Are National School Lunch Program Participants More Likely to be Obese? Dealing with Identification

Transcription

1 Are Natonal School Lunch Program Partcpants More Lkely to be Obese? Dealng wth Identfcaton Janet G. Peckham Graduate Student, Clemson Unversty Jaclyn D. Kropp Assstant Professor, Clemson Unversty Selected Paper prepared for presentaton at the Agrcultural & Appled Economcs Assocaton s 2012 AAEA Annual Meetng, Seattle, Washngton, August 12-14, 2012 Abstract: The Natonal School Lunch Program (NSLP) has been crtczed for provdng hgh calore lunches to over 31 mllon school-age students. Wth nearly 17 percent of chldren consdered obese, the relatonshp between NSLP partcpaton and chldhood obesty has been studed extensvely wthout conclusve evdence. Ths paper presents a revew of the lterature thus far and examnes dentfcaton ssues when estmatng the average treatment effect or local average treatment effect of the NSLP. Usng data from the Natonal Health and Nutrton Examnaton Survey (NHANES), the author fnds that when restrctve parametrc assumptons are removed, partcpaton n the NSLP reduces the probablty of beng obese n school age chldren. JEL: C14; I38; Q18 Keywords: Natonal School Lunch Program; Obesty; Regresson Dscontnuty; Monotone Instrumental Varable Copyrght 2012 by Janet G. Peckham & Jaclyn D. Kropp. All rghts reserved. Readers may make verbatm copes of ths document for non-commercal purposes by any means, provded that ths copyrght notce appears on all such copes.

2 I. Introducton Chldhood obesty has become a growng health concern n the Unted States, wth nearly 17 percent of two- to nneteen-year-old chldren consdered obese (Ogden & Carroll, 2010). Wth ths comes a greater rsk of health problems such as Type 2 dabetes, hgh blood pressure, and hgh cholesterol (Ogden & Carroll, 2010). Although the source of the obesty epdemc s debated n the lterature wth some authors pontng to a sedentary lfestyle (Blar & Brodney, 1999) and genetcs (Comuzz & Allson, 1998) as causes, most researchers cte ncreased consumpton as the man culprt (Chandon & Wansnk, 2007a and 2007b; Hll & Peters, 1998). There s also strong evdence that overweght 1 or obese chldren are more lkely to be overweght or obese as adults (U.S. Department of Health and Human Servces, 2001). These fndngs demonstrate the urgent need to mprove chldhood nutrton and take acton to reduce the rate of chldhood obesty. One way to acheve these ams may be through the Natonal School Lunch Program (NSLP) that provdes lunch for over 31 mllon school-age students at a cost of $10.8 bllon (U.S. Department of Agrculture, 2011). The NSLP was establshed n 1946 wth the dual-goal to reduce government commodty surpluses whle provdng low-ncome chldren a nutrtous meal (Ralston et al., 2008). Snce then, t has become one of the largest nutrton-assstance programs n the Unted States, wth over eghty percent of all prmary and secondary schools partcpatng. The current program provdes free and reduced-cost lunches for ncome-elgble students, as well as mnmally subsdzng pad lunches for students that are ncome-nelgble. Students wth a household ncome of 130 percent of the poverty lne or less are elgble for the free lunch. Students wth household ncomes between 130 percent and 185 percent of the poverty lne are 1 Chldren that are obese have a Body Mass Index (BMI) above the 95 th percentle. A chld s overweght f hs or her BMI falls between 85 th and 95 th percentle and s also sad to be at rsk of obesty. 1

3 elgble for the reduced-prce lunch. Students wth household ncomes over 185 are ncomenelgble but may purchase a full-prce lunch. 2 Thus the nutrtonal standards of the NSLP may mpact chldren of varous soco-demographc backgrounds. Whle all chldren are at rsk of obesty f calore consumpton and nactvty are left unchecked, low-ncome mnortes are at greater rsk than ther counterparts (Ogden & Carroll, 2010). Ths s partcularly troublng because recent studes have found a postve correlaton between partcpaton n the NSLP and chld weght (Mllmet et al., 2010; Schanzenbach, 2009). The correlaton may be due to selecton bas nto the program or because of ncreased fat consumpton of program partcpants relatve to non-partcpants at lunch. A School Nutrton Detary Assessment (SNDA) conducted by the Food and Nutrton Servce of the USDA found that less than one-thrd of schools were servng meals n complance wth the Detary Gudelnes for Amercans. These gudelnes requre no more than thrty percent of calores to come from fat and less than ten percent of calores to come from saturated fat (Ralston et al., 2008). Gleason and Sutor (2003) estmate that NSLP partcpants on average consumed nnety-fve percent more sodum than recommended whle non-partcpants consumed eghty-eght percent more sodum than recommended. The authors also fnd that NSLP partcpants consume more detary fat as a percentage of calores. Although the levels of nutrent defcences vary slghtly across studes, the majorty of the research concedes that NSLP partcpants consume more fats and sodum than non-partcpants, whch may lead to hgher rates of overweght and obesty. These fndngs hghlght the dffculty n determnng a causal relatonshp between the school lunch program and chldhood obesty. Ths paper examnes parametrc and nonparametrc approaches to dentfyng the average treatment effect (ATE) and local average 2 In 2011, the poverty lne for a famly of four was $22,340 (U.S. Department of Agrculture, 2011). 2

