Impact of relaxing flood policy interventions on fish production: lessons from earthen pond-based farmers in Southwest Nigeria

These days, aquatic (fish) welfare is a major issue and a significant component that affects fish output. Although numerous factors can be involved, climate-induced floods are one of the most critical limiting factors in the aquaculture and fisheries industry’s development. Understanding the extent of losses and damages caused by floods at the farm level will thereby exacerbate pre-emptive policy responses. Thus, the impact of floods on fish production by focusing on catfish earthen pond-based farmers in Southwest Nigeria is presented. A survey is conducted for 150 fish farms in the region. A marginal treatment effects (MTE) approach is employed to determine the heterogeneity across the households and the policy-relevant treatment effects (PRTE). The results show significant heterogeneity in the effects of floods on fish production, considering both observed and unobserved characteristics of the farmers. It is shown that flood significantly increases output loss. Furthermore, farmers with high propensity scores to flood tend to have a high likelihood of incurring output loss. The estimates of PRTE reveal that relaxing policy strategies, such as access to climate information and climate-related training and workshops, would significantly exacerbate output loss due to flood incidences. Thus, intensifying awareness and sensitization on climate change policies will address the flood menace and still increase food production.


Introduction
The world is still concerned about feeding nine billion people by 2050, especially in light of the negative effects of climate change (FAO 2016a;Oyebola et al. 2021;Adelesi and Baruwa 2022). Due to entire reliance on climate, limited modern technologies, and institutional deficiencies, it might develop worse in sub-Saharan Africa (SSA) (IPCC 2007;Mueller et al. 2017;Issahaku and Abdulai 2020;Liverpool-Tasie and Parkhi 2021). Despite contributing only around 5% of the world's greenhouse gases (GHG), the SSA is the area most susceptible to extreme weather caused by climate change (Tol 2018;World Bank 2019;Issahaku and Abdulai 2020;Oyebola et al. 2021). Thus, building climate resilience that incorporates a strong and sustainable adaptive capacity and mitigation measures is urgently needed to combat and maintain changes in the climate (Lebel et al. 2016;Liverpool-Tasie and Parkhi 2021).
The significant impacts of climate change on aquatic ecosystems, aquaculture, and fisheries have been documented in the literature (De Silva and Soto 2009;Badjeck et al. 2010;Bell et al. 2013;Lebel et al. 2016;Onyeneke et al. 2020). He et al. (2018) and Onyeneke et al. (2020) reported that aquaculture and fish farming accounted for about 7% of global agricultural GHG emissions, meaning that the sector also causes prominent changes in climate change. However, the rate at which climate change affects aquaculture and fisheries in return is not commensurate. Climate change has both directly and indirectly impacted agriculture, including aquaculture and fisheries (Nhemachena et al. 2010;Fatuase 2017;Asiedu et al. 2017). The direct impacts have been attributed to changes in climatic variables such as rainfall, sunshine hours, temperature, relative humidity, and wind, whereas the indirect impacts are climate extreme events such as drought and flooding (Asiedu et al. 2017;Oyebola et al. 2018;Kim et al. 2019;Onyeneke et al. 2020;Issahaku and Abdulai 2020). The resonance effects have devastated the growth and productivity of fish and fish products. Specifically, several studies have identified some of the negative impacts of climate extreme events, namely, high fish mortality, undesirable pond water quality, retard fish breeding, decreased fish production, increased pathogenic organisms, and low feeding and growth rates (Pimolrat et al. 2013;Lebel et al. 2016;Onyeneke et al. 2020).
Fisheries and aquaculture contribute immensely to food production and economic growth as the sector provides about 12% of global livelihoods (Alam and Guttormsen 2019;Lima et al. 2020) and essential nutrients for 3 billion people (Adhikari et al. 2018). Despite being viewed as a young business, aquaculture supplies roughly 52% of the world's fish meals (FAO 2016b;Alam and Guttormsen 2019), and its production is still projected to reach about 109.4 million tons by 2030 (FAO 2018;Lima et al. 2020). Africa's contribution to world aquaculture production is still very low (2.7%) as of 2019 (Chan et al. 2021) but it has experienced a significant increase between 1995 and 2018 with a compound annual growth rate of about 16% (FAO 2016b; Halwart 2020; Adeleke et al. 2020). According to Garlock et al. (2020), Africa's aquaculture production has tremendous potential to compete in the world's food industry.
