Spatial Misallocation across Chinese Firms PRELIMINARY, DO NOT QUOTE

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1 Spatial Misallocation across Chinese Firms Xiaolu Li Nanyang Technological University Yang Tang Nanyang Technological University February 29, 2016 Lin Ma National University of Singapore PRELIMINARY, DO NOT QUOTE Abstract In this paper, we develop a multi-city heterogenous firm framework to quantitatively evaluate how factor frictions affect productivity and welfare both at the aggregate and at the city level. We classify firms into state-owned and non-state ones to accommodate contemporary China conditions. Two types of frictions output and labor friction are assumed, and vary with firm types and across cities. Firm size distribution, real wage together with internal trade pattern are all endogenously determined in the model. We estimate city firm type specific output and labor frictions using individual firm data while taking into account various industry compositions. The trade cost are estimated using real world geography of transportation networks. We calibrate the model to 279 prefectural level cities in China We consider a counter-factual situation where both frictions are reduced proportionally to each firm s sales revenue and the total wage bill. We find that the total GDP increases by 80 percent related to the benchmark level. If we only reduce output or labor friction, the total GDP in turn increases by 5.5 and 76.2 percent, respectively. Moreover, if we only reduce frictions either on stateowned or non-state firms, GDP level is about 0.99 and 1.62 times of the benchmark level. A majority of cities gain in the counterfactual world in term of both productivity and welfare. The top winner cities are from less developed area in the western part of China, whereas cities that lose are mainly from the coastal area. Keywords: misallocation; regional trade; economic geography; productivity and welfare gain; JEL Classification: F1; F4;R1;O4; LI0005LU@e.ntu.edu.sg ecsml@nus.edu.sg tangyangs@ntu.edu.sg 1

2 1 Introduction It is widely recognized in the recent literature that the resource misallocation exerts great impact on the aggregate total factor productivity (TFP). 1 Distortions on firms with identical productivity can lead to substantial differences in total output. A prominent event in Chinese economy history is the series of reform on the state-owned firms since the late 1990s. Many state-owned firms were shut down or privatized. However, it is controversial that whether the government should continue this reform process or not. Some studies believe the state-owned firms still expose less distortion than the non-state ones, and thus a further reduction of distortion enables more efficient allocation. On the other hand, literature also argue that those remaining state-owned firms after the reform are among the most productive ones in China. As a result, it calls for serious quantitative study on whether a further reduction of distortion on state-owned firms is beneficial or harmful for economic growth as well as social welfare. Moreover, we argue it is also important to take into account the spatial dimension of the distortions. This is because in an economy where firms can freely choose the locations and goods are allowed to trade across space, policy change in one location may exert uneven impacts on different cities, and this may amplify or dampen the aggregate impacts. In this paper, we make some first attempts to address all the above issues. In this paper, we develop a quantitative framework with heterogenous firm to evaluate the role of factor distortions on the aggregate output, productivity and welfare. Our framework is based on the trade models with heterogeneous firms, following the ideas of Melitz [2003], Eaton and Kortum [2002], and Di Giovanni and Levchenko [2012]. We extend this line of models by introducing firm distortions and distinguishing state-owned and non-state firms. In our model, firms can freely choose which city to enter, and the set of cities they intend to trade. In the equilibrium, firm size distribution and real-wage in each city, together with internal trade pattern are all endogenously determined in the general equilibrium framework, which entail a series of rich quantitative analysis. 1 Examples include:hsieh and Klenow [2009], Restuccia and Rogerson [2008], Midrigan and Xu [2014] and Francisco, Joseph, Yongseok, Joseph, Francisco, et al. [2011] among others. 2

3 We calibrate the model into 279 largest prefectural-level cities in China The structural parameters are chosen to match the moments in input-output linkages, firm size distributions, internal trade patterns, and fraction of state-owned firms in the data. Our benchmark calibration successfully captures the key untargeted moments, such as city-size distributions and wage distributions across cities. We classify frictions into two types, namely, output and labor frictions. We denote output friction as the one that affects the overall sales revenue, and labor friction as the one that only affects the total wage bill. Intuitively, a larger value of output friction implies a more severe government restrictions on size, and a lower value of labor friction may suggest a better access to the labor market. We utilize firm-level data from the 2005 Annual Surveys of Industrial Firms to first estimate firm-level output and labor frictions following the approach in Hsieh and Klenow [2009] separately for state-owned and non-state ones. We also take into account the various industry compositions by assigning different labor share to firms in different industries. We then obtain industry-level frictions by aggregating firm-level frictions using firm employment as weight. Finally, we aggregate the industry-level frictions into the city-level using industry employment as weight. To our best knowledge, this is also the first attempt to estimate city-level frictions using individual firm data. We believe the findings can be widely applied to many other China-related studies. Our estimated frictions reflect the pattern that the share of state-owned firms is larger in cities where the state-owned firms receive more favorable treatment than the private ones. We find positive labor distortion on non-state firms in 275 out of 279 prefectural-level cities. In contrast, state-owned firms in most cities receive positive labor subsidy. The pattern sort of reverses in output friction. The results show non-state firms in a majority of coastal cities receive output subsidy, and state-owned firms in a majority of cities suffer output distortion. Overall, we do not observe favourable policy bias towards state-owned firms in year The geographical locations of cities, together with their relative positions in the traffic networks arguably play important roles in determining the bilateral trade flows and entry 3

