A Re-Examination of Multistage Economies in Hog Farming

Output Measure: Stage 2

FIN, the hundred weight gain at the feeder-to-finish stage, was calculated as the weight of market hogs sold/removed, plus the change in the weight of the inventory of hogs in the feeder-to-finish stage, minus the weight of feeder pigs supplied as inputs to the stage. Firms can acquire feeder pigs for input into their second stage production by transferring them internally or purchasing/placing them. No feeder pigs are produced under completely specialized feeder-to-finish operations so all must be acquired through purchase/placement, and the number of feeder pigs purchased or placed is reported in the survey. For all other firms, however, the number of head of feeder pigs entering the feeder-to-finish stage (HDFPIn) is not directly reported in the survey but can be determined by adding the outflow of market hogs exiting the stage due to sale (HDMHSold) or death loss (FeedFinDL) to the net change in market hog inventory (HDFeedFinΔInv):

where HDFPPurch is the number of head of feeder pigs purchased/placed.^[23] Given the number of feeder pigs used as a second stage input, the total weight is calculated by multiplying by the average weight of feeder pigs in hundred-weight (AvgCwtFP). For farms that purchased/placed or sold/removed feeder pigs, AvgCwtFP was set equal to the reported average weight of pigs involved in these transactions and was thus a measure specific to the farm. Fully-integrated farrow-to-feeder operations do not have external transactions in feeder pigs so, for these farms, AvgCwtFP was set equal to the sample average weight of feeder pigs purchase/placed or sold/removed by all farms, approximately 47 pounds. The hundred weight of feeder pig input to the second stage is then calculated as

Beginning-of-year and end-of-year head count inventories were reported separately in the survey for four size categories: 0–59 pounds, 60–119 pounds, 120–179 pounds, and 180 pounds and over. Hogs in the last three categories, and some of the hogs in the first category, are attributed to the feeder-to-finish stage. As the average weight of feeder pigs observed is less than 60 pounds, the inventory of hogs in the 0–59 pound category must be allocated between the farrow-to-feeder and feeder-to-finish stages. The allocation was based on the assumption that the pigs in this size category were uniformly distributed over weights of 0 to 60 pounds. This also implies that the average weight of the pigs in excess of 47 pounds is the average of 47 and 60, the category’s upper bound weight. Thus the hundred weight change in feeder-to-finish inventory of pigs weighing 47 to 60 pounds (CwtFeedFinΔInv47−59) is calculated as

where HDBegInv0−59 and HDEndInv0−59 are beginning and ending inventories of pigs under 60 pounds.

The representative weights of the other three categories, 100 pounds, 150 pounds, and 200 pounds, are the category weights implicit in the ERS/NASS calculations of the hundred-weight inventory variables from the reported head-count inventories. Thus, the hundred weight inventory changes in the remaining categories are constructed as:

where the new notation is defined in the obvious way. Summing these, we have the hundred weight change in feeder-to-finish inventory

Since both head of market hogs sold/removed (HDMHSold) and the average weight of market hogs sold/removed (AvgWtMH) were reported, the hundred weight of market hogs sold can be calculated as

Finally, the stage two output is

Output Measure: Stage 1

At the first stage, no output is produced by completely specialized feeder-to-finish operations. Since there is no intermediate input required for the farrow-to-feeder stage, the process of calculating hundred-weight gain is divided into only two parts: feeder pigs exiting the stage and change in inventory.

As previously mentioned, the survey reports head counts of pigs under 60 pounds in beginning-of-year (HDBegInv0−59) and end-of-year inventory (HDEndInv0−59). Just as before, we allocate these inventory totals between the farrow-to-feeder and feeder-to-finish stages based on the assumption of a uniform distribution of weights within the 0 – 60 pound category. With 47 pounds taken to be the top weight of the farrow-to-feeder stage, we have the following beginning- and end-of-year inventory head counts:

and

Assuming the average weight of feeder pigs in these beginning and ending inventories is half the average feeder pig weight, the hundred weight change in the pig inventory is

The outflow of feeder pigs from the first stage to the second (HDFPOut) occurs through either internal transfer or sale on the market. Thus, the number of feeder pigs exiting the farrow-to-feeder stage is

where HDFPSold, the number of feeder pigs sold/removed, is reported in the survey. The hundred-weight of feeder pigs exiting the farrow-to-feeder stage is then

From this, stage one output is given by

Death Loss Allocation

To determine the head count flows we require a measure of death loss at the feeder-to-finish stage. However, death losses were instead reported for pre-wean and post-wean periods – with weaning, of course, occurring during the farrow-to-feeder stage – so an allocation of the reported post-wean death losses (PstwDL) between the two stages was required for farms that operate at both stages. To achieve this, we calculated post-wean death loss ratios for completely specialized farrow-to-feeder and completely specialized feeder-to-finish operations as the number of weaned pigs that died before reaching market weight per feeder pig or per market hog sold/removed, respectively. These two producer types were selected as they operate exclusively on one stage or the other, and so reported death losses can be attributed entirely to a single stage of production. Sample averages of the post-wean death loss ratios were then generated for these two producer types. By dividing the average post-wean death loss ratio for feeder-to-finish operations by the sum of the average post-wean death loss ratios for both types of specialized operations, we obtained a rough estimate of the proportion of post-wean death losses that occur in the second stage of production (PstwPstfDLprop). This figure was then assumed to be applicable to all farms operating at both stages.

Completely specialized farrow-to-feeder farms have no second stage production so no death loss is allocated to the feeder-to-finish stage. Similarly, completely specialized feeder-to-finish farms operate exclusively on the second stage so all post-wean death loss is allocated to the feeder-to-finish stage. Since fully-integrated feeder-to-finish, partially-integrated backward, and partially-integrated forward firms operate on both stages, a portion of post-wean death loss is allocated to each stage. For these farms, farm-specific death loss at the feeder-to-finish stage (FeedFinDL) was calculated by multiplying the industry-wide proportion of post-wean death loss attributable to the second stage, PstwPstfDLprop, by the farm’s reported number of post-wean deaths: