ef="#f3" target="_self">Figure 3. In 2009, the average wage of urban workers was 32,244 yuan. In 2017, the average wage was nearly doubled in 2009, and the average wage of the labor force increased year by year. The changes in China’s labor wages are consistent with the characteristics of the labor shortage phase, but this does not mean that China’s “Lewis Turning Point” has arrived. The average wage increase of the labor force may be related to economic operations. The
Note: The data comes from the National Bureau of Statistics.
Figure 3. Average wages of urban workers (yuan).
economic development will increase the price of animals, and the average wage of employed people will also rise.
In order to further study the rise in the average wage of China’s labor force, it is mainly due to supply and demand or economic development. We analyze the changes in the GDP index and the consumer price index. If the economy develops rapidly at this stage, we will not be able to conclude that labor wages are caused by supply and demand. As shown in Figure 4, there is a significant increase in the GDP index and the consumer price index at this stage. In the case of a stable economy, the average wage of the labor force increases with economic development. Excluding the exogenous factors of economic development, is there still a correlation between per capita wages and the imbalance between labor supply and demand? In order to study this problem, we continue to analyze the changes in the number of employed people. If the increase in wages is accompanied by a decrease in the number of laborers, it can be said that the rise in wages is caused by labor shortages. Otherwise, this view will not hold. As shown in Figure 5, the number of employed people has risen slightly. It is worth noting that
Note: The data comes from the National Bureau of Statistics.1978 is the benchmark.
Figure 4. Consumer price index and gross domestic product index.
Note: The data comes from the National Bureau of Statistics.
Figure 5. Number of employed persons.
when distinguishing between urban and rural areas, we find that the number of employed people in urban areas is gradually rising, and rural employment is on the opposite trend. In summary, we preliminarily speculated that China has not yet entered the “Lewis second turning point”. At present, China is in the stage of rural labor migration to urban labor. In the following part, we will further verify this conclusion.
3. Data Description
The data in this paper is based on the 2009-2017 panel data published by the National Bureau of Statistics. The main variables include the fixed asset investment price index (based on 1990), the total fixed asset investment of the whole society, the fixed growth rate, the depreciation rate, the number of employed persons in the secondary industry, the total industrial production value, and the capital stock. Among them, the capital stock variable needs to be calculated by other variables. Since the value of the depreciation rate is missing, we need to use other methods to get the data. The currently used solutions are as follows: 1) Select a fixed depreciation rate   . 2) Using the PIM method, the depreciation rate is first classified and then weighted to obtain the total depreciation rate   . 3) Based on the national economic identity  . In this paper, the fixed depreciation rate method is used to select the same depreciation rate of 6% as  . The main variables are described in Table 1.
4. Model Construction
In this section, we describe the method of judging the Lewis inflection point and further define the efficiency.
4.1. The Method of Judging “Lewis Turning Point”
In the above, we conduct a preliminary analysis of the current situation in China. The following content, we choose a more standardized theoretical framework to judge. When labor is turned into a shortage, workers’ wages depend on the marginal productivity of labor. Some scholars have pointed out that if the marginal
Table 1. Main variable description.
productivity of labor in the industrial sector rises significantly from the base period, then it can be judged that this economy has surpassed the Lewis turning point during this period  . This article uses the same method to measure. Since the calculation of labor marginal productivity, the production function needs to be calculated. We assume that the production function conforms to the Cobb Douglas production function form, and the production function form is as in Equation (1):
In Equation (1), is the total output, K is the capital stock, L is the labor , , and . Since the capital stock in the Cobb Douglas production function cannot be directly obtained, further estimation is needed. The current perpetual inventory method is the most commonly used method for estimating capital stock. This paper uses this method to estimate. The basic formula is as follows:
In Equations (2) and (3), I is the fixed capital investment amount of the whole society, P is the fixed asset price index, d is the depreciation rate, and g is the fixed asset growth rate.
4.2. Definition of Efficiency
“Efficiency” generally adopts the Pareto optimal concept in economics, and there is no situation that increases one’s interests without harming other people’s interests.  pointed out that economic efficiency is divided into three kinds of efficiencies in microeconomic theory, namely, allocation efficiency, technical efficiency, and dynamic efficiency. Economic efficiency is defined as:
Economic efficiency refers to the ratio of the ideal minimum cost to the actual cost of the output level. When , it is called comprehensive effective, and when , it is called comprehensive invalid. In this paper, the economic efficiency values are obtained for each province. When the efficiency value is lower than 1, it indicates that the province still has inefficiency and needs further improvement. The lower the efficiency value, the higher the inefficiency of the province.
5. Empirical Results
5.1. Labor Marginal Productivity Calculation
Through the perpetual inventory method, we calculate the value of the capital stock, as shown in the second column of Table 2. Further, we estimate the production function. In order to facilitate the processing of the data, we take a logarithmic regression analysis of the Equation (1). Based on the estimated capital
Table 2. Capital stock and labor marginal productivity in the industrial sector.
stock and labor regression coefficient, we write Equation (1) as . The marginal productivity of labor is calculated according to the production function, as shown in the third column of Table 2. During the period from 2009 to 2017, the marginal productivity of industrial labor showed an upward trend, but it did not rise significantly. We believe that China will reach the “Lewis second turning point” during 2009-2017. At present, there is no shortage of labor in China, and the main reason for the rise in wages for workers is economic development. However, we do not deny that there is a heterogeneous view between cities. Some cities in China may have entered the “Lewis second turning point” in advance, which means that some cities have labor shortages, while in other cities, there are still surplus people to be employed. This phenomenon has caused the inefficiency of China’s labor force. The state can promote the transfer of labor between cities through reasonable policy guidance and further improve labor efficiency. In the next section, we analyzed the labor efficiency of China’s provinces in 2016.
5.2. Labor Efficiency in Different Provinces
This part of the study studied the labor efficiency of each province in 2016, including 31 research objects (22 provinces, 5 autonomous regions, 4 municipalities). The calculation method of the capital stock of fixed assets is calculated by  . In the frontier analysis method of measurement efficiency, it is divided into parameter and non-parameter methods according to the production function form. Stochastic frontier analysis (SFA) is a commonly used method in parameter method. Non-parametric method is represented by data envelopment analysis (DEA). In this paper, the stock of assets and the number of employed persons is used as input variables, and the gross national product of each province is the output variable. The efficiency values and rankings of each province are calculated by DEA and SFA, as shown in Table 3. Column (2) is a provincial efficiency value calculated using the DEA method, and columns (3)-(4) are ranking
Table 3. Efficiency value and ranking.
the efficiency values of the different methods. From the ranking point of view, the rankings of the two methods are similar, and the following analysis is based on the DEA efficiency value.
Table 3 shows that the provinces with lower rankings are mostly cities in the northwest, and the top cities are the eastern coastal cities. The economic development of the eastern coastal cities is rapid, so the resource allocation efficiency is generally higher than that of the northwestern cities. It is worth noting that the efficiency values of the top three are all higher than 0.9, but the fourth Jiangsu province is only 0.773, and the capital and labor input efficiency is obviously broken. Although Jiangsu ranks high, there is still a high inefficiency. Further analysis, we found that some cities in the central region ranked lower than the northwest region, which is inconsistent with its economic development level. For example, in 2016, the total GDP of Henan Province ranked fifth in the country, but its efficiency ranking was only 27. Since Henan is China’s most populous province, we further infer that the labor force is causing its inefficiency, and the large investment in labor has caused inefficiency.
6. Conclusions and Policy Recommendations
Through an analysis of the marginal productivity of China’s labor, we initially determined that China’s “Lewis second turning point” has not yet arrived. However, we do not object to the fact that some Chinese cities have entered the “Lewis Turning Point” ahead of schedule. This is mainly due to the uneven distribution of labor between cities. To this end, we have studied the efficiency of capital stock and labor input in cities. Studies have shown that the efficiency values in the Northwest are generally lower than those in the eastern coastal areas. This is mainly because the eastern coastal areas have absorbed more overseas and mainland investment due to their geographical advantages. The economic development of the eastern coastal areas is rapidly higher than that of the western regions. Although China has implemented partial support for the western plan, from the perspective of efficiency in 2016, the support for the west still needs to increase. On the other hand, some provinces with large populations are inefficient due to excessive labor input, while some cities have labor shortages. In response to this problem, we suggest that the state introduces policies to the populous provinces to support the flow of labor to the western and eastern coastal areas where the labor force is lacking. The rational allocation of labor also increases the efficiency of labor outflows and inflows, thereby increasing the average labor efficiency of the entire country.