THE EFFECTS OF U.S. DAIRY REGULATIONS
ON HERD IMPROVEMENT ACTIVITIES
by
Jeffrey Carl Olson
A thesis submitted in partial fulfillment
of the requirements for the degree
of
Master of Science
in
Applied Economics
MONTANA STATE UNIVERSITY
Bozeman, Montana
October 1987
APPROVAL
of a thesis submitted by
Jeffrey Carl Olson
This thesis has been read by each member of the thesis committee
and has been found to be satisfactory regarding content, English
usage, format, citations, bibliographic style, and consistency, and is
ready for submission to the College of Graduate Studies.
Date
Chairperson, Graduate Committee
Approved for the Major Department
Date
Head, Major Department
Approved for the College of Graduate Studies
Date
Graduate Dean
i ii
STATEMENT OF PERMISSION TO USE
In
presenting this thesis in partial fulfillment of the require-
ments for a master's degree at Montana State University,
the
I agree that
Library shall make it available to borrowers under rules
Library.
Brief
quotations
from this thesis are
allowable
of
the
without
special permission, provided that accurate acknowledgment of source is
made.
Permission
for extensive quotation from or reproduction of
thesis may be granted by my major advisor,
Dean of Libraries when,
the
material
or. in his absence,
by the
in the opinion of either, the proposed use of
is for scholarly purposes.
Any copying or use of
material in this thesis for financial gain shall not be allowed
out my written permission.
Signature ________________________________
Date
this
-------------------------------------
the
with-
iv
ACKNOWLEDGMENTS
would like to express my appreciation to my committee members,
Dr.
Bruce Beattie, and Dr. Michael Frank for their support during the
course
of this thesis.
Special acknowledgment goes to
my
committee
chairman, Dr. Jeffrey T. LaFrance, without whose patience and guidance
this project would not have been accomplished.
v
TABLE OF CONTENTS
Page
APPROVAL .
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STATEMENT OF PERMISSION TO USE ............................ .
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ACKNOWLEDGMENTS ........................................... .
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TABLE OF CONTENTS ......................................... .
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LISTOFTABLES.............................................
vii
LIST OF FIGURES ....................................... ,.....
viii
ABSTRACT.
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CHAPTER
INTRODUCTION ................................... , .
2
Introduction ................................. .
Statement of the Problem ... ;,, ............... .
Outline of Thesis ............................ .
2
5
REVIEW OF THE LITERATURE ........................ .
7
Studies of Technological Adoption ............ .
Studies of the U.S. Dairy Regulations ........ .
Basis for the U.S. Dairy Regulations ...... .
·Econometric Models of the Dairy Industry .. .
Investigation of Capitalization of
Dairy Program Rents ....................... .
Suggested Forms of the Milk
Production Function ....................... .
Questions of Interest Arising
in the Literature ......................... .
3
8
12
13
15
20
21
21
THE CONCEPTUAL MODEL AND DATA SOURCES ........... .
25
Dynamic Model of the U.S. Dairy Industry ..... .
25
vi
TABLE OF CONTENTS-Continued
Page
Theoretical Discussion of the Adoption
of DHIA Testing ..................... , ......... .
36
Hypothesized Relationship Between Profit
4
and Milk Cow Prices .......................... .
Data Sources . ...................... , ......... .
38
41
EMPIRICAL RESULTS ............................... .
43
Instrumental Variable Construction ........... .
Adoption of DHJA Testing ..................... .
Relationship between Profitability
43
63
and Milk Cow Prices ........................... .
72
CONCLUSIONS AND IMPLICATIONS .................... .
5
REFERENCES .. '
APPEND I X
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Original Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
89
vii
liST OF TABLES
Page
Table
1.
Comparison of Class I and Class II
Demand Restrictions ..................•........ , .. ,.
z.
Estimated Instrument Equations for the
Dynamic Dairy Model .........•.....................
3.
4.
49
59
Marginal Effects of Profit and Time in the
Adoption of DHIA .......... , ...................... .
68
Original Data ..................................... .
89
viii
LIST OF FIGURES
Figure
Page
1.
Classified Pricing Mechanism for Milk ..........•.
14
2.
Fixed Proportion Relationship of Milk
Production Inputs .................•..............
27
3.
Price Effects of an Increased Supply of Milk .....
39
4.
Observed Adoption of DHIA Testing ............... .
70
5.
Observed Return over Feed Cost .................. .
71
ix
ABSTRACT
In order to assure an adequate supply of milk and increase dairy
producers' incomes, the U.S. Government, through the Federal dairy
regulations, has increased the price of milk received by farmers above
that which would prevail under a competitive pricing system.
In
response to the higher price of milk, dairy producers have increased
the total amount of milk they supply.
Investigation of these responses and the factors causing them provides information about the impacts and effectiveness of the U.S. dairy regulations.
This study examines two aspects of dairy p~oducers' responses to
the dairy regulations.
These are: (1) What is the relationship between profit incentives created by the dairy program and farmers'
decisions to improve the productivity of dairy herds through herd
quality testing activities? and (2) Have the short run profits created
by the dairy regulations been capitalized into the market prices of
replacement dairy cattle?
The results of the investigation suggest that there is no significant relationship between dairy profitability, as defined in the
research, and the level of participation in Dairy Herd Improvement
Association t~sting of dairy cattle.
Further, the profitability
created by the dairy program appears to be completely capitalized into
the prices of dairy cattle implying that, in the long run, ·economic
profits to dairy producers are zero.
Consequently, the dairy regulations appear to have little impact on the adoption of herd improvement
activities. However, the U.S. Government efforts to achieve the goals
of the regulations are largely frustrated by the competitive nature of
the production sector in the U.S. dairy industry.
1
CHAPTER 1
INTRODUCTION
Introduction
This study is an analysis of responses of the U.S. dairy industry
to
Federal regulation of the dairy market.
Specifically,
the study
will address the nature of the rate of adoption of dairy herd improvement
the
testing,
and the impacts of the regulations on fluctuations
market pricing of dairy cattle.
estimate
Previous work has
attempted
in
to
dynamic supply and demand response relationships in the milk
markets and the various costs and benefits from the Federal dairy regulations.
This
approach has developed from the pioneering
work
of
Gaumnitz and Reed which formed the basis for the structure of the milk
regulatiori,
de
to the more recent,
Gorter.
Gorter
to
simulation framework of LaFrance and
This study will further the research of LaFrance and
investigate
questions which have received
attention in the previous literature.
foundation
of
LaFrance and de Gorter,
little
or
de
no
While employing the econometric
this project will extend
the
research to empirically investigate dairy farmers' responses to incentives created by Federal regulation of the dairy markets by
improving
the quality of their herds and bidding.up the market price of replacement
~airy
cattle.
2
Statement of the Problem
Federal
regulation of the Grade A production sector of the
dairy industry has existed since the Great Depression.
regulations were instituted to:
U.S.
Originally the
1) provide for "orderly marketing'' of
2) assure an adequate supply of milk throughout the year;
milk;
3) raise dairy farmers' incomes.
regulatory
A further criterion
and
stated that any
decisions must be in the public interest
[American
Agri-
cultural Economics Association Task Force].
In attempting to fulfill these goals,
tions,
fied
in
the form of federal and state marketing orders and classi-
pricing schemes,
farmers
the dairy industry regula-
have increased the price of milk
above that which would prevail in a competitive
received
by
marketplace.
Farmers have responded to this higher price with increased milk output
from larger dairy herds,
duction efficiency.
high
and improved pro-
Consumers have also responded to the artificially
prices for fluid milk products through decreased consumption
these products.
vergence
to buy.
of
more intensive input use,
surpluses have resulted from this di-
between what dairy producers supply and what consumers
want
The Commodity Credit Corporation (CCC) of the U.S. Department
Agricultur~
prices
Consequently,
of
(USDA) purchases surplus milk products
at
announced
and indirectly supports the prices of raw Grade B and
surplus
Grade A milk.
The
sulting
economic costs of the dairy industry regulations and the resurplus of dairy commodities are substantial.
These
costs,
3
including
direct
government expenses as well as lost
economic
pluses caused by higher consumer prices and lower consumer
have
purchases,
been estimated to be between $430 and $590 million per year
1980 dollars)
costs is,
[LaFrance and de GorterJ.
to a great extent,
dependent on the level of milk supplied
In order
fully understand the costs and economic impacts of the U.S.
support
programs,
(in
The level of these economic
by farmers and the resulting commodity surpluses generated.
to
sur-
one must investigate the supply response of
dairy
dairy
farmers to the production incentives created by the regulatory programs.
The
be
productive capacity
increased
placing
can
by culling low producing animals from the herd and
re-
animal's
milk
characteristics can be obtained through dairy testing
pro-
them with better cows.
producing
grams
of milk production in a given herd
Information about an
such as those offered by the Dairy Herd Improvement Association
(DHIA).
By participating in such a testing program,
a farmer learns
which animals are genetically poorer and should be culled.
are
then
replaced
with more productive animals
genetically superior offspring.
of the herd will be increased.
ting
program
might
which
In this way, the total
These cows
should
have
productivity
A farmer not participating in a
not gain this additional information
tes-
about
his
A farmer's decision to participate in DHIA testing and herd
im-
herd.
provement
is similar to a decision to adopt a technological
ment to a production process.
improve-
Dairy farmers were expected to respond
4
to
the higher,
nology
of
supported milk prices by adopting the available tech-
herd improvement activities.
dreases
the
ducts.
An
This response
further
in-
milk
pro-
supply of milk and the consequent surplus of
analysis of how and why farmers adopt
improvemerit
of
the
DHIA testing should provide insight
technological
into
production
incentives created by the dairy program regulations.
Finally,
long
run
in a competitive industry, economic theory asserts that
profits equal zero.
This occurs because firms can
freely
enter or exit the industry in response to short run profits or losses.
When short run profits are available,
industry
short
new firms attempt to enter
the
and existing firms attempt to expand to reap a share of
the
run
excess revenue.
When this occurs in an industry
with
a
relatively fixed stock of production assets, such as dairy cattle, the
firms bid with each other for the additional assets they desire.
This
bidding drives up the market prices and values of dairy cattle,
capi-
talizing the additional profits.
In
entry
the production sector of the dairy industry,
exist and the U.S.
available
expected
rents
few barriers to
dairy regulations have appeared
with the supported milk prices.
to bid for available,
share of the available profits.
to
create
Thus farmers
were
replacement dairy cattle to gather
a
An investigation of the relationship
between the level of profitability in the dairy industry and
fluctua-
tions in the market prices of replacement dairy cattle was expected to
confirm this assertion and provide additional evidence of the competitive
nature
of
dairy regulations.
dairy production and the effectiveness of
th~
U.S.
5
This
paper will investigate
responses to the dairy programs.
are:
(1)
created
What
the relationship between
the
profit
incentives
improve
the
of dairy herds through participation in herd improvement
testing activities?
dissipated
production
The questions of particular interest
by the dairy programs and farmers' decisions to
productivity
and
is
two aspects of farmers'
and (2) Have those increased
revenues
been
into the market prices of replacement dairy cattle due
to
the competitive nature of the dairy industry?
Outline of the Thesis
The
ture
next chapter of this thesis presents a review of the litera-
concerning the nature of technological adoption and
and
various aspects of the U.S.
The
third chapter contains the theoretical development of the dynamic
supply
lines
and
dairy industry and
its
innovation,
and demand models employed in this research project
the
investigations of the rate of adoption of DHIA
fluctuation
of the market prices of dairy
cattle.
regulation.
and
out-
activities
The
fourth
chapter discusses and summarizes the empirical results derived in
the
research.
summarizes
the
estimated instruments used in the final portions of the research.
The
The
first
section of the fourth chapter
second section discusses the findings of the investigation of participation
in the Dairy Herd Improvement Association.
The third section
presents the results concerning the relationship between profitability
and the prices of replacement dairy cattle in the long run.
The final
6
chapter
summarizes the main results and conclusions of the study
discusses possible implications for further research.
and
7
CHAPTER 2 '
REVIEW OF THE LITERATURE
This
chapter surveys previous research relating to the
of technological improvements in an industry,
of the dairy industry and regulatory programs.
cited in this review is not complete.
works
adoption
and to various
aspects
The list of references
However, it does contain those
considered by the author to be important to the development and
motivation of this project.
The literature review is divided into four sections.
section
presents
arguments concerning the adoption of
The
first
technological
improvements or innovations to production processes and the incentives
which motivate these adoptions.
tain
Further,
functional forms appropriate for the modelling of
logical adoption.
sing
various
research
second
on
such
questions of interest emanating from the regulation
whose findings the dairy
of
this section reviews early
legislations
are
based.
The
portion of this section addresses studies which suggest possi-
econometric models of the supply and demand sectors of
dairy
techno-
The second section summarizes several works addres-
the U.S. dairy industry. The first part of
ble
this section suggests cer-
industry
tions.
the
U.S.
regula-
The last portion of this. section reviews research of the capi-
talization
possible
used to research questions arising from
the
of
dairy
program rents.
The third
section
functional forms for milk production functions.
discusses
The
final
8
section relates possible questions of interest not investigated in the
prior literature.
Studies of Technological Adoption
Griliches
investigated
the adoption of hybrid corn
over
open-
pollinated varieties by farmers. The research determined that the rate
of adoption of hybrid corn followed an S-shaped curve.
slow
was
in the very early years with only a few innovative farmers using
the technology.
Over time, many other producers observed the benefits
of planting hybrids rather than the older varieties,
adoption increased significantly.
approached
new
Adoption
Griliches
fitted
slowed
of
Finally, as the planting of hybrids
an equilibrium level of use,
technology
and the rate
once again.
the rate of adoption of
To approximate
a transformation of the logistic
data.
The logistic function is specified
(1)
P=k/[1+e-(a+bt)J,
this
function
the
S-shape,
to
the
where P ig the percentage of corn acres planted with hybrid varieties,
k is a ceiling value, t is time, and a and bare parameters.
The research found that the earliest origins, quickest acceptance
rates,
and
highest
ceilings occurred where the
adopting the technology was the greatest.
bility
with
variables.
profitability
Griliches measured profita-
pre-hybrid yield per acre and average acres per farm
Specifically,
from
as
the use of hybrid corn started in Iowa and
9
Illinois
and over time,
spread to the entirety of the
corn
growing
a 1980 follow-up to Griliches' 1957 article,
reesti-
region of the United States.
Dixon,
in
mated the Griliches model with the additional data available and takes
issue with some of the original findings.
ling values were
than 1.0,
Dixon
all
priori and were,
years between the two studies,
replaced
revised
the
the 9pen-pollinated seeds.
ceiling values set at 1.0.
