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
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Effects of Subsidized Crop Insurance on Crop Choices · Introduction Total US Crop Insurance Subsidy is Increasing Total US crop insurance subsidy (million dollars) In 2014, total
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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?
Jisang Yu (UC Davis) Production Effects of Crop Insurance AAEA&WAEA 2015 2 / 19
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.
Jisang Yu (UC Davis) Production Effects of Crop Insurance AAEA&WAEA 2015 3 / 19
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.
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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
Jisang Yu (UC Davis) Production Effects of Crop Insurance AAEA&WAEA 2015 5 / 19
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)
Jisang Yu (UC Davis) Production Effects of Crop Insurance AAEA&WAEA 2015 6 / 19
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.
Jisang Yu (UC Davis) Production Effects of Crop Insurance AAEA&WAEA 2015 7 / 19
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.
Jisang Yu (UC Davis) Production Effects of Crop Insurance AAEA&WAEA 2015 8 / 19
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
Jisang Yu (UC Davis) Production Effects of Crop Insurance AAEA&WAEA 2015 9 / 19
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 .
Jisang Yu (UC Davis) Production Effects of Crop Insurance AAEA&WAEA 2015 10 / 19
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)).
Jisang Yu (UC Davis) Production Effects of Crop Insurance AAEA&WAEA 2015 11 / 19
Conceptual model Actuarially Fair Crop Insurance
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).
Jisang Yu (UC Davis) Production Effects of Crop Insurance AAEA&WAEA 2015 12 / 19
Conceptual model Actuarially Fair Crop Insurance
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.
Jisang Yu (UC Davis) Production Effects of Crop Insurance AAEA&WAEA 2015 13 / 19
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: