Final Project Milestone Two: Literature Review

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In Longitudinal Data From the Survey of Program Dynamics, 16.9% of the U.S.

Population Was Exposed to Household Food Insecurity in a 5-Year Period

PARKE E. WILDE,1 MARK NORD,2 and ROBERT E. ZAGER3 1Friedman School of Nutrition Science and Policy, Tufts University, Boston,

Massachusetts, USA 2USDA Economic Research Service, Washington, DC, USA

3Center for Social Development, Washington University, One Brookings Drive, St. Louis, Missouri, USA

This study provides US national-level estimates of exposure to and persistence of food insecurity in a period of 5 consecutive years. Based on longitudinal data from the Survey of Program Dynamics (SPD) (n = 12,185), 16.9% of the US population was exposed to household food insecurity in at least 1 year and 1.04% experienced persistent insecurity for 5 years from 1998 to 2002. Assuming that transition probabilities are stable, a Markov model allows fur- ther estimates for a longer period. From this approach, 25.9% of the US population was exposed to household food insecurity in a 10-year period. Supplemental materials are available for this arti- cle. Go to the Publisher’s online edition of Journal of Hunger & Environmental Nutrition to view the free supplemental file.

KEYWORDS household food security, food insecurity, dynamics, longitudinal data

This work was funded in part by USDA’s Economic Research Service through a coopera- tive agreement. The authors are grateful to Natalie Valpiani for excellent research assistance.

The views expressed here belong to the authors and may not be attributed to the Economic Research Service or USDA.

Address correspondence to Parke E. Wilde, Friedman School of Nutrition Science and Policy, Tufts University, 150 Harrison Ave., Boston, MA 02111. E-mail: [email protected]

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Longitudinal Household Food Security 381

INTRODUCTION

The federal government has provided cross-sectional estimates of the prevalence of household food insecurity in the United States each year since 1995, based on questions in a supplement to the Current Population Survey (CPS) about experiences of food hardship in a single 12-month period,1 Much less is known about exposure to and persistence of food insecurity longitudinally over multiple years. Using data from the Survey of Program Dynamics (SPD) from 1998 to 2002, this study provides the first US national-level estimates of transitions in household food security status over 5 consecutive years.

Although the CPS is most widely used for cross-sectional estimates of the prevalence of household food insecurity, the survey has some longitu- dinal structure. Wilde and Nord used December 2001 and 2002 CPS data in which approximately half the sample households were interviewed in 2 consecutive years.2 Although many food insecure households succeeded in making the transition to food security from one year to the next, others did not. The probability of being food insecure in 2002 was much higher if a household had been food insecure in 2001. Multivariate estimates using a longitudinal fixed effects version of logistic regression suggested that higher income and being married lowered the odds of becoming or remaining food insecure. Participation in the Food Stamp Program (now called the Supplemental Nutrition Assistance Program or SNAP) was associated with higher odds of being food insecure, but this was attributed to self-selection of needy households into program participation.

Jyoti et al used longitudinal data from the Early Childhood Longitudinal Study Kindergarten Cohort to estimate the effect of food insecurity on aca- demic performance, weight gain, and social skills.3 Of those children in food secure households in kindergarten, 7.7% were in food insecure households in third grade. Of those children in food insecure households in kinder- garten, 38.5% were in food insecure households in third grade. Again, past history of food insecurity was found to strongly influence future outcomes, yet a considerable share of households transitioned into and out of food insecurity over a period of several years.

Rank and Hirschl used longitudinal data from the Panel Study of Income Dynamics (PSID) to estimate the cumulative proportions of adults 20 years and older who participated in the Food Stamp Program over the course of the adult life cycle.4 In the 5-year period to age 25, 22% were estimated to participate in food stamps for at least one month. In a 10-year period to age 30, 29% were estimated to participate. Using a rough rule of thumb that about half of food stamp participants are food insecure, and implic- itly assuming that this relationship between food stamp participation and food insecurity is not subject to effect modification from other variables, the authors estimated lower bounds on the cumulative proportion of the

382 P. E. Wilde, M. Nord, and R. E. Zager

population exposed to food insecurity over time. In the 5-year period to age 25, the exposure to food insecurity was estimated at 15.7%. In the 10-year period to age 30, the exposure was estimated at 22%. Over the full period from age 20 to age 65, the exposure to food insecurity was estimated at 42%. These estimates were based on survey questions about food stamp participation, not household food security status. Rank and Hirschl called for future research to provide “a more definitive assessment of the life course risk of food insecurity (p. 145).”4

This article investigates how US households experience food insecurity over time. To break that larger objective into manageable steps, we pursue 7 specific aims: to (1) estimate the exposure to and persistence of food insecu- rity in a period of 5 years; (2) measure how these estimates of exposure and persistence change as the observation period is increased from 1 to 5 years; (3) measure how these estimates of exposure and persistence vary with eco- nomic and demographic variables; (4) estimate the probability of making a transition in food security status from one year to the next; (5) measure how these transition probabilities depend on the household’s food security status in the preceding 2 years; (6) measure how these transition probabilities vary with economic and demographic variables, and, based on these transition probabilities; (7) forecast the rates of exposure to and persistence of food insecurity over a longer period of 10 years.