4 decision made by firms. However, existing literature on China study has never taken the geography the road, railway, and waterway networks into account. One of our major contribution here is to estimate the between-city trade costs matrix based on the real world geography of China. Our estimation strategy follows the methods outlined in Allen and Arkolakis [2014]. We first digitize a set of highly-detailed maps on Chinese transportation networks with precision at around 1 square kilometers per pixel, and then compute the distance between any two cities conditional on a specific transportation mode using Fast Marching Methods (FMM). Lastly, we discipline the relative weight of different transportation modes by their mode-specific trade volumes in each city, and the overall scale of the matrix by the inter-city-trade/gdp ratio in China. The 279-by-279 iceberg trade costs matrix eventually is able to capture several key moments of internal trade in the data. We design a counter-factual experiment, where we decrease (increase) the positive (negative) output distortions to the extent that each firm s sales revenue increases (decreases) by 10 percent compared with the benchmark results. Similarly, we decrease (increase) the positive (negative) labor distortions such that each firm s total wage bill decreases (increase) by 50 percent relative to the benchmark results. In Figure 9, we present the the ratio of GDP and aggregate productivity in the counter-factual economy to the benchmark ones. GDP is found to be 1.80 times of the benchmark results, and aggregate productivity defined as the sum of all the operating firms conductivities is found to be 2.86 times of the benchmark results. To further understand the contribution of output and labor friction to the changes in aggregate variables, we perform another two set of counterfactual exercises, where we keep either output or labor frictions at their benchmark levels. Our results in Figure1 suggest that labor friction is the main obstacle of GDP growth: the reduction of output friction can only generate 1.05 and 1.15 times of GDP and aggregate productivity growth as opposed to the benchmark economy, while the reduction of labor friction can generate 1.76 and 2.80 times of growth in GDP and aggregate productivity. Similarly, in order to understand the role of state-owned firms in economic growth, we 4

5 300 Both τ y τ l % % 300 Both state owned non state % Growth relative to benchmark % % % % Growth relative to benchmark % 99.78% % % % 0 GDP Productivity 0 GDP Productivity (a) GDP (b) Aggregate Productivity Figure 1: Decomposition Results Note: Our benchmark economy is calibrated into 279 prefectural cities in China In the left panel, we run three counter-factual exercises, where we either reduce output friction or labor friction or both proportionally to each firm s sales revenue and total wage bill. We then report the GDP and aggregate productivity relative to the benchmark results. In the right panel, we similarly perform three counter-factual exercises where we either reduce friction on state-owned or non-state firms or both proportionally to each firm s sales revenue and total wage bill.we again report results relative to the benchmark level. For more details, please refer to Section 4. conduct another two sets of counter-factual exercises, where we either only reduce frictions on state-owned or non-state firms. As shown in Figure 1, if we only reduce frictions on stateowned firms, the total GDP level almost remains unchanged as the benchmark level. This result seem to suggest a further reduction of frictions on state-owned firms may not benefit the economic growth. Two potential reasons may support this seemingly surprising result: First, a reduction of positive distortion may make less productive firms easier to survive, overall this may hurt the aggregate efficiency; Second, distortion reduction may give rise to more small and non-trade firms gathering in small cities, as only serving home markets can make them survive. This may hurt the large firms in large cities, and hence the entire economy since less internal trade arise in the equilibrium. Our city-level decomposition results suggest that large cities such as Chongqing, Shanghai and Wuhan enjoyed the least gain when friction on state-owned firms are reduced. The impacts of reduction in distortion is not uniformly distributed across all the cities. Our results suggest that in the counter-factual world 275 out of 279 cities experienced growth 5

6 in real wage. 233 out of 279 cities experience growth in aggregate productivity. The winner cities in real wage are mainly from the western part of China, and the loser cities in aggregate productivity are mainly from Gansu and Inner Mongolia provinces. As for the contribution of labor friction, our results suggest that labor friction exerts the largest impacts mainly on coastal cities. When only frictions on state-owned firms are reduced, some coastal cities obtain the largest gain in both real wage and aggregate productivity. Our paper is most closely related to several papers that focus on the issue of misallocation in China. Tombe, Zhu, et al. [2015] study how misallocation due to goods and labor market frictions affect aggregate productivity in China at the province level. Brandt, Tombe, and Zhu [2013] measure the reduction in aggregate non-agricultural TFP due to distortions in the allocation of labour and capital across provinces and sectors in China for the period Hsieh and Klenow [2009] highlight that the misallocation of capital and output distortions have resulted in sizable loses in China s productivity. The first paper employs an Eaton-Kortum framework, which is abstract from analysis on firm size distribution and entry dynamics. The second paper does not consider the heterogeneity among state-owned and non-state firms. Moreover, they only conduct analysis at the province level. The last paper misses the important margins of internal trade and spatial dimension of the economy. We show in our work the linkage between city-specific frictions, city size and firm entry is at the core of driving both aggregate and city-level results. Moreover, our paper takes into account the real world geography, which are critical to firm s location decisions given the set of frictions. Our paper is broadly related to the large stream of literature on misallocation. Restuccia and Rogerson [2008] presents a model with balanced growth path to argue that differences in the allocation or resources across heterogenous firms may be an important factor in accounting for cross-country differences in output per-capita. Their definition of friction is similar to our notion of output friction, which can distort the sales revenue of each firm. Francisco, Joseph, Yongseok, Joseph, Francisco, et al. [2011] exams the role of final friction in explaining the aggregate productivity and output per worker differences across countries. 6

7 They define financial frictions as the strength of an economys legal institutions enforcing contractual obligations. Guner, Ventura, and Xu [2008]studies the size dependent policies on capital and labor. They find that the policies that restrict the size of the firms can leads to a costly adjustment of the new technology. Our work is broadly related to the large literature on Chinese economy. Brandt, Hsieh, and Zhu [2008] further document the process of industrial transformation and the role played by institutions and barriers to factor allocation. Song, Storesletten, and Zilibotti [2011] argue that the reduction in the distortions associated with state-owned enterprises may be responsible for the rapid economic growth starting in Hsieh and Song [2015] use detailed firm-level data to show that from 1998 to 2007 to find that the reforms of the state sector were responsible for 20 percent of aggregate TFP growth from 1998 to Our work conveys the following important messages. First, we do not observe favorable treatment in state-owned firm as opposed to non-state ones as of China Therefore, a further reduction of friction on state-owned firms may not be desirable. Second, a uniform reduction of distortion may not always be beneficial to the entire economy. This may induce small and less productive firms to concentrate in small cities, and thus indirectly hurt the productive firms in large cities through internal trade channel. If any, the policy aiming at reducing frictions should be location-specific. The rest of the paper is organized as follows: Section 2 presents the theoretical framework. We discuss estimation strategies for city-type specific distortions and bilateral trade costs, together with calibration strategy in Section 3. Section 4 describes the quantitative results. Conclusions are drawn in Section 5. 2 The Model We present the theoretical framework in this section. The production side of our model is simply an implication of Di Giovanni and Levchenko [2012], where they develop a multicountry framework. In this paper, we apply them into a multi-city context, and also go 7

8 beyond by introducing different types of firms and frictions. The economy contains a mass one of identical individual workers, and J > 1 geographically segmented cities, indexed by j = 1, 2...J. Individual workers obtain utilities from consuming the set of variety goods available in the city in which they reside. Specifically, the utility function of an individual worker in city j takes the following form: U j = k Ωj y (k) ε 1 ε ε ε 1 where ε represents the elasticity of substitution among all variety goods and y(k) denotes the consumption of variety goods k. Ω j denotes the set of available variety goods in city j. There are two types of firms in the economy, namely, state-owned firms and non-state firms. We will specify the differences between the two types of firms in details in later section. Each variety goods is monopolistically produced by a single firm. The production of each variety goods requires input bundles as inputs. To produce an input bundle in turn requires labor and all the available variety goods in the home city. Hereafter, we denote all the available variety goods in the home city as composite varieties. Specifically, the production function F (, ) for input bundle in city j takes standard Cobb-Douglas form: F (L j, Y j ) = L β j k Ωj y (k) ε 1 ε ε(1 β) ε 1 where β denotes the labor share of production, and 1 β is the share of composite varieties. Input bundle is the only input for production of variety goods. Firms are heterogenous in term of their input bundle requirements for producing one unit of output. In other words, firms with higher productivities need less input bundles to produce. Firms realize their input bundle requirements (productivities) after they pay certain entry fee to enter the market. We assume entry fee is paid in the unit of input bundles and is identical across all the cities. 2 We denote the entry fee to be f e. Given entry, firms then randomly draw their 2 Note that despite the quantity requirement is the same, the input bundle price may potentially be different across cities, so in the equilibrium the number of firms that choose to enter each city will be different. 8

9 input bundle requirement a from a distribution function G(a). We assume both types of firms state-owned and non-state ones draw from an identical type-1 Pareto distribution function: G( 1 ( µ a ) = 1 y where θ is the Pareto-index, and µ captures the lower bound of the firm productivity. We assume firms do not know their types when they decide to enter the market. After entry, they draw their productivities as well as their types. With probability λ (0, 1), the firm will become state-owned, and with probability 1 λ the firm will become non-state. Given entry, each firm needs to decide which city to serve. In order for a firm from city j to serve market in city i, a fixed operating cost f ij in term of input bundles of city j needs to be paid. Moreover, standard ice-berg trade cost assumption also applies to tradable intermediate goods here. In order to deliver 1 unit of intermediate goods from city j to city i, firms need to ship 1 + t ij units at city j. We follow Hsieh and Klenow [2009] by introducing two types of frictions in the economy, namely, output and labor friction. We denote frictions that increase the marginal products of labor and composite variety to the same magnitude as an output friction τ y. Intuitively, a larger value of τ y implies a more severe government restrictions on size or transportation cost. In contrast, a lower value of τ y implies a more generous public subsidies. In turn, we denote frictions that raise marginal product of labor relatively to composite varieties as the labor friction τ l. For example, a larger value of τ l corresponds to a better access to labor market. Frictions are city-specific. Moreover, state-owned and non-state firms are also subject to frictions in different magnitudes. We use τ S y,j and τ N y,j to denote output frictions in city j for state-owned and non-state firms, respectively. Similarly, we denote τ S l,j and τ N l,j to be the labor frictions in city j for state-owned and non-state firms, respectively. ) θ 2.1 Firm s decision We characterize firm s optimization problem in details in this subsection. Given the specification of production technology for input bundles, it is straightforward to obtain the 9

10 expenditure on an input bundle for firms of type d in city j as follows: c d j = [( 1 + τ d l,j ) wj ] β P 1 β j, d = S, N where P j denotes the price of composite variety and w j is wage rate in city j. 1 + τ d l,j unit of labor needs to be hired in order to having 1 unit of labor as production input. Note that we do not restrict the sign of τ d l,j to be positive. When τ d l,j < 0, this corresponds to the case of labor subsidy. Denote X i to be the total expenditure on composite variety in city i. Standard CES utility function yields the following demand function of individual workers in city i for goods k: q i (k) = X i P 1 ε i p i (k) ε Firm of type d located in city j with input bundle requirement a will serve city i iff the profit can cover the fixed operation cost, that is, π d ij(a) 0. π d ij(a) is the maximum profit level obtained from solving the following profit maximization problem: max ( ) 1 τ d y,j p d i (k) q i (k) a (k) t ij q i (k) c d j f ij c d j p d i (k) s.t. q i (k) = X i P 1 ε i p d i (k) ε where we have assumed that firms located in city j are always subjected to output friction τ y,j, and only purchase input bundle from city j regardless which city they serve. Standard monopolistic competition results apply: p d ε t ij c d ja (k) i (k) =, d = S, N ε 1 1 τ d y,j π d ij (k) = 1 ( ) ( 1 τ d y,j Xi ε t ij c d ja (k) ε ε 1 1 τ d y,j P 1 ε i ) 1 ε f ijc d j, d = S, N Moreover, we can derive the cutoff a d ij below which firm in city j will serve city i by 10

11 setting π d ij(a) equal to zero: a d ij = ε 1 ( ) 1 τ d y,j Pi ε t ij c d j (( 1 τ d y,j ) Xi εc d j f ij ) 1 ε 1, d = S, N Denote the number of each type s operating firms in city j as Ij d. Therefore, the total number of varieties in city i and sector d can be written as: J Ij d prob ( a ij (k) aij) d, d = S, N j=1 We assume free entry holds in the goods market. This implies in equilibrium the expected profit from entry should equal to the entry cost in each city. That is, [ J ] [ J ] λe 1[a < a S ij]π S ij (a) + (1 λ) E 1[a < a N ij ]π N ij (a) = f e c j (1) i=1 i=1 The first part of equation (1) is the expected profit from becoming a state-owned firm, whereas the second part describes the expected profit of a non-state firm. We assume there is no distortion before the realization of the firm type. c j is the expenditure on an input bundle at entry-stage, and thus it equals: c j = w β j P 1 β j Finally, the price index for composite variety in city i can be obtained as: P 1 ε i = 2.2 Equilibrium J j=1 d=s,n ( ε t ij c d j ε 1 1 τ d y,j We summarize the equilibrium definition in this subsection. ) 1 ε a d Ij d ij a 1 ε dg(a) 0 Definition: Given a series of fixed costs, entry fee {f ij, f e, t ij } in each city pair, and city-type specific frictions {τ S l,j, τ S y,j, τ N l,j, τ N y,j}, the equilibrium contains a series of prices {P j, w j } J j=1, and a sequence of quantities {I S j, I N j, q j (a)} such that the following conditions hold: 11

12 (a) Individual workers maximize their utilities by choosing consumption bundles. (b) Each intermediate goods producer maximizes their profits by choosing price and quantity of output. (c) Free entry condition holds in each city. (d) Goods market clearing in each city j: X j = w j L j + (1 β)x j In the Appendix A we explicitly solve the equilibrium under autarky situation. In the Appendix B we characterize equilibrium conditions without obtaining close-form solutions due to the complexity of the model. We seek numerical solutions in the next section. 3 Quantitative Analysis 3.1 Estimation of the Geographic Trade Cost We follow the approach in Allen and Arkolakis [2014] to estimate the matrix of geographic trade costs denoted as {T (i, j)} across cities. Our estimation takes three steps: We first propose a discrete choice framework to evaluate the relative cost of trade using different transportation modes. Second, we discuss our approach on measuring the shortest distance between a pair of any two cities using the fastest transportation modes. Third, we discuss our structural estimation strategy and present our final results on the trade cost matrix. Suppose there are M transportation modes indexed by m = 1, 2...M. For any pair of origin city i and destination city j, there exists a mass one of identical traders who will choose a particular transportation mode in order to minimize the iceberg trade costs incurred from shipping a unit of good from i to j using transportation mode m, denoted as τ m (i, j). Specifically, we let τ m (i, j) take the following form: τ m (i, j) = exp(t m d m (i, j) + f m + ν tm ) (2) 12

