Firm Entry and Exit and Aggregate Growth. Jose Asturias Georgetown University Qatar. Sewon Hur University of Pittsburgh

Transcription

1 Firm Enry and Exi and Aggregae Growh Jose Asurias Georgeown Universiy Qaar Sewon Hur Universiy of Pisburgh Timohy J. Kehoe Universiy of Minnesoa, Federal Reserve Bank of Minneapolis, and Naional Bureau of Economic Research Kim J. Ruhl Pennsylvania Sae Universiy Saff Repor 544 February 2017 Keywords: Enry; Exi; Produciviy; Enry barriers; Barriers o echnology adopion JEL classificaion: E22, O10, O38, O47 The views expressed herein are hose of he auhors and no necessarily hose of he Federal Reserve Bank of Minneapolis or he Federal Reserve Sysem. Federal Reserve Bank of Minneapolis 90 Hennepin Avenue Minneapolis, MN hps://

2 Federal Reserve Bank of Minneapolis Research Deparmen Saff Repor 544 February 2017 Firm Enry and Exi and Aggregae Growh* Jose Asurias Georgeown Universiy Qaar Sewon Hur Universiy of Pisburgh Timohy J. Kehoe Universiy of Minnesoa, Federal Reserve Bank of Minneapolis, and Naional Bureau of Economic Research Kim J. Ruhl Pennsylvania Sae Universiy ABSTRACT Using daa from Chile and Korea, we find ha a larger fracion of aggregae produciviy growh is due o firm enry and exi during fas-growh episodes compared o slow-growh episodes. Sudies of oher counries confirm his empirical relaionship. We develop a model of endogenous firm enry and exi based on Hopenhayn (1992). Firms ener wih efficiencies drawn from a disribuion whose mean grows over ime. Afer enering, a firm s efficiency grows wih age. In he calibraed model, reducing enry coss or barriers o echnology adopion generaes he paern we documen in he daa. Firm urnover is crucial for rapid produciviy growh. Keywords: Enry, Exi, Produciviy, Enry barriers, Barriers o echnology adopion. JEL Codes: E22, O10, O38, O47 *This paper has benefied from helpful discussions a numerous conference and seminar presenaions. We especially hank Pee Klenow for his insighs and suggesions. We also hank James Tybou, he Insiuo Nacional de Esadísica of Chile, and he Korean Naional Saisical Office for heir assisance in acquiring daa. All of he publicly available daa used in his paper can be found a hp://users.econ.umn.edu/~kehoe/. The views expressed herein are hose of he auhors and no necessarily hose of he Federal Reserve Bank of Minneapolis or he Federal Reserve Sysem.

3 1. Inroducion Underlying aggregae produciviy growh a fundamenal deerminan of aggregae oupu growh are he forunes of he firms ha produce in he economy. 1 These firms are creaed, hey produce, and, evenually, hey exi. Dubbed creaive desrucion by Schumpeer (1942), firm enry and exi is generally regarded as necessary for economic growh. Our empirical undersanding of he relaionship beween firm oucomes and aggregae produciviy comes largely from he decomposiion of aggregae produciviy growh ino a conribuion from incumben firms and a conribuion from firm enry and exi. In hese sudies, he role of enry and exi in accouning for aggregae produciviy growh, also referred o as he ne enry componen, varies considerably. Take, for example, wo widely cied empirical sudies: Foser, Haliwanger, and Krizan (2001) find ha plan enry and exi accouns for 25 percen of U.S. produciviy growh, while Brand, Van Biesebroeck, and Zhang (2012) find ha firm enry and exi accouns for 72 percen of Chinese produciviy growh. Why is firm urnover imporan for produciviy growh in some counries and imes and no in ohers? This wide range of findings presens a difficuly for researchers developing models in which firm enry and exi is explicily modeled. Should firm enry and exi play an imporan role in models? Models of firm enry and exi are ofen used o sudy he impac of economic reform on aggregae oucomes. An imporan mechanism in hese models is he exi of inefficien firms and he enry of efficien firms in response o reform. How can researchers discipline he role of enry and exi in models? In his paper, we argue ha enry and exi creaive desrucion is far more imporan during periods of rapid aggregae growh han i is during periods of slower growh. Our firs conribuion is empirical. Using plan-level daa from Chile and Korea, we find ha plan enry and exi accouns for a larger fracion of aggregae produciviy growh during periods of faser growh han during periods of slower growh. A mea-analysis of he produciviy lieraure, spanning a number of counries and ime periods, suppors his empirical regulariy. Figure 3, in which we plo oupu growh raes agains he conribuion of ne enry o aggregae produciviy growh, summarizes our findings. 1 In he absrac, we refer o producion unis as firms. When discussing specific daa, we refer o a single producion uni as a plan and a collecion of plans as a firm. 1

4 Our second conribuion is a dynamic general equilibrium model, based on Hopenhayn (1992), ha quaniaively accouns for he relaionship beween aggregae growh and firm urnover ha we find in he daa. In he model, new firms ener each period wih efficiencies drawn from a disribuion whose mean grows over ime. Noe ha we refer o he firm s producion funcion parameer as is efficiency, which is no he same as is measured produciviy. Afer enering, a firm s efficiency grows, bu more slowly han he new-firm average. We calibrae he model o U.S. plan-level daa and sudy is response o reducions in policy disorions ha generae aggregae oupu growh. When we reduce eiher he cos of firm enry or he barriers o echnology adopion, firm enry and exi accouns for a larger share of aggregae produciviy growh while he economy grows rapidly. No all reforms, however, generae he observed relaionship beween aggregae growh and ne enry. When we reduce he firm s fixed coninuaion cos, aggregae produciviy falls: A smaller coninuaion cos allows for less producive firms o ener and prevens less producive firms from exiing. Chile and Souh Korea are good candidaes for our analysis because boh counries have experienced periods of fas and slow aggregae growh. Real GDP per working-age person in Chile grew 4.0 percen per year during , slowing o 2.7 percen per year during In Souh Korea, real GDP per working-age person grew 6.1 percen per year in and slowed o 3.0 percen per year in Sudying periods of slow and fas growh wihin he same counry and same daase faciliaes comparisons. We use he decomposiion in Foser e al. (2001) o measure he conribuion of ne enry. (In Appendix B, we show ha our findings are robus o using oher decomposiions.) In his decomposiion, he ne enry erm is higher if enering plans are relaively producive compared o he overall indusry and exiing plans are relaively unproducive. The coninuing plan conribuion consiss of boh wihin-plan produciviy dynamics and he reallocaion of marke shares across coninuing plans. We find ha, in boh counries, ne enry plays a more imporan role during periods of fas growh. We furher decompose he ne enry erm and find ha he larges conribuor o changes in he ne enry erm is he change in he relaive produciviy of enering and exiing plans, raher han differences in heir marke shares. Our own analysis is limied by he availabiliy of producer-level daa. Forunaely, he Foser e al. (2001) decomposiion is widely used in he produciviy lieraure. To ge a more 2