In the
hybrid varieties had comTo account
for
updated the parameter estimates using the same model
of
cei-
in many instances, less
where the ceiling is equal to the total population.
intervening
pletely
specified~
In the original work
this,
but
The great majority
with
of
estimates of the slope or rate of acceptance parameters
the
were
less than Griliches' original figures due to the higher ceiling values
and the long tails exhibited by such diffusion curves.
Dixon also found that a significant number of states exhibited
rather than a symmetric growth curve.
skewed
used
by
ceiling
Griliches
value.
function for
The logistic
is forced to be symmetric about one half
To allow for asymmetry,
the model estimation.
Dixon specified a
The Gompertz function is
a
function
of
the
Gompertz
speci-
fied
(2)
t
P=k(aP ),
where P is the percentage of acres planted with hybrid varieties, k is
the ceiling value,
differential and
t is again time,
~ate
and a and p are parameters.
of growth equations for the Gompertz are
The
10
(3)
dP/dt=Pln(~)(ln(P/k)),
(4)
dP/dta(l/P)=ln(~)[ln(P)
where
the logarithm of the exponentiated parameter
- ln(k)J,
~
performs a simi-
lar role to the b coefficient in Griliches' logistic specification
that
it determines the rate at which P approaches the ceiling
Dixon
found
performed
of
the
only four of 31 states for which the
better than the Gompertz.
Gompertz
function
logistic
in
value.
function
Given the additional flexibility
function it may well be better
than
the
logistic
for the types of technological adoption and diffusion
ques-
tions of interest here.
Dixon further investigated Griliches' claim that a large
of
the
variability
in the rate of acceptance across states
plained by the profitability measures,·
average acres per farm.
portion
is
ex-
pre-hybrid yield per acre, and
Using his parameter estimates in a regression
of acceptance rates on the profitability variables,
Dixon was
unable
to refute Griliches' original findings.
A third discussion
undertaken by Mansfield.
factors
determining
was
In his paper Mansfield investigated certain
how rapidly the use of a new
from one firm to another.
ing
of technological adoption and diffusion
technique
spreads
Specifically, he presented a model explain-
differences in the rate of imitation among innovations and firms.
He estimated the model with data on three innovations in each of
different industries,
railroads.
bituminous coal,
iron and steel,
four
brewing, and
11
Mansfield's
hypothesis
asserted
that the proportion
of
firms
adopting an innovation in a given period of time is a function of:
1)
the
by
proportion of firms which had already adopted the
that period;
the
2) the
prof~tability
innovation
3) the size of
of the innovation;
investment necessary to implement the improvement;
unspecified
keenly
variables
competitive
industry,
such
markets,
as risk aversion in
an
financial health and
other
industry,
more
stability
and industry attitudes toward innovation.
Griliches,
and 4)
of
an
Mans fie 1d , 1 i ke
used a logistic function to estimate the parameters of the
5-shaped adoption path.
Mansfield
tance
further hypothesized that the slope or rate of
accep~
parameter is linearly related to the profitability of the inno-
vation
and
tested,
the size of the investment required to
adopt
it.
both the profitability and investment parameters were of
When
the
appropriate sign and significantly different from zero.
Another appropriate functional specification, though not directly
fitted
to
Taylor.
tion
a
question of technological
Taylor
adoption,
is
presented
by
used a transformation of the hyperbolic tangent func-
to approximate any 5-shaped curve.
The hyperbolic
tangent
is
specified
where
formed
-oo<x<oo and the function has range (-1.0,
the
function
+1 .0).
such that it was bounded by
retained the 5-shaped characteristic.
0.0
Taylor transand
His transformation is
1.0
but
12
(6)
= .5
F(x)
+ .5[(ex- e-x)/(ex +e-x)],
Given this specification, the hyperbolic tangent reduces to the logistic function, particularly
This research project employed the logistic specification for the
estimation of the DHIA adoption path.
The specified model was
where the polynomial P(x) is free to achieve the best fit to the data.
It
was expected a priori that the polynomial would include terms with
even powers.
This allowed the estimated curve to exhibit some asymme-
try.
Studies of the U.S. Dairy Regulations
Numerous
studies
have been done on the various aspects
dairy industry and its regulatory program.
works
in
or
~lternative
altering the current regulatory structure.
World War II research are nonpolicy studies,
estimating
In
this
placed
on
policy decisions
The rest of the
post-
primarily concerned with
supply and demand response relationships [Dahlgran
study,
the
Approximately half of the
the literature are policy studies with emphasis
examining the effects on dairy markets of
of
1981].
those works which derived econometric models of
the
U.S. dairy industry and investigate aspects of the questions of interest here are emphasized.
13
Basis for the U.S. Dairy
The
study which formed the basis for the original dairy
legislation
search the
and
Regul~tions
in 1937 was conducted by Gaumnitz and Reed.
autho~s
support
In the
analyzed milk cooperative market power before
re1937
developed a model to show how a monopolistic price discrimination
system such as the consequent classified pricing of milk could
lize
and
enhance
producer incomes given a fixed level of
stabi-
the
farm
supply of milk.
The demand for milk basically has two forms, for fresh fluid milk
products,
and
or far manufactured milk products such as
nonfat dry milk.
costly
to transport.
Fluid milk
butter,
is highly perishable,
cheese,
bulky,
Consequently the demand for milk used in
and
fresh
products is considerably less elastic than that far manufactured dairy
products which are easier to stare and less costly to
basic
transport.
The
element in Gaumnitz and Reed's model is that the price could be
raised for fluid uses of milk where the marginal revenue is relatively
low
and
demand is relatively inelastic.
The remainder of
the
milk
supplied is diverted into manufacturing uses where marginal revenue ishigher.
This principle underlies the milk marketing orders as legis-
lated in the Agricultural Adjustment Act of 1937.
The current classi-
fied pricing mechanism is presented in Figure 1.
In
price
the
PI and PII are the observed Class I
and the announced Class II support
intersection
private
illustration,
price,
respectively.
of the Class I and Class II prices with
demand schedules imply
a 1 and a 11 ,
the
milk
The
respective
the quantities of Class I
and Class II milk consumed by the private sector.
The average revenue
14
Figure 1.
Classified Pricing Mechanism for Milk
p
AR
~I
G
a
D1 =private demand for Class I milk
D1 + DII = horizontal summation of Class I and Class II milk demands
a 1 + DII =quantity of Class I milk consumed + Class II demand
a 11 =quantity of Class II milk consumed
as =quantity of milk supplied
G = fluid milk equivalent of government purchases of surplus milk products
S =total supply of milk
PI =Class I milk price
PII =announced support price for Class II milk
Pm =average price received by farmers for all milk
AR = average farm revenue
15
curve (AR) consists of the set of averages of the Class I and Class II
milk
prices,
consumption.
average
weighted
The
revenue
by the amount of milk used in each
class
intersection of the total milk supply (S) and
schedule determines the average
price
received
of
the
by
farmers for all milk (Pm) and the total amount of milk delivered (Qs).
Government purchases (G)
is the difference between the total delivery
of milk and total private consumption
ca 1
+
a 11 >.
Econometric Models of the Dairy Industry
LaFrance
and
de
Gorter provide an example of
using a simulation approach.
policy
research
The dairy industry model derived in this
study forms the foundations for the research
i~
this thesis and there-
fore will be reviewed in detail.
The
supply
authors
econometrically derive a model involving
and demand sides of the U.S.
.'
both
the
dairy industry and estimate
the
annual costs of the dairy program regulations. The specified model was
a
recursive
system
of equations with elements for
Class
I
(fluid
consumption) and Class II (manufacturing consumption) milk prices
private
demands;
net commercial removals of milk and dairy products;
the average price received by farmers for all milk
of milk per cow;
and
the aggregate U.S.
delivered;
output
dairy herd; and the total supply
of milk.
Prices
and quantities for the Class I and Class II milk
were simulated under unregulated,
1980.
The authors
markets
competitive conditions from 1965 to
then compared the simulation results with the his-
torical price and quantity data.
Using this comparison,
the authors
16
calculated
the
costs of the program in terms of higher
milk
prices
paid by consumers and lost economic surplus due to reduced consumption
of
milk
in response to the artificially high
costs
of
lated
net
prices.
Annual
the dairy program were determined as the sum of the
calcu-
economic
government
These
losses and the actual net
necessary
outlays
fluid
expenditures
to administer and operate
include
the
expenditures by the CCC to
dairy
of
the
program.
purchase
surplus
dairy products, less the value of domestic CCC donations, plus storage
and administration costs.
LaFrance
and de Gorter estimated total costs of the
U.S.
dairy
regulations to be between $430 and $590 million per year from 1965
to
1980
to
(in
varying
lower
1980 dollars).
choices
in the
estimate
measur~ments
of the
surplus
results from an ex ante measurement of
producer surplus,
operating
The range in the cost estimates is due
that is,
figures.
consumer
assuming that the dairy program had
The
and
been
and had already affected the supply and demand schedules in
previous years.
The higher calculation results from an ex post meas-
urement which assumes that competition had prevailed in the
years.
The
program
of
authors
preceding
also calculated a long run cost figure for
$560 million.
They determined this to be
a
the
reasonable
middle ground between the other two estimates.
The model used by LaFrance and de Gorter,
sults,
dairy
appear
to be fairly robust for several reasons.
First,
program cost estimates calculated by the authors compare
favorably
1980,
and its consequent re-
with other studies [Buxton,
Buxton and
Hammond,
the
quite
Dahlgran
Heien, and Ippolito and Masson]. Further, the simulation of the
17
competitive equilibrium situation appeared to result in a
stable
under
The authors tested this by simulating the model
equilibrium.
the assumption that the dairy program had been terminated
Each of these simulations resulted in
year from 1953 to 1965.
or
dynamically
each
equal
very nearly equal competitive price and quantity figures for
year
from 1965 to 1980,
each
revealing the long-run stability of the U.S.
dairy market.
Hein
specified
and estimated an econometric model of
the
U.S.
dairY industry to measure the effects of the Federal dairy support and
classified
pricing
regulations on consumer prices of dairy
over the period 1949-1974.
cost
He used the resulting price
products
chang~s
as
a
of living index to estimate the social costs and 6onsumer losses
Hein's model of the dairy industry is divided
due to these programs.
into three main sectors.
The
where
fed,
first
sector is a farm level supply
dairy herd inventory figures,
and time,
sured
and
to account for gradual
is a dynamic system where changes in the dairy herd figures
opportunity
by the market price of slaughter
not,
however,
long
term
profitability
are
past inventory figures, and
cost of keeping dairy animals in production as
does
hay
The dairy herd response relation-
influenced by the price of milk received,
the
relationship
total milk supplied ·is a function of the inputs grain
technical change and improvements.
ship
response
animals.
This
relationship
explicitly account for the present value of
streams such as future milk
income derived from the offspring of an animal.
mea-
production
any
or
18
The second sector of the model is composed of retail demand
tions for the six major dairy
frozen dairy products,
mi 1k.
fluid milk,
product~:
nonfat dry milk,
butter,
equa~
cheese,
and evaporated and condensed
In the model, the quantity demanded of each product is a func-
tion of its own price, prices of substitutes, the overall price level,
'
and lagged dependent variables
to account for persistence effects such
as habit formation.
Last,
the
retail prices of these six products are specified
functions of the price paid for milk,
sing
and distribution activities.
the
model
dairy
and the wage rates for
proces-
The supply and demand sectors
are linked by the identity where the quantity of milk
products
supplied
must equal private
consumption
as
of
and
plus
U.S.
government and military purchases, changes in private stocks held, and
net exports.
Hein calculated the total social cost of the dairy support
regu-
lations over the period 1949-1974 to be $15.011 billion, or an average
of
$577.0 million per year.
three
components.
expenditures
such
The first is $7.048 billion in direct
losses
due
ducts.
marketing
The second element of the social
cost
orders,
and
cost
determined by the model to be the consumer welfare
to elevated prices and reduced consumption of dairy
The
of
government
as CCC purchases of surplus dairy commodities
program administration costs.
is $3.405 billionJ
This total cost estimate is made up
of the classified pricing system and
the last component of the total social
calculated to be an additional $4.558 billion.
the
pro-
Federal
cost,
was
19
Salathe, Price, and Gadson present the structure, parameter estimates,
and
validation staiistics for the dairy sector submodel
tained in the USDA Food and Agricultural Policy Simulator.
con-
The model
the authors developed was used to examine and simulate the adjustments
in the supply and demand schedules of the U.S.
ting
from
dairy industry
resul-
a reduction of the dairy support level from 75X to 65X
of
parity in 1981.
The
to
dairy sector submodel is a simultaneous system of
endogeneously estimate dairy herd inventory
production;
supply,
farm level milk prices;
price,
figures;
equations
total
fluid milk consumption;
and consumptfon of butter,
cheese,
milk
and the
nonfat dry milk,
evaporated and condensed milk, and frozen dairy products.
The authors
estimated the levels of government purchases of surplus dairy products
necessary to support milk prices at their predetermined levels.
the
parameter estimates generated by the model
Salathe,
Using
Price,
and
Gadson predict the impacts of reducing the dairy support level.
The
simulated
resulted
in
reduction in the price supports to 65X of
predicted decreases in the farm level price of
$.11/cwt in 1981,
$.83/cwt in 1982,
$1.26/cwt in 1983.
parity
milk
By 1985, the
aggregate dairy herd was expected to decrease by .22 million head
the
total
necessary
mill ion
1983.
output of milk to fall by 3.0
USDA
and
billion
pounds.
and
Finally,
purchases of surplus commodities would fall
farmer cash receipts would decrease by $1.8
of
by
$820
billion· in
20
Investigation of Capitalization of
Dairy Program Rents
Masson
lations
and Eisenstat investigated the effects of the dairy regu-
in terms of the three goals for which the classified
system was enacted.
mers' incomes;
Again,
pricing
these goals are: 1) to raise dairy far-
2) to assure an adequate supply of milk throughout the
year; and 3) to provide for an orderly market.
The authors used the Gaumnitz and Reed model of price discrimination
to investigate how well the regulations have achieved the
enunciated in the initial legislation.
goals
Further, the authors assumed a
static equilibrium in the total dairy market and explore the questions
of interest under two supply scenerios,
a perfectly inelastic
supply
schedule and a positively sloped supply curve.
The
that
the
necessary
results of the research,
under either
scenerio,
dairy regulations set farm level prices
to
meet the first two goals.
higher
suggested
than
Masson and Eisenstat
that
found
that a substantial amount of the increased producer incomes are dissipated
through land markets into higher landowner
determined
rents.
They
also
that the support programs are set up so larger farmers and
landowners receive a greater benefit than smaller producers.
the authors cite large surpluses of
manufactu~ed
Further,
dairy products as
an
indication that farm level prices of milk are higher than necessary to
achieve the adequate supply stipulation.