SUBJECTS AND METHODS

The SPD was a longitudinal demographic survey collected by the US Census Bureau. The core purpose was to monitor the effects on low-income families of welfare reforms implemented during the 1990s. From 1998 through 2002, the SPD administered the same food security survey questions that are used to provide the federal government’s official estimates of the prevalence of food security in US households, based on responses in the annual food security supplement to the CPS.1 The food security data were released in cross-sectional public use files that could be linked by unique identifiers to longitudinal public use files for the SPD.

The SPD provided the longest existing panel of repeated annual obser- vations on household food security status in a national-level survey sample of the US population. By contrast, the Early Childhood Longitudinal Surveys would permit study of food insecurity in nonconsecutive years and only for households with children in school. The Child Development Supplement to the Panel Study of Income Dynamics would permit study of food inse- curity in nonconsecutive years and only for households with 2 or more children. The full PSID offered food security questions in 3 nonconsecutive years 1999, 2001, and 2003, which would not suffice for the analyses in the present article.

Longitudinal Household Food Security 383

The universe consisted of all noninstitutionalized people who resided in the United States in 1992 or 1993, building on earlier Survey of Income and Program Participation (SIPP) panels collected in those years. In 1997, a “bridge” survey was conducted to revisit sample persons from the 1992 and 1993 SIPP panels. The full SPD survey, including the food security questions, was administered from 1998 through 2002.

The SPD included individuals from 16 395 households in 1998 and 16 659 households in 1999, all of whom had participated in the 1992 or 1993 SIPP. Because of concerns with sample attrition over time, which may have reduced the representativeness of the SPD surveys by 1998 and 1999, the Census Bureau conducted an intensive effort in the 2000 and 2001 surveys to renew contact with additional cohorts of households that had previously been lost to attrition from the original SIPP samples, resulting in larger sam- ples of 18 716 households in 2000 and 22 340 households in 2001. Due to budget cuts, the sample was reduced again in 2002 by selecting households at random, evenly across the sample.

Because of this sampling history, the Census Bureau offered 2 sets of survey weights: (1) “traditional longitudinal” weights with positive values for individuals that were observed consistently through the years of the SPD and (2) “quasilongitudinal” weights with positive values for a larger fraction of the SPD sample, including many observations that were observed in some years but not others. The body of this article used the traditional longitudi- nal weights, because only these weights allow study of transitions in food security status over a 4-year or 5-year period. The analysis of attrition in the Online Supplemental Material used the quasilongitudinal weights, because only these weights allow study of observations that were missing in some years (Supplemental Material). The Census Bureau provided one version of the traditional longitudinal weights appropriate for the 4-year period from 1998 to 2001 (henceforth called “2001 traditional longitudinal weights”) and another version appropriate for the somewhat smaller sample available for the 5-year period from 1998 to 2002 (henceforth called “2002 traditional lon- gitudinal weights”). We rely on the Census Bureau’s weights to make our estimates as representative as possible of the original universe of noninstitu- tionalized people who resided in the United States in 1992 and 1993.

The Census Bureau noted that the SPD inherited SIPP panels with an accumulated attrition rate of about 27%, followed by additional attrition dur- ing the SPD years, leading to a cumulative attrition rate of 50% by 1999.5,6

There is some evidence that those who dropped out of the survey may be systematically different from those who were interviewed, and weight- ing only partly remedies the resulting response bias.5,7 For example, Social Security Administration earnings records for people sampled by the SPD indicate that the nonresponse pattern is not entirely random.7 On the other hand, counting attrition from the start of the survey, the attrition rate in the SPD may not be much different from that of other surveys that are widely accepted for social science research, such as the PSID and the National

384 P. E. Wilde, M. Nord, and R. E. Zager

Longitudinal Survey of Youth.6 Beyond attrition in the SPD overall, there is some further nonresponse to the food security questions in particular. Of the individuals with positive 2001 longitudinal weights in the SPD longitudi- nal file, 13% to 17% do not appear in public use files containing SPD food security data for 1998 to 2001. In 1998, 39% of these observations missing from the food security files had an entry in an SPD field describing a rea- son for noninterview (deceased, moved out of country, active duty armed forces, etc.), but 61% of these observations missing from the food security files had a missing value in the reason for noninterview field. Of the indi- viduals who do appear in the food security data files, moreover, 3% to 5% did not complete enough food security questions to compute the household food security status in 1998–2001.

It is difficult to analyze the statistical implications of complete nonre- sponse, in which a household could not be located or refused an interview in all years of the SPD, because there is no information at all about the food security status of such households. However, we were able to assess the extent of attrition bias for individuals who were observed in 2000 or 2001 (the years with the largest samples) but who were not interviewed in other years. The Online Supplemental Material reports statistically signifi- cant differences between interviewees who were “ever missing” and “never missing” in food security outcomes and the values of explanatory variables (Supplemental Material). There was less evidence of attrition bias in the coefficients of a multivariate logit model for food security status or in the esti- mated rates of transition from one food security state to another. For exam- ple, “never missing” observations were less likely than “ever missing” obser- vations to have low food security but, fortunately, never missing and ever missing observations with low food security in one year had approximately identical probabilities of transitioning to food security in the next year.

The final data file for the 4-year analysis in this study includes 28 000 individuals with positive 2001 longitudinal weights and valid food security measures in all years. The file for the 5-year analysis includes 14 000 individ- uals with positive 2002 longitudinal weights and valid food security measures in all years. In summary, the principal disadvantage of the SPD data source is attrition and nonresponse that is only partly remedied through weighting. The principal advantage is that the SPD provides the federal government’s only national-level survey sample with 4-year and 5-year longitudinal panels of consecutive annual food security status.

METHODS

Household Food Security Measurement

The federal government’s household food security survey module includes 10 survey items that refer to symptoms of food insecurity among adults in

Longitudinal Household Food Security 385

the household during the preceding 12 months.1 Another 8 items refer to symptoms of food insecurity among children and are asked only of house- holds with children. For ease of comparability across all households, this analysis used only the adult-referenced survey items. The individuals in the SPD were classified according to the food security status of the households in which they resided.

Each food security survey item is coded as a binary response, indicat- ing whether the household experienced a particular symptom of hardship. Based on the adult-referenced items, the household is classified as food secure with 0 to 2 affirmative responses and food insecure with 3 to 10 affirmative responses. Food insecurity may further be broken down into low food security with 3 to 5 affirmative responses and very low food security with 6 to 10 affirmative responses.

Cross-Sectional Prevalence Estimates in the SPD and CPS

The cross-sectional prevalence of food insecurity and very low food secu- rity each year from 1998 to 2001, based on adult-referenced items, was tabulated using the SPD and CPS. The CPS universe includes all noninsti- tutionalized civilians residing in the United States during each survey year, and the SPD universe represented by our analysis sample includes individ- uals who resided in the United States during 1993 and 1994, so the age distribution differs across the surveys. For greater comparability with the SPD, we reweighted the CPS data to estimate the cross-sectional prevalence that would have been observed if the CPS had the same age distribution as the SPD.

Fixed Longitudinal Observation Periods

For a longitudinal observation period of M years, we created frequency tables for the number of years with food insecurity and very low food secu- rity. To summarize these frequency tables more concisely, we estimated the exposure (having the condition of food insecurity or very low food security during some portion of any year out of M years) and persistence (having the condition during some portion of all years out of M years).

Of course, these estimates of exposure and persistence differ depending on the number of years M in the period of observation. Using the 2001 longitudinal weights, we created frequency tables for M = 1 (2001), M = 2 (2000–2001), M = 3 (1999–2001), and M = 4 (1998–2001). Using the smaller sample with positive 2002 longitudinal weights, we created the frequency table for M = 5 (1998–2002). This simple descriptive analysis necessarily is influenced by the choice of years, in addition to the length of the observation period.

386 P. E. Wilde, M. Nord, and R. E. Zager

Logit models were employed to investigate the relationship between food security status and selected time-invariant explanatory variables. The analysis used the 4-year longitudinal sample with the 2001 longitudinal weights. The dependent variables were binary indicators of food insecu- rity in a single year (2001), exposure during a 4-year observation period (1998–2001), and persistence during the 4-year observation period. The household-level time-invariant explanatory variables were mean income- to-poverty ratio, an indicator for having been in poverty during any year of the observation period, an indicator for containing a couple that was married for all years of the observation period, an indicator for contain- ing a college graduate, an indicator for containing a high school graduate (but no college graduate), an indicator for children present, an indicator for elderly present, and an indicator for disabled person present (having a health problem or disability that prevents work or limits the kind and amount of work). Categorical variables described the age in 1998 of the oldest nonelderly person in the household: 45–64 years, 30–44 years, 18–29 years, or no nonelderly adult in the household (household head is age 65 or older). Individual-level time-invariant explanatory variables described race and ethnicity.

Transition Models

The longitudinal data may also be analyzed in a way that is less depen- dent for interpretation on the length of the observation period. In a Markov transition model, the state of the world in time period t depends on the state of the world in the preceding period t − 1. For example, Klerman and Haider use such models to study the dynamics of entry into and exit from the welfare caseload in California.8

In the case of food security, suppose the (K × 1) vector yt contains the population fractions in K mutually exclusive states of household food security in time period t. The (K × K ) transition matrix C contains elements cij, which show the fraction of individuals in state j in time period t − 1 who transition to state i in time period t:

yt = C yt−1 (1) The simplest Markov analysis would define yt as the vector of population fractions in the three mutually exclusive food security states: (1) secure, (2) having low food security, and (3) having very low food security. For reasons given below, we estimate transitions to food security states in year t based on the preceding states in years t − 1 and t − 2 rather than year t − 1 alone. This extended Markov model easily may be brought within the framework of equation (1) by defining yt as a vector of the 9 mutually exclusive food

Longitudinal Household Food Security 387

security states in years t − 1 and t: (1) = “secure, secure,” (2) = “secure, low,” (3) = “secure, very low”, (4) = “low, secure,” and so forth through (9) = “very low, very low”.

