Shallow-loss policies take center-stage in many proposals for the current Farm Bill. We examine the choice of deductible coverage vs. coinsurance to show risk premiums and loss adjustment costs matter little when comparing policies. Thus, policy makers should base decisions more on costs to taxpayers than specific risk management features

Cooper, Joseph C.

Sproul, Thomas W.

Zilberman, David

English

DigitalCommons@URI

University of Rhode IslandDigitalCommons@URIEnvironmental and Natural Resource EconomicsFaculty Publications Environmental and Natural Resource Economics2013Deductibles vs. Coinsurance in Shallow-Loss CropInsuranceThomas W. SproulUniversity of Rhode Island, sproul@uri.eduDavid ZilbermanSee next page for additional authorsFollow this and additional works at: https://digitalcommons.uri.edu/enre_facpubsThe University of Rhode Island Faculty have made this article openly available.Please let us know how Open Access to this research benefits you.This is a pre-publication author manuscript of the final, published article.Terms of UseThis article is made available under the terms and conditions applicable towards Open Access PolicyArticles, as set forth in our Terms of Use.This Article is brought to you for free and open access by the Environmental and Natural Resource Economics at DigitalCommons@URI. It has beenaccepted for inclusion in Environmental and Natural Resource Economics Faculty Publications by an authorized administrator ofDigitalCommons@URI. For more information, please contact digitalcommons@etal.uri.edu.Citation/Publisher AttributionSproul, T.W., D. Zilberman, and J.C. Cooper. 2013. "Deductibles versus Coinsurance in Shallow-Loss Crop Insurance". Choices.Quarter 3. Available online: http://choicesmagazine.org/choices-magazine/theme-articles/current-issues-in-risk-management-and-us-agricultural-policy/deductibles-versus-coinsurance-in-shallow-loss-crop-insuranceAvailable at: http://choicesmagazine.org/choices-magazine/theme-articles/current-issues-in-risk-management-and-us-agricultural-policy/deductibles-versus-coinsurance-in-shallow-loss-crop-insuranceAuthorsThomas W. Sproul, David Zilberman, and Joseph C. CooperThis article is available at DigitalCommons@URI: https://digitalcommons.uri.edu/enre_facpubs/42	 Page	1	of	11	Deductibles	vs.	Coinsurance	in	Shallow-Loss	Crop	Insurance		Thomas	W.	Sproul,	David	Zilberman,	and	Joseph	C.	Cooper		Abstract	Shallow-loss	 policies	 take	 center-stage	 in	 many	 proposals	 for	 the	 current	Farm	Bill.	We	examine	the	choice	of	deductible	coverage	vs.	coinsurance	to	show	risk	premiums	and	loss	adjustment	costs	matter	little	when	comparing	policies.	 Thus,	 policy	 makers	 should	 base	 decisions	 more	 on	 costs	 to	taxpayers	than	specific	risk	management	features.		JEL	Classifications:	Q14,	Q18		 		 Page	2	of	11	Since	the	advent	of	the	Supplemental	Revenue	Assistance	Program	(SURE)	as	a	free	supplement	to	crop	insurance	in	the	2008	Farm	Bill,	shallow-loss	policies	have	become	an	area	of	increasing	focus	in	the	farm	safety	net.	These	policies	provide	coverage	for	smaller	revenue	losses	in	the	range	where	revenues	remain	higher	than	the	guarantee	provided	by	crop	revenue	insurance,	and	are	more	politically	palatable	than	direct	payments	in	times	of	record-high	farm	revenues.	While	SURE	is	history	(Smith	and	Hewlett,	2013),	debate	continues	in	Congress	over	a	range	of	policy	alternatives	including	deductible	and	coinsurance-style	revenue	insurance,	area	coverage,	whole	farm	vs.	single	crop,	and	even	price	supports,	all	of	which	are	heavily	subsidized	(CRS,	2012).		 