Data

The WBIA has been conducting bull performance tests and sales under its Bull Development and Sale Program since 1970. The bulls undergo carcass characteristic evaluation and must pass a breeding soundness test before being sold. A sale catalog is created, which includes detailed EPD profiles, performance data, and video documentation. The best-performing bulls are sold through in-person and online auctions (WBIA). The bull sale catalog contained detailed records on various performance measures, including breed, birth date, birth weight, final weight, on-test weight, weight per day of age, color, frame score, height, dam’s age, average daily gain, and ultrasound data such as average back fat, rib-eye area, and marbling score, along with detailed EPD profiles. The EPDs in the dataset included the calving ease direct EPD, birth weight EPD, weaning weight EPD, yearling weight EPD, and maternal milk EPD.

Data from 2012 to 2021 WBIA sale catalogs and testing records were compiled and analyzed. To avoid heterogeneity arising from breed differences and due to data availability, only polled Black Angus breed was included in the study. The number of bulls that passed the test during the study period was 470. After removing observations with no sales and missing values, our final dataset contained 398 observations. A summary of variables used in the analysis is presented in Table 1. Consistent with prior research (Tang et al., Reference Tang, Thompson, Boyer, Widmar, Lusk, Stewart, Lofgreen and Minton2023), the sale price ($/head) was adjusted to 2021 equivalents using the Producer Price Index for Slaughter Cattle from the Bureau of Labor Statistics. The bulls in the dataset are in the 351 to 457-day age range. The average sale price for bulls in the dataset is $3,022.6, and there is considerable variation in the sale price, with bulls selling for as low as $1,744.40 and as high as $7,629.96. The mean and standard deviation of bull attributes in our data were consistent with the values reported by earlier studies.

Table 1.

Summary statistics of Angus bull attributes (2012–2021 sale year)

Notes: Number of observations (N) = 398; Birth to yearling gain EPD is computed by subtracting the birth weight EPD from yearling weight EPD. The bull sale price is adjusted to 2021-dollar values.

Research methods

We used a hedonic regression framework for analysis, with the bull sale price as the dependent variable and genetic and phenotypic indicators, EPDs, and year dummies as independent variables (Dhuyvetter et al., Reference Dhuyvetter, Schroeder, Simms, Bolze and Geske1996; Kessler, Pendell, and Enns, Reference Kessler, Pendell and Enns2017; Tang et al., Reference Tang, Thompson, Boyer, Widmar, Stewart, Lofgren and Minton2020; Vanek, Watts, and Brester, Reference Vanek, Watts and Brester2008). To account for the non-normal price distribution, we applied a log transformation to the dependent variable (Boyer et al., Reference Boyer, Campbell, Griffith, DeLong, Rhinehart and Kirkpatrick2019; Jones et al., Reference Jones, Turner, Dhuyvetter and Marsh2008; Tang et al., Reference Tang, Thompson, Boyer, Widmar, Lusk, Stewart, Lofgreen and Minton2023) and used Ordinary Least Squares (OLS) to estimate the model. The model we used is the following semi-log model.

(1) $$y_{i}=\,\beta _{0}+\sum _{j=1}^{J}\beta _{j}X_{ij}+\,\sum _{k=1}^{K-1}\delta _{k}Z_{k}+\varepsilon _{i}.$$

Here, y _i is the natural log of the sale price ($/head) for the bull, i; X _ij represents the bull traits j = 1, …, J of bull i; and Z _k includes dummy variables that control for the K sale year fixed effects. β ₀ is the intercept term; β _j is the marginal valuation of each bull trait j by the producers to be estimated; δ _k are the shifts from discrete dummy variables; and ε _i is the i.i.d. error term.