Nigeria's fish industry is the second largest in Africa with an estimation of about 2.5 million tonnes of potential (FAO 2018). It is one of the fastest growing sub-sectors, making it an important source of livelihood, income generation, and job creation. Despite its economic relevance, the aquaculture in Nigeria is vulnerable to climate change extremes and variability as are other developing countries. According to the Climate Scorecard (2019) and World Bank (2021), Nigeria is ranked among the ten most vulnerable countries in the world to receive the impact of climate change and natural disasters. Since 2012, the country has experienced severe floods that resulted to about $17 billion in damages in most affected areas (World Bank 2021). The Emergency Events Database (EM-DAT) reported that flood situations in Nigeria between 1900 and 2020 have accounted for 1440 deaths with an estimated $645 million in damages (World Bank 2021). Echendu (2020) and the World Bank (2020) stated that over 40 million Nigerians are estimated to be living in high climate exposure areas, and the risk of flooding due to negative rainfall anomalies is expected to increase further. Chukwu-Okeah et al. (2018) reported that flooding would cause havoc and costly damages to the land use resources. Oyebola et al. (2021) added that fish farming will be greatly impacted than other agricultural sub-sectors because flood-prone marshy and wastelands are mostly used as fish ponds in the producing areas. Dubey et al. (2017) also reported that future climate change extremes would have disastrous consequences on inland fish production. Adejuwon (2005) and Durodola (2019) stated that Nigeria has been experiencing biodiversity depletion, yield decline, and land degradation. Again, flooding has reduced fish pond harvest and farm income (Enete 2014;Adejuwon 2005;Durodola 2019), leading to low productivity and food shortage (Ojo and Ilunga 2017).
According to Oyebola et al. (2021), Africa (Nigeria inclusive) is experiencing an increase in climate-induced floods. Therefore, various sustainable adaptation and mitigation strategies are urgently needed to combat flood consequences on farmers' productivity and food security (Navy et al. 2017;Durodola 2019;Alam and Guttormsen 2019). Oyebola et al. (2021) also affirmed that in the face of climate extremes such as flood, socioeconomic and technical capacity are needed for sustainable fish farming. Due to unprecedented variability to climate change, a vivid understanding of adaption strategies, especially in agrarian nations, is very crucial in climate change debate (Issahaku and Abdulai 2020). Also, sustainable development can never be achieved if only the adaptation and mitigation measures are well understood without the extent of losses and damages caused by climate extreme events (e.g., flood) at a farm level's productivity. Hence, the motivation for this study arises from the observed problem.
Prior studies have established the nexus between climate change and aquaculture (Dubey et al. 2017;Navy et al. 2017;Lebel et al. 2016;Adhikari et al. 2018). Many of these authors investigated the relationship broadly; that is, they combined the effects of all the climate variables and extreme events on aquaculture. Studies that focused on a particular extreme event, flood incidence in the case of this study, are very few in the literature (Chukwu-Okeah et al. 2018;Onyeneke et al. 2020;Oyebola et al. 2021). These authors investigated impacts from the perspective of adaptation strategies adopted by the fish farmers. The current study changes the narrative by not only identifying the fish farmers' floodbased adaptation strategies but also estimating the impacts from the perspective of floodexperienced farmers. That is, the impact of flood incidence on the productivity of the fish farmers. Based on these facts, the study has three research questions: What are the fish farmers' flood-based adaptation strategies? What is the heterogeneity in the impact of flood incidence on the output of the farmers? What is the expected loss if policy interventions on flood are relaxed, which changes the narrative from the previous studies?
Again, different econometric tools have been used by different authors in the literature in measuring impact, but they are not without limitations. For instance, propensity score matching (PSM) was documented to have a shortcoming of a selection bias as it is only accountable for the observable factors (Smith and Todd 2005;Abdulai 2016). Likewise, Heckman's treatment effect model also has a drawback of generating the heteroskedastic residuals which fail in the adjustments of consistent standard errors (Lokshin and Sajaia 2004;Shahzad and Abdulai 2021). Again, many studies (Abdulai 2016; Oparinde 2019; Tanimonure and Naziri 2021) on impact assessment promoted endogenous switching regression (ESR) as being a model that accounts for both selection bias (observable 1 3 and unobservable factors) and endogeneity. However, Cornelissen et al. (2016) reported that ESR has a limitation of aggregating the unobservable heterogeneity when accounting for selection bias. This is because, in the real sense, the heterogeneity varies across the individuals. Based on these limitations, the study adopted the marginal treatment effects (MTE) model following Shahzad and Abdulai (2021), Dubbert et al. (2021), and Li et al. (2021). The MTE model does not only account for observable and unobservable factors but also measures heterogeneity across individual households unlike ESR model. This study contributes to the body of knowledge because no previous research has modelled the effects of flood events on productivity, particularly in earthen pond-based catfish farmers in Nigeria and other parts of Africa using the MTE approach.

Location description
South-western Nigeria is the location of the study. The region is economically important, with an estimated population of over 30 million people and a land area of about 77,818km 2 . The region's latitude is 6°21′ and 8°37′ North, while the longitude is 2°31′ and 6°00′ East. From Fig. 1, the region has three agroecological zones (humid forest, derived savanna, and guinea savanna), and expected to often experience coastal flooding and urban flood (Nigeria Hydrological Services Agency [NIHSA] 2021). The climate is tropical and characterized by two distinct seasons, namely, wet (April-November) and dry (December-March) seasons. The annual rainfall is between 150 and 300 mm, while the temperature is between 21 and 34 °C. The practice of fish farming is prevalent in the area, and many individuals have either worked full-or part-time at it. The magnitude of losses and damages due to floods is enormous, which enlisted the area as being vulnerable (FAO 2012). Oyebola et al. (2018) stated that flood is one of the major threats to fish farming in the area.

