. The crosses map the combnaton of TFP and recovery rate of 90 countres n the data. Fgure 9 shows the mplcaton of the changng frm-sze dstrbuton for TFP. The calbraton to the Unted States s the pont wth TFP equal to and recovery rate equal to 80%. Varyng the recovery rate from 60 to 90% yelds large varatons n TFP. If the Unted States had a recovery rate of 60% as Italy does, ts TFP would be about 20% lower than ts current TFP. Alternatvely, the TFP of the U.S. would be 20% hgher f t mproved t s recovery rate to 87%, as n the UK. However, recovery rates lose eplanatory power 9 π s the sum of π j across all sectors. 25
below recovery rates of 60. For recovery rates between of 0 to 60, recovery rates generates small varatons n TFP. 6.2 Varaton n the ntal endowment, η Motvated by the lack of varaton of TFP n low recovery rate countres, I perform another eperment. In addton to varyng the recovery rate, I ask what level of ntal endowment would allow the model to match perfectly the TFP n the data (dashed lne n Fgure 0). I then hold recovery rate constant at the U.S. level and use the ntal endowment from the perfect match to ask how much varaton n ntal endowment alone could eplan TFP dfferences (red squares lne n Fgure 0). Intal endowment alone (red squares lne) eplans less n hgh recovery rate countres, but a substantal amount of TFP varaton n low recovery rate countres. One nterpretaton of ths result s that mprovements n bankruptcy procedures by tself has lttle mpact n low-ncome countres, unless t s accompaned by mprovements n ntal endowments. Put dfferently, the msallocaton of resources among entrepreneurs s of second order f the amount of resources to be allocated s low to begn wth. 7 Concluson Ths paper documents that frm-sze dstrbutons are an mportant drver of productvty dfferences between European countres, and t proposes dfferences n bankruptcy effcency as a drver of frm-sze dstrbutons. Low recovery rates, a measure of bankruptcy effcency, affect productvty dfferences by reducng the average qualty and total quantty of frms n an economy. The model calbrated to U.S. data suggests that dfferences n the recovery rate alone can generate TFP dfferences of smlar magntudes of those observed across European countres. The quanttatve eercse was also used to nvestgate the mpact of ntal endowments n eplanng TFP dfferences. The results suggest that mprovements n bankruptcy effcency have the hghest mpact on mddle and hgh-ncome countres. Other factors (such as corrupton, wars, health) that are not eplctly modeled but mght affect ntal endowments are most mportant for low-ncome countres. The fndngs suggest that n 26
0 0 20 30 40 50 60 70 80 90.4 0 0.2 0.4 0.6 0.8.2 Recovery Rate (Cents per Dollar, 2004-2009) TFP Relatve to U.S. Only ϕ Only η ϕ and η Fgure 0: Crosses: Countres n data. Hollow crcle (blue) lne: Only recovery rate φ vares. Square (brown) lne: Only ntal endowment η vares. Dashed (green) lne: Recovery rate and ntal endowment vary smultaneously. low-ncome countres reforms to mprove bankruptcy effcency must be accompaned by mprovements n other factors that affect low endowments n order to generate sgnfcant progress n aggregate productvty and ncome. A unque focus on the mprovng the bankruptcy code seems napproprate n low-ncome countres. 27
Append A Aggregate Total Factor Productvty and Frm Productvty Indvdual s endowed wth producton functon y, whch takes nputs k and n combnes them wth a Cobb-Douglas technology y (k, n ) = a k α nγ (A-) where α + γ <. The frst order condtons from the frm s problem are α y k = r, γ y n = w. (A-2) (A-3) The rato between margnal products s n = rγ k wα. (A-4) Obtan epressons for uncondtonal factor demand by substtutng (A-4) back nto the frst order condtons (A-2) and (A-3), Where B = k (r, w) = B α γ α r a α γ, (A-5) n (r, w) = B α γ γ w a α γ. (A-6) ( ( αr ) α ( γ w) γ ). Defne K = k π, N = n π and Y = y π, where π s the fracton of projects of type that are operated. Aggregate equatons (A-5) and (A-6) and dvde both sdes by π a K N ( ( π a π a α γ α γ ) = B α γ α r, ) = B α γ γ w. α γ to obtan (A-7) (A-8) 28