13 where d m (i, j) is distance from city i to j using transportation mode m. t m is the modespecific variable cost, f m is the mode-specific fixed cost, and ν tm is trader-mode specific idiosyncratic cost. We assume ν tm is i.i.d across traders and transportation modes, and follows a Gumbel distribution P r(e ν x) = e x θm. The specifications above allow us to explicitly obtain the fraction of trade shipped from city i to j using transportation mode m as follows: π m (i, j) = exp( a md m (i, j) b m ) k (exp( a kd k (i, j) b k )), where a m = θ m t m and b m = θ m f m. We next proceed to estimate the mode-specific distance matrix d m (i, j). We convert each transportation mode network into a raster image covering mainland China using the 2005 China Map from Sino Map Press. Each raster image has resolution 4431-by-4371, so that each pixel roughly corresponds to a 1.3km by 1.3km square. We then assign a cost value to every pixel on the map to indicate the relative difficulty to travel through the area using a specific transportation mode. For example, to construct the normalized road network cost raster, we assign pixels with no road access to be 10, all pixels with highways to be 2.5, all pixels with national level road to be 3.75, and all pixels with provincial and other road access to be 6.0. All the costs are chosen to roughly reflect differences in relative travel speeds. Similarly, we normalize those pixels with navigable waterways, including open seas, a cost of 1, and all other pixels a cost of 10. To construct the normalized railroad cost raster, we assign all pixels with rail road access to be 1 and otherwise to be 10. We then identify the central location of each of the 279 cities on the raster maps, and apply the Fast Marching Method (FMM) algorithm between all pairs of cities i and j to get a normalized distance between them for each transportation mode, d m (i, j). Given the mode-specific distance matrix, we next estimate the mode-specific parameters {a m, b m } in equation 3.1. From China City Statistics Yearbook 2005, we are able to observe the total trade volume of each city using transportation mode m. For instance, total trade volume in city i using rail includes the trade volume shipped from city i to all other cities by rail and the trade volume that delivered to city i from all other cities by rail. Formally, using the notation from our discrete choice framework the total trade volume of city i by 13

14 transportation mode m (V m (i)) equals to: V m (i) = J J exp( a m d m (i, j) b m ) + exp( a m d m (j, i) b m ). j=1 j=1 The share of total trade volume using transportation mode m in city i, s m (i), can thus be expressed as: s m (i) = V m (i) M k=1 V k(i) We estimate the sequence of {a m, b m } using a non-linear least square routine to minimize the distance between the simulated {s m (i)} J i=1 and the data counterpart. For the value of θ m, we follow the estimations in Allen and Arkolakis [2014] and set it to be Given {a m, b m } and θ m, we compute the mode-specific τ m (i, j) using equation 2. In Figure 2 we present the transportation mode-specific iceberg trade cost between any two cities against the distance between the two cities measured using the specific transportation mode. Finally, the discrete choice framework implies that the average iceberg cost from city j to i can be obtained as follows: T (i, j) = 1 ( ) ( ) 1 1 θm Γ exp( a m d m (i, j) b m ), θ m θ m m where Γ( ) is the standard Gamma function. We plot the estimated geographic costs matrix, T (i, j), against different measures of distance in Figure 2. Unsurprisingly, the trade costs increase with distance regardless of the transportation mode. Out of the three modes of transportation, the estimated T matrix mostly depends on the distance through the road network. This is because all the cities in our sample have access to the national road system, and the vast majority of intra-china trade goes through the road network as well. On the contrary, iceberg costs start to vary significantly between city pairs with similar rail or waterway distance. Traveling by river or coastal sea have the largest variation of iceberg cost, mainly because a large proportion of Chinese cities do not have easy access to any waterway. We plot the T matrix against the physical distance between two cities in the last panel 14

15 (a) Rail Distance (b) Waterway Distance (c) Road Distance (d) Physical Distance Figure 2: Geographic Trade Costs by Transportation Mode Note: The four panels above plot the estimated iceberg trade costs matrix, T, against the mode specific measures of distance obtained by FMM. The last panel plots the T matrix against physical distance between two cities, and the physical distances are normalized such that the distance between Beijing and Tianjin (110.9 KM) is 1. of Figure 2. The physical distance is measured by the Euclidean distance. We normalize the distance between Beijing and Tianjin, which is around km, to be 1, and report the normalized physical distance in the figure. The iceberg trade costs increase with physical distance, and the variation in iceberg costs increases with the physical distances as well. This is because cities trading with distant partners might diversify into different modes of transportation depending on the location of the partner, while they tend to exclusively rely on road transportation when trading with nearby neighbors. 15

16 3.2 Estimation of Output and Labor Frictions Our firm-level data comes from the 2005 Annual Surveys of Industrial Firms conducted by the Chinese government National Bureau of Statistics (NBS). The Survey includes all stateowned firms together with those non-state firms with more than 5 million RMB in sales revenue (about 600, 000). There are in total about thousand firms in our raw sample. We define the state-owned firms to be those firms whose registration type belongs to one of the following four categories: State-owned enterprises; State Joint Ownership Enterprises; Joint State-collective Enterprises, or wholly state-owned enterprises. In addition, for firms in other registration types, we define state-owned firms to be those ones with state paid-in capital ratio higher than a threshold level of 50%. In total, there are about 25.3 thousand state-owned firms in our sample state-owned firms are reported in the 2005 Statistics year book published by NBS, and thus this survey has covered a sufficiently large fraction of registered state-owned firms in We can further identify in which city the firm is located by examining the first 4-digit of the zip code reported by each firm in the survey. We restrict our analysis to those firms located in the prefecture-level cities. According to China City Statistics Yearbook, there are 286 prefectural cities in China at year In our dataset, the percentage of firms located in these 286 prefectural cities is as high as 98.1%. We also take into account the fact that labor intensity may be various across different industry structures while estimating the labor share. However, our survey data only reports the total wage bill of each firm. In principle, labor compensation should reflect more precisely the total labor cost, because certain non-monetary benefits such as health insurance and housing subsidy etc. are not included in the total wage bill but in the labor compensation. To address this issue, we turn to 2002 China input-output table, which contains detailed information on input expenditure for 24 industries. We assign each of the 39 industry in our sample to a specific industry in the 2002 input-output table. Appendix provides details on our matching procedure. We define the labor share in each industry as the ratio 16

17 of total labor compensation to the total input expenditure in each industry. In Figure 3, we plot the density distribution of labor share among our 24 industries. The results suggest the majority of industries have a labor within the range of [0.05, 0.25] Frequency labor share Figure 3: Labor Share Distribution Notes: We define labor share in each industry as the ratio of total labor compensation to the total input expenditure in each industry. We calculate labor share for 24 different industries from 2002 China inputoutput table. For more details, see the main text. In our theoretical framework, an operating firm s sale revenue must be able to compensate the total expenditure on production inputs. To ensure the consistency between the model and the estimation results, we drop the firms whose sales revenue are smaller than either their wage bill, or value of intermediate goods, or the sum of both. We also drop the firms with negative value added, which cannot arise as our equilibrium outcome either. We further drop those very small firms with employment no more than 20 person. These finally lead us to a sample size of 20.3 thousand, in which the fraction of state-owned firms is about 6.5 percent. In the following, we follow the approach in Hsieh and Klenow [2009] to estimate output and labor distortions denoted as {τ d l,j, τ d y,j} for each type of firms in each city, which j is 17

18 the city index and d specifies the type of the firm. Solving individual firm k s expenditure minimization problem on input bundle gives the following expression for τ t l,j,i (k): τ d l,j,i (k) = β i PjY t 1 β i ji (k) 1, d {S, N} w j L t ji (k) where i indexes the industry type and β i is the industry-specific labor share. P j Y d ji (k) is firm k s expenditure on intermediate goods and w j L d ji (k) is total wage bill. Both variables we can directly observe their data counter-parts. Similarly, from firm k s profit maximizing problem we can obtain the expressions for output friction, τ d y,ji (k), as follows: τ d y,ji (k) = 1 1 ε P j Yji d (k), d {S, N} 1 β i ε 1 (k) where R d ji (k) denotes firm k s sales revenue. Given the estimated output and labor frictions at firm-level, we first aggregate them into industry level using employment share as weight: R d ji τ d l,j,i = k τ d y,j,i = k τ d l,j,i (k) ω t ji (k) τ d y,j,i (k) ω t ji (k), d {S, N} where ω t ji (k) is employment weight for firm k of type d within industry i. Finally, we compute the city-level output and labor frictions by aggregating industry-level frictions obtained before: τ d l,j = i τ d y,j = i τ d l,j,iω d ji τ d y,j,iω d ji, d {S, N} where Ω d ji is employment weight within industry i and city j among type d firms. 18

19 We measure the difference in labor and output friction between state-owned and non-state firms, respectively: τ l,j = τ S l,j τ N l,j τ y,j = τ S y,j τ N y,j Intuitively, a smaller value of labor or output friction implies less distortion. Hence, when the distortion differences become negative, this suggests a more favorable policy treatment towards state-owned firms. In Figure 4, we plot τ l,j and τ y,j against employment share in state-owned firms, respectively. Unsurprisingly, the distortion difference significantly decreases with state-owned firms employment share in both panels slope = 1.62 t stat = slope = 0.09 t stat = Labor Distortion Difference Output Distortion Difference Employment Share in State owned Firms (a) Labor Distortion Difference vs. Employment Share State-owned Employment Share in State owned Firms (b) Output Distortion Difference vs. State-owned Employment Share Figure 4: Distortion Difference vs. State-owned Employment Share Notes: In the left (right) panel, we plot the difference between labor (output) friction on state-owned firms and non-state firms against the employment share of state-owned firms in each city. A negative value on the y-axis implies less distortion on state-owned firms than non-state ones. Both panels exhibit a significantly negative pattern between employment share of state-owned firms and differences in frictions, which can serve as a check of our estimation results. In Figure 5 we map the frictions for both types of firms. Labor distortion on non-state firms can be found in almost all the 279 cities in our sample except for Zhongshan and Yulin. In contrast, more cities grant labor subsidy to their state-owned firms. Those cities are mainly from coastal area as well as Yunan Province and Chongqing etc. Moving to output friction, our results show that non-state firms in a majority of coastal cities receive output 19

20 subsidy especially in Jiangsu and Zhejiang province, where non-state firms are found to be highly active. In contrast, interior cities in the western part of China, especially in Shanxi,Ningxia and Inner Mongolia province etc. suffer from severe output distortion on non-state firms. State-owned firms in a majority of cities suffer output distortion, and subsidy can only be intensively found in cities from Northeast provinces. Overall, in year 2005 we do not observe favorable policy bias towards state-owned firms. This is probably related to the policy grasp the large and let go of the small implemented since late 1990s during the process of state-owned firms reform. The correlation of labor (output) friction between state-owned and non-state firms is 0.21 (0.27). Among state-owned (non-state) firms the correlation between labor and output friction is found to be (-0.34). Legend Missing to to to to to 9.13 Legend Missing to to to to to 8.65 (a) Labor Friction on Non-state Firms (b) Labor Friction on State-owned Firms Legend Missing to to to to to 0.49 Legend Missing to to to to 0.57 (c) Output Friction on Non-state Firms (d) Output Friction on State-owned Firms Figure 5: Estimated Output and Labor Frictions 3.3 Calibration We calibrate the model into the Chinese economy. As of 2015, there were 334 prefectural level divisions and 2,852 county-level divisions. In this paper, we focus on a selection of 20

