Impact of floods on rice production in West Africa Micro-evidence from Benin

Floods are a climatic risk that can result in significant yield losses for smallholder farmers. In this study, the impacts of the 2012 floods on rice productivity in Benin were investigated. A socioeconomic and productivity survey of 150 rice farmers was conducted in 17 villages across 2 districts that are highly vulnerable to climate change. The generalised propensity score method was employed to account for the continuous nature of the treatment variable, with the results indicating a decrease in rice yield accompanied by an increase in flooded farm proportion. The expected rice yield for a 10% flooded rice land was 7.20 tons/ha throughout the year. Additionally, an increase in the proportion of flooded rice land from 10% to 20% resulted in a decrease of 1.19 tons/ha of rice yield. During the wet season, floods negatively impacted rice yield, irrespective of their severity. Conversely, flooding benefited rice production in the dry season following flooding. These findings offer policymakers insight into appropriate protection plans and adaptation strategies.


Introduction
Climate change is a global challenge that affects agriculture in many tropical regions, where it tends to be weather sensitive (Qiao et al., 2022).Smallholder farmers are unable to understand the potential impacts of climate change on their farming systems and anticipate sustainable adaptations.Climate predictions suggest that floods, droughts, aridity, and changes in rainfall will compromise agriculture (Serdeczny et al., 2017).With an increase in inundation depth and volume of up to 60%, the damage to agricultural areas is projected to rise by 2 to 6 times, while the associated loss value may surge from 2 to 38 times in river basins (Syldon et al., 2024).Moreover, forecasts have suggested continuous warming (1.5-6.5 °C) and precipitation uncertainty in West Africa (Sylla et al., 2016).Consequently, future climate events are expected to affect the yield of tropical crops, raising concerns regarding food insecurity, particularly in rural households (Palazzo et al., 2017;Waha et al., 2013).Furthermore, reductions in rice yields can be attributed to changes in atmospheric conditions.In 2018, the total rice yield loss in the Long Xuyen Quadrangle was estimated at 15,729 tons.This resulted in an economic loss amounting to approximately 1.47% of the total gross regional domestic product of the Long Xuyen Quadrangle in the Vietnam Mekong Delta (Bui & Nguyen, 2024).Consequently, adapting farming systems to climate change will require a thorough understanding of its impacts on the livelihoods of agricultural households (Devkota & Bhattarai, 2018).
Climate change is predicted to affect several aspects of rural livelihoods, such as sustainable agricultural production, food safety, and food quality (Gezie & Tejada Moral, 2019).Specifically, climate predictions indicate increasing trends in severe and moderate drought events by 2060, resulting in a 40% crop yield loss (Ahmed, 2020).Specifically, the maize yield is projected to decrease by approximately 85% in West Africa (Stuch et al., 2020).Therefore, there is significant interest in understanding the heterogeneous effects of climate change across different regions of the world, including within countries, to identify effective adaptation strategies against these adverse effects.
Climate change poses serious concerns for agriculture in Benin, a West African country.Climate simulation models have predicted a 13-15% reduction in precipitation in Northern Benin by 2100 (MEHU, 2011), which represents the primary crop cultivation region in the country.However, there is limited evidence regarding the impact of climate change on key staple crops, such as rice, in Benin.Rice cultivation typically occurs in favourable wet environments that are prone to both floods and droughts.Nevertheless, the impacts of flooding on yield reduction are significantly more pronounced than those of droughts (Meng & Qian, 2024).Moreover, because the majority of the favourable agroecological regions are located near rivers, lakes, or other water bodies, they are more susceptible to flooding promoted by climate change.Consequently, understanding the severity of the repercussions associated with climate change, such as flooding, is imperative for devising local adaptation strategies.
Agriculture plays a crucial role in the national economy, accounting for 88% of the export revenue and 70% of the country's workforce.The agricultural sector generates approximately 27.1% of the gross domestic product (GDP) (World Development Indicators, 2020), with cotton as the primary cash crop, representing approximately 40% of this contribution (World Development Indicators, 2020).Cereals are of paramount importance in the crop production subsector, mainly led by maize, sorghum, and rice.The economic importance of local rice production alone is underscored by its contribution of 1% to the GDP (MAEP, 2007).Additionally, rice is the fourth staple food product in terms of consumption.
In Benin, the extreme north is the most vulnerable region to climate change and climate-related disasters, justifying the focus of this study in this area.Its climate is transitionally tropical, with less rainfall than that in other areas at the same latitude.
One of the most severe flooding events in Benin occurred in August 2012.This natural disaster resulted from the overflow of rivers, particularly in Northern Benin, worsening the economy of local communities (Bonou et al., 2024).A prior flooding event occurred in 2010, with a nationwide area of farmland lost equalling approximately 50,764 ha and a decrease in food supply of up to approximately 2 million tons (World-Bank, 2011).The impacts of flooding on farming land exhibit significant variation depending on factors such as crop type, tolerance to excess water, and frequency, duration, depth, and seasonality of the flood (Morris & Hess, 1988).Within the study area, the area where rice is cultivated was the most affected by the 2012 flood (Figure 1).
Using survey data gathered from a highly climatevulnerable area in Benin, this study assessed the impact of flooding on rice farmlands in terms of both crop loss and yield reduction.Each surveyed rice farmer reported instances of flooding, and farmers were assumed to have potentially adopted adaptation strategies to mitigate their extent.Matching estimation techniques were employed to gauge the impacts of flooding on rice yield, which indicated that flooding had heterogeneous impacts on rice productivity depending on the growing season.Specifically, flooding substantially reduced rice productivity during the rainy season but promoted rice productivity during the dry season.These findings are significant for policymakers, offering additional insights into the magnitude of the impacts of floods on rice productivity.Such information is crucial for devising appropriate climate resilience programs aimed at sustaining the livelihoods of impoverished rural households in sub-Saharan Africa.

Study area
This study was conducted in March 2014 in the Republic of Benin, West Africa, which had its most severe flooding events 50 years ago.
Two adjacent rural municipalities within the Niger Basin that were affected by the 2012 flood were selected for this study: Malanville and Karimama (Figure 2).Malanville is located between 11°84'−11° 86' N and 3° 37'−3°40' E, at an altitude of 160 m, while Karimama is situated between 12°06'−12°07' N and 3°17'−3°18' E, at an altitude of 164 m.The climate of Northern Benin is characterised by a dry season from November to April and a rainy season from mid-April to October (Lawin et al., 2013).The average annual rainfall in both municipalities is 780 mm (Figure 3).

Sampling approach and data collection
This study used part of the PhD dataset of the first author, covering 228 households engaged in the production of various crops.These include cereals (rice, maize, millet, sorghum), legumes (groundnut, bean, soybean), vegetables (tomato, pepper, onion, okra), tubers/root (cassava, potato, sweet potato), fruits (banana, orange, mango, gourd), and cotton (Bonou et al., 2018).The data used in this paper comprises a subset of 150 households from the original 228, which was engaged in rice production during the 2012 flood.To reduce the sample of 228 households and select the villages and households, we used a multistage sampling approach.
Village sampling: During the exploratory phase, 19 villages were selected from both municipalities based on their extent of lost farmland.Selection was conducted via focus group discussions involving local and municipal authorities, as well as extension services, using a checklist of open questions.The stakeholders considered the consequences of the 2012 flooding when choosing the villages.Of the 19 villages, 2 did not engage in rice production and were therefore discarded, leaving 17 villages with rice farmlands.
Household sampling: The original sample consisting of 228 households was determined using the formula introduced by Dagnelie (1998).Using random sampling, 12 heads of households were selected from each of the 19 villages (Bonou et al., 2018).In this study, 150 households engaged in rice production from the 17 selected villages were used.The sample size varied across the villages where rice was produced (Tables 1  and 2), resulting in a non-self-weighted sample.
Data collection: Cross-sectional data were collected in March 2014, encompassing the period following the flooding events beginning in August 2012.Data collection relied on the memory of rice farmers and focused on the rainy and dry growing seasons of 2012-2013 using a questionnaire.Before its implementation, the questionnaire underwent a pre-testing phase in another region with similar characteristics to those of the study area, specifically, So-Ava village in southern Benin, which is adjacent to a floodplain.Subsequently, adjustments were made to some questions based on the feedback received, and the questionnaire was validated before deployment.The primary data collected included the sociodemographic characteristics of household members (e.g.household size, formal education, gender, and age of the head of household); experiences with flooding; characteristics of rice farms (e.g.area affected by flooding, production yield, area cultivated with rice, altitude of rice farm, area cultivated with rice and soil type); visits by extension services; and rice production costs (e.g.seed, labour, fertiliser, and pesticide costs as well as fuel costs for runoff/ drainage).
In addition to the researcher, three interviewers were enlisted for the survey.The questionnaire was designed and printed in French, but interviews were conducted entirely in the local languages of the farmers, i.e.Dendi, Gourmantche, and Fulani.
Microsoft Access 2020 was used for data processing, while the Stata 13 software was utilised for data analysis.

Review of impact evaluation framework
As cross-sectional data lack the temporal aspect necessary for applying methods such as randomisation (Linnemayr & Alderman, 2011) or difference-indifference (Khandker et al., 2009), we carried out an expost impact evaluation.This involved assessing the causal impact of the 2012 flood on a specific outcome to establish a connection between the observed changes in each outcome (such as production yield) and the extreme event (the flood).The impact equation used is as follows: where Gi represents the impact of the 2012 flood on household i, Y i denotes the outcome of household i, and T i is a dummy variable taking two values (when household i experienced a flood, T i = 1; otherwise, T i = 0).By comparing the same household with and without a flood event, we mitigated the influence of other factors, allowing G i to be entirely attributed to flooding.Unfortunately, because the realisation of the two outcomes mentioned above is mutually exclusive for any household, missing data present a challenge (Diagne, 2002;Rubin, 1974).Estimating the missing data requires identifying a comparison group that mirrors the counterfactuals of the flooded group.However, if systematic differences exist between the two groups, the estimated impact may be biased.
The primary objective of a robust impact assessment is to effectively mitigate or address selection bias.Unfortunately, in this study, identifying a suitable comparison group was challenging.Within the sample, only 31 households remained unflooded, whereas 150 households were affected by flooding.Consequently, the quasi-experimental propensity score matching could not be applied (Adégbidi, 2012;Rosenbaum & Rubin, 1983), owing to the insufficient size of the non-flooded sample.In the case of instrumental variable methods (Heckman & Vytlacil, 1999), the primary obstacle lies in determining the instrument.Here, a potential instrument is the proximity of each farm to the river.While this instrument is robust, as it is highly correlated with flooding, it is invalid because it also correlates with the error term.The proximity of farms to the river influences factors such as humidity and fertility, which, in turn, impact the outcome (production yield).
To address these challenges, this study focused on rice-producing households affected by flooding employing the generalised propensity score (GPS) to evaluate the impact of flooding on rice yield (Bia & Mattei, 2008;Guardabascio & Ventura, 2014;Hirano & Imbens, 2004).Although this method has numerous applications (Bia & Mattei, 2012;Carneiro & Rodrigues, 2009;Ciaian et al., 2011;Imai & Ratkovic, 2014;Kluve et al., 2012;Liu & Florax, 2014), its use in flood damage assessments is lacking.Thus, this study aimed to fill this gap and shed light on the challenges associated with such an application.

GPS framework
The causal model proposed by Rubin (1974) and tested by Imbens and Wooldridge (2009) has become the standard approach for impact evaluations using observational data when randomisation conditions are not met.The impact evaluation performed in this study presents a causal inference challenge, endeavouring to establish a causal relationship between observed changes in an outcome and an extreme event.By employing the potential outcome method for causal inference (Rubin, 1974(Rubin, , 1978)), a continuous dose-response function (GPS) was estimated, linking each dose value (i.e. the proportion of flooded rice farmland) to the post-flooding production yield (Hirano & Imbens, 2004) (see the Appendix for details).

Empirical specification
The production yield per ha values in flooded households during the 2012-2013 season were regressed on the percentage of flooded land and other covariates using the Stata package st0150 proposed by Bia and Mattei (2008).We assumed that unobserved variables did not significantly affect the level of treatment (flooding).
In the binary treatment case (flooding or no flooding), reducing the estimation bias critically depends on the quality and quantity of the control variables used in computing the GPS.If the test for normality of disturbances is not satisfied in the Stata package (Bia & Mattei, 2008), the results are no longer consistent.Guardabascio and Ventura (2014) overcame this limitation by proposing an alternative method of GPS estimation using a non-normal treatment variable.This helps overcome the challenge of failure to guarantee the normality of the treatment variable and its transformation.In other words, neither the treatment variable, the fraction of flooded rice farmland, nor its logarithm and other transformations were normally distributed, so the Stata package of Guardabascio and Ventura (2014) was used to overcome this challenge.
The treatment range was divided into three intervals based on flooding distribution; the control and background variables are presented in Table 3.Of the 213 ha cultivated by farmers in the sample, approximately 171 ha of rice farmland were flooded, representing 80.3% of the total cultivated rice land.The choice of covariates was based on economic and agronomic theories (Kabunga et al., 2012), presuming that these were the most relevant variables determining either the production yield or flooding intensity.Additionally, variables such as ethnicity, age, gender, social class, household composition, social capital level, tenure type, and property type were considered to potentially modify the economic consequences derived from floods (Walker, 2006).

GPS estimation and covariate balancing
The conditional distribution of the percentage of flooded rice farmland was calculated using covariates as arguments (Table 4).The selected covariates effectively explained the conditional distribution of flooding, with fertiliser and fuel costs during the post-flood period significantly associated with flood intensity (p < 0.05).The former was negatively associated with flooding intensity, whereas the latter was positively associated (Table 4).
According to the information available on T i , X i , the GPS value of each farmer was calculated using Eq.(A1) in the Appendix.X i is an observed vector of preflooding covariates for each unit i in the sample.Subsequently, an investigation was conducted to determine whether the GPS specification was adequate, i.e. if the covariates were balanced.To conduct balancing property tests, the flood intensity range was divided into three categories: category 1, a 0.125-0.5 fraction of flooded rice farmland; category 2, a 0.506-0.968fraction; and category 3, a fraction equal to 1.  Three blocks were defined based on the mean GPS of each support interval.Balancing tests are typically performed using t-statistics to ascertain whether a conditional mean difference exists for each pre-flooding covariate.The balancing property was fulfilled across all flooding intervals at p < 0.01 according to conventional two-tailed t-tests.Based on the score, there were no differences across the three categories of flood intensity.
To evaluate how effectively the GPS correction was in balancing the variables, a comparison of the covariate balance between the unadjusted and adjusted covariates for GPS was conducted.The results indicated that 12 out of the 39 covariates were unbalanced (p < 0.05) before GPS adjustment, whereas only 3 covariates remained unbalanced after the adjustment (Table 5).These findings demonstrate that the GPS derived at the mean point for all categories was consistent when considering the covariates and conditional density of flooding.
Table 6 presents the summary statistics of the GPS distribution computed at the mean points of each flooding interval.

Dose-response and treatment function estimation
To eliminate any bias in the estimation of the impact using GPS, we first used a quadratic function to approximate the conditional expectation of the result (production yield), concerning two scalar variables: the degree of treatment, T i and the projected GPS, Ri : Second, the dose-response relationship at each treatment level was estimated by averaging the conditional expectation function over the GPS at that specific degree of treatment: μ(t)=E[β(t, r(t, Xi))].
Using the observed data T i ð Þ and estimated GPS (R i ), the ordinary least squares method was used to estimate the model parameters.Block-wise bootstrapping was used to estimate the parameters (100 replicates) in Eq. (A4) in the Appendix.Table 7 presents the estimation results.
The model coefficients, calculated as per Hirano and Imbens (2004), do not allow a causal interpretation other than testing and determining whether the covariates contribute to any bias if the coefficients of variables involving GPS are equal to zero.The uncertainty intervals were calculated using 100 bootstrap replications and accounting for GPS estimation.
Figure 4a illustrates the average dose-response relationship for the production yield and 95% confidence bands for pooled data across the two seasons, whereas Figures 5  and 6 depict the separate impacts.The rice production yield exhibits a decreasing function concerning the fraction of flooded farmland (Figure 4a and Table 8).The average rice production yield was positive for each value of the fraction of flooded farmland, with narrow confidence bands.For example, the expected rice yield for a 10% flooded fraction was 7.20 tons/ha (standard error, SE = 1.11), while that for a 20% flooded fraction was 6.01 tons/ ha (SE = 0.8).This suggests that the average treatment effect of a 10% flooded fraction (20% − 10%) is 6.01-7.20 = −1.19(SE = 0.35).Therefore, increasing the fraction of flooded farmland from 10% to 20% decreases the rice yield by 1.19 tons/ha.Figure 4b illustrates the average impact of changing the percentage of flooded farmland by 10% on the rice production yield, presenting a dose-response function derivative.The observed estimations suggest that the marginal rice yield is negative and increases steeply, becoming null when 80% of the farmland is flooded.Thus, the marginal rice yield loss shifts from −1.19 tons/ha under a 10% flooded fraction to 0 tons/ha under an 80% flooded  fraction, becoming positive at a 100% flooded fraction.However, this 'positive' effect is not statistically significant.After surpassing a 70% flooded fraction, any additional flooding does not cause noticeable damage.
Table 8 reports the potential rice yield (dose_response in tons/ha) for each level of flooding (treatmen-t_level: fraction of flooded farmland).It also presents the treatment effect on rice yield (diff_dose_response in tons/ha) or the impact of each increment of 10% of flooded farmland fraction.Each impact was estimated by calculating the difference of potential rice yield between a treatment_level and treatment_level_plus (treatment_level plus an increment of 10% of the flooded farmland fraction).

