Finance and Development: A Tale of Two Sectors

Transcription

1 Finance and Development: A Tale of Two Sector Francico J. Buera Joeph P. Kaboki Yongeok Shin March 4, 2008 Abtract In poor countrie, total factor productivity (TFP) i particularly low in ector producing tradable good, and relative price of tradable are high. We document that an important difference between tradable and non-tradable ector i their average etablihment ize: tradable etablihment operate at much larger cale. We develop a model co-determining TFP, relative price and cale acro indutrial ector. In our model, financial friction diproportionately affect TFP in tradable ector where production require large etup cot. Our quantitative exercie how that financial friction explain 50% of the oberved cro-country pattern of TFP, relative price and relative cale acro ector. We have benefited from comment received at 2007 SED Meeting, Arizona State Univerity, FRB Minneapoli, and the Univerity of Chicago. Northwetern Univerity, f-buera@northwetern.edu. Ohio State Univerity, kaboki.1@ou.edu. Univerity of Wiconin, yhin@c.wic.edu. 1

2 It wa the bet of time, it wa the wort of time, it wa the age of widom, itwatheageoffoolihne,itwatheepochofbelief,itwatheepochof incredulity, it wa the eaon of Light, it wa the eaon of Darkne, it wa the pring of hope, it wa the winter of depair... Dicken (1859), p.1 EnglandandFrance,whichintermofthelevelofdevelopmentandtechnology were roughly comparable at the middle of the eighteenth century... went through radically different path of development. England went on to develop and benefithugelyfromthefactoryytemandlarge-cale production, wherea France remained a nation of mall farm and cottage indutrie for the next hundred year. Banerjee and Newman (1993), p Introduction Income per capita difference acro countrie are mainly accounted for by lower TFP in poor countrie (Klenow and Rodriguez-Clare, 1997, Hall and Jone, 1999). More diaggregated data how that the TFP gap between rich and poor countrie differ ytematically acro ector in the economy. Poor countrie are particularly unproductive in producing tradable. 1 Since equipment i tradable, low relative productivity in tradable increae the relative price of equipment in poor countrie and limit capital accumulation. 2 Thu, an important tak in development economic i to undertand the caue of uch ectoral difference in TFP. In thi paper, we propoe and quantify a theory of ectoral productivity difference baed on cro-ector difference in the optimal cale of etablihment and cro-country difference in financial development. We tart from the obervation that the ize of the typical etablihment, meaured a worker per etablihment, i one of the main characteritic ditinguihing technologie 1 Balaa (1964) and Samuelon (1964) are the claic citation for tradable and non tradable. Hieh and Klenow (2007) and Herrendorf and Valentinyi (2007a) are more recent contribution. 2 See again, Hieh and Klenow (2007), Eaton and Kortum (2001), and Jone (1994). 2

3 acro ector of an economy. Uing detailed ectoral data, we document that the average etablihment in the tradable ector i three time larger than that in the non-tradable ector. Large ectoral difference in a wide range of countrie, and o we argue that thee difference reflect technological difference acro ector. Furthermore, uing price data for a cro ection of countrie, we how that at a diaggregate level, poor countrie are relatively unproductive in indutrie with larger cale. Hence, etablihment cale appear to an important technological ditinction. Thee obervation lead u to tudy a model with ectoral cale difference, and to explore how financial friction ditort cale of operation in the different ector. We model production in which entrepreneur face a one-time etup cot to tart an etablihment. Entrepreneur face limited pan of control, however, o that average cot curve are U-haped. Sector differ in their etup cot, and hence their profit-maximizing cale. Tradable ector etablihment face a large etup cot, and hence operate at a large cale. Agent chooe ector and occupation. In a frictionle economy, the mot able individual become entrepreneur and the marginal product of capital i equalized acro ector and etablihment. With financial friction which we model with endogenou enforcement contraint entrepreneur invetment deciion are contrained by their available wealth. The deciion of whether to become an entrepreneur, in which ector, and how much capital to invet are driven not only by ability but alo wealth. Tighter financial friction hurt productivity, and diproportionately o in the large-cale tradable ector. Credit market imperfection are a natural candidate for ditortion diproportionately affecting large-cale ector. A central role of credit market i preciely to provide the financing that i critical for the viability of large-cale venture with ignificant etup cot. Indeed, it ha been widely recognized that well-functioning credit market are an important intitution miing from poor economie 3, and a large theoretical literature ha conidered 3 The literature here i vat. Banerjee and Duflo (2005) provide an excellent review. Banerjee and Duflo (2004) and Kaboki and Townend (2007) provide model-baed, quai-experimental evidence of credit contraint. Townend (forthcoming) give an in depth cae tudy of Thailand. 3

4 the role of credit market in economic development. Our quantitative exercie how that financial friction help explain the oberved pattern in relative TFP and the relative price of tradable (large-cale) v. non-tradable (mall-cale) output. The model explain roughly half of the relative price and income relationhip. In addition, financial friction lower overall output and wage. Lower wage make market labor le attractive, and, at the ame time, financial friction alo puh low wealth individual away from the high cale ector. Thu, entrepreneurhip in the mall-cale non-tradable ector well. Relative to the efficient allocation, economie with evere financial friction are characterized by too many entrepreneur in the non-tradable ector running uboptimally mall etablihment, and too few entrepreneur and too large of etablihment on average in the tradable ector. We purue thi a an important and novel tetable implication of our theory uing multiple data ource. Firt, we due a detailed comparion of the relationhip between etablihment ize and indutry in the U.S. and Mexico. Thee data are mot comparable becaue the North American Indutrial Claification Sytem i common to both countrie, and the exitence of a Mexican urvey of mall buinee to upplement the cenu of fixed location firm with mall-cale, mobile, informal entrepreneur. Uing the U.S. a a benchmark for comparion, the Mexican data how that mall-cale indutrie are even maller in Mexico, while large cale indutrie are even larger in Mexico (relative to the U.S.), but maller average cale in mall cale indutrie. Second, uing OECD data for a broader et of eleven countrie whoe level of development vary, we how that the relative cale of tradable etablihment i larger in poorer countrie. The paper i mot cloely related and complementary to two other in the literature that emphaize the differential effect of financial friction on manufacturing indutrie. 4 Rajan and Zingale (1998), an empirical paper, create an index of dependence on external ource 4 Thi paper alo contribute to a vat literature relating financial friction and entrepreneurhip to development, including: Aghion and Bolton (1997), Banerjee and Newman (1991),Buera and Shin (2007), Catro, Clemente and Mcdonald (2007), Lloyd-Elli and Burnhardt (2001), 4

5 of financing for each indutry and tet whether indutrie that are particularly dependent on financing grow relatively fater in countrie with trong financial ytem. Eroa and Hidalgo (forthcoming) i a theoretical paper howing how financial friction have differential effect on productivity in manufacturing indutrie with different fixed cot requirement. Our paper differ from thee in three way. Firt, our analyi explicitly combine data and theory by quantifying the effect of financial development on ectoral productivity. Second, we introduce cale a an empirical meaure related to etup cot and financing. Finally, we broaden the analyi to encompa the tradable and non-tradable ector, and emphaize their cale difference. The next ection document the key fact that motivate our analyi. Section 3 develop the model, and calibrate the model with no credit contraint. Section 4 preent the quantitative experiment and contrat the implication of the theory to detailed ectoral ize ditribution data of the US, Mexico and the SSIS panel. Section 5 conclude. 2 Fact Thi ection document the key fact in our tudy. Firt, we reviit the Balaa-Samuelon fact of the poitive relationhip between relative productivity in tradable and output per worker. Second, we how that a imilar relationhip hold between relative productivity and financial development. Third, we identify cale a a primary ditinction in technologie between ector. Finally, we how at a diaggregated level, that the relative price-income relationhip i related to cale. 2.1 Relative Productivity and Development The Balaa-Samuelon fact i that, in poor countrie, the price of tradable are high relative to thoe of non-tradable. Figure 1 confirmthifactforthe1996icpbenchmarkbyplotting 5

6 Log Relative Price: Tradable/Non-Tradable (each dot i a country) y = Ln(x) $1,000 $10,000 $100,000 GDP/Worker at PPP Figure 1: GDP/Worker the relative price of tradable againt real output per worker from the Penn World Table Here the relative price i produced by creating Geary-Khami aggregated price for tradable and nontradable ector uing 27 diaggregated product categorie. 6 Therelativepriceof tradable ha a trong negative relationhip with log output per worker. The regreion elaticity of i highly ignificant at the one percent level, and the relationhip ha an R 2 of Thi relationhip can be interpreted a reflecting a lower total factor productivity in tradable relative to non-tradable in poor countrie. Indeed, in model with contant return to cale aggregate production function, and equal factor hare acro ector, thee relative price equal the invere of relative TFP. 7 Difference in factor hare and the relative upply of factor (e.g., higher level of phyical capital or human capital per worker) could break 5 There are 115 ICP benchmark countrie in For the ake of maintaining a conitent ample, we preent reult baed on the 102 countrie for which we have data on financial development from Beck et al (2000). The reult uing all 115 countrie are virtually identical. 6 The tradable categorie conit of clothing, 9 food and beverage categorie, footwear, fuel, furniture/floor covering, houehold appliance, houehold textile and other houehold good, machinery/equipment, tobacco, and tranportation equipment. The non-tradable conit of communication, contruction, education, medical/health, recreation/culture, rent and water, retaurant/hotel, and tranportation ervice. We do not claify four final good price categorie: change in tock, collective conumption by government, net foreign balance, and other good and ervice. 7 See, for example, Hieh and Klenow (2007) who ue thi relationhip to identify aggregate ditortion between capital and labor and ectoral TFP difference. 6

7 thi invere relationhip, but empirically factor hare do not vary greatly acro ector, and if anything, the non-tradable ector tend to be intenive in human and phyical capital. 8 Explaining the ource of thi relative TFP v. output per worker relationhip i the goal of the paper. 2.2 Relative Productivity and Financial Development Financial development i a potential upect for explaining cro-country difference in relative productivity. A common meaure of a country level of financial development i it ratio of external financing (private credit+private bond market capitalization+tock market capitalization) to GDP (LaPorta et al, 1998, Rajan and Zingale, 1998). Figure 2 preent the ICP data of log relative price v. the ratio of external financingtogdptakenfrom Beck et al (2000). The relationhip i quite imilar with a lightly lower etimated elaticity of 0.32, but a lightly higher R 2 of Given the imilaritie between the relationhip, apriorifinancial development ha potential to explain the Balaa-Samuelon fact. In the theory, we preent financial development will be the caual force, however. A imple joint regreion of log relative price on both log GDP/worker and log external financing/gdp give uggetive evidence. In thi joint regreion, the elaticity with repect to external financing (0.23) i 50 percent higher than the coefficient with repect to output per worker (0.16) with a ubtantially maller tandard error Scale Difference Acro Sector To identify a reaon for financial development having a differential effect on ector, we conider a deep technological ditinction between the tradable and non-tradable ector of the 8 See Herrendorf and Valentinyi (2007b) for phyical capital and Buera and Kaboki (2007a) for human capital. 9 Meaurement error in either output per worker or financial development could confound thee etimate, to the extent that one i a mimeaured proxy for the other. 7

