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RETRACTED: Measurement and analysis of the distortion of factor prices in China

Retraction

After this article [1] was published, concerns were raised about potential manipulation of the publication process. Specifically:

  • The study reported in [1] appears similar to previously published work [2] (citation #44 of [1]); datasets (both data sources and timeframe of data collection), variables and methodology reported in [1], appear similar to [2], although the reported quantitative data are different.
  • The articles cited as References 2, 11–16, and 35 in [1] appear to be irrelevant to this article [1].
  • There are errors in the DOIs for References 17–19 of [1], and Reference 25 of [1] is a duplicate of Reference 20 of [1].
  • The PLOS One Editors identified concerns about the article’s peer review.

PLOS consulted a member of the PLOS One Editorial Board who advised that the contribution of [1] compared with [2] is insufficient to warrant a separate publication and the single reference to [2] (citation #44 in [1]) is insufficient to place the work in context. They also stated that the above references of concern (citations #2, 11–16, and 35 of [1]) did not appear to support the corresponding text.

The consulting Editorial Board Member also advised that there are issues in the reporting of the methodology used in [1]. Specifically, they noted that there is a lack of detail in the description of the panel data and how to access the data source, and that the limitations of the regression models used and the observed results require further discussion in relation to the statistical methodologies employed.

The authors of [1] did not respond to any communications from PLOS regarding the similarity with [2] or follow-up queries.

In light of the above cumulative unresolved concerns, the PLOS One Editors retract this article. We regret that the issues were not identified prior to the article’s publication.

All authors did not agree with the retraction.

4 Nov 2025: The PLOS One Editors (2025) Retraction: Measurement and analysis of the distortion of factor prices in China. PLOS ONE 20(11): e0335970. https://doi.org/10.1371/journal.pone.0335970 View retraction

Abstract

This study uses the extended C-D production function method to measure the total distortion of factor prices and the distortion of capital, labor and land factor prices in China’s provinces and cities. The results indicate that between 2000 and 2019, due to factors such as the dual economic structure between urban and rural areas, human intervention in the capital market, and lagging land marketization reform, both capital and land factor prices showed negative distortions, except for positive distortions in labor factor prices. The degree of this positive distortion began to gradually weaken, and even showed a negative distortion trend in some regions.

Citation: Lan G, Li S (2024) RETRACTED: Measurement and analysis of the distortion of factor prices in China. PLoS ONE 19(7): e0302825. https://doi.org/10.1371/journal.pone.0302825

Editor: Jabbar Ul-Haq, University of Sargodha, PAKISTAN

Received: July 5, 2023; Accepted: April 10, 2024; Published: July 23, 2024

Copyright: © 2024 Lan, Li. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant data are within the paper and its Supporting Information files.

Funding: This work has been supported by the Hunan Provincial Social Science Fund (Grant No: 23JD063). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

1. Introduction

Since the reform and opening up, China’s economic development has achieved remarkable results, with an average annual GDP growth rate of about 9.08%. The gross domestic product (GDP) has increased from 367.87 billion yuan in the early stages of reform and opening up to 121 trillion yuan in 2022. The proportion of the total economic output to the global economy has increased from 2.3% to 18%. The speed, scale, and duration of economic development have attracted widespread attention from the world, making it a "miracle of the Chinese economy" [1–3]. So, what created this Chinese economic miracle? Scholars usually analyze from the aspects of market economy, demographic dividend, import and export trade, urbanization, social stability, etc. Since 1978, China has taken a series of measures to adjust its material interests. For example, implementing progressive reforms. Among them, price reform, as a key step in progressive reform, has undergone three stages of reform: the planned price system as the main body, the mixed price system as the dominant force, and the establishment of a socialist market price system. As a result, the degree of marketization of Chinese products has significantly improved, and the price determination mechanism in the market has been basically established [4–6].On the one hand, micro level reforms have overcome the issues of non autonomy in management and incentive constraints, fully unleashing the previously suppressed market vitality in China’s social economy [7], On the other hand, it minimizes unnecessary transaction costs and promotes the improvement of socio-economic efficiency. Therefore, market-oriented reform is an important reason for achieving long-term high-speed economic growth in China. Although China’s gradual reform has achieved great success in promoting the growth of social wealth, the existence of path dependence in economic development has also exposed a series of drawbacks, with distorted factor prices being an important example [8, 9].Compared with the successful reform of product price marketization, the degree of marketization of factor prices in China is clearly insufficient, with prominent issues such as factor market segmentation, factor flow barriers, and factor price distortion between regions and industries [10]. From the perspective of factor market segmentation, China’s registered residence system forms a labor market segmentation, which leads to the failure of labor remuneration to follow the principle of equal marginal remuneration and marginal output in neoclassical economics, resulting in distortion of labor prices [11, 12]. From the perspective of factor industry segmentation, state-owned enterprises face ownership discrimination due to their monopoly advantage. Therefore, compared to non-state-owned enterprises, they are able to obtain the required capital at prices lower than the market, which damages the efficiency of capital allocation and worsens the negative distortion of capital.

Based on this, it is necessary to study the calculation and analysis of factor prices in China. From the perspective of economic operation, the distortion of factor prices in China is mainly manifested in traditional production factors such as capital, labor, and land. Among them, the central government mainly controls capital prices, local governments mainly affect land prices, and labor prices are mainly determined by the supply and demand of the labor market [13–15]. However, the degree of distortion in the labor market is also quite severe, mainly manifested in the disadvantaged position of workers in the labor market [16]. Therefore, it is necessary to further increase the intensity of market-oriented reform, remove institutional barriers and constraints that hinder the effective allocation of production factors.

2. Literature review

Economic theory posits that economic laws determine factor rewards and achieve efficient resource allocation through the price mechanism. Additionally, it is believed that markets, under conditions of perfect competition, can automatically achieve equilibrium, where the demand and supply for goods and factors are met, and resources are optimally allocated through the price mechanism. Thus, in a perfectly competitive market, there is no distortion, and therefore no such issue as distortion exists. However, in actual economic societies, it seems that there are few markets that are completely competitive without monopolies, externalities, or government intervention, and distortion becomes an economic norm. When factor markets are distorted under conditions of imperfect competition, the prices of production factors do not reflect the relative scarcity of resources under the particular supply and demand mechanism, leading to the inability to optimize factor resource allocation in the process of economic development, and a deviation occurs between factor prices and marginal outputs. Scholars generally define this deviation as factor price distortion(Bhagwati,1969)[17, 18]. In the course of research, the measurement of factor market distortions involves assessing the extent of price distortions of various factors within the factor market [19, 20]. In this context, distortions can be categorized into negative and positive distortions based on the varying relationships between factor prices and marginal outputs. Negative distortions are defined as those instances where the marginal output of a factor exceeds its price, while positive distortions are those where the marginal output of a factor is less than its price [21–26]. Based on the distinct objects, factor price distortions can be summarized into two categories: relative and absolute distortions. The deviation between the marginal product of a factor and its actual factor price is defined as the absolute distortion of factor prices, while the ratio of the absolute distortions of two or more factors is termed as relative distortion [27, 28]. From an empirical analysis perspective, investigating the potential impacts of factor price distortions on various aspects of the socio-economic system, the first issue to be addressed is how to quantitatively measure the extent of factor price distortions. Regarding the quantification of factor price distortions, notable differences exist among scholars in the selection of measurement methods. Most existing literature is based on the fundamental assumption that factor price distortions already exist in a market economy [29, 30]. Upon reviewing the relevant literature, it has been observed that both domestic and international scholars primarily employ production function methods, frontier technology analysis, and shadow price approaches to assess the degree of factor price distortion at the regional or national level [31, 32]. In the realm of production function methods, the most commonly used production functions include: the Cobb-Douglas production function (C-D), the translog production function, the time-varying elasticity production function, and the substitution elasticity production function. Each method has its own distinct advantages and limitations. For instance, foreign scholars employed the C-D production function method to analyze the total factor productivity (TFP) in China and India, assessing the impact of non-economic factors on the efficiency of factor misallocation in both countries (Peters, 2020) [33]. Chinese scholars have separately measured the degree of distortion in factors such as capital, labor, and land input in agriculture and industrial enterprises. They argue that in the long run, the factor shares in China have relative stability. However, there is a certain degree of distortion in all factors, whether capital, labor, or land, with the degree of distortion being higher for the land factor (Li et al.) [34]. In comparison to the production function approach, the translog production function method does not rely on strict unit substitution elasticity assumptions, minimizing the potential errors in estimation. Consequently, in recent years, this method has been increasingly employed by scholars both domestically and internationally in the measurement of factor price distortions (Saabneh & Tesfai, 2021) [35]. The time-varying elastic production function method differs from the traditional production function method. The primary difference in measurement arises from the fact that the output elasticity varies over time. Compared to fixed constants, this approach more objectively and genuinely reflects the changes in factor income shares over time. The aforementioned production function methods, the Translog production function, and the time-varying elastic production function all fall under the category of direct measurements. In contrast, the substitution elasticity method represents an indirect measurement approach. Its measurement principle differs from direct methods, primarily by utilizing factor substitution elasticity to assess marketization levels, which in turn are related to the extent of factor price distortions. In terms of frontier technical analysis methods, Mundlak (1970) was the first to introduce and develop the stochastic frontier analysis function model, which includes parametric stochastic frontier analysis and data envelopment analysis [36]. Subsequently, scholars employed unbalanced panel data at the firm level to investigate the distortion levels of input factors and technologies in agricultural sector firms. This distortion was further summarized into two types: allocation distortion in product markets and technical distortion in factor markets (Kopp & Diewert, 1982) [37]. Chinese scholars have employed parametric stochastic frontier analysis with industrial enterprise data to estimate the factor distortions within manufacturing firms. They argue that while the extent of factor price distortions within Chinese manufacturing firms has decreased, the issue of distortions remains prevalent. Additionally, data envelopment analysis is a frontier technical analysis method based on linear programming. Its measurement principle involves calculating the minimum convex envelope to achieve a measure of factor input and output distortions. For instance, some scholars have utilized data envelopment analysis to explore the microeconomic perspectives of the factors marketization reforms lagging in China during the process of opening up, which leads to barriers in factor flow and negative price distortions between industries and regions, subsequently impacting resource allocation efficiency and macroeconomic stability. They suggest that accelerating factor marketization reforms, reducing administrative interventions, and promoting free factor flows can improve China’s resource allocation efficiency and elevate the overall level of societal welfare [38, 39]. In the context of the shadow price method, its analytical principle is that resource allocation can automatically achieve equilibrium under the conditions of a free competitive market and the mechanism of price. Based on the aforementioned principle, it can be inferred that the shadow price method is used to estimate the deviation between the shadow price and the actual price in a free competitive market, thereby measuring the degree of distortion in factor prices [40]. Based on different estimated functions, the parameterized shadow price method can be categorized into the shadow profit function approach and the shadow cost function approach. Distinct from the production function method and the frontier technology analysis approach, the greatest advantage of this method is its ability to decompose and measure the price distortion levels of various factors through a parameterized approach, providing a more detailed analysis of the intrinsic factors behind the distortion. For instance, foreign scholars applied the shadow profit function approach to analyze the price distortions of capital, labor, and energy inputs in the US airline industry. They concluded that, compared to capital and labor factors, energy elements are more prone to having their allocation ratio on the low side under the background of factor price distortions [41–43]. Based on the generalization of cost models, Chinese scholars have investigated the impact of factor market distortions on economic efficiency. They argue that labor compensation in China is generally underestimated, while the compensation for capital and energy factors is artificially inflated [44–46]. Additionally, besides the aforementioned measures of price distortion, other methods include: model approaches, indicator decomposition methods, and benchmarking analysis.

According to the above analysis, the research results of scholars have discussed the causes of factor price distortion from different angles, as well as the advantages and disadvantages of different calculation methods, which has important theoretical reference for this paper to calculate the degree of factor price distortion in China. Different from the research of other scholars, the innovations of this paper are as follows: first, in terms of the calculation of the degree of factor price distortion, the existing studies rarely include capital, labor and land factors in the same production function for analysis. This paper includes land factors in the model, which helps to measure the contribution of various factors to total output more comprehensively and improve the accuracy of parameter estimation; Second, after comparative analysis, this paper uses the extended C-D production function method on the basis of the traditional Cobb Douglas production function to calculate the degree of factor price distortion in China, and analyzes the possible reasons for the distortion, and puts forward relevant policy suggestions.

The structure of this paper is as follows: the second part discusses the possible reasons for the measurement bias caused by previous measurement models; The third part introduces the model construction, variable description and data source of this study in detail; The fourth part calculates and analyzes the factor price distortion based on the content of the third part, and explains the relevant conclusions; The fifth part draws conclusions and gives relevant policy implications.

3. Theoretical analysis

Through sorting out the relevant studies of scholars at home and abroad, we can find that although the definition of factor price distortion is very simple and the relevant calculation methods are not complex, there are great differences in the calculation results due to various reasons. This paper believes that the possible reasons for this deviation include the following two aspects in addition to the defects of the measurement model itself.

First, the form of production function set in the process of calculation and the corresponding selection of factor input and output. The form of C-D production function is direct and relatively simple, but there is a strong assumption that the sum of unit output elasticity of capital and labor factors is 1, which makes the calculation results possibly biased. Therefore, many scholars will choose to calculate through the improved time variant elastic production function in practical research, but the time variant elastic production function may also have metrological defects such as significant multicollinearity between variables and insufficient model freedom due to too many estimated parameters, resulting in the problem of unable to measure effectively. For example, some scholars have quantitatively analyzed the relationship between industrial structure and factor price distortion through the three-factor time varying elastic production function model including energy factors, and concluded that the marginal output of labor is negative [34, 47, 48]. However, this conclusion is obviously inconsistent with the reality of China’s economic development. In addition, some scholars have made a comparative analysis of the time-varying elastic production function and the C-D production function respectively, and believe that in the calculation of factor price distortion, the results will be significantly different due to different model selection, so it is a rigorous behavior to adopt appropriate estimation methods [49, 50]. In the calculation and research of the price distortion of internal factors in the secondary industry, should output (y) be expressed by industrial added value or industrial output value? Should capital (k) be expressed in the net value of fixed assets or the original value of fixed assets? The choice of variable representation will lead to great differences in the estimation results. For example, some scholars express output (y) as gross industrial output and capital (k) as the original value of fixed assets when calculating the degree of distortion of capital factor prices, thus drawing the conclusion that the marginal output of capital is greater than 1, but if calculated by means of interest expenditure/liabilities, it will be found that the price of capital is actually less than 1. In order to make the research conclusion more credible, the author has to add 1 to the price of capital to explain it as the input consumption of capital itself. It is difficult to find the corresponding economic theory to support the absolute distortion of capital prices.

Second, the statistical caliber, processing method and data source of factor prices. In theory, capital price is the transaction cost of market participants when using funds, so compared with the statutory loan interest rate of national financial institutions, capital price should not be lower than its minimum interest rate level. Through the search of literature at home and abroad, this paper believes that Schneider and Schisler (1995) may be the first scholars to calculate capital prices by means of interest expenditure/debt. They use the cross section data of different economic types of enterprises to calculate capital prices, and the average capital price results of enterprises are acceptable, but there are large deviations in the relevant research results of different students [51]. For example, some scholars use panel data or time series data to calculate the capital price is significantly lower than the statutory loan interest rate of financial institutions, and even some research conclusions are lower than the deposit interest rate in the same period [50, 52, 53]. Later scholars also found this problem in their research, using compromise or twice elimination to correct the deviation of capital price calculation results: when the value of interest expenditure/liability is greater than 0.05, the value represents capital price; When the value of interest expenditure/liability is less than 0.05, the average value of loan interest rates of various ownership enterprises over the years is used to improve the rationality of the conclusion of capital price calculation, but whether it is a compromise method or a method of twice eliminating outliers in the final results, there may be insurmountable information loss problems [54]. When measuring the degree of labor price distortion, the labor wage level should correspond to the labor input to measure the marginal output of labor. In practical research, for the calculation of the degree of labor price distortion in the same industry, the corresponding situation between the wage level and the amount of labor input is better, but the problem is relatively prominent in the calculation of the degree of factor price distortion in the whole national economy. For example, some scholars choose labor input as the total number of employed people in the whole year and labor wage as the average annual wage when calculating the degree of factor price distortion of the whole national economy [53, 55, 56]. According to relevant data, it can be found that the total number of employed people in the whole year includes not only ordinary on-the-job workers, rural employees, urban unit employees and other employees, but also private business owners and individual business heads; The average wage only represents the average annual wage of employees in urban units, so the value is significantly higher than the average wage of the total number of employed people in the whole year. Through the above analysis, it is found that the difference of measurement caliber in the process of empirical research may cause the scientificity of the calculation results to be questioned.

4. Econometric model setting and variable explanation

4.1 Measurement model setting

From the above analysis, it can be seen that among the various methods for measuring factor price distortion, the production function method is widely used by scholars at present. Among them, Cobb Douglas (C-D) production function is the most commonly used production function method. The advantage of C-D production function is that the regression analysis of the basic model is the most direct and simple, and has been repeatedly verified by classical economic theory and empirical analysis, so the estimation result of factor marginal output obtained from this is more reasonable; Secondly, this method can not only measure the degree of price distortion of two or more factors at the same time, but also estimate the degree of relative price distortion between factors. In addition, as more and more economic factors are included in the production function, this method has also been applied to measure the price distortion of factors such as energy and land.

In previous studies, most scholars only considered the important role of capital and labor factors in China’s economic development, ignoring the possible impact of land factors. Based on the traditional Cobb Douglas production function, this paper uses the extended C-D production function method to measure the total factor price distortion degree and the factor price distortion degree of capital, labor and land in 30 provinces and cities in China from 2000 to 2019, except Hong Kong, Macao, Taiwan and the Tibet Autonomous Region. The main ideas of this method are as follows: firstly, the output elasticity coefficient of China’s input factors is obtained according to the production function; Secondly, according to the output elasticity coefficient of input factors, the marginal output of input factors in various regions of China is calculated; Finally, dividing the marginal output of input factors by the corresponding factor prices, we can measure the total distortion degree of factor prices in various regions and the price distortion degree of different factors. Therefore, the estimation of production function is the key to the effectiveness of this method. This paper assumes that the input factors in the production process of enterprises include: capital, labor and land, which is different from the C-D production function which only includes capital and labor factors in the past. This paper includes the land factor in the model, which helps to more comprehensively measure the contribution of each factor to the total output, and the calculation results are more accurate [57]. The specific form of the production function is set as follows: (1)

In Eq (1): A is the total factor productivity, which is constant as the comprehensive technological progress of the entire society remains unchanged in the short term; α、β and γ is the output elasticity coefficients of capital, labor, and land factors that do not change over time and region are fixed parameters; Yit is the total output of region i during period t, which is the regional gross domestic product; Kit and Lit represent the capital investment and labor investment of region i during the t period, respectively; Iit is the land input of region i during period t. After deriving the capital, labor, and land elements in Eq (1), the marginal output of these three elements in region i during period t can be obtained as follows: (2) (3) (4)

According to the definition of factor price distortion, assuming that the actual prices of capital, labor, and land are r, w, and s, respectively, combined with the marginal output of factors in Eqs (2) to (4), we can obtain the absolute distortion of these three factors and the specific form of factor price total distortion as follows: (5) (6) (7) (8)

In Eqs (5) to (8), DisKit, DisLit, and DisIit respectively represent the degree of absolute price distortion of production factor capital, labor, and land in region i during period t. When the value is equal to 1, there is no distortion in factor prices and resource allocation is reasonable; When the value is greater than 1, there is a negative distortion in factor prices; When the value is less than 1, there is a positive distortion in factor prices. Among them, rit、wit and sit are the actual prices of capital factors, labor factors, and land factors, respectively.

In order to facilitate empirical analysis and improve the accuracy of parameter estimation, this paper conducts logarithmic processing on the left and right sides of Eq (1), and obtains the specific form of production function as follows: (9)

In Eq (9), Yit is the total output of region i during period t, which is the regional gross domestic product; Kit and Lit represent the capital investment and labor investment of region i during the t period, respectively; Iit is the land input of region i during period t; εit is a random Error term.

4.2 Variable description

Through panel data, the total distortion of factor prices and the distortion of capital, labor, and land factor prices in 30 provinces and municipalities in China from 2000 to 2019, excluding Hong Kong, Macao, Taiwan, and the Tibet Autonomous Region, are measured. The main variables involved are the total output, capital, labor, and land factor inputs, and the corresponding actual factor prices

① Total output (Yit). Expressed as regional gross domestic product, deflated using the Industrial Producer Price Index (PPI) (2000 year = 100), and then logarithmically expressed as ln Yit. Among them, the regional GDP and industrial producer price index are sourced from the database of the National Bureau of Statistics of China, the Statistical Bulletin of each region over the years, and the statistical database of China Economic Network.

② Capital investment (Kit) and capital price (rit). Due to the fact that enterprises utilize all existing capital to organize production in actual operation, the capital investment here is a concept of stock (unit: 100 million yuan). There are many methods for estimating capital stock in existing research, among which the perpetual inventory method is the most commonly used and accurate one. Therefore, this article uses the perpetual inventory method to estimate the variable capital investment:

(10)

In Eq (10), Kit and Kt-1 represent the fixed capital stock during the t and t-1 periods, respectively; ηt and Pt are the depreciation rate and investment price index of fixed capital in period t, respectively; Ut represents the newly added investment amount during the period t. This equation mainly includes the base period capital stock (K0) and the depreciation rate of fixed capital (ηt) And increase investment volume (Ut/Pt) every year. Next, we will explain the processing methods of variable data involved in the estimation model: firstly, the base period capital stock (K0). Adopting The method of t is used for estimation (Hall & Jones 1999) [58], where U0 is the initial investment, which is the fixed capital formation amount starting from the year 2000 of this study; θ Is the annual average growth rate of fixed capital formation during the sample period; ηt is the depreciation rate of fixed capital, expressed as the ratio of the depreciation of fixed capital in year t to the original value of fixed capital in year t-1. The depreciation of fixed capital in year t is equal to the difference between the accumulated depreciation amount in each year and the accumulated depreciation amount in the previous year. The data is sourced from the China Statistical Yearbook and the China Industrial Economic Statistical Yearbook over the years. Secondly, increase the annual investment volume (Ut/Pt). This article replaces Ut and Pt with fixed capital formation and fixed capital investment price index, respectively. Subsequently, the fixed capital investment price index is used to convert the fixed capital formation into a constant price based on the year 2000, replacing the annual increase in investment. The data is sourced from the China Statistical Yearbook, China Industrial Economic Statistical Yearbook, and China Economic Census Yearbook over the years.

Capital Price (rit), In existing research, the determination of capital prices is mainly measured using interest rates or depreciation rates. Among them, the interest rate method includes two different methods: bank loan interest rate and enterprise current year interest expense/liability. For example, Hsieh and Klenow(2009) set interest rates at 0.1 instead of capital prices by directly assigning values [59]. Some scholars also use the average corporate loan benchmark interest rate of 6 months to 1 year (including 1 year) in each year, or calculate the cumulative daily interest rate level to obtain the annual average interest rate. In addition, in studies that use fixed asset depreciation rates instead of capital prices, capital prices are usually expressed as the ratio of fixed asset depreciation to actual fixed asset stock. Due to the relatively lagging financial marketization reform in China and the incomplete completion of interest rate marketization process. Therefore, financing constraints remain an important factor restricting the development of enterprises. This article believes that using interest rate levels may not be able to accurately and reasonably measure the cost of using corporate funds. Therefore, the depreciation rate method is chosen for measuring the determination of capital prices, and the data is sourced from the China Statistical Yearbook and the China Industrial Economic Statistical Yearbook over the years.

③ Labor input (Lit) and labor price (wit). The labor input (Lit) is measured by the total number of employees in enterprises above designated size (10000 people) in each year, and the data is sourced from the statistical yearbooks of various provinces and cities over the years. The labor price (wit) is the most commonly used measure of labor price in existing research, which is based on two different methods: the average wage of on-the-job employees or the average wage of the region. The measurement of regional average wages is achieved by weighting the income of non agricultural and agricultural employees, or by using the income method to calculate the ratio of labor remuneration to the total number of employed employees in the region in the gross domestic product. According to research needs, this article tends to use the average wage of on-the-job employees in various provinces and cities (in 10000 yuan) as an indicator to measure labor prices, because regardless of the average wage level in the region, the actual payment by the enterprise is the average wage of on-the-job employees, and this part of wage payment is included in the production cost of the enterprise. At the same time, in order to eliminate the impact of price levels on the actual wages of on-the-job workers, this article uses CPI to deflate the data based on the year 2000, which is sourced from the China Statistical Yearbook.

④ Land input (Iit) and land price (Sit). The amount of land investment (Iit), this article believes that in actual economic operation, local governments generally adopt the method of agreement transfer to increase the land required for production enterprises in order to encourage investment. Therefore, for the measurement of land factor input, the agreed land area transferred by each province over the years will be used as a substitute indicator, and the data is sourced from the China Land and Resources Statistical Yearbook over the years. The land price (Sit), because the enterprise obtains the required land by means of transferring the land through the agreement of the local government, this has caused the imperfection of the land market price determination mechanism to a certain extent. Therefore, the method of measuring land price is based on the income from land transfer through agreements between different provinces/the area of land transferred through agreements in corresponding years.

5. Calculation and analysis of factor price distortion

5.1 Data description

Based on the calculation methods for the total distortion of factor prices and the distortion of capital, labor, and land factor prices mentioned above, the variable symbols, variable names, and data sources appearing in the calculation functions of various factor price distortions will be explained, and descriptive statistical analysis will be conducted on the relevant data. The specific results are shown in Tables 1 and 2.

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Table 1. Variable names and data sources.

https://doi.org/10.1371/journal.pone.0302825.t001

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Table 2. Descriptive statistical analysis table.

https://doi.org/10.1371/journal.pone.0302825.t002

This article mainly calculates the total distortion degree of factor prices and the distortion degree of capital, labor, and land factor prices in 30 provinces and cities in China from 2000 to 2019, except for Hong Kong, Macau, Taiwan Province, and Tibet Autonomous Region. The descriptive statistical analysis results of each variable are shown in Table 2.

5.2 Calculation of factor price distortion

This paper uses typical panel data. According to the intercept and slope term of the estimation equation, the processing of panel data can be divided into three different regression methods: Pool Model, Fixed Effects Model and Random Effects Model. The specific model that should be used to estimate parameters effectively usually requires F-test and Hausman test. Therefore, in order to improve the rationality of calculating the degree of factor price distortion, this article will use Stata15.0 software to compare and analyze the regression results of three different regression models, and then determine the most suitable method. The specific regression results are shown in Table 3.

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Table 3. Parameter estimation results of three different models.

https://doi.org/10.1371/journal.pone.0302825.t003

From the estimation results of three different models in Table 3, it can be seen that the P-value corresponding to the F-statistic is 0, and the original hypothesis is rejected at a significance level of 1%. Therefore, it can be inferred that the fixed effects model is more suitable than the mixed effects model. Meanwhile, the Hausman test found that the random effects model rejected the original hypothesis at a significance level of 1%. Therefore, based on the test results of three different models, this article will choose the fixed effects model as the benchmark model for correlation regression analysis. From Model 2 (fixed effects model), it can be seen that the effects of capital, labor, and land factors on total output are all positive and significant at the 1% level. In addition, the estimated factor output elasticity coefficient α、β and γ, they are 0.414, 0.042, and 1.004, respectively. By using the marginal output elasticity coefficient of factors, the marginal output of input factors in various regions of China can be calculated. Then, by dividing the marginal output of input factors by the corresponding actual prices of factors, the total distortion of factor prices in each region and the degree of price distortion of different factors can be calculated.

5.3 Test results and analysis

Using the estimated factor output elasticity coefficient mentioned above to calculate the marginal output of capital, labor, and land factors, combined with Eqs (5) to (8), the total degree of factor price distortion in each region and the degree of price distortion of different factors can be calculated. Next, we will analyze the total distortion of factor prices, capital factor prices, labor factor prices, and land factor prices in various provinces and cities in China from 2000 to 2019. The total distortion of factor prices is shown in Table 4 below.

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Table 4. Total distortion of factor prices in various provinces and cities in China.

https://doi.org/10.1371/journal.pone.0302825.t004

From Table 4, it can be seen that the total distortion of factor prices in China during the sample period showed a negative distortion, meaning that the marginal output of factors was greater than the actual price of factors. At the same time, there are the following characteristics: firstly, there is a significant difference in the total distortion of factor prices among various provinces and cities in China, which is not only reflected in the comparative analysis of various provinces and cities over the years, but also remains very obvious in terms of time trend; Secondly, there are significant differences in the total distortion of factor prices between different regions, mainly manifested as the lower distortion of factor prices in the eastern and northeastern regions compared to the central and western regions during the same period; Thirdly, there is also a significant difference in the total distortion of factor prices within the region. For example, from the eastern region, the total distortion of factor prices in Guangdong, Fujian, and Hainan is significantly lower than that in provinces such as Hebei, Shandong, and Jiangsu, and even lower than that of the economically developed municipalities such as Shanghai, Beijing, and Tianjin; From the perspective of the central region, the overall distortion of factor prices in Jiangxi is significantly lower than other provinces within the region; From the perspective of the western region, the differences between provinces and cities within the region are more pronounced. Among them, there are not only Guangxi, Chongqing, Sichuan, and Yunnan with an average total distortion of factor prices exceeding 9.0, but also Ningxia with an average total distortion of factor prices of only 6.272.

The possible reasons for the occurrence of the above situation in the total distortion of factor prices in China are as follows: firstly, after 2003, the total distortion of factor prices in most regions of China has experienced a slow and fluctuating increase. This is because after the brief adaptation to WTO accession, in order to tap into the competitive advantages of the export industry and promote relatively strong economic development momentum, the state can only artificially lower the development costs of the manufacturing industry through administrative intervention and other means, Adopting policies of low labor prices, low capital usage costs, and low exchange rates, as well as implementing low-priced policies in areas such as energy, land, and raw materials to meet macroeconomic policy requirements and economic development goals; Secondly, after 2008, due to the impact of the international financial crisis caused by the US subprime mortgage crisis, China was forced to launch a 4 trillion yuan investment plan with a focus on increasing infrastructure construction in order to resist the crisis and maintain growth. The large-scale government investment and the "national advance and private retreat" in national income distribution ultimately led to a rapid increase in the overall distortion of factor prices in this round; Thirdly, with the continuous deepening of China’s market-oriented reform after 2013, the decisive mechanism of the market in the allocation of factor resources has been basically established, forming a unified, open, fair and orderly competitive market nationwide. Therefore, there is a clear downward trend in the overall distortion of factor prices in both the national, eastern, central, and western regions, as well as in the Northeast region.

From Table 5, it can be seen that China’s capital factor prices showed a negative distortion during the sample period, indicating that the marginal output of capital is greater than the actual price level of capital. From the perspective of the degree of distortion in national capital factor prices, there is a fluctuating increase in the degree of distortion in China’s capital factor prices, which began to show a slow downward trend after reaching a peak of 4.625 in 2010. This also confirms to some extent the viewpoint proposed by some scholars that the distortion of factor prices in China is an important reason for rapid investment growth, especially in 2008, due to the adverse impact of the international economic environment, China’s exports were greatly impacted. However, the government’s intentional intervention in the capital market did not significantly reduce economic growth. This approach, aimed at boosting economic development momentum and driving economic growth through investment, exacerbates the price distortion of China’s capital factors. From a regional perspective, the distortion of capital factor prices in various provinces and cities in China during the sample period was significant, manifested as a deeper negative distortion. Furthermore, from a regional perspective, there is a significant gap in the distortion of capital factor prices among different regions. Among them, the eastern region with the highest degree of distortion is 1.703 times that of the northeastern region.

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Table 5. Degree of distortion in capital factor prices in various provinces and cities in China.

https://doi.org/10.1371/journal.pone.0302825.t005

This article believes that the possible reason for the above-mentioned distortion in China’s capital factor prices is that the relatively lagging reform of factor marketization in China has led to a significant lack of marketization in factor prices. For example, state-owned enterprises face ownership discrimination due to their monopoly advantage. Therefore, compared to non-state-owned enterprises, being able to obtain the required capital at a price lower than the market undermines the efficiency of capital allocation and worsens the degree of negative distortion of capital. In addition, in order to promote regional economic development and increase investment and construction, the government usually takes strict control measures on the capital market to artificially lower the market price of capital elements. This government intervention in the factor market has seriously disrupted China’s investment consumption structure and suppressed the increase in consumer demand among residents.

From Table 6, it can be seen that firstly, there are significant differences in the degree of distortion of labor factor prices among provinces and cities in China over time. For the national labor market, most years of the sample period have seen positive distortions in labor factor prices. At the same time, there are many positive distortions of labor market prices in provinces and cities, including Hebei, Jiangsu, Zhejiang, Fujian, Shandong and Guangdong in the eastern region, Anhui, Jiangxi, Henan, Hubei and Hunan in the central region, and Guangxi, Sichuan, Guizhou and Yunnan in the western region, This indicates that the actual prices of labor factors in the labor market of these provinces are greater than the marginal output level. There are also some regions where labor factor prices have shifted from negative distortion to positive distortion, such as Beijing. This indicates that the rapid increase in worker wages in the labor market in the region has exceeded the increase in marginal output levels. This article argues that, This phenomenon may be related to the "Decision of the Central Committee of the Communist Party of China on Several Issues Concerning the Improvement of the Socialist Market Economic System (2003)" adopted at the Third Plenary Session of the Sixteenth Central Committee of the Communist Party of China and the "Opinions on Several Policies to Promote the Increase of Farmers’ Income (2004)" in the No. 1 central document There is a direct or indirect relationship between eliminating various institutional constraints on the employment of migrant workers in cities, improving the employment environment for farmers in cities, creating more employment opportunities for farmers, increasing labor remuneration income, and gradually forming a unified urban-rural labor market. During this period, in order to implement the above policies, local governments at all levels have successively formulated and introduced a series of supporting registered residence system reform measures, and most regions have cancelled the institutional constraints on the employment of migrant workers. The Chinese government has actively accelerated the process of labor market reform and promoted the continuous decline of labor factor price distortion. The labor factor prices in some provinces and cities have been negatively distorted and even deteriorated, such as Tianjin, Shanghai, and Hainan in the eastern region, and Qinghai, Ningxia, and Xinjiang in the western region. The actual labor factor prices in these regions have always been lower than the marginal output level, leading to long-term undervaluation of labor factor prices. In addition, there are also some provinces and cities where labor factor prices have changed from positive distortion to negative distortion, such as Shanxi in the central region, Inner Mongolia, Chongqing, and Gansu in the western region, and Liaoning, Jilin, and Heilongjiang in the northeast region. Throughout the entire sample period, the wage level of the labor market has not been correspondingly improved.

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Table 6. Degree of distortion in labor factor prices in various provinces and cities of China.

https://doi.org/10.1371/journal.pone.0302825.t006

The overall trend of the distortion of labor factor prices in China over time is an upward trend. Perhaps it is due to China’s long-term implementation of an outward oriented and extensive economic growth model driven by investment. This economic model is not based on technology driven economic development, but mainly adopts the method of artificially lowering labor factor prices and expanding the scale of the economy through increasing cheap inputs, achieving the goal of economic growth. At the same time, due to the existence of the "dual" economic structure between urban and rural areas in China, as well as the continuous transfer of relatively affluent surplus labor from rural areas to urban areas, it is also an important reason for the long-term high and increasing distortion of labor factor prices in China. From a time trend perspective, the degree of distortion in labor factor prices entered a slow decline period after reaching a phased high from 2004 to 2007. However, due to the impact of the 2008 international financial crisis, the degree of distortion in labor factor prices in China quickly turned to an upward turning point. This paper believes that the reason for the price distortion and decline of labor factors may be due to the dual impact of investment and export-oriented economy after China’s formal accession to the WTO in 2001. China’s manufacturing industry, especially labor-intensive industries, has developed rapidly. "Made in China" has thus gone to the world, forming a large demand for labor population in the short term. The registered residence system The existence of urban and rural "dual" economic structure makes the inflow of labor force into urban areas insufficient, and promotes the rise of labor market prices. For the rising inflection point of labor factor price distortion in 2008, it may be due to the impact of the international financial crisis, because the financial crisis led to a significant reduction in international import and export trade, the government was forced to promote 4 trillion yuan infrastructure construction investment in order to stimulate economic development, and the rapid growth of physical capital investment has significantly increased China’s per capita capital stock. At the same time, since the 18th National Congress of the Communist Party of China, a series of measures, such as Economic restructuring, transformation and upgrading, have actively promoted the increase of marginal output of labor factors directly or indirectly, but the labor market price has not risen synchronously, causing the expansion of distortion of labor factor prices. From the perspective of the degree of distortion in labor factor prices in various regions, the initial degree of distortion decreases sequentially from the eastern region, northeast region, western region, and central region, and the degree of distortion in the eastern and western regions and northeast regions is always higher than that in the central region. After surpassing the central region in 2004, the degree of distortion in the northeast region has always been higher than that in the central region, After surpassing the central region in 2012, the distortion of labor factor prices in the western region has always been higher than that in the central region. This article argues that the eastern region, as the forefront of reform and opening up, was first affected by the external economy. Although labor output has significantly increased, the wage levels of workers have not followed up, resulting in a relatively high degree of distortion; Although the marginal output of labor in the central region is not high, due to the relatively lagging economic reform in China, there has been no significant change in wage levels, resulting in a lower level of distortion.

From Table 7, it can be seen that during the sample period, China’s land factor prices showed a negative distortion, indicating that the marginal output of land factors is greater than the actual price level of the land market. From the perspective of the degree of distortion in the national land factor prices, the degree of distortion in China’s land factor prices shows a trend of first decreasing and then increasing, and gradually decreasing after reaching a peak of 10.295 in 2012. In terms of regions, there are significant differences in the degree of distortion in land factor prices among provinces and cities in China, but the land factor prices in all regions are negatively distorted. Furthermore, from a regional perspective, there are significant differences in the degree of distortion in land factor prices among different regions. For example, in 2012, the peak distortion of land factor prices in the western region reached 12.134, which is 1.396 times that of the northeast region. It is worth noting that before the international financial crisis, the degree of land factor price distortion in China was not severe. In this study, the degree of land factor price distortion in most regions except for the central region showed a downward trend from 2000 to 2008. However, after the outbreak of the 2008 international financial crisis, the government expanded investment in infrastructure construction in order to maintain stable economic growth, causing local governments to continuously increase administrative intervention in the land market. Land finance has even become the main source of government revenue in many regions, leading to a deterioration in the distortion of land factor prices. After 2013, with the promulgation and implementation of the Land Management Law (2013), accelerating land marketization reform, improving land acquisition compensation mechanisms, and clearly establishing a unified land market for urban and rural areas have received high attention from various parties. The degree of distortion in land factor prices nationwide has begun to show a slow downward trend. The land factor prices in China have a structural problem of high prices for commercial and residential land, and low or even zero prices for industrial land. On the one hand, the distortion of land factor prices caused by government intervention not only causes enterprises to mainly produce products with low technological content and low added value, but also lacks the motivation for new product research and development and technological transformation. Long term reliance on low-level production of factor inputs is not conducive to the transformation and upgrading of the overall industrial structure, and suppresses the optimization of consumption structure; On the other hand, in order to recover the costs of the process of agricultural land conversion and obtain more land fiscal revenue, the government often raises the prices of commercial and residential land, resulting in long-term high prices of commercial housing. House prices have become an important reason for reducing residents’ actual wealth, suppressing residents’ consumption demand, and is not conducive to the upgrading of the overall consumption structure of society.

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Table 7. Degree of distortion in land factor prices of various provinces and cities in China.

https://doi.org/10.1371/journal.pone.0302825.t007

6. Research conclusions and policy recommendations

After calculating the degree of distortion in the factor market, this article conducts an appropriate analysis of the possible reasons for the distortion. At the same time, measuring the degree of price distortion of each factor will also provide important data support for further empirical analysis in the following text. There are many methods to measure the distortion degree of factor prices in existing research, and the production function method is widely used by scholars at present. After comparative analysis, based on the traditional Cobb Douglas production function, this paper uses the extended C-D production function method to measure the total distortion of factor prices and the distortion of capital, labor and land factor prices in 30 provinces and cities in China from 2000 to 2019, except Hong Kong, Macao, Taiwan and Tibet Autonomous Region.

During the sample period, nationwide, except for positive distortions in labor factor prices, both capital and land factor prices showed negative distortions, indicating that only the actual price of labor factors in the Chinese labor market is greater than its marginal output level at this stage. This conclusion is similar to the research results of some scholars. However, the degree of positive distortion gradually weakens, and even shows a trend of negative distortion in some regions. Therefore, in the future, it is necessary to further eliminate the "dual" economic structure between urban and rural areas, strengthen the reform of the registered residence system, weaken the institutional constraints that restrict the free flow of labor, and improve the distortion of the labor market. In the calculation of capital factor price distortion, the actual price of capital factors in the Chinese capital market is significantly lower than its marginal output level, and the price of capital factors shows a significant degree of negative distortion. Due to the Chinese government’s artificial intervention in the capital market, for example, in order to promote regional economic development and increase investment attraction, the market price of capital factors has been seriously underestimated. At the same time, the degree of distortion in China’s capital factor prices is significantly greater than the degree of distortion in labor factor prices. The existence of negative distortion in the relative price of capital labor factors will have adverse effects on residents’ employment, income, and even consumption. The calculation results of land factor price distortion indicate that there is a serious problem of negative price distortion in China’s land factors, and the actual price of land factors in the land market is far lower than the marginal output level. Overall, although there has been a downward trend in the distortion of land factor prices in China in recent years, accelerating the process of land marketization reform still requires high attention from all parties.

Acknowledgments

The authors express their gratitude to the anonymous reviewers for their insightful comments.

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