The expected signs of parameter estimates are presented in Table 2. Previous studies have shown conflicting results on the impact of age and frame score attributes on bull sale prices (Boyer et al., Reference Boyer, Campbell, Griffith, DeLong, Rhinehart and Kirkpatrick2019). The value of older, mature bulls, which producers generally prefer, may decrease as the bull ages (Kessler, Pendell, and Enns, Reference Kessler, Pendell and Enns2017; McDonald et al., Reference McDonald, Brester, Bekkerman and Paterson2010). The preference for a bull’s frame may depend on the buyer’s inclination towards calving ease and weaning weight traits and the availability of feed resources (Dhuyvetter, Reference Dhuyvetter1995). Desirable traits in a bull, such as higher average daily gain, average back fat, rib-eye area, marbling score, scrotal circumference, calving ease direct EPD, and birth to yearling gain EPD are expected to have a positive effect on the sale price (Boyer et al., Reference Boyer, Campbell, Griffith, DeLong, Rhinehart and Kirkpatrick2019; Kessler, Pendell, and Enns, Reference Kessler, Pendell and Enns2017; Tang et al., Reference Tang, Thompson, Boyer, Widmar, Lusk, Stewart, Lofgreen and Minton2023). The impact of milk EPD can vary and may depend on weaning weights and feed costs targeted by the cow-calf operation (Boyer et al., Reference Boyer, Campbell, Griffith, DeLong, Rhinehart and Kirkpatrick2019; Tang et al., Reference Tang, Thompson, Boyer, Widmar, Lusk, Stewart, Lofgreen and Minton2023). The influence of the dam’s age on the sale price of the bull may depend on the producer’s preference for superior calving ease (Kessler, Pendell, and Enns, Reference Kessler, Pendell and Enns2017) and carcass traits of younger dams (Da Silva et al., Reference Da Silva, Musgrave, Nollette, Applegarth and Funston2016), as opposed to the emphasis on proven reproductive performance and weaning weight traits of older dams (Kessler, Pendell, and Enns, Reference Kessler, Pendell and Enns2017). It is also important to note that specific bull attributes, such as the age of the bull, average back fat, dam’s age, and scrotal circumference, may have a preferred range, affecting the sale price of the bulls in the sample. For a more detailed discussion of the potential impact of bull attributes on sale prices, readers are referred to 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), and Boyer et al. (Reference Boyer, Campbell, Griffith, DeLong, Rhinehart and Kirkpatrick2019).

Table 2.

Description of explanatory variables and expected sign of coefficients

Notes: Birth weight EPD is the sire’s ability to transmit birth weight to his progeny measured in pounds, and yearling weight EPD is the sire’s ability to transmit yearling weight to his progeny measured in pounds.

Bull traits are measured using different scales, and ranking them solely based on the magnitude of coefficient estimates from hedonic regression models can lead to incorrect conclusions (Tang et al., Reference Tang, Thompson, Boyer, Widmar, Lusk, Stewart, Lofgreen and Minton2023; Vanek, Watts, and Brester, Reference Vanek, Watts and Brester2008). Pindyck and Rubenfield (Reference Pindyck and Rubinfeld1998) recommended standardizing variables using their means and standard deviations before ranking coefficients from the regression. In the standardized model, the coefficients indicate how the standard deviation of the log bull price changes for each standard deviation change in the attribute, and the absolute value of the coefficients can be used to rank bull attributes by their importance in determining the log bull price.

Identifying latent classes and addressing unobserved heterogeneity

The heterogeneity in buyer preferences is addressed using a FMM. A mixture model is a probabilistic model that assumes that a bull’s price P _i arises from a population that is a mixture of a finite number of distributions called classes (S), in proportions π _s . The probabilities π _s are constrained such that $\sum _{s=1}^{S}\pi _{s}=1{\rm\ and}\ \pi _{s}\geq 0\ {\rm for\ } s=1,\ldots, S$ . (Tang et al., Reference Tang, Thompson, Boyer, Widmar, Lusk, Stewart, Lofgreen and Minton2023; Wedel and Kamakura, Reference Wedel and Kamakura2003). Class membership is not determined a priori and is assigned by the model from the data.

Following Tang et al. (Reference Tang, Thompson, Boyer, Widmar, Lusk, Stewart, Lofgreen and Minton2023), an S-component FMM of bull price is represented in the general form as

(2) $$f\left(y_{i}|{\boldsymbol{x}}_{i}, \boldsymbol{\beta }, \boldsymbol{\pi }\right)=\sum _{s=1}^{S}\pi _{s}\,f_{s}\left(y_{i}|{\boldsymbol{x}}_{i}, {\boldsymbol{\beta }}_{s}\right).$$

Here, X and Z from Equation (1) are concatenated into a single vector x _i ; y _i is the natural log of bull price; f _s (.) represents the probability density function for the s ^th latent class parameterized by β _s ; β = ( β ₁, β ₂,…, β _S ) is the vector representing the set of parameters for all latent classes; π _s represents the average probability that an observation i is assigned to a given class s; and π = (π ₁, π ₂,…, π _S ) is the vector of mixing proportions (weights) for all latent classes. Each class s is assumed to follow a normal distribution with mean μ _{i, s} = x _i β _s and variance σ _s ², and the probability density function

(3) $$f_{s}\left(y_{i}|{\boldsymbol{x}}_{i}, {\boldsymbol{\beta }}_{s}\right)={1 \over \sqrt{2\pi \sigma _{s}^{2}}}exp\left({-\left(y_{i}-{\boldsymbol{x}}_{i}{\boldsymbol{\beta }}_{s}\right)^{2} \over 2\sigma _{s}^{2}}\right).$$

For a mixture of linear regression models, the likelihood function for the observed bull price P _i , is given as

(4) $$L\left(\boldsymbol{\beta }, \boldsymbol{\pi }|\boldsymbol{x}\right)=\prod _{i=1}^{N}\left[\sum _{s=1}^{S}\pi _{s}\,f_{s}\left(y_{i}|{\boldsymbol{x}}_{i}, {\boldsymbol{\beta }}_{s}\right)\right],$$

and the log-likelihood function is

(5) $$Log\ L\left(\boldsymbol{\beta }, \boldsymbol{\pi }|\boldsymbol{x}\right)=\sum _{i=1}^{N}\log \left[\sum _{s=1}^{S}\pi _{s}\,f_{s}\left(y_{i}|{\boldsymbol{x}}_{i}, {\boldsymbol{\beta }}_{s}\right)\right].$$

An estimate of $(\hat{\boldsymbol{\beta }}, \hat{\boldsymbol{\pi }})$ can be obtained by solving the log-likelihood Equation (5) with respect to model parameters ( β , π ), subject to the restrictions on π _s discussed earlier. The first-order conditions of the log-likelihood function are solved numerically using the quasi-Newton method, and the posterior probability can be computed using Bayes’ Rule.Footnote ¹ The posterior probability of each observation i in class s is given by

(6) $$\hat{\pi }_{i, s}={\widehat{ \pi _{s}}\,f_{s}\left(y_{i}|{\boldsymbol{x}}_{i},\widehat{{\boldsymbol{\beta}} _{s}}\right) \over \sum _{s=1}^{S}\widehat{\pi _{s}}\,f_{s}\left(y_{i}|{\boldsymbol{x}}_{i},\widehat{{\boldsymbol{\beta}} _{s}}\right)}.$$

The FMM is estimated using PROC FMM in SAS 9.4 (SAS Institute, Inc., 2015). The final model selection is based on the Akaike Information Criterion (AIC), Corrected Akaike Information Criterion (AICC), and Bayesian Information Criterion (BIC). To further assess the separation of classes for different class models, we computed an entropy statistic (E _S ) using the formula

(7) $$E_{S}=1-{\sum _{i=1}^{N}\sum _{s=1}^{S}-\ \pi _{i,s}\ln\ (\pi _{i,s}) \over N\ln\ (S)}.$$

E _S is a relative measure and is bound between 0 and 1. A value close to one suggests a greater degree of separation between latent classes, and a value close to zero implies that the classes are not well separated (Tang et al., Reference Tang, Thompson, Boyer, Widmar, Lusk, Stewart, Lofgreen and Minton2023; Wedel and Kamakura, Reference Wedel and Kamakura2003). The entropy statistic cannot be used to choose the number of classes, but it is a helpful comparison tool to check the over-extraction of latent classes from the model (Tang et al., Reference Tang, Thompson, Boyer, Widmar, Lusk, Stewart, Lofgreen and Minton2023). According to Tang et al. (Reference Tang, Thompson, Boyer, Widmar, Lusk, Stewart, Lofgreen and Minton2023), the probability-weighted estimation of attribute valuations in the FMM does not allow for standardization within each class, making ranking based on standardized variables less meaningful. Additionally, the latent class models are not analyzed in subperiods due to the potential for class membership changes and sample size limitations.

