Discussion Paper No. 126
Privatization’s Influence on Agglomeration and Selection
Effects: Evidence from China’s Manufacturing Industry
Yikai Zhao and Jun Nagayasu

July, 2022

Data Science and Service Research
Discussion Paper

Center for Data Science and Service Research

Graduate School of Economic and Management
Tohoku University27-1 Kawauchi, Aobaku

Sendai 980-8576, JAPANPrivatization’s Influence on Agglomeration and Selection
Effects: Evidence from China’s Manufacturing Industry
Yikai Zhao* Jun Nagayasu†
June 2022

Abstract
We study the impact of state-owned enterprises’ (SOE) privatization on how firm productivity responds to agglomeration and selection effects, and investigate whether and how policymakers can utilize agglomeration and selection to benefit from privatization. As SOEs enjoy privileged treatment because of their government ties, we argue that the agglomeration advantages of
SOEs are rooted in their connection with local governments who regulate them, who share local information with surrounding SOEs, such as labor markets, resources, and tacit knowledge.
Overall, we attempt to answer the following questions: 1) Will the SOEs’ reform negatively(positively) influence enterprises’ agglomeration (selection) effects? 2) To what extent is this influence affected by the local government? 3) Is this adverse or favorable impact heterogeneous?
Keywords: Agglomeration Effect, Selection Effect, Productivity, Privatization, GovernmentTies
JEL Classification: D24, O18, O47, P25* Corresponding author, Tohoku University, Graduate School of Economics and Management, 27-1 Kawauchi,

Aoba-Ku, Sendai-city, Miyagi 980-8576 JAPAN; Tel: +81 22 795 6265; Fax: +81 22 795 6270; Email:zhao.yikai.p7@dc.tohoku.ac.jp.
† Tohoku University, Graduate School of Economics and Management, 27-1 Kawauchi, Aoba-Ku, Sendai-city,
Miyagi 980-8576 JAPAN; Tel: +81 22 795 6265; Fax: +81 22 795 6270; Email: jun.nagayasu.d8@tohoku.ac.jp.

11IntroductionMore than 100 countries have initiated extensive privatization programs since early 1980 (Megginson and Netter, 2001). Among them, China’s privatization is characterized by cautiousness andgradualism but stands out due to its sheer scale and extent (Svejnar, 2002; Kikeri and Nellis, 2004).
Large-scale privatization occurred in the country in the late 1990s. From 1995 to 2005, nearly
100,000 firms (two-thirds of China’s state-owned enterprises (SOE)) with 11.4 trillion RMB worthof assets were privatized (Gan, 2009). From 2009 to 2015, China has constantly been among the top
privatizers, being the second-largest privatizer in 2009, and the largest in 2013 and 2014 (Estrin andPelletier, 2018). Importantly, these privatized firms are a growing presence in international trade andinvestment. Considering its scale, extent, and impact, the Chinese experiences can provide valuable
insights into privatization design.
Most studies find a positive relationship between privatization and firm productivity (Brown etal., 2006); however, privatized SOEs rarely catch up with private firms (Boardman et al., 2016;
Harrison et al., 2019). Minimizing the negative effect of possible shocks in the early stage of theprivatization process and quickly reaping the outcomes of reforms are vital considerations for thegovernment while implementing reform policies. In this context, agglomeration economies andmarket selection may offer vital information. Specifically, with urbanization, large cities have economically outperformed small cities due to agglomeration advantages (Zhao et al., 2003; Syverson,2004). Then, privatizing SOEs in densely-populated cities can help in reducing the vulnerability
in the early stages of reform since these SOEs can benefit more from positive externalities throughsharing, matching, and learning from surrounding private firms; according to Marshall (2009) andJacobs (2016), these are the three fundamental channels of agglomeration. Moreover, fierce market
competition in urban areas motivates firms to raise productivity and eliminates low-quality firms(redistributing resources); thus, the surviving privatized SOEs are likely to be better.
To fully utilize the reform, policymakers can prioritize SOEs in urban cities where enhanced
agglomeration and selection effects can be leveraged by the post-privatization SOEs. Here, we
explore the impact of SOEs’ privatization by studying how firm productivity responds to agglomeration and selection effects. We ask: Will the SOEs’ reform negatively (positively) influence theenterprise’s agglomeration (selection) effect? To what extent is this influence affected by the local
government? Is this adverse or favorable impact heterogeneous? To address these questions, weestimate the differentials of agglomeration and selection effects between large and small cities forprivatized SOEs by employing a quantile specification proposed by Combes et al. (2012) and using
micro-data on Chinese manufacturing firms. An appropriate benchmark is required to validate ourresults to control the disturbance from changes in regulatory conditions and other factors that impact agglomeration and selection effects during SOEs’ reform. For this, referring to Boardman etal. (2016), we construct five comparable groups as contrasts to demonstrate the unique behavior of2privatized SOEs, i.e., Always-SOEs, Always-COEs, Always-POEs, SPs, and CPs.1
In addition to accounting for the agglomeration and selection effects during privatization, ourstudy has another advantage in that it considers having local information as an influencing factor.
We take inspiration from the seminal work of Huang et al. (2017), which is based on the conjectures of Hayek (1945) and Aghion and Tirole (1997). That is, one way to efficiently improve SOEs’
performance is to utilize local information by enhancing their interaction with the government. We
argue that this interaction is the primary source for SOEs to obtain agglomeration advantages. As
SOEs’ managers are usually appointed by the government, this gives SOEs more privileges in obtaining resources, industry licensing, and bank credits (Faccio, 2010). That is, most advantages of SOEs
come from the political connections; thus, the agglomeration gains of SOEs likewise stem primarily
from the government’s information sharing, matching, and learning regarding resources, financing,taxation, and labor pool. Importantly, these gains usually diminish with increasing geographic distance from the government. Huang et al. (2017) note that closer physical distance between an SOE
and the government/regulators which oversee it (hereinafter, “distance from oversight government”;
meanwhile, the governments overseeing the respective jurisdiction are referred to as “oversight governments”) can assure the availability of local information. Correspondingly, we use the physicaldistance to separate our sample into sub-groups (i.e., C-Group and F-Group as introduced in Section 3.3), and estimate the agglomeration and selection effects of each group.
Overall, while this study extends previous empirical work using a similar quantile approach(Arimoto et al., 2014; Accetturo et al., 2018; Ding and Niu, 2019; Adachi et al., 2021), it makes
three main contributions. First, we focus on the role played by agglomeration and selection effects
during the ownership transition period. The salient drop in general agglomeration benefits from preto post-privatized SOEs implies an adverse impact of privatization in the short term. In contrast,
the gradually increasing agglomeration that benefits only productive reformed SOEs has a positive
impact. This empirical evidence enriches the existing research on agglomeration effects and partiallyexplains why privatized firms have difficulties in improving productivity in the short term. Second,
we collect night-light satellite data and use them to proxy city density, which differs from Ding
and Niu (2019) who use population or population density. As indicated by Duranton and Puga
(2020), night-light data can measure crowding more directly. Third, based on the oversight agency
conjecture proposed by Hayek (1945) that governments have the motivation to decentralize distantSOEs, our study indicates that SOEs with fewer ex-ante government connections suffer less fromthe loss of agglomeration effects during the transition period; moreover, high-quality post-privatized
SOEs can respond quickly to agglomeration effects. In short, SOEs with weaker government ties
and higher productivity are most valuable for privatization.
1 SOE, COE, and POE are the abbreviations for state-, collective-, and private-owned enterprises, respectively. The

prefix Always- denotes firms where ownership does not change during the sample period. SPs are firms where ownershipchanges from state-owned to private-owned. Finally, CPs are firms where ownership changes from collective-owned to
private-owned. Section 3.2 elaborates the definition of each group.

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The remainder of this article is organized as follows. Section 2 reviews the literature aboutindustrial agglomeration and selection effects. Section 3 describes our data. The theoretical modeland empirical results from the various specifications for pre- and post-privatization for different
groups are explained and discussed in Section 4. Finally, Section 5 conducts robust checks. Section 6presents the conclusions of this study.

2

Literature Review

2.1

Agglomeration and Selection Effects

Large cities attract many firms despite high factor prices. These firms are more productive thantheir counterparts in small cities (Puga, 2010) and tend to innovate more significantly than those inrural regions (Naz et al., 2015). Seminal research (Marshall, 2009; Jacobs, 2016) on this area argues that one major cause are agglomeration advantages; urban areas are the outcome of a trade-off
between increasing returns and costs of urban congestion.2 Agglomeration can be of two types: localization economies and urbanization economics. The former refers to the Marshallian externalities
arising from a concentration of firms in the same industry (Marshall, 2009). In contrast, the latter
arises from an increase in city size that enables cross-fertilization of ideas among diverse economic
activities (Jacobs, 2016).
Apart from the improvement in enterprises, the excellent performance of metropolises can be
explained by the disappearance of inferior enterprises. Correspondingly, clustering weak firms thatare not expelled may hinder the positive externalities from agglomeration due to a crowded market.
Most of this evidence is presented by the inverted U-shaped productivity-to-agglomeration curve(Lin et al., 2011; Martin et al., 2011; Hu et al., 2015). This mechanism is named the selection effect,
which contributes to the urban area by forcing firms at the tail to withdraw from the market. It
serves to eliminate firms with low efficiency, thereby promoting urban productivity (Melitz, 2003;
Melitz and Ottaviano, 2008; Combes et al., 2012).3 This effect also hinders less productive firms
from entering large markets. Moreover, the selection process, because of tough competition and theinsolvency regime, can benefit society by reducing resource misallocation. Lam et al. (2017) notedthat approximately 30% of “zombie” firms in China continuously survive despite low productivity
and losses, crowding out private investment and hindering the market competition.4 The harm caused
2 Natural endowment is out of our discussion since man-made agglomeration (i.e., second nature) grants policymakers

more space and possibility to promote the local economy. Further, with the evolution of society, the importance of
natural resources has gradually weakened and can be ignored (Roos, 2005; Chasco et al., 2012); in addition, most of
the agglomeration in China’s manufacturing industry is the result of social outcomes and has little to do with natural
endowments (Wen, 2004; Ge, 2009).
3 Competition can also cause firms to initiate or continue their business in other cities (Gaubert, 2018), or spend
considerable investments in upgrading equipment to increase productivity (Jiang et al., 2015); however, this is not within
this study’s scope.
4 According to Lam et al. (2017), “zombies” are firms incurring persistent losses, with estimated interest payment

4

by zombie firms is even more severe because they worsen over-capacity by crowding out healthyfirms and stalling technological diffusion in the proximity (Shen and Chen, 2017; Andrews et al.,2017). Waiting for these firms to mature seems too costly; instead, market selection helps clear away
the zombie firms. This also limits productivity loss by reducing entry barriers in product markets,
thus generating significant gains (Andrews et al., 2017). Hence, when the agglomeration expansion
fails to deal with market congestion generated by zombie firms, examining the effect of the current
selection process on local economic production efficiency is worthwhile.
Overall, results of agglomeration can be similar to that caused by selection, for example, average
productivity improvement. Nevertheless, their mechanisms differ. On the one hand, we can roughly
distinguish three fundamental channels through which agglomeration works: sharing, matching, andlearning (Duranton and Puga, 2004); or labor, supplier, and knowledge spillovers (Marshall, 2009);
or goods, people, and ideas (Ellison et al., 2010). On the other hand, the selection process can cause
more efficient firms to be selected for a broader market, whereas less efficient firms serve the local
market only. Intuitively, more trade increases average profits per firm, attracting more entrepreneurs
to establish firms with certain fixed costs and employ workers, which increases wages in equilibrium.
Consequently, the cut-off productivity level increases. The least productive firms no longer makeprofits in the new trade equilibrium, and therefore, exit; only firms with productivity above the cutoff can enter the markets. Even if there are no newly-established firms, incumbent firms can expand
their production or reduce prices to seize market share, thereby strengthening competition. With thereallocation of market resources toward more efficient firms, the selection process contributes to an
aggregate productivity gain (Melitz, 2003; Melitz and Ottaviano, 2008).
Therefore, we extrapolate that both agglomeration and selection contribute to the efficiency ofurban cities, but act on different positions of the productivity distribution. A framework developed by
Combes et al. (2012) distinguishes between agglomeration and selection, and explains why average
productivity is higher in larger cities. Specifically, the agglomeration effect works at the mean value(the whole group of firms) or the right-hand tail (prominent firms), while the selection effect works
via shrinking the left tail (inferior firms) of the productivity distribution. In other words, large
cities differ from small ones by right-shifting, dilating, and left truncating the distribution of firm
productivity.
The magnitude of agglomeration advantages and selection gains has been compared in several
studies. Firm selection has outweighed agglomeration in the food industry in Chile (Saito and
Gopinath, 2009) and the Japanese silk-reeling industry (Arimoto et al., 2014). In contrast, others findthat the up-growing productivity is primarily due to agglomeration. Combes et al. (2012) developeda theoretical model and used the quantile regression to estimate the differentials of agglomerationand selection effects between large and small cities. Using data from French industries, the authors
found that the selection process could not explain spatial productivity differences. Applying a simicosts below market lending rates.

5

lar model to Italian manufacturing firms, Accetturo et al. (2018) showed that agglomeration effects
play a significant role, but there is also a substantial increase in the importance of the selection effectwithin several sectors. Ding and Niu (2019) and Zhang et al. (2020a) use the same method for examining China’s manufacturing and construction industries, respectively. There is strong evidence
for the agglomeration effect, while the selection effect contributes less to productivity.

2.2

Privatization and Firm Productivity in China

China’s SOE reform has been a gradual and selective process. Privatization started in the mid1990s, 15 years after the announcement of economic reforms in 1979 (Bai et al., 2006). Nevertheless, some scholars have advocated the role of state capitalism, underscoring that the remaining
SOEs are the largest firms driving China’s growth (Szamosszegi and Kyle, 2011; Hsieh and Song,2015). However, SOEs are believed to be generally less efficient than private firms due to policy
burdens, agency problems, and privileged licenses.5 Bai et al. (2000) and Bai et al. (2006) provided
a multitask theory of SOEs’ reform; this can explain the fact that even in the process of gradually
privatizing SOEs, China still emphasizes the importance of state capitalism. These authors suggested that because the Chinese SOEs have a crucial role in ensuring social stability, the governmentis cautious about reconstructing them. Even so, this stability is at the expense of firm performance,
which thus motivates the government to consider reforming SOEs.
Most studies agree that privatization in China has improved the performance of SOEs. Researchers find different channels of SOE reforms. Bai et al. (2009) showed that the layoff of surplus
labor is constrained even after privatization; however, privatized SOEs improve labor productivity
by increasing sales. Meanwhile, the authors indicated that reducing managerial expenses to sales
contributes the most to profit margins. Similarly, Sun and Tong (2003) reported that employee productivity has improved up to three years after privatization. The authors note that after privatization,
improving firms’ internal corporate governance can benefit their efficiency. Chen et al. (2021) also
found productivity improvements after privatization, which helped reduce bureaucratic noise (lessinterference from governments enables them to make better decisions and implement better schemes)
while denying the channels of downsizing or innovation. Su and He (2012) underlined lesser political influence and government administrative interference; the authors demonstrated the externalmarket’s positive impact during privatization, such as market competition.
Undoubtedly, the most notable feature of privatized SOEs is the reduced political connection(Huang et al., 2019), which is especially valuable in a transitional society with weak institutional
5 Policy burdens tend to instruct SOEs to serve specific political goals, such as hiring more employees to promotesocial stability (Wen, 2020); a government-oriented executive evaluation mechanism is another policy burden among
SOEs (Liu and Zhang, 2018), which can induce executives to abandon innovative investment projects that have higher
risks but can be more profitable (Gao et al., 2018). SOEs suffer from severe agency problems, such as satisfying themanagerial pursuit of personal benefits at the firm’s expense due to the lack of adequate incentives and supervision
for managers (Xu et al., 2005). Lastly, the administrative monopoly creates barriers through licenses, which reducescompetitors, resulting in the low productivity and efficiency of SOEs (Zhang et al., 2020b).

6

arrangements (Nee, 1992). In the guanxi research, Li et al. (2011) analyzed 250 Chinese firms andnoted that managers employed by SOEs possess more governmental tie channels than non-SOEs.
Using a meta-analytic framework with a sample of 20,212 organizations, Luo et al. (2012) demonstrated that government ties are more critical to SOEs than non-SOEs. Apart from bank credits
and better access to factor and product markets, the advantages of political connection subsume asounder understanding of regulations and policies, more information, and special protection (Guoand Miller, 2010; Luo et al., 2012). These advantages, caused by close ties with the government instead of the spillovers from non-SOEs, can be generalized as the agglomeration effect. One source of
agglomeration economies is knowledge spillover, specifically the tacit knowledge (Howells, 2002).
That is, the potential for knowledge spillover between the regulators and SOEs may be a strong
motivation for agglomeration since SOEs can exchange information quickly through the local government due to their close ties. Lower transaction and communication costs can be other reasons for
SOEs being located in the proximity of the local government. Huang et al. (2017) noted that due
to the distance–decay effect, when the distance to the government in the jurisdiction is farther, theSOE is more likely to be decentralized. The increased possibility of decentralization implies that the
government lacks information exchange with distant SOEs, weakening the agglomeration effect ofthese SOEs.
SOEs primarily rely on the central and local governments. Firms with different ownership types
may not usually have information exchange and technological diffusion (Zhu et al., 2019). Cognitive
proximity and technological relatedness can explain this finding because SOEs and non-SOEs are
subject to various operation codes, and confront distinct threats and opportunities (Peng et al., 2004;
Liao, 2015). Therefore, it is sensible to posit that after privatization, SOEs may enjoy fewer agglomeration benefits from clustering around local governments with other SOEs. Notwithstanding this,using firm-level data, Zhu et al. (2020) implied that compared with Always-SOEs, reformed SOEs
experience more knowledge spillovers from non-SOEs, and this effect strengthens year by year as
they successfully change their identity. In this case, the final change in the agglomeration effectfor privatized SOEs depends on which impact is more significant. For example, since privatized
SOEs are part of the private sector, they may suffer from selection stress; however, this may not
be clear in the short run. Based on the interview with factory directors and their accountants over
five years, Oi (2005) found that some privatized firms that have stopped production are denied theoption of declaring bankruptcy. Similarly, Boubakri et al. (2008) and Harrison et al. (2019) discovered that the government tends to offer privileged treatments to privatized SOEs compared to private
firms which were never state-owned. Hence, the selection effect may not have the same impact on
privatized SOEs as private firms.
To the best of our knowledge, no study has explored the agglomeration and selection effects
during the period of SOEs’ privatization. It may take several years to fully reap the benefits ofprivatization (Chen et al., 2021). By examining the role of agglomeration and selection effects

7

during privatization, our study sheds light on the methods to speed up the realization of benefits;that is, catching up with the private firms that were never state-owned. Given this background, we
propose the following hypotheses to answer our questions:Hypothesis 1a: Always-POEs enjoy agglomeration and selection effects, but their agglomeration
effect is smaller than that of Always-SOEs.
Hypothesis 1b: Always-SOEs enjoy an agglomeration effect; meanwhile, Always-SOEs in proximity to their regulating local governments have a more considerable agglomeration effect.
Hypothesis 2a: Post-privatization, SOE-to-POEs (SPs) enjoy a smaller (or more significant) agglomeration effect than pre-privatization; in addition, the change experienced by privatized SOEs
closer to and farther from their regulating local governments differ.
Hypothesis 2b: After privatization, SPs experience an improved selection effect, which is not detected for pre-privatized SOEs.
Although our interest is in the changes in the impact of agglomeration and selection effects onfirm productivity before and after SOEs’ reform, and the role of government connections, Hypotheses 1a and 1b are still necessary conditions before evaluating Hypotheses 2a and 2b. Consideringthat the goal of privatizing SOEs is to make them improve their performance by bringing moreprivate capital, we can see whether privatization helps SOEs in catching up with the private sector by comparing them with Always-POEs. Meanwhile, the predecessors of privatized SOEs arestate-owned enterprises, which allows us to accurately understand the influence of government connections on the agglomeration effect of SOEs and then reasonably predict the outcomes after losing
government support.

3

Data

3.1

Firm Data

Our total factor productivity (TFP) estimation extensively uses Chinese firm-level data. While
three industries (mining, manufacturing, and public utilities) are included in the data set, we only
use manufacturing because most sampled firms belong to this industry; moreover, the production behaviors of mining and public utilities are disparate. The Annual Survey of Industrial Firms Database(ASIF), maintained by the National Bureau of Statistics (NBS), covers all SOEs and non-SOEs withsales exceeding 5 million RMB in mainland China.6 7 Furthermore, the dataset has detailed in6 In the ASIF, a firm is defined as a legal unit.

It means that a qualified subsidiary can be considered as anothercompany and counted in the database. Fortunately, according to the Census, the vast majority of these companies(96.6% in 2007) do not have subsidiaries (Brandt et al., 2014). Therefore, we can justifiably suppose that an observation
is a unique single-plant firm.
7 In 2011, the designated size for non-state firms changed from 5 million to 20 million RMB.

8

formation on firms’ balance sheets and income statements, as well as basic information, such as
ownership, established time, and registration address.8 9 After matching firms each year following the method proposed by Brandt et al. (2012), cleaning data, and extracting our basic sample
according to Section 3.2, we obtain unbalanced panel data with 461,642 firms from 1998 to 2007
(1,653,782 observations in total) covering 28 two-digit manufacturing industries across 31 provincesand 287 prefecture-level cities (Appendix B details how we obtain the basic sample, Figure B.1 displays the distribution of firms with different ownership per year, and Figure B.2 demonstrates thetrends of employment, capital and value-added.)10

3.2

State-Owned and Private Firms

Many studies (Brandt et al., 2017; Khandelwal et al., 2013) find that Chinese SOEs have distinct
operation features that cannot be ignored; that is, SOEs’ production function and growth trajectory differ from those of private firms. Moreover, because China is implementing large-scale SOE
reforms during the sample period, it is necessary to consider the type of ownership.
ASIF reports the official registered enterprise structure but does not rightly reflect the type ofowner controlling firms. This is because firms rarely modify their registration status even if thecontrolling shareholder changes (Dougherty et al., 2007). Instead, we examine the shareholding
structure by capital share to understand the de facto owner of a firm. Following Dougherty et al.
(2007), we define a firm as an SOE when it directly reports that it is state held. Amongst non-stateheld firms, collective-owned enterprises (COEs) are those with a collective capital share greater than
50%, while the remainder are the private-owned enterprises (POEs).11 12 Furthermore, we divide
firms into five categories corresponding to changes in ultimate control. In line with Boardman et al.
(2016), we extract groups of Always-POEs, Always-SOEs, and Always-COEs; these firms have nochanges in ultimate control during our sample period. SPs refer to privatized firms that have changed
8 Table B.1 compares our original dataset with that of Brandt et al. (2014). As the database has been reviewed several

times (mainly to remove duplicate reports), the original data used here are slightly different from these authors but are
still very close to the statistics summarized in the Statistical Yearbook.
9 The database has been updated till 2013 from 1998; however, the data after 2007 are generally considered debatable
due to the small number of variables and the large discrepancy with the Statistical Yearbook contents. Therefore, weonly consider the period from 1998 to 2007.
10 According to Kamal-Chaoui et al. (2009), China has four de facto tiers of local governance: provinces, prefecturelevel cities, county-level cities, and townships. This article is based on the second tier but includes four municipalities
from the first tier (but without being broken into sub-areas): Beijing, Shanghai, Tianjin, and Chongqing. Henceforth, wecollectively refer to them as “prefecture-level” cities.
11 Private firms can be controlled by private companies (non-state legal persons), individuals, non-mainland agents,
or other shareholders, depending on which capital exceeds 50%. 50% is a common threshold to distinguish controlling
ownership, which can be seen in other studies (Liao et al., 2014).
12 Unlike simply dividing firms into SOEs and non-SOEs, we also distinguish COEs because compared with SOEs,
COEs are viewed as a competitive organizational form with remarkable performance under China’s partial reform; however, they still have to suffer from policy burdens and agency problems as local governments oversee them. Nevertheless,many COEs have also transitioned from collective ownership to private ownership during the SOE reform period (Xiaet al., 2009).

9

from being SOEs to POEs, while CPs are those that transition from COEs to POEs. Overall, we focus
on firms that have never changed ultimate control and those privatized only once, but exclude firms
whose ownership has changed multiple times or those which have been nationalized.