To estimate the transition probabilities for 3 states of food security status in period t, based on 9 possible states in periods t − 1 and t − 2, we must estimate 27 coefficients in matrix C , representing the transition probabilities or frequencies:

yt =

⎡ ⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

yt,1 yt,2 yt,3 yt,4 yt,5 yt,6 yt,7 yt,8 yt,9

⎤ ⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

⎡ ⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

c11 0 0 c14 0 0 c17 0 0 c21 0 0 c24 0 0 c27 0 0 c31 0 0 c34 0 0 c37 0 0 0 c42 0 0 c45 0 0 c48 0 0 c52 0 0 c55 0 0 c58 0 0 c62 0 0 c65 0 0 c68 0 0 0 c73 0 0 c76 0 0 c79 0 0 c83 0 0 c86 0 0 c89 0 0 c93 0 0 c96 0 0 c99

⎤ ⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

⎡ ⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

yt−1,1 yt−1,2 yt−1,3 yt−1,4 yt−1,5 yt−1,6 yt−1,7 yt−1,8 yt−1,9

⎤ ⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

= C yt−1 (2)

Because this extended Markov model requires 2 years of lagged food security status, our analysis of the 4-year longitudinal file estimated these transition frequencies using data for the years 2000 (based on food security status in 1998 and 1999) and 2001 (based on food security status in 1999 and 2000).

We conducted two hypothesis tests to investigate simplifying restrictions on this model. First, we tested a null hypothesis that the transition proba- bilities in year t depended only on status in t − 1 and not t − 2. If this assumption had been true, we could have used a simpler Markov model. Second, we tested a null hypothesis that food security transition probabili- ties were identical for households who were in different food security states before the current spell began but who shared the same length of time in their current spell. For example, if this second null hypothesis were true, then a household that had experienced very low food security for exactly one preceding year would have the same probability of continuing in this state for a second year, no matter whether its state before the current spell of very low food security had been food secure or low food security. If this second null hypothesis had been true, we could have pursued a model in the spirit of survival analysis. In survival analysis, the probability of con- tinuing in the current spell depends on the length of time in the current spell but not on events that preceded the current spell. However, both null hypotheses were rejected, so the extended Markov model in equation (2) was used.

388 P. E. Wilde, M. Nord, and R. E. Zager

As with the models for fixed observation periods, we used the transition model framework to investigate associations with the time-invariant explana- tory variables. Because the dependent variable includes 3 possible states of food security in year t, we used a multinomial logit model. The explanatory variables included indicator variables for the possible food security states in years t − 1 and t − 2, plus the same time-invariant explanatory covari- ates used in the logit analysis described previously. The coefficients of the multinomial logit model show how explanatory variables affect the relative risk of having low or very low food security. For example, the relative risk of having low food security is the ratio of the odds of having low food security to the odds of being food secure. In essence, this approach allows the time-invariant explanatory variables to serve as shifters to the transition probabilities in the extended Markov model in equation (2).

The extended Markov model offers a way to simulate the dynamics of food security transitions over time. Such simulation assumes that the transi- tion probabilities estimated for year t, as a function of food security status in years t − 1 and t − 2, are constants. Under this assumption, one may forecast the probabilities for each food security transition in periods t + 1, t + 2, and later years. In this application, the forecasts quickly converged to a steady state where yt equals yt-1. The steady state may be described as the national food security situation that would be reached if the current transi- tion pattern were maintained for several years and nothing else happened that affected food security. The steady state is not a real prediction about the future, because new external events will in fact influence food security. Rather, the steady state offers an intuitive way of explaining the practical implications of the transition pattern that is estimated using the extended Markov model in our 4-year sample.

In the steady state, we estimated the probability for each of the 35 = 243 possible food security histories during 5 years and the 310 = 59 049 possible food security histories during 10 years. From these estimates, we tabulated the probability of experiencing exposure to or persistence of food insecurity and very low food security during 5-year and 10-year periods.

The SPD data were arranged into analysis files using SAS version 9.1 (Cary, NC). The longitudinal analysis and steady-state simulations were programmed in Stata version 10 (College Station, Tex). The Institutional Review Board at Tufts University determined that this research with existing de-identified SPD survey data was exempt from review.

RESULTS

Preliminary Comparison to CPS

The cross-sectional prevalence estimates for food insecurity and very low food security were lower in the SPD than in the official estimates from the

Longitudinal Household Food Security 389

TABLE 1 A Comparison of the Estimated Prevalence of Food Insecurity and Very Low Food Security in the SPD and CPS, as Percentage of Population, 1998–2001

Survey of program dynamicsa,b Current population surveyc

Current population survey (adult-referenced,

reweighted)d

Year Food insecurity Very low food

security Food

insecurity Very low food

security Food

insecurity Very low food

security

1998 9.10 (0.31) 3.16 (0.21) 13.5 3.7 11.18 3.56 1999 6.88 (0.27) 2.16 (0.15) 11.5 2.9 9.36 2.61 2000 6.46 (0.24) 1.99 (0.15) 12.1 3.1 9.76 2.99 2001 6.25 (0.25) 1.90 (0.12) 12.2 3.3 9.94 3.12

aIndividual rate of household food insecurity and very low security based on adult-referenced questions. bThe SPD analysis uses 2001 traditional longitudinal weights; standard errors in parentheses are corrected for complex survey design. cOfficial individual rate of household food insecurity and very low security. dIndividual rate of household insecurity and very low security, based on adult-referenced questions and reweighted to have the same age distribution as SPD.

CPS (Table 1). This difference was only partly reconciled when, for compara- bility, we used the adult-referenced survey items in the CPS and reweighted the CPS data to have the same age distribution as the SPD data. There is some evidence that the SPD’s underestimation of the food insecurity preva- lence is worse in later years than earlier years. For example, the prevalence of food insecurity in 1998 is 11.18% in the reweighted CPS and 9.10% in the SPD, whereas the prevalence of food insecurity in 2001 is 9.94% in the reweighted CPS data and 6.25% in the SPD.

Food Insecurity in a Fixed Observation Period

The analysis for fixed observation periods shows that evidence of expo- sure to food insecurity increased as the length of the observation period increased (Table 2). For example, 6.3% of individuals lived in a household with food insecurity during a single year (2001), 16.2% ever experienced food insecurity during a 4-year observation period, and (using the smaller sample available for 5-year analysis) 16.9% ever experienced food insecurity during a 5-year observation period. The fraction that experienced persis- tent food insecurity in all years fell as the length of the observation period increased. Just 1.3% experienced food insecurity for 4 consecutive years, and 1.0% experienced food insecurity for 5 consecutive years.

Similarly, the exposure to very low food security increased as the length of the observation period increased, from 1.9% in a single year to 6.0% in 4 years and 6.1% in 5 years (Table 3). The fraction with persistent very low

390 P. E. Wilde, M. Nord, and R. E. Zager

TABLE 2 The Frequency Distribution for Multiple Years of Food Insecurity During Observation Periods That Vary From 1 to 5 Yearsa

Years in the observation period

1 2 3 4 5Classified as food insecure in: 2001 2000–2001 1999–2001 1998–2001 1998–2002b

Percentage 0 Years 93.7 (.29) 90.2 (.36) 87.3 (.44) 83.8 (.50) 83.1 (.65) 1 Year 6.25 (.29) 6.91 (.30) 7.60 (.34) 8.62 (.35) 8.54 (.47) 2 Years 2.90 (.17) 3.41 (.21) 4.05 (.23) 3.57 (.32) 3 Years 1.73 (.13) 2.26 (.18) 2.32 (.25) 4 Years 1.30 (.11) 1.38 (.16) 5 Years 1.04 (.13) Exposurec 6.25 9.81 12.7 16.2 16.9 Persistenced 6.25 2.90 1.73 1.30 1.04

aSE in parentheses, corrected for complex survey design using Taylor series linearization. bThe 5-year data are from a second SPD sample using 2002 longitudinal weights. cEver food insecure. dAlways food insecure.

TABLE 3 The Frequency Distribution for Multiple Years of Very Low Food Security During Observation Periods That Vary From 1 to 5 Yearsa

Years in the observation period

1 2 3 4 5Classified as very low food security in: 2001 2000–2001 1999–2001 1998–2001 1998–2002b

Percentage 0 Years 98.1 (.12) 96.8 (.18) 95.6 (.23) 94.0 (.28) 93.9 (.37) 1 Year 1.90 (.12) 2.42 (.17) 3.07 (.19) 3.80 (.21) 3.61 (.29) 2 Years .73 (.08) 1.00 (.09) 1.44 (.15) 1.36 (.18) 3 Years .33 (.05) .53 (.07) .62 (.09) 4 Years .24 (.04) .34 (.07) 5 Years .14(.04) Exposurec 1.90 3.15 4.40 6.01 6.07 Persistenced 1.90 .73 .33 .24 .14 N (individuals) 24 000 24 000 24 000 24 000 12 185

food security fell as the observation period increased. Just 0.2% experienced very low food security for 4 consecutive years, and 0.1% experienced food insecurity for 5 consecutive years.

In the logit analysis (Table 4), an increase in mean household income of 0.1 units (equivalent to 1/10 of the federal poverty standard) was asso- ciated with approximately 0.0136 units lower log odds of exposure to food insecurity in a 4-year period (OR = 0.986), 0.0253 units lower log odds of

Longitudinal Household Food Security 391

TABLE 4 Logit Estimates for Exposure to and Persistence of Food Insecurity During a 4-Year Observation Period, as a Function of Education and Demographic Variablesa

Logit models

Variable Mean or % of sample

Food insecurity in single year

Exposure in 4-year period

Persistence in 4-year period

Mean income-to- poverty ratio over time (mean)

4.06 (.04) −.253∗∗ (.050) −.136∗∗ (.017) −.614∗∗ (.107)

Household income fell below poverty line in any year

21.4 (.50) .500∗∗ (.131) .493∗∗ (.054) .624∗ (.287)

Someone in household was married in all years

61.9 (.52) −.794∗∗ (.098) −.450∗∗ (.055) −.751∗∗ (.240)

Someone in household was college graduateb

34.8 (.64) −1.24∗∗ (.221) −.659∗∗ (.100) −1.53∗∗ (.479)

Nobody was college grad, but someone was high school grad

56.7 (.65) −.464∗∗ (.137) −.431∗∗ (.079) −.450 (.251)

Child present in household

47.5 (.61) .240∗ (.100) .371∗∗ (.051) .075 (.224)

Elderly present in household

17.3 (.35) −.212 (.205) .092 (.121) .037 (.398) Oldest nonelderly

person is aged 45–64 yc

43.1 (.58) .992∗∗ (.220) .227 (.136) 1.51∗∗ (.443)

Oldest nonelderly person is aged 30–44 y

39.9 (.61) .913∗∗ (.210) .183 (.131) 1.58∗∗ (.453)

