United States

Department of

Agriculture

National

Agricultural

Statistics

Service

Research and

Development Division

Washington DC 20250

RDD Research Report

RDD-09-08

October 2009

Using FSA Data to 

Improve the Prices

Received for Grain

Program

William Cecere

This paper was prepared for limited distribution to the research community outside the United States

Department of Agriculture. The views expressed herein are not necessarily those of the National

Agricultural Statistics Service or of the United States Department of Agriculture.

i

EXECUTIVE SUMMARY

This paper looks at the feasibility of using Farm Service Agency (FSA) data to reduce response

burden associated with the National Agricultural Statistics Service (NASS) prices received for

grain questionnaire. Currently, NASS surveys grain elevators on the prices paid to farmers for

commodities for the previous month and the middle of the current month. The FSA daily price

estimates on these commodities were examined to determine whether they performed as well or

better at predicting the NASS whole-month price than the NASS summarized data from the midmonth price portion of the questionnaire. If so, the NASS mid-month price section could be

removed from the survey, thus reducing respondent burden.

The NASS mid-month and whole-month price data used for this research consisted of a price for

every state involved in a given commodity’s prices received program for each month over a three

year period. The FSA data contained prices for every day of the year (except weekends and 

holidays) for every county in each of the states for a given commodity. To get an accurate statewide price to correspond to the NASS data, the county prices were weighted by production and 

then averaged. To get an FSA mid-month price, prices for the three days out of each month

closest to the 15thwere selected and averaged. Also, another FSA price was evaluated that

averaged all FSA daily prices up to the 17thof the month.

Two prediction models were examined to possibly replace the NASS mid-month prices in 

forecasting the whole-month price. These models used the FSA mid-month price and the FSA

17-day average price. The models were evaluated on their percent of variation explained (Rsquared) and their mean squared error (MSE). Model validation was performed on the best

models for each commodity using 2005 NASS and FSA data.

The best performing models were chosen for each commodity and the overall performance was

determined to be good. Models tended to be more accurate for commodities such as corn and 

soybeans with more states in their prices received programs and less accurate for ones such as

sunflower for oil with fewer. All models met their normality assumptions.

Following validation, models were assessed using mean squared prediction error (MSPE) to

compare to the models’ original MSE and examine whether there was a large variance inflation

resulting in potential bias. Also, predicted prices were compared to actual prices in order to

check for consistency. With the exception of soybeans, the NASS mid-month price

outperformed the FSA price indicators for all commodities, indicating that the mid-month

portion of the prices received questionnaire should not be removed.
ii

RECOMMENDATIONS

1. This project’s findings support that while the NASS mid-month price is sometimes

inconsistent at forecasting the whole-month price for a few commodities, it is still the

best known way to predict the NASS whole-month price. Therefore NASS should keep

the mid-month portion of the prices received questionnaire.

2. Before considering the implementation of any future models that replace the mid-month 

portion of the prices received questionnaire, determine whether this will significantly

reduce respondent burden.
1

Using FSA Data to Improve the Prices

Received Questionnaire

William Cecere

1

Abstract

The United States Department of Agriculture’s National Agricultural Statistics Service (NASS)

conducts a prices received for grain survey each month. This survey is used to assess monthly 

prices received by farms for a given commodity at grain elevators. Prediction modeling was

performed that compared NASS mid-month prices to Farm Service Agency (FSA) prices in 

order to determine which did the best job of forecasting the NASS whole-month price,

potentially reducing respondent burden if the NASS mid-month price was not surveyed. This

was performed on nine commodities, comparing three models on each.

The prediction modeling and validation testing resulted in models for several commodities that

accurately predict the mid-month price over time with low model variance and little or no bias.

However, it was determined that the FSA prices did a relatively poor job at predicting the NASS

whole-month price and should not be used.

Key Words: prediction modeling; validation; model variance.

___________________

1 William Cecere is a mathematical statistician in the USDA’s National Agricultural Statistics Service (NASS) – Research and

Development Division (RDD), located in Room 305, 3251 Old Lee Highway, Fairfax, VA 22030.
2

1. INTRODUCTION

One of the primary goals of the National Agricultural Statistics Service (NASS) is to reduce

respondent burden associated with its survey questionnaires. Another goal of the agency is to 

use available administrative data effectively to enhance or supplement NASS data. This paper

addresses both of these goals in the context of the prices received survey.

Before the 15th of each month, NASS sends out a prices received questionnaire to sampled grain

elevators in the states involved in the prices received program for a targeted group of

commodities. The commodities for which the price information is requested varies by state. The

survey collects the average price farmers received per unit (usually bushel) on certain

commodities for the middle three days of the current month, as well as the quantity and value of

commodities for the entire previous month. A goal of this paper is to evaluate the feasibility of

reducing respondent burden by eliminating the mid-month portion of the survey instrument.

Currently, the NASS mid-month numbers are used to forecast the whole month’s prices.

Therefore, if the mid-month section of the questionnaire were removed, an alternate way of

obtaining mid-month estimates to forecast whole-month prices would need to be in place. Using

similar mid-month prices from other available data sources is one possibility. To assess the

potential of such a replacement model, price data from the Farm Service Agency (FSA) were

used as a source for testing. FSA price data contain a price, primarily gathered from auctions,

for commodities each day of the month except weekends and holidays. This paper examines

ways to use these data to compare with the NASS mid-month price and determines if they could 

potentially be used to better predict the NASS whole-month price.

The commodities used for this research are corn, soybeans, barley, oats, sorghum, durum wheat,

flaxseed, sunflower for oil, and sunflower not for oil.

2. METHODS

To investigate this problem, a series of statistical models were examined to determine how to

best predict the NASS whole-month price. These models are regression models where the

response is the whole-month price and the regressors vary depending on the model. Price data

from the NASS prices received questionnaire and FSA price data were used for the years 2001-

2004.

First Model

The first model that was investigated used the NASS mid-month price as a predictor for the

whole-month price. In this model (shown below), mprice is the mid-month price and wprice is

the whole-month price. This may be used as a benchmark for any model involving FSA data,

i.e., a model with FSA variables would not be considered unless it performs at least as well as a

standard model using only NASS data.
3

Model 1:

wprice = !0 + mprice!1

Second Model

The second model evaluated uses an FSA mid-month equivalent price to predict the NASS

whole-month price. Every county in every state had an FSA daily price for each crop whether or

not the crop was actually produced in the county. Also, each county had a price for every day of

the month except weekends and holidays. To obtain an overall state price for each month from

the FSA data sets, the prices were weighted by county production using NASS county 

production estimates from 2001 through 2004. The weighted FSA county prices were then

averaged to obtain an overall state price for each date.

To get a number that was compatible with the NASS mid-month price, the three days closest to

the 15th of each month were averaged to obtain an FSA mid-month price. For example, if the

weekend fell on the 15thand 16th of a certain month then the prices from the 13th, 14th, and 17th

were averaged and called the FSA mid-month price. This is somewhat similar to way the NASS

mid-month price is determined from the questionnaire, which collects the prices received for

each commodity purchased on the three days in the middle of the month.

Once the FSA mid-month prices were averaged, the data set was merged with the NASS data set.

In this second model (indicated below), the FSA mid-month price is labeled as FSA_mprice.

Model 2:

wprice = !0 + FSA mprice!1 _

Third Model

An alternative way that the FSA price data were used was to obtain an average price over all the

days of each month up to the 17th instead of only using the middle three days. This was then

used as the predictor of the NASS whole-month price. The FSA 17 day average price is denoted 

as FSAavg_price.

Model 3: wprice = !0 + FSAavg price!1 _

To check the consistency of the best selected models for each commodity, a validation process

was performed using data from 2005. Depending on the commodity, some months were missing.

In order to assess the results, charts were used to display differences between actual and 

predicted prices for US level prices. One commonly used statistical measure of model validation 

is the mean squared prediction error (MSPE). This is calculated as the mean of the squared 

predicted errors where the predicted value,Y i

^

, is obtained using the original prices received 

model. Then, this is compared to the mean squared error (MSE) of the model. The MSE is used 

as an unbiased estimate for the variance of the original fitted regression model and the MSPE is

used as a variance estimate for the validation. If the MSPE is much higher than the MSE, then 
4

the mean squared predicted error will be used. However, if they are relatively close, then the

model is stable and not noticeably biased.

3. RESULTS

The modeling results are summarized in Table 1.

Table 1: Modeling results for the best model by commodity

Commodity Best Model Model # R-squared MSE

Corn wPrice = 0.1469 + 0.9382 mPrice 1 0.942 0.0067

Soybeans wPrice = 0.5038 + 0.9166 FSAavg_price 3 0.960 0.0296

Barley wPrice = 0.4153 + 0.8355 mPrice 1 0.662 0.0748

Oats wPrice = 0.2202 + 0.8929 mPrice 1 0.748 0.0299

Sorghum wPrice = 0.2007 + 0.9527 mPrice 1 0.867 0.047

Durum Wheat wPrice = 0.1952 + 0.9611 mPrice 1 0.840 0.056

Flaxseed wPrice = 0.1738 + 0.9806 mPrice 1 0.966 0.0714

Sunflower Oil wPrice = 1.3534 + 0.892 mPrice 1 0.857 0.7281

Sunflower Non-oil wPrice = 2.727 + 0.7943 mPrice 1 0.731 1.4525

The models tested using corn data produced relatively strong results in terms of fit. This may be

in part to the relatively large number of states (18) involved with the prices received estimation 

for corn. The models using FSA variables produced a significantly poorer fit in the R-squared

values as well as increased model variance.

Soybean model results showed much promise as well. Like corn, a larger number of states were

used in the pricing estimates when compared to the rest of the crops. Here the third model with 

the FSA 17 day average price was chosen over the NASS mid-month. The model fit is just as

good as with Model 1, while the model variance is decreased significantly. The soybean models

were the only ones where FSA variables were comparable or better than the NASS mid-month

price at predicting the NASS whole-month price.

All remaining commodities (barley, oats, sorghum, durum wheat, flaxseed, sunflower oil, and 

sunflower non-oil) showed that the FSA data did nothing in terms of improvement from the first

model. Therefore, Model 1 was selected for those commodities. Appendix A shows the results

of all models for each commodity. The normality assumptions are shown to be valid for the

chosen models by probability plots or qq plots.

The results of variance estimation after model validation are shown in Table 2. Most MSPEs are

relatively close, indicating low bias and relative stability for those models. However, it is

evident from the validation process that the durum wheat, flaxseed, and sunflower oil models are

unstable and have significant bias. The corn and soybean models look as though there may be

problems for future predictions because of the higher than expected model variance.
5

Table 2: Results of model validation

Commodity MSPE MSE

Corn 0.0129 0.0067

Soybeans 0.1087 0.0296

Barley 0.0829 0.0748

Oats 0.0363 0.0299

Sorghum 0.0494 0.047

Durum

Wheat

1.2961 0.056

Flaxseed 1.085 0.0714

Sunflower

Oil

6.4209 0.7281

Figure 1 shows the actual US price (red) and the best model’s predicted US price (blue) for

soybean prices received for several months in the calendar year of 2005. It is evident that the

predicted prices are somewhat consistent with the actual prices and appear to capture changes in

price fairly well with the exception of the last two months. The rest of the price validation plots

are in Appendix B. There was no validation done on the sunflower non-oil model due to lack of

data.

Some commodities show little change between predicted and actual US prices, indicating a

strong prediction capability. However, the models for barley, flaxseed, durum wheat, and

sunflower oil showed a significant bias and little consistency in predicting the actual US level

prices. A possible reason for the relatively poor performance of the flaxseed model may be that

there is only one state, North Dakota, involved in the modeling.
6

Figure 1: Plot of predicted vs. actual prices for soybeans (dollars per bushel)

4. CONCLUSIONS

Prices received results on all commodities are important not only to NASS but also to grain 

elevators and consumers that use NASS’s published price data. Therefore, it is essential that

published estimates from all prices received surveys be as accurate as possible.

In order to replace the mid-month section of the prices received questionnaire with auxiliary FSA

data to predict the NASS whole-month price, the model must be consistently accurate over time

and be able to reflect upcoming economic changes for the entire month. The models using the

FSA mid-month and the 17 day average price did not perform as well as the NASS mid-month 

price at predicting the NASS whole-month price for any commodity except soybeans. The best

performing model for each crop is indicated in Table 3. Many of the best fitting models are

unstable when predicting the whole-month price.

A major factor that limits the net benefit of these results is the extent to which the respondent

burden would be reduced if the mid-month section of the questionnaire were to be replaced by an

FSA indicator. It does not appear that taking a small section of a short questionnaire will

significantly reduce respondent burden. As seen in Appendix C, the questionnaire is already 

short (two pages) and the respondents would still have to be contacted for the remaining data.

As this was one of the two agency goals listed in this paper, it is important to have information as

to the nature of the respondent burden. If there would be no significant respondent burden 

reduction due to elimination of the mid-month section, then the accuracy of the estimates would 

be jeopardized while gaining very little.
7

Table 3: Best Performing Models

Crop Model # Stable after validation (Yes/No)

Corn 1 Yes

Soybean 3 No

Barley 1 Yes

Oats 1 Yes

Sorghum 1 Yes

Durum Wheat 1 No

Flaxseed 1 No

Sunflower Oil 1 No

Sunflower Non-Oil 1 N/A

5. RECOMMENDATIONS

From the results of this study, the following recommendations are made:

1. This project’s findings support that while the NASS mid-month price is sometimes

inconsistent at forecasting the whole-month price for a few commodities, it is still the

best known way to predict the NASS whole-month price. Therefore NASS should keep

the mid-month portion of the prices received questionnaire.

2. Before considering the implementation of any future models that replace the mid-month 

portion of the prices received questionnaire, determine whether this will significantly

reduce respondent burden.

