Grading Error in the California
Prune Industry
by James A. Chalfant, Jennifer S. James, Nathalie Lavoie and Richard J.
Sexton
Food demand in the U.S. is rather stable. As their incomes rise, most people do not consume
more food; rather, they eat better, higher-quality foods. Thus, the quality dimension of the U.S.
food industry has become increasingly important. The most successful growers and marketers
have been those who are consistently able to provide high-quality products to consumers.
Grading of farm commodities is one way for the food industry to encourage production of
high-quality products, since prices will vary according to grade. In the absence of grades,
products of various quality levels are pooled and receive a common price based on the average
quality. This discourages growers from adopting the costly production practices necessary to
increase quality.
Unfortunately, grading is almost never done perfectly. Grading errors can emerge both as a
consequence of sampling errors and from imperfect testing. In a recent study, we showed that
grading with error can result in the same problems caused by the absence of grades, namely
reduced incentive to produce high quality.
California produces nearly all U.S. prunes and about 70% of the world's supply. Size is the
main quality criterion for dried prunes and is the crucial characteristic in determining prune
value. Official grading is done by the Dried Fruit Association (DFA), for purposes of
determining payments to growers, based on a 40 lb. sample collected at the time the prunes are
graded by the processor. Prunes are graded by size into one of five categories, A (largest) through
D (smallest) and U (undersized), and growers are paid based on a separate price negotiated for
each grade, with the U grade valued at zero. The largest prunes can be sold in gourmet retail
packs at a premium price. Moderately large prunes can be pitted and sold as pitted prunes, while
the smallest prunes are useful only for juice, paste and other industrial products and sell for a
lower price per pound.
Industry participants often complain of an "oversupply" of small prunes. Prune size may be
enhanced through cultural practices, such as pruning, shaker thinning and delaying harvest. Field
sizing may also be used to eliminate the smallest prunes and to avoid incurring the cost of
handling them. Growers have been encouraged to adopt these practices, with limited success to
date. Our study looks at the extent to which grading errors reduce the profitability of such
practices. Figure 1 represents the grader used for California prunes. As the figure suggests, small
prunes may not fall into their designated screen and may, instead, travel on to screens for larger
prunes, but large prunes cannot fall into the categories designated for smaller prunes. Thus, a
portion of lower quality prunes receives a higher quality ranking, but the reverse cannot
occur.
Grading Errors and Market
Prices
Errors in grading prunes mean that the measured quantity of prunes in each grade is not the
actual quantity of the prunes meeting the grade standard. As a result, the price paid to growers for
all grades except the lowest will be less, because of the "contamination" by prunes from the
lower grades.
We estimated the errors in valuation of prunes as the difference between the value of
correctly graded prunes and the grower price for a particular measured grade. The undervaluation
of a particular grade is determined by (a) the extent to which prunes from lower grades move up
in grade, and (b) the difference in value between prunes that are correctly graded and prunes of
lower grades. For example, the market price of grade B is discounted based on the relative
amounts of grades C, D and U prunes that receive a grade of B, and the differences in value
between grade B and these lower grades. There is an offsetting effect on the revenue from grade
B prunes-the grower is paid more than market value for grade B prunes that end up in grade A
due to grading error. A similar effect occurs for the lower grades, which can also move up and
receive the price associated with the higher grade. How do these effects play out on balance?
First, the average farm revenue for undersized prunes is higher than their actual value,
because some undersized prunes end up being measured and paid as higher grades. Second, grade
A prunes always earn less than their true value, because all grade A prunes receive the A-screen
price, which is discounted due to the presence of smaller prunes misclassified as grade A.
Offsetting effects of both types occur for the intermediate grades B, C and D. There is a gain in
revenue obtained by a portion of grades B, C and D product migrating into higher grades and a
loss in revenue from the reduction in grower prices relative to actual values.
