Federal Reserve Bank of Minneapolis Research Department Staff Report 544. February Firm Entry and Exit and Aggregate Growth*

Transcription

1 Federal Reserve Bank of Minneapolis Research Deparmen Saff Repor 544 February 2018 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 Applying he Foser, Haliwanger, and Krizan (FHK) (2001) decomposiion o plan-level manufacuring daa from Chile and Korea, we find ha a larger fracion of aggregae produciviy growh is due o enry and exi during periods of fas GDP growh. Sudies of oher counries confirm his empirical relaionship. To analyze his relaionship, we develop a simple model of firm enry and exi based on Hopenhayn (1992) in which here are analyical expressions for he FHK decomposiion. When we inroduce reforms ha reduce enry coss or reduce barriers o echnology adopion ino a calibraed model, we find ha he enry and exi erms in he FHK decomposiion become more imporan as GDP grows rapidly, jus as in he daa from Chile and Korea. Keywords: Enry, Exi, Produciviy, Enry coss, Barriers o echnology adopion. JEL Codes: E22, O10, O38, O47 *This paper has benefied from helpful discussions a numerous conference and seminar presenaions. We hank Paco Buera, V.V. Chari, Hal Cole, John Haliwanger, Boyan Jovanovic, Joseph Kaboski, Pee Klenow, Erzo Lumer, Ezra Oberfield, B. Ravikumar, Felipe Saffie, and Juan Sanchez for helpful discussions. We also hank James Tybou, he Insiuo Naional de Esadísica of Chile, and he Korean Naional Saisical Office for heir assisance in acquiring daa. All of he publically 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.

2 1. Inroducion Findings in empirical sudies vary widely on he imporance of he enry and exi of plans in accouning for aggregae produciviy growh. Consider, for example, wo widely-cied sudies: Foser, Haliwanger, and Krizan (FHK) (2001) find ha he enry and exi of plans accouns for 25 percen of U.S. manufacuring produciviy growh, while Brand, Van Biesebroeck, and Zhang (2012), using he same decomposiion, find ha enry and exi accoun for 72 percen of Chinese manufacuring produciviy growh. 1 In his paper, we accoun for he sark differences in he U.S. and Chinese daa boh by examining daa from oher counries and by developing a simple model in which we can undersand he driving forces behind hose differences. The firs conribuion of his paper is empirical. We apply he FHK decomposiion o manufacuring plan-level daa from Chile and Korea. We find ha plan enry and exi accouns for a larger fracion of aggregae manufacuring produciviy growh during periods of fas growh in GDP per working-age person. A mea-analysis of he produciviy lieraure, spanning a number of counries and ime periods, suppors his empirical regulariy. We summarize our findings in Figure 3, in which we plo growh in GDP per working-age person agains he conribuion of he enry and exi of plans o growh in aggregae manufacuring produciviy. This empirical relaionship is novel o he lieraure and suggess ha he enry and exi of plans plays an imporan role in explaining periods of fas growh. Our second conribuion is heoreical. We develop a dynamic general equilibrium model wih endogenous enry and exi, based on Hopenhayn (1992), ha can quaniaively accoun for he paerns we documen in he daa. Our model is simple enough ha here are analyical expressions ha correspond o erms in he FHK decomposiion. When we inroduce reforms ha reduce enry coss or reduce barriers o echnology adopion ino a calibraed model, we find ha he enry and exi erms in he FHK decomposiion become more imporan as GDP grows rapidly, jus as in he daa. Our simple model, mean o highligh he forces driving produciviy growh, performs surprisingly well in quaniaively maching he behavior we observe in he daa. Our general equilibrium model is of he enire economy, bu he produciviy decomposiions in boh he exising lieraure and our own work cover only he manufacuring secor. If we could 1 To calculae ha enry and exi accouns for 25 percen of U.S. manufacuring produciviy growh, see Table 8.7 in FHK and find he average ne enry share for he , , and windows. To find he conribuion of enry and exi in China, see Figure 7 in Brand, Van Biesebroeck, and Zhang (2012). 1

