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Crop Insurance, Premium Subsidy and Agricultural Output
Journal of Integrative Agriculture 2014, 13(11): 2537-2545
November 2014
RESEARCH ARTICLE
Crop Insurance, Premium Subsidy and Agricultural Output 1
2
XU Jing-feng * and LIAO Pu * 1 2
China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, P.R.China School of Economics, Nankai University, Tianjin 300071, P.R.China
Abstract This paper studied the effects of crop insurance on agricultural output with an economic growth model. Based on RamseyCass-Koopmans (RCK) model, a basic model of agriculture economic growth was developed. Extending the basic model to incorporate uncertainty and insurance mechanism, a risk model and a risk-insurance model were built to study the influences of risk and crop insurance on agricultural output. Compared with the steady states of the three models, the following results are achieved: (i) agricultural output decreases if we introduce uncertainty into the risk-free model; (ii) crop insurance promotes agriculture economic growth if insurance mechanism is introduced into the risk model; (iii) premium subsidy constantly improves agricultural output. Our contribution is that we studied the effects of crop insurance and premium subsidy from the perspective of economic growth in a dynamic framework, and proved the output promotion of crop insurance theoretically. Key words: economic growth, agriculture risk, crop insurance, premium subsidy
INTRODUCTION As agriculture plays an important role in the national economy, many countries and regions (e.g., United States, European Union, Canada, Japan and etc.) adopt various forms of subsidies to increase agricultural output (Barnett and Mahul 2007). Policy-based crop insurance is an important way of subsidy, which aims to help farmers manage agriculture risk and promote agricultural input and output. However, Goodwin (2001) claimed that the crop insurance policy is a way of income transfer rather than a risk management instrument. Whether crop insurance promotes agricultural output by means of managing risk is the research topic we are interested in. The significance of crop insurance has been recog-
nized and a lot of scholars have studied the effects of crop insurance empirically. Some literatures found that crop insurance increases the use of risk-increasing inputs, e.g., fertilizer, pesticide and so on (Horowitz and Lichtenberg 1993; Wu 1999; Chakir and Hardelin 2010). Some literatures showed that crop insurance more or less increases the plantings (Young et al. 2001; Goodwin et al. 2004; O’Donoghue et al. 2007). In addition, some literatures pointed out that crop insurance changes the planting structure (Wu 1999; Young et al. 2001). On the other hand, some scholars have studied the effects of crop insurance and premium subsidy theoretically. Ahsan et al. (1982) built an economic model with a single input and a single uncertain output to study the output effect and effectiveness of crop insurance. They believe that crop insurance promotes agricultural output, comparing to the economy without crop insurance.
Received 30 September, 2013 Accepted 5 December, 2013 Correspondence XU Jing-feng, E-mail: [email protected]; LIAO Pu, E-mail: [email protected] * These authors contributed equally to this study.
© 2014, CAAS. All rights reserved. Published by Elsevier Ltd. doi: 10.1016/S2095-3119(13)60674-7
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Extending the model of Ahsan et al. (1982), Nelson and Loehman (1987) constructed a more general production model with multiple inputs and uncertain outputs, and showed that the output effects of crop insurance depend on the substitution and risk properties of the production functions. Ramaswami (1993) decomposed the effect of insurance into a “risk reduction” effect as well as a “moral hazard” effect. He claimed that the directions and magnitudes of these effects depend on the parameters of the insurance contract, producer’s risk preferences, and the underlying technology. Similarly, Chambers and Quiggin (2001) developed a framework to analyze input adjustment for stochastic technologies and applied to the case of actuarially fair production insurance. They showed that the decomposition consists of a pure-risk effect and an expansion effect. Hau (2006) examined the output decision of a risk-averse producer facing profit risk in the presence of insurance or hedging, and derived the conditions under which the introduction of generic insurance increases output. Ye et al. (2012) studied the agriculture production behavior under premium subsidy by applying the Classic Insurance Model, and showed that the output effect depends on the revenue structure, which is determined by the price of the agricultural product, its foreign substitutes and the feasibility of inter-temporal storage. The above literatures studied the output effects of crop insurance and premium subsidy from different perspectives, but there is a common weakness in these literatures that almost all of studies were carried out in a static context (Ahsan et al. 1982; Nelson and Loehman 1987; Ramaswami 1993 and so on)1. Different with these researches, this paper studied the issue in a dynamic economic growth model and spelled out the importance of crop insurance and premium subsidy explicitly. The paper employed the classical Ramsey-Cass-Koopmans (RCK) model (Ramsey 1928; Cass 1965; Koopmans 1965) to generalize the growth process of agriculture economy. Extending the basic model to incorporate agriculture risk and crop insurance, we further built the risk model and the risk-insurance model. By comparing the steady states of the three models, we analyzed the output effects of agriculture risk and crop insurance. In 1
addition, based on the steady state of the risk-insurance model, we built the demand function of crop insurance and the relationship between agricultural output and crop insurance demand to analyze the output effect of premium subsidy. Our contribution is that we study the output effects of risk, crop insurance and premium subsidy from the perspective of economic growth, and prove the output promotion of crop insurance theoretically.
THE MODEL We started with an agriculture economy with a lot of identical farmers. In the agriculture economy, there is a representative farmer who lives forever and is endowed with unit labor, unit acreage and an initial capital k0. He chooses a sequence of consumptions and savings to maximize his lifetime utility which is given by: ∞
U=∑ βtu(ct)
(1)
t =1
Where, ct is the consumption in period t and β is the discount factor of utility. u(.) is the utility function satisfying u´(c)>0, u´´(c)<0 and Inada assumptions: u´(c)=∞, u´(c)=0. His savings augment the capital stock utilized in the production of agricultural production, where the production function is given by: y=f(k) (2) Where y is the agricultural output and k is the agricultural capital input. We assumed the production function satisfies f(0)=0, f ´(k)>0, f ´´(k)<0 and Inada assumptions: f ´(k)=∞, f ´´(k)=0. In this framework, the agricultural capital input k includes both the durable input (like farm machinery) and non-durable input (like seeds and chemicals), and the capital accumulation is the driving force of agriculture economic growth. Then the optimal allocation is determined by the maximization problem, max kt
∞
∑ β u (c ) t =1
t
t
(3)
with budget constraints (4) (1-d)kt-1+f(kt-1)=ct+kt; for t=1, 2, 3, … rf Proposition 1: The capital level, k (where the superscript “rf ” stands for the basic model), in the steady state of the basic model is determined by the following equation,
Scholars agreed on that crop insurance should be subsidized or sponsored by government. One reason is the important effects of crop insurance. Another important reason is that the private crop insurance market always fails because of moral hazard, adverse selection and correlated agriculture risk (Goodwin and Smith 1995). A lot of papers focus on the output effect of premium subsidy, for example, Goodwin et al. (2004), O’Donoghue et al. (2007), Ye et al. (2012), and Walters et al. (2012).
