### PCI and government responsiveness on flood fatalities

The regression results of FE negative binomial and FE Poisson estimates for Eq. (1) are reported in Table 1. The outcome variable is flood fatalities in all states. We use both regression models for estimation purposes because one model is advantageous over another. FE Poisson model controls more efficiently time-invariant unobserved state-specific heterogeneity. We introduce year dummy and state dummy to control time-variant and time-invariant unobserved state heterogeneity factors in all regression estimates. Also, we include cluster standard errors at the state level in all estimates.

The coefficient of per capita income (PCI) is positive, and its squared coefficient is negative and significant without taking into account control variables in FE Poisson estimation (see column C1 of Table 1). These results indicate a non-linear relationship between deaths from floods and per capita income, and it follows an inverted U-shaped relation with respect to per capita income. Our findings are mirror findings by^{7,9}. The turning point estimate of PCI is Rs. 38,803 (1268 US$), which lies at the 90th percentile distribution of our data sample (see column C1). The results imply that deaths from floods increase when per capita income is less than the turning point of PCI at Rs. 38,803 (1268 US$), and deaths decline further when income rises beyond the turning point of PCI at Rs. 38,803 (1268 US$).

Still, we find the inverted U-shaped relationship between flood fatalities and PCI after considering other control variables such as disaster adaptation measures and political factors (see column C2 of Table 1). The turning point of PCI is 38,424 (1256 US$), which is lower than Rs. 38,803 (1268 US$). In our final regression estimates, the relation for PCI remains inverted U-shaped after controlling flood magnitude in column C3. The coefficient plots are shown in Fig. 1a–c, which explain the non-linear relationship between per capita income and flood deaths for All, high-income, and low-income states. Here, we provide the plot for the key variables used in the study. The coefficient of PCI is positive, and the coefficient of its squared term is negative, which shows that flood fatalities in all states are higher in the initial phase, and then deaths decline as PCI increases further.

The turning points of per capita income are estimated using the linear and quadratic coefficients of the respective variables. Moreover, we use sample data to estimate the percentile value of the turning point of per capita income. In all states, the turning point of PCI is Rs. 26,980 (882 US$), which indicates that fatalities increase initially till the threshold income and thereafter decline with a further rise in PCI (see Fig. 2). We calculate the flood-related deaths using our sample data. The number of deaths from floods is 47,328 when the PCI is less than the turning point. When PCI crosses the turning point income, the flood fatalities reduce to 9408.

The magnitude of the turning point of PCI declines further from 1268 US$ to 882 US$ (lies at the 75th percentile distribution of our data) after controlling socio-economic and political covariates. Our estimates suggest that flood fatalities increase with increasing PCI up to 882 US$, then it declines when PCI is above 882 US$. We argue that we find the non-linear (inverted U-shaped) relationship in all three estimations (see columns C1, C2, and C3 of Table 1); however, the magnitude of the turning point of PCI varies.

We also estimate Eq. (1) using FE Poisson model to examine the non-linear (inverted U-shaped) relationship between per capita income and flood deaths for high-income and low-income states. The Poisson estimates are presented in Appendix Table A.3. To account for regional differences, we segregate our data into high-and low-income states. Higher flood fatalities and larger number of people are affected by floods in low-income states due to their higher poverty levels (measured by head count ratio) and inadequate disaster-resilient infrastructure (proxied by public expenditure on flood control and irrigation) (see Appendix Table A.1).

In the case of high-income states, we find that the coefficient of the linear term of per capita income is positive and statistically significant, and the coefficient of the squared term of income is negative and significant. This implies that the behavior of flood deaths is highly non-linear and follows the inverted U-pattern with respect to per capita income for high-income states (see Appendix Table A.3). This nonlinear relationship between flood deaths and income is presented in Fig. 1b. High-income states experience a lower level of flood deaths because higher income and stronger financial sectors help mitigate the effects of floods. Our estimates show a turning point of Rs. 40,764 (1332 US$), which suggests that flood deaths increase with a per capita income of less than Rs. 40,764 and then deaths decrease in per capita income for high-income states. Flood fatalities stood at 19,177 when the per capita income was less than the turning point income. As PCI crosses the turning point income, flood fatalities reduce to 3912 (see Fig. 2). Therefore, we find the existence of non-linearity (inverted U-shaped), as suggested by the theory.

For low-income states, the positive coefficient on per capita income and the negative coefficient on squared per capita income indicate the non-linear (inverted U-type) relationship between income and flood fatalities (see Appendix Table A.3). However, both coefficients are insignificant, implying that the non-linear relationship is weak. Our estimates show that deaths from floods are 25,025 when the PCI is less than the turning point income of Rs. 17,886 (585 US$). Furthermore, if PCI crosses the turning point income, flood fatalities reduce to 8622 (see Fig. 2). We find that low-income states experience higher deaths from floods than high-income states. This is because of the initial conditions of poverty and lack of adequate infrastructure in poor states.

