ATTACHMENT 6 SNAP-Participation-Rates-2022.pdf

ATTACHMENT 6

Empirical Bayes Shrinkage Estimates of State Supplemental Nutrition Assistance Program Participation Rates: Fiscal Year 2020 and Fiscal Year 2022

Final Report

February 2025

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Empirical Bayes Shrinkage Estimates of State Supplemental Nutrition

Assistance Program Participation Rates: Fiscal Year 2020 and Fiscal

Year 2022

Final Report

February 2025

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Submitted to: Submitted by:

U.S. Department of Agriculture

Food and Nutrition Service

1320 Braddock Place

Alexandria, VA 22314

Contract Number: 12-3198-23-F-0047

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Disclaimer

The findings and conclusions in this report are those of the authors and should not be construed to represent any official USDA or U.S. Government determination or policy.

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Acknowledgements

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Contents

Executive Summary .......................................................................................................................................................................................... ix

I. Introduction

II. A Step-by-Step Guide to Deriving State Estimates

A. From CPS ASEC data and SNAP administrative data, derive direct estimates of State SNAP participation rates

B. Using a regression model, predict State SNAP participation rates based on administrative, ACS, and other data

C. Using shrinkage methods, average the direct estimates and regression predictions to obtain preliminary shrinkage estimates of State SNAP participation rates

D. Obtain final shrinkage estimates of State SNAP participation rates and number of eligible people

III. State Estimates of SNAP Participation Rates and Number of Eligible People

References

Appendix A The Estimation Procedure: Additional Technical Details

Appendix B Data for Figures in Cunnyngham 2025

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Tables

III.1 Final shrinkage estimates of SNAP participation rates and number of people eligible for SNAP

III.2 Approximate 90 percent confidence intervals for final shrinkage estimates for FY 2020

III.3 Approximate 90 percent confidence intervals for final shrinkage estimates for FY 2022

A.1 Number of people receiving SNAP benefits, monthly average

A.2 Estimated percentage of participants who are correctly receiving SNAP benefits and eligible under Federal SNAP rules

A.3 Estimated number of participants who are correctly receiving SNAP benefits and income eligible under Federal SNAP rules, monthly average

A.4 Estimated percentage of people eligible for SNAP

A.5 Directly estimated number of people eligible for SNAP

A.6 CPS ASEC population estimate

A.7 State population on July 1

A.8 Direct estimates of SNAP participation rates and standard errors

A.9 Potential predictors

A.10 Predictors in current model

A.11 Values for first and second predictors

A.12 Values for third and fourth predictors

A.13 Values for fifth and sixth predictors

A.14 Values for seventh and eighth predictors

A.15 Regression estimates of SNAP participation rates, with standard errors

A.16 Preliminary shrinkage estimates of SNAP participation rates

A.17 Final shrinkage estimates of SNAP participation rates, with standard errors

A.18 Final shrinkage estimates of number of people eligible for SNAP, with standard errors

B.1a How many people were eligible in 2022? What percentage participated? (States)

B.1b How many people were eligible in 2022? What percentage participated? (Regions and national)

B.2a Estimates of participation rates (States)

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Tables

B.2b Estimates of participation rates (Regions and national)

B.3 How did your State rank in 2022?

B.4a How did your State compare with other States in 2022? (Illinois to Nevada)

B.4b How did your State compare with other States in 2022? (Iowa to Virginia)

B.4c How did your State compare with other States in 2022? (New Hampshire to Arkansas)

B.5 Estimates of participation rates varied widely

B.6 Supporting detail for Cunnyngham (2025)

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Exhibits

I.1 Example of a regression estimator

I.2 Shrinkage estimation

II.1 The estimation procedure

A.1 Algorithm to identify households with earnings

A.2 Direct estimates of national totals and adjustment factors

A.3 Estimated participation rates higher than 100 percent

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Executive Summary

The Supplemental Nutrition Assistance Program (SNAP) helps eligible individuals with low incomes buy food to feed themselves and their households. SNAP is the largest of the domestic nutrition assistance programs administered by the Food and Nutrition Service (FNS) of the U.S. Department of Agriculture

(USDA). During fiscal year 2024, the program served 41.7 million people in an average month and provided $93.7 billion in benefits.

This report presents estimates of the program’s effectiveness at reaching its target population in each

State and the District of Columbia for fiscal years 2020 and 2022. The program’s effective reach is measured by estimated SNAP participation rates, or the percentage of people eligible for SNAP benefits under Federal income and resource rules who participate in the program.

The COVID-19 public health emergency affected the quality of the data used to estimate SNAP participation rates from March 2020 through June 2021. As a result, the fiscal year 2020 participation rates reflect the pre-pandemic period of October 2019 through February 2020, and we did not estimate participation rates for fiscal year 2021 due to inadequate data for most of that year. Because of seasonality both in the data and introduced by our methodology, using 5 months rather than 12 months of fiscal year 2020 data resulted in an underestimate of SNAP participation rates for fiscal year 2020 (Vigil and Rahmi 2024). In addition, because of the smaller sample size for fiscal year 2020, this report does not include estimates of SNAP participation rates for any State subgroups, such as people in households with earnings. However, to maintain consistency with estimates for earlier years, we used estimates for people in households with earnings along with estimates of all eligible people to derive this report’s final shrinkage estimates.

