Impacts of the
Northeast Interstate Dairy Compact on New England Milk Supply
Charles F. Nicholson, Budy Resosudarmo, and Rick Wackernagel
Department of
Community Development and Applied Economics
The University
of Vermont
Background
During
the first year of the Northeast Interstate Dairy Compact, milk production in
the six New England states increased by about 57 million pounds, or about 1.3%
of production compared to the 12 months prior to the Compact (Figure 1). Increases in milk production were largest in
Connecticut (31 million pounds) and Vermont (21 million pounds), whereas Maine
and New Hampshire experienced increases of less than 10 million pounds. Production in Massachusetts and Rhode Island
declined by 9 million and 0.4 million pounds, respectively. Because the rate of increase for New England
was larger than the US average, the Compact Commission incurred obligations to
the CCC for purchases of dairy products.
The
increase in milk production in New England has led some observers to attribute
the increase to the Compact. However,
few formal studies to date have explored the role of factors other than the
Compact that also may have affected New England milk supply. The principal effects of the Compact that
are likely to influence milk production include higher milk prices (or the
expectation of higher prices), and the potential for lower price-related
risk. Due to falling grain prices and
higher milk prices, the milk-feed price ratio increased continuously starting
in the quarter before initiation of the Compact (Figure 2). The variance of the milk-feed price ratio in
previous periods is an indicator of price risk. Price risk is likely to have the effect of decreasing milk
production (Dillon, 1977). The variance
of the milk-feed price ratio increased during the first year of the Compact
relative to the same period a year earlier, so that changes in price risk may
not have contributed to an increase in milk production. Factors other than the prices and risk that
may have influenced milk production include weather conditions and higher hay
prices in the New England states.
Rationale and Objectives
The
impact of the Compact on milk supplied by New England farmers is important
because:
1)
Changes
in milk supply serve as an indicator of how well the objective of maintaining a
dairy production base in New England is being achieved;
2)
Changes
in milk supply affect the Compact Commission’s financial obligations, and it
would be helpful to determine to what extent changes in milk production have
resulted from the Compact as opposed to other factors;
3)
Information
on the responsiveness of dairy farmers to prices may help the Compact
Commission to better achieve its stated objectives.
Thus,
the objective of this study is to examine the impact of the Compact on milk
production in the six New England states.
An adequate study of the Compact’s impacts needs to control for factors
other than prices and risk that may have changed since the Compact came into
existence.
Methods
Econometric
models are an appropriate tool for analysis of the responsiveness of milk
supply to changes in various factors, including prices, weather conditions, and
risk. The analysis herein relies on a
two-equation ‘random coefficients’ model to predict the relationship between
milk production and price levels controlling for other factors. A random coefficient model allows the impact
of prices (and other factors) to differ for each of the six states (see the
Appendix for a summary of the random coefficients model). This is desirable given the differences in
farm characteristics and market proximity among the New England states. One equation in the model estimates the
relationship between cow numbers and factors such as prices, and the other
equation estimates the relationship between milk per cow and factors such as
prices. Cow numbers and milk per cow
predicted by the equations are multiplied to obtain an estimate of milk
production. This model is similar to
that used by Dixon et al. (1991) to examine the impacts of dairy policy changes
in the mid-1980s.
Quarterly
data from 1991 through the second quarter of 1998 were used to develop the
econometric model. The variables
explored in the process of constructing the econometric model included the
price of milk relative to the price of key inputs such as grain, hay, labor,
and interest rates (Table 1).
Environmental variables included inches of summer rainfall (which is
related to forage production), and the deviation of temperature from 50 degrees
F (which is the middle of the range described as optimal for dairy cows, Foley
et al., 1972). Price variation in the
previous year and two years was included to determine if price risk affected
cow numbers and(or) milk per cow. Due
to the biological lags inherent in dairy production, cow numbers and milk per
cow in the previous quarter were included in the models.
Because
in any given quarter milk production and milk prices are simultaneously
determined, single-equation econometric models typically use values of relative
prices in a previous period (in this case, the previous quarter) rather than
the relative prices in the current period.
The use of lagged price variables implies that the model does not need
to include a full set of equations and variables to estimate prices, production,
and demand simultaneously, as some previous studies of dairy policy options
have done (e.g., Kaiser, 1993). In
addition, the values of the lagged relative prices were transformed to natural
logarithms prior to model estimation, as in Dixon et al. (1991).
