Correction of Measurement Error in Monthly USDA Pig Crop: Generating Alternative Data Series

Journal of Agricultural and Applied Economics, Aug 2008 by Kim, In-Seck, Plain, Ronald L, Bullock, J Bruce, Jei, Sang Young

To solve underestimation problems without circular reference, SF were estimated with the use of PC numbers obtained from a 4-year moving average of GA. The components of PC^sub t-6^ (i.e., BHA^sub t^, PDL^sub t^, and NBGS^sub t^) are obtained from a 4-year moving average of GA rather than GA numbers generated directly from SF numbers in the calculation for SF^sub t-6^.

Use of the 4-year moving average of GA in generating PC^sub t-6^ in the calculation for SF^sub t-6^ resolves both underestimation and circular problems now that SF^sub t-6^ is not a simple function of the hog slaughter number in month t, but a function of PQ^sub t-6^ and PC^sub t-6^, which, in turn, is not a direct function of SF but is a function of the 4-year moving average of GA.

The study also regenerated other data series of FB, GA, etc. on the basis of this renewed SF^sub t-6^, which is consistent with PC^sub t-6^. These regenerated data series not only take observed slaughter numbers into account but also reflect imputed BHA, imputed NBGS, and imputed PDL in the data estimation process.

Weighting Procedure for Alternative Pig Crop Data over the January 2006-June 2006 Period

In this study, we developed the alternative PC on the basis of the observed slaughter hog numbers and known biological function for slaughter hogs, which is ignored in the USDA PC data projection system. Even though this approach would provide more biologically and logically consistent historical PC data than the USDA approach, the alternative PC data are not available in real time because they are generated from 6 months ahead of slaughter number.

Therefore, the latest available alternative PC data always lagged 6 months behind the USDA PC data. In fact, the latest month of alternative PC data generated on the basis of the previous data generation process was December 2005, whereas the latest USDA PC was June 2006 (end month of the sample period of PC).

In this study, we followed the weighting procedure of using the ratio of the alternative PC to the USDA PC (alternative PC/USDA PC) over the December 1995-December 2005 period to generate an alternative PC over the January 2006-June 2006 period. The study obtained mean, median, standard deviation, skewness, and kurtosis for the ratio of alternative PC to USDA PC in order to examine the distribution of the ratio. They are 0.99, 0.99, 0.04, 0.31, and 2.18, respectively, which indicates that the ratio over the December 1995-December 2005 period follows a normal distribution. Furthermore, the p-value of the Jarque and Bera normality test is 0.07,7 which supports the normality of this ratio.

The study multiplied 0.99, which is the same mean and median of the ratio, with the USDA PC over the January 2006-June 2006 period because the ratio is normally distributed. Additionally, this study also multiplied monthly average of the ratio (MA) over the January 1996-December 2005 period with the USDA PC over the January 2006-June 2006 period to preserve seasonality. That is, alternative PC^sub t-6^ = USDA PC^sub t^ × 0.99 × MA^sub t^, where t is January 2006-June 2006.