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Crop Insurance, Premium Subsidy and Agricultural Output
f ′(krf)=
1-(1-d) β
2539
(5)
β In the steady state, the consumption crf=f(krf)-dkrf. Additionally with the production function and utility function assumed, the dynamic process of the capital converges to the steady state. Proof: The basic model can be found in Stokey et al. (1989).
Agriculture economic growth: the risk model The basic model describes the characteristics of agriculture economic growth in the certain environment. However, there are a lot of risks in the real world and nature risk is one of the most important factors reducing agricultural output. Therefore, we extended the basic model to incorporate risk and built the risk model to describe agriculture economic growth in an uncertain environment. Referring to Ahsan et al. (1982), we assumed that the agricultural output suffers a risk loss ratio, which is a stochastic variable X. The risk loss ratio is between 0 and 1, i.e., X∈[0,1] and is identical and independent among different periods, i.e., X1=X2=…=X. Then the budget constraint (eq. (4)) becomes to: (6) (1-d)kt-1+(1-X)f(kt-1)=ct+kt Similar with the meaning of eq. (4), eq. (6) means that the farmer distributes his endowment, which consists of the capital after depreciation and the uncertain output, into consumption and capital re-input. Then the maximization problem becomes to: max E kt
∞
∑ β u (c ) t =1
t
t
(7)
s.t. (1-d) kt-1+(1-X) f (kt-1)=ct+kt; for t=1, 2, 3... Proposition 2: The capital level, kr (where the superscript “r” stands for the risk model), in the steady state of the risk model is determined by the following equation. f´(kr)=
1-(1-d) β β-βE[Xu´(cr)]/E[u´(cr)]
(8)
In the steady state, the consumption is cr=(1-X)f(kr)-
dkr. Additionally with the production function and utility function assumed, the dynamic process of the capital converges to the steady state. Proof: It is easy to prove Proposition 2 following the proving steps of Proposition 1. In order to highlight the influence of uncertainty, we artificially assumed the output in the basic model suffers a certain loss ratio EX, which is the expectation of X. Then the budget constraint of the basic model becomes to: (4´) (1-d)kt-1+(1-EX)f(kt-1)=ct+kt And a revised Proposition 1 is as follows. Proposition 1´: The capital level, krf, in the steady state of the basic model is determined by the following equation, 1-(1-d)β f ′(krf)= (5´) β-βEX In the steady state, the consumption crf=(1-EX)f(krf)rf dk . Additionally with the production function and utility function assumed, the dynamic process of the capital converges to the steady state.
Agriculture economic growth: the risk-insurance model Insurance is an important means of risk management, and crop insurance is an important means of agriculture risk management in agriculture economy. The farmer’s plan will be changed if he employs crop insurance to manage agriculture risk. Therefore, we introduced crop insurance into the risk model and built the risk-insurance model2. Let kt denote the capital as before and λt denote the insured proportion in period t. In period t-1, the risk loss is Xf(kt-1) and the insured proportion is λt-1, then the insurance indemnity is λt-1Xf(kt-1) after the loss. Assume that crop insurance is priced according to Expected Value Premium Principle. Then the premium is (1+θ)f(kt)EX in period t, where θ denotes the risk margin3. The budget constraint becomes to: (1-d)kt-1+(1-X)f(kt-1)+λt-1Xf(kt-1) (9) t=0, 1, 2, …, =ct+kt+λt(1+θ)f(kt)EX Where, λ0 is a constant denoting the initial insured
2
Crop insurance in our paper refers to crop-yield insurance in real practice, which is based on the crop yield. In the United States, crop-yield insurance is a broadbased crop insurance program regulated by the U.S. Department of Agriculture’s Risk Management Agency (RMA) and subsidized by the Federal Crop Insurance Corporation (FCIC). 3 When the risk margin θ is less than zero, the insurance premium refers to a subsidy, which is termed as “premium subsidy” later.
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proportion. Compared with eq. (6), the term added on the left denotes the insurance indemnity for the risk loss and the term added on the right denotes the insurance premium paid. Then the maximizing problem becomes
max E kt , λt
∞
∑ β u(c ) t
t =1
t
s.t. (1-d)kt-1+(1-X)f(kt-1)+λt-1Xf(kt-1) (10) =ct+kt+λt(1+θ)f(kt)EX and 0 λt 1; for t=1, 2, 3, ... Proposition 3: The capital level, kri (where the superscript “ri” stands for the risk-insurance model), and the insured proportion λ in the steady state of the risk-insurance model, are determined by the following equations:
f ′(kri)=
1-(1-d)β β-(1+θ)EX
(1+θ)EX=β
E[Xu′(cri)] E[u′(cri)]
(11)
u´(cr)=u´[(1-X)f(kr)-dkr]=u′[f(kr)-dkr-Xf(kr)] =u′[f(kr)-dkr]-Xf(kr)u´´[f(kr)-dkr] Then, E[u´(cr)]=u´[f(kr)-dkr]-f(kr)u´´[f(kr)-dkr]EX E[Xu´(cr)]=u´[f(kr)-dkr]EX-f(kr)u´´[f(kr)-dkr]EX 2 Therefore,
E[Xu′(cr)] E[u′(cr)] = =
-EX=
u′[f(kr)-dkr]EX-f(kr)u′′[f(kr)-dkr]EX 2 u′[f(kr)-dkr]-f(kr)u′′[f(kr)-dkr]EX
-f(kr)u′′[f(kr)-dkr]EX 2+f(kr)u′′[f(kr)-dkr](EX )2 u′[f(kr)-dkr]-f(kr)u′′[f(kr)-dkr]EX f(kr)u′′[f(kr)-dkr]Var(X ) E[u′(cr)]
Therefore,
1-(1-d)β (12)
In the steady state, the consumption is: cri=(1-X)f(kri)+λXf(kri)-dkri-λ(1+θ)f(kri)EX Moreover, with the production function and utility function assumed, the dynamic processes of the capital and the insurance proportion converge to the steady state. Proof: See Appendix.
RESULTS The effect of risk Comparing the steady state of the risk model to that of the basic model, we studied the output effect of risk. The result is stated in Conclusion 1. Conclusion 1: The introduction of risk reduces the agricultural output in the steady state, in other words, the capital input in the steady state of the risk model is lower than that of the basic model. Proof: Conclusion 1 means that krf ´(krf). From eqs. (5´) and (8), let f ´(k, A)=[1-(1-d)β]/(β-βA). It is obvious that f ´(k, A) is an increasing function of A. Therefore we just need to prove E[Xu´(cr)]/E[u´(cr)]>EX. With Taylor expansion of u′(cr)=u′[(1-X)f(kr)-dkr], and ignoring the higher-order terms, we obtained:
>0
β-βE[Xu′(c )]/E[u′(c )] r
r
>
1-(1-d)β β-βEX
i.e., f ´(kr)>f ´(krf). In addition that f ´´(.)<0, we get kr
The output effects of crop insurance Compared with the steady states of risk model and risk-insurance model, the output effect of crop insurance was analyzed, which is the content of Conclusion 2. Conclusion 2: If (1+θ)EX<βE[Xu′(cr)]/E[u′(cr)], the introduction of crop insurance increases the agricultural output, in other words, crop insurance promotes agricul© 2014, CAAS. All rights reserved. Published by Elsevier Ltd.