Statistical analysis of sensitivity
A sensitivity assessment of this estimation was conducted by considering both linear and higher-order approximations when estimating Eqs.(3) and (4).Specifically, linear and cubic approximations were employed, as depicted by the following equations: Although some differences were observed, the two graphs generally show that the dose-response function presents the same trends and shapes as those shown in Figure 4.However, the treatment impacts of all flood degrees were not statistically different from the no flooding treatment.

Impact on the rice yield for each growing season
All the rice farmers surveyed grew rice during the rainy season, while only 55% of them cultivated rice during the dry season.The rice yield during the rainy growing season was a decreasing function of the flooded fraction of farmland (Figure 5).The potential yield decreased from 3.56 tons/ha, reported by farmers who lost a 10% fraction of their farmland, to 0.01 tons/ha under a 100% flooded fraction.For instance, the expected rice yield under a 10% flooded fraction was 3.56 tons/ha (SE = 1.64), while that under a 20% flooded fraction was 3.05 tons/ha (SE = 1.14).This implies that the average treatment effect of a 10% flooded fraction during the rainy season (20% − 10%) is 3.05-3.56= −0.5 (SE = 0.5).Therefore, increasing the fraction flooded farmland from 10% to 20% decreases the rice yield by 0.5 tons/ ha.The average rice yield during the rainy season was positive for each fraction of flooded farmland, with very wide confidence intervals at lower treatment levels, which became narrow at higher treatment levels.Thus, the effect was statistically insignificant.
Figure 6 shows that the rice yield during the dry season was a slightly decreasing function of the fraction of flooded farmland.The average rice yield during the dry season was positive for each fraction of flooded farmland, with wide confidence bands, particularly at lower treatment levels.This indicates an increasing treatment effect; however, the effect is negative up to a 60% fraction, where it becomes null and subsequently turns positive.For instance, the expected rice yield for a 10% flooded is 6.53 tons/ha (SE = 4.7), while that for a 20% flooded is 5.29 tons/ha (SE = 3.23).This implies that the average treatment effect of 10% of rice land flooded during the dry season (20% − 10%) is 5.29-6.53= −1.23 (SE = 1.49).Therefore, increasing the fraction of flooded farmland from 10% to 20% decreases the rice yield by 1.23 tons/ha.However, this difference was not statistically significant.In summary, flooding during the rainy season is beneficial to rice farmers during the following dry season, particularly under flooded fractions greater than 60%.

Discussion
Approximately 171 of the 213 ha cultivated with rice by farmers in the sample were flooded, accounting for 80.3% of the total rice farmland in the study area in 2012.This flooding intensity aligns closely with those of Federica et al. (2022), who reported that 255 ha of rice yet to be harvested were submerged in Italy, with 211 ha affected by river overflowConsidering that the average rice yield in Benin is 5 tons/ha (Zannou et al., 2018), this resulted in a total rice production loss of 855 tons.In contrast, figures have been more substantial in Asia, where rice production is intensive.Between 2015 and 2019, approximately 3.72 million ha of cropland were damaged by floods due to the Monsoon of Southeast Asia, including Indonesia, the Philippines, and Malaysia.Moreover, a total loss of 20.64 million tons of crop production was reported (Venkatappa et al., 2021).
The potential annual rice yield in farms with up to a 10% flooded fraction is 7.2 tons/ha, whereas it averages 2.61 tons/ha for farmers losing 100% of their rice farmland.This suggests that the 2012 flood had an overall negative impact on annual rice production.Flooding has been reported to adversely affect crop yields in various regions, including Southeast Asia, Nigeria, Ghana, England, Germany, the United States, and Vietnam (Chau et al., 2014;Le Dang et al., 2014;Ojeh & Victor-Orivoh, 2014;Stein & Weisser, 2022).
Decreases in rice yield due to flooding affect the rice supply and, consequently, food security, given that rice ranks as the fourth staple food in terms of consumption in Benin, following yam, cassava, and maize (Lawin et al., 2013).Reduced farm yields and production lead to decreased food availability at both household and national levels (Badolo & Kinda, 2012), triggering a vicious cycle that impacts nutrition standards, rural migration, and the availability of agricultural labour (Armah et al., 2010).Additionally, production quality may also be affected, reducing its economic value.During the rainy season, immediately following the flood event, the potential rice yield for a farmer who lost 10% of their rice farmland is 3.56 tons/ha, whereas it is 6.53 tons/ha during the dry season following the flooding.Under a 100% flooding fraction, the potential rice yield is 0.01 tons/ha during the rainy season, whereas it is 3.58 tons/ha in the dry season.Assuming an average rice yield of 5 tons/ha (Zannou et al., 2018), our results suggest that a 10% flooded fraction reduces the rice yield by 1.5 points during the flooding and improves it by 1.5 points in the post-flood dry season.
Similarly, the complete loss of rice farmland due to flooding leads to a significant reduction in yield during the rainy season and a 1.5-point decrease during the subsequent dry season.This finding is consistent with that of Banerjee (2010) in Bangladesh.However, the results obtained for the rainy and dry seasons have certain limitations.The model for these growing seasons did not incorporate data on the input costs per season, which were unavailable.This discrepancy explains why the annual average production was unusually higher than the average yield during each growing season.Additionally, the inability to control the input costs per growing season may explain the relatively low positive impact of flooding during the subsequent dry season.This positive effect of flooding was not statistically significant, possibly owing to the pronounced negative impacts.Post-flooding advantages include the deposition of nutrients and salt seeping from agricultural fields, which have been documented to have a positive effect on yield in previous studies (Zhang et al., 2003).Flood-irrigated fields are typically more fertile and can support crop varieties that yield abundant fruit and vegetables (Rasid & Paul, 1987).The insights obtained here are particularly valuable for developing tools to mitigate flood hazards (Banerjee, 2010) and analysing post-disaster livelihood recovery (Karki et al., 2022).
Structural flood control measures, such as river embankments designed to stop floodwaters, may inadvertently disrupt natural processes of soil moisture replenishment and fertility (Brammer, 1990).Against the event of a flood, effective disaster management requires a thorough assessment of flood damage to inform budgeting and compensation decisions.Certain variables identified in this study showed significant associations with flood intensity, warranting the attention of policymakers.Specifically, fertiliser and fuel costs during the post-flood period exhibited noteworthy associations.Fertiliser costs were negatively correlated with flood intensity, whereas fuel costs were positively correlated with it.This implies that farmers may require financial assistance to procure fuel for drainage purposes, while fertilisers may not be as necessary owing to the nutrient deposition resulting from flooding.
Proactive measures, such as avoiding farming near floodplains and introducing water-resistant rice varieties that can withstand flooding, should also be implemented (Bairagi et al., 2021;Baishakhy et al., 2023).These rice varieties can withstand surplus water in the environment.Additionally, fast-growing, high-yield rice strains should be introduced in the region.Implementing the ridge-andfurrow farming techniques would also be beneficial; here, crops are planted on elevated ridges, while furrows serve as drainage channels to manage excess water.Moreover, efforts should be made to divert excess water from farmlands to nearby streams and rivers to effectively mitigate the impact of flooding on agricultural land in the area (Hussain et al., 2020;Yadav et al., 2017).
Historically, floodplains have been attractive for agricultural activities because of their fertile soils.It is commonly understood that agricultural areas generally receive lower protection levels than urban areas (Petsch et al., 2023).Consequently, policies focused on floodplain restoration and coexistence with floods imply that agricultural areas may face increased exposure to flooding (Fischer et al., 2021).Policies aimed at reducing flood damage should be coupled with measures aimed at enhancing asset resilience to mitigate vulnerability.In agriculture, these measures primarily involve improving equipment and livestock protection as well as implementing evacuation and post-flooding recovery plans.Additionally, afforesting riverbanks, particularly in the upstream areas of the basin, is advisable as a preventive measure (Ward et al., 2020).
Future research should focus on estimating flood insurance premiums, and developing and implementing flood insurance schemes.Additionally, expanding the scope beyond rice production loss to include other affected areas-such as other crops, pastures, fences, soil, buildings, equipment, stocks, and cleaning costs-would provide a more comprehensive understanding of flood damage.Moreover, evaluating the effectiveness of alternative protection strategies is crucial.Various post-flood funding mechanisms should be explored, such as market-based solutions (e.g. insurance and bonds), locally funded initiatives (e.g.microcredit schemes aimed at reducing vulnerability), and globally or regionally coordinated funding mechanisms.Research in this area should also address how these funding mechanisms can be scaled up, and how issues such as moral hazard and covariance can be mitigated.
This study has several limitations.First, because flooding is a natural event that tends to impact areas close to rivers, the selection of households in the treatment groupthose with flooded rice land-was not random.Second, because the number of rice-producing households varied across the selected villages, the sub-sample used was not self-weighted.Third, relying on the recall memory of farmers for data collection on flooding, yield, farm size, production costs, and socio-demographic characteristics introduces the risk of inaccurate or biased reporting.However, efforts were made to mitigate recall bias by employing random selection techniques for including riceproducing households in the sample.Despite these limitations, this study represents an important step towards understanding and responding to the impacts of flooding.

