Underwriting Area-based Yield
Insurance to Crowd-in Credit
Supply and Demand
Michael R. Carter
University of Wisconsin
The Problem
•
Risk rationing & restricted demand (and its
costs)
Restricted Credit supply (& its costs)
Insurance as solution, but moral hazard &
adverse selection can make standard insurance
(based on individual outcomes) infeasible
Can limited area-based yield insurance against
correlated risk solve credit market problems?
•
•
•
–
–
Should resolve credit supply problem (economic &
political-economic)
But will it help producers?
Outline of Remainder of Talk
1. Illustrate Two Types of Moral Hazard-Proof
Area-based Yield Insurance:
–
–
Based on Measured Average Yields
Based on Estimated Average Yields (weather index)
2. Estimate Benefits to Farmers/borrowers (using
data on rice in Peru’s Lambeyeque Valley)
3. Estimate benefits to lenders
4. Argue that must move results into policy &
practice by superseding past public good failures
Output Risk
1. Average Valley Yields & Sown Area
y t  yˆ ( t )   ty
,
s
ˆ
st  s ( t )   t
where t are measurable random weather-based variables that influence output (e.g,
river flow) and the tj capture residual (immeasurable) variation in valley averages.
2. Individual Yields & Sown Area for producer ‘i’
yit  iy  iy ( yt   y )   ity
,
s
s
s
s
sit  i  i ( st   )   it
where the i and the itj (pure basis risk) determine how closely individual yields
track average valley yields.
3. Estimation
35 year time series on valley information ( t , yt & st )
3 year panel on yit and sit
Estimate prob. dist. for t, functions yˆ and sˆ and parameters of individual yield
relationships
Insurance Contracts
1. Normalized yields
 st 
yt  yt  max
 (based on measured yields and sown area)
s 
ˆ
~yˆ  yˆ  st  (based on estimated yields and sown area: note that this is a
t
t  max 
s 
non-linear weather index)
2. Insurance Contract Structure
Payouts: t  max[0, y c  yt ] , where ~y c is strike/payout point
Actuarially fair premium:   E[ t ]
Insurance Contracts
1. Measured Area Based Yield Insurance:
Payouts based on ~y
Value of insurance to borrower depends on i (i=1 is best) and the
j
pure basis risk (the it )
2. Estimated Area Based Yield Insurance (weather index)
Payouts based on ~ŷ
Value of insurance to borrower depends on i (=1i is best), the pure
basis risk (the itj) and the risk of non-weather based average yield
j
variation (the t ).
Simulating the Value of Actual &
Estimated ARBY Insurance
Net income
Insurance payment
(5has)
Expected Indemnity
With Insurance
(Strike Point 100% of Expected
Yields)
Estimated ARBY
Measured ARBY
(Weather Index)
Mean
Mean
2,601
2,601
547
547
1,932
Consumption
[797]
669
Loan Repayment
[0]
Lending return (%)
21.7
Notes: Standard errors in square brackets.
Average loan: $ 550; Interest rate: 21.7%.
No
Insurance
Mean
2,601
514
0
514
1,945
[990]
656
[77]
19.4
0
1,971
[1276]
631
[118]
14.7
Simulating the Value of Actual &
Estimated ARBY Insurance
Consumption
Lending return (%)
With Insurance
No Insurance
(Strike Point 100% of Expected Yields)
Estimated ARBY
Measured ARBY
(Weather Index)
Mean
Mean
Mean
1,932
1,945
1,971
[797]
[990]
[1276]
21.7
19.4
14.7
Certainty Equivalent under Different Risk Aversion Assumptions
Low Risk Aversion
1904
Mid-Low Risk Aversion
1885
Middle Risk Aversion
1862
Mid-High Risk Aversion
1846
High Risk Aversion
1825
Notes: Standard errors in square brackets.
Average loan: $ 550; Interest rate: 21.7%.
1889
1849
1798
1742
1695
1878
1813
1726
1643
1565
Simulating the Value of Actual &
Estimated ARBY Insurance
Measured ARBY
Certainty
Equivalent ($)
No Insurance
1637
Insurance
Premium
($ per Ha)
0
Insurance Strike Point (% Expected Yield)
1615
11
40%
1670
20
50%
1770
55
75%
1817
86
90%
1843
109
100%
Assumes Mid-High Risk Aversion
Estimated ARBY Insurance
(Weather Index)
Certainty
Insurance
Equivalent ($)
Premium
($ per Ha)
1637
0
1640
1647
1695
1729
1741
5
11
42
75
103
Area-based Yield Insurance Simulation
(% probability of outcome less than indicated amount)
Typical Farmer, Strike Value = 100% mean
80
Cumulative Density
60
40
No Insurance
Insurance with Measured Avg Yields
Insurance with Est Yields (Weather Index)
20
0
0
1000
2000
3000
Income Available for Consumption ($US)
4000
So in Theory, Crowd-in
Credit Supply & Demand
1. Analysis above indicates that:
•
•
•
Substantial reduction in default risk for lenders
When default remains, should be largely idiosyncratic
Should crowd-in credit supply
2. Analysis also indicates that:
•
•
$100 ($200) typical smallholder willingness to pay
for estimated (measured) ARBY insurance above &
beyond the actuarially fair premium
Together with reduction in default risk, should reduce
risk rationing & crowd-in entrepreneurial risk taking
and demand for credit
3. Together imply large social & private returns
Market Failures Follow
Public Good Failures
1. So why is market not providing?
•
•
•
Costs of innovation
Scarcity of reliable data for probability estimates and
measurement of payoff condition
Costs of marketing product to smallholders
2. Note that all of these have a public good element
From Theory to Policy &
Practice
Time to stop wringing hands about past public good
failures and:
1.
2.
Follow example of micro-health insurance and bundle
product with MFI loans
Create a policy trajectory which
•
•
3.
Initially underwrites risk (& parameter uncertainty)
Creates institutions to collect better information and mover
from less to more valuable forms of ARBY
Paper illustrates risk exposure related to public
underwriting of initial risk