5 complee undersanding of he empirical relaionship beween growh and he role of ne enry, we survey papers in he lieraure ha use he Foser e al. (2001) decomposiion. We find ha coninuing plans consisenly accoun for he bulk of produciviy growh in slow-growing counries and periods. For counries ha grow a faser raes, he enry and exi of plans plays a more imporan role. Turning o our model, we find hree feaures o be imporan for generaing he relaionship beween firm enry and exi and aggregae produciviy growh. Firs, in each period, a mass of poenial enrans arrive, each of whom draws an efficiency from a disribuion wih a mean ha grows a rae ge 1. Second, coninuing firm efficiency improves wih age. This efficiency growh depends on an exogenous growh facor and spillovers from aggregae efficiency growh. Finally, firms opimally choose when o ener and exi producion. The economy is subjec o hree ypes of policy disorions. A poenial enran mus pay an enry cos in order o draw an efficiency, and, if i chooses o produce, i mus pay a fixed cos o coninue producion in each period. These coss are parly echnological and parly he resul of policy. We hink of hese policy-relaed coss as disorions ha can be reduced hrough economic reform. In he spiri of Parene and Presco (1994), new firms also face barriers o echnology adopion. Beer echnologies exis bu are no used because of policies ha resric heir adopion. Our disorions are moivaed by he experiences in Chile and Korea, which adoped reforms consisen wih lowering enry coss and barriers o echnology adopion. The model has a balanced growh pah on which oupu grows a he same rae as he mean of he efficiency disribuion for new enrans, ge 1, regardless of he severiy of he policy disorions. Income levels on he balanced growh pah, however, are deermined by he disorions: More severe disorions yield lower balanced growh pahs. The fracion of aggregae produciviy growh ha is due o ne enry he focus of our sudy is consan across balanced growh pahs. Afer enacing a reform ha decreases he enry cos or he barriers o echnology adopion, he economy ransis o a higher balanced growh pah. During his ransiion, oupu grows faser han i does on he balanced growh pah, and ne enry accouns for a larger share of aggregae produciviy growh. In his way, he model qualiaively accouns for he paern we observe in he daa: On he balanced growh pah, he oupu growh rae is relaively low, and so is he conribuion of ne enry o aggregae produciviy growh. During he ransiion beween 3

6 balanced growh pahs, he oupu growh rae increases, as does he conribuion of ne enry o aggregae produciviy growh. The model s balanced growh pah behavior is consisen wih he Unied Saes and oher indusrialized economies ha have grown a abou 2 percen per year for several decades, despie persisen differences in income levels. Kehoe and Presco (2002) provide an in-deph discussion of hese empirical regulariies. In our calibraed model, oupu grows a abou 5 percen per year during he ransiion beween balanced growh pahs and 2 percen per year on he balanced growh pah. Eichengreen e al. (2012) sudy episodes of fas growh followed by economic slowdowns and find ha, on average, he growh rae slowed from 5.6 o 2.1 percen per year. To deermine wheher removing disorions can quaniaively mach he imporance of enry and exi during periods of rapid growh, we calibrae he model o he U.S. economy. We calibrae he model so ha he balanced growh pah maches he long-run growh rae of he Unied Saes and he share of aggregae produciviy growh accouned for by coninuing plans. Our calibraion focuses on plan-level daa, such as he size disribuion of U.S. esablishmens and he employmen share of exiing plans. Afer calibraing he model, we creae hree separae disored economies. The spiri of he exercise is ha hese disored economies are exacly he same as he U.S. economy excep for he policy disorion ha we are sudying. We raise one of he hree disorions in each economy so ha he balanced growh pah income level is 15 percen below ha of he Unied Saes. I is imporan o noe ha, in he balanced growh pah, hese disored economies grow a 2 percen per year and ne enry accouns for 25 percen of aggregae produciviy growh. This maches he daa well: In our sample, counries we caegorize as slow-growing have, on average, annual oupu growh raes of 2.1 percen and ne enry accouns, on average, for 22 percen of aggregae produciviy growh. We hen remove he disorion in each economy and sudy he ransiion o he higher balanced growh pah. When we conduc reforms in he economies wih high enry coss and barriers o echnology adopion, here is rapid growh in oupu and aggregae produciviy immediaely afer he reform. During his period, he conribuion of enry and exi o produciviy increases. When we lower he enry cos, for example, he oupu growh rae rises o 4.6 percen per year for five years, and enry and exi accouns for 60 percen of produciviy growh. In our sample, counries ha we caegorize as fas-growing had an average oupu 4

