Subsidized Crop Insurance under Limited Access to Incomplete Financial Markets

Daniel C. Voica

doi:10.1515/bejeap-2021-0073

Published by De Gruyter November 29, 2022

Subsidized Crop Insurance under Limited Access to Incomplete Financial Markets

Daniel C. Voica

From the journal The B.E. Journal of Economic Analysis & Policy

https://doi.org/10.1515/bejeap-2021-0073

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Abstract

Almost universally, crop insurance uptake has been very low in the absence of significant governmental subsidies. We proposed an explanation for the low uptake by analyzing farmers’ optimal behavior in the presence of subsidized crop insurance and incomplete financial markets. Under specific replication conditions, farmers’ valuation of crop insurance is lower than insurers’ valuation if farmers have access to fewer financial assets than insurers. A potential rationalization is that farmers and insurers have dissimilar price formation processes. Our model implies that subsidized crop insurance changes farmers’ production choices by altering both the relative returns across states of Nature and their risk choices. However, because of the separation between consumption and production decisions, farmers will use crop insurance in a manner consistent with profit maximization, independent of risk preferences.

Keywords: uncertainty; portfolio analysis; incomplete financial markets

JEL Classification: D21; D81; G11

Corresponding author: Daniel C. Voica, School of Economics and Finance, Massey University, Palmerston North, New Zealand, E-mail: d.voica@massey.ac.nz

Acknowledgments

I thank two anonymous reviewers and the editor, Frans de Vries, for comments that greatly improved my work. I also thank Robert G. Chambers, Sue Cassells, Martin Berka, Reece Pomeroy, and conference and seminar participants at AAEA 2018, Massey University, and North Dakota State University for valuable feedback.

Appendix A

In this Appendix, we provide a proof for the pricing of insurance contract I in expression (19). For convenience, expression (19) is reproduced below.

(19′) WTP F = v F T P F ( I − ζ ) = v T P ( I − ζ ) < v T P I < v T P ( I + ε ) = WTS I

By assumption, insurers can access J < S assets (i.e. financial markets are incomplete), and farmers can access K < J financial assets. The insurer’s financial opportunities can be represented by the linear subspace, M ⊂ R Ω , spanned by the column vectors of the matrix A, where M is defined by

M = { y ∈ R Ω : A h = y , h ∈ R J }

Any contract I that falls in M can be replicated and priced in the financial market by insurers (e.g. this corresponds to case where the insurers value I in period 0 at PI). Similarly, the farmer’s financial opportunities subspace M F is defined as

M F = y ∈ R Ω : A F h F = y , h F ∈ R K

Any contract that falls in M F can be replicated and priced by the K financial assets, but since M F ⊆ M , it can also be replicated and priced in M . The reverse is not always true. The farmer may not be able to replicate contracts that fall in M \ M F . These risks fall in the orthogonal complement of M F , M F ⊥ . If the contract I falls outside the farmer’s market span M F , which is a closed subspace of M , then by Hilbert Projection Theorem, there exits a unique I F ∈ M F such that I = I _F + (I − I _F) and I − I F ∈ M F ⊥ .^[20] In words, I _F is the orthogonal projection of I onto M F and it is determined as the Least Square Estimate of I

(24) I F = A F P F I

from where it follows that

(25) I − I F = I − A F P F I = ( 1 Ω − A F P F ) I

where 1_Ω is the Ω dimensional identity matrix and P F = A F T A F − 1 A F T . Observe that P _F(I − I _F) = P _F(1_Ω − A _F P _F)I = 0 because P _F A _F = 1_Ω. Thus, the farmer’s period 0 valuation of I in M F is

(26) v F T P F I = v F T P F I F + v F T P F ( I − I F ) = v F T P F I F

The stochastic discount factor used by the farmer to price I in M F , v F T P F , is different than the stochastic discount factor used to price I in M , v ^T P. Also, only the orthogonal projection of I on M F , I _F, is actually priced. Recycling previous arguments, the period 0 value of the I in M is

(27) v T P I = v T P ( I F + ( I − I F ) ) = v F T P F I F + v T P ( I − I F ) > v F T P F I F

which says that the market valuation of I in M is higher than what the farmer is willing to pay for it in M F .^[21] Thus, without government intervention, no trade is possible because the farmer’s willingness to pay for I is lower than the insurers’ willingness to sell.

In our paper, I _F corresponds to I − ζ and I − I _F to ζ. This also covers the case when the contract I cannot be replicated by insurers in M and their valuation of insurance is v ^T P(I + ɛ).

References

Anderson, R. W., and J.-P. Danthine. 1983. “The Time Pattern of Hedging and the Volatility of Futures Prices.” The Review of Economic Studies 50 (2): 249–66. https://doi.org/10.2307/2297415.Search in Google Scholar

Arrow, K. 1964. “The Role of Securities in the Optimal Allocation of Risk-Bearing.” The Review of Economic Studies 31: 91–6. https://doi.org/10.2307/2296188.Search in Google Scholar

Babcock, B. A. 2016. Crop Insurance. A Lottery That’s a Sure Bet. The Environmental Working Group. Also available at https://www.ewg.org/research/crop-insurance-lottery (accessed September 26, 2020).Search in Google Scholar

Barnett, B. J. 2000. “The U.S. Federal Crop Insurance Program.” Canadian Journal of Agricultural Economics 48 (4): 539–51. https://doi.org/10.1111/j.1744-7976.2000.tb00409.x.Search in Google Scholar

Brown, J. P., and J. Weber. 2013. “The Off-Farm Occupations of U.S. Farm Operators and Their Spouses.” In USDA-ERS Economic Information Bulletin No. 117.Search in Google Scholar

Bulut, H. 2017. “Managing Catastrophic Risk in Agriculture through Ex Ante Subsidized Insurance or Ex Post Diaster Aid.” Journal of Agricultural and Resource Economics 42 (3): 406–26.Search in Google Scholar

Carter, M., A. de Janvry, E. Sadoulet, and A. Sarris. 2017. “Index Insurance for Developing Country Agriculture: A Reassessment.” Annual Review of Resource Economics 9: 421–38. https://doi.org/10.1146/annurev-resource-100516-053352.Search in Google Scholar

Chambers, R. G. 1989. “Insurability and Moral Hazard in Agricultural Insurance Markets.” American Journal of Agricultural Economics 71 (3): 604–16. https://doi.org/10.2307/1242016.Search in Google Scholar

Chambers, R. G., and J. Quiggin. 2000. Uncertainty, Production, Choice, and Agency. Cambridge: Cambridge University Press.Search in Google Scholar

Chambers, R. G., and J. Quiggin. 2009. “Separability of Stochastic Production Decisions from Producer Risk Preferences in the Presence of Financial Markets.” Journal of Mathematical Economics 45: 730–7. https://doi.org/10.1016/j.jmateco.2009.05.011.Search in Google Scholar

Chambers, R. G., and D. C. Voica. 2017. “Decoupled Farm Programs Payments Are Really Decoupled: The Theory.” American Journal of Agricultural Economics 99 (3): 773–82, https://doi.org/10.1093/ajae/aaw044.Search in Google Scholar

Connor, L., and A. L. Katchova. 2020. “Crop Insurance Participation Rates and Asymmetric Effects on U.S. Corn and Soybean Yield Risk.” Journal of Agricultural and Resource Economics 45 (1): 1–19.Search in Google Scholar

Danthine, J.-P. 1978. “Information, Futures Prices, and Stabilizing Speculation.” Journal of Economic Theory 17 (1): 79–98. https://doi.org/10.1016/0022-0531(78)90124-2.Search in Google Scholar

Debreu, G. 1959. Theory of Value. New Haven: Yale University Press.Search in Google Scholar

Du, X., H. Feng, and D. A. Hennessy. 2017. “Rationality of Choices in Subsidized Crop Insurance Markets.” American Journal of Agricultural Economics 99 (3): 732–57. https://doi.org/10.1093/ajae/aaw035.Search in Google Scholar

Du, X., J. Ifft, L. Lu, and D. Zilberman. 2015. “Marketing Contracts and Crop Insurance.” American Journal of Agricultural Economics 97 (5): 1360–70. https://doi.org/10.1093/ajae/aav024.Search in Google Scholar

Electronic Code of Federal Regulations, U. S. 2020. Title 17 Commodity and Securities Exchanges. Also available at https://www.ecfr.gov (accessed April 21, 2020).Search in Google Scholar

