Variable Markups and Misallocation in Chinese Manufacturing and Services

Transcription

1 Variable Markups and Misalloation in Chinese Manufaturing and Servies Jinfeng Ge Zheng Mihael Song Yangzhou Yuan eember 13, 216 Abstrat Cross-ountry omparison reveals an unusually small servie setor in China. Using firm-level data from China s 28 eonomi ensus, we find two fats that speak to a novel mehanism for misalloation within servie and between manufaturing and servie. First, ompared with the manufaturing setor, there are more state-owned enterprises and fewer entrants in the servie setor. Seond, markups inrease in firm size in both manufaturing and servie, and the inrease is more dramati among servie firms. We interpret these fats through the lens of a monopolisti ompetition model with heterogeneous firms and variable markups. Neessary and suffiient onditions are established for entry barriers and other fritions to ause misalloation via markups. We also extend the analysis to a multisetor environment, where the model implies a new hannel that translates asymmetri barriers to entry aross setors into setoral markups differenes, whih, in turn, ause setoral misalloation. To quantify the importane of the markups hannel, the model is alibrated to math the observed firm size and markups distributions. The alibration finds big variations in entry barriers aross industries. When reduing entry barriers for servie firms to the extent observed for manufaturing firms, the model predits a threeperentage-point inrease in the servie employment share. We thank John Hassler and seminar partiipants at the IIES, epartment of Eonomis Stokholm University, Chinese University of Hong Kong, Fudan University for helpful omments. Fudan University, Shool of Eonomis, jinfeng ge@fudan.edu.n. Chinese University of Hong Kong, epartment of Eonomis, zheng.mihael.song@gmail.om. Stokholm University, epartment of Eonomis, yangzhou.yuan@ne.su.se. 1

2 1 Introdution Less developed eonomies tend to have smaller servie setor. China is no exeption: Its servie industries aount for less than 4% of the total employment, about half of the share in the US. Yet, China s servie setor deserves speial attention for at least two reasons. First, China s servie employment as a share of the total employment is among the smallest when ompared to other ountries at the same inome level. When it omes to the servie share in the non-agriulture setor, China is atually ranked at the lowest see Figure 1. Seond, the mirror image of the dwarfed servie setor is China s extraordinarily large manufaturing setor, whih has made the ountry the world fatory. Understanding why China has a unusually small servie setor is among the first steps to rebalane the global eonomy. Figure 1: Panel A plots servie employment as a perentage of total employment y-axis and GP per apita PPP adjusted, x-axis in 211. Panel B plots servie employment as a perentage of non-agriulture employment y-axis and GP per apita PPP adjusted, x-axis in 211. ata soure: World Bank. Using firm-level data from China s 28 eonomi ensus, we doument two sets of fats that distinguish servie from manufaturing and may speak to the underdeveloped servie setor. First, the state share in the servie setor is about three times as high as that in the manufaturing setor. Moreover, there is a robust negative orrelation between the entry rate and the state share aross both manufaturing and servie industries. These patterns

3 are onsistent with the widely doumented heavy regulations and high barriers to entry in many Chinese servie industries see, e.g., Rutkowski, 215. We also find the dispersion of revenue-labor ratio among servie firms to be 6 perent higher than that among manufaturing firms, suggesting more severe misalloation within servie through the lens of the framework developed by Hsieh and Klenow Seond, revenue-labor ratio inreases in revenue among both manufaturing and servie firms. The orrelation is robust to within-industry heterogeneity in apital intensity. If we interpret variations in revenue-labor ratio, after ontrolling for apital intensity, as variations in markups, this finding would be in line with the reent models with variable markups e.g., Zhelobodko et al., 212; hingra and Morrow, 214 that predit higher markups for larger firms. More importantly, we find the inrease of revenue-labor ratio in revenue among servie firms to be about 5 perent more than that among manufaturing firms. Sine the average markups in an industry are mainly determined by markups hanged by large firms, the steeper revene-labor ratio profile suggests higher average markups in servie industries. In summary, there are more SOEs and fewer entrants in China s servie industries. Large servie firms tend to harge higher relative markups ompared to their ounterparts in manufaturing. These fats point to a potential onnetion between markups and distortions aused by fritions suh as barriers to entry. To lay down a theoretial foundation for suh onnetion, we add entry barriers and other fritions into a standard monopolisti ompetition model with heterogeneous firms and variable demand elastiity. We establish neessary and suffiient onditions for entry barriers to affet the average markups and misalloation in an industry. Interestingly, if firm produtivity follows Pareto distribution, entry barriers would have no effets due to the anellation of the seletion and variety effets. If, instead, firm produtivity follows log normal distribution, the variety effet would dominate the seletion effet, leading to the pro-ompetition effet that translates redution in entry barriers or other fritions to lower average markups and alleviation of misalloation. We apply the model to an multi-setor environment where the elastiity of substitution aross setors is onstant. The novel finding is that under ertain onditions, an asymmetry in fritions suh as barriers to entry aross setors may lead to setoral misalloation via markups. For instane, if the pro-ompetition effet exists, higher entry barriers in a setor would lead to higher average markups, resulting in too little resoures alloated to the setor as opposed to those in the effiient alloation. Notie that in the standard models with onstant markups, 1 Hsieh and Klenow 29 define revenue-labor ratio as labor revenue produtivity. Revenue produtivity is the produt of physial produtivity and a firm s output prie. It should be equated aross firms in the absene of distortions. 2

