The Yield Forecasting Program of NASS (revised January 2023)

United States
Department of
Agriculture

National
Agricultural
Statistics
Service
Methodology Division

THE YIELD
FORECASTING
PROGRAM OF
NASS

SEDMB Staff Report
Number SEDMB 23-01
May 2012
Revised January 2023

The Summary, Estimation, and
Disclosure Methodology Branch

THE YIELD FORECASTING AND ESTIMATING PROGRAM OF NASS, by the Summary,
Estimation, and Disclosure Methodology Branch, Methodology Division, National Agricultural
Statistics Service, U.S. Department of Agriculture, Washington, D.C., January 2023. NASS Staff
Report No. SEDMB 23-01.

ABSTRACT
The National Agricultural Statistics Service (NASS) is responsible for estimating production of
most crops grown in the United States. Additionally, early season forecasts are prepared for the
major crops. NASS conducts several surveys to obtain the basic data needed to fulfill this
obligation. These surveys are a mix of grower interviews and objective field visits employing
sophisticated survey sample designs and statistical methodology.
Large surveys designed to measure acreages are used to define prescreened subsampling
populations for the yield surveys. These surveys and the subsampling techniques are described,
and the data collection procedures are also outlined. Summary formulas are given, and regression
techniques employed in the forecasting process are discussed in detail.
Each survey produces indications of prospective yield which commodity specialists must interpret
to arrive at the official forecast or estimate of NASS and the USDA. This paper discusses in detail
the process of producing these indications by the Summary, Estimation, and Disclosure
Methodology Branch and outlines the review process used by the commodity specialists in the
Crops Branch. A brief discussion of acreage estimates is included to the extent that they impact
sampling and the calculation of production.

KEY WORDS
Yield, Forecast, Estimate, Regression, Outlier.

TABLE OF CONTENTS
THE YIELD FORECASTING PROGRAM OF NASS

CHAPTER 1 - OVERVIEW .........................................................................................................1

CHAPTER 2 - SAMPLE DESIGNS ............................................................................................4

CHAPTER 3 - AGRICULTURAL YIELD SURVEYS ...........................................................10

CHAPTER 4 - GENERAL YIELD FORECASTING PROCEDURES .................................20

CHAPTER 5 - CORN OBJECTIVE YIELD METHODS.......................................................28

CHAPTER 6 - SOYBEAN OBJECTIVE YIELD METHODS ...............................................44

CHAPTER 7 - COTTON OBJECTIVE YIELD METHODS .................................................60

CHAPTER 8 - WHEAT OBJECTIVE YIELD METHODS ...................................................77

CHAPTER 9 - PREPARATION OF OFFICIAL STATISTICS.............................................93

CHAPTER 1

OVERVIEW
CHAPTER 1 OVERVIEW
Introduction

Each month, the U.S. Department of Agriculture publishes crop supply and demand estimates for
the Nation and the world. These estimates are used as benchmarks in world commodity markets
because of their comprehensive nature, objectivity, and timeliness. The statistics that USDA
releases affect decisions made by businesses and governments by defining the fundamental
conditions in commodity markets. When using USDA statistics, it is helpful to understand the
forecasting and estimating procedures used and the nature and limitations of crop estimates.
Several agencies within USDA are responsible for preparing world crop statistics. The National
Agricultural Statistics Service (NASS) and the World Agricultural Outlook Board (WAOB) have
crop statistics among their primary focus. NASS forecasts and estimates U.S. crop production
based on data collected from farm operations and field observations. The WAOB is responsible
for monthly forecasts of supply and demand for major crops, both for the United States and the
world, and follows a balance sheet approach to account for supplies and utilization. The major
components of the supply and demand balance sheet are beginning stocks, production, domestic
use, trade, and end-of-season carry-out stocks. Forecasts and estimates of U.S. crop production
are independently prepared by NASS, while U.S. and foreign supply and demand forecasts are
developed jointly by several USDA agencies with WAOB coordinating.
This paper is dedicated to the crop production estimating program of NASS. A brief discussion
of acreage estimation is followed by a detailed presentation of yield forecasting and estimating.
This paper examines the NASS process from sample design to data collection to summarization
and data interpretation.
Definitions
Several variables, key to forecasting and estimating crop production, are defined below:
Planted acreage: Acreage planted for all purposes includes: (a) acreage planted that has been or
will be harvested; (b) acreage planted and replanted to the same crop (only the first planting is
included); (c) acreage planted and later plowed down, grazed, or abandoned; (d) volunteer
acreage, only if the acres will be harvested; and (e) acreage planted on land enrolled in
Government diversion programs.
Harvested acreage: Acreage harvested includes: (a) all acres already harvested or intended for
harvest and (b) the same crop acres (such as hay) harvested two or more times for the same
utilization from the same planting are included only once.
Biological Yield: The gross or total amount of a crop produced by plants expressed as a rate per
unit; for example, bushels per acre.
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CHAPTER 1

OVERVIEW

Net Harvested Yield: The portion of total crop production removed from the field, expressed as
a quantity per unit of area, and derived by deducting harvesting and other losses from the
biological yield.
Production: The total quantity of an agricultural commodity recovered or removed from the
field. In other words, net harvested production computed as harvested acres times net harvested
yield.
Preparing NASS Production Forecasts
Crop production forecasts and estimates have two components -- acres to be harvested and yield
per acre. A full program of forecasts and estimates includes determining acres planted at the
beginning of the growing season, estimates of acres to be harvested for grain, forecasts of yield
during the season, and final acres and yield after harvest. For example, corn and soybean planted
acreage estimates are made using data obtained from a survey of farmers conducted during the
first two weeks in June. Expected corn and soybean yields are obtained monthly using the Ag
Yield survey in August and two different types of yield surveys September through November.
Acres to be harvested for grain are measured in June and monitored through the season. Final
acreage and yield are measured in December.
Two types of crop forecast surveys are conducted, a grower-reported survey and objective
measurement surveys. The survey of growers, the Agricultural Yield Survey (AY), covers all
major field crops included in the NASS estimating program. Growers in the sample are asked,
monthly, to provide their assessment of yield prospects for the crops they grow. The objective
measurement surveys, known as Objective Yield (OY) Surveys, cover wheat, corn, soybeans,
and cotton. The OY surveys consist of a sample of fields in which counts and measurements are
made of plants in random plots laid out in each field.
Data collected from the yield surveys reflect seasonal growing conditions and weather events as
of the first of the month. An historical accumulation of monthly OY data collected under a
variety of growing conditions is an invaluable forecasting asset. The implicit relationship
between OY data and seasonal growing conditions is also explicitly evaluated using temperature
and precipitation relative to “normal”. Departures from normal are evaluated not only for the
current year but for the range of historic years under consideration. An assumption of "normal"
conditions is always held for the remainder of the growing season. Data collected from AY
surveys also reflects seasonal growing conditions and weather events up to the first of the month.
AY datasets have also been accumulated over time and form an integral part of yield forecasting.
In the context of AY surveys, the influence growing conditions and weather events have had
upon this year’s yield is given by the respondent’s collective perception, judgment, and
experience gathered over some given period of time.

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CHAPTER 1

OVERVIEW

NASS does not attempt to predict future weather conditions or events. Long-range weather
forecasts are not used in any forecast models and growing conditions and weather events after
the first day of the month are evaluated in the following months forecast. A significant change in
conditions or a weather event between the survey period and the report release date such as a
killing freeze, serious heat wave, beneficial rains, etc., will not alter the forecasted values based
on conditions existing on the first day of the month. NASS policy requires forecasts to be based
on conditions as of the first of the month, the period which corresponds to data collected in the
OY and AY surveys.

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CHAPTER 2

SAMPLE DESIGNS
CHAPTER 2 SAMPLE DESIGNS

Acreage and final production estimates for the major field crops are based on data collected from
a set of quarterly surveys designed to measure these items. The two yield forecasting surveys
documented in this manual use a subsample of operations and fields identified during these
quarterly surveys. Grower-reported yield surveys cover most major field crops included in the
NASS estimating program and are referred to as the Agricultural Yield Survey (AY). Objective
measurement surveys are conducted for corn, cotton, soybeans, and winter wheat and are
referred to as Objective Yield Surveys (OY).
Sampling Frames
The sample designs for these surveys utilize two different sampling frames. The area frame is
defined as the entire land mass of the United States and ensures complete coverage of the U.S.
farm population. The list frame is a roster of known farmers and ranchers and includes a profile
of each operation indicating the size of the operation and what commodities have historically
been produced. The main strengths of the area frame are its completeness and stability. The
weaknesses are its inefficiency for crops grown in small regions and its cost to build and collect
data. The list frame can be sampled more efficiently (commodity specific, if necessary) and data
can be collected using less expensive methods (e.g., mail, telephone, or web). The list frame does
not provide complete coverage of all farms and is not stable since farming arrangements are
constantly changing.
The area frame is stratified by land use for efficient sampling. All land in each State is classified
into land use categories by intensity of cultivation using a variety of map products, satellite
imagery, and computer software packages. These land use classifications range from intensely
cultivated areas to marginally cultivated grazing areas to urban areas. The land in each use
category is further divided into segments ranging in size from about 1 square mile in cultivated
areas to 0.1 square mile in urban areas. Different sampling rates are applied to different strata
with intensely cultivated land segments selected with a greater frequency than those in less
intensely cultivated areas.
All AY samples are selected from respondents to the March or June Agricultural Survey.
Objective Yield survey samples for corn, cotton, and soybeans are selected from the June Area
Survey (JAS) tracts having the commodity of interest. Objective Yield survey samples for winter
wheat are selected from March Agricultural Survey respondents with winter wheat planted for
harvest as grain.
Objective Yield samples are selected as soon as possible following the final summary of the
March Agricultural Survey or JAS. For geographic representation of the samples, the records are
first sorted by state, district, county, segment, tract, and crop. The sample select programs use
probabilities proportional to size to select a systematic random sample of acres from the reported
acres (multiplied by the inverse of the sampling fraction) of the parent survey. The selected acres
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SAMPLE DESIGNS

are used to determine sample fields. Two counting areas (plots) are then randomly selected in
each field.
The following example displays the area design for Nebraska. This frame was built with seven
land-use strata covering all 77,157 square miles. Each stratum is mutually exclusive and
independent. The stratum labeled commercial is made up of urban areas and the non-agricultural
contains mostly protected forest land. The expansion factors are inverses of the sampling
fractions. Note the allocation of the samples favors the more intensely cultivated areas with 200
of 207 segments falling in the first three strata. Strata with little or no agriculture are lightly
sampled.
Nebraska – 2019 JAS samples
Stratum
11

Square
Miles
22,878

Segment
Size
1

Segments
in Frame
22,867

Sample
Size
200

Exp
Factor
114

Stratum Definition

12

9,480

1

9,452

70

135

51-75% Cultivated

20

12,084

1

12,037

63

191

15-50% Cultivated

31

465

0.25

1,850

2

925

32

66

0.1

657

2

329

Commercial

40

5,147

2

2,567

6

428

0-15% Cultivated

42

26,775

4

6,690

12

558

50

262

pps

16

2

8

<15% Cultivated
Non-Agricultural

Total

77,157

56,136

357

>75% Cultivated

Agri-Urban

The Agricultural Survey list frame sample is selected using a multivariate probability
proportional to size (MPPS) sampling scheme. Each list frame record is assigned a measure of
size based on historic data for multiple specified commodities. The MPPS design makes it very
easy to target samples sizes for the commodities of interest. The desired number of samples for
each commodity can be controlled with a minimum overall sample size. The MPPS design
makes it easier to change samples to meet the needs of the crops program changes. The MPPS
design is a more efficient design because operations will have a more optimal probability of
selection based upon their individual commodities and size.

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CHAPTER 2

SAMPLE DESIGNS

The strata from a previously used stratified design are not being used for sampling, however they
are still used for nonresponse adjustments and item level imputation. Stratification for the
Agricultural survey sample is based on the frame data for total cropland, on-farm grain storage
capacity, and some rare or specialty crops (for each State). An example of the nonresponse
stratification for Illinois Agricultural Survey is shown below.
ILLINOIS
Agricultural Survey Strata
Strata

Boundaries

97

Capacity 500K+

95

Cropland 7,000+

79

Cropland 2,500-7,499

78

Capacity 50K-499,999

73

Sorghum 1+

72

Cropland 600-2,499

66

Capacity 10K-49,999

65

Cropland 100-599

62

Capacity 4K-9,999

Multiple frame statistical methodology has been developed that captures the efficiency of the list
frame and uses the area frame to measure incompleteness. This methodology was developed
jointly by NASS and Iowa State University with provisions to account for each farm or land area
once and only once. The survey process requires a check of all operations found in the area
sample against the entire list frame. Area operations not found on the list comprise the sample
from which incompleteness is measured.
Acreage and Final Production Surveys
The basic data for all NASS acreage estimates and final production estimates are collected on the
quarterly Agricultural Surveys. These surveys also cover the quarterly grain stocks data
requirements. NASS views the annual cycle of these surveys beginning in June with September,
December, and March completing the cycle. Each survey employs multiple frame methodology.
All surveys have list samples of about 70,000 operations. These samples are replicated, and
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SAMPLE DESIGNS

replicates are rotated from quarter to quarter with about 60 percent of the sample retained from
one quarter to the next. This scheme allows for response burden management while keeping the
ability to measure quarter to quarter change using matched reports.
The June Area survey (JAS) features complete enumeration of an area sample of about 9,000
segments. The June area sample forms a stand-alone survey from which a set of unbiased
indications are generated. They can also be married to the respective list samples to provide
another set of unbiased multiple frame indications. The September, December and March area
frame samples include only tracts that were not eligible to be included in the list frame crops
population. These tracts are referred to as non-overlap (NOL) tracts. Approximately 5,000 area
non-overlap tracts are sampled in these follow-on quarters.
Survey content differs each quarter to meet the varying requirements of the estimating program.
The June and March surveys also define subsampling populations for the yield forecasting
surveys. The following table outlines key data items collected on each survey, the yield surveys
subsampled from them, and from which frame the subsample is drawn.

Survey

Items Measured

Surveys Subsampled

June

Planted acres of spring planted crops.
Acres harvested and to be harvested for
spring crops and winter wheat.

Ag Yield (Aug. - Nov.) (list)
Corn Objective Yield
(area)
Soybean Objective Yield (area)
Cotton Objective Yield (area)

September

Final harvested acres and yield of small
grains.

None

December

Seeded acres of winter wheat (new crop).
Final harvested acres and yield for spring
crops.

None

March

Planting intentions for spring planted
crops. Winter Wheat acres for harvest as
grain.

Ag Yield (May - August) (list)
Winter Wheat OY (multiple frame)

Estimates of planted acres, made at the beginning of the season, include some acres left to be
planted at the time of the survey. Generally, these fields do get planted and planted acreage
estimates are not changed during the crop season. Occasionally, the planting season runs
extremely late causing abnormally large intentions in the data or some weather event alters
grower plans after the data are collected. When this happens, NASS may re-visit these farms
during late July to determine what was actually planted. If necessary, planted and harvested
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SAMPLE DESIGNS

acreage estimates are revised and published in the August Crop Production report.

Yield Forecast Surveys
As noted previously, there are two types of crop yield surveys conducted to obtain data for yield
forecasting, the grower-reported yield surveys or the Agricultural Yield Survey, and objective
measurement surveys, or the Objective Yield Surveys.
Agricultural Yield Surveys
Grower reported surveys, called the Agricultural Yield Surveys (AY), cover most of the field
crops estimating program. The survey covers most crop yield data needs for each State. The AY
program begins in May using a sample drawn from the list portion of the March Agricultural
Survey. This sample is used each month through August and focuses on the small grains: wheat,
oats, barley, and rye. The second AY sample is drawn from the list portion of the June
Agricultural Survey. This survey is conducted monthly from August through November and
includes numerous row crops like corn, cotton, and soybeans, as well as hay, tobacco, and
oilseeds.
The AY survey uses a multivariate probability proportionate to size (MPPS) sample design, with
list frame data used to determine a unit’s selection probability. A more detailed description of
this sample design is provided in “Chapter 3 - Agricultural Yield Surveys”.
Sample size targets are set for each commodity in AY. The overall sample size varies, depending
upon the month, from a maximum of 20,000 in August, to a minimum of 3,500 in June. In AY,
targeting is especially important for the commodities that are considered rare commodities or
specialty crops.
Objective Yield Surveys
Objective measurement surveys, called Objective Yield (OY), are conducted for corn, cotton,
soybeans, and winter wheat. These surveys are very costly and are conducted only in the top
producing States. The States in the OY program usually produce more than 75 percent of the
U.S. total. For each commodity, a series of monthly net yield forecasts culminates in a final net
yield at maturity
As noted in the previous table, all OY samples except winter wheat are drawn from an area
frame parent survey. JAS data are collected and recorded at the tract level, multiplied by the
inverse of the sampling fraction, and summed to obtain State totals. OY fields are selected
systematically from the acres of the crop of interest. In other words, OY samples are selected
with probability proportional to size, making them self-weighting samples. The detail of the
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recorded area data allows sample selection at the tract level. During the interview with the farm
operator, enumerators randomly select fields within the selected tract. Tracts with large acreages
or expansion factors may be selected for more than one sample. Separate plots are laid out for
each sample within a field up to four samples.
Winter wheat acres are collected at the farm level on the March Agricultural Survey
questionnaire, multiplied by the inverse of the sampling fraction adjusted for nonresponse, and
totaled in the summary program. Farms are selected probability proportional to size (expanded
acres). Fields are selected proportional to size within farm by the enumerator during an interview
with the farm operator making this, too, a self-weighting sample. Farms and fields within farms
may be selected more than once.

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CHAPTER 3

AGRICULTURAL YIELD SURVEYS
CHAPTER 3 AGRICULTURAL YIELD SURVEYS

The Agricultural Yield Survey (AY) collects farmer assessments of yield prospects monthly,
through the growing season. A sample of farmers who reported planting the crops of interest on a
parent survey (March or June Agricultural Surveys) are asked to predict their final yield for those
crops. The AY fills the yield forecasting needs of most field crops in the NASS estimating
program and provides data for all individually published State forecasts. In other words, this
survey provides yield indications to ensure the entire program is covered.
The AY survey uses a multivariate probability proportionate to size (MPPS) sample design, with
list frame data used to determine a unit’s probability of selection. A more basic PPS sample
design has their units selected by size depending on the proportion of the commodity of interest
the operation has in comparison with other operations on the list frame. The MPPS sample
design is similar to a traditional PPS sample design, but there are multiple commodities or frame
items used to determine a unit’s probability of selection. The MPPS design makes targeting of
samples to the desired commodities much easier, improves the sampling efficiency over the
traditional stratified design, and simplifies sample designs when there are multiple commodities.
In the MPPS sample design, a sample size is targeted for each commodity of interest that has
frame data available. A unit’s resulting probability of selection is determined by the commodity
that has the largest proportion of the total and the sample size for that commodity.
The AY samples are drawn from respondents in list strata in the March and June Agricultural
Surveys. A small grains (SG) sample, to be used May through August, is drawn from the March
Agricultural Survey from respondents who reported having a small grain crop of interest. A row
crops (RC) sample, to be used August through November, is drawn from the June Agricultural
Surveys from respondents who reported having a row crop of interest. All records to be included
in the AY SG sample were used only in the March quarter of the Agricultural Surveys (with
respect to June through March survey year). In a similar fashion, all records to be included in the
AY RC sample were used only in the June quarter of the Agricultural Surveys (with respect to
the June through March survey year). Excluded from the AY sampling are operations in the
largest (preselect) list strata, as well as the non-overlap area tracts – farms identified through our
area frame that were not on the list frame.
Since in some months (August in most states, for example) the AY sample includes operations
from both samples, a composite weighting methodology was developed. Using such an approach
allows maximum use of the information obtained from AY responses. That is, information about
SG crops that was obtained from AY RC only sample records can have that SG information used
in AY SG survey indications. Similarly, information about RC crops that was obtained from AY
SG only sample records can have that RC information used in AY RC survey indications. Under
the MPPS sample design, stratification is not used at all as an underlying component. The strata
are used, however, in computing nonresponse adjustment weights.

