# Natural Monopoly and Mixed Ownership Reform - Based on Natural Experiment and Cost Function Analysis Method

## - Based on Natural Experiment and Cost Function Analysis Method

Abstract: Despite a multitude of theoretical discussions on China’s mixed ownership reform, very few studies have addressed realistic questions concerning the implementation of the reform. The Resolutions of the Third Plenum of the 18th CPC Central Committee and other reform strategies have outlined the reform of sectors with natural monopoly, including urban public utility sectors. The question is how mixed ownership reform should be carried out in sectors of natural monopoly, or which public utilities sectors should enjoy priority of mixed ownership reform. To answer this question, this paper employs data of large public utility enterprises in China from 1998 to 2008, and estimates the natural monopoly attribute at the industry level and corporate total factor productivity (TFP) using cost function analysis method excluding the impact of product price factor. Based on the difference-indifferences-in-differences (DDD) method of natural experiment, an empirical test is carried out for the relationship among natural monopoly, mixed ownership reform and corporate productivity. Our results suggest that: (1) Statistically, mixed ownership reform cannot significantly increase corporate TFP in sectors with natural monopoly; (2) mixed ownership reform should not be carried out indiscriminately on a nationwide basis and for all public utilities sectors. Such an attempt of reform without distinguishing natural monopoly and the level of competitiveness is fraught with policy uncertainties; (3) relative to sectors with natural monopoly, corporate productivity in competitive sectors after mixed ownership reform will improve more significantly and enjoy greater “policy dividends” of institutional reform. Therefore, mixed ownership reform should be carried out first in competitive sectors.

Keywords: mixed ownership reform, natural monopoly, cost function, natural experiment, difference-in-differences-in-differences (DDD) method

JEL Classification Codes: H54; L98

DOI: 1 0.19602/j .chinaeconomist.2018.09.05

1. Introduction

Monopoly and competition, which compose a mainstream framework of economic theories, represent major issues facing socialist market economy. For instance, reform pathway for natural monopoly is discussed separately in two parts at length in the Resolutions of the Third Plenum of the

18th CPC Central Committee1. The Resolutions marks an attempt of top-level design2 for the reform of China’s mixed ownership sectors and monopolistic sectors: sectors of natural monopoly must be controlled by state capital, while private capital is permitted to enter “competitive sectors” without natural monopoly; reform pathway for sectors of natural monopoly is an improvement of previous regulatory approach, i.e. state-owned enterprises are separated from the government and operate under government sanction and oversight, but does not include mixed ownership reform.

Put simply, in sectors of natural monopoly, mixed ownership reform should not be carried out. Instead, existing government regulatory systems should be improved.

However, top- level design was not implemented in the reform process, resulting in the lack of coordination in the institutional reforms. First of all, the Ministry of Housing and Urban-Rural Development (MOHURD) as the regulatory authority for urban public utilities enacted the Implementing Opinions on Further Encouraging and Guiding the Entry of Private Capital in Public Utilities Sectors. This document calls for breaking monopoly without making any distinction of natural monopoly. It also states that “public utilities investment, construction and operation markets should be opened up” - such opening up naturally includes all sectors. Private capital is encouraged to participate in the mixed ownership reform of public utility sectors under MOHURD’s administration. In addition to removing monopoly, the new system also requires “standardization of market access in accordance with government licensed operations.” However, it does not specify which sectors need deregulation and which others require licensed operation due to natural monopoly. In fact, such a lack of clarity stems from the Opinions on Encouraging and Guiding the Healthy Development of Private Investment issued by the State Council in 2010, which is the upper policy regulation for MOHURD rules. This policy regulation also makes no distinction of natural monopoly in its policy statement that “private capital should be encouraged to proactively participate in the reorganization and reform of municipal public utility enterprises.” This lack of clarity increased when local governments formulated lower-level regulations.

The root cause behind such vagueness is the “Marshall Conflict” that has baffled economists for decades - should policymakers promote the economies of scale from natural monopoly or introduce other types of capital to inspire market competition. In the theories of modern natural monopoly, William Baumol employed “cost function analysis method” to mathematically prove the existence of natural monopoly (Baumol, 1977), and thus developed the contestable markets theory - economies of scale may lead to excessive entry (competition) and thus harm market dynamism and social welfare. Coincidentally, the Resolutions of the Third Plenum of the 18th CPC Central Committee identifies natural monopoly and economies of scale as critical questions in relevant institutional reforms. Hence, the Resolutions represents a top-level design of great theoretical importance.

The questions are: Whether mixed ownership reform should be carried out for sectors of natural monopoly? Should mixed ownership reform be carried out indiscriminately for all urban public utility sectors or for competitive sectors first? Theoretically, monopoly and competition represent a mainstream framework for economic research. The question is how to bring the discussions on mixed ownership

reform under this framework and seek a more reliable theoretical basis for mixed ownership reform (such as natural monopoly theory and cost function theory). The above practical and theoretical questions all contain great academic value. In addition, monopoly and state-owned economy are both critical questions of economic research and academic discussions in China. Under the research framework of cost function analysis created by William Baumol (Baumol et al., 1982), this paper investigates both questions in combination.

2. Theory and Hypothesis

In sectors of natural monopoly, mixed ownership reform could be fraught with more policy uncertainties. The reason lies in the difference of cost function for sectors of natural monopoly.

After the first Industrial Revolution, economists like John Stuart Mill and Alfred Marshall discovered that urban lighting, water supply and drainage and other municipal infrastructure networks were characterized by the dedicated use of assets, sunk cost and economies of scale (later economies of range), and developed the academic concept of “natural monopoly” - the fewer existing enterprises there are, the lower total cost of social production will be. Such sectors with special cost functions are entirely different from competitive sectors, i.e. only monopolistic or oligarchic market structure will maximize social welfare, because excessive competition may harm the level of social welfare for sectors of natural monopoly. This theory was comprehensively supplemented and improved by Baumol (1977), Panzar and Willig (1981) et al. using mathematical models. Afterwards, Willner (1994) attempted to break the cost function assumption of increasing marginal cost and diminishing return to scale in the mixed ownership reform theoretical model of De Fraja and Delbono (1989), and included the quadratic term cost function with variable average cost to examine the effect of economies of scale on mixed ownership reform. Since the economies of scale is a basic characteristic of natural monopoly (sufficient but not necessary condition), Willner’s study can be regarded as the first paper of theoretical exploration on the mixed ownership reform in sectors of natural monopoly.

Sunk cost and network externalities are also common characteristics of sectors of natural monopoly. Estrin and de Meza (1995) uses the former and Willner (2006a) simultaneously uses both as the model assumption for sectors of natural monopoly to investigate the relationship between natural monopoly and mixed ownership reform. Results indicate that unless a highly significant cost reduction occurs after SOE reform or the sunk cost is minimal ( weak attribute of natural monopoly), a higher proportion of state capital and government regulation should be retained in sectors of natural monopoly. Willner (2006b) further demonstrates that for sectors of natural monopoly with economies of scale, even if there is no difference of marginal cost between SOEs and private enterprises ( private enterprises do not have any comparative advantage in terms of efficiency), mixed ownership reform will still lead to greater total social welfare compared with a purely private or purely state-owned economic structure.

Existing theoretical studies suggest that the form of cost function influences every aspect of mixed ownership reform’s performance.

On the other hand, the most important criterion for the institutional performance of SOE reform is efficiency. There has been a protracted debate over the question of efficiency. Some scholars believe that SOE reform can bring about efficiency improvement (Yang, 1997; Zhang, 1999; Zhang, 2004; Xu and Zhang, 2015; Wu and Zhang, 2015). Others consider that SOE reform will not necessarily lead to an efficiency improvement, and still less overcome the problem of policy burden on the state sector of economy (Lin, et al., 1987; Lin and Liu, 2001). Empirical evidences provided by both sides also focus on efficiency. Some studies find that SOE reform is indeed conducive to corporate productivity (Shleifer et al., 1997, 1998; Liu, 2004; Liu and Li, 2005; Song and Yao, 2005; Jefferson and Su, 2006; Dong, et al., 2006; Li and Qiao, 2010; Liu and Shi, 2010; Yu et al., 2013; Li and Yu, 2015). Some studies hold

negative views on the efficiency effect of mixed ownership reform (Lin and Li, 2004; Bai et al., 2006; Zhang and Zhang, 2011; Liu and Sun, 2013).

Among various policy effects of mixed ownership reform, this paper will focus on efficiency discussions to investigate the efficiency improvement effect of reform.

In reality, products in sectors of natural monopoly have a strong nature of public goods. Their production, price and quality are of great importance to public welfare. Sectors of natural monopoly are of vital importance to the economy. In overseas institutional reform practices over recent years, ownership does not appear to be a major issue for reforming sectors of natural monopoly with the nature of public goods. For instance, in the United Kingdom where the mixed ownership reform for sectors of natural monopoly started in the 1970s, the reform was criticized by academicians for “turning state monopoly into private monopoly” and failing to achieve significant results (Xiao, 2001). Subsequently, the British government revamped institutional reform pathway: “The original massive and unified system was disintegrated to achieve effective competition in sectors without natural monopoly and effective regulation of sectors of natural monopoly” (Xiao, 2011). For competitive businesses in public utility sectors free from natural monopoly, ownership reform remains a feasible approach. Thus, mixed ownership reform in sectors of natural monopoly may have some uncertainties, and may not necessarily increase productivity for monopolistic firms.

Based on the above analysis, this paper puts forward Hypothesis 1 to be tested.

Hypothesis 1: In urban public utility sectors of natural monopoly, mixed ownership reform cannot substantially increase corporate productivity.

Chinese scholars extensively discussed the monopolistic and competitive segments of sectors of natural monopoly (Qie, 2002; Lin and He, 2004; Li, 2004; Chen and Jiang, 2008). For this reason, the Third Plenum of the 18th CPC Central Committee made the policy statement that “while state capital continues to control sectors of natural monopoly, reform should be carried out to separate government administration from enterprise management with government sanctions and oversight. Infrastructure network should be separated from operation according to the characteristics of different industries. Competitive sectors should be deregulated to promote market-based allocation of public resources,” and that “the scope of government pricing should be limited to critical public utilities, public-interest services and infrastructure networks of natural monopoly.” Recently, Zhang and Zhang ( 2011) finds that SOE efficiency is rather different in monopolistic and competitive sectors. Making no distinction between sectors with and without natural monopoly is likely a chief reason for the ineffective mixed ownership reform of urban public utility sectors and policy uncertainties.

Based on the above analysis, this paper puts forward Hypothesis 2 on the basis of Hypothesis 1.

Hypothesis 2: Without making distinction between sectors of natural monopoly and competitive sectors, mixed ownership reform cannot substantially increase corporate productivity.

According to extensive empirical evidences provided by the academia, mixed ownership reform in the general sense can increase corporate productivity (Liu, 2004; Song and Yao, 2005; Jefferson and Su, 2006; Dong, et al., 2006; Hu Yifan, et al., 2006; Li and Qiao, 2010, Yu, et al., 2013). Hence, if the public utility sectors of the city are free from natural monopoly and are competitive sectors in a socialist market economy, relaxing access threshold for private capital, encouraging employee stock ownership and implementing mixed ownership reform will naturally give rise to an efficiency improvement effect. Hence, we have Hypothesis 3.

Hypothesis 3: In competitive sectors free from natural monopoly, mixed ownership reform has a significantly positive effect on the productivity of municipal public utility enterprises.

Once the above hypotheses are proven, mixed ownership reform will not be the only option for institutional reform of urban public utility sectors of natural monopoly, and should instead be carried out first in competitive sectors free from natural monopoly.

3. Design of Study 3.1 Sample Selection

In China, urban public utility sectors that may have natural monopoly mainly include the sectors of power supply, heat supply, fuel gas supply, water supply, sewerage treatment, waste treatment, municipal landscaping, etc. Given data availability, this paper selects five four-digit-code sectors including “4420 Power Supply,” “4430 Heat Production and Supply,” “4500 Fuel Gas Production and Supply,” “4610 Tapwater Production and Supply” and “4620 Sewage Treatment” as research subjects. Data source is large Chinese enterprises during 1998-2008 from the “Database of China’s Industrial Enterprises.” In 2003, there was a change in the statistical scope of four-digit-code sectors. Using the sector codes after 2003, this paper has adjusted the sector codes of 1998-2002.

This paper identifies private enterprises by the final controllers of listed companies, and determines the ownership nature of enterprises according to the shareholding status. Without considering the impact of legal person capital, this paper identifies enterprises as state-owned enterprises, collective enterprises, private enterprises, enterprises with investment from Hong Kong, Macao and Taiwan, and foreign-invested enterprises if any of state capital, collective capital, personal capital, capital from Hong Kong, Macao and Taiwan, or foreign capital accounts for more than 50% in their “total paidin capital,” or if any of state capital, personal capital, capital from Hong Kong, Macao and Taiwan, or foreign capital is the maximum capital in their “total paid-in capital”; their “status of state controlling share” are accordingly registered as “absolute (relative) controlling share held by the State,” “privately held controlling share,” “controlling share held by investor from Hong Kong, Macao or Taiwan,” and “controlling share held by foreign investor” respectively. When a state-owned or collective enterprise introduces private capital and thus becomes controlled by private capital, this sample is defined as an enterprise having completed mixed ownership reform. Finally, we obtained 55,101 observations in five sectors, including 7,111 observations having completed mixed ownership reform. On average, there are 711 enterprises which completed mixed ownership reform each year, as well as 6,135 observations whose final controllers are “legal person’s capital” and whose ownership nature thus cannot be determined.

3.2 Natural Experiment, “Observation Period” Method and Econometric Model

As an earlier study, Bai et al. (2006) employs corporate level data from “Database of Chinese Industrial Enterprises,” and introduces the time-difference variable of “whether reform has been carried out” into its econometric model for the first time to depict the dynamic change in corporate performance before and after reform. Li and Qiao (2010), Yu, et al. (2013), Chen and Tang (2014), Yu, et al. (2016) and Sheng and Liu (2016) further combine the grouping difference variable of “participation in reform” with time-difference variable to carry out a difference-in-differences study based on natural experiment. However, the difference-in-differences method does not completely apply to the topic of research in this paper, since such a framework cannot examine the interactive effect between natural monopoly and SOE reform performance. In order to test Hypotheses 1 and Hypothesis 3, this paper will further employ the difference- in- difference- in- differences ( DDD) method. DDD method is extensively applied in international studies (Gruber, 1994; Meyer, 1995; Yelowitz, 1995; Huttunen, et al., 2013; Garthwaite, et al., 2014; Chen, 2017), and Chinese studies using this method include Deng, et al. (2014), Fu, et al. (2015), Wang (2016), etc.

Ordinary DDD studies are all based on the framework of natural experiment with “unique experimental period (simultaneous policy impact).” For instance, in Garthwaite et al. (2014), the policy impact occurred during the US public medical insurance reform of 2005. In Huttunen, et al. (2013), the policy impact occurred during the EU reform of salary tax subsidy implemented on the New Year’s

Day of 2006. In Yelowitz (1995), the policy impact occurred during the US women’s medical insurance expansion program in 1991. In Gruber ( 1994), the policy impact occurred during the US Federal government’s labor insurance reform of 1978. The above studies have the following things in common: The subjects of experiment suffered uniform policy impacts that were experienced throughout the United States and the European Union. Most relevant Chinese studies are also based on natural experiments of unique experimental period. However, mixed ownership reform was carried out in different periods of time across various localities in China. Different enterprises implemented mixed ownership reforms in different periods of time as well. Hence, referencing the “observation period” method of Yu, et al. (2013), this study organizes experiment group samples with inconsistent experimental periods into natural experiment samples with approximately consistent experimental periods.

First, the entire time span is roughly divided into three segments: 2002- 2005 ( four years) is observation period of public policy experiment; 1998-2001 (three years) is pre-reform period; 20062008 (three years) is post-reform period. Such differentiation of time periods aims to test the difference of performance between experiment group and control group and before and after the mixed ownership reform.

In order to test Hypothesis 2, this paper conducts regression of natural monopoly samples and nonnatural monopoly samples in a mixture to investigate whether the results of mixed ownership reform are affected, and designs a difference-in-differences econometric model. is explained variable; is the grouping variable of whether samples participated in mixed ownership reform; time-difference variable is a dummy variable which denotes the time periods before and after mixed ownership reform; is unobservable individual fixed effect; is the fixed effect of year (dummy variable of year); is the fixed effect of sector (sector dummy variable), which controls the unobservable factors between various sectors; is stochastic disturbance term. Considering the impact of entity and time fixed effects, this paper introduces referencing Chen (2017), Sun, et al. (2017), Shi and Wang (2017), Shi and Yue (2016), Fu, et al. (2015), Garthwaite, et al. (2014), Jian (2013) and Lu, et al. (2013), and introduces sector fixed effect referencing Wang (2016).

If a firm carried out mixed ownership reform during 2002-2005, it is then defined as experiment group, and the value of grouping dummy variable is 1; samples which did not carry out mixed ownership reform during 1998-2008 are defined as control group, 03. The value of timedifference variable before 2002 is 0, and the value after 2005 is 1. is a difference-in-differences estimator, and if mixed ownership reform can increase corporate productivity, its regression effect should be significantly positive. The specific values of grouping and time-difference variables are as follows:

DDD econometric model is specified as:

is grouping variable for natural monopoly, and is 0 when the urban public utility sector in the city where samples are located is of natural monopoly. Otherwise, it is 1. This variable reflects the level of natural monopoly and competitiveness of the sector of a firm. Specific estimation is shown below. DDD estimator is the basis for the assessment of whether the experiment treatment (policy implementation) has any significant impact on the experiment dependent variable ( explained variable). Its regression coefficient is the experimental effect of experimental variable (DDD estimator) on the dependant variable (explained variable) of experiment group, i.e. the integrated policy effects of natural monopoly and mixed ownership reform. If regression result is significant, it suggests that as long as samples are in a non-natural monopoly state, mixed ownership reform will have a significant effect on the explained variable.

The above is a natural experiment design whose time of experiment is not unique. This paper marks such a DID/DDD econometric model based on “observation period” method as DID( 1) ( DDD( 1)). This paper assumes that the government is the experiment’s operator, and that the experiment started in 1998 and finished in 2008 (i.e. the time span of data samples). The government’s purpose in conducting such an experiment was to examine whether the experimental variable (mixed ownership reform) was able to affect the experimental dependant variable (TFP) 4.

In the statistical sense, if the time of mixed ownership reform is inconsistent, the natural experiment’s 0 may not be guaranteed. Hence, natural experiments whose experimental periods are not unique usually compare an experimental group with relatively consistent policy impact periods with a control group. Based on the DID/DDD econometric model of “observation period” method, this paper excludes the enterprise samples whose reform period is too distant (during 19982001) and those whose reform period is too recent (2006-2008). In this manner, this paper creates a natural experiment with approximately consistent experimental period (the reform took place during 2002-2005), so as to investigate whether the experimental variable (mixed ownership reform and natural monopoly) can influence the experimental dependent variable (corporate productivity).

3.3 Panel Data DID/DDD Econometric Model

In order to ensure the robustness of results, this paper employs panel data DID/DDD econometric model to conduct a robustness test. Mixed ownership reform is a gradual process. Each year, it is carried out by a different number of enterprises in the public utility sectors of various cities. Therefore, this paper employs panel data DID econometric model to examine different periods of corporate reform

referencing the method of Lu, et al. (2013), Yu, et al. (2013), Lu and Yu (2015), Sheng and Liu (2016): is DID estimator, and examines the fixed effects of entity, time and sector. The experiment group of equation (5) is the total samples which carried out mixed ownership reform during 1999-2008 (1998 as the initial year), and the value of its grouping dummy variable

is 1. Samples that did not carry out mixed ownership reform during this period of time are defined as control group, 0. If experiment group samples i conducted mixed ownership reform in year t0 , then = 1, = 0 and of remaining samples is specified as 0. We have: DDD model is then created: For DDD estimator , its regression coefficient is expected to be significantly positive. The above DID/DDD model is marked as DID( 2) ( DDD( 2)).

Compared with “observation period” method DID( 1) and ( DDD( 1)), panel data DID/DDD model DID( 2) / DDD( 2) has certain problems of heteroscedasticity and time-series autocorrelation. Introducing may control for the above problems and reduce the risk of spurious regression to some extent. respectively denotes three differential variables , and . Due to multi- collinearity problem, fixed effect and differential variable ( , , ) normally will not simultaneously enter into regression equation.

The pairwise interaction effects of correspond to ,

and , and are simultaneously introduced into regression equation5 as equation (4).

The pairwise combination effect of fixed effect cannot be neglected, since the regression coefficient of pairwise cross-multiplying term of double difference in DDD(1) has specific experimental significance.

Mainstream DDD studies have all considered the DID variable or the joint effect of pairwise combination, and the former is more common. Among Chinese studies, Wang (2016) attempted to control the fixed effect of pairwise combination, and excluded the differential variable of experimental grouping (time). In addition to entity and time fixed effects, the paper also includes the fixed effects of province, sector, etc. Time of experiment is also not unique for the natural experiment created by Fan and Peng (2017). The study also excludes experiment grouping variable, replacing it with sector fixed effect and adding entity fixed effect to partially avoid the multi-collinearity problem. Garthwaite et al. (2014) only retains the third differential variable while excluding experimental grouping and time differential variables and adding entity and time fixed effects, but only controls for the fixed effect of

pairwise combination. Take the variable names of this paper for instance, the independent variable of the DID model of Garthwaite et al. (2014) is , and its is the dummy variable of province (prefecture). The cross-multiplying term containing in this paper’s enterprise panel data model does not have very strong economic significance, and its matrix calculation is hard to process. Thus, it is replaced with sector fixed effect .

In summary, this paper has created a panel data DDD economic model, which is expressed as DDD( 3):

3.4 Core Variable Treatment

(1) Measurement of natural monopoly

is the output of firm i in year t ; is the price of type j production factor obtained by firm i in year tk ; is the number of types of input factor, and is the total cost of firm production. The size of regression coefficient determines the characteristics of production function and its dual production function. In order to ensure that the cost function is second order differentiable,

. In order to satisfy the cost function’s homogeneousness of degree one with respect to factor price vector (i.e. total factor price increases with total cost by the same proportion), we must ensure that

0, and use Shephard’s Lemma, as the condition of regression constraint. is the share of the consumption of type production factor in total cost.

Based on data availability and previous research experience, this paper assumes that firm production conforms to DID production cost, and that capital K (municipal infrastructure networks and relevant equipment, etc.) and labor L are the two basic input factors for the production of urban public utility firms, i.e. the value of k is 2. The trans-log cost function of the two factors will employ seemingly unrelated regression models (SUR) method (Zellner, 1965). Since the production functions of the public utility sectors of five cities should be different, the regression of cost function should be carried out by sector grouping.

According to Baumol et al. (1982, page 17), when a sector reaches a certain aggregate output Q, once corporate production cost function satisfies = 0 , the sector will have a strict “cost sub-additivity,” i.e. natural monopoly. Cost weak additivity and natural monopoly are mutually sufficient and necessary conditions6. is the artificially embedded share of the total output of separated monopolistic sectors. For the simplicity of calculation, ’s value is 0.5.

Natural monopoly is a sector’s indicator, and urban public utility enterprises generally will not

engage in cross-regional competition. Thus, in estimating , Q is the annual total output of a public utility sector of a city. In fitting C(Q), coefficient obtained from regression of equation (10) will be employed, and capital and labor prices are the average levels of a certain public utility sector of a certain city.

When a certain public utility sector of a certain city 0, the implication is that its production meets cost sub-additivity, i.e. sector of natural monopoly; 1 suggests that the sector is a competitive sector of non-natural monopoly. More detailed studies on the measurement of natural monopoly of trans-log cost function include: Christensen et al. (1975), Evans and Heckman (1984), Gilsdorf (1995), Wilson and Zhou (2001), Fraquelli et al. (2004), Chen and Liu (2014), Wang and Liu (2016).

From the following calculations, we may obtain the natural monopoly attribute of the power supply sector (4420) of 3,214 cities above prefecture level, heat supply sector (4430) of 1,517 cities, gas supply sector (4500) of 1,680 cities, water supply sector (4610) of 3,680 cities, and sewage treatment sector of 364 cities (4620). On average, we are able to estimate the natural monopoly attribute of 948 cities for each year. Thus, we create the grouping variable of natural monopoly:

(2) Measurement of corporate productivity

In order to comprehensively evaluate overall corporate productivity, the explained variable in this paper follows total factor productivity (TFP). According to the definition of TFP and economic growth accounting equation, when cost function is constant return to scale, ,where

is the growth rate of capital and labor factor inputs; are the shares of capital and labor factor consumption in total cost; is TFP and output growth rates. According to the cost function derivation of variable return to scale by Wu et al. (2015) and Zhang et al. (2016), we obtain TFP growth rate on the basis of variable return to scale in equation (10):

By obtaining from equation ( 10), we may arrive at in equation ( 12). is the return to scale parameter often employed in academic research. When is small than 1, firm production will be in a stage of increasing return to scale. Otherwise, it is in a stage of diminishing return to scale.

However, the regression of equation (10) has a certain problem of error term contemporaneous correlation. Even if seemingly unrelated regression method is employed for control, the possibility of robustness problem in estimating cannot be excluded. In order to better control for simultaneity and selection bias problems, this paper attempts to introduce the semi-parametric estimation method proposed by Olley and Pakes (1996) (“OP method” for short) to re-estimate the second explained variable and conduct robustness test.

Since the production function under OP method has a constant return to scale, the cost function in equation (10) is regressed into constant return to scale, and referencing Chen and Zhu (2017), we have:

is the current investment of firms, and denotes unobservable productivity. conforms to first-order Markov process , i. e. , and is stochastic productivity impact that conforms to first-order Markov process. Expected productivity of a future phase is a function of current-phase productivity and capital price . Thus, we may assume that there exists a productivity threshold : if firm productivity is above the threshold, the firm will opt to stay in the market. Otherwise, it will opt to exit the market.

The specifications of investment decision equation and survival probability equation are consistent with Olley and Pakes (1996). Specifically, firm investment decision-making is subject to productivity level and capital price in the current phase . Survival probability is fitted using Probit model , i. e. to obtain fitted value of probability . Given the lack of fixed asset investment indicator in Chinese Industrial Enterprises Database, our estimation is conducted based on . is the net value of fixed assets, and is current-phase depreciation.

is the productivity which can be observed by firms but cannot be observed by researchers, and is the productivity volatility and measurement error which neither firms nor researchers are able to observe. Hence, will not affect firm decisions, while will influence the current phase decisions of firms. is a second-order polynomial which contains for approximation. Equation (13) employs OLS estimation. Since semi-parametric polynomial controls for observable productivity volatility, the estimation of its regression coefficient has consistency.

In the next step, we will estimate the elasticity coefficient of capital price. After the estimation results of and survival probability are known, equation (14) is created. Specifically, is approximated using the second-order polynomial which contains and . Based on non-linear OLS estimation, we may obtain the estimated value of and TFP estimation equation (15). According to equation (15), the estimated value of is negative, i.e. 1. may also be construed as the level of firm inefficiency. The higher it is (greater absolute value), the less efficient the firm is, i.e. smaller .

4. Empirical Test 4.1 Treatment of Other Variables and Data Explanations

is the labor price facing firms. Labor input employs current-year total amount of payable compensation. Labor price equals divided by the total number of employees , i.e. average employee wage. is capital price facing firms. This paper adopts a variation of fixed capital similar to a variation of perpetual inventory method (Oum and Zhang, 1995), and takes into account depreciation factor (Jara-Dı́az et al., 2004). Determination of the above-mentioned two methods and referencing Chen and Liu (2014) and Luo and Ni (2015), we have:

Where, is the quantity of capital factor input (consumption). is total capital stock (including fixed capital and active capital), measured by the asset aggregate indicator in the database of industrial enterprises. is the net value of fixed assets, and denotes the fixed capital stock of firms. r is the benchmark interest rate for one-year time deposits at the beginning of the year released by the People’s Bank of China, and denotes the opportunity cost of capital. is current-year depreciation8. is the number of years for the depreciation of fixed assets. Referencing China’s relevant accounting standards,

is the minimum number of years for the depreciation of houses and structures, i.e. 20 years. is current assets, and is inventory. Benchmark deposit interest rate data for estimating capital price is from the official website of the People’s Bank of China (China’s central bank).

Firm production cost . According to the cost category of industrial firms in the NBS Industrial Statistical Statement System ( manufacturing cost, inventory at the beginning of year, sales cost, management expenses, etc., without considering financial cost, etc.), the value is the sum of capital input , labor input , cost of primary business, inventory, sales cost and management cost.

Firm output is the physical output of municipal firms excluding the impact of product price, i.e. product sales revenue of products divided by the price of public utility products in the city. Household electric power consumption of 35 cities including provincial capitals in China Price Yearbook of 19992008 (yuan/kWh), natural gas (yuan/m³), pipeline gas (yuan/m³), household domestic water (yuan/m³, excluding sewage treatment cost) and sewage treatment cost (yuan/m³) are the prices of power supply, heat supply (natural gas price is used due to missing data), gas price, water supply and sewage treatment prices . Since China Price Yearbook of 1998 is not yet published, estimation is conducted using the price of 1999 for the same year deducting inflationary factor. Due to missing data, except for big cities such as Shenzhen, Xiamen, Dalian and Qingdao whose data is published in China Price Yearbook, the price data of other prefecture-level cities is the prices of provincial capitals. Without differentiation between industrial and civil prices of municipal products, product prices cited are civil prices. In 1999, sewage treatment cost and municipal water supply cost were not yet separated, and data of various localities was missing. Thus, estimation is carried out using the proportion of domestic water and sewage treatment cost for the same city in 2000. Household water tariff of Shenyang City for 2001-2003 is missing, and replaced with composite water tariff. Data not published in China Price Yearbook of 2007 and 2008 is replaced with year-end data provided by the Monitoring and Analysis Division of the Price Department of the National Development and Reform Commission (i.e. data source of China Price Yearbook).

Various capital stocks and depreciations are deflated by the fixed asset investment price index in various statistical yearbooks with 1998 as base period. In addition, monetary index variable is deflated by the ex-factory price index of industrial goods in the statistical yearbooks of various years. Refer to the working paper edition for variable statistical characteristics and relevant analysis.

This paper has 15,000 valid samples. After PSM, there are still around 2,000 samples in the experiment group and control group, which guarantees sample capacity. In 1998, only 171 out of 4,696 firms participated in mixed ownership reform, accounting for only 3.6%. With the advancement of mixed ownership reform, this proportion kept increasing year by year. By 2007, the number of

experiment group samples reached 864, accounting for 18.1% of total samples in the year, which more than doubled compared with 1998. Obviously, China’s economic reform was carried out with significant intensity during this period of time. Mixed ownership reform was carried out with the greatest intensity for gas supply sector, with the share of experiment group samples increasing from 13.1% in 1998 to 46.7% in 2007. About half of enterprises became mixed ownership enterprises. The experiment group samples of heat supply sector increased from 8.2% in 1998 to 35.4% in 2007, ranking the second. Then, the experiment group of sewage treatment sector increased from 7.7% in 2003 (all mixed ownership enterprises were established in 2003) to 29.6% in 2007. The experiment group of water supply sector increased from 3.4% in 1998 to 13.4% in 2007. Reform was carried out with the least intensity for power supply sector, whose experiment group samples increased from 1.7% in 1998 to only 3.9% in 2007.

Mixed ownership reform was carried out with the highest intensity in 2005, involving 1,025 enterprises. After 2005, however, reform encountered some resistance. During 2006-2008, samples that carried out reform reduced to 721, 694 and 764 respectively. Prior to 2005, the intensity of reform increased with volatility, up from 260 enterprises in 1999 and 190 enterprises in 2000 to 353 in 2002, 550 in 2003 and 544 in 2004.

In terms of capital structure, the annual average share of state capital in power supply and water supply sectors both accounted for over 80% in 2004 (state capital of all sectors divided by total capital); the shares dropped to 91.0% and 94.3% respectively in 1998, and started to decrease at a rapid pace after 2004, down to 75.7% and 67.8% respectively in 2008. Capital structure also shows that mixed ownership reform was carried out with greater intensity for heat and gas supply sectors: In 1998, their sector-wide share of state capital was 87.6% and 94.3% respectively. During 1998-2003, the shares decreased by 19.7 and 33.7 percentage points respectively in the five years from 1998 to 2003. After 2004, the average share of state capital further reduced to 44.6% and 29.9% respectively in 2008, and continued to reduce by 23.4 and 30.7 percentage points in the following five years.

4.2 Cost Function Regression and Core Variable Report

Refer to Table 1 for the cost function regression of equation (10) and equation (14). Econometric equation has a high goodness-of-fit, and regression coefficient is generally significant. Firm cost can be well fitted.

of public utility sectors in five cities is all greater than , which suggests that its sensitivity to production cost and labor price volatility is not strong, and that capital price hike has a major impact on corporate cost. This shows that municipal pipeline construction requires tremendous sunk cost, and involves significant economies of scope. Thus, the public utility sectors of five cities are all typical capital-intensive sectors.

Using regression coefficient of Table 1, we obtain the specific form of the cost function of urban public utility sectors in five cities, so as to calculate differential variable using equation (11), equation (12) and equation (15) respectively. Results of calculation are shown in the working paper edition.

As can be seen from the temporal trend of , the number of urban public utility sectors with natural monopoly shows a downward trend, down from 569 in 1998 to 462 in 2008. This is consistent with the mainstream views of academia: With the improvement of market-based economic system, production sectors with natural monopoly will reduce, and market competitiveness will increase gradually (Qie, 2002; Yu and Yu, 2004). In terms of sector distribution, power supply sector had the highest ratio of natural monopoly, i. e. 100%, and sewage treatment sector had the lowest ratio of monopoly, i.e. 13%. The ratio for water supply sector is the second-lowest, i.e. 27%, and heat and gas supply sectors had medium ratios of natural monopoly, i.e. 60% and 51% respectively. The proportions of natural monopoly samples for the latter four sectors reduced over time.

This paper obtains the natural monopoly grouping variable based on the criterion of

whether or not firm samples are in sectors of natural monopoly. Result shows that the natural monopoly samples have 0 similar distribution ratios at the level of urban sectors. The level of natural monopoly diminishes in the order of the sectors of power supply, heat supply, gas supply, water supply and sewage treatment.

Among the 10,425 urban public utility sector samples during 1998-2008, 6,003 are sectors of natural monopoly, but power supply sector accounts for the biggest share of natural monopoly. The natural monopoly attribute is insignificant for urban public utility sectors including heat supply, gas supply, water supply and sewage supply sectors. For these sectors, more cities are of non-natural monopoly, but cities of natural monopoly also exist.

Municipal public services of different cities and sectors have different natural monopoly attributes. Therefore, sector management must be carried out according to the specific conditions of various localities and sectors. Overlooking the natural monopoly attributes of specific public utilities sectors

will harm the efficiency of their regulation and management and jeopardize relevant economic reforms.

After estimating the regression coefficient of cost function , variables of firms such as are substituted using equations ( 12) and ( 15) to calculate at the firm level, which is shown in Figure 1. The “semi-parametric method TFP” sequence in Table 1 is the annual mean value of

. The “semi-parametric method TFP growth” is the mean value of growth rate, and “TFP growth rate” is the mean value of .

TFP growth rate of firms in urban public utilities sectors reduced at first and then increased. This finding is consistent with the manufacturer estimation result of Yang (2015). In general, the growth rates of estimated using cost function with variable return to scale and estimated using cost function with constant return to scale share a consistent time trend. From the perspective of TFP estimation, this study is an innovative attempt to c ompletely exclude product price effect.

4.3 DID Regression Result

According to DID econometric models of equations (1) and (2), Table 2 provides the test result of the correlation between mixed ownership reform and TFP. Line 3 of Table 2 shows that the regression result estimated using DID method is not robust. The model regression result with 2002- 2005 as observation period shows that mixed ownership reform has a certain positive effect on experiment group samples, but such an effect is insignificant (such as Columns 2-3). In Model DID( 2) with total sample participation, the policy effect of mixed ownership reform is not robust as well, and can be negative.

Causality between mixed ownership reform and TFP is statistically insignificant. Therefore, enterprises having completed mixed ownership reform may not necessarily improve their production efficiency. This finding is consistent with Hypothesis 2 that without differentiation between sectors of natural monopoly and competitive sectors, mixed ownership reform will not be able to significantly improve corporate production efficiency. In the real sense, indiscriminate mixed ownership reform for urban public utility sectors irrespective of natural monopoly attribute is subject to uncertain institutional performance. At least, it is not good for social production efficiency.

Hence, Hypothesis 2 is verified. The fundamental reason for Hypothesis 2 to hold true is that the grouping variable of natural monopoly has a critical effect on regression as a whole. Only by separating the natural monopoly attribute and competitiveness of sectors will this paper be able to accurately capture the policy effect of mixed ownership reform for urban public utility sectors.

4.4 DDD Regression Result

According to the DDD regression result in Table 3, DDD regression has improved the significance

of some explanatory variables, and the regression goodness- of- fit has also improved to some extent. This study is most concerned with DDD estimator . 1 is the urban public utility enterprise of non-natural monopoly which participates in mixed ownership reform, and its regression coefficient is the policy effect of mixed ownership reform in urban public utility sectors of nonnatural monopoly.

National monopoly has a significant influence on corporate TFP. First, in Model DDD( 1), once the natural monopoly attribute is not considered, the aggregate productivity improvement effect for the experiment group samples is relative to urban public utility enterprises which have not participated in the mixed ownership reform, i.e. reform will lead to approximately an additional -0.01 unit of TFP growth rate and about 0.24 units of TFP growth for experiment group samples. Second,

’s regression coefficient is significantly positive. Namely, a city’s public utilities sector being a competitive sector of nonnatural monopoly will significantly increase the city’s productivity. Third, with the improvement of market economic system, the efficiency losses caused by natural monopoly will diminish, as ’s regression coefficient is significantly negative. It can be learned based on that natural monopoly during 1998-2001 would cause 0.07 units of TFP growth loss of enterprises and about 0.27 units of TFP loss. During 2006-2008, such losses reduced to about 0.05 and 0.15 units respectively.

Based on the above analysis and the result that DID estimator is relatively insignificant and not robust, this paper considers that Hypothesis 1 is verified: In urban public utility sectors of natural monopoly, mixed ownership reform cannot significantly increase corporate productivity.

Consistent with Hypothesis 3, Table 3 shows that is all positive value and generally significant. The implication is that China’s mixed ownership reform during 1999-2008 has exerted a significant positive effect on competitive urban public utilities sectors of nonnatural monopoly and increased the TFP of municipal service enterprises.

’s aggregate effect on TFP is . Natural monopoly will cause additional 0.12 units of TFP growth rate of experiment group samples during 2006-2008 and about 0.21 units of TFP losses. In competitive sectors free from natural monopoly, mixed ownership reform has a significantly positive effect on the productivity of municipal public utility enterprises.

obtained based on Model DDD( 2) is also significantly positive. Thus, Hypothesis 3 is proven. Relative to sectors of natural monopoly, mixed ownership reform has a greater improvement effect on TFP and its growth rate in competitive sectors ( 0). In sectors of natural monopoly, mixed ownership reform led to about - 0.07 units of TFP growth rate and about 0.04 units of TFP growth ( ). In competitive sectors, mixed ownership reform brought about approximately 0.05 units of TFP growth rate and about 0.25 units of TFP growth (

).

Therefore, the positive effect of mixed ownership reform on corporate productivity mainly occurred under a competitive market structure rather than in sectors of natural monopoly. In other words, if competitive sectors carry out mixed ownership reform, the productivity of urban public utility enterprises will be greatly increased, unleashing more “policy dividends” of institutional reform.

Refer to Table 4 for the regression result of DDD model of panel data. Irrespective of whether or not the fixed effect of pairwise combination is controlled for, the regression coefficient of is all positive, i.e. mixed ownership reform will increase productivity in competitive sectors. Relative to the improvement effect of TFP , the improvement effect of its growth rate is not very significant. Refer to Column 2-3 of Row 3, Table 4.

5. Robustness Test 5.1 Further Causality Identification and Propensity Index Matching Method

The government will take into account the size and tax burden of enterprises in selecting the priority targets of reform. While the former involves reform difficulty and social stability issues, the latter is a matter of reform intent. Therefore, this paper identifies physical output, industrial valueadded, cost of primary business, payable income tax, payable VAT, government subsidy and amount of losses as characteristic variables9 to conduct core matching for the Gaussian kernel functions of experiment group and control group, with results shown in the working paper edition. After PSM treatment, all characteristic variables and standardization errors are smaller than 5% for the new control group and experiment group samples, and t test result basically does not reject the null hypothesis that the experiment group and control group have no systematic differences. This implies that after PSM treatment, sample heterogeneity of different groups has substantially reduced, which is of significant help to establishing the “counterfactual framework.”

After conducting a more stringent causality identification through PSM, Table 3 and Table 4 list relevant results. PSM- DDD( 1)’s regression result is generally consistent with previous result. In addition, the aggregate effect of on TFP growth rate becomes more evident (

), i.e. approximately 0.17 units of TFP growth loss. Compared with DDD( 2), despite a reduction in the observations of PSM-DDD( 2), the t statistic of its DDD estimator regression coefficient further increased, and the policy effect of mixed ownership reform is more significant.

Based on causality derivation of equation (18) and robustness test, this paper believes there is statistical causality among mixed ownership reform, natural monopoly and the TFP of urban public utility enterprises consistent with Hypotheses 1-3.

5.2 Change of Observation Period

In order to further test robustness, this paper shortens (prolongs) the observation period of reform into 2003-2004 (2001-2006), and conducts a test using DDD( 2) model. The test result is still generally consistent with the above, with the result shown in working paper edition.

5.3 Examination of Reform Performance on Other Dimensions

Dimensions for measuring policy gains are varied, since the same policy may have different dimensions of “policy dividends.” Therefore, this paper selects different operational performance indicators as criteria for evaluating the results of mixed ownership reform. Referencing the definition of Sheng and Liu (2016) on SOE performance, this paper selects sales profit margin (profits divided by income from primary business), share of management expenses (management expenses divided by income from primary business), labor productivity ( physical output divided by the number of employees), capital productivity ( physical output divided by total capital stock), as well as other corporate performance indicators as explained variables to examine the corporate business improvement effect of mixed ownership reform.

Regression results show that under the effect of natural monopoly, mixed ownership reform’s corporate performance improvement effect is significantly differentiated for various urban public utility sectors. Relative to sectors of natural monopoly, mixed ownership reform in a competitive market structure plays a bigger role in improvement of corporate profitability, share of management expenses, labor productivity and capital productivity. Thus, it can be learned that the positive effect of mixed

ownership reform on corporate performance occurs primarily under a competitive market structure, rather than in sectors of natural monopoly.

Except for the share of management expenses, the performance of DDD( 1) model with sales profitability, labor productivity and capital productivity as explained variables is not robust. This implies that reform may not directly improve financial indicators such as corporate labor productivity, capital productivity and sales profitability. Instead, reform should reduce redundant management expenses and improve corporate governance structure to indirectly improve productivity. Regression result 0 shows that mixed ownership reform will increase the share of management expenses for samples of natural monopoly sectors. It can be deduced that in less competitive sectors of natural monopoly, mixed ownership reform will not lead to any improvement in corporate governance structure.

6. Concluding Remarks

“Crossing the river by feeling your feet on the stones” is a concise summary of China’s institutional transformation since reform and opening-up. From the nationalization and planned economic system at the beginning of the founding of the People’s Republic of China in 1949 to the household contract responsibility system at the inception of reform and opening-up and the creation of market economic system in the 1980s, China’s institutional transformation has always been intermittent. From the perspective of institutional change, such an intermittent institutional change is fraught with more significant uncertainties of economic performance compared with a gradualist institutional change. Performance change arising from abrupt institutional change is often more surprising, but this seems to have become key to the success of China’s rapid growth over three decades. In its reform endeavors never experimented before, China has explored a unique path of its own. While the old system increased in size, each individual institutional reform addressing specific issues naturally had diminishing marginal return.

For urban public utility sectors and sectors of natural monopoly, the Third Plenum of the 18th CPC Central Committee attempted to introduce a fundamental change and designed a complete new system. State capital must maintain controlling shares in sectors of natural monopoly. Their mixed ownership reform must be carried out with caution. The priority targets of mixed ownership reform should be competitive sectors of nonnatural monopoly. However, since the proposition of mixed ownership reform in the 1980s, academic discussions have long focused on the necessity of reform without addressing the question as how reform should be carried out. This paper aims to address the question as how mixed ownership reform should be carried out in sectors of natural monopoly - an important theoretical and realistic question facing China’s current institutional reform, with a new approach of discourse that ownership reform cannot be carried out for ownership reform’s sake.

On the other hand, monopoly and competition have always been classical topics of discussion in economics. For natural monopoly as a special form of monopoly, mixed ownership reform should be well included into the framework of natural monopoly theory. This paper marks such an attempt.

Our key findings are as follows: 1) In urban public utilities sectors of natural monopoly, mixed ownership reform cannot significantly increase corporate productivity; 2) without differentiation between natural monopoly and competitive sectors, traditional DID econometric model will not be able to test the significant effects of mixed ownership reform, which means that indiscriminate implementation of mixed ownership reform is likely to be fraught with policy uncertainties; 3) in competitive sectors of nonnatural monopoly, mixed ownership reform has a significant positive effect on the productivity of municipal public utility enterprises. Relative to sectors of natural monopoly, the productivity of competitive sectors of the mixed ownership reform will be increased much more significantly with greater “policy dividends” of institutional reform. Therefore, the mixed ownership reform of urban public utility sectors

should be carried out first in competitive sectors of nonnatural monopoly.

Determining the natural monopoly attribute of specific public utilities sectors in specific cities is key to the implementation of mixed ownership reform. The accuracy and openness of cost data, which is the basis for such determination, are vitally important. Hence, this paper puts forward the following policy recommendations: The cost data of urban public utility enterprises must be made open to government departments. Such openness should be facilitated by recent legislative work. The departmental rule Administrative Measures for Infrastructure and Public Utility Licensed Operations enacted in 2015 stipulates that relevant information such as audited financial statements of the previous year should be made public in accordance with relevant provisions. This legislative approach is similar to the mandatory information disclosure clauses of price regulation agreement in the Price Regulation Agreement executed by the Government of Hong Kong Special Administrative Region with fuel gas supply enterprises over the years (“Information and Consultation Agreement”), which is a fairly advanced government regulatory rule. This paper considers that the Regulations on the Licensed Operations of Municipal Public Utilities currently under the State Council’s legislative process should put greater premium on the openness of cost data.

In the final analysis, mixed ownership reform cannot be carried out indiscriminately for public utility sectors which are of great relevance to public interest and welfare. Relevant institutional reforms should follow the “top-level design” approach of the Third Plenum of the 18th CPC Central Committee. Similarly, mixed ownership reform in other sectors should also be carried out in other sectors with specific priorities.

Nevertheless, this paper still has many deficiencies. For instance, such public utility sectors as waste treatment and landscaping are not brought under analysis due to lack of data. Data of 2009-2013 is not brought under analysis in this study due to poor quality of data. This paper is expected to serve as an initial study to inspire supplementary studies in the future.