4.2. Benchmark Analysis of Heterogeneous Food Price Risk Nonlinearity: Hypotheses H1–H2
By allowing for nonlinearity and spatial effects by including squared public opinion and spatial variables, we sought to test whether food safety incident has negative local and spatial spillovers to high-risk food price risk, which is heterogeneous in low- and high-risk food (hypothesis H1); and whether public health concern over food safety has nonlinear local and spatial spillovers to food price risk, which is heterogeneous in low- and high-risk food (hypothesis H2). We estimated Equation (3) (dynamic SDM, the second-best fit model) and Equation (4) (dynamic SAR, the first-best fit model) using QML estimator, excluding and including squared public health concern (lnphcb2), respectively, all with FE, as reported in
Table 4: (i) columns (1)–(4) report estimates of Equation (3) (dynamic SDM) excluding lnphcb2, Equation (3) (dynamic SDM) including lnphcb2, Equation (4) (dynamic SAR) excluding lnphcb2, and Equation (4) (dynamic SAR) including lnphcb2, respectively, with lnlrfp (low-risk food price risk) as DV (dependent variable); and (ii) columns (5)–(8) report estimates with lnhrfp (high-risk food price risk) as DV.
First, spatial specification diagnostic tests: (i) using spatial coefficients (ρ), we find that all columns are statistically significant, suggesting that spatially lagged effects of food price risk should be accounted for. (ii) using BIC, we find that dynamic SAR best fits the data; therefore, we restrict attention to dynamic SAR (columns (3)–(4) and (7)–(8)).
Second, empirical analysis for low-risk food: (columns (3)–(4)). (i) In columns (3)–(4), the short-run local spillovers (SR_Direct_lrid and SR_Direct_hrid), short-run spatial spillovers (SR_Indirect_lrid and SR_Indirect_hrid), long-run local spillovers (LR_Direct_lrid and LR_Direct_hrid), and long-run spatial spillovers (LR_Indirect_lrid and LR_Indirect_hrid) of low-risk incident and high-risk incident are all statistically insignificant, suggesting no significant local or spatial spillover of food safety incident. Thus, whether in the short run or in the long run, neither low-risk incident nor high-risk incident has a significant local or spatial spillover to low-risk food price risk.
(ii) First, in column (3), the short-run local spillover (SR_Direct_lnphcb) and short-run spatial spillover (SR_Indirect_lnphcb) of public health concern are both negative, suggesting negative local and spatial spillovers of public health concern on average; second, in column (4), the short-run local spillover (SR_Direct_lnphcb2) and short-run spatial spillover (SR_Indirect_lnphcb2) of squared public health concern are both negative, suggesting inverse U-shaped local and spatial spillovers of public health concern in general. Thus, in the short run, on average, public health concern over food safety has negative local and spatial spillovers to low-risk food price risk; in general, public health concern over food safety has inverse U-shaped local and spatial spillovers to low-risk food price risk.
(iii) First, in column (3), the long-run local spillover (LR_Direct_lnphcb) of public health concern is negative, and long-run spatial spillover (LR_Indirect_lnphcb) of public health concern is statistically insignificant, suggesting a negative local spillover but no significant spatial spillover on average; second, in column (4), the long-run local spillover (LR_Direct_lnphcb2) of squared public health concern is negative, and long-run spatial spillover (LR_Indirect_lnphcb2) of squared public health concern is statistically insignificant, suggesting an inverse U-shaped local spillover but no significant spatial spillover in general. Thus, in the long run, public health concern over food safety has a negative local spillover to low-risk food price risk on average, and an inverse U-shaped local spillover to low-risk food price risk in general; public health concern over food safety has no significant spatial spillover to low-risk food price risk.