Crop Insurance, Premium Subsidy and Agricultural Output
ture economy development. Proof: Conclusion 2 means kr0, we just need to prove f ′(kr)>f ′(kri). From eqs. (8) and (11), we know:
u′[f(k )-f ′(k )= r
ri
1-(1-d)β
-
1-(1-d)β
2541
insurance and output as well as the demand function of crop insurance in this subsection. Eq. (11) shows the effect of crop insurance premium on agricultural output. Differentiating both sides of eq. (11) with respect to θ,
df′(kri) dθ
β-βE[Xu′(cr)]/E[u′(cr)] β-(1+θ)EX
And if (1+θ)EX<βE[Xu′(cr)]/E[u′(cr)], f ′(kr)-f ′(kri)>0. In addition, f ′′(k)<0 and f ′(k)>0, then k r
The relationship between crop insurance and output Comparing with the basic model, risk model and risk-insurance model, we studied the effects of risk and crop insurance on the agricultural output in the above subsection. With the steady state of the risk-insurance model, we further analyzed the relationship between crop
=[1-(1-d)β]
EX [β-(1+θ)EX]2
>0
The above equation means that the marginal product function is an increasing function of risk margin θ, which suggests the output decreases as the risk margin increases. But when θ is large enough, satisfying (1+θ) EX βE[Xu′(cr)]/E[u′(cr)], the farmer will not buy crop insurance. Then the risk-insurance model degenerates to risk model and capital input is determined by eq. (8). From eqs. (11) and (12), we get the properties of the crop insurance demand function: (i) The insured proportion of crop insurance λ decreases as the risk margin θ increases; (ii) when θ becomes high enough, satisfying the above equation, risk-insurance model degenerates to risk model and the crop insurance demand is zero; (iii) when θ becomes low enough, the farmer transfers all of the risk and the insured proportion is one.
DISCUSSION With specific functions and parameters, we further discussed the effects of agriculture risk and crop insurance in this section.
The functions and parameters Assume that the production function is: f(k)=kα (13) Where, α represents the output elasticity of capital and satisfies 0<α<1, and the utility function is: u(c)=lnc (14) Which implies the relative risk aversion is a constant and equals one. From eqs. (5′), (13) and (14), the capital input in the steady state of the basic model is: 1
1-(1-d)β α-1 k = αβ-αβEX rf
(15)
From eqs. (8), (13) and (14), the capital input in the steady state of the risk model is:
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XU Jing-feng et al.
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k r=
2
- B + B - 4 AC 2A
Table 1 The parameters
1 α-1
(16)
Where, A=αβ(1-EX2), B=-αβd+αβdEX-[1-(1-d)β] (1+EX), C=[1-(1-d)β]d And the Lucas equilibrium price of the risk loss equals,
β
E[Xu′(cr)] E[u′(cr)]
=β
[(kr)α-dkr]EX+(kr)αEX 2
(17)
(kr)α-dkr+(kr)αEX
From eqs. (11)-(14), the capital input and the insured proportion in the steady state of the risk model are: 1
α-1 1-(1-d)β k = αβ-α(1+θ)EX
α 0.35
d 0.5
θ 0.2
EX 0.1
which is the content of Conclusion 1: the values of kr are always smaller than the values of krf. Table 2 also shows the effect of crop insurance on output, which is the content of Conclusion 2. In the first situation, market insurance premium is higher than the Lucas equilibrium price (0.12>0.1066), the farmer doesn’t buy crop insurance; in the second situation, the condition is satisfied (0.12<0.1408) and crop insurance promotes the economic development (0.4023>0.3870).
(18)
rf
λ=
β 0.95
The effect of the risk degree
(1+θ-β)[1-d(k ) ]EX+(1+θ)(EX) -βEX ri 1-α
2
(1+θ-β)(1+θ)(EX)2+(1+θ)(EX)2-βEX 2
2
(19)
According to Pecchenino and Pollard (2002), we assumed the utility discount factor is 0.95, i.e., β=0.95. Generally speaking, the output elasticity of capital in the developed countries is 0.3 and that in the developing countries is 0.5. We assumed the output elasticity of capital is 0.35, i.e., α=0.35. According to Gong (2012), the average depreciation rate is 8%, but considering the heavy depreciation of the non-durable capital inputs, like seeds, chemicals and so on, we assumed d=50%. We artificially assumed that the expectation of the risk loss ratio is EX=0.1, and the risk margin of the premium θ=0.2. Then the parameters are shown in Table 1.
The basic results According to the parameters in Table 1, we calculated the capital input and insured proportion in the steady states of the basic model, risk model and risk-insurance model, as shown in Table 2. Table 2 shows the effect of agriculture risk on output,
Following Conclusion 1, we first discussed the variation of the agricultural output as the agriculture risk becomes more uncertain. From eq. (16), it is hard to analyze the variation even if the functions are given. Therefore, we numerically simulated the variation of the agricultural output as the uncertainty increases, as shown in Fig. 1. Fig. 1 shows that the capital input decreases as the agricultural output becomes more uncertain, implying that the continuity of the risk aversion. Then Conclusion 1 is extended from “the effect of introduction of risk” to “the effect of the risk degree”, i.e., Conclusion 1*: If the expectation of the risk loss is identical, the output decreases as the risk loss becomes more uncertain; when the risk loss becomes a deterministic loss, the risk model degenerates to the basic model.
The demand of crop insurance In subsection “The relationship between crop insurance and output”, we analyzed the properties of the demand function of crop insurance without giving rigorous proof.
Table 2 The basic situations1) EX2=0.02 EX2=0.05
krf 0.4211 0.4211
kr 0.4124 0.3870
kri 0.4023
λ 0 0.5359
Insurance premium (1+θ)EX 0.12 0.12
Lucas equilibrium price of X 0.1066 0.1408
1)
We assumed there are two kinds of risk. For the first kind, the probability of the risk happens is 50%, and the loss ratio is 20%; for the second kind, the probability is 20%, and the loss ratio is 50%. When the simulation value of insured proportion λ is negative, it was set to be 0; when the simulation value of insured proportion is larger than 1, it was set to be 1. -, the data does not exist because market insurance premium is higher than the Lucas equilibrium price.
