Data

Each year, the Middle Tennessee Research and Education Center in Spring Hill, Tennessee markets performance-tested senior bulls in January (University of Tennessee Department of Animal Science, 2019). Senior bulls are born from the first of September to mid-December; therefore, these bulls are between 13 and 17 months old when sold. Breeders deliver their bulls to the test station in August before the sale. The bulls go through a 2-week adjustment period, and then an 84-day weight gain test where they are fed a commercial bull developing ration containing 12% crude protein.

After the test period, phenotypic measures for each bull are recorded including hip height, scrotal circumference, sale weight, frame score, and on-test average daily gain. These measurements, along with pretest information such as actual birth weight and weaning weight, the full suite of EPDs, and carcass ultrasound data (fat thickness, ribeye area, and intramuscular fat), are published in a catalog and online to potential buyers for each bull. Bulls are sold in a public first-price auction.

Data used in this study are from the 2013 to 2021 sales. Since most of the bulls in this sale being purebred Angus, we restrict this study to Angus animals. We used information from a total of five hundred Angus bulls that were sold over the 9-year time. This span of sale data included bulls with EPDs and GE-EPDs. From 2013 to 2016, none of the bulls in this study had a GE-EPD. From 2017 to 2021, all bulls used in this study had a GE-EPD. A description of variables considered to impact sale price is shown in Table 1. Table 2 shows the summary statistics for these variables. Bulls were only considered if their information in the data set was complete. The average sale price was $3,383 per head, with a range of $1,250–$8,250. Figure 1 shows the mean sale price for bulls in the years 2013–2021. The average weight was 1,403 pounds, and the average age was 433 days old.

Figure 1.

Average annual sale price of angus bulls sold from 2013 to 2021 in the University of Tennessee’s Middle Tennessee Research and Education Center Bull Sale.

Table 1.

Definition of independent and dependent variables

Table 2.

Summary statistics of independent and dependent variables

Statistical Analysis

A hedonic pricing model was used to determine whether, or not, phenotypic traits and EPD’s influence the sale price of bulls (Boyer et al., Reference Boyer, Campbell, Griffith, DeLong, Rhinehart and Kirkpatrick2019; Brimlow and Doyle, Reference Brimlow and Doyle2014; Dhuyvetter et al., Reference Dhuyvetter, Schroeder, Simms, Bolze and Geske1996; Jones et al., Reference Jones, Turner, Dhuyvetter and Marsh2008; Kessler, Pendell, and Enns, Reference Kessler, Pendell and Enns2017; Vestal et al., Reference Vestal, Lusk, DeVuyst and Kropp2013). We specify a log-level model by using the log-transformed the sale price to correct non-normal distribution (Wooldridge, Reference Wooldridge2013). Since all bulls are sold individually, we estimate the model using the bull as the experimental unit impacted over time. The model is shown as

(1) $$\ln \left( {{P_{it}}} \right) = \alpha + {\delta _1}G{E_{it}} + \mathop \sum \nolimits_{j = 1}^6 {\beta _j}{X_{itj}} + \mathop \sum \nolimits_{j = 1}^6 {\gamma _j}{X_{itj}}G{E_{it}} + \mathop \sum \nolimits_{k = 1}^7 {\theta _k}{Z_{itk}} + {v_t} + {u_l} + {\varepsilon _{it}}$$

where P _it is the sale price ($/head) of bull if in year t; ${\rm GE}_{it}$ is an indicator variable equal to one if the bull had GE-EPD and zero otherwise; and X _itj are j EPD covariates including weaned calf value, birth weight, milk, marbling, fat thickness, and ribeye area. The interaction between GE-EPD and EPD covariates is represented within the model multiplying X _itj by ${\rm GE}_{it}$ ; Z _itk are k phenotype covariates including sale weight, frame score, age, scrotal circumference, ribeye area, intermuscular fat, and fat thickness; v _t is the year trend variables (linear, squared, and cubic); u _l is the sale order effect; α, β, δ, γ, v, u, and θ are coefficients to be estimated; and ϵ _it ∼ N(0,σ _ϵ ²) is the random error term. Interaction between GE-EPD and EPD covariates to determine if the GE-EPD test was significant for any specific EPD although a GE-EPD test is for all EPDs.

Parameter estimates can be converted to a dollar change in the dependent variable with a one-unit change in the independent variable of interest by multiplying the parameter estimates by the average predicted selling price of the bulls in the sample (Wooldridge, Reference Wooldridge2013). This conversion yields a marginal effect of a change in the independent variable at the average price. A one-unit change in the independent variable would be unlikely for some bull traits. These marginal effects at the average price were converted into realistic unit changes for each variable of interest.

We also specify our model to have standardized independent variables with a level dependent variable (Kessler, Pendell, and Enns, Reference Kessler, Pendell and Enns2017; Lewis et al., Reference Lewis, Griffith, Boyer and Rhinehart2016; Mark, Schroeder, and Jones, Reference Mark, Schroeder and Jones2000; McDonald et al., Reference McDonald, Brester, Bekkerman and Paterson2010). This transforms regression coefficients from units to being standard deviations, which is helpful for making relative comparison of impact across the independent variables. This approach is commonly done for hedonic animal pricing models since independent variables are in different units. We standardized regression coefficients by subtracting the mean from the observed value and dividing that by the standard deviation. This is the same transformation followed by others (Brimlow and Doyle, Reference Brimlow and Doyle2014; Kessler, Pendell, and Enns, Reference Kessler, Pendell and Enns2017; Lewis et al., Reference Lewis, Griffith, Boyer and Rhinehart2016; Mark, Schroeder, and Jones, Reference Mark, Schroeder and Jones2000; McDonald et al., Reference McDonald, Brester, Bekkerman and Paterson2010). Therefore, the coefficients are interpreted as a one-unit standard deviation would result in a change in the standard deviation of the bull sale prices by the value of the coefficient.