4 distorting the average produtivity in a setor is the only hannel through whih entry barriers may ause setoral misalloation. In ontrast, our model entails both the standard produtivity hannel and the new markups hannel. A more stark omparison is to onsider the elastiity of substitution aross setors equal to one. The anellation of the inome and substitution effets would nullify the standard produtivity hannel. In other words, the markups hannel would be the only hannel through whih entry barriers ause setoral misalloation. To examine the quantitative importane of the markups hannel, we alibrate the model to math the observed firm size and markups distributions. The first finding is that although Pareto distribution fits well the right tail of the firm size distribution, it is a poor approximation for firms with size below the median level. Instead, log normal distribution that satisfies the neessary onditions for the markups hannel fits well the observed distributions. When reduing entry barriers in servie to the extent in manufaturing, the alibrated model predits a three-perentage-point inrease in the servie employment share. We find some auxiliary evidene for the mehanism that onnets markups to entry barriers. China has experiened two major reforms in the late 199s and early 2s that greatly redue entry barriers and foster domesti ompetition: i The restruturing of the state setor and ii the aession to WTO. Using the Annual Industrial Survey onduted by China s National Bureau of Statistis, we look for evidene whether suh reforms led to redution in markups among manufaturing firms. We find that the relative markups fell dramatially in most manufaturing industries from 1998 to 27. Moreover, the redution tends to be more dramati in those industries with a higher share of newly established private firms, onsistent with the mehanism that lowering barriers to entry would attrat entrants and ut markups. Our work ontributes to the misalloation literature in two aspets. The theory part points out a new soure of misalloation that arises from variable markups. When extended to the multi-setor environment, the theory illustrates the markups hannel that translates asymmetry in fritions aross setors into setoral misalloation. This provides a new perspetive from whih we understand resoure alloation effiieny aross setors. In the quantitative part, we use firm-level data from both manufaturing and servie to quantify the positive and normative impliations of misalloation within an industry and aross industries. Most of the existing work uses manufaturing firm data only and, hene, annot address setoral misalloation. We are not the first on setoral misalloation aused by markups differenes. Epifani and Gania 211 show that trade liberalization may worsen setoral misalloation by widening the gap of markups between tradable and nontradable setors. In a broader sense, this paper is part of the literature on strutural transformation see, e.g., Herrendorf, Rogerson, and 3

5 Valentinyi, 214. We provide a ase study, illustrating how fritions an retard strutural transformation. When it omes to misalloation in China, the literature has well doumented the poliies favoring state-owned enterprises as an important soure of misalloation. 2 There is also evidene linking entry barriers to the presene of state-owned enterprises aross ities see, e.g., Brandt, 216. Bai, Hsieh and Song 215 argue that large firms are more likely to be treated favorably through speial deals. Our findings suggest an asymmetry in favoring inumbent firms between manufaturing and servie an distort setoral alloation of resoures. Although Pareto distribution has widely been adopted in the literature, some reent studies explores some other distributions. For example, Fernandes et al. 215 and Bas et al. 215 argue for log normal distribution and Feenstra 213 suggest bounded Pareto distribution. Our theory part offers another example of the gains from moving beyond Pareto. Also, we provide evidene for log normal distribution as well as its quantitative importane. This paper also ontributes to a small but growing literature on fritions in the servie setor. Song, Thomas, Wang and Xu 216 develop a model where sales fritions an be redued by aumulating retail apital. They alibrate the model to math some empirial moments from their survey on Chinese footwear firms. One of their main findings is that sales fritions an generate large markups heterogeneity. In that sense, sales fritions play a role similar to entry barriers in our paper, though the markups heterogeneity arises from an entirely different mirofoudation. Finally, our paper is related to the reent literature on variable markups. Following Zhelobodko, Kokovin, Parenti and Thisse 212, Kihko, Kokovin and Zhelobodko 213 and hingra and Morrow 214, we adopt monopolisti ompetition model with additively separable utility funtions that allow the demand elastiity to be inreasing in quantity. 3 ontribution of our paper is two-fold. We haraterize how fritions affet the average markups and explore its impliations on setoral misalloation. In addition, to deliver quantitatively sensible results, we examine all the four lasses of utility in hingra and Morrow 214: CARA, Expo, quadrati and HARA utility. Interestingly, only HARA utility has the apaity of fitting the main patterns of firm-level markups from China s firm-level data. The rest of the paper is organized as follows. Setion 2 douments a set of fats regarding misalloation and markups in manufaturing and servie industries. We present the benhmark model in Setion 3 and extend it to a multi-setor environment in Setion 4. Setion 5 alibrates 2 See, e.g., Brandt and Zhu 21, Song, Storesletten and Zilibotti 211, Song and Wu 214, and Hsieh and Song Alternatively, Edmond, Midrigan and Xu 212 use a model of oligopoly and e Blas and Russ 212 adopt Bertrand ompetition. See also Holmes, Hsu and Lee 214 and Hsu, Lu and Wu 216 for different ways of generating variable markups. The 4

6 the model to the Chinese data and onduts ounterfatual exerises. Further evidene is provided in Setion 6. Setion 7 onludes. All the proofs are in the online tehnial appendix. 2 The Fats China s 28 Eonomi Census overs five million firms. 4 We use two samples from the ensus, one for above-sale manufaturing firms and one for all servie firms exluding finanial institutions. The threshold for manufaturing firms is revenue of five million Yuan, the standard adopted by China s National Bureau of Statistial for the Annual Survey of Industrial Firms. The servie sample has a lot more small firms, with more than two thirds below the sale. To make the two samples omparable, we drop all firms with revenue below five million Yuan. Table 1 reports the basi statistis of the two trunated samples. There are 29 and 34 twodigit manufaturing and servie industries, and a total of 363 and 549 thousand above-sale manufaturing and servie firms. The literature has found huge disparity between state-owned and non-state-owned firms in Chinese manufaturing. We identify state-owned enterprise SOEs heneforth by either of the following two onditions: i the firm is registered as a state-owned unit; ii its state paid-in apital share is equal to or above 5 perent. 5 All non-state-owned enterprises are referred to private firms. The strutural reforms initiated sine the mid of the 199s have greatly redued the state presene in manufaturing see, e.g., Hsieh and Song, 215. Our ensus data shows that only 4 perent of manufaturing firms are state-owned. Their employment as a share of the total manufaturing employment is 13 perent the top panel of Table 2. In ontrast, we find a muh larger state share in servie, where 11 perent firms are state-owned and they aount for 32 perent of the total servie employment. Entry barriers are obviously one of the reasons why the state setor remains sizable in some industries. Evidene that onnets state shares to entry rates has been found in manufaturing see, e.g., Brandt et al., 212, Hsieh and Song, 215 and Brandt et al., 216. The ensus data allows us to look further for the evidene in both manufaturing and servie industries. 4 Aording to the regulations, eonomi ensus surveys legal-person units, industrial units and self-employed individuals engaged in the seondary and tertiary industries within the territory of the People s Republi of China State Counil, eree No. 415, 24. Legal-person units, inluding legal-person enterprises and government bodies, refer to the formally registered units that an independently bear ivil liability. A legalperson enterprise may have single or multiple industrial units. 3.1 perent of the legal-person enterprises have multiple industrial units. In our sample, eah observation is a legal-person enterprise, in whih its industrial units are onsolidated. 5 Our definition of SOEs is broader than those using registration type only, for reasons stated in Hsieh and Song 215. However, their definition is still broader than ours. They identify SOEs by those satisfying any of the two onditions or those with the state as the main shareholder. We annot use their definition sine the ensus data does not report shareholding information. 5

7 Speifially, we use the employment share of new private firms in eah industry as a proxy for entry rate. New firms refer to the firms that were established after 1998 i.e., those with age below 1 in 28. Figure 2 shows that the employment share of new private firms x-axis in an industry is strongly orrelated with the employment share of SOEs in that industry. The orrelation is robust within manufaturing and servie and between two setors. Moreover, one an also see that servie industries dominate manufaturing industries in the northwest area with low shares of new private firms but high shares of SOEs. All manufaturing industry but one proessing of petroleum, oking and proessing of nulear fuel has the employment share of new private firms above 4 perent, while the share is below that level in 12 out of 34 servie industries. Figure 2: This figure plots the employment share of new private firms x-axis and the employment share of SOEs y-axis in manufaturing industries dots and servie industries triangles. The size of dots and triangles reflet the relative size of an industry by employment. Figure 3 plots the distributions of revenue, revenue-labor ratio and revenue-apital ratio. We measure effetive labor input by total wage bill. Revenue-labor ratio is thus equal to revenue per unit of total wages. Total assets are the only information related to apital in our samples. So, we use revenue per unit of total assets as a very rude measure for revenue-apital ratio. Most of the analysis in the following setions will be based on revenue and revenue-labor ratio. Revenue-apital ratio is only used for robustness hek. Revenue, revenue-labor ratio 6

8 and revenue-apital ratio are all in a relative sense, normalized by their orresponding median values in the industry. To redue the influene of outliers, we drop observations with labor or revenue-apital ratio in the top or bottom.5 perentile in eah industry. Figure 3: The dotted and solid lines in Panel A plot the revenue distribution of manufaturing and servie firms, respetively. Revenue is normalized by the median value in eah industry. Panel B and C plot the labor and revenue-apital ratio distributions. Revenue-labor ratio is revenue per unit of wage bill. Revenue-apital ratio is revenue per unit of assets. We normalize revenue, revenue-labor ratio and revenue-apital ratio by their median values in the industry. Observations are weighted by employment. The revenue dispersions are similar between manufaturing and servie firms. The variane of log revenue is 4.2 and 3.77 for manufaturing and servie firms, respetively. The differene is about 1 perent. The differene of the revenue-labor ratio dispersion is muh larger between the two setors: The variane of log revenue-labor ratio among servie firms is 1.18, about 6 perent higher than the variane of.74 for manufaturing firms. Bearing in mind the rudeness of the apital measure, we find an even larger differene in the revenue-apital ratio dispersion. The variane of log revenue-labor ratio is 1.2 and 2.75 for manufaturing and servie firms, respetively. The misalloation literature would interpret these statistis as evidene for worse misalloation in the servie setor. We next group firms into perentiles by their revenue in eah industry. The perentiles apture the within-industry firm size ranks. Panel A of Figure 4 plots the median of revenue- 7