Conclusion
This study provides insights regarding the challenges associated with conducting high-quality impact evaluations in the disaster sector.The paper investigated the impacts of the 2012 floods in Benin on rice production by estimating both the overall annual and seasonal impacts in the rainy and dry seasons.
The results indicated that rice yield decreases as the fraction of flooded farmland increases.The damage was more significant in the rainy season than in the dry season.The 2012 flood had overall harmful effects, impacting the rice supply and food security, especially when considering the importance of rice as the fourth staple food in Benin.However, this study had several limitations.Unlike the annual model, the models calibrated for the rainy and dry seasons did not account for the costs of inputs per growing season owing to missing information.This discrepancy may explain the abnormally higher annual average production compared to that in either season.Additionally, the inability to control the input costs per growing season may be attributed for the low positive impact of flooding during subsequent dry seasons.Nonetheless, these findings represent a crucial step towards modelling and responding to flooding impacts.

Appendix
Formally, consider a set of N rice farmers, and denote each of them by subscripts i, i = 1,. ..N.For each rice farmer i, there is a vector of pre-treatment variables, X i , a fraction of rice land flooded, T i , and the value of the outcome variable associated with this treatment level, Y i ¼ Y i T i ð Þ.In this application, the outcome variable,Y i ; is the rice yield.In order to formally describe the econometric framework, some additional notations are required.Let Y i t ð Þ denote a random variable that maps a particular potential treatment, t, to a potential outcome Y i .
Of interest is the average dose-response functionμ t The dose-response function measures the relationship between the 2012 flooding event as the cause and the potential outcomes as the effect.Following Hirano and Imbens (2004), the assumption is that Y i t ð Þ f g tεT , T i ; and X i , i ¼ 1; . . .; N are defined on a common probability space for which T i is continuously distributed with respect to a Lebesgue measure on T and Y i ¼ Y i T i ð Þ is a well defined random variable.As in the binary treatment context, propensity score methods in a setting with continuous treatments rely on the key assumption that adjusting for pre-treatment differences solves the problem of drawing a causal inference.Formally, the weak unconfoundedness assumption, which was introduced by Hirano and Imbens (2004) requires that the treatment assignment mechanism is conditionally independent of each potential outcome given the pre-treatment variables:Y i t ð Þ?T i jX i foralltεT .This assumption implies that all variables that affect the outcome (rice yield) and the likelihood of getting flooded are observed and that all the other variables are perfectly collinear with the observed variables.
In this study, the assumption of unconfoundedness holds conditional on all the pre-treatment variables, assuming that these variables are good proxies of factors that might affect the fraction of rice land flooded (Rubin, 2008).
Given unconfoundedness, the methods based on the GPS with continuous treatments introduced by Hirano and Imbens ( 2004) can be applied.The GPS is defined as the conditional density of the actual treatment given the observed covariates.
Formally, letr t; x ð Þ ¼ f TjX tjx ð Þbe the conditional density of the treatment given the covariates.Then, the GPS isR The GPS has a balancing property similar to that of the standard propensity score (e.g., Rosenbaum & Rubin, 1983), that is, within strata with the same value ofr t; X ð Þ, the probability that T=t is not dependent on the value of X.
The estimation is done through three steps:

st step: Modeling the conditional distribution of the treatment given the covariates This step consists of several routines
A key assumption in the Stata implemented version of the GPS methods is that the normality of the treatment variable (or its transformation) is conditional on the pre-treatment covariates (Bia & Mattei, 2008).In this application, the treatment or the logarithmic transformation of the treatment variable (fraction of rice land flooded) does not have a normal distribution, given the covariates.Therefore, the method of Guardabascio and Ventura (2014) is suitable in order to estimate the GPS, because the treatment variable 'fraction of rice land flooded' is a fractional variable.First, instead of using the maximum likelihood estimator to estimate the parameters of the treatment function (Bia & Mattei, 2008), the more flexible generalized linear model is used (Guardabascio & Ventura, 2014).The parameters θ and φ of the selected conditional distribution of the treatment are estimated given the covariates.The distribution of T is specified from the exponential family through the family () and link () functions.
Second, if the family selected is normal, one can assess the validity of the assumed normal distribution model by one of the following user-specified goodness-of-fit tests: the Kolmogorov-Smirnov, the Shapiro-Francia, the Shapiro-Wilk, or the Stata skewness and kurtosis test for normality.The user can skip the test by specifying the flag b(2) option.If the normal distribution model is not statistically supported, the user is noticed that the assumption of normality is not satisfied.The user is invited to customise the family () and link () options or a different transformation of the treatment variable.
Third, the score r(T, X) is estimated with the following equation: whereθ and φ are the estimated parameters in step 1, andX i is an observed vector of pre-flooding covariates for each unit iin the sample.
Fourth, the test for the balancing property of the estimated GPS function is done.This helps to determine whether and to what extent the balancing property is supported by the data.The test is done according to the following scheme: (a) The set of flooding values (i.e.flooding intensity: fraction of rice land flooded) is divided into k intervals according to a userspecified rule, which should be defined on the basis of the sample distribution of the treatment variable.(b) Within each flooding interval k, the median or mean intensity is calculated and the GPS at this representative point is computed.(c) The values of the GPS evaluated at the representative point of each flooding interval are subdivided into j blocks.(d) For each block j of the GPS scores and within each interval k, the mean difference of each covariate is calculated between units that belong to the flooding interval and units that belong to another flooding interval but are in the same GPS interval.
(e) Next, the differences in means calculated in the previous step are combined by using a weighted average with weights given by the number of observations in each GPS interval.(f) For each computed difference, at-test is performed, which indicates whether the mean difference of each covariate between units that belong to the given flooding interval k is statistically different from the mean difference of units that belong to another flooding interval but are from the same GPS block.If the mean differences for a given covariate are statistically significant, this would imply that, for this specific variable, the estimated GPS is not able to completely eliminate a selection bias (although some reduction of bias could be achieved).If adjustment for the GPS properly balances the covariates, one would expect all differences to be statistically insignificant.
2nd step: In order to estimate the conditional expectation of the outcome given the flooding intensity and the GPS using a flexible function (a quadratic function) of T i and R i , one may use a polynomial approximation of order not higher than three.
The information obtained from this equation is used later to derive the average dose-response function and the derivative doseresponse functions.
3 rd step: Estimating the dose-response function μ t ð Þ ¼ E β t; r t; X ð Þ f g ½ �; tεT by averaging the estimated conditional expectations, β t; r t; X ð Þ f g, over the GPS at each level of the treatment the user is interested in:

Figure 1 .
Figure 1.Distribution of flooded farmland per crop.

Figure 2 .Figure 3 .
Figure 2. Study area showing the two sampled municipalities and villages.

Figure 4 .
Figure 4. Average dose-response function and treatment effect function using a quadratic approximation.

Figure 5 .
Figure 5. Impact of floods on rice production yield during the rainy season.

Table 1 .
Sample size distribution among the selected villages in Malanville municipality

Table 2 .
Sample size distribution among the selected villages in Karimama municipality

Table 3 .
Descriptive statistics of the control variables

Table 5 .
Common support and covariate balance results

Table 6 .
Summary data of GPS

Table 8 .
Impact of floods on rice yield during the dry season.Potential yield and average/marginal treatment effect