Quantitative Forecasting and Development Pathways of the Linkages between the Shellfish Industry and Fishermen's Income in Liaoning Province: An Empirical Analysis Based on the GM(1,1) Model

This study takes Liaoning Province, a core fishery region in Northeast China, as a case study to quantify the contribution and long-term impact mechanisms of the shellfish aquaculture industry on regional fishermen's household business income. Addressing the typical characteristics of limited data samples and incomplete system information, the research employs the GM(1,1) prediction model from grey system theory to independently model and forecast shellfish production and fishermen's household business income for the period 2010-2033. The empirical results indicate: using the original, non-translated data, the Liaoning shellfish production prediction model passed the ratio test, with a development coefficient (a) of -0.01885, forecasting a sustained and steady expansion of the industry scale, with production projected to reach approximately 3.19 million tons by 2033. The fishermen's household business income series, due to initial high volatility, required the application of a translation constant C=265,410 to establish a viable GM(1,1) model, which yielded a development coefficient (a) of -0.02986, also predicting a long-term growth trend for income. Model accuracy evaluation showed that the shellfish production forecast had a mean relative error of 4.839%, a posterior variance ratio C of 0.502, and a small error probability P of 0.786, achieving an accuracy grade between "qualified" and "good". Although the income prediction model had a higher mean relative error (20.125%), its posterior variance ratio C was 0.272, and the small error probability P was 1, indicating a robust trend in the forecasted sequence. Integrating a literature review on Liaoning's fishery industrial structure—where the primary sector dominates but the secondary and tertiary sectors' shares are gradually increasing—and fishermen's income composition—where household business income is the core pillar—this study further elucidates the transmission mechanisms through which the shellfish industry influences fishermen's income via multiple pathways, including direct sales, value-added processing, and linkages with recreational fisheries. Finally, based on the forecast results and the current industrial landscape, the study proposes countermeasures and suggestions, such as promoting intensive and ecological shellfish aquaculture, deepening aquatic product processing, fostering industrial integration, and strengthening scientific, technological, and policy support. These recommendations aim to provide a theoretical basis and decision-making reference for the sustainable and inclusive development of the marine fishery economy in Liaoning Province and similar regions in China.