3 compue he FHK decomposiions using economy-wide daa for Chile and Korea and we could find comparable resuls for oher counries in he lieraure, hen we would no need o resric ourselves o he manufacuring secor. Due o he availabiliy of daa, we assume ha he FHK decomposiion for aggregae manufacuring produciviy growh assigns he same proporions o enry and exi of plans as would a decomposiion of aggregae produciviy growh for he whole economy. This assumpion allows us o make comparisons beween he model and he daa. In our empirical work, Chile and Souh Korea are good candidaes for our analysis because boh counries have experienced periods of fas and slow 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 by 6.1 percen per year in and by 4.3 percen per year in and slowed o 3.0 percen per year in Sudying periods of slow and fas growh in he same counry allows us o avoid cross-counry differences and use consisen daases hrough ime, which reduces issues of measuremen. We use he FHK decomposiion o measure he conribuion of ne enry. 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 GDP growh. During periods of slow growh, when GDP per workingage person grows a less han 4 percen per year, enry and exi accoun for less han 25 percen of aggregae manufacuring produciviy growh on average, similar o he average conribuion of enry and exi in he Unied Saes. During periods of fas GDP growh, however, enry and exi accoun for a larger fracion of aggregae manufacuring produciviy growh, ranging from 37 o 58 percen. We also find ha he increasing imporance of enry and exi is mainly driven by he change in he relaive produciviy of enering and exiing plans, raher han differences in heir marke shares. Our findings are robus o using alernaive decomposiions. Our own analysis is limied by he availabiliy of esablishmen-level daa. Forunaely, he FHK decomposiion is widely used in he produciviy lieraure. To ge a broader undersanding of he empirical relaionship beween growh and he role of ne enry, we survey papers in he lieraure ha use he FHK decomposiion. We find ha coninuing esablishmens plans in 2

4 four of he papers, firms in he oher papers consisenly accoun for he bulk of aggregae manufacuring produciviy growh when GDP per working-age person grows slowly. During episodes of fas GDP growh, he enry and exi of plans play a more imporan role. Moivaed by our empirical work wih he FHK decomposiion, we build a simple model ha has hree sources of produciviy growh. Firs, in each period, poenial enrans draw efficiencies from a disribuion wih a mean ha grows a rae ge 1. Second, coninuing firm efficiencies improve wih age. This efficiency growh depends on an exogenous growh facor and spillovers from average efficiency growh. Finally, firms opimally choose when o exi producion, which induces a selecion effec in which inefficien firms exi. The economy is subjec o hree ypes of policy disorions. Firs, a poenial enran mus pay an enry cos o draw an efficiency. Second, a successful enran mus pay a fixed cos o coninue producion in each period. These wo 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. Third, new firms face barriers o echnology adopion in he spiri of Parene and Presco (1994). Beer echnologies exis bu are no used because of policies ha resric heir adopion. We show ha he model has a balanced growh pah on which income grows a he same rae 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. These resuls are consisen wih he daa from he Unied Saes and oher indusrialized economies. These economies 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. Similarly, Jones (1995) discusses he sable growh raes shown by he Unied Saes over exended periods of ime. The simpliciy of our model allows us o analyically characerize he FHK decomposiions of he model on he balanced growh pah. The decomposiions highligh he ways ha firm urnover, selecion, and he efficiency advanage of enrans affecs he conribuion of ne enry o aggregae produciviy growh. These forces are presen in many of he growh models in he lieraure and our model allows us o undersand how hey map ino empirical decomposiions. We furher show ha, in he balanced growh pah, he conribuion of enry and exi o produciviy growh, jus like GDP growh raes, is he same for all economies on he balanced 3

5 growh pah regardless of he level of disorions in he model. We also show ha, under cerain parameers, he imporance of enry and exi is decreasing in he efficiency growh of coninuing firms, a fac ha we use in our calibraion sraegy. Afer enacing a reform, he economy grows quickly and evenually converges o a higher balanced growh pah. This overall paern is also consisen wih empirical evidence of episodes of fas growh. For example, Eichengreen e al. (2012) sudy episodes of fas growh followed by economic slowdowns. Using daa ha sars in 1957, hey consider a slowdown o have occurred if: he seven-year average GDP per capia growh rae is a leas 3.5 percen for seven years prior o he slowdown, and he growh rae exhibied a decline of a leas 2 percenage poins in he subsequen seven years afer he slowdown. The auhors resric he sample o counries wih GDP per capia of a leas $10,000 in 2005 consan dollars a he ime of he slowdown. They find ha, in he average counry ha experienced a slowdown, he growh rae slowed from 5.6 o 2.1 percen per year. We calibrae he model o esablishmen-level daa for he enire U.S. economy. The major excepion o using economy-wide daa in he calibraion of our model is ha we arge he fac ha enry and exi accoun for 25 percen of U.S. aggregae manufacuring produciviy growh according o FHK, which we assume o be he fracion of growh due o enry and exi in he enire economy. Our model also includes spillovers from growh of enering firms o coninuing firms. In esimaing hese spillovers, we rely on manufacuring daa from Chile and Mexico, which also is an excepion o calibraing o esablishmen-level daa of he enire U.S. economy. Afer calibraing he model, we documen he reforms ha ook place in Chile and Korea during he periods of fas GDP growh. We find ha he majoriy of reforms during hese periods can be inerpreed as he lowering of enry coss and he barriers o echnology adopion in he conex of our model. We creae hree separae disored economies o evaluae reforms o enry coss, barriers o echnology adopion, and fixed coninuaion coss. 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 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. 4

