Beef and pork processing plant labor costs

Funding information 58‐0111‐21‐019; Office of the Chief Economist; U.S. Department of Agriculture Abstract Federal and state legislators recently enacted policies to fund new and renovated small and local meat processors expansion with the aim of increasing the meat‐processing sector's resiliency. Wages must be competitive to attract employees for these new and renovated plants to be competitive. No previous studies have examined what has happened to employee labor costs at United States (US) meat‐processing plants since the early 2000s. This study estimates how meat‐processing firm size affects employee wages in the US. We use average employee wages for beef and pork processing plants from 2007 to 2019. We find larger plants pay higher wages than smaller ones, which is likely attributable to lower fixed costs resulting from economies of scale. Findings suggest that facilities with more than 500+ employees will most likely offer wage that are high enough to recruit workers in for this industry. Small plants will need to increase real wages that are higher than historical averages. Thus, if smaller facilities increase the sector's resiliency, then it will likely come at a cost in terms of higher wage bills. [EconLit Citations: Q12, Q18].


| INTRODUCTION
Examining the resiliency and flexibility of the United States (US) meat processing supply chain emerged as an important research topic in the initial wake of COVID-19 (Bina et al., 2022;Ma & Lusk, 2021;Ijaz et al., 2021;Wahdat & Lusk, 2023). Across the US, meat-processing plants experienced numerous COVID-19 outbreaks, resulting in temporary shutdowns and a reduction in output. These events led to serious disruptions along protein supply chains (Krumel & Goodrich, 2022;Taylor et al., 2020) and rapid declines in animal prices combined with higher meat prices (Martinez et al., 2021). Policy makers focused efforts on to expand industry capacity (United States [US] Department of Agriculture [USDA], 2021b). Along with these investments, additional funding targeted meat processing workforce development and supported the development of lending programs to finance the capital needed to build these plants (USDA, 2021a).
State and federal initiatives share the same goal of providing more opportunities for meat processing at smaller plants that cater to local demand for their services. A rationale of policies to expand smaller and more localized meat processing plants is to increase supply chain resiliency and flexibility or the time it takes for a firm to return to performance levels after experiencing a shock. Bina et al. (2022) found that such policies may generate unintended outcomes, given that labor is a key constraint for US meat processors (Bina et al., 2022;Hobbs, 2021;Ma & Lusk, 2021;Wahdat & Lusk, 2023). Meat processing industry employment has decreased over the last decade (Luckstead et al., 2022). More recently, the risk of COVID-19 spreading among meat processing employees and the shutdown of production lines due to a reduction in workers were the primary drivers of these disruptions (Luckstead et al., 2021(Luckstead et al., , 2022Ramsey et al., 2021). The pandemic exposed how vulnerable the animal slaughtering and the processing industry are to labor shocks in terms of gross output (Wahdat & Lusk, 2023).
These proposed policy goals also reverse a general trend in the meat-processing sector over the past halfcentury of consolidation toward fewer large processing plants. Crom (1988) reported the number of US livestock physical slaughter plants declined by 46% from 196746% from to 198646% from . Crom (1988 noted that a few large plants were built and operated more intensively using double shifts and 6-day work weeks. This trend continued through the 1990s (Hornung, 2004;Ward & Hornung, 2005). Hornung (2004) concluded that, by 1980, there were 520 beef federally inspected (FI) slaughtering plants that harvested 24.5 million head of steers and heifers annually. By 2000, total FI steer and heifer slaughter increased to 29.39 million head per year from fewer larger plants. After 2000, the US FI cattle slaughter industry saw a permanent decline in physical capacity following the closure of several plants, for example, Conagra in 2001, Tyson in 2008, and Cargill in 2013. A similar trend of fewer, but larger processing plants developed for the pork industry as well . The primary drivers of this structural change in the US meatpacking industry were economies of scale and size. Aggregate industry average total costs decreased as slaughter facility output increased (Koontz & Lawrence, 2010;Ward, 1990Ward, , 1993. Previous research suggests that these new and renovated small and local meat processors will need to offer sufficiently higher wages to attract workers in their effort to reduce the threat of labor vulnerabilities and increase the resiliency of the meat-processing supply chain. Wages must also be economically sustainable for the processing plant to remain profitable.  showed that labor costs at pork processing plants increased as the volume of processing increased from the 1970s to 1992, with larger plants paying employees more than smaller processors due to economies of scale. However, MacDonald and Ollinger (2005) found hourly wages were lower for large beef and hog processors than small plants in 1997 and 2002. A recent study by Luckstead et al. (2022) found that the current average wage for a meat-processing employee was lower than employee willingness to accept these jobs. They concluded that the average willingness to accept a wage offer at a meat processing facility was $22.77 per hour, which is higher than the national average of $15 per hour. Since the early 2000s, no previous studies have examined what happened to employee labor costs at US meat-processing plants across firm sizes.
The objective of this study is to determine how several factors, including the size of meat processing facilities, affect employee wages in the US. We use average employee wages for beef and pork processing plants from the Statistics of US Business data tables, 2007 to 2019. The results provide insight into meat-processing wages across different plant sizes and locations. These findings could inform policy maker and agency decisions regarding the distribution of program funds to support wages in effort to stabilize the meat-processing labor force. Results also provide insight into the value of detailed labor data that could address important questions pertaining to the resiliency of the US meat processing supply chain.  These statistics are similar to Luckstead et al.'s (2022) industry average estimates but are below the employee willingness to work in a processing facility. Table 1 also shows there are more processing plants with less than four employees than any other size category. The number of firms declines as size increases, which aligns with the industry concentration reported in previous studies.
Firm size and salary have changed over time. Figure  smaller processing plants. This trend has been documented since the late 1960s (Crom, 1988;Hornung, 2004;. This could indicate that, while the plants with less than four employees increased wages, the increase was well below the industry average. However, higher wage costs might be associated with the decline in small establishments. This is a researchable question but outside the scope of the current study. Figure 2 reports the average adjusted salary from 2007 to 2019. The figure shows that larger firms are able pay higher wages compared to firms with a smaller payroll.

| METHODS AND PROCEDURE
We estimate a log-linear regression of adjusted salary per employee per year by firm size on observed covariates using a Bayesian procedure introduced by Geweke (1993). Geweke's procedure models the distribution of heteroskedastic disturbances as a mixture of normal models, which, under certain regularity conditions, is equivalent to a Student-t distribution for the error terms. Koop  The response model with Student-t errors is: where y itj is the natural logarithm of average annual salary per employee in 2019 dollars for i = 1, …, n states; t indexes years; j indexes establishment size according to employees; μ itj is a mean function for the log of salary; σ is the standard deviation for the model errors; and ω itj is heteroskedastic term that varies across observations. Note that this parameterization is agnostic concerning any formalized heteroskedastic function.
The mean response is parametrized as: (2) with s j fixed effects for facility size class j = establishment with less than 4 employees, 5-9 employees, 10-19 employees, 20-99 employees, and 100-499 employees (500 plus employees are the reference group); c n are fixed effects for state n = 1, …, 42 (Wyoming is the reference state); and τ t are yearly fixed effects for t = 2007…2018 (2019 is the reference year). The variable estab is the number of animal processing establishments.
Priors for the population effects are normal, weakly informative, and centered on zero with a standard deviation of 100: β β s c τ , , , ,~Normal(0, 100).
The normal distribution is used as the prior for the model parameters because (1) the probability the parameter lies below or above zero is the same, and (2) it is centered on zero, which corresponds with our null hypotheses, β = 0 (McElreath, 2020). The prior for the model's error standard deviation is Half-Cauchy with a lower bound of zero and a relatively diffuse prior on the scalar term's variance: σ~Half Cauchy(0,100).
(4) F I G U R E 2 Average annual salary per employee (in 2019 dollars) of beef and hog processing firms by size from 2007 to 2019.
The Cauchy distribution has wide, flat tails and is amenable to modeling potential residual outliers.
The prior for the heteroskedastic terms, ω, is: which is a function of a degrees-of-freedom parameter, ν. The model's degrees of freedom are estimated jointly with the other model parameters. Joint estimation of the degrees of freedom parameter with the other model parameters allows the data to determine the width of the Student-t tails for the error terms. Chung et al. (2013) recommended the following prior for the degrees-of-freedom term: with a lower bound of two. This parametrization ensures that the likelihood estimate is roughly one standard deviation from zero when the estimate of ν is approximately zero.

| Modeling missingness
The US Census Bureau's data does not disclose wages and salaries paid to employees when the number of firms in a reporting district is small enough to identify employers. For this analysis, the number of records was 2514 observations, of which 41% (1025) observations for the dependent variable, salary, were suppressed due to administrative protocol. Isserman and Westervelt (2006) found that suppression is particularly common for establishments located in rural communities since one or several firms may employ a significant share of the community's population.
The effect of missingness on inference depends on the mechanism causing missing values. If records with missing data are dropped, one implicitly assumes that the missing values are missing completely at random (MCAR) (Rubin, 1976). The MCAR assumption maintains that missing patterns are independent of other missing values and of other observed covariates. In this case, dropping records with missing values could reduce the power of tests but otherwise inference proceeds as usual.
The other case, which is relevant here, assumes that suppressed salary records are missing at random (MAR). Unlike MCAR, MAR assumes that the likelihood of suppression is unrelated to other missing values for salary but its missingness is related to other observed data (Rubin, 1976). US Census suppresses employment and salary when an establishment, or several establishments, are identifiable in a surveyed region. Naturally, the pattern of missingness is a function of the number of firms because this is a leading criterion for suppression. Other factors, such as the categorical number of employees, annual-, and state-level effects could ostensibly codetermine suppression along with establishment count. The missing firm information is not "not missing at random" (NMAR) because the missing data mechanism is uncorrelated with missing values for salary and for the reason why the number of firms is candidate predictor of missingness.
Several methods are available for contending with suppressed data issues. The first includes two imputation methods. The first imputation method, proposed by Isserman and Westervelt (2006), uses a hierarchical mathematical programming procedure to impute missing employment and salary information. Lower levels of missingness are filled in using matrix-balancing algorithms such as RAS (Schneider & Zenios, 1990). For example, state level totals are downscaled to county levels, conditioned on variation in employment across industry sectors and states as targets. Use of Isserman and Westervelt's procedure in this study would entail a two-step estimation procedure of the statistical model, with imputation of missing salaries in the first stage, and estimation of the statistical model in the second stage. The second imputation approach uses statistical procedures to generate pseudo-datasets with missing values replaced with predicted values estimated with complete cases. Examples of this procedure include "hot deck" imputation (Lohr, 2010) or the use of multiple imputation by chained equations ("mice") (Zhang, 2016). These procedures also entail a two-step estimation procedure, with imputation in the first stage and estimating the statistical model with the imputed data sets in the second stage.
We use a model-based approach to estimate simultaneously the statistical model and to impute MAR values for the dependent variable; salary. The model-based approach taken here considers missing records as unknown but estimable parameters that share a joint distribution with the population effects and other model components. The advantage of the model-based approach over the previously mentioned imputation procedures is that it specifies a joint density function of the missingness mechanism and the statistical model.  (7) Let w index all observations and W the total number of observations. The variable y* w is observed and equal to y w for w = 1, 2, …, m, m < W . The dependent variable is missing for all other w = m + 1, m + 2, …, W observations. In this case, the joint distribution for the observed and missing values for salary is:

| Estimation procedures
The complete cases (n = 1025) and missing at random models (n = 2514) are estimated with R-Stan's Hamiltonian Monte Carlo and No U-turn Sampler (HMC-NUTS) (Stan Development Team, 2022). The performance of the HMC-NUTS algorithm is superior to Gibbs or standard Metropolis-Hastings algorithms in terms of the number of iterations typically required to achieve convergence and the relative speed the algorithm affords compared to other samplers (Hoffman & Gelman, 2014).
We ran the HMC-NUTS sampler on four parallel chains with 5000 iterations per chain and a warm-up ("burn in") period of 5000 iterations. Every fifth sample was saved following the warm-up period, resulting in 4000 posterior samples for each model parameter. Gelman and Rubin's (1992) R-statistic is used to confirm chain convergence. A R diagnostic approaching one indicates convergence.

| RESULTS
We organize the results by first discussing significant independent variables included in both models, followed by discussion of estimated salaries for workers at different sized facilities. Finally, we connect these findings back to the literature to build on the discussion of labor costs for hog and beef processing facilities. Table 2 reports the model statistics and estimated parameters. All R-statistics are less than 1.01, indicating that both models converged.
The posterior log likelihood value was larger for the model using the completed cases than when modeling with missingness; however, there is little difference in the estimated parameters and their significance.
Annual salary varied across time and state, but the year and state fixed effects are not reported or discussed here. The year fixed effects are included to capture variation in beef and pork demand changes, wage inflation, and employment. State fixed effects are difficult to interpret because employment laws vary across states, but these variables serve as a proxy for this unobserved heterogeneity. Predicted values of salaries by state are reported in an appendix figure.
For both models, the sign and significance of the estimated parameters were similar. These data are MAR, but there does not seem to be any inferential differences in salary for hog and beef processing facilities with or without the missing salary data. This finding is important, considering 41% of the salary data were missing.
The number of firms in a state and by size was not significant in either model. However, the estimated parameters for beef and hog processing facilities with less than 4 employees, 5-9 employees, 10-19 employees, and 20-99 employees were significant and negative. Thus, the labor costs at smaller-sized processing facilities were lower than the labor cost at facilities with 100-499 employees and 500+ employees. There was no difference in annual labor costs for at facilities with 100-499 employees and 500+ employees. Regardless, facilities with more than 500 employees are the size that will most likely achieve wage levels needed to recruit workers in for this industry. surveyed results and found that other benefits, like a signing bonus, could be another way to attract meat-processing workers. Smaller plants currently promoted through newly implemented polices might consider how to utilize other types of employee benefits.

| CONCLUSIONS
Recently, federal and state policies have been enacted to fund the expansion of small and local meat processors. For these policies to increase the meat-processing sector's resiliency, new and renovated plants will need to offer competitive wages to attract employees. However, to our knowledge, no previous study has examined what happened to employee labor costs at US meat-processing plants across various sizes since the early 2000s. This study determined how the size of meat processing facilities affects employee wages in the US. We used average employee wages for beef and pork processing plants from the Statistics of US Business data tables, 2007-2019.
These findings could help policy makers and agency funders make decisions regarding the distribution of funding to the meat-processing sector that would support wages to stabilize the meat-processing labor force.
Results could also provide insight into the value of detailed labor data that could address important questions pertaining to the resiliency of the US meat processing supply chain.
We find annual employee wages vary across meat processing plant size. Larger plants can pay a higher wage than the smaller plants, which is likely due to lower fixed costs attributable to economies of scale. The paper finds that small plants, which are the target of these proposed and active policies, have historically been unable to pay F I G U R E 3 Predicted average annual salary per employee (in 2019 dollars) of beef and hog processing firms by size.
employees the wages needed to retain workers. The results suggest that policies that add physical processing capacity to improve resiliency may generate unintended outcomes, given labor constraints.
A shortcoming of this study is that employee wages at a plant were modeled as an average of all employees.
We know that not all jobs within a meat processing facility are created equally, and thus wages will vary by job title within a plant. Some jobs will, which require more skill in processing, likely get paid a higher wage than other positions (i.e., the person splitting the carcass vs. the person that collects trimmings). High skill jobs are the ones that will have the biggest implications on meat processing resiliency. These are the employees that are harder to train, retain, and replace. This study is unable to estimate wages by job across plant size. That said, the results provide insight into the challenges smaller new or renovated plants will face with labor costs.