21 279 prefectural level cities due to data restrictions: our sample contains all the cities that are included in both the Chinese City Statistical Yearbooks, Chinese 1 percent mini census in 2005, and the 2005 China Annual Survey of Industrial Firms. We illustrate cities in our sample in Figure 6. The vast majority of cities in China proper are included in our study. The missing cities are mainly those in Tibet, Xinjiang, Inner Mongolia, and various autonomous cities dominated by ethnic minorities in southwest China. Legend Missing In Sample Figure 6: Prefectural-level Chinese Cities Note: This graph plots the 279 prefecture level cities included in our sample. All the cities that are included both in the Chinese Statistical Year Books and the percent population census are in our sample. Our parameter space contains the following structural parameters: {ε, θ, µ, β, λ, f e }, population distribution {L j }, and two series of origin-destination specific matrices {f ij, τ ij }. ε is the elasticity of substitution among all available variety goods. This parameter generally ranges from 3 to 10 in the literature, and we pick the middle value of 6. θ is the tail index of firm s productivity distribution. In our model the firms employment follows a power law distribution with a tail index of θ/(ɛ 1). We follow Di Giovanni and Levchenko [2012] by setting θ to be 5.3 so that the tail equals to 1.06, the value documented in Axtell [2001]. The value of β reflect the share of labor in total output, and we calibrate it using China 2002 input-output table. We use the basic flow table of 42 industries, and compute β = 0.35 as the average ratio between total labor compensation and total output. We directly obtain population distribution {L j } by matching the data counterpart from 2005 China City Statistics Yearbook. Chongqing, Shanghai and Beijing are the three largest cities 21

22 with a population size at around 3169, 1360 and 1184,0000, respectively. {θ, ε, β} are calibrated without solving the model. The calibration targets of the other parameters depend on the equilibrium outcome of the model, and thus calls for joint calibration. For the fixed operating costs matrix f ij, we first turn to the Chinese 1 percent mini census in 2005, and approximate 1/f ii by using the fraction of entrepreneurs in each city among all working population. Following Di Giovanni and Levchenko [2012] we set the off-diagonal elements, f ij, as the sum of the two diagonal elements f ii and f jj. At this stage f ij matrix is not yet in the unit of local labor, and to convert the f ij matrix into the correct unit, we again follow Di Giovanni and Levchenko [2012] by scaling the entire matrix with a factor ζ. We set ζ to ensure interior solutions in all the counter-factual simulations. 3 We assume that the fixed cost of entry, f e, is the same across different cities. f e is the cost paid to reveal one s ability as an entrepreneur, which is unlikely to be affected by the differences in infrastructures and institutions across Chinese cities. We calibrate this parameter to match the number of firms in Beijing in 2005, which is around 22 thousands. λ governs the probability of becoming state-owned firms given entry. We obtain the value by matching a fraction 21.2 percent of State-owned firms among all registered firms according to China Economic Census Yearbook The geographic iceberg trade cost matrix, T, describes the relative difficulties of transportation between different city pairs. We still need to pin down the overall scale of the T matrix to obtain a meaningful iceberg cost matrix, which we denote as τ. We again multiply the off-diagonal elements of the T matrix by τ, and calibrate this multiplier to match the overall volume of inter-city trade in China. We estimate the overall weight of internal trade with the Investment Climate Survey in China from China-Investment Climate Survey 2005 published by World Bank. This survey covers 12,500 firms in all 31 provinces of China, and it asks the firms to report the percentage of their sales by regions: within the city, within the province, within China, and overseas. We find that 62.5 percent of total sales of the firms surveyed went into cities other than their home city, and thus calibrate τ to reach the same 3 Interior solution here means a ij <= 1/µ, where 1/µ is the theoretical upper bound of the unit cost distribution. We calibrate ζ such that the number of entering firms is about twice the size of the number of operating firms in the benchmark model to guarantee that not all firms that enter choose to operate. 22

23 trade/gdp ratio in our model. We summarize all the parameter value and their corresponding targets in Table 1. Table 1: Benchmark Parameterizations Para. Targets Para. Value β labor share in non-tradable sectors 0.47 θ Pareto index in emp. distribution 5.3 ɛ elasticity of substitution 6.0 f e number of firms, Beijing 1.30 λ probability of becoming State-owned 0.17 τ internal trade/gdp ratio 2.15 ζ entrants/operating firm ratio {L j } Population distribution Note: The calibration targets for β comes from the 2002 Chinese input-output table for 42 industries. The target for θ comes from Axtell [2001], the values for ɛ and ζ comes from Di Giovanni and Levchenko [2012]. The targets for f e comes from 2005 mini census. The targets for τ from the China-Investment Climate Survey 2005 published by World Bank. 4 Quantitative Results We discuss quantitative results in this section. We first conduct a counter-factual exercise where we reduce output and labor frictions proportionally to each firm s sales revenue and total wage bill. We further decompose the contribution of output and labor frictions to growth in GDP and aggregate productivity by studying two separate cases, where only one type of friction is reduced in each case. We also perform similar exercises to evaluate the role of state-owned and non-state firms. 4.1 Counter-factual Simulation In this section, we construct a counter-factual economy in which we reduce the output and labor friction among all the operating firms proportionally to their sales revenue and total wage bill, respectively. Recall that in our model economy, τ y > 0 (τ l > 0) implies a output (labor) distortion, and τ y < 0 (τ l < 0) implies a output (labor) subsidy. In the following exercise, when τ y > 0 we uniformly decrease the output distortion to the extent that all the 23

