Why Do Inefficient Firms Survive? Management and Economic Development

Transcription

1 Why Do Inefficient Firms Survive? Management and Economic Deveopment Michae Peters January 2012 Abstract There are arge and persistent productivity differences across firms within narrowy defined industries. This is especiay true in poor countries. Why do productivity differences decine as the economy deveops? In this paper I propose a theory where productivity differences exist because different firms use different technoogies. The negative correation between economic deveopment and productivity dispersion occurs because the set of economicay viabe techniques shrinks as the economy deveops. My mechanism stresses the roe of manageria inputs. If managers are essentia to increase the scae of production, inefficient techniques survive in manageria-scarce economies as productive firms do not have the means to repace them. As the aggregate suppy of managers increases, efficient firms expand, best-practice technoogies dominate the industry and productivity differences decine. Using firm-eve pane data from Chie, I test both cross-sectiona and time-series impications of the theory and evauate different approaches of how to introduce management in firms production function. 1 Introduction There are arge and persistent differences in abor productivity across firms within narrowy defined industries. Whie this has aso been estabished in deveoped economies, this seems to be particuary true in poor countries Foster, Hatiwanger, and Syverson, 2008; Hsieh and Kenow, 2009; Bartesman, Hatiwanger, and Scarpetta, 2009). As an exampe, consider Tabe 1, where I report the within-sector dispersion of revenue abor productivity in Indonesia, Coombia, Chie and France. It is not ony seen that the dispersion is substantia but more interestingy, the dispersion is much ower in rich countries. The dispersion of abor productivity within an industry in Indonesia is more than 60% higher than in France. And even compared to a midde-income country ike Chie, Indonesia has a 17% higher dispersion in abor revenue productivity. What is it about the growth process that reduces this heterogeneity across producers? In this paper I argue that such differences in the average product of abor exist because different firms use different production technoogies. Furthermore, the negative correation between economic I especiay thank my advisors Daron Acemogu, Abhijit Banerjee and Rob Townsend for many hepfu discussions and their ongoing support. I aso thank Nick Boom, Ricardo Cabaero, V.V. Chari, Roberto Fatta Jaef, Danie Keniston, Amir Kermani, Ben Mo, Michae Powe, Ivan Werning, participants of the MIT macro unch and especiay Joaquin Baum and Feipe Iachan for their comments. I aso thank Caire Learge for providing me with the data from France. 1

2 Labor Productivity France Chie Coombia Indonesia 2005) 1992) 1989) 1992) sd Prod diff GDP capita Notes: The tabe shows the within-industry dispersion of og abor productivity. An industry is a 4-digit sector. Labor productivity is cacuated as py w, where py is the firm s rea vaue added and w denotes the firm s tota wagebi. See appendix for detais of the construction of the data. Tabe 1: Differences in Labor Productivity Dispersion Within Industries Across Countries deveopment and productivity dispersion occurs because the set of economicay viabe techniques shrinks as the economy deveops. My mechanism stresses the roe of the avaiabiity of manageria inputs. In particuar, I argue and provide empirica evidence that managers are essentia to increase the scae of production. If managers are scarce in poor countries, inefficient techniques survive as productive firms do not expand sufficienty to repace them. This aows different technoogies to coexist and causes the dispersion in abor productivity to be high. As the aggregate suppy of managers grows, productive firms wi have the means to expand and previousy used technoogies wi cease to be economicay viabe. This reaocation process causes a concentration of production factors in best-practice -technoogies and thereby reduces the within-sector dispersion of abor productivity. I want to stress that it is the heterogeneity of technoogies and not the heterogeneity of firms, which is at the heart of the mechanism. The data presented in Tabe 1 is about revenue measures of productivity and not about quantity measures. 1 In a canonica heterogeneous firms mode a a Lucas 1978) or Meitz 2003), firms differ in their physica productivity but revenue-based productivity measures ike abor productivity wi be equaized across a firms. Precisey because a margina products are equated, physicay) more productive firms wi end up not having a higher abor productivity but they wi be bigger. With heterogeneous technoogies being active in the market however, there can sti be ampe heterogeneity in the average product of abor, despite a margina products being equaized. It is ony when the set of economicay viabe techniques shrink, that the dispersion of abor productivity decines. To study this mechanism and to derive additiona empirica predictions, I propose a highy tractabe genera equiibrium mode, which formaizes this intuition. The mode features withinsector heterogeneity in that each sectora commodity can be produced using two technoogies. Whie the what I ca) traditiona technoogy uses ony production workers, the modern technoogy has an efficiency advantage but aso requires manageria inputs to produce. The ony heterogeneity across sectors is the factor-neutra efficiency advantage of modern producers. In the competitive equiibrium, the avaiabe suppy of managers is aocated according to the sectors comparative advantage. Whie there are modern firms in a sectors of the economy, more managers wi be aocated to those sectors, where the efficiency advantage is high and it is ony in those sectors, 1 In the terminoogy of Foster, Hatiwanger, and Syverson 2008), this paper is about the dispersion of T F P R and not about the dispersion in T F P Q. 2

3 that modern firms can achieve a sufficienty arge scae to fuy repace traditiona production techniques. In a other sectors, both technoogies coexist and abor productivity differs across firms within the industry. Such productivity differences precisey exist, because manageria suppies are imited in the aggregate. With ony few managers avaiabe to the economy as a whoe, manageria demand of some sectors is ow as they compete with other sectors where manageria productivity is comparativey high. As the aggregate suppy of manageria inputs grows, within-sector productivity differences decine as the economy can afford to aocate managers to more and more sectors of the economy, which enabes modern firms to repace traditiona producers. Besides this time-series comparative static resut, the mode aso makes cross-sectiona predictions. In particuar, the mode impies on the sectora eve a positive correation between the average abor productivity and the average manageria intensity and a negative correation between the within-sector empoyment share of ow productivity units and the average manageria intensity. The key object generating those correations are the equiibrium reative prices. Whenever different technoogies coexist in a given sector, the equiibrium price is determined by the margina agent within the sector. In the mode, the margina agent wi aways be a traditiona producer so that reative prices do not depend on the efficiency of manageria firms. Manageria firms in more efficient sectors wi therefore earn a premium as they benefit from reativey high prices. This induces them to increase their manageria intensity and expand their scae. By doing so, they increase the sector s average productivity and reduce the empoyment share of ow-productivity, traditiona producers. To test those predictions empiricay, I anayze a comprehensive pant-eve pane dataset of manufacturing firms in Chie. Cruciay for this paper, this data has information on manageria inputs at the firm-eve. This aows me to not ony test the impications of the theory but to aso provide some evidence on different ways to introduce management in the production function. Both in the time-series and the cross-section I show evidence, that is consistent with the mode. In the cross-section, I show that the above mentioned predictions across sectors are borne out in the data. In the time-series, I show that the aggregate manageria intensity increased over time and that both the productivity dispersion and the empoyment share of ow-productivity units within sectors decined as the mode predicts. Finay, I use the micro-data and the equiibrium impications of the mode to evauate different ways to introduce management in a neocassica production function. The cross-sectiona equiibrium impications are very informative to distinguish different approaches as they have strong impications for the correation between firms inframargina rents and the direction of reaocation - are resources moving from high to ow abor productivity units or the other way round. In particuar I show that thinking about management as an increase in a Lucas-type span of contro is consistent with the micro-data within industries, but has counterfactua impications for the cross-sectora impications. Reated Literature The idea that manageria inputs might be centra for firms abiity to efficienty expand has a ong tradition in economics. Of specia importance for the particuar mechanism of this paper is Edith Penrose s andmark study The Theory of the Growth of the Firm Penrose, 1959). Penrose not ony argues that manageria resources create a fundamenta and inescapabe imit to the amount of expansion a firm can undertake at any time but aso that it is precisey this scarcity of manageria inputs which provide so caed interstices for sma firms as the bigger firms have not got around to mopping them up Penrose, 1959, p. 221). My mode has exacty these two features: the scope of expansion is determined by the aggregate suppy of manage- 3

4 ria resources and traditiona producers survive in those sectors of the economy where bigger firms are imited in the amount of manageria resources they want to buy at at the current market price. However, the precise mechanism how manageria inputs are aocated across producer differs from Penrose s origina work. Whie she argues that manageria inputs are to a arge degree firm-specific, my mode wi ony feature frictioness spot-market transactions. In her work the suppy-botteneck for managers is therefore at the eve of the individua firm. I am focusing on a simper probem - what are the consequences of manageria scarcity at the aggregate eve. The view that manageria inputs were the crucia factor determining the efficiency with which firms coud expand features aso prominenty in the work of Chander 1977) and Robinson 1934). Especiay the scarcity of manageria suppies in poor countries is discussed by the atter, who argues that if we contrast the highy industriaized with the unindustriaized countries we may perhaps fee justified in hoping that industria probems are very graduay producing men of the abiity necessary to hande them. Robinson, 1934, p. 255) The interest in cross-country differences in manageria inputs has been revived recenty. Boom and Reenen 2007, 2010) provide evidence that manageria quaity differs markedy across countries and argue that such differences might be important to account for the income differences across countries. 2 Boom, Eifert, McKenzie, Mahajan, and Roberts 2010) report experimenta evidence from India that providing manageria know-how increases productivity and argue that one reason why better run firms do not dominate the market is constraints on growth through manageria span of contro as effective managers outside the famiy) are in short suppy given the contractua environment. This is aso suggested by Hsieh and Kenow 2011) to expain differences in firms ifecyce growth experience across countries. That manageria capita is missing in deveoping countries is aso argued in Bruhn, Karan, and Schoar 2010). These authors however focus on manageria inputs increasing productivity instead of being a necessary ingredient to expand scae. Finay, there is a arge and growing iterature on productivity differences across firms see Syverson 2011) for a recent survey). The majority of the iterature foows Restuccia and Rogerson 2008) and Hsieh and Kenow 2009) to interpret differences in the average product of abor as dispersion in margina products and hence concudes that poor countries are characterized by a arger degree of misaocation. 3 There is a vast iterature trying to provide a theoretica foundation for this pattern through financia frictions recent contributions incude Buera, Kaboski, and Shin 2011); Mo 2010); Banerjee and Mo 2010) and Midrigan and Xu 2010)), differences in mark-ups Peters, 2010) or the presence of adjustment costs Coard-Wexer, Asker, and De Loecker, 2011). These contributions are of course very different than this paper. There productivity differences are a sign of misaocation as some firms are not at their efficient size. In this paper, the economy is fuy efficient and differences in productivity precisey stem from the fact that the efficient size is different for firms using different technoogies. The structure of the paper is as foows. In the next section I provide empirica evidence about the two crucia ingredients of the mode, namey that economic deveopment is correated with an increase in the aggregate suppy of managers and that managers are essentia to expand the scae of production. Then I turn to the description of the mode. After describing how I incorporate management in the production function, I discuss a very simpe exampe to iustrate the main 2 In fact, aready 35 years Afred Chander argues that administrative coordination heps to account for a significant segment of what economists have defined as a residua, that is the proportion of output that cannot be expained by the growth of input Chander, 1977, p. 490) 3 One recent paper that expicity inks measured productivity differences to the eve of deveopment is Ziebarth 2011) who appies the framework of Hsieh and Kenow 2009) to US pant eve data from the 19th century and finds simiar eves of productivity dispersion as in modern day India and China 4