Oldest nonelderly person is aged 18–29 y

6.36 (.29) .774∗∗ (.248) .109 (.150) 1.18∗ (.516)

Hispanicd 9.18 (.34) −.402 (.318) .212 (.184) −.746 (.486) Black 11.5 (.55) −.204 (.320) .173 (.186) −.580 (.524) White 75.9 (.66) −.777∗ (.296) −.329∗ (.165) −.847 (.493) Someone in

household had a disability in at least one year

33.7 (.62) .986∗∗ (.114) .602∗∗ (.057) .810∗∗ (.252)

Constant −2.01∗∗ (.412) −.289 (.233) −3.62∗∗ (.665) aSE in parentheses, corrected for complex survey design using Taylor series linearization. bThe omitted category is nobody in household was a high school graduate. cThe omitted age category is no nonelderly working-age adult (household head is aged 65 years or older). dNon-Hispanic other race is the omitted race/ethnicity. ∗P < 0.05. ∗∗P < 0.01.

392 P. E. Wilde, M. Nord, and R. E. Zager

food insecurity in a single year (OR = 0.985), and 0.0614 units lower log odds of continuous food insecurity for 4 years (OR = 0.940). Holding mean income constant, the experience of ever having income below the poverty standard was associated with 0.493 units higher log odds of exposure to food insecurity in a 4-year period (OR = 1.64), 0.500 units higher log odds of food insecurity in a single year (OR = 1.65), and 0.624 units higher log odds of continuous food insecurity for 4 consecutive years (OR = 1.87). Likewise, having a disabled person in the household substantially increased the odds of all 3 food insecurity outcomes. Having a steadily married couple or a person with high education reduced the odds of all 3 food insecurity outcomes.

Extended Markov Transition Model Results

The extended Markov transition models below show the probability of tran- sitioning to each food security state in year t as a function of the state in 2 previous years, t − 1 and t − 2. As a preliminary analysis, we also tabulated selected transition probabilities as a function of the food security state in 3 previous years (t − 1, t − 2, and t − 3; Table 5). For example, if a household had very low food security for just 2 consecutive years but not earlier, the probability of remaining with very low food security is 45%. If a household has had very low food security for 3 consecutive previous years, the prob- ability of remaining in this state is higher, 60%. Our main extended Markov transition model uses just 2 years of history, because of concerns about com- plexity and sample size, given that we only have 4 years of longitudinal data in the largest analysis file (for 1998–2001).

Based on the main extended Markov transition model, of those indi- viduals who were food secure for 2 consecutive years, 97.4% will remain food secure for the next year, 2.1% will change to low food security, and

TABLE 5 Probability of Continuing in Current State of Food Security or Very Low Food Security, in Percentagea

Probability of remaining:

Conditional on having been: Food secure

Secure 1 year 96.5 (.15) Secure 2 years 97.4 (.14) Secure 3 years 97.8 (.19)

Conditional on having been: Very low food security Very low food secure 1 year 33.0 (1.81) Very low food secure 2 years 45.2 (.04) Very low food secure 3 years 59.5 (7.14)

aSE in parentheses, corrected for complex survey design using Taylor series linearization.

Longitudinal Household Food Security 393

TABLE 6 Transition Matrix for the Probability of Each Possible Food Security Status in Year t, as a Function of Food Security Status in Years t − 1 and t − 2

Proportion in period t with food security status . . .

Food security status in year . . . (1) Secure (2) Low (3) Very low

t − 2 t − 1 In percentage (standard error)a

Secure Secure 97.4 (.14) 2.12 (.12) .49 (.05) Secure Low 73.7 (2.0) 18.4 (1.82) 7.92 (1.19) Secure Very low 46.8 (4.0) 24.8 (3.12) 28.4 (3.84) Low Secure 77.7 (1.78) 17.8 (1.71) 4.51 (.91) Low Low 52.6 (3.0) 37.7 (3.02) 9.66 (1.70) Low Very low 37.0 (4.50) 34.9 (5.22) 28.1 (4.59) Very low Secure 73.6 (3.33) 14.4 (2.72) 12.0 (2.17) Very low Low 44.4 (4.26) 29.7 (3.96) 25.9 (3.72) Very low Very low 29.9 (.03) 24.8 (3.35) 45.2 (3.83)

N = 49 629 observation years. aSE in parentheses, corrected for complex survey design using Taylor series linearization.

only 0.5% will change to very low food security (Table 6). By contrast, of those individuals who had very low food security for 2 consecutive years, 29.9% will become food secure in the next year, 24.8% will move to low food security, and 45.2% will remain in their current state of very low food security.

For individuals who had highly variable food security histories during 2 years, the food security status in the following year depended to a greater extent on their most recent state. For example, of those individuals who had very low food security one year and then became food secure, 73.6% remained food secure in the following year. By contrast, of those individuals who were food secure one year and then changed to very low food security, only 46.8% were food secure in the following year (Table 5).

Specification tests rejected two simpler models. First, we rejected the null hypothesis that food security status in year t depends only on previous status in year t − 1 and not on earlier history in year t − 2 (P value less than 0.0001). Second, we rejected a hypothesis that food security probabilities depended only on the length of time in the current food security spell, not on food security status in time periods that preceded the current spell (P value = 0.0483). The rejection of these two null hypotheses favors the full model in Table 6 over simpler models.

The multinomial logit estimates within the transition model framework (Table 7) are similar in several respects to the logit estimates reported earlier. For example, having experienced poverty at some point was associated with an increased relative risk of having low food security instead of food security in year t (relative risk [RR] ratio = 1.40). Compared with having only low education in the household, having a college graduate in the household was associated with a decreased relative risk of having low food security

394 P. E. Wilde, M. Nord, and R. E. Zager

TABLE 7 Multinomial Logit for Odds of Having Low and Very Low Food Security in Period ta

Compared to odds of being secure . . .

Variables Low Very low

Food security status in yearb

t − 2 t − 1 Relative risk ratio (standard error) Secure Low 4.48 (.64) 9.65 (2.32) Secure Very low 9.17 (1.98) 44.8 (11.9) Low Secure 4.55 (.69) 5.52 (1.48) Low Low 12.6 (2.23) 16.0 (4.12) Low Very low 13.7 (3.78) 51.7 (16.8) Very low Secure 3.39 (.90) 12.6 (3.38) Very low Low 10.1 (2.36) 44.5 (10.7) Very low Very low 14.3 (3.40) 97.4 (24.1) Mean income-to-poverty ratio over time .82 (.03) .87 (.06) Household income fell below poverty line in any

year 1.40 (.15) 1.44 (.25)

Someone in household was married in all years .65 (.06) .44 (.06) Someone in household was college graduatec .43 (.08) .38 (.12) Nobody was college grad, but someone was

high school grad .74 (.09) .78 (.13)

Child present in household 1.52 (.15) .91 (.13) Elderly present in household 1.15 (.20) .83 (.18) Oldest nonelderly person is aged 45–64 yd 2.02 (.39) 2.05 (.55) Oldest nonelderly person is aged 30–44 y 1.75 (.35) 2.38 (.64) Oldest nonelderly person is aged 18–29 y 1.37 (.30) 2.54 (.75) Hispanice 1.31 (.36) .36 (.13) Black 1.19 (.32) .50 (.18) White .73 (.18) .46 (.16) Someone in household had a disability in at least

one year 1.70 (.16) 2.36 (.36)

N = 49 592. aSE in parentheses, corrected for complex survey design using Taylor series linearization. bSecure–Secure is the omitted combination. cThe omitted category is nobody in household was a high school graduate. dThe omitted age category is no nonelderly working-age adult (household head is aged 65 years or older). eNon-Hispanic other race is the omitted race/ethnicity.

instead of food security in year t (RR ratio = 0.43). These estimates control for 2 previous years of food security history. Compared with a household that had experienced 2 previous years of food security, a household with 2 previous years of very low food security has greatly increased relative risk of having low food security instead of food security in year t (RR ratio = 14.3).

In the steady state, without controlling for covariates, the extended Markov transition probabilities in Table 6 support simulations of the proba- bilities for food security histories over several years. For example, during a 5-year period, the estimated probability of being food secure for all 5 years was 84.5%, and the estimated probability of having very low food security for

Longitudinal Household Food Security 395

TABLE 8 Simulated Steady State Exposure to and Persistence of Food Insecurity and Very Low Food Security in Years 5 and 10, in Percentage

Years in the simulationa period

5 10

Food insecurity Exposure 15.5 25.9 Persistence .44 .03

Very low food security Exposure 5.06 8.91 Persistence .05 <.01

aSimulation uses transition parameters from Table 6.

all 5 years was 0.05%. We can also estimate the probability for more idiosyn- cratic histories, such as being secure for 4 years followed by a single year of low food security (1.83%). Because there are too many of these possible his- tories to tabulate conveniently, a useful approach is to present the same sum- mary measures of exposure and persistence that were used previously in the analysis of fixed observation periods. During a 5-year period in the steady state, the Markov transition model suggests that 15.5% of individuals would be exposed to food insecurity in one or more years (Table 8). This estimate is slightly lower than the fixed-observation-period estimate of 16.9% reported earlier in Table 2. The Markov transition model suggests that 0.4% would have persistent food insecurity for 5 consecutive years (Table 8), which is lower than the fixed-observation-period estimate of 1.0% reported in Table 3. One possible reason that these steady-state estimates are lower than the estimates with a fixed observation period is that the prevalence of food inse- curity was falling during the observation period (Table 1). Holding constant the average yearly food insecurity prevalence during the period, the steady- state estimates for exposure to food insecurity would have been higher if the observation period had shown a rising prevalence of food insecurity.

Similar estimates of exposure and persistence can be generated for longer time periods. During a 10-year window, the transition probabili- ties imply that 25.9% of individuals would ever experience food insecurity (including either low food security or very low food security) and 8.9% would ever experience very low food security in one or more years (Table 8). Only 3 out of 10,000 individuals would experience food insecurity persistently for 10 consecutive years.

DISCUSSION

With a fixed observation period, we estimate that 16.9% of individuals lived in a household that was exposed to food insecurity at some point during

396 P. E. Wilde, M. Nord, and R. E. Zager

5 years and 1.04% of individuals lived in a household that experienced per- sistent food insecurity for 5 consecutive years. These estimates with a fixed observation period have the advantage of simplicity, but they depend for interpretation on careful attention to the length of the observation period. Clearly, the probability of being exposed to food insecurity in a longer observation period was greater than in a shorter period.

By contrast, Markov transition probability estimates have the advantage of being less dependent for interpretation on the length of the observa- tion period, and they support simulations for any time window chosen by the analyst. However, these forecasts require the assumption that transition probabilities are constant. From the extended Markov transition model, in the steady state, we estimate that 15.5% of individuals lived in a household that is exposed to food insecurity at some point during a 5-year period. In the steady state, we estimate that 25.9% of individuals live in a household that is exposed to food insecurity at some point during a 10-year period.

Our estimates of exposure to food insecurity over 5-year and 10-year periods are much higher than the single-year probability of being food inse- cure, estimated at 6.3% to 9.1% during the years of the SPD sample. The 10-year estimate of exposure to food insecurity is in the neighborhood of 3 to 4 times as large as the single-year prevalence of food insecurity (depend- ing which single year is used as the base). The important implication is that single-year estimates substantially understate the fraction of the US popula- tion with personal experience of food insecurity over a longer period, such as a decade or a lifetime.

Earlier research by Rank and Hirschl used a very different methodol- ogy, relying on Food Stamp Program participation status in the PSID rather than food security questions to generate estimates of exposure to food insecurity.4 Rank and Hirschl provided estimates for specific stages of the life cycle starting with age 20, whereas our estimates in Table 8 reflect averages across all ages combined. Yet, Rank and Hirschl’s lower bound estimates for the 5-year period to age 25 and the 10-year period to age 30, summarized earlier, are remarkably close to and slightly lower than our SPD estimates above.

For the 4-year observation window, and for the extended Markov tran- sition model, we estimated multivariate versions of these models. Higher household income, not having been in poverty, having a steadily married couple, having a person with higher education, and not having a person with a disability in the household lowered the probability of being food insecure, the probability of exposure to food insecurity in a 4-year period, the probability of persistent food insecurity for 4 consecutive years, and the relative risk of transitioning to food insecurity.

The most important limitation in this study is the gap in prevalence estimates between the SPD data used here and the CPS data used in official federal government estimates. One possible explanation is differences in the

Longitudinal Household Food Security 397

universe of US residents when the SPD sample was drawn (in 1993 and 1994) and when the CPS was drawn (in 1998 through 2001). Another, less favorable, explanation is that, by necessarily selecting a sample of nonattrit- ers that is comparatively stable over multiple years of survey participation, the SPD sample may be selected systematically in the direction of greater food security.

We nevertheless used the SPD data, because they provide unique sup- port for national-level longitudinal estimates of food security transitions over periods as long as 5 and 10 years. Important public policy decisions depend not only on the cross-sectional prevalence of food insecurity but on the dynamics of food insecurity transitions over time. For example, if 10% of the population were food insecure one year, and the prevalence were again 10% five years later, the sensible policy response may differ depending on the dynamics. If the same individuals were food insecure in both periods, there would seem to be a great need for food assistance and antihunger programs to reach a population group with persistent hardship. If completely new people fell into food insecurity in the second period, while others recov- ered, then it might be better to think of SNAP and other food assistance programs as a form of social insurance that may be needed by a large frac- tion of Americans who experience food insecurity for comparatively short periods of their life.

The evidence from this study falls somewhere in between these two scenarios. There is a very small fraction of the US population (far below 1%) that experiences food insecurity steadily for 10 consecutive years and a large fraction of the US population (estimated at about 74.1% in the Markov approach) that never experiences food insecurity in a decade. Yet, the frac- tion of the population with some exposure to food insecurity in a decade (estimated at 25.9% in the Markov approach) is much larger than one might expect knowing only the cross-sectional estimates. We estimate that food insecurity is an experience that happens to more than a quarter of the US population at some point during a decade.

REFERENCES

1. Nord M, Andrews M, Carlson S. Household food security in the United States, 2007. Washington, DC: USDA, Economic Research Service; 2008. Report No. ERR-66.

2. Wilde PE, Nord M. The effect of food stamps on food security: a panel data approach. Rev Agric Econ. 2005;27:425–432.

3. Jyoti DF, Frongillo EA, Jones SJ. Food insecurity affects school children’s academic performance, weight gain, and social skills. J Nutr. 2005;135:2831–2389.

4. Rank MR, Hirschl TA. Likelihood of using food stamps during the adulthood years. J Nutr Educ Behav. 2005;37:137–146.

398 P. E. Wilde, M. Nord, and R. E. Zager

5. US Census Bureau. Survey of Program Dynamics Users’ Guide. Washington, DC: US Department of Commerce; 2002.

6. Weinberg DH, Shipp SS. The Survey of Program Dynamics: A Mid-term Status Report. Washington, DC: US Census Bureau, US Department of Commerce; 2000.

7. Hall D, Smanchai S-U, Tin J. Earned income and longitudinal attrition in the SIPP and SPD. Paper presented at: the American Statistical Association Section on Survey Research Methods, August 9, 2004, Toronto, Ontario, Canada; Joint Statistical Meetings.

8. Klerman JA, Haider SJ. A stock-flow analysis of the welfare caseload. J Hum Resour. 2004;39:865–886.

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