24 firms now enjoy 10 percent more of sales revenue compared with the benchmark economy. Similarly, when τ y < 0 we increase τ y to the extent that all the firms now only obtain 90 percent of the sales revenue as in the benchmark economy. Therefore, we simulate a counterfactual world with less frictions: firms that suffer output distortion can gain more and firms that enjoy output subsidy gain less. Specifically, the relation between τ d y in the benchmark economy and counter-factual world denoted as τ d y can be expressed as follows: 1.1τ d τ d y 0.1 if τ d y > 0 y = 0.9τ d y if τ d y < 0 Similarly, we also reduce labor friction uniformly across all the cities. Note that the distribution of our estimated labor frictions is more dispersed than that of output friction, in order to capture a sizeable change in τ l among all the cities, we let labor friction decrease a larger extent. 4 Specifically, the relation between τ d l in the benchmark economy and counterfactual world τ d l can be expressed as follows: 1.5τ d τ d l l = 0.5 if τ d l < 0 0.5τ d l if τ d l > 0 The above implies cities with positive labor distortion will spend 50 percent less on labor than in the benchmark economy, whereas for firms with labor subsidy will spend 50 percent more on labor. We start with evaluating changes in GDP. Our results suggest a uniform deduction in both types of frictions can lead to a 80.4 percent increase in total GDP. 5 We further decompose 4 Assume in a benchmark economy, τ l [1, 2]. If in the counterfactual world, we let all the firms only need to pay 90 percent of their original wage bill, then the adjusted τ l will fall into the interval [0.8, 1.7]. Now if the benchmark τ l is instead distributed over a larger range [2.6, 4.4], we then need all the firms to pay 50 percent of their original wage bill in order to maintain the same interval which τ l originally belongs to. 5 To make sure the two cases are comparable, we add back the frictions that are collected by someone outside the economy. So total GDP is expressed as: Y = J w j L j + j=1 J j=1 d=s,n [ ] τ d yxj d + τ d l w j L d j where X j denotes the sales revenue collected by type d firm in city j, and L d j denotes employment level at 24

25 the contribution of state-owned and non-state firms to the output growth as follows: Ỹ Y = Ỹ S Y S Y S Y S + Y N } {{ } state-owned Y N } Y N Y {{ S + Y N } non-state + Ỹ N (3) where the first and the second part equation (3) represents the contribution of state-owned and non-state firms to growth in total output, respectively. Our results suggest that output among state-owned and non-state firms is about 1.65 times and 1.88 times of its benchmark level. These together imply that the contribution of state-owned and non-state to output growth is about 30.6 percent and 69.4 percent, respectively. We also construct an index to measure aggregate productivity in each city, which is an weighted sum between state-owned and non-state firms: A = j d {S,N} I d j E[a a a d jj] (4) The aggregate productivity is found to be 2.86 times of its benchmark level. We further decompose the contribution of state-owned and non-state firms: aggregate productivity among state-owned and non-state firms is about 2.72 and 2.90 times of its benchmark level. This implies that the contribution of state-owned and non-state firms to productivity growth is 19.6 percent and 80.4 percent, respectively. We summarize the results in Table C.1 and C.2. We next turn to exam the changes in total welfare. We measure total welfare by the sum of real-wage across all the cities: W = j L j w j P j (5) Our results suggest that despite some firms may obtain less output or labor subsidy, the overall social welfare is about 3.89 times of its benchmark level. We again decompose the changes into contributions of prices and nominal wages, respectively. If we keep the price level the same as the benchmark level, the total welfare is only 85 percent of the benchmark level, and this implies nominal wage rate actually declines in the counter-factual world. In contrast, keeping the wage rate at its benchmark level the total welfare is 4.54 times of type d firm in city j. 25

26 its benchmark level. Therefore, the surge in social welfare is purely driven by decline in price level, and the magnitude is large enough to compensate the decline in wage level. We summarize the results in Table C.3. A summary of changes in other aggregate variables include: trade openness measured by the percentage of trade volume in total GDP increases from 62.5 percent to 63.4 percent. The total number of operating firms increases from thousands in the benchmark economy to thousands in the counterfactual world, which corresponds a percentage of increase. City-level Impacts The aggregate gains are not uniformly distributed across cities. Out of 279 cities in our sample, 275 cities experience growth in real wage. The only four cities that suffer real wage loss are Zhongshan,Jianyuguan, Jiaxing, and Yichun. There are 233 cities experience growth in total productivity, in which 200 cities have labor distortion on both state-owned and non-state firms, and 109 cities have output friction on both types of firms. Cities may still suffer productivity loss despite of the reduction in distortion due to the fact that reduction makes it easier for less productive firms to survive, and this in turn make those cities less competitive. The 46 cities that suffer productivity loss in fact have encountered at least one type of distortion in our benchmark economy. Overall, the winner cities in real wage are mainly from the middle part of China including Jiangxi, Hunan and Inner-mongolia provinces. In term of aggregate productivity, the loser cities are mainly from Gansu and Inner Mongolia provinces. We map the results in Figure 7. Legend Missing to to to to to 1.73 Legend Missing to to to to to 2.02 (a) Real Wage (b) Aggregate Productivity Figure 7: Real Wage and Productivity 26