7 growh rae of 5.8 percen per year, and ne enry accouned, on average, for 47 percen of aggregae produciviy growh. Decreasing barriers o echnology adopion in he model is quaniaively similar. No all reforms, however, generae he dynamics consisen wih he daa. Lowering he fixed coninuaion cos also leads o rapid oupu growh, bu his rapid growh is accompanied by a decline in aggregae produciviy. Lowering he fixed coninuaion cos allows less producive firms o ener and prevens less producive firms from exiing, which resuls in a decline in aggregae produciviy during periods of fas growh. Our empirical analysis is broadly relaed o he produciviy decomposiion lieraure, including Baily e al. (1992), Griliches and Regev (1995), Olley and Pakes (1996), Perin and Levinsohn (2012), and Meliz and Polanec (2015), which develops mehodologies for decomposing aggregae produciviy. These ypes of decomposiions are ofen used o sudy he effec of policy reform (Olley and Pakes 1996; Pavcnik 2002; Eslava e al. 2004; Bollard e al. 2013). Our work is he firs o documen he relaionship beween he imporance of plan enry and exi and aggregae oupu growh. Our modeling approach is relaed o a series of papers ha use quaniaive models o sudy he exen o which enry coss can accoun for cross-counry income differences, such as Herrendorf and Teixeira (2011), Poschke (2010), Barseghyan and DiCecio (2011), Bergoeing e al. (2011), D Erasmo and Moscoso Boedo (2012), Moscoso Boedo and Mukoyama (2012), D Erasmo e al. (2014), Bah and Fang (2016), and Asurias e al. (2016). Disorions in our model also drive differences in balanced growh pah oupu levels, bu our focus is on he behavior of produciviy and enry/exi dynamics during he ransiion beween balance growh pahs. Closer o our approach, Garcia-Macia e al. (2016) use a model of firm enry, innovaion, and exi o decompose U.S. produciviy growh, bu heir focus is on innovaion and he creaion of new varieies. In Secion 2, we use produciviy decomposiions o documen he posiive relaionship beween he imporance of firm ne enry in aggregae produciviy growh and he aggregae growh rae in he economy. Secion 3 lays ou our dynamic general equilibrium model, and Secion 4 discusses he exisence and characerisics of he model s balanced growh pah. In Secion 5 we show how our calibraed model replicaes he empirical relaionship we find in Secion 2. Secion 6 concludes. 5

8 2. Produciviy Decomposiions In his secion, we decompose changes in aggregae produciviy in Chile and Korea ino conribuions from he produciviy of enering and exiing plans and from changes in he produciviy of coninuing plans. We find ha, compared o periods of slow oupu growh, he ne enry of plans accouns for a larger share of produciviy growh during years of fas oupu growh. We hen analyze previous work on plan enry and exi and aggregae produciviy. This lieraure was no explicily focused on he role of enry and exi during differen kinds of growh experiences. We find, however, ha previous sudies suppor our finding ha fas-growing counries end o have a larger share of produciviy growh accouned for by he enry and exi of plans. To be clear, we use he erms fas growh and slow growh only in a descripive sense o ease exposiion. We find i illusraive o caegorize counries as relaively fas- or slow-growing and make comparisons across he groups. In our final analysis, boh oupu growh raes and he conribuion of ne enry are coninuous (see Figure 3) Decomposing Changes in Aggregae Produciviy Growh Our aggregae produciviy decomposiion follows Foser e al. (2001). We define he indusrylevel produciviy of indusry i a ime, Z i, o be log Z = s log z, (1) i ei e e i where s ei is he share of plan e s gross oupu in indusry i and z e is he plan s produciviy. The indusry s produciviy change during he window of 1 o is log Zi = log Zi log Zi, 1. (2) The indusry-level produciviy change can be wrien as he sum of wo componens, NE C log Z = log Z + l og Z, (3) i i i where log Z NE i is he change in indusry-level produciviy aribued o he enry and exi of plans and log Z C i is he change aribued o coninuing plans. The firs componen in (3), log Z NE i, is 6

9 where (, 1 ), 1 (, 1, 1) NE log Zi = sei log ze log Zi sei log ze log Zi, (4) e Ni e Xi (((( (((( ((((( ((((( enering N i is he se of enering plans and exiing X i is he se of exiing plans. We define a plan as enering if i is only acive a, and exiing if i is only acive a 1. The firs erm, he enering plan componen, posiively conribues o aggregae produciviy growh if enering plans produciviy levels are greaer han he iniial indusry average. The second erm, he exiing plan componen, posiively conribues o aggregae produciviy growh if he exiing plans produciviy levels are less han he iniial indusry average. where The second componen in (4), log Z C i, is wihin ( ) C log Zi = sei, 1 log ze + log ze log Zi, 1 se, (5) e Ci e Ci (( (( (((( (((( reallocaion C i is he se of coninuing plans. We define a plan as coninuing if i is acive in boh 1 and. The firs erm in (5), he wihin-plan componen, measures produciviy growh ha is due o changes in he produciviy of exising plans. The second erm in (5), he reallocaion componen, measures produciviy growh ha is due o he reallocaion of oupu shares among exising plans The Role of Ne Enry in Chile and Korea We decompose aggregae produciviy in wo counries ha experienced rapid growh in he 1990s followed by a slowdown in he 2000s: Chile and Korea. We plo GDP per working-age person in Chile and Korea in Figure 1. GDP per working-age person in Chile grew a an annualized rae of 4.0 percen during and, in Korea, GDP per working-age person grew a 6.1 percen during and 4.3 percen during GDP growh in Chile slowed o 2.7 percen during and, in Korea, GDP growh declined o 3.0 percen during Using plan-level daa from hese periods, we examine how he imporance of ne enry in produciviy growh evolves in an economy ha grows quickly and hen experiences a slowdown. The benefi of looking across muliple periods in he same counry is ha we can avoid cross-counry differences and use consisen daases. 7

10 Figure 1: GDP per working-age person in Chile and Korea. 400 slow growh (3.0%) fas growh (4.3%) Index (1985=100) 200 fas growh (6.1%) Korea Chile fas growh (4.0%) slow growh (2.7%) We use manufacuring plan-level daa for Chile and Korea. For Chile, we use he Encuesa Nacional Indusrial Anual daase provided by he Chilean saisical agency, he Insiuo Nacional de Esadísica. The panel daase covers all manufacuring esablishmens in Chile wih more han 10 employees for he years For Korea, we use he Mining and Manufacuring Surveys provided by he Korean Naional Saisical Office. This panel daase covers all manufacuring esablishmens in Korea wih a leas 10 workers. We have hree panels: , , and The full deails of he daa preparaion can be found in Appendix A. The firs sep in he decomposiion is o compue plan-level produciviy. For plan e in indusry i, we assume he producion funcion is log y log i log i log i ei = zei + βk kei + β ei + βm log mei, (6) where y ei is gross oupu, z ei is he plan s produciviy, k ei is capial, ei is labor, m ei is i inermediae inpus, and β j is he indusry-specific coefficien of inpu j in indusry i. To define an indusry, we use he mos disaggregaed classificaion possible. For he Chilean daa, his is 4-digi Inernaional Sandard Indusrial Classificaion (ISIC) Revision 3. 8

11 For he Korean daa, depending upon he sample window, his is a Korean naional sysem ha is based on 4-digi ISIC Revision 3 or Revision 4. To ge a sense of he level of disaggregaion, noe ha ISIC Revisions 3 and 4 have, respecively, 127 and 137 indusries. We consruc measures of real facor inpus for each plan. Gross oupu, inermediae inpus, and capial are measured in local currencies, and we use price deflaors o build he real series. For labor, we use man-years in he Chilean daa and number of employees in he Korean i daa. Following Foser e al. (2001), he coefficiens β j are he indusry-level facor cos shares, averaged over he beginning and end of each ime window. We calculae he indusry-level produciviy, log Z, for indusry i in each year using (1), and decompose hese changes ino ne enry and coninuing erms using (4) and (5). To compue he aggregae (manufacuring-wide) produciviy change, log Z, we weigh he produciviy change of each indusry by he fracion of nominal gross oupu accouned for by ha indusry, averaged over he beginning and end of each ime window. We follow he same process o compue he aggregae enering, exiing, and coninuing erms. Before we compare he resuls, we mus make an adjusmen for he varying lenghs of he ime windows considered. We face he consrain ha our daa for Chile ha covers he fas growh period is hree years: The daa begin in 1995, and he period of fas growh ends in Furhermore, in Secion 2.3 we will describe how we supplemen our own work wih sudies from he lieraure, which also use windows of varying lenghs. The lengh of he sample window is imporan because longer sample windows increase he imporance of ne enry in produciviy growh. We use our calibraed model (discussed in Secions 3 5) o conver each measuremen ino 5-year equivalen windows. To do so, we compue he conribuion of ne enry generaed by he model (on he balanced growh pah) using window lenghs of 5, 10, and 15 years. The conribuion of ne enry o aggregae produciviy growh in he model is 25.0 percen when measured over a 5-year window, 41.1 percen when measured over a 10-year window, and 54.0 percen when measured over a 15-year window. Using hese poins, we fi a quadraic equaion ha relaes he imporance of ne enry o he window lengh, which we plo in Figure 2. We use he fied curve o adjus he measuremens ha do no use 5-year windows. i 9

12 Figure 2: Ne enry under various windows in he model. Conribuion of ne enry o aggregae produciviy Window lengh (years) The conribuion of ne enry o aggregae produciviy in Chile , for example, is 35.5 percen. To adjus his 3-year measuremen o is 5-year equivalen, we divide he model s ne enry conribuion o aggregae produciviy a hree years (17.6 percen, he blue square in Figure 2) by he ne enry conribuion a five years o arrive a an adjusmen facor of 1.42 (=25.0/17.6). The 5-year equivalen Chilean measuremen is 50.4 (=1.42*35.5) percen. We summarize he Chilean and Korean produciviy decomposiions in Table 1. We find ha periods wih faser oupu growh are accompanied by larger conribuions of ne enry o aggregae produciviy growh. From 1995 o 1998, Chilean manufacuring produciviy experienced annual growh of 3.3 percen compared o 1.9 percen growh during he period. During he period of fas growh for Chile, ne enry accouns for 50.4 percen of aggregae produciviy growh, whereas i accouns for only 22.8 percen during he period wih slower growh. In Korea, he manufacuring secor experienced annual produciviy growh of 3.6 percen during and 3.3 percen during , compared o 1.5 percen during During he periods of fas growh, ne enry accouns for 48.0 percen of aggregae produciviy growh in and 37.3 percen in , compared o only 25.1 percen in

13 Period Table 1: Conribuion of ne enry in produciviy decomposiions. Counry GDP per annual growh (percen) Aggregae produciviy annual growh (percen) Conribuion of ne enry (percen) Chile * Chile Korea Korea Korea * Measuremens adjused o be comparable wih he resuls from he 5-year windows. In Appendix B, we consider alernaive produciviy decomposiions described in Griliches and Regev (1995) and Meliz and Polanec (2015). Our finding ha ne enry is a more imporan conribuor o aggregae produciviy during periods of fas growh is robus o hese alernaive mehods. We also show ha his fac is robus o using he Wooldridge (2009) exension of he Levinsohn and Perin (2003) mehodology (Wooldridge-Levinsohn-Perin) o esimae he producion funcion. I is also robus o using value added as weighs, as opposed o gross oupu weighs. As a nex sep, we decompose boh he enering and exiing erms in (4) ino he produciviy differences of enering and exiing firms and heir marke shares. Appendix C conains addiional deails regarding his decomposiion. We repor he decomposiions in Table 2. The enering erm increases during periods of fas growh. The relaive produciviy of enrans increases during periods of faser growh in boh counries, bu marke share paerns are less clear. Enran marke shares rise in Korea and fall in Chile. The exiing erm ends o be more negaive during periods of fas growh. Exiing firm marke shares end o be larger in Korea in imes of fas growh, whereas marke shares are relaively unchanged in Chile. 11

14 Table 2: Enering and exiing erms decomposed muliplicaively. Enering erm Exiing erm Period Relaive Enran Relaive Enering Exiing Exier marke produciviy marke produciviy erm erm share of enrans share of exiers Chile * Korea * Measuremens adjused o be comparable wih he resuls from he 5-year windows The Role of Ne Enry in he Cross Secion In Secion 2.2 we sudied he conribuion of ne enry o aggregae produciviy growh in Chile and Korea, counries ha experienced boh fas growh and a subsequen slowdown. This is an ideal siuaion because we eliminae problems ha migh arise from cross-counry differences. We would like o sudy he deerminans of produciviy growh in as many counries as possible, bu access o plan-level daa consrains he se of counries ha we are able o consider. Forunaely, several researchers have used he same mehodology ha we describe in Secion 2.1 o sudy counries ha are growing relaively slowly (Japan, Porugal, he Unied Kingdom, and he Unied Saes) and counries ha are growing relaively fas (Chile, China, and Korea). These sudies are no focused on he quesions ha we ask here, bu heir use of TFP as he measure of produciviy, gross oupu producion funcions, gross oupu as weighs, and he Foser e al. (2001) decomposiion make heir calculaions comparable o ours for Chile and Korea. Table 3 summarizes our findings as well as hose in he lieraure. The fifh column in he able conains he conribuions of ne enry o aggregae produciviy growh as repored in he sudies, and he sixh column conains he adjused 5-year equivalens. In he firs panel of Table 3, we gaher resuls from counries wih moderae oupu growh raes. In his se of counries, he conribuion of ne enry ranges from 12 percen o 35 percen, wih an average of 22 percen. 12