5 Manageria share in the US economy Year Manageria empoyment share ETH BDI UGA MWI RWA Manageria Occupations across Countries 1990s) BGD NPL HUN IRQ BGR PRY URY COL BLZ CHL SURHRV MDV EGY PER PAN GTM DOMKD JAM MYS CRI POL VEN SVK TTO VCT SYR BOL ZAF TON LTU ECU BWA LVA MEX NGA LKA CPV HND NAM SLV IRN MUS CHN PAK PHL IND IDN THA TUR BRA HTI CIV BMU DNK FIN AUS NLD USA PRI ISR FRA CAN NOR LUX NZL GBR SGP BEL AUT CHE BRN IRL JPN KWT CYP MLT MAC HKG SWE ISL PRT SVN GRC BRB ESP QAT KOR CZE BHRBHS ITA OMN ARE og gdp Notes: The top pane depicts the time-series evoution of the manageria empoyment share of the US. The data is taken from the IPUMS fies from the US Census. Manageria occupations are defined using the Census occupationa category Managers, Officias and Proprietors. The bottom pane depicts the manageria empoyment share across countries. The GDP data comes from the Penn Word Tabes. Manageria empoyment is taken from the Internationa Labor Organization ILO). Manageria occupations are defined using the ILO occupationa categories Manageria, administrative, cerica and executive occupations. Figure 1: Manageria Suppiers and Economic Deveopment mechanism of this paper. Then I present the genera muti-sector genera equiibrium mode and derive its empirica impications. In Section 4 I test those impications using the Chiean pant eve data. Finay I go back to the management production function and use both the equiibrium impications of the mode and the micro data to try to distinguish different specifications. Section 6 concudes. 2 Empirica Motivation for the Mechanism This paper argues that manageria inputs into production are essentia to expand firms scae of production. In such a word, the aggregate suppy of managers determines the reaocation process across firms. If managers are scarce, the scope for expansion is imited and productivity differences across firms persist. Once manageria suppies grow, productive firms can expand and repace inefficient production techniques. Whie I wi be presenting more empirica evidence about the particuar mechanism suggested by the mode beow, I want to first present two pieces of evidence, which motivate the particuar mechanism I am going to expore. Consider first the variation in manageria suppies. For differences in the scarcity of manageria inputs to pay an important part for the pattern of within-sector productivity differences across countries depicted in Tabe 1, it better be the case that the economywide suppy of managers is positivey correated with economic deveopment. That this seems to be the case is seen in Figure 1 beow. In the top pane I depict the manageria empoyment share in the time series of the US. The data stems from the US census and I define workers in manageria occupations as a individuas that are assigned the occupationa category Managers, Officias and Proprietors in the Census. There is a strong positive correation in the time series in that the growth experience of the US 5

6 Dep. Variabe: Manageria empoyment share ny) ) ) ) ) nk) ) ) ) ) nh) ) ) 0.392) 0.431) years of schooing ) ) abor share ) 0.116) Regiona contros No No No No Yes N R Notes: Robust standard errors are shown in parentheses. and denotes significance at the 5% and 10% eve respectivey. The dependent variabe is the manageria empoyment share from the Interna Labor Organization. n y), n k) and n h) are the og of) income per capita, the per-capita capita stock and a measure of human capita. years of schooing are the average years of schooing. The regiona contros in coumn 5 contain dummy variabes for the OECD, Africa and Asia. A the independent variabes are taken from Casei 2005). Tabe 2: Determinants of manageria empoyment shares across countries since the mid 19th century has been characterized by a trend of manageria deepening. Whie hardy 5% of the aborforce have been working in manageria occupations in the 19th century, in 1970, amost a quarter of the US aborforce has been empoyed in manageria occupations. The same pattern is apparent in the cross-country comparison. In the bottom pane of Figure 1 I show the simpe correation between income per capita and the manageria empoyment share in the 1990s. The empoyment data comes from the Internationa Labour Organization ILO) and I define as manageria workers a empoyees which work in manageria, executive, administrative and cerica occupations according to the ILO. Like for the US time series, there is a strong positive correation between economic deveopment and the reiance of manageria inputs. 4 Furthermore, the cross-sectiona reationships is not entirey driven by a simpe correation between manageria occupations and measures of human or physica capita. In Tabe 2 I take the cross-sectiona deveopment accounting data from Casei 2005) and show that whie measures of the stock of human and physica capita are highy correated with the manageria empoyment share coumn 2), they do not expain the correation with income. In the remaining coumns it is seen that this correation is robust to other contros used in the traditiona deveopment accounting exercises. In the preceding paragraph I took care in caing the reationship depicted in Figure 1 as an increase in the manageria empoyment share - and not an increase in manageria suppies. To 4 The cassification of the ILO and the US Census is somewhat different in that the cassification of the ILO is more encompassing. I experimented with different measures of manageria empoyment shares both for the Census and the ILO data) and they a have the same message: Economic deveopment is positivey correated with empoyment in manageria occupations both in the cross-section of countries and the time series within countries. 6

