2. Industry background

In 1998, a reduction in slaughter capacity during a wave of packer consolidation resulted in a dramatic fall in hog prices. The cause was a sudden 8% drop in hog processing capacity as several U.S. packing plants closed or reduced capacity, which increased production costs at the plant level (Fabiosa and Kaus, Reference Fabiosa and Kaus2015). At the same time, federally inspected (FI) hog slaughter increased 10% from 1997 to 1998 (USDA-NASS, n.d.-a). Despite taking measures to mitigate the situation in 1998, many producers went out of business (Barboza, Reference Barboza1998). The structure of the pork industry changed dramatically following 1998. Fewer operations produced more hogs, and each stage of the supply chain became more tightly integrated (Haley, Reference Haley2024). However, as FI hog slaughter levels grew 28% from 1998 to 2023 (USDA-NASS, n.d.-a), capacity constraints at the packer level remained an ongoing issue for the live-animal segment of the pork supply chain.

A “positive” structural change was the unprecedented addition of hog processing capacity in the late 2010s. Large plant openings in 2017 and 2019 may have increased capacity by as much as 32,200 head per day (Meyer, Reference Meyer2017; Meyer, Reference Meyer2019). One estimate suggests an additional increase of 2,300 head per day from fall 2019 to fall 2020, despite COVID-19-related challenges (Meyer, Reference Meyer2020b). For context, FI hog slaughter levels in 2020 were 11% higher than in 2016 and 1% higher than in 2019 (USDA-NASS, n.d.-a). While the relationship between slaughter capacity and actual slaughter depends on a variety of factors, the 2020 bottleneck could have certainly been worse without the large expansion of physical packing plant capacity that occurred.

Unlike prior hog processing capacity disruptions related to market conditions, the situation in 2020 was predicated on labor challenges (Ramsey et al., Reference Ramsey, Goodwin, Haley, Ramsey, Goodwin and Haley2023). One key component of understanding this situation is to consider the volume of market-ready hogs not delivered during intended marketing windows due to reduced pork packing operations. The National Pork Producers Council estimated that at the height of slaughter disruptions “up to 10,069,000 market hogs will need to be euthanized between the weeks ending on April 25 and September 19” (NPPC, 2020). A less pessimistic scenario was euthanizing about five to six million head (Meyer, Reference Meyer2020a; Miller, Reference Miller2020). While actual euthanasia was much smaller, at the time it was difficult to project the likelihood, duration, and extent to which the collective hog processing industry could operate at particular levels, which caused a large range in estimates regarding the backlog of market hogs. Other unknowns were the success and prevalence of adjusting pigs’ diets, increasing stocking densities, sorting or topping off pens, finding additional facilities to house pigs, and selling into alternative markets to partially mitigate live-animal supply chain disruptions (Hayes et al., Reference Hayes, Schulz, Hart and Jacobs2020).

Subsequent to COVID-19 disruptions, the pork industry entered a high price, high-cost period of production. A key structural change during this period was the closure or reduction of several slaughter facilities. Smithfield Foods announced in July 2021 and June 2022, respectively, that it would cease slaughter operations at its Gwaltney, Virginia, and Vernon, California, plants (Meyer, Reference Meyer2021, Reference Meyer2022). By 2023, a relatively high supply and softening demand environment placed downward pressure on pork prices (Tonsor, Reference Tonsorn.d.). This filtered upstream into markets for hogs and pigs, driving down prices in those markets as well. Responding to these unfavorable conditions, Smithfield Farms closed 35 sow farms in Missouri (Hess, Reference Hess2023). An additional closure in 2023 was Hylife’s Windom, Minnesota, pork processing plant (Schulz & Crespi, Reference Schulz and Crespi2024). Then in March 2024, Tyson announced it was closing its Perry, Iowa, slaughter plant in June 2024 (Meyer, Reference Meyer2024). Processing plant and farm closures do not necessarily reduce hog processing capacity or inventories in the aggregate. Market hogs can be transported to other facilities for slaughter, and sows can be repopulated at new or expanded farms elsewhere. Additionally, pork cold storage capacity can serve as a cushion against short-term imbalances in supply and demand (Tonsor et al., Reference Tonsor, Schulz and Lusk2020; Schulz, Reference Schulz2025).

In the wake of disruptions and structural changes, there was increased public interest in the pork industry. Legislative and executive action addressed a host of issues at varying levels of the supply chain (Executive Order No. 14,036, 2021; The White House, 2022), and industry initiatives sought to increase pork demand and develop trade opportunities (Even, Reference Even2023). At the same time, market participants sought new ways to manage risk (Carlson, Reference Carlson2022; Grebner, Reference Grebner2025). However, evaluating the effects of processing capacity changes, demand fluctuations, herd management decisions, and other factors, both internal and external to the pork industry, requires an end-to-end model of the live-animal segment of the pork supply chain. In a dynamic business environment, decision-makers need reliable tools to accurately assess and respond to evolving market conditions. We propose a model that connects production stages along the pork supply chain so that the effects of various disruptions, business decisions, and industry initiatives and policies can be better understood.

3. Conceptual model

While not particularly esoteric, the steps in bringing a hog to market are necessary to understand the structure of the pork supply chain and the importance of early weaned pig and feeder pig markets. There are four key stages in producing a market hog (Hoar and Angelos, Reference Hoar and Angelos2015; Pork Checkoff, n.d.; Haley, Reference Haley2024) (Figure 1). First is gestation, or pregnancy, which takes 115 days. When a sow or gilt gives birth, or farrows, the lactation phase begins, which is typically three weeks in length and concludes when producers wean pigs. Once weaned, pigs enter the nursery phase for the next three to seven weeks. The final phase can be split into two subphases, growing and finishing. The growing phase takes pigs from 35 – 60 pounds to 120 – 150 pounds, and the finishing phase takes pigs from 120 – 150 pounds to their market (live) weight of 250 – 300 pounds. Growing and finishing takes approximately four months. In total, it takes six months from birth to market or ten months including gestation.

