## 4 Results
### Impact of NGCL Level on ADR  
Combined with the Hausman test (Statistic = 188.91, Prob > chi2 = 0.0000), the fixed effect model was selected. The software Stata17 was used to test the significance of a single threshold, double threshold, and triple threshold of four alternative threshold variables (Table 3).  
The results in Table 3 showed that the variables of \(clplf\) and \(pal\) passed the single threshold test of 5%, whereas the threshold test results of \(rng_{1}\) and \(ampc\) were insignificant. Therefore, the \(clplf\) and \(pal\) were selected as the threshold variables. OLS was used to estimate the regression model parameters with different threshold variables (Table 4). OLS is a mathematical optimization technique; its principle is choosing a set of parameters of a linear function of the explanatory variables, and minimizing the sum of squared residuals between the dependent variable (the predicted variable) and the predictor variable observed in a given data set. This method easily facilitates determining the parameters to be estimated and minimizing the sum of squared residuals for all observations.  
Meanwhile, the time-space dual fixed effect Model (1) was established, and Model (2) without control variables and Model (3) with control variables were also built (Table 4). The regression result of Model (1) showed that NGCL has a positive and significant effect on ADR, which was higher than the results of other models. The regression results of Models (2) and (3) showed that the impact of NGCL on ADR was further increased after adding control variables with basically similar threshold characteristics. It indicated that the regression result of Model (3) was basically robust.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & \multicolumn{2}{c}{**Single Threshold**} & \multicolumn{2}{c}{**Double Threshold**} & \multicolumn{2}{c}{**Triple Threshold**} \\ \cline{2-7}  & **LR\_F** & **LR\_P** & **LR\_F** & **LR\_P** & **LR\_F** & **LR\_P** \\ \hline Cultivated land per labor & 49.15 & 0.0000 & 4.01 & 0.8600 & 3.31 & 0.8667 \\ force (\(clplplf\)) & 4.23 & 0.963 & 4.84 & 0.8900 & 6.09 & 0.7833 \\ Rate of non-grain of & & & & & & \\ cropland (\(rng_{1}\)) & 4.23 & 0.963 & 4.84 & 0.8900 & 6.09 & 0.7833 \\ Proportion of agricultural & & & & & & \\ laborens (\(plf\)) & 18.58 & 0.0300 & 20.33 & 0.0500 & 6.30 & 0.5500 \\ Agricultural machinery per capita (\(ampc\)) & 10.86 & 0.3467 & 7.35 & 0.4867 & 8.12 & 0.6167 \\ N & 350 & & 350 & & 350 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Detection results of alternative threshold variables.  
Furthermore, the regression results showed that in the study area, NGCL had no negative influence on ADR from 2011 to 2020. According to the study, the NGCL in Northeast China may have been driven by changes in planting trends and changes in residents' diets, which somewhat encouraged rational allocations of agricultural production factors. As far as the threshold regression results, due to the scale of regional agricultural labor force, a threshold effect occurred on the impact of NGCL on ADR. The influence of NGCL on ADR had a significant negative effect when it was less than 7.07%. When the proportion was higher than 7.07% and less than 9.80%, the effects had a positive recessive cumulative effect, when the proportion was greater than 9.8%, the influence had a dominant accelerating effect. The regression result with \(clplf\) as the threshold variable showed that the occurrence of NGCL had a significant positive effect on ADR, when the \(clplf\) was less than 2.034 ha. Meanwhile, the \(clplf\) was larger than a certain scale, the effect showed an invisible negative accumulation feature. According to the estimated results of the control variables, the local general public budget expenditure, grain output, and industrial structure all had negative effects on ADR (Table 4).