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AGRICULTURAL YIELD SURVEYS
Data Collection

The reference date of every AY survey is the first of the month. The data collection period must
span the first, and States are expected to collect data as close to this reference date as reasonable.
In practice, the data collection period begins around the 25th of the previous month and ends no
later than the 7th of the survey month. This amounts to about seven working days with
allowances for weekends.
Survey instruments are prepared in paper and electronic forms. Most data are collected in the
electronic form using Computer Assisted Telephone Interviewing (CATI) techniques. Many
States will collect some data by mail; however, the short data collection period limits this
activity. A small number of samples are interviewed face to face due to special reporting
arrangements or other considerations. Computer Assisted Self Interviewing (CASI) via the
internet began with the 2006 crop year.
The complete questionnaire for AY includes acres for harvest and yield for each crop of interest.
For most crops, planted acres will also be asked in either the initial month of the survey - May
for SG and August for RC, the first month the crop appears if it is not asked in the base month,
or the first time an operator is interviewed. Actual survey instruments are customized for each
month in each State. Some differences may also exist between the paper and CATI version.
Acreage responses are retained in the dataset from month to month and these items are not asked
on later interviews. The acreage questions are printed on all paper versions of the questionnaire
and enumerators are responsible for managing the flow of the interview and recognizing when to
ask the acreage questions and when to skip them. The CATI software easily tracks previously
reported data and manages the flow of the interview accordingly. The paper and CATI versions
also include a question on whether each crop has been harvested and the reported yield is final.
Once harvested, the yields for those crops are not asked on subsequent interviews but are brought
forward and used in subsequent month’s summaries. The AY survey has an additional ability to
measure harvested acreage changes during the crop year due to extreme weather conditions when
necessary. This distressed acres sub-survey estimates the current acres for harvest versus
previously reported acres for harvest and can be targeted at specific crops and States.
The small grains are surveyed May-August and the row crops August-November. The small
grains and row crops probability samples overlap in August. A single survey instrument is
prepared, and respondents are asked all questions regardless of the sampling base.
States are expected to achieve a minimum response rate of 80 percent. In order to meet this
minimum level, States are expected to conduct a telephone follow-up for operations that have not
responded. States must also monitor response by crop to determine the amount of follow-up
necessary to achieve 50 complete reports for major crops.

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Analysis

All AY data are processed through an interactive edit program as the first step in data review.
This edit performs all within-record data (micro level data) checks. Data from paper versions are
manually reviewed, key entered, and merged with CATI data. Any CASI data is also merged
with the CATI data prior to editing. The edit program checks that reported data are within
absolute limits, compares acres reported on AY and the parent survey, and compares yields
reported by the same reporting unit in consecutive months. This ensures data review is consistent
across States. States provide customized edit limits for their data. Most of the edit checks are also
performed by the CATI software during the interview which allows enumerators to probe for
additional information and correct errors when suspect values are recorded.
The next step is an across-record (macro level data) review of the raw data via the Interactive
Data Analysis and Review Tool (iDART). Reported data for all responses are listed for each crop
as well as data expanded by probability weights. This allows statisticians to examine data
distributions and to identify extreme values that may overly influence the summary results. Data
are displayed graphically by district so statisticians can also analyze yield relationships
geographically within their State. Statisticians re-examine these values before allowing them to
pass to the summary. Some follow-up may be necessary to validate a response. If the data are
deemed correct, no action is taken.
iDART displays extreme differences between surveys. In May and August, AY acreage values
are compared to acres reported on the parent survey for review. Similarly, month-to-month yield
differences are displayed beginning in June for small grains and in September for row crops.
The output is displayed in graphical and tabular form. The graphs show the frequency
distribution of the positive data while the tabulations show actual record level data
Summarization
The AY summary program is really two summaries combined. The first part is a probability
summary that applies a combination of the appropriate MPPS sample weight and a nonresponse
adjustment to produce an indication with associated measurable statistical error. The second part
is a non-probability indication which pools the complete reports from all respondents for each
crop within an Agricultural Statistics District (ASD). These respondents’ yields are then
reweighted based on their harvested acres and the acres in their respective ASD for that specific
crop. This produces an indication but, because of a lack of probability sampling design, has no
measurable error associated with it. The probability and non-probability indications are both
sorted by ASD prior to output for comparative purposes.

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Probability Summary

The probability summary computes three types of indications:
1.
2.
3.

Average expected yield.
The ratio of yields reported on consecutive AY surveys.
The ratio of any two acreage items from the AY, the parent survey, or both.

Average expected yield
Average expected yield is defined as the expected total production divided by the total acres
standing for harvest. For an individual report, production is acres for harvest times expected yield
per acre.
The nonresponse weight is calculated using the Agricultural survey stratum each respondent is
associated with and is based on the total number of expected respondents within the stratum
divided by the total number of complete respondents. The kth stratum nonresponse weight would
be calculated as:
𝑘
∑𝑁
𝑖=1 𝑤𝑀𝑃𝑃𝑆𝑖
𝑤𝑛𝑟𝑘 = 𝑛𝑘
∑𝑖=1 𝑤𝑀𝑃𝑃𝑆𝑢
where
𝑤𝑛𝑟𝑘 = nonresponse weight for stratum k
𝑁𝑘
= total sample size for stratum k
𝑛𝑘
= number of complete responses within stratum k
𝑤𝑀𝑃𝑃𝑆𝑖 = MPPS weight for sample i within stratum k
𝑤𝑀𝑃𝑃𝑆𝑢 = MPPS weight for complete responses u within stratum k
The total probability weight for the ith individual record within stratum k would then be the
product of the MPPS weight and the nonresponse weight:
𝑤𝑖 = 𝑤𝑀𝑃𝑃𝑆𝑖 𝑤𝑛𝑟𝑘
where
𝑤𝑖
= total weight for record i
𝑤𝑀𝑃𝑃𝑆𝑖 = MPPS weight for record i
𝑤𝑛𝑟𝑘 = nonresponse weight for stratum k
Production is the product of reported current month yield and harvested acreage:

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AGRICULTURAL YIELD SURVEYS
𝑝𝑖 = 𝑌𝑖 ℎ𝑖

where
𝑝𝑖
𝑌𝑖
ℎ𝑖

= production for record i
= record i yield
= acres of harvested or to be harvested for record i

Production is calculated for each ASD using the total probability weight and production for each
record, then summed to the State using the following formula:
𝑁𝐷

𝑃𝑆 = ∑ ∑
𝑗=1

𝑁𝑖𝐷
𝑖=1

𝑝𝑖𝐷 𝑤𝑖 𝑢𝑖

where
𝑃𝑆
𝑁𝐷
𝑁𝑖𝐷
𝑝𝑖𝐷
𝑤𝑖
𝑢𝑖

= production for State S
= number of ASD in State S
= total number of sampled records in ASD D
= production for record i in ASD D
= total weight for record i
= 1 if sample i is complete, else 0

Similarly, the total number of acres harvested or to be harvested is determined for each ASD and
summed to the State:
𝑁𝐷

𝐻𝑆 = ∑ ∑
𝑗=1

𝑁𝑖𝐷
𝑖=1

ℎ𝑖𝐷 𝑤𝑖 𝑢𝑖

where
𝐻𝑆
𝑁𝐷
𝑁𝑖𝐷
ℎ𝑖𝐷
𝑤𝑖
𝑢𝑖

= acres harvested or to be harvested for State S
= number of ASD in State S
= total number of sampled records in ASD D
= acres harvested or to be harvested for record i in ASD D
= total weight for record i
= 1 if sample i is complete, else 0

The average expected yield for the State would be:
𝑌̂𝑆 =

𝑃𝑆
𝐻𝑆

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where
𝑌̂𝑆
= average expected yield for State S
𝑃𝑆 𝑎𝑛𝑑 𝐻𝑆 were previously described
Ratio of Yields
The ratio of yields reported on consecutive AY surveys quantifies the change in the collective
judgment of the respondents. Computations are made by converting the current and previous
month’s sample reported yields to a sample level production value using the last reported acres
for harvest and the total weight wi . ASD and State totals are obtained for each month and the
ratio of current over previous provides the measure of change. The bth complete value is1 if
complete for current and previous month, and 0 if not complete for both months. The equation
for State S:
𝑅𝑆 =

𝑁𝑖𝐷
𝐷
∑𝑁
𝑗=1 ∑𝑖=1 𝑦𝑖𝐷𝑐 ℎ𝑖𝐷𝑐 𝑤𝑖 𝑏𝑖
𝐷
∑𝑁
∑𝑁𝑖𝐷
𝑗=1 𝑖=1 𝑦𝑖𝐷𝑝 ℎ𝑖𝐷𝑝 𝑤𝑖 𝑏𝑖

where
𝑅𝑆
𝑁𝐷
𝑁𝑖𝐷
𝑦𝑖𝐷𝑐
ℎ𝑖𝐷𝑐
𝑤𝑖
𝑏𝑖
𝑦𝑖𝐷𝑝
ℎ𝑖𝐷𝑝

= ratio of current month’s expected yield to previous month’s expected yield for
State S
= number of ASD in State S
= total number of sampled records in ASD D
= current expected yield for record i in ASD D
= current acres harvested or to be harvested for record i in ASD D
= total weight for record i
= 1 if sample i is complete for current and previous month, else 0
= previous expected yield for record i in ASD D
= previous acres harvested or to be harvested for record i in ASD D

Ratio of two acreage items
The ratio of any two acreage items from AY and the parent survey offers several key indicators.
Any ratio of AY reported acres to the acres reported on the parent survey provides a link
between the AY and the parent survey. Every AY probability sample unit matches a parent
survey response. This affords the opportunity to calculate ratios of acres reported on both
surveys. The acres used vary between crops. For most crops ratios of harvested acres are
computed, for a few crops planted acres are used, and a few crops have both. Acreage ratios
provide an assessment of the presence or absence of reporting errors in the data used to
determine the AY subsampling population. This ratio is expected to be near 1.0. Deviation from
1.0 can indicate a reporting error and/or changes in growing conditions such as delayed planting.
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In a drought year, harvested to previous harvested ratios provide an indication of increasing
abandonment. Under these conditions, reporting errors become confounded with true change in
the acreage level. The AY survey is not designed to provide clean measurement of current year
acreage changes; however, it can provide limited information about current acreage changes.
The general formula for the ratio between surveys for State S is shown below. Note that the
current AY weights apply in all instances.

𝐴𝑆 =

𝑁𝑖𝐷
𝐷
∑𝑁
𝑗=1 ∑𝑖=1 𝑎𝑖𝐷𝑐 𝑤𝑖 𝑏𝑖
𝐷
∑𝑁
∑𝑁𝑖𝐷
𝑗=1 𝑖=1 𝑎𝑖𝐷𝑝 𝑤𝑖 𝑏𝑖

where
𝐴𝑆
𝑁𝐷
𝑁𝑖𝐷
𝑎𝑖𝐷𝑐
𝑤𝑖
𝑏𝑖
𝑎𝑖𝐷𝑝

= ratio of current month’s acreage to the parent survey acreage in State S
= number of ASD in State S
= total number of sampled records in ASD D
= current acreage for record i in ASD D
= total weight for record i
= 1 if sample i is complete for current and previous month, else 0
= parent survey acreage for record i in ASD D

The formula for the harvested to planted acreage ratio for State S is:
𝑁𝑖𝐷
𝑁𝐷
𝐻𝑆 ∑𝑗=1 ∑𝑖=1 ℎ𝑖𝐷 𝑤𝑖 𝑏𝑖
=
𝑃𝑆 ∑𝑁𝐷 ∑𝑁𝑖𝐷 𝑝𝑖𝐷 𝑤𝑖 𝑏𝑖
𝑗=1 𝑖=1

where
𝐻𝑆
𝑃𝑆

𝑁𝐷
𝑁𝑖𝐷
ℎ𝑖𝐷𝑐
𝑤𝑖
𝑏𝑖
𝑝𝑖𝐷𝑝

= ratio of acres harvested to acres planted in State S
= number of ASD in State S
= total number of sampled records in ASD D
= acres harvested for record i in ASD D
= total weight for record i
= 1 if sample i is complete, else 0
= acres planted for record i in ASD D

Although all calculations in the probability summary are performed within design stratum, the
printed output presents the results by ASD. This facilitates the interpretive process by making it
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easier to compare AY results to other data sources reported by ASD. Temperature, precipitation,
and crop progress data provide additional evidence to support the AY indications to build a
complete picture of current conditions. An additional analytical benefit is gained from the ability
to see a geographic breakdown.
The summary program derives yields and ratios by expanding the sample level data and grouping
the samples by ASD. Key variables are summed to obtain ASD totals and the yields and ratios
are computed. It is important for commodity analysts to remember that even though the summary
shows the results by ASD, the calculations performed at the sample level follow the design
strata.
Non-Probability Summary
The non-probability portion of the summary treats the pooled dataset as a simple random sample.
The data are partitioned by ASD. Sample weights are 1.0 for all reporting units. Reported yields
are weighted by acres for harvest when computing ASD means. ASD means and ratios are
weighted to the State level using externally provided historical district harvested acreage
estimates.
The same three types of indications are calculated. The non-probability formulas similar to the
probability at the ASD level, with design weights (wi) eliminated. State level formulas use the
ASD level calculations and then applies external weights.
Average expected yield
Average expected yield is a weighted average of reported yields with harvest acres serving as
weights. The yield for ASD D would be calculated as follows:
𝑌̂𝐷 =

𝑖𝐷
∑𝑁
𝑖=1 𝑦𝑖𝐷 ℎ𝑖𝐷 𝑘𝑖
𝑖𝐷
∑𝑁
𝑖=1 ℎ𝑖𝐷 𝑘𝑖

where
𝑌̂𝐷
𝑁𝑖𝐷
𝑦𝑖𝐷
ℎ𝑖𝐷
𝑘𝑖

= expected yield for ASD D
= total number of sampled records in ASD D
= yield for record i in ASD D
= parent survey acreage for record i in ASD D
= 1 if sample i is complete, else 0

Ratio of Yields
Similarly, the ratio of yields reported on consecutive AY surveys is:

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𝑅𝐷 =

𝑖𝐷
∑𝑁
𝑖=1 𝑦𝑖𝐷 𝑐 ℎ𝑖𝐷 𝑘𝑖
𝑖𝐷
∑𝑁
𝑖=1 𝑦𝑖𝐷 𝑝 ℎ𝑖𝐷 𝑘𝑖

where
𝑅𝐷
= ratio of current to expected yield to previous month’s expected yield for ASD D
𝑁𝑖𝐷 , ℎ𝑖𝐷 , and 𝑘𝑖 were previously described
𝑦𝑖𝐷𝑐 = current yield for record i in ASD D
𝑦𝑖𝐷𝑝 = previous yield for record i in ASD D
Ratio of two acreage items
The ratio of acreage items between AY and the parent survey and the harvested to planted ratio
for ASD D are derived as:
𝐴𝐷 =

𝑖𝐷
∑𝑁
𝑖=1 𝑎𝑖𝐷𝑐 𝑘𝑖
𝑖𝐷
∑𝑁
𝑖=1 𝑎𝑖𝐷𝑝 𝑘𝑖

where
𝐴𝐷
𝑁𝑖𝐷
𝑎𝑖𝐷𝑐
𝑘𝑖
𝑎𝑖𝐷𝑝

= ratio of current month’s acreage to the parent survey acreage in ASD D
= total number of sampled records in ASD D
= current acreage for record i in ASD D
= 1 if sample i is complete for current and previous month, else 0
= parent survey acreage for record i in ASD D

The formula for the harvested to planted acreage ratio for ASD D is:
𝑁𝑖𝐷
ℎ𝑖𝐷 𝑘𝑖
𝐻𝐷 ∑𝑖=1
= 𝑁𝑖𝐷
𝑃𝐷 ∑ 𝑝𝑖𝐷 𝑘𝑖
𝑖=1

where
𝐻𝐷
𝑃𝐷

𝑁𝑖𝐷
ℎ𝑖𝐷𝑐
𝑘𝑖
𝑝𝑖𝐷𝑝

= ratio of acres harvested to acres planted in ASD D
= total number of sampled records in ASD D
= acres harvested for record i in ASD D
= 1 if sample i is complete, else 0
= acres planted for record i in ASD D

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State Level Estimates
The ASD level non-probability estimates shown above are weighted to the State level using
external weights. These external weights are derived from historical district harvested acreage
estimates. Let 𝐸𝐷 denote any ASD level non-probability estimate shown above. The State S level
estimate, 𝐸𝑤 is:
𝐸𝑤 =

𝐷
∑𝑁
𝑖=1 𝑤𝐷 𝐸𝐷
𝐷
∑𝑁
𝑖=1 𝑤𝐷

where
𝐸𝑤
𝑁𝐷
𝑤𝐷
𝐸𝐷

= weighted State S estimate 𝐸𝐷
= total number of ASD in State S
= external weight for ASD D
= ASD D level non-probability estimate

Survey Bias
Note that AY data are the respondents’ expected yield. The crop may not be mature and ready
for harvest for another several weeks after the respondent has been contacted. Experience has
shown these responses tend to be conservative (biased down). Under drought conditions, this
bias gets much larger as respondents’ perceptions of a crop are influenced by current weather
conditions. Therefore, the interpretation phase of the review must recognize this tendency and
factor it into the final deliberations.

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CHAPTER 4
OBJECTIVE YIELD SURVEY AND
GENERAL YIELD FORECASTING PROCEDURES

This chapter presents basic sampling, data collection, and mathematical methods commonly
employed to forecast the yield and production of any economically valuable agricultural crop.
The sampling review will emphasize the reliance objective yield survey forecasts have to a welldefined population and the traditional sampling methods employed in objective yield studies.
Data collection will focus on the plant characteristics and measures commonly collected for
objective yield programs. Finally, the mathematical methods review will center on
mathematical/statistical estimation principles common to forecasting any crop’s yield and
production.
Sampling
NASS currently expends federal funds to forecast crop yields in 24 of the lower 48 states. NASS
also supports yield forecasting for fruits and nuts in Florida and California. For most crops, yield
forecasting begins with partitioning each states’ land area into uniquely identifiable pieces called
segments. The resulting collection of segments is a complete population of all land area in each
state and is referred to as an “Area Frame”. This painstaking segmentation of land area into
uniquely identifiable segments makes possible the selection of a probability-based sample of
crop acres for objective yield (OY) field enumeration.
The most important statistical result of area frame construction is that any crop acre can be
assigned a known inclusion probability for OY studies. For annual crops like corn, NASS’s
Area Frame explicitly identifies and separates each corn acre from every other possible
utilization and makes probability calculations possible. For perennial crops like Florida citrus, a
Citrus Area Frame allows separation of citrus acres from other possible utilizations allowing
probabilities of selection to be established. The effort required to identify and separate each type
of utilization from another is a common feature of agricultural area frames. In return for the
effort, statistically defensible estimates of crop yields are obtainable.
Accurate inferences from probability-based surveys require the construction of a sampling
population and, in addition, a method to select a representative sample from that population.
Probability proportional to size (PPS) is the most common statistical method employed by NASS
for selecting crop acres to be included in objective yield studies. Since a given crop acre is most
often embedded within an individual field composed of multiple acres, PPS sampling ensures
that a proper accounting is made for the size of field. In agriculture a field is one, continuous
acreage of land devoted to the same use. Since fields are the unit of selection for objective yield
studies and because fields vary in acreage, PPS sampling is ideally suited to selecting a sample
that perfectly reflects the population characteristics of the particular crop. For example,
employing PPS sampling implies a crop field accounting for twice the percentage of total state
corn acres relative to a neighboring corn field, will also carry twice the probability of selection as
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the neighbor. The representative acre selected from a sampled field is finally accomplished with
simple random sampling. Since a selected acre is too large for complete enumeration, a selected
sample will be enumerated and expanded up to the one-acre level.
Data Collection
A full OY survey collects data at different times during the growing season. The following
paragraphs describe the data collected and the how the data are used in the forecasting and
estimating process.
During the initial OY survey, the operator is asked to verify the acreage reported in the parent
survey. This is accomplished on a field-by-field basis. Changes may be due to recording or
reporting errors in the parent survey, failure to fulfill planting intentions, or switching to other
utilizations. Other data concerning the crop, for example planting date and use of genetically
modified seed, are collected at this time. The final question asks for permission to enter the
sample field and make counts and measurements through the growing season.
The initial visit to the sampled acre involves precise selection of plants from which fruit counts,
measurements, and maturity determinations are to be made for the remainder of the growing
season. Each sample is identical in its dimensions according to crop. Extra precautions during
sample layouts ensure the exact same plants are revisited in subsequent months. Plant counts and
a variety of plant characteristics collected from these samples will be used to forecast gross yield
and the components of yield such as number of fruit and weight per fruit. The final visit obtains
all harvestable yield, which will determine final gross yield. The counts and measurements from
all visits are added to a five-year historical database which will be used to forecast gross yields
the following season.
After the farmer has harvested the sample field, postharvest gleaning data are collected. All unharvested fruit and loose grains are gleaned from specially prepared plots that are separate from
the original sample plot. The calculations from these plots will be used as a deduction from gross
yield which provides a net yield number. Before gleanings data become available, a five-year
average harvest loss is assumed for the calculation of net yield.
Models
Linear statistical models are used extensively in forecasting and estimating crop yields and
production. Other methods employed are variable plots, scattergrams, and tables. The basic
agronomic model used to conceptualize final net yield per acre is:
Y = (F * W)-L

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where
Y = the population net yield per acre,
F = the population average number of fruit per acre,
W = the population average net fruit weight per unit, in industry standard moisture, and
L = the population average harvest loss per acre.
This model can be estimated as follows:
First, forecast the average number of fruit per sample as
𝑓𝑖 = 𝛽0 + 𝛽1 𝑥𝑖 + 𝜀𝑖
Where 𝑓𝑖 is the estimate for average number of fruit for sample i, 𝛽0 and 𝛽1 are historic
coefficients estimated by ordinary least squares from five years of data, 𝑥𝑖 is some characteristic
such as plant count for sample i, and 𝜀𝑖 is an error term exhibiting classical properties. Each 𝑓𝑖 is
expanded to the acre level after the forecast is made.
Secondly, forecast the average weight of fruit per unit as:
𝑤𝑖 = 𝛽2 + 𝛽3 𝑧𝑖 + 𝜀𝑖
Where 𝑤𝑖 is the estimate for average weight of fruit per unit, e.g., weight of corn per ear, weight
of soybeans per pod, weight of cotton per boll, weight of wheat per head, etc., 𝛽2 and 𝛽3 are
historic coefficients estimated by ordinary least squares from five years of data, 𝑧𝑖 is some
characteristic such as average fruit size from sample i, and 𝜀𝑖 is an error term exhibiting classical
properties. Each 𝑤𝑖 is converted to industry standards for moisture when required.
Third, forecast the average yield loss per sample as:
𝑁𝐿

1
𝐿̅ =
∑ 𝐿𝑖
𝑁𝐿
𝑖

Where Li is the historic sample harvest loss in the ith sample expanded to one acre, then summed
from the first sample to the NL sample and divided by NL which gives 𝐿̅, the average historic loss
per acre. After the current years’ final harvest, each sample’s harvest loss reflects this years’ loss
statistics.
Finally, substitute each component back into the agronomic model:
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GENERAL YIELD FORECASTING PROCEDURES
𝑁

𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 1.