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Crop Insurance, Premium Subsidy and Agricultural Output
2543 2
0.44 0.42
1.5
0.38
Insured proportion
Capital input
0.4
0.36 0.34 0.32 0.3
1
0.5
0
0.28 0.26
0
0.02 0.04 0.06 0.08
0.1
0.12 0.14 0.16 0.18
0.2
EX 2
Fig. 1 The effect of the risk degree.
With specific functions and parameters, the demand curve of crop insurance is drawn in Fig. 2. There are two lines in Fig. 2, the full line and the dotted line. The full line shows the real demand of crop insurance in real world. The dotted line shows the demand relationship suggested by eq. (19), which has something different. Following eq. (19), the farmer is willing to transfer more than his total risk if the crop insurance is very cheap because of premium subsidy. But the insured proportion will never be greater than 1 because of the insurable interest principle4, as shown in Fig. 2. On the other hand, when the risk margin is very high, the farmer is willing to purchase negative crop insurance, i.e., λ<0. But that is not permitted in the real world. Therefore, we set 0 λ 1. When the risk margin is moderate, the demand of crop insurance is just suggested by eq. (19). Therefore, the full line shows the real demand curve considering the two aspects. The downward sloping demand curve shows the general law of demand, i.e., the demand decreases as the price increases. And when the risk margin is very high, the demand decreases to zero. The scale of risk margin is one of the reasons of deficient demand for crop insurance5. As the interdependency of agriculture risks, the actuarial price of the crop insurance may be very expensive, even exceed the individual’s reservation price. And the high risk margin reduces the demand of crop insurance. 4 5
-0.5 -0.5 -0.4 -0.3
-0.2 -0.1
0
0.1
0.2
0.3
0.4
0.5
Risk margin
Fig. 2 The demand curve of crop insurance (EX 2=0.05). The negative risk margin means that the farmer transfers agriculture risk at a price which is lower than the expectation of risk loss. The situation may be resulted from premium subsidy.
The output effect of premium subsidy As mentioned above, scholars agree on that crop insurance program should be subsidized or sponsored by government to succeed and some scholars directly focus on the output effect of premium subsidy. Employing the risk-insurance model, we further analyzed the output effect of premium subsidy. The relationship between capital input and risk margin is shown in Fig. 3. Fig. 3 shows that the capital input decreases as the risk margin increases. When the market price is higher than the Lucas equilibrium price, the farmer will not purchase crop insurance and the risk-insurance model degenerates to the risk model. There are two implications in Fig. 3. On one hand, as the risk margin decreases, both the insured proportion and capital input increase at the same time, showing the positive relationship between the two. But the result doesn’t show the causal relationship between the insured proportion and capital input. Exactly as Chakir and Hardelin (2010) pointed out, the demand of crop insurance and the capital input are determined by each other. On the other hand, crop insurance premium subsidy has an obvious promoting effect on the output. Given a constant insurance price, Fig. 3 shows that capital input
Insurable interest principle demonstrates that, people have an insurable interest in their property up to the value of the property, but not more. Deficient demand is one of the reasons that private crop insurance market fails (Glauber and Collins 2002).
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XU Jing-feng et al.
2544 0.5 The basic model
0.48
Capital input
0.46 0.44
The risk-insurance model
0.42 0.40 The risk model 0.38 -1.0 -0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Risk margin
Fig. 3 The output effect of premium subsidy (EX2=0.05). That the risk margin is -1 means that the crop insurance is free for the farmer, which is available in the real world. But it is called disaster assistance instead of crop insurance.
increases as premium subsidy increases, even exceeding the level of the basic model. At the moderate level, premium subsidy reduces the individual’s cost of managing risk and changes the insured proportion and capital input. After the insured proportion reaches 1, premium subsidy becomes a way of income transfer rather than a risk management instrument. From eqs. (5) and (11), the capital input of the risk-insurance model recovers to that of the basic model if θ=β-1.
CONCLUSION Based on the RCK model, we built the basic model, the risk model and the risk-insurance model of agriculture economic growth to study the output effects of risk, crop insurance and premium subsidy. Our focus is whether agricultural insurance and premium subsidies increase agricultural output. For this purpose, we compared the steady states of the three models. Our contribution is that we studied the output effects of risk and crop insurance from the perspective of economic growth and proved the output promotion of crop insurance theoretically. The theoretical results show that the introduction of agriculture risk decreases the capital input and the introduction of crop insurance increases the capital input. But the output effect of crop insurance depends on the condition, that the market price of crop insurance is lower than individual’s reservation price. Numerical analysis
complements the theoretical results: (i) the capital input decreases as the uncertainty of agriculture risk increases; (ii) there are positive relationships between the insured proportion and capital input, but we can’t judge the causal relationship between them; (iii) crop insurance premium subsidy has an obvious promoting effect on the output. Issues related to agricultural insurance will certainly continue to be a hot topic. Based on the relationship between capital input and premium subsidy we built, the optimal premium subsidy will be solved if the agricultural externality is reasonable measured in the future research. Appendix associated with this paper can be available on http://www.ChinaAgriSci.com/V2/En/appendix.htm
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Crop Insurance, Premium Subsidy and Agricultural Output
Hau A. 2006. Production under uncertainty with insurance or hedging. Insurance: Mathematics and Economics, 38, 347-359. Horowitz J K, Lichtenberg E. 1993. Insurance, moral hazard, and chemical use in agriculture. American Journal of Agricultural Economics, 75, 926-935. Koopmans T C. 1965. On the concept of optimal economic growth. [2013-03-01]. http://cowles.econ.yale.edu/P/cd/ d01b/d0163.pdf Nelson C H, Loehman E T. 1987. Further toward a theory of agricultural insurance. American Journal of Agricultural Economics, 69, 523-531. O’Donoghue E J, Key N D, Roberts M J. 2007. Does risk matter for farm businesses? The effect of crop insurance on production and diversification. [2013-03-01]. http:// purl.umn.edu/19397 Pecchenino R A, Pollard P. 2002. Dependent children and aged parents: funding education and social security in an aging economy. Journal of Macroeconomics, 24, 145-169. Ramaswami B. 1993. Supply response to agricultural insurance: Risk reduction and moral hazard effects.