6. REFERENCES

Neter, J., Kutner, M., Nachtsheim, C., & Wasserman, W. (1996). Applied Linear Statistical

Models: Fourth Edition. Boston, MA: McGraw-Hill
8

APPENDIX A: Results of model testing by commodity

*- indicates selected model

Table A1: Corn

Model number R2

(n=709)

Root

MSE

QQ plot

1 * 0.942 0.0817

wPrice = 0.1469 +0.9382 mPrice

N

709 

Rsq

0.9422

AdjRsq

0.9421

RMSE

0.0817

-3

-2

-1

0

1

2

3

Studentized Residual

-5 -4 -3 -2 -1 0 1 2 3 4

2 0.799 0.1383

3 0.824 0.1293
9

Table A2: Soybean

Model number R2

(n=593)

Root

MSE

QQ plot

1 0.968 0.262

2 0.959 0.173

3 * 0.960 0.172

Table A3: Barley

Model number R2

(n=475)

Root

MSE

QQ plot

1 * 0.662 0.2735

wPrice = 0.4153 +0.8355 mPrice

N

475 

Rsq

0.6618

AdjRsq

0.6611

RMSE

0.2735

-3

-2

-1

0

1

2

3

Studentized Residual

-5 -4 -3 -2 -1 0 1 2 3 4 5 6

2 0.25 0.4081

3 0.251 0.4076

wPrice = 0.5038 +0.9166 FSAavg_price

N

593

Rsq

0.9602

AdjRsq

0.9601

RMSE 0.1718

-3

-2

-1

0

1

2

3

Studentized Residual

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5

3
10

Table A4: Oats

Model number R2

(n=522)

Root

MSE

QQ plot

1 * 0.748 0.1729

wPrice = 0.2202 +0.8929 mPrice

N

522 

Rsq

0.7479

AdjRsq

0.7474

RMSE

0.1729

-3

-2

-1

0

1

2

3

Studentized Residual

-4 -3 -2 -1 0 1 2 3 4

2 0.328 0.278

3 0.306 0.2879

Table A5: Sorghum

Model number R2

(n=331)

Root

MSE

QQ plot

1 * 0.867 0.2169

wPrice = 0.2202 +0.8929 mPrice

N

522 

Rsq

0.7479

AdjRsq

0.7474

RMSE

0.1729

-3

-2

-1

0

1

2

3

Studentized Residual

-4 -3 -2 -1 0 1 2 3 4

2 0.754 0.2865

3 0.768 0.2782
11

Table A6: Durum Wheat

Model number R2

(n=115)

Root

MSE

QQ plot

1 * 0.840 0.2367

wPrice = 0.1952 +0.9611 mPrice

N

115 

Rsq

0.8404

AdjRsq

0.8390

RMSE

0.2367

-3

-2

-1

0

1

2

3

Studentized Residual

-5 -4 -3 -2 -1 0 1 2 3

2 0.524 0.3848

3 0.524 0.3641

Table A7: Flaxseed

Model number R2

(n=45)

Root

MSE

QQ plot

1 * 0.966 0.2673

wPrice = 0.1738 +0.9806 mprice

N

45 

Rsq

0.9663

AdjRsq

0.9655

RMSE

0.2673

-3

-2

-1

0

1

2

3

Studentized Residual

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

2 0.868 0.2756

3 0.91 0.3606
12

Table A8: Sunflower Oil

Model number R2

(n=173)

Root

MSE

QQ plot

1 * 0.857 0.7381

wPrice = 1.3534 +0.892 mPrice

N

173 

Rsq

0.8569

AdjRsq

0.8560

RMSE

0.7381

-3

-2

-1

0

1

2

3

Studentized Residual

-3 -2 -1 0 1 2 3 4 5

2 0.790 0.9459

3 0.804 0.9131

Table A9: Sunflower Non-oil

Model number R2

(n=159)

Root

MSE

QQ plot

1 * 0.7310 1.2052

wPrice = 1.3534 +0.892 mPrice

N

173 

Rsq

0.8569

AdjRsq

0.8560

RMSE

0.7381

-3

-2

-1

0

1

2

3

Studentized Residual

-3 -2 -1 0 1 2 3 4 5

2 0.426 1.6246

3 0.433 1.6146
13

APPENDIX B: Validation plots at US level by commodity, calendar year 2005

Figure B1: Plot of predicted vs. actual corn prices (dollars per bushel)

Figure B2: Plot of predicted vs. actual prices for soybeans (dollars per bushel)
14

Figure B3: Plot of predicted vs. actual prices for barley (dollars per bushel)

Figure B4: Plot of predicted vs. actual prices for durum wheat (dollars per bushel)
15

Figure B5: Plot of predicted vs. actual prices for flaxseed (dollars per bushel)

Figure B6: Plot of predicted vs. actual prices for oats (dollars per bushel)
16

Figure B7: Plot of predicted vs. actual prices for sorghum (dollars per bushel)

Figure B8: Plot of predicted vs. actual prices for sunflower oil (dollars per bushel)
17

APPENDIX C: Prices received example questionnaire
18