The research on the BTC in mariculture mainly involves three factors: labor, capital and resources. This paper fits labor and resource factors into non-resource factors and uses Cobb-Douglas production function to represent them. The CES production function is used between the non-resource elements represented by ‘ labor-capital ‘ and the resource elements.

Referring to the research of Liao and Ren (2020) and Hassler et al. (2021), the double nested CES production function is represented as follows.

In the expression, Y t is total output, K t is capital inputs, L t is labor inputs, A t is capital-labor-enhancing technological progress, R t is resource inputs, A t R is resource biased technological progress, ϵ denotes the elasticity of substitution of capital-labor for resources, and α is the share of capital income as a proportion of the joint share of labor and capital.

The following can be obtained by assuming that factor markets are perfectly competitive, that is, the marginal output of a factor is equal to its real price.

From Equations 2, 3, the level of technological progress for the two categories is as follows.

As can be seen from the above equations, the level of TC in the two categories can be found by setting the values of α 、 ϵ 、 γ and utilizing the data Y t 、 K t 、 L t 、 R t 、 L t s h a r e   and R t s h a r e . For the value of γ , this research refers to Hassler et al. (2012), assuming γ = 0.05 .

From Equations 4, 5, it can be observed that the prerequisite for studying the level of technological progress of factors is to estimate the elasticity of substitution between them.

Given the level of TC satisfies the following conditions.

If a t = l o g ( A t ) , a t R = l o g ( A t R ) , ϖ t A ∼ N ( 0 , Σ ) , ϖ t R ∼ N ( 0 , Σ )

Then from Equations 4, 5, the following can be deduced.

The logarithm of Equations 8, 9 is taken and substituted into Equations 6, 7. The following equations are obtained.

Let s t A = log ( Y t K t α L t 1 − α ) − log ( Y t − 1 K t − 1 α L t − 1 1 − α ) , s t R = log ( Y t R t ) − log ( Y t − 1 R t − 1 ) , z t A = log L t s h a r e − log L t − 1 s h a r e , z t R = log R t s h a r e − log R t − 1 s h a r e

So Equations 10, 11 can be abbreviated as follows.

For Equations 12, 13, the value of the elasticity ϵ can be estimated by seemingly uncorrelated regression.

The value of α can be obtained by the following equations.

Then L t s h a r e K t s h a r e = 1 − α α can be obtained.

This paper takes the data of mariculture industry in ten coastal areas from 2008 to 2020 as the research sample. Based on the availability of data, it does not consider Shanghai, Hong Kong, Macao and Taiwan. The relevant data mainly come from China Fishery Statistical Yearbook, China Statistical Yearbook, China Rural Statistical Yearbook and China Fixed Asset Investment Statistical Yearbook. The specific indicators are as follows.

Output (Y): This paper uses the output value of mariculture in coastal areas to measure output, and uses the regional GDP index to deflate to obtain the actual output value of mariculture.

Labor (L): This paper selects the number of employees in the marine aquaculture industry to measure the labor input of the marine aquaculture industry. Regarding labor prices, the per capita net income of fishermen is approximately used as the wage level of mariculture practitioners. For the labor income share, this paper uses the product of the number of workers and the labor price to calculate.

Capital (K): the capital stock of mariculture industry is estimated by perpetual inventory method (Ji et al., 2022). On the capital price, using the method of Doraszelski and Jaumandreu (2014), capital price = investment price index * (loan interest rate + depreciation rate-inflation rate), in which the investment price index, loan interest rate, depreciation rate and inflation rate are replaced by the price index of agricultural means of production, the loan interest rate of 3-5 years, the depreciation rate of fixed assets and the change rate of consumer price index respectively. For the capital income share, this paper uses the product of capital stock and capital price to calculate.

Resources (R): This paper selects the area of marine aquaculture to measure the input of marine resources. Regarding the price of resources, considering that the sea area use fee levied on the sea for aquaculture in various regions has policy preferences and exemptions, it is difficult to accurately measure. Therefore, this paper uses the residual value of mariculture output value after deducting labor income share and capital income share to approximate the resource income share. The resource price is the ratio of sea area resource income share to mariculture area.

Regression analysis was first performed on the data of the full sample from 2008 to 2020, and seemingly uncorrelated regression estimation was carried out on Equations 12, 13. The estimation results of parameter coefficients are shown in Table 1 .