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American Journal of Agricultural Economics, 75, 914-925. Ramsey F P. 1928. A mathematical theory of saving. Economic Journal, 38, 543-559. Stokey N L, Lucas R E, Prescott E C. 1989. Recursive Methods in Economic Dynamics. Harvard University Press, Massachusetts, USA. Walters C G, Shumway C R, Chouinard H H, Wandschneider P R. 2012. Crop insurance, land allocation, and the environment. Journal of Agricultural and Resource Economics, 37, 301-320. Wu J J. 1999. Crop insurance, acreage decisions, and nonpointsource pollution. American Journal of Agricultural Economics, 81, 305-320. Ye T, Yokomatsu M, Okada N. 2012. Agricultural production behavior under premium subsidy: Incorporating crop price when subsistence constraint holds. International Journal of Disaster Risk Science, 3, 131-138. Young C E, Vandeveer M L, Schnepf R D. 2001. Production and price impacts of U.S. crop insurance programs. American Journal of Agricultural Economics, 83, 11961203. (Managing editor WENG Ling-yun)
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November 2014
RESEARCH ARTICLE
Crop Insurance, Premium Subsidy and Agricultural Output 1
2
XU Jing-feng * and LIAO Pu * 1 2
China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, P.R.China School of Economics, Nankai University, Tianjin 300071, P.R.China
Abstract This paper studied the effects of crop insurance on agricultural output with an economic growth model. Based on RamseyCass-Koopmans (RCK) model, a basic model of agriculture economic growth was developed. Extending the basic model to incorporate uncertainty and insurance mechanism, a risk model and a risk-insurance model were built to study the influences of risk and crop insurance on agricultural output. Compared with the steady states of the three models, the following results are achieved: (i) agricultural output decreases if we introduce uncertainty into the risk-free model; (ii) crop insurance promotes agriculture economic growth if insurance mechanism is introduced into the risk model; (iii) premium subsidy constantly improves agricultural output. Our contribution is that we studied the effects of crop insurance and premium subsidy from the perspective of economic growth in a dynamic framework, and proved the output promotion of crop insurance theoretically. Key words: economic growth, agriculture risk, crop insurance, premium subsidy
INTRODUCTION As agriculture plays an important role in the national economy, many countries and regions (e.g., United States, European Union, Canada, Japan and etc.) adopt various forms of subsidies to increase agricultural output (Barnett and Mahul 2007). Policy-based crop insurance is an important way of subsidy, which aims to help farmers manage agriculture risk and promote agricultural input and output. However, Goodwin (2001) claimed that the crop insurance policy is a way of income transfer rather than a risk management instrument. Whether crop insurance promotes agricultural output by means of managing risk is the research topic we are interested in. The significance of crop insurance has been recog-
nized and a lot of scholars have studied the effects of crop insurance empirically. Some literatures found that crop insurance increases the use of risk-increasing inputs, e.g., fertilizer, pesticide and so on (Horowitz and Lichtenberg 1993; Wu 1999; Chakir and Hardelin 2010). Some literatures showed that crop insurance more or less increases the plantings (Young et al. 2001; Goodwin et al. 2004; O’Donoghue et al. 2007). In addition, some literatures pointed out that crop insurance changes the planting structure (Wu 1999; Young et al. 2001). On the other hand, some scholars have studied the effects of crop insurance and premium subsidy theoretically. Ahsan et al. (1982) built an economic model with a single input and a single uncertain output to study the output effect and effectiveness of crop insurance. They believe that crop insurance promotes agricultural output, comparing to the economy without crop insurance.
Received 30 September, 2013 Accepted 5 December, 2013 Correspondence XU Jing-feng, E-mail: [email protected]; LIAO Pu, E-mail: [email protected] * These authors contributed equally to this study.
© 2014, CAAS. All rights reserved. Published by Elsevier Ltd. doi: 10.1016/S2095-3119(13)60674-7
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Extending the model of Ahsan et al. (1982), Nelson and Loehman (1987) constructed a more general production model with multiple inputs and uncertain outputs, and showed that the output effects of crop insurance depend on the substitution and risk properties of the production functions. Ramaswami (1993) decomposed the effect of insurance into a “risk reduction” effect as well as a “moral hazard” effect. He claimed that the directions and magnitudes of these effects depend on the parameters of the insurance contract, producer’s risk preferences, and the underlying technology. Similarly, Chambers and Quiggin (2001) developed a framework to analyze input adjustment for stochastic technologies and applied to the case of actuarially fair production insurance. They showed that the decomposition consists of a pure-risk effect and an expansion effect. Hau (2006) examined the output decision of a risk-averse producer facing profit risk in the presence of insurance or hedging, and derived the conditions under which the introduction of generic insurance increases output. Ye et al. (2012) studied the agriculture production behavior under premium subsidy by applying the Classic Insurance Model, and showed that the output effect depends on the revenue structure, which is determined by the price of the agricultural product, its foreign substitutes and the feasibility of inter-temporal storage. The above literatures studied the output effects of crop insurance and premium subsidy from different perspectives, but there is a common weakness in these literatures that almost all of studies were carried out in a static context (Ahsan et al. 1982; Nelson and Loehman 1987; Ramaswami 1993 and so on)1. Different with these researches, this paper studied the issue in a dynamic economic growth model and spelled out the importance of crop insurance and premium subsidy explicitly. The paper employed the classical Ramsey-Cass-Koopmans (RCK) model (Ramsey 1928; Cass 1965; Koopmans 1965) to generalize the growth process of agriculture economy. Extending the basic model to incorporate agriculture risk and crop insurance, we further built the risk model and the risk-insurance model. By comparing the steady states of the three models, we analyzed the output effects of agriculture risk and crop insurance. In 1
addition, based on the steady state of the risk-insurance model, we built the demand function of crop insurance and the relationship between agricultural output and crop insurance demand to analyze the output effect of premium subsidy. Our contribution is that we study the output effects of risk, crop insurance and premium subsidy from the perspective of economic growth, and prove the output promotion of crop insurance theoretically.
THE MODEL We started with an agriculture economy with a lot of identical farmers. In the agriculture economy, there is a representative farmer who lives forever and is endowed with unit labor, unit acreage and an initial capital k0. He chooses a sequence of consumptions and savings to maximize his lifetime utility which is given by: ∞
U=∑ βtu(ct)
(1)
t =1
Where, ct is the consumption in period t and β is the discount factor of utility. u(.) is the utility function satisfying u´(c)>0, u´´(c)<0 and Inada assumptions: u´(c)=∞, u´(c)=0. His savings augment the capital stock utilized in the production of agricultural production, where the production function is given by: y=f(k) (2) Where y is the agricultural output and k is the agricultural capital input. We assumed the production function satisfies f(0)=0, f ´(k)>0, f ´´(k)<0 and Inada assumptions: f ´(k)=∞, f ´´(k)=0. In this framework, the agricultural capital input k includes both the durable input (like farm machinery) and non-durable input (like seeds and chemicals), and the capital accumulation is the driving force of agriculture economic growth. Then the optimal allocation is determined by the maximization problem, max kt
∞
∑ β u (c ) t =1
t
t
(3)
with budget constraints (4) (1-d)kt-1+f(kt-1)=ct+kt; for t=1, 2, 3, … rf Proposition 1: The capital level, k (where the superscript “rf ” stands for the basic model), in the steady state of the basic model is determined by the following equation,
Scholars agreed on that crop insurance should be subsidized or sponsored by government. One reason is the important effects of crop insurance. Another important reason is that the private crop insurance market always fails because of moral hazard, adverse selection and correlated agriculture risk (Goodwin and Smith 1995). A lot of papers focus on the output effect of premium subsidy, for example, Goodwin et al. (2004), O’Donoghue et al. (2007), Ye et al. (2012), and Walters et al. (2012).