15 Figure 3: The conribuion of ne enry and GDP growh. 60 CHN * CHN * Conribuion of ne enry (percen) PRT * USA KOR * KOR USA JPN * KOR CHL PRT * USA GBR CHL * KOR CHL * GDP (per 15-64) growh rae (percen) * denoes 5-year equivalens In he second panel of Table 3, we gaher he resuls from counries wih relaively high oupu growh raes. In his se of counries, he conribuion of ne enry o aggregae produciviy growh ranges beween 37 and 58 percen, wih an average of 47 percen. In Figure 3, we summarize our findings. On he verical axis, we plo he conribuion of ne enry, and on he horizonal axis we plo he economy s oupu growh rae. The figure shows a clear posiive correlaion: The ne enry of plans is more imporan for aggregae produciviy growh during periods of rapid GDP growh. Combining our resuls wih sudies from he lieraure yields a more complee picure of he relaionship beween aggregae produciviy growh and he conribuion of ne enry. 13

16 Counry Period GDP/WAP growh rae Table 3: Produciviy decomposiions. Window Ne enry conribuion Ne enry conribuion, 5-year equivalen Japan years Fukao and Kwon (2006) Porugal years Carreira and Teixeira (2008) Porugal years Carreira and Teixeira (2008) Unied Kingdom years Disney e al. (2003) Unied Saes years Foser e al. (2001) Unied Saes years Foser e al. (2001) Unied Saes years Foser e al. (2001) Chile years Auhors calculaions Korea years Auhors calculaions Average China years Brand e al. (2012) China years Brand e al. (2012) Chile years Bergoeing and Repeo Korea years Ahn e al. (2004) Chile years Auhors calculaions Korea years Auhors calculaions Korea years Auhors calculaions Average Noes: The hird column repors annual growh raes of real GDP per working-age person (in percen) over he period of sudy. The fourh column repors he sample window s lengh. The fifh column repors he conribuion of ne enry (in percen) during he sample window using he decomposiion described in (3). The sixh column repors he ne enry conribuion (in percen) normalized o 5-year sample windows. The sevenh column repors he source of he informaion. All sudies use TFP as he measure of produciviy, use he gross oupu producion funcion, and use gross oupu shares as weighs. All sudies use plans excep for Brand e al. (2012), Fukao and Kwon (2006), and Carreira and Teixeira (2008), which use firms. Source 14

17 3. Model In his secion, we consruc a general equilibrium model of firm enry and exi based on Hopenhayn (1992). We model a coninuum of firms in a closed economy. These firms are heerogeneous in heir marginal efficiencies and produce a single good in a perfecly compeiive marke. Time is discree and here is no aggregae uncerainy. In our model, as in Parene and Presco (1994) and Kehoe and Presco (2002), all counries grow a he same rae when hey are on he balanced growh pah, bu he level of he balanced growh pah depends on he disorions in he economy. We incorporae hree disorions ha we inerpre as being he resul of governmen policy. Firs, poenial firms face enry coss. Second, new firms face barriers ha preven hem from adoping he mos efficien echnology. Third, here is a fixed coninuaion cos ha firms mus pay o operae each period. When hese policy-induced barriers are reduced, he economy ransiions o a higher balanced growh pah. The model has hree key feaures. Firs, he disribuion from which poenial enrans draw heir efficiencies exogenously improves each period. Second, he efficiency of exising firms improves boh hrough an exogenous process and hrough spillovers from he res of he economy. Finally, firm enry and exi are endogenous, alhough we also allow for exogenous exi. In erms of linking he empirical work and he model, we make wo poins. Firs, firms in he model are heerogeneous in heir efficiencies. These efficiencies are no he same as he produciviy ha we measure in he daa. When we decompose aggregae produciviy growh in he model, we mus compue a firm s produciviy using he same process described in Secion 2.2. Second, our plan-level daa do no disinguish beween single and muli-plan firms. Given his lack of daa, we rea a plan in he daa as being equivalen o a firm in our model Households The represenaive household inelasically supplies one uni of labor o firms and chooses consumpion and bond holdings o solve max s.. = 0 β log C PC + q B = w + B C 0, no Ponzi schemes, B given, 15 + D 0 (7)

18 where β is he discoun facor, C is household consumpion, P is he price of he good, q + 1 is he price of he one-period bond, B + 1 are he holdings of one-period bonds purchased by he household, for all. w is he wage, and 3.2. Incumben Producers D are aggregae dividends paid by firms. We normalize P = 1 In each period, poenial enrans pay a fixed enry cos, κ, o draw a marginal efficiency, x, from he disribuion F ( x ). This enry cos is paid by he household, eniling i o he fuure dividends of firms ha operae. Afer observing heir efficiencies, poenial enrans choose wheher o operae. Poenial enrans ha choose o operae may exi for exogenous reasons (wih probabiliy δ ), or hey may endogenously exi when he firm s value is negaive. We firs characerize he profi maximizaion problem of a firm ha has chosen o operae. A firm wih efficiency x uses a decreasing reurns o scale producion echnology, y = x α, (8) where is he amoun of labor used by he firm and 0< α < 1. Condiional on operaing, firms hire labor o maximize dividends, d( x ), a d ( x) = max x ( x) w ( x) f, (9) where f is he coninuaion cos, which is denominaed in unis of he consumpion good. Boh he enry cos, κ = κg, and he coninuaion cos, e f = fg, grow a he same rae as he poenial enran s average efficiency. In he nex secion, we show ha hese assumpions imply ha he fixed coss incurred are a consan share of oupu per capia and hus ensure he exisence of a balanced growh pah. 2 T κ We assume ha he cos of enry, κ κ ( 1 τ ) e = +, is T composed of wo pars. The firs, κ, is echnological and is common across all counries. The κ second, τ 0, is he resul of policy. The coninuaion cos is defined analogously as f ( 1 ) T f f τ = +. The soluion o (9) is given by 2 This formulaion is similar o Acemoglu e al. (2003), who assume ha fixed coss are proporional o he fronier echnology. 16