Finally,
disorderly marketing in the 1930's meant lockouts, dis-
ruptive violence, and milk withholding actions.
of
today
this goal is somewhat
obsolete,
For the dairy markets
Therefore,
the
authors
21
concluded
that
the
classified pricing system
eliminated without violating the
go~ls
could
be
completely
of the dairy program.
Suggested Forms of the Milk Production Function
Numerous
researchers
.
have
. investigated the production
for milk to estimate a supply response.
employed
linear
a
of the studies
quadratic specification of the production
and
reviewed
function
quadratic terms in the inputs grain and hay plus
other factors.
with
various
The general· specification used is
Y is the output of milk,
wh~re
Al~
function
g is the input grain fed,
h is
the
input hay fed, and · · · are the other factors varying among researchers
[see,
e.g.
Jacobson,
Paris,
Heady,
Jacobson,
and Freeman;
Schnittker, and Bloom;
Hoover,
Heady, Madden,
Kelly, Ward, Feyerman, and Chaddha;
Malossni, Pilla, and Romita; and LaFrance and de Gorter].
research here,
The
follows the pertinent literature and employs a quadra-
tic form of the production function to model the output of milk.
Questions of Interest Arising in the Literature
Several
on
the
points of interest were evident in the prior
technological adoption and innovation and the various
dairy program to motivate this research
the adoption of a technological improvement,
testing, should follow some 5-shaped path.
tion
of
project.
literature
aspects
of
Particularly,
such as herd improvement
Further, the rate of adop-
a new technology was expected to depend on
several
factors
22
such
as expected profitability from the improvement,
investment required to install it,
the size of the
the number of firms already
using
the innovation, and various, other unspecified factors.
The
literature concerning the effects of the dairy support regu-
lations and the classified pricing system analyzes an extensive
of
questions,
of
the dairy supply and demand and deriving estimates of the
though primarily addressing the response relationships
iocial costs and benefits incurred due to the legislation.
however,
tigated
range
various
There are
other questions of particular interest which were not invesor
were explored only briefly in the course
of,
or
as
an
extension of the primary research.
The
first
of these questions involves determining
the
factors
influencing the rate of adoption of a technological improvement in the
U.S.
dairy industry.
herd quality testing.
played
In this case, the technological improvement was
Both Hein and Salathe,
Price,
and Gadson em-
a time trend as an explanatory variable to account for
quality
animals and improved management practices.
tempted
to explain a portion of the variations in the level
output
due to technological improvements.
higher
This merely
of
atmilk
No literature reviewed ex-
plicitly researched the factors affecting farmers decisions to .improve
the
productive
capacity of their herds.
Such an
investigation
necessary to determine the rates of adoption of such improvements
to
is
and
better understand the forces and incentives inducing dairy farmers
to undertake such investments.
23
Another
question
determining
the
which has yet to be
fully
forms of dissipation of the short run
created by the Federal dairy regulations.
eluded
that
in~olves
analyzed
profitability
Masson and Eisenstat
attempts to achieve the goal of raising
dairy
con-
farmers'
incomes increased the price of land used in dairy production. In other
words,
the rents from the dairy regulation were capitalized into land
values.
Thus
landowners,
not necessarily dairy farmers
themselves,
were the final recipients of the benefits of the dairy program.
the research failed to refute this claim,
specialized
itself.
assets
Land
in the production of milk,
that
of
even more
namely the dairy
always has a number of good alternative uses
tilling for crop production,
dairy cow,
there are other,
however,
While
such
cow
as
or pasturing other types of livestock. A
has few good alternative uses.
Thus one expects
any short run rents or profits to be capitalized into the prices
replacement
Investigation
dairy cows even more quickly than into
of
a relationship between program
land
created
values.
rents
and
fluctuations in replacement cow prices is absent from the literature.
This
dairy
research
project builds an econometric model of
industry following LaFrance and de Gorter and investigates
incentives
created
by the Federal
milk marketing orders.
dairy price support
program
U.S.
the
and
The research will address and empirically test
two basic questions of interest.
respond
the
These are: (1) How do dairy farmers
to incentives created by the dairy support program by attemp-
ting to improve their herds with quality testing? and (2) How does the
dairy
program
impact the driving forces behind fluctuations
price of a specialized asset,
in this case,
a dairy cow?
in
The
the
next
24
chapter
employed
outlines the theoretical development of the empirical
in this research and describes the
nature and
of the data used to estimate the economic relationships.
models
construction
25
CHAPTER 3
THE CONCEPTUAL MODEL AND DATA SOURCES
Dynamic Model of the U.S. Dairy Industry
The
model that is employed in this research project has a recur-
sive structure.
production
The foundation for the model is a milk output per cow
function.
This yield per cow equation is specified as
a
quadratic function where milk output is determined by the inputs grain
and concentrated feed per cow (g),
and
participation
measured
three
reflect
by
in
herd improvement activities
the proportion of total cows on
years previously.
the
hay and roughage fed per cow
Yt
period for a tested animal to produce a
= a0
+
(DHIA).
DHIA
is
testing
programs
The DHIA regressor is lagged three years to
heifer maturing into milk production.
C10)
DHIA
(h),
calf
and
that
Specifically the equation is
~ 1 DHIAt_ 3 + ~ 2 gt + p3 ht + 1/2cr 1 DHIAt_ 32 + 2r 2
DHIAt_ 3egt + 2t 3DHIAt_ 3oht + t 4gt + 2t 5 gt•ht + r 6 ht),
and r 1 are parameters. This specification results in
where the a 1 ,
~i•
closed
expressions
form
for the factor demand functions
research suggests that it tends to fit the data well.
to be strictly concave in g and h,
and
prior
It was assumed
having the desirable properties of
26
a well-behaved production function
ductivities
of the inputs,
such as diminishing marginal
pro-
which results in finite solutions for the
choice variables.
However,
monitored
since the amount of hay and roughage fed per cow is not
in usual dairy feeding practices and is not a directly
servable variable,
derive
well
one must use this quadratic production function to
a reduced form supply equation where output is a
input
prices rather than input levels.
as
labor
function,
search
sumed
ob-
function
of
The inputs grain and hay,
as
which does not explicitly appear
in
the
are employed in some complementary fashion.
production
In prior
re-
complete nonsubstitutability between all three inputs was
as-
[LaFrance and de Gorter].
relaxed
In this study,
that constraint was
so that the nonsubstitutability between grain and hay was not
initially imposed.
However,
with grain and hay,
as well as the fourth factor, DHIA participation,
in
fixed
proportions
labor will still be assumed to
from a translated
origin.
The
combine
relationship
between labor and the other factors is specified as
where all of the inputs are measured in units per cow.
This relation-
ship is illustrated in Figure 2 where labor and a bundle of the
inputs grain,
hay, and DHIA participation are necessarily combined in
fixed proportions along the production function for milk. This
that for each level of the inputs grain,
some fixed,
other
states
hay, and DHIA, there will be
positive level of labor necessary to be combined with the
other inputs for the production of milk.
27
Figure 2. Fixed Proportion Relationship between Milk Production Inputs
A
f(g,h,DHIA)
~ = labor per cow
f(g, h, DHIA) = assumed bundle of other milk production factors
A = set of least cost labor/other factor combinations
28
An individual dairy farmer is assumed to maximize profits.
·Par-
ticularly, the farmer maximizes the objective function
subject to the constraints imposed by the production function (10) and
the complementarity of the inputs (11).
of
milk,
feed,
Pm is the average farm
price
Pg is the price per hundredweight of grain and concentrated
Ph
is
the price per ton of hay and roughage,
and P£
is
the
average farm wage.
Maximization
minimization
between
the profit per cow
of cost and factor usage.
labor anq the other
Substituting
bine
of
inp~ts
in the complementary
equation
implies
(12),
a
This forces the relationship
(11) to assume a strict
a~ounts
of
l~bor
equality.
necessary to
with each of the other factors in the profit function
com-
(12)
im-
p 1 i es
(13)
rrt
= Pm•Yt-
(Pg + a 1 ,£P£)gt- (Ph+ a 2 ,£P£)ht- (ao,£ +
a 3 ,£DHIAt_ 3 )P£.
Maximization
conditions
of (13) and simultaneously solving the first
for the inputs grain and hay results in the factor
equations for those inputs
(14)
g*
= e1[((Pg
+ a 2 ,£P£)/Pm) (15)
=
+
~3
a 1 ,£P£)/Pm)
- ~2
-
r 2DHIAt_ 3 J
- r 3DHIAt_ 3 J,
- ~2
+
order
demand
29
where
= r 6 t<r 4 r 6 - r 25 ),
2
e2 = -r5t<o4r6- r5),
2
e3 = o4t<r4o6- r5),
e1
and
the
optimal level of use for each factor is a
of the inputs and the level of
function
DHIA
of
the
deflated
prices
participation.
Assuming
that these equations have been derived from the profit maxi-
mization hypothesis qnd that the structural production function,
f(gt,
ht,
=
bHIAt_ 3 ) is strictly concave, certain properties of factor
demand equations are implied.
are
y
homogeneous
These are:
(1) equations (14) and (15)
of degree zero in prices;
(2) they
are
negatively
sloped, that is, the first derivative of each demand equation with respect
to own price is less than zero.
less than zero and
the
o4 o6
-
og
This occurs if
o4
and r 6
> 0; and (3) cross price symmetry exists,
partial derivative of a given factor demand equation with respect
to the price of the other factor equals the partial derivative of
other
are
the
factor demand equations with respect to the given factor price,
particularly, ag*taPh
Substitution
= ah*taPg = e2 = -r 5 tcr 4 r 6
- o~).
of the optimal input levels (14) and (15) into
the
initial production function (10) results in a reduced form output
per
cow equation, which is a product supply function in classical economic
production
theory,
output price,
where milk produced per cow is a function of
the factor prices,
tion is specified
and DHIA participation.
the
This func-
30
( 16)
Yi
= ¢o
2
+ .PtDHIAt-3 + ¢ 2 DHIAt_ 3 +
e1 E(Pg
+
a 1 ,£P£)/PmJ 2 +
e2
a 1 ,£P£)/PmJE(Ph + a 2 ,fPQ)/PmJ + e 3 E(Ph + a 2 ,£P£)/PmJ 2 ,
[ ( pg
+
.Po
= ao -
¢1
= {31
¢2
-
where
( {3~ a- 6
2
2
- o5)J,
- 2 f32f33r5 + f33o4)1E2(o416
2
- Ef32 12r6 - ({32°3 + f33 1 2l 1 5 + f33r3o4J/Cr4r6 - 05),
2
2
- a-5)].
a-1 - ( 0~06 - 2r 2 r 3r 5 + 1314)/[2(1416
From (11), the relationship between the inputs, a 1 ,R and a 2 ,R are
constrained to be non-negative. The assumption of the strict concavity
of the production function (10) imposes constraints on el, e2, and e3.
Specifically,
e 1 < 0,
e3
< O, and
e1 e3
> e~.
The parameters for the
flnal reduced form yield equation are redefined to assure satisfaction
of a weak inequality form of these restrictions.
The coefficients are
redefined as
(17a)
e1 -- - rp2 1 ,y '
( 1 7b)
282 = rp2 'y'
( 1 7c)
e3 = -(rp22,y + rp 3,yl 1 ~ l,y•
(17d)
2
al,£ = rp 4,y'
(17e)
2
a2,£ = rp 5,y·
2
Substitution
of
2
these new coefficients into
the
reduced
form
yield per cow equation (16) results in the final estimable form of the
yield equation.
This reduced form yield equation, which is nonlinear
in the parameters, is
31
( 18)
In this specification, optimal output of milk per cow is a function of
an
intercept,
a linear and quadratic term in the DHIA
participation
variable, and quadratic terms in the real input price variables.
The real input price variables reflect the perfect
ity
between
labor and the linear function of grain,
participation.
For
example,
complementarhay,
and
DHIA
the input price for grain includes
the
price per unit of grain and concentrated feed used plus the wage times
a
factor for the amount of labor necessary to feed
the
grain.
The
input price for hay and roughage is defined in a similar manner.
Again,
assuming
the
through profit maximization,
plied.
The
function
upward
sloping,
supply per cow function has
been
derived
the usual, desirable properties were im-
is homogeneous of degree zero
in
prices,
that is the first derivative of the supply
and
function
with respect to product price is greater than zero.
The
yield
per cow equation was used in the determination
profitability measure,
defined as returns over variable
cost.
of
a
This
measure is
(19)
where profit,
the
optimal
n*
'
in this case,
is determined by the interaction of
levels of the output milk and the
various
inputs.
32
The avergae price
where
of all milk is defined by
Pm is the average price per
farmers;
PI
hundredwei~ht
of milk
milk,
by
and P 11 are the average farm prices per hundredweight of
(fluid consumption) and Class II (manufacturing
Class
received
respectively;
o1
and
o11
consumption)
are the private consumption levels for
Class l-and Class II milk, defined as the total U.S. population multiplied by the per capita demands for Class I and Class II milk,
q 1 I;
qi and
NCR is net commercial removals; and NGR is the fluid milk equiv-
alent of net government purchases of manufactured milk products.
However
supply
of
calculation
(20),
(QI
the
average price received for all milk and
milk are determined jointly due to
of the price of milk.
+
the
Specifically,
the
weighted
total
average
the denominator of
a 11 *NCR+ NGR) equals the total quantity of milk
sup-
plied and (Orr+ NCR+ NGR) equals the total supply of milk less Class
I
private consumption.
Consequently,
endogeneous variables on
the
right hand sides of the equations are correlated with the error terms.
To break this simultaniety and derive consistent parameter
the
model
estimates,
equations were estimated with instrumental variables in
a
two stage least squares procedure.
In
the
endogeneous
are
two stage procedure,
the
various
components entering the equations of the recursive
estimated and calculated as functions of exogeneous or
mined variables.
on
predicted values for
model
predeter-
Observed values of these elements are then regressed
their predicted counterparts.
Predicted values of the
variables
33
from
this
second estimation then
form the two stage
squares
These instruments are then used as predetermined varia-
instruments.
bles in subsequent recursive equations.
the
least
endogeneous
This technique corrects
right hand side variables,
resulting in
for
consistent
parameter estimates.
The
actual
lated to the
prices of Class I and Class II milk are closely
~upport
price exogeneously determined in the milk
re-
marke-
t1ng orders due to the purchase,
storage, and disposition of manufac-
tured milk products by the CCC.