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Crop Insurance, Premium Subsidy and Agricultural Output
f ′(krf)=
1-(1-d) β
2539
(5)
β In the steady state, the consumption crf=f(krf)-dkrf. Additionally with the production function and utility function assumed, the dynamic process of the capital converges to the steady state. Proof: The basic model can be found in Stokey et al. (1989).
Agriculture economic growth: the risk model The basic model describes the characteristics of agriculture economic growth in the certain environment. However, there are a lot of risks in the real world and nature risk is one of the most important factors reducing agricultural output. Therefore, we extended the basic model to incorporate risk and built the risk model to describe agriculture economic growth in an uncertain environment. Referring to Ahsan et al. (1982), we assumed that the agricultural output suffers a risk loss ratio, which is a stochastic variable X. The risk loss ratio is between 0 and 1, i.e., X∈[0,1] and is identical and independent among different periods, i.e., X1=X2=…=X. Then the budget constraint (eq. (4)) becomes to: (6) (1-d)kt-1+(1-X)f(kt-1)=ct+kt Similar with the meaning of eq. (4), eq. (6) means that the farmer distributes his endowment, which consists of the capital after depreciation and the uncertain output, into consumption and capital re-input. Then the maximization problem becomes to: max E kt
∞
∑ β u (c ) t =1
t
t
(7)
s.t. (1-d) kt-1+(1-X) f (kt-1)=ct+kt; for t=1, 2, 3... Proposition 2: The capital level, kr (where the superscript “r” stands for the risk model), in the steady state of the risk model is determined by the following equation. f´(kr)=
1-(1-d) β β-βE[Xu´(cr)]/E[u´(cr)]
(8)
In the steady state, the consumption is cr=(1-X)f(kr)-
dkr. Additionally with the production function and utility function assumed, the dynamic process of the capital converges to the steady state. Proof: It is easy to prove Proposition 2 following the proving steps of Proposition 1. In order to highlight the influence of uncertainty, we artificially assumed the output in the basic model suffers a certain loss ratio EX, which is the expectation of X. Then the budget constraint of the basic model becomes to: (4´) (1-d)kt-1+(1-EX)f(kt-1)=ct+kt And a revised Proposition 1 is as follows. Proposition 1´: The capital level, krf, in the steady state of the basic model is determined by the following equation, 1-(1-d)β f ′(krf)= (5´) β-βEX In the steady state, the consumption crf=(1-EX)f(krf)rf dk . Additionally with the production function and utility function assumed, the dynamic process of the capital converges to the steady state.
Agriculture economic growth: the risk-insurance model Insurance is an important means of risk management, and crop insurance is an important means of agriculture risk management in agriculture economy. The farmer’s plan will be changed if he employs crop insurance to manage agriculture risk. Therefore, we introduced crop insurance into the risk model and built the risk-insurance model2. Let kt denote the capital as before and λt denote the insured proportion in period t. In period t-1, the risk loss is Xf(kt-1) and the insured proportion is λt-1, then the insurance indemnity is λt-1Xf(kt-1) after the loss. Assume that crop insurance is priced according to Expected Value Premium Principle. Then the premium is (1+θ)f(kt)EX in period t, where θ denotes the risk margin3. The budget constraint becomes to: (1-d)kt-1+(1-X)f(kt-1)+λt-1Xf(kt-1) (9) t=0, 1, 2, …, =ct+kt+λt(1+θ)f(kt)EX Where, λ0 is a constant denoting the initial insured
2
Crop insurance in our paper refers to crop-yield insurance in real practice, which is based on the crop yield. In the United States, crop-yield insurance is a broadbased crop insurance program regulated by the U.S. Department of Agriculture’s Risk Management Agency (RMA) and subsidized by the Federal Crop Insurance Corporation (FCIC). 3 When the risk margin θ is less than zero, the insurance premium refers to a subsidy, which is termed as “premium subsidy” later.
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XU Jing-feng et al.
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proportion. Compared with eq. (6), the term added on the left denotes the insurance indemnity for the risk loss and the term added on the right denotes the insurance premium paid. Then the maximizing problem becomes
max E kt , λt
∞
∑ β u(c ) t
t =1
t
s.t. (1-d)kt-1+(1-X)f(kt-1)+λt-1Xf(kt-1) (10) =ct+kt+λt(1+θ)f(kt)EX and 0 λt 1; for t=1, 2, 3, ... Proposition 3: The capital level, kri (where the superscript “ri” stands for the risk-insurance model), and the insured proportion λ in the steady state of the risk-insurance model, are determined by the following equations:
f ′(kri)=
1-(1-d)β β-(1+θ)EX
(1+θ)EX=β
E[Xu′(cri)] E[u′(cri)]
(11)
u´(cr)=u´[(1-X)f(kr)-dkr]=u′[f(kr)-dkr-Xf(kr)] =u′[f(kr)-dkr]-Xf(kr)u´´[f(kr)-dkr] Then, E[u´(cr)]=u´[f(kr)-dkr]-f(kr)u´´[f(kr)-dkr]EX E[Xu´(cr)]=u´[f(kr)-dkr]EX-f(kr)u´´[f(kr)-dkr]EX 2 Therefore,
E[Xu′(cr)] E[u′(cr)] = =
-EX=
u′[f(kr)-dkr]EX-f(kr)u′′[f(kr)-dkr]EX 2 u′[f(kr)-dkr]-f(kr)u′′[f(kr)-dkr]EX
-f(kr)u′′[f(kr)-dkr]EX 2+f(kr)u′′[f(kr)-dkr](EX )2 u′[f(kr)-dkr]-f(kr)u′′[f(kr)-dkr]EX f(kr)u′′[f(kr)-dkr]Var(X ) E[u′(cr)]
Therefore,
1-(1-d)β (12)
In the steady state, the consumption is: cri=(1-X)f(kri)+λXf(kri)-dkri-λ(1+θ)f(kri)EX Moreover, with the production function and utility function assumed, the dynamic processes of the capital and the insurance proportion converge to the steady state. Proof: See Appendix.