19 1 1 α α x ( x) =. (10) w Noice ha labor demand is increasing in he efficiency of he firm. An imporan mechanism in our model is he increase in he wage ha resuls from an inflow of relaively producive new firms. A he beginning of each period, an operaing firm chooses wheher o produce in he curren period or o exi. If he firm chooses o exi, is dividends are zero and he firm canno reener in subsequen periods. The value of a firm wih efficiency x is V ( x) = max{ d ( x) + q (1 d ) V ( xg ),0}, (11) c, + 1 where g c, + 1 is he firm s efficiency growh facor from o + 1. This efficiency growh facor is characerized by g c = gg ε, (12) where g is a consan, g is average efficiency growh, and ε measures he degree of spillovers from he aggregae economy o he firm. These spillovers are no imporan for our heory, bu hey are imporan for our quaniaive resuls. Since d( x ) is increasing in x, V( x) is also increasing in x, and firms operae if and only if hey have an efficiency above he cuoff hreshold, x ˆ, which is characerized by V( x ˆ ) = 0. (13) I is also useful o define he minimum efficiency of firms in a cohor of age j, x ˆ j. For all firms age j = 1, we have ha xˆ 1 = xˆ since firms will only ener if he firm s value is posiive. For all firms age j 2, x ˆ j is characerized by { 1, 1 } xˆ = max xˆ, xˆ g. (14) j j c If here are firms in a cohor ha choose o exi, hen xˆ j = xˆ. If no firms in he cohor choose o exi, hen he minimum efficiency evolves wih he efficiency of he leas-efficien operaing firm adjused for efficiency growh, xˆ ˆ j = xj 1, 1gc. 17

20 3.3. Enry Upon paying he fixed enry cos, κ = κg, a poenial enran draws is efficiency, x, from a Pareo disribuion, e ϕ x F ( x) = 1 ge g, (15) for x g / ϕ. The parameer γ governs he shape of he efficiency disribuion. We assume ha ( α) e γ 1 > 2, which ensures ha he firm size (employmen) disribuion has a finie variance. In he spiri of Parene and Presco (1994), he parameer ϕ characerizes he barriers o echnology adopion faced by poenial enrans. When ϕ > 1, poenial enrans draw heir efficiencies from a disribuion ha is sochasically dominaed by he fronier efficiency disribuion. The mean of (15) is proporional o g / ϕ, so increasing barriers o echnology adopion lowers he mean efficiency of poenial enrans. The mass of poenial enrans, µ, is deermined by he free enry condiion, [ ( )] e E V x = κ. (16) x We refer o he mass of draws aken from he disribuion as poenial enrans because some of he efficiencies drawn are no large enough o jusify operaing. A ime, he mass of firms of age j in operaion, η j, is j 1 where g j =, g s= 1 c s+ 1 ( ) j 1 ( 1 ) 1 F ( x j / g j ) η = µ δ, (17) ˆ j + 1 j + 1 j is a facor ha convers he ime- efficiency of an operaing firm o is iniial efficiency, which is needed o index he efficiency disribuion. The oal mass of operaing firms is η = η. (18) i= 1 i 18

21 3.4. Equilibrium The economy s iniial condiions are he measures of firms operaing in period zero for ages j = 1,...,, given by { j ˆ 1, x j 0, g c, j 1} j 1 µ + + = and he households bond holdings B 0. Definiion: Given he iniial condiions, an equilibrium is sequences of minimum efficiencies ˆ j = 0 { x } for j = 1,...,, masses of poenial enrans { µ } = 0, masses of operaing firms { η } = 0, firm allocaions, { y( x), ( x)} = 0, x > 0, prices { w, q 1} 0, aggregae dividends and oupu {, } + = D Y = 0, and household consumpion and bond holdings {C, B 1} + = 0, such ha, for all 0 : 1. Given { w, D, q 1} + = 0, he household chooses { C, B 1} 0 + = o solve (7). 2. Given { w } = 0, he firm wih efficiency x > 0 chooses { ( x )} = 0 o solve (9). 3. The mass of poenial enrans is characerized by he free enry condiion in (16). 4. The mass of operaing firms is characerized by (17) and (18). 5. The labor marke clears, 1 = µ j 1 d ( +. (19) x + j 1 j j j= 1 j 1 ( 1 ) x) df ( x/ g ) ˆ 6. Enry-exi hresholds { } 0 x ˆ j = saisfy condiions (13) and (14) for all j = 1,...,. 7. The bond marke clears, B + 1 = The goods marke clears, ( 1 j 1 α 1 ) ( ) 1 ( / + + ) C + η f + µκ = Y = µ d x x df x g. (20) j ˆ j j x j j= 1 9. Aggregae dividends are he sum of firm dividends less enry coss, D j ( ) 1 µ 1 1 d d ( x) df 1( x / g + + ) µκ. (21) = j ˆ j j x j j= 1 4. Balanced Growh Pah In his secion, we define a balanced growh pah for he model described in Secion 3 and prove is exisence. We also conduc comparaive saics exercises o show how he oupu level on he balanced growh pah depends on enry coss, coninuaion coss, and barriers o echnology adopion. 19

22 Definiion: A balanced growh pah is an equilibrium, for he appropriae iniial condiions, such ha he sequence of wages, oupu, consumpion, dividends, and enry-exi hresholds grows a rae ge 1, and bond prices, measures of poenial enrans, and measures of operaing firms are consan. In he balanced growh pah, for all 0 and j 1, and q = + 1 β / g, e µ = µ, η = η. w ˆ 1 Y 1 C 1 D x j, + 1 = = = = = ge, (22) w Y C D xˆ Proposiion 1. A balanced growh pah exiss. Proof: On he balanced growh pah, he profiabiliy of a firm declines over ime because of he coninual enry of firms wih higher efficiencies. Thus, once a firm becomes unprofiable, i will exi, which implies ha he cuoff efficiency is characerized by he saic zero-profi condiion, d ( x ˆ ) = 0. Furhermore, we can show ha firms of every age will endogenously exi each j period, so xˆ j = xˆ for all j 1. The mass of operaing firms is where λ( κ, f, ϕ) g / Y ( κ, f, ϕ) e (, f, ϕ) η κ γ(1 α) 1 =, (23) λ κ ϕ fγ (, f, ) =, which is consan in he balanced growh pah. Since λκ (, f, ϕ ) is consan on he balanced growh pah, i follows ha he fixed enry cos is a consan share of oupu per capia, (, f, ) λ κ ϕ κ =. (24) Y κ ( κ, f, ϕ) An analogous argumen proves ha he fixed coninuaion cos is also a consan share of oupu per capia. The mass of poenial enrans is µ ( κ, f, ϕ) = ξ λ κ ϕ κγω, (25) (, f, ) where ξ and ω are posiive consans ha do no depend on κ, f, and ϕ. The cuoff efficiency o operae is given by 20

23 ( κ f ϕ) xˆ,, (, f, ) (, f, ϕ ) g µ κ ϕ e = ω ϕ η κ which, because µκ (, f, ϕ ) and λκ (, f, ϕ ) are consans, grows a rae g 1. 1 g, (26) Since he cuoffs grow a rae ge 1, he oher aggregae variables relaed o income also grow a rae ge 1, The bond price is q = + 1 β / g. Finally, e γ ( 1 α ) ( 1 α ) 1 α Y( κ, f, ϕ) = η κ, f, ϕ x, f, γ 1 w ( κ, f, ϕ) αy ( κ, f, ϕ) ( ) ˆ ( κ ϕ) e, (27) =, (28) ω ξ D( κ, f, ϕ) = Y( κ, f, ϕ). (29) γω (, f, ) γ( α) 1 αγ α αγ λ κ ϕ = f ϕ κ ν, (30) where ν is a posiive consan. Appendix D conains furher deails. How does he improving efficiency disribuion of new firms generae growh? Each enering cohor of firms has a higher average efficiency han he previous cohor. These moreefficien firms increase he demand for labor, as seen in (10), increasing he wage and he efficiency needed o operae. Thus, inefficien firms from previous generaions are replaced by more efficien firms. The balanced growh pah has he ineresing feaure ha, alhough here is efficiency growh among coninuing firms, long-run oupu growh in he economy is solely driven by he improving efficiency of new enrans, g e. Furhermore, if wo economies have he same g e, hey will grow a he same rae, regardless of heir enry coss and barriers o echnology adopion. The cross-counry differences in enry coss and barriers o echnology adopion manifes as differences in he level of oupu on he balanced growh pah. 21

24 4.1. The Impac of Reform We conduc comparaive saics o highligh he mechanisms hrough which lowering disorions raises oupu. Three poins are worh menioning. Firs, as seen in (27), income can rise because of an increase in he mass of operaing firms or an increase in he efficiency cuoffs. Second, each policy change has boh direc and indirec effecs. The indirec effec is summarized by ( f ) λ κ,, ϕ, which relaes fixed coss o oupu, as in (24). Finally, i is useful o know ha ξ, ω, and ν are posiive consans ha do no depend on κ, ϕ, or f, whereas λκ (, f, ϕ ) is increasing in each of is argumens. Consider an economy ha decreases is enry cos, κ. The associaed decrease in λκ (, f, ϕ ), which capures he decrease in he fixed coss relaive o oupu, increases boh he mass of operaing firms and he mass of poenial enrans. The increase in he mass of operaing firms increases oupu. From (23) and (25), we see ha he mass of poenial enrans increases more han he mass of operaing firms, which increases he cuoff efficiency in (26). The indirec effecs, summarized by λκ (, f, ϕ ), cancel ou, and he direc effec of κ on he mass of enrans remains. The increase in he cuoff efficiency increases oupu. When a counry lowers he barriers o echnology adopion, ϕ, i also increases he mass of operaing firms and he mass of poenial enrans hrough he induced decrease in λκ (, f, ϕ ). As in he reform o κ, he increase in he mass of operaing firms increases oupu. The effec of ϕ on he efficiency hreshold, however, is differen from ha in he κ reform. Since he change in ϕ only effecs µ and η indirecly hrough λκ (, f, ϕ ), he mass of poenial enrans and he mass of operaing firms grow a he same rae and do no affec he efficiency hreshold. The efficiency hreshold changes only hrough he direc effec of ϕ. Firms have access o a beer echnology disribuion, which increases he efficiency hreshold, hereby increasing oupu. As in he oher wo reforms, lowering he fixed coninuaion cos, f, increases he mass of operaing firms and he mass of poenial enrans hrough a decrease in λκ (, f, ϕ ). The increase in he mass of operaing firms increases oupu. In his case, he mass of poenial enrans grows less han he mass of operaing firms lowering he coninuaion cos encourages firms o say in he marke so he efficiency hreshold falls. The lower efficiency hreshold decreases oupu. The wo effecs, he increase in he mass of operaing firms and he decrease in he 22

