Analysts spend a lot of time scrutinizing estimates in USDA’s Hogs and Pigs reports. Amid our disagreement, or agreement, over a specific number, we can easily overlook the fact that every number is an estimate that falls within a statistical range.

A USDA point estimate is just one plausible value within a particular confidence interval. All estimates that are based on survey data have a statistical margin of error.

Computing the root mean square error, 90% confidence interval, and the difference between the first and last estimate can help evaluate the reliability of current estimates. USDA publishes these reliability metrics for the all hogs and pigs inventory, pig crop, and expected sows farrowing estimates in every report.

## Interest in statistical analysis

USDA’s estimates of the two heaviest weight categories on Sept. 1 came in well above the average trade guess in advance of the report. The 180-pound-and-over inventory was up 9.8%. Analysts pegged it up between 1% and 6.6% from a year ago, with an average of up 2.6%. Market hogs weighing 120 to 179 pounds were up 6.1% compared to an average of pre-report expectations of up 1.5%. All market hogs, at 72.766 million head, were up 0.8% from last year, which was closer to the average trade guess of up 0.1%.

Declines in the lightweight hog inventories restrained growth in the all-market hog number. The under-50-pound category was down 3.5% from Sept. 1, 2019, which was 1.5 percentage points lower than expected. Inventories of hogs weighing 50 to 119 pounds were down 3.5% instead of the expected 0.3% decrease.

Those differences raise the question as to just how many market hogs are on farms and at what weights. Those numbers obviously have implications for market prices.

USDA makes its first estimate in the quarter when data are collected. As more information, such as final slaughter data, becomes available, USDA may revise the estimate each quarter until one-year post-data collection, which is the final estimate. The largest changes, if any, usually occur in the first revision. The second and third reviews usually result in minimal revisions.

A measure of accuracy, or margin of error, is then the consistency between the first and final estimate. Differences for the all hogs and pigs estimates during the last 20 quarters have averaged 573,000 head, ranging from zero to 1.710 million head. The first all hogs and pigs inventory estimate has been below the final estimate 10 times, above eight times and unchanged twice. No bias is obvious. Estimates are not consistently different in any direction. If they were, the market would build this pattern into its expectations.

## Meaning behind statistical measures

The root mean-square error for the all hogs and pigs inventory estimate over the past 20 quarters is 1%. This means the chances are 2 out of 3 that the final estimate will not be above or below the Sept. 1 estimate of 79.099 million head by more than 1%. This equates to 790,990 head. The 90% confidence interval is another view. It says chances are 9 out of 10 that the difference will not exceed 1.7%, which equates to 1.345 million head.

Determining implications for the market hog inventory requires some extrapolation beyond the detail provided in the report.

Suppose for illustration purposes, that the statistical measures for the market hog inventory match the all hogs and pigs measures. The root mean-square error of 1% means there is a 67% chance the market hog inventory will not fluctuate by more than 727,660 head when comparing it to the final estimate. The 90% confidence interval of 1.7% over the last 20 quarters suggests we can be 90% sure that the current estimate of the market hog inventory will not vary by more than 1.237 million head.

The 72.766 million head for the Sept. 1 market hog inventory estimate was above pre-report expectations. Suppose the market hog inventory would have come in at the bottom of the 90% confidence interval. That would have been 1.237 million head lower at 71.529 million head, which would have been down 0.9% from last year. Would there be any more agreement or disagreement with this estimate? That’s hard to say.

## Slaughter offers some confirmation

Hog slaughter since Sept. 1 suggests USDA might revise the Sept. 1 heavyweight market hog inventory estimate downward in the December report. Most of the 180-pound-and-over hogs have already come to market. Since Sept. 1, weekly federally inspected hog slaughter is down 1.2% compared to the same period in 2019. That is far below the 9.8% rise implied by the report.

A downward revision in the heaviest-weight market hog inventories, within the 90% confidence interval, would roughly explain the difference in the estimates with the average of pre-report expectations and the actual slaughter numbers.

## Blurred lines

Obviously, 2020 has unusual dynamics. Slower growth rates could mean hogs are more evenly spread across market weight categories than front-end loaded as the report implies. USDA tallied the 180-pound-and-over category up 9.8% from a year ago, 120-to-179-pound up 6.1%, and 50-to-119-pound along with under-50-pound both down 3.5%.

Consequently, slaughter rates could change by 3.8 percentage points and then by 9.6 percentage points in a matter of weeks. The 13.3 percentage point change between market weight categories is the largest in the history of the current weight category data back to 2008.

The market eventually provides truth on value. Futures market prices are the collective opinion of everyone who is in the market as to what the price should be. So far, during the time the heaviest weight hogs were going to slaughter, prices have risen. In fact, nearby contracts have surged. On Sept. 1, October CME lean hog futures traded at $55.025 per cwt. On Oct. 8, that contract was at $77.350 per cwt. That’s a 41% gain in just over a month. December 2020 futures rose 20% over that time. Contracts for 2021 are up about 10%.

*Schulz is the ISU Extension livestock economist. Email *lschulz@iastate.edu.

# Are finishing facilities looking for feeders?

Factors such as expected market hog prices, feed prices, pig supply, availability of nursery and finishing space, and interest rates drive variation in feeder pig values over time. The cash or spot market can be thought of as a residual market and will often react preemptively to many of these factors. As such, cash prices tend to lead formula prices in both rising and falling markets. Prices derived or determined from the futures market or from a formula based on the cost of production show less variability than is observed in cash prices.

USDA’s weekly National Direct Delivered Feeder Pig report (NW_LS255) provides prices quoted on a per head basis delivered to the buyer’s farm and include freight and fees. The cash price for 10- to 12-pound pigs fell to about $6 per head on average in April and held there until late July. The lower end of the price range was $1 per head for several sales. Cash 40-pound feeders averaged $16 per head over that same time period. Formula prices averaged $28 per head for 10- to 12-pound pigs. Formula trade for 40-pound pigs is rarely reported.

For the week ending Oct. 2, cash 10- to 12-pound pigs averaged $29.75 per head and 40-pound pigs were $40.82 per head. Those are 373% and 157% increases, respectively, from this spring and summer. Prices are about 5% lower than the same time in 2019.