Data and sampling procedure
Primary data were gathered through a well-designed questionnaire and scheduled interview. The data were obtained from the 2020/2021 production season in thirty (30) communities across three states in Southwest Nigeria. The selection involves a multistage sampling procedure to select and interview 150 catfish farmers across the following states: Lagos (LA), Ogun (OG), and Oyo (OY). The three states were purposively selected based on the prediction of flood risk and the history of affected Local Government Areas (LGAs) in Southwest Nigeria in 2020 (NIHSA 2021). At least, seven LGAs were affected by floods in each state in 2020 as reported by NIHSA. A simple random sampling method was used to select two floods affected LGAs from each state in 2020 (Ikorodu and Ibeju-Lekki in LA, Abeokuta South and Obafemi-Owode in OG, Ibadan North-East and Egbeda in OY). The NIHSA report does not contain the affected communities, and there is no official record that identifies the communities. Therefore, the study sought the subjective opinions of the government officials at each State Agricultural Development Programme (SADP) as also employed in related studies by Wang et al. (2018) and Onyeneke et al. (2020) carried out in China and Nigeria, respectively. Based on this, five flood-affected communities were purposively selected from each LGA. Again, it was observed that most farmers were neither registered based on the agricultural enterprises nor the flood-affected individuals. It was very difficult to identify farmers let alone the earthen pond-based catfish farmers in each community. Thus, the sampling of catfish farmers was carried out using snowball sampling technique. With the help of the SADP officials, the key informants from the farmer's groups in each community were introduced to the enumerators. With the help of each farmer's group, fifty earthen pond-based catfish farmers were able to be interviewed successfully. Therefore, one hundred and fifty (150) respondents (3 × 2 × 5 × 5 = 150) were used for the analysis of the study. To validate the responses from the farmers, the interview was also conducted in local language, particularly with the uneducated farmers. Also, the reliability of the instrument was done by a test-retest method and subjected to a Cronbach's alpha coefficient with a value of 0.82. The questionnaire was divided into four sections: socioeconomic characteristics, production, climate change, and flood information. For the information on climate change and flood event, awareness and perception of the farmers were first interrogated. For the farmers that perceived climate change, it was asked if they adapted to climate change or not. To be sure of the farmers' responses, the same questions were asked on the flood event. The farmers were asked if they experienced floods in the last production season (2020/2021) or not. The information provided the two groups used as treatment in this study: flood experienced (FEP) and non-flood experienced (NFE) farmers. In addition, the study merged farmers that were not aware of, perceived, and adapted to climate change with the non-flood experienced (NFE) farmers. The outcome variable was the output (quantity of fish harvested) of the farmers. This was captured in kilograms for all the farmers. Again, it is worthy of noted that the adaptation strategies adopted by the farmers were not imposed or suggested. The farmers were allowed to describe and define the adaptations in their own ways. All the adaptation strategies were given to the extension agent in each LGA for proper identifications. At the end, 12 adaptation strategies were mainly employed by the catfish farmers to combat and cope with the flood events in the areas sampled for the study.

Concepts and data estimations
The econometric tool, MTE, is used to model flood incidence by earthen pond-based catfish farmers following Heckman andVytlacil (2005, 2007). The concept dwells on the generalized Roy model which involves both observed and unobserved components of the treatment, as reported by Heckman and Vytlacil (2007). In this study, the binary treatment (D) is the flood incidence and the outcome variable (H) is defined as the output (kg) of the fish farmers. The treatment (D) groups are the non-flood experienced (NFE) and flood experienced (FEP) catfish farmers with the code of zero (0) and one (1), respectively. This means that the ith farmer assumes the value of one when the farmer experienced flood (FEP) and zero when s/he did not experience flood incidence (NFE). The two treatment groups are associated with the potential outcomes H 1 and H 0 . Thus, the outcome equation of the farmer's output for the two treatment groups is expressed as: where Z contains the vectors of socioeconomic, climatic, institutional, and farm-level factors, γ is the parameter to be estimated, D takes 1 when farmer is FEP, and 0 when farmer is NFE, and U D is the error terms. H 1 denotes the output of FEP and H 0 denotes the output of NFE. Again, the unobserved heterogeneity (U D ) will be split into U 1 and U 0 for unobserved heterogeneity under the conditions of FEP and NFE, respectively. However, it is assumed that the two treatment groups cannot be observed simultaneously in the same household. Therefore, the observable response, that is, FEP can be expressed as: The expected heterogenous returns (losses) are conditional on observed and unobserved factors. Thus, the return is the change in the outcome (H) of the two groups as H 1i -H 0i = According to Mogstad and Torgovitsky (2018), it is unlikely to assume that the D is exogenously determined by the outcomes (H 1 and H 0 ). When D is endogenous, comparing the distribution of H for the treated (D = 1) and control (D = 0) groups confounds the effect of the treatment with other differences between these two groups. Conditioning on observed covariates, Z, can conceivably unconfound the effect of D on H. It is expected that there are important factors that could influence the option of D. For instance, the individual's beliefs and knowledge about H 0 and H 1 that are fundamentally difficult to observe and therefore not part of Z. Thus, instrumental variable (V) was introduced to indirectly shift D while holding Z fixed. If V is exogenous, then the resulting variation in H is solely due to the causal effect of D on H, that is, from the difference between H 1 and H 0 . Due to essential heterogeneity that often arises in solving endogenous problem, Heckman (2010) suggested that the MTE should be considered. MTE is an important unifying concept for instrumental variable methods that maintain the weakly separable choice model (Mogstad and Torgovitsky 2018) as in Eq. (3). This makes Heckman and Vytlacil (2005) and Carneiro et al. (2011) to suggest a standard latent variable discrete selection model to represent whether a farmer is categorized as treatment or not. Let D denotes the choice of flooding and this is dependent on the selection of equation D* as: The propensity to be affected by flood event depends on the net return from the treatment D* and this can be depicted as: where G is the vector of both exogenous variable, Z, and instrumental variable, V; U D is the random error term induced by the observable factors of the farmers. Therefore, D = 1 when G < U D , meaning that the farmer is FEP; and D = 0 when G ≥ U D , indicating that the farmer is NFE.