Third, empirical analysis for high-risk food: (columns (7)–(8)). (i) First, in columns (7)–(8), the short-run local spillovers (SR_Direct_lrid and SR_Direct_hrid) and short-run spatial spillovers (SR_Indirect_lrid and SR_Indirect_hrid) are all negative, suggesting negative local and spatial spillovers of food safety incident; second, in column (7), the short-run local spillover (SR_Direct_lnphcb) and short-run spatial spillover (SR_Indirect_lnphcb) of public health concern are both negative, suggesting negative local and spatial spillovers of public health concern on average; third, in column (8), the short-run local spillover (SR_Direct_lnphcb2) and short-run spatial spillover (SR_Indirect_lnphcb2) of squared public health concern are both negative, suggesting inverse U-shaped local and spatial spillovers of public health concern in general. Thus, in the short run, both low-risk incident and high-risk incident have negative local and spatial spillovers to high-risk food price risk; on average, public health concern over food safety has negative local and spatial spillovers to high-risk food price risk; in general, public health concern over food safety has inverse U-shaped local and spatial spillovers to high-risk food price risk.
(ii) In columns (7)–(8), the long-run local spillovers (LR_Direct_lrid, LR_Direct_hrid, LR_Direct_lnphcb, and LR_Direct_lnphcb2) and long-run spatial spillovers (LR_Indirect_lrid, LR_Indirect_hrid, LR_Indirect_lnphcb, and LR_Indirect_lnphcb2) are all statistically insignificant, suggesting no significant local or spatial spillover of food safety incident and public health concern. Thus, in the long run, neither low-risk incident nor high-risk incident has a significant local or spatial spillover to high-risk food price risk; public health concern over food safety has no significant local or spatial spillover to high-risk food price risk.
Fourth, turning point for public health concern: We compute the turning point for public health concern in the inverse U-shape using the main coefficients (β
3 and β
4) following Wooldridge [
35]. We obtain the turning point values for public health concern (turning_lnphcb) from column (4) (dynamic SAR for low-risk food) and column (8) (dynamic SAR for high-risk food), which are −2.3420 and −2.9651 (well within the range of the observed data on lnphcb), respectively, as also reported in
Table 4.
Fifth, plots of marginal effects of public health concern: We further plot the marginal effects of public health concern on low-risk food price risk (column (4) of
Table 4) and high-risk food price risk (column (8) of
Table 4), respectively, using the main coefficients (β
3 and β
4) and turning point values for public health concern (turning_lnphcb), as depicted in
Figure 4. In both panels, the curves exhibit a pronounced inverse U-shaped pattern, lending further support to hypothesis H2.
In summary, these results show that (i) food safety incident alone only triggers high-risk food price risk, not low-risk food price risk; and (ii) public health concern amplifies nonlinear food price risk triggered by food safety incident. Overall, food safety incident itself does not necessarily determine food price risk, whereas it is actually public health concern that directly causes nonlinear food price risk. Therefore, hypotheses H1–H2 are generally supported.
4.3. Further Analysis of Heterogeneous Food Price Risk Mechanism: Hypotheses H3–H4
4.3.1. Further Analysis of Heterogeneous Food Price Risk Moderation: Hypothesis H3
By allowing for the interaction between food safety incident and public health concern following Hayes [
36], we seek to test whether expected moderation exists, that is, whether food safety incident negatively moderates the negative local and spatial spillovers of public health concern over food safety to food price risk, which is heterogeneous in low- and high-risk food and incidents (hypothesis H3). We estimate Equations (5) and (6) (dynamic SAR, the first-best fit model) using QML estimator, excluding and including the interaction terms between low risk incident and public health concern (lrid*lnphcb), and high risk incident and public health concern (hrid*lnphcb), respectively, all with FE, as reported in
Table 5: (i) columns (1)–(2) report estimates of Equation (5) only including lrid and lnphcb (Step 1), and Equation (6) further including lrid*lnphcb (Step 2), respectively, with lnlrfp as DV; (ii) columns (3)–(4) report estimates of Equation (5) only including hrid and lnphcb (Step 1), and Equation (6) further including hrid*lnphcb (Step 2), respectively, with lnlrfp as DV; and (iii) columns (5)–(8) report estimates with lnhrfp as DV.
First, spatial specification diagnostic tests: Using spatial coefficients (ρ), we find that all columns are statistically significant, suggesting that spatially lagged effects of food price risk should be accounted for.