The State participation rate estimates for all eligible people were derived by using empirical Bayes shrinkage estimation methods and data from the Current Population Survey Annual Social and Economic

Supplement (CPS ASEC), the American Community Survey (ACS), and administrative records. The shrinkage estimator averaged direct estimates of participation rates with predictions from a regression model. The regression predictions were based on observed indicators of socioeconomic conditions in the

States, such as the percentage of a State’s population receiving SNAP benefits. Shrinkage estimators improve precision by “borrowing strength,” that is, by using data for several years from all the States to derive each State’s estimates for a given year and by using data from multiple sources, including sample surveys and administrative data. On average, 90 percent confidence intervals for fiscal year 2022 shrinkage estimates were 41 percent narrower than the corresponding confidence intervals for direct estimates. This report describes the shrinkage estimator in detail.

Final shrinkage estimates for fiscal year 2020 presented in this report differ slightly from the estimates presented in Cunnyngham (2023a) and Cunnyngham (2023b) because of annual updates to the years of data and regression model used. As a result, the estimates presented in this report should not be compared to those published in earlier reports.

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I. Introduction

The Supplemental Nutrition Assistance Program (SNAP) provides nutrition assistance to eligible individuals and households that need this assistance. SNAP is the largest of the domestic nutrition assistance programs administered by the Food and Nutrition Service (FNS) of the U.S. Department of

Agriculture. During fiscal year (FY) 2024, the program served 41.7 million people in an average month, providing $93.7 billion in benefits annually.

This report presents estimates that measure the program’s effectiveness at reaching its target population in each State and the District of Columbia for FY 2020 to FY 2022. Cunnyngham (2025) also reports the estimates presented here and compares them with one another. The program’s effective reach is measured by estimated SNAP participation rates—the percentage of people eligible for SNAP benefits under Federal income and resource rules who participate in the program.

The COVID-19 public health emergency affected the quality of the data used to estimate SNAP participation rates from March 2020 through June 2021. As a result, the fiscal year 2020 participation rates reflect the pre-pandemic period of October 2019 through February 2020, and we did not estimate participation rates for fiscal year 2021. Because of seasonality both in the data and introduced by our methodology, using 5 months rather than 12 months of fiscal year 2020 data resulted in an underestimate of SNAP participation rates for fiscal year 2020 (Vigil and Rahmi 2024). In addition, because of the smaller sample size for fiscal year 2020, this report does not include estimates of SNAP participation rates for any

State subgroups, such as people in households with earnings. However, to maintain consistency with estimates for earlier years, we used estimates for people in households with earnings along with estimates of all eligible people to derive this report’s final shrinkage estimates.

We derived estimates for each State in both fiscal years by using empirical Bayes shrinkage estimation methods. Specifically, we used a shrinkage estimator that optimally averaged direct estimates of SNAP participation rates with predictions from a regression model. We obtained the direct estimates (1) by applying

SNAP eligibility rules to households in the

Current Population Survey Annual Social and

Economic Supplement (CPS ASEC) to estimate numbers of eligible people and (2) by using

SNAP Quality Control (QC) data to estimate numbers of participating people. The regression predictions drew on data from the American

Community Survey (ACS), individual tax returns, population estimates, and administrative records.

The rest of this introductory chapter provides an overview of indirect estimation and our

U.S. Census Bureau data

The Current Population Survey is conducted monthly for the Bureau of Labor Statistics and is the primary source of current information on the labor force characteristics of the U.S. population. The survey’s Annual Social and Economic Supplement includes additional data on work experience, income, and noncash benefits and is based on a sample size of just under 100,000 households.

The American Community Survey is conducted monthly. Designed to replace the decennial census long form, it collects economic, social, demographic, and housing information on about 3 million households annually.

The Census Bureau develops annual population estimates by using decennial census population estimates along with administrative records and other data on births, deaths, net domestic migration, and net international migration.

More information on these data sources is available at http://www.census.gov.

http://www.census.gov/

Chapter I Introduction

Mathematica® Inc. 2 shrinkage estimator. In Chapter II, we describe, step by step, how we derived the shrinkage estimates presented here; in Chapter III, we present State SNAP participation rate estimates. Technical details and additional information about our estimation methods appear in Appendix A. The figures presented in

Cunnyngham (2024) appear in Appendix B.

Direct estimates. The principal challenge in deriving State estimates such as those presented in this report is the small sample size of the CPS ASEC. The optimal survey for estimating State SNAP eligibility

(1) would be based on a large sample for all States, (2) would be representative at the State level, and (3) would contain detail on the household relationships and income sources needed to estimate program eligibility. Among the three leading surveys, the CPS ASEC comes closest to meeting these standards despite its small sample size for most States. Another national household survey, the Survey of Income and Program Participation, contains more detail on relationships and income than the CPS ASEC, but it is not representative at the State level and is based on even smaller State samples than the CPS ASEC. The third candidate, the ACS, is much larger than the CPS ASEC, but it has fewer details on relationships and income sources. In addition, unlike the CPS ASEC’s fixed reference period of the previous calendar year for all households, the ACS’s reference period is the previous 12 months and therefore varies across households by up to a year, depending on when respondents completed the survey. For these reasons, we use the CPS ASEC to estimate SNAP eligibility.

However, for many States, estimates of SNAP eligibility and participation rates based solely on the CPS

ASEC sample for the State and time period in question, or “direct” estimates, are imprecise. For example, to directly estimate the number of people in New Jersey who were eligible for SNAP in FY 2022, we used only FY 2022 CPS ASEC data on households from New Jersey. Given the potential errors introduced by the

CPS ASEC surveying a small number of families in New Jersey, we can be confident—by a commonly used standard, a 90 percent confidence interval—that New Jersey’s SNAP participation rate in FY 2022 ranged between about 76 and 89 percent. This range is wide, although typical, reflecting our substantial uncertainty about New Jersey’s actual participation rate.

Indirect estimators. To improve precision, statisticians have developed indirect estimators, which borrow strength by using data from additional States, time periods, or data sources. The assumption underlying indirect estimation is that what happened in other States and in other years is relevant to estimating what happened in a particular State in a particular year.

One type of indirect estimator is the shrinkage estimator, which averages estimates obtained from different methods. In an early application of shrinkage methods, Fay and Herriott (1979) developed a shrinkage estimator that combined direct sample and regression estimates of per capita income for small places that were used to allocate funds under the General Revenue Sharing Program. For FNS, Schirm and

DiCarlo (1998) developed a shrinkage estimator to derive estimates of State participation rates for the

Food Stamp Program (the previous name for SNAP) and found that the shrinkage estimates were substantially more precise than the corresponding direct estimates—the shrinkage 90 percent confidence intervals were, on average, about 64 percent as wide as (or 46 percent narrower than) the corresponding sample confidence intervals. FNS has been publishing annual estimates of State participation rates for the

Food Stamp Program and later, SNAP, since Schirm (2000) estimated rates for September 1997.

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Regression estimates. Regression estimates are predictions based on either non-sample or highly precise sample data. In Exhibit I.1, we illustrate how a regression estimator works. The simple example in the exhibit involves only nine States and data for just one year on one predictor—the SNAP “prevalence” rate—that will be used to predict each State’s SNAP participation rate. The SNAP prevalence rate is the percentage of all people (eligible and ineligible combined) who received SNAP benefits, in contrast to the

SNAP participation rate, which is the percentage of eligible people who received SNAP benefits. The triangles in the exhibit correspond to direct sample estimates; a triangle shows the prevalence rate in a

State (horizontal axis) and the direct estimate of the participation rate in that State (vertical axis).

Exhibit I.1. Example of a regression estimator

Not surprisingly, the graph suggests that prevalence and participation rates are systematically associated.

States with higher percentages of all people participating in SNAP tend to have higher percentages of

Mathematica® Inc. 4 eligible people participating in the program, although the relationship is far from perfect. To measure the relationship between prevalence and participation rates and derive predictions, we can use a technique called “least squares regression” to draw a line through the triangles. Regression estimates of participation rates are points on that line, as indicated by the circles in Exhibit I.1. The predicted participation rate for a particular State is obtained by moving up or down from the State’s direct sample estimate (the triangle) to the regression line (where there is a circle) and reading the value from the vertical axis. For example, the regression estimator predicts a participation rate of just under 60 percent for both States with prevalence rates of about 5.5 percent. In contrast, for the State with a prevalence rate of about 9.5 percent, the predicted participation rate is nearly 70 percent.

Comparison of direct and regression estimators. A comparison of how the direct and regression estimators use data illustrates how the regression estimator borrows strength to improve precision. With

Tennessee as an example again, we used only one year of CPS ASEC sample data from the State to estimate Tennessee’s participation rate in that year. To derive regression estimates, we estimated a regression line from sample, administrative, and ACS data for several years and all the States and used the estimated line (with administrative and ACS data for Tennessee) to predict Tennessee’s participation rate in a given year. In other words, the regression estimator not only uses the direct estimates from every

State for several years to develop a regression estimate for a single State in a single year, but it also incorporates data from outside the sample—namely, data in administrative records systems and the ACS.

To improve precision even further, the estimator borrows strength across groups—all eligible people and people in households with earnings—by deriving estimates for the groups jointly.

The regression estimator can improve precision by using additional data to identify States with direct estimates that seem too high or too low because of sampling error (error from drawing a sample of the population that has a higher or lower participation rate than does the entire State population). For example, when a State has a low SNAP prevalence rate and values for other predictors that are consistent with a low SNAP participation rate, our regression estimator will predict a low participation rate for that

State. If the direct estimate for that State is high, the regression estimate will be lower than the direct estimate. On the other hand, if the sample data for a State show a lower participation rate than expected in light of the SNAP prevalence rate and the other predictors, the regression estimate for that State will be higher than the direct estimate.

A limitation of the regression estimator is bias. Some States actually have higher or lower participation rates than predicted with the regression estimator. Such errors in regression estimates reflect bias.

Although the regression estimator borrows strength by using data for all the States and several years as well as administrative and ACS data, it makes no further use of the sample data after estimating the regression line. It treats the entire difference between the sample and regression estimates as sampling error (that is, error in the direct estimate). It makes no allowance for prediction error (that is, error in the regression estimate). Although not all, if any, true State participation rates lie on the regression line, the assumption underlying the regression estimator is that the rates do lie on the regression line.

Shrinkage estimator. The shrinkage estimator strikes a compromise between the limitations of the direct estimator (imprecision) and the regression estimator (bias) by combining the two estimates. As illustrated in Exhibit I.2, the shrinkage estimator takes a weighted average of the direct and regression estimates, Mathematica® Inc. 5 weighting them according to their relative precision. When the direct estimate is more precise than the regression estimate, the estimator gives more weight to the direct estimate. On the other hand, when the regression estimate is more precise than the direct estimate, the estimator gives more weight to the regression estimate. The larger samples drawn in large States support more precise direct estimates; as a result, shrinkage estimates tend to be closer to the direct estimates for large States. The weight given to the regression estimate depends on how well the regression line “fits.” If we find good predictors reflecting why some States have higher participation rates than other States, we say that the regression line “fits well.” The shrinkage estimate will be closer to the regression estimate when the regression line fits well than when the line fits poorly (Appendix A describes the methods used to produce the estimates in this report.)

The direct and regression estimates are optimally weighted to improve accuracy by minimizing a measure of error that reflects both imprecision and bias. By accepting a little bias, the shrinkage estimator may be substantially more precise than the direct sample estimator. By sacrificing a little precision, the shrinkage estimator may be substantially less biased than the regression estimator. The shrinkage estimator optimizes the trade-off between imprecision and bias.

Exhibit I.2. Shrinkage estimation

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II. A Step-by-Step Guide to Deriving State Estimates

Here, we describe our procedure for estimating State SNAP participation rates and the number of people eligible for SNAP benefits. The procedure, summarized by the flowchart in Exhibit II.1, involves the following four steps:

1. From CPS ASEC data, SNAP administrative data, and population estimates, derive direct estimates of

State SNAP participation rates

2. Using a regression model and the direct estimates derived in Step 1, predict State SNAP participation rates based on SNAP administrative, individual income tax, and ACS data and population estimates

3. Using a shrinkage estimator, average the direct estimates from Step 1 and the regression predictions from Step 2 to obtain preliminary shrinkage estimates of State SNAP participation rates

4. Obtain final shrinkage estimates of State SNAP participation rates by using national estimates of eligible people derived from the CPS ASEC to adjust the preliminary shrinkage estimates from Step 3

We describe each step in the remainder of this chapter, with additional technical details in Appendix A.

A. From CPS ASEC data and SNAP administrative data, derive direct estimates of

State SNAP participation rates

A SNAP participation rate is obtained by dividing an estimate of the number of people participating in

SNAP by an estimate of the number of people eligible for SNAP, with the resulting ratio expressed as a percentage. We used SNAP QC data to estimate numbers of participants in an average month in the fiscal year and CPS ASEC data to estimate numbers of eligible people in an average month. Because the CPS

ASEC collects income data for the previous calendar year, we obtained estimates of eligible people in a fiscal year by using two years of CPS ASEC data. For example, we used the 2022 CPS ASEC to estimate

SNAP eligibility for October to December 2021 and the 2023 CPS ASEC to estimate SNAP eligibility for

January to September 2022. Appendix A presents direct estimates and their standard errors in each State for both fiscal years.

B. Using a regression model, predict State SNAP participation rates based on administrative, ACS, and other data

To derive regression estimates, we included both years and all States, not just one year and nine States as in our example in Chapter 1. We also used eight predictors, not just one. The eight predictors used for the estimates in this report measure the following:

1. The percentage of the population that correctly received SNAP benefits according to administrative data and population estimates.

2. The percentage of families with income under $20,000 in the past 12 months according to ACS one-year estimates.

3. The median household income according to ACS one-year estimates.

Chapter II A Step-by-Step Guide to Deriving State Estimates

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4. The percentage of the civilian employed population over age 16 who are private wage and salary workers according to ACS one-year estimates.

5. The change in the estimated population on July 1 compared to the previous year according to Census

Bureau population estimates.

6. The percentage of people not claimed on tax returns or claimed on tax returns with adjusted gross income under the federal poverty level according to individual income tax data and population estimates.

7. The percentage of individuals over age 65 that received Supplemental Security Income according to administrative records and population estimates.

8. An indicator of whether a State had a broad-based categorical eligibility (BBCE) policy that did not have a resource test and covered all income-eligible people.

Exhibit II.1. The estimation procedure

CPS ASEC = Current Population Survey Annual Social and Economic Supplement; SNAP = Supplemental Nutrition

Assistance Program; ACS = American Community Survey.

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These eight predictors were selected as the best from a longer list in Table A.9, which provides complete definitions and sources for the predictors. The second, fourth, and seventh predictors were included in the model that estimated rates for fiscal years 2018 to 2020. In addition, the first, sixth, and eighth predictors are similar to predicators included the previous model. Those previous predictors were, respectively, (1) the percentage of the population receiving SNAP benefits according to administrative data and population estimates, (2) the percentage of all children not claimed on tax returns or claimed on tax returns with adjusted gross income under the federal poverty level according to individual income tax data and population estimates, and (3) an indicator of whether a State had a resource test because it either did not use BBCE or included a resource test in its BBCE policy. Other predictors used in the previous model but not the current one are (1) the percentage of individuals age 25 and older who have completed a bachelor's degree and (2) the percentage of individuals over age 65 with household income under 100 percent of the federal poverty level according to ACS one-year estimates.