P 11 , the Class II price is defined as
the Class II support price plus some random variation,
where
Psup is the Class II support price as announced in the
milk marketing orders and Ell is unobservable error.
expects a 0 , 11 to equal zero and
~l,II
support price,
market
conditions,
Psup'
A priori,
one
to equal unity. The actual price
received by farmers for manufacturing grade milk,
the
Federal
P 11 , need not equal
in every period and in fact has not due to
measurement errors in reporting the actual
price
received, and aggregation, etc.
The
Class
I price of milk is defined as the
Class
II
support
price plus a differential and an error term
Here,
one
specified
expects
in
a 0 , 1 to equal the average
the milk marketing orders and
Class
~l,I
differential
should equal
unity.
34
The
Class
Federal
I differential is a markup above the Class II price
Milk
processing
plant
[USDA,AMSJ.
served
Marketing
and
Order depending on the location
its
distance
to
a
In the estimation of (22),
major
of
in
a
consuming
milk
center
P 1 was constructed from
variables because it is not reported by the USDA.
a
ob-
By solving
(20} for the Class I price, one determines
where
the
Class I price is a functt·on of
variables
with
available
data.
The
per capita demand equations for Class I and Class II consump-
tion are
<24 )
=
qi
~o,I
+ ~t,r<Pr 1 Pnt> +
~2,r<Prr 1 Pnf)
+
~3,r<Pb 1 Pnt>
+ r4,r(AGE) + rs,I(TJ + r6,I(INC/Pnf) + ~7,I(qr,t-l> + E24'
(25)
q1I
= rO,II
+ ~2,I(PI/Pnf) + ~2,II(PII/Pnfl + ~3,Il(Pfo/Pnf)
+ ~4,II(AGE) + ~5,II(T) + r6,II(INC/Pnf) + r7,II(qii,t-1) +
E251
where
P 1 /Pnf'
flated
by
PI 1/Pnf are the Class I and Class II milk
prices
de-
the Consumer Price Index for nonfood items to reflect
own
and cross price effects in the demands;
Consumer
and
Pb/Pnf•
Price Indices of other beverage prices,
oils excluding butter,
respe~tively,
and Pf 0 /Pnf are
the
and prices of
fats
again deflated by the non-
food price index to reflect substitution effects;
AGE is the
average
age of the U.S. population to reflect changes in preferences as people
age;
ql,t-l and qii,t-l are lagged dependent variables to account for
35
persistence
effects such as habits;
and T is a time trend to reflect
the over time growth in the consumption of dairy products.
The
var-
ious prices in the demands for milk are deflated by the non-food price
index
so
the
deflator is not affected by the price
net
commercial removals in (20),
variable
being
deflated;
NCR,
commercial
the
inventories and net commercial exports,
Government purchases,
ports.
price
government
represents increases
stocks,
exports less
im-
NGR is the control instrument by which
of Class II milk is supported and
owned
in
represents
foreign and domestic
changes
donations,
in
and
net
government export sales.
Commercial removals were specified
=
(26)
where NGRt, government purchases, accounts for the replacement of private
inventories with government stocks and NCRt-l is a lagged depen-
dent
variable
to account for the effects of last
current period's decisions.
of
year's
stocks
on
Equation (26) was specified without price
milk regressors because the price effects on net commercial
remo-
vals have been shown to be nonsignificant due to the effects of import
and export restrictions on dairy products [LaFrance and de Gorter].
NGR,
Class
been
ducts
the net government purchases, are the residual amount after
I and Class II consumption,
and net commercial
deducted from the total milk supplied.
removals
have
The amount of dairy pro-
purchased by the government each year is jointly determined
the interaction of supply and demand forces within the dairy
by
industry
36
and a predicted instrument for it must be constructed.
Net government
removals were specified
=
(27)
where
+
Psup is the Class II support price;
+
Pfo is the Consumer
Price
Index for fats and oils excluding butter to reflect the costs of close
substitutes for manufactured milk products;
disposable
milk
income
to reflect any income effects in the
and milk products;
items;
INC is average per capita
demands
Pnf is the Consumer Price Index for
for
nonfood
Tis a linear trend; and NGRt-l is the level of net government
removals in the previous period.
When (21)-(27) had been estimated,
mates
w~re
the resulting parameter esti-
used to derive predicted values for P 1 ,
and
NCR.
was
constructed
P11 ,
a 1 , a 11 ,
A predicted instrument for the average farm price of
as a form of (20) using the predicted
values.
NGR,
milk
This
instrument is
(28)
~m
= [p 1a1
-
-
-
+ P 11 <a 11 +NCR+ NGR)J/(QI +
-a11
- -
+NCR+ NGR).
Theoretical Discussion of the Adoption of DHIA TestinQ
Prior
literature
suggests
that the rate of
adoption
of
some
technological improvement, such as herd improvement testing activities
will be dependent on expected profitability from the improvement, size
of the required investment,
In the dairy industry,
and past levels of use of the innovation.
expected profitability is largely dependent on
37
the
supported prices for milk and the input expenses,
the
profitability measure (19).
in
as evident
in
Since the investment to participate
DHIA testing is basically a nominal fee per cow,
inflation is nearly constant,
which when
counted
for
the hypothesis
portion
of the research is that the rate of adoption of DHIA
for
disthis
testing
is directly related to the level of profitability created by the dairy
support program.
This hypothesis was investigated by estimating a rate of adoption
function for DHIA participation.
The rate of adoption was
initially
specified
(29)
where
DHIA~
= ko[exp(a
e~p(a
+
the
dependent
level of
+
*2
~2nt
~articipation
estimation as a linear trend;
study,
equilibrium
(29)
and
and k,
activities
time,
is
measure
entering
an interaction term between return
which is the ceiling value.
the ceiling was defined to be 1.0,
level of use equals the available
where
For
the· long-run
population,
Equation
particularly the estimated coefficients on the return
variable cost regressors, were
the
in herd improvement
linear and quadratic terms in T,
over variable CQst and time;
this
*
+ ~3T + ~4T2 + ~5ntoT)J,
on linear and quadratic terms in the profitability
calculated in (19);
the
*
~lnt
+ ~ 1 n~ + ~ 2 n~ 2 + ~ 3 T + ~ 4 T 2 + ~ 5 n~eT)J/[1 +
over
used to test the hypothesis concerning
relationship between the rate of DHIA adoption and expected
pro-
fitability in the dairy industry. Specifically, the null hypothesis is
that profitability in the
dai~y
industry has no effect on the rate
of
38
adoption
of
DHIA testing,
w~ile
the alternative hypothesis
asserts
that the level of expected profits do affect the adoption of herd
provement testing.
im-
This hypothesis was tested by regressing the par-
ticipation in DHIA as a function of profits.
Hypothesized Relationship Between Profit and Milk Cow Prices
The final thrust of this project was to investigate the impact of
the
u.s.
program
the U.S.
dairy regulations on the value of a dairy cow.
dairy
The
appears to enhance production incentives and profitability in
dairy industry in the short run.
However over time, due to
the competitive nature of the production sector in the industry,
cer-
tain
term
forces
in the market will tend to dissipate
these
rents and in the long run, economic profits will be zero.
ly,
there are
the
milk
two forces at work here.
supply curve from
short
Particular-
First, a rightward shift in
s 0 to s 1 will reduce the blend
milk received by farmers from Pm,O to Pm,l'
price
as seen in Figure 3.
of
The
reduction in output price will reduce somewhat the short term profits.
However, this alone will not drive economic profits to zero.
The second force tending to dissipate profits is the
tion
capitaliza-
of those profits into the market price of a dairy cow.
As
new
firms strive to enter the dairy industry, or as existing firms attempt
to expand their operations,
inventory
increase
the market prices of the relatively fixed
of producing dairy cattle will be bid up.
in
The
consequent
prices of replacement animals will tend to increase
average total cost of producing milk.
For long run profits to
the
equal
zero, the competitive equilibrium condition where the marginal cost of
39
Figure 3.
Price Effects of an Increased Supply of Milk
Os,o
s0 = initial supply of milk
s 1 = increased supply of milk
Os,1
Pm,O =initial average price for all milk delivered
Pm,l = average price for milk after supply increase
G0 = initial fluid milk equivalent government purchases of surplus
mi 1k products
G1 = government purchases after supply increase
as,O = initial quantity of milk supplied
0 5 , 1 = increased quantity of milk supplied
40
milk
production
.~verage
equals
the minimum average total
cost
equals
the
price received from producing milk must exist.
In this study, long run total profit is specified
(30)
TI =
n*ec*
+ P~ull COW?eCS- P~ceCP- c(C*),
where TI is long-run total profit;
over
n*ec* is long-run,
per cow, return
variable cost multiplied by the long-run inventory of
producing
cows;
Pcull
* cows•CS is the long-run price of utility cull cows multi-
plied
by
the
number of culls sold to reflect the salvage
cattle
at the end of their productive life;
market
price
of
pruchased;
animals
in a producing herd.
inventory
P~c•CP is the . long
milk cows multiplied by the number
animals
value
of
and c(C*) is the opportunity cost of
of
run
replacement
keeping
c*
Differentiating (30) with the long run
of producing cows and setting equal to zero determines
the
long-run competitive equilibrium condition
n* + P~ull cows= P~c + c'(C*).
( 3 l)
Empirically,
the opportunity cost in (31),
and was eliminated·from the equation.
equilfbrium
as
condition,
c'(C*),
was unobservable
Consequently,
in the long-run
the long-run price of milk cows was specified
a function of the return over variable cost and the price of
cull
cows
(32)
where
COWS'
a*,
~*,
and
r* are long run parameters.
For the
long
run
41
equilibrium to hold the price of milk cows must be a linearly homogeneous function of the return over variable cost and price
The long run intercept a*
regressors.
cant
of cull cows
was expected to be nonsignifi-
in a statistical test of the relationship in (32).
run
If the
constant term was significant the competitive equilibrium
tion
would not exist and long run profitability would not
long
condi-
be
dissi-
the
years
pated away.
Data Sources
The
period
1950-1985
gathered
of data observation for this project is
inclusive.
The data to be used in the estimation has
from a number of sources.
trated feed per cow,
The amount of grain and
the number of cows on DHIA test,
of Class I and Class II milk consumption,
the
amount
the
been
concen-
quantitie~
the average farm wage,
of labor used for dairy operations are found in the
and
USDA
publication Agricultural Statistics.
Data for the total milk produc-
tion, milk per cow, average farm
for all milk, average price for
grain and feed concentrates,
p~ice
and replacement cow prices are found
in
Agricultural Statistics, and the Economic Research Service/USDA publication Dairy Situation and Outlook.
on
farms
in
Statistics,
January and annual average are
the Dairy Situation and Outlook,
bulletins 'Dairy Statistics 1949-1960,
The
average
Agricultural
ASCS'
The number of producing milk cows
support
in
Agricultural
and the ERS statistical
and Dairy Statistics 1960-1967.
and farm price for Class II milk are
Statistics,
Commodity
found
tMe Dairy Situation and
Fact Sheet:
Dairy Program,
Outlook,
found
and
while the Class I
in
the
farm
42
level price is a constructed data series as previously mentioned.
average price per ton of hay and roughage;
The
the price per bushel of #2
yellow corn at Omaha, Nebraska; the price per short ton of 44% protein
soybean
meal at Decatur,
price of utility
tural Prices,
Illinois;
and the ASCS' Feed Situation and Outlook.
Economic
The consumer
non-food items, non-alcoholic beverages,
fats and oils appear in Food Consumption,
tures,
hundredweight
cull cows are found in the USDA publication Agricul-
price indices for all items,
and
and the Omaha per
Prices,
and
the Bureau of Labor Statistics' CPI Detailed Report,
Report
of the President.
Finally,
and
The index of all prices paid
farmers is found in Ag,ricultural Statistics,
of the President.
Expendi-
data on the 1,.1.5.
the
by
and the Economic .ReRort
population,
incomes appear in the Economic Report of the President.
age,
and
43
CHAPTER 4
EMPIRICAL RESULTS
The
previous
chapter developed the theoretical basis
for
this
study.
This chapter summarizes the empirical results. The estimation
of
model is completed using the statistical
the
packages
analysis
Dynreg EBurt, Townsend, and LaFrance], and Shazam [WhiteJ.
This
chapter is divided into three sections.
The first section
and
constructing
discusses
summarizes
the results derived
in
various two-stage least squares instruments used in the
tigations of the study.
the
final
inves-
The second section contains the results from
investigation of the hypothesis concerning the adoption of
Herd
Improvement
final
Association quality testing of dairy
section summarizes the investigation of the
bility
in
the
Dairy
cattle.
long-run
the dairy industry and its impact on the market
The
profitaprice
of
dairy cattle.
Instrumental Variable Construction
As stated in the previous chapter, many of the prices and quantity
This
figures
results
within the U.S.
dairy industry are
of
constructed
jointly.
in correlation between the dependent variables and
error terms of the estimated equations.
taniety
determined
the variables,
the
In order to break the simul-
predicted values of these
as instruments for a two-stage least
variables
squares
are
estimation
44
This section reviews and discusses each estimated instru-
technique.
ment,
its
relationship
to the theoretical counterpart specified
in
Chapter 3, the alterations of the theoretical specifications that were
mage during the estimation, and reasons why such changes were made.
Class I and Class II milk price equations estimated to
The
con-
struct predicted instruments are
=
(33)
+ Et,33 1
P11 =all+ Pt,II 0 73 + ~2,11°74 +~3,11°75 + ~4,11°76 +
(34)
~5,11
Psup + Et,34•
where
P1 and P 11
~re
and Class II milk,
the average prices per hundredweight of Class
respectively;
Psup is the Class II support price,
as announced in the Federal milk marketing orders;
and
o76 ,
sample.
strijcture
and
o73 , o74 , o75 ,
are binary indicator variables equal to one in each of
respective years 1973,
These
of
1974~
the
1975, and 1976, and zero elsewhere in the
indicator variables reflect possible changes
th~
I
in
the
dairy industry in these years due to factors such as
the Nixon Administration wage and price freeze,
the OPEC oil embargo,
and the concurrent and subsequent economic disarray.
Net
specified
governm~nt
in
removals
in the current y•ar are
the theoretical model.
hypothesized to be
Net
government
estimated
as
removals
are
45
(35)
= aNGR
NGRt
(INC/Pnfl
+ ~1,NGR(Psup 1 Pnf) + ~2;NGR(Pfo 1 Pnfl + ~3,NGR
+ P4,NGRT + P5,NGRNGRt-1 + Et,35'
where Psup is the Class II support price of milk;
Pfo is the Consumer
Price
INC is the
per
Index for fats and oils excluding butter;
capita
disposable income
nonfood items;
average
Pnf is the Consumer Price Index
T is a linear trend;
and
for
NGRt-l is the level of
net
government removals in the previous period.
Net
net
commercial removals,
comme~cial
except
that
played
as
exports,
the increases in commercial stocks and
are estimated as specified
in
Chapter
the predicted net government removals instrument is
a regressor,
rather than its
observed
counterpart.
3,
emThe
estimable form of this equation is
=
(36)
where
and
o66 _85
+
+
is a binary variable equal to one in the years
zero in the earlier years of the sample;
variable equal to one during the years 1973,
elsewhere
in the sample;
o73 _ 75
is an
1966-1985
indicator
1974, and 1975, and zero
NGRt is the predicted level of current
net
government purchases as derived in (35); and NCRt-l is a lagged dependent variable.
The binary variables in (36) reflect possible structural
in
the dairy market.
exports
in
changes
The first accounts for changes in storage
the later years of the sample period.
The second
and
again
represents possible changes in market structure caused by the wage and
46
price freeze of the Nixon Administration,
the OPEC oil
embargo,
and
consequent economic disarray.
The
Class
instruments
for the per capita consumption of Class
II milk are estimated as a joint system of equations.
pothesized
milk
in the previous chapter,
an index
index
of
~f
prices
equation,
of fats and oils excluding butter in the
the average age of the U.S.
per capita disposable income.
income
be
estimation,
Class
I
the
equation
statistically
II
II
Class
II
population to
and average
The demand equations are further speci-
homogeneous of degree zero by deflating
regressors
hy-
other beverage prices in the Class I equation, the
a linear trend,
to
As
the Class
reflect changes in consumption preferences as people age,
fied
and
per capita Class I and Class
demands are functions of the Class I milk price,
price,
I
by the index of non-food prices.
all
In
price
the
initial
estimated coefficients for the age variable
and the trend in the Class II
equation
and
in
the
were
not
different from zero and were omitted from those respec-
tive equations.
The system of demand equations was estimated in four fashions
to
test the significance of two restrictions required to satisfy a set of
sufficient
one
linear
effects
in
conditions for the integrability of a system of more
demand function.
These conditions are (1)
the demand functions;
and (2) symmetry
effects across the equations [LaFrance].
of
than
zero
income
cross
price
47
The four versions of the demand system specified are:
(1)
non-zero income effects
and
unrestricted
~
(37a)
ql,t = ai +
cross price effects;
~
~l,I(PI/Pnf) + ~2,I(PII 1 Pnf) + ~3,l(Pbev 1 Pnf) +
P4,1T + P5,1<INC/Pnf) + Alql,t-1 + Et,37a'
~
(37b)
qll,t =all+ Pt,II(PI/Pnf> + P2,11(PII 1Pnf> + P3,11 (Pfo 1Pnf)
+ ~4,IIAGE + P5,11(INC/Pnf> + AJiqii,t-1 + Et,37b 1
(2) zero income effects and unrestricted cross
~
price effects;
~
~l,I(PI/Pnf> +
P2,r<Px1 1Pnf> +
~3,I(Pbav1Pnf> +
(3aar
ql,t = al +
(38b)
qll,t =ali+ Pt,II(PI/Pnf) + P2,II(P11/Pnf) + P3,11 (Pfo 1Pnf)
~
~
+ ~4,IIAGE + Allqll,t-1 + Et,38b 1
(3) zero income effects and cross price effects restricted to be equal
in the short run;
~
(39a) ql,t = al + ~1,1(P1/Pnf) + P2,I(P11 1Pnf> + ~3,I(Pbev 1 Pnf) +
P4,1T + Alql,t-1 + Et,39a'
~
(39b)
qll,t
~
=all + P2,1(P1/Pnf> + P2,11(PII/Pnf) +
P3,II(Pfo/Pnf>
(4) zero income effects and cross price effects restricted to be equal
in the long run;
48
(40a) q1,t
= ai
~
~
+ P1,1<Pr 1Pnfl + ( 1 · 0 -~rl~2,I(Pir 1 Pnf> + ~3,1
(Pbev/Pnf> + ~4,IT + ~Iql,t-1 + Et,40a'
=
(40b)
The
+
various restrictions were tested using the estimated results
of the four models with a likelihood-ratio test.
for
each
The null hypothesis
test is that the restricted model performs as well
unrestricted specification.
as
the
The formal statistical hypothesis is
Ho: Rrestricted
= Runrestricted
Ha: Rrestricted < Runrestricted
R is the value of the respective models' likelihood
where
functions.
The tests and comparisons are summarized in Table 1.
Neither
the
zero
income effects and long run symmetry
cross price effects restrictions significantly affect the
of
the system of milk demand
equ~tions
at the 1 percent
of
the
performance
level.
The
predicted values from the fourth model are used as the instruments for
the
per
capita Class I and Class II milk demands in the rest of
the
study.
A nominal predicted blend price received by farmers for all
is ·calculated as specified in (28),
Clas~
using the predicted values of the
I and Class II prices and demands,
net commercial removals
milk
net government removals, and
Tabie 1. Comparison of Class I and Class II Demand Restrictions
Calculated
X2 Test
Statistic
Conclusion
a = .01
Model
Log-Likelihood
1. Unrestricted
-186.62
2. Zero Income Effects
~5,1 = ~5,II = 0 · 0
-189.96
6.68
fail to reject
3. Zero Income effects
~5,1 = ~5,II = 0 · 0
-191.33
9.42
fail to reject
A
\0
Short Run Cross Price Symmetry
1 = ~l,II (short run)
~2 ,
4. Zero Income Effects
~5,1 = ~5,II = 0 · 0
Long Run Cross Price Symmetry
1 = ~l,II (long Run)
~2 ,
-192.2393
11.24
fail to reject
50
(41)
Pm
= (P 1a 1
where
a1
and
a 11
- -
-
-
- -
are the per capita Class I and Class II milk
multiplied by the U.S. population. The observed
milk
demands
average price for all
is then estimated as a function of this calculated prediction to
derive a two-stage least squares
milk
-
+ P 11 <a 11 + NCR+ NGR))/(a 1 + a 11 + NCR+ NGR),
received by farmers.
instrument for the average price
of
The estimable form of the average price of
milk is
The
predicted
instrument
for
the
by farmers for all milk in the remainder of
the
re-
the estimable reduced form of the output per
cow
equation specified milk per cow as a function of quadratic prices
for
price
received
values from (42) are used as the
search.
In
Chapter 3,
grain and concentrated feeds,
hay and roughage, and labor.
The tunc-
tion also specified linear and quadratic terms reflecting the level of
Dairy Herd Improvement Association testing three years past.
On
dairy
dairy farms,
the most common feeding practice for
cows is to monitor and control the animal's intake of grain and
concentrated feed and then allow the cow to eat hay or other
until
producing
it is full.
roughage
Therefore the amount of hay and roughage consumed
is some complementary function of the amount of grain and concentrated
feed
per cow.
The intake capacity of a dairy cow is assumed to be
function of the levels of DHIA testing three years ago.
grain
hage
The amount' of
and concentrated feed per cow plus the amount of hay and
fed will then equal the intake capacity,
assuming
a
the
rougfeeding
51
practices
above are implemented.
Specifically this relationship
is
assumed to be
After subtracting the amount of grain fed from both sides of (43), hay
and
roughage is shown to be a function of the amount of grain fed and
the past level of DHIA testing
This,
along
with the assumed complementarity of labor with the
inputs in (11),
feed
suggests that the reduced form output of milk per cow
should be driven by the levels of DHIA testing three years ago and the
price
per hundredweight of grain and concentrated feed,
deflated
by
the average blend price of milk.
The
estimation of the reduced form supply equation
assertion
and found it to be valid.
tested
A complete output per.cow equa-
tion was estimated with linear and quadratic terms in DHIA
tion
three
labor
and
complete
model
various
years past,
along with quadratic prices of
their cross products as regressors.
model
cross
omitting the prices of hay and
product interaction terms.
complete model, (18) is
participagrain,
The results
were then compared with the estimates
specification
this
of
labor,
a
of
hay,
the
smaller
and
the
The estimated form of
the
52
(45)
=
Yt
4.5294 + 2.2468P~- .32658PgePh- 12.665PgePR +
(16.333) (3.2392)
(.73481)
(1.5296)
.39445e10- 10 P~ + .86786PhoPR- 1.5984P~ + 41.366DHIAt_ 3 (.2215e10- 9 )
(.69793)
(.63704) (17.965)
2
43.920(DHIAt_
3
(6.52'11)
log-likelihood= 23.344479,
where the numbers in parentheses are asymptotic t-ratios.
The
effect of restricting the coefficients of the squared prices
of hay and labor
and the grain-hay, grain-labor, and hay-labor inter-
action terms to zero in the smaller equation reduced the value of
log-likelihood of the equation from 23.344479
~o
19.70005.
the
Performing
a likelihood ratio test on these values results in a test statistic of
The
7.287958.
esis
that the restricted model performs as well as
model
the
conclusion is that at the 1 percent level the
cannot be rejected.
interaction
the
hypoth~
unrestricted
Inclusion of the hay and labor prices and
terms does not significantly contribute to
the
ex-
planatory power of the model.
Economic
theory and the profit maximization
hypothesis
dictate
that
input demand and reduced form output supply functions be derived
from
a
input
production function and imposes certain
demand
and
supply.equations.
constraints
As discussed in
the
on
the
previous
chapter, the estimable forms of the input demand for grain and concantrated feed,
and the supply of milk in this study are derived from
quadratic milk production function.
must
In the estimation, both equations
be functions of the same explanatory
degree zero in all
prices,
a
variables,
homogeneous of
and negatively sloped with respect to the
53
real input,
ficient
grain and concentrated feed,
on the
stricted
grain price variable in
Also,
prices.
~he
Specifically,
the
coef~
grain input demand is re-
to be twice the corresponding parameter in the
equation.
the
milk
supply
reduced form equations that were esti-
mated are
(46)
(47)
gt
~
= ~g
+ ~t,y<Pg/Pm) + ~ 2 ,gDHIAt-J + Et, 47 .
After estimating this system,
significantly
sign,
different
examination
statistic
although the coefficients were all
from zero and of the
theoretically
of the calculated residuals and the
correct
Durbin-W~tson
suggested the existence of serial c9rrelation.
The
auto-
regressive errors were particularly evident in the grain input demand.
The
Durbin-Watson statistics for the supply of milk and grain
equations are 1.5591 and .3603,
related
errors
can
respectively.
be corrected by specifying
equation with an autoregressive error process.
In many
and
~ases
demand
autocor-
estimating· the
However, serial cor-
relation as severe as that in the grain per cow equation is suggestive
of
misspecification
of the model and further
investigation
of
the
appropriateness of the explanatory variables is necessary.
Further
estimation of the milk and grain per cow system of equa-
tions employs the price per bushel of #2 yellow corn at Omaha, Nebraska and the price per short ton of 44/. protein soybean meal at Decatur,
Illinois
as proxy variables for the price of grain
and
concentrated
54
The
feecjs.
·meal
to
soybean
are the primary components of the concentrated feed rations
fed
The price of corn is specified as a reg-
producing dairy cattle.
ressor
soy
rationale for these choices being that corn and
throughout the sample period
and both the price of
meal are included as indicator variables equal to the
corn
and
respective
prices for the years 1979-1985 and zero elsewhere in the sample.
are
They
specified in the system to reflect changes in the nature of dairy
farmers'
responses to price changes during the late .1970's and
early
1980's when price movements of agricultural commodities were extremely
wide and volatile,
after remaining relatively stable during the
liar years of the sample period.
(48)
(49)
This system is specified as
=
Yt
+
=
gt
ear-
+
+
...
P2,g((Psm 0 79-85)/Pm)
...
+ ~3,g<<PcornD79-85)/Pm) + P4,gDHIAt-3 + Et,49'
The
system using these price variables and the lagged values· of
DHIA testing is estimated in two forms.
system
The
The first is an unrestricted
with no constraints being imposed on the parameter
second
variables
model
restricts the coefficients of
the
estimates.
various
in the grain demand equation to be twice those on the
price
cor-
responding variables in the milk per cow equation. The significance of
these
values
restrictions is then examined in a likelihood ratio test.
of the log-likelihood function for the restricted
tricted systems are 28.011 and 57.080,
ratio
test
respectively.
statistic is calculated to be 58.138 and
and
The
unres-
The 1 ikel ihood
the
hypothesis
55
that
is
the restricted model performs as well as the unrestricted
rejected by the data at the 1 percent level.
model
Therefore the
unre-
stricted system is used in the remainder of the study.
Some
serial
correlation still existed in the system
prices of corn and soybean meal.
grain
demand equation,
To
1.3171.
using
the
Again, this is more prevalent in the
as evidenced by a Durbin-Watson statistic
achieve efficient estimates of the system
of
coefficients,
this serial correlation must be accounted for in the estimation of the
grain equation.
To
account for the serially correlated errors,
transformed
by
a
consistent estimate of the
relation coefficient,
mated p is .48290.
then
transformed
p,
the data must be
first
order
autocor-
from the estimated grain demand.
The esti-
The data observations for the years 1955-1985 are
with the serial correlation
coefficient
by
sub-
tracting from each observation, the previous observation multiplied by
0.48290.
The
(.48290) 2 )
first
observation,
for its transformation.
1954,
was multiplied by
J<1.0
Applying the usual least
squares
techniques to the data transformed in this manner produces generalized
least
squares estimates of the coefficients which are best linear un-
biased [Judge, Hill, Griffiths, Lutkepohl, and Lee, p.440-41J.
Reestimation
transformed
appears
data
of
the
milk and grain per cow
system
using
the
revealed that accounting for the serial correlation
to be sufficient.
The new Durbin-Watson statistics for
the
transformed milk and grain equations are 1.8802 and 2.091, respectively.
56
As stated previously,
economic theory dictates that the marginal
effect of an input price be negative in output supply and input demand
functions.
tions
were
the
signs of the coefficients on the price of
expected
However,
bles
In the reestimation of the milk and grain system of aqua-
to be negative and consistent
with
corn
variables
economic
the estimated parameters on the price of soybean meal varia-
were expected to be positive in (48) and (49) This is
because
meal.
theory.
the
variable
measures the price of high (44%)
explained·
protein
soy
As the price of soybean meal increases, farmers must substitute
other, less nutritious grains and feeds for the relatively more expensive
high protein meal.
rations,
the
a
meal,
increase.
To maintain the same nutrient value of
the
greater amount of the other feed must be substituted
for
causing the quantity,
or weight,
of the feed
ration
to
This will lead to a positive sign on the soybean meal coef-
ficients.
Predicted
values to be used as a two-stage least squares instru-
ment for the price per hundredweight
are
determined
of grain and concentrated
feeds
by regressing the observed grain and feed price as
a
function of the feed ration components specified in the milk and grain
system.
The estimable form
~
(50)
of this equation is
~
Pg/Pm
= apg
~
+ ~l,Pg<Psm/Pm) + ~2,Pg<Pcorn 1 Pm) + €t,50'
where Pg is the observed price per hundredweight of grain and
trated feeds,
Pcorn
is
concen-
Psm is the price per short ton of 44% soybean meal, and
the price per bushel of #2 yellow corn.
All three of
the
57
price
variables
are
deflated by the predicted
instrument
for
the
average price of milk received by farmers.
After the predicted price par hundredweight of grain and
trated
feeds
was
determined,
a predicted nominal profit
defined as returns over'faed cost,
par
cow,
was calculated using the construe-
ted instruments for the average blend price of milk,
grain
concan-
and concentrated feed per cow,
output per
cow,
and the price of the grain
and
feed rations. Predicted nominal profit per cow is specified as
~t
(51)
The
-Pg•9t·
-
= -Pm•Yt-
calculation of nominal profit per cow is a condensed form of
(28) as specified in Chapter 3.
The hay and labor components of (28)
are eliminated due to the exclusion of the hay and labor prices in the
estimation of the output per cow
and
milk
concentrated
equation (45).
The price of
feeds is the primary factor driving the
grain
output
of
is thus a reasonable proxy for feed costs in the calculation
of
nominal profit per cow in (51).
To
construct a two-stage least squares instrument for profits as
defined in (51),
the observed returns over feed cost are regressed as
a function of the calculated prediction.
Specifically, the relation-
ship is estimated as
where
~t
is defined as (PmYt- Pggt) in observed units and
~t
is
the
58
predicted counterpart from (51).
ification
the
The predicted values from this
~pac­
of nominal profit per cow is used in the investigations
adoption
of DHIA quality testing and
in
profitability
the
relationship
of
between
the dairy industry and fluctuations in the
market
price of dairy cattle.
A summary of the constructed instruments is listed in
The
estimation
equations
procedure
for the Class I and Class
was ordinary least squares.
the Class I per capita consumption,
centrated teeds,
squares.
The
milk
2.
price
The procedure for the net gov-
ernment removals is nonlinear least squares.
for
II
Table
The estimation procedure
the price of grain and
con-
and nominal profit per cow is linear two-stage least
remainder of the equations were estimated using
non-
linear two-stage least squares.
In the table, the numbers in parentheses are the respective coefficients' asymptotic t-ratio statistics in absolute value;
R2 is
the
coefficient of multiple determination; ~ 2 is the coefficient of multiple
determination adjusted for the degrees of freedom;
Durbin-Watson
D.W.
statistic for first order serial correlation;
the number of degrees of freedom;
is
d.f.
the
is
and s.e.e. is the standard error of
the estimate.
Serial correlation among the residuals appeared to be present
many of the estimated equations.
corrected,
sistent,
If the autoregressive errors are not
the estimated coefficients,
are
in
while being unbiased and con-
neither efficient nor asymptotically efficient [Kmenta,
59
Table 2. Estimated Instrument Equations for the Dynamic Dairy Model
Class I Milk Price
=
1.8328
(14.321)
+
.64215073
( 4.1246)
.771970 76 + 1.0410Psup
(4.9557)
(56.958)
+
1.2469074
(6.8320)
+
• 52015075
(2.8463)
+
€t = .65976€t-1 + Ut
(5.2677)
R2=.99861, ~2=.99822, D.W.=1.690, d.f.=29, s.e.e.=.156264
Class II Milk Price
P 11
=
.21018 + .826220 73 + ,795810 74 + 1.30100 75 + .573900 76
(2.5336) (4.6664)
(4.2417)
(6.9187)
(3.2320)
.96576Psl,lp
(81.806)
+
Et = .32864€t-1 + Ut
(2.0878)
R2=.99798, ~ 2 =.99757, D.W.=1.765, d.f.=29, s.e.e.=.174567
Net Government Removals
=
25.385 + 3.2082(Psup/Pnt>- 9.9519(Pf 0 /Pnf) + .71863T
(4.7194)(6.2101)
(3.1404)
(4.6027)
+ .015358(INC/Pnt> + .60904E(NGRt-t>
(5.3739)
(2.0878)
R2 =.81040, ~ 2 =.77771, D.W.=2.595, d.f.=29, s.e.e.=1.88695
Net Commercial Removals
=
~
5.0468 - 3.3249066-85
(6.3785) (5.3501)
- 1. 8242073-75
(2.6434)
- . 16208NGRt
(2.0536)
- .42445ECNCRt_ 1 )
(2.5331)
R 2 ~.74090, ~ 2 =.69622, D.W.=1.992, d.f.=29, s.e.e.=.855049
.60
Table 2 (continued)
Class I Per Capita Consumption
=
-
153.81 - 13.335(P 1 /Pnf) + 33.264(1.0-.70264)(PII/Pnf)
(3.7873)(4.9212)
(1.6472)
+
2.2188(Pbev1Pnt>- 1.9861T + .70264qi t-l
(.99477)
(4.3310) (6.4216) '
R2=.996969, D.W.=1.903248, d.f.=28
Class II Per Capita Consumption
qii,t = -316.38 + 33.264(1.0-.80828)(PI/Pnf)- 18.599(PII/Pnf)
(3.8333)(1.6472)
(3.1271)
57.639(Pf 0 /Pnf) + 10.963AGE + .80828E(qii t- 1 >
(4.6467)
(4.1828) (14.639)
J
R2=.938462, D.W.=2.503937, d.f.=28
Average Farm Price for All Milk
Pm = -.017516 + .99391Pm
( .2562)(115.94)
R2=.99755, ~2=.99748, D.W.=1.737, d.f.=33, s.e.e.=.179711
Output of Milk per Cow
Yt
=
4.4634
(31.729)
+
+ 42.672DHIAt_ 3 - 44.221(DHIAt_ 3 ) 2
(25.700)
(7.5863)
R2 =.9982, ~ 2 =.9979, D.W.=1.8802, d.f.=27, s.e.e.=.093524
+
61
Table 2 (continued)
Grain and Concentrated Feeds per Cow
9t
-
= 1.3627-
-
1.3680(Pcorn/Pm) + .15622((P 5 mo 79 _85 )/Pm) (5.5403) (2.0544)
(5.9461)
-
12.437((Pcorno 79 _ 85 )/Pm) + 17.782DHIAt_ 3
(6.1897)
(22.209)
R2 =.9665, R2 =.9623, D.W.=2.091, d.f.=28 s.e.e.=.11490
Price of Grain and Concentrated Feeds
-
P 9 /Pm
-
=
.35115 + .97915(Pcorn/Pm) + .0047675(Psm/Pm)
(9.0580)(10.036)
(5.5667)
Et = .51658£t-1 + .38411£t-2 + Ut
(3.1650)
(2.3534)
R2 =.92696, R2:.91610, D.W.=1.834, d.f.=27, s.e.e.=.020331
Nominal Profit per Cow
-
n = -.17258 + .87847n
(.1431)(57.737)
Et = .45720et_ 1 + ut
(2.9081)
R2 =.99706, ~2=.99686, D.W.=1.963, d.f.=29, s.e.e.=2.23553
62
This invalidates any hypothesis tests performed with parame-
p. 278].
ter
coefficients derived from ordinary least squares techniques
when
autoregressive disturbances are present.
To
correct serially correlated errors,
milk price equations,
the Class I and Class II
and the nominal profit per cow estimation
The price
specified with a first order autoregressive error process.
per
were
hundredweight of grain and concentrated feeds required the speci-
fication of a second order autoregressive error process to remedy
the
autocorrelated disturbances.
When
serially
correlated
errors appear to exist
in
the
data
employed to estimate a difference equation with ordinary least squares
techniques,
observed values of the dependent variable entered on
the
right
side of the equation result in inconsistent estimates
of
the.
hand
equation parameters.
lagged
This is due to the correlation between
dependent variable and the error term.
nonstochastic difference equation,
of
the
Using
correct
this,
a
with the unconditional expectation
lagged dependent variable specified as a
played.
pends
To
the
regressor, . is
the expectation of the dependent variable,
only on the systematic portion of the regression,
em-
which de-
rather
than
the observed values, eliminates the correlation with the error process
providing consistent parameter estimates [Burt, 1980].
The net government removals, net commercial removals, and the per
capita
Class
correlation
difference
II
of
consumption equations appeared
the 'disturbances and are estimated
equations using nonlinear least squares
to
exhibit
as
serial
nonstochastic
techniques.
The
63
Class I per capita consumption regression appeared to exhibit
cal
"white
specified
classi-
rioise" residuals and a stochastic difference equation
with observed values of the lagged dependent
variable
is
en-
tered as a regressor on the right hand side.
Adoption of DHIA Testing
The
theoretical model for this research asserted that the
of Dairy Herd Improvement Association
of
dairy
testing to improve the
herds is a function of the expected level of
level
quality
profitability
within the dairy industry and time. To investigate this assertion, the
current
levels of DHIA testing are estimated as a function
of
those
factors.
The
DHIA
adoption equation is estimated as a transformation
the logistic function, ·as specified in Chapter 3.
of
The original logis-
tic function for the adoption of DHIA testing is
(53)
~
DHIAt = Eexp(a +
~l,DHIA(nt/PPft)
P3,DHIAT + P4,DHIAT
2
~
+ P2 ,DHIA(nt/PPFt)
2
+
~
+ P5,DHIA<nt/PPFt)•T + Et,53)] I E1.0+
The estimable form of the DHIA equation is
~
(54)
lnEDHIAt/(1.0- DHIAt)l =a+ Pt,DHIA(nt/PPFt) +
~
P2,DHIA(nt/PPFt)
2
+ P3,DHIAT + P4,DHIAT
2
+ ~5,DHIA(nt/PPFt)•T
where lnEDHIAt/(1.0- DHIAt)] is the natural (base e) logarithm of the
64
ratio of the proportion of dairy cattle on DHIA test to the proportion
of
animals
not on test;
-
(nt/PPFt) is the predicted
instrument
for
profit per cow constructed in (52), defined as returns over feed cost,
and
deflated by
the index of all prices paid by farmers;
and Tis a
linear trend.
The ceiling or equilibrium level of use is specified to
be
error terms in (53) are assumed to be additive
1.0.
The
in
the
exponential to allow the linear transformation.
This
transformation,
while linearizing the
response
does not exhibit a constant variance of the error terms,
a heteroskedastic model [Dixon].
function,
resulting in
Under heteroskedasticity, the least
squares assumption of constant variance of the error terms is violated
and
the
parameter estimates derived from ordinary least squares
not efficient and not best linear unbiased estimates.
dastic errors,
test
like serially correlated errors,
are
With heteroske-
hypothesis tests and
statistics are biased and correction of the error
term~
is · re-
qui red.
To
correct
variance,
each
the
heteroskedastic
errors and derive
a
constant
Weighting
a weighted least squares procedure is required.
observation
of
the dependent and
the
independent
variables,
including the constant term, by the square root of the variance of the
dependent
variable results in best linear unbiased estimates
of
the
parameters. For DHIAt > 0.0, the approximate variance of the logarithm
df
the
ratio of proportions in the logistic transformation has
shown to be
(55)
been
65
with the appropriate weights specified as
(56)
where nt is the total inventory of producing cows on farms in time
and
t.
'
DHIAt is the proportion of all producing cows on DHIA test in the
current period [Neter, Wasserman, and Kutner, pp.362-63; Berkson].
The weighted least squares adoption path exhibited serially
related
errors
when
estimated with a "white noise"
error
Reestimation of (54) with a second order autoregressive error
appeared to correct the correlated disturbances.
cor-
process.
process
The results of this
estimation are
(57)
- DHIA.t) J
=
-2.4268
( 7 . 188 5)
.10090(TTt/PPFt)
(1 • 0012)
+ .005393CitiPPFt) 2 + .1061T -
.0008959T 2 ~
(4.6962) (2.3989)
(.71787)
-
.0010633(TTt/PPFt>•T
(.32221)
€t
= 1.3207et-l(11.313)
.75093et_ 2 + ut
(6.4324)
R2 =.99761, R2=.99691, D.W.=2.156, d.f.=24, s.e.e.=.0342861.
The
search is
hypothesis of interest for this portion of
the
re-
66
null
The
hypothesis asserts that the estimated coefficients
real
profit per cow regressors are not significantly
zero
and
expected
different
profits have no impact on farmers'
begin to test the quality of their dairy herds
~sing
on. the
from
decisions
DHIA
to
procedures.
The alternative hypothesis states that the parameters are statistically
significant
and
DHIA participation is affected by the
level
of
expected profitability within the U.S. dairy industry.
Equation (57) was reestimated with the coefficients of the return
over
feed cost variables restricted to equal zero in order to
calcu-
late
an F-statistic based on the difference between the error sum
of
squares without the profitability regressors and that with return over
feed cost variables included. This difference is divided by the number
of restrictions to calculate a mean square error for the restrictions.
This is then divided by the mean square error for the complete specification
including the profitability variable to form the F-statistic.
The calculated test statistic is then compared with the table value of
the
F-distribution at the appropriate level of
cance
and degrees of freedom.
statistical
signifi-
The results from the reestimation
of
(57) are
ln[DHIAt/(1.0- DHIAt)J = -2.8208 + .089706T- .00082173T2
(103.65) (21.453)
(6.3242)
(58)
Et = 1.3128et-l - .68696et_ 2 + ut
(10.219)
(5.3475)
R2 =.99741, ~ 2 =.99703, D.W.=2.2221, d.f.=27, s.e.e.=.03373481.
The null hypothesis that the reduced specification with the coefficient
of
the return over feed cost regressor restricted
to
equal
67
zero
is
identical to the complete model is tested at the
level of confidence.
cance
of
5
percent
The calculated F-statistic to test the signifi-
the estimated parameter of the predicted profitability
re-
gressor is
F(3,24)
and
= .71288
at the 5 percent level the null hypothesis that the
variable
cannot
return
over
cost coefficients are not significantly different from
zero
be
rejected.
variable cost are,
the sample,
the
Although the marginal effects of
over
as expected, positive for the last twenty years of
the nonsignificance of the profit coefficients contradict
assertion from the theoretical model that the rate of adoption of
DHIA testing activities
is directly related to the level of
bility available in the U.S.
(58)
return
with
dairy industry.
profita-
The marginal effects of
respect to the profit variable and time are
presented
in
Table 3.
The
results here suggest that the level of participation in
Dairy
herd
time,
independent
mers
receive
improve
Improvement Association is determined
exogeneously
the
over
of the dairy program and the supported prices far-
for milk.
Dairy producers appear to be
attempting
the productive capacity of their herds without regard to
available level of profitability as defined here.
In this case,
primary factor affecting the rate of adoption of DHIA testing
to
the
the
activi-
ties is time, reflecting the period for a farmer to gather and analyze
68
Table 3. Marginal effects of Profit and Time iri the Adoption of DHIA
Year
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
a[ln(DHIAt/1.0 - DHIAtJ_l
a ( nt >
-.03143
-.02421
-.01854
-.01525
-.01661
-.01487
-.00726
.00394
-.00669
-.00654
-.00321
-.00199
.01043
.02001
.02866
.02503
.03560
.03688
.03062
.03377
.03137
.03379
.03481
.04302
.04180
.04573
.06065
.04834
.04992
.03789
.02901
.02549
aEln(DHIAt/1.0 - DHIAtll
a(T)
. 10510
.1 0409
.10301
.1 0189
. 10073
.09957
.09820
.09681
.09544
.09415
.09298
.09160
.09056
.08931
.08807
.08693
.08587
.08434
.08306
.08143
.08006
.07878
.07757
.07576
.07403
. 07245
.07050
.06828
.06618
.06459
.06310
.06266
69
information about the DHIA testing procedures and to begin to participate in the programs.
cost
omitted
Estimation of (58),
with return over variable
still explains 99.5% of the variation in the
dependent
This situation would result in a monotonically
variable.
adoption path in the early stages of development,
increasing
as over time,
more
producers become familiar with and adopt DHIA testing techniques.
As
evident in Figure 4,
cattle
on
period
until 1982 when the structural effects of the Federal
ment
DHIA
the observed proportion of total
test has increased steadily
throughout
the
sample
govern-
dairy herd buyout begin to impact the dairy industry.
years
dairy
Over the
of the sample the level of DHIA participation increased
five-fold.
cost,
In
contrast,
as seen in Figure 5,
nearly
the increase in the real return over
feed
has been much smaller and subject to much
greater fluctuation throughout the sample period.
However,
making decisions such as whether to begin
to test
and
improve
the quality of a dairy herd without regard to available reve-
nue
profits
or
profit
appears to be inconsistent with
maximization
factors may
responding
the
assumption
made in the theoretical model and
a
number
of
of
account for the unexpected result. Dairy producers may be
to a level of profitability, ·but not that as defined
and
calculated here.
The
were
constructed instruments and the final DHIA adoption equation
estimated
quantities.
using aggregated data for the respective
Consequently,
return over variable cost measure
profitability
employed
figure.
rate of adoption of DHIA testing is however,
The
in
the
prices
the investigation is
also
an
and
of
aggregate
based
on
Figure 4. Observed DHIA Participation
0. 320001
o. 300021
0. 280041
o. 260051
I
<(
0. 240071
0. 22009 -l
~
I
0.20011
z
0
- o.
10::
0
n.
0
~
n.
18012
-.1
0
0. 16014
o.
140161
o.
12018l
I
0. 10019 ~
I
o. 08021 -1
0. 06023
~-r-
1950
r
,
,
,
,
,
0
0
I
1960
,
,
, -,
1
,
---r--r--o1
1970
YEAR
I
I
1-r-r--r--,--y-
1
l .--,---,-·.,---r-r
1980
71
0
m
m
.-t
f
~I
Ii\
~
I
~
I
r
I
r-
0
£"...
m
.-t
I
t
r
I
t
+>
lfJ
~
0
u
(J}
.0
ld
(...
I
ld
rl
>
~
(...
(J}
~r
>
0
r::
(...
:;s
+>
(J}
"0
(J}
L
(J}
r
i
lfJ
t
.0
0
~
ll'l
(J}
(...
. u..
.-t
I
>
(...
Ol
m
r
0::
:;s
0
(0
............--
-r
(f)
.-t
N
....
....
......
.LSOO
0
......
0
lO
,---·-··,----·-.,-·--r-·-T·---·-·-.1- m
m
318'v'l~'v'A
m
~3AO
£"...
(0
N~n.L3~
lO
.-t
0::
<
UJ
>-
72
individual
dairy producer deci~ions.
This inconsistency may,
to an
extent, explain the insignificant relationship.
Further,
adoption
the
research completed here assumed the rate
of
DHIA
to be a function of a general level of profitability for all
producers of dairy products.
Mansfield showed that.the rate of adop-
tion.of a technological improvement is impacted by the expected
itability
from the adoption of the improvement [Mansfield].
profitability
particularly
profIf
the
figures were gathered from individual dairy operations,
from
those operations already using
the
DHIA
testing
procedures, a significant, direct relationship may arise.
Finally,
profitability
defined
as
return over feed
cost
may
simply not be the appropriate revenue measure to which dairy producers
respond
in deciding to test and improve the qual.ity of
Factors
other than feed costs such as fixed costs or costs of capital
may
enter the decision making process.
sponding
only
received
by
farmers for all milk may be the
research
results
derived
the
average
appropriate
of this question is necessary to
in
herds.
Possibly farmers may be
to the level of gross revenue and
Further
their
reprice
regressor.
substantiate
this study or determine the correct
the
measure
of
profitability to which dairy producers respond.
Relationship between Profitability and Milk Cow Prices
The
final
thrust of this thesis investigates
the
relationship
between
profitability and fluctuations in the market prices of
cattle.
As discussed in the theoretical chapter, as the level of pro-
fitability increases,
the market prices of replacement milk cows
dairy
are
73
expected
try
to be bid up by farmers attempting to enter the dairy
or
to
expand existing herds.
The bidding up of
the
indus~
cost
of
replacement cattle shifts up the average total cost schedules of dairy
production, dissipating the additional returns.
Economic
theory
dictates that firms in a
competitive
industry
must earn zero economic profits in the long run. This follows from the
existence
of
a
long run equilibrium condition where
marginal
cost
equals minimum average total cost equals price.
The dairy industry, though regulated and supported by the Federal
government
cause
mandates,
can be examined in a competitive framework
a basically homogeneous product is supplied and there
barriers
condition
where
linearly
run
to
exist,
investigate
this assertion,
a long run price of
to
cost
zero.
milk
cows
The long run equation follows that specified by
Burt for the capitalization of rents into long run land prices
(59)
a
implying
economic profits are dissipated and driven
equation is derived.
1984].
of
the long-run price of replacement dairy cattle is
homogeneous function of the long-run return over fixed
long
To
few
Therefore a long-run competitive equilibrium
the price of utility cull cows was expected
that
are
to entry other than the relatively fixed short run stock
producing dairy cattle.
and
be-
[Burt,
The estimable form of the long run price of cows equation is
Pmc,t =a +~tnt+ P2nt-1 + rlpcull cows,t + AlPmc,t-1 +
A2Pmc,t-2 + Et,59•
where
Pmc,t'
Pmc,t-l'
and Pmc,t- 2 ,
are current and lagged
nominal
74
prices of milk cows; nt, and nt_ 1 are the current and lagged levels of
predicted
per
cow
return over feed
profitability proxy;
~ost
constructed in
as
a
and Pcull cows is the current, nominal price per
hundredweight of utility cull cows at Omaha.
is
(52)
The price for cull cows
specified in (59) as a salvage value for culled heifers and
older
cattle to reflect the impact on milk cow prices of fluctuations in the
beef market.
In the long run,
bles
across
time
there is assumed to be no change in the
periods and equilibrium values
Pcull cows' can be defined.
=n
~*
ting
,
the
Specifically, Pmc,t
and Pcull cows,t
= Pcull
cows,t-1
of
Pmc,
varian,
*
= Pmc,t- 1 = Pmc'
= P~ull
equilibrium values into (59) and rewriting
and
~
nt
=
Substitu-
cows·
determines
the
long run price of milk cows equation
where
(60a)
a* = C£1 (1
•0 -
(60b)
~*
= (/31
+ /32)/(l.O- ).1 - ).2),
(60c)
r*
= a"/(1.0->..1
For
italized
).1 -
-
>..2)'
).2).
the assertion that profits from the dairy industry are
into the prices of replacement dairy cattle and
the long run price of milk cows equation (60)
cap-
dissipated,
must be homogeneous
of
degree one in~* and P~ull cows·
In this case, from the properties of
linearly homogeneous functions,
increasing the level of profitability
and
the price of cull cows by the same positive factor will
increase
75
the market price of milk cows by that same factor and the
competitive
equilibrium condition will continue to hold [Chiang, p.410-14].
The hypothesis tested here is
H0 :
a*
=o
Ha: a* t 0.
The
null
hypothesis states that the estimated intercept in the
long
run
price of milk cows equation are not significantly different
from
zero.
The
alternate
hypothesis asserts that the constant
term
is
statistically significant.
The estimated form of (59) is
(61)
Pmc t
'
= -45.483-
57.4610 81 _85 - 38.1600 73 + 250.660 79 (1.4953) .(1.4532)
(.72552)
(3.8689)
1.9954nt
(.80954)
-
+ 3.2333nt-l + 5.9233Pcull cows+ 1.0838E(Pmc t- 1 )
(.93549)
(2.1034)
(8.6606)
'
- .41007E(Pmc t- 2 )
(2.0494)
'
R2=.99526, ~ 2 =.99345, O.W.=1.805, d.f.=21, s.e.e.=27.6138,
where
o81 _85 , o73 ,
structural
and
changes
o79 ,
are binary indicator variables to reflect
in the dairy industry due to the effects
Federal government dairy herd buyout in 1981-1985,
unexpected
1979,
movements
respectively;
of
of
the
and the sharp
and
agricultural commodity prices in
1973
and
and E<Pmc,t- 1 ), and E<Pmc,t- 2 ) are unconditional
76
expectations of the first and second order lag on the
ble, respectively.
ified
dep~ndent
varia-
Again a nonstochastic difference equation is spec-
because (61) appeared to exhibit serial correlation
among
the
disturbances when observed values for Pmc,t-l and Pmc,t- 2 were used.
To
test
the significance df the long run
reestimated with the intercept omitted.
intercept,
Further,
(61)
was
the 1981-1985,
and
1973 indicator variables and the current return over variable cost did
not
appear
consequently
cept,
to be statistically different from zero in (61)
omitted from the reestimations.
two binary variables,
and
are
Omission of the inter-
and current profitability
coefficients
resulted in
= 312.120 79
(62)
(11.139)
+ 1.9481nt-l + 2.2085Pcull cows+ 1.2216
(5.9125)
(6.9749)
(30.789)
E<Pmc t- 1 )- .57678E(Pmc t- 2 )
'
(11.694)
'
R2 =.99402, R2 =.99306, D.W.=1.812, d.f.=25, s.e.e.=28.48618.
The hypothesis that the specification with the four
restricted
tested
coefficients
to equal zero performs as well as the full model (60)
at the 5 percent level of significance.
The calculated
was
test
statistic here is
F(4,21)
The
conclusion
= 1.401301.
is that the null hypothesis is not rejected at the
percent level of significance.
The calculated long run price of milk cows equation is,
5
77
Pmc
* = 5.5129t * + .47830Pcull
* cows
(63)
Elasticityn = .6298a
where
ElasticitYpc~ll
cows= .3198,
the coefficient on the price of cull cows is divided by 13.0 to
transform
the
consistent
per hundredweight cull cows price into per
with the other variables in the equation.
The
cow
U.S.
units
De-
partment of Agriculture assumes that the live weight of culled utility
dairy cows is 1300 lbs. each [USDA, NEWSJ.
The
market
tion
in the long
run,
the
price or value of dairy cattle is a linearly homogeneous funcof the return over variable cost and the price of
cows.
nal
empirical results here suggest that,
utility
cull
Consequently, the long run competitive equilibrium where margicost equals marginal revenue appears to exist and long run econo-
mic profits are driven to zero.
These
conclusions hold rather important implications
the effectiveness of the U.S.
program
and
supporting
dairy support program.
the mandates of the Federal Milk
the
concarni~g
While the dairy
Mar~eting
prices of milk received by farmers above
Orders
that
are
which
would exist under a competitive framework, the results of this portion
of the research suggest that the increased returns farmers receive are
capitalized
into the market price of replacement dairy cattle.
the long run,
economic profits to the dairy industry,
milk price supports provided by the government,
virtue of
the
competitive natura
a Elasticities
are
of
the
the
are driven to zero by
the industry.
calculated at
even with
Over
In
effect, the
sample means.
78
support
efforts
of the U.S.
government,
incurred from the dairy programs,
and
net
worth
and the
associated
costs
appear to be supporting the incomes
of those producers who raise and
market
replacement
dairy cattle.
The final chapter of this thesis summarizes the main results
tained during the course of this research.
discussing
sults.
ob-
The thesis is completed by
possible implications and extensions of these research re-
79
CHAPTER 5
CONCLUSIONS AND IMPLICATIONS
In this·study an attempt was made to estimate a dynamic model
of
the U.S. dairy industry and use those empirical results to investigate
the
factors impacting the adoption of Dairy Herd Improvement Associa-
tion quality testing of dairy cattle.
examine
The model was also employed to
the relationship between the level of profitability
and
the
market price of milk cows.
The
as
empirical research recursively constructed predicted
instruments
for various price and quantity figures of the
and demand sectors of the U.S.
trumental
procedure.
supply
The constructed ins-
variables attempted to break the simultaneity
various. price
ted
dairy industry.
values
and quantity components in a two-stage
between
least
the
squares
The constructed instruments were used to derive a predic-
profit per cow,
defined as return over feed cost,
to be used in
the investigations concerning the rate of adoption of DHIA testing and
the market prices of dairy cattle.
In the theoretical model, the rate of adoption of DHIA activities
was hypothesized to be directly related to the level of
available
creased,
in
an
the dairy industry.
As the return over feed cost
increase in participation in the Dairy Herd
Association was expected.
profitability
Improvement
To investigate this assertion the level
DHIA participation was estimated as a
t~ansformed
in-
of
logistic function of
80
return over variable cost and time, which entered as a linear trend.
The
these
results
of
the empirical research appeared
initial expectations.
to
The estimated parameter of
contradict
the
return
over feed cost regressor was not statistically different from zero and
only the linear trend appeared to affect the level of participation in
the Dairy Herd Improvement Association.
The
is
results suggested that the rate of adoption of DHIA
determined exogeneously,
U.S. dairy program.
testing
unaffected by the support efforts of the
However,
making decisions concerning inputs to a
production process without considering the expected level of
profita-
bility appears to be inconsistent with the optimization assumption
profit
maximization and a number
of
of factors such as aggregation bias
and misspecification of the profitability measure may be
contributing
to its lack of effect on the participation in DHIA activities.
The research here also investigated the relationship between
nominal
price of replacement dairy cattle and nominal profits,
defined as predicted returns over feed cost.
economic
profits in the
d~iry
of
industry ware hypothesized to be
dairy
production,
producing
replacement dairy cattle,
milk,
was
expected to equal the marginal
defined as the sum of per cow return
mic profits are driven to zero.
substantiate
the
capi-
In the long run,
defined to be marginal
cost and the price of utility cull cows,
again
In the theoretical model
talized into the market prices of dairy cattle.
price
the
cost
revenue
over
the
of
from
variable
implying the long run econo-
The empirical results of the research
hypothesized relationship.
The long run price
of
81
milk cows equation was estimated,
as expected, to be a linearly homo-
geneous
function
utility
cull cows and the equilibrium condition appears to hold.
The
results
implications
programs.
of nominal return over feed cost and the
of
this portion of the research
concerning the effectiveness of the U.S.
One
price
significant
support
of the underlying goals of the Federal dairy
regula-
To achieve this goal the
farmers receive for all milk is supported
which
would exist in a competitive environment.
sults
obtained
here,
The
suggest that the increased
above
empirical
revenue
Rather,
the
profits
dairy production are capitalized into market prices
the
government
Thus,
to support prgducers incomes are.,
renot
raise producers incomes in the long
replacement dairy cattle and dissipated away.
run.
that
does
significantly
from
of
dairy
tions is to increase dairy farmers' incomes.
average
hold
price
the efforts
in the
long
of
of
run,
frustrated by the competitive nature of the U.S. dairy industry.
A number of implications for further research have arisen in the
investigations
adoption
accomplished here.
Further analysis of the
rate
of
of Dairy Herd Improvement Association testing activities
is
required to either substantiate the unexpected results derived in this
thesis,
or
to determine the appropriate measure of profitability
to
which dairy producers ultimately respond in adopting DHIA procedures.
Viewed
process,
for
more
as a technological improvement to a
DHIA
production
testing may hold potential long run economic
benefits
consumers due to the increased supply of milk resulting from
productive dairy herds.
Additional research may
determine
nature, size, and distributions of such economic benefits.
the
the
82
Finally,
from
dairy
placement
incomes
the investigation here suggests that additional revenue
production is dissipated into the market prices
dairy
cattle and consequently does not
in the long run.
increase
of
re-
producer
Possible extensions of this portion of the
thesis could attempt to more exactly determine the nature and the rate
of the capitalization of the dairy program rents over time.
83
REFERENCES
84
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Occasional Paper #3.
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Beattie, B.R., and C.R. Taylor. The Economics of Production.
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New
Berkson, J. "A Statistically Precise and Relatively Simple Method of
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Washington
D.C.
Burt,
O.R.
"Estimation of Distributed Lags as Nonstochastic Difference Equations." Department of Agricultural Economics and Economics Staff Paper 80-1. Montana State University, Bozeman, Montana, ( 1980).
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O.R.
"Econometric Modelling of the Capitalization Formula for
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Burt,
0.~.
S. Townsend, and J.T. LaFrance. "Instruction Manual for
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Buxton, B.M. "Welfare Implications of Alternative Classified Pricing
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Lev e 1s . "
_A_m_e_r_i_c_a_n_ _J_o_u_r_n_a_l__o_f__A_..g_r.. :. i_c_u..;_l_t...:..u..;..r_a...:..l----"E-=-c-'-o-'-n-omics. 56(1974):279-87.
Chiang, A.C.
Fundamental Methods of
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Mathematical
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New
85
Dahlgran, R.A. "Welfare Cost~ and Interregional Income Transfers due
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____ , "Dairy Marketing and Policy Analysis: a Critical Review of
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Dixon, R.
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Gaumnitz, E.W. and O.M. Reed. Some Problems Involved in Establishing
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Griliches, Z.
"Hybrid Corn: an Exploration in the Economics
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Harris, E.S. Classified Pricing of Milk: some Theoretical Aspects.
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E.O. Heady, and J.L. Dillon. Iowa State University Press, Ames,
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Heady, E.O., J.P. Madden, N.L. Jacobson, and A. E. Freeman. "Milk
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Hein,
D.
"The Cost of the U.S.
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Hoover, L.M., P.L. Kelly, G.M. Ward, A.M. Feyerman, and R. Chaddha.
"Economic Relationships of Hay and Concentrate Consumption to
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(1967) :64-78.
Ippolito, R.A. and R.T. Masson. "The Social Cost of Government Regulation of Milk." Journal of Law and Economics. 21(1978):33-65.
Judge, G.J., R.C. Hill, W.E. Griffiths, H. Lutkepohl, and T.C. Lee.
Introduction to the Theory and Practice of Econometrics. New
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Kmenta, J. Elements of Econometrics. New
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Publishing
86
LaFrance, J.T. "Linear
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LaFrance, J., and H. de Gorter. "Regulation in a Dynamic Market: the
U.S. Dairy Industry." American Journal of Agricultural Economics. 67(1985): 821-32.
Mansfield, E. "Technical Change and the Rate of Imitation." Econometrica. 29(1961):741-66.
Masson, R.T., and P.M .. Eisenstat. "Goals and Results of Federal Milk
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Neter, J., W. Wasserman, and M.H. Kutner. Applied Linear Statistical
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Paris, 0., F. Malossni, A.M. Pilla, and A. Romita. "A Note on Milk
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Agricultural Economics. 64(1982):1-7.
Taylor, C.R. "A Simple Method for Estimating Empirical Probability
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Western Journal of Agricultural Economics. 9(1984):66-76.
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______ ,ASCS. Dairy Program,
(various issues).
_______ ,ERS.
issues)
Commodity Fact Sheet.
Dairy Situation and Outlook.
,ERS. Dairy Statistics through 1960.
Washington D.C. (1962).
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Washington D.C. (1968).
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Washington
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D.C.
(various
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303.
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430.
87
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---issues).
Feed Situation and
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D.C.
(various
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D.C. (various issues).
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- - -D.C.
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Washington
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_____ ,Statistical Reporting Service.
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Agricultural Prices. Washington
White, K.J. "A General Computer Program for Econometric Methods
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88
APPENDIX
ORIGINAL DATA
89
Table 4. Original Data
Avg.
Year
Avg.
Milk
Price
Price
Mfg.
Avg.
Milk
cl . 1
Price .Price
1950
1951
1952
1953
1954
1955
1956
1957
195.8
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
3.89
4.58
4.85
4.32
3.97
4.00
4. 14
4.21
4 ..13
4.16
4.21
4.22
4.09
4.10
4. 15
4.23
4.78
5.02
5.24
5.49
5.11
5.87
6.07
7.14
8.33
8.75
9.66
9. 72
10.60
12.00
13.05
13.76
13.59
13.58
13.46
12.75
3.07
3.47
3.79
3. 77
3.30
3.15
3.23
3.25
3. 11
3.06
3.11
3.37
3.18
3.13
3.15
3.22
3.69
4.00
4.21
4.28
4.57
4.86
4.93
5.31
6.33
7.36
8.06
8.82
9.42
10.70
12.33
13.12
13.10
13 .. 06
12.60
11.98
3.16
3.85
4.06
3.48
3.14
3.15
3.25
3.27
3.15
3.17
3.25
3.36
3.20
3.21
3.26
3.34
3.94
4.06
4.22
4.45
4.70
4.86
5.08
6.20
7.13
8.62
8.56
8.70
9.65
11 . 10
12.05
12.73
12.66
12.61
12.49
11.72
Sup.
4. 77
5.40
5. 71
5.31
4.94
4.97
5. 15
5.26
5.21
5.25
5.28
5.24
5.14
5. 12
5 .18
5.22
5.66
6.07
6.34
6.63
6.88
7.08
7.23
8.18
9.79
10.10
11.06
11 . 07
11.85
13.22
14.55
15.41
15.17
15.23
15.00
14.50
Avg.
Grain
Price
#2
Corn
Price
3.08
3.52
3.75
3.43
3.30
3.10
3.00
3.00
2.89
2.89
2.90
2.91
2.93
3.03
3.02
3.03
3.15
3. 23
3.10
3.15
3.28
3.44
3.52
4.88
6.23
6.25
6.30
6.20
6.08
6.68
7.42
8.02
7.45
7.88
8.16
7.35
1. 21
1. 59
1. 77
1. 53
1.46
1.46
1. 38
1. 30
1.12
1.09
1.07
1. 01
1.03
1.13
1.17
1.26
1.29
1. 30
1.14
1.20
L28
1. 44
1.23
1.80
2.79
3.05
2.66
2 .15
2.09
2.28
2.49
3.13
2.46
2.82
3.20
2.60
Uti 1.
Cows
Price
NonFood
CPI
19.50
0.711
24.03
0.757
18.54
0.775
12.04
o. 790
11. 11
0. 795
10.99
0.797
10.91
0.811
13.40
0.838
17.87· 0.857
17.47
0.873
15.31
0.888
15.65
0.897
15.3'7
0.908
14. 7,3
0.920
13.24
0.932
14.44
0.945
17.83
0.967
17.22
1 .000
17.94
1.044
20.29
1. 101
21.32
1. 167
21.62
1 . 221
25.21
1.258
32.82
1.307
25.56
1.437
21.09
1 . 5 71
25.31
1. 675
25.32
1.784
36.78
1. 912
50.10
2.130
45.72
2.440
41.93
2.706
39.96
2.884
39.35 . 2.983
39.81
3 .113
38.31
3.233
Beverage
CPI
0.867
0.955
0.961
0.988
1 . 173
1. 051
1.099
1. 091
1. 014
0.921
0.915
0.915
0.901
0.912
1. 023
1. 015
1 .009
1. 000
1. 019
1.046
1. 174
1. 216
1. 213
1. 302
1. 556
1.790
2. 1.40
3.224
3.398
3.561
3.958
4.126
4·.242
4.322
4.430
4.532
90
Table 4. (continued)
Fats &
Oils
CPI
Milk
Cows
Price
Per Cap.
Disp.
Income
0.885
1. 035
0.878
0.882
0.929
0.901
0.920
0.961
0.950
0.906
0.865
0.926
0.925
0.899
0.896
0.961
0.998
1 .000
0.978
0.979
1.053
1 . 152
1 .166
1.290
1.794
1 .986
1.737
1. 914
2.100
2.266
2.412
2.671
2.596
2.631
2.875
2.939
198.
247.
243.
177.
149.
146.
153.
166.
210.
233.
223.
224.
221.
215.
209.
212.
246.
260.
274.
300.
332.
358.
393.
496.
500.
412.
478.
504.
675.
1040.
1190.
1200.
1110.
1030.
895.
860.
1267.
1349.
1396.
1458.
1477.
1560.
1608.
·1666.
1692.
1786.
1829.
1857.
1940.
2017.
2133.
2268.
2428.
2534.
2752.
2949.
3121.
3330.
3609.
3950.
4285.
4689.
5178.
5707.
6304.
6960.
7608.
8324.
8825.
9503.
10235.
10810.
Total
u. 5.
Pop.
Average
152.271
154.878
157.553
160.184
163.026
165.931
168.903
171.984
174.882
177.830
180.671
183.691
186.538
189.242
191.889
194.303
196.560
198.712
200.706
202.677
205.052
207.661
209.896
211.909
213.854
215.973
218.035
220.239
222.585
225.055
227.738
230.043
232.345
234.538
236.681
238.816
Age
Yield
per
Cow
Grain
per
Cow
32.06660
32.01794
31.99775
31.95212
31.90199
31.84348
31.76767
31.68051
31.59908
31.54801
31.50865
31.44578
31.40061
31.40973
31.42435
31.46332
31.53852
31.67012
31.82273
31.95431
32.07092
32.15747
32.34636
32.54675
32.75930
32.97404
33.19138
33.38777
33.56360
33.72565
33.85603
33.98249
34. 11340
34.24668
34.37798
34.50845
5.314
5.333
5.374
5.542
5.657
5.842
6.090
6.303
6.585
6.815
7.029
7.290
7.496
7.700
8.099
8.304
8.507
8.797
8.992
9.434
9.751
10.015
10.259
10.119
10.293
10.360
10.894
11 . 206
11.243
11.488
11.889
12.177
12.306
12.585
12.506
13.031
1.629
1. 605
1.628
. 1.670
1 .659
1.758
1. 825
1.945
2.003
2.050
2.259
2.404
2. 723
2.646
3.040
2.953 .
3.200
3.374
3.519
3. 726
3.979
4.070
4.298
4. 389
4.384
4.357
4.545
4.709
4.803
5.070
5.260
5.300
5.380
5.438
5.253
5.430
u.s.
91
Table 4. (continued)
Producing
Milk Cows
on Farms
21.944
21 • 505
21. 338
21 . 691
21 . 581
21.044
20.501
19.774
18.711
17.901
17.515
17.243
16.842
16.260.
15.677
14.954
14.093
13.501
13.038
12.307
12.000
11.839
11 . 700
11.413
11.230
11 . 139
11 . 032
10.945
10.803
10. 743
10.810
10.923
11.033
11.098
10.833
11.025
Per Cap.
Class I
Demand
Per Cap.
Class I I
Demand
347.40918
349.32523
348.46079
343.98801
344.74295
345.32632
345.76672
341.90021
334.51508
327.27884
322.68774
312.48297
309.33362
308.60281
305.39920
302.62479
297.61902
286. 14563
280.66763
273.20273
264.86221
259.55887
262.80432
258.23499
243.81575
243.59865
242.62716
239.29528
235.28619
232.97045
227.68191
223.87411
216.06267
215.32427
211.67822
212.72141
385.50601
365.68735
349.31131
336.82105
339.65768
342. 14426
337.71463
331.14316
322.84421
323.15131
324.40915
320.73056
302.64835
302.33035
307.54114
294.61142
313.21732
272.18054
277.08020
273.25699
275.52304
274.89645
276.66873
276.18216
287.63150
285.22479
294.84473
288.25.317
298.98013
305.03442
301.20755
293.03598
302.72443
307.87106
324.20990
335.92813
Net
Com.
Rem.
Net
Govt.
Rem.
3.999
3.821
2.036
1.793
4. 544
3.993
4.320
2.495
3.936
2.889
3.074
1.363
1.349
1. 815
1.672
2.462
-.821
.388
.140
.870
.420
.297
1.445
.062
.584
-.856
1. 759
.388
-.200
.213
-.844
.999
.683
. 151
-.029
-. 537
1 .000
.125
2.700
9.375
5.975
4.875
5.100
6.375
4.325
3.425
3.115
8.022
10.748
7. 772
7.677
5.665
.645
7.427
5.150
4.479
5. 774
7.268
5.345
2 .185
1.346
2.036
1.236
6.080
2.743
2. 119
8.800
12.861
14.282
16.814
8.645
13.174