Impacts of the Northeast Dairy Compact on Retail Prices
Daniel
A. Lass, Mawunyo Adanu, and P. Geoffrey Allen[1]
University of Massachusetts, Amherst
Introduction
In July of 1997, the Northeast Dairy Compact Commission began instituting an over-order price premium for dairy farmers. The Compact affected the blend price that farmers receive by effectively establishing a price floor for Class I milk in the New England milk market. The announcement of the over-order premium attracted a significant amount of media attention and encouraged a great deal of speculation about the impacts on retail prices of fluid milk. When the over-order premium was instituted, retail prices increased. While the furor has died, questions remain about impacts the Compact had on retail fluid milk prices and whether observed effects were warranted given the actual effects that the Compact has had on the Class I price of milk. In the analysis below, we attempt to provide some objective assessment of the impacts the Compact has had on retail fluid milk prices in the New England region.
Our approach to assessing the impact of the compact on retail prices is as follows. First, the relationship between retail and farm prices in New England will be modeled using econometric techniques applied to historic data. The data available will be broken into two subsets; one sample will be used for estimation (the bulk of the data) and a second sample will be used for out-of-sample forecasting. Once the relationship between farm and retail prices has been estimated, we will forecast retail prices for the period immediately prior to the Compact and immediately following the Compact. Forecasts will be developed for retail prices with and without the known impacts of the Compact on the Class I price of fluid milk. Using these forecasts, we can assess the impacts the Compact should have had on retail prices and compare those predicted effects with the effects that actually occurred in the New England region.
This paper is organized as follows. First, we discuss briefly the theory of farm-to-retail price adjustments and the procedure used to model that adjustment process. We then discuss the modeling approach followed in this study. Next, our estimation results are presented and implications of the results discussed. Finally, forecasts for the period immediately prior to and following the Compact Commission action are presented and implications of the forecasts for retail prices are discussed. In the final section, we discuss some general conclusions about the relationships between farm and retail prices of fluid milk.
Modeling Retail Prices
The basic model of retail prices for fluid milk is a mark-up price model. The model presumes that the retail price
represents the farm price plus a mark-up to account for additional processing,
handling and marketing costs (Heien, et al.).
The model of retail prices can be represented by the following simple
mathematical expression:
where 
is the retail price
of fluid milk in period t, 
is the farm price of
fluid milk in period t, and 
represents
processing costs. Processing costs
might represent expenditures on labor, packaging, transportation and other
processing inputs by the processor. The
model suggests that the farm price is marked-up according to the value of
processing and marketing inputs required to bring the product to the retail
shelf. The parameters, 
, determine the degree to which the farm price and processing
costs are included in the retail price.
Kinnucan and Forker developed an important adjustment to the basic mark-up price model. They found that response of retail prices to farm prices was asymmetric with respect to rising versus falling farm prices. In other words, rising farm prices were incorporated rapidly in retail prices, while the effects of decreases in farm prices took much longer to be assimilated into the retail price. Retail prices were slow to adjust to decreases in farm prices. Kinnucan and Forker also found that falling farm prices were not incorporated in retail prices to the same degree as rising farm prices. Holding all other factors constant, retail prices would rise rapidly with rising farm prices, but would fall more slowly with falling farm prices and, for equal farm price increases and decreases, the retail price would not return to its previous level.
The results of Kinnuncan and Forker have been generally accepted and represent important considerations for any analysis of farm-to-retail price transmission. In order to incorporate their additions to the basic mark-up price model, farm prices must be separated into rising and falling categories. Rising and falling farm prices are then incorporated into the model separately to allow for the possibility of different effects on retail prices. To account for potential differences in retail price speeds of adjustment to rising versus falling farm prices, lagged values are used in addition to current period values. The basic mark-up price model in the equation above is expanded to:
where T is a time trend variable. In this model, 
, indicates a rising farm price in period t - l, and 
indicates a falling
farm price in period t - l. In practice, any number of lags might be
included. The model presented in the
equation above is completely general, allowing different lag lengths for rising
(L1) and falling (L2) farm prices. Figure 1 provides a graphic depiction of our
model. We included current price
(period t) and two lagged prices (for
periods t - 1 and t - 2) in our illustrations and the
discussions that follow.[2]
To determine whether price asymmetry exists in the structure of pricing retail milk in the New England market, we need to conduct hypothesis tests on the estimated parameters. In particular, we are interested in the following hypotheses:
The first set of hypotheses tests the speed of adjustment for rising versus falling farm prices. For example, if we find that the estimated parameter for rising current farm price is greater than the
estimated parameter for falling current farm price, then the results will provide evidence that upward adjustments in retail prices due to rising farm prices occur more rapidly than do downward adjustments due to falling farm prices. The second hypothesis will provide evidence about whether retail prices return to the same level after equivalent farm price increases and decreases. Rejection of either hypothesis, will constitute evidence of retail price asymmetry in the New England market.
In addition to these tests of asymmetry, mean lags for rising and falling farm price effects will be computed. The mean lag for rising farm price effects was computed as follows (Rao and Miller, 1971):
|
|
Where 
is the maximum lag
length for rising farm prices and 
is the mean lag for
rising farm prices. The mean lag for
falling farm prices was computed similarly.
A mean lag for rising farm prices that is smaller than the mean lag for
falling farm prices will provide additional evidence that the upward speed of
adjustment is more rapid than the downward speed of adjustment.
The final set of measures that indicate relative speeds of adjustment are the short-run and long-run elasticities of retail price with respect to rising and falling farm prices. The short and long-run elasticities were computed as follows:
; and 
.
The short-run and long-run elasticities differ in that the latter incorporates all lagged farm price effects on the retail price. Short and long-run elasticities for falling farm prices were calculated using a similar formula.
Data
Monthly time-series data were collected for the New England region for the period 1982 - 1997. The data were divided into two samples, one for estimation and a second for forecasting. The sample used for estimation included data for the period January 1982 through June 1996. The sample retained for forecasting included data for July 1996 through December 1997. This allows a period of eighteen months for forecasting, one year prior to the Compact and six months during which the Compact was in effect.
A consistent series of retail price data proved somewhat difficult to obtain. After discussions with economists responsible for regional Consumer Price Indexes and economists at the GAO, we chose to use the USDA Agricultural Marketing Service (AMS) retail price series for Boston, Massachusetts, and Hartford, Connecticut. These data were available monthly and were provided for our estimation and forecasting periods, 1982 – 1997, by the AMS staff. Changes in retail prices were determined from this monthly series and a variable measuring the accumulated changes was created for use as the dependent variable in estimation.
The farm price of milk is measured by the Class I price for the New England market. The Class I price of milk was used because we are concerned only with changes in retail fluid milk prices and the Class I price represents the cost of fluid milk as an input for the fluid milk processing industry.
Indicators of changes in the costs of processing inputs were provided by the USDA Economic Research Service. These indexes represent producer price indexes for inputs used in processing and marketing. Indexes were available for labor, packaging and transportation inputs. In addition, a composite index of these three components was provided. It is very likely that these three variables will be closely linked. Thus, it is may be difficult to identify individual effects when all three are included in the model due to problems with multicollinearity. By using the composite index, estimation problems may be avoided without encountering the problems associated with omitting important variables.
Data for two additional variables were also collected to test the validity of the Kinnucan and Forker specification. The consumer price index for nonalcoholic beverages was included to capture effects of price changes for substitutes (Bureau of Labor Statistics). Quarterly data for total generic fluid milk advertising expenditures were also included to capture two possible effects; an additional cost of marketing fluid milk and possible effects from shifts in the demand for fluid milk. The generic dairy advertising data, which was deflated by the media cost index, was Leading National Advertisers data and was provided by Dr. Harry Kaiser of the Cornell Commodity Promotion Research Program.
Econometric Estimation and Results
The work of Houck (1977) and Kinnucan and Forker (1987) was central to the model specification used in this study. Estimation of a retail price model that allowed for asymmetry was accomplished by first transforming the data into first differences. Variables were then created that measured accumulated increases or decreases for all variables (Houck, 1977). For example, in period 5 of the data set, the current cumulative rising farm price variable represents the sum of all price increases for periods 1 - 5. Cumulative change variables were created for all independent variables: farm prices, consumer prices, marketing cost indexes and advertising costs. Cumulative change variables were also created for the lagged farm prices. These accumulated increase and decrease variables were used in the estimation procedure to determine the different effects of rising versus falling farm prices.
Retail price models were estimated for Boston and Hartford using a polynomial distributed lag model and maximum likelihood methods to correct for autocorrelation. Ideally, sufficient data would be available to use separate samples for model specification, estimation and forecasting. We used U.S. level data to specify the lag structure for fluid milk. Several different polynomial lag structures were investigated; a polynomial lag of order two was selected with rising and falling farm prices lagged zero, one and two periods. We assume that both U.S. and New England retail price models follow the same lag structure.
A number of tests were applied to assess the adequacy of the Kinnucan-Forker model for these two data sets. Two specification tests were included for the residuals: the Jarque-Bera statistic for normality, and the Ljung-Box Q -statistic for white noise. A Chow test was also conducted to assess the stability of the coefficients during a period of change in dairy policy, specifically, whether the model coefficients changed after 1988 due to changes in dairy policy.
Tests for white noise
confirmed that the model was well specified; calculated values of the Q-statistics fell short of the critical
value for the 
distribution.[3] Normality tests lent empirical support for
normality of the residuals for the Boston model. The same was not true for the Hartford model residuals. For both models, the stability tests
suggested the coefficients were not different for the two time periods
considered. On the whole, the
specification tests suggest the Boston and Hartford models were well specified.
The measures of farm-to-retail price asymmetry were calculated from the estimated econometric model results. Tables 1 and 2 present summary results for the Boston and Hartford models. The estimated coefficients for the Boston econometric model show that retail prices rise rapidly in response to a current period rise in the farm price. There then appears to be an adjustment that occurs in subsequent periods after the initial rapid increase. However, the estimated coefficients for one-period and two-period lags were not statistically significant. The response to a current period decline in farm price is of a much smaller magnitude. In fact, the greatest impact of falling farm prices occurs with a one-period lag. Only the current period effect is statistically different from zero for rising farm prices, while the current period and one-period lag effects are statistically different from zero for falling farm prices.
Hypothesis tests were conducted to determine whether single period rising effects were different from single period falling effects. If the single period effects are not statistically different from zero, then there is no statistical difference between the retail price time-paths of adjustment to farm price changes. As indicated in Table 1, the direction of the price change matters for both the current period effect and the one-period lag effect. The positive calculated t-statistics indicates that the current period rising coefficient is statistically greater than the current period falling coefficient, while the negative t-statistic for the one-period lag indicates the opposite. The two-period lag coefficients were not statistically different. Thus, there is empirical evidence in the Boston retail price series that adjustments to rising farm prices is much more rapid than adjustments to falling farm prices.
The second aspect of farm-to-retail price asymmetry is the net effect after the time-paths of adjustment to both rising and falling farm prices have had time to complete their impacts. In other words, if farm prices rose, but subsequently fell to their previous level, would retail prices also rise and then return to their previous level? This hypothesis requires a comparison of the sums of the rising and falling coefficients. The sums of the rising estimated coefficients and the falling coefficients for Boston retail prices are reported in Table 1. As can be observed, there is little difference between these sums. A test of the hypothesis confirms what is apparent; there is no statistical difference between the sums of rising and falling price coefficients. Thus, while the time-path of adjustment to rising farm prices is more rapid that the time-path for falling farm prices, the net retail price effect is statistically not different from zero for equal increases and decreases in farm prices.
The same analyses (Table 2) were conducted for Hartford retail price data for the period 1982 - 1996. Individual estimated coefficients indicated only current period effects were statistically different for rising versus falling farm prices. The two current period coefficients indicated that retail prices respond more rapidly to increases in the farm price than to decreases in the farm price. The current period effect of a rising farm price was statistically greater than the current period effect of a falling farm price. Estimated coefficients for one-month and two-month lags were not found to be statistically different. We again compared sums of coefficients to determine whether retail prices return to the same level after equivalent farm price increases and decreases. While the rising sum of farm price coefficients appears greater than the falling sum, we can not conclude that the sums of the coefficients were statistically different. Thus, that aspect of farm-retail price asymmetry appears not to be present in the Hartford area.
Two additional measures of asymmetry investigated were mean lags, and short-run and long-run elasticities. These measures were presented earlier in equations (4) and (5). The mean lags were calculated as a weighted lag-length for rising price and falling farm prices. For rising farm prices, most impact occurs in the current period, which places the heaviest weight on the lag of zero. For falling farm prices, stronger effects occur for lags of one-month and two-months. The mean lags (Table 3) show that the strongest effects occur during the current period for rising farm prices in contrast to falling farm prices. Statistical tests revealed no differences in the values of the mean lag; however, it is important to remember that the current period coefficients provide weights for the lag of zero.
Short-run elasticities represent the immediate (current period) effects of a farm price increase or decrease on the retail price. The long-run elasticities represent the sum of the lagged effects. These elasticities, measures of the percentage change in retail price given a percentage increase or decrease in farm price, provide another way of considering current and aggregate effects of farm price increases and decreases. The elasticities presented in Table 4 show that the immediate effect of a farm price increase is greater than the immediate effect of a farm price decrease, while over time the aggregate effects of increases and decreases are approximately the same.
Analyses of the farm-retail price relationship in both the Boston and Hartford markets lead us to conclude that asymmetry does exist. The asymmetry appears in the form of a relatively rapid upward adjustment of retail prices in response to a increase in the farm price. Retail prices fall more gradually in response to a decrease in farm prices. However, after three periods (three months time), retail prices would return to the same level given equivalent increases and decreases in the farm price of fluid milk.
Forecasting Results
The final aspect of the farm-retail price analysis is to consider out-of-sample forecasting using the econometric model. By predicting out-of-sample, we can determine whether there appears to have been a change in the farm-retail price relationship. The data that were saved for out-of-sample forecasting include the months June, 1996, through June, 1998. The Compact was instituted in July 1997. Thus, there are 12 months prior to and 12 months following the Compact for which we can forecast.
Forecasts for Boston are presented in Figure 2 and forecasts for Hartford appear in Figure 3. The graphs of forecasts show that the model did well in predicting retail prices. Forecasting performance was measured by the mean absolute percentage error. The values were 1.16% and 0.77% for Boston and Hartford, respectively.[4]
While the models forecast well, there do appear to be immediate responses to the Compact over-order premium that the models did not predict completely. A unique policy change occurred during the forecast period, which was measured in the model by the change in farm price. Participants in the fluid milk market knew perfectly the magnitude of the change, and knew that the change was rather permanent, at last for the duration of the compact. It appears that participants may have reacted differently than they may have had the permanence of the change been uncertain. Thus, differences between predicted and actual prices in July 1997 likely reflect perfect anticipation of a well-known policy impact on farm price by processors and retailers. There was no need for processors and retailers to form expectations of changes or to make any additional adjustments during the subsequent months as the model would predict. While these individuals had such information, the econometric model did not, and the model required some time to fully adjust to the changes that occurred. Farm prices were eventually stabilized by the compact, and current and lagged changes diminished to zero as the Class I price became an administered price. The auto-regressive error correction component of the model also subsides and the model forecasts converge to the stable values of the actual retail prices. The fact that the econometric model converges on the actual prices suggests that the retail behavior does not depart permanently from the process that was predicted using the 1982-1996 data for estimation. If the retail price mark-ups continued out of the ordinary, then the model would not converge on actual retail prices.
One method of evaluating impacts of the Compact on retail prices would be to forecast retail prices with and without an administered farm milk price. The differences in forecasts would then represent the impacts of setting a price floor for fluid milk at the farm level. The forecasts presented in Figures 2 and 3 can not be used to measure effects of the Compact on retail prices. Retail prices did increase in response to the increase in farm level price caused by institution of the Compact. In forecasting with the farm price of milk at the Class I level, rather than the floor established by the compact, the error correction component of the model incorporates any differences not explained by the model into the following (next month’s) forecast. Forecasts based on Class I prices rather than the administered price include a large initial error for July 1997, the month the Compact was instituted. The error correction component of the model then incorporated that large error into all following forecasts. Thus, the with and without compact forecasts converge in just one month due to the error correction component of the model.
Our solution is to develop predictions “with the Compact” and “without the Compact” based only on the structural components of the model. These predictions are based on values for the independent variables of the model and estimated parameters listed above. Values for the marketing cost variable are the same in both predictions. The differences between the “with Compact” and “without Compact” forecasts are due the different farm-price of fluid milk. Thus, differences in predictions throughout the forecast period are due to differences between the Compact administered fluid milk price (Zone 21 fluid price set at $16.22 after June 1997) and the Class I price as announced by the Market Administrator.
The differences between predictions “with the Compact” and “without the Compact” are detailed in Table 5. The greatest Compact effects were predicted for the first month of the Compact, July 1997. The effects declined after that and are closely associated with the over-order premium. The average predicted monthly Compact effect was 6.9 cents per gallon for Boston and 5.7 cents per gallon for Hartford. Figures 4 and 5 provide a graphic depiction of the association between the over-order premiums and predicted compact effects. Numeric measures of these associations are provided by correlation coefficients. The estimated correlation coefficients were 0.98 and 0.91 for Boston and Hartford, respectively. Another method of summarizing the relationship between retail price differences and over-order premiums is through regression analysis. A simple regression model relating the Compact effect to the over-order premium predicts that a one dollar increase in the over-order premium would lead to a 5.9 cent per gallon increase in Boston retail prices during the 12 months the compact was in effect. Regression results for Hartford predicted that a one dollar increase in the over-order premium would lead to a 3.7 c ent per gallon increase in retail price.
What policy implications do these results carry? They suggest changes the Compact should have had on retail prices based on 14 years of farm-retail price behavior in the Boston and Hartford areas. These predicted Compact effects could be used in measuring the impacts of the Compact or in establishing magnitudes for reimbursements to the Women, Infants and Children (WIC) program and school milk programs. However, it is important to remember that these predictions are based upon a model developed to measure farm-retail price relationships and forecast retail prices that was estimated using historic data. The value of the predictions depends upon evaluation of the model and continuation of the historic farm-retail price relationship. The model does not capture changes that may have occurred in the farm-retail price relationship during the forecast period. However, all measures of model fit and performance suggest that the model was well specified and that it predicted the farm-retail price relationship accurately.
Summary and Conclusions
The Kinnucan and Forker econometric model fit the monthly data for both Boston and Hartford well. Specification tests indicated that the model was well specified in general and forecasts suggest that the model predicted retail prices well. Key features of the analysis of retail prices were investigations into possible asymmetric responses of retail prices to farm price changes. Farm to retail price asymmetry was investigated in two ways. First, the effects (estimated coefficients) of rising versus falling farm prices for the current period, a one-month lag and a two-month lag were compared. If retail prices increase (in response to a farm price increase) more rapidly than they fall (in response to a farm price decline), then the current period coefficient for rising farm prices should be greater than the current period coefficient for falling farm prices. In addition, the lagged effects of rising farm prices should be smaller than the lagged effects for falling farm prices, indicating that downward adjustments take more time to be completed. These individual parameter tests were conducted and empirical evidence supported the existence of this form of asymmetry in both Boston and Hartford. In particular, the current period effects of rising farm prices was greater than the current period effects for falling farm prices for both the Boston and Hartford data.
A second aspect of asymmetry is the net effect of equal farm price increases and decreases. To determine whether retail prices will eventually return to the same level after equal increases and decreases in farm prices, the sums of rising and falling farm price coefficients were compared. These tests indicated that retail prices do return to the same level upon allowing adequate time for the upward and downward adjustments. Thus, empirical evidence suggests that this second aspect of price asymmetry does not exist in Boston and Hartford.
Finally, a number of observations were saved for forecasting. These “out-of-sample” data saved for forecasting included 12 months prior to the Compact and 12 months following institution of the compact. The model forecasted actual prices well during this period; mean forecast errors were 1.6% and 0.77% for Boston and Hartford, respectively. The ability of the model to forecast actual prices suggests no structural change in the farm-retail price relationship during the out-of-sample period, June 1996 through December 1997.
We also used the econometric model to predict the magnitudes of retail price changes that should occur due to institution of the Compact. The predicted effects were smaller than expected based on the number of gallons of fluid milk per hundredweight. The predictions suggest that retail prices would not rise as much as anticipated. However, the institution of the Compact may have altered the reactions of retail prices to farm prices. One possible explanation for a change in behavior is that farm prices became more certain for processors.
In conclusion, we find that the Compact does affect retail prices. The Compact directly affects the farm price of fluid milk by establishing a floor for the farm price of fluid milk. The increases in farm price that occurred during the late summer and fall of 1997 were then transmitted to the retail price. Predicted impacts of the Compact on retail prices did not exceed those that would be expected given the farm-retail price relationship.
Table 1. Results for the Boston Econometric Retail Price Model, 1982 - 1996
|
|
Estimates |
Hypotheses |
Test Statistic |
|
Rising Farm Price Coefficients: |
|
|
2.6542 - 1.9272 - 0.390 |
|
Falling Farm Price Coefficients: |
|
||
|
Sum of Rising Coefficients: |
2.697 (0.615) |
|
0.006 |
|
Sum of Falling Coefficients: |
2.691 (0.585) |
1 Numbers in parentheses are standard errors.
2 Statistically different from zero at the 5% level of significance.
Table 2. Results for the Hartford Econometric Retail Price Model, 1982 - 1996
|
|
Estimates |
Hypotheses |
Test Statistic |
|
Rising Farm Price Coefficients: |
|
|
2.3992 -1.317 0.818 |
|
Falling Farm Price Coefficients: |
|
||
|
Sum of Rising Coefficients: |
2.509 (0.501) |
|
0.859 |
|
Sum of Falling Coefficients: |
1.908 (0.472) |
1 Numbers in parentheses are standard errors.
2 Statistically different from zero at the 5% level of significance.
Table 3. Comparison of Mean Lags for Rising and Falling Farm Price Effects
|
|
Mean Lags |
|
Statistical Results |
||
|
Rising |
Falling |
|
Test Statistic |
Conclusion1 |
|
|
Boston |
0.424 |
0.613 |
|
- 0.353 |
Fail to Reject |
|
Hartford |
0.505 |
0.624 |
|
- 0.488 |
Fail to Reject |
1 Conclusions for a t-test of the null hypothesis: rising mean lag equals falling mean lag. Tests conducted at the 5% level of significance.
Table 4. Short-Run and Long-Run Retail Price Elasticities of Farm Price Changes
|
|
Rising Elasticities |
|
Falling Elasticities |
||
|
Short-Run |
Long-Run |
|
Short-Run |
Long-Run |
|
|
Boston |
0.457 |
0.351 |
|
0.140 |
0.350 |
|
Hartford |
0.300 |
0.333 |
|
0.150 |
0.253 |
Retail Milk Price Figure 1. Conceptual Retail Milk Price Model