The regression equations do not express causal relationships. Rather, they imply only statistical associations. For this reason, predictors are often called “symptomatic indicators.” They are symptomatic of differences among States in conditions associated with higher or lower participation rates.

Appendix A presents the regression estimates and their standard errors. The standard errors tend to be similar across the States and much smaller than the largest standard errors for direct estimates, reflecting substantial gains in precision from regression for States with the most error-prone direct estimates.

C. Using shrinkage methods, average the direct estimates and regression predictions to obtain preliminary shrinkage estimates of State SNAP participation rates

To derive preliminary estimates of State SNAP participation rates, we used an empirical Bayes shrinkage estimator to average the direct estimates calculated in Step 1 and the regression predictions from Step 2.

(Appendix A describes the empirical Bayes methods we used.) We call the estimates from this step preliminary because we make some adjustments to them in the next step. Appendix A presents the preliminary shrinkage estimates of State SNAP participation rates.

D. Obtain final shrinkage estimates of State SNAP participation rates and number of eligible people

We adjusted the preliminary shrinkage estimates of participation rates in two ways. First, we adjusted the rates so that the counts of eligible people implied by the rates sum to the national count of eligible people estimated directly from the CPS ASEC. Second, we adjusted the rates so that no State’s estimated rate exceeded 100 percent. We carried out these adjustments separately for each year; the following description of the adjustments focuses on the FY 2022 estimates. In Appendix A, we describe the results of the adjustments for other years and discuss our adjustment method in more detail.

To implement the first adjustment, we calculated preliminary estimates of the number of eligible people from the preliminary estimates of participation rates derived in Step 3 and the administrative estimates of the number of SNAP participants obtained in Step 1. For FY 2022, the State estimates of eligible people summed to 39,330,801, whereas the national total estimated directly from the CPS ASEC was 38,278,702.

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To obtain estimated numbers of eligible people for States that sum (aside from rounding error) to the direct estimate of the national total, we multiplied each of the State preliminary estimates of eligible people by the ratio of 38,278,702 divided by 39,330,801, or 0.9732. Such benchmarking of estimates for smaller areas to a relatively precise estimated total for a larger area is common practice. (See, for example, Doppelt and Haley [2020] for a discussion of the Bureau of Labor Statistics benchmarking of the Current

Employment Statistics.)

After carrying out this first adjustment, the District of Columbia and eight States—Illinois, Massachusetts, New Mexico, Oregon, Pennsylvania, Rhode Island, Washington, and Wisconsin—had fewer estimated eligible people than estimated eligible participants in FY 2022, incorrectly implying participation rates over

100 percent. To cap participation rates at 100 percent, we performed a second adjustment. Specifically, we increased the number of eligible people in the District of Columbia and the eight States listed above so that the number of eligible people in those States equaled the number of participants. We reduced the number of eligible people in the other 42 States by an equivalent number and in proportion to their number of eligible people. The adjustment raised the participation rates of the 42 States by between 1.4 and 2.4 percentage points but did not change the national total or State rankings.

Applying this adjustment, we obtained our final shrinkage estimates of the number of people eligible for

SNAP. From those estimates and our administrative estimates of the number of SNAP participants, we derived final shrinkage estimates of participation rates. We present those estimates in the next chapter.

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III. State Estimates of SNAP Participation Rates and Number of Eligible

People

In Table III.1, we present our final shrinkage estimates of SNAP participation rates and the number of people eligible in each State for FY 2020 and FY 2022. The shrinkage estimates are relatively precise; they have much smaller standard errors and narrower confidence intervals than the CPS ASEC direct estimates.

In Tables III.2 and III.3, we provide approximate 90 percent confidence intervals showing the uncertainty remaining after using shrinkage estimation to derive the estimates in Table III.1. One interpretation of a 90 percent confidence interval is that there is a 90 percent chance that the true value—that is, the true participation rate or the true number of eligible people—falls within the estimated bounds. For example, although our best estimate is that New Jersey’s participation rate was 91 percent in FY 2022 (Table III.1), the true rate may have been higher or lower. However, according to Table III.3, the chances are 90 in 100 that the true rate was between 85 and 98 percent, an interval that is 44 percent narrower than the interval

(76 and 99 percent, as cited in Chapter I) around the direct estimate. A narrower interval means we are less uncertain about the true value. On average, shrinkage confidence intervals for FY 2022 participation rates for all eligible people were 41 percent narrower than the corresponding direct confidence interval.

Thus, shrinkage estimation substantially improves precision and reduces our uncertainty.

Despite the impressive gains in precision, substantial uncertainty about the true participation rates for some States remains even after application of shrinkage methods. Nevertheless, as discussed in

Cunnyngham (2024), the shrinkage estimates are sufficiently precise to show, for example, whether a

State’s SNAP participation rate was probably near the top, near the bottom, or in the middle of the distribution of rates in a given year. That is enough information for many important purposes, such as guiding an initiative to improve program performance.

Final shrinkage estimates presented in this report for FY 2020 differ slightly from the estimates presented in Cunnyngham (2023a) and Cunnyngham (2023b) for two reasons:

1. The shrinkage estimator uses data from multiple years to estimate participation rates for each year. Annually, data for the most recent year are added and data for the oldest year are dropped. As a result, the FY 2020 estimates presented in this report are based on 2020 and 2022 data, while the corresponding estimates published in Cunnyngham (2023a) and Cunnyngham (2023b) are based on

2018 to 2020 data.

2. The shrinkage estimator incorporates a regression model that is updated each year. Each year, we choose a regression model that best predicts participation rates for all years being estimated.

Although we place a premium on maintaining consistency in regression predictors from year to year, differences between the data used in the previous estimates and data used in the current estimates resulted in the use of a different regression model. Different regression models lead to slight differences in predicted participation rates, which in turn lead to slight differences in estimated participation rates.

Given these updates, the none of the estimates in this report should be compared to those published in earlier reports.

Chapter III State Estimates of SNAP Participation Rates and Number of Eligible People

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Table III.1. Final shrinkage estimates of SNAP participation rates and number of people eligible for SNAP

Participation rate (percent) Number of eligible people (thousands)

FY 2020 FY 2022 FY 2020 FY 2022

Alabama 88 90 762 797

Alaska 81 73 91 70

Arizona 73 77 920 822

Arkansas 64 59 505 454

California 67 81 5,290 4,618

Colorado 80 100 483 428

Connecticut 93 98 315 305

Delaware 96 91 96 92

District of Columbia 96 100 106 124

Florida 77 81 3,094 2,927

Georgia 76 92 1,618 1,535

Hawaii 85 81 162 161

Idaho 83 73 159 156

Illinois 100 100 1,464 1,540

Indiana 76 89 694 625

Iowa 89 98 277 224

Kansas 67 79 282 231

Kentucky 65 75 704 633

Louisiana 87 99 889 776

Maine 85 94 147 126

Maryland 91 85 579 543

Massachusetts 100 100 629 816

Michigan 84 100 1,185 1,027

Minnesota 80 93 429 372

Mississippi 63 74 661 546

Missouri 86 92 747 651

Montana 78 75 112 99

Nebraska 84 93 168 144

Nevada 89 98 370 350

New Hampshire 81 82 78 68

New Jersey 80 91 746 775

New Mexico 100 100 403 439

New York 84 91 2,651 2,558

North Carolina 73 95 1,468 1,273

North Dakota 67 81 56 46

Ohio 85 99 1,438 1,307

Oklahoma 89 98 602 597

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FY 2020 FY 2022 FY 2020 FY 2022

Oregon 100 100 503 483

Pennsylvania 100 100 1,520 1,387

Rhode Island 100 100 119 112

South Carolina 72 76 750 733

South Dakota 83 84 92 80

Tennessee 87 84 939 869

Texas 74 74 3,895 3,846

Utah 78 76 203 197

Vermont 96 99 57 55

Virginia 79 83 834 804

Washington 100 100 657 625

West Virginia 91 98 291 255

Wisconsin 97 100 522 528

Wyoming 52 63 47 47

United States 81 88 40,807 38,279

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Table III.2. Approximate 90 percent confidence intervals for final shrinkage estimates for FY

Lower bound Upper bound Lower bound Upper bound

Alabama 81 95 703 820

Alaska 74 87 83 98

Arizona 66 79 837 1,002

Arkansas 58 69 462 548

California 65 70 5,067 5,512

Colorado 74 87 443 523

Connecticut 86 100 292 338

Delaware 90 100 89 102

District of Columbia 88 100 97 114

Florida 73 81 2,931 3,256

Georgia 70 81 1,504 1,731

Hawaii 79 92 149 175

Idaho 77 90 146 172

Illinois 93 100 1,383 1,546

Indiana 71 81 648 741

Iowa 83 96 257 296

Kansas 61 73 255 309

Kentucky 59 70 642 765

Louisiana 82 92 837 941

Maine 78 91 135 159

Maryland 84 98 535 623

Massachusetts 93 100 586 671

Michigan 79 90 1,111 1,258

Minnesota 74 86 396 463

Mississippi 58 68 604 717

Missouri 79 93 686 808

Montana 72 84 104 121

Nebraska 78 91 155 180

Nevada 83 95 345 395

New Hampshire 73 88 71 85

New Jersey 74 86 686 806

New Mexico 92 100 375 432

New York 80 88 2,524 2,778

North Carolina 68 78 1,367 1,569

North Dakota 62 73 51 61

Ohio 80 91 1,345 1,531

Oklahoma 83 95 562 643

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Oregon 93 100 469 536

Pennsylvania 93 100 1,436 1,605

Rhode Island 93 100 112 126

South Carolina 67 77 699 802

South Dakota 76 90 84 100

Tennessee 82 93 877 1,001

Texas 70 77 3,697 4,092

Utah 72 85 186 220

Vermont 89 100 52 61

Virginia 73 86 766 903

Washington 91 100 602 712

West Virginia 84 98 268 314

Wisconsin 90 100 484 560

Wyoming 46 58 42 53

United States 79 82 40,161 41,452

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Table III.3. Approximate 90 percent confidence intervals for final shrinkage estimates for FY

