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Effects of Subsidized Crop Insurance on Crop

Choices

Jisang Yu

Department of Agricultural and Resource Economics, UC Davis

UC Agricultural Issues Center

2015 AAEA&WAEA Annual Meeting, San Francisco, CA, July 27

Jisang Yu (UC Davis) Production Effects of Crop Insurance AAEA&WAEA 2015 1 / 19

Introduction

Research Questions

1 How do subsidized crop insurance programs affect which cropsto grow?

2 What is the role of premium subsidies on the production effectsof subsidized crop insurance?


Introduction

Total US Crop Insurance Subsidy is Increasing

Total US crop insurance subsidy (million dollars)

In 2014, total US crop insurance subsidy was 6.2 billion dollars.


Introduction

Global Crop Insurance Market

About 89% of the total premium for crop insurance programs in 38countries was paid into subsidized crop insurance programs during2003-2007 (World Bank Survey, 2008).

The number of crop insurance programs is growing globally.


Introduction

Why Do Crop Insurance Subsidies Matter?

“The problem with subsidized crop insurance is that it allows farmersto operate in ways that increase the risk of crop and other forms offinancial loss because they know that any losses they incur will becovered by taxpayers.” - Vince H. Smith

“But the insurance provides farmers with the income securitynecessary to secure the loans they need to produce crops.” - W.Robert Goodman

The Wall Street Journal, July 12

http://www.wsj.com/articles/should-washington-end-agriculture-

subsidies-1436757020


Introduction

Previous Studies on Crop Insurance and Portfolio

Choices

1 Theoretical Studies Investigate the Demand for Insurance andthe Interaction with Portfolio Choice (Eeckhoudt, Meyer, andOrmiston 1997; and Hennessy 1998)

2 Empirical Studies Provide Some Evidence on the PositiveProduction Effect of Insurance (Goodwin, Vandemeer, and Deal2004; Cole, Gine, and Vickery 2013; Karlan et al. 2014; andElabed and Carter 2014)


Introduction

Potential Contributions of This Paper

The conceptual framework of this paper separates the effect ofsubsidized crop insurance into two channels:

1 Actuarially Fair Crop Insurance Effect

2 Premium Subsidy: Encouragement Effect and RelativeProfitability Effect

Also, the paper explains the interaction between self-insurance andsubsidized crop insurance.


Conceptual model

Assumptions for the Model

Farmers allocate their initial capital endowment (single input) into a“safe” crop production and a “risky” crop.

Risk-averse farmers maximize expected utility.

I compare three cases 1) without insurance, 2) with actuarially faircrop insurance, and 3) with subsidized crop insurance.


Conceptual model

Notation

K0: Initial Capital Endowment

Kr and Ks : Allocations into the “Risky” and the “Safe” Crops

r and s: The Stochastic Rate of Return from the “Risky” Cropand the Non-stochastic Rate of Return from the “Safe” Crop

θ: Insurance Coverage

π, γ, and I (r): Insurance Premium, Subsidy Rate, and Indemnity


Conceptual model

Expected Utility Maximization Problem without

Access to Insurance

The optimization problem without access to insurance:

MaxKr U(Kr ) = Eu(x(Kr ))

subject to Kr − K0 ≤ 0

where x(Kr ) = sKs + rKr and Ks = K0 − Kr .


Conceptual model Actuarially Fair Crop Insurance

Actuarially Fair Crop InsuranceInsurance Demand

The optimization problem with actuarially fair crop insurance:

MaxKr , θ U(Kr , θ) = Eu(x(Kr , θ))

subject to (1 + θπ)Kr − K0 ≤ 0

−θ ≤ 0

where x(Kr , θ) = sKs + (r + θI (r))Kr and Ks = K0 − (1 + θπ)Kr .

The demand for actuarially fair insurance is positive if and only if

sπEu′(x |θ=0) < Eu′(x |θ=0)(I (r)).



Actuarially Fair Crop InsuranceSubstitutability

By applying the implicit function theorem to the first orderconditions, I obtain Proposition 1.

Proposition 1The demand for actuarially fair crop insurance decreases as the rateof return from the “safe” crop increases if farmers have ConstantAbsolute Risk Aversion (CARA) preference or Decreasing AbsoluteRisk Aversion (DARA) preference with Rr (x) ≤ 1 whereRr (x) = −u′′(x)x/u′(x).



Actuarially Fair Crop InsuranceEffects on the allocation to the “risky” crop

By treating insurance coverage, θ, as an exogenous variable, I obtainProposition 2a and 2b.

Proposition 2aCARA and DARA preferences are sufficient for the positive actuariallyfair crop insurance effect on the “risky” crop investment (likeHennessy 1998).

Proposition 2bThe increase in the rate of return from the “safe” crop investmentreduces the actuarially fair crop insurance effect on “risky” cropinvestment if the farmers have CARA preference or DARA withRr (x) ≤ 1.


Conceptual model Premium Subsidy

Premium SubsidyInsurance Demand

Now, the premium becomes π(1− γ).

Farmers who satisfy the following condition only purchase insurancewith the premium subsidy γ:

sπ(1− γ)Eu′(x |θ=0) < Eu′(x |θ=0)I (r) < sπEu′(x |θ=0).

Thus, the minimum effective premium subsidy is

γ > γT = sπ − Eu′(x |θ=0)I (r)

Eu′(x |θ=0).



Premium SubsidyEffects on the allocation to the “risky” crop

The premium subsidy effect can be decomposed into1) encouragement effect and 2) relative profitability effect:

∂Kr

∂γ=

(1− ∂Kr

∂θ

∂θ

∂Kr

)−1

∂Kr

∂θ

∂θ

∂γ Kr constant︸︷︷︸Encouragement Effect

+∂Kr

∂γ θ constant︸︷︷︸Relative Profitability Effect

.



Premium SubsidyEffects on the allocation to the “risky” crop - Encouragement Effect

Kr

Ks

Kr =K0−Ks

(1+θ0π)

A

I0



Premium SubsidyEffects on the allocation to the “risky” crop - Encouragement Effect

Kr

Ks

Kr =K0−Ks

(1+θ1π(1−γ))

Kr =K0−Ks

(1+θ0π)

A

I0

I ′1

B

I1



Premium SubsidyEffects on the allocation to the “risky” crop - Relative Profitability Effect

Kr

Ks

Kr =K0−Ks

(1+θπ)

A

I0



Premium SubsidyEffects on the allocation to the “risky” crop - Relative Profitability Effect

Kr

Ks

Kr =K0−Ks

(1+θπ(1−γ))

Kr =K0−Ks

(1+θπ)

C

A

I0

I ′0



Premium SubsidyPositive Effects on the Allocation to the “Risky” Crop

Proposition 3aCARA or DARA with Rr (x) ≤ 1 is sufficient for ∂Kr

∂θ∂θ∂γKr constant

> 0

(encouragement effect).

Proposition 3bCARA or DARA preference are sufficient for ∂Kr

∂γ θ constant> 0

(relative profitability effect).


Conclusions

Conclusions

The rate of return from the “safe” crop investment is crucial forboth insurance demand and the effect on the allocation to the“risky” crop.

The premium subsidies affect the allocation to the “risky” cropby encouraging farmers to purchase insurance and making thesubject crop more lucrative.