Second, empirical analysis for low-risk food: (columns (2) and (4)). (i) In column (2), the short-run local spillover (SR_Direct_lrid*lnphcb), short-run spatial spillover (SR_Indirect_lrid*lnphcb), long-run local spillover (LR_Direct_lrid*lnphcb), and long-run spatial spillover (LR_Indirect_lrid*lnphcb) of interaction lrid × lnphcb are all statistically insignificant, suggesting no significant moderation of local or spatial spillover of public health concern by low-risk incident. Thus, whether in the short run or in the long run, low-risk incident doesn’t moderate the local or spatial spillover of public health concern over food safety to low-risk food price risk.
(ii) In column (4), the short-run local spillover (SR_Direct_hrid*lnphcb) and short-run spatial spillover (SR_Indirect_hrid*lnphcb) of interaction hrid × lnphcb are both negative, suggesting negative moderation of local and spatial spillovers of public health concern by high-risk incident. Thus, in the short run, high-risk incident negatively moderates the negative local and spatial spillovers of public health concern over food safety to low-risk food price risk.
(iii) In column (4), the long-run local spillover (LR_Direct_hrid*lnphcb) of interaction hrid × lnphcb is negative, and long-run spatial spillover (LR_Indirect_hrid*lnphcb) of interaction hrid × lnphcb is statistically insignificant, suggesting negative moderation of local spillover but no significant moderation of spatial spillover of public health concern by high-risk incident. Thus, in the long run, high-risk incident negatively moderates the negative local spillover of public health concern over food safety to low-risk food price risk; high-risk incident doesn’t moderate the spatial spillover of public health concern over food safety to low-risk food price risk.
Third, empirical analysis for high-risk food: (columns (6) and (8)). (i) In column (6), the short-run local spillover (SR_Direct_lrid*lnphcb), short-run spatial spillover (SR_Indirect_lrid*lnphcb), long-run local spillover (LR_Direct_lrid*lnphcb), and long-run spatial spillover (LR_Indirect_lrid*lnphcb) of interaction lrid × lnphcb are all statistically insignificant, suggesting no significant moderation of local or spatial spillover of public health concern by low-risk incident. Thus, whether in the short run or in the long run, low-risk incident doesn’t moderate the local or spatial spillover of public health concern over food safety to high-risk food price risk.
(ii) In column (8), the short-run local spillover (SR_Direct_hrid*lnphcb) and short-run spatial spillover (SR_Indirect_hrid*lnphcb) of interaction hrid × lnphcb are both negative, suggesting negative moderation of local and spatial spillovers of public health concern by high-risk incident. Thus, in the short run, high-risk incident negatively moderates the negative local and spatial spillovers of public health concern over food safety to high-risk food price risk.
(iii) In column (8), the long-run local spillover (LR_Direct_hrid*lnphcb) and long-run spatial spillover (LR_Indirect_hrid*lnphcb) are both statistically insignificant, suggesting no significant moderation of local or spatial spillover of public health concern by high-risk incident. Thus, in the long run, high-risk incident doesn’t moderate the local or spatial spillover of public health concern over food safety to high-risk food price risk.
In summary, these results show that high-risk incident intensifies negative pressure of public health concern on food price risk. Therefore, hypothesis H3 is generally supported.
4.3.2. Further Analysis of Heterogeneous Food Price Risk Mediation: Hypothesis H4
By using an extended spatial causal steps approach motivated by the Baron and Kenny method [
33], we seek to test whether expected mediation exists; that is, whether public health concern over food safety mediates the negative local and spatial spillovers of food safety incident to food price risk, which is heterogeneous in low- and high-risk food and incidents (hypothesis H4). We estimate Equations (7)–(9) (dynamic SAR, the first-best fit model) using QML estimator, following the causal steps approach in Baron and Kenny [
33], respectively, all with FE, as reported in
Table 6: (i) columns (1)–(3) report estimates of Equation (7) including lrid with lnlrfp as DV (Step 1), Equation (8) including lrid with lnphcb as DV (Step 2), and Equation (9) including lrid and lnphcb with lnlrfp as DV (Step 3); (ii) columns (4)–(6) report estimates of Equation (7) including hrid with lnlrfp as DV (Step 1), Equation (8) including hrid with lnphcb as DV (Step 2), and Equation (9) including hrid and lnphcb with lnlrfp as DV (Step 3); and (iii) columns (7)–(12) report estimates with lnhrfp as DV.
First, spatial specification diagnostic tests: Using spatial coefficients (ρ), we find that all columns are statistically significant, suggesting that spatially lagged effects of food price risk should be accounted for.
Second, empirical analysis for low-risk food: (columns (1)–(6)). In columns (1) and (4), the short-run local spillovers (SR_Direct_lrid and SR_Direct_hrid), short-run spatial spillovers (SR_Indirect_lrid and SR_Indirect_hrid), long-run local spillovers (LR_Direct_lrid and LR_Direct_hrid), and long-run spatial spillovers (LR_Indirect_lrid and LR_Indirect_hrid) of lrid and hrid with lnlrfp as DV are all statistically insignificant (thereby not passing Step 1), suggesting no significant mediation of local or spatial spillover of low-risk incident and high-risk incident by public health concern. Thus, whether in the short run or in the long run, public health concern over food safety doesn’t mediate the local or spatial spillover of low-risk incident to low-risk food price risk; public health concern over food safety doesn’t mediate the local or spatial spillover of high-risk incident to low-risk food price risk.
Third, empirical analysis for high-risk food: (columns (7)–(12)). (i) First, in columns (7) and (10), the short-run local spillovers (SR_Direct_lrid and SR_Direct_hrid) and short-run spatial spillovers (SR_Indirect_lrid and SR_Indirect_hrid) of lrid and hrid with lnhrfp as DV are all negative (thereby passing Step 1); second, in columns (8) and (11), the short-run local spillovers (SR_Direct_lrid and SR_Direct_hrid) and short-run spatial spillovers (SR_Indirect_lrid and SR_Indirect_hrid) of lrid and hrid with lnphcb as DV are all negative (thereby passing Step 2); third, in columns (9) and (12), the short-run local spillovers (SR_Direct_lnphcb) and short-run spatial spillovers (SR_Indirect_lnphcb) of lnphcb with lnhrfp as DV are both negative (thereby passing Step 3); fourth, in columns (9) and (12), SR_Direct_lrid, SR_Direct_hrid, and SR_Indirect_hrid are all negative, while SR_Indirect_lrid is statistically insignificant, suggesting partial mediation of local spillover of low-risk incident by public health concern, complete mediation of spatial spillover of low-risk incident by public health concern, and partial mediation of local and spatial spillovers of high-risk incident by public health concern. Thus, in the short run, public health concern over food safety partially mediates the negative local spillover and completely mediates the negative spatial spillover of low-risk incident to high-risk food price risk; public health concern over food safety partially mediates the negative local and spatial spillovers of high-risk incident to high-risk food price risk.
(ii) In columns (7) and (10), the long-run local spillovers (LR_Direct_lrid and LR_Direct_hrid) and long-run spatial spillovers (LR_Indirect_lrid and LR_Indirect_hrid) of lrid and hrid with lnhrfp as DV are all statistically insignificant (thereby not passing Step 1), suggesting no significant mediation of local or spatial spillover of low-risk incident and high-risk incident by public health concern. Thus, in the long run, public health concern over food safety doesn’t mediate the local or spatial spillover of low-risk incident to high-risk food price risk; public health concern over food safety doesn’t mediate the local or spatial spillover of high-risk incident to high-risk food price risk.
Fourth, mediation effect and ratio of mediation effect to total effect: We further compute mediation effect (ME) and ratio of mediation effect to total effect (MR) using the main coefficients following Mackinnon, Warsi, and Dwyer [
37]. We obtain ME and MR from columns (9) and (12) where mediation is statistically significant, as also reported in
Table 6. Results show that, (i) for column (9), the mediation effect of spillover of low-risk incident to high-risk food price risk by public health concern is −0.0162 (ME = −0.0162), accounting for 12.45% of the total spillover (MR = 0.1245); and (ii) for column (12), the mediation effect of spillover of high-risk incident to high-risk food price risk by public health concern is −0.0075 (ME = −0.0075), accounting for 6.44% of the total spillover (MR = 0.0644).
In summary, these results show that food safety incident indirectly affects high-risk food price risk through public health concern. Therefore, hypothesis H4 is generally supported.
Moreover, we subject our analyses to a variety of robustness checks as described in
Table 2, finding that all results are robust to using alternative measurement of food safety incident, alternative measurement of public health concern, and alternative spatial weighting matrix.