The
criteria used to select a specific econometric model among possible
alternatives are subjective (Judge et al., 1980). Typically, model development includes decisions about which
variables to include and which to leave out, as well as choices about whether
models will be linear, non-linear, or linear in logarithms. Economic theory, practical knowledge, and
comparisons of results from alternative models guide the choice of variables
included. To develop the random
coefficients model, we began by using all variables (Table 1) and then
evaluated model results to guide the process by which variables were
excluded. The two most important
criteria used to evaluate the models are:
a)
Explanatory
power of the model, that is, how much of the variance in the cow numbers or
milk per cow was explained by the included variables (as measured by the
adjusted R2);
b)
Signs
(negative or positive effect) and statistical significance of key variables
such as the milk feed price ratio for both the overall model and for the
individual states.
Once
a satisfactory relationship between factors such as relative prices and cow
numbers or milk per cow has been determined, the model can be used to estimate
the impacts of the Compact on milk supply.
To do this, an estimate of the prices that would have occurred had the
Compact not existed must be developed.
These price estimates are used with the coefficients from the random
coefficients model to predict milk production that would have occurred in the
absence of the Compact. The difference
between milk production under the actual prices and the predicted milk
production under ‘non-Compact’ prices provides an estimate of the impact of the
Compact on milk production.
A
number of different methods could be used to estimate prices that would have
prevailed in the absence of the Compact.
For the analyses reported in the next section, we developed two
independent estimates of the milk prices that would have prevailed without the
Compact. For New England, state
all-milk prices are calculated as the sum of the Zone 21 Order 1 blend price,
butterfat premiums based on butterfat differentials and mean butter fat tests,
handler over-order premiums from a survey of handlers in each state,
state-mandated payments (currently applicable only in Maine) and the Compact
over-order premium[1] (Sharon
Slayton, NASS, personal communication).
Using this calculation as a base, one estimate of the prices that would
have prevailed without the Compact is the state all-milk price less the
over-order premiums paid to farmers by the Compact Commission. This estimate ignores effects that the
Compact may have on the Order 1 blend price (the principal component of the
state all-milk price in New England) and any interactions that may have
occurred between Compact-mandated over-order premiums and voluntary premiums
paid by milk handlers. If the Compact’s
price regulation decreased the blend price and resulted in a decrease in
average handler over-order premiums, this price estimate will overstate the
impact of price enhancement under the Compact on milk production. (A more detailed and mathematical treatment
regarding estimation of milk prices in the absence of the Compact is found in
the Appendix.)
The
second estimate of the state all-milk price in absence of the Compact is the
sum of an estimated ‘non-Compact’ blend price, applicable butterfat premiums,
and an estimated ‘non-Compact’ handler premium. The estimated ‘non-Compact’ blend prices use an adjustment to
actual blend prices based on class utilization by quarter for the Compact
period and the previous six years.
These estimated non-Compact blend prices are $.05 to $.06 higher than
the actual blend prices. The estimated
‘non-Compact’ handler premiums are calculated as the mean weighted average
handler premiums for all classes of milk by quarter during the three years
prior to the implementation of the Compact.
For the purpose of this calculation, handler premiums are estimated as
the state all-milk price less the Zone 21 blend price, butterfat premiums, and
the Compact over-order premium. In
states other than Maine, estimated handler premiums are about the same or
somewhat higher as in the period prior to implementation of the Compact[2]. For Maine, handler over-order premiums
calculated in this way were sometimes negative—an unlikely value—and efforts to
discuss the result with NASS staff to determine the source of the discrepancy
were not successful. Thus, no price
estimate based on this method is reported for Maine.
Results
Model Results
The
variables included in the random coefficients model of cow numbers include cow
numbers in the previous quarter, the milk-feed price ratio in the previous
quarter, the milk-land price ratio for two quarters previous, summer rainfall,
and summer rainfall squared (Table 2).
Although this model contains relatively few variables, it has high
explanatory power, theoretically consistent signs, and statistically
significant model coefficients. All
variables have a positive impact on milk production with the exception of the
square of summer rainfall, which indicates, essentially, that too much rain can
lower summer forage production. The low
probability value for the c2 indicates that the
coefficients are statistically different for the six states.