9 labor ratio in eah perentile. It is immediate that revenue-labor ratio inreases in revenue for both manufaturing and servie firms. These findings are in line with the models where markups are variable and inrease in firm size. More interestingly, the profile is steeper for servie firms. The revenue-labor ratio of the top one perent manufaturing firms relative to that of the bottom one perent manufaturing firms is 3.5, while the ratio is 4.7 for servie firms. Column 1 of Table 2 regresses log revenue-labor ratio against log revenue and the interation term between log revenue and the dummy variable for servie firms. Both of the estimated oeffiients are positive and highly signifiant. In partiular, the results suggest the revenuelabor ratio profile for servie firms is about 5 perent steeper than that for manufaturing firms. Figure 4: We group firms into perentiles by their revenue in an industry. Panel A plots the median revenue-labor ratio in eah perentile for manufaturing firms dotted line and servie firms solid line. Panel B plots the median revenue-labor ratio in eah perentile for stateowned manufaturing firms dotted line and private manufaturing firms solid line. Panel C plots the revenue-labor ratio profiles for servie firms. A different reading of Panel A is to think of the upward-sloping revenue-labor ratio profile as larger firms adopting less labor-intensive tehnology. The hypothesis would predit a negative orrelation between revenue-apital ratio and firm size. 6 This is obviously inonsistent with the findings in Panel A of Figure 5. As a robustness hek, we add the apital-labor ratio into 6 This an be seen through the lens of 5 below under α <. 8

10 the benhmark regression. One an see from Column 2 of Table 2 that the apital-labor ratio has the expeted sign. Its effet on revenue-labor ratio is stronger for manufaturing firms. The estimated oeffiients of our main interests appear to be very robust. Figure 5: We group firms into perentiles by their revenue in an industry. Panel A plots the median revenue-apital ratio in eah perentile for manufaturing firms dotted line and servie firms solid line. Panel B plots the revenue-apital ratio profiles for manufaturing firms. Panel C plots the revenue-apital ratio profiles for servie firms. Panel B in Figures 4 and 5 plots the revenue-labor ratio and revenue-apital ratio profiles by ownership for manufaturing firms. Consistent with the findings in the literature, private firms are assoiated with higher revenue-labor ratio and revenue-apital ratio. Panel C plot the results for servie firms. There, revenue-labor ratio and revenue-apital ratio are also higher for private firms. The revenue-labor ratio profile is always upward-sloping, regardless of setor or ownership. Columns 3 and 4 of Table 2 onfirms the finding by inluding the SOE dummy and its interations with log revenue and the apital-labor ratio as additional ontrols. The revenue-apital ratio profile shows a similar pattern, though it beomes muh weaker for state-owned manufaturing firms. To onlude, we find the following fats: 1. The state employment share is a lot higher in servie industries than that in manufaturing industries. There is a negative orrelation between the state share and entry rate aross both manufaturing and servie industries. 9

11 2. The firm size distribution is similar between the manufaturing and servie setors, while the revenue-labor ratio and revenue-labor ratio distributions are more dispersed in servie. 3. The revenue-labor ratio is inreasing in revenue, regardless of setor and ownership. The revenue-labor ratio profile is substantially steeper for servie firms than that for manufaturing firms. 3 The One-Setor Model In this setion, we lay out a simple monopolisti ompetition model with heterogeneous firms and variable markups. Our main purpose is two-fold. First, the one-setor version of the model demonstrates a novel hannel through whih fritions may lead to higher markups. A set of neessary and suffiient onditions will be established for the hannel to funtion. The model will be extended to a multi-setor environment, where different magnitudes of fritions aross setors may lead to setoral misalloation. Seond, using Chinese ensus data, we estimate the model and ondut ounterfatual experiments to quantify the importane of the markup hannel. In addition, the model generalizes the framework in Hsieh and Klenow 29 by introduing variable markups. Our approah an thus isolate misalloation aused by variable markups from the Hsieh-Klenow estimator of misalloation. There are N firms. Eah produes a single variety. Labor is the only input fator, an assumption that will be relaxed below. The prodution tehnology is l i = i l q i, where l >, l, q i is the quantity of the good, l i denotes the labor input and 1/ i aptures the firm TFP. We abstrat apital input for simpliity in the benhmark model and will bring it bak for robustness hek. goods: Consider a representative onsumer who has the following preferenes over differentiated U = N u q i di, 1 where u is ontinuously differentiable, monotonially inreasing, stritly onave and u =. Here we do not assume speifi form of u. 7 The downward-sloping demand urve is haraterized by p q i = u q i /λ, where λ is the shadow prie of onsumer onstraint. 8 And demand elastiity is: dq i dp i p i q i = u q i q i u q i 7 The CES utility is a speial ase with an iso-elasti u. 8 See Appendix 8.2 for detailed derivation of household problem. 1

12 We define the inverse of the demand elastiity as µ q i : µ q i q iu q i u q i. 2 Under the general assumptions of u, µ q i is allowed to be a variable funtion of q i. As a onsequene, firms harge variable markups under variable demand elastiity. The speial ase is CES utility, whih implies a onstant µ and, hene, onstant markups. 9 The variable demand elastiity here establishes the mirofoundation that links markups to firm size. In a symmetri ase where q i is the same for all i, µ q i represents the inverse of the elastiity of substitution. µ is also referred to as the relative love for variety in Zhelobodko et al 212 or private markup in hingra and Morrow All firms fae the same demand urve, p i = p q i, and need to pay taxes. The after-tax revenue is 1 τ i p i q i. τ i has two omponents: i the rate that applies to all firms; and ii the rate that is firm-speifi. Without loss of generality, the ommon tax rate is normalized to zero. We then interpret τ i as fritions aused by distortionary poliies. Aordingly, we will refer to misalloation aused by τ i as poliy-indued misalloation. 11 Firms make prodution deision by max q i 1 τ i p q i q i w i l q i. 3 efine markup as prie over marginal ost, the first-order ondition implies p q i w i l = 1 1 q i 1 τ }{{} i 1 p q i q i pq i Markups = 1 1 τ i 1 1 µ q i, 4 4 shows that markups, the LHS of the equation, are o-determined by τ i and µ q i. 4 an be rewritten as log p q i q i w i l }{{ i } = log 1 τ i log 1 µ q i e q i, 5 revenue-labor ratio where e q i l q i / l q i q i is the output elastiity. When the demand and output elastiities are invariable, 5 redues to the one in Hsieh and Klenow 29. Another way to think of 5 is to interpret the LHS as the inverse of labor inome share. By adding τ i, 5 9 With CES power utility: u q = q s 1 s, we have µqi = 1/s. 1 Under Assumption 1 stated below, onsumers will pereive varieties as being less differentiated when their onsumption is higher. 11 Alternatively, one may interpret τ i as firm-speifi labor inome tax rate, whih is observationally equivalent to τ i in the model. For expositional ease, we assume a ommon wage rate, denoted by w, for all firms and load all the distortions to τ i. 11

13 extends the well-known formula that equates markups to the ratio of output elastiity to fator share see, e.g., e Loeker and Warzynski, 212. Finally, variable markups would invalidate the welfare alulation in Hsieh and Klenow 29 sine τ i would distort resoure alloation through variable markups, a hannel that is absent in their model. For simpliity, we speifially assume that l q i = q i through the following setions. Sine p q i is a funtion of u q i, rewrite 4 and u q i an be expressed as a funtion of We make the following assumption throughout the rest of the paper. Assumption 1: µ 1, and µ >, where µ is defined in 2. i 1 µq i. Lemma 1 Under Assumption 1, q i, markups, revenue and profits are all stritly dereasing in. revenue-labor ratio is hene inreasing in revenue. See Appendix 8.1 for proof. Lemma 1 is onsistent with the third fat in Setion Entry Barriers We now onsider a partiular type of fritions: barriers to entry. Ative firms ome from a pool of N potential produers. We use N, as a measure of entry barriers. 12 To begin with, we shut down poliy-indued misalloation i.e., τ i = i. Eah potential produer from N draws a produtivity from a distribution G. For simpliity, we assume there is no fixed osts for prodution. The firms that are indifferent between entering and staying outside the market must make zero profits. Without fixed ost, existene of these break even firms requires u <. 13 Notie CES utility does not satisfy this ondition and we are fousing on utility funtions with variable elastiity. 14 Moreover, there exists a unique utoff produtivity, denoted by, suh that only firms with will make profits and be ative. A formal proof is provided in the online appendix. The zero-profit ondition implies that q i assoiated with the utoff produtivity is also zero. The first-order ondition beomes: u q i 1 µ q i = i λ, 6 12 N is similar to fixed entry ost setting. With entry ost setting, potential entrepreneurs pay entry ost, draw produtivity and then start prodution. With free entry ondition, entry ost equals to expeted profits after entry. In equilibrium, a higher entry ost indiates a higher expeted profits after entry. As a onsequene, less firms an survive with higher expeted profits in equilibrium. Chaney 28 uses similar setting. Instead of free entry ondition, total mass of potential entrants in ountry is proportional to ountry size. 13 u < implies demand urve intersets vertial axis when q =. At intersetion points, firms fae zero demand and make zero profits. However, when u =, all firms are ative. 14 All utilities listed in setion 5 satisfy this ondition. 12

14 whih implies u q i 1 µ q i u 1 µ = i., 7 We an establish that q i = q i / and q < see the online appendix for proof. The lowest markups are thus equal to 1/ 1 µ. There exists a ompetitive labor market where labor supply is inelasti and equal to L. The market learing ondition pins down : N q efine Φ as the average markups. dg = L. 8 Φ Y L = 1 µq/ q q dg dg q 1 dg. q dg 1 µ q }{{}}{{} employment share markups 9 For analytial onveniene, we define Ψ / as the relative produtivity distribution of ative firms, where / [, 1]. Proposition 1 Consider two distributions, Ψ 1 and Ψ 2. If Ψ 1 first-order stohastially dominates Ψ 2, i the average markup assoiated with Ψ 2 will be higher than that assoiated with Ψ 1 ; ii the revenue-labor ratio distribution assoiated with Ψ 2 will be more dispersed than that assoiated with Ψ See the online appendix for proof. The first-order stohasti dominane implies that for any x [, 1], there will be more ative firms i.e., those with the relative produtivity / > x, in the equilibrium with Ψ 2. In other words, the equilibrium with Ψ 2 has a higher employment share of high-produtivity firms. Sine high-produtivity firms are larger and harge higher markups, the omposition effet leads to higher average markups. For example, assume that follows a Pareto distribution with G = / κ, where [, ]. Then, Ψ / = / κ. The first-order stohasti dominane holds if κ 1 > κ 2. Proposition 1 guarantees that a lower κ will lead to higher average markups and more dispersed revenue-labor ratio. Assumption 2: Ψ / 1 first-order stohastially dominates Ψ / 1 if 1 < We use the onept Lorenz omination to measure dispersion, see Appendix 8.2 for detailed definition. 13

15 Proposition 2 Under Assumption 2, a high N i.e., low entry barrier or a less dispersed τ i will redue the average markup and the dispersion of revenue-labor ratio. Proposition 2 is a key that onnets fritions to markups. The seletion effet inreases the produtivity and output of ative firms, resulting in higher average markups. However, there is an opposite effet via variety. A higher N leads to more varieties, implying less labor alloated to eah variety, whih, in turn, lowers markups. A ounterexample to Assumption 2 is Pareto distribution. We an show that if is Pareto distributed, a higher N will redue but leave Ψ / 1 unhanged see the online appendix for proof. In this ase, the seletion effet and the variety effet anel out with eah other under the Pareto distribution. Melitz and Ottaviano 28 and Behrens et al. 214 establish that under quasi-linear or CARA preferenes and Pareto distribution, the average markup is independent of trade fritions. Our result is more general sine it applies for all additive preferenes. Moreover, it suggests that the fat-tailed nature of the Pareto distribution is the key: It strengthens the seletion effet. If instead follows a log-normal distribution with a less fat tail that satisfies Assumption 2, the seletion effet will not be strong enough to balane the variety effet. 4 The Multi-Setor Model We apply the above model to a multi-setor environment. Assume there are J setors and U is a CES aggregator of U j of setor j: J U = γ j U j σ 1 σ j where J j γj = 1, U j = 1 q uj j i di and σ > is the elastiity of substitution aross setors. There are N j potential firms in setor j, where the produtivity distribution is G j. The utoff-level produtivity in setor j is j. The labor market learing ondition 8 beomes j N j q j dg j = L j = L. 1 j j Our fous is on the setoral alloation of resoures between manufaturing and servie. To sharpen the results, we establish the following proposition in a two-setor environment with J = 2. Setor 1 and 2 are referred to as manufaturing and servie, respetively. All the results an easily be extended to J > 2. For analytial onveniene, we will also assume that u j and G j are the same aross setors. The online appendix proves that Proposition 1 and 2 arry over to the multi-setor environment. 14 σ σ 1,

16 Proposition 3 Under Assumption 2 and σ 1, a higher N 1 lower entry barrier in manufaturing or a less dispersed τ 1 i flow from servie to manufaturing. will inrease the average markup in servie and ause labor to Under Assumption 2, a lower entry barrier in manufaturing will inrease the average produtivity and redue the average markup in the setor Proposition 2. Holding the relative prie of manufaturing goods unhanged, the lower average markup would inrease the demand for manufaturing goods, ausing labor to flow towards the manufaturing setor. We refer to this as the markups hannel, whih is absent in the models with onstant markups. addition, the standard produtivity hannel is also present. The higher average produtivity in manufaturing lowers the relative prie of manufaturing goods. When σ > 1, the substitution effet of the lower relative pries will dominate the inome effet. This will also ause labor to realloate from servie to manufaturing. In the following quantitative exerise, we will assume σ = 1 in the benhmark ase so that the inome and substitution effets anel out eah other. The overall effet beomes ambiguous when σ < 1. To see the mehanism more transparently, we obtain the following equation that governs setoral labor alloation: L j γ j σ 1 σ j = Γ where Ω j is stritly inreasing in the average markups see the online appendix for details. The term with j aptures the standard produtivity hannel, where the average produtivity in setor j inreases in the utoff produtivity, 1/ j. The diretion of the produtivity effet hinges on the value of σ. The term with Ω j aptures the markups hannel. In the speial ase with σ = 1, the markups hannel would be the only mehanism through whih entry barriers affet resoure alloation aross setors. It is worth mentioning what would happen if the produtivity distribution is Pareto. There, a lower entry barrier or a less dispersed output wedge in manufaturing will still inrease the average produtivity i.e., 1/ j in manufaturing. However, Ωj that reflets the average markup remains unhanged. The omparative statis is analogous to that in Ngai and Pissaridis 27. In other words, Pareto produtivity distribution will shut down the markup effet and, thus, the new hannel for setoral resoure alloation with variable markups. Ω j In 15

17 5 Quantitative Results 5.1 Utility Funtion We first examine the empirial preditions of the four lasses of utility funtion in hingra and Morrow 214 that satisfy the assumptions that µ q [, 1] and µ q >. Although all the utility funtions an generate a upward-sloping size-markup profile, their preditions on the dispersions of size and markup turn out to be very different. CARA Utility: u q = 1 exp αq, with α > and µ q = αq. In the limiting ase with, q 1/α as µ q [, 1] and, hene, p/. In words, the most produtive firm will harge infinitely high markups. This is obviously inonsistent with the empirial regularity that labor inome share is quantitatively sizable even among the top one perent firms in eah industry. Moreover, firm employment is not monotonially inreasing in firm produtivity. As, l = q. Expo Utility: u q = 1 exp αq 1 ρ, with α >, ρ, 1 and µ q = α 1 ρ q 1 ρ ρ. The assumption that µ q [, 1] implies q [, 1/α 1 ρ] and, p/. So, if ρ is suffiiently large, Expo utility an generate large output and revenue dispersion. Bùt a larger ρ also implies higher markups harged by the firms at the utoff-level produtivity: p/ = 1/ 1 ρ. Therefore, to math the observed size dispersion, Expo utility has to resort to large ρ that will generate unrealistially high markups for the smallest firms. Similar to CARA utility, the relationship between firm produtivity and employment is ambiguous. Quadrati Utility: u q = αq β 2 q2, where α >, β > and µ q = βq/ α βq. The assumption that µ q [, 1] implies q [β/α, β/ 2α]. In the limiting ase with, q β/ 2α and, hene, p/. So, the size-markups profile implied by quadrati utility is similar to that implied by CARA utility and, hene, subjet to the same ritique. HARA Utility: u q = [q/ 1 ρ α]ρ α ρ, 11 ρ/ 1 ρ 16