4 treatment effect (LATE) of partcpaton n the NSLP on the rate of obesty. Usng data from the Natonal Health and Nutrton Examnaton Survey (NHANES), we fnd estmaton of the effect depends on the model: OLS regresson and bvarate probt model fnd a postve effect of partcpaton n the school lunch program on the lkelhood of beng obese. Contrarly, regresson dscontnuty desgn and nonparametrc bounds estmaton procedures dentfy a negatve, but nsgnfcant, effect of partcpaton on the lkelhood of beng obese. The postve effect of the NSLP on obesty s removed when nonparametrc estmaton s used. II. Lterature Revew Identfcaton ssues are nherent n many economc problems, and estmatng the relatonshp of the NSLP on chldhood obesty s no excepton. To begn, selecton nto the NSLP s not random; many of the same populatons at hgher rsk for obesty are more lkely to choose to partcpate n the NSLP (Curre, 2003; Ogden & Carroll, 2010). Furthermore, partcpants are not a homogenous group. Unlke most government programs provdng food for low-ncome chldren, any chld can partcpate n the NSLP regardless of ncome. However, due to the threeter prcng structure, all partcpants do not face the same prces. Whle all prevous studes have controlled for ncome when assessng the mpact of partcpaton on chldhood obesty, most have not dstngushed between partcpants recevng free or reduced prce lunches (referred to as ncome-elgble students) and partcpants recevng a full prce lunch (ncome-nelgble students). Two exceptons nclude Gunderson et al. (2012), who analyzes the mpact for ncome elgble students and Schanzenbach (2009), who analyzes the effect of partcpaton for ncomenelgble students. There has been a sgnfcant amount of research about the NSLP wthn the economcs lterature as well as the nutrton scence lterature. Untl recently, results have been descrptve 3

5 n nature and have not consdered the effects of non-random selecton nto the program. Current analyses of the relatonshp between the NSLP and nutrtonal outcomes (ncludng the rate of obesty) use a varety of methods to control for selecton on unobservables, ncludng fxed effects (Gleason & Sutor, 2003), two-step Heckman procedures (Long, 1991), regresson dscontnuty (Schanzenbach, 2009), and propensty score matchng (Campbell et al., 2011). Instrumental varables have, for the most part, been rejected due to mnmal predctve power (Bhattacharya et al., 2004). Usng data from the Natonal Health and Nutrton Examnaton Survey (NHANES) 1999 to 2006, Campbell et al., (2011) estmate the average treatment effect of the treated (ATET) usng propensty score matchng. Instead of lookng at the effect of partcpaton on weght, the authors look at specfc nutrtonal ntakes such as fat, sodum, and vtamns and fnd that students partcpatng n the NSLP fve days a week report consumng more Vtamn A, calcum, proten, and fat at lunch than non-partcpants. These results support prevous research by Gleason & Sutor (2003) usng fxed effects model. Campbell et al. also determne that these ncreases n nutrents come from consumng a hgher-quantty det (not a hgher-qualty det) than non-partcpants at lunch. The dfferences between partcpants and non-partcpants food consumpton at breakfast and dnner are nsgnfcant. These results suggest that partcpaton n the NSLP may ncrease the probablty of beng obese through consumng larger quanttes of food at lunch. Schanzenbach (2009) uses panel data from the Early Chldhood Longtudnal Study Kndergarten Cohort (ECLS-K) to assess the causal effect of the NSLP on obesty. The author separates ndvduals nto rsk categores dependng on ther weght upon enterng kndergarten and observes that ncome-nelgble NSLP partcpants are 1 to 2 percentage ponts more lkely to 4

6 be obese by end of frst grade. Addtonally, takng advantage of the sharp ncome-elgblty cutoff of 185 percent, Schanzenbach uses regresson-dscontnuty desgn (RD) to observe that ncome-elgble students are more lkely to be obese than ncome-nelgble students. Due to the lmtatons of RD, ths result only holds for students wth household ncome around 185 percent. Usng the same dataset, Mllmet et al. (2010) assess the mpact of both the NSLP and the School Breakfast Program (SBP). They fnd smlar results to Schanzenbach, even though ther sample ncludes ncome-elgble and nelgble students. Mllmet et al. then use a bvarate probt model to estmate the mpact of postve selecton nto the SBP. When controllng for postve selecton, the authors fnd that the school lunch program contrbutes to obesty rates whle the breakfast program does not. Another way to account for endogenety n treatment not captured by covarates s by computng bounds on average treatment effect. Gunderson et al. (2012) calculate bounds on average treatment effect of the NSLP on three negatve health outcomes: self-reported poor health, household food nsecurty, and obesty. The data are collected from NHANES 2002 to 2004 and the sample s lmted to ncome-elgble students. The authors use a monotone nstrumental varable assumpton that each outcome s non-ncreasng wth ncome such that non-partcpants have weakly lower outcomes. Usng ths nonparametrc method, the authors fnd that under weak assumptons, the NSLP reduces the rate of poor health, food nsecurty, and obesty. Specfcally, partcpaton n the NSLP by ncome-elgble students reduces the rate of obesty by 17 percent (3.2 percentage ponts), contradctng Schanzenbach and Mllmet et al. s results. Ths bref revew of the prevous lterature llustrates the complexty n determnng a causal effect of the NSLP on chldhood obesty. It appears that the school lunches provde a 5

7 larger lunch wth more nutrents than lunches from home (Gleason & Sutor, 2003; Campbell et al., 2011). For low-ncome students comng from households unable to provde breakfast or dnner, partcpatng n the NSLP may reduce malnutrton and be benefcal to overall health. For other students, the NSLP may contrbute to obesty but only by a small amount. The remander of ths paper s organzed as follows. The next secton descrbes the data and provdes summary statstcs of varables used n the analyses. The fourth secton presents four approaches to estmatng the effect of the NSLP on chldhood obesty. Methods are results are reported for 1) ordnary least squares regresson (OLS), 2) recursve bvarate probt model, 3) nonparametrc bounds estmaton, and 4) regresson dscontnuty desgn. The fnal secton offers concludng remarks. III. Data Data are obtaned from the Natonal Health and Nutrton Examnaton Surveys (NHANES). NHANES ncludes ntervews and medcal examnatons of a natonally representatve sample of about 5,000 Amercans annually; about half are chldren. Clusters of households wthn predetermned countes are selected and one or more persons from each household are chosen to partcpate n the survey. Samplng weghts are used to fnd accurate estmates and standard errors. To ncrease the sample sze and account for any unobserved changes over tme, we use a pooled cross-sectonal sample of chldren who attended elementary, mddle, and hgh school between 2001 and 2008 and nclude survey year as a dummy varable. All data used n the analyss come from the household ntervews, wth the excepton of body measurements obtaned n the medcal examnatons. These measurements are used to calculate three measurements of obesty used as outcomes n the analyses: body mass ndex (BMI), percent body fat, and wast to heght rato. The head of household, defned as a 6

8 household member 18 years or older that rents or owns the resdence, provdes all nformaton pertanng to the household and may assst mnors n ther ndvdual ntervew (NHANES 2009). Lke all self-reported data, NHANES may have relablty ssues. For example, the respondent may be unfamlar wth the specfc household management, such as household ncome. Furthermore, under-reportng of partcpaton n government programs such as the NSLP may occur, basng estmates (Gunderson et al, 2012). Outcomes Prevous research has usually measured obesty through an ndvdual s BMI. A chld s defned as obese f hs or her Body Mass Index (BMI = kg/m 2 ) s greater than the age and gender-specfc threshold, BMI, 95%. Ths threshold s calculated by the Center for Dsease Control s (CDC) as greater than the 95 th percentle for weght based on growth charts. BMI does not allow dstnctons between fat and muscle, possbly creatng measurement error of very muscular ndvduals as obese. However, t s the most prevalent measure of overweght because t s easy to calculate usng standard equpment. The ndcator varable BMI measures whether the th chld s obese (BMI =1) or not (BMI =0). In addton, we nclude two other ndcators of obesty used n the nutrton scence lterature: body fat and wast to heght rato. Percent body fat s measured usng the Slaughter et al. equaton of body densty (Slaughter, et al. 1988). Ths equaton uses trceps and subscapular sknfold measurements to calculate percent body fat and s consdered to be a vald measure for chldren (Relly et al., 1995). Body fat measurements requre specalzed equpment to measure and therefore are less often used than BMI. However, ths more refned measurement does dstngush between muscle and fat. A chld s consdered to have a hgh body fat f the total 7

9 percent of body fat s greater than 30 percent. The ndcator varable Body Fat measures whether the th chld has hgh percent body fat (Body Fat =1) or not (Body Fat =0). The thrd outcome used n the analyss s wast to heght rato. Ths measure of central adposty (fat dstrbuton) s easy to calculate and may be a more senstve predctor of cardovascular dsease and dabetes than BMI (Brownng et al., 2010). A person wth a wast to heght rato greater than 0.5 s consdered obese and at rsk of cardovascular dsease (Brownng et al. 2010), thus the ndcator varable WtH Rato measures whether chld has a large (greater than 0.5) wast to heght rato (WtH Rato =1) or not (WtH Rato =0). Control Varables A chld s body composton depends on age, gender, race, calores consumed and calores burned, and genetcs. For example, females are more lkely to store energy as fat nstead of muscle and chldren wth obese parents may be genetcally predsposed to obesty. NHANES ncludes myrad health, soco-economc, and nutrtonal outcomes, but nformaton on parental heght, weght, or health s unfortunately not provded and thus the genetc component of body composton remans unobserved. Instead, brth weght s ncluded to control for genetc and bologcal factors. An approprate measure of calores burned (exercse) s not avalable across all years, so two measures of nactvty are ncluded n the analyss: average daly hours watchng televson and usng the computer. We expect that the more tme spent at ether actvty, the fewer hours spent engaged n physcal actvty and thus the more lkely a chld s obese. Twoday detary recall nformaton s provded for only a very lmted number of ndvduals, so a measure of calore nput s not ncluded n the analyses. To control for characterstcs across households, educaton, ncome, and martal status of the household reference are ncluded as covarates. Household educaton s measured by the 8

10 educaton attanment of the female head of household. Female educaton level s used nstead of male because we assume that n most households the female adult makes most decsons about food, ncludng whether the chld brngs a lunch from home nstead of eatng a school lunch. Household ncome s measured as the ncome to poverty rato (PIR); a PIR of 2 means a household s ncome s 200% of the poverty lne. Measurng ncome relatve to poverty s helpful n some of the analyses because t dentfes ncome elgble students (PIR < 1.85). Addtonally, because the poverty lne changes annually, PIR does not need to be adjusted by the consumer prce ndex (CPI). Table 1 provdes detals of all varables used n the analyss. Not all varables selected are deal. Household educaton level s measured by the educaton level of the female head of household and does not nclude a measure of the male head of household s (f present) level of educaton. Therefore, f the female head of household has only graduated hgh school but her spouse attended college, the household s reported to have the same level of educaton as a household wth two hgh school graduates. Ths may bas the estmates postvely or negatvely. Summary Statstcs The sample ncludes 6,410 students n elementary, mddle, or hgh school who partcpated n the NHANES ntervew and medcal examnaton. Only students attendng schools that serve school lunch are ncluded. Descrptve statstcs of key varables can be found n table 2. The average age wthn the sample s 10.6 years old and 47 percent of the sample attends elementary school. The average PIR for all students s 252 percent of the poverty level. For a famly of four n 2008, ths s equvalent to approxmately $53, percent of all students sampled are obese, 16.8 percent have hgh percent body fat, and 29.2 percent of all students sampled have large wast to heght ratos. Ths result suggests that Body Fat s more closely correlated wth BMI than WtH 9

11 Rato; n fact, 17.2 percent of students dentfed as not obese have large wast to heght rato whle only 7.6 percent of students classfed as not obese have hgh body fat percent of all students partcpate n the school lunch program 5 days per week. Smlarly to prevous research, we fnd sgnfcant dfferences wth NSLP partcpants and non-partcpants as well as between obese and non-obese chldren (Dunfon and Kowalesk- Jones, 2001; Ogden & Carroll, 2010). Both obese students and NSLP partcpants are more lkely to come from lower-ncome households: on average non-partcpants have a household ncome of 313 percent of the poverty lne compared to 216 percent for NSLP partcpants. The dfference between household ncome among obese and non-obese students s smaller but stll sgnfcant. On average, obese students n the sample are 0.23 pounds heaver at brth than nonobese students, suggestng the possblty of an unobserved genetc component of obesty. The majorty of students sampled are non-hspanc whte. Although Mexcan Amercans make up only percent of the sample, 53.9 percent of all NSLP partcpants are Mexcan Amercan, 18.7 percent are whte, and 14.9 percent are black. The summary statstcs for household educaton seem unusual percent of the students sampled come from households where the female head of household s a college graduate. Interestngly, 25.7 percent of NSLP partcpants sampled come from households where the female s a college graduate whle only 10.9 percent of non-partcpants s come from households where the female s a college graduate. It may be possble that as the female s level of educaton ncreases, her tme s more valuable and she chooses not to prepare a lunch for the chld. IV. Measurng the Effect of NSLP Ths secton presents four approaches to estmatng the effect of Natonal School Lunch Program 10

12 partcpaton on chldhood obesty measured through BMI, percent body fat, and wast to heght rato. We begn wth OLS regresson. Second, results of the recursve bvarate probt model smlar to Mllmet et al. (2010) are presented. The thrd approach recreates the nonparametrc bounds approach used by Gunderson et al. (2012) but ncludes two new outcomes. Lastly, the fourth approach borrows from Schanzenbach (2009) by usng RD desgn to estmate the local average treatment effect of partcpaton. For the sake of brevty, we focus on the nterpretaton of the treatment effect and do not dscuss the effects of the other covarates. However, all results are presented n tables 3 through 7. Approach One: Ordnary Least Squares Regresson The frst approach n determnng the effect of partcpatng n the NSLP on chldhood obesty s the OLS regresson. It s well known that a lnear regresson model wll not provde consstent estmates when modelng bnary outcomes because t gnores the dscreteness of the varable; ths approach serves prmarly as a baselne comparson for the subsequent methods. The regresson models are defned as: (1.1) BMI =! BMI + x" # BMI + h" $ BMI + g" % BMI + NSLP & BMI + ',BMI (1.2) Body Fat =! BF + x" # BF + h" $ BF + g" % BF + NSLP & BF + ',BF (1.3) WtH Rato =! WtH + x" # WtH + h" $ WtH + g" % WtH + NSLP & WtH + ',WtH Let x! be a vector of ndvdual covarates ncludng age, gender, and race. Let h! be a vector of health ndcators that contrbute to ncreased measures of obesty (brth weght, daly televson use, and daly computer use) and g! be a vector of household demographcs ncludng educaton, ncome, martal status, and survey year. The ndcator varable NSLP measures whether student partcpates n the school lunch program (NSLP =1) or not (NSLP =0). Let BMI, Body Fat, and WtH Rato be the dscrete obesty measurements of student, as prevously defned. Let!! 11

13 be the error term. Results of the OLS regresson are smlar across all three models (table 3). The overall ft of the models s very low wth R 2 between 3.5 percent and 6.7 percent. The estmates n table 3 are not weghted to account for survey desgn, however we fnd no sgnfcant dfference between weghted and non-weghted results. We fnd statstcally nsgnfcant and small coeffcents NSLP rangng from to Ths suggests that partcpatng n the NSLP ncreases your probablty of beng obese (measured by BMI) by less than 1 percentage pont. Contrarly, partcpatng n the NSLP decreases your probablty of havng hgh percentage of body fat by 0.7 percentage ponts. These estmates are smlar n magntude to results n Schanzenbach (2009). Smlar results are found when health and household characterstcs are not controlled (.e., when h! and g! are not ncluded n equatons ). Ths model assumes that partcpaton n the NSLP s exogenous. However, t s lkely that many of the observable covarates and unobservable characterstcs mpactng the decson to partcpate may also mpact the probablty of beng obese. The next approach tres to account for potental endogenety of NSLP due to nonrandom selecton. Approach Two: Recursve Bvarate Probt Model The recursve bvarate probt model allows for the endogenety of NSLP partcpaton but requres strong dstrbutonal assumptons of the error term. Mllmet et al. (2010) use ths model to assess the mpact of postve selecton nto the School Breakfast Program and note that whle the model s dentfed wthout excluson restrctons, the bvarate probt model wll not provde consstent estmates wthout a vald nstrument. We are currently attemptng to determne a vald nstrument and present our prelmnary results here. Even wthout a vald nstrument for partcpaton, the bvarate probt model should be an mprovement from the OLS 12

14 regresson. We use the same outcome varables and covarates as descrbed above n ths twoequaton model. (2.1) BMI * = x! " BMI + h! # BMI + g! $ BMI + NSLP % BMI + & 1,BMI, BMI = 1 f BMI * > BMI, 95%, else 0 NSLP * = x! ' BMI + g! $ BMI + & 2,BMI, NSLP = 1 f NSLP * > 0, else 0 (2.2) Body Fat * = x! " BF + h! # BF + g! $ BF + NSLP % BF + & 1,BF, Body Fat = 1 f Body Fat * >.30, else 0 NSLP * = x! ' BF + g! $ BF + & 2,BF, NSLP = 1 f NSLP * > 0, else 0 (2.3) WtH Rato * = x! " WtH + h! # WtH + g! $ WtH + NSLP % WtH + & 1,WtH, WtH Rato = 1 f WtH Rato * > 0.5, else 0 NSLP * = x! ' WtH + g! $ WtH + & 2,WtH, NSLP = 1 f NSLP * > 0, else 0 Because NSLP s endogenous to the three outcomes, BMI, Body Fat, and WtH Rato, NSLP s smultaneously determned n ths model. The frst equaton n each model ncludes vectors of ndvdual, health, and household explanatory varables defned n the prevous secton as x!, h! and g!, respectvely. envronmental factors. These varables are selected to control for possble household and The second equaton n each model does not nclude covarates controllng for health. To fnd consstent estmators of the model, the log lkelhood functon for each bvarate probt model s maxmzed: ( ) n (2.4) LLF = ln! 2 q 1 ( x" # Y1 + h " $ + g" % + NSLP& ), q Y1 Y1 Y1 2 ( x" ' Y1 + g " % ), q Y1 1 q 2 ( Y1 where ) =1 "# $% = & z 2 (, z, ' 1 2 Y 1 )dz 1 dz 2! 2 ( ) = Pr Y 1 = y 1, NSLP = y 2 x,h,g, NSLP x* 0+ * / () g - x* ++ h*, + g* - +. NSLP / () 13

15 " $ q j = 1 f y j = 1 # %$!1 f y j = 0 & j = 1, 2 The log-lkelhood functon, LLF, s the summaton of the four possble combnatons of Y 1 and NSLP. Let Y 1 be the chosen measure of obesty (ether BMI, Body Fat, or WtH Rato). The standard normal bvarate dstrbuton,! 2 ( ), requres both error terms!!,!! and!!,!! have a mean of zero and varance of one. The covarance (or dsturbance term) between!!,!! and!!,!! s!!!. If the!!! = 0, the model reduces to a recursve probt model where NSLP s stll determned smultaneously. If!!! 0, the error terms!!,!! and!!,!! are postvely or negatvely correlated, dependng on the sgn of!!!. Ths may ndcate selecton bas on unobservables as well (Altonj et al., 2005; Mllmet et al., 2010). It s mportant to note that a non-zero dsturbance term may be due to true correlaton between chldhood obesty and NSLP partcpaton as well as specfcaton error wthn the model. Table 4 provdes the estmated coeffcents for the recursve bvarate probt model. Agan, results across the three models are smlar. The coeffcent!!! ranges from s to and s statstcally sgnfcant n the BMI and WtH Rato models, suggestng that partcpaton n the school lunch program ncreases the lkelhood of beng obese. The coeffcent!!"#$ s not sgnfcant when Body Fat s the outcome. The dsturbance term s estmated to be negatve and statstcally dfferent than zero. Ths s a surprsng and a somewhat counterntutve result: after accountng for ndvdual and household characterstcs and the effect of NSLP partcpaton on obesty rates, there s a sgnfcant negatve correlaton between unobservables n the two equatons. Recall that ths term s due to ether true correlaton or specfcaton error n the model. If the model s specfed approprately, ths result may ndcate negatve selecton nto the school lunch program. 14

16 The margnal effects of NSLP partcpaton on the three health outcomes are also ncluded n table 4. All three margnal effects are postve and statstcally sgnfcant. The probablty of beng obese (Y 1 =BMI) s 11.7 percentage ponts hgher for students partcpatng n the school lunch program. The probablty of havng a hgh percentage of body fat ncreases 9.0 percentage ponts for partcpants and the probablty of havng a large wast to heght rato ncreases 18.3 percentage ponts for students partcpatng n the NSLP. Ths estmate s sgnfcant and supports studes fndng ncreased fat ntake of NSLP partcpants (e.g. Gleason & Sutor, 2003; Campbell et al., 2011) and those fndng postve relatonshps between partcpaton and obesty (e.g. Mllmet et al., 2010; Schanzenbach, 2009). However, wthout a vald nstrument, a causal effect of partcpaton n the NSLP on chldhood obesty cannot be determned wth the bvarate probt model. The next approach uses nonparametrc methods to partally dentfy the average treatment effect wthout restrctve parametrc assumptons. Approach Three: Nonparametrc Bounds The prevous models have dealt wth endogenous treatment selecton by mposng strct parametrc assumptons (recursve bvarate probt model) or gnorng them completely (OLS regresson). In contrast, the thrd approach uses nonparametrc bounds to partally dentfy the ATE. We observe x = ( w,z), a set of covarates wthn X = W! Z defnng each subpopulaton. Let y 1 be a student s potental health outcome f partcpatng n NSLP and let y 0 be a student s potental health outcome f not partcpatng n NSLP. For ths analyss, y t ncludes BMI, Body Fat, and WtH Rato. The average treatment effect s (3.1) ATE = E!" y 1 x#$ % E!" y 0 x#$ where 15

17 E!" y 1 x# $ = pe!" y 1 x, NSLP = 1# $ + ( 1% p)e!" y 1 x, NSLP = 0# $ E!" y 0 x# $ = pe!" y 0 x, NSLP = 1# $ + ( 1% p)e!" y 0 x, NSLP = 0# $ ( ) [ ] &[ 0,1] p = Pr NSLP = 1 x E y t For each student, we observe ether y 1 or y 0, a bnary outcome, but we do not observe the counterfactual where E "# y t x, NSLP! t $%. We know, however, that the expectaton must le between 0 and 1. Unless partcpaton n the NSLP s random, a pont estmate of ATE wll be based due to potental selecton on unobservables. Wthout ncludng any further assumptons, Mansk (1990) developed worst-case bounds by replacng the unobserved expectatons wth the bounded values of y t. For each value of x, let ATE WC be defned as: (3.2) ATE WC! " # pe "# y 1 x, NSLP = 1$% & p & ( 1& p)e "# y 0 x, NSLP = 0$%, pe "# y 1 x, NSLP = 1$% + ( 1& p) & ( 1& p)e " # y 0 x, NSLP = 0$% $. % The worst-case bounds are not very nformatve. By defnton, they must cover zero and have a wdth of one n the case of bnary outcomes. The ATE WC for y t = BMI, y t = Body Fat, and y t = WtH Rato are shown n table 5. The sample s dvded nto 20 groups defned by the PIR and an approprately weghted ATE WC calculated for each group. 3 Covarates n x lmt the sample to students between the age of 6 and 17 attendng school that offers NSLP; unlke Gunderson et al., we nclude ncome-elgble and nelgble students. In fnte samples, bounds other than ATE WC are based. However, wth more than 400 observatons n each group, the bas should be neglgble (Kreder et al., 2011). At worst, partcpaton n the NSLP ncreases the obesty rate by 42.6 percentage ponts. At best, partcpaton decreases the obesty rate by 57.4 percentage ponts. Smlar results are found for Body Fat (-0.595, 0.405) and WtH Rato (-0.539, 0.461). 3 Because some x are empty sets, the sample must be dvded nto groups. Estmates are smlar when usng 10 groups. 16