8 economy: the difference in the cale of technologie. Two empirical proxie are ued for the cale of technologie: worker per etablihment and worker per enterprie. Etablihment are location of buine, o that a ingle enterprie, Walmart, for example, may have multiple etablihment. 10 Table 1 preent meaure of average cale acro broad final good ector of the U.S. economy 11.Thefirt two column are baed on 2002 data from the OECD Structural Statitic for Indutry and Service (SSIS) databae. Thee data are ueful becaue they provide both etablihment and enterprie data in a comparable ISIC digit claification which can ued for comparion acro OECD countrie. The third column i baed on data from the 2002 U.S. economic cenu, which i on an etablihment bai uing the NAICS 8-digit claification. 12 We preent unweighted average, the meaure of interet implied by implied by the model we preent, but worker-weighted average how imilar pattern. 10 The different data ource alo include two different meaure of worker: number of employee and total number of peron engaged. The major difference i that the latter include proprietor, while the former may include ome type of temporary or contract worker. For ome countrie, we have both meaure, and the two mirror eachother well. 11 Thee ector are contructed to reflect final good categorie covered in the ICP data. Manufacturing conumption include food, beverage, textile, clothing, medicine, furniture, appliance, TV and radio, car, houehold item, and media. Equipment include all manufactured equipment not included in conumption. Together, thee two encompa tradable. Service include accomodation/food ervice, art/entertainment, communication, education, FIRE, health, retail, ewage, tranportation, and wholeale. 12 There are alo ubtle difference in definition of worker acro the two ample. In particular, the SSIS data meaure number of peron engaged, which include proprietor. The cenu data i number of employee and exclude proprietor. 8

9 OECD SSIS Data U.S. Cenu Data Worker per Etab. Worker per Enterp. Worker per Etab. Manuf. Con. (m) Service () Equip. Invet. (e) Cont. Invet. (c) Tradable (m+e) Non-tradable (+c) Table 1: Scale by Sector, U.S. 13 Whether etablihment or enterprie i ued a the unit of meaure, average cale varie coniderably acro thee broad ector of the U.S. economy. The top break out cale by diaggregated ector: manufactured conumption, ervice, equipment invetment, and contruction. Manufactured conumption and equipment invetment tend to be large cale, while ervice and contruction are maller cale. Thi ditinction i preciely the tradable v. non-tradable ditinction in the two row below. 14 Hence, the tradable ector i ubtantially larger cale than the non-tradable ector. In the SSIS data for worker per etablihment, the tradable ector i over 3.5 time a large (43 v. 12). The ratio of tradable cale to nontradable cale i maller uing enterprie a the unit, but till over 3 (48 v. 15). Finally, the U.S. cenu etablihment data, yield larger number for cale, but the ratio i till above 3 (again 48 v. 15). 15 In the model we develop in the next ection, difference in cale will be driven by difference in et-up cot acro ector. We view thee cot a the cot of etting up and learning 13 The average are unweighted average acro 4-digit indutrie (OECD SSIS data) and 8-digit indutrie in the U.S. cenu data. One ource of the larger value for the U.S. cenu data come from the fact that air tranportation and rail tranportation have been dropped from the SSIS data to ait cro-country comparion. 14 We lack comparable cale data for agriculture, a third component of tradable. In advanced economie, land/capital invetment per farm are ubtantial, but worker/farm may not be large. 15 Buera and Kaboki (2007b) build on the related cale ditinction between manufacturing and ervice. 9

10 to operate a particular technology. Given thi interpretation, etablihment i our preferred unit of reference becaue we think it more often reflect the technology of production, but for ome technologie (e.g., Walmart), thee cot may be at the firm level. 2.4 Relative Price and Scale In the United State, where capital market are relatively well-functioning, we view the oberved cale of technologie a cloely mirroring the optimal cale of different technologie. 16 A natural quetion to ak i how the relative price relate to the cale of technologie. We ran cro-country regreion of the price of diaggregated ICP price data (relative to country PPP) on log output per worker for each category: log p i, PPP i = α + β log (real GDP/WOK i )+ε i, where p i, i the 1996 price of ector in country i, PPP i i the 1996 PPP price level of country i, andrealgdp/wok i i the output per worker in 1996 international price. Categorie with highly negative coefficient are categorie whoe relative price fall markedly with output per capita (a with the tradable ector). We then mapped thee diaggregated ICP categorie into meaure of cale uing the U.S. Economic Cenu data. 17 Figure 2 preent the pattern between thee etimated coefficient from the price regreion β (vertical axi) and worker per etablihment (logarithmic horizontal axi). The data trend downward with a coefficient of -0.15, again ignificant at the 1 percent level. Thu, the larger cale categorie are thoe that behave mot imilarly to tradable; their relative price decreae the mot with output per worker. Realizing the implication for TFP, relative TFP for thee large cale technologie increae the mot with output per worker. Why might poor countrie be particularly unproductive in operating technologie with 16 At a diaggregated level, there i a high correlation between the cale in the United State and the cale in other countrie. We return to thi pattern in Section Thi mapping i limited by our lack of data on agriculture, o only the cale of food manufacturing etablihment could be ued. It i at leat comforting that none of the food categorie appear to be outlier. 10

11 Cro-country Income Elaticity of Relative Price (each point i an "indutry") Tranport. Service 0.2 Medical Communication Furniture 0 Retaurant/hotel Houehold Contruction Footwear Tobacco appliance -0.2 Clothing Fuel Bread/cereal FihDairy/egg Meat -0.4 Oil/fat Fruit/vegetable -0.6 Recreation Alcoholic bevnon-alcoholic bev y = -0.15ln(x) Machinery/equipment -1 Automobile Worker/Etablihment in the U.S., 2002 Figure 2: Cro-Country Relative Price Elaticity v. Scale large optimal cale? Again, to the extent that cale reflect large et-up cot, we view cale a being related to financial dependence. 18 A final fact, which ha been well-documented in other exiting paper, i that poor countrie tend to have lower level of financial intermediation and lower level of invetor protection (ee King and Levine, 1993, and LaPorta et al,1998). The next ection develop a model to potentially explain thee pattern baed on poor countrie having tighter credit contraint. 3 Model We model an economy with two ector, = NT (mall-cale, non-tradable ector),t (large-cale, tradable ector); and, in each ector, two occupation (worker and entrepreneur/manager). The economy i open and take the price of tradable a fixed; in the end, withonlyonetradablegood,opennewillimplyetthepriceofthetradableoutput. There i a continuum of dynatie. At the beginning of a generation, dynatie only differ in term 18 Indeed, our model i baed on a different meaure of financial dependence than Ranjan and Zingale (1998), ince the et up cot in our model meaure abolute need, while they meaure the fraction of invetment that i externally financed. The two are nonethele related; for the manufacturing indutrie they conider, log average worker/etablihment i poitively related to their financial dependence index for young firm, and mildly ignificant at the 6 percent level. 11

12 of their wealth (a). At that time, individual make an irreverible deciion to pecialize in a particular ector. After chooing a ector, they draw a ector-pecific entrepreneurial idea z from the ditribution μ(z). Agent then decide whether to work for a wage or tart a buine in their ector. Entrepreneurial idea die with probability 1 γ, in which cae, a new generation within a dynaty again get to chooe ector and draw a new entrepreneurial ability Preference Dynatie preference are decribed by the following expected utility function over equence of pair of ectoral conumption c t =(c NT,t,c T,t ), " # X U (c) =E u (c t ) t=0 where u (c t )= 1 1 σ c 1 ε NT + 1 σ c1 ε 1 ε T. The expectation i over the realization of the draw of entrepreneurial idea (z) andthe death of thee idea. 3.2 Occupational Choice and Technology Individual from a new generation tarting with wealth a mut firt decide the ector in which to pecialize. Thi aumption capture, in a very implified way, the fact that individual obtain ector-pecific kill early in their career that may allow them to manage a technology (Chari and Hopenhayn, 1993). 20 To reduce the dimenionality of the problem, we collape thi initial training period into an infiniteimal moment. 19 Thi can be due to the fact that the current generation die and i replaced by omeone that doe not hare the ame talent, or due to the fact that the market condition change making the kill of the current generation obolete. 20 Thi aumption capture alo the idea that many new firm i a ector are tarted by former employee of firm in thi ector, i.e., pin-off. See Franco and Filon (forthcoming) for a model of pin-off along thee line, and evidence of thi mechanim from the rigid dik-drive indutry. 12

13 After drawing the ector-pecific productivity z aociated with their entrepreneurial idea, individual chooe whether to work for a wage or tart a buine in ector. If they chooe to work for a wage, they can do it in either of the ector. Thi aumption guarantee that there i a ingle labor market with wage w. Alternatively, agent can tart a buine in the ector where they pecialized. To tart a buine, they mut pay a fixed etup cot of κ unit of the ector output. The crucial aumption i that κ T >κ NT. After paying the etup cot, they produce uing capital (k) and labor (l) according to the following production function: zf (k, l) =zk α l θ Per-period profit of an entrepreneur operating in ector are: π (k, l; r, w) =p zk α l θ Rk wl The value of being a worker v w (a, z, ) depend on an agent aet a, butalothe productivity z and ector of an agent idea which may be implemented at a later date. The value of being an entrepreneur v e (a, z,, b) depend on thee a well, but alo on b {0, 1}, an indicator of whether or not the buine ha already been tarted by paying the et-up cot. Thu, the tate vector of individual problem i decribed by a quadruple (a, z,, b).the value of an agent facing the choice between working an entrepreneurhip i then: v (a, z,, b) =max{v w (a, z, ),v e (a, z,, b)} (1) The value of a new generation facing the choice of pecializing in a ector depend only on aet: v 0 (a) =max{e [v (a, z,, 0)]} (2) 13

14 3.3 Credit and Rental Market Individual have acce to competitive credit and rental market. Financial intermediarie receive depoit, accumulate and rent capital at a rental rate R, and lend to entrepreneur. Borrowing i between period, while capital rental i within period. We aume that, while aet are tranferred acro generation, debt do not carry over to future generation. 21 Hence, the probability of death γ introduce a wedge between the depoit (r d ) and borrowing rate (r b ). Free entry and, therefore, zero profit for financial intermediarie imply: 1+r d = γ 1+r b R = r d + δ where δ i the depreciation rate. Both borrowing and the rental of capital by entrepreneur are limited due to enforcement problem. The enforcement problem i characterized by the following limited enforcement contraint: u (c)+β [γv (a 0,z,,1) + (1 γ) v 0 (max {0,a 0 })] (1 φ) v e a d,z, + φv ww (0) where a d [k +(1 b) p κ ] i the wealth that i kept by an individual if defaulting and v ww (0) i defined a the value function of an individual left with no aet who i excluded from becoming an entrepreneur for the ret of hi life. The left-hand ide repreent the value of complying with the contract, and the righthand ide repreent the value of reneging on rental and debt obligation. Thi latter value i a function of the contant φ, capturing the everity of the punihment aociated with default a meaured by the excluion from credit and buine opportunitie (φ), and the 21 One can view thi a reflecting either limited liability for firm or a prohibition on debt being tranfered from parent to children, which i cutomary in modern ocietie. 14

15 fraction of the borrowed money that can be teel by borrower upon defautl (φ). To focu on the production role of credit market, we abtract from borrowing by worker and require that they have a poitive net-worth. 3.4 Recurive Repreentation of Agent Problem We are ready to tate the Bellman equation that define the value function of worker and entrepreneur, v w (a, z, ) and v e (a, z,, b). The problem of an individual that work for a wage in the current period olve: v w (a, z, ) = max c,a 0 0 (a0,z,,0) (3).t. pc + a 0 w + 1+r d a and the value function of being an entrepreneur olve 22 v e (a, z,, b) = max c,k,l (a0,z,,1) (4).t. pc + a 0 p f (e, k, l) Rk wl (1 b) p κ +(1+ˆr) a v w (φ [p κ (1 b)+k],z,) u (c)+β [γv (a 0,z,,1) + (1 γ) v 0 (max {0,a 0 })] (5) where ˆr = r d (a 0) + r b (a<0). Again, the tradable good ector, which produce invetment good, i the numeraire, o that p {p 1, 1}. 22 Thi value function will not be well defined for certain value of the tate, a the contraint et might be empty. In that cae, the proper way to etup the problem would be to explicitely introduce a dicrete choice. We chooe the purely Bellmanized notation to better hightlight the tructure of the problem. 15