6 We hen remove he disorion in each economy and sudy he ransiion o he higher balanced growh pah. When we lower enry coss, he GDP growh rae rises o 4.6 percen per year for five years, and enry and exi accoun for 60 percen of produciviy growh. In ha sense, he model maches he increasing imporance of firm enry and exi during periods of fas GDP growh, even hough he model is calibraed so ha enry and exi are relaively unimporan in he balanced growh pah. We also find ha he model has paerns ha are similar o he neoclassical growh model. For example, immediaely afer a reform here is an increase in ineres raes due o a boom in invesmen from more poenial enrans paying he enry cos. The increase in ineres raes discourages consumpion and consumpion growh emporarily declines immediaely afer he reform. Decreasing barriers o echnology adopion in he model is quaniaively similar. No all reforms, however, generae he dynamics consisen wih he daa. When we lower fixed coninuaion coss in his economy, he economy experiences GDP growh, bu his fas 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 in GDP. The reform also resuls in capial deepening: GDP increases, labor inpu remains fixed, and aggregae produciviy falls, which implies ha here are increases in he capial sock. The increase in he capial sock is due o he increased number of firms in he economy. Wha do we learn from comparing he differen simulaions? Consider he resuls from he experimen in which we lower enry coss and he resuls of he experimen in which we lower barriers o echnology adopion. Excep for an increase in poenial enry, he ransiions in he wo experimens are he same. The reason is ha he increasing number of firms ha ry o ener and fail when enry coss are lowered push up he efficiency cuoff for successful firms o operae. This mechanism is very much in he spiri of Schumpeer (1942). Thus, we find ha lowering enry coss is almos equivalen o improving he poenial echnology from which firms draw. Resuls from he experimen in which we lower he fixed coninuaion cos shows ha reforms ha increase GDP do no always increase aggregae produciviy. Our resul ha he drop in aggregae produciviy is mosly due o an increase in he ne enry erm of he FHK decomposiion sill holds even in his experimen. The experimen in which we lower fixed coninuaion coss is no as ineresing as he oher wo, however, because i resuls in aggregae 5

7 produciviy falling a he same ime ha GDP is rising. This is no he case in any of he episodes we sudy in Chile and Korea. Nor is i he case in any of he episodes we sudy in he lieraure. 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 GDP per working-age person growh. These empirical resuls sugges ha he enry and exi of firms is an imporan ingredien if we wan o explain fas economic growh. I also provides empirical facs ha can be used o discipline models ha sudy produciviy growh in fas growing counries. In a relaed paper, Garcia-Macia e al. (2016) use a calibraed model o deermine ha he bulk of aggregae produciviy growh in he Unied Saes is due o incumbens raher han enering firms. Our model is relaed o oher works ha aemp o undersand how he FHK decomposiion is relaed o srucural models of firm enry and exi. For example, we are he firs o analyically characerize he FHK produciviy decomposiion along he balanced growh pah of a general equilibrium model wih firm enry and exi. The characerizaions show how he parameers of he model are relaed o he FHK decomposiions. In oher papers, such as Acemoglu e al. (2013), Arkolakis (2015), and Lenz and Morensen (2008), he auhors numerically compue he FHK decomposiion using a calibraed model and compare i o he daa. Our modelling approach builds on he endogenous growh lieraure in which produciviies are drawn from a disribuion ha improves over ime (see Alvarez e al. 2017; Buera and Oberfield 2016; Lucas and Moll 2014; Perla and Tonei 2014; Sampson 2016). Relaive o hese papers, we ake a simplified approach where he produciviy disribuion ha enrans draw from improves a an exogenous rae, which is similar o Lumer (2007). The idea ha poenial enrans in any economy can draw heir produciviy from he fronier produciviy disribuion is relaed o he lieraure on echnology diffusion and adopion (see Parene and Presco 1999; Eaon and Korum 1999; Alvarez e al. 2017). 6

8 Finally, our paper is also 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 income levels, bu our focus is on he behavior of produciviy and enry and exi dynamics during he ransiion beween balanced growh pahs. In Secion 2, we use produciviy decomposiions o documen he posiive relaionship beween he imporance of enry and exi in aggregae manufacuring produciviy growh and he growh in GDP per working-age person 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 discuss he measuremen of produciviy in he model. In Secion 6, we presen analyical characerizaions of he FHK decomposiion of he model on he balanced growh pah. In Secion 7, we conduc quaniaive exercises o show ha he calibraed model replicaes he empirical relaionship ha we find in Secion 2. Secion 8 concludes and provides direcions for fuure research. 2. Produciviy Decomposiions In his secion, we use Chilean and Korean manufacuring daa o decompose changes in aggregae manufacuring produciviy ino he conribuion of enering and exiing plans and he conribuion of coninuing plans. We find ha, compared o periods of slow growh in GDP per working-age person, he enry and exi of plans accouns for a larger share of aggregae manufacuring produciviy growh during years of fas growh in GDP per working-age person. We hen analyze previous work on plan enry and exi and aggregae manufacuring 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 counries wih fas-growing GDP per working-age person also end o have a larger share of aggregae manufacuring produciviy growh accouned for by he enry and exi of plans. 7

9 We use manufacuring daa because i is more widely available han daa for services. For example, we are no aware of any plan-level panel daa on he service secor for Chile and Korea. Furhermore, he wider availabiliy of manufacuring daa allows us o conduc a survey of he lieraure o expand he analysis o a greaer se of counries. We consider a counry o be in fas growh if i has a GDP per working-age person growh rae of a leas 4 percen per year. 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 afand make comparisons across he groups. In our final analysis, we regard boh GDP per working-age person growh raes and he conribuion of enry and exi as coninuous (see Figure 3). In our model, we consider a counry o be slow-growing if i is on a balanced growh pah and o be fas-growing if i is in ransiion o a higher growh balanced growh pah Decomposing Changes in Aggregae Produciviy Growh Our aggregae produciviy decomposiion follows FHK. We define he indusry-level produciviy of indusry i a ime, Z i, o be log Z s log z, (1) i ei e ei 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, 1, 1, 1, 1 NE log Zi sei log zelog Zi sei log ze log Zi, (4) eni exi enering exiing 8

10 where N i is he se of enering plans and 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 wihin, is C log Zi sei, 1 log ze log ze log Zi, 1 se, (5) eci eci 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 manufacuring produciviy in wo counries ha experienced fas growh in he 1990s followed by a slowdown in he 2000s: Chile and Korea. We plo real 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 aggregae manufacuring produciviy growh evolves in an economy ha has fas growh in GDP per working-age person 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. 9

11 Figure 1: Real 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%) The Chilean daa is drawn from 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 k kei ei m 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 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. For he Korean daa, depending upon he sample window, his is a Korean naional sysem ha is based 10

12 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 daa. i Following FHK, he coefficiens 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 i, 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 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 7) 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 53.9 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. 11

13 Figure 2: Conribuion of 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 manufacuring produciviy growh 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 five years (25.0 percen) by he ne enry conribuion a hree years (17.6 percen, he square on he curve a 3 years in Figure 2) o arrive a an adjusmen facor of 1.42 (=25.0/17.6). The 5-year equivalen Chilean measuremen is 50.4 (= ) percen. We summarize he Chilean and Korean manufacuring produciviy decomposiions in Table 1. We find ha periods wih faser GDP growh are accompanied by faser manufacuring produciviy growh, and larger conribuions of ne enry o aggregae manufacuring 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 manufacuring 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 12

