## 4 Findings
### Results of the Spatial Econometric Models  
Table 3 presents the empirical results from the application of the SLM and its lagged version, \(\text{SLM}_{\text{t}-1}\). These models play a pivotal role in shedding light on the impact of sectoral economic activities on income, particularly focusing on the spatial lag effect, denoted by lambda (\(\lambda\)). The consistently positive and statistically significant \(\lambda\) values in both models (0.989 and 0.994, with \(p\)-values < 0.001) reveal the presence of spatial spillover effects. Specifically, they indicate that household income in one province is positively correlated with the income levels in nearby provinces. This finding implies that the economic health of a region can be, in part, influenced by the financial success of its surrounding areas. The analysis indicates that certain sectors consistently exhibit a positive correlation with average household income. Notably, the _agricultural_ sector--which includes a range of activities from farming to fishing--display a strong positive link with household income across both models. This relationship highlights the essential role of agriculture in sustaining rural economies and suggests that variations in agricultural output are directly connected to the economic health of provincial households. However, the earlier Granger causality tests cautions against interpreting this link as strictly predictive or causal. It likely points to a symbiotic relationship, where the success of the sector and the growth in household income are mutually reinforcing. Additionally, the _real estate_ sector, encompassing property development and sales, shows a significant positive association in both models. This relationship may reflect the immediate economic benefits derived from real estate activities, which could suggest the sector's impact on employment opportunities and local income levels in the short term--and the potential feedback effect of these economic conditions on the real estate sector itself. _Professional, scientific, and technical services_, which range from legal and accounting to architectural services, exhibit variability in their influence on household income. They are significantly associated with the average household income in the SLM model. _Administration and support services_, essential to the functioning of both public and private sectors, also show a positive association with income in the \(\text{SLM}_{\text{t}-1}\) model. Finally, the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Independent Variables** & **SLM** & \(\text{SLM}_{\text{t}-1}\) \\ \hline Spatial lag coeff. (\(\lambda\)) & 0.989 *** & 0.994 *** \\ \hline Agriculture & 0.172 ** & 0.188 ** \\ Mining & \(-\)0.038 & \(-\)0.018 \\ Manufacturing & 0.001 & 0.009 \\ Electricity & \(-\)0.016 & \(-\)0.075 \\ Water & \(-\)0.714 & \(-\)0.140 \\ Construction & 0.034 & \(-\)0.028 \\ Retail & \(-\)0.056 & \(-\)0.061 \\ Transport & \(-\)0.022 & \(-\)0.040 \\ Food & 0.024 & 0.041 \\ Information & \(-\)0.034 & \(-\)0.007 \\ Finance & \(-\)0.031 & 0.026 \\ Real estate & 0.560 *** & 0.705 *** \\ Professional & 0.471 *** & 0.051 \\ Support & 0.175 & 0.470 ** \\ Public & 0.071 & 0.038 \\ Education & 0.207 & 0.076 \\ Health & \(-\)0.379 ** & \(-\)0.514 ** \\ Leisure & 0.289 * & 0.561 ** \\ Others & \(-\)1.030 ** & \(-\)1.581 *** \\ \hline Pseudo R\({}^{2}\) & 0.872 & 0.874 \\ RMSE & 2457 & 2444 \\ \hline \hline \end{tabular} \({}^{*}\)\(p\) < 0.1; **\(p\) < 0.05; *** \(p\) < 0.001.  
\end{table} 
Table 3: The Results of Spatial Lag Models. _leisure_ sector, which includes arts, entertainment, and recreation, presents a significant positive relationship with household income in the \(\text{SLM}_{\text{t-1}}\) model. This pattern indicates a short-term relationship between leisure-related economic activities and income. While the SLM and \(\text{SLM}_{\text{t-1}}\) models' results point to significant sectoral associations with household income, the simultaneity and the presence of bidirectional causality emphasise the need for careful interpretation.