Measurement of Yield distribution: A Time-Varying Distribution Model

Regarding the nature of yield data, there are two basic characteristics that needs to be accommodated while we are about to model a yield distribution. The first one is the nonstationary nature of the yield distribution, which causes the heteroscedasticity related problems. The second one is the left skewness of the yield distribution. A common approach to this problem is based on a two-stage method in which the yields are detrended first and the detrended yields are taken as observed data modeled by various parametric and nonparametric methods. Based on a two-stage estimation structure, a mixed normal distribution seems to better capture the the secondary distribution from catastrophic years than a Beta distribution. The implication to the risk management is the yield risk may be underestimated under the common selection -- Beta distribution. A mixed normal distribution under a time-varying structure, under which the parameters are allowed to vary over time, tends to collapse to a single normal distribution. The time-varying mixed normal model fits the realized yield data in one step that avoids the possible bias caused by sampling variability. Also, the time-varying parameters imply that the premium rates can be adjusted to represent the most recent information and that lifts the efficiency of the insurance market.