Jones et al.: Value of Bull Characteristics
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price data. Ordinary least squares (OLS)
regression models were applied to the data to
determine the contribution of each of the
variables presented in the conceptual model to
purebred Angus bull prices. Heteroscedasticity
concerns were tested for using the approach
suggested by Breusch and Pagan and were
addressed by estimating the models using
White’s Correction procedure.
Results
Here we present specific empirical models and
report the results obtained from the estimation
of the models. The parameter estimates
reported represent changes in the dependent
variable, natural log of price, for a one-unit
change in the respective independent variable.
As an alternative, the reader may choose to
view the parameter estimates as percentage
changes in the linear form of the dependent
variable, price. This interpretation of the
results is helpful but fails to provide dollar
values for changes in the variables.
One way to address this issue is to multiply
the parameter estimates for the continuous
variables in each model by the average price
for that model. This procedure resulted in
dollar values for each continuous variable,
representing the marginal effect for one-unit
changes. We include these results for compar-
ison with previous research; however, the
marginal effects must be interpreted with
caution. For example, large absolute values
can result from variables that are by nature
small in magnitude (i.e., a ‘‘one-unit’’ change
is unlikely). In addition, different distributions
(higher or lower degrees of variability) can
impact the likelihood of a one-unit change in a
particular variable, making it difficult to
compare the marginal effects across variables.
As a second alternative, elasticities were
calculated for each of the continuous variables
by multiplying the parameter estimates by the
average of each continuous variable. Elastic-
ities are commonly used and easily interpreted
(percentage impact of a 1% change in the
respective variable); however, they suffer some
of the same shortcomings as the marginal
effects calculations. That is, different distribu-
tions of alternative variables result in dissim-
ilar likelihoods of a 1% change. In addition,
elasticity estimates depend on the point of
calculation (in this case the means of the
respective variables). Elasticity results must be
interpreted with these caveats in mind,
prompting us to explore another approach to
examining relative impacts (discussed later).
Shifts for discrete (i.e., dummy) variables
were also calculated using the procedure
suggested by Halvorsen and Palmquist for
the interpretation of discrete variables in
semilogarithmic equations. The values calcu-
lated for each variable show the effect of
including the variable when all other discrete
variables are equal to zero. The results are
reported in dollars and provide a useful means
of comparing between discrete variables.
Model of Actual and EPD Physical
Performance Measures
The first model specification included actual
performance measures (birth, adjusted wean-
ing, and adjusted yearling weights) and their
corresponding EPDs. Restricting the model to
include adjusted weights decreased the number
of usable observations to 4,150, primarily
because of missing values for adjusted yearling
weights. The model is specified as
In price ~ b0 z b1age z b2age2 z b3birthwt
z b4adjweanwt z b5adjyearwt
z b6 birthepd z b7 weanepd
z b8milkepd z b9yearepd
z b10saleorderz b11picture
(2)
z b12et z b13sementhird
z b14semenhalf z b15fullbrother
z b16pathfinder z b17seasonofsale
25 40
z aksrk z cj salej z e:
k~ 1 j~ 1
Results are reported in Table 3, and sum-
mary statistics for variables included in this
model specification are included in Table 4.
The model R2 of 0.6363 indicates reasonable
explanatory power for a cross-sectional study.