18 where α >, ρ, 1 and µ q = q/ α q/ 1 ρ., q and pq but p/ 1/ρ. In the limiting ase with Moreover, q = and p/ = 1 at the utoff produtivity. These are two important properties. First, HARA utility an generate large output dispersion. Seond, revenue and employment are monotonially inreasing in produtivity. It is also worth noting that ρ has two opposite effets on the average markups in a setor. On the one hand, a lower ρ tends to inrease the average markups by making larger firms harge higher markups. On the other hand, it also implies less substitutability aross varieties, making the firm size distribution less dispersed. This tends to lower the average markups. We show in the online appendix that the former effet dominates the latter effet and the average markups are always dereasing in ρ. We then adopt HARA utility in our quantitatively exerise and assume ρ j to be industryspeifi. The model predits a upperbound of 1/ρ j 1 for markups. 16 We will alibrate ρ j to math the observed markups and revenue distributions. In addition to ρ j, HARA utility has another parameter α j. But it does not affet any of the revenue, employment and markup distributions. 17 So, we simply set it to unity. The results are robust to various values of α j. 5.2 Calibrating Produtivity istributions When markups are onstant, the firm size distribution would be isomorphi to the underlying produtivity distribution. Our simulations show that although variable markups affet firm size, the differene between the firm size and produtivity distributions are quantitatively small. In partiular, if produtivity follows Pareto or log normal, then the firm size distribution would also be niely fitted by a Pareto and log normal distribution. The similarity allows us to hek if the produtivity distribution satisfies Assumption 2 by looking at the firm size distribution. Although Pareto distribution has been widely adopted in the literature, some reent studies hallenge the appliability of the assumption. 18 Figure 6 plots the log size and log rank for manufaturing and servie firms, where size is employment relative to the median value in the industry. It is immediate that the power law doesn t apply for firms with employment below the industry median. Following Eekout 24, we use the Kolmogorov-Smirnov K-S test to hek the goodness of fit for log normal distribution. This gives the K-S statisti of This an easily be extended to the Cobb-ouglas prodution tehnology with apital and intermediate inputs. To see this, denote e < 1 the labor output elastiity. The orresponding labor inome share for the firms with and those with the utoff produtivity is ρe and e, respetively. 17 We an write q j /α j as a funtion of j / j and ρj. 18 See Feenstra 213, Fernandes et al. 215 and Bas et al

19 and.54 for manufaturing and servie firms, respetively. The orresponding p value is less than 1 perent in both ases. That is to say, log normal distribution fits well the firm size distribution in the ensus. Figure 6: This figure plots log employment relative to the median employment in the industry against log rank. The dotted and solid lines are for manufaturing and servie firms, respetively. Let G j follow log normal distribution, where G j = erf ln ϕ j s j 2 where ϕ j and s j denotes the mean and standard deviation, respetively. exp ϕ j is normalized to unity. Then,, Ψ j x j 1 erf 1/ s j 2 ln x j ln j = 1 erf 1/ s j 2, ln j where x j = / j. We then estimate j and sj 2by mathing the revenue and markup distributions. Speifially, we stimulate 1, firms for eah industry and group firms into perentiles by their revenue. We then generate the revenue and markups profiles, whih plot the median value of revenue or markups in eah perentile relative to that in the bottom perentile. Nonlinear least square is used to estimate j and sj 2 to minimize the distane between the stimulated and empirial profiles. 18

20 5.3 Calibrating Entry Barriers We assume that the number of potential firms, N j, equals N S,j N P,j, where the supersript S or P represents state-owned and private firms, respetively. Without loss of generality, we let N S,j = N S,j, namely, there is no entry barrier for SOEs and all potential SOEs are ative. Private firms fae entry barriers. N P,j / N P,j measures the magnitude of entry barriers in industry j. To bak out N P,j, we rewrite the labor market learing ondition as N j = N S,j N P,j = 1/2 j [ 1 1 erf L j ln j s j 2 ]. xqj x dψ j x Given j and sj, the above equation would pin down N j and, hene, N P,j. 5.4 Calibrating Preferene Parameters We set σ = 1 as the benhmark ase. The household onsumption deision implies j is a funtion of γ j U j 1/σ : [ j = Υ γ j N j G j j 1 u j q j x 1/σ ] dψ j x Given j, sj and N j, we an bak out γ i by the above equation and the onstraint that Σ j γ j = Results The results are reported in Table 3. The fitness is very good. The average R square is.94 and.95 for the markups and sales profiles, respetively. The alibrated eonomy implies severe setoral misalloation and large effiieny losses. We now ondut ounterfatual experiments to illustrate the quantitative importane of one partiular distortion over the extensive margin. 4.1% and 25.4% of manufaturing and servie firms are state-owned. In the ounterfatual exerise, we inrease the number of potential private firms in eah servie industry by the same proportion suh that the number of ative SOEs relative to that of ative private firms in the servie setor is idential to that ratio in the manufaturing setor. The results an be seen from Figure 7. The first finding is that the extensive margin an generate quantitatively sizable effets. The average markups in the real estate industry, for instane, would drop by 9.2 perent. Figure 7 also reveals a linear pattern between the perentage hanges in the average markups and total employment. The real estate industry would gain employment by 17%. Overall, the employment share of the servie setor would inrease by 3 perentage 19

21 points. The aggregate welfare gain would be inreased by 32 perent. The big inrease is largely driven by the inrease in the average produtivity. The deomposition shows that our markups hannel aounts for about one fifth of the welfare gain. In other words, holding the average produtivity onstant, reduing entry barriers would inrease the aggregate welfare by 6 perent through the variable markups hannel. Figure 7: This figure plots the results of the ounterfatual experiment see the text for details. The x- and y-axis represent the perentage hange of the average markups and total employment in eah servie industry. 6 isussion We disusses in this setion some of the potential reasons why entry barriers tend to be lower in Chinese manufaturing industries. Moreover, we will provide evidene that onnets entry barriers to hanges in the average markups. The Chinese authorities have been implementing the SOE reforms under the poliy slogan of Grasping the Large, Letting Go of the Small sine the mid of the 199s. While many SOEs in manufaturing industries were shut down or privatized Hsieh and Song, 215, some servie industries suh as banking, teleommuniation and transportation are still heavily regulated to favor inumbent SOEs. The offiial reason is to support the industries of vital importane to the eonomy and people s livelihood. China s aession to WTO in 21 is another major breakthrough that lowers barriers for Chinese firms 2

22 to enter the global markets and enhanes domesti ompetition see, e.g., Brandt et al., 214. While most trade barriers have been removed for many manufaturing industries, it is often hard to open up servie industries to foreign ompetition for politial reasons. This has been seen in many ountries. 19 These observations prompt us to look into the orrelation between entry barriers and hanges in the average markups aross industries. The model predits that i the average markups should deline in manufaturing industries due to the SOE reforms and aession to WTO; ii the average markups should deline more in the industries where the share of new firms is higher. We use the firm-level data from the annual industrial survey onduted by China s National Bureau of Statistis from The annual industrial survey allows us to keep trak of hanges in the average markups. The disadvantage is that the survey overs industrial firms only. We do not have a diret measure on the average markups. Under HARA preferenes, the firms with the utoff produtivity would always make zero profits. Higher barriers to entry inrease the average markups by inreasing the markups harged by high-produtivity firms. Hene, we proxy the average markups by the relative markups i.e., the ratio of revenue-labor ratio of the firms with revenue in the top five perentiles to that of the firms with revenue in the bottom five perentiles. Figure 8 plots the employment share of new private firms x-axis and the ratio of the relative markups in 27 to that in 1998 y-axis aross manufaturing industries. First notie that the relative markups fall dramatially in most manufaturing industries in the sample period from 1998 to 27. There is only one industry manufature of rubber where the relative markups go up. Moreover, the negative orrelation illustrated in the figure attests to the mehanism that lower barriers to entry may redue the average markups. 7 Conlusion To reapitulate, this paper ontributes to the literature in two aspets. On the theoretial front, we establish the onditions for distortions over extensive and intensive margins to affet the average markups. Moreover, we illustrate how the within-industry distortions an lead to setoral misalloation. On the other hand, we show the quantitative importane of the hannel by alibrating the model to the Chinese eonomy. In partiular, we find that removing entry barriers for private servie firms to the extent for private manufaturing firms would be able to inrease the employment share of China s servie setor by three perentage points. Suh 19 One example is the restritions on foreign investment in servies see, e.g., Rutkowski,

23 Figure 8: his figure plots the employment share of new private firms in manufaturing industries in 27 x-axis and the ratio of the relative markups in that industry in 27 to that in 1998 y-axis. deregulation would also inrease the aggregate welfare by 3 perent, from whih one fith is ontributed from the variable markups hannel. There are ertainly many other ways to think of variable markups within and aross industries and to understand the underdevelopment of China s servie setor. A major task to be done in the future is to show our mehanism and quantitative results are robust to alternative setups. Also, we want to explore the other hannels through whih China s servie setor is underdeveloped. 22

24 Referenes [1] Arkolakis, C., A. Costinot, ave onaldson, and A. Rodriguez-Clare 212: The Elusive Pro-Competitive Effets of Trade, Working Paper. [2] Atkeson, Andrew, and Ariel Burstein 28: Priing-to-Market, Trade Costs, and International Relative Pries, Amerian Eonomi Review, 985, [3] Auerbah, Alan J. 1985: The Theory of Exess Burden and Optimal Taxation, in Handbook of Publi Eonomis, Vol. 1. A.J. Auerbah and M. Feldstein, eds. Amsterdam: North Holland, [4] Brandt, Loren, Van Biesebroek, Johannes and Zhang, Yifan, 212: Creative Aounting or Creative estrution? Firm-level produtivity growth in Chinese manufaturing, Journal of evelopment Eonomis, 972, , [5] Brandt, Loren, Johannes Von Biesebroek and Yifan Zhang, 215: WTO and the Effet of Trade Liberalization on Produtivity in Chinese Manufaturing, Working Paper. [6] Brandt, Loren, Gueorgui Kambourov and Kjetil Storesletten, 216: Firm Entry and Regional Growth isparties: The Effets of SOEs in China, Working Paper. [7] Brandt, Loren, Trevor Tombe and Xiaodong Zhu, 213: Fator Market istortions Aross Time, Spae, and Setors in China, Review of Eonomi ynamis, 161, [8] Brandt, Loren & Zhu, Xiaodong, 21. Aounting for China s Growth, IZA isussion Papers [9] Bernard, A. B., J. Eaton, J. B. Jensen and S. Kortum, 23: Plants and Produtivity in International Trade, Amerian Eonomi Review, 934: [1] Behrens, Kristian and Yasusada Murata, 212: Trade, ompetition, and effiieny, Journal of International Eonomis, 871, [11] Behrens Kristian, Giordano Mion, Yasusada Murata, and Jens Sudekum, 214: Trade, wages, and produtivity, International Eonomi Review, forthoming. [12] Bas, Maria, Thierry Mayer, and Mathias Thoenig, 215: From Miro to Maro: emand, Supply, and Heterogeneity in the Trade Elastiity, Working Paper [13] Chaney Thomas, 28: istorted Gravity: The Intensive and Extensive Margins of International Trade, Amerian Eonomi Review, 984: