Reprinted from:
Proceedings of the Beltwide Cotton Production Conference
(1992):399-402.
Ethridge, D., C. Engle, J. Brown. "An Econometric
Approach for Estimating Daily Market Prices."
Beltwide Cotton Conference, 1992.
AN ECONOMETRIC APPROACH FOR ESTIMATING DAILY MARKET PRICES
Don Ethridge, Carlos Engels, ana Jeff Brown Professor and Research Assistants, respectively, Department of Agricultural Economics, Texas Tech
University, Lubbock, TX
Abstract
Procedures for hedonic model determinations of market prices, premiums, and discounts fo~ cotton fi~er attributes have been developed for da~ly market pr~ce reporting. Model ~esul ts for t~e two Texas-Oklahoma price reporting reg~ons are descr~bed and presented and compared to the current Daily spot Cotton Quotations. Evidence to date indicates that both the model and the quotations accurately track market prices in the two markets the model provides a more detailed set of quality' premiums and discounts and avoids a systematic bias which occurs in the Quotations. Plans for further research are described.
Introduction
In cotton marketing, the system of grading cotton by its characteristics or attributes has changed from subjective measures of cotton attributes to objective measures of a larger number of attributes. Advancements in measurement technology of cotton attributes led to the development and adaptation of new, rapid, accurate, and objective measurement of the same quality attributes previously evaluated, plus measurements of se~eral important quality attributes not previously prov~c:ted. This new system, High volume Instrument (HVI) grad~n~, has been used to grade over 95 percent of the cotton ~n Texas and Oklahoma for several years and was adopted industry-wide in the U.S. 1991.
These changes in the grading system impact m~ny parts of the cotton marketing system, one of them be~ng price reporting activities. By law, the Agricultural Marketing Service (AMS), U.S.D.A. must report prices f~r all qualities of cotton in each of the seven des~gnated markets in the U.S. for each trading day. The new system will require price quotations, including premiums and discounts for the attributes of trash content, color (yellowne~s and grayness), fiber length, micronaire, strength, and length uniformity. The previous system was for grade (a composite of trash content and color), fiber length, and micronaire.
The changes in the infrastructure of cotton marketing with HVI grading will require, among other adjustments, a new system to support price reporting activiti~s. Development and testing of a new system to support da~~y market reporting has been underway for three years. Th~s new system involves applying hedonic price analysis to reporting daily spot cotton prices. The objectives of this paper are to review the hedonic price framework as developed for this application in daily price reporting and to report on the performance of the hedonic system in the only market where HVI is already in predominant use, the Texas-Oklahoma market.
The Hedonic concept of Hedonic Prices
The underlying concept of hedonic price analysis is that a product is a collection of characteristics or attributes, and that the price of the product is the aggregated prices of those characteristics. Explici t prices of products are observed in the marketplace, but implicit prices of attributes are not observable. These implicit (marginal) prices may be obtained by regressing the product's price against its attributes and then differentiating the resulting equation with respect to each attribute. The relationship may be expressed as:
where p. = explicit market price of product i, and Zn = amount of the nth attribute contained in the
product. oP./oZn is the marginal implicit price (market value) of attribute n.
Early research which focused on product attributes included Waugh's 1929 study on the effects of quality attributes of vegetables (color, size, shape) on vegetable prices and Clark and Bressler's 1938 study on strawberry and egg prices as functions of size,
CoHon Economics and Marketing Conference 399
condition, uniformity, color and variety. Many durable goods have been analyzed ,fr,om ~he hedonic price perspective (Adelman and Gr~l~c;:hes, Ladd and Zober; Dhrymes; Fettig; Freeman; palmqu~st).
Hedonic price studies relate~ t~ agricultur~l commodities and identified as hedon~c, f~rst appeared ~n 1982 (Ethridge and Davis) and are related ~o, cotton. Hedonic analyses of other agricultural commod~t~es have been subsequently performed, but will not be covered here. Subsequent analyses on cotton (Ethridge and Mathews; Hembree et al.; Ethridge and Neeper; Bowman) provided substantial prior knowledge of stru?tural forms of hedonic equations for the present analys~s.
A Dail~ Model for Cotton
In the Texas-Oklahoma regional cotton market, the use of HVI and availability of daily observations of aver~ge lot price and average values for each of ~he qual~ ty attributes provide the necessary data requ~rements to develop an hedonic pricing model for cotton. Arrangements were madEt to obtain the sales data ~rom Telcot (Ethridge) and The Network, two computer~~ed electronic spot markets, for the two Texas-Oklahoma pr~ce reporting regions (West Texas and Eas~ Texas/Oklahom~). The Telcot and Network data sets prov~de the sale pr~ce of each mixed lot the average quality attributes (trash content, color, fiber length, micron~ire, strength, and length uniformity) on each lot, lot s~ze (no. of bales), and market area (West Texas or East Texas/Oklahoma). Both systems provide the sales data on a daily basis. The Telcot system merchandises cotton from throughout Texas and Oklahoma: The N~twork operates primarily in the Texas Rolling Plains.
Prior research on hedonic cotton models provided some insight on mathematical stru?ture; Most pri~r mod~ls found that a quadratic relat~onsh~p between m~crona~re and price works consistently well. Other variables have shown a linear relationship with price when a highly aggregated data were used (Hembree et, al.: Bo~a~)! but a non-linear relationship between pr~ce and ~nd~v~dual quality attributes when disaggregated data (individual sales) were used (Ethridge and Mathews: Ethridge and Neeper,) •
Several hedonic model structures were estimated and evaluated. These models were estimated using data in two ways. One was using each day's observed mixed lot sales data, estimating relationships based on the one day of observed sales. The other approach used the five most recent days of observed sales, weighting the second most recent day's sales half as much as the most recent day's sales, the third day half as much as the second, etc. This procedure was designed to alleviate an anticipated problem of enough sales data for statistically reliable estimates on thin market days. Recognizing that lot size may affect average market values, observed sales were also weighted by lot size, the rationale being that sales of large lots may have more influence on average market values than small lots.
Based on the criteria for model selection, consideration was narrowed to two model structures after the first year's work. One was a "linear difference" model which estimated price differences from a base price as a function of quality difference from a defined set of baseline characteristics (see Bowman for an example of this structure). The other model, which was eventually selected as the better model, was the "double log" model:
1nP. = 1nao + a,1nTR. + a,1n (C. + 1) + a3 1nL. + a.M. + a.M.· + a.1nS. + a,1nU. + a.R
(this is the logarithmic transformation of
where p. price of mixed lot i in cents/lb., TR. average of the first digit of the grade code
1992 Beltwide Cotton Conferences
(proxy for trash) in mixed lot i, C, average of the second digit of the grade code
+ 1 (proxy tor color) in mixed lot i (1 is added because color codes range from 0 to 7, and InO is undefined,
L, - average staple length of cotton in mixed lot i in 32nds inch,
H, - average micronaire index reading of mixed lot i,
S, - average strength reading of cotton in lot i in grams/tex,
ul _ average length uniformity index of cotton in mixed lot i,
R _ binary indicator variable denoting region (R - 0 if market reporting region is West Texas; R 1 if market region is East Texas/Oklahoma).
This model is simpler than the linear difference model in its mathematical configuration and has some a priori conceptual appeal; the patterns of premiulIls and discounts are curvilinear rather than linear and the coefficient magnitudes suggest decreasing marginal productivity of the attributes. It also has all the quality attributes interactive in their effects on price (Le., the implicit price of each fiber attribute depends on the levels of all other quality attributes in the lot of cotton).
Estimation Results
Hodel parameters have been estimated for each trading day since late March, 1989, exceptions being the days for which there were insufficient numbers of sales to obtain reliable estimates. The rule of thuab of 5 observations per variable, or 40 observed sales on a given day, was chosen as the minimum for estimation. There have been days when no recorded sales occurred, but this occurrance has been relatively rare except for the period from March to october, 1991. However, aside fro. the thin market problem (which is little, if at all, different from the problem in providing quotations in the current system), the model usually produces intuitively reasonable estillates of base prices (price for grade 41, staple length 34, micronaire range 3.5-4.9, strength 24.5, and uniformity 80) and quality premiums and discounts. Limits were placed on parameter signs such that Q lI Q2t
and Q • .s 0 and Q" Q., Q. and Q,. ~ O. If the first Ilodel run resulted in wrong signs, the variable was deleted from the equation.
To examine the prelliums and discounts of the fiber attributes, a spreadsheet program was developed to calculate the average premium/discount for each attribute at mean quality levels in the market on each day. Examples of a portion of these for fiber strength and low .icronaire and for base prices for selected periods are shown graphically in Figures 1-3. Blank spaces in the graphs occur when there was inSUfficient sales data for aodel estimation.
It is notable that all of the large daily aovellents through tim. occurred on a light trading (thin .arket) day. Also, there appear to be movements in the general level of some premiums and discounts over ti1le. There is also more daily variation in market pre.iUBs/discounts for individual fiber attributes than many aarket observers have presumed. This last observation may be interpreted as an indicator that the market responds quickly (daily) to shifts in both supply of and demand for individual fiber attributes.
A spreadsheet was developed to present the model estimates in a tabular fora siailar to the Daily Spot Cotton Quotations (U.S. Dept. of Agriculture). Table 1 shows an example result from one day. The grade (trash, color) and staple price matrix shows the base price (cents/lb.) for grade 41, staple length 34 and pre.iu.s (+) and discounts (-) in points/lb. (1 point - .01 cent) with lIicronaire fixed at the midpoint of the 3.5-4.9 range, strength - 24.5 grams/tex, and uniformity index -80. The micronaire discounts are for base values of grade, staple, strength. and uniformity. strength premiums and discounts assume base qualities for all other attributes as well. The specific reason for developing the tabular estimates was to accommodate industry habits .
Model Evaluation
To test the model's performance, several model
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estimates and the Spot Quotations were compared to actual, observed sale prices to determine how well both track the daily spot market. (Comparison of model resul ts with the current market quotations provide no reliable benchmark because the accuracy of the Spot Quotations is not known.) A random sample of 200 from over 20,000 mixed lot sales during the period from March 31, 1989 through April 6, 1990 was drawn. The model prediction based on the regression equation (model equation prediction) was calculated for each sale from both the data set using five days of weighted data and the unweighted single day data set. The model prediction of each lot price was also calculated from the tables generated with the model (model table prediction), again with both the one-day and five-day data sets; this invol ved interpolating between discrete points in the table. The spot Quotations prediction (quotations prediction) price for each lot was calculated in the saae manner as the model table prediction, but premiums and discounts for strength and length uniformity were ignored because the spot quotations do not report these premiuas/discounts. Only 171 of the 200 sales sampled were usable because the spot quotations provided no estimates for one or more qualities in 29 sales of the sample.
Analysis of how well each estimate tracks the actual price took two forms: (a) a test of the mean difference between estimated and actual prices from each source of estimated prices and (b) regressing the price estimates from each source against the actual prices.
Average predicted and actual price differences were not statistically different from 0 at the .05 significance level for three predictors--the quotations predictions and the model and table predictions using five days at data. Because the quotations have no explicit premiums/discounts for strength and uniformity, the results suggest that these premiums/discounts are being impliCitly absorbed into the premiUllS/discounts for the other fiber properties. They may also suggest that strength and uniformity premiums and discounts are not yet having much influence on average lot prices. However, standard errors of estill8tes about the means were smallest with the model equation, indicating that the model equation esti.ates had less variation fro. actual prices than estimates with the model table (second smallest standard error) or the quotations.
The differences from actual prices with model and table predictions fro. one day of data were both statistically different from 0 at the .05 significance level. Both predictors underestimated actual prices by 0.4-0.5 cents/lb. on the average. The reason(s) for these differences is not yet known.
The purpose of regressing the predicted price from each procedure against actual prices was to evaluate potential for systematic bias with each procedure. Using a simple linear regression, an unbiased predictor should have a 0 constant term and a slope coefficient of 1; deviation from either condition ia evidence at soae type of systematic bias in the procedure. Results are presented in Table 2.
Three sets at predictiona--both model table predictions and the model equation prediction fro. one day of data-contain no evidence of consistent bias in their predictions. Both the quotations and the .odel equation from five days of data show evidence of a consistent bias, although they are in opposite directions and the model prediction bias ia about half the size of the quotations bias (Figure 4). The AMS quotations tended to underestimate low prices (prices for lower qualities) and ove:estiaate prices at the high end of the price range (pr~ces for high qualities of cotton). The model equation with five days of data erred in the opposite direction, but by about half as much. The reason that the transition froa the equation to the table removes the bias may lie in the reduced interaction between quality attributes implicit in the transforaation; the various premium/discount structures in the table are computed with other attributes held constant. This interpretation suggests that the double log structure may impose interaction where it does not exist. However, the same structure with one day of data (no weighting) exhibits no biasedness, suggesting that the source of bias aay lie in the data or its manipulation with the weighting procedures.
1992 Beltwide Cotlon Conferences
Further analysis to identify more of the nature of the biases has included correlating errors (estimated price minus actual price) with each type of price estimate with each of the fiber properties. Errors in the Spot Quotations price estimates were significantly correlated with all fiber properties except trash. None of the errors from model estimates were significantly correlated with any of the individual fiber properties. This indicates that there are systematic errors in the Spot Quotations prices which are related to color, fiber length, strength, length uniformity, and micronaire, but the source of the errors is unknown.
Automation of the System
With a view to possible implementation, the system has been automated so that users have model estimates on a timely basis. In general, the system works as follows. The two suppliers of sales data offload, via telephone connection, the day's sales from their computers to our computer during the night following the trading day. Our computer runs the regression program, then loads parameter estimates into a spreadsheet that generates tables of premiums and discounts, then FAXes of the tables are sent to the two cooperators and the AMS Market Hews Office in Memphis, TH. These groups then examine the estimates and decide how to use them . The procedures tor estimation were temporarily modified to adjust for chronically thin markets in the latter part of the 1990/91 marketing year. The 1990/91 crop was almost sold out by February, 1991, resulting in only a few sales on many days and no sales on many days. The procedure was modified by "stacking" sales for as many days as necessary to obtain 40 mixed lot sales, then running the model without weighting the data by day or lot size. That procedure generally produced unreliable estimates. The original procedures are currently being used and evaluation of the model output is progressing at the present time.
Conclusions and Future Work
Work reported here represents the first attempt to develop an econometrically-based system to support daily market price reporting. While it is not a panacea for the problems of daily price reporting, it provides estimates for a large number ot quality combinations of cotton which are repeatable and the manner in which they are obtained is objective. The hedonic model approach provides premium/discount estimates for more quality attributes than the current systea of reporting prices, and does it in a manner which can be replicated and checked. Based on comparative tests, the model can track market prices without the systematic bias in the current quotations.
The problems with the system are associated largely with thin market days, which produce few sales on which to estimate the structure of prices, premiums, and discounts. This is the same problem currently faced by market reporters, but the econometric approach makes the problem more obvious than does the current, more intuitive approach used by AMS Market News.
Several aspects of the hedonic modeling approach need further analysis, which is planned for the future. We plan to re-evaluate model performance against Daily Spot Cotton Quotations using a larger sample. We also hope to recruit more cooperators for providing sales data. Additional analysis is planned on statistical properties of estimates, as well as comparisons of behavior between model estimates and Daily Spot Cotton Quotations. Work is also being done on developing a more precise representation ot color than the second digit of the grade code currently being used. This matter of color is being approached by attempting to break color into its component parts (Rd and +b) within the hedonic framework.
Acknowledgements
The authors acknowledge the contributions of Ken Bowman, Steve Morse, Ron Cole, Billy Freeman, Melanie Gillis, Kevin Kesecker, Preston Sasser, and Dale Shaw to the work reported in the paper. They also thank Eduardo Segarra, Terry Ervin, and Phil Johnson for their suggestions on the manuscript . This research was supported by the Federal-State Market Improvement Program, Agricultural Marketing Service, USDA. Texas Tech University College of Agr. Sciences Pub. No. T-1-349.
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References
1. Adelman, I., and Z. Griliches. liOn an Index of Quality Change." Jour. Amer, stat Assn. 56(1961): 535-48
2. Bowman, K.R. "A Multi-stage Hedonic Market Model of Cotton Characteristics with Separable Supply and Demand. II Unpublished Ph.D. Dissertation, Texas Tech University, Hay 1989.
3. Clark, C.B., and R.G. Bressler. Prices as Related to Quality on the Connecticut strawberry Auctions. Bulletin 227, Univ. of Connecticut Agri. Experiment Station, 1938.
4. Dhrymes, P. "Price and Quality Changes in Consumer Capital Goods: An Empirical Study." Price Indexes and QUali~y Change; Studies in New Methods of Measurement. Z. Gr11iches, ed., Cambridge: Harvard University Press, 1971.
5. Ethridge, D.E. "A Commodi ty Market; Telcot." (1978): 177-182.
Computerized Remote-Access South. J. "gri. Econ . 10
6. Ethridge, D.E., and B. Davis. "Hedonic Price Estimation for commodities: An Application to cotton." .w~e~s~tu.~JL.~A~ggr~i"-~E~c~Q~nLc. 7(1982): 156-163.
7. Ethridge, D.E., and K.H. MatheWS. "Reliability of Spot Cotton Quotations for Price Discovery in the West Te~as cotton Market." Texas Tech Univ. College of Agr. SC1. Pub. No. T-1-212, Aug. 1983.
8. Ethridge, D.E., and J.T. Neeper. "Producer Returns from Cotton Strength and Uniformity: An Hedonoic Price Approach." South. J. Agr Econ. 19(1987): 91-97.
9. Fettig, L. "Adjusting Quality Changes, 1950-1962." 599-611.
Farm Tractor Prices for J. Farm Eeon. 45( 1963):
10. Freeman, A.M. "Hedonic Prices, Property values and Measuring Environmental Benefits: A Survey of the Issues." Scandinavian J. Econ 81(1979): 154-173.
11. Hellbree, J.F., D.E. Ethridge, and J.T. Neeper. "Market Values of Fiber Properties at Southeastern Mill Point." Textile Res. J. 56(1986): 140-144.
12. Ladd, G.W., and M. Zober. "A Model of Consumer Reaction to Product characteristics." .Jour. Consumer Research 4(1977): 89-101.
13. Palmquist, R.B. "Estimating the Demand for the Characteristics of Housing." Rey, ECOD, and stat, 66(1984): 394-404.
14. U.S. Department of Quotations." Market Agricultural Marketing issues.
Agriculture, "Daily Spot Cotton News Branch, Cotton Division, Service, Memphis, TN. Daily
15. Waugh, F. V. "Quality Factors Influencing Vegetable Prices." J, FOrm Econ. 10(1929): 185-196.
2
1.5
-0.5
Figure 1. All Fiber 12-27-89.
Daily Strength Premiums at Average Values of Attributes, West Texas Market, 3-22-89 to
1992 Beltwide Cotton Conferences
11,--------------.----,
• 0-
• C • u
10 -
9
8
5-
4 -
3 -
2
0-1------- 1 ......................... , ... "._.-......... , ....... , ............ _ ..... , ...... _. _. J-U-It ,_ ~_" 6-11-19 '_1_8') 9·20-" 10- I O-1t U-27-19
Figure 2. Low «3.5) Micronaire Discounts at Average Values of All Other Fiber Attributes, East Texas/ Oklahoma Market, 3-22-89, to 12-27-89.
8 4r-----82 80 78
76
~74 il72 0-,70 ~68 -~ 66 ~ 64'
62-
60 -58 56 -
I
5A __ .......... _ •• " ... ,., .......... , .... , ........ , ............ " ............... I._OWIM
280(C89 13rEB90 30MAR90 16~AY90 02JUl90 29AUG90 150CT90
Figure 3. Daily Base Prices, East Texas/ Oklahoma, 12-28-89 to 10-15-90.
100
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80
60
u 40 0-
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o / ,
Plode! Equa t ion ~ ~ Pred ictlon . "
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20 40 60
Actual p r i ce (c/lb.
80 100
Figure ... Prices .
Relationships Between Estimated and Actual
Cotton Economics and Marketing Conference 402
Table 1. Sample Price Schedule From the Econometric system for EstImating Prices Premiums and Di scounts
Illll sra f COHill 'IUCE SOOI.' h l .. llu" U. kpI,l_t .1 "rle.ltll. 1 (e_,,", f.u , IKt 1I''' .... lt,
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m~ 1m sm 11:.6 sus un nn 14;"1 1m un ~ IS" ... ,. m. $511 " " '~2 ,,:It
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Table 2. on actual saDgle of
Regression parameters of estimated lot prices sales prices, Texas-Oklahoma markets, based on 171 mixed lot sales.
Source of Estimated Price
Quotations
Hodel Equation, 5 days of data
Intercept
Model Table from 1.82" 5 days of data
Hodel Equation, 1 day of data
Hodel Table from -0.80-1 day of data
Slope
0.939'
0.997-
1. 006-
R'
0.93
0.92
0.91
0.88
0.90
F Value
2253.2 1
1867.01
1721.1
1189.31
1472.51
lOifferent from 0 at the .0001 significance level . 20ifferent from 1 at the .0001 significance level . SOifterent from 0 at the .01 significance level. 40ifterent from 1 at the .01 significance level. -Not different from 0 at the .10 significance level. -Not different from 1 at the .10 significance level.
1992 Beltwide Cotton Conferences