RESULTS The effect of risk Comparing the steady state of the risk model to that of the basic model, we studied the output effect of risk. The result is stated in Conclusion 1. Conclusion 1: The introduction of risk reduces the agricultural output in the steady state, in other words, the capital input in the steady state of the risk model is lower than that of the basic model. Proof: Conclusion 1 means that kr
>0
β-βE[Xu′(c )]/E[u′(c )] r
r
>
1-(1-d)β β-βEX
i.e., f ´(kr)>f ´(krf). In addition that f ´´(.)<0, we get kr
The output effects of crop insurance Compared with the steady states of risk model and risk-insurance model, the output effect of crop insurance was analyzed, which is the content of Conclusion 2. Conclusion 2: If (1+θ)EX<βE[Xu′(cr)]/E[u′(cr)], the introduction of crop insurance increases the agricultural output, in other words, crop insurance promotes agricul© 2014, CAAS. All rights reserved. Published by Elsevier Ltd.
Crop Insurance, Premium Subsidy and Agricultural Output
ture economy development. Proof: Conclusion 2 means kr
u′[f(k )-f ′(k )= r
ri
1-(1-d)β
-
1-(1-d)β
2541
insurance and output as well as the demand function of crop insurance in this subsection. Eq. (11) shows the effect of crop insurance premium on agricultural output. Differentiating both sides of eq. (11) with respect to θ,
df′(kri) dθ
β-βE[Xu′(cr)]/E[u′(cr)] β-(1+θ)EX
And if (1+θ)EX<βE[Xu′(cr)]/E[u′(cr)], f ′(kr)-f ′(kri)>0. In addition, f ′′(k)<0 and f ′(k)>0, then k r
The relationship between crop insurance and output Comparing with the basic model, risk model and risk-insurance model, we studied the effects of risk and crop insurance on the agricultural output in the above subsection. With the steady state of the risk-insurance model, we further analyzed the relationship between crop
=[1-(1-d)β]
EX [β-(1+θ)EX]2
>0
The above equation means that the marginal product function is an increasing function of risk margin θ, which suggests the output decreases as the risk margin increases. But when θ is large enough, satisfying (1+θ) EX βE[Xu′(cr)]/E[u′(cr)], the farmer will not buy crop insurance. Then the risk-insurance model degenerates to risk model and capital input is determined by eq. (8). From eqs. (11) and (12), we get the properties of the crop insurance demand function: (i) The insured proportion of crop insurance λ decreases as the risk margin θ increases; (ii) when θ becomes high enough, satisfying the above equation, risk-insurance model degenerates to risk model and the crop insurance demand is zero; (iii) when θ becomes low enough, the farmer transfers all of the risk and the insured proportion is one.
DISCUSSION With specific functions and parameters, we further discussed the effects of agriculture risk and crop insurance in this section.
The functions and parameters Assume that the production function is: f(k)=kα (13) Where, α represents the output elasticity of capital and satisfies 0<α<1, and the utility function is: u(c)=lnc (14) Which implies the relative risk aversion is a constant and equals one. From eqs. (5′), (13) and (14), the capital input in the steady state of the basic model is: 1
1-(1-d)β α-1 k = αβ-αβEX rf
(15)
From eqs. (8), (13) and (14), the capital input in the steady state of the risk model is:
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XU Jing-feng et al.
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k r=
2
- B + B - 4 AC 2A
Table 1 The parameters
1 α-1
(16)
Where, A=αβ(1-EX2), B=-αβd+αβdEX-[1-(1-d)β] (1+EX), C=[1-(1-d)β]d And the Lucas equilibrium price of the risk loss equals,
β
E[Xu′(cr)] E[u′(cr)]
=β
[(kr)α-dkr]EX+(kr)αEX 2
(17)
(kr)α-dkr+(kr)αEX
From eqs. (11)-(14), the capital input and the insured proportion in the steady state of the risk model are: 1
α-1 1-(1-d)β k = αβ-α(1+θ)EX
α 0.35
d 0.5
θ 0.2
EX 0.1
which is the content of Conclusion 1: the values of kr are always smaller than the values of krf. Table 2 also shows the effect of crop insurance on output, which is the content of Conclusion 2. In the first situation, market insurance premium is higher than the Lucas equilibrium price (0.12>0.1066), the farmer doesn’t buy crop insurance; in the second situation, the condition is satisfied (0.12<0.1408) and crop insurance promotes the economic development (0.4023>0.3870).
(18)
rf
λ=
β 0.95
The effect of the risk degree
(1+θ-β)[1-d(k ) ]EX+(1+θ)(EX) -βEX ri 1-α
2
(1+θ-β)(1+θ)(EX)2+(1+θ)(EX)2-βEX 2
2
(19)
According to Pecchenino and Pollard (2002), we assumed the utility discount factor is 0.95, i.e., β=0.95. Generally speaking, the output elasticity of capital in the developed countries is 0.3 and that in the developing countries is 0.5. We assumed the output elasticity of capital is 0.35, i.e., α=0.35. According to Gong (2012), the average depreciation rate is 8%, but considering the heavy depreciation of the non-durable capital inputs, like seeds, chemicals and so on, we assumed d=50%. We artificially assumed that the expectation of the risk loss ratio is EX=0.1, and the risk margin of the premium θ=0.2. Then the parameters are shown in Table 1.
The basic results According to the parameters in Table 1, we calculated the capital input and insured proportion in the steady states of the basic model, risk model and risk-insurance model, as shown in Table 2. Table 2 shows the effect of agriculture risk on output,
Following Conclusion 1, we first discussed the variation of the agricultural output as the agriculture risk becomes more uncertain. From eq. (16), it is hard to analyze the variation even if the functions are given. Therefore, we numerically simulated the variation of the agricultural output as the uncertainty increases, as shown in Fig. 1. Fig. 1 shows that the capital input decreases as the agricultural output becomes more uncertain, implying that the continuity of the risk aversion. Then Conclusion 1 is extended from “the effect of introduction of risk” to “the effect of the risk degree”, i.e., Conclusion 1*: If the expectation of the risk loss is identical, the output decreases as the risk loss becomes more uncertain; when the risk loss becomes a deterministic loss, the risk model degenerates to the basic model.
The demand of crop insurance In subsection “The relationship between crop insurance and output”, we analyzed the properties of the demand function of crop insurance without giving rigorous proof.
Table 2 The basic situations1) EX2=0.02 EX2=0.05
krf 0.4211 0.4211
kr 0.4124 0.3870
kri 0.4023
λ 0 0.5359
Insurance premium (1+θ)EX 0.12 0.12
Lucas equilibrium price of X 0.1066 0.1408
1)
We assumed there are two kinds of risk. For the first kind, the probability of the risk happens is 50%, and the loss ratio is 20%; for the second kind, the probability is 20%, and the loss ratio is 50%. When the simulation value of insured proportion λ is negative, it was set to be 0; when the simulation value of insured proportion is larger than 1, it was set to be 1. -, the data does not exist because market insurance premium is higher than the Lucas equilibrium price.
