Managing farm-centric risks in agricultural production at the flood-prone locations of Khyber Pakhtunkhwa, Pakistan

Abstract

The agriculture sector in Pakistan is confronted with massive floods and other climate-induced disasters. Resultantly, the farmers are compelled to adopt several risk-management activities to cope with these risks. Therefore, the study aims to explore the risk management tools and their association with farmers’ risk perception, risk-averse attitude, and other socio-economic factors. We collected data from 200 respondents from two districts in Khyber Pakhtunkhwa. The study employed a multivariate probit model to investigate the association among dependent variables (risk management tools) and explanatory variables. Findings indicated that floods and heavy rains were not the sources of risk for most of the large farmers. The majority of small farmers were risk-averse. The multivariate probit model results exposed that farmers' age, their risk perception about the heavy rains, and the size of landholding were positively associated with the adoption of assets depletion as a risk management tool. Farmers’ age, education, off-farm income, and farmers’ risk-averse attitude were positive, while the farming experience was negatively associated with consumption reduction. Moreover, farming experience, risk perception about the floods and heavy rains, and risk-averse attitude are positively associated with the adoption of diversification. Farmers in the study area were vulnerable, and they were relying on traditional tools of risk management. Hence, the government is suggested extending agricultural credit and crop insurance facilities to these farmers.

Appendix

These include the von Neumann−Morgenstern (N−M) model, Equally Likely Certainty Equivalent (ELCE) method, a modified version of the N-M model, and the Equally Likely but risky outcome method. Based on the above discussion, we have adopted the interview method of the direct approach with the ELCE, using a Purely Hypothetical Risky model. The farmers are categorized into three groups. First is risk-preferring farmers are those who are willing to take risks, or the expected outcome is preferred over the sure outcome. The second is risk-neutral: those indifferent to certain and uncertain outcomes but have the same expected income. The third is risk-averse, where farmers give preference to guaranteed income over income that is uncertain. It is assumed that the selection of expected or sure outcomes is based on utility. Farmers opt for that choice, which gives them more utility. Farmers maximize utility (Eq. 6). In our case, utility is a function of wealth (Eq. 7), but we use it as a function of income (Hardaker et al. 2004; Olarinde et al. 2007).

$$U = u\left( w \right)$$

(6)

The individual wants to maximize utility with respect to income.

$$U\prime \left( w \right) \ge 000$$

(7)

The first differential is positive and indicates that more is preferred over less (also called convex utility function). Likewise, risk aversion is a state of a utility function that shows a decrease in marginal utility as the payoff increases (also called concave utility function). Risk neutral has a linear utility function (Hardaker et al. 2004).

The expected utility theory is defined by Von Neumann and Morgenstern (1944). According to this theory, there are reasons behind individual choices involving risks. The decision-makers compare the expected utility in risky and uncertain prospects. Levy (2006) and Gill (2007) argued that individuals are reluctant to accept choices with uncertain payoffs, but rather, are willing to accept another choice with a low and sure payoff. Farmers will try to maximize utility within the constraints:

$$U = u\left( {y,c} \right)$$

(8)

where y is income, and c is consumption. The TUF will show the nature of individual behavior based on convexity or concavity of the utility function. This will further lead to risk aversion, which is the central behavioral concept in the expected utility theory (Musser and Patrick 2002). Risk aversion attitude measures a decision-makers’ unwillingness to accept outcomes with uncertain payoffs. Instead, they prefer certain outcomes, although with the probability of lower expected payoffs. A decision-maker’s utility function will shape their risk preferences (Hardaker et al. 2004). A decision-maker’s utility function will have a positive slope, which means that a higher payoff is always preferred to a lesser one. The nature of risk attitude is further explained by Arrow (1970) and (Pratt 1964a).

From each respondent, certainty values were obtained, and then for each value, their corresponding utility values were calculated. Furthermore, the CE² values were regressed on utility values, which were in the cubic utility function. After solving the regression model, the absolute risk aversion coefficient was calculated by taking the first and second derivatives obtained.

The advantage of ELCE is that it is based on ethically neutral probabilities of (0.5) (Hardaker et al. 2004). People find 50/50 risky prospects much easier to conceptualize than probabilities with ratios. After deriving CEs, place them into the cubic utility function to obtain the utility of each individual, following the model below:

$${\text{u}}\left( {\text{w}} \right) = { }\alpha_{1} + { }\alpha_{2} {\text{w}} + { }\alpha_{3} {\text{w}}^{2} + { }\alpha_{4} {\text{w}}^{3}$$

(9)

Cubic utility function showed risk attitude, risk preference, risk aversion, and risk indifference attitudes (Binici et al. 2003). The utility was converted into a quantitative measurement of risk aversion called absolute risk aversion (Hardaker et al. 2004; Pratt 1964b). The following formula can derive the absolute risk aversion.

Important note We are mentioning here that several papers had reported Eq. 10 as reciprocal of ${\mathrm{R}}_{\mathrm{a}}\left(\mathrm{W}\right)$, which is wrong. The researchers are recommended in the future to use the correct form of equation (Hardaker et al. 2004; Ogurtsov et al. 2008; Pratt 1964b) as mentioned below or go to the original source.

$${\text{ R}}_{{\text{a}}} \left( {\text{W}} \right) = { } - \frac{{{\text{U}}^{\prime \prime} \left( {\text{W}} \right)}}{{{\text{U}}^{\prime }\left( {\text{W}} \right)}}{ }$$

(10)

${\mathrm{R}}_{\mathrm{a}}\left(\mathrm{W}\right)=\mathrm{coeffecient of risk aversion}$

${\mathrm{U}}^{{^{\prime}}\left(\mathrm{W}\right)}=\mathrm{first order differential of a utility function}$

${\mathrm{U}}^{\prime \prime}\left({\mathrm{W}}\right)={\mathrm{second order differential of a utility function}}$

If:

${\mathrm{R}}_{\mathrm{a}}\left(\mathrm{W}\right)>0\mathrm{ or positive}$

Positive means that the individual is risk-averse.

${\mathrm{R}}_{\mathrm{a}}\left(\mathrm{W}\right)=0$

Then the individual is indifferent or neutral to risk.

${\mathrm{R}}_{\mathrm{a}}\left(\mathrm{W}\right)<0\mathrm{ or negative}$

The individual is risk seekers or risk preferred.

As an example, one of the regression results obtained for the first respondent is given based on the above methodology, and absolute risk aversion is calculated.

Example of elicitation of certainty equivalents and computation of utility values

Step	Elicited CE	Utility calculation
	Scale	u(0) = 0 and u(200,000) = 1
1	(120,000; 1.0) ~ (0, 200,000; 0.5, 0.5)	u(120,000) = 0.5u(0) + 0.5u(200,000) = 0.5
2	(60,000; 1.0) ~ (0, 120,000; 0.5, 0.5)	u(60,000) = 0.5u(0) + 0.5u(120,000) = 0.25
3	(30,000; 1.0) ~ (0, 60,000; 0.5, 0.5)	u(30,000) = 0.5u(0) + 0.5u(60,000) = 0.125
4	(20,000; 1.0) ~ (0, 30,000; 0.5, 0.5)	u(20,000) = 0.5u(0) + 0.5u(30,000) = 0.0625
5	(140,000; 1.0) ~ (200,000, 140,000; 0.5, 0.5)	u(140,000) = 0.5u(200,000) + (0.5u(140,000) = 0.75
6	(170,000; 1.0) ~ (200,000, 170,000; 0.5, 0.5)	u(170,000) = 0.5u(200,000) + (0.5u(170,000) = 0.875
7	(180,000; 1.0) ~ (200,000, 180,000; 0.5, 0.5)	u(180,000) = 0.5u(200,000) + (0.5u(180,000) = 0.937

1. Authors’ calculations

Parameter estimation from simple regression model from cubic utility function

Parameter	Value	t (ratios)	P (value)
α1	36.67821	3.378728	0.043132
α2	−0.00218	−3.08772	0.05381
α3	4.22E-08	2.800944	0.0678
α4	−2.6E-13	−2.49192	0.088334
R2	0.96

1. Source Author’s calculations
2. Based on the above data, the absolute risk is calculated as under
3. R_a $\left(\mathrm{W}\right)= 0.16336$
4. The R_a value is positive here, which means that he is risk-averse