Feng, H., X. Du, and D. A. Hennessy. 2020. “Depressed Demand for Crop Insurance Contracts, and a Rationale Based on Third Generation Prospect Theory.” Agricultural Economics 51: 59–73. https://doi.org/10.1111/agec.12541.Search in Google Scholar

Foreign Intelligence, U. S. 1851. “Crop Insurance Participation Rates and Asymmetric Effects on U.S. Corn and Soybean Yield Risk.” Journal of the Institute of Actuaries 1 (2): 78–81. https://doi.org/10.1017/S2046164X00054909.Search in Google Scholar

Ghosh, R. K., S. Gupta, V. Singh, and P. S. Ward. 2021. “Demand for Crop Insurance in Developing Countries: New Evidence from India.” Journal of Agricultural Economics 72 (1): 293–320. https://doi.org/10.1111/1477-9552/12403.Search in Google Scholar

Giné, X., and D. Yang. 2009. “Insurance, Credit, and Technology Adoption: Field Experimental Evidence from Malawi.” Journal of Development Economics 89 (1): 1–11. https://doi.org/10.1016/j.jdeveco.2008.09.007.Search in Google Scholar

Goodwin, B. K. 1993. “An Empirical Analysis of the Demand for Multiple Peril Crop Insurance.” American Journal of Agricultural Economics 75 (2): 425–34. https://doi.org/10.2307/1242927.Search in Google Scholar

Goodwin, B. K. 2001. “Problems with Market Insurance in Agriculture.” American Journal of Agricultural Economics 83 (3): 643–9. https://doi.org/10.1111/0002-9092.00184.Search in Google Scholar

Goodwin, B. K., and V. H. Smith. 2013. “What Harm is Done by Subsidizing Crop Insurance?” American Journal of Agricultural Economics 95 (2): 489–97. https://doi.org/10.1093/ajae/aas092.Search in Google Scholar

Halcrow, H. G. 1949. “Actuarial Structures for Crop Insurance.” Journal of Farm Economics 31 (3): 418–43, https://doi.org/10.2307/1232330.Search in Google Scholar

Hazell, P., C. Pomareda, and A. Valdes. 1986. Crop Insurance for Agricultural Development: Issues and Experience. Baltimore: Johns Hopkins University Press.Search in Google Scholar

Hennessy, D. A. 1998. “The Production Effects of Agricultural Income Support Policies under Uncertainty.” American Journal of Agricultural Economics 80: 46–57. https://doi.org/10.2307/3180267.Search in Google Scholar

Holthausen, D. M. 1979. “Hedging and the Competitive Firm Under Price Uncertainty.” The American Economic Review 69 (5): 989–95.Search in Google Scholar

Just, R. E., L. Calvin, and J. Quiggin. 1999. “Adverse Selection in Crop Insurance: Actuarial and Asymmetric Information Incentives.” American Journal of Agricultural Economics 81 (4): 834–49. https://doi.org/10.2307/1244328.Search in Google Scholar

Kramer, R. A. 1983. “Federal Crop Insurance.” Agricultural History 57 (2): 181–200.Search in Google Scholar

Luenberger, D. G. 1969. Optimization by Vector Spaces Methods. New York: John Willey and Sons.Search in Google Scholar

Machina, M. J. 1982. “‘Expected Utility’ Analysis without the Independence Axiom.” Econometrica 50: 277–323, https://doi.org/10.2307/1912631.Search in Google Scholar

Magill, M., and M. Quinzii. 1996. Theory of Incomplete Markets. Cambridge: MIT Press.Search in Google Scholar

Mahul, O., and C. J. Stutley. 2010. Government Support to Agricultural Insurance: Challenges and Opportunities for Developing Countries. Washington, DC: The World Bank.10.1596/978-0-8213-8217-2Search in Google Scholar

Makki, S. S., and A. Somwaru. 2001. “Farmer’s Participation in Crop Insurance Markets: Creating the Right Incentives.” American Journal of Agricultural Economics 83 (3): 662–7. https://doi.org/10.1111/0002-9092.00187.Search in Google Scholar

Miranda, M. J. 1991. “Area-Yield Crop Insurance Reconsidered.” American Journal of Agricultural Economics 73 (2): 233–42. https://doi.org/10.2307/1242708.Search in Google Scholar

Miranda, M. J., and K. Farrin. 2012. “Index Insurance for Developing Countries.” Applied Economic Perspectives and Policy 34 (3): 391–427. https://doi.org/10.1093/aepp/pps031.Search in Google Scholar

Miranda, M. J., and J. W. Glauber. 1997. “Systemic Risk, Reinsurance, and the Failure of Crop Insurance Markets.” American Journal of Agricultural Economics 79 (1): 206–15. https://doi.org/10.2307/1243954.Search in Google Scholar

Mishra, A. K., and M. J. Morehart. 2001. “Off-Farm Investment of Farm Households: A Logit Analysis.” Agricultural Finance Review 61 (1): 87–101. https://doi.org/10.1108/00214770180001118.Search in Google Scholar

Nelson, C. H., and E. T. Loehman. 1987. “Further Toward a Theory of Agricultural Insurance.” American Journal of Agricultural Economics 69 (3): 523–31. https://doi.org/10.2307/1241688.Search in Google Scholar

Nixon, R. 2012. Crop Insurance Proposal Could Cost U.S. Billions. The New York Times. Also available at https://nyti.ms/L3kEHe (accessed August 23, 2018).Search in Google Scholar

Quiggin, J. 1992. “Some Observations on Insurance, Bankruptcy and Input Demand.” Journal of Economic Behavior & Organization 18: 101–10. https://doi.org/10.1016/0167-2681(92)90055-g.Search in Google Scholar

Risk Management Agency. 2021. History of the Crop Insurance Program. Also available at https://legacy.rma.usda.gov/aboutrma/what/history.html (accessed December 5, 2021).Search in Google Scholar

Risk Management Agency, U. S. D. A. 2017. The Risk Management Safety Net: Market Penetration and Market Potential. Also available at https://www.rma.usda.gov/-/media/RMAweb/Publications/Market-Penetration-and-Market-Potential-2017.ashx (accessed April 22, 2020).Search in Google Scholar

Seidman, L. R. 1991. “Sec Rule 144a: The Rule Heard Round the Globe - or the Sounds of Silence?” The Business Lawyer 47 (1): 333–54.Search in Google Scholar

Sjostrom, W. K. 2008. “The Birth of Rule 144a Equity Offerings.” UCLA Law Review 56: 409–49.Search in Google Scholar

Skees, J. R., and M. R. Reed. 1986. “Rate Making for Farm-Level Crop Insurance: Implications for Adverse Selection.” American Journal of Agricultural Economics 68 (3): 653–9. https://doi.org/10.2307/1241549.Search in Google Scholar

Smith, V. H., and J. W. Glauber. 2012. “Agricultural Insurance in Developed Countries: Where Have We Been and where Are We Going?” Applied Economic Perspectives and Policy 34 (3): 363–90. https://doi.org/10.1093/aepp/pps029.Search in Google Scholar

Takahashi, K., M. Ikegami, M. Sheahan, and C. B. Barrett. 2016. “Experimental Evidence on the Drivers of Index-Based Livestock Insurance Demand in Southern Ethiopia.” World Development 78: 324–40. https://doi.org/10.1016/j.worlddev.2015.10.039.Search in Google Scholar

Wang, M., T. Ye, and P. Shi. 2016. “Factors Affecting Farmers’ Crop Insurance Participation in China.” Canadian Journal of Agricultural Economics 64 (3): 479–92. https://doi.org/10.1111/cjag.12088.Search in Google Scholar

Yu, J., A. Smith, and D. A. Sumner. 2018. “Effects of Crop Insurance Premium Subsidies on Crop Acreage.” American Journal of Agricultural Economics 100 (1): 91–114. https://doi.org/10.1093/ajae/aax058.Search in Google Scholar

Yu, J., and D. A. Sumner. 2018. “Effects of Subsidized Crop Insurance on Crop Choices.” Agricultural Economics 49 (4): 533–45. https://doi.org/10.1111/agec.12434.Search in Google Scholar

Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/bejeap-2021-0073).

Received: 2021-02-28

Revised: 2022-11-02

Accepted: 2022-11-03

Published Online: 2022-11-29

Subsidized Crop Insurance under Limited Access to Incomplete Financial Markets

Abstract

Acknowledgments

References

Supplementary Material

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