Heteroscedasticity is a frequent problem for estimating cattle hedonic pricing models (Jones et al., Reference Jones, Turner, Dhuyvetter and Marsh2008; Kessler, Pendell, and Enns, Reference Kessler, Pendell and Enns2017). The likelihood ratio test was used to determine if heteroscedasticity was present from year and actual weight. If heteroscedasticity was present, we corrected it using multiplicative heteroscedasticity in the variance equation (Wooldridge, Reference Wooldridge2013). Additionally, multicollinearity is an issue in hedonic pricing models for bulls (Boyer et al., Reference Boyer, Campbell, Griffith, DeLong, Rhinehart and Kirkpatrick2019; Brimlow and Doyle, Reference Brimlow and Doyle2014; Kessler, Pendell, and Enns, Reference Kessler, Pendell and Enns2017; Vanek et al., Reference Vanek, Watts and Brester2008). Failing to correct for this issue can result in flawed conclusions. Person correlation coefficients were estimated for all variables. As anticipated, birth weight EPD and calving ease direct EPD were highly correlated. Therefore, we dropped calving ease direct EPD and included birthweight EPD in the model. Additionally, this study includes weaned calf value index, which is an index that expresses in dollar per head of predicted profitability differences in progeny due to genetics from birth to weaning. This value is highly correlated with weaning weight EPD. Therefore, we drop weaning weight EPD to contribute to the literature by analyzing weaned calf value index.Footnote ¹ These models were estimated using maximum likelihood with the MIXED procedure in SAS 9.4 (SAS Institute, 2013).

Hypotheses for Variable Sign

We hypothesize that bull sale price will increase as weaned calf value EPD increases. We base this hypothesis on the weaned calf value index indicates higher profit potential per offspring. Previous studies have shown that weaning weight EPD positively correlated the sale price of bulls (Chvosta, Rucker, and Watts, Reference Chvosta, Rucker and Watts2001; Dhuyvetter et al., Reference Dhuyvetter, Schroeder, Simms, Bolze and Geske1996). However, no study has explored the impact of the weaned calf value economic selection index on bull sale price.

Studies have shown that an increase in birthweight EPD can decrease the price of bulls (Brimlow and Doyle, Reference Brimlow and Doyle2014; Jones et al., Reference Jones, Turner, Dhuyvetter and Marsh2008; Vestal et al., Reference Vestal, Lusk, DeVuyst and Kropp2013). Likely, a producer selecting sires to be used on all females or exclusively virgin heifers will desire a bull with a lower birth weight for calving ease. Calving ease direct EPD is highly correlated with birthweight EPD, as calves with smaller birth weights are less likely to have calving complications. As mentioned above, we chose to use birthweight EPD in our analysis due to this correlation. Studies have used either calving ease direct EPD (Boyer et al., Reference Boyer, Campbell, Griffith, DeLong, Rhinehart and Kirkpatrick2019), but it is more common in the literature to see birth weight EPD (Brimlow and Doyle, Reference Brimlow and Doyle2014; Kessler, Pendell, and Enns, Reference Kessler, Pendell and Enns2017; Tang et al., Reference Tang, Thompson, Boyer, Widmar, Stewart, Lofgren and Minton2020, Reference Tang, Thompson, Boyer, Olynk Widmar, Lusk, Stewart, Lofgreen and Minton2022). We follow these studies and hypothesize that an increase in birth weight EPD is correlated with decreased sale price.

An increase in milk EPD has also been reported to increase bull sale price (Boyer et al., Reference Boyer, Campbell, Griffith, DeLong, Rhinehart and Kirkpatrick2019; Jones et al., Reference Jones, Turner, Dhuyvetter and Marsh2008; Vestal et al., Reference Vestal, Lusk, DeVuyst and Kropp2013); however, Kessler, Pendell, and Enns (Reference Kessler, Pendell and Enns2017) found the converse to be true. Milk production also requires a higher nutritional demand, which can increase feed costs for a sire’s daughters. A moderate milk EPD is ideal, but the optimum will rely on an operation’s environment and management. Marbling, ribeye, and fat thickness EPD were hypothesized to be insignificant based on previous work (Tang et al., Reference Tang, Thompson, Boyer, Widmar, Stewart, Lofgren and Minton2020, Reference Tang, Thompson, Boyer, Olynk Widmar, Lusk, Stewart, Lofgreen and Minton2022).

For the phenotypic traits, studies have reported that higher sale weights tended to increase a bull’s sale price (Boyer et al., Reference Boyer, Campbell, Griffith, DeLong, Rhinehart and Kirkpatrick2019; Brimlow and Doyle, Reference Brimlow and Doyle2014; Kessler, Pendell, and Enns, Reference Kessler, Pendell and Enns2017). The expected impact of frame score is unclear since studies commonly find this trait to be insignificant factors for influencing the price of a bull (Kessler, Pendell, and Enns, Reference Kessler, Pendell and Enns2017; Vestal et al., Reference Vestal, Lusk, DeVuyst and Kropp2013). Scrotal circumference is an estimate of reproductive performance and is sometimes found to be positive (Tang et al., Reference Tang, Thompson, Boyer, Widmar, Stewart, Lofgren and Minton2020). This is important to many producers since reproductive failure can result in substantial economic losses (Boyer, Griffith, and DeLong, Reference Boyer, Griffith and DeLong2020).