Results and discussion – Pooled model and models in subperiods

We used the Pearson correlation coefficient to assess correlations and dropped highly correlated variables from the model to control multicollinearity.Footnote ² Prior research has established the role of weight in determining the price of the bull (Bekkerman, Brester, and McDonald, Reference Bekkerman, Brester and McDonald2013; Jones et al., Reference Jones, Turner, Dhuyvetter and Marsh2008). However, the final weight and weight per day of age attributes of the bull were correlated with several attributes of interest, including age, rib-eye area, weaning weight EPD, and the yearling weight EPD, and were therefore dropped.Footnote ³ A new variable, the birth to yearling gain EPD, was constructed by subtracting the birth weight EPD from the yearling weight EPD (Bekkerman, Brester, and McDonald, Reference Bekkerman, Brester and McDonald2013), and the highly correlated weaning weight EPD and yearling weight EPD attributes were dropped. The birth to yearling gain EPD was used as the primary indicator of the sire’s ability to transmit higher growth and weight to its progeny compared to other sires. Calving ease direct EPD is a comprehensive measure computed using birth weight and the calving score and was used as the primary indicator of calving ease. Consequently, the correlated birth weight and birth weight EPD variables were dropped.

The final model included age, average daily gain, average back fat, rib-eye area, marbling score, scrotal circumference, frame score, dam’s age, birth to yearling gain EPD, calving ease direct EPD, and milk EPD attributes. Year dummy variables with 2021 as the base year were included to account for changes in cattle inventory, fat cattle price, feed cost, labor cost, and other marketing and environmental factors that may influence a bull’s sale price (Bekkerman, Brester, and McDonald, Reference Bekkerman, Brester and McDonald2013; Chvosta, Rucker, and Watts, Reference Chvosta, Rucker and Watts2001; Kessler, Pendell, and Enns, Reference Kessler, Pendell and Enns2017; Tang et al., Reference Tang, Thompson, Boyer, Widmar, Lusk, Stewart, Lofgreen and Minton2023). Assessing multicollinearity in the final pooled model using the Variance Inflation Factor (VIF) showed a value lower than five for all variables with an overall VIF of 1.8, indicating no severe multicollinearity issues. Consistent with prior research, robust Huber-White standard errors were used to calculate reliable estimates of standard errors in the presence of heteroskedasticity related to variables included in the model (Jones et al., Reference Jones, Turner, Dhuyvetter and Marsh2008; Kessler, Pendell, and Enns, Reference Kessler, Pendell and Enns2017; Tang et al., Reference Tang, Thompson, Boyer, Widmar, Lusk, Stewart, Lofgreen and Minton2023).Footnote ⁴ Residual diagnostics using the Q-Q plot showed a mild departure from normality.Footnote ⁵