With	so	many	alternative	insurance	policies	proposed	for	the	new	farm	safety	net,	it	is	easy	to	assume	that	the	exact	risk-management	features	of	each	policy	should	drive	the	discussion.	This	is	not	the	case.	Using	the	deductible	vs.	coinsurance	choice	as	a	motivating	example,	we	find	that	both	risk	premiums	and	changes	in	loss	adjustment	costs	are	economically	insignificant	across	a	broad	range	of	shallow-loss	policies,	crops,	and	counties,	relative	to	differences	in	the	expected	value	of	claims	payments.	This	result	is	driven	largely	by	the	nature	of	shallow-loss	policies,	which	act	on	smaller,	more	frequent	claims	around	the	peak	of	the	revenue	distribution.	Thus,	our	research	suggests	that	policy	specifics	can	be	ignored	if	they	do	not	materially	affect	the	level	of	claims	payments,	and	policy	makers	should	focus	almost	exclusively	on	the	expected	cost	of	proposed	shallow-loss	programs.	We	do	not,	however,	address	distributional	issues	of	which	constituencies	are	the	primary		 Page	3	of	11	recipients	of	subsidies.	Differences	in	the	House	and	Senate	bills	along	these	lines	are	discussed	in	detail	in	Smith	et	al.	(2012).		Deductibles	vs.	Coinsurance	We	motivate	the	discussion	by	focusing	on	the	choice	of	deductible	vs.	coinsurance	policy	because	this	choice	leads	to	changes	in	both	risk	characteristics	and	claims	adjusting	costs,	even	when	expected	claims	payments	are	held	constant.	It	has	been	well	known	by	economists	since	at	least	the	1960s	that	a	risk-averse	decision	maker	will	strictly	prefer	deductible	insurance	to	coinsurance	when	the	two	policies	have	the	same	expected	value	of	payments	and	the	same	premium.	Figure	1	compares	the	cumulative	distribution	of	revenues	under	deductible	insurance	and	a	coinsurance	of	the	same	fair	value;	since	the	outcomes	under	coinsurance	are	more	spread	out	to	the	downside,	the	coinsurance	policy	exposes	the	policyholder	to	additional	risk	relative	to	a	deductible.	The	risk	premium	is	then	defined	as	the	amount	of	higher	expected	value,	in	terms	of	claims	payments,	that	the	coinsurance	policy	must	provide	to	attain	indifference	between	the	two	policies.	This	comparison	applies	to	shallow-loss	crop	insurance	policies	as	well,	which	are	generally	written	“stacked”	on	top	of	an	underlying	deductible	coverage.		 For	example,	consider	a	farmer	who	takes	the	standard	crop	insurance	with	a	guarantee	of	80%	of	mean	revenues	per	acre.		This	arrangement	would	provide	dollar-for-dollar	payments	for	losses	below	the	80%	threshold.	If	we	choose	parameters	similar	to	the	original	SURE	policy	and	ignore	the	disaster	component,	we	would	have	a	coinsurance	policy	with	a	shallow-loss	coverage	threshold	at	90%	of	mean	revenues,	and	with	a	60%	reimbursement	rate.	In	the	insurance	literature,		 Page	4	of	11	this	policy	would	be	identified	as	carrying	40%	coinsurance,	which	is	the	insured	party’s	share	of	the	loss.	The	policy	would	pay	sixty	cents	for	every	dollar	of	losses	below	the	90%	threshold,	down	to	the	80%	threshold	where	the	standard	crop	insurance	kicks	in.	In	contrast,	the	farmer	may	view	a	shallow-loss	deductible	policy	with	an	86%	threshold	as	equally	appealing,	or	indifferent.	The	deductible	policy	pays	dollar-for-dollar	losses	below	86%	of	mean	revenues,	effectively	just	increasing	the	crop	insurance	guarantee.	The	indifferent	deductible	threshold	will	always	be	lower	than	the	coinsurance	threshold,	but	its	exact	level	will	depend	on	the	farmer’s	risk	aversion.	For	winter	wheat	farmers	with	moderate	risk	aversion	in	Hyde	County,	South	Dakota,	we	estimate	that	the	expected	value	of	claims	payments	is	$17.23	per	acre	under	the	coinsurance	program	above,	but	only	$17.22	under	the	indifferent	deductible	program	with	86%	threshold,	so	the	risk	premium	is	$0.01	per	acre.	