14 manufacuring produciviy growh in and 37.3 percen in , compared o only 25.1 percen in Period Table 1: Conribuion of ne enry in manufacuring produciviy decomposiions. Counry Real GDP per working-age person annual growh (percen) Aggregae manufacuring 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 manufacuring produciviy during periods of fas growh in GDP per working-age person 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 furher decompose boh he enering and exiing erms in (4) o invesigae wheher he increased imporance of enry and exi is associaed wih changes in he relaive produciviies of enering and exiing plans or heir marke shares. Appendix C conains addiional deails regarding his decomposiion. Table 2 repors he resuls. We find ha during periods of fas growh in GDP per working-age person, we end o see boh he enering and exiing erm conribuing more o aggregae manufacuring produciviy growh. I is useful o noe ha, as shown in (4), if he exiing erm is negaive hen i has a posiive effec on produciviy growh. We find ha he relaive produciviy of enran and exiing plans, raher han heir marke shares, ends o be he mos consisen driver of changes in boh of hese erms. 13

15 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 manufacuring produciviy growh in Chile and Korea, counries ha experienced boh fas growh in GDP per working age person and a subsequen slowdown. This is ideal because we eliminae problems ha migh arise from cross-counry differences. We would like o sudy he deerminans of aggregae manufacuring 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). As menioned before, we consider a counry o grow relaively fas if i has a GDP per working-age person growh rae of a leas 4 percen per year. 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, manufacuring daa, and he FHK decomposiion make heir calculaions comparable o ours for Chile and Korea. Table 3 summarizes our findings as well as hose in he lieraure. The sixh column in he able conains he conribuions of ne enry o aggregae manufacuring produciviy growh as repored in he sudies, and he sevenh column conains he adjused 5-year equivalens. In he firs panel of Table 3, we gaher resuls from counries wih relaively slow growh raes in GDP per working-age person. In his se of counries, he conribuion of ne enry ranges from 12 14

16 percen o 35 percen, wih an average of 22 percen. In he second panel of Table 3, we gaher he resuls from counries wih relaively high growh raes in GDP per working-age person. In his se of counries, he conribuion of ne enry o aggregae manufacuring produciviy growh ranges beween 37 and 58 percen, wih an average of 47 percen. Figure 3: The conribuion of ne enry and GDP growh. 60 CHN * CHN * Conribuion of ne enry (percen) PRT * USA KOR USA JPN * KOR * KOR CHL CHL * KOR PRT * USA GBR CHL * GDP (per 15-64) growh rae (percen) * denoes 5-year equivalens In Figure 3, we summarize our findings. On he verical axis, we plo he conribuion of ne enry o aggregae manufacuring produciviy growh and on he horizonal axis we plo he economy s GDP per working-age person growh rae. The figure shows a clear posiive correlaion: The ne enry of plans is more imporan for aggregae manufacuring produciviy growh during periods of fas GDP per working-age person growh. Combining our resuls wih sudies from he lieraure yields a more complee picure of he relaionship beween GDP per working-age person growh and he conribuion of ne enry o aggregae manufacuring produciviy growh. Noe ha here is also a posiive relaionship beween aggregae produciviy growh in manufacuring and ne enry. This is no a surprise as he correlaion beween GDP per working-age person growh raes and aggregae manufacuring produciviy growh raes is 0.73 and if we remove one oulier observaion (Porugal ) his correlaion rises o

17 Counry Period GDP/WAP growh rae Table 3: Produciviy decomposiions. Aggregae manufacuring produciviy growh rae Window Ne enry conribuion Ne enry conribuion, 5-year equiv. Japan years Fukao and Kwon (2006) Porugal years Carreira and Teixeira (2008) Porugal years Carreira and Teixeira (2008) U.K 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 (2006) 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 aggregae manufacuring produciviy growh (in percen) in he manufacuring secor as described in (2). The fifh column repors he sample window s lengh. The sixh column repors he conribuion of ne enry (in percen) during he sample window using he decomposiion described in (3). The sevenh column repors he ne enry conribuion (in percen) normalized o 5-year sample windows. The eighh column repors he source of he informaion. All sudies use TFP as he measure of produciviy, use he gross oupu producion funcion, use gross oupu shares as weighs, and use manufacuring daa. All sudies use plans excep for Brand e al. (2012), Fukao and Kwon (2006), and Carreira and Teixeira (2008), which use firms. Source 16