16 3.4.1 Stationary Competitive Equilibrium A tationary competitive equilibria given by an invariant ditribution of wealth, entrepreneurial idea, ector, and buine ownerhip G (a, z,, b), policy function (a), c (a, z,, b), a 0 (a, z,, b), l (a, z,, b), k (a, z,, b) and price w, r d, r b, p uch that: 1. Given w, r d, r b and p, (a), c (a, z,, b), a 0 (a, z,, b), l (a, z,, b), k (a, z,, b) olve (1), (2),, (4), and (3); 2. Financial intermediarie have zero profit 1+r d = γ 1+r b ; 3. Credit, labor, and good market clear: X Z ag (da, dz,, e) = X Z k (a, z,, e) G (da, dz,, e), X Z G (da, dz,, b) (a,z) W(,b) = X Z l (a, z, ) G (da, dz,, b), c NT = X b Z (a,z) E(NT,b) hzk (a, z, NT, b) α l (a, z, NT, b) θ (1 b) κ NT i G (da, dz, NT, b) c T + δ X b Z k (a, z, T, b) G (da, dz, T, b) = X b Z (a,z) E(T,b) hzk (a, z, T, b) α l (a, z, T, b) θ (1 b) κ T i G (da, dz, T, b) (a,z) E(T,b) 16

17 where W (, b) {(a, z) :v w (a, z, ) v e (a, z,, 0)} and E (, b) {(a, z) :v w (a, z, ) v e (a, z,, 0)}; 4. The joint ditribution of wealth, entrepreneurial idea, ector and buine ownerhip i a fixed point of the equilibrium mapping: G (a, z,, b) = γ X Z G b {0,1} ã, z X 1 +(1 b)(1 γ) μ (z) ³ dã, d z,, b X Z, b {0,1} ã, z X 2 ( ) ³ G dã, d z,, b ³ o where X 1 = nã, z : z z,a 0 ã, z,, b a, (v e (a, z,, 0) v w (a, z, )) = b,andx 2 ( ) = ³ nã, z : a 0 ã, z,, b ³ a, ³a 0 ã, z,, b o = Firt Bet Benchmark To clarify the baic mechanic of the model it i intructive to analyze the unditorted firt bet allocation. Thi i alo the benchmark economy that we ue to calibrate the technological parameter of the model, by matching key apect of the ize ditribution of etablihment in the US economy. In writing thi problem, we tart by olving for the optimal allocation of capital and labor within ector for a given fraction of the population pecializing in the ector, n,a given threhold idea productivity for tarting a buine, ẑ, and a given amount of capital and labor in the ector K and L : max k(z),l(z) n R ẑ zk (z) α l (z) θ dμ (z).t. n R ẑ n R ẑ k (z) dμ (z) K l (z) dμ (z) L whoe olution i the (gro) ectoral production function for a given ditribution of firm 17

18 defined by n and ẑ : Z 1 Ỹ (K,L ; n, ẑ )= n z 1 α θ dμ (z) 1 α θ K α L θ ẑ Realizing that n NT =1 n T, the Bellman equation characterizing the firt bet allocation can be written: 23 v (K) = max c, K 0, n, ẑ NT, ẑ T u (c)+βv (K 0 ).t. c NT Ỹ NT (K NT,L NT ; n NT, ẑ NT ) (1 γ) κ NT n NT (1 μ (ẑ NT )) c T + K 0 Ỹ T (K T,L T ;1 n NT, ẑ T ) (1 γ) κ T (1 n NT )(1 μ (ẑ T )) K T + K NT K L T + L NT n NT μ (ẑ NT )+(1 n NT ) μ (ẑ T ) We next preent two reult characterizing the firt bet allocation for the cae in which we aume idea follow a Pareto ditribution, z ηzmz η (η+1). Thi aumption yield cloed form olution for the net ectoral production function, i.e., the output of a given ector net of the reource ued to etup plant, the factor hare, and the ize ditribution of etablihment acro ector. The reult alo provide key inight that are ued to calibrate the technological parameter of the model to match baic fact about the ize ditribution of etablihment acro ector. The firt reult how that net output of a ector a a function of the fraction individual pecializing in a ector (n ), the ectoral capital (K )andlabor(l ) input, i Cobb-Dougla with contant return to cale: Propoition 1 Provided that idea are ditributed Pareto z ηz η mz (η+1), the output of a 23 To implify the expoition we abtract from the irreveribility in the ectoral choice deciion, i.e., the contraint γn 1 n 0 1 γn 1 +1 γ, and do not carry the ditribution of previouly active entrepreneur a a tate variable. Thi information will only be relevant to analyze the tranitional dynamic of the model. 18

19 ector net of etup cot equal: Y (K,L ; n ) = Ỹ (K,L ; n, ẑ ) (1 γ) κ n (1 μ (ẑ )) = A n 1/η α+θ+1/η K α α+θ+1/η L θ α+θ+1/η where A = A η 1+η(α+θ) h i 1 h (1 α θ) η(1 α θ) 1 ηzη 1+η(α+θ) m 1 (1 γ) p κ w i (1 γ) p κ w ³1 α θ 1 (1 γ) pκ w +1 η +1 η(1 α θ) 1 1+η(α+θ) and n o ẑ =argmax p Ỹ (K,L ; n, ẑ ) ((1 γ) p κ + w) n (1 μ (ẑ )). ẑ From thi reult it follow that, a in the tandard neoclaical ectoral growth model, the α elaticitie of output with repect to capital and labor are contant, and θ, α+θ+1/η α+θ+1/η repectively. Unlike in the tandard model, however, the elaticitie are not equal to the correponding factor hare, ince entrepreneur earn rent. In particular, payment to capital a a hare of income equal: K, = = RK Y (K,L ; n ) α 1 p κ /w p κ /w+1 ³ 1 α θ 1 η. Even though factor hare are not contant, for realitic parametrization of the model 1 α θ 1 η 0, implying that factor hare are contant for practical purpoe. We finih thi ection by tudying the ize ditribution of etablihment in the firt bet economy. In particular, we how that, within a ector, etablihment are ditributed Pareto with tail coefficient η (1 α θ), while the ize ditribution over the entire economy i given by a mixture of Pareto ditribution. We alo how that there i a one-to-one mapping between the value of the etup cot relative to the labor cot p κ /w and the ratio of the 19

20 average employment per etablihment l acro ector. Propoition 2 The ditribution of employment in each ector follow a power law: i Pr h l >l = µ l (ẑ ) l η(1 α θ) where l (ẑ ) i the employment in the marginal etablihment; while the ditribution of employment in the aggregate economy i given by a mixture of Pareto ditribution: i Pr h l >l µ η(1 α θ) µ l (ẑ1 ) = n 1 +(1 n 1 ) l l (ẑ 2 ) max {l, l (ẑ 2 )} η(1 α θ), l l (ẑ 1 ) ; and the ratio of average employment per etablihment acro ector equal: l l 0 = p (1 γ)κ +1 w p 0(1 γ)κ w Thi reult ugget a imple way to calibrate the relative importance of etup cot acro ector and the parameter of the ditribution of idea by matching the ratio of average employment per etablihment acro ector and the tail of the ize ditribution of etablihment. In the next ection, we ue thi inight to calibrate the model, and then tudy how credit friction affect the relative productivity acro ector, and the ize ditribution of etablihment. 4 Quantitative Analyi In thi ection we calibrate the perfect credit benchmark to the United State economy. We then conduct experiment varying only φ, the parameter which capture the extent of financial friction, to obtain variation in debt/gdp ratio that are quantitatively reaonable given the range oberved in the cro-ection of countrie. We ae the model prediction for TFP, price, output and cale acro ector. Finally, we ae a tetable implication of 20

21 the model about variation in the relative cale of ector vi-a-vi the data. 4.1 Calibration We calibrate the preference and technological parameter o that the firtbeteconomy matche tandard macroeconomic aggregate and key feature of the ize ditribution of etablihment acro ector in the U.S. We chooe a degree of return to cale to the variable factor, capital and labor, of 1 α θ =0.85, a value that fall in the range of value in the literature 24. Given thi choice, the value of α i choen to match an aggregate hare of capital of 1/3. We calibrate the etup cot, κ NT =0.05 and κ T =6.75, to match the average employment per etablihment in the non-tradable and tradable ector of 15 and 48, repectively. We aume that z i ditributed Pareto, z ηz η mz (η+1), and ymmetrically for each ector. We normalize z m = η 1, and chooe the tandard deviation of the ditribution of entrepreneurial idea, η η =8.6667, to match the hare of employment accounted by the top 10% of etablihment of A period in the model i et to 2 year, and we let γ =0.93othattheaveragedurationof working live i 30 year. Calibrating to the working life, which i longer than the life of the typical etablihment, i conervative in the ene that entry cot will be a maller fraction of total output. The 2-year depreciation rate i et at δ =0.11 and et β =0.9 to match the 2-year interet rate. We let σ = 1.5 following the tandard practice. The aumption of a unitary elaticity of ubtitution between tradable and non-tradable i conitent with the etimate of 1.24 by Otry and Reinhart (1991) for a group of developing countrie and Mendoza (1995) etimate of 0.74 for a group of indutrialized countrie. 24 For example, thi i the value ued by Atkeon, Ohanian and Kahn (1996), Atkeon and Kehoe (2005), and Amaral and Quintin (2006). The et of alternative value range from 0.10 (Cagetti and De Nardi, 2006) and 0.19 (Buera and Shin, 2007). 21

22 Parameter Value Target α 0.33 capital hare θ 0.52 diminihing return κ avg. cale in tradable ector κ avg. cale in non-tradable ector η 9.33 top 10% employment hare z m 0.67 normalized γ 0.93 working life δ year depreciation β year dicount rate ε 1 trad./non-trad. elat. of ubt. Table 2: Benchmark Parameter Value Figure 3 how the ize ditribution of etablihment implied by the calibrated model, and compare them with their data counterpart. The model i able to fit the tail of thee ditribution, the ditance between the ectoral ditribution, and the initial concavity in the aggregate ditribution of etablihment. The model cannot capture the initial concavity in ditribution of etablihment within a ector, preumably due to our abtracting from within-ector heterogeneity in the etup cot. 4.2 Numerical Example Table 3 give a ummary of our empirical target in the cro-country data. Here we have divided the ample into quintile by output per worker, and lited the tatitic regarding output per worker, external finance to GDP ratio and log relative price of tradable in each quintile, a well a a repreentative country for each quintile. One can ee that both the ratio of external finance to GDP and the log relative price of tradable varie coniderably within output per worker quintile, and indeed overlap ubtantially acro quintile. Indeed, even the average value are non-monotonic. 22

23 ln(fraction of etablihment to the right of ) Sector 1-6 Sector 2 All -7 Non-tradable Tradable = employment (log cale) Figure 3: Size ditribution of etablihment acro ector, in the data (* and +) and model (olid and dah line). We compare thee empirical reult to our numerical example. We how numerical example for two level of financial friction a well a the firtbetbenchmark. Thecae of mild financial friction yield an external finance/gdp ratio of 2.22, while the tighter financial friction yield The firt correpond well to a typical top quintile country (e.g., Belgium), while the latter i in between the firt and econd quintile, roughly Spain. All of the value come directly out of the model except for output and ectoral productivity, A, which we calculate a typically meaured in the data. Output i meaured at contant ( international, i.e., firt-bet) price, while ectoral TFP i calculated a A = Y /K 1/3 L 2/3. ThereultforkeyvariablearehowninTable4. 23

24 Low Financial Friction High Financial Friction High-Low Percent Difference φ External Financing/GDP % A NT % A T % A T /A NT % p T /p NT % z NT,avg % z T,avg % Fraction Specializing in Non-tradable Sector Etab. per Capita in Non-tradable Sector Etab. per Capita in Tradable Sector % % % l NT,avg % l T,avg % l T,avg /l NT,avg % w % r % K % Y % Table 3: Experimental Reult The firt row how the particular value of φ choen, which i the only parameter that i varied. The econd row how the above mentioned effect on the ratio of external financing 24

25 to GDP. The third and fourth row how the effect on ectoral TFP, which, in the economy with tighter financial retriction, i lightly lower (1.5 percent) in the non-tradable ector, but ubtantially (15.0 percent) lower. Conequently, the relative TFP of the tradable ector in row 5 i about 14 percent lower in the economy with tronger financial friction. Likewie, the relative price of the tradable ector increae about 10 percent a well. Thi i ubtantial. Uing thee two value for relative price and external financing to GDP would yield an elaticity of (10.5/41.5=) 0.25 or roughly three-fourth of empirical etimate of (Clearly, further example that pan the range of financial development are neceary.) The row that follow how the ource of thi change in relative TFP. Firt, the average quality of entrepreneur (z T,avg ) fall in the tradable ector becaue there are profit to be made, even for low-kill entrepreneur, provided one can ha enough mean to tart and run the large-cale, tradable project. The number of people pecializing in the tradable ector fall, a low wealth individual elect into the mall-cale ector. Thi election i ubtantial leading to fewer etablihment in the large-cale tradable ector, even given the lower threhold for productivity, and more etablihment in the mall-cale ector. Thi highlight the econd force affecting TFP: fewer firm are tarted in the tradable ector becaue of reduced credit. Given the higher price, there are profit to be had for thoe with mean. Thi lead to larger etablihment, which are le productive. The average number of worker per etablihment in the large-cale ector rie from 59.4 to 151.8, while the ize of nontradable fall from 6.8 to 5.8. The relative cale of tradable i therefore larger in the economy with higher financial friction, 26.1 v Finally, wenotetheeffect on wage, capital and output. Wage fall by 17 percent, or omewhat more than ectoral TFP. The lower wage are an additional force leading to more firm in the low-cale, non-tradable ector. The drop in output i imilarly 16 percent. About half of thi decline i driven by the fall in TFP, while the remaining half i driven by a decline in capital. Capital fall by 25 percent, and ince it hare i 1/3, it contribute about 8 percent to the output decline. 25

26 4.3 A Tetable Implication The imulation confirm the intuition that financial friction are relatively more harmful to TFP in the high entry cot, large-cale ector. A urpriing reult, however, i the effect of financial friction on average cale in equilibrium; tighter financial friction lead to greater diparity in cale in between the high- and low-entry cot ector. Thi i the reult of the lower average wage. Given low wage, (very) mall-cale entrepreneurhip i more deirable becaue the opportunity cot (i.e., the income from being a worker) i lower. Converely, thoe who have the mean to finance the large cale entry cot face high output price and lower labor cot that lead to larger cale etablihment. While abolute cale of ector are governed by abolute productivity level, which preumably vary acro countrie, the prediction that the relative average cale of the tradable ector i decreaing with income (or financial friction) i a tetable implication. Evaluating thi require data ource for cale that are comparable acro countrie. We have two ource. Firt, the Economic Cenue in the U.S. and Mexico are both baed on the NAICS 2002, an etablihment level claification, very well documented, and broadly comparable. We drop thoe indutrie that are not collected on a comparable bai. 25 Second, the OECD SSIS data i le well-documented but i deigned for comparability. It contain data on worker, etablihment, and enterprie according to the common ISIC3.2 claification. Unfortunately, not all countrie have complete coverage of indutrie, and only the U.S. provide both etablihment and enterprie data. For comparion, we choe two group of countrie: the three large advanced economie (Britain, France and Germany) and the eight pooret countrie available (Czech Republic, Hungary, Poland, Portugal, Slovak Republic, South Korea, and Turkey). 26 Korea and Turkey provide etablihment data, while the other provide enterprie data. Given our focu on financing, we drop government 25 Contruction, mining, tranportation, FIRE, telephone, potal ervice, electricity and water are all collected at the firm level in Mexico. 26 The data i for When not available we ue 2001 or Data on three advanced economie (Autralia, Canada, Japan) and one poorer country (Mexico) lacked coverage of broad ector of the economy. 26

27 Etablihment unit, Cenu Etablihment unit, SSIS Enterprie unit, SSIS 100 Scale of Tradable/Scale of Non-tradable (Logarithmic Axi) KOR TUR DEU MEX CZK FRA POL HUN 10 SVK PRT GBR USA 1 $0 $10,000 $20,000 $30,000 $40,000 $50,000 $60,000 $70,000 $80,000 GDP per Worker at PPP, 2002 Figure 4: Relative Scale v. Output per Worker, 12 Countrie a well a indutrie that are extreme outlier and are ubtantially government financed: air tranportation, central banking, potal ervice, and rail tranportation. For all meaure we calculate the unweighted average cale for the tradable and non-tradable ector, and take the ratio of the two. The reult for thee three comparion are hown in Figure 3, which plot the cale of tradable relative to non-tradable on the logarithmic vertical axi and output per worker on the horizontal axi. 27 The U.S. i in the lower right-hand corner, and ha fairly imilar value for all three meaure of cale. Focuing on the triangle, we ee that in Mexico the relative cale of tradable etablihment i larger in Mexico than in the U.S. Thi i alo true of etablihment in Korea and Turkey v. the U.S., which are plotted uing the diamond. The lope between relative cale and external finance in thee data are comparable to that calculated in the numerical example (roughly -18), but the lope for Mexico i much flatter than in the numerical example. The quare how that in the poorer countrie alo have the relative cale of tradable 27 GDP per worker taken from PWT 6.2. SSIS i the OECD Structural Statitic for Indutry and Service uing ISIC 3-digit claification. The Cenu data i from U.S. and Mexican Economic Cenue uing the NAICS claification. Exclude government run indutrie uch a air and rail tranportation, central banking, and public utilitie. 27

