Estimating the Fair Insurance Premium for Dungeness Crab Yields in the Western U.S. Coast

The Dungeness is a popular food and the most commercially important crab in the western states in the U.S. Like all agricultural production, the crab fisherman face yield risks and must manage these risks. In addition to weather risk, crab fisherman may experience low yields if the crabs are over fished in previous years. Farmers for many traditional agricultural crops can purchase crop insurance to insure against low yields. However, crab fishermen at this time do not have this option. The purpose of this paper is to estimate a fair insurance premium based on the historical yields of the Dungeness crab. This information can then be used in risk/return models for crab fishing to determine if it would be optimal for fisherman to purchase crop insurance. An important input into the fair insurance premium estimation is the yield distribution. Sherrick et al. estimated alternative yield distributions to evaluate traditional crop insurance. However, no one has looked at the yield distributions for the Dungeness crab nor explored possible crop insurance. Much of the past literature for the fishing industry has focused on production functions, cost function models, and optimal catching yields for specific fish species. Moreover, most research has focused on the endangered commercial ocean species such as tuna and swordfish. Data and Methodology This research collects the annual landing data including metric tons, pounds, and price per pound from NOAA's National Marine Fisheries Service (NOAA Fisheries Service) to analyze the yield distributions of Dungeness crab in California, Oregon, Washington, and Alaska from 1950 to 2009. Dickey Fuller test is conducted for each state to test if the data is stationary. The Durbin-Watson test was used to make sure the data did not have autocorrelation problems. We find that the detrended data has positive Skewness contrary to traditional crop yield data. The positive Skewness indicates that the tail on the right sides is longer than the left side and the mass of the distribution is concentrated on the left. It also has relatively few high values. The candidate distributions used include normal, Gamma, Weibull, logistic, lognormal, and loglogistic distributions. The fitted distributions are compared with formal goodness- of- fit tests including Chi-Square, Anderson-Darling, and Kolmogorov-Smirnov. The loglogistic distribution is best to estimate the yield losses of Alaska, Oregon, and California respectively while the logistic is best for Washington. The Gamma and normal distribution are the worst for the four states. Actual Production History (APH) policies insure crop producers against yield losses due to natural causes. After Just and Weninger found that crop yield losses were nonnormally distributed, many agricultural researchers use parametric (Goodwin and Ker) and nonparametric distributions (Sherrick et al) and the insured price to estimate the insurance premium. The premium refers to the periodic payment made on the insurance policy. When the yields are below the insured level (the predicted level each year), the insurance company has to pay indemnities to the producers to compensate them for their losses. Our study uses different parametric distributions to forecast the crab yields. Along with the yield distributions and yield forecasts, we assume that the crop insurance insures up to 80% of the yield distribution. We also assume that the insured price is the predicted price per pound for 2010 (since the price model are Pth-order autoregressive (AR(p)) processes) to estimate the fair insurance premium. The insured prices per pound of the four states from north to south are $1.88, $2.39, $1.94, and $1.99 respectively. If the random value (that the realized yields fall below the guaranteed yields) generated by the best distributions which may generate different parametric value for the four states falls below zero, it will means that the fisherman suffer yield losses, and that the insurance company has to compensate the fishermen’s revenue. The insurance company pays the fishermen the dollars that the insured price times 80% of the yield that the fishermen suffer from loss. The indemnities will be either zero or positive. Next, we adopt Latin hypercube sampling (LHS) to simulate the indemnities 500 times to calculate the average indemnities. If we don’t consider the capital and administration fees of the insurance company, the average indemnities will be the actuarially fair insurance premium. The average indemnity and thus the actuarially fair premiums of the overall crab industry are $1,380,924, $702,344, $2,823,855, and $3,470,998 one year for the all ships in Alaska, Washington, Oregon, and California respectively. Unlike traditional crop insurance that estimates the premium per acre, we use the total premium shared by all fishing vessels in the state and account for the total tons that the fishing vessels load because the crabs and the fishing vessel move everywhere. After simulated, half of the time the insurance company must pay indemnities. To avoid the high risk of yield losses and uncertainty, the existence of insurance is necessary to protect the fishermen’s revenue. Finally, we will try to use non-parametric method to estimate the fair premium and compare the results of the parametric and non-parametric distributions for the rigorous study. We will also estimate the potential welfare gain of fishermen from this insurance policy.