The pooled model presented in Table 3. has an R² of 0.51.Footnote ⁶ All bull attributes except scrotal circumference and dams’ age were statistically significant at an α = 0.05 and had expected signs.Footnote ⁷ The model coefficients were transformed to estimate the dollar change in bull price from a unit change in each attribute and are reported as the “Value ($)” in Table 3.Footnote ⁸ For example, the premium paid for a bull in the sample increased by an average of $4.36 as the age increased by a day. The bull’s age signifies biological maturity, and its positive sign is consistent with the buyer’s preference for larger mature bulls mentioned in other studies (Boyer et al., Reference Boyer, Campbell, Griffith, DeLong, Rhinehart and Kirkpatrick2019; Thompson et al., Reference Thompson, Boyer, Martinez, Rowan and Rhinehart2022). The average daily gain increased the bull’s expected sale price, showing the value producers attach to growth. Rib-eye area and marbling score attributes increased the bull’s sale price, revealing the producer’s interest in improving carcass quality. While Brimlow and Doyle (Reference Brimlow and Doyle2014) and Thompson et al. (Reference Thompson, Boyer, Martinez, Rowan and Rhinehart2022) reported a negative relationship between average back fat and sale price, our results showed a positive relation. The sample mean of the average back fat attribute is 0.39 inches and within the range that increases a bull’s premium, which likely explains this result. A higher frame score led to increased sale prices for the bulls in the sample, indicating a preference for greater bull weight and maturity. The birth to yearling gain EPD attribute increased the sale price of a bull, showing the importance of growth-related attributes in deciding the sale price of the bull. The bull’s value also increased with higher calving ease direct EPD and milk EPD, signifying the value producers attach to reproductive and maternal traits.Footnote ⁹ While the magnitude of estimated coefficients and our overall findings are comparable to other contemporary studies (Bekkerman, Brester, and McDonald, Reference Bekkerman, Brester and McDonald2013; Boyer et al., Reference Boyer, Campbell, Griffith, DeLong, Rhinehart and Kirkpatrick2019; Brimlow and Doyle, Reference Brimlow and Doyle2014; Tang et al., Reference Tang, Thompson, Boyer, Widmar, Lusk, Stewart, Lofgreen and Minton2023; Thompson et al., Reference Thompson, Boyer, Martinez, Rowan and Rhinehart2022), the effect of bull attributes on the sale price may be overestimated due to variables omitted from the model.Footnote ¹⁰ Nonetheless, our results show that consumer preferences are transferred upstream, and producers pay premiums for value-enhancing bull attributes.

Table 3.

Results from the full sample and the subperiods

Notes: The dependent variable is the natural log of bull price adjusted to 2021-dollar values. Value ($) is the impact of a one-unit increase in the independent variable on the bull sale price. N is the number of observations. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% levels, respectively. The model is estimated using Stata/MP 18.

Data for the pooled model spans a 10-year period, which may cause potential changes in producer valuation of bull attributes (Boyer et al., Reference Boyer, Campbell, Griffith, DeLong, Rhinehart and Kirkpatrick2019; Tang et al., Reference Tang, Thompson, Boyer, Widmar, Stewart, Lofgren and Minton2020). The interaction of variables with time in the pooled model was evaluated using a linear time trend variable (t = 1, …, 12) and its square without including the sale year dummies. The results indicated changes in the way producers valued calving ease direct EPD and average daily gain attributes over time. Time interaction with calving ease direct EPD was significant at α = 0.05 when the time trend variable was used. However, the time interaction with other variables was insignificant. On the other hand, only the average daily gain attribute showed significant interaction at α = 0.10 when both time and time square interactions were introduced. We examined the temporal differences in producer marginal valuation of bull attributes by analyzing data in two subperiods: 2012–2016 and 2017–2021. To enable comparison, a specification similar to the pooled model was adopted.

The results from different periods are also presented in Table 3. The most significant changes were observed in the buyers’ valuation of the marbling score, frame score, birth to yearling gain EPD, and calving ease direct EPD attributes, which nearly doubled in value in the second subperiod. The buyer valuations for average daily gain and rib-eye area decreased slightly, while those of average back fat decreased moderately in the second subperiod. In the second subperiod, age was no longer significant, possibly due to increased valuations of the marbling score and frame score, which became more correlated with age. The milk EPD attribute was not important in explaining the bulls’ sale price in the second subperiod. Tang et al. (Reference Tang, Thompson, Boyer, Widmar, Stewart, Lofgren and Minton2020) also found similar results, which they attributed to varying producer preferences for the milk EPD trait. The dam’s age and scrotal circumference attributes did not influence the bull’s sale price in either subperiod.

The rankings of bull attributes by their importance in explaining the bull sale price in different periods are presented in Table 4. Calving ease direct EPD, average daily gain, and rib-eye area were consistently the top predictors of bull value. Birth to yearling gain EPD, marbling score, and frame score attributes increased in importance in the latter subperiod, while average back fat, milk EPD, and age decreased in ranking. Scrotal circumference and the dam’s age attributes were consistently ranked lower. The findings align with other recent studies and show that producers value calving ease, growth, production weight, and carcass merit attributes in their cattle. However, as Tang et al. (Reference Tang, Thompson, Boyer, Widmar, Lusk, Stewart, Lofgreen and Minton2023) noted, using pooled data may impact producers’ valuation of bull attributes if there is heterogeneity in producers’ demand for specific bull traits.

Table 4.

Ranking of bull attributes

Notes: The dependent variable is the natural log of bull price adjusted to 2021-dollar values. The ranking is based on the absolute value of estimated coefficients from the model using standardized variables. N is the number of observations. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% levels, respectively. The model is estimated using Stata/MP 18.

Results and discussion – Latent class model

The sample size and the degree of separation among latent classes presented challenges for parameter estimation in the FMM. As a result, unobserved heterogeneity is addressed to the extent possible after careful data analysis. Models from two to six latent classes were estimated, and rigorous evaluation was performed before choosing the number of classes.Footnote ¹¹ The results from the FMM are presented in Table 5. The AIC, AICC, and BIC values were lower for the 2-Class FMM compared to the 3-Class FMM. Additionally, the entropy statistic was higher for the 2-Class FMM (0.91) relative to the 3-Class FMM (0.68), suggesting an over-extraction of classes with the 3-Class FMM. Based on the AIC, AICC, and BIC values and the computed entropy statistic values, we used the 2-Class FMM for further discussion.Footnote ¹²

Table 5.

Latent class model results

Notes: The dependent variable is the natural log of bull price adjusted to 2021-dollar values. Value ($) is the impact of a one-unit increase in the independent variable on the bull sale price. N is the number of observations in each class. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% levels, respectively. The model is estimated using PROC FMM in SAS 9.4.

The bulls were categorized into two classes based on their estimated posterior probabilities. Class 1 is the smaller of the two classes, comprising 16.08% of the observations with 64 bulls, and is difficult to characterize. Meanwhile, Class 2 includes 83.92% of the observations with 334 bulls and shared similarities with the typical cow-calf producers in the upper Midwest. The average price per head for bulls in Class 1 is $2,480.39, lower than the average price of $3,126.58 for Class 2. In Class 1, all attributes except the marbling score and milk EPD are statistically significant. The effect of attributes on the bull’s sale price is much lower in Class 1 compared to Class 2. Class 1 likely consists of buyers who do not prioritize specific bull attributes but focus on buying low-priced bulls that are easy to manage. The producers in this class may also include uninformed market participants and buyers focusing on bull attributes not included in the model. The negative signs of average daily gain and frame score attributes in Class 1 suggested that producers may be selecting bulls based on herd characteristics such as lower forage and feed requirements and higher calving ease. The negative sign of the average back fat attribute is consistent with the demand for bulls with lower frame sizes. Small to medium-frame cattle require lower forage and feed resources (Barham, Reference Barham2011) and can reduce calving issues, which is highly valued by producers facing labor constraints. This result is also supported by the insignificance of milk EPD, a preferred trait for operations targeting heavier calves with high nutritional demand and feed costs. Producers in this category tend to favor bulls born out of older dams, which aligns with their desire for proven reproductive performance and higher weaning weight traits in their herds. The emphasis on scrotal circumference is also consistent with the preference for improved reproductive efficiency. Another noticeable characteristic of Class 1 was the lower effect of calving ease direct EPD, birth to yearling gain EPD, rib-eye area, and marbling score traits on the bull’s sale price. The operations in Class 1 likely represent the “value buyer” segment, including smaller, part-time operators, as highlighted in the study by Tang et al. (Reference Tang, Thompson, Boyer, Widmar, Lusk, Stewart, Lofgreen and Minton2023).

In Class 2, all attributes are significant at a 5% significance level, except for scrotal circumference and dam’s age. The coefficients for average daily gain, rib-eye area, marbling score, frame score, birth to yearling gain EPD, calving ease direct EPD, and milk EPD attributes had the expected signs and are larger in magnitude in Class 2 than Class 1. The higher magnitude of the calving ease direct EPD signifies the importance of the calving ease to producers in this segment. Producers in Class 2 focus on growth and production weight attributes, as indicated by the significance and positive sign of average daily gain, frame score, birth to yearling gain EPD, and milk EPD attributes. The higher magnitude of the coefficients of rib-eye area and marbling score indicates that producers in Class 2 are willing to pay premiums for better carcass quality. The lack of significance of the dam’s age and scrotal circumference attributes is likely due to the stronger influence of other attributes on the sale price of bulls in this class. These results suggest a clear preference among producers in Class 2 for traits associated with higher calving ease, growth, production weight, and carcass quality. These findings align with the upper Midwest cow-calf operations, selling calves post-weaning or retaining them on the farm for additional weight gain.

Given the temporal heterogeneity in producer demand for specific bull attributes (Boyer et al., Reference Boyer, Campbell, Griffith, DeLong, Rhinehart and Kirkpatrick2019; Tang et al., Reference Tang, Thompson, Boyer, Widmar, Stewart, Lofgren and Minton2020, Reference Tang, Thompson, Boyer, Widmar, Lusk, Stewart, Lofgreen and Minton2023), assessing whether it affects the class membership assigned by the 2-Class FMM was essential. We analyzed the number of observations in each year and each class and performed a χ ² test with a null of no change in proportions across years, which we failed to reject (χ ² = 9.68; P − value = 0.38). The distribution of class membership was consistent across the years in the data, suggesting that temporal heterogeneity did not influence class membership even though the producer valuation of attributes changed over time.

Conclusions and implications

The hedonic regression analysis of pooled data from the WBIA Bull Sale and Development Program showed that producers in the region are willing to pay more for traits related to higher growth, production weight, calving ease, and carcass quality. The importance of growth and production weight for cow-calf producers has been well established and is consistent with our findings on average daily gain, birth to yearling gain EPD, frame score, and milk EPD traits. Increasing pounds per cow stems naturally from calving ease or a high calving percent, which results in more pounds per cow, as does weaning or yearling weight. The increased importance of calving ease over time is also consistent with the potential for financial loss during calving. While not all cow-calf operations may benefit from superior carcass traits, buyers who focus on producing higher-quality calves and those who retain calves for weight gain would prefer these traits. Most cow-calf producers in the region may not be large enough to consider retaining ownership of calves, but buying bulls with better carcass traits provides operations with the option to build a sound genetic base, maintain the reputation as quality producers, and realize higher returns on sales through value-addition when market conditions are favorable (Tang et al., Reference Tang, Lewis, Lambert, Griffith and Boyer2017). Given the beef industry’s focus on carcass merit, it is poised to play a more significant role in cattle marketing.

The FMM identified two latent classes or segments, revealing heterogeneity in producer preferences. The first class of bull buyers comprised a smaller segment that prioritizes lower-priced bulls with limited emphasis on specific traits. The second, more prominent segment valued traits related to calving ease, growth, production weight, and carcass qualities. Our findings do not necessarily invalidate the presence of a distinct third segment focused primarily on superior carcass qualities, as identified by Tang et al. (Reference Tang, Thompson, Boyer, Widmar, Lusk, Stewart, Lofgreen and Minton2023). However, this segment may not be large enough in smaller markets, highlighting the broader relevance of regional-level analysis of heterogeneity in the cattle industry. Although temporal heterogeneity does not affect the number of buyer segments in our study, it is important to note that the marginal values assigned to specific attributes by producers change over time, emphasizing the need to evaluate industry trends continuously.

The findings of this study have several practical implications for cow-calf producers, seed stock producers, and the beef industry. Producers can benefit from investing in economically important traits relevant to their production system by selecting bulls based on their phenotype, performance, and EPDs. The estimates from the study can serve as a benchmark for producers to assess their performance against that of other regional operators. Understanding the bull attributes within each segment enhances the selection process by avoiding undesirable traits and incorporating preferred ones, ultimately leading to increased long-term profitability for operations. The WBIA can use this study to provide bull sellers with an estimate of how well their bulls performed in the auction. Seed stock producers in the region can use the information to identify the specific traits in demand and focus on incorporating them into their breeding programs. Finally, customizing future educational programs and marketing strategies for different segments can help expedite these changes and benefit the beef industry in the long term.