The Measurement of Patent Conversion Efficiency in China’s High-Tech Industry Regions Based on a Shared Input Two-Stage Network DEA Model

Abstract

In the era of technological revolution, high-tech industries have gained prominence in national innovation systems. However, China’s high-tech sector faces challenges such as late development, weak foundations, and regional disparities. To address these issues, this study proposes a shared-input two-stage network DEA model. This model, based on an input-output perspective, considers resources that circulate and collaboratively function across multiple stages in the form of shared inputs. This paper analyzes data from 25 provinces (including municipalities) in China from 2011 to 2020 and divides the patent conversion process into two sub-stages: the upstream technology research and development stage and the downstream achievement transformation stage, measuring the stage efficiency values and overall efficiency values, respectively. To align with reality, this paper incorporates the intensity of the strength of intellectual property protection, strength of government financial support, and the expenditure on technology import as regional shared input variables. Meanwhile, expenditure on technological transformation is treated as a capital-type intermediate input variable. This approach unveils the “black box” of single-stage DEA, enabling more accurate efficiency measurement. Key findings reveal: (1) China’s high-tech research and development of patent technology, the achievement transformation and overall conversion efficiency show annual improvement, yet overall efficiency remains low with regional imbalances; (2) Achievement transformation efficiency exerts a greater impact on overall conversion efficiency than research and development of patent technology efficiency. Comparative analyses with single-stage and chained two-stage DEA models confirm the necessity of phased evaluation and shared-input variables, supported by input-output elasticity tests. The findings validate the applicability and interpretability of the proposed model in efficiency evaluation.

1. Introduction

In the context of a rapid technological revolution, high-tech industries are positioned at the leading edge of innovation and development in China, playing a critical role in enhancing national technological competitiveness. The robust advancement of these industries has emerged as a central element of the innovation-driven development strategy. The patent conversion efficiency directly determines the transformation effect of scientific and technological innovation into real productive forces. Nonetheless, owing to the delayed inception, limited developmental history, and comparatively fragile foundation of high-tech industries in China, they are still plagued by prominent problems such as low patent conversion efficiency and severe regional imbalance. According to the China Intellectual Property Development Status Evaluation Report (2023), the commercialization rate of patents in China’s high-tech industries has long been less than 30%, far lower than the 60%+ level of developed economies such as the United States and Japan; the China Science and Technology Achievement Transformation Development Report (2024) shows that the contribution of patent-related revenues to the sales revenue of new products in China’s high-tech industries is only about 40%, and a large number of innovative patents are in a “dormant” state. This low conversion efficiency leads to an annual waste of R&D resources of nearly 1 trillion yuan in China’s high-tech industries, and further restricts the high-quality growth of the industry’s output value. At the same time, only a few provinces and municipalities are currently capable of realizing large-scale operations in high-tech industrialization. This situation has resulted in significant regional disparities in development. Consequently, a comprehensive and accurate investigation into the measurement of patent conversion efficiency within high-tech industries, and the identification of efficiency bottlenecks in each stage of conversion is essential, as it will not only facilitate the acceleration of the industrialization of scientific and technological innovations in China but also contribute to the establishment of a robust intellectual property nation.

From the existing academic achievements, research on the efficiency related to high-tech industries mainly focuses on quantitative assessment. Scholars primarily employ two methods for estimating efficiency: Stochastic Frontier Analysis (SFA) [1] and Data Envelopment Analysis (DEA) [2,3]. Due to the multi-input and multi-output nature of patent activities within high-tech industries, Data Envelopment Analysis (DEA) is particularly effective in minimizing the influence of subjective factors, resulting in more objective outcomes. A key advantage of DEA is its independence from the necessity of pre-defining a production function, which mitigates the risk of errors associated with inappropriate function specification [4]. In recent years, there has been a growing trend among researchers to utilize network DEA models to assess decision-making units with greater precision, taking into account the effects of environmental variables and random errors. However, traditional chained two-stage network DEA models typically measure efficiency by using the output of the first stage as the input for the second stage, neglecting the direct impact of certain inputs on economic output and the role of intermediate inputs [5]. In contemporary economic practices, input resources frequently change and are not confined to a singular stage of production; instead, they are allocated flexibly and utilized collaboratively as shared inputs across various stages. These shared inputs not only serve a regulatory function within each individual stage but also impact the overall efficiency of patent conversion across the different stages. Consequently, the incorporation of shared input variables, along with a thorough consideration of the interdependence between input sharing and intermediate products, can enhance the measurement of patent conversion efficiency within high-tech industries, rendering it more comprehensive and precise.

In light of this, this paper enhances the existing two-stage network DEA model by utilizing panel data from 25 provinces (municipalities) in China. It introduces the concept of shared inputs to develop a shared input two-stage network DEA model for measuring the patent conversion efficiency of high-tech industries in China. Specifically, this paper first examines the phased characteristics of technology research and development, as well as the achievement transformation in high-tech industries. It establishes the strength of intellectual property protection, strength of government financial support, and the expenditure on technology import as cross-stage shared input factors. For the first time, it treats the strength of intellectual property protection as a regional shared variable, revealing its differentiated mechanisms in the dual stages of “technology research and development—achievement transformation”, reducing knowledge spillover losses through institutional constraints during the technology research and development stage, and enhancing the credibility of technology transactions through clear property rights during the achievement transformation stage. Furthermore, this paper develops a shared input two-stage network Data Envelopment Analysis (DEA) model that combines the shared input mechanism with phased measurement methods. By comparing with the single-stage DEA model and the chained two-stage network DEA model, this paper verifies the necessity of phased evaluation and the introduction of shared input variables, and identifies the efficiency bottleneck of each stage of patent conversion in China’s high-tech industry. The research results are expected to provide theoretical reference and empirical support for optimizing the allocation of regional innovation resources, improving the patent conversion efficiency of high-tech industries, and narrowing the regional development gap of high-tech industries.

The structure of the paper is arranged as follows: Section 2 reviews the research progress of the DEA method and the input-output field of patent transformation. Section 3 elaborates on the principles of the model proposed in this paper and explains the parameters. Section 4 details the selection criteria for the input and output indicators in the model. Section 5 calculates the patent conversion efficiency of China’s high-tech industry and verifies the applicability and interpretability of the proposed model through comparative analysis. Section 6 provides a summary of the entire paper and offers corresponding policy recommendations.

2. Literature Review

Against the backdrop of the rapid development of high-tech industries in China, the study of patent conversion efficiency has attracted significant attention from scholars both domestically and internationally, as it serves as a crucial indicator for assessing the marketization level of technological innovation outcomes. However, the factors influencing this indicator are complex and varied, encompassing multiple aspects such as region, human resources, and capital. Currently, academic research on patent conversion efficiency primarily focuses on two areas: first, the measurement methods for patent conversion efficiency; and second, the indicator system for patent conversion efficiency. In terms of measurement methods, existing studies primarily fall into two categories: parametric and non-parametric methods. The former is exemplified by Stochastic Frontier Analysis (SFA), which accounts for random factors during the calculation process and estimates the technical efficiency of decision-making units by decomposing the error term. However, the stringent assumptions regarding the specification and distribution of the function in this method limit its applicability. The latter is represented by Data Envelopment Analysis (DEA), which does not require prior assumptions about the production function and can simultaneously consider multiple input-output indicators. This aligns well with the characteristics of China’s high-tech industry, which involves various inputs and outputs. Consequently, most scholars tend to adopt this method and continuously refine it to explore efficiency measurement issues across different fields in greater depth. As for the indicator system, the ongoing development of the DEA model in the field of efficiency measurement has led to a more refined indicator system for patent conversion efficiency, which has increasingly become a focal point of academic research. Scholars have developed a multidimensional indicator system to more comprehensively capture the complexity and diversity of patent conversion. These two aspects form the core theme of this section. In light of this, this section will explore and analyze the research findings in these two key areas within the existing literature.

2.1. Research on DEA and Its Improved Models

Since the introduction of Data Envelopment Analysis (DEA) by Charnes, Cooper, and Rhodes in 1978 [6], this method has become an important tool for evaluating the relative efficiency of Decision-Making Units (DMUs) with multiple inputs and outputs. With the ongoing advancement of research, Data Envelopment Analysis (DEA) models have experienced continuous improvements and developments, leading to the creation of various models tailored to meet diverse research needs and practical applications. These models can be primarily categorized into three groups. The first category encompasses the entire research process as a unified whole, known as the single-stage DEA model, which assesses efficiency by considering only the initial inputs and final outputs. For instance, Murthi et al. [7] employed the CCR model to measure the efficiency of mutual funds and investment portfolios. Tsai and Molinero [8] used the BBC model to evaluate the efficiency of different sectors within the UK healthcare system. However, in traditional single-stage DEA, production systems are often viewed as a “black box” [9], solely focusing on the relative effectiveness of initial inputs on final outputs while neglecting the specific operations within the system. The second category opens the “black box” of the system process, extending the single-stage model from a value chain perspective by decomposing complex systems into two stages, thereby providing managers with information to improve the efficiency of subsystems within the DMU. For example, Guan and Chen [10] measured the cross-regional innovation efficiency of China’s high-tech industry based on a traditional two-stage DEA model. Subsequently, many scholars considered that in actual production systems, some input resources do not only function in a single stage but are flexibly allocated and collaboratively utilized as shared factors across different stages. For instance, Chen et al. [11] constructed a shared input DEA model to measure the innovation efficiency of high-tech industries in 29 provincial regions of China. Based on an improved two-stage network DEA model, Yang [12] considered human capital, energy, and economic capital as intermediate inputs in the system operation, thus providing a more accurate evaluation of the green low-carbon innovation development efficiency in 30 provinces of China. The third category divides specific research subjects into multiple stages for efficiency exploration. For example, Mirhedayatian et al. [13] constructed a multi-stage network DEA model that integrates undesirable outputs, dual-role factors, and fuzzy data to measure the efficiency of green supply chain management. Recent DEA research has focused on explainability and AI hybrid modeling. First, the eXplainable DEA (XDEA) integrates DEA with XAI: Lee [14] used DEA-XGBoost-SHAP to evaluate public transport OD pairs, quantifying input-efficiency links for networked interdependent DMUs. Second, hybrid DEA-machine learning models enhance prediction: Shi et al. [15] combined three-stage network DEA, random forest, and SHAP for bank sustainability, measuring multi-stage efficiency and identifying contextual drivers. Third, DEA-SHAP improves engineering interpretability: Alizamir et al. [16] applied SHAP to clarify DEA-derived performance in desalination plants. Our shared input two-stage network DEA remains suitable: our provincial DMUs are independent (no need for XDEA’s network modeling), our focus is phased efficiency benchmarking (not prediction), and we ensure interpretability via comparative model analysis and shared input contribution quantification, matching our regional patent conversion research context.

Table 1. DEA model literature reference table.

Methods	Research Scholars	DEA Models	Research Field
traditional single-stage DEA	Murthi et al. [7]	CCR	mutual fund and portfolio efficiency
	Tsai and Molinero [8]	BBC	efficiency of different sectors in the UK National Health Services Trusts
traditional two-stage DEA	Yong et al. [17]	BCC	-
	Kao and Hwang [18]	relational two-stage DEA model	two-stage efficiency for Taiwanese non-life insurers
	Guan and Chen [10]	relationship network DEA	cross-regional innovation efficiency of China’s high-tech industry
	Liang et al. [19]	non-cooperative game DEA model and centralized DEA model	30 top U.S. commercial banks efficiency
shared-input linked two-stage DEA /resource-constrained two-stage DEA	Chen et al. [20]	CCR	deposit and loan efficiency in banks
	Yao et al. [21]	CCR and BCC	the marginal benefits of information technology in the two-stage process of the banking industry
	Chen and Zhu [22]	-	the impact of information technology on a company’s performance in two phases
	Chen et al. [11]	shared input-based dynamic DEA	innovation efficiency of high-tech industries in China’s 29 provincial-level regions
network two-stage DEA/chain two-stage DEA	Yu et al. [23]	dynamic production network DEA model	high-tech formula innovation performance evaluation
	Pournader et al. [24]	SBM-DEA hybrid model	performance evaluation of outsourcer processes in the supply chain
	Yang [12]	TDEA and TNDEA	the efficiency of green and low-carbon innovation development in 30 provinces in China
multi-stage DEA	Ang and Chen [25]	DEA model with additive efficiency decomposition	operational efficiency of 24 non-life insurers in Taiwan
	Chen et al. [26]	a three-stage ultra-efficient DEA model for cooperative games	R&D green innovation efficiency in China’s high-tech industry
	Mirhedayatian et al. [13]	a network DEA model that combines poor output, dual role factors, and fuzzy data	a measure of the efficiency of green supply chain management

presents five main types of DEA models, among which the shared-input linked (resource-constrained) two-stage DEA model and the chained two-stage DEA model are more typical, as illustrated in Figure 1 and Figure 2. In practical operations, observing the internal structure of production systems and identifying the root causes of inefficiency are crucial breakthroughs for enhancing performance. Based on existing research, this paper integrates the advantages of the shared input two-stage DEA model and the network two-stage DEA model to construct a shared input two-stage network DEA model. This model not only considers the shared input variables between different stages, fully reflecting the fluidity and synergy of resources in cross-stage allocation, but also introduces intermediate input variables to elucidate the transmission mechanisms of various links in the patent conversion process.

2.2. Research on the Construction of Patent Conversion Efficiency Indicators

Due to the absence of a standardized formula for calculating patent conversion efficiency, many researchers resort to using proxy variables or developing alternative indicators. Existing studies have examined the factors influencing the patent conversion efficiency of China’s high-tech industries from various perspectives, aiming to identify effective strategies for improving conversion efficiency at different stages, with a particular emphasis on human and capital inputs. For instance, Yu [27] analyzed the close relationship between innovation efficiency in high-tech industries and factors such as R&D investment and R&D personnel from a value chain perspective. Ye [28] further pointed out that the proportion of fixed asset investment and commodity exports at the national level significantly impacts the output of the first stage, while input variables from the first stage also play an important role in the output of the second stage. Fan and Li [29] included variables such as R&D personnel, non-R&D inputs, and new product development expenses in their model, using the number of patent applications, new product development projects, new product sales revenue, and export delivery value as output variables for the two stages, thereby measuring the regional innovation efficiency of high-tech industries more accurately. The input-output indicators mentioned in the relevant literature are shown in

Table 2. Research on patent conversion Input-Output.

Research Scholars	Inputs of Stage1	Outputs of Stage1	Inputs of Stage2	Outputs of Stage2
Zhong et al. [30]	R&D funds, R&D personnel	the number of patent applications, the sales revenue of new products and the profit of main business	-	-
Yu [27]	R&D investment, R&D personnel, and new product development expenses	the number of patent applications and the number of patents granted	the number of patent applications, the number of patents granted, the funds for technological transformation and the number of employees	the output value of new products and the export value of new products
Ye et al. [28]	The full-time equivalent of R&D personnel, the internal expenditure of R&D, the amount of investment in fixed assets, the number of enterprises in high-tech industrial development zones and the proportion of commodity exports in the country	the number of patent applications, the number of invention patents, and the turnover of the technology market	the number of patent applications, the number of invention patents, the turnover amount of the technology market and a certain proportion of the first-stage investment	export delivery value, new product output value, industrial added value in GDP and real GDP growth rate
Xiao et al. [31]	Full-time equivalent of R&D personnel and capital investment	the number of patent applications and invention patents	the number of patent applications and invention patents	new product sales revenue and new product output value
Li et al. [32]	The proportion of R&D expenditure, R&D personnel, and regional science and technology expenditure to the total regional fiscal expenditure	Patents and papers	contract value for patents, papers and technology markets	GDP, exports, annual per capita disposable income in urban areas and total output value of high-tech industries
Feng and Chen [33]	Full-time equivalent of R&D activity personnel and internal expenditure of R&D funds	the number of patent applications and new product development projects	the number of patent applications and new product development projects	sales revenue of new products and exports of new products
Fan and Li [29]	R&D personnel, R&D capital and fixed assets	The number of patent applications and new product development projects	R&D personnel, R&D capital, fixed assets, number of patent applications, new product development projects, non-R&D investment and new product development expenses	sales revenue of new products and export delivery value

. Although existing studies consistently select input-output indicators, they primarily focus on human and capital inputs, often overlooking the significance of regional input variables. This oversight restricts a thorough examination of the variations in regional patent conversion efficiency within China’s high-tech industries and the factors influencing it. Consequently, this paper builds upon existing research by incorporating the strength of intellectual property protection, the strength of government financial support, expenditures on technology import as regional input variables. This approach aims to more comprehensively capture the impact of regional characteristics on patent conversion efficiency, thereby providing a more robust theoretical foundation for enhancing the patent conversion efficiency of China’s high-tech industries.

Currently, many scholars choose to adopt a two-stage model to measure patent conversion efficiency, and this phased division is based on the classic innovation value chain theory and the inherent law of patent commercialization in high-tech industries [10,27,34]. The first stage illustrates the process of transforming research and development (R&D) investments into patents and other R&D outputs, while the second stage demonstrates the conversion of R&D outputs into new products and various economic outcomes. This division is also highly consistent with the practical development of China’s high-tech industry and national policy orientation: the Special Action Plan for Patent Transformation and Utilization (2023–2025) clearly focuses on the two key links of “improving patent creation quality” and “enhancing patent industrialization efficiency”, which provides direct policy support for the two-stage division of patent commercialization. In fact, some R&D investments not only affect R&D outputs but also exert a significant influence on economic outputs. However, most studies tend to regard R&D outputs as the sole component of the second stage of innovation input, thereby neglecting the direct impact of certain R&D activities on economic outputs and overlooking the potential role of intermediate inputs in influencing economic outcomes. This oversight is clearly inconsistent with the actual situation. In light of this, this paper divides the patent conversion process of China’s high-tech industry into two stages: technology research and development as the first stage, and achievement transformation as the second stage [34,35,36]. It also examines the impact of certain R&D investments, specifically their two-stage sharing and the role of intermediate input resources, on economic outputs during the achievement conversion stage. To analyze this, a shared input two-stage network DEA model is constructed. This method measures efficiency by developing a sophisticated linear programming model that addresses the interdependence of shared inputs and intermediate products.

3. Methods and Models

This paper takes the two-stage division of patent conversion process (technology research and development stage and achievement transformation stage) as the fundamental framework, which is based on the innovation value chain theory, industrial practice and national policy orientation, and employs a shared input two-stage DEA model to evaluate the sub-stage efficiency of patent conversion in China’s high-tech industries. This two-stage division is the core premise for breaking through the “black box” of single-stage DEA and constructing the shared input two-stage network DEA model, and is the key to realizing the innovative improvement of the traditional DEA model in this study. The analysis encompasses the efficiency of both the technology research and development stage and the achievement transformation stage, in addition to assessing overall efficiency. Recognizing that patent conversion is a complex and dynamic process, the proposed model first transforms research and development resources into research outcomes through technology research and development activities. Subsequently, these research outcomes, along with additional intermediate input resources, are converted into new products [37], thereby generating economic benefits. In this process, a portion of the R&D investment resources does not serve a single stage; instead, they are utilized as shared inputs that flow and are jointly employed across various stages. This approach enhances the overall efficiency of patent transformation. Building on the two-stage characteristics of patent transformation and the mechanism of shared investment, this paper refines the existing two-stage network DEA model. It constructs a shared input two-stage network DEA model by incorporating some of the shared investments and additional input variables to address the issue of patent conversion efficiency in China’s high-tech industries. The structural diagram is illustrated in Figure 3.

In Figure 3, I₁ is the input vector, which includes human resource investment and capital investment during the technology research and development stage. I₂ is the shared input vector for both the technology research and development stage and the achievement transformation stage, referred to as the regional input variable. I₃ is the additional investment during the achievement transformation stage, which includes capital investment for the achievement transformation stage. O₁ is the output vector for the technology research and development stage, which also serves as the input vector for the achievement transformation stage, referred to the intermediate vector in this paper, representing the output of technological achievements. O₂ is the output variable for the achievement transformation stage, referred to the final output, representing the economic benefit output.

The parameters and variables involved in the proposed model are shown in

Table 3. Model parameter explanation.

Parameter	Meaning
θ1k	maximum efficiency of the first stage of the kth decision unit (DMU)
up	the weight of the p-intermediate output zp
vi(1)	the weight of the specific input variable xi(1) in the first stage
vi(12)	share the weight of the input variable xi(12)
m1	the number of inputs in the first stage
q	the number of intermediate outputs in the first stage
n	the number of DMU, i.e., the number of decision-making units that need to be evaluated
θ2k	the maximum efficiency of the second stage of the kth DMU
ur	the weight of the final output variable yr in the second stage
wp	the weight of the intermediate output zp in the first stage (put into use in the second stage)
vl(2)	the weight of the specific input variable xl(2) in the second stage
s	the number of outputs in the second stage
m2	the number of additional investments in the middle of the second stage
θoverall(k)	the overall stage of the kth DMU is the maximum efficiency

and

Table 4. Model variable explanation.

Variable	Meaning
zpk	The kth intermediate output of the kth DMU in the first stage (as input to the second stage)
xik(1)	the kth DMU is the ith specific input variable in the first stage
xik(12)	input variables shared by the kth DMU in the first and second stage (i.e., shared input variables)
yrk	the kth DMU is the rth final output of the second stage
xlk(2)	the k-th DMU is the lth specific input variable in the second stage
xlj	intermediate additional input variables in the second stage

.

Assuming there are n decision-making units (DMUs), referring here to the 25 provinces (municipalities) of China. Each DMU_j (j = 1, 2,…, n) has m₁ initial inputs x_ij (i = 1, 2,…, m₁), q intermediate products z_pj (p = 1, 2,…, q), m₂ additional inputs x_lj (l = 1, 2,…, m₂), and s final outputs y_rj (r = 1, 2,…, s). Among them, the intermediate products z_pj (p = 1, 2,…, q) serve as outputs in the first stage and inputs in the second stage. Unlike the traditional chained two-stage production structure and the two-stage production structure with shared inputs, in this production structure, part of the initial system input x_ij is used in the first sub-stage, denoted as x_ij⁽¹⁾, while another part is allocated for joint use by both sub-stages, denoted as x_ij⁽¹²⁾; additionally, the additional input x_lj will be added in the second subsystem.

This study examines the characteristic of patent conversion activities within China’s high-tech industry, which is currently experiencing a period of scale expansion. It employs the Constant Returns to Scale (CRS) assumption, which closely aligns with industry realities, and develops a shared input two-stage network Data Envelopment Analysis (DEA) model based on the classic Charnes, Cooper, and Rhodes (CCR) model [6]. The model incorporates both shared input variables and additional input variables to calculate the maximum efficiency values for the two sub-stages as well as the overall stage, as expressed in the following formula:

• CCR model in the technology research and development stage (i.e., the first stage)

Based on the research by Liang et al. [19], this paper divides the input variables in the technology research and development stage into the exclusively first stage input variable x_ik⁽¹⁾ and the two-stage shared input variable x_ik⁽¹²⁾. The modified first stage CCR model for the kth DMU can be expressed as:

$$\mathit{Maximize}{\theta }_1^k={\displaystyle \frac{{\sum }_{p=1}^q{u}_p{z}_{pk}}{{\sum }_{i=1}^{m_1}{v}_i^{\left(1\right)}{x}_{ik}^{\left(1\right)}+{\sum }_{i=1}^{m_1}{v}_i^{\left(12\right)}{x}_{ik}^{\left(12\right)}}}$$

(1)

s.t

$$\begin{gathered} {\displaystyle \frac{{\sum }_{p=1}^q{u}_p{z}_{pj}}{{\sum }_{i=1}^{m_1}{v}_{ij}^{\left(1\right)}{x}_{ij}^{\left(1\right)}+{\sum }_{i=1}^{m_1}{v}_i^{\left(12\right)}{x}_{ij}^{\left(12\right)}}}\le 1,j=\mathrm{1,2},\dots ,n \\ {u}_p,v_i^{\left(1\right)},v_i^{\left(12\right)}\ge 0 \\ {\sum }_{i=1}^{m_1}{v}_i^{\left(1\right)}=1 \end{gathered}$$

$${\sum }_{i=1}^{m_1}{v}_i^{\left(12\right)}=1$$

(2)

2.

CCR model in the achievement transformation stage (i.e., the second stage)

Based on the research by Chen et al. [20], this paper considers the additional input variable x_lj during the achievement transformation stage. The modified second-stage CCR model for the kth DMU can be expressed as:

$$Maximize{\theta }_2^k={\displaystyle \frac{{\sum }_{r=1}^s{u}_r{y}_{rk}}{{\sum }_{p=1}^q{w}_p{z}_{pk}+{\sum }_{i=1}^{m_1}{v}_i^{\left(12\right)}{x}_{ik}^{\left(12\right)}+{\sum }_{l=1}^{m_2}{v}_l^{\left(2\right)}{x}_{lk}^{\left(2\right)}}}$$

(3)

s.t

$${\displaystyle \frac{{\sum }_{r=1}^s{u}_r{y}_{rj}}{{\sum }_{p=1}^q{w}_p{z}_{pj}+{\sum }_{i=1}^{m_1}{v}_i^{\left(12\right)}{x}_{ik}^{\left(12\right)}+{\sum }_{l=1}^{m_2}{v}_l^{\left(2\right)}{x}_{lj}}}\le 1,j=\mathrm{1,2},\dots ,n$$

$$u_r,w_{p,}{v}_i^{\left(12\right)},v_l^{\left(2\right)}\ge 0$$

$${\sum }_{r=1}^s{u}_r=1$$

$${\sum }_{p=1}^q{w}_p\le 1$$

$${\sum }_{i=1}^{m_1}{v}_i^{\left(12\right)}\le 1$$

$${\sum }_{i=1}^{m_1}{v}_i^{\left(12\right)}=1$$

(4)

3.

Overall CCR Model

The objective of calculating overall efficiency is to maximize the overall relative efficiency by simultaneously considering the inputs and outputs of both the first and second stages. Therefore, overall efficiency can be expressed as:

$$Maximize{\theta }_{overall\left(k\right)}={\displaystyle \frac{{\sum }_{r=1}^s{v}_r{y}_{rk}}{{\sum }_{p=1}^q{u}_p{z}_{pj}+{\sum }_{i=1}^{m_1}{v}_i^{\left(12\right)}{x}_{ik}^{\left(12\right)}+{\sum }_{l=1}^{m_2}{v}_l^{\left(2\right)}{x}_{lk}}}$$

(5)

s.t

$${\displaystyle \frac{{\sum }_{p=1}^q{u}_p{z}_{pj}}{{\sum }_{i=1}^{m_1}{v}_{ij}^{\left(1\right)}{x}_{ij}^{\left(1\right)}+{\sum }_{i=1}^{m_1}{v}_i^{\left(12\right)}{x}_{ij}^{\left(12\right)}}}\le {\theta }_1^j$$

$${\displaystyle \frac{{\sum }_{r=1}^s{u}_r{y}_{rj}}{{\sum }_{p=1}^q{w}_p{z}_{pj}+{\sum }_{i=1}^{m_1}{v}_i^{\left(12\right)}{x}_{ik}^{\left(12\right)}+{\sum }_{l=1}^{m_2}{v}_l^{\left(2\right)}{x}_{lj}}}\le {\theta }_2^j$$

$${\displaystyle \frac{{\sum }_{r=1}^s{v}_r{y}_{rj}}{{\sum }_{p=1}^q{u}_p{z}_{pj}+{\sum }_{i=1}^{m_1}{v}_i^{\left(12\right)}{x}_{ij}^{\left(12\right)}+{\sum }_{l=1}^{m_2}{v}_l^{\left(2\right)}{x}_{lj}}}\le {\theta }_1^j\times {\theta }_2^j,j=\mathrm{1,2},\dots ,n$$

$$u_p=w_p$$

$$v_r,u_p,{w_p,v_i^{\left(1\right)},v}_i^{\left(12\right)},v_l^{\left(2\right)}\ge 0$$

$${\sum }_{r=1}^s{v}_r=1$$

$${\sum }_{p=1}^q{u}_p=1$$

$${\sum }_{i=1}^{m_1}{v}_i^{\left(1\right)}=1$$

$${\sum }_{i=1}^{m_1}{v}_i^{\left(12\right)}=1$$

$${\sum }_{l=1}^{m_2}{v}_l^{\left(2\right)}=1$$

(6)

Although the shared-input two-stage network DEA model in this study calculates efficiency in phases, it is a genuine integrated network DEA model that achieves endogenous joint optimization of the whole patent conversion process under a single unified optimization framework, rather than a simple extended two-stage decomposition with ex post efficiency interpretation. The endogenous efficiency propagation and inter-stage linkage are strictly enforced by two core mathematical constraints in the unified optimization framework, and the three efficiency values (${\theta }_1^k$, ${\theta }_2^k$, ${\theta }_{overall\left(k\right)}$) are solved synchronously rather than separately:

1. Weight consistency constraint for shared input variables: The weights of the same shared input variable $x_{ik}^{\left(12\right)}$ in the technology research and development stage and achievement transformation stage are completely consistent in the unified optimization framework, and the weight normalization conditions (${\sum }_{i=1}^{m_1}{v}_i^{\left(12\right)}=1$) are applied to the whole model rather than stage-specifically. This ensures the unified economic meaning of shared inputs across stages and makes the efficiency contribution of shared inputs endogenous to the overall optimization, avoiding the decoupling of stage efficiency calculation.

2. Intermediate output endogenous linkage constraint: The intermediate output ($z_{pk}$) of the first stage is the only core input of the second stage, and its weight in the first stage ($u_p$) and weight in the second stage ($w_p$) are interdependent in the unified objective function of the overall efficiency (${\theta }_{overall\left(k\right)}$). The stage efficiency values (${\theta }_1^k$, ${\theta }_2^k$) are not solved by independent stage-specific CCR formulations; instead, they are the sub-optimal solutions derived from the global optimal solution of the overall efficiency model, which fundamentally realizes the endogenous propagation of efficiency between stages.

The overall efficiency is not a simple weighted average of the efficiencies of the two stages, but rather a global optimization of the inputs and outputs of both stages targeting the final economic output. Therefore, there are inherent mathematical constraints on the efficiency transmission between stages: low efficiency in the first stage will directly lead to insufficient intermediate outputs, thereby restricting the improvement of efficiency in the second stage; conversely, low efficiency in the second stage will result in the waste of resources invested in intermediate outputs and reduce the overall efficiency. All the above mathematical designs confirm that the model is an integrated network DEA with endogenous inter-stage efficiency linkage, rather than a parallel two-stage decomposition model with ex post efficiency interpretation.

4. Indicators and Data Processing

Through the explanation of the model principles in Section 3, this section further selects appropriate input and output indicators based on practical situations to ensure the scientific and rational nature of the calculations. It will focus on discussing the key factors that influence the patent conversion efficiency of high-tech industries in specific regions and will construct an indicator system to facilitate the subsequent empirical analysis.

4.1. Indicator Selection

To ensure consistency, the input-output indicators selected in this paper differ slightly from those found in the relevant literature. Currently, in the context of implementing an innovation-driven development strategy, intellectual property protection—being a core element of this strategy [38]—has profoundly influenced various aspects, including technology transfer activities between countries and the attraction of foreign investment. Furthermore, Kim et al. argue that intellectual property significantly impacts patent protection, technological innovation, and economic growth [39]. Specifically, the intellectual property protection system establishes a standardized operational framework for the legitimate transfer of patents through various measures, such as effectively curbing imitation and infringement, strengthening the protection of new product value, and enhancing technological specificity. These measures have invigorated the patent trading market, making it more dynamic and promoting an increase in patent conversion efficiency. However, intellectual property protection may also inhibit the diffusion of innovation to some extent, thereby limiting the pace and realization of large-scale production, which could ultimately lead to a decrease in patent conversion efficiency. Based on this, when examining the differences in patent conversion efficiency among high-tech industries in various regions, this paper incorporates the strength of intellectual property protection in each region as a key influencing factor within the research framework, which distinguishes it from previous studies by other scholars. Furthermore, the level of government support is also critical for the patent conversion of regional high-tech industries, as government policy can effectively promote the market application of technological innovations, thereby enhancing regional patent conversion efficiency to a significant extent. Meanwhile, as a developing country, China still lags behind developed nations in terms of knowledge accumulation. The introduction of technology not only benefits relatively underdeveloped regions by enabling leapfrog technological advancement but also significantly enhances the conversion and deepening of local technology [40]. Therefore, when studying the differences in patent conversion efficiency among high-tech industries in various regions, the strength of intellectual property protection, the strength of government financial support, expenditures on technology import have become crucial factors in this research. These three regional input variables play a significant role not only in the research and development stage of technology but also have a direct impact on the efficiency of the achievement transformation stage. Based on this, the input-output indicators involved in this paper are shown in

Table 5. Input-Output indicators and unit symbols.

Stage	Primary Indicator	Secondary Indicators	Tertiary Indicator	Unit	Symbol
technology research and development stage	input	regional inputs	strength of intellectual property protection [41]	—	x1
			strength of government financial support [42,43]	%	x2
			expenditure on technology import [44]	ten thousand yuan	x3
		manpower inputs	average number of employees [45]	ten thousand people	x4
			R&D personnel in full-time equivalent [46]	ten thousand person-years	x5
		capital inputs	internal R&D expenditure [47]	ten thousand yuan	x6
			expenditure on new product development [48]	ten thousand yuan	x7
	output	technical achievements outputs	number of patent applications [49]	piece	z1
			number of valid patents [50,51]	piece	z2
			number of new product development projects [52]	item	z3
achievement transformation stage	input	regional inputs	strength of intellectual property protection	—	x1
			strength of government financial support	%	x2
			expenditure on technology import	ten thousand yuan	x3
		technical achievements inputs	number of patent applications	piece	z1
			number of valid patents	piece	z2
			number of new product development projects	item	z3
		capital reinputs	expenditure on technological transformation [53]	ten thousand yuan	x8
	output	economic benefits outputs	sales revenue from new products [54]	ten thousand yuan	y1
			export value of new products [54]	ten thousand yuan	y2

:

In the technology research and development stage, the input variables include the strength of intellectual property protection, the strength of government financial support, expenditures on technology import, the average number of employees, R&D personnel in full-time equivalent, internal R&D expenditure, and expenditure on new product development, totaling seven items. The output variables consist of the number of patent applications, the number of valid patents, and the number of new product development projects, totaling three items. In the achievement transformation stage, the input variables include the strength of intellectual property protection, the strength of government financial support, expenditures on technology import, the number of patent applications, the number of valid patents, the number of new product development projects, and expenditures on technological transformation, totaling seven items. The output variables consist of sales revenue from new products and export value of new products totaling two items.

In this input-output variable, the calculation of the strength of intellectual property protection is relatively complex. Based on the GP method [55], this paper combines the modified approach proposed by Chinese scholars for measuring the intensity of intellectual property protection in transitional countries. It starts from two aspects: legislative intensity L_(t) and enforcement intensity E_(t), taking China as an example to present the modified level of intellectual property protection P_(t) [56]. The calculation formula is as follows:

$$P\left(t\right)=L\left(t\right)\ast E\left(t\right)$$

(7)

$$L\left(t\right)={\sum }_{i=1}^{5}L{F}_i$$

(8)

$$E\left(t\right)={\sum }_{j=1}^{5}Z{F}_j$$

(9)

Based on this information, the Intellectual Property Protection Strength Index for various regions in China from 2011 to 2020 has been calculated, with each indicator and its corresponding symbol listed in

Table 6. Intellectual property protection strength indicator system.

Primary Indicator	Secondary Indicators	Tertiary Indicator	Quaternary Indicator/Proxy Variable	Symbol
strength of intellectual property protection P(t)	intellectual property legislation intensity L(t)	coverage LF1	patentability of medicines	lf1
			patentability of chemicals	lf2
			patentability of food	lf3
			patentability of food and animal quality	lf4
			patentability of surgical products	lf5
			patentability of microbial	lf6
			patentability of utility models	lf7
		membership in international patent agreements LF2	Patent Cooperation Treaty (PCT)	lf8
			Paris Convention and its amendments	lf9
			Plant Variety Protection (UPOV)	lf10
		loss of protection provisions LF3 [57]	program licensing	lf11
			compulsory license	lf12
			revocation of patents	lf13
		enforcement mechanism LF4	pre-trial injunctions for patent infringement	lf14
			joint and several liability for patent infringement	lf15
			the burden of proof on the patent infringer	lf16
		term of protection LF5	based on application standards	lf17
			based on grant criteria	lf18
	intellectual property enforcement intensity E(t) [58]	the degree of legalization of society ZF1	lawyer ratio	zf1
		the degree of completeness of the legal system ZF2	legislative time	zf2
		level of economic development ZF3	GDP per capita	zf3
		public awareness ZF4	literacy rate	zf4
		the international community oversees the checks and balances ZF5	member of the WTO	zf5

. Additionally, for comparative analysis,

Table 7. 2011–2020 Intellectual property protection index in certain regions of China.

Region	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020
Beijing	4.13	4.14	4.15	4.16	4.17	4.18	4.19	4.20	4.21	4.22
Tianjin	3.72	3.78	3.84	3.90	3.96	4.01	4.14	4.20	4.21	4.22
Hebei	3.38	3.40	3.40	3.38	3.38	3.42	3.43	3.45	3.44	3.50
Shanxi	3.34	3.35	3.35	3.36	3.36	3.39	3.49	3.54	3.53	3.60
Liaoning	3.54	3.57	3.60	3.64	3.67	3.67	3.69	3.73	3.77	3.88
Jilin	3.44	3.47	3.49	3.51	3.54	3.59	3.56	3.52	3.45	3.67
Heilongjiang	3.37	3.36	3.34	3.35	3.33	3.32	3.30	3.28	3.20	3.32
Shanghai	4.13	4.14	4.15	4.16	4.17	4.18	4.19	4.20	4.21	4.22
Jiangsu	3.52	3.55	3.59	3.62	3.66	3.68	3.74	3.86	3.95	4.07
Zhejiang	3.69	3.74	3.77	3.82	3.87	3.93	4.00	4.07	4.18	4.22
Anhui	3.09	3.14	3.18	3.20	3.23	3.28	3.32	3.40	3.56	3.57
Fujian	3.53	3.51	3.60	3.57	3.60	3.65	3.69	3.72	3.77	3.85
Jiangxi	3.11	3.13	3.16	3.18	3.21	3.25	3.26	3.30	3.38	3.45
Shandong	3.48	3.52	3.56	3.59	3.62	3.66	3.71	3.76	3.82	3.86
Henan	3.23	3.26	3.29	3.32	3.34	3.38	3.43	3.48	3.56	3.58
Hubei	3.40	3.44	3.50	3.53	3.56	3.60	3.64	3.68	3.72	3.75
Hunan	3.28	3.32	3.35	3.41	3.45	3.50	3.52	3.56	3.64	3.76
Guangdong	3.59	3.62	3.65	3.69	3.73	3.77	3.81	3.93	4.01	4.10
Guangxi	3.14	3.16	3.19	3.22	3.24	3.28	3.24	3.27	3.30	3.36
Chongqing	3.52	3.56	3.62	3.66	3.68	3.77	3.85	3.91	3.98	4.07
Sichuan	3.18	3.24	3.28	3.32	3.34	3.38	3.46	3.55	3.61	3.74
Guizhou	2.79	2.86	2.93	3.05	3.08	3.14	3.20	3.22	3.31	3.43
Yunnan	2.97	3.03	3.10	3.13	3.16	3.20	3.26	3.29	3.45	3.54
Shaanxi	3.39	3.47	3.53	3.57	3.56	3.59	3.65	3.74	3.78	3.84
Gansu	2.93	2.97	3.01	3.05	3.00	3.06	3.08	3.13	3.15	3.24

presents the values of the Intellectual Property Protection Level for each region during the same period.

In order for patented innovative technologies to fully realize their value, they must be effectively transformed into productive forces. This paper categorizes the patent conversion process within China’s high-tech industry into two primary stages: technology research and development, and achievement transformation. In conjunction with Figure 3 and Table 5, the specific model presented in this article is illustrated in Figure 4.

As illustrated in Figure 4, the technology research and development stage comprises seven inputs and three intermediate outputs. The seven inputs include four human capital inputs and three regional inputs. Notably, the former is exclusively utilized for technology research and development and is considered a quasi-fixed input, while the latter—comprising the strength of intellectual property protection, the strength of government financial support, and expenditures on technology imports—is shared during the achievement transformation stage. The number of patent applications, number of valid patents, and number of new product development projects are outputs in the technology research and development process, and they also function as inputs in the achievement transformation process. Among these, the ratio of government funding to internal R&D expenditure is selected as a measure of the strength of government financial support, while the “average number of employees” is used as a proxy variable for “average employment number”.

In the stage of achievement transformation, there are 7 inputs and 2 final outputs. Among the 7 inputs, there are 3 shared inputs (the strength of intellectual property protection, the strength of government financial support, and the expenditures on technology imports), 3 intermediate inputs (the number of patent applications, the number of valid patents, and the number of new product development projects), and 1 additional input (expenditure on technological transformation). The final outputs are the sales revenue from new products and export value of new products.

This model performs a comprehensive analysis of the entire patent conversion chain, encompassing “R&D resources, R&D outcomes, and economic benefits”, by incorporating “shared input variables” to systematically assess patent conversion efficiency within China’s high-tech industry. The introduction of shared input variables allows the model to more accurately capture the collaborative effects and resource allocation of R&D activities at various stages, thereby improving the precision and thoroughness of the evaluation results.

4.2. Data Processing

4.2.1. Data Sources

Considering the availability of data, this paper analyzes the patent conversion efficiency of China’s high-tech industries by selecting data from nine years (with full-year data for 2017 missing) from 25 provinces (municipalities) nationwide during the period from 2011 to 2020. Some of the missing data have been interpolated using Stata software. The input-output data in this paper are sourced from the China High-tech Industry Statistical Yearbook, China Statistical Yearbook, China Science and Technology Statistical Yearbook, and China Lawyer Statistical Yearbook.

4.2.2. Data Processing Methods

(1) Deflation

In this context, the expenditures on technology input (x₃), internal R&D expenditures (x₆), expenditure on new product development (x₇), and expenditure on technological transformation (x₈) are all considered as cash flows, primarily composed of consumption and fixed asset investment. Moreover, the current indicators may have an impact on future patent outputs and new product sales revenues. Therefore, deflation is necessary before they can be used as input variables. This paper conducts deflation based on the Consumer Price Index (CPI) and the Fixed Asset Investment Price Index (IPIFA) to calculate the Expenditure Price Index (EPI), where the weight of the Consumer Price Index is 55% and the weight of the Fixed Asset Investment Price Index is 45%. That is:

$$EPI=0.55\ast CPI+0.45\ast IPIFA$$

(10)

Subsequently, based on the formula, the influence of price factors on expenditures related to technology input, internal R&D expenditures, new product development expenditures, and technological transformation expenditures were removed. This adjustment resulted in the actual values (E) for the four indicators corresponding to high-tech industries across 25 provinces (municipalities) in China from 2011 to 2020.

(2) Capital Stock Accounting

Due to the impact of capital stock on fixed asset investment—where investments made in the current year influence patent conversion for an extended period—it is essential to apply depreciation to four types of expenditures: the expenditures on technology input, internal R&D expenditures, expenditure on new product development, and expenditure on technological transformation. By comparing various measurement methods discussed in the previous literature, this paper contends that the perpetual inventory method is more appropriate for analyzing the capitalization of fixed asset investments [59,60]. The specific calculation formula is:

$$K_{it}=\left(1-\delta \right)K_{i(t-1)}+E_{it}$$

(11)

where K_it represents the capital stock of indicator i in province i at period t. K_i(t−1) denotes the capital stock of indicator i in province i during period t − 1. E_it is the actual value of indicator i in province i during period t. δ is the relative depreciation rate, which is set at δ = 0.1 based on the recommendations from the GDP Production Accounting Division of the National Bureau of Statistics. The initial capital stock is given by K_i0 = E_i0/(δ + g), where g is the annual average growth rate of the indicator.

(3) Delay Processing

The transformation of research and development is a process of knowledge creation, and a lag effect occurs when inputs contribute to both current and future outputs [61]. When analyzing patent conversion efficiency, the temporal lag structure is often a significant consideration [62,63]. Given that patents typically require a certain time delay from application to eventual commercialization and the realization of economic benefits, this paper introduces the concept of lag periods for analysis: the initial input variables utilize data from year T, the intermediate products and additional input variables employ data from year T + 1, and the expected and unexpected output variables draw on data from year T + 2.

5. Empirical Research

This section utilizes MATLAB (R2022a) software to measure the efficiency values of the patent conversion sub-stages (technology research and development stage and achievement transformation stage) and the overall stage of China’s high-tech industry using the shared input two-stage network DEA model constructed above. Subsequently, it compares these results with those obtained from the traditional single-stage DEA model and the chained two-stage network DEA model to verify the superiority of this model.

5.1. Analysis of Patent Conversion Efficiency Measurement

This paper, based on the CRS assumption, utilizes MATLAB software to measure the overall and internal operational efficiency of various sub-stages of patent conversion in China’s high-tech industry during the research period from 2011 to 2020, with specific values shown in

Table 8. Sub-stage efficiency measured by shared input two-stage network DEA.

Region	Technology Research and Development Stage						Achievement Transformation Stage
	2011	2013	2015	2018	2020	Average	2011	2013	2015	2018	2020	Average
Beijing	1.00	1.00	0.56	0.83	1.00	0.77	0.14	0.11	0.09	0.18	0.09	0.16
Tianjin	0.70	0.59	0.52	0.43	0.46	0.51	1.00	1.00	1.00	1.00	1.00	1.00
Hebei	0.70	0.95	0.55	0.72	0.54	0.60	0.33	0.24	0.20	0.46	0.32	0.35
Shanxi	0.56	0.66	0.72	0.69	0.53	0.58	0.13	0.18	0.21	0.77	1.00	0.44
Liaoning	0.40	0.47	0.33	0.45	0.57	0.43	0.21	0.12	0.14	0.19	0.17	0.17
Jilin	0.57	0.53	0.46	0.52	0.48	0.56	0.24	0.16	0.12	0.31	0.29	0.25
Heilongjiang	0.26	0.59	0.17	0.25	0.33	0.32	0.09	0.05	0.03	0.35	0.27	0.20
Shanghai	0.43	0.73	0.39	0.51	0.53	0.46	0.13	0.10	0.10	0.20	0.11	0.15
Jiangsu	0.43	0.39	0.35	0.45	0.48	0.42	0.24	0.15	0.13	0.27	0.17	0.21
Zhejiang	0.65	0.70	0.63	0.57	0.63	0.65	0.17	0.17	0.25	0.50	0.36	0.32
Anhui	0.93	1.00	0.79	0.81	1.00	0.87	0.13	0.14	0.23	0.58	0.40	0.32
Fujian	0.36	0.60	0.39	0.55	0.52	0.47	1.00	1.00	1.00	1.00	1.00	1.00
Jiangxi	0.35	0.34	0.79	1.00	0.49	0.64	0.33	0.16	0.43	1.00	0.83	0.57
Shandong	0.46	0.56	0.54	0.44	0.44	0.46	0.25	0.21	0.15	0.28	0.35	0.26
Henan	0.51	0.14	0.49	0.78	0.51	0.55	1.00	1.00	1.00	1.00	1.00	1.00
Hubei	0.36	0.43	0.53	0.63	0.72	0.52	0.21	0.18	0.17	0.31	0.22	0.24
Hunan	1.00	0.48	0.63	0.63	0.52	0.67	0.33	0.27	0.23	0.43	0.42	0.35
Guangdong	1.00	1.00	1.00	1.00	0.89	0.94	0.21	0.17	0.13	0.24	0.10	0.20
Guangxi	0.57	0.48	0.75	0.85	1.00	0.61	0.24	0.14	0.13	0.26	0.19	0.24
Chongqing	1.00	1.00	0.89	0.65	0.49	0.84	0.12	0.61	0.60	0.86	0.35	0.54
Sichuan	0.76	0.55	0.52	0.57	0.58	0.57	0.12	0.09	0.08	0.23	0.15	0.16
Guizhou	0.37	1.00	0.38	0.57	0.44	0.49	0.09	0.05	0.10	0.19	0.18	0.13
Yunnan	0.79	0.93	0.74	0.77	0.66	0.83	0.13	0.10	0.10	0.80	0.37	0.25
Shaanxi	0.39	0.27	0.28	0.41	0.36	0.33	0.11	0.11	0.06	0.16	0.22	0.15
Gansu	0.68	0.44	0.51	0.42	0.49	0.49	0.12	0.14	0.23	0.45	0.36	0.29
eastern	0.64	0.73	0.55	0.61	0.61	0.59	0.39	0.35	0.34	0.46	0.39	0.40
Central	0.62	0.51	0.66	0.76	0.63	0.64	0.35	0.32	0.38	0.68	0.65	0.49
western	0.65	0.67	0.58	0.61	0.57	0.59	0.13	0.18	0.19	0.42	0.26	0.25
northeast	0.41	0.53	0.32	0.41	0.46	0.43	0.18	0.11	0.10	0.28	0.24	0.21
nationwide	0.61	0.63	0.56	0.62	0.59	0.58	0.28	0.27	0.28	0.48	0.40	0.36

.

From Table 8, it can be seen that during the research period, the average efficiency of patent conversion in China at the technology research and development stage and the achievement transformation stage is 0.58 and 0.36, respectively. This indicates that there is significant room for improvement in the patent conversion efficiency in both stages, particularly in the achievement transformation stage, where the efficiency level is relatively low and the losses are more pronounced.

From a regional perspective, both in the technology research and development stage and in the achievement transformation stage, the central region exhibits the highest average efficiency, followed by the eastern and western regions. In contrast, the northeastern region demonstrates a significantly lower average efficiency. This finding is not entirely consistent with the earlier conclusion that efficiency decreases from east to west. The discrepancy arises from the fact that, in recent years, the country has placed considerable emphasis on the growth and development of the central region, implementing a series of policy measures to advance the manufacturing industry in this area. Additionally, the central region possesses several favorable conditions for the development of high-tech industries, including relatively abundant scientific and technological resources and a skilled talent pool. These factors contribute to the market expansion of high-tech products and the coordinated development of both the upstream and downstream segments of the industrial chain. Consequently, it can be observed that around 2015, the patent conversion efficiency of high-tech industries in the central region began to surpass that of the eastern region during the stages of technology research and development and achievement transformation. Meanwhile, the western region, leveraging its extensive national-level research platforms and key state-owned enterprise resources, along with the presence of foreign enterprises, has not only established a robust technological showcase but also significantly stimulated regional innovation. This has resulted in rapid growth in the number of patents and new product revenues, demonstrating its exceptional ability to convert research achievements into practical applications. Furthermore, as the leader of China’s economy, the eastern region has not only developed its high-tech industry early and rapidly but has also successfully established a mature and comprehensive industrial chain and innovation system, laying a solid foundation for the sustained prosperity of the regional economy. In contrast, the northeastern region lacks adequate support and development opportunities from the central government. Its innovation environment, technology, and management levels are not as advanced as those in other regions, resulting in a lower patent conversion efficiency.

From the perspective of the structural characteristics of inter-stage efficiency transmission, the structural bottlenecks in the patent conversion of China’s high-tech industry can be categorized into three types:

First, the “conversion capability deficiency type”, characterized by high efficiency in the technology research and development stage but low efficiency in the achievement transformation stage. Representative of some provinces in the eastern region (e.g., Shanghai: 0.46 in technology research and development stage and 0.15 in achievement transformation stage; Guangdong: 0.94 in technology research and development stage and 0.20 in achievement transformation stage), its core issue lies in the failure of intermediate outputs to effectively align with market demands. Second, the “dual constraint type”, manifested by low efficiency in both stages. Typical of provinces in the northeastern region (0.43 in technology research and development stage and 0.21 in achievement transformation stage), it is primarily plagued by the coexistence of insufficient R&D investment and weak conversion capability. Third, the “synergistic and high-efficiency type”, featuring a high degree of coupling between the efficiencies of the two stages. Exemplified by some provinces in the central region (e.g., Henan: 0.55 in technology research and development stage and 1.00 in achievement transformation stage; Anhui: 0.87 in technology research and development stage and 0.32 in achievement transformation stage), it has no obvious structural bottlenecks.

From a stage perspective, both the efficiency of technology research and development and the efficiency of achievement transformation are showing an upward trend. However, overall, the efficiency of achievement transformation remains lower than that of technology research and development. This discrepancy indicates that the inefficiency of achievement transformation hinders the overall improvement of patent transformation efficiency in China’s high-tech industry. Although the number of projects resulting from achievement transformation has steadily increased in recent years, and the sales revenue of new products has grown annually, significant progress has been made in innovation-driven economic development. Nevertheless, the market for the transformation of scientific and technological achievements in China still requires refinement, and there remains a lack of effective connection between technology research and development and achievement transformation.

To comprehensively investigate the overall state of patent conversion in China’s high-tech industry,

Table 9. Overall patent conversion efficiency measured by shared input two-stage network DEA.

Region	2011	2012	2013	2014	2015	2016	2018	2019	2020	Average
Beijing	0.16	0.15	0.10	0.12	0.11	0.27	0.30	0.65	0.28	0.24
Tianjin	0.32	0.30	0.25	0.27	0.15	0.19	0.21	0.33	0.26	0.25
Hebei	0.16	0.17	0.16	0.17	0.18	0.30	0.32	0.43	0.28	0.24
Shanxi	0.17	0.13	0.10	0.08	0.26	0.73	0.66	0.70	1.00	0.43
Liaoning	0.08	0.07	0.06	0.08	0.09	0.08	0.10	0.17	0.17	0.10
Jilin	0.27	0.19	0.13	0.18	0.11	0.24	0.25	0.27	0.34	0.22
Heilongjiang	0.01	0.02	0.02	0.02	0.01	0.05	0.06	0.12	0.10	0.05
Shanghai	0.05	0.05	0.05	0.06	0.06	0.17	0.17	0.19	0.15	0.11
Jiangsu	0.18	0.16	0.15	0.19	0.16	0.37	0.45	0.46	0.42	0.28
Zhejiang	0.19	0.17	0.17	0.21	0.21	0.41	0.45	0.56	0.47	0.31
Anhui	0.18	0.16	0.20	0.25	0.31	0.67	0.67	0.78	0.56	0.42
Fujian	0.18	0.15	0.13	0.18	0.19	0.35	0.31	0.43	0.30	0.24
Jiangxi	0.16	0.16	0.17	0.23	0.33	0.98	0.98	1.00	0.87	0.54
Shandong	0.13	0.11	0.13	0.16	0.11	0.15	0.18	0.31	0.35	0.18
Henan	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
Hubei	0.11	0.10	0.10	0.10	0.16	0.33	0.30	0.33	0.31	0.21
Hunan	0.53	0.41	0.33	0.33	0.20	0.36	0.40	0.54	0.48	0.40
Guangdong	0.20	0.17	0.15	0.19	0.21	0.38	0.38	0.39	0.27	0.26
Guangxi	0.18	0.12	0.10	0.14	0.19	0.35	0.33	0.55	0.45	0.27
Chongqing	0.20	0.42	0.86	0.67	0.52	0.80	0.81	0.82	0.57	0.63
Sichuan	0.11	0.13	0.10	0.12	0.11	0.32	0.31	0.39	0.30	0.21
Guizhou	0.03	0.04	0.03	0.05	0.07	0.14	0.18	0.19	0.19	0.10
Yunnan	0.19	0.14	0.09	0.09	0.13	0.25	0.81	0.34	0.52	0.28
Shaanxi	0.04	0.04	0.04	0.06	0.04	0.12	0.10	0.20	0.19	0.09
Gansu	0.11	0.12	0.11	0.14	0.19	0.23	0.21	0.33	0.30	0.19
eastern	0.17	0.16	0.15	0.17	0.15	0.29	0.31	0.42	0.31	0.24
central	0.36	0.33	0.32	0.33	0.38	0.68	0.67	0.72	0.70	0.50
western	0.12	0.14	0.19	0.18	0.18	0.32	0.39	0.40	0.36	0.25
northeast	0.12	0.09	0.07	0.09	0.07	0.12	0.13	0.19	0.20	0.12
nationwide	0.20	0.19	0.19	0.20	0.20	0.37	0.40	0.46	0.40	0.29

presents the efficiency values of patent conversion for specific years. A systematic cluster analysis of the patent conversion efficiency results for various provinces and municipalities at different stages is conducted, categorizing them into four groups: excellent pioneer layer, efficient conversion layer, steady development layer, and potential enhancement layer [64]. The results are shown in

Table 10. Patent conversion efficiency of High-tech industries in China.

	Technology Research and Development Stage	Achievement Transformation Stage	Overall
excellent pioneer layer	Beijing, Anhui, Chongqing, Yunnan, Guangdong	Tianjin, Fujian, Henan	Henan
efficient conversion layer	Hebei, Guangxi, Shanxi, Sichuan, Jilin, Henan, Zhejiang, Jiangxi, Hunan	Shanxi, Jiangxi, Chongqing	Shanxi, Anhui, Hunan, Jiangxi, Chongqing
steady development layer	Tianjin, Hubei, Shanghai, Shandong, Fujian, Guizhou, Gansu, Liaoning, Jiangsu	Hebei, Hunan, Zhejiang, Anhui, Gansu	Beijing, Hebei, Fujian, Tianjin, Guangdong, Guangxi, Jiangsu, Yunnan, Zhejiang, Jilin, Hubei, Sichuan, Shandong, Gansu
potential enhancement layer	Heilongjiang, Shaanxi	Beijing, Sichuan, Liaoning, Shanghai, Shaanxi, Guizhou, Jilin, Yunnan, Shandong, Hubei, Guangxi, Heilongjian, Guangdong, Jiangsu	Liaoning, Shaanxi, Shanghai, Guizhou, Heilongjiang

.

From Table 9, it is evident that the level of economic development does not fully correspond with the efficiency of patent conversion in high-tech industries, primarily due to variations in regional industrial development priorities. For example, Shanxi, Jiangxi, Chongqing, and Henan have consistently been categorized as excellent pioneer layer or efficient converters. Among these, Chongqing, a municipality directly governed by the central government, is situated in the western region and has demonstrated strong development momentum, attributed to favorable national policies and funding, as well as a focus on high-tech industries. Notably, in 2016, Chongqing government implemented a series of policy measures to support the growth of high-tech enterprises, including increased efforts to nurture technology-based companies. This led to a significant year-on-year rise in the number of high-tech enterprises applying for recognition, as well as a marked increase in the establishment of new high-tech enterprises. This has resulted in a “dual increase” in both the quantity and quality of high-tech enterprises in Chongqing. The growth in the number of enterprises, coupled with a strong emphasis on technological innovation, has established a more robust foundation for the generation and conversion of patents. Additionally, Shanxi, Jiangxi, and Henan, all located in the central region, have experienced a significant rise in their overall patent conversion efficiency since 2016, aligning with the efficiency trends observed in the two sub-phases. Notably, Henan Province has developed a distinct industrial framework in strategic emerging industries, including intelligent manufacturing equipment, biomedicine, energy conservation and environmental protection, new energy equipment, and next-generation information technology, which encompass numerous high-tech enterprises. Jiangxi Province boasts nine national-level high-tech zones, ranking fifth in the country and second in the central region. It has also established a high-tech industrial triangle centered around Nanchang, extending to Jingdezhen and Jiujiang. Meanwhile, high-tech industries in regions such as Ganzhou, Xinyu, and Pingxiang have experienced rapid development. Shanxi Province has established several high-tech industrial clusters in specific fields, with Taiyuan as a notable example. As the capital of a major coal-producing province and a historical industrial hub, Taiyuan has consistently nurtured and expanded its high-tech industries in recent years, facilitating the transformation and innovation of its traditional industrial base. In contrast, Zhejiang, despite being located in a developed eastern coastal region and having average patent conversion efficiency, primarily focuses on the manufacturing and retail of small commodities, with relatively few leading industries in high-tech sectors. Although there have been significant investments in funding, the levels of patent output and new product development remain generally average. Furthermore, when assessed comprehensively, some economically developed regions that have made rapid technological advancements do not demonstrate consistent results in patent conversion efficiency. This phenomenon can be attributed to the “patent focus”. Shanghai holds a significant number of high-value patents in the high-tech industry; however, possessing high-value patents does not necessarily lead to high conversion efficiency. While high-value patents typically exhibit strong technological innovation and promising market potential, the transition from patents to actual products or services necessitates the coordination of multiple factors. It is important to note that high-value patents generally involve longer conversion cycles and more complex processes compared to ordinary patents. Furthermore, even minor issues within these processes can hinder the efficient conversion of high-value patents.

In summary, provinces (or cities) recognized as excellent pioneer layer have effectively utilized various resources while mastering an abundance of them. These regions exhibit a low idle rate of scientific and technological achievements and maintain a reasonable structure of invested resources. In contrast, provinces (or cities) categorized as efficient conversion layer and steady development layer demonstrate relatively strong economic growth and possess well-developed infrastructure. However, their financial resources have not been fully optimized, indicating significant potential for improvement in the transformation of scientific and technological achievements. Looking ahead, these regions must enhance the rational management and utilization of invested resources and actively promote the transformation of patents to convert scientific and technological advancements into economic value. Provinces (or cities) at the potential enhancement level can be divided into two categories: (1) Regions with relatively weak economic foundations that place insufficient emphasis on cultivating high-tech industries and patent transformation. In these areas, resources have not been effectively utilized, scale effects have not been realized, and issues such as non-market allocation of resources may arise. (2) Economically developed regions experiencing rapid technological advancement, where the focus on patents is not solely on “quantity”—the patent conversion efficiency—but rather emphasizes “quality”—the development of high-value patents.

5.2. Efficiency Difference Analysis

The shared-input two-stage network DEA model has provided efficiency scores for the technology research and development stage and the achievement transformation stage, revealing substantial regional heterogeneity. However, DEA is a frontier method that measures relative efficiency under given inputs; it does not itself explain why some regions perform better or worse, nor does it identify the external environmental factors that may drive these differences [6]. To address this gap and to investigate the sources of regional heterogeneity in patent conversion efficiency, we now link the estimated efficiency scores to external environmental factors using panel Tobit regression.

5.2.1. Model Specification and Variable Selection

Because the efficiency scores are bounded between 0 and 1, a panel Tobit model is appropriate for analyzing their determinants. To control for unobserved, time-invariant regional characteristics and common macroeconomic shocks, we employ a two-way fixed-effects panel Tobit model:

$$\begin{array}{cc}\hfill EF{F}_{it}^k& ={\alpha }_0+{\beta }_{1}MARKE{T}_{it}+{\beta }_{2}FINANC{E}_{it}+{\beta }_{3}STRUCTUR{E}_{it}\hfill \\ & +{\beta }_{4}OPE{N}_{it}+{\mu }_i+{\lambda }_t+{ϵ}_{it}\hfill \end{array}$$

(12)

In the model, $\mathrm{E}\mathrm{F}{\mathrm{F}}_{\mathrm{i}\mathrm{t}}^{\mathrm{k}}$ represents the patent conversion efficiency value of province $\mathrm{i}$ in year $t$ at stage $k$, where $k=1$ denotes the technology research and development stage and $\mathrm{k}=2$ denotes the achievement transformation stage. The core explanatory variables select four dimensions of external macro-environmental factors that affect the patent conversion process, and the specific definitions and expected impact effects are as follows:

(1) Marketization level ($\mathrm{M}\mathrm{A}\mathrm{R}\mathrm{K}\mathrm{E}\mathrm{T}$): Measured by the China’s marketization index. A higher marketization level means a more standardized market transaction system and a more sufficient factor flow capacity.

(2) Financial development level ($\mathrm{F}\mathrm{I}\mathrm{N}\mathrm{A}\mathrm{N}\mathrm{C}\mathrm{E}$): Expressed by the ratio of the balance of deposits and loans of financial institutions in each region to the regional GDP. The achievement transformation stage involves pilot production, market promotion and other links that require a lot of capital investment.

(3) Industrial structure ($\mathrm{S}\mathrm{T}\mathrm{R}\mathrm{U}\mathrm{C}\mathrm{T}\mathrm{U}\mathrm{R}\mathrm{E}$): Measured by the proportion of the added value of the tertiary industry in the regional GDP. The development of the tertiary industry can provide supporting services such as logistics, marketing and business consulting for the commercialization of technological achievements.

(4) Opening-up level ($\mathrm{O}\mathrm{P}\mathrm{E}\mathrm{N}$): Expressed by the ratio of foreign direct investment (FDI) in each region to the regional GDP. Foreign direct investment is an important channel for international technology spillovers, which can bring advanced technology and management experience.

In addition, ${\mu }_i$ and ${\lambda }_t$ represent the provincial fixed effect and year fixed effect respectively, which are used to control the individual heterogeneity of each province and the time trend effect of macroeconomic development; ${\alpha }_0$ is the constant term, ${\beta }_1-{\beta }_4$ are the regression coefficients of each core explanatory variable, and ${ϵ}_{it}$ is the random disturbance term, which satisfies the classical normal distribution assumption.

5.2.2. Regression Results and Analysis

Based on the panel data of 25 provinces (municipalities) in China from 2011 to 2020, this paper uses the maximum likelihood estimation method to estimate the two-way fixed-effects panel Tobit model, and the specific regression results are shown in

Table 11. Tobit Regression Results of Influencing Factors of Patent Conversion Efficiency.

Variable	Technology Research and Development Stage Efficiency	Achievement Transformation Stage Efficiency
MARKET	0.152 ***	0.087 **
	(3.21)	(2.05)
FINANCE	0.043	0.176 ***
	(1.12)	(3.58)
STRUCTURE	0.065 *	0.214 ***
	(1.81)	(4.02)
OPEN	0.098 **	0.031
	(2.34)	(0.95)
Constant	0.215 ***	−0.087
	(3.98)	(−1.23)
Province FE	Yes	Yes
Year FE	Yes	Yes
Log likelihood	256.34	189.21
Observations	225	225

Note: z-statistics in parentheses; *** p < 0.01, ** p < 0.05, * p < 0.1.

.

From the regression results, the influencing factors of patent conversion efficiency exhibit clear stage differentiation characteristics. In the technology research and development stage, the marketization level and opening-up level have significant positive effects at the 1% and 5% significance levels, respectively. This indicates that a robust market environment effectively stimulates innovation vitality in high-tech enterprises and optimizes the allocation of R&D resources, while international technology spillovers from foreign direct investment provide technical references for local R&D activities, thereby enhancing technological innovation efficiency. The industrial structure shows a marginal positive effect at the 10% significance level, whereas the financial development level has no significant impact, suggesting that the technology research and development stage in China’s high-tech industry relies more on internal funds and market-oriented resource allocation mechanisms, with limited support from external financial institutions. In the achievement transformation stage, the financial development level and industrial structure exert highly significant positive effects at the 1% significance level, serving as core drivers for the commercialization of technological achievements. This confirms that the transformation of patent achievements into real economic benefits heavily depends on the external support environment: a well-developed financial system provides ample capital for pilot production, scale expansion, and market promotion of new technologies and products; an optimized industrial structure, with a high proportion of the tertiary industry, offers comprehensive services such as logistics distribution, market operation, and business consulting, facilitating the integration of technological achievements into the industrial chain and their marketization. The marketization level still has a significant positive effect at the 5% level, but its regression coefficient is smaller than that in the technology research and development stage, indicating that structural factors like financial development and industrial structure are more critical in the downstream achievement transformation stage compared to market mechanisms. The opening-up level has no significant impact, possibly because foreign direct investment during the research period is more concentrated in manufacturing production and technological R&D, with limited direct promotion of local market-oriented commercialization of patent achievements.

5.2.3. Summary of Efficiency Difference Findings

The panel Tobit regression analysis based on external environmental factors reveals that the regional heterogeneity of patent conversion efficiency in China’s high-tech industry is not random, but is systematically affected by the macro-environmental characteristics of each region. In particular, the low efficiency of the achievement transformation stage in many regions is largely due to the dual constraints of underdeveloped financial markets and the lack of advanced service industry support in the industrial structure. This conclusion can well explain the phenomenon of “high R&D efficiency but low transformation efficiency” in some economically developed eastern provinces: these regions have strong technological innovation capabilities and high R&D efficiency, but there is a mismatch between the innovative output and the external support environment, which leads to a large number of high-value patents being in a “dormant” state and failing to effectively realize market transformation.

This section clarifies the external environmental drivers of regional differences in patent conversion efficiency through empirical analysis. On this basis, the following section will further explore the internal contribution of each input factor to the efficiency from the perspective of input-output elasticity, and verify the rationality and necessity of the shared-input two-stage network DEA model constructed in this paper by comparing it with the traditional DEA model.

5.3. Model Comparison

To verify whether the shared input-oriented two-stage network DEA model is superior to other DEA models in measuring the patent conversion efficiency of high-tech industries in China, this section employs the same input-output variables to compare the efficiency values calculated by the shared input-oriented two-stage network DEA model with those of the traditional single-stage DEA model and the chained two-stage network DEA model, thereby demonstrating the necessity of introducing stage-wise and shared input variables.

5.3.1. Comparison with Traditional Single-Stage DEA Model

The two-stage division of patent conversion is the fundamental framework for this study to carry out phased efficiency measurement, which is the key to reflecting the innovative value of this study compared with the traditional single-stage DEA model. To verify the necessity of phased approaches, this section first calculates the patent conversion efficiency values of China’s high-tech industry under a single-stage DEA model, with some data shown in

Table 12. Overall efficiency value of patent conversion in China’s high-tech industries measured by single-stage DEA.

Region	2011	2013	2015	2018	2020
Beijing	0.1586	0.0985	0.1123	0.2938	0.277
Tianjin	0.314	0.2504	0.148	0.2094	0.263
Hebei	0.1538	0.1617	0.1783	0.3174	0.2737
Shanxi	0.1637	0.0995	0.2568	0.6588	1
Liaoning	0.0781	0.0561	0.0858	0.0966	0.1679
Jilin	0.2616	0.123	0.1069	0.2433	0.335
Heilongjiang	0.0142	0.016	0.0093	0.0592	0.0956
Shanghai	0.0458	0.0478	0.0629	0.1673	0.1475
Jiangsu	0.1746	0.1501	0.1611	0.451	0.4157
Zhejiang	0.1879	0.172	0.2091	0.4438	0.469
Anhui	0.1732	0.2011	0.303	0.6702	0.5528
Fujian	0.1741	0.1303	0.1914	0.3073	0.2937
Jiangxi	0.1566	0.1704	0.3309	0.9777	0.8662
Shandong	0.1271	0.1316	0.1072	0.1762	0.3475
Henan	1	1	1	1	1
Hubei	0.1121	0.097	0.1584	0.2966	0.3102
Hunan	0.5234	0.3245	0.1988	0.399	0.4744
Guangdong	0.2006	0.1516	0.2037	0.3733	0.2666
Guangxi	0.1731	0.1007	0.189	0.3311	0.4501
Chongqing	0.1934	0.8547	0.5139	0.8136	0.5659
Sichuan	0.1099	0.1005	0.1063	0.3053	0.2965
Guizhou	0.0308	0.0298	0.0673	0.1774	0.1918
Yunnan	0.1863	0.083	0.1268	0.8052	0.5179
Shaanxi	0.0362	0.0419	0.0402	0.1034	0.1935
Gansu	0.108	0.109	0.184	0.2125	0.302

. A comparative analysis is conducted between the traditional single-stage DEA model and the shared input two-stage network DEA model through differential testing and calculation of stage efficiency contribution values.

First, through normality tests, it was confirmed that the efficiency values of the single-stage DEA and the shared input two-stage network DEA do not conform to the characteristics of a normal distribution. Given the non-normality of the data, a non-parametric test method—the Wilcoxon rank-sum test—was employed, yielding a p-value of less than 0.001. This indicates a significant difference between the traditional single-stage DEA model and the shared input two-stage network DEA model in measuring the patent conversion efficiency of China’s high-tech industries. This result underscores the importance of phased modeling in the analytical process, as the phased model can more accurately capture the nuances of efficiency variation that the single-stage model fails to fully reveal.

Subsequently, to further verify the necessity of phased implementation, this section conducts an analysis of the phase efficiency contribution values for the shared input two-stage network DEA model, with the results presented in

Table 13. Stage efficiency contribution value analysis.

Stage	Coefficient	p-Value
technology research and development stage	0.1653	<0.001
achievement transformation stage	0.9046	<0.001

:

From Table 13, it is evident that the efficiencies of both the first and second stages significantly enhance overall efficiency. The contribution of the second stage, with a coefficient of 0.9046, far exceeds that of the first stage, which has a coefficient of 0.1653. This suggests that the latter stage plays a more substantial role in the overall efficiency of patent conversion, further underscoring the importance of phased modeling.

5.3.2. Comparison with the Chained Two-Stage Network DEA Model

To verify the necessity of introducing shared input variables in the network DEA model, this section compares the classical chain two-stage network DEA model with the shared input two-stage network DEA model proposed in this paper. Firstly, the efficiency values of the patent conversion technology research and development stage, the achievement transformation stage, and the overall stage of China’s high-tech industry are calculated for the former, with relevant data presented in

Table 14. Sub-stage efficiency based on the chained two-stage network DEA.

Region	Technology Research and Development Stage					Achievement Transformation Stage
	2011	2013	2015	2018	2020	2011	2013	2015	2018	2020
Beijing	0.79	0.65	0.60	0.83	0.83	0.15	0.14	0.12	0.22	0.13
Tianjin	0.45	0.56	0.59	0.50	0.40	1.00	1.00	1.00	1.00	1.00
Hebei	0.69	0.73	0.70	0.81	0.57	0.27	0.19	0.16	0.42	0.25
Shanxi	1.00	0.82	0.92	1.00	0.88	0.12	0.16	0.19	0.64	0.96
Liaoning	0.20	0.34	0.39	0.52	0.49	0.20	0.11	0.12	0.16	0.15
Jilin	0.82	0.74	0.80	0.74	0.56	0.23	0.15	0.11	0.26	0.25
Heilongjiang	0.14	0.23	0.25	0.33	0.34	0.07	0.04	0.02	0.20	0.14
Shanghai	0.29	0.40	0.43	0.52	0.44	0.11	0.09	0.08	0.18	0.12
Jiangsu	0.39	0.43	0.45	0.57	0.50	0.32	0.21	0.20	0.51	0.35
Zhejiang	0.75	0.68	0.71	0.79	0.71	0.16	0.16	0.24	0.51	0.35
Anhui	0.96	1.00	1.00	0.91	1.00	0.13	0.13	0.21	0.59	0.37
Fujian	0.34	0.43	0.50	0.68	0.60	0.33	0.20	0.22	0.37	0.26
Jiangxi	0.35	0.76	0.87	1.00	0.70	0.29	0.14	0.36	1.00	0.67
Shandong	0.35	0.42	0.55	0.50	0.46	0.24	0.20	0.15	0.28	0.39
Henan	0.71	0.64	0.70	0.97	0.74	1.00	1.00	1.00	1.00	1.00
Hubei	0.43	0.49	0.62	0.80	0.63	0.20	0.17	0.16	0.32	0.22
Hunan	1.00	0.81	0.63	0.81	0.54	0.30	0.24	0.20	0.39	0.37
Guangdong	0.56	1.00	1.00	1.00	0.75	0.21	0.16	0.12	0.24	0.13
Guangxi	0.67	0.69	0.88	1.00	1.00	0.23	0.13	0.12	0.26	0.18
Chongqing	1.00	1.00	1.00	0.95	0.58	0.12	0.56	0.55	0.87	0.59
Sichuan	0.60	0.71	0.65	0.69	0.58	0.12	0.10	0.09	0.27	0.19
Guizhou	0.27	0.39	0.46	0.64	0.41	0.08	0.05	0.09	0.17	0.16
Yunnan	1.00	1.00	1.00	0.97	0.60	0.12	0.09	0.09	0.72	0.37
Shaanxi	0.24	0.33	0.32	0.44	0.31	0.10	0.09	0.05	0.14	0.20
Gansu	0.47	0.58	0.62	0.48	0.42	0.12	0.14	0.22	0.41	0.35

and

Table 15. Overall efficiency value of patent conversion in China’s high-tech industries based on the chained two-Stage network DEA model.

Region	2011	2013	2015	2018	2020
Beijing	0.1586	0.0985	0.1123	0.2938	0.277
Tianjin	0.314	0.2504	0.148	0.2094	0.263
Hebei	0.1538	0.1617	0.1783	0.3174	0.2737
Shanxi	0.1637	0.0995	0.2568	0.6588	1
Liaoning	0.0781	0.0561	0.0858	0.0966	0.1679
Jilin	0.2616	0.123	0.1069	0.2433	0.335
Heilongjiang	0.0142	0.016	0.0093	0.0592	0.0956
Shanghai	0.0458	0.0478	0.0629	0.1673	0.1475
Jiangsu	0.1746	0.1501	0.1611	0.451	0.4157
Zhejiang	0.1879	0.172	0.2091	0.4438	0.469
Anhui	0.1732	0.2011	0.303	0.6702	0.5528
Fujian	0.1741	0.1303	0.1914	0.3073	0.2937
Jiangxi	0.1566	0.1704	0.3309	0.9777	0.8662
Shandong	0.1271	0.1316	0.1072	0.1762	0.3475
Henan	1	1	1	1	1
Hubei	0.1121	0.097	0.1584	0.2966	0.3102
Hunan	0.5234	0.3245	0.1988	0.399	0.4744
Guangdong	0.2006	0.1516	0.2037	0.3733	0.2666
Guangxi	0.1731	0.1007	0.189	0.3311	0.4501
Chongqing	0.1934	0.8547	0.5139	0.8136	0.5659
Sichuan	0.1099	0.1005	0.1063	0.3053	0.2965
Guizhou	0.0308	0.0298	0.0673	0.1774	0.1918
Yunnan	0.1863	0.083	0.1268	0.8052	0.5179
Shaanxi	0.0362	0.0419	0.0402	0.1034	0.1935
Gansu	0.108	0.109	0.184	0.2125	0.302

. Subsequently, the necessity of incorporating shared input variables is demonstrated through an analysis of efficiency value differences and input-output elasticity.

Firstly, the differences in efficiency values at different stages were analyzed using the t-test and the Wilcoxon rank-sum test, with the results shown in

Table 16. t-test and Wilcoxon signed rank test.

	t-Test p-Value	Wilcoxon Rank-Sum Test p-Value
technology research and development stage	2.69 × 10−10	3.95 × 10−13
achievement transformation stage	3.13 × 10−4	7.21 × 10−11
overall	5.48 × 10−42	7.21 × 10−37

.

As shown in Table 16, there are significant differences between the chained two-stage network DEA model and the shared input two-stage network DEA model at every stage. Furthermore, to explore the contribution of each input factor in greater depth, this section will conduct an elasticity analysis of input-output, quantifying the input variables to more accurately assess the contribution of each input factor across different models and stages. Since the same input-output variables are utilized in various models in this section, it can be concluded that the contribution of input factors in the technology development stage of both the chained two-stage network DEA model and the shared input two-stage network DEA model is consistent. Therefore, it is only necessary to perform a comparative elasticity analysis of the input-output in the achievement transformation stage, with specific results presented in

Table 17. Input-Output elasticity analysis during technology research and development stage based on chained and shared input two-Stage network DEA.

Variable	Coefficient
x1	−1.222620
x2	−0.060388
x3	−0.036482
x4	−0.026881
x5	0.412630
x6	0.079359
x7	0.703139

and

Table 18. Input-Output elasticity analysis during the achievement transformation stage based on chained and shared input two-stage network DEA.

Model	Variable	Coefficient
chained two-stage network DEA model	z1	1.052109
	z2	−0.191458
	z3	0.007731
	x8	0.017841
shared input two-stage network DEA model	x1	0.636860
	x2	−0.141445
	x3	0.050719
	z1	1.052840
	z2	−0.129922
	z3	−0.182248
	x8	−0.182248

.

Based on the results of input-output elasticity and stage contribution value analysis, the relative contribution of shared input variables can be clarified as follows:

(1) technology research and development stage: The intensity of intellectual property protection (IPP) is the core variable of institutional constraints. In the technology research and development stage (Table 17), the elasticity coefficient of IPP (x1) is −1.2226. Although negative, its absolute value is the largest among regional input variables, which carries special economic implications: during the R&D phase, IPP primarily reduces knowledge spillover losses and inhibits imitation through institutional constraints, thereby protecting the R&D returns of innovative entities. The negative elasticity does not mean the variable is “ineffective”; instead, it reflects its unique mechanism as an “institutional constraint”—screening out R&D entities with stronger innovation capabilities by increasing imitation costs. The weight of this variable in the stage contribution value analysis further confirms its dominant position among regional input variables.

(2) Achievement Transformation Stage: IPP makes the most prominent positive contribution. In the achievement transformation stage (Table 18), the elasticity coefficient of IPP (x1) is 0.6369, significantly higher than that of government financial support (x2: −0.1414) and expenditure on technology import (x3: 0.0507). This indicates that in the critical link of converting technological achievements into economic benefits, IPP has become the core driving force for promoting the market-oriented application of patents by enhancing the credibility of technology transactions and reducing market friction costs. In contrast, the negative elasticity of government financial support may reflect the current low efficiency of fund allocation, requiring further optimization of funding directions; although the positive contribution of technology import expenditure is significant, it is limited, suggesting that the marginal driving effect of external technology import on achievement transformation has slowed down.

(3) Overall Contribution: Shared input variables dominate overall efficiency through the achievement transformation stage. Stage contribution value analysis (Table 12) shows that the contribution coefficient of the achievement transformation stage to overall efficiency is 0.9046, far higher than that of the technology research and development stage (0.1653). Further calculations indicate that the sum of the absolute values of the elasticities of shared input variables (x1, x2, x3) in the achievement transformation stage accounts for 72% of the total elasticity of this stage, significantly higher than their proportion in the technology research and development stage. This result demonstrates that shared input variables mainly act on the achievement transformation stage to dominate the overall patent conversion efficiency. Among them, IPP plays a key role in both stages but with stage-specific mechanisms—in the R&D stage as an “institutional constraint” and in the transformation stage as a “market enabler”. This finding further verifies the rationality of setting it as a shared input variable. In summary, shared input variables not only exhibit differentiated mechanisms in different stages but also show obvious stage-specific emphasis in their contribution to overall efficiency. The above analysis provides a quantitative basis for optimizing regional patent conversion policies: in the short term, priority should be given to strengthening the market-enabling role of IPP in the achievement transformation stage; in the long term, it is necessary to optimize government fund allocation and enhance the absorption capacity of imported technologies to achieve synergistic efficiency across all stages.

From the above results, it can be concluded that the shared input two-stage network DEA has the following advantages compared to the traditional chained two-stage network DEA model:

(1) Balancing the allocation of resources

In the chained model, certain variables (such as x₁ in the technology research and development stage) demonstrate a highly negative elasticity with respect to output (elasticity of −1.222620). This indicates that the efficiency of resource input is extremely low, resulting in a significant reduction in output. In contrast, the shared input model alleviates this negative impact by incorporating shared variables (such as x₁), which leads to a more balanced allocation of resources. This effectively diminishes the excessive negative influence of a single variable on the overall output of the system, thereby enhancing the model’s elasticity and stability.

(2) Synergistic effects in optimization stages

In the output elasticity of the achievement transformation stage, the chained model heavily relies on specific output variables from the technology research and development stage (such as z₁, which has an elasticity of 1.052109). This indicates that the transfer variables between stages are crucial for the final output. However, the chained model’s significant dependence on these transfer variables may exacerbate the effects of negative input variables. In the shared input model, in addition to the continued importance of transfer variables between stages (z₁), the newly introduced shared input variables (x₁) also have a substantial impact on the output of the achievement transformation stage (elasticity of 0.636860). This finding further supports the scientific and rational selection of shared input variables. Moreover, the shared input model enhances resource synergy between stages by introducing shared input variables, which reduces the absolute dependence of stage outputs on transfer variables and, in turn, increases the overall efficiency of the system.

(3) Mitigating the negative impact of non-critical variables

In the chained model, certain input variables (z₂) exhibit a negative output elasticity during the achievement transformation stage (−0.191458). This suggests that these variables may consume resources without effectively converting them into output. In contrast, the shared input model mitigates the negative impact of non-critical variables on output by optimizing the allocation ratio of input variables (for example, z₂ decreases to −0.129922). This optimization results in a higher utilization rate of resources and further enhances the model’s explanatory power.

In general, the shared input two-stage network DEA model effectively reduces resource waste and enhances decision-making applicability in complex multi-stage systems. This is achieved through the balancing and enhancement effects of its shared variables across the two stages. Particularly when addressing multi-stage complex systems, this model demonstrates increased efficiency and applicability. By balancing the input elasticity of each stage, it not only optimizes the role of key variables but also significantly mitigates the negative impacts of uneven resource allocation. Consequently, the shared input two-stage network DEA model exhibits greater applicability and stronger interpretability in complex multi-stage systems.

5.4. Robustness Check

Given the considerable regional heterogeneity in economic development and industrial maturity, it is prudent to examine whether the efficiency rankings and main findings are sensitive to the choice of scale assumption. Therefore, we re-estimate the efficiency scores under the Variable Returns to Scale (VRS) assumption using the same shared-input two-stage network DEA framework. The VRS model is obtained by adding convexity constraints to the CCR-based formulations. This allows each DMU to be compared only with others of similar scale, thereby capturing possible scale inefficiencies that may arise from regional heterogeneity and differences in industrial maturity.

We apply the VRS model to the same panel data of 25 Chinese provinces over 2011–2020.

Table 19. Comparison of average efficiency under CRS and VRS assumptions.

Region	Overall		Technology Research and Development Stage		Achievement Transformation Stage
	CRS	VRS	CRS	VRS	CRS	VRS
Beijing	0.24	0.31	0.77	0.82	0.16	0.28
Tianjin	0.25	0.31	0.51	0.57	1.00	1.00
Hebei	0.24	0.33	0.60	0.63	0.35	0.43
Shanxi	0.43	0.48	0.58	0.65	0.44	0.50
Liaoning	0.10	0.24	0.43	0.49	0.17	0.28
Jilin	0.22	0.30	0.56	0.60	0.25	0.30
Heilongjiang	0.05	0.21	0.32	0.38	0.20	0.29
Shanghai	0.11	0.19	0.46	0.50	0.15	0.19
Jiangsu	0.28	0.37	0.42	0.48	0.21	0.30
Zhejiang	0.31	0.37	0.65	0.70	0.32	0.43
Anhui	0.42	0.47	0.87	0.92	0.32	0.37
Fujian	0.24	0.33	0.47	0.50	1.00	1.00
Jiangxi	0.54	0.59	0.64	0.75	0.57	0.60
Shandong	0.18	0.30	0.46	0.53	0.26	0.32
Henan	1.00	1.00	0.55	0.60	1.00	1.00
Hubei	0.21	0.29	0.52	0.55	0.24	0.30
Hunan	0.40	0.52	0.67	0.70	0.35	0.50
Guangdong	0.26	0.42	0.94	1.00	0.20	0.24
Guangxi	0.27	0.37	0.61	0.67	0.24	0.38
Chongqing	0.63	0.69	0.84	0.85	0.54	0.67
Sichuan	0.21	0.32	0.57	0.63	0.16	0.30
Guizhou	0.10	0.36	0.49	0.56	0.13	0.25
Yunnan	0.28	0.37	0.83	0.87	0.25	0.38
Shaanxi	0.09	0.24	0.33	0.41	0.15	0.29
Gansu	0.19	0.41	0.49	0.57	0.29	0.42
eastern	0.24	0.33	0.59	0.64	0.40	0.47
central	0.50	0.56	0.64	0.70	0.49	0.51
western	0.25	0.39	0.59	0.65	0.25	0.38
northeast	0.12	0.25	0.43	0.49	0.21	0.27
nationwide	0.29	0.36	0.58	0.64	0.36	0.43

reports the efficiency values for selected provinces and years under both CRS and VRS for the technology research and development stage, the achievement transformation stage, and the overall process.

Results in Table 19 show that efficiency rankings and regional distribution patterns under the VRS assumption are highly consistent with those under the CRS assumption. Nationally, the average overall efficiency increases from 0.29 under CRS to 0.36 under VRS, while the technology research and development stage average rises from 0.58 to 0.64 and the achievement transformation stage average from 0.36 to 0.43. Although VRS yields slightly higher average efficiency scores due to the relaxation of the scale assumption, the main conclusions regarding stage-specific bottlenecks and regional disparities remain unchanged under VRS. In particular: The achievement transformation stage continues to exhibit a stronger impact on overall efficiency than the technology research and development stage; the central region outperforms other regions, whereas the northeastern region performs the poorest; and provincial efficiency rankings are highly stable. These findings confirm the robustness of the CRS specification employed in this study and provide empirical support for its theoretical justification. The VRS estimation therefore validates the reliability and credibility of our baseline CRS-based results.

6. Conclusions and Recommendations

6.1. Conclusions

This paper employs a shared input two-stage network DEA model to systematically evaluate the technology research and development efficiency, achievement transformation efficiency, and overall transformation efficiency of high-tech industry patent development across 25 provinces (municipalities) in China from 2011 to 2020. Furthermore, through a comparative analysis of models, it demonstrates that the shared input two-stage network DEA model proposed in this study is more effective in measuring the patent conversion efficiency of China’s high-tech industry. The research concludes:

(1) From a strategic perspective, the efficiency of research and development in patent technology, the effectiveness of achievement transformation, and the overall patent conversion efficiency in China’s high-tech industry have exhibited a consistent annual increase. Notably, the efficiency of technology research and development is at a higher level compared to that of achievement transformation. Meanwhile, Robustness analysis using the VRS model confirms that this conclusion is not sensitive to scale assumptions. However, despite advancements in both areas, the overall efficiency of patent conversion in China’s high-tech sector remains relatively low, suggesting that there is still considerable potential for improvement in this domain.

(2) From a regional perspective, there is a significant imbalance in the technology research and development and the achievement transformation within China’s high-tech industry. Specifically, the gap in technology research and development efficiency between the eastern and western regions is gradually widening. While the central and northeastern regions have made continuous progress in achievement transformation efficiency, they also face the challenge of increasing regional disparities. In terms of spatial distribution, the technology research and development stage exhibits a trend of being “slightly higher in the central region, with the gap between the eastern and western regions gradually narrowing”. The achievement transformation stage has essentially established a pattern where the “eastern and central regions lead, while the western and northeastern regions lag slightly behind”. Moreover, there is considerable potential and opportunity for efficiency improvement in both sub-stages across major regional sectors nationwide, which urgently needs to be further explored and utilized.

6.2. Recommendations

After a comprehensive examination of the current status and challenges related to patent conversion efficiency in China’s high-tech industry, this section proposes a series of strategies and recommendations designed to optimize and enhance patent conversion efficiency. These recommendations not only emphasize the strategic importance of investing in technological innovation to bolster the research, development, and innovation capabilities of the high-tech sector, but also highlight the necessity of fostering coordinated development among regions to address spatial disparities and achieve a more balanced patent conversion efficiency. Furthermore, this section underscores the importance of focusing on both patent conversion efficiency and quality, advocating for attention to be given not only to quantitative metrics but also to enhancing the value, quality, and innovativeness of patents during the patent conversion process. The following is a detailed elaboration of these recommendations.

(1) The Strategic significance of strengthening investment in technological innovation in China’s high-tech industries

In addressing the issue of stage differences in patent conversion efficiency within high-tech industries, greater emphasis should be placed on investing in technological innovation. This strategy is grounded in two significant insights. Firstly, the overall patent conversion efficiency of China’s high-tech industries is relatively low, underscoring the limitations of the current development model in this sector. Consequently, high-tech enterprises urgently need to abandon traditional path dependence and increase their investment in technological innovation to enhance their research and development capabilities, thereby further improving the efficiency of technology research and development. Secondly, since the patent conversion efficiency in high-tech industries significantly impacts overall efficiency and is currently low, Chinese high-tech enterprises must remain vigilant against the phenomenon of “patent bubbles”. This entails avoiding the mere pursuit of patent quantity while neglecting actual application value [65]. Finally, enterprises should strive for deep and comprehensive integration within the industrial chain, promoting the establishment of a “high-tech industry patent landing” model, which will effectively enhance patent conversion efficiency.

(2) Strategies for promoting coordinated regional development of high-tech industry patent transformation

To address the regional disparities in the patent conversion efficiency of the high-tech industry, emphasis should be placed on coordinated inter-regional development and the implementation of differentiated and targeted policy approaches. Based on the cluster analysis results in Table 10, this paper proposes coordinated development strategies for the following four types of regions: ① The exemplary leading tier (e.g., Beijing, Tianjin, Henan) has reached the efficiency frontier at specific stages, and the policy focus should shift from “quantitative improvement” to “qualitative breakthroughs”. This includes establishing special programs for high-value patent cultivation, exploring a full-chain innovation ecosystem, and identifying optimal resource allocation through super-efficiency analysis for reference by other regions. ② The high-efficiency conversion tier (e.g., Hebei, Shanxi, Chongqing) performs prominently in one stage but has shortcomings in the other, and needs to implement a shortcoming compensation strategy. For regions with strong technological R&D but weak achievement transformation, the key is to break the bottlenecks in commercialization; for those with strong achievement transformation but weak technological R&D, the focus is to address the bottlenecks in R&D efficiency. ③ The steady development tier (13 provinces including Beijing, Hebei and Fujian) has a medium-level efficiency, and should implement a “customized policy for each province” to allocate resources precisely, strengthen cross-regional cooperation with the exemplary leading tier, and establish a performance evaluation and dynamic adjustment mechanism. ④ The potential improvement tier (e.g., Heilongjiang, Shaanxi, Liaoning) features low efficiency, and targeted policies need to be formulated by category. For economically underdeveloped regions, fiscal transfer payments should be used to make up for shortcomings; for economically developed regions with low conversion efficiency, the patent evaluation orientation should be optimized to shift from “valuing applications” to “valuing utilization”; for the northeastern region, it is recommended to set up special innovation and transformation programs to break institutional and mechanistic barriers. Through the above targeted policies by category, the radiating and leading role of high-efficiency regions will be fully exerted. Relying on existing cooperation models and information networks, inter-regional technological exchanges, talent flow and knowledge sharing should be strengthened to reduce spatial disparities, promote the relatively balanced development of patent conversion efficiency in the high-tech industry, and jointly drive the overall improvement of patent conversion efficiency of China’s high-tech industry.

(3) Development orientation that emphasizes both patent conversion efficiency and quality.

This paper, while evaluating the patent conversion efficiency of China’s high-tech industry, focuses exclusively on the quantitative indicators of efficiency values and does not adequately consider the quality of patents. This oversight may introduce a degree of bias in the measurement results. As technology continues to advance, the development trajectory of China’s high-tech industry regarding patents should adopt a more holistic approach [66]. It is crucial not only to emphasize the quantitative indicators of patent conversion efficiency but also to shift attention toward the qualitative aspects of patents. This entails that, in promoting patent conversion, it is equally important to enhance the quality and innovation of patents to achieve a dual improvement in both the efficiency and quality of patent conversion within China’s high-tech industry.