7 distinguish demand and suppy factors in the changing empoyment shares of skied workers in genera and manageria personne in particuar is subject of a arge iterature and this paper does not have much to add to this debate Murphy and Wech, 1993; Autor and Katz, 1999; Godin and Katz, 1999). In contrast, I take the evidence presented in Figure 1 as being consistent with a positive correation between economic deveopment and manageria suppies and the mode wi expore the economic impications of these differences in manageria suppy on within-industry productivity differences across firms. The mode is aso sient on why manageria suppies differ across countries. Of first order importance are surey differences in aggregate human capita suppies. This is aso suggested by the strongy positive correation between the manageria empoyment share and human capita reported in Tabe 2. A second potentia determinant of manageria suppies are differences in the institutiona environment, for exampe the ega system. Boom, Eifert, McKenzie, Mahajan, and Roberts 2010) for exampe present evidence that firms in underdeveoped countries do not hire managers as deegating authority seems to be infeasibe given the contractua environment. Such a mechanism can be thought of a reduction in suppy of manageria efficiency units. Whie the human capita expanation woud impy that manageria skis are iteray absent in poor countries, this mechanism woud argue that marketabe manageria skis are in short suppy. The second important ingredient I want to capture in the mode is a strong form of compementarity between manageria inputs and firms expansion decision.the pant-eve data from Chie, which I wi describe in more detai beow, aows me to study if managers are indeed an essentia input to expand. If such compementarities are important, changes in the non-manageria abor force shoud be predictive for changes in the number of managers a firms empoys. To test this prediction, I ook at a regression of the form g M i,t,s = α + βg BC i,t,s + γ BC i,t 1,s + δ t + δ s + u i,t,s, 1) where gi,t,s M and gbc i,t,s are the growth rates of the number of managers and bue-coar workers of firm i between t 1 and t in sector s, i,t 1,s BC is the firm s agged eve of bue-coar empoyment and δ s and δ t are set of year and sector fixed effects. 1) is a regression akin to Doms, Dunne, and Troske 1997), who study compementarities between firms ski demand and technoogy adoption. The resuts are contained in Tabe 3 beow. In the first three coumns I test of firms expand their manageria workers whenever they increase their bue-coar empoyment. In terms of 1), I regress an indicator if gi,t,s M > 0 on an indicator if gbc i,t,s > 0. Tabe 3 shows that there is a strong positive correation. In coumn 4 I iteray estimate 1), which confirms the earier resuts: the two growth rates are strongy positivey correated. To put these effects into perspective, coumns 5 and 6 repeat this exercise when I use the growth rates of non-manageria white coar workers as a dependent variabe. Whie coumn 5 aso shows a positive correation between times of expansion, the coefficient is ony a third as big as for manageria personne. This is even stronger in coumn 6, where I show that there is a negative correation between the growth rate of bue and white-coar non-manageria empoyment. I interpret this as saying that managers and bue-coar workers are compements, whie bue-coar workers and non-manageria personne are more substitutabe. In coumn 7 I show that this negative correation is not driven by a different sampe of firms. Even those firms that report a negative correation between the bue-coar and non-manageria growth rates report a positive one with manageria empoyment. I view these resuts as generay supportive of the idea that managers are an important compementary factor for firms to grow. 7

8 Dep. Variabe 1[g M > 0] g M 1[g W C > 0] g W C g M 1[g BC > 0] ) ) ) ) n BC t 1) ) ) ) ) ) g BC ) ) ) N R Notes: Robust standard errors are shown in parentheses. and denotes significance at the 5% and 10% eve respectivey. A regression except for coumn 1 contain year and sector fixed effects 4 digit). g j s,t denotes the growth rate of managers, bue coar workers and white-coar non manageria workers respectivey. 1[g j s,t > 0] is an indicator variabe if gm s,t > 0. n ) t 1 BC is the og of agged bue coar empoyment. 3 The Mode Tabe 3: Management as an essentia input for expansion Motivated by the evidence above, I wi now study the economic impications of differences in manageria suppies if managers are an essentia input for firms to expand. 3.1 How to mode management? This paper interprets the observed within-sector differences in abor productivity as stemming from differences of techniques used. It then interprets the negative correation between productivitydispersion and income per capita as being generated by a process of reaocation: as rich countries are manager-abundant, manager-intensive firms repace other technoogies used and thereby reduce the dispersion of abor productivity within narrowy defined industries. To mode this phenomenon, I not ony have to specify how managers enter the production function, I aso have to specify how the manageria-intensive technoogy itsef differs from the non-manageria technoogy. It is this difference between technoogies that determines which firms wi earn the inframargina rents. For the most part of this paper I wi assume that the traditiona, non-manageria firms produce using abor ony and that their technoogy is inear y T =. 2) Manageria firms in contrast have access to a production function of the form y M = qf, m), where q is a factor-neutra productivity term and and m denote the number of workers and managers empoyed. I wi now put more structure on f. In accordance with resuts of Tabe 3, I want to capture that manageria inputs are essentia for firms to increase their scae of production. Hence, f shoud have a ow easticity of substitution 8

9 so that managers and production workers are strong compements. Additionay, given that the traditiona technoogy is assumed to have constant returns, f has to have decreasing returns - otherwise, ony the technoogy with the owest margina costs at given factor prices) wi prevai and there were not any differences in abor productivity within sectors. In order to emphasize that it is the scarcity of manageria suppies that imit the expansion of management-intensive firms, I wi take f to take the foowing form f, m) = α σ 1 σ ) + 1 α) m γ ) σ 1 σ σ 1 σ, 3) where σ is sma in particuar σ < 1) and γ < 1. Putting the decreasing returns directy on the manageria input inside the CES aggregator has the convenient property that f can aso be expressed as ) σ 1 ) σ σ 1 ) m γ σ m γ f, m) = α + 1 α) A. This stresses the interpretation that the tota factor productivity of abor A ) m γ decreases in scae if managers are scarce. However, it wi be cear in the mode beow, that a formuation of ) f, m) = α σ 1 σ + 1 α) m σ 1 σ σ 1 γ σ wi have amost identica resuts. There is one specia case of 3) which is particuary interesting. This is the case of σ = 0, where f, m) = min {, m γ }. 4) 4) is an interesting formuation, precisey because it focuses on the roe of managers being necessary to expand scae. In contrast to 3), managers do not affect the margina or average product of abor but if firms want to increase their scae, they require manageria inputs to do so. In the main section of the paper, I wi anayze mosty the case of 4) in order to focus on that particuar margin what managers are usefu for. However, I aso state the main resuts of the mode for the genera CES case of 3). It wi be seen that the economy is continuous in σ so that a the resuts are entirey anaogous. Finay, consider the productivity term q. Throughout the paper I wi assume that q > 1. For the case of 4) it is obvious that q > 1 is necessary for manageria firms to be wiing to produce. 5 I aso think that q > 1 is the economicay interesting case as I want to think of manageria scarcity preventing efficient firms to expand. As mentioned above, it is not essentia where I put the decreasing returns to scae given that it wi be the manageria firms that earn inframargina rents in this economy. That it is the manageria technoogy which has decreasing returns however is crucia. I wi come back to this in Section 5 beow, where I discuss the case of traditiona producers having a decrease returns technoogy. In particuar, I wi show the genera equiibrium impications of this case differ markedy from the setup described above and that these impications are at odds with the pant-eve data. 3.2 A simpe exampe Before I present the genera mode, et me consider the simpest exampe that can iustrate the economic mechanism that is at the heart of this paper. Consider an economy, which consists of a 5 For the genera CES case, q coud be smaer than one precisey because manageria firms earn inframargina rents. In fact I wi show beow that the condition for manageria firms making positive profits is given by q 1 σ ` 1 σ α > 1. For σ = 0, this impies that q > 1. 9

10 unique fina good. The economy has access to two production techniques. In particuar, there is a measure one of entrepreneuria firms that produce according to the production function y = qmin {, m γ }, q > 1, γ < 1, where as above denotes the amount of production workers and m is the number of managers. The economy has aso access to a traditiona production technoogy, which transforms production abor into output, i.e. y =. Workers and managers are in fixed suppy L and M respectivey and a markets are competitive. Characterizing the equiibrium is straight-forward. If both techniques are active, the equiibrium wage for production workers wi be equa to the price of the fina good, which is taken to be the numeraire. Given w L = 1, profits of modern producers are given by π = q 1) m γ w M m, as the Leontief structure of the production function impies that = m γ. Manageria demand is therefore determined from the first-order condition γ q 1) m γ 1 = w M. 5) Now consider the differences in abor productivity in this economy which wi of course triviay correspond to within-sector productivity differences). Foowing Foster, Hatiwanger, and Syverson 2008, 2011) I measure productivity as revenue per adjusted abor input. This invoves weighing different types of abor by their reative wage. Formay, abor productivity is measured as Simpy appying 6) to the different firms in this economy yieds that py ξ + w M wl m. 6) ξ T = y = 1 7) and ξ M = y + w M wl m = qmγ m γ + w M m = q > 1, 8) 1 + γ q 1) where the ast equaity uses 5). Hence, entrepreneuria firms produce at a higher abor productivity precisey because they earn some inframargina rents. Note that ξ M = 1 if γ = 1, which again stresses that abor productivity is not primariy a statement about firm-specific factor neutra productivity here q) but about the inframargina rents different producers earn. The reason why I assumed that it is the manageria firms that earn inframargina rents is seen in Tabe 4 beow. There I report the resuts from running a regression of og abor productivity n ξ)) on firms manageria intensity and a fu set of industry fixed effects. Hence, the coefficient on the manageria intensity is the within-industry correation between the manageria intensity and the inframargina rents the firm earns. According to the mode, the variation in the manageria share is generated 10

11 Dep. Variabe og abor productivity ξ) Manageria intensity ) ) ) n k ) ) ) ) ) Manageria expenditure share ) ) ) N R Notes: Robust standard errors are shown in parentheses. and denotes significance at the 5% and 10% eve respectivey. A regression contain year and sector fixed effects. A sector is a 4-digit industry. The dependent variabe is og abor productivity see 6)). Manageria intensity is the firm s manageria empoyment share m i, where m i is the number of i managers and i denotes tota empoyment. n ` k denotes the og of firm s capita intensity. Manageria expenditure share is given by firm s manageria compensation over the tota wagebi. Tabe 4: Manageria intensity and inframargina rents by technoogica differences within the industry. The strong positive correation suggests that inframargina rents are earned by the - in the mode - modern firms and not the traditiona firms. 6 Note aso that measured productivity does not depend on any variabes determined in equiibrium - in fact to derive 7) and 8) I did not even use the factor market cearing conditions. Once we impose market cearing, the equiibrium quantities are determined as m = M, M = M γ and T = L M γ, and the equiibrium wage for managers is simpy given by w M = q 1) γm ). Now consider an increase in the aggregate suppy of managers M. There are three main impications: 1. The dispersion in abor productivity vanishes once traditiona technoogies are fuy repaced. 2. The empoyment share in ow productivity estabishments decines as more and more workers wi be working in units that do earn inframargina rents. 3. The economy s average abor productivity increases as high-productivity units expand their scae. 7 Whie admittedy simpe, there are a coupe of properties, which wi aso feature in the more genera mode. In particuar, these three main impications wi have their counterpart in the cross-sectora dimension and the impications of manageria deepening are sighty more nuanced as the aocation of managers across sectors wi respond. It is this mode where I turn now. 6 However, I wi come back to this point in Section 5 when I present some other conficting evidence. 7 One way to see that this reaocation to high productivity units is mainy about increasing the inframargina rents in the economy, is to note that the aggregate abor share w LL+w M M Y = L+q 1)γM γ L+q 1)M γ is decreasing in M. 11

