The Dynamics of Technological Complexity and Its Growth Effect

1. Data Generation ProtocolThis study adopts the network structural diversity method proposed by Broekel to measure the overall technological complexity in China. This approach utilizes information theory to evaluate the diversity of knowledge component combinations within a technology. New knowledge and technologies are viewed as networks formed by the combination of existing knowledge, comprising nodes that represent distinct knowledge components and edges that denote knowledge associations. In this context, complexity is defined as the degree of interweaving among various knowledge components and ideas. Consequently, more complex technologies exhibit denser and more diverse networks of interconnected ideas and components. The specific measurement process consists of four stages:Construction of Technological Networks: Based on IPC classifications of patents, technological association networks are constructed using co-occurrence relationships to capture all knowledge components constituting a specific technology and their interconnections.Calculation of Technological Complexity Scores: Introducing information theory, we calculate the network diversity score for each technology by assessing the network's module share, subgraph ratios, and variability via random sampling and random walk algorithms. To ensure stability, a three-year moving window is employed, and the scores are logarithmically transformed to ensure that higher values correspond to greater technological complexity.Construction of City-Level Technological Distributions: Patents are matched to specific cities, and the complexity scores of all technologies within a city are aggregated and sorted in descending order to form a distribution sequence of technological complexity.Calculation of City-Level Technological Complexity: Distinct from traditional simple summation or averaging, this study sums the scores of the top 20% most complex technologies within a city's distribution. Drawing on the research framework of Mewes and Broekel, this approach simultaneously accounts for the characteristics of "high complexity" and "technological scale," effectively mitigating measurement bias arising from disparities in regional patent volumes.2. Data BackgroundFrom a knowledge perspective, technological complexity reflects the difficulty of cross-domain combinations of knowledge elements. It emphasizes the interdependence of knowledge elements and their role in the "mix and match" process of technological creation. Unlike traditional technological scale metrics, technological complexity captures structural information that cannot be described by simple aggregate indicators. For instance, according to the Herfindahl index or information entropy, a region with 80% complex and 20% simple technologies is considered identical to one with 20% complex and 80% simple technologies. The technological complexity index breaks this symmetry by incorporating the complexity level of each technology, thereby revealing more details about how technological innovation drives economic growth. Therefore, analyzing the evolution and economic performance of technological complexity helps to deeply understand regional technological structural differences and potential, providing a theoretical basis for formulating more scientific high-quality development policies.Research related to technological complexity is mainly divided into two streams: one focuses on the measurement of technological complexity. Hidalgo and Hausmann pioneered the use of regional export product portfolios to assess Economic Complexity (ECI) and provided specific calculation methods. Subsequent studies have used the ECI index to approximate technological complexity. In addition to export data, recent literature has begun to use knowledge data such as patents and papers to estimate technological complexity, including metrics based on patent citations, classifications, and knowledge combinations. The other stream explores the relationship between technological complexity and economic growth. Currently, there is no consensus on how technological complexity affects economic growth. On one hand, regions with higher technological complexity are more likely to acquire long-term growth potential and quasi-monopoly rents, implying that complexity promotes growth. On the other hand, opposing views suggest that complexity reflects the difficulty of technological application, which may cause productivity losses and hinder growth. Furthermore, the strong exclusivity of high-complexity technologies exacerbates regional imbalances, where a few regions master the most complex technologies, influencing the spatial distribution of economic growth. Thus, it is necessary to further explore the spatial heterogeneity of technological complexity's impact on regional economic growth.3. Data File ContentThe dataset contains variables used for the regression analysis in the paper, including explanatory variables, the dependent variable, and control variables.4. File Naming Convention and Variable DefinitionsData files and variables are named using Pinyin or English abbreviations corresponding to their definitions:year: Yearlngdp_w: Economic Growthlnfzd_w: Technological Complexitylnpat_w: Technological Scalelnpdiv_w: Technological Diversityczzc_w: Level of Fiscal Expenditureer_w: Share of Secondary Industry in GDPrenkmd_w: Population Densityroad_w: Road Densityfin_w: Financial Environmentsc_w: Share of Tertiary Industry in GDPHSR_w: High-Speed Rail Operationmarket_w: Marketization Leveleducation_w: Education Levelcityid: City ID5. Value of the DataSpecifically, the value of this dataset is reflected in the following three dimensions:Upgrade in Measurement Dimension: From "Quantity" to "Structure"Traditional indicators (such as total patent counts or R&D investment) can only measure the scale of innovation, whereas this data measures the depth of innovation.Revealing Implicit Knowledge Barriers: Based on the co-occurrence network of IPC classifications, this data captures the degree of "interweaving" among knowledge elements. It reflects the difficulty of "mixing and matching" in technological creation.Identifying Core Advantages: By summing the "top 20% most complex technologies," this data filters out the noise of low-level repetitive innovation, precisely identifying whether a city has mastered high-threshold, high-barrier core technologies, rather than simply possessing a large volume of simple technologies.Methodological Superiority: Solving the "Average Trap"This data addresses the blind spots of traditional statistical methods through its algorithmic design, offering higher academic rigor:Breaking Symmetry: Traditional Herfindahl indices or information entropy cannot distinguish the regional differences between "80% complex + 20% simple" and "20% complex + 80% simple." Through weighted sorting, this data can keenly capture these structural nuances.Eliminating Scale Bias: Through specific calculation methods (balancing high complexity with technological scale), it effectively mitigates measurement errors caused by differences in regional patent totals. This means it is suitable not only for cross-sectional comparison (between different cities) but also for longitudinal comparison (different periods for the same city), even if the city's patent output fluctuates significantly.Economic Explanatory Power: Predicting Growth Potential and RentsFrom an economic perspective, this data serves as an important leading indicator for predicting regional economic futures:Proxy for Quasi-Monopoly Rents: High technological complexity implies that technologies are difficult to imitate or substitute. Cities with high values are more likely to secure long-term growth potential and "quasi-monopoly rents" (i.e., excess profits).Benchmark for High-Quality Development: The data background notes that the relationship between technological complexity and economic growth is controversial (promoting growth vs. hindering productivity). Using this data, researchers can deeply analyze this "spatial heterogeneity," determining whether a city is in a "growing pain period due to high difficulty" or a "dividend period due to high barriers," thereby providing a basis for formulating differentiated high-quality development policies.