Alabama 84 96 738 856

Alaska 66 79 63 77

Arizona 72 83 763 882

Arkansas 54 63 417 491

California 77 85 4,383 4,852

Colorado 93 100 395 461

Connecticut 92 100 283 326

Delaware 85 98 85 99

District of Columbia 90 100 116 133

Florida 76 85 2,747 3,107

Georgia 86 98 1,428 1,642

Hawaii 73 88 146 177

Idaho 68 78 145 168

Illinois 93 100 1,466 1,614

Indiana 83 95 581 670

Iowa 91 100 207 241

Kansas 72 86 210 251

Kentucky 69 81 579 688

Louisiana 93 100 726 826

Maine 87 100 116 137

Maryland 77 93 492 595

Massachusetts 92 100 771 861

Michigan 94 100 965 1,089

Minnesota 86 100 344 401

Mississippi 69 78 508 585

Missouri 85 99 600 701

Montana 69 81 90 108

Nebraska 86 100 132 156

Nevada 92 100 326 375

New Hampshire 75 90 62 75

New Jersey 85 98 716 833

New Mexico 90 100 409 470

New York 86 96 2,415 2,700

North Carolina 89 100 1,194 1,352

North Dakota 75 88 42 50

Ohio 92 100 1,217 1,397

Oklahoma 92 100 556 639

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Oregon 92 100 455 512

Pennsylvania 93 100 1,311 1,463

Rhode Island 93 100 104 120

South Carolina 70 82 674 792

South Dakota 76 92 72 89

Tennessee 78 90 804 934

Texas 70 77 3,654 4,039

Utah 70 82 180 214

Vermont 92 100 51 59

Virginia 77 90 737 871

Washington 93 100 579 671

West Virginia 92 100 239 272

Wisconsin 92 100 495 560

Wyoming 55 70 41 53

United States 86 89 37,609 38,948

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References

Cunnyngham, Karen. “Empirical Bayes Shrinkage Estimates of State Supplemental Nutrition Assistance

Program Participation Rates in Fiscal Year 2018 to Fiscal Year 2020.” Prepared by Mathematica, Contract No. 12-3198-22-F-0020. U.S. Department of Agriculture, Food and Nutrition Service, Office of

Policy Support, August 2023a.

Cunnyngham, Karen. “Reaching Those in Need: State Supplemental Nutrition Assistance Program

Participation Rates in 2020.” Prepared by Mathematica, Contract No. 12-3198-22-F-0020. U.S.

Department of Agriculture, Food and Nutrition Service, Office of Policy Support, August 2023b.

Cunnyngham, Karen. “Reaching Those in Need: State Supplemental Nutrition Assistance Program

Participation Rates in 2022.” Prepared by Mathematica, Contract No. 12-3198-23-F-0047. U.S.

Department of Agriculture, Food and Nutrition Service, Office of Policy Support, February 2025.

Doppelt, Lawrence, and Shane Haley. “CES National Benchmark Article: BLS Establishment Survey National

Estimates Revised to Incorporate March 2019 Benchmarks,” 2020.

https://www.bls.gov/web/empsit/cesbmart.htm.

Fay, Robert E., and Roger Herriott. “Estimates of Incomes for Small-Places: An Application of James-Stein

Procedures to Census Data.” Journal of the American Statistical Association, vol. 74, no. 366, June 1979,

pp. 269–277.

Leftin, Joshua, Mia Monkovic, Francisco Yang, Nima Rahimi, Andrew Wen, and Alma Vigil. “Technical

Documentation for the Fiscal Year 2022 Supplemental Nutrition Assistance Program Quality Control

Database and QC Minimodel.” Prepared by Mathematica, Contract No. 12-3198-23-F-0016. U.S.

Department of Agriculture, Food and Nutrition Service, Office of Policy Support, March 2024.

Schirm, Allen L. “Reaching Those in Need: Food Stamp Participation Rates in the States.” Final report submitted to the U.S. Department of Agriculture, Food and Nutrition Service. Mathematica Policy

Research, July 2000.

Schirm, Allen L., and John V. DiCarlo. “Using Bayesian Shrinkage Methods to Derive State Estimates of

Poverty, Food Stamp Program Eligibility, and Food Stamp Program Participation.” Final report submitted to the U.S. Department of Agriculture, Food and Nutrition Service. Mathematica Policy

Research, March 1998.

U.S. Census Bureau. “Current Population Survey: Design and Methodology, Technical Paper 66.” October

2006. https://www2.census.gov/programs-surveys/cps/methodology/tp-66.pdf.

Vigil, Alma and Nima Rahimi. “Trends in Supplemental Nutrition Assistance Program Participation Rates:

Fiscal Year 2020 and Fiscal Year 2022.” Prepared by Mathematica, Contract No. 12-3198-23-F-0047.

U.S. Department of Agriculture, Food and Nutrition Service, Office of Policy Support, October 2024.

https://www.bls.gov/web/empsit/cesbmart.htm https://www2.census.gov/programs-surveys/cps/methodology/tp-66.pdf

Appendix A

The Estimation Procedure: Additional Technical Details

Appendix A The Estimation Procedure

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This appendix provides additional information and technical details about our four-step procedure to estimate State SNAP participation rates. Each step is discussed in turn.

1. From CPS ASEC data and SNAP administrative data, derive direct estimates of State SNAP participation rates for the three fiscal years

We derived direct estimates of participation rates for all eligible people for a given fiscal year1 according to the following formula:

Pi (1,i / 100)

(1) Y1,i = 100

(E

1,i

/ 100)Ti where Y1,i is the estimated participation rate for all eligible people for State i(i = 1,,51); Pi is the number of people participating in SNAP according to adjusted SNAP Program Operations data; 1,i is the percentage of participating people who are correctly receiving benefits and eligible under federal SNAP rules according to SNAP Quality Control (SNAP QC) data; E1,i is the estimated number of people who are eligible for SNAP according to a microsimulation model based on CPS ASEC data, expressed as a percentage of the CPS ASEC population; and Ti is the estimated resident population according to decennial census and administrative records (mainly vital statistics) data.

We estimated Pi by adjusting SNAP program operations data to exclude people who received SNAP benefits only because of a natural disaster. Data on participants, including counts of participants eligible only through disaster assistance, were provided by the U.S. Department of Agriculture’s Food and

Nutrition Service. SNAP Program Operations data include the full population of SNAP cases, so participant counts are not subject to sampling error.

We estimated 1,i (the correctly eligible rate for all households) from the SNAP QC sample data as follows:

mi,h1,i,h

(2) = 100 h , 1,i mi,h h where h indexes households in a State’s SNAP QC sample; mi ,h equals the number of people in household h times the weight for household h; and 1,i,h is an indicator that household h is eligible to receive SNAP benefits. We excluded from our estimates of participants two groups that are not included in our estimates of eligible people: (1) ineligible participants who received SNAP benefits in error and (2) participants who were eligible through State-expanded categorical eligibility policies but would not meet federal SNAP income and resource criteria.

We used the following formula to estimate the percentage of people who were eligible for SNAP:

1 The COVID-19 public health emergency affected the quality of the data used to estimate SNAP participation rates from March 2020 through June 2021. As a result, the fiscal year 2020 participation rates reflect the pre-pandemic period of October 2019 through February 2020 and we did not estimate participation rates for fiscal year 2021.

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(3) E = 100 Z i where Z1,i is the CPS ASEC estimate of the number of eligible people, and Ni is the CPS ASEC estimate of the population. Estimated percentages are more precise than estimated counts because the sampling errors in the numerators and denominators of percentages tend to be positively correlated and therefore partially cancel each other out.

We derived SNAP eligibility estimates (Z1,i ) by applying SNAP rules to CPS ASEC households. However, some key information needed to determine whether a household is eligible for SNAP is not collected in the CPS ASEC. For example, there are no data on resources or expenses deductible from gross income.

Also, it is not possible to ascertain directly which members of a dwelling unit purchase and prepare food together or which members may be categorically ineligible for SNAP. Yet another limitation is that only annual, rather than monthly, income amounts are recorded.

We have developed methods, described in Vigil and Rahimi (2024), to address these data limitations.

These methods include procedures for identifying the members of the SNAP household within the

(potentially) larger CPS ASEC household, taking into account the restrictions on participation by noncitizens, distributing annual amounts across months, and imputing net income. Vigil and Rahimi

(2024) also describes how we applied SNAP gross and net income tests and calculated the benefits an eligible household would qualify for.

To derive fiscal year estimates of eligibility, we combined two years of the CPS ASEC. For example, to estimate Z1,i for FY 2022, we used data from the 2022 CPS ASEC (simulating October through December

2021) and the 2023 CPS ASEC (simulating January through February 2022). We restricted the FY 2020 eligibility simulation to October 2019 through February 2020 to match the available months of SNAP QC data. To estimate Ni , we used a weighted average of population estimates from the two CPS ASEC files.

The Census Bureau derives population estimates (Ti ) by subtracting from decennial census counts people

“exiting” the population (due to death or net out-migration) and adding people “entering” the population

(due to birth or net in-migration).

SNAP participation rates for people in households with earnings. This report does not present estimates of State SNAP participation rates for people in households with earnings because of the smaller sample size for FY 2020. However, to maintain consistency with estimates for prior years, we used direct estimates for people in households with earnings, along with direct estimates of all eligible people, to derive shrinkage estimates for all eligible people. We derived direct estimates of participation rates for people in households with earnings for a given year according to the following formulas:

(4) Y = 100 P i

2,i / 100)

2,i (E 2,i

/ 100)Ti

(5) mi,h

2,i,h

= 100 h , 2,i mi,h

N

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(6)

E = 100 Z2,i

2,i i where Y2,i is the estimated participation rate for people in households with earnings for State i; 2,i is the percentage of SNAP participants who are in households with earnings, correctly receiving SNAP benefits, and eligible under federal SNAP rules according to SNAP QC data; E2,i is the percentage of people who are in households with earnings and eligible for SNAP according to the CPS ASEC; Z2,i is the CPS ASEC estimate of the number of eligible people in households with earnings, and Pi , Ti , h, mi,h , and Ni are as defined in the opening paragraphs of this appendix.

We defined households with earnings as those that were eligible for SNAP and had a member who earned money from a job. Households with earnings were identified slightly differently in the SNAP QC data than in the CPS ASEC.