Introduction

Given these considerations, it is useful to have a straightforward method of measuring and reporting the genetic value of dairy bulls. This would provide dairy producers with an additional tool to be used in making breeding decisions, in order to improve the genetic quality of their herd and thereby improve their profitability. Such a system would also be of value to managers of artificial insemination (AI) units and other related businesses by providing a method to set standards by which breeding stock, semen, embryos, etc., may be valued for marketing purposes.

The Lifetime Profit Index (LPI) is a measure of genetic valuation that is currently being used by the AI industry in Canada to rank dairy bulls. The LPI makes use of information concerning production and type scores to provide an index of the expected contribution of a bull's offspring to dairy enterprise profitability. However, the LPI suffers from some weaknesses related to its construction and the representativeness of the index for all Canadian dairy producers.

This study examines an alternative approach in measuring genetic value. Specifically, hedonic pricing is used to determine the value of genetic traits for purebred Holstein dairy bulls in Alberta, through the statistical analysis of market price data for semen. Through this analysis, the value of individual relevant production and type traits may be identified, based on Alberta production and marketing characteristics. This is the primary objective of the study. A secondary objective is to suggest ways in which this information may be used by the dairy industry to evaluate the genetic quality of dairy bulls.

The Lifetime Profit Index

The LPI represents one method of linking selection for genetic characteristics and the economic value of those traits. The LPI measures the expected contribution of a bull's offspring to dairy enterprise profit over a five year period, using a combination of production and longevity characteristics. The current formulation of the LPI is based on research by Gibson et al. (5) where the relative values of various milk components (e.g., fat and protein) were estimated using costs and returns for Ontario dairy farms. These values were used to develop economic weights and a single selection index, based on milk production traits for the bull.

The LPI currently used by the dairy industry is based on a combination of production and type proofs, using BCA scores for each bull. The value to a farmer of using a bull with an improved set of genetic traits is estimated by projecting the changes in profit from increasing the production value per animal . The LPI is currently being used by AI units in Canada as an overall measure of genetic merit.

The LPI is an appealing measure, as it combines production and type proofs into a single index. However, this approach has some weaknesses. First, the costs and returns of the representative (average) farm derived from the Ontario data are not likely to be representative of all dairy producers in Canada. Second, the Ontario records yield estimates of the average cost associated with a given change in milk production, whereas producers concerned with improving their profits should consider the marginal costs of genetic improvements. Third, although the longevity traits of each bull will be different, the relevant lifetime of the offspring for every bull is defined to be five lactations. Finally, the weights on each component of the LPI are determined on an ad hoc basis; that is, they have no basis in optimal economic behavior. This is another way of stating that the method assumes a fixed production technique even though the level of technology is constantly changing in the industry.

Hedonic Pricing for Evaluating Dairy bulls

The demand for livestock sires has been examined using hedonic pricing models. Studies such as Kerr (8; beef) and Walburger and Foster (14; hogs) model sire prices as functions of individual animal characteristics. In contrast to the beef and pork industries, however, there is no comparable active market for dairy herd sires. Producers typically buy frozen genetic material from artificial insemination (AI) units in the form of a vial or straw. Using a hedonic pricing model, Schroeder et al. (12) estimate the marginal values of several purebred dairy bull traits by using published bull proofs to explain the price for a dose of a bull's semen. Their approach forms the basis for the hedonic pricing model used in the current study.

A hedonic pricing model for dairy bulls may be expressed as a mathematical function where the price of a bull's semen is defined as the sum of the values for each of the genetic characteristics. Cows are bred in the expectation that their offspring will produce for several years and that the offspring will, in turn, transmit their genetic traits to future generations. Thus, breeding decisions are made with a goal of maximizing not the current flow of profits from the cow, but the present value of the dairy herd as a whole. The marginal value of a genetic improvement can be expressed as the increment to the maximum present value of the farm from increasing the herd's milk productivity, milk composition, and/or longevity. An expression for the maximum present value of the farm may be defined as follows:

where the decision variable is x, defined as the addition to the quality of the herd's genetic stock through artificial insemination services. The index of genetic "quality" for the herd is z and the rate of change in z is equal to x. Component corrected milk production per year for the herd is represented by f, p is the component corrected milk price, w is the price of breeding services, R is the "rental price" of cattle of a genetic level indexed by z, and r is the annual interest rate.