25 efficiency hreshold, have opposing influences on oupu, bu i is sraighforward o show ha he increase in he mass of operaing firms dominaes he change in he efficiency hreshold. A decrease in f increases oupu. 5. Quaniaive Exercise We now ake our model o he daa. We begin by calibraing he model so ha i replicaes key feaures of he U.S. economy, which we ake o be he fronier economy ( ϕ = 1 ) and on a balanced growh pah. We hen creae hree disored economies ha have income levels ha are 15 percen below ha of he Unied Saes by increasing enry coss, barriers o echnology adopion, and he coninuaion cos. Finally, we inroduce a reform ino each of hese disored economies o deermine wheher he reforms can quaniaively mach he relaionships ha we observe in he daa regarding oupu growh, produciviy growh, and he imporance of enry and exi Measuring Produciviy We need o define he capial sock of firms in he model so ha we can measure produciviy in he model in he same way we measure i in he daa. When a new firm is creaed, he firm invess κ + f unis of consumpion o creae κ + f unis of capial. We assume ha, in each period, he capial sock depreciaes by f ( κ + 1 κ) and, if he firm coninues o operae, i invess f + 1. This implies ha he firm s capial sock in + 1is ( ( )) k = k + f f k k + f = k + f. (31) This formulaion implies ha all firms have he same capial sock, which keeps he model racable. The complee deails are available in Appendix E. In Appendix F, we also repor he resuls from a model in which labor is an amalgam of variable labor and variable capial. Our main findings are robus o his alernaive calibraion. The produciviy z of a firm wih efficiency x is measured as log z( x) = log y( x) α log ( x) αk log( k ) (32) where α = w / Y is he labor share, α = RK / Y is he capial share, R = 1/ q 1+ δ is he i renal rae of capial, k K is he aggregae capial sock, and δ k is he aggregae depreciaion rae. 23 k

26 This is idenical o he way produciviies and facor shares are compued in Secion 2, wih he excepion ha we do no have inermediae goods in our model. The depreciaion rae is consan in he balanced growh pah (BGP) bu no in he ransiion. In Appendix E, we provide he derivaion of he aggregae depreciaion rae. Once we measure firm produciviy, we calculae aggregae produciviy and he Foser e al. (2001) (FHK hereafer) decomposiions using he model-generaed daa as described in (4) and (5). I is useful o discuss how measured produciviy is relaed o efficiency in he model. We subsiue he producion funcion (8) ino (32) and use he fac ha α = α o obain log z ( x) = log x α log( k + f ). (33) Thus, measured produciviy and efficiency are ighly linked, he only difference being he las erm, which is common across all firms. Noe ha, in models of monopolisic compeiion wih consan markups or in models ha do no have fixed coss, measured produciviy is generally consan across firms in he cross secion. In our model, he fixed componen of a firm s capial sock generaes dispersion in firm produciviy Calibraion We choose parameers so ha he model maches key feaures of he U.S. economy, paying paricular aenion o he size disribuion of esablishmens and he imporance of ne enry in U.S. aggregae produciviy growh. We hink of he U.S. economy as being disorion-free, f κ τ = τ = 0 and ϕ = 1, so he calibraion idenifies he model s echnological parameers. We summarize he parameers in Table 4. A period in he model is five years, he same lengh as he ime window for he produciviy decomposiions. We se he fixed coninuaion cos, f T k, so ha he model maches he average esablishmen size in he Unied Saes of 14.0 employees, as found in U.S. Census Bureau (2011) for Barseghyan and DiCecio (2011) survey he empirical lieraure on fixed enry and coninuaion coss, and find ha he average enry-coninuaion cos raio is T T T We se κ so ha he raio of he enry cos o he annual fixed coninuaion cos, κ / ( f / 5), is

27 Table 4: Calibraed parameers. Parameer Value Targe Operaing cos (echnological) Enry cos (echnological) T f Average U.S. esablishmen size: 14.0 T κ 0.38 Enry cos / coninuaion cos: 0.82 Tail parameer γ 6.10 S.D. of U.S. esablishmen size: 89.0 Firm growh g Effec of coninuing firms on growh: 75 percen 5 Deah rae δ Exiing plan employmen share: 19.3 percen Enran produciviy growh 5 g e 1.02 BGP growh rae: 2 percen Discoun facor β Real ineres rae: 4 percen Reurns o scale α 0.67 BGP labor share: 0.67 We canno calibrae ε, which characerizes he relaionship beween coninuing-plan and aggregae efficiency growh, so we esimae ε direcly from he plan-level daa. In he daa, we observe an increase in he produciviy growh of coninuing plans when here is an increase in indusry-level produciviy growh. To quanify his relaionship, ake he logarihm of (12), log g = log g + ε log g, (34) c o arrive a an equaion ha we can esimae using plan-level daa. Using ordinary leas squares (OLS), we esimae log g c, i 0 i i = β + ε log g + υ, (35) where g c, i is he produciviy growh of coninuing plans of indusry i (weighed by he gross oupu of plans), g i is he aggregae produciviy growh in indusry i, and υ i is an error erm. In he daa, a coninuing plan is one ha is presen a boh he beginning and he end of he sample window. Alhough ε governs he growh rae of coninuing-firm efficiency, we use produciviy daa o esimae (35). Since produciviy is a linear ransformaion of efficiency, he esimaed ε is correc, bu he consan erm in he regression is no an esimae of g. Table 5: Produciviy spillover esimaes. Chile 25 Korea

28 Indusry produciviy growh *** *** *** *** *** (0.051) (0.054) (0.079) (0.036) (0.043) Observaions Adj. R-squared Noes: Esimaes of (35) using plan-level daa from Chile and Korea. Sandard errors are repored in parenheses. *** Denoes p<0.01. Ideally, we would like o esimae (35) using daa for U.S. plans, bu wihou access o hose daa, we use daa from Chile and Korea. The OLS esimaes of ε range from 0.38 o 0.70 for Korea and 0.72 o 0.83 for Chile (Table 5). We use he average over he five esimaes, ε = In Appendix F, we explore he robusness of our resuls o changing his parameer Simulaing Policy Reforms In his secion, we consider policy reforms ha move he economy o a higher balanced growh pah by lowering enry coss, barriers o echnology adopion, or he firm coninuaion cos. The goal of hese experimens is o undersand he kinds of reforms ha can quaniaively accoun for he conribuion of enry and exi o produciviy growh during periods of rapid aggregae growh. We creae hree separae disored economies. Each economy is parameerized as he U.S. economy, wih one excepion. In he firs disored economy, we increase he policy-relaed porion of he enry cos, κ τ, so ha oupu on he balanced growh pah is 15 percen lower han in he nondisored economy. In he second and hird disored economies, we raise he barriers o echnology adopion, ϕ, and he policy-relaed porion of he fixed coninuaion cos, f τ, so ha oupu on he balanced growh pah is 15 percen lower han in he nondisored economy. This requires seing κ = 0.74, ϕ = 1.12, and f = in he hree disored economies (he benchmark values of hese parameers are repored in Table 4). 26