Figure 1.

Production phases in the pork supply chain. Opportunities for marketing are denoted with an “M”: after weaning, at the end of the nursery phase, and finally once the hog has reached market weight.

From an industry segment perspective, the pork supply chain begins with farrowing operations that keep sows for the purpose of farrowing pigs. We focus on two types of operations that have farrowing: farrow-to-wean and farrow-to-feeder. Farrow-to-wean operations sell pigs after weaning, typically around 21 days of age and 10 to 12 pounds. Farrow-to-feeder operations keep pigs after weaning, feed them, and then sell them following the nursery stage when they weigh 40 to 60 pounds. Finishing operations buy pigs as an input in raising hogs. Wean-to-finish producers buy early weaned pigs from farrow-to-wean operations and feed them for five months before they are ready for slaughter. Feeder-to-finish operations buy feeder pigs from farrow-to-feeder operations and feed them for four months, at which point they are ready for slaughter. When ready for slaughter, hogs are procured by packers and processed into pork that is then sold into end-user markets. According to the 2022 Census of Agriculture, farrow-to-wean operations accounted for 29% and farrow-to-feeder operations accounted for 2% of all hog and pigs sales. Relative to only pig sales, the representation was 71 and 4%, respectively (USDA-NASS, 2024).

Price discovery for early weaned and feeder pigs occurs through negotiation (cash) or formulas.Footnote ¹ Conceivably, then, there are four markets for pigs: cash- and formula-priced early weaned pigs, and cash- and formula-priced feeder pigs. Formula pricing for feeder pigs was common before 2012, but publishing of this data since then is infrequent, so we exclude it from our analysis. Formula pricing for early weaned pigs is common, but formula terms are not well understood. Contracts for early weaned formula pigs may rely on cash prices for pigs or other market prices, such as feed, hog, or pork prices. Since we use aggregated data, we cannot identify heterogeneous contract terms. Hence, we also exclude formula-priced early weaned pigs and focus on cash-priced early weaned pigs and feeder pigs. To the extent that formulas depend on cash prices or an operation participates in both formula and cash markets, the model may be underspecified. Despite this, buyers and sellers predetermine formulas in an earlier negotiating stage, so separating cash and formula markets at the time of sale is reasonable.

We model the live-animal segment with one system of nine equations that relate inverse demand, supply, and market clearing conditions for market hogs, feeder pigs, and early weaned pigs. For clarity, we use superscripts M, CN, and CEW to denote market hogs, cash feeder (nursery) pigs, and cash early weaned pigs, and D and S to denote demand and supply. McKendree et al. (Reference McKendree, Tonsor, Schroeder and Hendricks2019) similarly construct a system of supply and inverse demand equations for feeder and fed cattle. Our model is analogous with salient features of the pork supply chain that builds upon the work of Reid and Reed (Reference Reid and Reed1982) and Parcell et al. (Reference Parcell, Mintert and Plain2004).

3.1. Conceptual model for hog market

The market for hogs is specified as:

(1) $$P_{t}^{M}=\phi \; \left({\matrix{Q_{t}^{M,D},\textit{WholesaleDeman}d_{t},\textit{PlantUtilizatio}n_{t},\textit{ColdStorageUtilizatio}n_{t}, \cr \textit{Technolog}y_{t},\textit{Seasonalit}y_{t} \cr } } \right)$$

(2) $$Q_t^{M,S} = \phi \; \left( {\matrix{{{E_{t - 17}}[P_t^{M,}],{E_{t - 22}}[P_t^{M,}],P_{t - 17}^{CN},P_{t - 22}^{CEW},P_{t - 17}^F,P_{t - 22}^F,Q_{t - 17}^{M,S},Q_{t - 22}^{M,S},PackerShar{e_t},} \cr {Technolog{y_t},Seasonalit{y_t}} \cr } } \right)$$

(3) $$ Q_{t}^{M,D}=Q_{t}^{M,S}=Q_{t}^{M} $$

Equation (1), the inverse demand for market hogs, models the price of a market hog as a function of the quantity demanded by processors ( $Q_t^{M,D}$ ), demand for wholesale pork (WholesaleDemand _t ), hog processing plant capacity utilization (PlantUtilization _t ), pork cold storage capacity utilization (ColdStorageUtilization _t ), technological change (Technology _t ), and seasonal effects (Seasonality _t ). Demand for wholesale pork is derived from consumers’ demand for pork but omits price and quantity variation that is specific to retailing, foodservice, or export. Hog processing plant capacity utilization is necessary to evaluate how the market responds when plants run at varying levels of capacity. When a plant is running near full capacity, its marginal cost of processing an additional hog will be high. Similarly, pork cold storage capacity utilization is necessary to evaluate how the market responds when stocks are built up and drawn down. In the inverse demand equation, technological change measures the trend of prices over time and seasonal effects capture variation in prices related to the time of year.

Equation (2), the supply of market hogs, models the quantity of market hogs supplied as a function of past decisions by feeder-to-finish and wean-to-finish operations $\left({E_{t - 17}}[P_t^M],{E_{t - 22}}[P_t^{M,}],P_{t - 17}^{CN},P_{t - 22}^{CEW},P_{t - 17}^F,P_{t - 22}^F,Q_{t - 17}^{M,S},Q_{t - 22}^{M,S}\right)$ . The price a feeder-to-finish or wean-to-finish operation expected to receive for a market hog $\left({E_{t - 17}}[P_t^{M,}],{E_{t - 22}}[P_t^M]\right)$ is the expected price of a market hog at the time that operation purchased a pig to raise. These terms are the expected prices of a market hog from 17 and 22 weeks prior, the time required to raise a feeder or early weaned pig for market, respectively. The price a feeder-to-finish (wean-to-finish) operation paid for a feeder (early weaned) pig is $P_{t - 17}^{CN}\left(P_{t - 22}^{CEW}\right)$ , which is simply the cash price of a feeder (early weaned) pig from 17 (22) weeks prior. Similarly, feed prices $(P_{t - 17}^F,P_{t - 22}^F)$ were paid 17 or 22 weeks prior when the pigs were purchased. The quantity of market hogs from 17 and 22 weeks prior $\left(Q_{t - 17}^{M,S},Q_{t - 22}^{M,S}\right)$ capture the flow of animals from finishing operations to processors at the time a finishing operation purchased its current group of pigs.Footnote ²

Packers’ share of owned or sold hogs is included to account for short-term changes in flows of pigs as packers can prioritize slaughtering packer-owned hogs or producer-owned hogs and accounts for longer-term structural changes as vertical integration has increased. In the supply equation, technological change measures the trend of quantity supplied over time, and seasonal effects capture variation in quantity supplied related to the time of year. Equation (3) is the market clearing condition that relates inverse demand for market hogs (1) with the supply of market hogs (2).

3.2. Conceptual model for feeder pig market

The market for feeder pigs is specified as:

(4) $$ P_{t}^{CN}=\phi \left(Q_{t}^{CN,D},E_{t}\left[P_{t+17}^{M}\right],P_{t}^{F},\textit{SmallLotShar}e_{t}^{CN},\textit{Technolog}y_{t},\textit{Seasonalit}y_{t}\right) $$

(5) $$ Q_{t}^{CN,S}= \phi \left({\matrix{{c} P_{t}^{CN},P_{t-25}^{F},E_{t-45}\left[P_{t}^{CN}\right],P_{t-25}^{SOW},Q_{t-28}^{CN,S},\textit{Diseas}e_{t},\textit{ContractShar}e_{t},P_{t-5}^{CEW}, \cr \textit{Technolog}y_{t},\textit{Seasonalit}y_{t} \cr}} \right) $$

(6) $$ Q_{t}^{CN,D}=Q_{t}^{CN,S}=Q_{t}^{CN} $$

Equation (4), the inverse demand for cash-priced feeder pigs, models the cash price for feeder pigs as a function of the quantity demanded by feeder-to-finish producers $\left(Q_t^{CN,D}\right)$ , the market hog price those producers expect to receive when pigs are ready for slaughter $\left( {E_t}\left[ {P_{t + 17}^M} \right]\right)$ , current feed prices ( $P_t^F$ ), and the share of feeder pigs marketed in lots of fewer than 1,200 pigs ( $SmallLotShare_t^{CN}$ ). The time period on expected prices for market hogs reflects the 17 weeks from nursery until slaughter. Feed prices capture the variable input costs of raising a pig for market. Producers evaluate the price they expect to receive for a pig and the cost of raising that pig when choosing the quantity to purchase. When pigs are marketed in small lots, a buyer may have to purchase multiple lots to fill a barn. The small lot share variable proxies for increases in transaction costs due to farrow-to-feeder operations marketing pigs in lots smaller than a conventional feeder-to-finish barn.

Equation (5), the supply of cash-priced feeder pigs, models the quantity of cash-priced feeder pigs as a function of the current cash price for feeder pigs $\left(P_t^{CN,}\right)$ , past decisions made by farrow-to-feeder operations that affect current inventories of early weaned pigs $\left( P_{t - 25}^F,{E_{t - 45}}\left[ {P_t^{CN}} \right],P_{t - 25}^{SOW},Q_{t - 28}^{CN,S},P_{t - 5}^{CEW}\right)$ , and the share of hogs raised under production contracts (ContractShare _t ). The current cash price for feeder pigs ( $P_t^{CN}$ ) is the opportunity cost of selling today versus retaining and selling in the next few weeks. Farrow-to-feeder operations incur feed costs from the beginning of gestation $\left(P_{t - 25}^F\right)$ . The opportunity cost of retaining a gilt for farrowing $\left({E_{t - 45}}[P_t^{CEW}]\right)$ is the expected price of a cash-priced feeder pig when making the decision whether to retain that gilt. This period is 45 weeks, which includes 20 weeks from the retention decision until she is ready to be bred, 17 weeks for gestation, 3 weeks from farrowing to weaning, and then 5 weeks in a nursery. The opportunity cost of retaining a sow for farrowing $\left(P_{t - 25}^{SOW}\right)$ is the price of a sow 25 weeks in the past, which includes 17 weeks for gestation, 3 weeks from farrowing to weaning, and 5 weeks in a nursery. The term $\left(Q_{t - 28}^{CN,S}\right)$ accounts for the flow of feeder pigs from farrow-to-feeder operations to feeder-to-finish at the time a farrow-to-feeder operation bred its current group of pigs. This is accounted for in the lag structure: 3 weeks between weaning a litter and the beginning of the next gestation cycle, 17 weeks for gestation, 3 weeks from farrowing to weaning, and 5 weeks in a nursery.

In principle, a farrow-to-feeder operation can sell a pig after weaning. The opportunity cost of retaining an early weaned pig for the nursery stage $\left(P_{t - 5}^{CEW}\right)$ is the price a farrow-to-feeder operation could have received for a pig 5 weeks prior when that pig was weaned. This captures the inventory effect of past prices for early weaned pigs on the current supply of feeder pigs. Intuitively, this could be a farrow-to-feeder operation choosing to take a first cut of pigs that are sold on a 10- to 12-pound basis and then a second cut that are sold on a 40-pound basis.

Disease prevalence (Disease _t ) is included as it directly affects inventories of feeder pigs, which are susceptible to viral infections such as PEDV and porcine reproductive and respiratory syndrome that have high mortality rates (Pospischil et al., Reference Pospischil, Stuedli and Kiupel2002; Leedom Larson, Reference Leedom Larson2016). Finally, to account for the flow of hogs under different ownership structures, we include the share of hogs raised under a production contract (ContractShare _t ). A production contract shifts some risk and control from the contract grower or contractee to the contractor or integrator but can reduce risk exposure for both parties (Key and MacDonald, Reference Key and MacDonald2006). Equation (6) is the market clearing condition that relates the inverse demand (4) and supply (5) equations for cash-priced feeder pigs.

3.3. Conceptual model for early weaned pig market

The market for early weaned pigs is specified as:

(7) $$ P_{t}^{CEW}=\phi \left(Q_{t}^{CEW,D},E_{t}\left[P_{t+22}^{M}\right],P_{t}^{F},\textit{SmallLotShar}e_{t}^{CEW},\textit{Technolog}y_{t},\textit{Seasonalit}y_{t}\right) $$

(8) $$Q_t^{CEW,S} = \phi \left( {\matrix{ {{E_{t - 20}}\left[ {P_t^{CEW}} \right],P_{t - 20}^F,{E_{t - 45}}\left[ {P_t^{CEW}} \right],P_{t - 20}^{SOW},Q_{t - 23}^{CEW,S},Diseas{e_t},} \cr {ContractShar{e_t},Technolog{y_t},Seasonalit{y_t}} \cr } } \right)$$

(9) $$ Q_{t}^{CEW,D}=Q_{t}^{CEW,S}=Q_{t}^{CEW} $$

Equation (7), the inverse demand for cash-priced early weaned pigs, is similar to equation (4), the inverse demand for cash-priced feeder pigs. Its terms are specified for early weaned pigs. The period for expected prices, 22 weeks, is increased by the 5 weeks an early weaned pig will spend in a nursery.

Equation (8), the supply of cash-priced early weaned pigs, is similar to equation (5), the supply of cash-priced feeder pigs. Periods are shortened by 5 weeks since farrow-to-wean operations do not include a nursery stage.Footnote ³ The supply of cash-priced early weaned pigs, equation (8), specifies the quantity of cash-priced early weaned pigs supplied as a function of expected pig prices $\left(E_{t-20} [P_t^{CEW} ]\right)$ and feed prices ( $P_{t - 20}^F$ ) at the beginning of gestation. In contrast, the supply of cash-priced feeder pigs, equation (5), specifies the quantity of cash-priced feeder pigs as a function of contemporaneous cash prices for feeder pigs ( $P_t^{CN}$ ). This is because pigs rapidly outgrow the farrowing pen after weaning and the transition to feed, more than doubling in weight in the three weeks after weaning (Schinckel et al., Reference Schinckel, Ferrel, Einstein, Pearce and Boyd2004). In the nursery phase, however, pigs can be commingled at the risk of exposing younger pigs to pathogens from older pigs (Fangman & Tubbs, Reference Fangman and Tubbs1997). Equation (9) is the market clearing condition for cash-priced early weaned pigs.

4. Data

We collect data used in this analysis from publicly available sources. Unless otherwise specified, all data are at a weekly level and span January 2013 to December 2023. Prices are deflated by the Prices Paid Index for Commodities and Services, Interest, Taxes, and Wage Rates (PPITW) published by the USDA’s National Agricultural Statistics Service (USDA-NASS), and all monthly or quarterly variables are imputed to a weekly level using linear interpolation. Table 1 contains descriptive statistics for the variables used in the analysis.

Table 1.

Descriptive statistics for variables. Frequency is weekly. Data period is from January 2013 to December 2023. Number of observations is 516. All prices deflated by the USDA-NASS prices paid index for commodities and services, interest, taxes, and wage rates, with January 2013 as the base period

Producers voluntarily report feeder pig sales to USDA’s Agricultural Marketing Service (USDA-AMS). USDA-AMS groups feeder pigs into 10 – 12-pound pigs (early weaned) and 40-pound (feeder) pigs. For each category, USDA-AMS further classifies transactions as either cash or formula. Quoted prices are on a per head basis delivered to the buyer’s farm and include freight and fees. USDA-AMS adjusts prices by a slide to conform to the 10- to 12- and 40-pound reporting categories.Footnote ⁴ Data are published in the USDA-AMS National Direct Feeder Pig report. The Livestock Marketing Information Center (LMIC) compiles the weekly data into a spreadsheet. These data provide cash prices and quantities for early weaned and feeder pigs ( $P_t^{CEW},Q_t^{CEW},P_t^{CN},Q_t^{CN}$ ). Over the period of this study, cash prices averaged $57.36 per head for feeder pigs and $38.70 per head for early weaned pigs. The average weekly volume of cash-priced early weaned pigs is around four times the volume of cash-priced feeder pigs.

For the opportunity costs of retaining a gilt ( $E_{t-45} [P_t^{CEW} ],E_{t-45} [P_t^{CN} ]$ ), we adopt a naïve expectations approach, similar to McKendree et al. (Reference McKendree, Tonsor, Schroeder and Hendricks2019), and use a 45-week lag of the relevant feeder pig price ( $P_{t-45}^{CEW},P_{t-45}^{CN}$ ). The feeder pig report dataset also contains the number of pigs sold by lot size: <600, 600 – 1,200, and >1,200 head. We construct the SmallLotShare _t variables as the number of cash-priced early weaned (feeder) pigs sold in lots of <600 or 600 – 1,200 divided by the total number of cash-priced early weaned (feeder) pigs sold in a given week. The average share of cash-priced feeder pigs sold in small lots is roughly three times that of early weaned pigs.

We assume that USDA-reported data on pig sales is representative of all pig transactions. Producers report data to USDA voluntarily. Pigs imported from Canada are included in the data and typically comprise 30% of the published volume. Published volumes of cash-priced early weaned and feeder pigs range between 1.9 and 3.6 million head per year. For context, FI slaughter of barrows and gilts averaged around 120 million head per year (USDA-AMS, n.d.), so published pig cash sales cover fewer than 3% of hogs raised for slaughter.Footnote ⁵ Since reporting is voluntary, there are pig sales not accounted for in USDA data. Pigs within an integrated system are transferred inter-farm but not marketed. This is a growing share as more pigs are raised under production contracts. In 2022, 35% of hog and pig sales were from independent growers, and 65% were from contract growers (contractees) or contractors or integrators (USDA-NASS, 2024). As the pork industry has integrated, pig markets have become residual markets defined by thinness of trade. However, residual markets can serve an important role in facilitating inventory adjustment in addition to price discovery (Peterson, Reference Peterson2005; Franken and Parcell, Reference Franken and Parcell2012).

USDA does not grade feeder pigs; thus, we cannot control for variation in health and other characteristics. USDA takes steps to ensure data quality and representativeness, and we are unaware of any evidence that reported and nonreported prices or attributes are systemically different (USDA-AMS, 2021).

For market hog prices ( $P_t^M$ ) and quantities ( $Q_t^M$ ), we use the Chicago Mercantile Exchange (CME) Lean Hog Index. This is a representative price, and volume, for hogs that are marketed in the cash negotiated market or use formulas that establish prices in reference to negotiated hog prices and/or pork cutout values.Footnote ⁶ Data are compiled by LMIC and then aggregated to a weekly level by taking a volume-weighted average of the daily data. Under the assumption of naïve expectations, these prices are also used for the expected price of a market hog in the market hog supply and feeder pig demand equations. That is, we use $P_{t-22}^M$ for $E_{t-22} [P_t^M ]$ in equation (2) and $P_t^M$ for $E_t [P_{t+22}^M ]$ in equation (4), and $P_{t-17}^M$ for $E_{t-17} [P_t^M ]$ in equation (8) and $P_t^M$ for $E_t [P_{t+17}^M ]$ in equation (10). Prices are dollars per hundredweight, and volumes are in hundredweight for consistency. This is because the average weight for market hogs varies over the period. In contrast, pig prices and volumes conform to 10 – 12- and 40-pound categories, so prices in dollars per head and volumes in head are consistent. For the period of this study, the CME Lean Hog Index averaged $70.85 per hundredweight with a weekly volume of 1,580,246 hundredweight. This volume is around one third of weekly FI slaughter of barrows and gilts (USDA-AMS, n.d.).

Structural change in the pork industry is a key motivation of this study. Figures 2 and 3 display the relationships among price and volume data for market hogs, feeder pigs, and early weaned pigs that are included in the model. Prices exhibit seasonal variation and are highest in 2014 and lowest in 2020, corresponding to the initial porcine epidemic diarrhea virus (PEDV) outbreak and COVID-19 disruptions, respectively. Volumes of cash-priced early weaned pigs exhibit an upward trend, while market hog volumes, measured by the CME Lean Hog Index volume, decline. This is consistent with increased packer ownership of hogs, increased marketing and production contract use, as well as classification changes to USDA reporting categories (Butcher and Schulz, Reference Butcher and Schulz2021).

Figure 2.

Prices for hogs and pigs. Market hog prices are from the CME lean hog index ($ per hundredweight). Feeder and early weaned pig prices ($ per head) are cash prices from the USDA-AMS national direct feeder pig report.

Figure 3.

Volumes for hogs and pigs. Market hog volumes are taken from the CME lean hog volume (hundredweight). Feeder and early weaned pig volumes (head) are for cash-priced pigs from the USDA-AMS national direct feeder pig report.

We calculate a wholesale demand index (WholesaleDemand _t ) using the pork cutout value and its associated volume from the USDA-AMS National Daily Pork FOB Plant – Negotiated Sales – Afternoon (LM_PK602) report. Data are compiled and aggregated to a weekly level by LMIC. This data was incorporated into Livestock Mandatory Reporting in 2013 but reported voluntarily prior to that. The wholesale demand index is calculated similarly to the retail demand index in McKendree et al. (Reference McKendree, Tonsor, Schroeder and Hendricks2019) and for the own-price elasticity we use −0.471 from Lusk et al. (Reference Lusk, Marsh, Schroeder and Fox2001). Following McKendree et al., consumer sentiment is used as an instrument for the wholesale demand index in the empirical model. Consumer sentiment data is taken from the monthly Index of Consumer Sentiment published by the University of Michigan’s Survey of Consumers and linearly interpolated to a weekly level. This index (ConsumerSentiment _t ) captures consumers’ assessment of current and expected economic conditions in the United States.

Corn and soybean meal prices are the average prices for the next expiring CME futures contract for all days within a week, data which LMIC compiles. We use these data to construct feed prices by assuming a constant feed ratio of one bushel of corn per nine pounds of soybean meal (Christensen and Schulz, Reference Christensen and Schulz2022). Our feed price variable ( $P_t^F$ ) is then the cost per bushel of corn plus nine times the cost per pound of soybean meal.

We derive sow prices from USDA-AMS Daily Direct Prior Day Sow and Boar Report. This report provides daily head counts and weighted average prices in dollars per hundredweight for purchased sows, grouped into weight ranges. We use the price series for sows purchased on a live basis via negotiation. LMIC compiles these data and aggregates daily prices and volumes to a weekly level by taking the head count weighted average. We then take the head count weighted average of sow prices for three weight ranges – 300 to 449 pounds, 450 to 499 pounds, and 500 pounds and above – to construct our sow price variable ( $P_t^{SOW}$ ).

To proxy for disease prevalence, we use preweaning mortality (PreweaningMortality _t ) data from PigCHAMP (n.d.). This data represents the percentage of pigs that are born alive but die before weaning. PigCHAMP collects these data every quarter from thousands of sows farrowing across hundreds of farms that implement its data collection and management software. We linearly interpolate to a weekly level. Postweaning mortality data is not readily available. Therefore, preeaning mortality is also a proxy for postweaning mortality, which is relevant for operations that buy or sell pigs on feed. The average preweaning mortality rate is 15.27% and ranges from 14.44% to 16.97% for the period of this study. There is an upward trend in preweaning mortality over time, and the preweaning mortality data is only weakly correlated with the monthly dummy variables included in the model to capture seasonality.

Production contract share is taken directly from USDA-NASS Quarterly Hogs and Pigs reports and linearly interpolated to a weekly level. These shares are the total number of hogs under contract owned by operations with over 5,000 head, but raised by contractees, divided by the total all hogs and pigs inventory on the U.S. farms.

Packer hog share (PackerShare _t ) is derived from data in the USDA-AMS National Daily Direct Hog Prior Day Report - Slaughtered Swine (LM_HG201), also compiled and aggregated to a weekly level by LMIC. The variable is simply the number of slaughtered hogs owned or sold by a packer – that is, not producer-sold – divided by the total slaughter hog volume published in the report.

Hog processing plant capacity utilization is calculated from the USDA-AMS Actual Slaughter Under Federal Inspection (SJ_LS711) report,Footnote ⁷ compiled by LMIC. We construct a hog processing plant capacity utilization variable (PlantUtilization _t ) by dividing the current week’s slaughter volume of barrows and gilts by the maximum slaughter volume having occurred over the prior three years for the same week, following the approach used by Tonsor and Schulz (Reference Tonsor and Schulz2020).

Pork cold storage capacity utilization is calculated from the USDA-NASS Cold Storage report. This report contains the total pounds of frozen pork in public and private cold storage warehouses at the end of each month, which we linearly interpolate to a weekly level. We construct a cold storage capacity utilization variable (ColdStorageUtilization _t ) similarly to the hog processing plant capacity utilization variable. It is the current week’s pork stocks in cold storage divided by the highest stocks for the current week from the prior three years.

5. Empirical model

For estimation of the empirical model we implement a two-step GMM procedure (Wooldridge, Reference Wooldridge2002, Chapter 8). We use the IVSystemGMM module of the linearmodels package in Python 3.8 to conduct estimation. In all cases, we use heteroskedasticity-robust standard errors. All equations are specified in log-log form, excluding share and deterministic variables; thus, we can interpret coefficients as elasticities or flexibilities. Finally, the vector of deterministic variables ( D _t ) includes a linear time variable and monthly dummy variables with January excluded to account for Technology _t and Seasonality _t , respectively. The deterministic vector also includes a year dummy variable for 2020 to adjust for any reporting changes by producers for the USDA-AMS National Direct Feeder Pig report and other issues related to COVID-19 not captured in the model.

We specify the system of equations as:

(10) $$\eqalign{ \ln P_t^M = \; & \alpha _0^M + \alpha _1^M\ln Q_t^M + \alpha _2^M\ln WholesaleDeman{d_t} + \alpha _3^M\ln PlantUtilizatio{n_t} \cr & + \alpha _4^M\ln ColdStorageUtilizatio{n_t} + {\boldsymbol \alpha _m^M{D_t}} + \varepsilon _t^{M,D} \cr} $$

(11) $$\eqalign{ \ln Q_t^M = \; & \beta _0^M + \beta _1^M\ln P_{t - 17}^M + \beta _2^M\ln P_{t - 22}^M + \beta _3^M\ln P_{t - 17}^{CN} + \beta _4^M\ln P_{t - 22}^{CEW} + \beta _5^M\ln P_{t - 17}^F + \beta _6^M\ln P_{t - 22}^F \cr & + \beta _7^M\ln Q_{t - 17}^M + \beta _8^M\ln Q_{t - 22}^M + \beta _9^MPackerShar{e_t} + {\boldsymbol \beta _m^M{\boldsymbol {D_t}}} + \varepsilon _t^{M,S} \cr} $$

(12) $$ \ln P_{t}^{CN}=\alpha _{0}^{CN}+\alpha _{1}^{CN}lnQ_{t}^{CN}+\alpha _{2}^{CN}\ln P_{t}^{M}+\alpha _{3}^{CN}\ln P_{t}^{F}+\alpha _{4}^{CN}\textit{SmallLotShar}e_{t}^{CN}+\boldsymbol {\alpha _{m}^{CN}D_{t}}+\varepsilon _{t}^{CN,D} $$

(13) $$\eqalign{ \ln Q_t^{CN} =& \; \beta _0^{CN} + \beta _1^{CN}\ln P_t^{CN} + \beta _2^{CN}\ln P_{t - 25}^F + \beta _3^{CN}\ln P_{t - 45}^{CN} + \beta _4^{CN}\ln P_{t - 25}^{SOW} + \beta _5^{CN}\ln Q_{t - 28}^{CN} \cr & + \beta _6^{CN}PreweaningMortalit{y_t} + \beta _7^{CN}ContractShar{e_t} + \beta _8^{CN}\ln P_{t - 5}^{CEW} + \boldsymbol \beta _m^{CN}{\boldsymbol{D_t}} + \varepsilon _t^{CN,S} \cr} $$

(14) $$\eqalign{ \ln P_t^{CEW} =& \; \alpha _0^{CEW} + \alpha _1^{CEW}{\rm{ln}}Q_t^{CEW} + \alpha _2^{CEW}{\rm{ln}}\; P_t^M + \alpha _3^{CEW}{\rm{ln}}\; P_t^F + \alpha _4^{CEW}SmallLotShare_t^{CEW} \cr & + {\boldsymbol \alpha _m^{CEW}{\boldsymbol {D_t}}} + \varepsilon _t^{CEW,D} \cr} $$

(15) $$\eqalign{ \ln Q_t^{CEW} = & \; \beta _0^{CEW} + \beta _1^{CEW}\ln P_{t - 20}^{CEW} + \beta _2^{CEW}\ln P_{t - 20}^F + \beta _3^{CEW}\ln P_{t - 45}^{CEW} + \beta _4^{CEW}\ln P_{t - 20}^{SOW} \cr & + \beta _5^{CEW} \ln Q_{t - 23}^{CEW} + \beta _6^{CEW}PreweaningMortalit{y_t} + \beta _7^{CEW}ContractShar{e_t} + {\boldsymbol \beta _m^{CEW}{\boldsymbol {D_t}}} \cr & + \varepsilon _t^{CEW,S} \cr} $$

Equation (10) is the inverse demand for market hogs. It is analogous to equation (1). Equation (11) is the supply of market hogs. It is analogous to equation (2). Equation (12) is the inverse demand for cash-priced feeder pigs, and equation (13) is the supply of cash-priced feeder pigs; these correspond to equations (4) and (5). Equations (14) and (15) are the inverse demand for and supply of cash-priced early weaned pigs. They are analogous to equations (7) and (8). We estimate equations (10)–(15) jointly.

In equation (10), the endogenous variables are the quantity of market hogs ( ${\rm ln}\; Q_t^M$ ), wholesale demand index (lnWholesaleDemand _t ), hog processing plant capacity utilization (lnPlantUtilization _t ), and pork cold storage capacity utilization (lnColdStorageUtilization _t ). In equation (11), all variables are exogenous by construction. We use all unshared independent variables as excluded instruments, so the system is overidentified. For equation (10), the excluded instruments are ${\rm ln} \; P_{t-17}^M$ , ${\rm ln} \; P_{t-22}^M$ , ${\rm ln} \; P_{t-17}^{CN}$ , ${\rm ln} \; P_{t-22}^{CEW}$ , ${\rm ln} \; P_{t-17}^F$ , ${\rm ln} \; P_{t-22}^M$ , ${\rm ln} \; Q_{t-17}^M$ , ${\rm ln} \; Q_{t-22}^M$ , and PackerShare _t . We include consumer sentiment (ConsumerSentiment _t ) as an additional instrument for the wholesale demand index to ensure we accurately capture shifts in wholesale pork demand that are derived from shifts in consumer demand for pork.

Equation (12) is the inverse demand for cash-priced feeder pigs, and equation (13) is the supply of cash-priced feeder pigs. In equation (12), the endogenous variables are the quantity of cash-priced feeder pigs ( $\ln Q_t^{CN}$ ) and the price of market hogs ( $\ln P_t^M$ ), and the endogenous variable for equation (13) is the cash price of feeder pigs ( ${\rm{\ln}}\,\,P_t^{CN}$ ). As before, we use exogenous independent variables not common to both equations as excluded instruments, and this system is overidentified. For equation (12), the excluded instruments are ${\rm{\ln}}\,\,P_{t - 25}^F,\,\,{\rm{\ln}}\,\,P_{t - 45}^{CN}$ , ${\rm{\ln}}\,\,P_{t - 25}^{SOW},\,\,{\rm{\ln}}\,Q_{t - 28}^{CN}$ , PreweaningMortality _t , ContractShare _t , and ${\rm{\ln}}\,\,P_{t - 5}^{CEW}$ . For equation (13), the excluded instruments are ${\rm{\ln}}\,\,P_t^F$ and ${SmallLotShare_t^{CN}}$ .

In equation (14), the endogenous variables are the quantity of cash-priced early weaned pigs $\left( {{\rm{\ln}}\,Q_t^{CEW}} \right)$ and the price of a market hog ( ${\rm{\ln}}\,\,P_t^M$ ). In equation (15), all variables are exogenous by construction. We again use all unshared independent variables as excluded instruments, so the system is overidentified. For equation (14), excluded instruments are ${\rm{\ln \;}}P_{t - 20}^{CEW},\,{\rm{\ln}}\,P_{t - 20}^F,\,{\rm{\ln }} \; P_{t - 45}^{CEW},\,{\rm{\ln }} \; P_{t - 20}^{SOW},\,{\rm{\ln }}\; Q_{t - 23}^{CEW}$ , PreweaningMortality _t , and ContractShare _t .

7. Simulations

Two key periods of disruption that motivate this paper are 2020 and 2023. While the drivers of events during these years are distinct, the common outcome was lower profit levels for hogs and pigs (Schulz, Reference Schulzn.d.). We use the model’s results to find the effects of three hypothetical scenarios:

1. 1. What if hog processing plant capacity did not expand and remained at 2016 levels during the second and third quarter of 2020?

2. 2. What if wholesale pork demand in 2023 had remained at 2022 levels?Footnote ¹⁰

3. 3. How much would the supply of hogs and pigs have needed to be reduced in order for producers to breakeven in 2023?

Because the system of equations relies on lags of prices and quantities, model outputs become model inputs in the future. Hence, a simulation procedure is necessary.

For scenarios 1 and 2, the simulation is similar to McKendree et al. (Reference McKendree, Tonsor, Schroeder and Hendricks2019). Baseline values for each scenario are found by predicting prices and quantities for market hogs, feeder pigs, and early weaned pigs using observed values for other variables at the start of the period. These predictions are stored, and the next week is predicted. This continues, and predicted prices and quantities are eventually picked up as lagged prices and quantities in the model. The steps for simulating the 2020 capacity scenario are the same as the 2020 baseline scenario but incorporate a shock to hog processing capacity. This shock comes from substituting the observed hog processing plant utilization-to-capacity ratio in 2020 for a hog processing plant utilization-to-capacity ratio calculated with 2016 capacity levels, that is, as if capacity were not expanded from 2016 to 2020. The 2023 demand scenario is also simulated like the baseline but substitutes observed levels of wholesale pork demand from 2023 for levels from 2022.

For scenario 3, reducing the hog and pig supply in 2023, the baseline is found as before, but the procedure for simulating shocks differs. This scenario considers the effect of supply on prices, taking demand as given. As such, we fix prices at particular levels where hog and pig producers would breakeven and then solve for the quantity that satisfies this relationship. Based on Iowa State University’s Estimated Livestock Returns - Swine (Schulz, Reference Schulzn.d.), in 2023 the breakeven prices are assumed to be $95 per hundredweight for finishing operations, $75 per head for farrow-to-feeder operations, and $45 per head for farrow-to-wean operations.Footnote ¹¹ For market hogs, the resulting calculation is derived from equation (10) as

(18) $$\ln Q_t^M = {1 \over {\alpha _1^M}} \times \left[ \matrix{\ln \left( {95} \right) - \alpha _0^M - \alpha _1^M - \alpha _2^M\ln WholesaleDeman{d_t} \hfill \cr - \;\alpha _3^M\ln PlantUtilizatio{n_t} - \alpha _4^M\ln ColdStorageUtilizatio{n_t} - {\boldsymbol {\alpha _m^M{{D_m}}}} \hfill \cr} \right]$$

Similar expressions for the quantity of feeder pigs and early weaned pigs are derived from equations (12) and (14).Footnote ¹² Like shocks for other scenarios, predicted quantities are stored and used in subsequent predictions. Unlike other scenarios, however, prices remain fixed at the breakeven level.

Results for each scenario are shown in Table 5. In the first scenario, had processing capacity in the second and third quarter of 2020 been at 2016 levels, market conditions would have been far worse for producers. In the short term, feeder pig supply is responsive to market conditions, but early weaned pig and market hog supplies are fixed. In turn, shocks are transmitted through both prices and quantities for feeder pigs but primarily prices for early weaned pigs and market hogs. Price declines in this scenario are relatively larger on a percentage basis for market hogs (19%) and early weaned pigs (20%) than feeder pigs (15%). Only feeder pigs had a nonnegligible decrease in quantity (42%).

Table 4.

Inverse demand and supply coefficient estimates for early weaned pigs. Coefficients are interpreted as the percent change in the dependent variable for a one-percent change in the independent variable for log-transformed variables, a one-percentage-point change for contract production share and mortality variables, and a one-unit change for deterministic variables

* p < 0.1, ** p < 0.05, *** p < 0.01.

The second scenario quantifies the effects of falling wholesale pork demand in 2023. If wholesale pork demand had stayed at 2022 levels in 2023, prices would have been higher for market hogs (4%), feeder pigs (4%), and early weaned pigs (5%). As in the first scenario, only feeder pigs would have had a nonnegligible supply response, increasing the number of feeder pigs purchased by 10%. This is because there is a contemporaneous decision to sell feeder pigs, whereas the supply of market hogs and early weaned pigs is affected through lagged price expectations.

The third scenario finds the quantity of market hogs, feeder pigs, and early weaned pigs at which the price paid for each would be equal to the cost of production. It mirrors the second scenario in the sense that it finds the supply shock necessary to achieve certain price levels rather than how a demand shock is transmitted through prices. In contrast with the first and second scenarios, supply shifts are relatively large in each market. To reach a price of $95 per hundredweight for market hogs, a 14% increase over the baseline, supply would have to fall by 19%. To reach prices of $75 per head for feeder pigs, 29% over the baseline, and $45 per head for early weaned pigs, 39% over the baseline, the supply of each would have to fall by 31 and 23%, respectively. Extrapolating the market hog supply shock – 19% decrease – to annual hog slaughter at FI facilities in 2023 – 116,558,200 head (USDA-NASS, n.d.-b)– a reduction of around 22 million market hogs would have been required for finishing operations to breakeven. At a rate of 27 pigs weaned per sow per year (PigCHAMP, n.d.), this translates to removing around 800,000 sows from the breeding herd. Using the December 2022 breeding herd as the denominator (USDA-NASS, n.d.-a), this reduction would be 800, 000 ÷ 6, 203, 500 ≈ 13% of the domestic breeding herd. For comparison, one industry analyst estimated that the domestic sow herd would need to be reduced between 6 and 10% to make pork production profitable (Eller, Reference Eller2024).

The second and third scenarios consider two paths for making hog producers more profitable, increasing demand or decreasing supply. Note that these scenarios are not intended to be comprehensive or directly compared. Conceptually, there is a level of wholesale pork demand that would push prices to their breakeven level in the model. Rather, these scenarios illustrate the effects of demand- and supply-side drivers in shifting market outcomes in the context of particular events and initiatives within the pork industry. Turning to the results, had wholesale pork demand remained at 2022 levels in 2023, market hog prices would have been $86.79 per hundredweight. However, neither feeder pig prices ($60.29 per head) nor early weaned pig prices ($33.86 per head) would have been close to their breakeven price. This is because market hog prices in 2023 were closer to their breakeven than feeder and early weaned pig prices. While keeping wholesale pork demand at higher 2022 levels could have made finishing operations more profitable in 2023, it would not have been sufficient for farrow-to-feeder or farrow-to-wean operations to reach their breakeven thresholds.

Key to understanding this result is considering how costs changed from 2022 to 2023. Based on Iowa State University’s Estimated Livestock Returns – Swine (Schulz, Reference Schulzn.d.), total costs per pig for farrow-to-wean operations increased from around $41 in 2022 to $44 in 2023. The incremental cost of the nursery phase was consistent at around $28 per pig in both 2022 and 2023, so total costs per pig increased from $69 to $72 from 2022 to 2023 for farrow-to-feeder operations. However, total costs per hundredweight fell from $102 to $97 for wean-to-finish operations and $105 to $92 for feeder-to-finish operations because early weaned and feeder pig prices were lower. In sum, total production costs increased for farrow-to-wean and farrow-to-feeder operations but decreased for finishing operations. Stronger wholesale pork demand would have attenuated losses for pig producers, but cost increases in pig production offset some of this gain. Because hog finishing costs fell due to lower pig placement prices, stronger wholesale pork demand would have pushed hog prices close to their breakeven.