The use of dynamic programming to solve the optimization problem expressed by (E1) yields the following Bellman equation (8):

Equation (2) may be totally differentiated with respect to the genetic quality index (z) to yield an expression for the marginal current value of genetic improvement:

The rate of change for the dynamic shadow value of the genetic index may be determined by totally differentiating Vz with respect to time.

Equation 4 describes the marginal value of an increase in the genetic merit of the dairy herd. Equations 3 and 4 may be combined (using the equivalence of and x) to provide an expression for Vz; that is, the marginal present value of investing in genetic improvement. This is provided by the following relationship:

Equation 5 suggests that the marginal present value of investing in genetic improvement is equal to the discounted value of an annual stream of benefits from higher current milk production less the opportunity cost of resources used to improve the genetic makeup of the herd plus the value of improving the genetic value of all future generations. This present value, in equilibrium, is the market price that farmers are willing to pay for an increase in the genetic quality of their herd.

The index of overall genetic quality, z, is constructed from the performance of cows sired by several different bulls. Each of these bulls has a unique vectorof genetic characteristics. Therefore, the value of each trait is given by its marginal impact on the price associated with the z index.Assuming that the z index is constructed in such a way that it is homogeneous of degree one in the characteristics, the price paid for a given index level (i.e., level of z) may be written in terms of the marginal values of the component characteristics:

where Pz is the price (i.e., value) of a given level of genetic quality z, is the level of the ith characteristic for z, and all other variables are defined as before.

In this way Pz measures not only the "lifetime" value of breeding an improved cow as the LPI claims to do, but also measures the value of a breeding program over the investment horizon of the farmer. As this investment horizon extends beyond the lifetime of one cow, the hedonic approach is constructed from a more plausible assumption concerning the motivation underlying producers' breeding decisions. This specification (E6) provides the basis for the empirical model that is estimated in this study.

Empirical Hedonic Pricing Model

The data used to estimate the implicit proof characteristic prices represent a cross sectional sample of 692 purebred Holstein bulls, obtained from the July, 1994 volume of the Who's Who sire guide. Available production proof data consist of milk, fat, and protein BCA deviation for each bull, as well as fat and protein percentage predicted deviations. The proofs for milk, final class, and milking speed are all measured by the deviation from breed average and use a "rolling base" for comparison. Protein deviation is the contribution that a chosen sire would be expected to make in increasing an offspring's protein content above that of her cohort, expressed in terms of a percentage deviation from herd protein content average.

Repeatability measures for production and type proofs are not included in these data. However, daughter and herd numbers provide acceptable proxies for measuring the reliability of the proof . Type proofs consist of all major and minor traits. For those traits that include both a numerical and qualitative description, only the numerical value is included in the statistical model.

Semen price data are obtained from SEMEX Canada, the cooperative marketing arm of all major Canadian artificial insemination firms, and are reported in terms of dollars per straw . Hedonic pricing models generally require price data obtained from competitive bidding in an open market framework. In Canada, semen prices are set by individual AI units in order to allocate their supplies among producers. However, some AI units are producer-owned cooperatives and because cooperatives operate on a not-for-profit basis, the price they charge should be the minimum price possible (i.e., the competitive price). The "competitive yardstick" effect refers to the ability of cooperatives to discipline competing investor owned firms from charging more than the minimum cost price. As a result, semen prices should behave as if they are determined through a purely competitive bidding process.

Empirical Model Specification

Most hedonic price model applications do not specify an a priori functional form for the price index. In the current study, however, the model is restricted to the general class of homogeneous functions. Initially, therefore, the semen price index is specified as a double-log, or Cobb-Douglas, function of the proof characteristics:

where Ps is the observed price of a bull's semen, Ci is the value of the ith characteristic, and u is a random error term, herein assumed to be log-normally distributed.

Two potential sources of statistical bias exist if the basic model described above is used to estimate the implicit value of characteristics. First, if a bull cannot command a price of at least $5 in the market, it is not included on the SEMEX "active list". As a result, no price is recorded for 80.5% of the bulls in the sample. The sample of observed prices is said to be censored at $5, so the expected value of the error term is positive. Walburger and Foster (14) confront a similar problem in that their data include several boars that do not receive a minimum $300 bid, and are therefore not sold. Their solution for this problem is to estimate unbiased marginal characteristic values using a Tobit approach. A Tobit model is also adopted in this study.

In the Tobit model, the dependent variable is observed as either positive or zero, with a large cluster of observations at zero. In this case, P* is the price that is expected in the log-linear function (E7). The observed price will equal this expected price only if the expected price is greater than the censoring, or limit, value of $5. Below this value, the observed price will be zero. Equation 8 describes this logic, using the notation developed above:

A maximum likelihood procedure is used to estimate the parameters of this Tobit model. Because of the censored sample, the log likelihood function (LLF) must be broken into components describing the positive observations and the limit observations, as follows:

where Ki is the censoring point, Fi is the cumulative normal distribution function, Zi = 1 if Ps* less then 5, and is zero otherwise, and all other parameters are defined as in (7).

A second potential source of bias arises from the fact that SEMEX officials feel that the supply of a bull's semen is often considered to be a factor in determining its price. The usual assumption in hedonic models is that the supply of the commodity is fixed for the time period under consideration so that the price of each characteristic is entirely determined by its demand. Rosen (11) develops a general framework within which the marginal value of a commodity is determined by both the supply and demand of each characteristic. Bowman and Ethridge (2) incorporate this notion in their study by specifying a structural model of cotton characteristics wherein the price-dependent hedonic price equations are estimated simultaneously with a series of quantity-dependent characteristic supply equations.

In terms of the semen pricing problem, determining the supply of each characteristic is not possible, as SEMEX does not record inventories of semen on hand at the unit level. Instead, an alternative method is used to account for possible supply pressures. SEMEX officials are able to make a qualitative assessment as to whether or not the supply of a given bull represents a constraint that is likely to affect the price charged for his semen. Based on this information, a dummy variable is constructed that is equal to one when supply may be a limiting factor, and zero when it is not. However, this dummy variable cannot be assumed to be exogenous. Besides the isolated cases of premature death of the bull, the decision to collect and market semen is made simultaneous to the pricing decision. Again, if this "self selection" behavior is not accounted for in the empirical model, the estimated parameters will be biased.

The two-stage estimation method of Heckman (6) is used to correct for the endogeneity of the dummy variable. In the first stage, a bull's proof is used to establish a latent or unobserved variable measuring the potential for supply to influence the price. For example, if a bull's proof is very strong, the demand for its services is likely to be high. If semen for this bull is in relatively short supply, then the tendency for supply to be a factor in determining the market price is expected to be significant. If this unobserved value is greater than a threshold level determined by the marketer, then the dummy variable will take on a value of one. Otherwise, the dummy variable will be equal to zero. This is illustrated as follows:

where S* is the estimated unobserved value defined above, and L is the threshold value.

In this first stage, a probit model is used to estimate the marginal contribution made by each proof element, in addition to the LPI value for each bull, to the probability that the supply of a bull may be a limiting factor. The fitted probabilities from the probit model are then used in the second stage hedonic pricing model as instruments for the unobserved supply factors. In terms of the Tobit log likelihood function (LLF), the fitted probabilities are included as right hand side variables in the pricing equation:

Consistent estimates of the hedonic model are obtained by maximizing (E11) with respect to each of the parameters. The resulting parameter estimates are corrected for both the censored sample and the endogeneity of the supply dummy variable.

Estimates of the optimal parameter vector are obtained by maximizing the log likelihood function (E11) with the non-linear solver in SHAZAM (15). Starting values for each parameter are supplied by a preliminary OLS regression. The first stage probit estimates are established using the probit procedure within SHAZAM. Several alternative specifications are estimated for this model in order to determine the set of variables which best explain AI units' semen allocation behavior.

In the second stage of the analysis, the Tobit procedure within SHAZAM is used to estimate the parameters for the hedonic pricing model. The results of the first stage are incorporated through the supply dummy variable. Alternative variables are considered for the repeatability proxies, the fat and protein content variables, and several closely related type variables. One problem common to all of the models is the presence of multicollinearity between many of the type variables and final class. The final variable set is selected on the basis of not only goodness of fit, but also the consistency of coefficient estimates with their a priori expected signs (i.e., positive or negative).