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Crop Insurance, Premium Subsidy and Agricultural Output
2543 2
0.44 0.42
1.5
0.38
Insured proportion
Capital input
0.4
0.36 0.34 0.32 0.3
1
0.5
0
0.28 0.26
0
0.02 0.04 0.06 0.08
0.1
0.12 0.14 0.16 0.18
0.2
EX 2
Fig. 1 The effect of the risk degree.
With specific functions and parameters, the demand curve of crop insurance is drawn in Fig. 2. There are two lines in Fig. 2, the full line and the dotted line. The full line shows the real demand of crop insurance in real world. The dotted line shows the demand relationship suggested by eq. (19), which has something different. Following eq. (19), the farmer is willing to transfer more than his total risk if the crop insurance is very cheap because of premium subsidy. But the insured proportion will never be greater than 1 because of the insurable interest principle4, as shown in Fig. 2. On the other hand, when the risk margin is very high, the farmer is willing to purchase negative crop insurance, i.e., λ<0. But that is not permitted in the real world. Therefore, we set 0 λ 1. When the risk margin is moderate, the demand of crop insurance is just suggested by eq. (19). Therefore, the full line shows the real demand curve considering the two aspects. The downward sloping demand curve shows the general law of demand, i.e., the demand decreases as the price increases. And when the risk margin is very high, the demand decreases to zero. The scale of risk margin is one of the reasons of deficient demand for crop insurance5. As the interdependency of agriculture risks, the actuarial price of the crop insurance may be very expensive, even exceed the individual’s reservation price. And the high risk margin reduces the demand of crop insurance. 4 5
-0.5 -0.5 -0.4 -0.3
-0.2 -0.1
0
0.1
0.2
0.3
0.4
0.5
Risk margin
Fig. 2 The demand curve of crop insurance (EX 2=0.05). The negative risk margin means that the farmer transfers agriculture risk at a price which is lower than the expectation of risk loss. The situation may be resulted from premium subsidy.
The output effect of premium subsidy As mentioned above, scholars agree on that crop insurance program should be subsidized or sponsored by government to succeed and some scholars directly focus on the output effect of premium subsidy. Employing the risk-insurance model, we further analyzed the output effect of premium subsidy. The relationship between capital input and risk margin is shown in Fig. 3. Fig. 3 shows that the capital input decreases as the risk margin increases. When the market price is higher than the Lucas equilibrium price, the farmer will not purchase crop insurance and the risk-insurance model degenerates to the risk model. There are two implications in Fig. 3. On one hand, as the risk margin decreases, both the insured proportion and capital input increase at the same time, showing the positive relationship between the two. But the result doesn’t show the causal relationship between the insured proportion and capital input. Exactly as Chakir and Hardelin (2010) pointed out, the demand of crop insurance and the capital input are determined by each other. On the other hand, crop insurance premium subsidy has an obvious promoting effect on the output. Given a constant insurance price, Fig. 3 shows that capital input
Insurable interest principle demonstrates that, people have an insurable interest in their property up to the value of the property, but not more. Deficient demand is one of the reasons that private crop insurance market fails (Glauber and Collins 2002).
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XU Jing-feng et al.
2544 0.5 The basic model
0.48
Capital input
0.46 0.44
The risk-insurance model
0.42 0.40 The risk model 0.38 -1.0 -0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Risk margin
Fig. 3 The output effect of premium subsidy (EX2=0.05). That the risk margin is -1 means that the crop insurance is free for the farmer, which is available in the real world. But it is called disaster assistance instead of crop insurance.
increases as premium subsidy increases, even exceeding the level of the basic model. At the moderate level, premium subsidy reduces the individual’s cost of managing risk and changes the insured proportion and capital input. After the insured proportion reaches 1, premium subsidy becomes a way of income transfer rather than a risk management instrument. From eqs. (5) and (11), the capital input of the risk-insurance model recovers to that of the basic model if θ=β-1.
CONCLUSION Based on the RCK model, we built the basic model, the risk model and the risk-insurance model of agriculture economic growth to study the output effects of risk, crop insurance and premium subsidy. Our focus is whether agricultural insurance and premium subsidies increase agricultural output. For this purpose, we compared the steady states of the three models. Our contribution is that we studied the output effects of risk and crop insurance from the perspective of economic growth and proved the output promotion of crop insurance theoretically. The theoretical results show that the introduction of agriculture risk decreases the capital input and the introduction of crop insurance increases the capital input. But the output effect of crop insurance depends on the condition, that the market price of crop insurance is lower than individual’s reservation price. Numerical analysis
complements the theoretical results: (i) the capital input decreases as the uncertainty of agriculture risk increases; (ii) there are positive relationships between the insured proportion and capital input, but we can’t judge the causal relationship between them; (iii) crop insurance premium subsidy has an obvious promoting effect on the output. Issues related to agricultural insurance will certainly continue to be a hot topic. Based on the relationship between capital input and premium subsidy we built, the optimal premium subsidy will be solved if the agricultural externality is reasonable measured in the future research. Appendix associated with this paper can be available on http://www.ChinaAgriSci.com/V2/En/appendix.htm
References
Ahsan S M, Ali A G, Kurian N J. 1982. Toward a theory of agricultural insurance. American Journal of Agricultural Economics, 64, 520-529. Barnett B J, Mahul O. 2007. Weather index insurance for agriculture and rural areas in lower-income countries. American Journal of Agricultural Economics, 89, 12411247. Cass D. 1965. Optimum growth in an aggregative model of capital accumulation. Review of Economic Studies, 32, 233-240. Chakir R, Hardelin J. 2010. Crop insurance and pesticides in French agriculture: an empirical analysis of multiple risks management. [2013-03-01]. http://halshs.archivesouvertes.fr/hal-00753733/ Chambers R G, Quiggin J. 2001. Decomposing input adjustments under price and production uncertainty. American Journal of Agricultural Economics, 83, 20-34. Glauber J W, Collins K J. 2002. Crop insurance, disaster assistance, and the role of the federal government in providing catastrophic risk protection. Agricultural Finance Review, 62, 81-101. Gong G. 2012. Growth and development in a harrodian economy: with evidence from China. Metroeconomica, 64, 73-102. Goodwin B K. 2001. Problems with market insurance in agriculture. American Journal of Agricultural Economics, 83, 643-649. Goodwin B K, Smith V H. 1995. The Economics of Crop Insurance and Disaster Aid. The AEI Press, Washington, D.C., USA. Goodwin B K, Vandeveer M L, Deal J L. 2004. An empirical analysis of acreage effects of participation in the federal crop insurance program. American Journal of Agricultural Economics, 86, 1058-1077.
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Crop Insurance, Premium Subsidy and Agricultural Output
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© 2014, CAAS. All rights reserved. Published by Elsevier Ltd.