Figure	1:	Effect	of	Deductible	and	Coinsurance	on	the	Cumulative	Distribution	of	Revenues			 Page	5	of	11		 The	deductible	vs.	coinsurance	choice	also	affects	the	size	and	frequency	of	claims,	which	may	affect	the	administrative	costs	associated	with	claims	payments.	When	comparing	insurance	policies	of	equal	expected	value,	the	coinsurance	guarantee	must	be	higher	than	the	deductible	guarantee,	so	switching	from	deductible	to	coinsurance	will	lead	to	more	frequent	claims	of	smaller	size.	A	well-known	model	for	claims	adjustment	costs	(Raviv,	1979)	includes	a	fixed	cost	per	claim,	a	variable	cost	based	on	the	size	of	the	claims	payment,	and	possibly,	returns	to	scale.		Thus,	whether	the	change	from	deductible	to	coinsurance	will	lead	to	higher	loss	adjustment	costs	depends	on	the	exact	cost	structure	of	the	insurer.			Estimating	the	Distribution	of	Revenues	Per	Acre	To	evaluate	these	tradeoffs,	we	started	by	estimating	probability	distributions	of	per	acre	revenues	for	representative	farmers	of	various	crops	in	a	number	of	U.S.	counties.	County-level	and	national-level	yield	data	are	drawn	from	the	National	Agricultural	Statistical	Service	(NASS)	for	the	period	1975-2011,	and	expected	and	realized	prices	are	taken	from	grain	futures	prices,	according	to	USDA	Risk	Management	Agency	(RMA)	definitions.	We	used	copula	methods	to	estimate	the	joint	distribution	of	yields	and	prices	at	the	county	level,	following	Cooper,	Delbecq,	and	Davis	(2012),	and	to	forecast	the	empirical	distribution	for	the	2012	crop	year,	just	following	the	final	year	of	the	dataset.	Farm-level	conditions	are	represented	by	adding	Gaussian	white	noise	to	inflate	the	standard	deviation	of	county-level	yields	until	it	matches	RMA-calculated	fair	premiums	for	the	2012	crop	year	(following		 Page	6	of	11	Coble	and	Dismukes,	2008).	A	sample,	per-acre	gross	revenue	distribution	for	winter	wheat	in	Hyde	County,	South	Dakota,	is	shown	in	Figure	2.		Figure	2:	Kernel	Density	of	the	Empirical	Revenue	Distribution	for	Winter	Wheat,	Hyde	County,	S.D.		Policy	Indifference	and	Risk	Premiums	We	identify	 indifferent	policies	using	an	exponential	utility	 function	of	wealth	and	the	full	range	of	reasonable	risk	aversion	coefficients,	as	identified	in	Babcock,	Choi,	and	 Feinerman	 (1993).	 For	 each	 risk	 aversion	 coefficient,	 we	 used	 a	 numerical	optimization	 procedure	 to	 identify	 the	 deductible	 guarantee	 that	 makes	 the	representative	farmer	indifferent	to	the	coinsurance	parameters	of	SURE.	We	found	that	the	indifferent	deductible	guarantee	was	quite	stable,	often	varying	by	less	than	0.1%	of	mean	revenues	across	most	of	the	range	of	risk	aversion	coefficients	when	baseline	coverage	was	70%	or	above,	and	by	less	than	0.2%	at	extreme	levels	of	risk	aversion.			 Page	7	of	11		 Estimated	 risk	 premiums	 were	 stable	 as	 well,	 and	 small.	 For	 nearly	 all	combinations	 of	 crop,	 county,	 underlying	 coverage,	 and	 risk	 aversion,	 risk	premiums	were	estimated	 to	be	 less	 than	$0.15	per	acre,	and	 in	many	cases	were	less	 than	 $0.05	 per	 acre.	 These	 values	 are	 economically	 insignificant	 when	compared	to	 insurance	policies	with	fair	values	ranging	from	$10	up	to	$100+	per	acre	 in	 some	 high	 revenue	 corn	 counties.	 The	maximum	 risk	 premium	 estimated	was	$0.19	per	acre	 for	DeKalb,	 IL,	where	per	acre	revenues	were	$974.44	and	the	90/60	coinsurance	policy	had	a	fair	value	of	$48.31.	Table	1	below	shows	estimated	means	 and	 standard	 deviations	 of	 revenues	 for	 select	 crops/counties,	 and	 the	highest	 risk	 premium	estimated.	 The	highest	 risk	 premiums	were	 observed	when	risk	aversion	was	sufficient	to	turn	down	a	$100	gamble	with	3:1	odds	of	winning.	Table	1:	Means,	Standard	Deviations	and	Maximum	Risk	Premiums	Estimated,	Select	Counties	and	Crops	County	 Crop	 Mean	 Std.	Dev.	 Max	Risk	Premium	DeKalb,	IL	 Corn	 $974.44		 $304.25		 $0.19		McLean,	IL	 Corn	 $1,009.80		 $202.87		 $0.17		Howard,	NE	 Corn	 $905.61		 $449.42		 $0.13		Beadle,	SD	 Corn	 $619.02		 $319.81		 $0.06		Montgomery,	MS	 Cotton	 $942.76		 $512.72		 $0.13		Hoke,	NC	 Cotton	 $850.92		 $364.65		 $0.12		Howard,	TX	 Cotton	 $373.59		 $373.89		 $0.01		Logan,	IL	 Soy	 $697.53		 $198.33		 $0.11		Sumner,	KS	 Soy	 $395.42		 $306.86		 $0.02		Sanilac,	MI	 Soy	 $570.16		 $256.83		 $0.06		Logan,	KY	 Winter	Wheat	 $470.77		 $248.70		 $0.04		Marion,	OH	 Winter	Wheat	 $449.92		 $165.73		 $0.04		Hyde,	SD	 Winter	Wheat	 $225.34		 $74.48		 $0.03					 Page	8	of	11	Loss	Adjustment	Expenses	We	obtained	crop	insurance	performance	data	from	the	RMA	Summary	of	Business	for	years	1995-2010.	These	data	included	premiums,	indemnities,	and	number	of	units	with	claims	by	crop,	county,	coverage	level	and	year,	for	all	U.S.	counties.	We	also	obtained	a	crop	insurance	industry	report,	the	2011	Grant-Thornton	Report,	which	uses	a	survey	of	U.S.	crop	insurers	to	estimate	loss	adjustment	expenses	as	a	percentage	of	gross	premiums	(also	for	1995-2010).	Loss-adjustment	expenses	were	only	available	on	a	national	aggregate	basis,	so	we	aggregated	the	RMA	data	and	combined	the	two	into	a	simple	regression	model	estimating	the	structure	of	loss	adjustment	costs,	as	described	above.			 The	model	performed	quite	well.	At	a	99%	significance	level,	we	estimated	per-claim	fixed	costs	of	$132.41,	variable	costs	of	4.39%	of	indemnity	payments,	and	returns	to	scale	of	0.025	cents	per	claim,	on	a	national	scale.	Given	estimated	distributions	of	per	acre	revenues,	these	results	can	be	used	to	estimate	expected	savings	(or	costs)	from	switching	between	deductible	and	coinsurance	shallow-loss	coverage.	Variable	costs	will	be	identical	for	two	policies	with	the	same	fair	value,	so	comparing	deductibles	vs.	coinsurance	means	assessing	fixed	costs	saved	against	lost	economies	of	scale.		We	will	use	our	estimated	data	for	wheat	in	Hyde	County,	South	Dakota,	as	a	back-of-the-envelope	example.	Before	adjusting	for	claims	frequency,	fixed	costs	average	$1.64	per	acre	per	claim,	while	economies	of	scale	average	$1.86	per	acre	per	claim	when	counting	only	the	599K+	insured	units	of	farmed	wheat	in	the	United	States,	and	using	an	average	of	80.67	acres	per	insured	unit.	Transition	from		 Page	9	of	11	our	example	coinsurance	policy	with	SURE	parameters	to	a	deductible	policy	of	equal	fair	value	actually	results	in	higher	claims	costs,	though	they	are	tiny	(about	$0.002	per	acre).	The	higher	costs	arise	because	lost	returns	to	scale	outweigh	the	savings	of	fixed	costs,	when	comparing	larger	claims	under	a	deductible	policy	against	smaller,	more	frequent	claims	under	a	coinsurance	policy.		 	As	with	the	risk	premium	differences	estimated	above,	these	values	are	economically	insignificant,	even	when	extended	to	policies	with	different	expected	values	of	claims	payments.	If	we	consider	an	89%	shallow-loss	deductible	guarantee	with	base	coverage	at	80%,	it	has	an	expected	value	$2.11	per	acre	higher	than	our	sample	90/60	coinsurance	policy.	In	this	scenario,	the	higher	expected	value	of	payments	will	lead	to	higher	variable	loss	adjustment	costs,	averaging	$0.033	per	acre.	So,	while	variable	costs	are	likely	their	largest	component,	any	changes	in	loss	adjustment	costs	are	likely	to	be	dwarfed	by	increases	in	expected	claims	payments.		What	Next?	As	we	witness	the	continued	transition	of	the	farm	safety	net	away	from	direct	payments	and	towards	subsidized	insurance-style	products	like	shallow-loss	policies,	it	is	important	to	remember	that	risk	management	may	not	be	the	primary	concern	driving	these	innovations.	This	article	has	presented	evidence	that	farmers	are	not	likely	to	care	about	the	exact	risk	management	characteristics	of	shallow-loss	crop	insurance,	and	that	efficiency	gains	from	saved	loss	adjustment	expenses	are	not	likely	to	arise	from	subtle	differences	between	policies.	Thus,	shallow-loss		 Page	10	of	11	policies	can	be	judged	almost	exclusively	on	the	expected	value	of	claims	and	subsidy	payments.		For	More	Information:		Babcock,	B.,	Choi,	E.,	and	Feinerman,	E.	(1993).	Risk	and	Probability	Premiums	for	CARA	 Utility	 Functions.	 Journal	 of	 Agricultural	 and	Resource	 Economics,	 18(1),	17-24.		Coble,	 K.,	 and	 Dismukes,	 R.	 (2008).	 Distributional	 and	 Risk	 Reduction	 Effects	 of	Commodity	Revenue	Program	Design.	Review	of	Agricultural	Economics,	30,	543-553.			Cooper,	J.C.,	Delbecq,	B.,	and	Davis,	C.	Fiscal	and	Farm	Level	Consequences	of	‘Shallow	Loss’	Commodity	Support	Programs.	 Presented	 as	 a	 Selected	 Paper	 in	 the	 2012	AAEA	Annual	Meeting,	Seattle,	WA,	August	12-14,	2012.		Raviv,	A.	(1979).	The	Design	of	an	Optimal	Insurance	Policy.	The	American	Economic	Review,	69(1),	84-96.		Shields,	D.A.,	and	Schnepf,	R.	(2012).	CRS	Report	R42040:	Farm	Safety	Net	Proposals	in	the	112th	Congress,	a	Report	of	the	Congressional	Research	Service.			Smith,	 V.	 H.,	 Babcock,	 B.,	 and	 Goodwin,	 B.	 (2012).	 Field	 of	 Schemes	Mark	 II:	 The	Taxpayer	 and	 Economic	 Welfare	 Costs	 of	 Price	 Loss	 Coverage	 and	Supplementary	 Insurance	Coverage	Programs.	Working	paper	#2012-03	 in	 the	American	 Enterprise	 Institute	 for	 Public	 Policy	 Research	 Series	 “American	Boondoggle:	Fixing	the	2012	Farm	Bill.”		Smith,	V.H.,	and	Hewlett,	J.P.	(2013).	Farm	Policy	and	Disaster	Aid	Programs:	The	Path	Looking	Forward.	Choices,	28(1).			Author	Information/Acknowledgements:		Thomas	W.	Sproul	(sproul@mail.uri.edu)	is	Assistant	Professor,	Department	of	Environmental	&	Resource	Economics,	at	the	University	of	Rhode	Island.	David	Zilberman	is	Professor	and	holds	the	Robinson	chair	in	the	Department	of	Agricultural	&	Resource	Economics	at	the	University	of	California,	Berkeley.	Joseph	C.	Cooper	is	Chief	of	the	Agricultural	Policy	and	Models	Branch,	Market	and	Trade	Economics	Division,	at	the	U.S.	Department	of	Agriculture	Economic	Research	Service.				 Page	11	of	11	The	authors	would	like	to	thank	the	members	of	the	AAEA	Annual	Meeting	sessions,	the	SCC-76	Risk	Group	Annual	Meeting	sessions,	guest	editor,	Joshua	Woodard,	and	an	anonymous	reviewer	for	their	insightful	feedback.		We	are	grateful	for	research	support	from	USDA	Cooperative	Research	Agreement	No.	58-3000-8-0069	and	USDA-NIFA	Hatch	Project	Number	RI00H-108.	The	views	expressed	herein	are	those	of	the	authors	and	not	necessarily	those	of	the	Economic	Research	Service	or	the	USDA.	Of	course,	any	errors	or	omissions	are	our	own.					

Deductibles vs. Coinsurance in Shallow-Loss Crop Insurance

https://digitalcommons.uri.edu/cgi/viewcontent.cgi?article=1042&amp;context=enre_facpubs

Deductibles vs. Coinsurance in Shallow-Loss Crop Insurance

Abstract

Similar works

Full text

Available Versions

DigitalCommons@URI