Finally, a Tobit model is estimated with only the LPI as an explanatory variable for the price of semen. As with the hedonic pricing model, the log of the LPI is used in order to allow a direct comparison between the models. If the fit with this model proves better than the fit with the hedonic price specification, then the LPI can be concluded to be a superior measure of genetic merit, and vice versa. The basis for the comparison between the two models is the correlation between the observed semen price vector and the predicted semen price; that is, the measure of the predictive ability for each model.

Results and Discussion of the Semen Pricing Problem

Results from the first stage probit model are presented in Table 1. These coefficients represent the marginal contribution made by each variable to the probability that semen supply may be a limiting factor. Conceptually, the supply decision should include the complete information set, including all proof elements and the LPI. Although many of the proof traits are found to be insignificant in this initial analysis, they remain in the final model based upon a priori expectations of their relevance to the semen buying decision. For example, the "feet and legs" variable does not appear as a significant independent influence on the perceived marketability of a bull when 'final class' is already included, but a reputation for transmitting poor legs can shorten a bull's active career. Thus, it remains as an explanatory variable in the probit and Tobit analyses.

The Ym parameter estimates in Table 1 do not indicate the marginal increase in the probability of supply influencing the price due to a one-unit change in the given characteristic, but depend upon the initial values of all other explanatory variables. If P is the probability, then the marginal impact of the mth characteristic (Cm) on P is shown by:

where f is the normal probability density function.

Table 2 presents the second stage results from the Tobit model. These are the parameter estimates for the hedonic pricing model. As both the price and the explanatory variables are in logs, the coefficients may be interpreted as elasticities. For example, the coefficient for the milk proof variable is 0.707, which implies that a 10% change in the milk proof will cause the expected price of semen to rise by 7%. If a bull currently has a milk proof of +10 and its semen sells for $20/straw, then another bull that is similar in all other respects, with a milk proof of +11 should be expected to have a semen price of $21.40. Similar interpretations may be made for the other coefficient estimates.

The negative coefficients for feet and legs and mammary system should be interpreted carefully. Because "final class" is an all-encompassing measure of type, it is influenced by the quality of an animal's feet and legs and mammary system. Therefore, the marginal effect of a plus deviation bull for the more detailed class categories (e.g., feet and legs) is small when final class is included as an explanatory variable. One possible interpretation for these negative coefficients would be to suggest that feet and legs and mammary system are over-represented in the marginal value of the final class characteristic .

The effect of supply on the price of semen is measured by the coefficient for the PROBABILITY variable in Table 2. If an AI unit decides to take a previously active bull out of service, for example, the probability of being in short supply could conceivably rise from 0 to 100%. The price of semen would then be expected to rise by 22%, on average. Future research in this area would benefit from more complete data on the supply of each characteristic. Perhaps an index of the aggregate stock of each characteristic could be constructed to measure the marginal effect of each bull on this supply.

Table 3 presents the results obtained from applying the Tobit model to a double-log pricing equation with only the LPI as an explanatory variable. The results suggest that the LPI represents a highly significant explanatory variable for the semen price. However, the explanatory ability of the LPI index is inferior to the hedonic pricing model. This conclusion is based upon a comparison of the correlation between the observed semen prices and those predicted by the model. A correlation coefficient of 0.56 is achieved with the LPI model, whereas the fitted hedonic pricing model yields a correlation of 0.72. The superiority of the hedonic price model over the LPI is supported by comparing the values of the likelihood function between the two models. While the hedonic price model produces a log-likelihood function value of -384.549, the maximum value using the LPI variable is -711.922.

Implications and Extensions

These results suggest that the hedonic pricing model provides a better explanation of semen price than does the LPI. The hedonic model may be a superior sire selection tool in several other respects as well. Rational decision makers will utilize an information source only up to the point where the marginal benefit of additional information equals the marginal cost of obtaining that information. The low cost and simplicity of the hedonic pricing method means that bull rankings may be updated more frequently than with the LPI. In this respect, the LPI seems to be a "black box" for most potential users. Its construction, output, and interpretation are somewhat of a mystery, so it may be less likely to be trusted as a source of information. Furthermore, the hedonic pricing model is derived from semen prices that are determined by market-sensitive AI units reacting to buying pressures from profit-maximizing farmers. Rather than being told what the value of a given genetic trait should be, the model measures what the value of that trait actually is to all members of the trade.

In determining the value of a bull's genetic contribution to the herd, the hedonic pricing model suggests that farmers buy semen as if they regard only a few components of the proof breakdown as critically important. The most important considerations are the ones included in Table 2. These include milk volume, protein content, fat content, general conformation, some measure of body capacity, the "popularity" of the bull, and the probability that the bull's semen may be in short supply. Producers appear to regard the number of daughters sired by a bull as a good indicator of the reliability of the proof; that is, they allow popularity to stand as an indicator of the intangible aspects of a bull's genetic value.

One of the advantages that has been attributed to the LPI is its role as a measure of the lifetime contribution of the offspring for a given sire. Lifetime, in the context of the LPI, simply means that the index is constructed by assuming five lactations of production. Longevity considerations in the hedonic pricing model are more consistent with economic theory. Dairy producers make breeding decisions with longevity as a major consideration, and this is incorporated in the hedonic model. A bull that has a reputation of siring long-lived daughters, or that has a package of type traits suggesting problems with feet and legs or the mammary system are not likely to arise, will sell for more than one noted for siring "one lactation wonders". In this way, the hedonic pricing model implicitly embodies the multi-period consequences of any breeding decision.

Similarly, the hedonic price implicitly measures producers' tendency to be risk averse. A young sire will sell for less due to the uncertainty over the longevity of his daughters. Risk aversion also explains the significance of the DAUGHTERS variable (i.e., number of daughters) in the Tobit model results.

This method is not restricted to estimating the values of only quantifiable traits; that is, traits that are assigned numerical proofs. Qualitative traits may be included, and would act to "shift" the whole function up or down. Traits such as breed or color (e.g., the "red" factor in Holsteins) could be incorporated in the Tobit analysis through the use of a characteristic variable. This variable would take on the value of 1 when the trait is present and 0 otherwise. This results in an equation being estimated for all bulls, but with a premium or a discount incorporated for the particular trait.

The hedonic method discussed and used in this study can constitute a powerful marketing tool in determining the price for bulls that are just coming on to the system. However, this method also has a further value to the industry as a whole in helping to design a new method of ranking bulls according to their relative genetic value. Instead of creating a 'synthetic' value for bulls, the hedonic price index is a direct estimate of how each trait should be reflected in terms of increased profit for the dairy farmer. If the price is set according to the estimates from this model, the price itself indicates the total value to the producer of buying that dose of semen. If the price does not reflect this, then producers are not making the most profit from buying and using semen in their herds. Therefore, it is a simple matter to create an index from the hedonic price estimates as the price itself already is the best index that could possibly be used!

This model may also be used as an indirect test of the effect of policy on genetic progress in the dairy industry. Conversations with industry members regarding the trends in selection between production and type by Canadian dairy breeders suggest that breeders are now selecting bulls more for production than type, as compared to a decade ago. At that time, the future of supply management, and the virtual guaranteed return on investment in dairy, was assured.With the threat of having to deal with competition in dairy products from the U.S., breeders in Canada have begun to emphasize productivity gains over aesthetics.

The hedonic pricing model may be used to test this hypothesis directly by estimating two equations; one for 1993 and another for 1983. The alternative sets of trait valuations may be compared to show whether the relative valuation of type traits versus production traits has changed over the ten year period. If data are available, an equation may be estimated for each year. Comparing the trends in trait valuation over time would be a very valuable exercise in predicting the future needs of producers. From the perspective of the AI unit, these predictions could be used in selecting prospective mates for future bulls. Rather than using intuition, the market could help to guide mating decisions.

Conclusions

The hedonic pricing model will prove a valuable tool to both AI units' marketing managers and dairy breeders alike. The AI units can use the model to forecast a possible market price for semen from a young sire exhibiting a given set of proof characteristics. Breeders will be able to obtain a true index of the likely contribution to the profit of their herd made by any combination of proof characteristics using a simple, low-cost, easy to understand calculation.

Additional applications of the hedonic pricing model include the ability to test for changes in breeders selection criteria over time. For example, if producers expect multiple component pricing for milk to be instituted in the near future, this should be reflected in a higher implicit value for the protein proof of a given sire. The changes in these valuations can be linked to expected changes in the environment (policy and otherwise) within which producers must manage their farms.

Acknowledgements

Notes

Additional Readings

Applied Dairy Science Course - University of Alberta:
Dairy Cattle Breeds and Programs for Genetic Improvement

References