28 enterprie i larger than in the U.S. that are more in line with the numerical example, but the relationhip i not a trong or ytematic. In particular, relative cale i maller in France and epecially Britain, although their ratio of external finance to GDP are lower than in the United State. In contrat, relative cale of tradable i larger in Germany, driven by automobile manufacturing enterprie, which are ubtantially larger in Germany (2803) than in the U.S. (162) and other countrie. 5 Concluion The paper ha developed an explicit theory linking countrie level of financial development to their relative productivity in the tradable ector, and the equilibrium relative price of tradable. Tradable productivity i more enitive to financial friction becaue tradable require entail large et-up cot that often require external financing. Moreover, we have hown that thi mechanim i quantitatively important, potentially explaining three-quarter of the oberved relationhip between financial development and relative price in the cro-country data. Through thi channel, both productivity and capital accumulation are lowered by financial friction, thu financial development become quantitatively important for income per capita. Finally, we have hown that the implied mechanim i conitent with the large difference in average cale acro ector oberved in poor countrie. Thu, the analyi how how emphai on the ize ditribution of microtechnologie (firm or etablihment) i informative about macroiue uch a productivity, relative price and capital accumulation. 28

29 ProofofPropoition1. Netoutputofector equal Y = N Z ẑ za k (z) α l (z) θ ηz η mz (η+1) dz (1 γ) κ N (1 μ (ẑ )). Uing k (z) = z 1 Z 1 α θ 1 1 α θ K N and l (z) = z 1 1 Z 1 α θ 1 α θ L N, Z " z Y = N za ẑ = A N 1 α θ Z α+θ 1 α θ 1 1 α θ Z 1 1 α θ K α L θ Z ẑ K N # α " z α θ Z 1 1 α θ L N # θ ηz η mz (η+1) dz (1 γ) κ N (1 μ (ẑ )) z 1 α θ ηz η m z (η+1) dz (1 γ) κ N (1 μ (ẑ )) = A N 1 α θ K α L θ Z (1 γ) κ N (1 μ (ẑ )) or Y = A N 1 α θ K α L θ Z (1 γ) κ N (1 μ (ẑ )) (6) h R 1 1 α θ. where Z = z 1 α θ ηz η m z dzi (η+1) Theoptimalẑ olve ẑ max ẑ z with firt order condition A N 1 α θ K α L θ Z µ(1 γ) κ + wp N (1 μ (ẑ )) (1 α θ) A 2 N 1 α θ Z α+θ 1 α θ K α L θ ẑ 1 1 α θ = µ(1 γ) κ + wp N implying ẑ = ³ (1 γ) κ + w p h (1 α θ) η(1 α θ) 1 ηzη m (1 α θ) A 2 N α θ K α L θ i α+θ 1 1+η(α+θ). (7) Subtituying into (6) Y = A N 1 1+η(α+θ) K αη 1+η(α+θ) L θη 1+η(α+θ) 29

30 where A = A η 1+η(α+θ) h i 1 h (1 α θ) η(1 α θ) 1 ηzη 1+η(α+θ) m 1 (1 γ) p κ w i (1 γ) p κ w ³1 α θ 1 (1 γ) pκ w +1 η +1 η(1 α θ) 1 1+η(α+θ) Proof of Propoition 2. From the firt order condition of an entrepreneur of productivity z and that of the marginal entrepreneur (ẑ )weobtain µ z l (z) = ẑ 1 1 α θ l (ẑ ). Thu, i Pr h l >l = P " µ z ẑ 1 # 1 α θ l (ẑ ) >l " µ # 1 α θ l = P z> ẑ z ẑ l (ẑ ) µ η(1 α θ) l (ẑ ) =. l The aggregate ditribution of employment i then given by a mixture of Pareto: i Pr h l >l µ η(1 α θ) µ l (ẑ1 ) = n 1 +(1 n 1 ) l for l l (ẑ 1 ). Finally, by integrating l (z) = z 1 L N, we obtain that the average employment per etablihment in ector equal Z 1 α θ 1 1 α θ l (ẑ 2 ) max {l, l (ẑ 2 )} η(1 α θ) l = L N (1 μ (ẑ )). (8) 30

31 The optimal allocation of labor (L ) and etablihment (n ) to ector implie θp n 1 α θ Z K α L θ 1 = w and (1 α θ) p n α θ Z K α L θ =(1 γ) p κ (1 μ (ẑ )) + wμ (ẑ ) (9) Takentheratiooftheetwoconditionimplie 1 α θ θ L n (1 μ (ẑ )) =(1 γ) p κ w + μ (ẑ ) 1 μ (ẑ ). (10) Subtituying (9) into (7) we obtain ³ h (1 γ) κ + w (1 α θ) p η(1 α θ) 1 ηzη m ẑ = (1 γ)p κ (1 μ(ẑ ))+ w p μ(ẑ) Z i α+θ 1 1+η(α+θ) rearrenging (1 γ) p κ w + μ (ẑ ) 1 μ (ẑ ) = (1 γ) p κ w + μ (ẑ ) η (1 α θ) 1 1 μ (ẑ ) η (1 α θ) (11) uing (8), (10) and (11) we obtain the deired expreion. l l 0 = (1 γ)p κ w +1 (1 γ)p 0κ 0 w +1 31

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