Substtute back nto (A-5) and (A-6), k (K) = K a α γ π a α γ n (N) = N a α γ π a α γ Pluggng back nto the ndvdual producton functon (A-) yelds y = a α γ ( π a α γ, (A-9). (A-0) ) α γ K α N γ. (A-) Aggregatng one last tme we fnd the epresson for sector output, Y = AK α N γ (A-2) where Append B A ( π a α γ ) α γ. Ouput of False Report Substtute the margnal ratos (A-4) nto the producton functon (A-) and solve for condtonal factor demand ( r ) y (w, r, k ) = a B k α y (w, r, n ) = a B ( w γ ) n (A-3) (A-4) wth B as defned n A. Solvng for factors, we get condtonal factor demand, k (w, r, y ) = α r B n (w, r, y ) = γ w B a a y y (A-5) (A-6) 29
Substtutng nto the cost functon, κ (w, r, y ) = rk (w, r, y ) + wn (w, r, y ) + f and substtutng n for B, (( α ) α ( γ γ ) κ (w, r, y ) = (α + γ) r w) a y + f (A-7) Fnd output by pluggng the cost functon nto the frm problem and mamze to get (( α y (w, r) = r ) α ( γ w) γ ) α γ a α γ (A-8) We can rewrte the cost functon as κ (w, r, y ) = ψ y + f where ψ a ( ( (α + γ) rα ) ( ) α γ ) wγ. An entrepreneur who msrepresents hs type s gven funds ψ y producton costs are ψ (y F) + f. Makng these two equal yelds y F + f but hs real = a a y. Append C Soluton to the Contract The soluton begns wth the no-prvate-nformaton problem, and then adds prvate nformaton. Rewrte the problem as a lnear programmng problem, wth L e L ma e l,e h, L l, L h, L l F, L h F s.t. E[c] = ν(e l (y l w) L l ) + ( ν)(e h (y h w) L h ) + w e l (y l w) L l e h (yl F w) L l F e h (y h w) L h e l (yh F w) L h F νe l (κ l ) + ( ν)e h (κ h ) νl l + ( ν) L h + η (A-9) (A-20) (A-2) (A-22) 0 L e φy (A-23) 0 L F e φy F (A-24) 0 e (A-25) 30
No-prvate-nformaton In the no-prvate-nformaton envronment, (A-20) and (A-2) are absent. Notce the effect of L l and L h s neutral: Increasng ether reduces (A-9) by the same amount t relaes (A-22) so ther values are ndetermnate. The proporton of hgh ablty projects funded s the mamum possble snce t ncreases (A-9) by more than t reduces (A-22) because y h κ h w > 0. The amount of funded projects e h e l because y h κ h w > y l κ l w. The proporton of low projects funded s e l = 0 f low type s unproftable because t constrants (A-22) by more than t ncreases (A-9) y l κ l w < 0, and postve otherwse. Prvate nformaton If w > a l a h y h ( φ) then the no-prvate-nformaton allocatons are ncentve compatble. Recall the ncentve compatblty constrant for low type, e l (y l L l ) + ( e l )w e h (y F l LF l ) + ( e h)w. (A-26) If low ablty agent s unproftable (y l κ l < w) or there are suffcent hgh-ablty agents (e h < ), then e l = 0 n the no-prvate-nformaton allocaton. Ths allocaton s ncentve compatble f w e h (y F l LF l ) + ( e h)w. (A-27) A low-productvty entrepreneur who les obtans output yl F = a l a y h h (B). To deter lyng, t s optmal to set the punshment for lyng as hgh as possble, Ll F = φyf l = φ a l a y h h. Substtute ths epresson n (A-27) to obtan, w e h a l a h y h ( φ) + ( e h )w. (A-28) Substract ( e h )w and dvde by e h from both sdes to obtan the threshold wage beyond whch the no-prvate-nformaton allocaton s always ncentve compatble. 3
w a l a h y h ( φ). (A-29) Incentve compatblty bnds: w < a l a h y h ( φ) Frst, settng L F = e φy F for all s optmal snce t relaes (A-20) and (A-2) but has not other effects elsewhere. Net, (A-20) bnds and, rearrangng, we obtan e h e l = y l L l w ( φ) a l a y h h w. (A-30) Feasblty always bnds, so combnng (A-30) wth (A-22) one obtans e h = ( a ( φ) l ν(κ l L l ) a h y h w y l L l w η ) ) (A-3) + ( ν) (κ h L h and the amount of low-ablty projects funded, e l = η ( )( ν(κ l L l ) + ( ν) κ h L h yl L l w ( φ) a l a y h w h ). (A-32) The remanng arguments of the contract are L h and L l. We already argued that the drect effect of L h n the objectve functon and feasblty constrant s neutral. Yet, ncreasng L h has another ndrect effect on the objectve functon by ncreasng the quantty of projects e h and e l. To see ths, notce that e h L h and (A-32). Snce e ce > 0 and ce l e h L h s pnned down by (A-2) wth equalty. > 0 and e l L > 0 n epressons (A-3) h > 0 n (A-9), L h = φy h, unless (A-2) bnds and then L l s also drectly neutral on the objectve functon and the feasblty constrant. Its ndrect effect on the objectve functon through e l s postve, as e l L > 0. However, ts l ndrect effect through e h depends on the proftablty of low-productvty projects. If κ l L l y l w L l low-type projects are proftable (y l κ l > w) then e h L > 0 because l L < 0 n l the denomnator of epresson (A-3). Hence ncreasng L l has an overall postve effect on the objectve functon, and L l = φy l. However, f low types are unproftable, then e h L l < 0 by the opposte argument. Snce hgh-productvty projects are more benefcal 32