18 3. Model In his secion, we develop a simple dynamic general equilibrium model of firm enry and exi based on Hopenhayn (1992). We model a coninuum of firms in a closed economy. In he conclusion, we discuss how our model can be exended o an open economy model. Openness was undoubedly imporan in he growh experiences of Chile and Korea. In his paper, however, we wan o focus on he simples possible model so ha we can undersand he economics of he FHK decomposiion. Furhermore, when we look a he reforms implemened in boh Chile and Korea during he episodes ha we sudy, we do no find major rade reforms. In our model, he 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, a porion of which 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 ransis 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. 17

19 3.1. Households The represenaive household inelasically supplies one uni of labor o firms and chooses consumpion and bond holdings o solve max s.. 0 logc PC q B w B 1 1 C 0, no Ponzi schemes, B given, D 0 (7) where 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, w is he wage, and for all. D are aggregae dividends paid by firms. We normalize P Producers In each period, poenial enrans pay a fixed enry cos,, o draw a marginal efficiency, x, from he disribuion, F ( x ), whose mean grows exogenously by g 1. 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. We refer o poenial enrans ha draw a high enough efficiency o jusify operaing as successful enrans. Poenial enrans ha do no draw a high enough efficiency are failed enrans. Firms ha operae may exi for exogenous reasons (wih probabiliy ), 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 18 e x, (8) where is he amoun of labor used by he firm and 0 1. Condiional on operaing, firms hire labor o maximize dividends, d ( x ), d ( x) max x ( x) w ( x) f, (9) where f is he fixed coninuaion cos, which is denominaed in unis of he consumpion good. The soluion o (9) is given by

20 1 1 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 ) V ( xg ),0}, (11) 1 1 c, 1 where gc, 1is he coninuing firm s efficiency growh facor from o 1. This efficiency growh facor is characerized by g c gg, (12) where g is a consan, g is he growh facor from 1 o of he unweighed mean efficiency of all firms ha operae in each period, and 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. We assume ha in he balanced growh pah. g 1 g e, which ensures endogenous exi 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 ( xˆ ) 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 x늿 1 x since firms only ener if he firm s value is posiive. For all firms age j 2, x ˆ j is characerized by j j1, 1 c x늿 max x, x? g. (14) 19

21 If here are firms in a cohor ha choose o exi, hen x늿 j x. 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, x늿 j x j 1, 1g c Enry Upon paying he fixed enry cos,, a poenial enran draws is efficiency, x, from a Pareo disribuion, x F ( x) 1 ge, (15) for x g /. The parameer governs he shape of he efficiency disribuion. We assume ha e 1 2, which ensures ha he firm size (employmen) disribuion has a finie variance. In he spiri of Parene and Presco (1994), he parameer characerizes he barriers o echnology adopion faced by poenial enrans. When 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 /, so increasing barriers o echnology adopion lowers he mean efficiency of poenial enrans. We assume ha boh he enry cos, g, and he fixed coninuaion cos, e 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. Our formulaion is similar o ha of Acemoglu e al. (2003), who assume ha fixed coss are proporional o he fronier echnology. In Appendix F, we consider an alernaive model in which fixed coss are denominaed in unis of labor, which has he same propery. We assume ha he cos of enry, T T 1, is composed of wo pars. The firs,, is echnological and is common across all counries. The second, 0, is he resul of policy. The fixed coninuaion cos is defined T f analogously as f f 1. The mass of poenial enrans,, is deermined by he free enry condiion, e 20

22 E V ( x). (16) x A ime, he mass of firms of age j in operaion, j, is j1 where g j, g s1 c s1 j F x j / g j, (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. (18) i1 i 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 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 { } 0, masses of operaing firms { } 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}, he household chooses 0 { 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 j 1 ( j 1 j. (19) x j j1 j1 1 x) df x/ g ˆ ˆ j 6. Enry-exi hresholds { x } 0 saisfy condiions (13) and (14) for all j 1,...,. 7. The bond marke clears, B The goods marke clears, 21

23 1 j / C f Y x x df x g. (20) j ˆ j j x j j1 9. Aggregae dividends are he sum of firm dividends less enry coss, D j d ( x) df 1x/ g. (21) j ˆ j j x j j1 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, fixed coninuaion coss, and barriers o echnology adopion Definiion and proof of exisence Definiion: A balanced growh pah is an equilibrium, for he appropriae iniial condiions, such ha he sequences of wages, oupu, consumpion, dividends, and enry-exi hresholds grow 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 / g, e,. w ˆ 1 Y 1 C 1 D x 1 j, 1 ge, (22) w Y C D xˆ j 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 exis, which implies ha he cuoff efficiency is characerized by he saic zero-profi condiion, d ( ˆ x) 0. Furhermore, firms of every age endogenously exi each period, so x늿 j x for all j 1. The mass of operaing firms is (1 ) 1, f,, (23), f, f 22

24 where, f, g / Y, f, e enry cos is a consan share of oupu per capia,, which is consan in he balanced growh pah. Thus, he, f, Y, f,. (24) An analogous argumen proves ha he fixed coninuaion cos is also a consan share of oupu per capia. The mass of poenial enrans is, f,, f,, (25) where and are posiive consans. The cuoff efficiency o operae is given by g, f, e xˆ, f,, f, which, because (, f, ) and (, f, ) are consans, grows a rae g 1. 1, (26) Since he cuoffs grow a rae ge 1, he oher aggregae variables relaed o income also grow a rae ge 1, Y, f,, f, x, f, 1 w, f, Y, f, ˆ e, (27), (28) D, f, Y, f,. (29) From he household s firs order condiions, he bond price is given by q 1 / g. Finally, e , f, f, (30) where 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 23

25 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 deermined by he improving efficiency of poenial enrans, g e. This is due o endogenous selecion: Because inefficien firms exi, he remaining incumbens are more efficien han he previous cohor of incumbens by a facor of g e. Furhermore, if wo economies have he same g e, hey grow a he same rae, regardless of heir enry coss, barriers o echnology adopion, or fixed coninuaion coss. The cross-counry differences in hese parameers map ino differences in he level of oupu on he balanced growh pah Comparaive Saics We conduc comparaive saics o undersand 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 changes in f,,, which relaes he size of fixed coss o oupu, as shown in (24). Finally, i is useful o know ha,, and are posiive consans ha do no depend on,, or f, whereas (, f, ) is increasing in each of is argumens. We now show ha each reform operaes hrough differen channels. We focus on he direc effec and hus hold, f, fixed. Firs, consider an economy ha decreases is enry cos,. Lower enry coss lead o an increase in he mass of poenial enrans in (25), which increases he cuoff efficiency in (26). The increase in he cuoff efficiency resuls in an increase in oupu in (27). Second, when a counry lowers he barriers o echnology adopion,, here is an increase in he efficiency hreshold in (26), which increases oupu. In conras o he decline in enry coss, he mass of poenial enrans remains unchanged. Raher, efficiency hresholds increase due o firms having access o a beer efficiency disribuion. Finally, consider a reducion in he fixed coninuaion cos, f. Equaion (23) shows ha his leads o an increase in he mass of operaing firms. There are wo resuling conradicory effecs. On one hand, he 24

26 increase in he mass of operaing firms lowers he efficiency cuoffs in (26) which lowers oupu in (27). On he oher hand, he increase in he mass of operaing firms also raises oupu in (27). We can show ha he laer effec dominaes. Thus, lowering fixed coninuaion coss raises oupu and, in conras o reforms o enry coss and barriers o echnology adopion, lowers efficiency cuoffs. All of he reforms we discuss above have he same indirec effec hrough changes in (, f, ). A reducion in enry coss, barriers o echnology adopion, or fixed coninuaion coss have he indirec effec of decreasing he fixed coss relaive o oupu. This increases boh he mass of operaing firms in (23) and he mass of poenial enrans in (25). The increase in he mass of operaing firms resuls in an increase in oupu in (27). Noe ha hese indirec effecs have no impac on efficiency hresholds. To see how his is he case, subsiue (23) and (25) ino (26). 5. Measuremen 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 f unis of consumpion o creae f unis of capial. We assume ha, in each period, he capial sock depreciaes by f ( 1 ) and, if he firm coninues o operae, i invess f 1. This implies ha he firm s capial sock in 1 is k f f ( ) f 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 G, we also repor he quaniaive resuls from an alernaive model in which labor is a composie of variable labor and variable capial. We find ha he resuls are qualiaively similar bu he conribuion of enry and exi o aggregae produciviy growh during periods of fas GDP growh is larger. The produciviy z of a firm wih efficiency x is measured as z x y x x k log ( ) log ( ) log ( ) log, (32) k where w / Y is he labor share, k R K / Y is he capial share, R 1/ q 1 k is he renal rae of capial, K is he aggregae capial sock, and k is he aggregae depreciaion rae.