12 3.3 The genera mode I wi now take the basic environment of this simpe mode and put it in a muti-sector environment. Doing so is usefu for three reasons. First of a, the mode generates additiona economic insights, which are absent from the simpe mode. In particuar, it aows me to study how different sectors in the economy bear the burden of manageria scarcity in the aggregate economy. Which sectors wi absorb the few managers the economy has? How are different sectors affected by an increase in in the aggregate suppy of managers in the economy? And which sectors are characterized by within-sector productivity differences, precisey because they have to compete with other sectors for managers - the scarce resource in the economy? These are a questions, which the singe-sector mode above can not address. Secondy, the mode generates additiona empirica prediction on the sector eve, which I can test using the pant eve data. Finay, it turns out that it is these cross-sectora predictions, which wi be informative about the management production function and I wi come back to this in Section 5 beow. Environment The environment is the foowing. The economy consists of a continuum of sectors in the unit interva. I wi denote sectors by i [0, 1]. Individuas aggregate this unit mass of intermediate products according to a Cobb-Dougas aggregator 1 ) Y = exp n Y i)) di, 9) 0 where y i) is the tota eve of consumption of sector i s production. The specific Cobb-Dougas form is convenient but not essentia. 8 There are three type of agents. There is a measure µ of entrepreneurs in each sector i and hence aso in the aggregate) that have access to a technoogy to produce variety i. Additionay there is a measure λ of managers and a measure 1 λ of production workers. Each manager worker) has M L ) λ λ of efficiency units of abor so that the aggregate suppy of manageria worker) efficiency units is given by M and L respectivey. Like in the exampe of Section 3.2, each sector s output Y i) can be produced by two technoogies. Which of these technoogies wi prevai wi be determined in equiibrium. More specificay, in each sector i production workers have access to a traditiona technoogy, whose production function is given by y T i) = A i). 10) Here, denotes the amount of production workers empoyed and A i) denotes the productivity in sector i. The distribution of A i) is unrestricted. Note that ony production workers have access to this technoogy. Hence, I assume from the outset that managers wi never want to run those technoogies in equiibrium. Essentiay this as an assumption on the parameters of the mode that the reative wage of managers wi be sufficienty high in particuar higher that the wage for production workers). I aso assume that the technoogy in 10) is common knowedge among production workers and that there is free entry in a sectors. Traditiona producers in sector i compete with entrepreneurs. As in the singe-sector exampe entrepreneurs have access to the technoogy y M i) = q i) A i) min {, m γ }. 11) 8 In the Appendix I derive the resuts for the more genera CES specification with non-unitary demand easticities. 12

13 Hence, A i) is a technoogy-neutra productivity term that appies to both the manageria and the traditiona technoogy and q i) parametrizes the sector-specific comparative advantage of entrepreneurs. Whie the main anaysis wi focus on the specific Leontief case given in 11), I aso state the resuts for the more genera case of y M i) = q i) A i) α σ 1 σ + 1 α) m γ σ 1 σ ) σ σ 1, whose anaysis is reegated to the Appendix. It wi be seen that a the resuts are continuous in σ so that nothing is ost to focus on the notationay simper case of σ = 0. Note aso that I coud aow entrepreneurs access to the traditiona technoogy 10). However, precisey because entrepreneurs do earn inframargina rents, they wi stricty prefer to run the manageria technoogy. Finay, I assume that a markets are perfecty competitive, i.e. a agents in the economy take wages w L, w M ) and sectora prices [p i)] 1 i=0 as given when making their decisions. Equiibrium Consider now the equiibrium of this economy. An equiibrium has the obvious forma definition. Definition 1. Consider the economy above. An equiibrium are wages for workers and managers w L, w M ) and sectora prices [p i)] 1 i=0 such that entrepreneurs and workers running the traditiona technoogy maximize profits there is free entry in the traditiona technoogy in a sectors factor markets for managers and production workers cear reative prices and quantities are consistent with demands generated from 9) To characterize the equiibrium it is usefu to take the productivity advantage q as the main state variabe in this economy. In particuar, as q is the main source of heterogeneity across sectors, et us index sectors directy by q and et A q) be the corresponding factor neutra productivity term which appies to a producers. I wi denote the distribution of q by G q and the support of q is given by [q L, ), where q L > 1. Simiary, sectora prices can be expressed directy as a function of q, i.e. the coection of sectora prices is given by [p q)] q. Taking a prices as given, the entrepreneuria demand for production workers is given by and the scae of each firm is determined from M q) = m q) γ m q) = argmax m {p q) A q) q w L m γ w M m} { ) p q) A q) q = argmax m 1 m γ w } M m. 12) w L w L As ceary seen from 12), I can express manageria demands as a function of the wage premium w M wl and the statistic p q) A q) q z q) 1, 13) w L which I wi refer to as the revenue productivity premium in sector q. In particuar, a the sectora characteristics are fuy contained in z q). 12) then directy impies that the manageria demand m z, ψ) is defined by m z q), ψ) = γψz q), 13

14 where ψ w L w M is the reative wage of production workers. This directy impies that m z, ψ) is increasing in both the revenue productivity premium z and in the reative wage of production workers. The decision probem of traditiona producers is straight-forward. Profits of traditiona producers in sector q are given by π T = p q) A q) w L ), which directy impies that equiibrium prices [p q)] q and wages w L have to satisfy the condition { = w L Aq) if traditiona producers are active in sector q p q) < w L Aq) if traditiona producers are not active in sector q. 14) Hence, the main question is in which sectors traditiona suppiers are active. In this economy, the answer is easy in that there wi be a simpe cutoff rue. In particuar, et Ω T w L, w M ) be the set of sectors where traditiona suppiers produce at wages w L, w M ) and prices [p q)] q satisfying 14). Then there is ˆq w L, w M ) such that q Ω T w L, w M ) q ˆq w L, w M ). 15) To see why 15) is true, note first that the Cobb-Dougas demand system in 9) impies that tota sectora revenues are equaized in a sectors, i.e. As tota production in sector q is given by 16) appied to q, q Ω T w L, w M ) impies that p q) Y q) = x for a q. 16) Y q) = A q) T q) + µqa q) m z q), ψ) γ, p q) A q) [ T q) + µqm z q), ψ) γ ] = p q ) A q ) [ T q ) + µq m z q ), ψ) γ]. As p q) A q) = p q ) A q ) = w L, 13) impies that z q) = q 1 so that T q) = T q ) + µq m q 1, ψ) γ µqm q 1, ψ) γ, which impies that tota empoyment in traditiona technoogies T q) is stricty decreasing in q. Hence, there is ˆq such that in a sectors with q > ˆq ony entrepreneuria, management-intensive technoogies wi be active. This cutoff ˆq is the key endogenous variabe, which wi be determined equiibrium. In particuar, I can characterize the entire equiibrium aocations as a function of this cutoff ˆq. Consider first a sectors where ony entrepreneurs are active, i.e. q ˆq. The demand system 16) and the expression for z q) see 13)) impies that 1 + z q)) m z q), ψ) γ = 1 + z ˆq)) m z ˆq), ψ) γ for a q ˆq, which directy shows that the revenue productivity premium z q) is equaized for a entrepreneuria firms, which do not compete against traditiona suppiers within their sector. In terms of equiibrium prices, this together with 14) impies that p q, ˆq) = = { wl Aq) w L ˆq Aq) q if q < ˆq if q ˆq w L min {q, ˆq}, 17) A q) q 14

15 where the notation p q, ˆq) stresses that the equiibrium price of sector q products depend on the aggregate statistic ˆq. Given the equiibrium pricing schedue in 17), the revenue productivity premium z q) of entrepreneuria firms is given by z q, ˆq) = p q) A q) q w L 1 = min {q, ˆq} 1 and the aocation of managers across entrepreneuria firms of different sectors is given from 12) as m q, ˆq, ψ) = γψz q, ˆq)) 1 = γψ) 1 min {q, ˆq} 1) 1. 18) Tota production-worker empoyment in entrepreneuria firms is simpy given by M q, ˆq, ψ) = m q, ˆq, ψ) γ. To finay determine aggregate empoyment in traditiona technoogies, use again the demand system 16) and the expression for equiibrium prices 17) to arrive at T q, ˆq, ψ) = µ ˆq M ˆq, ˆq, ψ) q M q, ˆq, ψ)). 19) According to 3.2, traditiona technoogies wi - in equiibrium - be used to account for the output not produced by arge scae producers. Hence, the coexistence of heterogeneous technoogies stems entirey form the demand side - ess efficient producers survive because firms with a higher abor productivity are not wiing to hire compementary factors managers) to expand sufficienty. This keeps prices high and creates interstices for sef-empoyed firms to survive Penrose, 1959). Finay, consider the equiibrium wage for production workers in this economy. With the fina good being the numeraire, the eve of reative prices has to satisfy q n p q)) dg q = 0. Substituting 17) yieds that n w L ) = q L n A q)) dg q q) + ˆq n q) dg q q) n ˆq) ˆq dg q q), 20) which shows that wages are decreasing in ˆq. This is just the fip-side of traditiona suppiers keeping prices high and is reminiscent of a ong tradition of dua economy modes in deveoping economics Lewis, 1954). Given ψ, ˆq) this fuy characterizes a the aocations in the economy. Now et us again measure abor productivity in this economy. In this economy we have that and that ξ M q, ˆq) = ξ T q, ˆq) = p q) A q) T q, ˆq) T q, ˆq) = w L 21) p q) A q) qm q, ˆq, ψ) γ p q) A q) q M q, ˆq, ψ) + w = M wl m q, ˆq, ψ) 1 + γz q, ˆq) = w 1 γ) z q, ˆq) L + w L 1 + γz q, ˆq) = w L + w L 1 γ) min {q, ˆq} 1) 1 + γ min {q, ˆq} 1) > w L 22) Hence, akin to the simpe singe-sector mode of Section 3.2, manageria firms earn a productivity premium precisey because they earn inframargina rents γ < 1). However, 21) and 22) now aso contain resuts about the correation of productivity across sectors. For traditiona producers, abor productivity is equaized across sectors, precisey because the sectora differences in productivity 15