3.3

Distance From Oversight Government

Here, we regard the SOEs’ decentralization as a loss of agglomeration advantages as they can nolonger leverage local information. Huang et al. (2017) used the physical distance between SOEs andthe corresponding oversight governments to proxy the availability of local information exchange.
This was based on the assertion of Hayek (1945) that one way to improve SOE performance isby taking advantage of local information when the government urges them to improve efficiency.
Intuitively, firms may be able to access more local information in proximity. This points to more
relation-based government ties, which strengthens the agglomeration advantages from the interaction
between SOEs and government officials, and the inextricable connection among SOEs through therelationship with the government.
Thus, following Huang et al. (2017), we consider three levels of affiliations: central, provincial,
and municipal. Using Google Maps API, we obtain each government’s geo-location (WGS84). For
the central level, we use the location of the China State Council. For others, we use the location of
the People’s governments of provinces and cities. We rank firms at each level from the smallest tolargest based on distance, and compare the top 50% and bottom 50% (top-1/2 versus bottom-1/2),
and the top third and bottom third (top-1/3 versus bottom-1/3). The geographically close group isdenoted as C-Group and the distant one as F-Group.

3.4

Market Size

Market size is essential to measure agglomeration and selection effects in our setting. Two questions arise regarding this issue: 1) the choice of the index (e.g., population or light-night data) and 2)
spatial unit (e.g., provinces or cities). Agglomeration always occurs on a local scale. Hence, we takethe prefecture-level city as the spatial unit in our benchmark model.13 Regarding the first question,
instead of using population, we employ nighttime lights data to measure the market size; these data
have been demonstrated to reflect and project the trajectory of urban development directly (Ma et al.,2012; Duranton and Puga, 2020). Chan (2007) stated that in many Chinese statistical publications,
the National Bureau of Statistics’ definition (NBS-defined) of urban areas—an average population
density of at least 1,500 per sq km or contiguity of the built-up area—can be an appropriate criterion
13 Provinces with low average population density also have densely-populated capital cities.

Therefore, we use
prefecture-level city data. Intuitively, the city boundaries may impede the agglomeration impact caused by mutualinteraction even inside a province. As Puga (2010) noted, the agglomeration effect usually operates within restrictedspatial boundaries. The indicators we use to classify cities are at the prefecture-level, which is distinct from Ding and
Niu (2019) who use local data. Hence, our results may differ from them, especially when identifying dilation effects.

10

to reflect the de facto population density. This is because the population of a city administrative
unit (shi) includes both an urbanized core and extensive rural areas (which are primarily agriculturalareas and sometimes are quite broad). Thus, using city (shi) population or population density is not
an ideal measure for the market size or urbanization. Meanwhile, the hukou system in China does
not count workers who migrate from rural areas to urban cores. Hence, the hukou population of theurban areas (labeled as chengzhen renkou) may underestimate the actual population. According to
Chan (2007), approximately 150 million people in Chinese cities belonged to this category in 2005.
Therefore, remotely sensed nighttime lights datasets are more reasonable for measuring the market
size and have been tested for robustness. In addition, we use employment data as a proxy for urban
population.14 15

3.5

TFP Estimation

Based on the standard Cobb–Douglas production function for firm i at time t, TFP can be estimated using: ln TFPit = ln(value-added)it − βk ln(Capital)it − βl ln(Labor)it . The coefficients are
estimated by Equation (1)ln Yisct = β0 + βk ln X1,isct + βl ln X2,isct + γs + θc + µt + εisct(1)

where Y, X1 and X2 stand for industrial value-added, capital, and labor, respectively. s and c denoteindustry and city, respectively. γs , θc and µt represent industry, city, and time effects. When theordinary least squares (OLS) method is applied to estimate firm-level TFP, unavoidable measurement
technical problems emerge. The most noticeable one is the simultaneity of production decisionmaking. To ensure the reliability of the results, we conduct a group-by-group regression (using theultimate control as grouped in Section 3.2) based on the Olley-Pakes (OP) method (Olley and Pakes,
1992). In Section 5, we use labor productivity and productivity estimated by the OLS method tocheck the robustness.
Next, following Combes et al. (2012), we calculate the average productivity to reduce noise.
Moreover, as our interest is whether ownership (ultimate controller) affects agglomeration and selection effects, we consider the manufacturing industry as a whole. However, the productivity ofdifferent 2-digit industries is not comparable (Van Beveren, 2012), as well as the industrial structureof each city. Before computing average TFP, expressed as Equation (2), across years 1998 to 2007,
we standardize productivity by industry to reduce the variability caused by different industries. Fur14 DMSP-OLS nighttime lights nighttime data are downloaded from https://ngdc.noaa.gov/eog/download.

html.
15 To verify the reliability of the light brightness, we also used other measures of city size: the number of employees inthe secondary industry (employment density) and population (population density) in the urban areas (shi xia qu). These
data are collected from the city statistic yearbooks (Table A.1 presents the top five and last but five cities by different
criteria).

11ther, the cities are grouped into large city and small city by median values of light brightness in 2003,
as discussed in Section 3.4.16
ln TFPic =T
1(ln TFPisct )∑(T − t + 1) t

4

Methodology

4.1

Agglomeration, Selection and Dilation Effects(2)

Based on the firm data and estimated TFP, we investigate the discrepancies between firms inlarge and small cities by identifying agglomeration, dilation, and selection effects; these effects canimprove productivity through diverse channels (Combes et al., 2012).17
Agglomeration effect (Ai ): Each worker is more productive in large cities by interacting witheach other, represented as Ai = ln[a(Ni + δ ∑i̸=i N j )], where δ is a decay parameter and Ni is the sizeof city i.18
Dilation effect (Di ): Workers are more productive when they work for a more efficient firm,
expressed as Di = ln[d(Ni + δ ∑i̸=i N j )]. Then, φi (h) = Ai − Di ln(h) where h stands for labor requirement per output (or marginal cost), and higher h means lower productivity φi . This effect hints
that agglomeration benefits are also related to individual productivity and not just to city size.
Selection effect (Si ): This effect is estimated as the probability of a firm exiting from the local
market. It is represented as Si = 1 − G(h̄i ),19 where G(.) is the cumulative density function (CDF)from which a firm randomly draws its h and is assumed to be the same across cities, and h̄ is theprice threshold such that only firms with h ≤ h̄ can sell their products.20 We can easily understandthat lower h̄i (higher φi ) leads to higher Si . Entry barriers keep potential entrants out of the market
because of high sunk costs or productivity pressures.
Then, the CDF of the city i can be written as a function of CDF (F̃(.)) without Ai , Di , or Si :16 For sample period analysis, t starts from 1998 and ends at 2007.

However, for a certain period of time, say the,three-year average for 1998–2000 in Table 1, t starts from 1998 and ends at 2000.
17 STATA codes are based on Kondo (2017), who also elaborated on the correctness of the estimation process.
18 δ ∈ [0, 1] δ = 0 means that workers in city i can only interact with people in the same place. δ = 1 means thatworkers enjoy interactions with the same intensity with workers from everywhere; in this case, there are no difference
in dilation or agglomeration effects among cities: Di = D j , Ai = A j
19 Low-efficiency firms may also relocate to smaller cities; however, we do not consider these dynamic sorting effects. We analyzed the sample and found that only 2% (10326/513500) of the companies have changed their locations(prefecture-level city level) during 1998–2007.
2
R
N j R h̄ j /τ
20 h̄ is the function of Ni h̄i h̄ − h 2 g(h)dh +h̄ j − τh g(h)dh = s This means that city size, marginal∑ j̸=i 4γ 0i
4γ 0distribution (g(.)), sunk entry cost s, and degree of product differentiation parameter γ influence h̄ and thus, the selection
effect. Accetturo et al. (2011) also extended this equation into various si and found no changes in the results. Specifically,
if there is no additional cost when they sell in other cities (τ = 1), then there are no differences in selection density:
Si = S j .

12





i

 F̃ φ −A−SiDi
Fi (φ ) = max 0,
1 − Si(3)This is impossible to estimate because of the lack of the exact underlying distribution F̃(.). Nevertheless, Combes et al. (2012) showed that by comparing the distribution of log productivity across
two cities of different sizes i and j, F̃(.) can be eliminated. That is:
D≡

Di
,
Dj

A ≡ Ai − DA j ,S≡

Si − S j
1−Sj(4)Then, Equation (3) can be arranged as follows: Fj φ −A−SDFi (φ ) = max 0,


1−S
(
Fj (φ ) = max 0,−S
Fi (Dφ + A) − 1−S

Si > S j

if

(5)

)

−S
1 − 1−Sif

Si < S j(6)

Finally, we rewrite these two equations in quantiles and estimate the following function:
λi (rS (u)) = Dλ j (S + (1 − S)rS (u)) + Au ∈ [0, 1]
(7)
 

−S
−S
+ 1 − max 0, 1−Su.
where λi (u) ≡ Fi−1 (u) is the uth quantile of Fi and rS (u) = max 0, 1−S
Using this method, we can obtain the relative shift parameter A, relative dilation parameter D, andthe relative truncation parameter S. Back to the Equation (4), the hypothesis of no agglomeration,
dilation, or selection effect between two cities can be denoted as follows:
H0 : A = 0,

D = 1,

for

S=0

(8)

Figure 1 displays the CDF of the productivity between large and small cities with a certain A, D,
and S. Here, the selection effect is the result after comparison. If there is no trade cost (i.e., τ = 1,
see footnote 20), S will be 0. This is seemingly contrary to the finding in Syverson (2004) that the
reduction in transportation costs will enhance the competition via selection. This may be because
what Syverson (2004) described is an absolute raise (or Si instead of S). If two cities are compared,
there is probably no difference (S = 0).

13

FIGURE 1. M ONTE C ARLO S IMULATIONS , D ISTRIBUTIONS IN L ARGE AND S MALL C ITIES
Notes: Created by the authors. In panel (a), Ai = 0, A j = 0.2, Di = D j = 1, Si = S j = 0 and thus A = 0.2, D = 1, S = 0, it corresponds to thedifferences in agglomeration that are required to move the entire (only right-shift); in panel (b), Ai = 0, A j = 0.2, Di = 1, D j = 1.2, Si = S j = 0,
it additionally dilates the distribution by stretching out the productivity especially at the right-side tail (right-shift and dilation); in panel (c),Ai = A j = 0, Di = D j = 1, Si = 0, S j = 0.1, it corresponds to the differences in selection required to left truncate the productivity by taking
probability away from the left of the distribution (left-truncation); the panel (d) identifies right-shift, dilation and left-truncation by visualcomparison of two distributions of ln TFP distributions in large cities and small cities.

14

4.2

Empirical Results

4.2.1

Agglomeration and Selection Effects of Different Ownership

Estimates of A, D and S using light brightness as a criterion to group cities are reported in Table 1
and Table 2. Note that R2 are often above 0.90, indicating that the agglomeration (A and D) andselection effects (S) can explain the majority of divergence in productivity between large and small
cities. Moreover, we find positive agglomeration effects on productivity for all firms controlled byvarious ownership types. Based on bootstrapped standard errors, estimates of A differ significantly
from zero. Further, generally, there are different trajectories of productivity on agglomeration effects
over time (column (1) in Table 1). The agglomeration effect from shifting gradually fades awayamong the private sector and benefits toward SOEs slightly drop, while collective firms still enjoy
more and more agglomeration effects.
Meanwhile, owing to an insignificant Ŝ at most times, no evidence of stronger firm selection inlarger cities is detected among Always-COEs. In contrast, SOEs unsurprisingly have negative valuesof S, corresponding instead to greater truncation in less dense areas. SOEs with the government’s
extensive support are less likely to exit the local market, even on the verge of a break-down. Better
access to credit markets may explain the fact that growing firms, such as Chinese SOEs, with low
productivity, survive (Hu et al., 2015). Nevertheless, urban cities tend to have the ability to provide
more bank credit.
We find evidence of fierce selection in larger cities for Always-POEs, where Ŝ is always positiveand statistically significant.21 Thus, without considering the selection effect, productivity gains
from agglomeration advantages may be overestimated. Even so, the selection effect on productivity
is far less than the agglomeration effect. As Brandt et al. (2012) reckoned, there is market selectionin the Chinese market; however, limited efficiency-enhancing input re-allocations may curtail thisfunction. Overall, Table 1 supports Hypothesis 1a that Always-POEs have statistically significant
agglomeration and selection effects, though the agglomeration effect for this group is smaller thanthat for Always-SOEs.
Table 2, where firms are divided by the distance from their overseeing government, provides
more information about the sources of SOEs’ agglomeration effects. As specified by Huang etal. (2017), a longer distance implies fewer direct observations of firm-specific information as well
as fewer interaction activities. Moreover, stimulated by the tax sharing system and the lack ofenough POEs, supporting SOEs in the jurisdiction is the main way for the local government toobtain tax revenues.22 The agglomeration effect (Â) shows that the 95% confidence interval (CI)21 This result is similar to Arimoto et al. (2014) who investigated the Japanese silk-reeling industry, Accetturo et al.

(2018) who controlled for market access, and Ding and Niu (2019) who examined a couple of Chinese manufacturingindustries. Notably, Ding and Niu (2019) used the provincial population density as the standard and found that 15 out of
29 industries exhibit a significant S regardless of enterprise ownership.
22 As an important fiscal reform, the 1994 tax reform replaced the previous fiscal contracting system with a tax sharing
system (the previous one was a tax contracting system): central, local, and shared taxes. This tax system drives local

15

of Always-SOEs classified to C-Group is [0.1754, 0.2619], while that of being classified to F-Groupis [0.0817, 0.1416] (column (1), Panel A). These two CIs significantly differ. This is more obvious
in Panel B ([0.1957, 0.2755] for Always-SOEs of C-Group and [0.0651, 0.1508] for Always-SOEs of
F-Group). Furthermore, in Panel B, the selection effect for SOEs close to the government is significantly negative, but is insignificant for distant SOEs. We attribute the pronounced discrepancy
to the agglomeration advantages from political ties intensified by proximity. As the government isalways located in the center of an urban city, one may question whether this discrepancy simply
comes from economic agglomeration. This concern is reinforced because while we use the lightbrightness of a city to proxy the density, the density is not evenly distributed within a city. Then,firms classified in the same density tier may have higher economies of scale because they are closer
to the city center. Nevertheless, if this reason holds, all firms close to the local government should
exhibit a significantly larger Â or D̂ value. Especially for Always-POEs, the Ŝ should be larger aswell due to tougher competition (e.g., high land costs). However, we see no difference between Cand F-Groups for Always-POEs and Always-COEs. Therefore, we argue that Always-SOEs that arecloser to their overseeing regulator enjoy more agglomeration advantages through their interaction
with the government. Table 2 also demonstrates that Hypothesis 1b is supported.
4.2.2

After Privatization

Now, we investigate the extent to which privatization impacts productivity through agglomeration and selection effects. Private ownership is believed to be necessary for improving firm efficiency(Xu and Wang, 1999). Table 3 reports A, D, and S before and after privatization by distance from thecorresponding oversight government (Panel A shows top versus bottom half, while Panel B shows
top versus Bottom one-third). Their agglomeration effects A and D with CI are plotted in Figure 2
and Figure 3, respectively. Here, t = 0 stands for the year when an SOE changed its ultimate control
from state- to private-owned, while t = −1 is one year before the reform and t = +1 is one year
after.
In column (1) of Table 3, the estimates of A are always significantly positive before the SOE
reform, except in one case (t = −4 in F-Group (bottom-1/3)). We find the largest value Â = 0.249 at
t <= −5 and the smallest value Â = 0.215 at t = −2 in Panel A for pre-privatized SOEs in proximity
to the local government. This implies an approximately 30% productivity increase if they move toa denser area.23 For those located far from the oversight government, the increase is almost halved
to nearly 15 percent with Â around between 0.193 (t <= −5) to 0.122 (t = −2). These results aregovernments to generate revenues within their jurisdictions efficiently and transparently (Park et al., 2006; Shen et al.,2012).
23 Following Combes et al. (2012), we have φ (h) = A −D ln(h) and A = A −DA = φ (h)−D ln(h)−φ (h)+D ln(h)
i
i
i
i
j
i
i
j
j
If D = DDij = 1, then A = φi (h) − φ j (h), where φi (h) refers to ln TFPi . Thus, we re-write this equation as eA − 1 =FPi( TT FP− 1) This implies an increase in mean TFP if a firm relocates from a small city to a large city due to a generaljagglomeration effect A.

16

TABLE 1. I NTER - TEMPORAL E STIMATION R ESULTS FOR D IFFERENT U LTIMATE C ONTROL F IRMS ,C ITIES ARE G ROUPED BY M EDIAN VALUE OF L IGHT B RIGHTNESS(1)
Agglomeration Effects

(2)

(3)
Selection Effects

A

D

S

(4)
R2

(5)
Obs.

(6)

Big City

Small City

Always-SOEs
1998-2000
1999-2001
2000-2002
2001-2003
2002-2004
2003-2005
2004-2006
2005-2007

0.143***
0.162***
0.168***
0.176***
0.182***
0.196***
0.164***
0.135***[0.1142,0.1730][0.1325,0.1920][0.1336,0.2028][0.1418,0.2107][0.1473,0.2182][0.1513,0.2409][0.1107,0.2181][0.0731,0.1979]

1.010
1.046***
1.073***
1.062***
1.066***
1.082***
1.069***
1.082***[0.9844,1.0352][1.0218,1.0702][1.0418,1.1046][1.0262,1.0983][1.0343,1.0970][1.0478,1.1153][1.0236,1.1144][1.0378,1.1261]-0.014***-0.012***-0.009**-0.013***-0.013***-0.013***-0.014**-0.030***[-0.0186,-0.0098][-0.0164,-0.0068][-0.0150,-0.0036][-0.0197,-0.0071][-0.0176,-0.0085][-0.0179,-0.0074][-0.0227,-0.0043][-0.0398,-0.0199]

0.950
0.938
0.924
0.925
0.943
0.948
0.926
0.976

27,61924,553
21,837
17,173
17,664
15,29812,94010,196

11,455
10,053
8,300
6,129
5,768
4,596
3,484
2,576

Always-COEs
1998-2000
1999-2001
2000-2002
2001-2003
2002-2004
2003-2005
2004-2006
2005-2007

0.125***
0.166***
0.135***
0.182***
0.140***
0.234***
0.181***
0.180***[0.0977,0.1541][0.1308,0.2025][0.0914,0.1798][0.1277,0.2377][0.0823,0.1990][0.1641,0.3053][0.1084,0.2546][0.1252,0.2362]

0.960***
0.985
1.056***
1.019
1.092***
1.065***
1.116***
1.101***[0.9347,0.9856][0.9441,1.0278][1.0152,1.0975][0.9618,1.0768][1.0439,1.1409][1.0087,1.1213][1.0517,1.1805][1.0430,1.1604]

0.001-0.012**-0.004-0.0050.003
0.009-0.002-0.002[-0.0044,0.0062][-0.0196,-0.0042][-0.0119,0.0041][-0.0148,0.0046][-0.0043,0.0104][-0.0020,0.0195][-0.0123,0.0078][-0.0158,0.0122]

0.981
0.964
0.981
0.970
0.982
0.963
0.960
0.968

18,105
15,728
12,170
9,149
9,370
8,106
6,498
5,603

3,577
2,778
2,249
1,675
1,572
1,244
847
870

Always-POEs
1998-2000
1999-2001
2000-2002
2001-2003
2002-2004
2003-2005
2004-2006
2005-2007

0.130***
0.124***
0.132***
0.153***
0.094***
0.102***
0.079***
0.034***[0.1109,0.1504][0.1015,0.1478][0.1187,0.1465][0.1394,0.1684][0.0835,0.1058][0.0902,0.1150][0.0686,0.0909][0.0232,0.0454]

0.984
1.012
1.000
1.017***
1.031***
1.016***
1.017***
1.027***[0.9609,1.0080][0.9872,1.0368][0.9852,1.0156][1.0004,1.0348][1.0190,1.0430][1.0052,1.0281][1.0089,1.0267][1.0184,1.0368]

0.006**
0.009***
0.003*
0.008***
0.005***
0.003**
0.002*
0.003***[0.0015,0.0107][0.0049,0.0147][0.0002,0.0068][0.0050,0.0113][0.0021,0.0081][0.0014,0.0057][0.0001,0.0050][0.0014,0.0057]

0.949
0.951
0.946
0.965
0.931
0.930
0.875
0.613

55,581
72,32785,717
102,966
176,519
193,043
214,605
235,966

7,208
9,666
11,715
14,884
22,26026,59830,96638,033

Notes: The prefix Always- denotes firms without changing ultimate control during the sample period as Section 3.2; The null hypothesis H0 is
A = 0, D = 1, S = 0; Bootstrap replication (50); 95% confidence intervals in brackets; ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001.

17

TABLE 2. M EAN E STIMATION R ESULTS FOR D IFFERENT U LTIMATE C ONTROL F IRMS BY D ISTANCEF ROM OVERSIGHT G OVERNMENT, C ITIES ARE G ROUPED BY M EDIAN VALUE OF L IGHT B RIGHTNESS(1)
Agglomeration Effects

(2)

(3)
Selection Effects

A

D

S

(4)
R2

(5)
Obs.

(6)

Big City

Small City

Panel A: top-1/2 vs. bottom-1/2
Always-SOEs:
C-Group
F-Group0.219***
0.112***[0.1754,0.2619][0.0817,0.1416]

1.050***
1.038***[1.0118,1.0891][1.0130,1.0633]-0.013***-0.010***[-0.0184,-0.0087][-0.0146,-0.0063]

0.976
0.948

17,69816,564

6,045
7,330

Always-COEs:
C-Group
F-Group

0.124***
0.143***[0.0878,0.1596][0.0947,0.1906]

1.003
0.951

[0.9719,1.0342][0.9012,1.0003]

0.001-0.005[-0.0054,0.0066][-0.0148,0.0041]

0.973 12,880
0.937 12,945

2,381
2,466

Always-POEs:
C-Group
F-Group

0.153***
0.157***[0.1395,0.1660][0.1474,0.1657]

1.004
0.978***[0.9938,1.0151][0.9687,0.9874]

0.002
0.000

[-0.0007,0.0039][-0.0018,0.0013]

0.979
0.990

148,992
149,001

23,49423,651Panel B: top-1/3 vs. bottom-1/3
Always-SOEs:
C-Group
F-Group0.236***
0.108***[0.1957,0.2755][0.0651,0.1508]

1.049***
1.085***[1.0087,1.0883][1.0510,1.1193]-0.015*** [-0.0214,-0.0085]-0.002[-0.0066,0.0032]

0.981 11,809
0.960 10,959

3,852
5,131

Always-COEs:
C-Group
F-Group

0.141***
0.186***[0.0921,0.1901][0.1311,0.2415]

1.004
0.920***[0.9570,1.0518][0.8826,0.9568]-0.002-0.010*[-0.0101,0.0062][-0.0194,-0.0023]

0.972
0.960

8,509
8,707

1,511
1,721

Always-POEs:
C-Group
F-Group

0.148***
0.159***[0.1359,0.1607][0.1437,0.1751]

0.993
0.966***[0.9792,1.0071][0.9541,0.9783]

0.001
0.000

[-0.0011,0.0040][-0.0029,0.0026]

0.980
0.991

99,24899,404

15,58515,853

Notes: The prefix Always- denotes firms without changing ultimate control during the sample period as Section 3.2; Firms are ranked fromnearest to farthest by distance from the corresponding oversight government in Section 3.3, and thus, top-1/2 (top-1/3) are the nearest 50%(33%) firms, while bottom-1/2 (bottom-1/3) are the farthest 50% (33%) firms. The null hypothesis H0 is A = 0, D = 1, S = 0; Bootstrap
replication (50); 95% confidence intervals in brackets; ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001.

18

consistent with the findings for Always-SOEs discussed in Section 4.2.1: productivity rises in denser
areas relative to less dense areas because of agglomeration; being proximate to the government
additionally intensifies this effect. Furthermore, we find a conspicuous drop in the value of A aftert = 0, A starts to become insignificant for both C-Group and F-Group firms in the next few years.
That is, the productivity improvements in all firms due to agglomeration advantages gradually fadeaway once SOEs are privatized. According to Siegel (2007), political networks burdened firms after
a change in political regime in Korea because the way they accessed information and resources in
the past was outdated in the new environment. Song et al. (2022) likewise demonstrated that during
China’s transition period, firms’ close ties with the pre-reform institutions impeded new activities
as firms’ operations were constrained by the connections established in the past and employees
continued following old business norms. Rather, there is little evidence about considerable laid-off
staff after SOEs’ reform (Omran, 2004; Bai et al., 2009) (demonstrated in Figure B.2 as employment
scarcely changes around t = 0). SOEs with close ties before the reform would have likely maintained
the old way of acquiring information and resources even after the privatization. Thus, the fall in the
agglomeration effect of post-privatization SOEs is understandable.
By contrast, comparing column (2) of C-Group with that of F-Group in Panels A and B (Table 3), D is insignificantly less than one pre-privatization but becomes above one significantly forpost-privatized SOEs located far from their oversight governments. A value of D above one demonstrates that more productive firms benefit more from being in denser areas, while D smaller than one
indicates that more productive firms benefit less from being in denser areas. Figure 2 and Figure 3
complement this finding, and show a steady increasing tendency of D̂ starting from t = 0 This holds
significantly only for post-privatized SOEs far from the oversight government. For post-privatized
SOEs close to the oversight government, except for estimates at t = +1, D estimates are insignificantly above one. Briefly, according to columns (1) and (2) in Table 3, after transitioning to a private
firm, agglomeration benefits that come from the rightward shift of the productivity distribution (represented by Â) decline, while agglomeration benefits stemming from dilation (represented by D̂)
increases. That is, only pre-privatized SOEs with high quality (e.g., hiring efficient workers) can
improve productivity through the agglomeration effect after the reform; this is especially true for
F-Group firms.
Next, we ask whether agglomeration economies (or, more generally, productive advantages)
shared by post-privatized SOEs are weakened after they lose the privileged treatment. Specifically,
we weigh the gain (due to dilation D̂) and loss (due to shift Â) from agglomeration economies atdifferent quantiles of the log productivity distribution. Figure 4 depicts ln TFP differences at the
25th, 50th, and 75th quantiles between large and small cities. The sample is grouped by the distancefrom the corresponding oversight government, where thick arrows stand for C-Groups (top half) andthin arrows for F-Groups (bottom half). The direction of each arrow is from small to large cities.
We see two facts. First, productivity increases substantially when SOEs are privatized (t = 0).

19However, after this jump in productivity at t = 0, the 25th and 50th percentiles of the ln TFP distribution of these privatized SOEs do not exhibit a gratifying high-speed increase movement; rather, only
distant firms at the 75th percentile productivity show a steady increase (as shown by F-Group p=75
in Figure 4). Second, we observe discrepancies between large and small cities regarding the size of
productivity increases if a firm relocates from small to large cities as a response to agglomeration
benefits. After privatization, the difference in production efficiency between large and small cities
narrows significantly, as shown by the most paired-coordinate plots in Figure 2. This indicates thatthe scale effect brought by large cities is not efficiency accretive for mediocre privatized SOEs.24
Nonetheless, the advantages of agglomeration effects still exist for more efficient and distant firms(F-Group p=75), specially between the [t = −3] and [t = +3] windows. From the agglomeration effect perspective, most SOEs have instantly lost this advantage after privatization, which may further
affect productivity growth. Instead, high-quality SOEs with weak government relations can maintain or even enhance the agglomeration benefit. This does not last for a long time and recedes four
years after SOEs’ reform (as shown by F-Group p=75 in Figure 2). Nevertheless, outstanding privatized SOEs (such as firms at the 95th percentile) which are distant from the oversight government
demonstrate a lasting agglomeration effect, which is accompanied by a steady increase in efficiency(see F-Group p=95 in Figure 5). This discovery is of interest because privatized SOEs absorb theadvantages of large cities through the agglomeration effect, implying the possibility of improving
firm productivity in a relatively straightforward way.
Column (3) reports the estimates of selection effects S. Unlike the agglomeration effect shownby Â and D̂, the values of S are insignificant and negligible in all periods. This suggests that privatization fails to enhance the selection process significantly. However, the sign of Ŝ changes fromnegative to positive in some cases. Moreover, by linking column (3) of Always-SOEs in Table 1 tocolumn (3) in Table 3, notice that Ŝ among Always-SOEs is significantly negative but insignificant
among soon-to-be-privatized SOEs. This suggests that governments in large cities tend to protect
SOEs on the brink of bankruptcy while selectively privatizing enterprises that they are not willingto support. For example, strategically important enterprises are all backed by state capital (Huang
et al., 2017). By contrast, as reported in Panel B, the pre-privatization values of S are often negative; meanwhile, after privatization, Ŝ has some positive values. For F-Group, this change is quite
noticeable. Before the privatization reform, Ŝ values are negative, except for the third year; after
the privatization, Ŝ values exceed zero. These results provide reliable evidence, regardless of SOEs’
reform, that denser and less dense areas show no significant differences in the truncation of the distribution of firm productivity. Market selection appears to have a similar intensity across cities inmainland China, irrespective of the market size. Moreover, residual government connections within
newly privatized SOEs may likewise explain the poor performance (Boubakri et al., 2008). Harrison
et al. (2019) discovered that privatized SOEs are still favored by low-interest loans and government
24 Here, mediocre firms are those with productivity below the 50th percentile.

20

subsidies relative to Always-POEs in China. This favoritism from the government regarding resources means that privatized SOEs continue to operate even if their performance is not outstanding.
Thus, privatizing SOEs without creating a competitive market environment may have little effecton their productivity (Konings et al., 2005). Nevertheless, regarding the negative-to-positive changeof Ŝ in F-Group firms, we optimistically expect that privatization can contribute to improving theefficiency of firms in large cities if the government can also change their behavior (e.g., less credit);
however, this may take longer. Unlike Always-POEs, SPs barely have significant selection effects;
however, the positive Ŝ partially indicates that SOEs’ reform contributes to market selection. Thus,
Hypothesis 2b is still supported.
Moreover, SPs generally exhibit a smaller agglomeration effect after privatization and this decrease varies with the distance from the oversight governments. Furthermore, firms distant from thegovernment and hiring employees with higher efficiency respond better to the agglomeration effectafter privatization. After privatization, they can enjoy more agglomeration advantages and gradually
increase their productivity even in the short term. Even so, the changing value of Ŝ from negative topositive implies a gradual improvement in the market exit mechanism. Conclusively, without finding
a similar pattern among CPs as reported in Table 4, this feature is unique to SPs. It shows that: 1)
Always-SOEs in proximity to oversight governments have a more substantial agglomeration effect;2) after privatization, middle SPs have a smaller agglomeration effect than before; 3) the decreased
contribution from the agglomeration of privatized SOEs farther from oversight governments is lessthan those who are closer; 4) Outstanding SOEs that employ highly productive employees and are
distant from oversight governments can enhance agglomeration benefits after privatization, and show
steady productivity growth.

5

Robustness

Our primary variables are the division of the ownership and productivity of firms.25 Here, we
use productivity and labor productivity (industrial value-add divided by employment) for testing
the robustness of our results. Following Liao et al. (2014), we distinguish firm ownership by theratio of state-owned equity to total equity. Firms are assigned by their state ownership into fourgroups: Non-SOEs, L-SOEs, M-SOEs, and H-SOEs. Non-SOEs include firms without any stateowned equity. The rest are ranked ascendingly by low, medium, and high firm ownership as L-SOEs,
M-SOEs, and H-SOEs, respectively. Privatization is equivalent to selling state-owned equity; thatis, the transition from H-SOEs to Non-SOEs directly (only one change). Firms that have undergone
25 There may be endogeneity concerns due to the government’s preference for the privatization of high-efficiency

firms or loss-making firms. However, the dilation effect (denoted as D in Equation (8)) already addresses this issue.
Specifically, the agglomeration effect consists of two parts: the increase in the average agglomeration effect (denoted
as A Equation (8)) of SOEs after privatization, and the benefits that only high-quality SOEs can obtain (marked as D
Equation (8)).

21TABLE 3. E STIMATION R ESULTS OF SP S BY D ISTANCE F ROM OVERSIGHT G OVERNMENT, TOP -1/2
(1/3) VS . BOTTOM -1/2 (1/3), C ITIES ARE G ROUPED BY M EDIAN VALUE OF L IGHT B RIGHTNESS(1)
Agglomeration Effects

(2)

(3)
Selection Effects

A

D

S

(4)
R2

(5)
Obs.

(6)

Big City

Small City

Panel A: top-1/2 vs. bottom-1/2
C-Group (top-1/2)
t<=-5 0.249*** [0.1850,0.3140]
t=-40.219*** [0.1561,0.2811]
t=-30.256*** [0.1906,0.3224]
t=-20.215*** [0.1241,0.3063]
t=-10.247*** [0.1767,0.3168]
t=00.159*** [0.0890,0.2292]
t=+1
0.062
[-0.0016,0.1257]
t=+2
0.078
[-0.0102,0.1660]
t=+3
0.080
[-0.0232,0.1827]
t=+4
0.059
[-0.1195,0.2373]
t>=+5 0.006[-0.1233,0.1348]

1.011
0.914
1.008
1.003
0.985
1.039
1.077***
1.104
1.057
1.040
1.023

[0.9318,1.0910][0.8089,1.0195][0.9166,1.0997][0.9356,1.0697][0.9157,1.0550][0.9643,1.1133][1.0131,1.1409][0.9982,1.2088][0.9735,1.1397][0.8600,1.2208][0.9153,1.1308]-0.003-0.004-0.002-0.003-0.009-0.008-0.0030.001-0.015-0.014-0.004[-0.0156,0.0104][-0.0390,0.0309][-0.0194,0.0146][-0.0143,0.0085][-0.0189,0.0017][-0.0206,0.0040][-0.0117,0.0063][-0.0134,0.0162][-0.0302,0.0000][-0.0641,0.0371][-0.0710,0.0634]

0.966
0.968
0.955
0.978
0.970
0.958
0.842
0.857
0.846
0.721
0.474

2,326
1,409
1,931
2,628
3,267
3,592
2,634
2,095
1,752
1,221
1,858

787
530
710
971
1,182
1,300
963
795
622
444
622

F-Group (bottom-1/2)
t<=-5 0.193*** [0.1202,0.2663]
t=-40.158*** [0.0653,0.2499]
t=-30.130** [0.0497,0.2100]
t=-20.122*** [0.0646,0.1799]
t=-10.165*** [0.0964,0.2344]
t=00.118*** [0.0613,0.1739]
t=+10.110** [0.0429,0.1766]
t=+20.103** [0.0278,0.1785]
t=+3
0.053
[-0.0525,0.1579]
t=+4-0.020[-0.1237,0.0830]
t>=+5 -0.047[-0.1477,0.0534]

0.973
0.993
0.985
0.957
1.029
1.082***
1.169***
1.098***
1.197***
1.142***
1.152***[0.9062,1.0401][0.9070,1.0789][0.9053,1.0654][0.9040,1.0103][0.9625,1.0946][1.0334,1.1297][1.0743,1.2630][1.0177,1.1781][1.1202,1.2729][1.0432,1.2412][1.0611,1.2428]

0.001-0.0040.003
0.000-0.0040.001
0.002-0.002
0.003
0.003
0.003

[-0.0200,0.0225][-0.0212,0.0126][-0.0122,0.0173][-0.0116,0.0107][-0.0161,0.0084][-0.0089,0.0112][-0.0128,0.0177][-0.0188,0.0138][-0.0140,0.0207][-0.0165,0.0221][-0.0160,0.0211]

0.979 1,708
0.965 1,084
0.924 1,546
0.890 2,146
0.964 2,783
0.949 2,983
0.938 2,171
0.911 1,746
0.937 1,434
0.823 975
0.836 1,675

797
535
737
1,005
1,220
1,343
1,012
821
678
483
677

Panel B: top-1/3 vs. bottom-1/3
C-Group (top-1/3)
t<=-5 0.269*** [0.1795,0.3593]
t=-40.183** [0.0724,0.2938]
t=-30.230*** [0.1451,0.3146]
t=-20.167*** [0.0776,0.2562]
t=-1
0.204*** [0.1368,0.2713]
t=00.136** [0.0438,0.2290]
t=+1
0.029
[-0.0784,0.1363]
t=+2
0.050
[-0.0351,0.1356]
t=+3
0.046
[-0.0822,0.1750]
t=+4-0.004[-0.1688,0.1609]
t>=+5 -0.112[-0.2553,0.0307]

1.065
0.835
0.959
0.924
0.946
1.001
1.049
1.089
1.062
1.064
1.025

[0.9571,1.1720][0.6552,1.0139][0.8279,1.0911][0.8398,1.0075][0.8648,1.0279][0.9315,1.0708][0.9603,1.1371][0.9750,1.2030][0.9519,1.1721][0.8346,1.2928][0.9073,1.1426]

0.013-0.009-0.005-0.010-0.012-0.007-0.0070.006-0.015-0.0030.002[-0.0059,0.0317][-0.0648,0.0462][-0.0277,0.0186][-0.0243,0.0038][-0.0270,0.0035][-0.0189,0.0051][-0.0288,0.0156][-0.0145,0.0264][-0.0325,0.0021][-0.0524,0.0467][-0.0316,0.0357]

0.979
0.960
0.928
0.960
0.961
0.913
0.806
0.851
0.814
0.467
0.812

1,696
1,035
1,381
1,839
2,291
2,526
1,855
1,486
1,257
860
1,257

538
350
477
637
779
865
629
520
408
296
432

F-Group (bottom-1/3)
t<=-5 0.149*** [0.0679,0.2303]
t=-4
0.082
[-0.0292,0.1926]
t=-3
0.096*[0.0079,0.1847]
t=-20.088*[0.0047,0.1704]
t=-10.119** [0.0455,0.1931]
t=00.081*[0.0001,0.1616]
t=+1
0.073
[-0.0217,0.1674]
t=+2
0.043
[-0.0721,0.1578]
t=+3
0.001
[-0.1265,0.1295]
t=+4-0.105[-0.3549,0.1444]
t>=+5 -0.102[-0.6336,0.4301]

0.917
0.956
0.980
0.946
0.985
1.053
1.147***
1.104***
1.171***
1.161
1.183

[0.7907,1.0428][0.8125,1.0997][0.8736,1.0855][0.8891,1.0025][0.9107,1.0586][0.9824,1.1243][1.0403,1.2539][1.0187,1.1883][1.0356,1.3074][0.9480,1.3731][0.7627,1.6023]-0.012-0.0100.003-0.004-0.005
0.000
0.005
0.001
0.013
0.016
0.004

[-0.0438,0.0199][-0.0913,0.0718][-0.0158,0.0211][-0.0208,0.0128][-0.0245,0.0136][-0.0133,0.0142][-0.0153,0.0246][-0.0178,0.0194][-0.0229,0.0489][-0.0505,0.0825][-0.1874,0.1955]

0.967
0.796
0.821
0.823
0.933
0.877
0.892
0.847
0.876
0.740
0.821

1,178
750
1,079
1,454
1,848
1,985
1,428
1,152
942
631
1,078

570
380
528
701
846
931
699
572
462
323
449

Notes: SPs are firms change their ownership from stated-owned to private-owned, as Section 3.2; t = 0 denotes the year when a firm privatizes
from a SOE to a POE, and t = −1 is one year prior to the privatization while t + 1 one year after, and so forth; Firms are ranked from nearest to
farthest by distance from the corresponding oversight government in Section 3.3, and thus, top-1/2 (top-1/3) are the nearest 50% (33%) firms
denoted by prefix C-, while bottom-1/2 (bottom-1/3) are the farthest 50% (33%) firms denoted by prefix F-; The null hypothesis H0 is A = 0,
D = 1, S = 0; Bootstrap replication (50); 95% confidence intervals in brackets; ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001.

22

FIGURE 2. PARAMETERS OF SP S AGGLOMERATION E FFECTS BY D ISTANCE F ROM OVERSIGHTG OVERNMENT, TOP -1/2 VS . BOTTOM -1/2, C ITIES ARE G ROUPED BY M EDIAN VALUE OF L IGHT
B RIGHTNESS
Notes: SPs are firms change their ownership from state-owned to private-owned, as Section 3.2; t = 0 denotes the year when a firm privatizes
from a SOE to a POE, and t = −1 is one year prior to the privatization while t + 1 one year after, and so forth; Firms are ranked from nearest
to farthest by distance from the corresponding oversight government in Section 3.3, and thus, top-1/2 are the nearest 50% firms denoted by
prefix C-, while bottom-1/2 are the farthest 50% firms denoted by prefix F-; The null hypothesis H0 is A = 0, D = 1; Bootstrap replication (50);
Estimated values with 95% confidence intervals are plotted.

FIGURE 3. PARAMETERS OF SP S AGGLOMERATION E FFECTS BY D ISTANCE F ROM OVERSIGHTG OVERNMENT, TOP -1/3 VS . BOTTOM -1/3, C ITIES ARE G ROUPED BY M EDIAN VALUE OF L IGHT
B RIGHTNESS
Notes: SPs are firms change their ownership from state-owned to private-owned, as Section 3.2; t = 0 denotes the year when a firm privatizes
from a SOE to a POE, and t = −1 is one year prior to the privatization while t + 1 one year after, and so forth; Firms are ranked from nearest
to farthest by distance from the corresponding oversight government in Section 3.3, and thus, top-1/3 are the nearest 33% firms denoted by
prefix C-, while bottom-1/3 are the farthest 33% firms denoted by prefix F-; The null hypothesis H0 is A = 0, D = 1; Bootstrap replication (50);
Estimated values with 95% confidence intervals are plotted.

23

FIGURE 4. P RODUCTIVITY D IFFERENCE OF SP S AT 25 TH , 50 TH AND 75 TH P ERCENTILE BY
D ISTANCE F ROM OVERSIGHT G OVERNMENT, TOP -1/2 VS . BOTTOM -1/2
Notes: SPs are firms change their ownership from state-owned to private-owned, as Section 3.2; Firms are ranked from nearest to farthest by
distance from the corresponding oversight government in Section 3.3, and thus, top-1/2 are the nearest 50% firms denoted by prefix C- (deepcolor), while bottom-1/2 are the farthest 50% firms denoted by prefix F- (light color); The paired-coordinate arrows point from small cities tolarge cities.

FIGURE 5. P RODUCTIVITY D IFFERENCE OF SP S AT 95 TH P ERCENTILE BY D ISTANCE F ROM
OVERSIGHT G OVERNMENT, TOP -1/2 VS . BOTTOM -1/2
Notes: SPs are firms change their ownership from state-owned to private-owned, as Section 3.2; Firms are ranked from nearest to farthest by
distance from the corresponding oversight government in Section 3.3, and thus, top-1/2 are the nearest 50% firms denoted by prefix C- (deepcolor), while bottom-1/2 are the farthest 50% firms denoted by prefix F- (light color); The paired-coordinate arrows point from small cities tolarge cities.

24

TABLE 4. E STIMATION R ESULTS OF CP S BY D ISTANCE F ROM OVERSIGHT G OVERNMENT, TOP -1/2
VS . BOTTOM -1/2, C ITIES ARE G ROUPED BY M EDIAN VALUE OF L IGHT B RIGHTNESS(1)
Agglomeration Effects

(2)

(3)
Selection Effects

A

D

S

C-Group (top-1/2)
t<=-5 0.042
t=-4
0.140
t=-3
0.154***
t=-2
0.097*
t=-1
0.106***
t=00.086**
t=+10.117***
t=+20.141***
t=+3
0.158
t=+4
0.109*
t>=+5 -0.014

(4)
R2

(5)
Obs.

(6)

Big City

Small City[-0.0549,0.1380][-0.0733,0.3524][0.0761,0.2316][0.0179,0.1763][0.0440,0.1681][0.0319,0.1402][0.0640,0.1706][0.0646,0.2169][-0.0481,0.3638][0.0247,0.1932][-0.0906,0.0625]

1.144***
1.074
1.06
1.011
1.048
1.063*
1.058*
1.027
1.006
1.061
1.050

[1.0184,1.2689][0.8810,1.2680][0.9726,1.1466][0.9205,1.1011][0.9927,1.1030][1.0122,1.1136][1.0031,1.1127][0.9546,1.1001][0.8506,1.1609][0.9813,1.1406][0.9947,1.1051]

0.015-0.0130.010-0.003
0.010
0.002
0.001
-0.012-0.012-0.0010.008[-0.0022,0.0330][-0.1085,0.0831][-0.0076,0.0278][-0.0196,0.0134][-0.0000,0.0201][-0.0087,0.0122][-0.0084,0.0099][-0.0259,0.0024][-0.0913,0.0673][-0.0177,0.0155][-0.0053,0.0212]

0.960
0.974
0.969
0.851
0.934
0.906
0.916
0.944
0.885
0.865
0.611

2,802
2,150
3,365
5,621
9,457
9,944
7,353
5,863
4,515
3,492
6,259

418
334
549
851
1,455
1,509
1,082
844
635
476
857

F-Group (bottom-1/2)
t<=-5 0.050[-0.0397,0.1392]
t=-40.136*[0.0089,0.2637]
t=-30.152*[0.0226,0.2815]
t=-20.128** [0.0484,0.2084]
t=-1
0.184*** [0.1343,0.2342]
t=00.092*** [0.0471,0.1359]
t=+10.105** [0.0270,0.1821]
t=+2
0.039
[-0.1444,0.2219]
t=+3
0.075
[-0.0243,0.1739]
t=+4
0.036
[-0.5926,0.6651]
t>=+5 -0.015[-0.1215,0.0909]

1.157**
1.02
1.031
1.014
0.994
1.045**
1.01
1.074
1.063
1.108*
1.181*[1.0699,1.2446][0.9074,1.1334][0.9322,1.1304][0.9328,1.0954][0.9358,1.0516][1.0011,1.0892][0.9404,1.0800][0.9301,1.2171][0.9746,1.1512][0.6922,1.5242][1.0821,1.2809]

0.012
0.005
0.004
0.012
-0.002-0.001-0.011
0.010
0.003-0.0020.029[-0.0049,0.0292][-0.0222,0.0323][-0.0261,0.0350][-0.0013,0.0244][-0.0120,0.0084][-0.0083,0.0065][-0.0335,0.0109][-0.0546,0.0746][-0.0254,0.0321][-0.2117,0.2078][-0.0002,0.0588]

0.911
0.951
0.959
0.955
0.984
0.943
0.871
0.603
0.747
0.781
0.787

2,586
2,160
3,507
5,864
10,156
10,580
7,879
6,368
4,831
3,691
6,833

485
341
545
891
1,617
1,684
1,222
958
719
547
889

Notes: CPs are firms change their ownership from collective-owned to private-owned, as Section 3.2; t = 0 denotes the year when a firm
privatizes from a SOE to a POE, and t = −1 is one year prior to the privatization while t + 1 one year after, and so forth; Firms are ranked fromnearest to farthest by distance from the corresponding oversight government in Section 3.3, and thus, top-1/2 are the nearest 50% firms denotedby prefix C-, while bottom-1/2 are the farthest 50% firms denoted by prefix F-; The null hypothesis H0 is A = 0, D = 1, S = 0; Bootstrap
replication (50); 95% confidence intervals in brackets; ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001.

25

multiple transitions are not included in the robustness test because the preceding section (Section 4.2)
only incorporates firms that have been privatized once. Table 5 uses different firm productivity
estimation methods, while Table 6 uses another firm ownership classification. These tables showthat our results continue to hold and suggest that the market competition and withdrawal mechanisms
have gradually improved after the SOE reform.

6

Conclusion

Employing a large firm-level dataset and following the generalized firm selection model (Melitz,
2003; Melitz and Ottaviano, 2008), we examine the impact of SOEs’ privatization on Chinese firms’
productivity in response to agglomeration and selection effects. We use extensive manufacturing
firm data with a quantile specification (Combes et al., 2012). This specification allows us to estimate
a relative change in shift (A, agglomeration benefits shared by all firms), dilation (D, productivity
benefits shared by top firms), and left truncation (S, selection that eliminates the least productive
firms) in the productivity distribution between small and large cities. We find that agglomeration
explains a large part of productivity differentials across cities in China’s manufacturing industry foreach ownership type, in line with most of the literature that uses the same measures (Combes et al.,2012; Arimoto et al., 2014; Ding and Niu, 2019; Zhang et al., 2020a). We also find a statisticallysignificant selection effect among Always-POEs, which is a specific result relative to Ding and Niu(2019) and Zhang et al. (2020a). We attribute this to the classification of the sample by firm ownership. In the five sub-samples (Always-SOEs, Always-COEs, Always-POEs, SPs, and CPs), only
Always-POEs display a significantly positive selection effect while the selection effects of the othergroups are insignificant (or even negative).
We also find that Always-SOEs enjoy a statistically significant agglomeration effect which isgreater than that for Always-POEs. This differs from research (Hu et al., 2015) which argues thatprivate enterprises benefit the most from agglomeration. A possible reason is that these studies do
not consider the agglomeration enjoyed by SOEs as the government supports them by sharing local
information, such as tacit knowledge, labor markets, and resources. Intimate ties with the government characterize SOEs; we assume that the agglomeration effect of SOEs will increase with accessto more local information. Following Huang et al. (2017), we use the geographic distance between
firms and their corresponding oversight governments to proxy the capability to access local knowledge such that firms far from the oversight governments have less interaction with the government
and less information sharing, and thus, hinting at a lower level of agglomeration advantages. In
contrast, firms close to the oversight government enjoy more agglomeration gains.
Regarding the selection effects, we only detect a statistically significant but minor selection effectamong Always-POEs. Moreover, we fail to find a significant selection effect after SOEs are privatized. Residual government ties that provide preferential credit policies may explain the disparity in

26

TABLE 5. E STIMATION R ESULTS OF SP S BY D ISTANCE F ROM OVERSIGHT G OVERNMENT, TOP -1/2
VS . BOTTOM -1/2, C ITIES ARE G ROUPED BY M EDIAN VALUE OF L IGHT B RIGHTNESS , P RODUCTIVITY
ARE E STIMATED BY OLS M ETHOD AND L ABOR P RODUCTIVITY(1)
Agglomeration Effects

(2)

(3)
Selection Effects

A

D

S

(4)
R2

(5)
Obs.

(6)

Big City

Small City

Panel A: LnTFP, OLS method
C-Group (top-1/2)
t<=-5 0.281*** [0.2124,0.3505]
t=-40.347*** [0.2760,0.4175]
t=-30.322*** [0.2403,0.4040]
t=-20.314*** [0.2209,0.4066]
t=-1
0.309*** [0.2404,0.3780]
t=00.201*** [0.1281,0.2737]
t=+10.107** [0.0278,0.1862]
t=+20.092*[0.0021,0.1813]
t=+30.101*[0.0002,0.2014]
t=+4
0.054
[-0.1023,0.2099]
t>=+5 0.039[-0.1110,0.1896]

1.034
0.877*
1.016
0.963
0.976
1.065*
1.061
1.149*
1.090*
1.108
1.036[0.9557,1.1128][0.8096,0.9435][0.9359,1.0953][0.8900,1.0360][0.9004,1.0519][1.0107,1.1193][0.9645,1.1567][1.0495,1.2495][1.0108,1.1692][0.9339,1.2821][0.9423,1.1293]-0.001 [-0.0140,0.0128]-0.013 [-0.0273,0.0005]-0.006[-0.0252,0.0133]-0.014* [-0.0255,-0.0021]-0.011[-0.0246,0.0036]-0.003 [-0.0116,0.0065]-0.002[-0.0174,0.0129]
0.012[-0.0011,0.0249]-0.012[-0.0250,0.0008]
0.002[-0.0475,0.0511]
0.001[-0.0642,0.0653]

0.966
0.980
0.980
0.986
0.981
0.986
0.877
0.912
0.909
0.673
0.533

2,326
1,409
1,931
2,628
3,267
3,592
2,634
2,095
1,752
1,221
1,858

787
530
710
971
1,182
1,300
963
795
622
444
622

F-Group (bottom-1/2)
t<=-5 0.255*** [0.1671,0.3422]
t=-40.204*** [0.1248,0.2827]
t=-30.174*** [0.1002,0.2484]
t=-20.178*** [0.0952,0.2614]
t=-10.161*** [0.1024,0.2205]
t=00.158*** [0.0957,0.2203]
t=+10.160*** [0.0937,0.2268]
t=+20.139*** [0.0570,0.2211]
t=+3
0.097
[-0.0126,0.2072]
t=+4
0.007
[-0.1357,0.1492]
t>=+5 -0.026[-0.9574,0.9061]

1.035
1.017
1.018
0.998
1.082*
1.080*
1.171**
1.118*
1.184**
1.159**
1.183[0.9412,1.1295][0.9034,1.1314][0.9382,1.0985][0.9091,1.0878][1.0122,1.1524][1.0283,1.1311][1.0743,1.2684][1.0383,1.1973][1.1115,1.2557][1.0061,1.3112][0.6363,1.7304]

0.011-0.0010.005
0.001-0.0020.000
0.001-0.002
0.001
0.001
0.003

[-0.0141,0.0370][-0.0272,0.0256][-0.0172,0.0271][-0.0240,0.0253][-0.0144,0.0111][-0.0090,0.0084][-0.0116,0.0138][-0.0225,0.0176][-0.0190,0.0215][-0.0362,0.0385][-0.3039,0.3103]

0.967
0.961
0.892
0.933
0.973
0.973
0.971
0.932
0.960
0.857
0.835

1,708
1,084
1,546
2,146
2,783
2,983
2,171
1,746
1,434
975
1,675

797
535
737
1,005
1,220
1,343
1,012
821
678
483
677

Panel B: LnTFP, Labor Productivity
C-Group (top-1/2)
t<=-5 0.312*** [0.2329,0.3903]
t=-40.299*** [0.2017,0.3954]
t=-30.336*** [0.2565,0.4163]
t=-20.304*** [0.2391,0.3682]
t=-1
0.340*** [0.2745,0.4046]
t=00.221*** [0.1639,0.2772]
t=+10.120** [0.0481,0.1918]
t=+20.133** [0.0494,0.2156]
t=+30.093*[0.0112,0.1746]
t=+4
0.098
[-0.0096,0.2053]
t>=+5 0.022[-0.0727,0.1174]

1.081***
0.922
1.058
1.055
1.009
1.073**
1.047
1.106**
1.04
1.108
1.038

[1.0083,1.1528][0.7973,1.0464][0.9816,1.1354][0.9891,1.1210][0.9324,1.0856][1.0172,1.1292][0.9874,1.1072][1.0391,1.1730][0.9472,1.1319][0.9700,1.2451][0.9519,1.1232]

0.000
0.001
-0.0010.004-0.0100.000-0.003-0.001-0.0110.001-0.002[-0.0119,0.0120][-0.0473,0.0498][-0.0152,0.0122][-0.0077,0.0150][-0.0229,0.0021][-0.0087,0.0083][-0.0144,0.0078][-0.0115,0.0102][-0.0375,0.0152][-0.0307,0.0332][-0.0246,0.0213]

0.983
0.984
0.990
0.984
0.986
0.982
0.957
0.950
0.635
0.759
0.317

2,326
1,409
1,931
2,628
3,267
3,592
2,634
2,095
1,752
1,221
1,858

787
530
710
971
1,182
1,300
963
795
622
444
622

F-Group (bottom-1/2)
t<=-5 0.278*** [0.2032,0.3521]
t=-40.205*** [0.1158,0.2938]
t=-30.174*** [0.1021,0.2459]
t=-2
0.199*** [0.1274,0.2701]
t=-10.201*** [0.1418,0.2596]
t=00.145*** [0.0702,0.2199]
t=+10.142*** [0.0754,0.2079]
t=+20.113*[0.0135,0.2121]
t=+3
0.087
[-0.0125,0.1864]
t=+4
0.002
[-0.1072,0.1111]
t>=+5 -0.01[-0.1001,0.0809]

1.027
1.057
1.049
1.005
1.067**
1.093**
1.179***
1.105**
1.149*
1.126***
1.153***[0.9535,1.1011][0.9439,1.1709][0.9335,1.1650][0.9528,1.0571][1.0101,1.1244][1.0424,1.1427][1.1034,1.2549][1.0375,1.1721][1.0415,1.2572][1.0126,1.2398][1.0656,1.2401]

0.004
0.001
0.010
-0.002
0.001
0.003
0.002
-0.001-0.001
0.002
0.005[-0.0129,0.0210][-0.0324,0.0350][-0.0132,0.0340][-0.0144,0.0113][-0.0107,0.0136][-0.0069,0.0132][-0.0098,0.0147][-0.0136,0.0113][-0.0287,0.0274][-0.0151,0.0186][-0.0085,0.0188]

0.958
0.918
0.878
0.922
0.977
0.960
0.958
0.956
0.871
0.862
0.838

1,708
1,084
1,546
2,146
2,783
2,983
2,171
1,746
1,434
975
1,675

797
535
737
1,005
1,220
1,343
1,012
821
678
483
677

Notes: SPs are firms change their ownership from state-owned to private-owned, as Section 3.2; t = 0 denotes the year when a firm privatizes
from a SOE to a POE, and t = −1 is one year prior to the privatization while t + 1 one year after, and so forth; Firms are ranked from nearest to
farthest by distance from the corresponding oversight government in Section 3.3, and thus, top-1/2 are the nearest 50% firms denoted by prefix
C-, while bottom-1/2 are the farthest 50% firms denoted by prefix F-; The
27null hypothesis H0 is A = 0, D = 1, S = 0; Bootstrap replication (50);95% confidence intervals in brackets; ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001.

TABLE 6. E STIMATION R ESULTS S NON S BY D ISTANCE F ROM OVERSIGHT G OVERNMENT, TOP -1/2
VS . BOTTOM -1/2, C ITIES ARE G ROUPED BY M EDIAN VALUE OF L IGHT B RIGHTNESS(1)
Agglomeration Effects

(2)

(3)
Selection Effects

A

D

S

C-Group (top-1/2)
t<=-5 0.991**
t=-4
0.422
t=-3
0.452***
t=-2
0.451***
t=-1
0.371***
t=00.264***
t=+1
0.115*
t=+20.152**
t=+3
0.155
t=+4
0.011
t>=+5 0.047

(4)
R2

(5)
Obs.

(6)

Big City

Small City

[0.2388,1.7427][-0.0393,0.8833][0.3308,0.5723][0.3030,0.5997][0.2828,0.4596][0.1860,0.3417][0.0195,0.2113][0.0492,0.2555][-0.0025,0.3117][-0.1437,0.1659][-0.0752,0.1685]

0.481*
0.860
1.016
1.120**
1.002
1.044
1.142**
1.149**
1.099
1.141*
1.058[0.0818,0.8802][0.5016,1.2176][0.8913,1.1403][1.0167,1.2228][0.9373,1.0672][0.9747,1.1138][1.0323,1.2518][1.0138,1.2843][0.9624,1.2363][1.0032,1.2795][0.9468,1.1701]-1.014 [-2.1164,0.0885]-0.031[-0.6569,0.5957]-0.013[-0.0469,0.0212]-0.016 [-0.0396,0.0084]
0.002[-0.0129,0.0160]-0.017* [-0.0307,-0.0028]
0.014* [0.0005,0.0276]
0.008[-0.0128,0.0298]-0.004[-0.0438,0.0365]-0.002[-0.0298,0.0261]-0.015[-0.0338,0.0042]

0.932
0.970
0.988
0.960
0.994
0.970
0.947
0.906
0.853
0.879
0.819

748
541
882
1,707
3,225
3,584
2,366
1,831
1,402
1,081
2,055

182
162
274
525
917
1,049
659
506
381
298
520

F-Group (bottom-1/2)
t<=-5 0.191[-0.1828,0.5647]
t=-4
0.398
[-0.2512,1.0470]
t=-3
0.482*** [0.3345,0.6287]
t=-2
0.328*** [0.1961,0.4603]
t=-1
0.261*** [0.1824,0.3395]
t=00.131*** [0.0583,0.2044]
t=+10.122*[0.0212,0.2221]
t=+20.120*[0.0108,0.2284]
t=+3
0.096
[-0.0348,0.2261]
t=+4
0.028
[-0.1429,0.1991]
t>=+5 -0.027[-0.1354,0.0809]

1.323***
1.167
1.181
1.077
1.05
1.106**
1.232*
1.188**
1.214**
1.188**
1.158***[1.0078,1.6376][0.4987,1.8360][0.9932,1.3684][0.9068,1.2478][0.9640,1.1362][1.0182,1.1935][1.0844,1.3791][1.0804,1.2961][1.0563,1.3718][1.0220,1.3548][1.0540,1.2620]

0.045-0.017-0.001
0.003-0.002
0.015
0.012
0.008
0.014
0.005
0.018

0.923
0.945
0.969
0.951
0.944
0.897
0.938
0.914
0.945
0.870
0.752

367
327
630
1,381
2,661
2,984
1,881
1,463
1,126
892
1,829

151
135
235
503
928
1,056
670
501
369
308
520

[-0.0871,0.1778][-0.7279,0.6937][-0.0609,0.0588][-0.0562,0.0622][-0.0168,0.0127][-0.0047,0.0339][-0.0072,0.0312][-0.0099,0.0250][-0.0100,0.0383][-0.0439,0.0545][-0.0038,0.0399]

Notes: SnonS are firms transition from H-SOEs to Non-SOEs as discussed in Section 5; t = 0 denotes the year when a firm privatizes froma SOE to a POE, and t = −1 is one year prior to the privatization while t + 1 one year after, and so forth; Firms are ranked from nearest to
farthest by distance from the corresponding oversight government in Section 3.3, and thus, top-1/2 are the nearest 50% firms denoted by prefix
C-, while bottom-1/2 are the farthest 50% firms denoted by prefix F-; The null hypothesis H0 is A = 0, D = 1, S = 0; Bootstrap replication (50);95% confidence intervals in brackets; ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001.

28

the selection effect of Always-POEs and SPs (Boubakri et al., 2008; Harrison et al., 2019). However,the negative-to-positive change of Ŝ suggests that privatization can improve firm efficiency in large
cities through tougher competition; however, this can take longer, and require a well-established firm
exit and resource reallocation mechanism.
Finally, based on the above methodology and results, we show that Hypotheses 1a, 2a, 1b, and2b are supported: First, the SOE reforms negatively influences the agglomeration effect for mediocre
privatized SOEs, but positively improves the selection effect. Second, weakened government ties
after SOEs’ reform account for the drop in agglomeration advantages, and the more or less improved
market selection of post-privatized SOEs. Finally, privatization can reinforce the agglomeration
advantages for SOEs with high ex-ante productivity and less close ties to the government.
In summary, to smoothly transition and catch up with the productivity levels of private firms
sooner, the government can utilize the agglomeration and selection effects of the urban areas by prioritizing the privatization of SOEs that are efficient and not closely linked to the government. After
privatization, SOEs may lose privileged treatment and face the dilemma of sharply reduced agglomeration benefits, such as productivity improvements generated by labor market matching, resource
sharing, and knowledge spillovers. To allow privatized SOEs to maintain their original agglomeration advantages and consistently increase productivity, the government should reduce political ties
with pre-privatized SOEs, prompting them to adapt to a market that is characterized by both cooperation and competition with private firms. The government should also privatize high-quality SOEs
with efficient employees or managers so that these firms can better leverage the post-privatization
agglomeration benefits. Meanwhile, the government should reduce the preferential credit support
for SOEs that have already been privatized, allowing market competition-induced selection effects
to play out. That is, constructing a competitive market environment is necessary for improving firm
productivity.

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33

Appendix A
Rank

Table

Province

City

Employment(secondary industry)

Employment
Density

Population(hukou)Population
DensityLight

Sort by employment of the secondary industry in the urban areas
1
2
3
4
5

Tibet
Yunan
Gansu
Yunan
Qinghai

Lasa
Lincang
Longnan
Lijiang
Haidong

695
1,600
2,600
3,100
3,100

13
42
397
102
389

181,991
288,307559,049
153,023
416,148

3,321
7,500
85,351
5,057
52,214

8,545
6,913
2,964
6,016
5,749

283
284
285
286
287

Shandong
Helongjiang
Tianjin
Shanghai
Beijing

Guangzhou
HarbinTianjin
Shanghai
Beijing

763,900
913,500
928,400
1,434,800
1,651,700

1,256
3,021
1,905
2,611
1,400

5,882,553
4,754,753
7,912,385
13,091,515
11,453,643

9,676
15,723
16,232
23,821
9,706

231,834
110,809
276,413364,622383,236

Sort by employment density of the secondary industry in the urban areas
1
2
3
4
5

Tibet
YunnanInner Mongolia
Inner Mongolia
Yunnan

Lasa
Lincang
UlanqabHulunbuir
Lijiang

695
1,600
6,700
10,400
3,100

13
42
60
66
102

181,991
288,307298,887
263,005
153,023

3,321
7,500
2,681
1,662
5,057

8,545
6,913
16,04836,640
6,016

283
284
285
286
287

SichuanJiangxi
Henan
FujianHenanPanzhihua
Xinyu
Pingdingshan
PutianPuyang141,500
125,100
188,000
125,600
152,600

3,369
3,475
3,547
3,873
4,348

664,700
821,919
1,104,000
2,016,300
516,600

15,826
22,831
20,83062,174
14,718

16,8478,301
41,15633,33537,515

Sort by population (hukou) in the urban areas
1
2
3
4
5

Yunan
Tibet
Helongjiang
Gansu
Jiangxi

Lijiang
Lasa
Heihe
Jinchang
Yintan

3,100
695
9,200
42,000
5,400

102
13
497
1,712
284

153,023
181,991
191,440
198,401
201,787

5,057
3,321
10,348
8,088
10,6206,016
8,545
15,207
7,241
7,049

283
284
285
286
287

Tianjin
Hubei
BeijingShanghai
Chongqing

Tianjin
Wuhan
BeijingShanghai
Chongqing

928,400
621,800
1,651,700
1,434,800
677,400

1,905
2,824
1,400
2,611
1,293

7,912,385
8,282,137
11,453,643
13,091,515
15,260,234

16,23237,608
9,706
23,821
29,139276,413
105,769
383,236
364,622
113,443

Sort by population density (hukou) in the urban areas
1
2
3
4
5

Inner Mongolia
Guangdong
Inner Mongolia
Inner Mongolia
Guangdong

Hulunbuir
Zhaoqing
Ordos
UlanqabShenzhen

10,40052,80025,9006,700
576,600

66
271
284
60
809

263,005
477,428
243,429
298,887
2,168,453

1,662
2,453
2,669
2,681
3,041

36,64037,04035,097
16,048
176,437

283
284
285
286
287

Guangxi
FujianGuizhou
SichuanGansu

LaibinPutianBijie
Bazhong
Longnan

12,700125,600
12,70022,700
2,600

698
3,873
605
1,437
397

1,023,100
2,016,300
1,415,638
1,332,929
559,049

56,21462,17467,411
84,36385,351

7,364
33,335
6,633
2,524
2,964

Sort by light brightness
1
2
3
4
5

SichuanSichuan
Gansu
Shaanxi
Hunan

Yaan
Bazhong
Longnan
Shangluo
Zhangjiajie

20,10022,700
2,600
5,400
5,300

1,267
1,437
397
470
277

350,987
1,332,929
559,049
552,900
497,957

22,11684,36385,351
48,07826,071

2,431
2,524
2,964
3,418
3,998

283
284
285
286
287

JiangsuGuangdong
Tianjin
Shanghai
BeijingSuzhouGuangdong
Tianjin
Shanghai
Beijing249,600
763,900
928,400
1,434,800
1,651,700

1,675
1,256
1,905
2,611
1,400

2,940,849
5,882,553
7,912,385
13,091,515
11,453,643

19,737
9,676
16,232
23,821
9,706

226,203
231,834
276,413364,622383,236

TABLE A.1. C ITY R ANKS ACCORDING TO D IFFERENT C RITERIA

34

Appendix B

Data Cleaning Process

The firm linkages over time are made using the methods by Brandt et al. (2012, 2014) and Brandt
et al. (2017), who made do-files available online, including programs of matching firms over years
and tables of industrial concordance codes.26 After matching firms, we follow standard procedures
documented in the previous literature to clean the data (Wei and Liu, 2006; Brandt et al., 2012, 2014;
Yang, 2018):
1. Only keep the manufacturing industry;
2. Exclude the tobacco industry;
3. Use observations with positive industrial value-added, intermediate inputs, and net fixed assets;
4. Keep observations with no-less-than eight employees;
5. Drop observations not under accounting principles: liquid assets, fixed assets, or net fixed
assets larger than total assets;
6. Make 4-digit industrial numerical codes uniform across the entire period following the practice
introduced by Brandt et al. (2014). And also update the renamed or merged city to the latest
city name.27
7. Firms that changed their locations are deleted.28
8. Observations without population data, another critical variable collected from city statistical
yearbooks, are deleted.
9. According to the method of distinguishing the firm ownership instructed in Section 3.2, we
exclude firms that have changed their ownership many times and have been nationalized.
we finally obtain an unbalanced panel data with 461,642 (specifically, there are 50,041 Always-SOEs,
30,854 Always-COEs, 347,056 Always-POEs, 23,717 CPs, 756 SCs, and 9,218 SPs) unique firms
from 1998 to 2007 (totally 1,653,782 observations) covering 28 two-digit manufacturing industries
across 31 provinces and 287 prefecture-level cities.29
26 Online

website:https://feb.kuleuven.be/public/u0044468//CHINA/appendix/, accessed March 13th2021.
27 During analysis period from 2000 to 2007, Industrial standard classification for national economic activities wasrevised in 2002 from GB/T 4754—1994 to GB/T 4754—2002 where some 4-digit industries were merged while others
were divided.
28 Firms whose addresses have changed accounted for only 0.16% of the whole sample. Hence, we can assume thatthe firm does not have the possibility of relocation; it can only go bankrupt and cannot change its official place to reopen.
29 SCs are those change from SOEs to COEs, but we do not analysis this group firms due to few observations.

35

36

1998
1999
2000
2001
2002
2003
2004
2005
2006
2007

Year

165,118
162,033
162,833
169,030
181,557
196,222
279,092
271,835
301,961
336,768

165,116
162,033
162,885
171,256
181,557
196,222274,886
270,043
301,961
336,768

Number of firms
Brandt et al. (2014) Dataset

2
0
-52
-2226
0
0
4206
1792
0
0

Diff.

6.41
6.99
8.42
9.24
10.95
14.32
20.43
24.69
31.36
39.97

0.00
0.00
0.00
-0.13
0.00
0.00
0.55
-0.13
-0.06
-0.09

Diff.
6.77
7.27
8.57
9.41
11.08
14.23
20.16
25.16
31.66
40.52

6.77
7.27
8.57
9.54
11.08
14.23
20.10
24.99
31.66
40.51

OutputBrandt et al. (2014) Dataset
0.00
0.00
0.00
-0.13
0.00
0.00
0.06
0.17
0.00
0.01

Diff.
1.94
2.16
2.54
2.79
3.30
4.20
6.62
7.22
9.11
11.70

1.94
2.16
2.54
2.83
3.30
4.20
5.67
7.14
9.11
11.70

Value added
Brandt et al. (2014) Dataset
0.00
0.00
0.00
-0.04
0.00
0.00
0.95
0.08
0.00
0.00

Diff.
56.44
58.05
53.68
52.97
55.21
57.49
66.27
68.96
73.58
78.75

56.44
58.05
53.68
54.41
55.21
57.49
66.26
69.09
73.58
79.27

Employment
Brandt et al. (2014) Dataset
0.00
0.00
0.00
-1.44
0.00
0.00
0.01
-0.13
0.00
-0.52

Diff.

4.41
4.73
5.81
5.45
5.95
6.61
7.97
8.95
10.58
12.34

4.41
4.73
5.18
5.54
5.95
6.61
7.96
10.53
10.58
12.34

0.00
0.00
0.63
-0.09
0.00
0.00
0.01
-1.58
0.00
0.00

Net value of fixed assets
Brandt et al. (2014) Dataset Diff.

TABLE B.1. O RIGINAL DATA VS. TABLE .4 IN B RANDT ET AL . (2014)

6.41
6.99
8.42
9.37
10.95
14.32
19.88
24.82
31.42
40.06

Sales
Brandt et al. (2014) Dataset

1.08
1.16
1.46
1.61
2.01
2.69
4.05
4.77
6.05
7.34

1.08
1.15
1.46
1.62
2.01
2.69
4.05
4.77
6.05
7.34

ExportBrandt et al. (2014) Dataset

0.00
0.01
0.00
-0.01
0.00
0.00
0.00
0.00
0.00
0.00

Diff.

FIGURE B.1. P ERCENTAGE OF FIRM WITH DIFFERENT ULTIMATE OWNERSHIP PER YEARFIGURE B.2. AVERAGE F IRM PERFORMANCE GROUPED BY ULTIMATE OWNERSHIP

37

Appendix C

OP Method

We start with the production function:ββ

Yit = Ait Kit k Litl

(C.9)
β

β

β

where Yit stands for value-added; the revenue production function looks like: Yit = Ait Kit k Litl Mit m ,where Yit is gross output. Taking natural logs of Equation (C.9) results in a linear production function:
yit = β0 + βk kit + βl lit + εit(C.10)and εit includes two parts ωit + uit , where ωit represents firm-level productivity and uit is i.i.d. Direct estimation using OLS will cause endogenous problems and selection bias and lead to biased
productivity results.
Olley and Pakes (1992) assumes that investment decisions at the firm level can be shown todepend on capital (Iit = Kit+1 − (1 − δ )Kit ) and productivity (higher expectation, higher investment
decision):ωit = ht (kit , iit )(C.11)
Since this is a monotonically increasing function, it can be written as ht (.) = it−1 (.):
yit = βl lit + β0 + βk kit + ht (kit , iit ) + uit(C.12)

The first term on the right side of the equation represents the contribution of labor, and the latterterm represents the contribution of capital and can be further written as:
ϕ (iit , kit ) = β0 + βk kit + ht (iit , kit )(C.13)

yit = βl lit + ϕ (iit , kit ) + uit(C.14)

Through the estimation of Eq.(C.14), an unbiased labor coefficient can be obtained. Then, the estimated coefficient is used to fit the polynomial term (ϕ (iit , kit )) formed by investment and capitalstock:
yit+1 − βl lit+1(C.15)q=β0 + βk kit+1 + g (φit , βk kit ) + ξit+1 + uit+1
The second stage estimation includes the estimation of high-order polynomials, and the current
period and the lag period of the capital stock exist simultaneously, which needs to be completed by
the nonlinear least square method.

38