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

Monthly U.S. Slaughter Hog Model

In addition to the pure comparison between USDA data and the alternative data series by basic descriptive statistics in Table 4, we compare the relative empirical performance of each PC data set by putting it into a monthly slaughter hog model.

Monthly variations in slaughter hog supply in month t are governed by the biological production process once the size of the breeding herd is determined in (t - 11).8 However, as mentioned earlier, there is some flexibility in the timing of slaughter. Therefore, the domestic hogs slaughtered commercially in month t should be specified not only by PC^sub t-6^ but also WD^sub t^,

(4) CDBGS^sub t^ = α^sub 0^ α^sub 1^PC^sub t-6^ α^sub 2^ WD^sub t^ ε^sub t^,

where ε^sub t^ is the error term. Definitions for other variables are reported in Table 3.

On the basis of the slaughter hog model in Equation (4), two empirical models are specified to evaluate empirical performances of USDA and alternative PC data series.

(5) CDBGS^sub t^ = a^sub 0^ a^sub 1^PC^sup U^^sub t-6^ a^sub 2^WD^sub t^ a^sub 3^TU^sub t-6^ V^sub t1^

(6) CDBGS^sub t^ = b^sub 0^ b^sub 1^PC^sup A^^sub t-6^ b^sub 2^WD^sub t^ b^sub 3^TA^sub t-6^ V^sub t2^

where PC^sup U^^sub t-6^ is the size of the USDA PC^sub t-6^; TU^sub t-6^ is the product of the annual time trend and size of USDA PC^sub t-6^; PC^sup A^^sub t-6^ is the size of the alternative PC^sub t-6^; TA^sub t-6^ is the product of the annual time trend and size of the alternative PC^sub t-6^; and V^sub t1^, V^sub t2^ are error terms for Equations (5) and (6). Definitions for other variables are the same as Equation (4).

TU^sub t-6^, TA^sub t-6^ are included to capture the increasing growing/finishing period of pig from birth to slaughter because of the increasing slaughter weights in recent years. We expect negative signs in both TU^sub t-6^ and TA^sub t-6^.

Empirical Results

Equations were estimated with CDBGS, WD for the June 1996-December 2006 period (127 months), 11 years annual time trend, and both USDA and alternative PC for the December 1995-June 2006 period (127 months).

We conducted the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) stationary test for all variables before estimation.9 The null hypothesis of stationary was rejected for all variables except PC^sup A^ and WD. All variables were first differenced for consistency in evaluating the empirical performance of PC^sup U^ and PC^sup A^ in Equations (5) and (6), even though PC^sup A^ and WD are stationary and the first differenced variables were found to be stationary. Table 5 reports estimation results of Equations (5) and (6) by OLS coupled with various test results.

All estimated variables in Equations (5) and (6) had expected signs, but the parameter estimates in the two sets of data exhibit quite distinct differences between them, as expected.

Parameter estimates of Equation (5) in the first column indicate that, on average, 74.3% of pigs born in the 6 months previous are slaughtered, and about 302,000 domestic slaughter hogs are slaughtered commercially per day on the basis of the reported USDA pig crop data series over the sample period. This is not quite consistent with our observations of the U.S. swine industry. Moreover, a TU^sub t-6^ term with a value of -.0078 modifies the average hog slaughtered number per pig crop in the 6 months previous to .66 in year 2006.