M1 represents a disaggregate model such as an auction model, and model M2 represents
an aggregate model such as the traditional NEIO model. To account for weekly changes
in demand and supply of cattle that are observed imperfectly within the experimental
cattle market, an additional error term is appended to the nested model (M3) to capture
these time random effects, as:
M3 : prjt - p wjtf = ω0 + ω1shwlst jt + ω2todem jt +ω3 fdlt1jt + ω4 fdlt2jt +ω5 fdlt3 jt
+ω6 fdlt4jt +ω7 fdlt5jt +ω8 fdlt6jt + ω9 fdlt7 jt +ω10GenMjt
+ω11GenHjt + ω12wt1150jt + ω13wt175 jt + ω14bid1jt
+ ω15bid2jt + ω16bid3 jt + ω17HHI jt +ηt + εjt.
where subscript j represents a lot of cattle, subscript t indicates a week within which the
jth lot is sold prj is beef price, pwjf is winning bid, todemj is total demand for cattle, fdlt1,
fdlt2, fdlt3, fdlt4, fdlt5, fdlt6, and fdlt7 are zero-one indicator variables that equal one if
the cattle are bought from feedlots 1, ..., 7, respectively; shwlst is the inventory of cattle
available for sale in a given week, wt150 , and wt175 are zero-one indicator variables that
equal one if steer’s weight is 1500, and 1175 lbs., respectively; GenM, and GenH are
zero-one indicator variables that equal one if the generic type of carcass quality is
medium, and high, respectively; bid1, bid2 and bid3 are zero one indicator variables that
equal to one if there were one, two, or three bidders on the lot; HHI is industry
concentration, the ωjt's are parameters to be estimated, ηt ~ N(0,ση2In) is a week
specific random error term to capture imperfectly measured changes in weekly demand
and supply of cattle, εjt ~ N(0,σε2 I), is a observation- specific error term that accounts
jt
for possible heteroskedasticity inherent to time-series cross-sectional data, with
σ2 = exp(b0 + b1shwlst + b2todem ) and cov(ε ,η ) = 0. Notice that models M1 and
ε jt j j j
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