Estimated Effects of Grading
Errors
We estimated the differences between the actual value and the grower price, and between the
average farm revenue and the actual value, for each grade of prunes for the 1996 crop year. These
estimates were based on the grade sheets completed for all 1,487 samples graded by the DFA in
1996 and on detailed information for two 40-lb. samples of prunes provided by the Prune
Bargaining Association (PBA). These samples consisted of prunes from a variety of Sacramento
Valley sites and conformed closely in size distribution to the overall harvest.
After each PBA sample was graded, the weight of each individual prune was recorded. Thus,
for each prune in the PBA samples, we knew which screen it fell through and its actual size. In
other words, the measured and actual size distributions were known for these two samples.
We also obtained the grading sheets for all 1,487 actual shipments made in the 1996 crop
year. Each sheet reports the total weight and the average prune size in each of the measured
grades A, B, C, D and U based on the 40-lb. sample taken from each shipment after drying. We
used the detailed information from our two 40-lb. PBA samples to infer the size distributions for
each actual shipment.
We estimated the proportions of prunes of each grade that were measured in each of the five
grades. The averages of these proportions over all 1996 shipments are reported in tables 1 and
2.
Table 1 contains the measured and actual proportion of prunes in a grade for each grade.
Differences between the actual and measured proportions are readily apparent, but the degree of
measurement error is further clarified in table 2. Each row of table 2 refers to the actual prune
grade, and each column refers to the measured prune grade. Individual cells in the table contain
the proportion of the prunes actually belonging to a particular grade that received any other
grade, so that the diagonal elements represent proportions of correctly graded prunes. The
numbers below the diagonal represent the percentage of prunes of each actual grade migrating to
higher grades.
Table 2 shows that the probability of grading errors is greatest in the lower grades. This
result is not surprising, because products in these grades have the greatest opportunity to migrate
into higher grades. All A-quality prunes were graded correctly by construction of the grading
process, and 85% of B-quality prunes were graded correctly, with the remaining 15%
masquerading as A-quality prunes. However, only 56% of C-quality prunes were graded
correctly, with 42% masquerading as B prunes. Only 38% of true D-quality prunes were graded
as D, with 50% and 12% migrating into the C and B screens, respectively.
The information contained in tables 1 and 2 and the actual grower prices for each grade,
determined through negotiations between the handlers and the PBA, enable us to solve for the
actual value of each grade. Grower prices, actual values, and average grower revenue for each
grade are presented in columns 2, 3, and 4 of table 3. The differences between grower prices and
actual values for each grade indicate the extent to which grower prices were discounted because
of grading error and are listed in column 5 of table 3. For all grades except the lowest, U, the
grower price is lower than the actual value. The price of grade A prunes is lower than its true
value by 2.28 cents/lb., or 4%, while B-grade prunes are undervalued by 3.43 cents/lb., or
7.7%.
The difference between the average grower revenue and the actual value of prunes in each
grade is shown in the last column of table 3. Since A-grade prunes cannot masquerade as any
other grade, their average grower revenue equals their price, and the difference is again 2.28
cents/lb. The average grower revenue of undersized prunes is higher (by over 6 cents/lb.) than the
actual value of zero. The average grower revenue is lower than the actual value for grade B (by
3.4%), but higher for grades C and D (by 16.7% and 73.2%, respectively). The negative spread
for grade B indicates, for example, that the decrease in average grower revenue for grade B
prunes, associated with the migration of lower grades into grade B, more than offsets the gain in
revenue associated with some of the B prunes being classified as grade A.
These findings are consistent with the pattern of "oversupply" of small prunes in recent years
and illustrate that continuing to produce relatively greater numbers of small prunes, rather than,
for example, shaker thinning to produce larger prunes, may well be a rational response to current
incentives. The industry can partially address the problem of oversupply of small prunes by
improving the accuracy of the grading process. Examples include increasing screen length or
adding additional screens on the DFA grader. Alternatively, the industry might consider a
graduated payment system that offers premiums and discounts based on average prune size
within each measured grade, rather than a single price per grade, as is the current practice.