A
different set of variables is included in the equation for milk per cow (Table
2). In this model, milk per cow in the
previous quarter, the milk-feed price ratio in the previous quarter, the
deviation from temperature away from 50 degrees F, and a constant are all
statistically significantly different from zero and have theoretically
consistent signs. The explanatory power
of the milk per cow equation is lower than that for cow numbers, but is still
good for models of this type. In
contrast to the cow numbers equation, the c2 test provides evidence that
the relationship between the included variables and milk per cow does not
differ by state. Although important in
theory, the variance of milk-feed price ratios (i.e., risk variables) were not
included in the final models because they were statistically
insignificant. Thus, risk (as measured
by past price variance) appears to have relatively little impact on cow numbers
or milk per cow.
Estimates of Non-Compact Prices
Milk
prices in the absence of the Compact are predicted to be lower in most cases
than actual prices (Table 3 and Figure 3).
For most states and for most quarters, the price estimated by
subtracting the Compact over-order premium from the state all-milk price
(subsequently referred to as estimate 1) is higher than the estimated price
based on an estimate of the ‘non-Compact’ blend price, the butter premium, and
estimated ‘non-Compact’ handler premiums (subsequently referred to as estimate
2). The estimated influence of the
Compact on state all-milk prices is given by the difference between actual
prices and the two estimated prices.
Price estimate 1 is closer to the actual prices during the Compact
period for most states and quarters, so the estimated aggregate impact of the
Compact on all-milk prices is slightly smaller than that predicted by estimate
2 prices.
In
addition, because of variations in the underlying blend prices during the
Compact period—and therefore changes in the amount of the Compact over-order
premium—the difference between the actual prices and price estimates is smaller
later in the Compact period. In
Vermont, for example, the difference between actual and estimated prices was
more than $1.00 in the third quarter of 1997, but narrows to about $0.20 in the
first quarter of 1998. Thus, the impact
of the Compact on milk prices, and therefore milk production, is likely to be
larger earlier in the Compact period.
Estimates of Cow Numbers and Milk Per Cow
The increase in milk prices under the Compact is estimated
to have increased the number cows on farms in New England compared to cow
numbers that would have been observed without the
Compact (Table 4). The impact of the
Compact on total number of animals is small, about 700—0.2% of actual cow
numbers—and is concentrated in Massachusetts and New Hampshire. Connecticut and Maine are estimated to have
retained about 100 more cows than they would have without the Compact, and
Rhode Island and Vermont are estimated to have essentially no change in cow
numbers as a result of the Compact.
As
expected, higher milk prices under the Compact are estimated to have increased
milk per cow in all six New England States (Table 4). The estimated increases range from about 20 pounds per cow per
quarter in Rhode Island to just under 50 pounds per cow per quarter in
Connecticut. The percentage increase
over the milk per cow that would have been expected in the absence of the
Compact range from 0.4% in Rhode Island to 1.2% in Connecticut. Milk per cow is estimated to have increased
0.7% for the New England region due to the increase in milk prices under the
Compact. Because these percentage
increases are higher than those for cow numbers, more of the increase in total
milk production is attributable to changes in milk per cow than cow numbers.
Estimates of Milk Production
Using
the coefficients from the random coefficients models for cow numbers and milk
per cow and prices estimated in the absence of the Compact allows estimates of
milk production by state. The
difference between the estimated values and actual milk production provides an
estimate of the impact of the Compact on milk production for each of the six
New England states.
The
total increase in milk production for the six New England states attributed to
increased milk prices under the Compact is 45 million pounds under price
estimate 1, and 43 million pounds for the states other than Maine under price
estimate 2 (Table 5). These amounts
represent increases of 1.0% over the milk production predicted in the absence
of the Compact. To put these increases
into perspective, it is helpful to compare them to the total increase in milk
production during the Compact period compared to the previous year. The increase in production using estimate 1
equals 79% of the increase in milk production from the previous year, and the
increase in production using price estimate 2 for the 5 states other than Maine
equals about 90% of the increase in milk production from the previous year.
The impact of the price increases on milk production varies by state. The largest increase in milk production occurs in Vermont, but New Hampshire and Rhode Island experience the largest percentage increases due to the Compact (Table 5). The proportion of the change in milk production from the previous year also differs by state. In Vermont, the increase in milk production from 1996-97 accounted for by the increase in prices under the Compact accounted for 101 to 113% of the increase of 21 million pounds from 1996-97 to 1997-98. That is, our results suggest that milk production in Vermont would have declined somewhat in 1997-98 if milk prices had been at the levels estimated without the Compact. For New Hampshire, the increase in milk production due to the Compact was nearly equal to the increase from 1996-97 to 1997-98. In the other states, the proportion of the increase accounted for by increased prices under the Compact tends to be lower. In Connecticut and Maine, price increases under the Compact are estimated to have contributed between one-quarter and one-half of milk production increases compared to the year before the Compact. A detailed summary of the results for cow numbers, milk per cow, and milk production by state and quarter is provided in Appendix Tables 1 and 2.
References
Chavas, J-P., A. F. Kraus,
and E. V. Jesse. 1990. A Regional Analysis of Milk Supply Response
in the United States. North Central
Journal of Agricultural Economics, 12:149-164.
Dillon, J. 1977.
The Analysis of Response in Crop and Livestock Production. 2nd ed. Oxford: Pergamon Press.
Dixon, B. L., D. Susanto,
and C. R. Berry. 1991. Supply Impact of the Milk Diversion and
Dairy Termination Programs. American Journal of Agricultural Economics,
73:633-640.
Foley, R. C., D. L. Bath, F.
N. Dickinson, and H. A. Tucker.
1972. Dairy Cattle: Principles, Practices, Problems, and
Profits. Philadelphia: Lea and Febiger.
Judge, G. G., W. E.
Griffiths, R. C. Hill, and T-C. Lee.
1980. The Theory and Practice of
Econometrics. New York: John Wiley and Sons.
Kaiser, H. M. 1993.
An Analysis of Alternatives to the Dairy Price Support Program. Department of Agricultural Economics,
Cornell University, Ithaca, NY.
(Agricultural Economics Research 93-9, July 1993)
Swamy, P. 1974.
Linear Models with Random Coefficients, in Zarembka, P. (ed.), Frontiers
in Econometrics. New York: Academic Press.
Table 1. Variables Examined for Inclusion in Random
Coefficients Model of Milk Supply in Six New England States
|
Variable |
Description |
Source of base data |
Dependent
|
|
|
|
Cow
numbers |
|
NASS |
|
Milk
cow |
|
NASS |
Independent
|
|
|
|
Milk-feed
price ratio |
State
all-milk price divided by grain prices for Vermont |
NASS
|
|
Milk-hay
price ratio |
State
all-milk price divided by hay prices in the northeast |
NASS
|
|
Milk-cow
price ratio |
State
all-milk price divided by milk cow herd replacements |
NASS |
|
Milk-beef
price ratio |
State
all-milk price divided by slaughter beef prices in New York |
NASS
|
|
Milk-wage
price ratio |
State
all-milk price divided by farm labor wage rates for hired workers in New
England and New York |
NASS |
|
Milk
price -interest rate |
State
all-milk price divided by prime rate |
NASS
and Federal Reserve |
|
Milk
price-land value ratio |
State
all-milk price divided by land value per acre |
NASS |
|
Temperature
deviation from 50 degrees F, degrees |
Square
of the quantity mean monthly temperature minus 50. |
NASS |
|
Summer
rainfall, inches |
Sum
of rainfall in June, July and August |
NASS |
|
Summer
rainfall squared, inches |
Square
of summer rainfall |
NASS |
|
Price
risk in the previous 4 quarters |
Variance
of milk-feed price ratio in previous 4 quarters |
NASS |
|
Price
risk in the previous 8 quarters |
Variance
of milk-feed price ratio in previous 8 quarters |
NASS |
Note: Dependent variables are the information to
be explained, whereas independent variables are the variables that are
hypothesized to determine the values of the dependent variables
Table 2. Results of Random Coefficients Models of Cow
Numbers and Milk Per Cow, Aggregated Estimates1
|
|
Dependent variable |
|
Independent Variable |
Cow numbers |
Milk per cow |
|
|
|
|
|
Cow
numbers in previous quarter |
+0.83 |
-- |
|
|
(20.89) |
|
|
Milk
per cow in previous quarter |
-- |
+0.86 |
|
|
|
(19.17) |
|
Milk-feed
price ratio in previous quarter |
+0.07 |
+0.08 |
|
|
(1.89) |
(2.41) |
|
Milk-land
price ratio 2 quarters previous |
+0.02 |
-- |
|
|
(1.20) |
|
|
Summer
rainfall |
+0.48 |
-- |
|
|
(3.42) |
|
|
Square
of summer rainfall |
-0.09 |
-- |
|
|
(-3.18) |
|
|
Squared
deviation from 50 degrees F |
-- |
-0.004 |
|
|
|
(-1.83) |
|
Constant |
-- |
1.10 |
|
|
|
(2.93) |
Model Evaluation Characteristics |
|
|
|
Adjusted
R2 |
.97 |
.74 |
Number of observations |
240 |
240 |
|
Number
of groups |
6 |
6 |
|
Residual
standard deviation |
0.22 |
.03 |
|
c2 for test of homogeneity
of state coefficients |
74.23 |
13.84 |
|
Probability
value for c2 |
.000 |
.838 |
1 Aggregated estimates
indicate responsiveness for the region as a whole, whereas state-level
coefficients (not reported) indicate differences in responsiveness among
states.
Note: All variables expressed in natural
logarithms.
Note: t-statistics in parenthesis below
coefficient values.
Table 3. Comparison of Actual and Estimated
Non-Compact Milk Prices,
by State and Quarter
|
|
Year:Quarter |
|||
State, Price |
97:3 |
97:4 |
98:1 |
98:2 |
|
|
|
|
|
|
Connecticut |
|
|
|
|
Actual all-milk price |
14.53 |
15.80 |
15.43 |
15.00 |
Estimate 11 |
13.22 |
15.25 |
15.25 |
14.59 |
|
Estimate 22 |
13.18 |
15.20 |
15.28 |
14.76 |
Maine |
|
|
|
|
Actual all-milk price |
14.43 |
15.57 |
15.20 |
14.57 |
|
Estimate 1 |
13.12 |
15.02 |
15.02 |
14.16 |
|
Estimate 2 |
3 |
3 |
3 |
3 |
Massachusetts |
|
|
|
|
Actual all-milk price |
14.67 |
15.97 |
15.43 |
15.40 |
|
Estimate 1 |
13.35 |
15.42 |
15.49 |
14.76 |
|
Estimate 2 |
13.24 |
15.30 |
15.49 |
14.91 |
New Hampshire |
|
|
|
|
Actual all-milk price |
14.57 |
15.87 |
15.57 |
15.20 |
|
Estimate 1 |
13.25 |
15.32 |
15.39 |
14.79 |
|
Estimate 2 |
13.23 |
15.27 |
15.42 |
14.92 |
Rhode Island |
|
|
|
|
Actual all-milk price |
14.50 |
15.73 |
15.53 |
14.90 |
|
Estimate 1 |
13.19 |
15.18 |
15.35 |
14.61 |
|
Estimate 2 |
13.18 |
14.97 |
15.36 |
14.65 |
Vermont |
|
|
|
|
Actual all-milk price |
14.17 |
15.57 |
15.27 |
14.93 |
|
Estimate 1 |
12.85 |
15.02 |
15.09 |
14.53 |
|
Estimate 2 |
12.80 |
14.85 |
15.05 |
14.56 |
1 Price estimate 1 equals the
state-all-milk price minus the Compact over-order premium.
2 Price estimate 2 equals the
sum of an estimated ‘non-Compact’ blend price, butterfat premiums, and an
estimated ‘non-Compact’ handler premium.
3 Not reported due to
discrepancies between estimated handler premiums and those mentioned in
personal communications with Sharon Slayton, NASS.
Table 4. Estimated Impact of the Compact on Cow
Numbers and Milk Per Cow, by State
|
|
|
Predicted Without Compact |
Difference With and
Without Compact |
||
|
Price |
Price |
Price |
Price |
||
Cow Numbers, 000 3
|
|
|
|
|
|
Connecticut |
29.8 |
29.6 |
29.6 |
0.1 |
0.1 |
|
Maine |
39.5 |
39.4 |
4 |
0.1 |
4 |
|
Massachusetts |
25.3 |
25.1 |
25.1 |
0.2 |
0.2 |
|
New Hampshire |
18.3 |
18.0 |
18.0 |
0.2 |
0.2 |
|
Rhode Island |
2.0 |
2.0 |
2.0 |
0.0 |
0.0 |
|
Vermont |
157.8 |
157.8 |
157.8 |
0.0 |
0.0 |
|
Total, All States |
272.5 |
271.9 |
4 |
0.6 |
4 |
|
Total, States excluding Maine |
|
|
|
|
|
|
|
|
|
|
|
|
Milk Per Cow5
|
|
|
|
|
|
Connecticut |
4,397 |
4,351 |
4,350 |
46 |
47 |
|
Maine |
4,189 |
4,166 |
4 |
22 |
4 |
|
Massachusetts |
4,218 |
4,195 |
4,192 |
23 |
26 |
|
New Hampshire |
4,482 |
4,457 |
4,456 |
26 |
26 |
|
Rhode Island |
3,938 |
3,919 |
3,918 |
18 |
20 |
|
Vermont |
4,131 |
4,097 |
4,094 |
34 |
38 |
|
Weighted Average, All States |
|
|
|
|
|
|
Weighted Average, States excluding Maine |
|
|
|
|
|
1 Price estimate 1 equals the
state-all-milk price minus the Compact over-order premium.
2 Price estimate 2 equals the
sum of an estimated ‘non-Compact’ blend price, butterfat premiums, and an
estimated ‘non-Compact’ handler premium.
3 Mean quarterly value of
actual and estimated cow numbers for each state during 1997:3 to 1998:2.
4 Not reported because no
price estimate 2 was made for Maine.
5 Mean quarterly value of
actual and estimated milk per cow for each state during 1997:3 to 1998:2.
Table
5. Estimated Impact of the Compact on
Milk Production, by State, 1997:3 to 1998:2
|
|
Annual Milk Production,
million pounds |
Difference With and
Without Compact |
|||
|
State |
Actual With Compact |
Predicted Without Compact,
Price |
Predicted Without Compact,
Price |
Price |
Price |
|
|
|
|
|
|
|
|
Connecticut |
523.0 |
515.6 |
515.4 |
7.4 |
7.6 |
|
Maine |
662.0 |
656.8 |
3 |
5.2 |
3 |
|
Massachusetts |
426.0 |
421.0 |
420.5 |
5.0 |
5.5 |
|
New
Hampshire |
327.0 |
321.4 |
321.3 |
5.6 |
5.7 |
|
Rhode
Island |
31.5 |
30.9 |
30.8 |
0.6 |
0.7 |
|
Vermont |
2,607.0 |
2,585.7 |
2,583.5 |
21.3 |
23.5 |
|
|
|
|
|
|
|
|
Total,
All States |
4,576.5 |
4,531.4 |
3 |
45.1 |
3 |
|
Total,
States excluding Maine |
3,914.5 |
3,874.6 |
3,871.5 |
39.9 |
43.0 |
1 Price estimate 1 equals the
state-all-milk price minus the Compact over-order premium.
2 Price estimate 2 equals the
sum of an estimated ‘non-Compact’ blend price, butterfat premiums, and an
estimated ‘non-Compact’ handler premium.
3 Not reported because no
price estimate 2 was made for Maine.
Appendix
Model Specification
The
underlying theory supporting the variables considered for inclusion in the
random coefficients model can be found in Dillion (1977). The variables used in most previous studies
of milk supply response include the price of milk relative to other prices
(usually input prices), risk measures, time trends, seasonal dummy variables
and lagged values of cow numbers and milk per cow (Dixon et al.,1991; Chavas et
al., 1990). The random coefficients
model developed for this study uses more explicit representations of biological
factors underlying seasonal variation in milk per cow and cow numbers by
including summer rainfall and temperature deviation variables rather than
seasonal dummies.
The
random coefficients model (Swamy, 1974) can be specified as:
Where
yi is a dependent
variable, Xi is a matrix
of independent variables, bi is a vector of coefficients
relating yi and Xi for each i=1,…,N group, b is
a constant, ei and vi are error terms, E[
] indicates the expected value operator, Var[ ] indicates the variance-covariance matrix, s2 is a constant, and G is a matrix. This model allows the relationship between yi and Xi to vary for each group (states in this case).
The
model estimated herein contains two equations, one for cow numbers and the
other for milk per cow. The
relationship between these variables and the independent variables reported in
Table 2 can be specified as follows:
Where
MPCst is milk per cow in
state s during quarter t and the superscript C indicates this is the
actual value with the Compact, PMFs,t-1
is the milk-feed price ratio during quarter t-1, TEMPDEVt
is the squared deviation from a temperature of 50 degrees F during quarter t, CNst
is the number of milk cows in state s
during quarter t and the superscript C indicates this is the
actual value with the Compact, SRAINst
is inches of summer rainfall, and e and x are error terms.
Predicted Values of Cow Numbers, Milk Per Cow, and Milk Production
Model
predictions of cow numbers and milk per cow are computed as follows:
Where the ^ indicates
that MPC and CN are predicted values and that the values of the b and a are estimated by the random
coefficients model. Predicted milk
production is equal to:
To
predict the values of MPC and CN that would have been observed in the
absence of the Compact, the equations use the values of PMFs,t-1 estimated without the Compact (the
derivation of these variables is discussed in more detail subsequently), and
the values of MPC and CN predicted in previous periods without
the Compact. Thus
Where
the superscript NC indicates that
these are the values that would have prevailed in the absence of the
Compact. Note that because the values
of milk per cow and cow numbers in the previous period affect current milk per
cow and cow numbers, the effect of the Compact in a given quarter carries over
into subsequent quarters. As an
example, consider cow numbers. If
higher prices result in increased cow numbers in the first quarter, this larger
number of cows then influences subsequent values of cow numbers through the
term CNs,t-1.
The
impact of the Compact on milk per cow and cow numbers is then estimated as the
difference between the predictions that use PMF
with the Compact and the predictions that use the estimated PMF without the Compact, or:
Where
DC indicates the estimated
change due to price increases under the Compact, and the other variables are as
defined previously.
The
estimate of milk production that would have occurred in the absence of the
Compact is given by
And
the difference in milk production attributable to price increases under the
Compact is given by:
Estimates of Non-Compact Prices
As a starting point for consideration of the impacts of the Compact on state all-milk prices, consider the definition of the all-milk price prior to the implementation of the Compact (for states other than Maine, which has additional mandated premiums):
Where
Pst is the price in state s during quarter t, BFCst is
the mean butterfat content of milk from state s during quarter t (as
reported by Order 1), BFDt
is the butterfat differential per 0.1% butterfat (as reported by Order 1), OOPst is the weighted average
amount of all over-order premiums paid by handlers in state s for all classes of milk during quarter
t.
If
the Compact over-order premium is defined as Ct, then the impact of the Compact on the state all-milk
price can be expressed mathematically as:
Where
as above DC indicates the impact of the Compact, and the ¶P/¶C and ¶P/¶OOP represent the changes in P and OOP that result from over-order premiums under the Compact. This equation explicitly recognizes that the
Compact over-order premiums may result in changes in the blend price and
over-order premiums paid by handlers.
Although the equation as written specifies that the Compact over-order
premium in quarter t has possible effects
on the blend price and handler premiums in that same quarter, it would be easy
to generalize this to allow for impacts across quarters. The above equation also assumes that the
Compact has no impact on butterfat content of New England milk or the butterfat
differentials specified under Order 1.
The
Compact may have an effect on the blend price if C affects total utilization in the four classes of milk specified
by Order 1, or if the total size of the pool for Order 1 is increased because
milk supplies increase as a result of higher prices. Mathematically, the blend price is equal to:
Where Pi is the classified price for class i=I,II,III,IIIA in New England, UTILi is the amount of milk used in making products of class i, t represents adjustments to the value of milk such as inventory reclassification or transportation credits, and POOLt is the sum of all producer milk pooled under the order. If the Compact increases prices for Class I products at the retail level, class I utilization may fall. This may result in the use of milk for other (usually lower-valued) products. To the extent that it occurs, this will lower the numerator of the expression for the blend price. If the size of the pool increases either because milk production in New England increases or the higher price attracts additional milk supplies from states like New York, the denominator of the expression for the blend price will become larger. Both of these potential effects would tend to lower the blend price, all other things being equal.
In
addition, the Compact over-order premium may affect the weighed average of
premiums paid by handlers for all classes of milk in the New England
States. This is supported by a
graphical analysis of estimated weighted average handler premiums for selected
states (Appendix Figure 1 below), which indicates different types of changes in
different states.
The
estimated weighted average of handler premiums paid for all classes of milk
shown in Appendix Figure 1 are calculated as the NASS-reported state all milk
price less the blend price, butterfat differentials, and the Compact over-order
premium (during the Compact period).
These estimates of handler premiums are approximate because state all
milk prices are rounded to the nearest $0.10.
In part this rounding reflects the fact that NASS data collection
procedures rely on a small number of cooperating handlers in each state. The estimated weighted average premiums show
relatively modest changes during the Compact period compared to previous years. In Vermont, handler premiums during the
Compact period are somewhat higher than prior to July 1997. In most other states, the average handler
premium is nearly the same in the years before and after the Compact.
Anecdotal
evidence from key contacts in the New England dairy industry, however,
indicates that Class I premiums initially disappeared when Compact price
regulation began in July 1997. Although
handler premiums for other classes of milk did not disappear, the decrease in
Class I handler premiums should have been reflected in a decrease in weighted
average premiums paid by handlers, but this is not observed in the data
reported by NASS. Due to the
discrepancies in the NASS and industry estimates of changes in handler premiums
with the implementation of the Compact, it is difficult to accurately assess
the Compact’s impacts on the weighted average of handler premiums during the
Compact period. As discussed below,
this complicates efforts to assess the Compact’s impact on the milk price
received by dairy producers.
Mathematically, hypotheses about the relationship between Compact over-order premiums and the blend price and handler over-order premiums can be expressed as:
When the signs of
these terms are entered into the equation relating Compact over-order premiums
to changes in the state all-milk price, that equation can be re-written as:
Where
gt is the effect of the Compact over-order premium on
the blend price and is less than zero, and hst is the effect of the
Compact over-order premium on over-order premiums paid by handlers, which may
be positive, negative, or zero.
Now,
consider the two specifications of the prices used to examine the all-milk
prices that would have prevailed without the Compact. Estimate 1 is expressed as
Which
assumes that DC = C,
or alternatively that gt=0
and hst=0. For states in which the impact of the Compact on
handler over-order premiums might be negative (i.e., the Compact premium
substitutes in part for premiums previously paid by handlers), Ct overstates the difference
between the actual price and the price that would have prevailed under the
Compact because the effects on the blend price and handler over-order premiums
are ignored. Overstating the impact of
the Compact on milk prices has the effect of overestimating the impact of the
Compact on milk production, because prices affect both milk per cow and cow
numbers. Alternatively, if average
handler premiums were positively affected by the Compact (perhaps because
higher total premiums become part of farmers’ expectations), the use of
Estimate 1 may overstate or understate the difference in prices, depending on
whether the effect of the decrease in blend price is offset by the increase in
handler over-order premiums.
In
order to provide an alternative estimate as a check on the estimate 1, which
essentially ignores the effects of the Compact on the blend price and handler
over-order premiums, estimate 2 attempts to explicitly define the impacts of
the Compact on the blend price and handler over-order premiums. Estimate 2 sums the individual components of
the state all-milk price estimated without the Compact, and is defined as:
Where
BFCst and BFDt are the elements of the
butterfat premium that are assumed not to change with the Compact over-order
premium, and
Where
The
impact the Compact on utilization in the tth
quarter of the Compact period is assumed to be
and
the initial quarter of observations is the first quarter of 1991. That is, the changes in the percentage of
class utilization are the differences between the values observed during
quarter t during the Compact period,
and the mean values of class utilization of the same quarters in the previous
six years. Note that the value of DCU is negative, so that the
estimated non-Compact blend price is larger than the actual blend price.
Handler
over-order premiums in the absence of the Compact during the tth quarter of the Compact period are
estimated as the mean value for the same quarters during 1995 to 1997:2, or
where the initial observation is the first quarter of 1991. The estimates of the non-Compact blend price and handler premiums assume that 1) mean values in previous periods are representative of what would have occurred in the absence of the Compact, and 2) all changes from mean values in previous years are attributable to the Compact. This latter assumption means that the impact of the Compact on the blend and handler premiums is likely to be overstated, because it does not include other factors that may have affected the blend price. The net effect on the price estimate of overstating the individual components depends on the relative sizes of the two, as well as on whether the effects on the blend price and handler premiums are positive or negative.