Following Eq.
(2), the MTE is the treatment effect associated with farmers who are indifferent between treated (D = 1) and control (D = 0), which is conditional on the covariates, Z and unobserved response, U D .
The treatment effect for an individual farmer with observed factors, Z = z who are at u D th quantile distribution of the unobserved, G D with a propensity score P(Z, V) = u D . This is the probability that a farmer with observed factors Z and excluded instrument V will be affected by the flood event negatively. The assumption that MTE is additively separated into observed and unobserved parts can be derived from Eq. (5) above as: where z 1 − 0 is the observed component and E U 1 − U 0 |U D = u D is the unobserved component. Therefore, given Eq. (2) and the propensity score, the outcome equation can be estimated as a function of the observed factors (Eq. (6)) and the propensity score as: where H measures the output of the farmers with different levels of observed factors, Z = z, the propensity score, P and K(P) is a nonlinear function of the propensity score. Following Heckman and Vytlacil (2005), Shahzad and Abdulai (2021), and Li et al. (2021), the derivative of Eq. (7) with respect to P will give the MTE. Using a probit model in Eq. (3), the first stage involved the estimation of treatment effects on the selection equation to obtain P(Z, V) as P , while the second stage estimated outcome equation as: The derivative of Eq. (9) is taken to obtain the MTE curve with respect to P . Following the studies of Heckman and Vytlacil (2005) and Shahzad and Abdulai (2021), the MTE is aggregated over U D in various ways to derive the average treatment effects , average treatment effects on the treated (ATT), average treatment effects on the untreated (ATU), and local average treatment effects (LATE). The equations of the treatment effect aggregates are presented in Table 1. Furthermore, the study models the policy-relevant treatment effects (PRTE) to measure the impact of relaxing policy intervention on the output of fish farmers based on the flood experience. The PRTE is estimated using an MTE estimation to stimulate baseline and alternative policies on climate change adaptation on flood incidence. PRTE is defined by Heckman and Vytlacil (2005), Carneiro et al. (2011), andLi et al. (2021) as the mean effect of per farmer shift from a baseline policy to alternative policy, that is, the ATT weight difference between baseline and alternative policies. The PRTE measures the average returns of responding to flood event if certain policies are made. Following Cornelissen et al. (2016) and Shahzad and Abdulai (2021), the PRTE equation is stated as: Tables 6 and 7 in the appendix depict the definitions, scale measurements, and summary statistics of the dependent variables and selected explanatory variables used for the study. It is worthy of noted that the significant mean difference in some of the variables between NFE and FEP farmers is not enough to make a conclusion. The reason is that the summary statistics do not capture the confounding factors that influence the choice of the farmers' flood experience. Thus, a robust econometric method is required to conclude and justify the effect of flood incidence on the output of the fish farmers.

