A Better Approach to Calculate Approved Yield - Indexing

1. A Better Approach to Calculate Approved Yield - Indexing Dr. Myles J. Watts Professor, Montana State University Agricultural Economics & Economics Department Economic Consultant, Watts and Associates, Inc.

2. Crop Insurance • A risk management tool for producers to alleviate financial stress from: • Low yields. • Unexpected price declines.

3. Concerns • Producers ability to obtain meaningful crop insurance is eroded after a series of poor yielding years. • After unusually good or bad years, rates are actuarially less sound. • Technologyimprovements resulting in increasing yield are ignored by current system.

4. Current Method of Calculating Indemnity Trigger • Approved yield = simple average of 4-10 years of producer supplied yield history. • (Approved yield)*(Coverage level) = Indemnity trigger. • If yield outcome falls below the indemnity trigger, an indemnity is paid.

5. Current Method • Pros • Easy to administer. • Easy to understand.

6. Current Method • Cons • Does not account for technological increases • Biased. • Small sample size • Efficiency of approve yield estimates. • Series of unusually low yielding years will dramatically lower approved yield, making an indemnity payment less likely. • Series of high yields increases probability of an indemnity payment.

7. U.S. Corn Historic Yields

8. U.S. Wheat Historic Yields

9. Wheat Yield, Petroleum County, Montana

10. Objectives • Develop an approved yield as accurate as possible point estimate of expected yield. • Reduce bias of a simple average. • Increased efficiency over a simple average. • Reduce adverse selection and moral hazard. • Administratively feasible.

11. Proposed Alternative – Indexing • Longer term (e.g. > 50 years) regional data (NASS) sets used along with producer actual production history. • Method overview • Statistically estimate trend line from long term regional data to forecast expected regional yield. • Calculate average of farm level and regional series for given time period. • Difference between two is added (subtracted) to (from) expected regional yield to calculate the producers approved yield.

12. Detailed Discussion • Let

13. Bias • Simple average of current method is biased because of technology. Bias is • Indexed yield predicted from linear regression has no bias.

14. Efficiency • Variance of simple average = . • Variance of indexed yield has two components which are orthogonal and additive. • Variance of regional expected yield ( ) in year =

15. Efficiency cont. • Variance of difference between farm & regional average yield = Therefore, variance of Indexed yield is

16. Efficiency Gain • Large number of observations at regional level increases the efficiency of indexing. • The efficiency of the simple average and indexing is the same when the number of observations satisfies • The Indexed yield will provide a more efficient estimate of the approved yield if the length of the regional data series is greater than approximately four times the length of the farm data series.

17. Illustration of Efficiency Let • For approved yields to be efficient (stable) and unbiased, the distribution of approved yields must be concentrated around the expected yield (small variance).

18. Critical Component Indexing • Estimation of yield trend lines. • ‘s are parameters to be statistically estimated.

19. Estimating Trend Lines • Form is flexible. For example:

24. Model Selection • Model chosen by: • Standard statistical tests such as F-test. • Visual inspection of graphs. • Model choice experience • Have estimated 100’s of trend lines for crop yields in the US and other countries.

25. Wheat Yield, Petroleum County, Montana

26. Petroleum County, Montana • Estimated trend line equation is • Scale t • Expected regional indexed yield 2005 = 22.6.

27. Adjustment to Indexed Method • Indexed Farm Yield = Indexed Regional Yield = (Farm Average – Regional Average).

28. Regional (county) and Hypothetical Farm Yields for Petroleum County

29. Petroleum County Simple Farm Average and Indexed Yield *Most Recent Years