1
𝑦̅ = ∑(𝑓𝑖 ∗ 𝑤𝑖 – 𝐿̅)
𝑁
𝑖

Where 𝑦̅ is now an estimate of the population average net yield per acre in industry standard
moisture and volume.
The models used to forecast fruit count and fruit weight above may also be independently
evaluated from the general agronomic model as in:
𝑁

𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 2.

1
𝑓 ̅ = ∑ 𝑓𝑖
𝑁
𝑖

Where 𝑓 ̅ is now an estimate of the population average number of fruit per acre, or:
𝑁

𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 3.

1
𝑤
̅ = ∑ 𝑤𝑖
𝑁
𝑖

Where 𝑤
̅ is now an estimate of the population average fruit weight per unit in industry standard
moisture.
Component forecasts, represented by equations 2 and 3, are evaluated with statistical plots,
charts, and scatter grams to assist statisticians forecasting yields. Analysts will investigate
component fruit counts and weights relative to the current years growing conditions and compare
to previous years’ conditions. An in-depth examination is made relative to potential impacts of
outliers on component forecast and in turn on net yield forecasts. In addition to component
forecasting, other more esoteric relationships are examined during the course of yield
forecasting.
Regressed to Board Indications
Time series models are also estimated for each aggregate using the expression:
𝑌𝑡 = 𝛽4 + 𝛽5 𝑦̅𝑡 + 𝜀𝑡
Where 𝑌𝑡 , is the known population final net yield per acre in time period t, 𝛽4 , and 𝛽5 are
coefficients to be estimated using fifteen years of data, 𝑦̅𝑡 is the average net yield aggregate from
Equation 1 for time period t , and 𝜀𝑡 is an error term exhibiting classical properties. Individual
years’ that have absolute studentized deleted residuals (see Neter, Wasserman, and Kutner [2],
page 406) greater than three are not used for estimating 𝛽4 and 𝛽5 . Similarly, other models are
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estimated, such as:
𝐹𝑡 = 𝛽6 + 𝛽7 𝑓𝑡̅ + 𝜀𝑡
Where 𝐹𝑡 , is the known population final fruit count per acre in time period t, 𝛽6, and 𝛽7 are
historic coefficients to be estimated from fifteen years of data, 𝑓𝑡̅ is the aggregate average
number of fruit per acre from Equation 2 for time period t , and 𝜀𝑡 is an error term exhibiting
classical properties.
Strengths and Weaknesses of Each Model
The strength of the sample level models is that each model is estimated at every level of
maturity, for example the sample level model estimating fruit count per acre, as given above
was:
𝑓𝑖 = 𝛽0 + 𝛽1 𝑥𝑖 + 𝜀𝑖
which is estimated for each crop maturity classification. For example, corn has six forecasting
classes, thus up to six equations are estimated for every month and geographic area represented
in the survey. A similar set of equations are estimated for weight of fruit per unit by maturity
class. If xi is one plant characteristic used to forecast fruit count per acre, but ri is an alternative
plant characteristic, which can also predict fruit count per acre, the process repeats. This
approach to estimation allows for a high degree of complexity. The weaknesses of sample level
models are that plant measurements are very sensitive in nature and require extra caution in their
collection and the data typically exhibit large variation within and across years.
A statistical benefit of aggregate level models like Equations 1, 2, and 3 is the reduction in mean
variation of net yield, or fruit count, or fruit weight as sample sizes increases across all maturity
classes. Additionally, aggregated survey means are well correlated with general changes in
agricultural technology across time. Disaggregated sample level models cannot capture
technological change from relatively short five-year time periods, limited geographic area, and
single maturity classifications. Another advantage for aggregate models is that their dependent
variables have very small measurement error due to end of year administrative data. A noted
weakness of aggregated models is that maturity levels across many years are never equal as of a
date certain on the calendar. By their nature, aggregated models also have few degrees of
freedom.
Acreage Indications
Acreage adjustment ratios are another byproduct of objective yield surveys. Data collected in the
initial interview may be compared to data obtained in the parent survey. Acreage adjustments are
not the main purpose of OY surveys and thus are not designed for great precision but to detect
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gross changes in acreage.
There are three acreage adjustment ratios:
1. The R1 ratio is a harvest intentions ratio. For crops sampled from the area frame, it is the
ratio of total acres intended for harvest in the tract to total acres planted in the tract.
Acres intended for harvest are reported on the initial OY interview and acres planted are
reported on the base survey.
2. For cotton, the R2 is the ratio of planted acres to the planted acreage from the JAS. Thus,
the R2 measures the change in planting intentions for cotton since the JAS.
3. The abandonment ratio is used each month to adjust for samples destroyed or abandoned,
that is, "lost" samples. The numerator of the ratio equals the total number of lost
samples, and the denominator is the total number of samples, including lost samples. An
active sample is where harvest has occurred or is expected to occur.

Model Based Yield Indication
The Agricultural Statistics Board (ASB) examines each indication to decide the best
forecast in any given month. One such indication introduced in 2015 is a model-based
yield indication that combines the farmer reported survey, the objective yield survey, and
a linear covariate model with crop condition, weather data, and trend as predictor
variables. This additional indication has proved to be a valuable piece of information
when forecasting crop yields. The ASB’s procedures for selecting the official forecast has
not changed; however, this new indication provides additional insight in considering the
official forecast for any given month. Currently, winter wheat, corn, soybeans, and cotton
have this model-based yield indication. There are no plans to introduce any other crops.
Three components are used to generate this indication: farmer reported survey, objective
yield survey, and a linear regression model using crop condition, weather data, and trend
as predictor variables. The linear regression will be hitherto referred as the covariate
model. The farmer reported survey and the objective yield survey are adjusted for bias for
each state and for each month. In most cases, the farmer reported survey is adjusted
upward while the objective yield survey is adjusted downward. This bias is an average
bias comparing the final ASB yield to those respective indications for that month.
The covariate model has four predictor variables that are regressed to the final ASB yield.
The simplest of these is a trend variable. Because crop yields have shown a strong linear
trend upward, this trend variable is simply the forecasting year minus a constant for easy
calculation. Monthly average temperature and precipitation observed in the prior month
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CHAPTER 4

GENERAL YIELD FORECASTING PROCEDURES

are also used as predictors. For corn, only July weather data are used for this covariate
model because July is the most crucial month for corn development. For soybeans, July
weather data are used for the August forecast whereas August weather data are used for
the September and later forecasts. For wheat, the weather data used are specific to the
state because weather across the wheat speculative region is quite different. The final
predictor variable in this model is the crop condition measures from the NASS weekly
Crop Condition report. For corn, only the percentage of good to excellent corn in week 30
is used for all forecasting months. For soybeans, week 34 is used for each month. Wheat
varies by state. The following table shows a timeline for updating the covariate model for
wheat.

State/
FIPS
CO

8

IL

17

KS

20

MO

29

MT

30

NE

31

OH

39

OK

40

TX

48

WA

53

May Covariates
Week
Weather
#
Month
15
April
15
April
15
April
15
April
15
April
15
April
15
April
15
April
15
April
15
April

June Covariates
Week
Weather
#
Month
21
May
19
May
19
May
19
May
19
May
21
May
21
May
17
April
17
April
22
May

July Covariates
Week
Weather
#
Month
21
May
19
May
19
May
19
May
24
June
21
May
21
May
17
April
17
April
22
May

August Covariates
Week
Weather
#
Month
21
May
19
May
19
May
19
May
24
June
21
May
21
May
17
April
17
April
22
May

A model is also calculated at the speculative region level. The covariate component is
simply a weighted average of the state level covariates with weights being the harvested
acreage. The survey components are directly inputted from the summaries of those
respective surveys which generate a speculative regional yield. Because the speculative
region has less variability, each state’s model-based indication must be adjusted to match
the speculative region as a whole.
Given all three indications (the bias adjusted farmer reported survey, the bias adjusted
objective yield survey, and the covariate model), weights are then assigned to each
indication to calculate a single model-based yield indication. These weights are
determined by how well each indication does at predicting the final ASB yield. The
weights are determined in proportion to the inverse of the variance for each indication
according to the formula below:

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𝑤𝑘 =

1⁄
𝑉𝑘
1⁄
1
1
𝑉𝑂𝑌 + ⁄𝑉𝐴𝑌 + ⁄𝑉𝐶𝑂𝑉𝐴𝑅

Where k in {OY, AY, COVAR}.
Generally, the weights for the covariates and farmer reported survey are the greatest early
in the forecasting season. As the season progresses, more weight is assigned to the farmer
reported survey and the objective yield survey as less weight is attributed to the
covariates. The covariate model all but drops out in the last two months of the season as
more weight is given to each of the two survey indications.
For more information on this indication please refer to the paper “A Bayesian Hierarchical
Model for Combining Several Crop Yield Indications” by Cruze (2016).

Remotely Sensed Empirical Model Indication
The latest indication considered by the ASB, introduced in 2019, is a within-season, remotely
sensed-based corn and soybean yield estimation. This indication is made available to the ASB
from August through October and uses a linear regression model for prediction as a function of
the Normalized Difference Vegetation Index (NDVI) values accumulated over the growing
season. The NDVI measurements come from NASA’s Moderate Resolution Imaging
Spectroradiometer (MODIS) which provides a landscape-level snapshot of vegetation conditions
every eight days. The imagery is refined further by constraining it to crop-specific areas via an
ancillary bitmask image derived from the NASS Cropland Data Layer. Ultimately, the NDVI
data are averaged to the state or regional area of interest annually and related to the NASS
historically published yields going back to 2002, the start of the MODIS era, to build the
empirical model. The image handling is currently performed through the USDA supported
NASA Global Agricultural Monitoring website and statistical aspects undertaken within NASS.

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CHAPTER 5

CORN OBJECTIVE YIELD METHODS
CHAPTER 5

CORN OBJECTIVE YIELD METHODS

This chapter presents basic sampling, data collection, and mathematical methods utilized to
estimate U.S. corn yield and production. The sampling review will emphasize NASS’s unique
Area Frame and its suitability for sample selections intended to measure U.S. corn yields. Data
collection will focus on the variety of data collected and how data collection changes as corn
crop maturity changes. The mathematical methods review will center on mathematical/statistical
estimation of final corn yields utilizing measurable plant characteristics observed at specific
points during the growing season. The end results of careful sampling, data collection, and
mathematical methods are numeric indications suitable to establishment, and/or revision, of U.S.
corn acreage, yield, and production.
Sample Design
Corn Objective Yield (COY) surveys are conducted in Illinois, Indiana, Iowa, Kansas,
Minnesota, Missouri, Nebraska, Ohio, South Dakota, and Wisconsin. On average, over the last
three years, these ten states produced more than 80 percent of the U.S. corn crop. As described
in Chapter 2, NASS partitions each of these states’ land area into approximately one square mile
pieces and calls the pieces segments. The resulting collection of segments is referred to as the
“Area Frame”. This painstaking segmentation of land area into uniquely identifiable segments
makes possible the selection of a probability-based sample of U.S. corn acres.
Probability based surveys require the explicit identification and separation of all elements
contained in a population of interest. For yield surveys like COY, the most important result of
constructing a population of corn acres is that any acre of corn, in a given state, can be assigned a
known probability of selection. This result allows statistical samples to be extracted, population
parameters to be estimated, hypotheses to be tested, and inferences to be made. NASS’s Area
Frame is the vehicle that transports us from a very large population of U.S. corn acres to a
representative sample of U.S. corn acres. The sample is both statistically defensible and
economically feasible to enumerate. The procedure for identifying every U.S. corn acre is to
first, select a subsample of Area Frame segments, and secondly, to account for all agricultural
activity occurring within those segments. Each selected segment will have all its acres inspected
by and accounted for by professional enumerators with assistance from the owner/operator. In
this manner, a new listing of corn acres is constructed each year. This listing is the COY sample
population. No other purveyor of U.S. corn estimates can construct such a sample population.
Accurate inferences from a probability-based survey require the construction of a sampling
population and, in addition, a means to select a representative sample from that population. The
statistical method used to select corn acres to be included in COY is probability proportional to
size (PPS). In statistics, this method ensures a representative sample is selected when sample
elements vary in their size. A simple explanation should be given as to how sample elements in
the corn acres population can differ in size. During constructing of the corn acres sample
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CHAPTER 5

CORN OBJECTIVE YIELD METHODS

population, the explicit identification and separation of corn acres, from all other acres, is made
according to fields. In agriculture a field is one, continuous acreage of land devoted to the same
use. Therefore, the sample elements in the corn population are fields. Since fields of corn vary in
acreage, the sample selection method of PPS ensures the probability of selection is adjusted for
field size. For example, employing PPS sampling, a corn field that is twice the size of its
neighbor will also be twice as likely to be included in the sample. After the determination of
which fields are included in the sample, the representative acre is selected with simple random
sampling designed to give every acre in the selected field, an equal chance of selection. Since a
selected acre is too large for complete enumeration, a selected sample will be enumerated and
expanded up to the one-acre level.
In mid-July of each year, professional statisticians in the ten COY states train field enumerators
to properly identify and prepare selected samples for data collection. Generally, enumerators will
have many years of experience in COY data collection and are well qualified to conduct their
assignments. Practical field training is also available through relationships developed among
individual enumerators and their supervisors. Overall, the preparation for data collection is
rigorous and includes quality control processes that continue through the corn growing season. In
late July, field enumerators will begin visiting and enumerating samples and will continue
personal visits at monthly intervals throughout the season until final harvest.
Each sample consists of two units (or plots) to be utilized in forecasting final net yield per acre.
Each unit consists of two parallel 15-foot sections of row. During each visit, enumerators count
or measure each required plant characteristic, the required characteristics being determined
according to the units’ maturity level. For example, at early maturities enumerators will count
plants and measure row spacing. At later maturities, ear lengths, diameters, and weights are
measured and recorded. After each data collection period, a forecast of each unit’s final net yield
is constructed. Essentially forecasts of corn yields depend on two items: One, the current year’s
measurable plant characteristics and, two, the historic relationship between plant characteristics
measured in the past, at the same level of maturity, and final plant characteristics that result in
harvestable yield. Each item is needed to forecast a samples final net yield per acre. In cases
where one or the other of the two required items is missing, a five-year average of the final plant
characteristic is substituted. During some early forecasts there may be no plant characteristic that
NASS measures that can be related the final plant characteristic. Ear weight is the prime
example. In these cases, historic averages are used to forecast final net yield.
Data Collected
Field enumerators count and measure several items within or near the units. The size of the unit
(square feet), the number of ears, grain weight, and harvest loss. The following lists the data
items collected and what it is used to measure.
Data items used to measure the size of each unit:
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CORN OBJECTIVE YIELD METHODS

Distance between two rows (one row middle)
Distance between five rows (four row middles)
Data items used to forecast or estimate the number of ears:
Number of stalks in each row
Number of stalks with ears or silked ear shoots in each row
Number of ears and silked ear shoots in each row
Number of ears with kernel formation
Data items used to forecast or estimate grain weight:
Kernel row length from the first five ears beyond the unit in a specified row
Ear diameter at a point one inch from the butt on the same five ears beyond the unit
Weight of the first five ears in the dent stage (when the sample reaches this maturity)
Weight of shelled grain from the five dent stage ears
Moisture content of grain from the five dent stage ears
Field weight of all ears in the two units at maturity (crop cutting)
Lab weight of sample of four mature ears harvested
Weight of grain shelled from the four mature ears
Moisture content of shelled grain from the four mature ears
Data items used to estimate harvest loss:
Distance between two rows (one row middle)
Distance between five rows (four row middles)
Grain weight of ears between Row 1 and Row 3
Grain weight of loose kernels between Row 1 and Row 2
Maturity Categories
At each visit, the enumerator makes maturity assessments within the units and a maturity
category is established for the sample. If necessary, ears outside the unit may be husked to make
this determination. Forecast equations are derived using data collected during the previous 5years for each maturity in each month. The maturity definitions used by the enumerators are:
Maturity

Definition

1 - no ear shoots

No ears or ear shoots are present.

2 - pre-blister

Ear shoots are present with some silks showing. Most silks are yellow to
white in color. Spikelets contain little or no liquid.

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CHAPTER 5

CORN OBJECTIVE YIELD METHODS

3 - blister

Most silks protruding from husks are beginning to turn brown. Spikelets
have swollen and contain clear to white liquid.

4 - milk

Silks protruding from husks have turned brown and dry. Plant or shuck is
green. Ears are erect. Kernels contain a milk-like substance and show
little or no denting.

5 - dough

Shucks starting to take on a light rust color. Ears beginning to lean away
from stalks. About half the kernels are dented and contain a milk or
dough-like substance. Maturity line has not moved halfway to the cob on
a majority of the kernels.

6 - dent

Shucks are dry but not opening up. Nearly all kernels are dented.
Maturity line on kernels has not reached the cob.

7 - mature

Shucks are dry and opening up. Ears are hanging down from the stalk.
Maturity line on kernels has reached the cob.
Analysis of Raw Data

In the following sections estimation at the sample level is discussed. All sample level regression
equations are derived from the previous 5 years' survey data using multiple regression
techniques. Certain influential data points (i.e., "outliers") are excluded from the dataset prior to
deriving the coefficients. These influential data points are identified using a "deleted residual"
analysis or the "Cook's D" statistic (Belsley, Kuh, and Welsch, [4]). There is usually very little
change in the regression equations from year-to-year because roughly 80 percent of the data for
each class were used in the analysis the previous year. Classes that do change significantly from
one year to the next are usually those with very few observations. If a class has little data and a
plausible forecast equation cannot be derived, the equation from the previous year is used.
Forecasting and Estimating Number of Ears for Sample Fields
The mathematical expression for calculating the number of ears per acre from a sample plot is
straightforward, i.e., a specific count of ears per 60 linear feet and a measurement of average row
spacing for the sample results in a unique value of ears per acre. The formula for calculating the
number of ears per acre is:
ears per acre = (ears in sample plots) (43,560)
(60) (average row space)

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CORN OBJECTIVE YIELD METHODS

Where 43,560 is the number of square feet in an acre, 60 is the total length of rows in two units,
and average row space is the sum of the two 4-row space measurements divided by 8.

In the equation above, forecasts for ears per acre are dependent on the number of ears in the
sample plots. Should the ears in a sample plot not be observable due to immaturity, then a
forecast of the final number of ears before farmer harvest is required. NASS bases this prediction
on the historic relationship between observable plant characteristics and the eventual outcome for
number of ears. NASS carefully considers which plant characteristics are used to make ear count
forecasts based on the historic performance of the particular plant characteristic in question.
When samples are in maturities categories 1-4, two models are used to forecast the number of
ears in each sample. The first model uses five years of historic data to estimate the relationship
between final ears per sample and the historic stalk count from the same month.
𝑦𝑖 = 𝛽0 + 𝛽1 𝑥𝑖 + 𝜀𝑖
where xi is the number of stalks in sample i, yi is the final number of ears for sample i, and 𝜀𝑖 are
random departures from the relationship. The coefficients 𝛽0 and 𝛽1 are estimated by ordinary
least squares from data collected during the previous five years. This model produces historic
results with R2’s typically in the 80 to 90 percent range for all states. The second model uses five
years of historic data to estimate the relationship between final ears per sample and the ratio of
stalks with ears to total stalk counts per sample. This model may be represented by,
𝑦𝑖 = 𝛽2 + 𝛽3 𝑧𝑖 + 𝜖𝑖
Where zi is the number of stalks with ears or silked ear shoots (maturity category 1-4) divided by
the total number of stalks in the sample, yi is the final ratio, measured at or before maturity
category 4, of stalks with ears to total stalks and 𝜖𝑖 are random departures from the relationship.
The coefficients 𝛽2 and 𝛽3 are estimated by ordinary least squares and a forecasted number of
ears per sample is formulated by dividing the current count of stalks with ears by the predicted
value of the ratio. This model produces R2’s that are much lower than the simple stalks model
and, in addition, are generally variable across states and within states across maturity categories.
The forecast models for ears per sample are a weighted combination of the two regressions.
Model 1:

𝑦𝑖 = 𝛽0 + 𝛽1 𝑥𝑖 + 𝜀𝑖

Model 2:

𝑦𝑖 = 𝛽2 + 𝛽3 𝑧𝑖 + 𝜖𝑖

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A composite is constructed for forecasting ears per sample as follows:

𝑌̂𝑖 =

𝑅12 (𝑦̂𝑖1 ) + 𝑅22 (𝑦̂𝑖2 )
𝑅12 + 𝑅22

where, 𝑌̂𝑖 is the weighted forecast of ears per sample from Model 1 and 2, and R12 and R22 are
the multiple correlation coefficients for Model 1 and 2 respectively. Typically, the performance
of Model 1 completely dominates Model 2.
Samples classified in dough stage or higher use the actual count of ears with evidence of kernel
formation as the forecasted number of ears in the sample. Also, for the final visit to the sample,
the actual ear count is used, regardless of the maturity category.
Forecasting and Estimating Grain Weight Per Ear for Sample Fields
Corn is no exception to the general rule of objective yield surveying, i.e., successfully
forecasting fruit weight is more difficult than forecasting fruit count. Therefore, it should be no
surprise that over the course of time and program development, one model has been successfully
employed for ear count predictions whereas multiple models are utilized forecast final weight per
ear. The sensitivity of final net yield to grain weight per ear necessitates a careful consideration
of all plant characteristic which may contribute to successfully forecasting final grain weight per
ear.
When samples are in maturity categories 1 and 2 the grain weight per ear will be forecasted to
the final utilizing the 5-year historical average grain weight per ear. For the September 1 survey,
this average is computed from all samples with final lab grain weights during the last 5-years.
For the October 1 and later surveys, this average is computed using only samples that were in
maturity category 1 or 2 (no ear shoots and pre-blister stage) for October 1 or later surveys from
the last 5-years. The October 1 historic average is rarely used.
Corn samples in maturity categories 3 through 6 use historic regression models to forecast final
grain weight per ear. There are currently three models calculated that are based on the following
plant characteristics: kernel row length, ear volume, and maturity code 6 harvested ears. Kernel
row length measurements are taken just beyond the 15-foot count section of each unit. Kernel
row length measures the average length of five cobs from one inch above the butt to the end of
the cob. These measurements, collected over a series of years, can be utilized to forecast future
sample grain weights. Ear volume measures are calculated by combining kernel row length
measures with cob diameter measurements. These too are historically related to final grain
weights. Lastly, maturity code 6 harvested ears are collected just beyond the 15-foot count

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CHAPTER 5

CORN OBJECTIVE YIELD METHODS

section and are then laboratory weighed and adjusted to 15.5 percent moisture. These MC6
weights are also related to final grain weights by means of regression.

In general, the form of the three models discussed above is:
𝑤𝑡𝑖 = 𝛽0 + 𝛽1 𝑥𝑖 + 𝜀𝑖

Where xi is the average kernel row length for sample i or the computed volume measurement of
the ears in sample i, or the MC6 grain weight for sample i. wti is the final grain weight for sample
i and 𝜀𝑖 is a random departure from the relationship. The coefficients 𝛽0 and 𝛽1 are estimated by
ordinary least squares from the previous five years of data.
Parameter estimates (𝛽0 and 𝛽1) are calculated for each maturity category in each month for each
State. Each of these models exhibits significant variation but, in general, each improves in
predictive ability over the course of a growing season. R2‘s are in the 20’s, 30’s and 40’s for ear
volume and slightly less for kernel row length. The R2 for MC6 weights does show the expected
improvement given the later maturity, however, by statistician standards, has considerable
remaining variation. Ultimately, it is difficult to make both an early and confident prediction of
final grain weights per ear utilizing kernel row length, ear volume, and MC6 weights.
A sample is enumerator harvested when three or more ears of the first ears beyond a unit are
mature or the farmer intends to harvest the sample within three days. If a final harvest sample is
missed by an enumerator, its most recent forecast is perpetuated. The average field weight per
ear is an average of the combined ear weight (cob and kernels) from all ears harvested in sample
i:
𝐹𝑖𝑒𝑙𝑑 𝑊𝑡 = [

𝑇𝑜𝑡𝑎𝑙 𝑤𝑡 𝑜𝑓 𝑒𝑎𝑟𝑠
]
𝑐𝑜𝑢𝑛𝑡 𝑜𝑓 𝑒𝑎𝑟𝑠

A conversion must be made to adjust this field weight to a shelled ear weight at 15.5 percent
moisture. The conversion factor is calculated in one of two ways:
1. When lab data are available, the adjusted weight per ear is calculated by:
1 − 𝑚𝑖
𝑊𝑡
𝑤𝑠
= 𝐹𝑖𝑒𝑙𝑑 𝑊𝑡 ∗ [
] ∗ [ 100 ]
𝐸𝑎𝑟
𝑤4 − 𝑏
. 845

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34

CHAPTER 5

CORN OBJECTIVE YIELD METHODS

where, for sample i, ws is the weight of all grain shelled from four ears, w4 is the weight of four
ears (including cob), plastic bags and rubber bands (as mailed), b is the weight of plastic bags
and rubber bands, mi is the moisture content of the shelled grain, and .845 = (100 - 15.5/100)
adjusts to standard moisture.

2. If lab data are not available, a 5-year historical average shelling fraction and moisture
adjustment is applied to the average field weight.
Independent Variables used in Sample Level Forecasts and Estimates
The following table summarizes the data items used to estimate or forecast the number of ears,
weight per ear and harvest loss for each of the 7 maturities:

Maturity

Number of Ears

Weight per Ear

Harvest Loss

1 No ears or ear shoots

Stalks

5-year average

5-year average

2 Pre-blister

Stalks

5-year average

5-year average

3 Blister

Stalks

Kernel row length/
Volume

5-year average

4 Milk

Stalks

Kernel row length/
Volume

5-year average

5 Dough

Ears with kernels

Kernel row length/
Volume

5-year average

6 Dent

Ears with kernels

Kernel row length
Grain weight per ear

5-year average

7 Mature

Ears with kernels

Grain weight per ear

Realized Harvest Loss

Final

Ears with kernels

Grain weight per ear

Realized Harvest loss

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CHAPTER 5

CORN OBJECTIVE YIELD METHODS
Forecasting Yield for Sample Fields

The gross yield for sample i is calculated by:
̂𝑖 =
𝐺𝑌

̂𝑖
𝑦̂𝑖 ∗ 𝑤𝑡
56

̂ 𝑖 is the forecasted or final
Where 𝑦̂𝑖 is the forecasted or final estimate for ears per acre, 𝑤𝑡
average grain weight per ear in pounds at 15.5 percent moisture, and 56 converts the numerator
to bushel per acre
State Average Forecasts and Estimates
The sample level gross yield forecasts are averaged to the State level. Since the sample is selfweighting, the simple mean of the sample forecasts is an unbiased estimate of the State gross
yield. Therefore, gross yield for a State is given as 𝐺̅ ,
𝑁𝐺

1
𝐺̅ =
∑ 𝐺𝑖
𝑁𝐺
𝑖

where
𝐺̅ = State mean gross yield
𝑁𝐺 = number of samples with gross yield forecasts (estimates)
𝐺𝑖 = gross yield for sample i
The standard error of 𝐺̅ is:
NG

𝑆𝐺̅ = √∑
𝑖

̅ )2
(Gi − G
NG (NG − 1)

Simple means are also appropriate for Stalks per Acre, Ears per Acre, and Harvest Loss. No
weighting is required when calculating State level averages for these items:
State Average Stalks per Acre =  (Sample Field Stalks per Acre) / NG
State Average Ears per Acre =  (Sample Field Ears per Acre) / NG

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CHAPTER 5

CORN OBJECTIVE YIELD METHODS

State Average Harvest Loss =  (Sample Field Harvest Loss) / NL
The State average grain weight per ear is calculated using a weighted mean. The weighting
variable is the sample field Ears per Acre.
State Average Grain Wt per Ear =  (sample field grain weight * sample field ears per acre)
/  (sample field ears per acre)

Harvest Loss
Harvest loss data are collected from every fourth sample. If less than 10 samples have current
harvest loss data then harvest loss, L, is the 5-year average harvest loss, expressed as a
percentage of gross yield. This 5-year average is used during the early months of the forecast
season.
AVG. PERCENT LOSS = 100* (1/5) *  (Avg Loss in bu. / Avg Gross Yield in bu.)
The percentage loss is applied to the current year gross yield indication to calculate an indicated
loss per acre.
INDICATED HARVEST LOSS = AVG. PERCENT LOSS * INDICATED GROSS YIELD
Later in the season, when 10 or more samples have harvest loss data, sample harvest loss
calculations are made with the following expression:

𝐿𝑖 =

𝑚𝑖
(𝑤𝑒 + 2𝑤𝑔 ) (1 − (100
)) ∗ 43,560
(𝑅̅𝑖 )(453.6)(60)(56)(.845)

Where 𝐿𝑖 is the forecasted harvest loss of sample i, we is the weight of ears between Row 1 and
Row 3 for sample i, wg is the weight of grain between Row 1 and Row 2 for sample i, 𝑅̅𝑖 is the
average row spacing, sample i, (sum of the two 4-row space measurements divided by 8), mi is
the moisture content of the shelled grain for sample i, and the following conversion factors:
453.6= conversion of grams to pounds
43,560 = square feet per acre
60 = row feet in 2 units
56 = pounds of corn in a bushel
.845 = converts to standard moisture (15.5) percent.
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State average harvest loss is calculated using data from the individual samples as:
𝑁𝐿

1
𝐿̅ =
∑ 𝐿𝑖
𝑁𝐿
𝑖

Where Li is the harvest loss in sample i and NL is the number of harvest loss samples and
standard error of harvest loss can be understood as:
NL

𝑆𝐿̅ = √∑
𝑖

(Li − L̅)2
NL (NL − 1)

State Level Net Yield
Net yield for the State is computed by subtracting the estimated State level harvest loss from the
mean of all sample level gross yield forecasts and estimates. Thus, estimated average net yield
is:
𝑌̅ = 𝐺̅ − 𝐿̅
Where G
¯ and L
¯ are State level gross yield and state level harvest loss
The standard error of the estimate is:
𝑆𝑌̅ = √𝑆𝐺2̅ + 𝑆𝐿̅2 −

2
𝐶𝑂𝑉(𝐺, 𝐿)
𝑁𝐺

Where 𝑆𝐿̅ and 𝑆𝐺̅ were defined previously, and

NL

COV (G,L) =


1

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(Gi - G )(Li - L )
NL -1

CHAPTER 5

CORN OBJECTIVE YIELD METHODS

When less than 10 Form E's are completed, and historical average loss is used, the standard error
is:
𝑆𝑌̅ = 𝑆𝐺̅
Production for the State

Production (P) for the State is the product of estimated State level net yield and acres to be
harvested for grain:
P = (Aharv) ( 𝑌̅),
with standard error:
𝑆𝑃 = √(𝐴2ℎ𝑎𝑟𝑣 )(𝑆𝑌2̅ ) + (𝑌̅ 2 )(𝑆𝐴2ℎ𝑎𝑟𝑣 ) + (𝑆𝑌2̅ )(𝑆𝐴2ℎ𝑎𝑟𝑣 )

Gross Yield for Samples with Incomplete Data
Gross yield is forecasted from the current month's survey data. In some cases, current data are
unavailable and data from a previous month may be used to forecast gross yield, or no gross
yield is forecasted for the sample. The specific cases are discussed below.
Refusals
If the farmer refuses permission to enter the field, the sample is lost for the season. In this case
the yield for this sample is left missing. Consequently, the refused sample contributes nothing to
the State level average yield. Stated another way, the assumption is made that if the sample had
not been a refusal, its gross yield would have been equal to the State's average gross yield.
Inaccessible Samples
Occasionally, some samples are inaccessible due to scheduling or field conditions. If data from a
previous visit are available, the previous forecast is carried forward. Otherwise, the sample is
excluded from gross yield calculations. The sample must still be intended for harvest as grain.
Early Farmer Harvest

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CHAPTER 5

CORN OBJECTIVE YIELD METHODS

If a sample is harvested by the farmer before current data can be collected, the previous month's
predicted yield is brought forward.
Lost, Abandoned, Destroyed Samples
If a sample is lost, abandoned, destroyed, and so forth, no gross yield is computed for the sample.
The sample contributes nothing to the sample-level yield indication.

Removing Bias from State Level Calculations
Forecasts of state or regional yields are inherently subject to differ from the final,
administratively-determined, yield. The difference is due to weather and crop conditions yet to
be encountered at the time the forecast is made, the difference between weather and crop
conditions in the current year and the historic weather and crop conditions utilized to predict
current yields, and systematic non-sampling errors which contribute to forecast error. NASS
makes every attempt to minimize the impact of these three sources of error by means of
administratively determine final values. These final, sometimes referred to as official, values are
used as dependent variables to estimate an ordinary least squares equation with the averages
calculated from objective yield samples as the independent variable. For example, each state will
have an administratively-determined, official corn yield for all previous years. To forecast the
official corn yield for the current year, NASS regresses the objectively determined State level
average corn yields from previous years to the corresponding official corn yields. This process
provides a historical context for weather, biases, and non-sampling errors.
The regression equation is:
𝑦𝑖 = 𝛽0 + 𝛽1 𝑥𝑖 + 𝜀𝑖
where yi is the official state yield and xi is the calculated State average net yield, 𝛽0 and 𝛽1 are
historic least squares estimates, and 𝜀𝑖 is a random departure from the relationship.
Computational Examples
Sample Field Yield Examples
Suppose data have been collected for the following four samples. Calculations of gross yield
will be demonstrated. The maturity categories are defined earlier in this chapter.

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CHAPTER 5
1.

CORN OBJECTIVE YIELD METHODS

Sample 1
Maturity category
1, no ear shoots
Stalk count
79
8-row space width (ft.)
20.3
Historical 5-year avg grain weight per ear (lbs.)
0.29
Suppose regression models for samples with no ear shoots are:
Ears
Grain Wt

=
=

8.6 + 0.86 (stalk count)
Historical average grain weight

=
=

8.6 + 0.86 (79) = 76.54 ears
0.29 pounds

Then
Ears
Grain Wt

Then forecasted gross yield for sample 1 is:
Gross Yield = [ (76.54)(0.29)(43560) ] / [ (56)(15)(20.3)/(2) ] = 113.4 bu/acre

2.

Sample 2
Maturity category
Stalk count
8-row space width (ft)
Average kernel length (in.)

3, blister
81
20.3
5.8

Ears Model = 7.2 + 0.87 (stalk count)
Grain Wt = 0.23 + 0.02 (kernel row length)
Therefore,
Ears
Ears Model
Grain Wt
and

=

7.2 + 0.87 (81) = 77.67 ears

=
=

89 / [ 1.2 + 0.09 * (76 / 81) ] = 69.29
0.23 + 0.02 (5.8) = 0.346 lbs

Gross Yield = [ (73.65)(0.346)(43560) ] / [ (56)(15)(20.3)/(2) ] = 130.2 bu/acre

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CHAPTER 5
3.

CORN OBJECTIVE YIELD METHODS

Sample 3
Maturity category
Ears with kernel formation
8-row space width (ft)
Average kernel length (in.)

5, dough
70
19.5
5.2

Suppose regression models for samples in dough stage are:

Ears
Grain Wt

=
=

count of ears with kernel formation
0.10 + 0.04 (kernel row length)

=
=

70 ears
0.10 + 0.04 (5.2) = 0.308 lbs.

=

[(70)(0.308)(43560) ] / [ (56)(15)(19.5)/(2) ] = 114.7

Therefore,
Ears
Grain Wt
and
Gross Yield

bu/acre

4.

Sample 4
Maturity category
Ears with kernel formation
8-row space width
Ears husked with grain
Field weight of husked ears (lbs.)
Wt. of ears in sealed bags (grams)
Wt. of bags and rubber bands (grams)
Wt. of grain at moisture test(grams)
Moisture content (percent)

6, dent
50
20.3
22
12.1
1042.2
45.2
758.9
25.0

Suppose models for enumerator harvested samples are:
Ears
Grain Wt

=
=

Therefore,
THE YIELD FORECASTING PROGRAM OF NASS
42

count of ears with kernel formation
(field wt per ear)(fraction dry grain wt of
field wt) / (0.845)

CHAPTER 5

CORN OBJECTIVE YIELD METHODS

Ears

=

50 ears

Field weight per ear

=

12.1 / 22 = 0.55 lbs

Fraction dry weight of field weight =
=
Grain Wt
=

[ (758.9)(1-(25.0/100)) ] / [ (1042.2 - 45.2) ]
0.571
[ (0.55)(0.571) ] / 0.845 = 0.372 lbs.

And,
Gross Yield = [ (50)(0.372)(43560) ] / [ (56)(15)(20.3)/(2) ] = 95.0 bu/acre

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CHAPTER 6

SOYBEAN OBJECTIVE YIELD METHODS
CHAPTER 6

SOYBEAN OBJECTIVE YIELD METHODS

This chapter presents basic sampling, data collection, and mathematical methods utilized to
estimate U.S. soybean yield and production. The sampling review will emphasize NASS’s
unique Area Frame and its suitability for sample selections intended to measure U.S. soybean
yields. Data collection will focus on the variety of data collected and how data collection
changes as soybean crop maturity changes. The mathematical methods review will center on
mathematical/statistical estimation of final soybean yields utilizing measurable plant
characteristics observed at specific points during the growing season. The end results of careful
sampling, data collection, and mathematical methods are numeric indications suitable to
establishment, and/or revision, of U.S. soybean acreage, yield, and production.
Sample Design
Soybean Objective Yield (SOY) surveys are conducted in Arkansas, Illinois, Indiana, Iowa,
Kansas, Minnesota, Missouri, Nebraska, North Dakota, Ohio, and South Dakota. On average,
over the last three years, these eleven states produced more than 80 percent of the U.S. soybean
crop. As described in Chapter 2, NASS partitions each of these states’ land area into
approximately one square mile pieces and calls the pieces segments. The resulting collection of
segments is referred to as the “Area Frame”. This painstaking segmentation of land area into
uniquely identifiable segments makes possible the selection of a probability-based sample of
U.S. soybean acres.
Probability based surveys require the explicit identification and separation of all elements
contained in a population of interest. For yield surveys like SOY, the most important result of
constructing a population of soybean acres is that any acre of soybeans, in a given state, can be
assigned a known probability of selection. This result allows statistical samples to be extracted,
population parameters to be estimated, hypotheses to be tested, and inferences to be made.
NASS’s Area Frame is the vehicle that transports us from a very large population of U.S.
soybean acres to a representative sample of U.S. soybean acres. The sample is both statistically
defensible and economically feasible to enumerate. The procedure for identifying every U.S.
soybean acre is to first, select a subsample of Area Frame segments, and secondly, to account for
all agricultural activity occurring within those segments. Each selected segment will have all its
acres inspected by and accounted-for by professional enumerators with assistance from the
owner/operator. In this manner, a new listing of soybean acres is constructed each year. This
listing is the SOY sample population. No other purveyor of U.S. soybean estimates can construct
such a sample population.
Accurate inferences from a probability-based survey require the construction of a sampling
population and, in addition, a means to select a representative sample from that population. The
statistical method used to select soybean acres to be included in SOY is probability proportional
to size (PPS). In statistics, this method ensures a representative sample is selected when sample
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SOYBEAN OBJECTIVE YIELD METHODS

elements vary in their size. A simple explanation should be given as to how sample elements in
the soybean acres population can differ in size. During constructing of the soybean acres sample
population, the explicit identification and separation of soybean acres, from all other acres, is
made according to fields. In agriculture a field is one, continuous acreage of land devoted to the
same use. Therefore, the sample elements in the soybean population are fields. Since fields of
soybeans vary in acreage, the sample selection method of PPS ensures the probability of
selection is adjusted for field size. For example, employing PPS sampling, a soybean field that is
twice the size of its neighbor will also be twice as likely to be included in the sample. After the
determination of which fields are included in the sample, the representative acre is selected with
simple random sampling designed to give every acre in the selected field, an equal chance of
selection. Since a selected acre is too large for complete enumeration, a selected sample will be
enumerated and expanded up to the one-acre level.
In mid-July of each year, professional statisticians in the eleven SOY states train field
enumerators to properly identify and prepare selected samples for data collection. Generally,
enumerators will have many years of experience in SOY data collection and are well qualified to
conduct their assignments. Practical field training is also available through relationships
developed among individual enumerators and their supervisors. Overall, the preparation for data
collection is rigorous and includes quality control processes that continue through the soybean
growing season. In late July, field enumerators will begin visiting and enumerating samples and
will continue personal visits at monthly intervals throughout the season until final harvest.
Each sample consists of two units (or plots) to be utilized in forecasting final net yield per acre.
Each unit consists of two parallel 3.5-foot sections of row partitioned into a 3-foot section and a
6-inch section. During each visit, enumerators count or measure each required plant
characteristic, the required characteristics being determined according to the units’ maturity
level. For example, at early maturities enumerators will count plants and measure row spacing.
At later maturities, lateral branches, flowers, and pod weights are measured and recorded. After
each data collection period, a forecast of each unit’s final net yield is constructed. Essentially
forecasts of soybean yields depend on two items: One, the current year’s measurable plant
characteristics and, two, the historic relationship between plant characteristics measured in the
past, at the same level of maturity, and final plant characteristics that result in harvestable yield.
Each item is needed to forecast a samples final net yield per acre. In cases where one or the other
of the two required items is missing, a five-year average of the final plant characteristic is
substituted. During some early forecasts there may be no plant characteristic that NASS
measures that can be related the final plant characteristic. Pod weight is the prime example. In
these cases, historic averages are used to forecast final net yield.
Data Collected

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SOYBEAN OBJECTIVE YIELD METHODS

Field enumerators count and measure several items within or near the units. The size of the unit
(square feet), the number of pods, pod weight, and harvest loss. The following lists the data items
collected and what it is used to measure.
Data items used to measure the size of each unit:
Distance between two rows (one row middle)
Distance between five rows (four row middles)

Data items used to forecast or estimate the number of pods:
Number of plants in each section of each row
Number of main stem nodes in the 6-inch section
Number of lateral branches in the 6-in section
Number of dried flowers and pods in the 6-inch section
Number of pods with beans in the 6-inch section
Data items used to forecast or estimate bean weight per pod:
Weight of beans harvested by enumerator
Moisture content of beans harvested
Data items used to estimate harvest loss:
Distance between two rows (one row middle)
Distance between five rows (four row middles)
Weight of beans gleaned from harvest loss units
Moisture content of beans gleaned
Maturity Categories
At each visit, the enumerator makes maturity assessments within the units and a maturity
category is established for the sample. Forecast equations are derived using data collected
during the previous 5-years for each maturity in each month. The maturity definitions used by
the enumerators are:
Maturity 2,

Pods set, leaves still green, or earlier

Maturity 3,

Pods filled, leaves turning yellow

Maturity 4,

Pods turning color, leaves shedding

Maturity 5,

Pods brown, almost mature or mature

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SOYBEAN OBJECTIVE YIELD METHODS

In analysis, these categories are further refined into 10 forecasting categories, based on the
counts made by the enumerators. The 10 forecasting categories form a more homogeneous
grouping and are defined as:
0 No plants present in either row of the 6-inch section
1 Field maturity 2, no pods with beans in 6-inch section and the ratio
of total fruit to main stem nodes is less than .20.
2 Field maturity 2, no pods with beans in 6-inch section and the ratio
of total fruit to main stem nodes is between 0.20 and 1.75
inclusive.
3 Field maturity 2, no pods with beans in 6-inch section and the ratio
of total fruit to main stem nodes is greater than 1.75.
4 Field maturity 2, pods with beans are present in the 6-inch section
and the ratio of pods with beans to total fruit is less than 0.05.
5 Field maturity 2 and the ratio of pods with beans to total fruit is at
least 0.05 but less than 0.20.
6 Field maturity 2 and the ratio of pods with beans to total fruit is at
least 0.20 but less than 0.65.
7 Field maturity 2 and the ratio of pods with beans to total fruit is at
least 0.65 but at most 0.85.
8 Field maturity 2 and the ratio of pods with beans to total fruit is
greater than 0.85, or Field maturity 3 (and plants present in the 6inch section).
9 Field maturity 4 and plants present in the 6-inch section.
10 Field maturity 5, regardless of whether there are plants in the 6inch section.
Analysis of Raw Data
In the following sections estimation at the sample level is discussed. All sample level regression
equations are derived from the previous five years' survey data using multiple regression
techniques. Certain influential data points (i.e., "outliers") are excluded from the dataset prior to
deriving the coefficients. These influential data points are identified using a "deleted residual"
analysis or the "Cook's D" statistic (Belsley, Kuh, and Welsch, [4]). There is usually very little
change in the regression equations from year-to-year because roughly 80 percent of the data for
each class were used in the analysis the previous year. Classes that do change significantly from
one year to the next are usually those with very few observations. If a class has little data and a
plausible forecast equation cannot be derived, the equation from the previous year is used.
Forecasting Gross Yield
Forecasting soybean yields is somewhat different, but follows similar patterns, to corn and cotton
yield forecasting. The difference results from two features of soybeans: one, their typical row
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CHAPTER 6

SOYBEAN OBJECTIVE YIELD METHODS

space pattern and two, their fruit size and count. Soybean producers exhibit more variation with
respect to row spacing than either corn or cotton producers. This variation is a direct result of
soybeans flexibility to be used as either a single or double crop. Another unique feature of
soybeans that alter yield forecasting patterns is fruit size and counts. Corn ears are large and
most often singular to individual plants. Even cotton bolls are large compared to soybean pods
and cotton’s fruit counts are not unmanageable. On the other hand, individual soybeans pods are
much smaller, more prolific, and therefore, more difficult to count. In addition, other plant
characteristics for soybeans are almost unmanageable due to prolific counts, e.g., flowers. These
two differences alter the methods NASS employs to count and measure soybeans. The most
important change is a reduction in the size of the count area for soybean samples. Another
change is the conversion of all soybean sample measures to a common denominator of 18 square
feet.
The forecast for soybean yield per acre is expressed as follows:
Gross yield per acre = (pods per 18 square feet)*(weight per pod)* (43,560)
(18)(453.6)(60)
Where 43,560 is the number of square feet in an acre, 60 converts pound of beans to bushels, and
453.6 converts grams to pounds.
In the equation above, forecasts for gross yield per acre depends on the number of pods per 18
square feet and the weight per pod. Should the pods per 18 square feet in a sample plot be
unobservable due to immaturity, then stochastic models are employed to “predict” the number of
future pods per 18 square feet. The prediction is based on the historic relationship between past
observable plant characteristics and the eventual outcome for pods. These historic models are
stochastic because a range of potential pods per 18 square feet exists for each value of the
observable plant characteristic. NASS gives careful consideration to plant characteristics that are
proven performers in terms of prediction and forecasting. Table 1 illustrates the plant
characteristics utilized for predicting gross yields at alternative time and maturity levels:

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CHAPTER 6

SOYBEAN OBJECTIVE YIELD METHODS
Table 1. Soybean Objective Yield Models
Sample Level Models

models based on previous 5 years
maturity

maturity 2
1

Fruit/

Forecasting
Category

Node

2

Fruit/

Node

0 to .2 .2 to 1.75

3

4

3,4

5

Pods/

Fruit

.65 to

yellow

brown

Pods

Pods

Pods

Pods

Pods

Pods

Pods/

Pods/

Pods/

1.75+

0 to .05

.05 to .2

.2 to .65

Fruit

Fruit

7

6

Fruit/

Node

maturity 5

Fruit
.85

8

9

10

enumerator
harvested

Laterals,
Pods per Sep
Plant

Plants,
Nodes

Plants,

Laterals

Laterals,
Fruit

Plants,

Laterals

Laterals,
Fruit

Oct

Fruit,
Pods

Pods

Nov
Weight per pod

5-year average

Lab Data

fruit = blooms + dried flowers + pods

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CHAPTER 6

SOYBEAN OBJECTIVE YIELD METHODS

To form a complete gross yield expression, a value is needed for pods per 18 square feet which is
only observable at or just before harvest. Therefore, yield forecast made before final harvest
require some method to forecast final pods per 18 square feet. NASS forecasts pods per 18
square feet with the following expression:
Pods per 18 square feet = Final Plants per 18 square feet * Final Pods per Plant
But ‘Final Plants per 18 square feet’ is also unobservable before harvest, as well as ‘Final Pods
per Plant’. NASS forecasts these two subcomponents in the following manners.
1. Forecasting Final Plant Count per 18 Square Feet
A simple linear (one variable) regression model is used to forecast the final number of plants per
18 square feet. The form of the model is:
𝑦𝑖 = 𝛽0 + 𝛽1 𝑥𝑖 + 𝜀𝑖
The independent variable, xi, is the current period, total plant count in the 3-foot and 6-inch
sections of unit i and yi is the final plant count from the same area. These counts are available
from previous years’ data collections and therefore are available to calculate parameters 𝛽0 and
𝛽1 by ordinary least squares. As might be expected, the R2’s from this model, in any state, is
rarely below 90 percent.
If the forecasted number of plants exceeds the number obtained during the monthly visit, the
forecast is replaced with the monthly visit value. A negative forecast is replaced with zero.
2. Forecasting Final Pods per Plant
The final number of pods per plant is forecasted using one or two variable regression models.
The independent variables used to predict pods per plant depend upon the forecasting category of
the unit and are shown in Table 1. There are five possible forecasting variables:
V1 = Plants per 18 square feet (the same variable used to forecast the final number of plants
per 18 square feet)
V2 = Main stem nodes per plant
V3 = Lateral branches with blooms, dried flowers, or pods per plant
V4 = Blooms, dried flowers, and pods per plant
V5 = Pods with beans per plant
Thus, the general form of the model is:
𝑦𝑖 = 𝛽0 + 𝛽1 𝑉1 + 𝛽2 𝑉2 + 𝛽3 𝑉3 + 𝛽4 𝑉4 + 𝛽5 𝑉5 + 𝜀𝑖
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CHAPTER 6

SOYBEAN OBJECTIVE YIELD METHODS

where three or four of the coefficients (𝛽1, 𝛽2, 𝛽3, 𝛽4 , 𝛽5) are zero. y is the final (at-harvest)
number of pods per plant in the 6-inch section for sample i.
If a unit is classified as forecasting category 0, no counts are possible in the 6-inch sections so
there are no forecasting variables. The average number of pods with beans per plant in all other
forecasting categories (1-10) is substituted for units in category zero. In all States separate
averages are computed for "wide" row units (row width at least 1.5 feet, broadcast, or blank) and
narrow row units (row width less than 1.5 feet) for category zero substitutions.
Recall the expression for final gross yield given above was:
Gross yield per acre = (pods per 18 square feet)*(weight per pod)* (43,560)
(18)(453.6)(60)
Together, the two sub-component forecasted values for final plants per 18 square feet and final
pods per plant may be used to forecast a final pods per 18 square feet. Now, if a final weight per
pod is also known, the yield may be calculated. Unfortunately, the final weight per pod is
unknown until just before, or at, harvest. As Table 1 shows, weight per pod is forecasted at a 5year average over all forecasting categories, allowing for shifts in the five-year average
according to whether the sample has wide or narrow row spacing. The average is carried until
laboratory data make the weight per pod final.
State Average Forecasts and Estimates
The sample level gross yield forecasts are averaged to the State level. Since the sample is selfweighting, the simple mean of the sample forecasts is an unbiased estimate of the State gross
yield. Therefore, gross yield for a State is given as G,
𝑁𝐺

1
𝐺̅ =
∑ 𝐺𝑖
𝑁𝐺
𝑖

where
𝐺̅ = State mean gross yield
𝑁𝐺 = number of samples with gross yield forecasts (estimates)
𝐺𝑖 = gross yield for sample i

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And the standard error of 𝐺̅ is:
NG

𝑆𝐺̅ = √∑
𝑖

̅ )2
(Gi − G
NG (NG − 1)

Simple means are also appropriate for Pods per 18 Square Feet, Plants per 18 Square Feet,
Harvest Loss, etc. No weighting is required when calculating State level averages for these
items:

Harvest Loss
For one quarter of the samples, an additional plot is laid out near each unit and gleaned after
farmer harvest of the field. If less than 10 harvest loss samples have been completed for a State,
a 5-year historical average (bu/acre) is the State-level estimate of harvest loss. When a sampling
gleaning has been completed, harvest loss (bu/acre) is computed for each sample as follows:

𝐿𝑖 =

𝑚𝑖
(𝑤𝑙𝑜𝑜𝑠𝑒/𝑡ℎ𝑟𝑒𝑠 ) (1 − (100
)) ∗ 43,560
(3)(𝑅̅𝑖 )(453.6)(60)(.875)

Where wloose/thres is the weight of loose and threshed beans, mi is moisture, and 𝑅̅𝑖 is the 4-row
spacing for unit 1 plus the 4-row spacing for unit 2, divided by 2. If a unit is broadcast, 6.0 is
used for its 4-row space width.
These sample-level harvest loss estimates are averaged to the State level, with mean
𝑁𝐿

1
𝐿̅ =
∑ 𝐿𝑖
𝑁𝐿
𝑖

Where Li = harvest loss in sample i, and NL = number of harvest loss samples.

N

̅)2
(Li −L

And the standard error is given by 𝑆𝐿̅ = √∑𝑖 L N

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L (NL −1)

CHAPTER 6

SOYBEAN OBJECTIVE YIELD METHODS
State Level Net Yield

Net yield for the State is computed by subtracting the estimated State level harvest loss from the
mean of all sample level gross yield forecasts and estimates. Thus, estimated average net yield
is:
𝑌̅ = 𝐺̅ − 𝐿̅
Where G
¯ and L
¯ are the State level gross yield and state level harvest loss respectively.
The standard error of the estimate is:
𝑆𝑌̅ = √𝑆𝐺2̅ + 𝑆𝐿̅2 −

2
𝐶𝑂𝑉(𝐺, 𝐿)
𝑁𝐺

Where 𝑆𝐿̅ was defined previously, and
NG

𝑆𝐺̅ = √∑
𝑖

̅ )2
(Gi − G
NG (NG − 1)
NL

COV (G,L) =



(Gi - G )(Li - L )

1

NL -1

When less than 10 Form E's are completed, and historical average loss is used, the standard error
is:
𝑆𝑌̅ = 𝑆𝐺̅
Production for the State
Production (P) for the State is the product of estimated State level net yield and acres to be
harvested for grain:
𝑃 = (𝐴𝐻𝐴𝑅𝑉 )(𝑌̅)
with standard error:
𝑆𝑃 = √(𝐴2ℎ𝑎𝑟𝑣 )(𝑆𝑌2̅ ) + (𝑌̅ 2 )(𝑆𝐴2ℎ𝑎𝑟𝑣 ) + (𝑆𝑌2̅ )(𝑆𝐴2ℎ𝑎𝑟𝑣 )
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SOYBEAN OBJECTIVE YIELD METHODS
Removing Bias from State Level Calculations

Forecasts of State level yields are inherently subject to differ from the final, and in most cases
administratively-determined, yield. The difference is due to weather and crop conditions yet to
be encountered at the time the forecast is produced, the difference between weather and crop
conditions in the current year and the historic weather and crop conditions utilized to predict
current yields, and also systematic non-sampling errors which contribute to forecast error. NASS
makes every attempt to minimize the impact of these sources of error by means of
administratively determine final values. These final, sometimes referred to as official, values are
used as dependent variables and are related to corresponding State level averages of net yield to
estimate historic linear regression equations. For example, each state will have an
administratively-determined, official soybean yield and a State level soybean yield for all
previous years. To forecast the official soybean yield for the current year, NASS takes the State
level average soybean yields from previous years surveys and regresses them to the
corresponding official soybean yields. This process provides a historical context for weather,
biases, and non-sampling errors.
The following table shows the variety of independent and dependent variables for which historic
biases are evaluated:

Dependent variable

Independent variable
September - average number of pods per acre

Official Final Yield

October - December - average net yield per
acre
September - December - average number of
pods per acre

Final Number of pods per acre
September - average number of pods per acre
Final weight per pod

October - December - average weight per pod
September - November - average of previous
5 years harvest loss

Final Harvest Loss

December - Harvest Loss for current year
Laboratory Weight Measures
Bean weight per pod is calculated using the harvested data from the sample. The weights from
both units are combined, so only one weight is calculated for the sample.

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CHAPTER 6
WC
N 
 C

 WB 
W 
 12

SOYBEAN OBJECTIVE YIELD METHODS
1.0-(moisture content /100)


0.875



where
Wc = weight of the pods and beans from Row 1 of the 3-foot section of Unit 1. If there are
no plants in Row 1 of Unit 1, then Row 2 is used. If that is also blank, then the same
process is applied to Unit 2.
Nc = the number of pods with beans from the row counted above.
W12 = weight of pods and beans from Row 1 of the 3-foot sections of Units 1 and 2.
WB = weight of the threshed beans form Row 1 of the 3-foot sections of Units 1 and 2.
0.875 = conversion to 12.5 percent moisture (1.0 - .125).
Number of Pods with Beans per 18 Square Feet is computed for each unit from the harvested
data:

Unit 1:

(W1)(Nc)(18)
───────────────────────
(Wc)(3)(4-row space width)/(4)

Unit 2:

(W2)(Nc)(18)
───────────────────────
(Wc)(3)(4-row space width)/(4)

Where
Wi = weight of pods and beans from Row 1 of the 3-foot section of Unit i (i = 1 or 2),
Nc and Wc were defined previously, and the expression “(3)(4-row space width)/(4)” is the area
of the rectangular unit formed by Row 1 of the 3-foot section and its row middle. If the unit is
broadcast, a 4-row space of 6.0 is used.
Example
Suppose Unit 1's pods are counted in the lab, and the following data are obtained:
Wc = 103.2 grams =
W1
Nc = 221
WB = 134.8 grams
W12 = 236.4 grams
moisture content = 10.6 percent
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SOYBEAN OBJECTIVE YIELD METHODS

4-row space width = 11.0 feet
Then, the estimated weight of beans per pod is:
(103.2)(134.8) (1-(10.6/100))
───────────────────── = 0.272 grams.
(221)(236.4) (0.875)
The estimated number of pods per 18 square feet is:
(103.2)(221)(18)
────────────────────── = 482.18 pods/18 square feet.
(103.2)(3)(11.0)/(4)
Then the estimate of gross yield for the unit is:
(482.18)(0.272)(43560)
────────────────────── = 11.66 bu/acre
(18)(453.6)(60)
Gross Yield for Units with Incomplete Data
Gross yield is forecasted or estimated from the current month's survey data. In some cases,
current data are unavailable and data from a previous month may be used to compute gross yield,
or no gross yield may be computed for the unit. The different cases are discussed below.
Refusals
If the farmer refuses permission to enter the field, the sample is lost for the season. In this case,
the yield for this sample is left missing. Consequently, the refused sample contributes nothing to
the State-level average yield. Stated another way, the assumption is made that if the sample had
not been a refusal, its gross yield would have been equal to the State's average gross yield.
Inaccessible Samples and Units
Occasionally, some or both units are inaccessible due to scheduling or field conditions. If data
from a previous visit are available, the previous forecast is carried forward. Otherwise, the
sample is excluded from gross yield calculations. The sample must still be intended for harvest
as beans.
Early Farmer Harvest

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If a previously laid out unit is harvested by the farmer before current data can be collected, the
previous month's predicted yield is brought forward.
Lost, Abandoned, Destroyed Units
If a unit is lost, abandoned, destroyed, and so forth, no gross yield is computed for the unit. The
unit contributes nothing to the sample-level yield indication.
Computational Examples
An example will now be given showing how gross yield per acre is forecasted for a sample.
Assume that the following data were obtained for a sample.

Sample Data
Unit 1

Unit 2

Field maturity

2

2

Four-row space measurement (ft.)

12.8

12.5

Plants in the 2 3-foot row sections

41

40

Plants in the 2 6-inch row sections

11

9

Nodes on the main stems of the plants

96

74

Lateral branches with blooms, dried flowers, or pods

5

Blooms, dried flowers, and pods

50

37

Pods with beans

0

0

2

Before gross yield is computed, a forecasting category is computed for each unit. In this
example, both units would be category 2 (no pods with beans in the 6-inch section, fruit/nodes
ratio between 0.20 and 1.75 inclusive).
To forecast plants per 18 square feet, the current number of plants is scaled to the standard 18
square feet:
(plants in the 3-foot and 6-inch sections)(18)
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SOYBEAN OBJECTIVE YIELD METHODS

X = ──────────────────────────────────────────────
(3.5)(4-row space width)/(2)
Where 18 is standard area, (3.5) is the length of row counted, and (4-row space width)/(2) is the
width of a 2-row unit. If the unit is broadcast, the 4-row space width is 6 feet.
The current plant count per 18 square feet for each unit in the example is:

Unit 1:

Unit 2:

(41+11)(18)
X = ────────────
(3.5)(12.8)/(2)

= 41.8

(40+9)(18)
X = ────────────
(3.5)(12.5)/(2)

= 40.3

Suppose that the values for bo and b1 in the forecasting equation are 1.2 and 0.92, respectively.
Then the forecasted number of plants per 18 square feet for each unit is:
Unit 1:

P1 = 1.2+(0.92)(41.8)=39.656

Unit 2:

P2 = 1.2+(0.92)(40.3)=38.276

To forecast pods with beans per plant, a two-variable regression model is used for forecasting
category 2 (see previous table), containing the following variables:
V1 = current month's plant count expanded to 18 square feet (x)
V3 = lateral branches with blooms, dried flowers, or pods per plant for the 6-inch section
so, the model is:
Y = bo+b1V1+b3V3.
Given, the following forecast equation:
Y = 42.2 - (0.6) V1 + (4.8)V3,
the forecast of pods per plant for each unit is:
Unit 1: 42.2 - (0.6)(41.8) + (4.8)(5/11) = 19.30
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Unit 2: 42.2 - (0.6)(40.3) + (4.8)(2/9) = 19.09
To forecast bean weight per pod, a 5-year historical average weight is used. Assume that the 5year historical average weight is 0.437 grams for the wide row samples for this State. The
expression for each unit’s yield per acre is:

Unit 1:
Y1 =

(39.656)(19.30)(.437)(43560)
────────────
= 29.74 bu/acre
(18)(453.6)(60)

Y2 =

(38.276)(19.09)(.437)(43560)
────────────
= 28.39 bu/acre
(18)(453.6)(60)

Unit 2:

And the gross yield forecast for the sample is:
(29.74+28.39)/2 = 29.06 bu/acre

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CHAPTER 7

COTTON OBJECTIVE YIELD METHODS
CHAPTER 7 COTTON OBJECTIVE YIELD METHODS

This chapter presents the procedures and formulae used to calculate cotton yield indications. The
scope of the Cotton Objective Yield Survey, sample plots, and data collected are briefly
described. More detail is given to the formulae that use the data to forecast and estimate yield.
Early in the growing season, some or all of the three components of net yield (number of bolls,
average boll weight, and harvest loss) cannot be obtained directly and must be forecast. The
procedures used to forecast these components are described in the following sections.
Sample Design
Cotton Objective Yield (CtOY) surveys are conducted in major cotton producing States:
Arkansas, Georgia, Mississippi, and Texas. As described in Chapter 2, NASS partitions each of
these states’ land area into approximately one square mile pieces and calls the pieces segments.
The resulting collection of segments is referred to as the “Area Frame”. This painstaking
segmentation of land area into uniquely identifiable segments makes possible the selection of a
probability-based sample of U.S. cotton acres.
A probability-based survey requires the explicit identification and separation of all elements
contained in the population of interest. NASS’s Area Frame is the vehicle for explicitly
identifying and separating each acre of cotton produced in the U.S. Every year, during late
spring, all four CtOY states screen a statistically selected sample of Area Frame segments for all
agricultural activity, including cotton acreage planted. Each acre in every selected segment will
be visually inspected and/or accounted-for by the owner/operator with respect to agricultural
activity. In other words, every year a new listing of every cotton acre is constructed. This listing
is the CtOY sample population. This listing is an important step towards employing probability
theory to randomly select a sample of cotton acres from which inferences will be made about all
cotton acres. The most important result of constructing a sample population is that any acre of
cotton, planted in each state, has a chance to be selected for the CtOY survey. No other purveyor
of U.S. cotton estimates can make an equivalent statement.
Accurate inferences from a probability-based survey require the construction of a sampling
population and, in addition, a means to select a representative sample from that population.
The statistical method used to select cotton acres to be included in CtOY is probability
proportional to size (PPS). In statistics, this method ensures a representative sample is selected
when sample elements vary in their size. During constructing of the cotton acres sample
population, the explicit identification and separation of cotton acres, from other acres, is made
according to fields. In agriculture a field is one, continuous acreage of land devoted to the same
use. Since fields of cotton are the unit of selection for CtOY samples and because cotton fields
vary in acreage, probability proportional to size is ideally suited to selecting a sample that
perfectly reflects the population characteristics of cotton. For example, employing PPS sampling
implies a cotton field accounting for twice the percentage of total state cotton acres relative to a
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COTTON OBJECTIVE YIELD METHODS

neighboring cotton field, will also carry twice the probability of selection as the neighbor. The
representative acre selected from a sampled field is finally accomplished with simple random
sampling. Since a selected acre is too large for complete enumeration, a selected sample will be
enumerated and expanded up to the one-acre level.
In mid-July of each year, professional statisticians in the four CtOY states train field enumerators
to properly identify and prepare selected samples for data collection. Generally, enumerators will
have many years of experience in CtOY data collection and are well qualified to conduct their
assignments. Practical field training is also available through relationships developed among
individual enumerators and their supervisors. Overall, the preparation for data collection is
rigorous and includes quality control processes that continue through the cotton growing season.
Data are collected from each sample at monthly intervals starting in late July and continuing
through December or until the sample has been harvested. Each month during the Objective
Yield Survey, data collected from the sample fields are used to produce indications of planted
acres (September only), acres for harvest, and yield.
A sample consists of two independently located units (or plots), each of which consists of two
parallel 10-foot sections of row. An additional 3-foot section is appended to one row of each
unit. This extra section is used when making detailed fruit counts. Field enumerators use a
random number of rows along the edge of the field and a random number of paces into the field
to locate each unit. At each visit, enumerators count all fruit and fruiting positions. Any mature
bolls found in the 10-foot sections of the sample plots are picked and sent to a NASS lab where
boll weight is determined. The count of bolls picked, and the weight of these bolls are
accumulated through the season. Just before farmer harvest, all remaining open bolls are picked
and weighed to establish gross yield. The yield is measured as pounds of lint per acre at 5
percent moisture. Harvest loss is measured in separate units located near the monthly yield plots.
Data Collected
Field enumerators count and measure several items within or near the units. Data items are used
to measure the size of the unit, number of bolls, weight per boll, and harvest loss. The following
lists the data items collected and objective of these measurements:
Data items used to measure the size of each unit:
Distance between two rows (one row middle)
Distance between five rows (four row middles)
Data items used to forecast or estimate the number of bolls:
Number of plants in each row (all sections)
Number of squares (3-foot sections)
Number of small bolls and blooms (3-foot sections)
Number of large unopen bolls (10-foot sections)
Number of open bolls (10-foot sections)
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Data items used to estimate weight per boll:
Weight of lint harvested by enumerators
Weight of lint dried to zero moisture
Data items used to estimate harvest loss:
Distance between two rows (one row middle)
Distance between five rows (four row middles)
Number of unopen bolls left in the field
Weight of lint gleaned from harvest loss units
Weight of dried lint
Maturity Categories
To forecast each sample’s yield per acre, regression models are developed by maturity category
for each survey month. For cotton, the maturity categories are defined by the raw counts
obtained in the sample. These categories are:

1

In 10-foot sections
No fruit present

In 3-foot sections
No fruit present

2

No fruit present

Squares only

3

0 < RATIO < 0.5

Blooms or Bolls

4

0.5 < RATIO < 2.0

----

5

2.0 < RATIO

----

6

Sample field has been harvested or harvest immanent.

RATIO is the ratio of large bolls counted to plants counted in the 10-foot sections of the sample.
Large bolls include burrs, open bolls, partially open bolls, and large unopened bolls.
Sample Level Yield Forecasts
Forecasting the Number of Large Bolls
The expected number of large bolls for each sample is forecast using a regression model:
𝑌̂𝑖 = 𝛽0 + 𝛽1 𝑋1 + 𝛽2 𝑋2 + 𝛽3 𝑋3

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where:
𝑌̂𝑖 =
𝑋1 =

forecasted number of large bolls in ith unit
observed number of burrs, open bolls, partially open bolls, and large unopened
bolls (40-foot equivalent) in ith unit
𝑋2 = observed number of small bolls and blooms (40-foot equivalent) in ith unit
𝑋3 = observed number of squares (40-foot equivalent) in ith unit
𝛽0 − 𝛽3 = least squares regression coefficients
Small bolls are defined as boll less than one inch in diameter. Enumerators use a gauge with a
one-inch hole to determine whether a boll is small or a large unopened boll. A square is an
observable fruiting position that has not reached the bloom stage.
Forecast equations for each model are derived for each maturity category for each month for
each district for each State. Not all possible independent variables are used in each model. For
instance, for maturity category one only the intercept is fit. For later maturities and or months,
squares and small bolls are excluded from the models. Data from the previous 5 years are used to
estimate the regression coefficients. If a unique set of coefficients cannot be determined for a
given class (due to insufficient data), the previous month's coefficients are used.
The actual count of large bolls is used for any sample in maturity category six in any month, and
for all samples in December and later months. All samples in maturity category one use a 5-year
historical average.
Analysis of Raw Data
The regression equations are derived from the previous 5 years' survey data using multiple
regression techniques. Certain influential data points (i.e., "outliers") are excluded from the
dataset prior to deriving the coefficients. These influential data points are identified using a
"deleted residual" analysis or the "Cook's D" statistic (Belsley, Kuh, and Welsch, [4]). There is
usually very little change in the regression equations from year-to-year because roughly 80
percent of the data for each class were used in the analysis the previous year. Classes that do
change significantly from one year to the next are usually those with very few observations. If a
class has little data and a plausible forecast equation cannot be derived, the equation from the
previous year is used.
Forecasting Boll Weight
Early in the season, until 20 percent of the projected number of large bolls have been picked and
weighed by the enumerator, a 5-year historical average is used. When 20 to 85 percent of the
projected number of large bolls has been picked, one model is used to forecast boll weight for all
maturity categories in a district in a State:
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CHAPTER 7

COTTON OBJECTIVE YIELD METHODS
̂𝑠𝑑 = 𝑤𝑠𝑑 (𝛽0 + 𝛽1 𝑋𝑠𝑑 )
𝑊

where:
̂𝑠𝑑 = forecast boll weight for the sth State and dth district
𝑊
𝑤𝑠𝑑 = observed boll weight
𝑋𝑠𝑑 = ratio of bolls picked and weighed to large bolls forecasted
𝛽0 − 𝛽1 = regression coefficients
When more than 85 percent of the projected number of large bolls has been picked and weighed
by the enumerator, actual boll weight is used.
The following table shows the independent and dependent variables for the State level indication
models used during the 1996 growing season.
Dependent variable

Independent variable

Official Final Yield

Average estimated net yield per acre over all
samples

Final Number of Bolls

August - Average small bolls and blooms per acre
over all samples
September - Average small bolls and blooms plus
cumulative large bolls per acre over all samples
October - January - Average cumulative large
bolls per acre

Final boll weight

August - September - Weight derived from
average estimated final gross yield and average
estimated final large bolls per acre
October - January - average cumulative net
weight per boll

Final Harvest Loss

August - November - average of previous 5 years
harvest loss
December - January - OY B Harvest Loss for
current year

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COTTON OBJECTIVE YIELD METHODS
Cotton Objective Yield Models
Sample Level Models
models based on previous 5 years
1
no fruit
present

2
squares
present

August

5-year
average

squares

September

5-year
average

squares

Forecast Category

Number of
Bolls

October

3
ratio
0 to 0.5

4
ratio
0.5 to 2.0
cumulative large bolls
small bolls & blooms
squares
cumulative large bolls
small bolls & blooms
squares
cumulative large bolls
small bolls & blooms
cumulative large bolls
cumulative large bolls

5
ratio
2.0+

November
December
<20%
5-year average
picked
Weight
20-85%
cumulative net weight x smoothing parameter
per boll
picked
>85%
cumulative net weight
picked
ratio = cumulative large bolls / plants in 10-foot units
large bolls = burrs + large opened bolls + large partially opened bolls + large unopened bolls
smoothing parameter = value <1 that approaches 1 as percent picked approaches 85 percent

THE YIELD FORECASTING PROGRAM OF NASS

65

6
harvested or soon
to be harvested

cumulative large
bolls

CHAPTER 7

COTTON OBJECTIVE YIELD METHODS
Forecasting Directly to State Level

The discussion in the previous sections centers on processing data at the sample level. Modeling
and yield calculations are done at the sample level and averaging is done as the last step.
Additionally, averages of the raw counts and component forecasts can be computed for
supporting analysis.
A second approach to forecasting State yield, using the same data, can be applied by doing the
averaging first and the modeling last. Averages per acre at the State level can be calculated for
each of the count variables (plants, squares, small bolls and blooms, large unopen bolls, and open
bolls. Average weight per boll can also be calculated, weighting the average weight per boll in
each sample by the number of bolls in that sample. This process creates State level independent
variables and leads to State and regional level models. The State and regional level independent
variables can be regressed to final official yield, final bolls per acre, and final weight per boll.
The distinction is State and regional averages are used as independent variables in regression
models that predict State and regional level final yields, bolls per acre, and weight per boll. In
these models, one year and month represents one observation, so instead of partitioning
thousands of sample level points into forecasting categories, we have one data point per month
per year. A 15-year dataset is used for these models. The models are simple one variable
regression models and are called the State level models, referring to the fact that they are State
and regional level models, not sample level models as described in the previous sections.
Gross Yield
The estimate of final gross yield is computed by multiplying the forecasted number of large bolls
at harvest by the forecasted average weight per boll, expanding to a per acre basis, and
converting to a standard unit. The standard unit for cotton is pounds of lint at 5 percent moisture.
Production is reported in 480-pound bales.
The formula for computing gross yield is:
𝐺̂𝑖 =

(2.401)𝑍𝐵𝑖 𝑊𝑖
𝑅𝑖

where
𝐺̂𝑖 = estimated gross yield (lbs. of lint per acre) for sample i
Z = lint/seed ratio (3-year average)
𝐵𝑖 = number of large bolls at harvest in 40 feet for sample i
𝑊𝑖 = average boll weight for sample i (grams at 5 percent moisture, gin equivalent)
𝑅𝑖 = average row spacing for sample i
2.401 = 43,560 / (40 * 453.59) = which converts grams of seed cotton per 40 feet of row
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to pounds of seed cotton per acre.
The Objective Yield samples are selected in such a way that each acre has equal probability of
selection within districts. Therefore, the average of the sample level yields across all samples in a
district provides a forecast of mean gross yield per acre for the district.
Mean Gross Yield for State
The sample level gross yield forecasts (estimates) are averaged to the State level. Since the
sample is self-weighting, the simple mean of the sample forecasts (estimates) is an unbiased
estimate of the State gross yield. Therefore,
𝑁𝐺

1
𝐺̅ =
∑ 𝐺𝑖
𝑁𝐺
𝑖

where
𝐺̅ = State mean gross yield
𝑁𝐺 = number of samples with gross yield forecasts (estimates)
𝐺𝑖 = gross yield for sample i
The standard error of the estimate is:
𝑁𝐺

𝑆𝐺̅ = √∑
𝑖

(𝐺𝑖 − 𝐺̅ )2
𝑁𝐺 (𝑁𝐺 − 1)

Gross Yield for Units with Incomplete Data
Gross yield is forecasted or estimated from the current month's survey data. In some cases,
current data are unavailable and data from a previous month may be used to compute gross yield,
or no gross yield may be computed for the unit. The different cases are discussed below.
Refusals
If the farmer refuses permission to enter the field, the sample is lost for the season. In this case
the yield for this sample is left missing. Consequently, the refused sample contributes nothing to
the State-level average yield. Stated another way, the assumption is made that if the sample had
not been a refusal, its gross yield would have been equal to the State's average gross yield.
Inaccessible Samples and Units
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Occasionally, some or both units are inaccessible due to scheduling or field conditions. If data
from a previous visit are available, the previous forecast is carried forward. Otherwise, the
sample is excluded from gross yield calculations. The sample must still be intended for harvest
as cotton.
Early Farmer Harvest
If a previously laid out unit is harvested by the farmer before current data can be collected, the
previous month's predicted yield is brought forward.
Lost, Abandoned, Destroyed Units
If a unit is lost, abandoned, destroyed, and so forth, no gross yield is computed for the unit. The
unit contributes nothing to the sample-level yield indication.
Harvest Loss
The harvest loss is computed from gleanings obtained from one quarter of the samples. The
sample level harvest loss is found by determining the total weight of seed cotton gleaned,
expanding to a "per acre" basis, and converting to standard units.
The formula for harvest loss is:
𝐿𝑖 =

(2.401)𝑊𝑖 𝑍
𝑅𝑖

where
𝐿𝑖 = harvest loss (lbs. of lint per acre) for the ith sample
𝑊𝑖 = weight of cotton left in units for sample i which is computed as: (partially opened
and large unopened bolls left in the units) * (average net weight per boll) +
(weight of cotton gleaned adjusted to 5 percent moisture)
Z = lint/seed ratio (3-year average)
𝑅𝑖 = row space measurement for sample i
2.401 = conversion factor (defined above)
For each month, if fewer than 10 harvest loss samples have been completed within a district, a 5year average harvest loss is used as an estimate.
These sample-level harvest loss estimates are averaged to the State level, with mean:
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𝑁𝐿

1
𝐿̅ =
∑ 𝐿𝑖
𝑁𝐿
𝑖

where
𝐿̅ = State level mean harvest loss
𝐿𝑖 = harvest loss in sample i
𝑁𝐿 = number of samples with Form E data
The standard error of the estimate is:
𝑁𝐿

𝑆𝐿̅ = √∑
𝑖

(𝐿𝑖 − 𝐿̅)2
𝑁𝐿 (𝑁𝐿 − 1)

Net Yield for the State
Net yield for the State is computed by subtracting the estimated State-level harvest loss from the
mean of all sample-level gross yield forecasts and estimates. Thus, estimated average net yield
is:
𝑌̂ = 𝐺̅ − 𝐿̅
where
𝑌̂= estimated average State net yield
𝐺̅ = State mean gross yield
𝐿̅ = State level mean harvest loss

The standard error of the estimate is:
𝑆𝑌̂ = √𝑆𝐺2̅ + 𝑆𝐿̅2 −
where
𝑆𝐺̅ and 𝑆𝐿̅ were previously defined, and

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69

2
𝐶𝑂𝑉(𝐺, 𝐿)
𝑁𝐺

CHAPTER 7

COTTON OBJECTIVE YIELD METHODS
𝑁𝐿

𝐶𝑂𝑉(𝐺, 𝐿) = ∑
𝑖

(𝐺𝑖 − 𝐺̅ )(𝐿𝑖 − 𝐿̅ )
𝑁𝐿 − 1

When less than 10 gleanings are completed, and historical average loss is used, the standard error
is:
𝑆𝑌̅ = 𝑆𝐺̅
Production for the State
Production for the State is the product of estimated State-level net yield and acres harvested:
𝑃 = 𝑌̂𝐴
where
P = State production
𝑌̂= State level net yield
𝐴 = acres harvested
with standard error:
𝑆𝑃 = √𝐴2 𝑆𝑌2̂ + 𝑌̂ 2 𝑆𝐴2 + 𝑆𝑌2̂ 𝑆𝐴2
Removing Bias from State Level Calculations
Forecasts of State level yields are inherently subject to differ from the final, administrativelydetermined, yield. The difference is due to the three possible reasons: weather and crop
conditions yet to be encountered at the time the forecast is produced, the difference between
weather and crop conditions in the current year and the historic weather and crop conditions
utilized to predict current yields, or systematic non-sampling errors which contribute to forecast
error. NASS makes every attempt to minimize the impact of these three sources of error by
means of administratively determine final values. These final, sometimes referred to as official,
values are used as dependent variables to estimate an ordinary least squares equation with the
averages calculated from objective yield samples as the independent variable. For example, each
state will have an administratively-determined, official cotton yield for all previous years. To
forecast the official cotton yield for the current year, NASS regresses the objectively determined
State level average cotton yields from previous years to the corresponding official cotton yields.
This process provides a historical context for weather, biases, and non-sampling errors.
The regression equation is:

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𝑦𝑖 = 𝛽0 + 𝛽1 𝑥𝑖 + 𝜀𝑖

where
yi = Official state yield
xi = calculated State average net yield
𝛽0 and 𝛽1 = ordinary least squares estimates
𝜀𝑖 =random departure from the relationship
Computational Yield Example
Yield (computed for a single sample)
September 1 Data
8-row space measurement

25.8

Counts Within 10-foot Units
Number of plants (4 rows)
Number of burrs (2 units)
Total open bolls (4 rows)
Weight of seed cotton picked (2 units)
Number of partially open bolls (4 rows)
Number of large unopened bolls (4 rows)

87
113
130
650
48
121

3-foot Tag Section Beyond Unit 1
Number of plants
Number of burrs and open bolls
Number of large unopened bolls
Number of small bolls and blooms
Number of squares

11
33
14
4
2

3-foot Count Section Beyond Unit 2
Number of plants
Number of burrs and open bolls
Number of large unopened bolls
Number of small bolls and blooms
Number of squares
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8
27
11
6
1

CHAPTER 7

COTTON OBJECTIVE YIELD METHODS

Current Month Lab Form
Weight of seed cotton before drying
Weight of seed cotton after drying

56
52

Previous Months= Data Brought Forward
Accumulated burrs within unit
Accumulated bolls picked within unit
Accumulated adjusted weight seed cotton

20
50
257

Maturity Category Determination
𝑟𝑎𝑡𝑖𝑜 =

(𝐵𝑐 + 𝐵𝑎 ) + (𝑇𝑐 + 𝑋𝑎 ) + 𝑉𝑐 + 𝑈𝑐
𝑃𝑐

where
𝐵 𝑐 = current burrs within 10-foot units
𝐵 𝑎 = accumulated burrs within 10-foot units
𝑇𝑐 = current total open bolls within 10-foot units
𝑋𝑎 = accumulated bolls picked within unit
𝑉𝑐 = current partially open bolls in 10 foot-units
𝑈𝑐 = current large unopened bolls within 10-foot units
𝑃𝑐 = current number of plants within 10-foot units
Using the example data 𝑟𝑎𝑡𝑖𝑜 =
thus the maturity category is 5.