16 A q) wi shift reative prices equaize revenue per worker. This is different for management-intensive firms. As seen from 22), productivity is increasing in q as ong as q < ˆq. This is of course precisey due to the fact that reative prices do not depend on q as ong as traditiona producers are present. Hence, manageria firms earn rents for two reasons: first of a they earn inframargina rents simpy due to their technoogy. But secondy, they earn rents because traditiona firms which are the margina agents in this economy) put a foor on reative prices. This prevents reative prices from faing as sectora productivity q increases and hence increases the revenue productivity premium, which entrepreneuria firms face. Once productivity differences within sectors vanish, i.e. for q > ˆq, productivity manageria productivity ξ M is constant across sectors because prices then do depend on entrepreneuria productivity q which causes revenue per production unit to be constant. For future reference, I gather these resuts in the foowing Proposition. Proposition 2. Consider the economy above. Any equiibrium is characterized by a productivity cutoff ˆq, such that T q) = 0 if and ony if q ˆq. Given this cutoff ˆq and the reative wage ψ = w L w M, equiibrium prices [p q)] q are given by 17), the aocation of managers m q) is given in 18), empoyment in traditiona technoogies T q) is given in 19) and abor productivity ξ T and ξ M are given in 21) and 22). Proposition 2 characterizes the entire aocation as a function of the productivity cutoff and reative wage. To show that an equiibrium exists and that it is unique I ony have to show that there exists a unique tupe ˆq, ψ) which cears the abor markets for both managers and production workers. Before doing so however, I want to reiterate that nothing in the simpe characterization contained in Proposition 2 reied on the specia Leontief structure. In particuar, if I were to consider the genera CES production function, the characterization of the equiibrium was essentiay identica. It is contained in the foowing Proposition and the agebraic detais can be found in the Appendix. Proposition 3. Consider the economy above and assume that the entrepreneuria technoogy is ) given as a genera CES production function f, m) = α σ 1 σ + 1 α) m γ ) σ 1 σ σ 1 σ. Any equiibrium is characterized by a productivity cutoff ˆq, such that T q) = 0 if and ony if q ˆq. Given this cutoff ˆq and the reative wage ψ = w L w M, equiibrium prices [p q)] q are given by 17), the revenue productivity premium z q, ˆq) is given by ) σ 1 z CES q, ˆq) = min {q, ˆq}) 1 σ 1, α the aocation of managers and production workers in entrepreneuria firms is given by m CES q, ˆq, ψ) = CES M q, ˆq, ψ) = 1 α α 1 α α ) σ θ γ ψ z q, ˆq) θ ) σ θ γ γ 1 θ γ ψ z q, ˆq) θ where θ = 1 γ) 1 σ). Empoyment in traditiona technoogies is given by CES T q, ˆq) = ) σ 1 ˆq 1 σ M CES q, ˆq, ψ) q 1 σ M CES q, ˆq, ψ) ) α 16

17 and abor productivity ξt CES and ξm CES are given by Proof. See Appendix. ξ CES T q, ˆq) = w L ξ CES M q, ˆq) = w L + w L 1 γ) z CES q, ˆq) 1 + γz CES q, ˆq) From Propositions 2 and 3 it is easy to see that the economy is essentiay continuous in σ. In particuar, im σ 0 z CES q, ˆq) = z q, ˆq) = min {q, ˆq} 1 and that the same hods true for a the aocations. To fuy characterize the equiibrium, I have to find the tupe ˆq, ψ), which ensures that the abor markets for both managers and production workers cear. Consider first the market for managers. Given that there are M units of manageria efficiency units to be hired in the market and that manageria demand ony stems from entrepreneuria firms given in 18)), the market cearing condition is given by M µ = m q, ˆq, ψ) dg q q) = ψ 1 1 γ ). z q, ˆq) 1 dg q q). Equiibrium on the market for production workers in turn requires that L = µ ˆq M q, ˆq, ψ) dg q q) + T q, ˆq, ψ) dg q q). q L Using 19) it can be shown see Appendix) that the abor market cearing condition can be written as [ ) ] L µ = ψ γ γ γ 1 + z ˆq, ˆq) z q.ˆq) 1 z q.ˆq) 1 dg. z ˆq, ˆq) For future reference it is usefu to rewrite these conditions as M µ = γ 1 ψ 1 Ψ ˆq) 23) L µ = γ γ ψ γ D ˆq) Ψ ˆq)), 24) where Ψ ˆq) = D ˆq) = q z q, ˆq) 1 dg q q) 1 + z ˆq, ˆq) z ˆq, ˆq) ) z q.ˆq) 1. 25) 23) and 24) are two equations in the two remaining unknowns ψ, ˆq). That an equiibrium exists and it is unique is contained in the foowing Proposition. Proposition 4. Consider the economy above. There is a unique equiibrium ψ, ˆq) as 23) and 24) have a unique intersection. The equiibrium is characterized by two functions 17

18 M ˆq = ˆq w L w M = ψ ) µ, L µ, [q]ˆq q L M µ, L ) µ, [q]ˆq q L with ˆq M µ w L w M M µ < 0, > 0, ˆq L µ w L w M L µ > 0, < 0, ˆq > 0 [q]ˆq q L w L w M < 0. [q]ˆq q L In particuar, the equiibrium vaues ψ, ˆq) do neither depend on [A q)] q H q L Proof. See Appendix. nor on [q] q H ˆq. The most important comparative static resut for this paper is that productivity cutoff ˆq is decreasing in the reative manageria suppy of the economy. Hence, akin to the simpe singe sector mode, as the aggregate suppy of manageria resources grows, there wi be more and more sectors in which traditiona technoogies are repaced. This comparative static resut is contained in the foowing reationship, which determines the cutoff ˆq as a function of reative manageria suppies. Using 23) and 24) it foows that ) γ M µ L µ ) = Ψ ˆq) γ Q ˆq). 26) D ˆq) Ψ ˆq) In the Appendix I show that Q ˆq) is stricty decreasing which is essentiay the proof of Proposition 4)) and that imˆq ql Q ˆq) = 1 imˆq Q ˆq) = 0. Q ˆq) is exacty the aggregate reative demand for manageria inputs. As entrepreneuria firms are management intensive, this reative demand is decreasing in ˆq as a decine in ˆq impies that more and more of the economy s output is produced using traditiona techniques. It is in that sense that 26) exacty determines how much repacement of traditiona technoogies the economy can afford given that manageria suppies are imited. As with every scarce resource, managers are aocated according to their comparative advantage, which is parametrized by q. Hence, there wi be managers in every sector of the economy but the reative importance of manageria firms is higher, the higher the productivity advantage of the technoogy they run. If managers are scarce, ony a sma pocket of the economy is characterized by technoogica homogeneity where traditiona suppiers are fuy repaced. As the manageria suppy accumuates over time, this part of the economy grows, more and more traditiona techniques wi cease to be economicay profitabe and a smaer share of the economy wi be characterized by a coexistence of different techniques and productivity differences. With that intuition, the other comparative static resuts contained in Proposition 4) are aso intuitive. First of a, note that the reative demand for managers Q ˆq) does neither depend on 18