As can be seen from the table, − ϵ ϵ − 1 = 0.6539 , the elasticity of substitution between the non-resource factors aggregated by “capital-labor” and the marine resource factors can be calculated as 0.3954. This result is in line with the meaning of economics, indicating that there is a certain substitutability between resource factors and non-resource factors, that is, the increase in the input of non-resource factors such as labor and capital or marine resource factors will promote each other ‘s marginal output, but the degree of substitution is weak, showing a complementary relationship as a whole. From the perspective of a completely free market, the ratio of the marginal output of factors is the ratio of the price of factors. Therefore, this complementarity between resource factors and non-resource factors indicates that as the price of resources increases, the production cost of mariculture activities also increases. In order to cope with the cost pressure caused by the increase in the price of resource factors, producers can only moderately adjust the proportion of input of resources and non-resource factors, such as appropriately reducing the input of resources and reducing the marginal output of capital-labor, resulting in a decline in total output. Therefore, in order to maintain the total output of the mariculture industry will not decrease with the decrease of resource input, it is necessary to increase the marginal output by improving technological progress.

The level and growth rate of RBTC in mariculture industry from 2009 to 2020 can be calculated by bringing the obtained substitution rate into Equation 5. The results are shown in Table 2 .

From the table, it can be found that the RBTC of mariculture industry generally shows a trend of decreasing first and then increasing. The growth rate of resource biased technological progress has experienced a trend of “sharp rise-sharp decline-slow rise”. Since 2015, the level of technological progress of marine resources has gradually increased, and the growth rate of resource biased technological progress has fluctuated around 5%, which is basically consistent with the actual situation of mariculture. From 2015 to 2020, the Ministry of Agriculture and Rural Affairs has announced six batches of national marine ranching demonstration areas, a total of 136, marine ranching construction and management standard system basically established, to a certain extent, promote the development of mariculture. During this period, the development of mariculture industry attaches great importance to the protection of fishery resources, mariculture industry pays more and more attention to green aquaculture in production practice, and the technological progress level of marine resource elements has been steadily improved. As far as the level of BTC is concerned, because the TC of non-resource factors such as “resources-labor” is greater than the technological progress level of marine resource factors, and the substitutability between the two types of factors is weak, there is a certain complementarity. It can be concluded that in the production process of mariculture, the marginal production of non-resource factors is greater than the marginal production of marine resource factors. Increasing one unit of non-resource factor input requires more than one unit of marine resource factor input, and the overall TC is RBTC. This result also reflects that the TC of mariculture industry tends to increase the use of sea area resources as a whole.

On the basis of estimating the elasticity of substitution and resource biased technological progress for the full sample, this research divided the regions into the Bohai rim region, the East China Sea and Yellow Sea region and the South China Sea region, and performed seemingly uncorrelated regression estimation of the time-series data for each region respectively. The parameters obtained are shown as Table 3 .

Thus, the elasticity of substitution of each region was further calculated as Table 4 .

It can be seen from the table that the factor elasticity of substitution is less than 1 in all three regions and has relatively small values. This result suggests that there is a complementarity between marine resource factors and non-resource factors, i.e., that an increase in either marine resource factors or non-resource factors can lead to marginal outputs of the other type of factor in each of the three coastal regions. Comparing the elasticity of substitution of the three major coastal regions, it can be found that the South China Sea region has the smallest elasticity of substitution, the Bohai rim region has the second highest, and the East China Sea and Yellow Sea region has the highest elasticity of substitution. This result evinces the very weak substitutability between resource and non-resource factors in the South China Sea and Bohai rim regions. Therefore, when the price of marine resources fluctuates relative to the price of non-resource factors, producers cannot effectively achieve the goal of reducing costs and ensuring output simply by adjusting the ratio of inputs between resource and non-resource factors. For the East China Sea and Yellow Sea region, on the other hand, the elasticity of substitution is 0.4492, and although the two types of factors also show a complementary relationship, the degree of substitutability between resource and capital-labor factors is significantly higher than in other regions. This result suggests that when there is a relative change in the price of marine resources to the price of non-resources, there will be a relatively larger change in the ratio of marine resources to the inputs of capital and labor.

Table 5 shows resource biased technological progress and its growth rates for the three regions. Significant differences can be found between the three regions in terms of resource biased technological progress. TC in the South China Sea region is much higher than that in the East China Sea and Yellow Sea region and the Bohai rim region, with RBTC in the South China Sea region averaging about 0.317 over the sample period, which is 7 times higher than that in the Bohai rim region and 40 times higher than that in the East China Sea and Yellow Sea region. This is mainly due to the fact that the South China Sea region is more richly endowed with marine resources, and technological progress communicates itself in a resource biased manner, while the level of TC in the resource factors in the Bohai rim and the East China Sea and Yellow Sea regions need to be further improved. In terms of growth rates, RBTC in the South China Sea region achieves steady growth at an average rate of 3.272%, while resource biased technological progress in the East China Sea and Yellow Sea region grows at a slightly slower rate than that of the South China Sea region, at 1.303%, and in the Bohai rim region, at -1.912%. In addition, the figure depicted that the growth rate of resource biased technological progress in the three major coastal regions peaked in 2012, with both the South China Sea region and the Bohai rim region growing at more than 20%. The reason may be that in 2012, the country proposed to build a strong marine nation and strengthen the development and utilization of marine resources, which to a certain extent promoted the growth rate of RBTC.

As indicated by the definition of share of resources (Chen et al., 2015), the resource share is expressed as follows.

Then unite Equations 3, 16, 17 is yielded.

In this research, resource efficiency is defined as the ratio of output to resource consumption. From Equation 17, it can be assumed that resource efficiency is closely linked to resource biased technological progress and resource prices. Therefore, drawing on the study of the relationship between resource biased technological progress and resource efficiency and accommodating the variable of marine resource price, the research establishes an econometric model to study the influence of the two on resource efficiency.

As evident by  Figure 1 , the resource efficiency of mariculture increased from 6.81 in 2009 to 7.50 in 2020, with an overall increase of 10.18%, a result which indicates that the resource efficiency of mariculture has shown an upward trend, and the output of marine resources per unit has been increasing during the study period. Further detailed analysis shows that from 2009 to 2011, the resource efficiency of mariculture showed a sharp decline, followed by a sharp increase from 2011 to 2012, and a fluctuating upward trend from 2012 to 2020. The reason is mainly due to the extensive aquaculture in the early stage of mariculture, and the increase of economic benefits at the expense of a large amount of resources. Moreover, due to the decrease of aquaculture density and the backwardness of technology, the output efficiency per unit sea area is relatively low. In 2011, the resource efficiency reached its lowest point, mainly due to natural disasters, such as typhoons, resulting in a decrease in aquaculture area and social resource, which directly led to a decline in the efficiency of mariculture resources. While in other years, the resource efficiency of mariculture industry is higher than 6.5, and reaches its peak of 7.50 in 2020.

To reduce the possible heteroskedasticity in the data, this research takes the natural logarithm of the sequence Y t R t 、 A t R 、 P t R , to obtain lny, lna and lnp. The stationarity of the data needs to be tested before constructing the vector autoregressive model. The ADF unit root test is performed to determine its stationarity, and the results are shown in Table 6 .

To construct a vector autoregressive model, it is first and foremost to determine the optimal lag order. If the optimal lag order is too small, it will cause the error to have strong autocorrelation, which will affect the reliability of the parameter being estimated. And if the optimal lag order is too large, it will lead to the reduction of the degree of freedom and the validity of the parameter estimation will be significantly affected. The LR test is implemented to determine that the lag order is 1. Further, this research constructs the VAR (1) model and results grabbed as shown below:

It can be noted that the elasticity coefficient of resource efficiency with respect to resource biased technological progress is -1.2172 at lag 1, which indicates that in the short run, the level of resource biased technological progress in mariculture has a significant dampening effect on resource efficiency. When the level of technological progress rises by 1%, there is a corresponding decline in resource efficiency of -1.2172%. In terms of the impact of resource prices on resource efficiency, the lag 1 elasticity coefficient is -3.0604, which suggests that there is a negative impact of the price of marine resources on resource efficiency. When the price of marine resources rises by 1%, it will result in a decrease in resource efficiency of -3.0604%. The reason may be that resource biased technological progress, resource prices and resource efficiency have not yet been in a synergistic growth situation. In the short term, due to the pressure of rising costs, farmers may not be able to immediately adjust their production methods and improve resource utilization efficiency, resulting in a decline in resource efficiency.

In order to further investigate the long-run equilibrium relationship between resource biased technological progress, resource price and resource efficiency, the three variables lny, lna, lnp are first tested for cointegration. The results of the cointegration trace test indicate that there is only one linearly independent cointegration variable. The results of the maximum eigenvalue test demonstrated that the null hypothesis of “cointegration is 0” can be rejected at the level of 5%, but the null hypothesis of “cointegration is 1” cannot be rejected. It can be concluded from the test results that there is a cointegration relationship among the three variables, which implies that there is a long-run equilibrium relationship among the three.

Using Johansen’s MLE approach to estimate the cointegration equation.

As a comparison, the EG-ADF two-step method is used to estimate the long-run equilibrium relationship of the three variables, and the co-integration equation is obtained.

The two estimates are similar, but the MLE estimate is theoretically more efficient. According to the MLE estimation results, the coefficient of elasticity of technical progress for resource efficiency is 0.5733, suggesting that when the level of resource biased technical progress increases by 1%, it will contribute to an increase in resource efficiency by 0.5733%. The price elasticity coefficient of resource efficiency is 0.8006, importing that when prices increase by 1%, it will contribute to an increase in resource efficiency by 0.8006%. This result reveals that both resource biased technological progress and marine resource prices promote resource efficiency in mariculture in the long-run, with marine resource prices contributing slightly more than resource biased technological progress.

Taking the data of China’s mariculture industry from 2008 to 2020 as research samples, this research introduced marine resource factors into the input-output system of mariculture industry to study the technological progress level of marine resource factors. On this basis, an econometric model was built to study the impact of resource biased technological progress and resource price on resource efficiency. The main research results are summarized as follows.

Firstly, a double-nested CES production function was constructed to estimate the elasticity of substitution between non-resource factors represented by labor and capital factors and resource factors, so as to measure the level of resource biased technological progress in the mariculture industry, which yielded that there was a complementary relationship between resource and non-resource factors in marine areas, and that the level of technological progress of non-resource factors was higher than that of resource factors. resource biased technological progress among the three major coastal regions presents heterogeneous characteristics, with the level of resource biased technological progress in the Bohai rim region showing a small downward trend, the level of resource biased technological progress in the South China Sea region basically remaining stable, and the level of resource biased technological progress in the South China Sea region being the highest among the three major regions and showing a steady growth.

Secondly, the research analyzed the relationship between resource biased technological progress, resource prices and resource efficiency and fount that, in the short term, resource biased technological progress and resource prices had a negative impact on resource efficiency; in the long term, there was a long-term equilibrium relationship between the three, and resource biased technological progress and resource prices had a positive impact on resource efficiency. Moreover, the improvement of resource price on resource efficiency could reflect greater utility. When the level of resource biased technological progress increased by 1%, the resource efficiency would increase by 0.5733%, whereas 1% increase in the price of marine resources would lead to a 0.8006% increase in resource efficiency.

The first is to improve the technological progress level of marine resource elements. R & D and promotion of resource-saving mariculture technology, coastal areas can increase efforts to R & D and promotion of resource-saving mariculture technology, improve the ability of independent innovation, strengthen the development and utilization of green aquaculture technology. This includes optimizing the aquaculture structure, developing multi-level comprehensive aquaculture, making full use of the three-dimensional space of seawater, and improving the utilization efficiency of marine resources. In addition, in the field of key technology research, technical research on fish industrial ships and deep-water cage culture was carried out, and technical specifications for ship-borne cabin culture and deep-water giant cage fish culture were established. This helps to improve breeding efficiency and resource utilization efficiency. At the same time, the integration and demonstration of aquaculture platform should be carried out, the industrialization platform should be established, and the technical mode of large-scale aquaculture in deep sea should be constructed.

The second is to build a perfect marine resource price evaluation system. Coastal areas need to improve the management system of marine resource price assessment, establish and improve the procedures and methods of marine resource price assessment, and establish a database of transaction information including the price of marine resources sold by various places and types, so as to fully and truly reflect the market price of marine resources. Moreover, coastal areas can consider introducing differentiated sea area resource price policies to make full use of regional differences to improve the utilization of sea area resources in various regions. This means that according to the resource situation, economic development level and ecological environment requirements of different regions, different sea area resource prices are formulated to promote the rational allocation and efficient utilization of resources.