18 Incluson of addtonal assumptons allows these bounds to be tghtened to produce a more nformatve result wthout dependng on strong dstrbutonal assumptons (Mansk, 1990; Mansk & Pepper, 2000). A common assumpton (and an underlyng assumpton for vald nstrumental varables) s mean-ndependence: the mean outcome for each treatment s equal across all subpopulatons. If covarate z s an nstrumental varable, then the worst-case bounds for each x can be tghtened to: (3.3) " ATE IV! sup #' z ( ) & nf pe "# y 1 x, NSLP = 1$ % ( ( ) ) & sup nf pe y 1 x, NSLP = 1 z "# $% + 1& p z ( p + ( 1& p)e "# y 0 x, NSLP = 0$ % ), z ( ) $ % (. ( 1& p)e "# y 0 x, NSLP = 0$% ATE IV are ncluded n table 5 usng household PIR as an nstrument for partcpaton n NSLP. The ATE IV on Body Fat states that assumng students from households wth varyng ncome have the same mean health outcome, partcpaton n the NSLP wll at worse ncrease the probablty of havng hgh percent body fat by 10.7 percentage ponts and at best decrease the probablty of havng hgh percent body fat by 31.0 percentage ponts. However, t s much more lkely that PIR s a monotone nstrumental varable (MIV). That s, we expect that the probablty of negatve health outcomes Body Fat, BMI, and WtH Rato weakly decrease wth PIR, as n Gunderson et al. (2012). Formally, the negatve MIV assumpton states that for each treatment t, E!" y t w,z = z 1 # $ % E!" y t w,z = z 2 # $, where z s an ordered set and. z 1! z! z 2. The average treatment effect usng the MIV assumpton produces bounds that are smaller than worstcase bounds but larger than IV bounds. Let ATE MIV be (3.4) # ATE MIV!) sup pe #$ y 1 x,z = z 1, NSLP = 1% z 1 ( "z & ) ' nf p + ( 1' p)e y 0 x,z = z 2, NSLP = 0 z 2 ( (z #$ % & ), $ nf( pe #$ y 1 x,z = z 2, NSLP = 1 % & + ( 1' p )) ' sup ( 1' p)e #$ y 0 x,z = z 1, NSLP = 0% & z 2 (z z 1 "z ( ) % & *. 17

19 ATEMIV bounds are also unnformatve. The ATEMIV on WtH Rato states that assumng students from households wth lower ncome have weakly hgher negatve health outcomes, partcpaton n the NSLP wll at worse ncrease the probablty of havng a large wast to heght rato by 22.8 percentage ponts and at best decrease the probablty of havng a large wast to heght rato by 51.7 percentage ponts. Whle the MIV assumpton may seem nnocuous (Gunderson et al., 2012), our sample data suggest that even ths assumpton s ncorrect. Fgure 1 graphs each expected outcome by PIR. The relatonshp does not appear monotone (negatve or postve) across any values of PIR. Even f analyss s restrcted to ncome-elgble students, the expected values of BMI, Body Fat, and WtH Rato appear to fluctuate between PIR values of 0 and A more common assumpton n the lterature s selecton on unobservables. Models that assume exogenous selecton (e.g., OLS regresson) wll calculate based treatment effect estmates f postve or negatve selecton exsts. Although the bvarate probt model estmated above found possble negatve selecton through the covarance term!, t s generally assumed that unobserved characterstcs assocated wth obesty are postvely related to partcpaton n the NSLP (Curre, 2003). We now formalze the assumpton of postve selecton, or monotone treatment selecton (MTS) assumpton (Mansk & Pepper, 2000) wthn the ATE framework. In terms of ths analyss, the MTS assumpton states that a student partcpatng n the NSLP s lkely to have no better negatve health outcome on average than non-partcpants. Thus the bounds of the expected outcomes are now: 0! E "# y1 x, NSLP = 0 $%! E "# y1 x, NSLP = 1$%! 1 1 & E "# y0 x, NSLP = 1$% & E "# y0 x, NSLP = 0 $% & 0. The MTS assumpton does not change the lower bound of ATEWC but does decrease the upper bound. Ths result s ntutve: f postve selecton exsts, we expect estmates assumng 18

20 exogenous selecton to be based upward. Thus the ATE MTS has the same lower bound of equaton 3.2 and the upper bound s now (3.5) ATE MTS! pe "# y 1 x, NSLP = 1$ % + ( 1& p)e "# y 1 x, NSLP = 1$ % & pe "# y 0 x, NSLP = 0$% & ( 1& p)e "# y 0 x, NSLP = 0$%. The estmates of ATE MTS for each outcome are n table 5. Includng the MTS assumpton tghtens the lower bounds for all outcomes and fnds negatve upper bounds for Body Fat and WtH Rato. Assumng postve selecton, at worst partcpatng n the NSLP 1) ncreases the probablty of beng obese by less than 1 percentage pont, 2) decreases the probablty of havng hgh percent body fat by 3.7 percentage ponts, and 3) decreases the probablty of havng a large wast to heght rato by 1.6 percentage ponts. Unlke the MIV assumpton, the authors know of no test or fgure used to evaluate the valdty of the MTS assumpton. However, the assumpton of postve MTS seems much more lkely than exogenous treatment selecton or negatve MTS. Lastly, although we queston the valdty of the MIV assumpton, we present the combned MIV and MTS assumpton because t may be applcable n other research scenaros. Let ATE MIV+MTS be % (3.6) ATE MIV +MTS!' sup & z 1 "z where LB 1 z 1 UB 1 z 2 ( LB 1 ( z 1 )) # nf ( ) = pe y 1 x,z = z 1, NSLP = 1 ( ) = pe y 1 x, NSLP = 1 ( ) = pe y 0 x, NSLP = 0 ( ) = p + 1% p LB 0 z 1 UB 0 z 2 z 2 ( UB z 0 ( 2 )), nf UB z 1 2 $z z 2 $z ( ( )) # sup!" # $!" #$ + 1% p)e " y 1 x, NSLP = 1#$!" #$ % 1% p)e " y 0 x, NSLP = 0#$ ( )E!" y 0 x,z = z 2, NSLP = 0# $. z 1 "z ( LB 0 ( z 1 )) ( ) * 19