Frequency of utilizing adaptation measures to combat flood event
It has been established in the literature that a rational farmer adopts multiple adaptation strategies, and there are synergies among the strategies (Mulwa et al. 2017;Chukwu-Okeah et al. 2018;Onyeneke et al. 2020;Oyebola et al. 2021). Based on the premise of the information, the study presents how frequent the farmers utilize each strategy to combat flood events in the area. For ranking, the relative adoption intensity index (RAII) was adapted to suit the intention of this study as it was done in some studies (e.g., Akadiri 2011;Oseni et al. 2018;Rooshdi et al. 2018). According to the Table 2, the highly subscribed strategies include siting ponds far from flood-prone areas, and livelihood diversification. The awareness of the effect of climate change extremes, especially floods, have made farmers to site pond far away from flood-prone areas. Onyeneke et al. (2020) reported that siting ponds far away from the flood-prone area is an effective measure used by fish farmers to manage flood-related risks in the Niger Delta area of Nigeria. It was also observed that most fish farmers diversified into off-farm activities (e.g., fish processing, fish marketing, input supplying, crop and livestock) and non-farm activities. Oyebola et al. (2021) reported similar findings in Uganda, where many of the fisher farmers diversified into not or less flood prone enterprises to improve their adaptability. Furthermore, six of the strategies attested by the farmers included high-moderately (H-M) adopted. Early warning information about climate change has been reported to give very vital information on the recurrence and persistence of climate risks in Nigeria which has improved resilience (Adefolalu 2007;Durodola 2019;Oyebola et al. 2021). As also observed by Onyeneke et al. (2020), early warning information has helped fish farmers to consistently monitor pond water and adjust their management practices toward climate risks. Planting economic trees around the pond site and increasing pond dykes' height are also adopted by the farmers. Some of these economic trees, especially fruit crops, have generated extra income for the farmers. At the same time, the height of pond dykes is increased to prevent the escape of stocked fish and the entry of predators during flooding. Dubey et al. (2017) reported that fish farmers in India frequently adopted the strategies and also planted fruit trees on pond dykes because of the sensitivity of pond dykes during extreme weather events. The interdependence of adaptation strategies is very useful in helping farmers to know when to stock based on the early warning information about climate change. It was observed that the stocking or breeding times had varied over the years based on the weather forecast for the production year. This has also helped to build a 3-tier step-cutting inward slopes and proper drainage systems as management strategies for mitigating flood risks. Change in the quantity of stocking or breeding density is moderately (M) adopted by the fish farmers. Again, the use of pumping saline water and artificial covering of the pond from direct rainfall and  (1-4); H is the highest weight (4); S is the number of observations. RAII value ranges from 0 to 1. The higher the value of RAII, the more utilized the adaptation strategy by the farmers. Following Akadiri (2011)  erosion are adopted moderately-low (M-L). The cost implications and the stress involved in the adoption of these two strategies, especially when the pond site is far from home, might contribute to their adoption level. Lastly, insurance as a climate adaptation strategy is rarely adopted in the area. Insurance in agriculture and climate change has not been harnessed in Nigeria and other developing countries. Many studies from developing countries recorded low patronage of insurance in combating climate risks and also advocated for weather-based insurance (Isife and Ekeremor 2015;Asiedu et al. 2017;Onyeneke et al. 2020;Olorunfemi et al. 2020). It either signifies that many are yet to appreciate the function of insurance, or the insurance institutions denied farmers this provision due to the subsistence nature of farming in the area.

Determining the heterogeneity in the impact of flood on the output of the farmers
This section is the main focus of this study. Here, the selection equation estimates were first discussed, which depicts the determinants of flood incidence. The second component of the analysis involved the impact of the floods on the output of the fish farmers based on observable and unobservable characteristics. The MTE curves with the ATT, ATE, ATUT, and LATE were also presented for discussion. Finally, PRTE was conducted to quantify the negative impact of the floods when policy strategies are relaxed. The study further ensures that the basic assumptions of ordinary least squares (OLS) are not violated. The values of variance inflation factor (VIF) for the individual variable range from 1.11 to 4.00, with an average of 1.82, suggesting that the model is free from multicollinearity problems (Table 3). Likewise, the null hypothesis of homoscedasticity failed to be rejected in favor of the alternative using Breusch-Pagan/Cook-Weisberg test for heteroscedasticity (check the Appendix, Tables 8, 9, 10, 11, and 12 for details).

Selection equation results-determinants of flood event
The estimates of the first-stage (probit selection equation) are shown in Table 3 in column (B). According to the methodology, the study's instrumental variables are access to climate information and participation in climate-related training. The result of a Wald statistic test (15.61) shows that the instrumental variables jointly influence the treatment (flood event) at a 1% probability level. Likewise, the insignificant influence of instrumental variables on the outcome variable (output) using the F-statistic test confirms the validity of the instrumental variables (check the Appendix for details). Again, Fig. 2 depicts the common support of the propensity score for treated and untreated observations. The common support values are between nearly 0.1 and 0.9, showing a sufficient overlap between the NFP and FEP farmers. Thus, the result satisfies the assumption of MTE identification that the MTE curve requires to overlap between the two groups (Dubbert et al. 2021). The probit estimates of the selection into flood events are presented in column (B) in the table. The results show that the variable representing pond size is significant but negative in determining being flood-experienced. It suggests that the larger the pond size, the lesser the probability of being flood-experienced in the area. This is because pond size determines the stock size, and stock size determines the scale of the enterprise. Thus, Onyeneke et al. (2020) observed that large-scale fish farmers were more inclined to implement a variety of adaptation measures that could help mitigate flood risk. The coefficient of the pond location variable is positive and significant in determining flood experience. This indicates that siting Table 3 Estimates of selection equation and outcome equations Flood experienced (FEP) and non-flood experienced (NFE) farmers 10% significant level = *; 5% significant level = **; 1% significant level = *** Observations 150 a fish pond in a flood-prone area will likely increase the likelihood of being flood-experienced. Floods commonly occur in flood-prone areas in Nigeria (Niger Delta), threatening fish farming (Onyeneke et al. 2020). The variable representing the adaptation strategies adopted by the farmers is negative but significant, suggesting that an increase in the number of adaptation strategies adopted will reduce the probability of being flood-experienced. The finding supports the results reported by Durodola (2019) and Onyeneke et al. (2020) that mitigating the negative effects of climate extremes, particularly floods, on agricultural productivity will require several adaptation and mitigation strategies. Thus, adaptations are critical in addressing climate change by smallholders (Asiedu et al. 2017). The coefficient of the perceived rainfall variable is significant and positive in determining the flood experience, suggesting that farmers that perceived an increase in the amount of rainfall over the years might likely be flood-experienced compared with those that perceived a decrease in the amount of rainfall. Here, many farmers believe that a decrease in rainfall always comes with heavy rains that lead to flooding. Irrespective of the weight attached by the respondents, several studies (Asiedu et al. 2017;Chukwu-Okeah et al. 2018;Onyeneke et al. 2020;Oyebola et al. 2021) have reported that rainfall patterns will affect water quality, quantity, and mortality in the smallholder farms. The variable representing belief is negative but statistically significant in influencing flood experience. This suggests that those fish farmers that believe that climate change exists might likely not experience floods compared with those that do not believe. The belief of farmers will determine their actions and inactions. Thus, the decisions to take up adaptations against flood events will be easier when the farmers believe that flood is also climate-induced. The coefficient of the age of the farmers is positive and significant in determining being flood-experienced. This indicates that as the fish farmer gets older, the chance of being flood-experienced is also increased. It has been reported that productivity gets low at old age, and most adaptation strategies require costs and energy (stresses) which might not be favorable for aged farmers. This is in contrast to Alam and Guttormsen (2019) finding, who reported that older farmers adopted more farm management practices to reduce risks. The credit access variable shows a significant coefficient but negative in addressing the flood incidence, suggesting that those having access to credit are more likely less flood-experienced than those that do not have access. Credit availability is correlated with financial management practices (Alam and Guttormsen 2019). Thus, the financial well-being of the farmers will determine their adaptive capability to flood events (Arimi 2014;Onyeneke et al. 2020). From the Table, the significant effects of access to climate information and participation in workshops and training variables on the flood events are expected being the instrumental variables. The coefficient of access to climate information is negative and significant at a 5% level, suggesting that having access to climate information reduces the probability of being flood experienced by about 44%, ceteris paribus. Also, the coefficient of participating in workshops and training is negative and highly significant at a 1% level. All things being equal, this suggests that fish farmers participating in climate-related workshops and training are less likely to experience floods by approximately 157%. The results have been consistent with previous climate-related studies such as Asiedu et al. (2017)

Outcome equation results-impact of flood on farmers' output
The results of the impact of flood event on output in the non-flood experienced (NFE = untreated 0 ) and flood experienced (FEP = treated 1 − 0 ) farmers are presented in columns (C) and (D) of Table 3, respectively. Following Andresen (2018) and Dubbert et al. (2021), the average differences in output (outcome variable) are directly interpreted from 0 , while 1 − 0 is interpreted as the treatment effects (FEP), which can be termed as a loss from flood events. Several studies in the literature (e.g., Mendelsohn et al. 2006;Nhemachena et al. 2010;FAO 2012;Onyeneke et al. 2020;Chonabayashi et al. 2020;Oyebola et al. 2021) reported that flood experience always led to loss of assets and properties. The results reveal that pond size tends to have significant differential effects on the NFE and FEP farmers. In the NFE group, a unit increase in the size of the pond will likely increase the fish output by 0.6%, while the treatment effects show that an increase in the pond size of the FEP farmers reduces output loss by about 0.6%. A similar result is reported by Onyeneke et al. (2020) that pond size increased the net returns from fish production. The negative and significant coefficient of pond location implies that farmers who site their pond in a flood-prone area reduce the output by 66.2% in the NFE group. However, the treated group is not significant but positive, implying that farmers who locate their pond in a flood-prone area may suffer more losses from flood events. The number of adaptations adopted variable shows a positive and significant coefficient in the untreated group, implying that an increase in the number of adaptation strategies adopted by the fish farmers tends to increase fish output by 6.8%, ceteris paribus. Although, the adaptation adopted variable is not significant but negative in addressing treated group, suggesting that FEP farmers might reduce output loss by adopting multiple adaptation measures. The coefficient of belief variable has significant differential effects on NFE and FEP farmers. In the NFE group, the output for farmers that believed that climate change exists is 2.2% higher than those that did not. However, when FEP farmers believe climate change exists and experience floods, their output loss will be reduced by 70%. The probable reason might be that believing that climate change exists will motivate the preparedness of the farmers against climate extremes such as flood events by adopting multiple adaptation measures. The variable representing education is positive and significant in the untreated group, indicating that higher education tends to increase output by 9.3%. Although not significant, education in the treated group reduces output loss by 4%. The importance of education in reducing risks has been reported by Oparinde (2019) and Olutumise (2022). The coefficient of the age variable is negative and significant in the treated group, suggesting that the output loss of older FEP farmers will likely increase by 8.8%, ceteris paribus. The finding agrees with the result of Olutumise et al. (2022), who also reported a negative relationship between age and the farmers' output. However, the finding disagrees with the study of Alam and Guttormsen (2019), who stated that older farmers were more risk averse than younger ones. With the family size variable, the results imply that in the untreated group, the output of the fish farmers increases with family size by approximately 18%. In contrast, the treated group shows that larger family size of FEP farmers decreases output loss by about 47%. A large family size helps farmers to meet labor requirements (Heise et al. 2015); thus, labor availability in adopting adaptation measures against flood events might prevent output loss. Access to credit is positive and significant in determining the untreated group, suggesting that output increases by approximately 70% among credit-accessed farmers compared with their counterparts. However, when credit-accessed farmers experienced floods, output loss was reduced by about 8%, though not statistically significant. This reiterates that credit availability is critical in fighting against climate extremes, particularly flood events (Alam and Guttormsen 2019).

MTE estimates
The advantage of MTE over other impact econometric tools is that it captures how a flood incidence tends to impact fish output and how this effect varies with the unobservable characteristics of the farmers. Thus, the MTE curve at 95% confidence intervals is presented in Fig. 3. The curve illustrates the distribution of marginal returns to treatment over varying levels of unobserved resistance to treatment (i.e., resistance to flooding (U D )) among fish farmers, according to Dubbert et al. 2021). According to Shahzad and Abdulai (2021), the higher the value of U D in the MTE curve, the lower the probability of being flood experienced, that is, resistance to flood incidence. The line graph shows an upward trend from the negative treatment effect of about 18 and finally attains a positive effect at nearly 20 by the right-hand side of the distribution. This affirms that the effect of flood event on fish output varies with levels of unobservable characteristics. The fish farmers who are most likely to experience floods might also experience more output loss. Thus, the loss from flood event decreases with resistance to flooding since the curve shows a sloping trend upward. 1 3 The impact of flood incidence on fish output based on the baseline specification is presented in Table 4. The selection pattern of the test of essential (unobservable) heterogeneity in return to flooding is statistically significant at a 10% level (see Table 3). It measures the treatment effects of flood incidence on the outcome variable (output). Thus, fish farmers with a low resistance to treatment (i.e., high propensity to flood event) seem to experience more output loss. This is expected because many studies (e.g., Mendelsohn et al. 2006;Nhemachena et al. 2010;FAO 2012;Onyeneke et al. 2020;Chonabayashi et al. 2020;Oyebola et al. 2021) reported that floods caused losses in farm income and assets which is also projected to increase due to climate change (NIHSA 2021). The standard estimates ATE, ATT, ATUT, and LATE are derived from the weighted averages of the MTE. The different treatment effect estimates follow the same pattern, confirming the positive selection on output loss, as shown in Fig. 3. The value of ATE revolves around 1.12, and the upward sloping pattern implies a positive selection on the unobservable loss. The effect can be interpreted as, given the unobservable characteristics, fish farmers who are most likely to experience floods tend to incur more output loss on their farm. According to the table, experiencing floods increases the likelihood of incurring output loss by about 16% for average farmers (ATE). The ATT parameter puts more weight on the fish farmers with high propensity scores for experiencing floods. This means that for an average FEP farmer, flood incidence significantly increases output loss by approximately 4%. The ATUT focuses on the untreated (NFE farmers), and its value is higher than that of ATE and ATT, as shown in the table. This confirms the positive selection of unobserved losses from experiencing floods. For an average non-flood experience (NFE) farmer, this implies that floods would significantly increase output loss by about 23%. LATE indicates the fish farmers who experienced floods because of less or no access to climate information and participation in climate-related workshops and training. The result implies that those groups of farmers would significantly increase output loss by about 13%, ceteris paribus.

Effects of relaxing policy intervention on flood incidence
The study examines and predicts the gravity of havoc that could arise if policy interventions are relaxed in tackling flood events. This is necessary to proactively put more pressure on the concerned authority to address climate change, especially flood climate-related risks. It is observed from Table 3 that the two instrumental variables play a significant and negative role in affecting flood incidence; that is, they reduce the probability of experiencing floods. As a result of the increased returns to flooding, policies that cause low-resistance fish farmers to flood may result in significant losses. This study considered the two Table 4 Impact of flood event on output of the farmers ATE, average treatment effect; ATT , average treatment effect on the treated; ATUT , average treatment effect on the untreated; LATE, local average treatment effects on the treated; 10% significant level = *; 5% significant level = **; 1% significant level = *** instrumental variables as policy interventions. Since they have negatively influenced flood incidence, it is assumed that relaxing the two policies will cause more havoc on fish farmers. On this note, the expected losses of relaxing the two policy interventions are quantified by increasing the baseline by 5%. It provides insights into what the gravity of the danger or havoc to the fish production would be if the two variables are relaxed by lessening the actions on access to climate information and participation in climate-related training and workshops. As a result, the study adopts PRTE as weighted average estimations of the MTE curve (Carneiro et al. 2011;Cornelissen et al. 2018;Shahzad and Abdulai 2021). It computes the weights of the number of fish farmers that shift from non-flood experience baseline due to policy changes. Therefore, Table 5 presents the PRTE that reflects the effect of relaxing policy variables on the outcome variable under the alternative policy.
The study simulates a policy that increases the average flood-experienced (FEP) farmers by 5% (from 0.37 to a level of 0.41) while access to climate information and participation in climate-related training and workshops are relaxed. This means that there is a shift in the number of FEP farmers from 37% to a level of 41% due to lowering or not intensifying the policy variables. According to the findings, relaxing action on access to climate information will shift the average FEP farmer from 37 to 41% which would aggravate output loss by around 12%. Similarly, relaxing action on climate-related training and workshops to raise the average FEP farmer from 37 to 41% will increase output loss by about 18%. It is worth emphasizing that reduced policy measures on access to climate information and climate-related training and workshops would result in an increase in flood occurrences relative to production loss due to an increase in the number of casualties.

Conclusion and policy implications
Weather extremes, especially flood events, cause huge economic losses due to widespread damage and dysfunction of agricultural production systems. Despite the potential of aquaculture production to compete in the world's food industry, the negative impacts of flooding could devastate the sector in terms of high mortality rate, yield decline, food shortage, land degradation, and biodiversity depletion. Thus, estimating the trade-off effects of not taking proactive policy interventions with the expected havoc and costly damages will propel decisive adaptation and mitigation strategies to abate the extreme climate events. Against this background, the study utilizes survey data of earthen pond-based catfish farmers from Southwestern Nigeria to investigate the impact of relaxing flood policy interventions on fish production. Even though the strategies are interdependent, the RAII reveals that siting ponds far from flood-prone areas, livelihood diversification, and seeking early warning climate information are highly subscribed as the adaptation strategies to combat flooding by the fish farmers. However, the adaptive capacity of the farmers to know their level of resilience to flood impacts could not be ascertained from the above information. Thus, the study employs the MTE model to examine the heterogeneity in the impact of flood incidence on farmers' output. The MTE accounts for selection bias and heterogeneity of the farmers' observable and unobservable characteristics. The results of the probit selection equation reveal that pond size, location, number of adaptations adopted, perceived rainfall, belief in climate change, age, and credit access are significant determinants of experiencing floods. The instrumental variables (access to climate information and participation in climaterelated training and workshop) are negative and strongly related to experiencing flood incidence, which confirms their inverse relationship with loss from flood incidence. The finding further reveals the heterogeneity in the returns (losses) from flood events. A pattern of positive selection is noticed on unobserved losses from flood events in the outcome variable. It is observed that fish farmers who are more likely to experience floods show a tendency to experience losses (ATE). The ATT reveals that average FEP farmers significantly increase output loss due to floods, while an average NFE farmer would significantly increase output loss due to flood incidence (ATUT). Output loss is also recorded from the farmers who experience floods due to less or no access to climate information and participation in climate-related training and workshops. Thus, the findings have confirmed that flood incidence significantly increases fish output loss. The expected losses if policy interventions on flood events are relaxed are also estimated using the PRTE approach. The instrumental variables are adopted as the policy strategies since they are strongly significant in reducing the effect of flood incidence.
To support this claim, several studies have recommended the adoption of adaptation strategies, access to climate information, and participation in climate-related training and workshops as sure policy interventions to curb flood events (Chukwu-Okeah et al. 2018;Adhikari et al. 2018;Durodola 2019;Onyeneke et al. 2020;Oyebola et al. 2021). Thus, relaxing efforts to intensify the dissemination of climate information and climaterelated training on flood risks will aggravate flood incidence and cause at least 12% output loss on each experience. Again, variables such as pond size, belief in climate change, family size, credit access, and age are very germane in addressing the negative impacts of floods in the area. The economic losses of relaxing flood policy interventions will be unbearable for smallholder farmers and can cause more havoc in food production. Thus, government and policymakers should intensify the policy strategies on climate information and climaterelated training on flood events to abate the consequences and still provide expected yield amidst climate change. Government should make early warning climate information more accessible through affordable and functioning channels such as local radio, television, and social media. Government and private agencies should develop location-specific weather forecasts in preparedness for flood extremes. Investing more in farmers' capacity through extension agents and other educational systems is also important. This could be achieved by engaging farmers through constant training and workshops on climate-related risks, especially floods. Also, this study provides useful opportunities for understanding flood hazards. Based on this fact, developing flood adaptation policies and implementation will be essential, especially in developing countries, and prioritizing aquaculture in flood-prone scenarios. The adoption of insurance as one of the adaption strategies is observed to be very low. The government should revisit the agricultural insurance scheme not only to prioritize flooding but to create more awareness and sensitize farmers on the benefits involved. 10% significant level = *; 5% significant level = **; 1% significant level = *** Table 8 Table 7    Table 10  Table 11  Table 12 Author contribution The author was responsible for the survey (fieldwork) with the help of hired enumerators, wrote the manuscript text, and paid for the analysis.
Funding Open access funding provided by Walter Sisulu University.
Data Availability All data and materials not included in the manuscript are available on request.

Competing interests
The authors declare no competing interests.

Conflict of interest
The author declares no competing interests.
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