(113+20)+(130+50)+48+121
87

= 5.54. The ratio is greater than 2.0,

Forecast Number of Large Bolls
Multiple Regression Model
𝑌̂ = 𝛽0 + 𝛽1 𝑋1 + 𝛽2 𝑋2 + 𝛽3 𝑋3
Where
𝑌̂ =
𝑋1 =
𝑋2 =

forecasted number of large bolls
number of burrs, open bolls, partially open bolls, and large unopened bolls (40foot equivalent)
number of small bolls and blooms (40-foot equivalent)

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𝑋3 = number of squares (40-foot equivalent)
𝛽0 − 𝛽3 = least squares regression coefficients derived from the previous 5 years of
sample level data
The multiple regression model uses 40-foot equivalents for the number of bolls. Each boll
measurement must first be converted to this standard.
Burrs and open bolls, partially open bolls, and large unopened bolls are counted in a total of 46
feet of row (four 10-foot units and two 3-foot units).
𝑋1 =

40
[(𝐵𝑐 + 𝐵𝑎 ) + (𝑇𝑐 + 𝑋𝑎 ) + 𝑉𝑐 + 𝑈𝑐 + (𝐶1 + 𝑈1 ) + (𝐶2 + 𝑈2 )]
46

where
𝑋1 = number of burrs, open bolls, partially open bolls, and large unopened bolls (40-foot
equivalent)
𝐵 𝑐 = current burrs within 10-foot units
𝐵 𝑎 = accumulated burrs within 10-foot units
𝑇𝑐 = current total open bolls within 10-foot units
𝑋𝑎 = accumulated bolls picked within unit
𝑉𝑐 = current partially open bolls in 10 foot-units
𝑈𝑐 = current large unopened bolls within 10-foot units
𝐶1 = burrs and open bolls within 3-foot Unit 1
𝑈1 = large unopened bolls within 3-foot Unit 1
𝐶2 = burrs and open bolls within 3-foot Unit 2
𝑈2 = large unopened bolls within 3-foot Unit 2
Using the example data:
𝑋1 = ⌊(113 + 20) + (130 + 50) + 48 + 121 + (33 + 14) + (27 + 11)⌋ = 493.043
Small bolls and blooms are counted in six feet of row (both 3-foot units)
𝑋2 =

40
(𝐷 + 𝐷2 )
6 1

where
𝑋2 = number of small bolls and blooms (40-foot equivalent
𝐷1 = small bolls and blooms within 3-foot Unit 1
𝐷2 = small bolls and blooms within 3-foot Unit 2

Using the example data: 𝑋2 =

40
6

(4 + 6) = 66.667

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Squares are counted in six feet of row (both 3-foot units)
𝑋3 =

40
(𝑄 + 𝑄2 )
6 1

where
𝑋3 = number of squares (40-foot equivalent)
𝑄1 = squares within 3-foot Unit 1
𝑄2 = squares within 3-foot Unit 2
Using example data: 𝑋3 =

40
6

(2 + 1) = 20.000

Least squares regression coefficients (𝛽0 − 𝛽3 ) are derived from the previous 5 years of sample
level data, for this example let:
𝛽0 = 14
𝛽1 = 0.933
𝛽2 = 0.300
𝛽3 = 0.110
The estimate of number of bolls using the regression model for this sample is:
𝑌̂ = 14 + (0.933 ∗ 493.043) + (0.300 ∗ 66.667) + (0.110 ∗ 20.000) = 496.209
Forecast Boll Weight
̂ = 𝑤(𝛽0 + 𝛽1 𝑋)
𝑊
where:
̂ = forecast boll weight
𝑊
w = observed boll weight at 5% moisture (gin equivalent)
𝑋 = ratio of bolls picked and weighed to large bolls forecasted
𝛽0 − 𝛽1 = regression coefficients

Determine the observed boll weight at 5% moisture:

𝑤=

𝑗
[𝑟 (𝑗𝑎 ) (1.0526) + 𝐾𝑎 ]
𝑏

(𝑋𝑎 + 𝑇𝑐 )

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where
w = observed boll weights at 5% moisture (gin equivalent)
r = weight of seed cotton picked in 10-foot section
𝑗𝑎 = weight of seed cotton after drying
𝑗𝑏 = weight of seed cotton before drying
1.0526 = conversion factor to 5% moisture (gin equivalent)
𝐾𝑎 = accumulated adjusted weight of seed cotton
𝑋𝑎 = accumulated bolls picked within unit
𝑇𝑐 = current total open bolls within 10-foot units
Using the example data:
52
[650 ( ) (1.0526) + 257]
56
𝑤=
= 4.957
(50 + 130)
Determine the ratio of picked to forecasted large bolls:
𝑋=

(𝑇𝑐 + 𝑋𝑎 )
𝑌̂

where
𝑋 = ratio of bolls picked and weighed to large bolls forecasted
𝑇𝑐 = current total open bolls within 10-foot units
𝑋𝑎 = accumulated bolls picked within unit
𝑌̂ = forecasted number of large bolls
Using the example data:
𝑋=

(130 + 50)
= 0.363
496.209

For this example, let:
𝛽0 = 0.882
𝛽1 = 0.131
The forecasted boll weight using the calculated inputs:
̂ = 4.957(0.882 + 0.131 ∗ 0.363) = 4.608 𝑔𝑟𝑎𝑚𝑠 𝑝𝑒𝑟 𝑏𝑜𝑙𝑙
𝑊
Forecast Gross Yield per Acre
The estimated gross yield for this example sample is:

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𝐺̂ =

(2.401)𝑍𝐵𝑊
𝑅

where
𝐺̂ = estimated gross yield (lbs. of lint per acre)
Z = lint/seed ratio (3-year average)
B = number of large bolls at harvest in 40 feet
W = average boll weight (grams at 5 percent moisture, gin equivalent)
R = average row spacing
2.401 = 43,560 / (40 * 453.59)
which converts grams of seed cotton per 40 feet of row to pounds of seed cotton
per acre.
For this example, let:
Z = 0.368
𝐺̂ =

(2.401) ∗ 0.368 ∗ 496.209 ∗ 4.608
= 626.45 𝑝𝑜𝑢𝑛𝑑𝑠 𝑜𝑓 𝑙𝑖𝑛𝑡 𝑝𝑒𝑟 𝑎𝑐𝑟𝑒
(25.8⁄8)

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CHAPTER 8

WHEAT OBJECTIVE YIELD METHODS

This chapter presents basic sampling, data collection, and mathematical methods utilized to
estimate U.S. winter wheat yield and production. The sampling review will emphasize the
technical differences in winter wheat sampling relative to techniques employed for corn,
soybeans, or cotton. Data collection will focus on the variety of data collected and how data
collection changes as the wheat crop matures. The mathematical methods review will center on
mathematical/statistical estimation of final winter wheat yields utilizing measurable plant
characteristics observed at specific points during the growing season. The end results of careful
sampling, data collection, and mathematical methods are numeric indications suitable to
establishment, and/or revision, of U.S. wheat acreage, yield, and production.
Sample Design
Wheat Objective Yield (WOY) surveys are conducted in the 10 major winter wheat producing
States: Colorado, Illinois, Kansas, Missouri, Montana, Nebraska, Ohio, Oklahoma, Texas, and
Washington. These ten states, on average over the last three years, have accounted for more than
65 percent of U.S. production. A sample of wheat producers to be included in WOY is selected
each year from among all producers with positive wheat acreage reported during the March
Agricultural survey. Thus, the major sampling difference in WOY compared to other crops is
that producers are the sample element for WOY, whereas fields are the sample element for corn,
cotton, and soybeans. The difference is necessary since Area Frame records are unavailable for
the current years’ winter wheat plantings. In the past, NASS sampled and enumerated segments
from the Area Frame during late November to early December specifically for winter wheat
plantings but discontinued the practice for budgetary reasons. A reasonable alternative to Area
Frame records for winter wheat yield sampling are the Multiple Frame records collected during
the March Agricultural survey. The Multiple Frame combines an exhaustive listing of
agricultural producers, called the List Frame, with producers identified by the Area Frame in a
manner that producer duplication is minimized, and producer omission is satisfactorily resolved.
The resulting Multiple Frame is a satisfactory sampling frame for winter wheat yield forecasting.
Accurate inferences from a probability-based survey require the construction of a sampling
population and, in addition, a means to select a representative sample from that population. The
statistical method used to select wheat acres to be included in WOY is probability proportional to
size (PPS). In statistics, this method ensures a representative sample is selected when sample
elements vary in their size. The wheat acres sample population is constructed by explicitly
identifying and separating producers with winter wheat plantings and noting their whole farm
wheat plantings. Based on this producer record, PPS sample selection assigns higher
probabilities to producers with a larger percentage of the state’s total wheat plantings. Recall the
sample design for WOY selects the producer first whereas, for corn, soybeans, and cotton the
field is selected first. Then for each selected producer, a listing of wheat fields is constructed
from which the representative field is selected and finally the representative acre is selected by
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simple random sampling. Since a selected acre is too large for complete enumeration, a selected
sample will be enumerated and expanded up to the one-acre level.
In mid-April of each year, professional statisticians in the ten WOY states train field enumerators
to properly identify and prepare selected samples for data collection. Generally, enumerators will
have many years of experience in WOY data collection and are well qualified to conduct their
assignments. Practical field training is also available through relationships developed among
individual enumerators and their supervisors. Overall, the preparation for data collection is
rigorous and includes quality control processes that continue through the wheat growing season.
In late April field enumerators will begin visiting and enumerating samples and will continue
personal visits at monthly intervals throughout the season until final harvest.
Each sample consists of two units (or plots) to be utilized in forecasting final net yield per acre.
Each unit consists of three parallel 21.6-inch sections of row. During each visit, enumerators
count or measure each required plant characteristic, the required characteristics being determined
according to the units’ maturity level. For example, at early maturities enumerators will count
plants and measure row spacing. At later maturities, head weights are measured and recorded.
After each data collection period, a forecast of each unit’s final net yield is constructed.
Essentially forecasts of wheat yields depend on two items: 1. the current year’s measurable plant
characteristics and, 2. the historic relationship between plant characteristics measured in previous
years, at the same level of maturity, and final net yield. Each item is needed to forecast a samples
final net yield per acre. In cases where the historic relationship is missing, a five-year average of
the final plant characteristic is substituted. During some early forecasts there may be no plant
characteristic that NASS measures that can be related to the final net yield. Head weight is the
prime example. In these cases, historic averages are used to forecast final net yield.
Data Collected
Field enumerators count and measure several items within or near the units. Data items are used
to measure the size of the unit, number of heads, weight per head, and harvest loss. The
following lists the data items collected and objective of these measurements.
Data items used to measure the size of each unit:
Distance between two rows (one row middle)
Distance between five rows (four row middles)
Data items used to forecast or estimate the number of heads:
Number of stalks in each row
Number of late boot heads in each row
Number of emerged heads in each row

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Data items used to forecast or estimate grain weight per head:
Number of fertile spikelets on 10 heads
Number of grains on 10 heads
Weight of mature heads (before threshing) and weight of late boot heads
Weight of grain threshed from mature heads
Moisture content of the threshed grain
Data items used to estimate harvest loss:
Distance between two rows (one row middle)
Distance between five rows (four row middles)
Grain weight of heads between Row 1 and Row 4
Grain weight of loose kernels between Row 1 and Row 4.
Maturity Categories
At each visit, the enumerator makes maturity assessments within the units and a maturity
category is established for the sample. Forecast equations are estimated using data collected
during the previous five years, by month, and by maturity classification. The maturity
definitions used by the enumerators are:
Maturity

Definition

1 - Pre-Flag

There is no swelling in the stalks and no flag leaf is present.

2 - Flag or early boot

A flag leaf is present, and the collar of the flag leaf has emerged
above the top foliage leaf. The enclosed head is located below the
collar of the top foliage leaf.

3 - Late boot or Flower

The wheat is in the late boot stage from the point where the
swelling has occurred above the top foliage leaf until the head has
emerged and will show a water clear liquid turning milky white.

4 - Milk

The kernels are soft, moist, and filled with a milky liquid.

5 - Soft dough

The contents of the kernels are soft and can be kneaded like dough.

6 - Hard dough

The grain is firm and can be dented with the thumbnail, but not
easily crushed.

7 - Ripe

The grain is hard and breaks into fragments when crushed.

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Forecasting and Estimating Number of Heads and Grain Weight per Head for Sample Fields
Wheat is no exception to the general rule of objective yield surveying, i.e., successfully
forecasting fruit weight is more difficult than forecasting fruit count. Therefore, it should be no
surprise that over the course of time and program development, one model has been deemed
sufficient for predicting number of heads whereas two are employed to forecast final weight. The
regression equations for all three models are developed at the sample level by relating counts and
measurements of plant characteristics made during the growing season to actual counts,
measurements, or weights made at harvest time. For example, the April stalk count of a sample
may be easily related to the number of heads recorded just before farmer harvest in July. Many
relationships like this are developed for forecasting and each relationship is estimated from the
most recent five years of data.
The major early season independent variable used to forecast the final number of heads (used for
pre-flag and flag or early boot maturities) is the observed stalk count. At this stage of
development there are very few observable plant characteristics that are associated with final
weight per head. Consequently, to forecast a yield, it is necessary to rely on the historical head
weight (5-year average) as the forecast of end-of-season head weight.
As the crop develops toward mid-season, more plant characteristics appear that can be accurately
defined, measured, and related to final yield. It is in this period of early head development (late
boot or flower) that the plant enters a transition stage. The plant shifts from development of
vegetative growth to grain development. At this time, it is possible to accurately forecast final
head numbers. The maximum fruit load has been or is nearly set. The number of emerged and
late boot heads are used to forecast the final number of heads. It is also possible to make the first
forecast of head weight based on observable and measurable plant characteristics. Wheat heads
have spikelets which are clearly distinguishable when the stalk reaches the boot stage. Within
most of these spikelets one to three grains will form. Therefore, using the number of spikelets in
a regression equation provides the first current indication of the end of season head weight.
When the wheat plant reaches the late stages of development (milk and soft dough), the
physiological processes of the wheat plant are directed totally toward kernel development. Head
development has also reached the point where kernels are filling and can be accurately identified
and counted. The observed number of grains per head and the observed clip unit green weight
per head of emerged and late boot heads are weighted together by their R-square values and used
at this stage for predicting the final head weight. At this time, forecasts become more precise
since the effect of unfavorable weather or environmental conditions on final biological yield is
reduced considerably.
When a field reaches the hard dough or ripe stage (maturity codes 6 and 7), the sample units are
harvested. Number of heads, average grain weight per head, and the moisture content of the
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grain are determined for each sample. The number of heads in the sample units is expanded to
heads per acre and grain weight per head is adjusted to industry standard moisture of 12 percent.
These actual yield components are used to compute the final sample gross yield per acre.
Table 1 illustrates the independent variables used to forecast the final number of heads and the
grain weight per head over all maturity classes.

Table 1. Variables Used to Forecast the Components of Final Yield
Maturity
Category

Final Number of Heads

Final Weight per Head

Independent Variable

Independent Variable(s)

Pre-Flag
Flag or Early Boot
Late Boot or Flower

Number of stalks
Number of stalks
Emerged heads plus
heads in late boot

Milk

Emerged heads plus
heads in late boot

Soft Dough

Emerged heads plus
heads in late boot

Hard Dough and Ripe

Actual count of emerged
heads, detached heads, and
heads in late boot

Historical Average
Historical Average
1. Fertile spikelets per
head, and
2. Historical Average
1. Grains per head, and
2. Clip Unit Green
Weight per head
1. Grains per head, and
2. Clip Unit Green
Weight per head
Actual threshed weight per
head adjusted to standard
moisture determined from the
laboratory work.

The forecast model for final heads per sample has the following form for each maturity class:
𝑦𝑖 = 𝑎 + 𝑏𝑥𝑖 + 𝜀𝑖
where xi is the number of stalks in sample i if maturity is 1 or 2, and a combination of emerged
heads and late boot heads in higher maturity classes, yi is the number of heads for sample i, and
𝜀𝑖 ’s are random departures from the relationship. The historic coefficients a and b are estimated
by ordinary least squares from data collected during the previous five years. This model
produces R2’s between 50 and 80 percent for maturity class 1 and 2, in the 80’s and 90’s for class
3, and in the 90’s to high 90’s for classes 4 and 5.
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The forecast models for final weight per head are a weighted combination of two regressions for
each maturity except maturity class 1 and 2 which rely solely on historic weights. The form for
each model is:
Model 1:
𝑤𝑦𝑖 = 𝑎 + 𝑏𝑥𝑖 + 𝜀𝑖
Model 2:

𝑤𝑦𝑖 = 𝑐 + 𝑑𝑧𝑖 + 𝜖𝑖

where xi is one plant measure such as the number of fertile spikelets, or the number of grains per
head, or the weight of harvested green heads, and zi is the other; yi is the final weight of heads
for sample i, and 𝜀𝑖 and 𝜖𝑖 are random departures from the relationship and there is no
specification for the relationship between 𝜀𝑖 and 𝜖𝑖 . The coefficients (i.e., a, b, c, and d) are
estimated by ordinary least squares from data collected during the previous five years. Table 1
highlights the variables used for estimating Model 1 and Model 2 for each maturity. Generally
speaking, Model 1 and Model 2 have poor diagnostics, the R2 values begin at 0 percent for
maturity class 3 and neither model is regularly above 50 percent even for maturity class 5. Since
Model 1 and Model 2 sometimes lead to performance ambiguity, a composite is constructed for
each maturity class as follows:

̂𝑖 =
𝑊𝑌

𝑅12 (𝑤𝑦
̂ 𝑖1 ) + 𝑅22 (𝑤𝑦
̂ 𝑖2 )
2
2
𝑅1 + 𝑅2

̂ 𝑖 is the weighted forecast of grain weight per head for sample i from Model 1 and 2,
where, 𝑊𝑌
2
and R1 and R22 are the multiple correlation coefficients for Model 1 and 2 respectively. In class
3, the 5-year historic grain weight per head is manually assigned an R2 of .2.

Forecasting Yield for Sample Fields
̂𝑖 = (𝑦̂𝑖 ) ∗ (𝑊𝑌
̂ 𝑖) ∗
𝐺𝑌

𝐶𝐹𝑖
𝑅𝑆𝑖

where, RSi is the row spacing measurement across eight rows and CFi is a conversion factor
defined as [ (43560)(8)(12) ] / [ (6)(60)(453.58)(21.6) ] = 1.186 adjusts for area measured and
weight changes from metric to English. The parts are as follows:
43,560 is the number of square feet per acre,
8 adjusts for measuring across 8 row spaces,
12 converts inches to feet,
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6 is rows counted in the sample units,
60 converts pounds to bushels,
453.58 converts grams to pounds and
21.6 is the width of the wheat frame in inches.
State Average Forecasts and Estimates
In each month, the sample level gross yield forecasts are averaged to the State level. Since the
sample is self-weighting, the simple mean of the sample forecasts is an unbiased estimate of the
State gross yield. Therefore,
𝑁𝐺

1
𝐺̅ =
∑ 𝐺𝑖
𝑁𝐺
𝑖

Where 𝐺̅ represents the mean gross yield for each state,
and the standard error of the estimate is:
NG

𝑆𝐺̅ = √∑
𝑖

̅ )2
(Gi − G
NG (NG − 1)

Simple means are also calculated for most all independent variables and harvest loss measures.
These calculations are used to support analysis of the State level gross, or net, yield. Notably, the
State average grain weight per head is calculated using a weighted mean. The weighting variable
is the sample’s Heads per Square Foot.
State Average Grain Wt. per Head = ∑(Sample Field Grain Wt. per Head * Sample Field Heads
per Sq. Ft) / ∑(Sample Field Heads per Sq. Ft)

Harvest Loss
State level harvest loss is forecasted as the mean of all sample level harvest losses.
𝑁𝐿

1
𝐿̅ =
∑ 𝐿𝑖
𝑁𝐿
𝑖

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where Li is the harvest loss in sample i and NL = number of samples with gleaning data.
NL

𝑆𝐿̅ = √∑
𝑖

(Li − L̅)2
NL (NL − 1)

State Level Net Yield
Net Yield is a direct extension of the State level aggregates.

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̅̅̅̅ = 𝐺̅ - 𝐿̅
𝑁𝑌
And the standard error of the State level net yield :

2
2
𝑆𝑁𝑌
̅̅̅̅ = √𝑆𝐺̅ + 𝑆𝐿̅ −

2
𝐶𝑂𝑉(𝐺, 𝐿)
𝑁𝐺

Where
NL

COV (G,L) =



(Gi - G )(Li - L )

1

NL -1

Production for the State
Production, P, for the State is the product of estimated State-level net yield and acres to be
harvested for grain
̅̅̅̅),
P = (Aharv) ( 𝑁𝑌
And a standard error of:
2
2
2
̅̅̅̅ 2 2
𝑆𝑃 = √(𝐴2ℎ𝑎𝑟𝑣 )(𝑆̅̅̅̅
𝑁𝑌 ) + (𝑁𝑌 )(𝑆𝐴ℎ𝑎𝑟𝑣 ) + (𝑆̅̅̅̅
𝑁𝑌 )(𝑆𝐴ℎ𝑎𝑟𝑣 )

Gross Yield for Samples with Incomplete Data
Gross yield is forecasted or estimated from the current month's survey data. In some cases,
current data are unavailable and data from a previous month may be used to compute gross yield,
or no gross yield may be computed for the sample. The different cases are discussed below.
Refusals
If the farmer refuses permission to enter the field, the sample is lost for the season. In this case
the yield for this sample is left missing. Consequently, the refused sample contributes no new
information to the state level average yield. The sample, and the acreage represented by it, is
assumed to be the state’s average gross yield.

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Inaccessible Samples
Occasionally, some samples are inaccessible due to scheduling or field conditions. If data from a
previous visit are available, the previous forecast is carried forward. Otherwise, the sample is
excluded from gross yield calculations. The sample must still be intended for harvest as grain.
Early Farmer Harvest
If a previously laid out sample is harvested by the farmer before current data can be collected,
the previous month's predicted yield is brought forward.
Lost, Abandoned, Destroyed Samples
If a sample is lost, abandoned, destroyed, and so forth, no gross yield is computed for the sample.
The sample contributes nothing to the sample-level yield indication.
Removing Bias from State Level Calculations
Forecasts of State level yields are inherently subject to differ from the final, administrativelydetermined, yield. The difference is due to weather and crop conditions yet to be encountered at
the time the forecast is produced, the difference between weather and crop conditions in the
current year and the historic weather and crop conditions utilized to predict current yields, and
systematic non-sampling errors which contribute to forecast error. NASS makes every attempt to
minimize the impact of these three sources of error by means of administratively determine final
values. These final, sometimes referred to as official values are used as dependent variables to
estimate an ordinary least squares equation with the averages calculated from objective yield
samples as the independent variable. For example, each state will have an administrativelydetermined, official wheat yield for all previous years. To forecast the official wheat yield for the
current year, NASS regresses the objectively determined State level average wheat yields from
previous years to the corresponding official wheat yields. This process provides a historical
context for weather, biases, and non-sampling errors.

The regression equation is:
𝑦𝑡 = 𝑎 + 𝑏𝑥̅𝑡 + 𝜀𝑡
where yt is the Official state yield in time period t, 𝑥̅𝑡 is the calculated State average net yield in
time period t, a and b are ordinary least squares estimates, and 𝜀𝑡 is a random departure from the
relationship.

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Computational Examples

Yield
Yield indications are derived by initially calculating the two yield components, number of heads,
and weight per head. These components are forecasted by applying linear regression models to
sample data. The models used by a State vary by class of wheat, geographic district, and
maturity category. The parameters for these regression models are computed from the 5 most
recent years of historical sample data for that State.
The following pages will demonstrate, by example, how models are used to forecast yield in the
various sample maturity categories.
Maturity Category 1, pre-flag:
For samples in the pre-flag maturity category, the sample variable used to forecast number of
heads is number of stalks. The variable to forecast the weight per head is the historical average
weight per head.
Suppose the appropriate regression models are:
Number of heads = 180 + .2 * (total number of stalks),
and
Weight per head = .64
If the sample has 920 stalks, then the forecasted number of heads = 180 + .2 * (920) = 364.
Therefore, the forecast of gross yield per acre from a sample with an 8-row width of 6.4 would
be:
Gross yield

= [(number of heads)(weight per head)(conversion factor)] / (8-row width)
= [ (364)(.64) (1.186) ] / 6.4 = 43.17.

Maturity Category 2, flag or early boot:
For samples in the flag or early boot maturity category, the sample variable to forecast number of
heads is number of stalks. The variable to forecast the weight per head is the historical average
weight per head.
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Suppose the appropriate regression models are:
Number of heads = 90 + .4 * (total number of stalks)
and
Weight per head = .64
If the sample unit has 650 stalks, then the number of heads = 90 + .4 * (650) = 350.
Therefore, the forecast of gross yield per acre from a sample with an 8-row width of 6.4 would
be:
Gross yield

= [(number of heads)(weight per head)(conversion factor)] / 8-row width
= [ (350)(.64) (1.186) ] / 6.4 = 41.51

Maturity Category 3, late boot or flower:
For samples in the late boot or flower maturity category, the variable to forecast number of heads
is the sum of emerged heads and heads in late boot. Two models are used to forecast weight per
head. The first model uses the number of fertile spikelets per head and the second model uses
the historical average head weight. These are weighted together using R-square of the first
model and a weight of 0.2 for the second.
Suppose the appropriate regression models are:
number of heads = 23 + .9 * (total number of emerged heads + heads in late boot)
weight per head (Model 1) = .12 + .04 * (number of fertile spikelets), with an R-square
of .31
weight per head (Model 2) = .64
If the sampled unit has a total of 336 emerged heads and heads in late boot, and 15 fertile
spikelets per head,
then,

number of heads = 23 + .9 * (336) = 325,
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and weight per head (Model 1) = .12 + .4 * (15) = .72
The composite weight per head forecast is:
weight of heads = R2 Model 1(wt per head Model 1) + R2 Model 2(wt per head Model 2)
R2 Model 1 + R2 Model 2
so that in this example:
weight per head = [.31(.72) + .20 (.64) ] / [ .31 + .20 ] = .69
Therefore, with 8-row width of 6.4,
Gross Yield per Acre = [ (number of heads)(wt per head)(conversion factor) ] / 8-row
width
= [ (325)(.69)(1.186) ] / 6.4
= 41.56
Maturity Category 4, milk:
For samples in the milk maturity category, the variable to forecast number of heads is the sum of
emerged heads and heads in late boot. Two models are used to forecast weight per head. The
first model uses the number of grains per head and the second model uses the clip unit green
weight per head. There are weighted together using the R-squares of the models.
Suppose the appropriate regression models are:
number of heads = 6 + 1.0 * (total number of emerged heads + heads in late boot),
weight per head (Model 1) = .59 + .003 * (number of grains per head), with an R-square
of .95,
and
weight per head (Model 2) = .5 + .16 * (clip unit head weight), with an R-square of .97
If the sampled unit has a total of 331 emerged heads and heads in late boot, 18 grains per head,
and a clip unit green weight of .74,

then

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number of heads = 6 + 1.0 * (331) = 337,
weight per head (Model 1) = .59 + .003 * (18) = .64,
and
weight per head (Model 2) = .5 + .16 * (.74) = .62
The composite weight per head forecast is
wt per head = R2 model 1(wt per head Model 1 )+R2 Model 2(wt per head Model 2)
R2 Model 1 + R2 Model 2
so that in our example
weight per head = [ .95 (.64) + .97 (.62) ] / [ .95 + .97 ] = .63
Therefore, with 8-row width of 6.4,
Gross yield per acre = [ (number of heads)(wt per head)(conversion factor) ] / 8-row
width
= [ (337) (.63) (1.186) ] / .64 = 39.34
Maturity Category 5, soft dough:
For samples in the soft dough maturity category, the variable to forecast number of heads is the
sum of emerged heads and heads in late boot. Two models are used to forecast weight per head,
one using the number of grains per head and the other using the clip unit green weight per head.
These are weighted together using the R-squares of the models.
Suppose the appropriate regression models are:
number of heads = 7 + 1.0 * (number of emerged heads + head in late boot),
weight per head (Model 1) = .33 + .02 * (number of grains per head),
with an R-square of .98,
and
weight per head (Model 2) = .37 + .33 * (clip unit green wt.),
with an R-square of .99.
If the sample unit has a total of 332 emerged heads and heads in late boot, 21 grains per head,
and a clip unit head weight of .93,
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then
number of heads = 7 + 1.0 * (332) = 339,
weight per head (Model 1) = .33 + .02 * (21) = .75,
and
weight per head (Model 2) = .37 + .33 * (.93) = .68
The composite weight per head forecast is
wt per hd = R2 model 1(wt per hd Model 1) + R2 Model 2(wt per hd Model 2)
R2 Model 1 + R2 Model 2
so that in the example
weight per head

= [ .98 (.75) + .99 (.68) ] / [ .98 + .99 ]
= .71

Therefore, with an 8-row width of 6.4,
Gross Yield Per Acre = [ (number of heads)(wt per head)(conversion factor) ] / 8-row
width
= [ (339) (.71) (1.186) ] / 6.4 = 44.60
Maturity Categories 6 and 7, hard dough and ripe:
Actual number of heads and actual head weight are used to calculate gross yield per acre. The
following final lab data and gleaning counts and measurements are obtained for a sample:
number of emerged heads, detached heads, and heads in late boot = 350,
moisture content of enumerator harvested grain = 12%,
number of heads threshed = 250, and
threshed weight of grain = 180
weight of gleaned grain = 20
moisture content of post-harvest gleaning grain = 14%
Calculate weight per head, gross yield per acre, harvest loss per acre, and net yield.
Wt. per Head = [(threshed wt of grain)(1.0 - moisture) ] / [ (number of heads threshed)
(.880)]
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= [ (180) (1.0-.12) ] / [ (250) (.880) ]
= .72

Assuming an 8-row width of 6.4,
Gross Yield Per Acre = [ (number of heads)(wt per head)(conversion factor) ] / [ 8-row
width ]
= [ (350) (.72) (1.186) ] / 6.4
= 46.70
Harvest loss per acre = [(wt of threshed grain)(1.0-moisture content of grain)
(conversion factor) ] / [(.880)(8-row width)]
= [ (20) (1-.14) (1.186) ] / [ (.880) 6.4 ]
= 3.62
Net Yield = Gross Yield - Harvest Loss
= 46.70 - 3.62
= 43.08

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CHAPTER 9 PREPARATION OF OFFICIAL STATISTICS
Overview

A fundamental principle behind the estimation process is that precision of the sample survey
estimates is greatest at the aggregated regional and U.S. levels. The precision of a sample survey
estimate is measured by the estimated sampling error. In theory, many independent sample
surveys could be conducted simultaneously, each producing estimates of acreage, yield, or
production. The extent to which these independent estimates would differ from each other is
called the sampling error and can be estimated from each sample. For NASS surveys, the
sampling error at the U.S. level for corn acres is about 1.0 percent, 2.3 percent in major States
and 10-15 percent in other States.
The sample surveys are designed to produce State level estimates of acreage, expected yields,
final yields, and total production. The surveys are conducted by each State, and the first level of
analysis is done by each State. Each Regional Field Office does its independent appraisal of the
relationships between the survey estimates and the final official statistics and forwards this
information to Headquarters.
While each Regional Field Office is analyzing its survey data, statisticians in Headquarters are
doing a parallel analysis of all survey data at the State, U.S., and regional levels. For the major
field crops discussed in this paper, a formal Agricultural Statistics Board is convened to review
regional indications and determine the official forecast or estimate. This Board is made up of 7 to
10 statisticians representing different divisions of NASS. Each Board member evaluates the
regional survey indications and supporting data and determines their forecast or estimate. Each
member brings their individual perspective to the review which can result in different
conclusions being drawn. Through review and discussion, the Board must collectively reach a
consensus and establish the National number. The Board process ensures all perspectives are
examined and the national or regional forecast or estimate is the result of a thorough analysis.
The summation of the individual State estimates as prepared by each State is compared to the
Board number. The Headquarters statisticians will re-examine all national and State data
relationships and either adjust State estimates, so they sum to the U.S. or change the previously
determined U.S. number.
Domestic supply is a key factor in the marketing of any commodity and affects the day-to-day
business decisions of the industry. As a result, crop production forecasts and estimates are
extremely sensitive data. Premature or privileged disclosure of NASS numbers would give
individuals or groups an unfair advantage in the marketplace. NASS must ensure that all official
numbers are made available to everybody at the same time, making security a very big issue. All
data, both individual and summary, are protected against disclosure at every step of the
forecasting and estimating process. Data access must be always restricted in the Regional Field
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Offices and Headquarters. As data are summarized and aggregated to regional or national levels,
the security is heightened. Yield forecasts and estimates from the largest producing States are
encrypted before transmission to Headquarters. As data are received in Headquarters and
commodity statisticians begin the review process, offices are designated as secure offices and
visitors are denied access.
The formal meeting of the ASB to establish the final numbers and prepare the report is
conducted under “lock up” conditions. Lock up begins with a complete isolation of all facilities
required by the Board. All doors are locked, windows and elevators are covered and sealed,
phones are disconnected, and the computer network inside “lock up” is isolated from the full
network. Transmitters are not permitted, and the area is monitored for electronic signals. Highly
speculative data are decrypted only after the area is secure. Only after all security is in place does
the Board begin final deliberations. The area remains locked up until a prescribed release time
(12:00 p.m. for Crop Production) at which time the report is disseminated in electronic and paper
forms.
This chapter is devoted to describing the interpretation process followed by commodity
statisticians to arrive at the best number. A brief discussion of acreage estimates is followed by a
detailed explanation of forecasting yields. The last two parts address end of season estimates of
acreage, yield, and production followed by an overview of how balance sheets are used as a
check on the final estimates.
Acreage Estimates
The summary programs provide point estimates of acreage planted, called direct expansions,
and measures of change from a previous estimate, called ratio estimates.
Direct expansions measure the level of the value of the item being estimated. For area frame
surveys, every segment of land selected from the area frame has a known probability of
selection. The inverse of the probability of selection for each sample unit (expansion factor)
multiplied times the acres found in the segment are summed across the sample to determine a
direct estimate of acres planted to each crop. List samples also have known probabilities of
selection and their data can be similarly expanded to provide direct expansions in a multiple
frame design.
Ratio estimates are used to measure change from a previous estimate of the same item
(preliminary acres for harvest) or a related item (previous year’s planted acres). These types of
ratios rely on matched reports from both surveys. The area frame sample is divided into five
independent rotation groups with four groups carried over from one year to the next. The
consecutive year’s data from these four rotation groups can be matched to provide a measure of
the percent change in acres planted. The list sample can be similarly structured to provide survey
to survey matched samples and ratios can be computed in the multiple frame design.
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The determination of the official estimates of acres planted is based on an analysis of the
historical and current direct expansions and ratio estimates as they compare to the final estimates
of planted acres. The analysis is based on “difference” estimates which measure the average
difference between the survey indications and the final estimates. This analysis is done at both
the State and U.S. levels with any differences being reconciled in Headquarters.
The June Area Survey (JAS) and the June Agricultural Survey provide the benchmark estimates
of acres planted. In some years, weather related problems delay planting activities which means
farmers are reporting acres they still intend to plant. When this occurs, subsamples of farms
included in the JAS are re-surveyed in July to determine the acres actually planted. These
updated acreage estimates are reviewed similarly to the procedures followed in June. Yield
surveys provide ratio indications which are used to monitor changes in acreages.
Acres harvested and to be harvested are key variables for deriving production forecasts and
estimates, respectively. Direct expansion and ratio of change estimators are also used to estimate
harvested acres. In addition, the ratio of harvested to planted acres as provided by the survey can
be multiplied times planted acres for another indication of harvested acres. The “difference”
analysis described above is also used to determine the official harvested acreage estimates.
Yield Forecasts
Arguably, the most watched publications of NASS are the Crop Production Reports containing
the early season forecasts of production for the major field crops. Early season production
forecasts are key pieces in the price discovery mechanism for these billion-dollar crops. This
kind of scrutiny demands a review as comprehensive as the security provisions to ensure the best
forecasts and estimates.
The yield surveys produce vast amounts of data for analysis. The modeling processes described
in previous chapters produce multiple indications of net yield per harvested acre. The first
monthly forecasts for a crop feature some key indications that include but not limited to average
field level yield regressed to official estimates, average counts regressed to official estimates,
average projected yield reported by farmers in the Agricultural Yield (AY) Survey regressed to
official estimates, and model-based indications. Once harvest begins, average realized farmer
yields are regressed to official estimates. In addition to the point estimates, forecast errors of the
regression equations and models are also computed. Adding and subtracting these forecast errors
from the forecast value forms a forecast range for each indication. Usually, the ranges for these
indications overlap defining the range that simultaneously satisfies all forecasts.
Merely selecting a yield from within the overlapping range is not the end of the process.
Commodity statisticians must determine if all of the other pieces of available data support the
“candidate” yield forecast. Some of the more important things to evaluate are:
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1.

Average maturity category - Enumerators determine the maturity category of each OY
sample. The average maturity category helps commodity statisticians align the crop
calendar with the monthly report calendar. This maturity should be consistent with
weekly crop progress data. Extremely late (below average maturity) crops and extremely
early (above average maturity) crops often produce data that lie in the fringes of the
historical data and may result erratic forecasts due to extrapolating the forecast equations.

2.

Forecasted fruit count - Even in the first survey month, plant counts are obtained for all
OY samples and forecasts of the number of fruit per acre can be made every month for
every crop regardless of maturity. As the fruit develop, counts of immature fruit are used
to provide even more precise forecasts of fruit expected at harvest. Experience has shown
that forecast equations for fruit count have very high R-square values and produce very
accurate forecasts. In fact, the linear relationship is so strong these equations are robust
against extrapolation.

3.

Forecasted fruit weight - As easy as it is to forecast count, forecasting weight is equally
difficult. In the early months, there is no measurable characteristic to use in a model and
historical average fruit weights must be used. Even after the fruit set and measurements
can be made, data are extremely variable, and correlations are not very high. Thus, fruit
weight forecasts have much larger forecast errors than fruit count. Extreme maturities can
significantly impact weight models. Fruit weight often becomes the key discussion factor
in Board deliberations.

4.

Averages of the raw data - The raw counts are definitionally stable across years. As noted
in earlier chapters, parameter estimates for the forecast equations are recomputed each
year using a “rolling” dataset. Changes in forecasts from one year to the next are a
combination of changes in the current raw counts and new equations. These changes are
confounded in the forecast and isolating the changes in farmer practice from the
differences in the crop season from the trends in yield is difficult. The raw counts give
insight into true shifts in the components of yield like planting patterns and plant
populations, fruit per plant, size of ears, etc. When the number of plants per acre is higher
than ever recorded before, a record fruit count forecast and, possibly, a record yield
should be no surprise.

5.

Interaction of fruit count and fruit weight - Statisticians can obtain insight into yield
levels by looking at the interaction of the two main components, count and weight. The
final yield may be the same for 2 years, but they may be a result of different components.
A simple scatterplot of count against weight with points labeled as to year clearly show
how the current forecasts compare to the final estimates of previous years.

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6.

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Month to month shifts - Each of the five items discussed above can apply to a standalone, single month analysis. However, after the first forecast month, each can be applied
in a month-to-month analysis. The second and third forecasts are measured against the
previous forecast and the statistician must understand what is causing the indications to
move up or down. Are the raw counts and measurements changing? Are the models
forecasting the components at a different level? How are the farmer assessments of their
yield prospects in the AY survey changing? What effect is final harvest data having on
the indications?

This process is done independently in each State and at the combined level in Headquarters.
Headquarters statisticians make the final determination, and, when necessary, will establish
forecast or estimate that differs from the State(s) recommendations so the State numbers are
additive to the U.S. level.
Final Estimates - Acres, Production, Stocks
Chapter 2 contains a discussion of the Agricultural Surveys and how they relate to yield surveys.
The September and December Agricultural Surveys are the vehicles by which final acreage,
yield, and production data are obtained. Final end-of-year estimates are prepared from these data.
The September survey focuses on the small grains and is timed to be conducted as harvest is
nearly complete. The December survey collects the row crops end of season data, and it is also
timed to occur as harvest winds down. Respondents to these surveys report actual acres
harvested and the actual yield or production realized from harvest. Grain in storage data are
collected at this time and are used to estimate “carry out” stocks which are used in balance sheet
reviews of the major crops.
The OY sample plots are harvested at crop maturity. A sample of plots are gleaned for harvest
loss after the sample fields are harvested. These crop cuttings form a secondary final yield
indication, but, more importantly, they are used to compute parameter estimates in future years.
The final OY observations serve as the values of the dependent variables of the regression
models.
Balance Sheets
The end-of-season estimates of acres harvested, yield, production, and stocks are reviewed in
combination using a balance sheet approach. Up to this point, the approach is to consider acres
and yield independent of the supply and demand relationship. The balance sheet offers a more
global look at how the estimates fit into the bigger picture. Using estimates from NASS surveys,
and administrative data from outside sources, commodity statisticians can construct a balance
sheet to see if the estimates reconcile with these sources. Using corn as an example, a December
1 balance sheet analysis would look as follows:

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Quantity carried over from previous year (September 1 on-farm and off-farm stocks for
corn and soybeans, June 1 for wheat)
Plus

Imports since September 1
Current Production (NASS estimate)
Equals Beginning supply as of December 1
Minus Disappearance since September 1
Exports
Processing
Feed and seed
Balance Sheet Indication of December 1 stocks
Survey Indications of December 1 stocks (on farm and off farm)
Residual
The residual component of the balance sheet is the difference between the survey indicated
stocks and the balance sheet stocks. Each survey component of the balance sheet contains
sampling and non-sampling errors. The disappearance items such as exports and processing are
based on administrative sources with varying levels of completeness. For these reasons, it is not
reasonable to expect a zero residual; however, an unreasonable residual is cause for alarm and
triggers a second review of the elements in the balance sheet. The objective is to have a
reasonable balance and still have the estimates within the range indicated by the surveys.

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