Apart from income’s role in preventing flood fatalities, government responsiveness (proxied by government expenditure on natural calamities) plays a crucial role in mitigating flood fatalities (see Table 1). The coefficients of natural calamity expenditure are positive, and the squared terms are negative and insignificant. This implies an inverted U-shaped relationship between natural calamity expenditure and flood fatalities; however, this relationship is weak (see column C1 of Table 1). Furthermore, the relation remains inverted U-type with respect to natural calamity expenditure after considering other control variables (columns C2–C3 of Table 1). Moreover, it can be observed that the parametric estimates of the FE Poisson model are larger than their negative binomial estimates. The larger magnitudes of coefficients of variables in the FE Poisson estimate can be attributed to complete control for unobserved state-specific effects^{9}. The coefficient plots are shown in Fig. 1a–c, which explain the non-linear relationship between government responsiveness and flood deaths for All, high-income, and low-income states. Flood fatalities increase with government responsiveness at low levels of governance and decrease with responsiveness at high levels of governance.

The turning point of the natural calamity expenditure as a percentage of GSDP is 0.87 (lies at 97% percentile, column C3 of Table 1). The estimates suggest that flood fatalities increase when natural calamity expenditure (NCE) as a percentage of GSDP is less than 0.87%, then it declines further when natural calamity expenditure as a percentage of GSDP is above 0.87%, but the relationship is weak. The inverted U-type relationship between NCE and deaths from floods is shown in Fig. 3. The results suggest that the current government expenditure for the mitigation of flood risk is not adequate. Around 53,200 people have been killed in all states due to floods when natural calamity expenditure as a percentage of GSDP is lower than 0.87% (turning point). Nearly 3536 people have died when the turning point of NCE as a percentage of GSDP reaches above 0.87%. Therefore, higher government spending to protect citizens against natural calamities is essential to reduce flood mortality.

In high-income states, flood fatalities are 22,883 when natural calamity expenditure as a percentage of GSDP is lower than 1.46% (turning point). Flood deaths reduce to 206 when natural calamity expenditure as a percentage of GSDP crosses the turning point. The results suggest that rich states with better spending on natural disasters suffer less death from floods. Greater government spending helps mitigate the effects of floods. However, low-income states with relatively lower ability to spend on disasters experience a U-shaped relationship between flood fatalities and government responsiveness. The governance responsiveness turning point lies outside our dataset, suggesting that government responsiveness provides protection but at a diminishing rate. This implies that states with lower income and inadequate government responsiveness are more likely to suffer greater flood-related deaths than developed states. This is consistent with^{4} findings, which suggest that countries with higher economic development are less likely to experience disaster deaths.

Additionally, disaster adaptation measures such as financial development, forest cover, and flood control expenditure are not sufficient to alleviate flood fatalities. The state election and existing political alignment between State and the Centre help to minimize flood fatalities. This finding is consistent with the results of^{11}. The findings suggest that the central government releases favorable grants and soft loans to respective state governments with the same or coalition political party ruling the State. Moreover, if a flood disaster occurs in the state election year, incumbent state governments try to manage the flood calamity efficiently. The management work further helps the ruling government to enhance its prospects of winning the election. Also, the flood magnitude dummy (moderate, high, and severe) is positively related to flood fatalities (see column C3). This is in line with the findings of^{9} and^{11}. The less developed states with a higher poverty ratio and higher population density are likely to experience higher flood fatalities.

### PCI and Population affected by floods

We evaluate the impact of PCI and government responsiveness on the population affected by floods, controlling for socio-political and flood magnitudes in high-and low-income states. The FE Poisson method is used to estimate Eq. (2), and the results are reported in Tables 3 and Appendix A.2. Our results show that an inverted U-type relationship between per capita income and the population affected by floods exists in all states, high-income, and low-income states. However, the inverted U-shaped relationship with respect to income is not significant for the low-income states. Therefore, a significant increase in PCI is required to mitigate the effects from floods in the poor states. The coefficient plots are shown in Fig. 4a–c, which shows the non-linear relationship between PCI and the population affected by floods in All, high-income, and low-income states.

We estimate the turning point of PCI at which the population affected by floods is the maximum (see Fig. 5). The population affected was 855.9 million in all states when the PCI was less than the turning point PCI (578 US$). Thereafter, the population affected by floods declined by 343.7 million when income crossed the turning point PCI. The population affected in high-income states was 179.7 million when the PCI was less than the turning point PCI (647 US$). When income crossed the turning point PCI, the population affected reduced to 126.1 million. In low-income states, the population affected was 839.7 million when the PCI was less than the turning point PCI (850 US$). When income crossed the turning point PCI, the population affected reduced to 54.2 million. We conclude that poor states require higher turning point PCI to lessen the number of people affected by floods than rich states.

In addition, we employ the FE Poisson estimation method to examine the non-linear relationship between government responsiveness and the population affected by floods in All, high-income, and low-income states using Eq. (2). The results of Poisson estimates are shown in Table 2 and Appendix Table A.3, and the coefficient plot of the key variables is shown in Fig. 4a–c. The estimated results show an inverted U-shaped relationship between government responsiveness and the population affected by floods in high-income and low-income states; however, the inverted U-type relation is weak for both states. The result concludes that government responsiveness is still ineffective in mitigating the disastrous flood impact in Indian states.

We also estimate the turning point of government responsiveness and the number of people affected by floods below and above the turning point of government responsiveness (see Fig. 6). In all states, population affected was 1149.6 million when natural calamity expenditure as a percentage of GSDP was lower than 0.9% of GSDP (turning point). The number of persons affected reduced to 50.02 million when natural calamity expenditure as a percentage of GSDP crossed the turning point. In high-income states, the population affected was 278.6 million when natural calamity expenditure as a percentage of GSDP was lower than 1.15% of GSDP. If government responsiveness crossed the turning point, the number of persons affected reduced to 17.1 million. In low-income states, the population affected was 256 million when natural calamity expenditure as a percentage of GSDP was lower than 0.13% of GSDP. If government responsiveness crossed the turning point, the population affected reduced to 637.9 million.

Moreover, financial development, forest cover, and flood control expenditure have no significant effect on lowering the population affected by floods. On the other hand, the occurrences of state elections have significantly declined the flood impacts. Furthermore, the flood magnitude dummies remain significant in all Poisson specifications, implying that a larger population is affected due to severe flooding.

We estimate Eq. (2) using FE negative binomial for robust results, and results are presented in columns C4–C6 in Table 2. This exercise is done only for all Indian states. The inverted U-shaped relationship remains the same with respect to PCI. However, the turning point of income moderately varies with the FE Poisson estimate. In addition, non-linear relation is continued with respect to natural calamity expenditure throughout the models (see Table 2). Moreover, results show that severe floods adversely affect the population in Indian states. In sum, the FE negative binomial produces mirror results of FE Poisson estimates.

### PCI and government responsiveness on flood damages

We evaluate the effect of PCI and government responsiveness on flood damages, controlling socio-political and severity of floods. Using the FE Tobit model, we estimate Eq. (3), and the results are presented in Table 3. The outcome variable is flood damage over GSDP, which consists of many zeros, and the data is truncated from below. Therefore, it is appropriate to use Tobit estimation in our dataset. The flood damages include damage to crops, houses, and public infrastructure, all expressed in monetary values. We control year and state fixed effects, and standard errors are clustered at the state level in all regression models. The coefficient on the lag of PCI is positive and significant, and its squared term is negative and significant without considering control variables.

The results confirm that an inverted U pattern with respect to PCI has been established (see column C1 of Table 3). The inverted U pattern is sustained with respect to PCI after considering economic, political, and flood severity variables (see columns C2–C3 of Table 3). The estimated turning point of PCI in all models exceeded the PCI’s maximum value in our sample, implying that a higher PCI is needed to reduce flood damage. These results are consistent with the findings of^{8}. They found an inverted U-shaped relationship between damages due to floods and per capita income using a cross-country dataset spanning 1980–2004. Besides PCI’s role in mitigating the flood damages, government responsiveness (measured by government expenditure on natural calamity) plays an essential role in mitigating flood damages in Indian states. The coefficient of natural calamity expenditure is positive, and its squared term is negative and significant, except for the model shown in column C1. The results follow an inverted-U pattern with respect to natural calamity expenditure throughout the models. We also estimate the non-linear relationship between PCI and flood damages in high and low-income states. The Tobit estimates show an inverted U-shaped relation between PCI and flood damages in high and low-income states. However, the relationship is weak for the low-income states. The coefficients plot of these results is shown in the Appendix Fig. A.1 (see Supplementary Information).

The turning point of natural calamity expenditure as a percentage of GSDP marginally increased from 0.81% in column C1 to 1.1% in column C3. This suggests that flood damages increase with a rise in natural calamity expenditure as a percentage of GSDP up to 1.1%; thereafter, it declines with increasing natural calamity expenditure. In addition, a higher flood magnitude yields greater flood damage. Controlling flood magnitude and total area under forest cover, we find that financial development and expenditure on flood control measures have no impact on flood damage. Furthermore, we find that the state election year and political alignment have little effect on reducing flood damages to some extent.

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