3.1. Model Setup
The fixed effects model, the difference model, and the random effects model constitute the three principal methodologies for the analysis of panel data. The fixed effects model posits a scenario wherein all variables are directly related to the explanatory variable, while the dependent variable demonstrates temporal variability. Fixed-effect models can be further categorized into three distinct types:
- (1)
Individual Fixed Effect Models: In these models, the intercept term is the only element that alters across the temporal sequence. Within the framework of panel regression models, the marginal effect of explanatory factors on the dependent variables remains consistent. However, it is noteworthy that, besides the explanatory variables incorporated within the model, there exist additional significant variables influencing the explanatory variables which exhibit variation across individuals but remain stable over time.
- (2)
Time Fixed-Effect Model: This model is characterized by distinct temporal markers in diverse cross-sectional data. Should the model’s intercepts be consistent throughout the timeline yet exhibit substantial differences across various cross-sections, a time-specific fixed-effect model is warranted. This approach acknowledges the temporal consistency of intercepts while allowing for significant variances between different cross-sectional analyses.
- (3)
Time-point Individual Fixed-Effect Model: This model delineates a scenario where intercepts among various horizontal time points and time series show significant disparities. It advocates for the creation of a unique fixed effects model for specific time points, contingent upon the intercepts demonstrating notable variability across different cross-sections and throughout the timeline.
Each category delineates a refined approach to analyzing panel data, offering nuanced insights into the dynamics of variables over time and across different populations or conditions. By employing these models, researchers can effectively dissect and interpret the complex interrelationships between explanatory and dependent variables, taking into account temporal and individual variations.
The selection of the model is guided by two primary objectives: to account for unobservable heterogeneity and to encapsulate the dynamic interactions stipulated in the research hypothesis. The fixed-effect model excels in managing unobservable heterogeneity among entities (such as countries, regions, etc.) and, temporally, is a pivotal aspect in examining the realms of ocean governance and marine economic development. Factors inherent to each entity, including geographical location, policy frameworks, and historical backdrop, alongside temporal elements like global economic trends and environmental shifts, considerably affect the study’s variables.
The implementation of this model is particularly relevant to the study at hand. Utilizing the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) for model selection facilitates the identification of a model that adeptly balances complexity with accuracy, thereby mitigating the risk of overfitting. The penalization mechanisms of AIC and BIC against superfluous parameters guarantee that the model remains streamlined yet proficient in delineating the relationship between ocean management (OMN) and Ocean Gross Domestic Product (OGDP). This methodology, given the intricacies of marine economic structures and governance systems, assures the model’s robustness and applicability. The integration of both entity-specific and temporal fixed effects enables a more precise depiction of the nuanced and evolving relationship between ocean governance and marine economic growth.
Descriptive statistical analysis plays a foundational role in illuminating the dataset’s characteristics, including the mean, median, and standard deviation of crucial variables such as OGDP, Urbanization (URB), foreign direct investment (FDI), human resources (HR), industrial structure (IS), and Ocean Marine Industry (OMI). This analysis accentuates both the variability and consistency present within the dataset, underscoring the necessity for a model adept at accommodating these variances effectively.
Both the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) incorporate a penalty term that is directly related to the number of parameters within the model. Notably, BIC assigns a more substantial penalty than AIC, with the added consideration of sample size. This feature of BIC makes it particularly adept at preventing the model from becoming overly complex, thereby mitigating the risk of overfitting, especially in analyses involving a large dataset. In the process of model selection, it is imperative to balance the likelihood function of the model pair against its complexity. The introduction of a penalty term for model complexity in numerous information criteria aims to address and prevent overfitting.
In this research, we utilize two prevalent methodologies for model selection. The first approach involves the Akaike Information Criterion (AIC), which evaluates the complexity of a statistical model. The primary objective is to select the model with the minimum AIC value, thus reducing the likelihood of overfitting. The second method employs the Bayesian Information Criterion (BIC), analogous to AIC, yet distinct in that BIC’s penalty for the number of model parameters is more severe, with sample size playing a role in its calculation. This characteristic allows BIC to effectively curtail the complexity of the model, ensuring its simplicity and applicability when dealing with extensive datasets.
Use of a dual fixed effects model: compared to a single fixed effects model, this study uses a dual fixed effects model, which allows for controlling for both firm fixed effects that do not vary over time and time fixed effects that vary over time, reducing omitted variable bias and improving the accuracy and robustness of the estimation results. In addition, in contrast to broader sustainable development or environmental economics studies, this study focuses on the relationship between marine environmental governance and marine economic development, providing insights specific to the marine sector.
However, the model also has shortcomings: the present model may provide static correlation analyses rather than dynamic causality. This means that it may not capture the dynamic interaction between marine environmental governance and economic development over time, and furthermore, the accuracy of the model may be limited by data quality, availability and sample size. For example, if the data have measurement errors or are not representative, the conclusions of the model may be affected.
Based on the comprehensive analysis conducted, the dual fixed-effect model has shown a notable advantage over the single fixed-effect model, highlighting its increased reliability and robustness. The results obtained from the dual fixed-effect model not only validate its efficacy but also reinforce its credibility, underscoring its potential to provide nuanced insights into the relationship between marine economic development and ocean governance. This model has been carefully designed, incorporating contemporary scholarly discourse and an extensive review of the relevant literature to ensure its scientific rigor. We construct the model as follows:
In the preceding equation,
I point to the individual,
t points to the year,
ocean governance (
OMN) is the core explanatory variable,
the level of ocean economic development (
OGDP) is the explanatory variable,
control is the related control variable:
the level of urbanization (
URB),
the level of foreign investment (
FDl),
human resources (
HR),
industrial structure (
lS), and
the share of ocean industry (
OMl), and
is the random perturbation term.
The variable signifies the kth control variable for individual i at time t, enhancing the original model by integrating an expanded array of control variables. The coefficients and quantify the interaction effects between ocean governance and human resources, as well as ocean governance and foreign direct investment, respectively. These interaction terms provide insights into how the influence of governance on economic development may differ across varying levels of human resources and international investment. Additionally, incorporates further variables or indicators pertinent to the marine economy, including technological innovation within marine sectors, environmental sustainability initiatives, or overarching maritime policies, each denoted by their respective coefficients φ.
This analytical framework examines how the dynamics between ocean governance and marine economic growth are potentially influenced or intensified by these variables. For example, the efficacy of governance strategies in fostering economic expansion might be more distinct in regions endowed with a richer pool of skilled human resources or substantial foreign investment. By broadening the spectrum of control variables to encompass a more diverse array of factors, the model offers a comprehensive portrayal of the marine economy’s intricacies. This approach enables a sophisticated understanding of the myriad factors that individually and cumulatively affect marine economic development, from technological breakthroughs to efforts aimed at environmental preservation.
Furthermore, the model supports a dynamic analysis, tracking changes over time and across various entities, thereby capturing the fluid nature of ocean governance and its repercussions on the marine economy. Such a dynamic viewpoint is crucial for discerning trends, projecting future developments, and crafting policies that adapt to evolving circumstances.
3.2. Variable Description
Marine environmental governance (OMAN) [
26]: Basis for selection: The level of marine environmental governance is a key indicator of the efficiency of the protection and management of marine resources. By analyzing the number of protected marine areas, it is possible to assess the importance that countries attach to marine ecosystems and the effectiveness of conservation measures.
Data source: The data comes from the Global Marine Protected Areas Statistical Database (Global Ocean Database), which provides detailed information on MPAs globally, including area, type and level of protection.
Level of marine economic development (OMG) [
27]: Rationale for selection: The level of marine economic development is an important indicator for assessing the contribution of marine economic activities to a country’s economy. By calculating the logarithm of OMG, the growth trend of the marine economy can be more accurately measured.
Data source: The data is obtained from the National Bureau of Statistics (NBS) through the collection and collation of economic statistics at the national level, including Gross Marine Product (GMP) and indicators related to marine economic activities.
Urbanization level (URB) [
28]: Selection basis: The level of urbanization reflects the trend of population migration from rural to urban areas, which has a direct impact on the use of marine resources and the governance of the marine environment. Areas with a high level of urbanization may face more serious problems of marine environmental pollution and overexploitation of resources.
Data source: Data from the World Bank database, which provides detailed data on the level of urbanization in countries around the world, including urban population as a percentage of the total population and related indicators of the urbanization process.
Foreign Direct Investment Level (FDI) [
29]: Selection basis: The level of FDI is an important indicator of a country’s ability to attract foreign investment, which has a significant impact on the development of marine resources and the development of the marine economy. High levels of FDI are usually associated with faster economic growth and more advanced technology transfer.
Data source: Data are sourced from national statistical offices through the collection and collation of economic statistics at the national level, including the amount of FDI and FDI as a percentage of GDP.
Human Resources (HR) [
30]: Selection basis: Human resources are an important support for ocean governance and ocean economic development. Highly educated marine professionals are essential for the sustainable use of marine resources and marine environmental protection.
Data source: The data comes from the University of Science and Technology of China (USTC) by collecting and collating the number of graduate students graduating from marine science-related majors in the university, which is used as a proxy variable for marine human resources.
Industrialization level (IND) [
31]: Selection basis: the industrialization level reflects the transformation and upgrading of the national economic structure, which has a far-reaching impact on the way marine resources are developed and utilized. High industrialization levels are usually accompanied by more intensive industrial activities and more complex marine environmental issues.
Source of data: Data are obtained from national statistical offices through the collection and collation of economic statistics at the national level, including the amount of investment in fixed assets and relevant indicators of the industrialization process.
3.3. Results of Descriptive Statistics
Initially, a descriptive statistical analysis was conducted to elucidate the foundational characteristics of the dataset under examination, with
Table 1 and
Table 2 presenting the findings. The analysis reveals that the mean value for ocean governance (OMN) stands at 1.907, with a median of 1.609 and a standard deviation of 1.219, indicating a relatively low level of ocean governance within the sample, accompanied by notable variability. In terms of marine economic development (OGDP), the mean is recorded at 8.420, the median at 8.523, and the standard deviation at 0.882, suggesting that while the marine economy’s development level is comparatively high, disparities exist within the dataset.
The urbanization level (URB) manifests a mean of 0.654, a median of 0.650, and a standard deviation of 0.124, implying a consistent degree of urbanization across the sample. This consistency may be attributed to urbanization processes, infrastructure development, and demographic movements, all of which potentially enhance urbanization levels, subsequently influencing societal development and economic structuring.
Foreign direct investment (FDI) exhibits a mean of 0.0260, a median of 0.0210, and a standard deviation of 0.0180, illustrating a modest and stable level of foreign investment. An increase in foreign investment can introduce technology, capital, and management expertise, thus fostering economic growth and facilitating international collaboration.
Human resources (HR) presents a mean of 4.688, a median of 5.147, and a standard deviation of 1.305, indicating relative stability in human resource levels. This stability could be associated with educational attainment and labor market dynamics, underscoring the pivotal role of human resources in driving economic development, innovation, and competitive advantage in industries.
The industrial structure (IS) showcases a mean of 0.368, a median of 0.395, and a standard deviation of 0.0930. The composition of the industrial structure, reflecting the proportion of various industrial sectors and their adjustments, can significantly impact economic growth, employment generation, and the broader economic reshaping process.
Finally, the marine industry share (OMI) demonstrates a mean of 0.646, a median of 0.650, and a standard deviation of 0.234, pointing to a relatively consistent representation of the marine industry within the dataset. This stability in marine industry share, encompassing sectors such as fisheries, marine energy, and marine tourism, holds promising implications for economic enlargement and the enhancement of marine economic activities’ efficiency.