21 Agan, the postve MTS assumpton only changes the upper bounds of each ATE MIV+MTS. The lower bounds are dentcal to the ATE MIV lower bounds. Assumng students from households wth lower ncome have weakly hgher negatve health outcomes n addton to assumng postve selecton on unobservables, at worst partcpatng n the NSLP 1) decreases the probablty of beng obese by 5.4 percentage ponts, 2) decreases the probablty of havng hgh percent body fat by 14.7 percentage ponts, and 3) decreases the probablty of havng a large wast to heght rato by 9.8 percentage ponts. When ncludng ncome-elgble and nelgble students, the average treatment effect for BMI s 2.2 percentage ponts hgher than estmated by Gunderson et. al (2012). The nonparametrc bounds approach suggests that under weak assumptons, the average treatment effect of partcpaton n the NSLP on ndcators of hgh percent body fat, obesty, and large wast to heght rato s at worst negatve. Ths result contradcts the results from approach 1 and 2 n ths paper as well as results n the prevous lterature (ncludng Mllmet et al. (2010) and Schanzenbach (2009)). The fnal approach to treatment evaluaton s regresson dscontnuty desgn. Approach Four: Regresson Dscontnuty Regresson dscontnuty takes advantage of the large dsparty between the prce of a school lunch for ncome-elgble students and ncome-nelgble students that ncreases the probablty of partcpaton for ncome-elgble students. By law, the reduced prce lunch can cost the student no more than $0.40 whle a full prce meal on average costs $ (School Nutrton Assocaton, 2007). Because ncome-elgble students are not requred to partcpate and ncome- 4 The cost of a full prce meal s set locally and thus vares from school to school. As of 2012, each full prce lunch served s federally subsdzed $0.26, much lower rate than the subsdy rate for free and reduced prce lunches. State and local governments can choose to subsdze full prce meals even more. For example, full prce meals n New York Cty are currently set at $

22 nelgble students may choose to partcpate and pay full prce, we use a fuzzy regresson dscontnuty desgn (FRD) such that lm Pr ( NSLP PIR!PIR 0 = 1 PIR = PIR ) 0 " lm Pr ( NSLP PIR#PIR 0 = 1 PIR = PIR ) 0 where PIR 0 =1.85 s the threshold. In our sample, the probablty of partcpatng n NSLP decreases from 59 percent to 73.3 percent around the threshold, PIR 0. Let the relatonshp between the three outcomes and partcpaton n the NSLP be (4.1) BMI =! BMI + NSLP " BMI + f ( PIR ) +#,BMI (4.2) Body Fat =! BF + NSLP " BF + f ( PIR ) +#,BF (4.3) WtH Rato =! WtH + NSLP " WtH + f ( PIR ) +#,WtH where NSLP and PIR are defned as before,! y s the local average causal effect (LATE) of partcpaton, and!,y s a vector of covarates nfluencng the outcome varable (age, gender, race, and brth weght). The estmand of! y s the rato of the magntude of the dscontnuty n the probablty of each outcome to the magntude of the dscontnuty n the probablty of partcpatng n the school lunch program 5 (Imbens & Lemeux, 2007): (4.4)! y = lm E # y PIR"PIR $ 0 PIR = PIR 0 % & ' lm E # y PIR(PIR $ 0 PIR = PIR 0 % & lm E # NSLP PIR"PIR $ 0 PIR = PIR 0 % & ' lm E # NSLP PIR(PIR $ 0 PIR = PIR 0 % & where y s student s obesty outcome (BMI, Body Fat, or WtH Rato). The LATE estmand! s determned by usng local lnear regressons to estmate the outcome varable on ether sde of the threshold PIR=1.85 (the numerator of! y ) and then usng local lnear regresson agan to estmate the treatment effect on ether sde of the threshold (the denomnator of! y ). 5 The sharp regresson dscontnuty desgn s a specal case of FSD where the dscontnuty n regresson of the treatment ndcator s 1. 21

23 Results are presented n table 6 and fgures 2 through 4. Optmal bandwdth s defned by the IK bandwdth (Imbens & Kalyanaraman, 2009). Standard errors are estmated usng the delta method. Fgure 2 graphs the smoothed probablty of beng obese over all values of PIR. The vertcal lne represents the threshold value of PIR=1.85, wth ncome-elgble students to the left of the cutoff and ncome-nelgble students to the rght of the cutoff. A dscontnuty s present at the cutoff, but t appears small. Unlke Schanzenbach (2009), we fnd that students just above the threshold are more lkely to be obese. That s, partcpaton n the school lunch program decreases the probablty of beng obese by 78 percentage ponts. Although the result s nsgnfcant and the magntude hghly mprobable, the negatve sgn s congruent wth the nonparametrc bounds estmated above. Fgures 3 and 4 show smlar results for ndcators of hgh body fat and large wast to heght rato. Partcpaton n the NSLP reduces the probablty of hgh percent body fat by 132 percentage ponts and reduces the probablty of large wast to heght rato by 198 percentage ponts. Agan, these estmates seem very unrealstc and are not sgnfcantly dfferent than zero. The authors calculate standard robustness checks on the valdty of the FRD desgn. To make sure the dscontnuty s not present at other thresholds,! y s estmated at PIR 0 =2 (ncluded n table 6), PIR 0 =2.5, and PIR 0 =1. The coeffcents at each false threshold are not sgnfcant. Another specfcaton test s calculated by runnng regressons on baselne covarates Brth Weght and Black, non-hspanc that should not affect partcpaton n the NSLP and thus we expect contnuty n each of these covarates at the threshold. As expected, nether of these coeffcents s sgnfcant. The coeffcent estmates do not depend on bandwdth: decreasng the bandwdth to half the sze of the IK optmal bandwdth and ncreasng t to twce as large produces smlar results. Lastly, local lnear regressons estmated wth and wthout 22

24 covarates also produce smlar results. If the ncluson of covarates changes the sgnfcance or sgn of the estmated LATE, ths may ndcate msspecfcaton of the FRD or a potental dscontnuty n one or more covarates. Whle our specfcaton tests ndcate vald FRD desgn, the estmated treatment effects for BMI, Body Fat, and WtH Rato are all nsgnfcant. It may be the case that the small dscontnuty s caused by non-lnearty of the condtonal mean functon. As shown n fgure 1, the expected value of each of the outcomes s not monotonc across all values of PIR. A test of monotoncty n the condtonal mean outcomes for students just above and just below the threshold should be calculated. V. Summary and Conclusons The Natonal School Lunch Program s one of the largest food-assstance programs n the Unted States, provdng lunch for over 31 mllon students. Recent research suggests that the NSLP s no longer provdng nutrtous meals and at least one-thrd of schools do not meet complance set by the Detary Gudelnes of Amerca (Crepnsk et al., 2009). Wth chldhood obesty close to 17 percent for two- to nneteen-year olds, t s mperatve to understand how partcpaton n the NSLP may be mpactng chldhood obesty. Prevous studes have shown that partcpaton n the NSLP contrbutes to chldhood obesty, most lkely through the hgh fat and calore content of the school lunch as well as due to selecton on unobservables. However, under weaker assumptons, the postve effects of partcpaton on negatve health outcomes dsappear. Ths paper revews the current lterature on the causal mpacts of the NSLP on obesty and other nutrtonal outcomes and then offers four approaches to estmaton. We add to the economcs lterature two addtonal measures of obesty: percent body fat and wast to heght rato. However, the fndngs are nconclusve. Usng OLS regresson, the estmated effect of partcpaton on obesty s less than 1 percentage 23

25 pont; usng a recursve bvarate probt model, partcpaton n the NSLP ncreases the probablty of beng obese by 12 percentage ponts. When strong normalty dstrbutons are removed, these estmates reverse sgn: under MIV and MTS assumptons, partcpaton n the NSLP at worst decreases the probablty of beng obese 5 percentage ponts; estmaton of a local average treatment effect around the ncome-elgblty threshold of 185 percent of the poverty lne ndcates that partcpaton n the NSLP decreases the probablty of beng obese by 78 percentage ponts. The causal relatonshp between partcpaton n the NSLP and rates of chldhood obesty s stll unclear, partly due to concerns about the valdty of each model. The smplstc OLS regresson does not account for the endogenety of partcpaton, however the more complex bvarate probt model requres a vald nstrument to correctly dentfy the causal effect and results may depend heavly on the strong dstrbutonal assumptons. Unfortunately, even the most nnocuous assumpton of condtonal mean monotoncty s not supported by the data, thus nvaldatng the nonparametrc MIV bounds and possbly the fuzzy regresson dscontnuty results. These conclusons underscore the complexty n determnng a causal effect of the NSLP on chldhood obesty. Future research may focus on determnng the precse mechansm through whch the school lunch program has an effect on obesty. VI. References Altonj, J.G., Elder, T.E., Taber, C.R., An evaluaton of nstrumental varable strateges for estmatng the effects of Catholc schoolng. Journal of Human Resources 46 (4), Bhattacharya, J., Curre, J., Hader, S., Evaluatng the mpact of school nutrton programs: fnal report. USDA Economc Research Servce Washngton, D.C. 24

26 Blar, S., Brodney, S., Effects of physcal nactvty and obesty on morbdty and mortalty: current evdence and research ssues. Medcne & Scence n Sports & Exercse 31 (11), S646-S662. Brownng, L.M., Hseh, S.D., Ashwell, M., A systematc revew of wast-to-heght rato as a screenng tool for the predcton of cardovascular dsease and dabetes: 0.5 could be a sutable global boundary value. Nutrton Research Revews 23(2), Campbell, B.L., Nayga Jr., R.M., Park, J.L., Slva, A., Does the Natonal School Lunch Program mprove chldren s detary outcomes? Amercan Journal of Agrcultural Economcs 93 (4), Comuzz, A.G., Allson, D.B., The search for human obesty genes. Scence 280, Crepnsk, M. K., Gordon, A. R., McKnney, P. M., Condon, E. M., Wlson, A., Meals offered and served n US publc schools: do they meet nutrent standards? Journal of Amercan Detetc Assocaton 109, S31-S43. Chandon, P., Wansnk, B., 2007a. Is obesty caused by calore underestmaton? A psychophyscal model of meal sze estmaton. Journal of Marketng Research 44 (1), Chandon, P., Wansnk, B., 2007b. The basng health halos of fast-food restaurant health clams: lower calore estmates and hgher sde-dsh consumpton ntentons. Journal of Consumer Research 34 (3), Chburs, R.C., Semparametrc bounds on treatment effects. Journal of Econometrcs 159(2010),

27 Curre, J., U.S. food and nutrton programs. Means-Tested Transfer Programs n the Unted States. Ed. R.A. Mofftt. Unversty of Chcago Press. Dunfon, R., Kowalesk-Jones, L., Assocatons between partcpaton n the Natonal School Lunch Program, food nsecurty, and chld well-beng. Workng Paper No Northwestern Unversty/Unversty of Chcago Jont Center for Poverty Research. Gleason, P., Sutor, C., Eatng at school: how the Natonal School Lunch Program affects chldren s dets. Amercan Journal of Agrcultural Economcs 85(4), Gundersen, C., Kreder, B., Pepper, J., The mpact of the Natonal School Lunch Program on chld health: a nonparametrc bounds analyss. Journal of Econometrcs 166 (1), Hll, J.O., Peters, J.C., Envronmental contrbutons to the obesty epdemc. Scence 280 (5368), Imbens, G.W., Lemeux, T., Regresson dscontnuty desgns: A gude to practce. Journal of Econometrcs 142 (2008), Imbens, G., Kalyanaraman, K., Optmal bandwdth choce for the regresson dscontnuty estmator. NBER Workng Paper # Kreder, B., Pepper, J., Gunderson, C., Jollffe, D., Identfyng the effects of food stamps on chld health outcomes when partcpaton s endogenous and msreported. Workng Paper. Lee, D.S., Lemeux, T Regresson dscontnuty desgns n economcs. Journal of Economc Lterature 48 (2), Long, S., Do the school nutrton programs supplement household food expendtures? Journal of Human Resources 26 (4),

28 Mansk, C.F., Nonparametrc bounds on treatment effects. The Amercan Economc Revew 80 (2) Mansk, C.F., Pepper, J.V., Monotone nstrumental varables: wth an applcaton to the returns to schoolng. Econometrca 68 (4), Mllmet, D.L., Tcherns, R., Husan, M., School nutrton programs and the ncdence of chldhood obesty. Journal of Human Resources 45 (3), NHANES, About NHANES. Ogden, C., Carroll, M., Prevalence of obesty among chldren and adolescents: Unted States, trends through Center for Dsease Control. Ralston, K., Newman, C., Clauson, A., Guthre, J., Buzby, J., The Natonal School Lunch Program: background, trends, and ssues. ERR-61, U.S. Department of Agrculture, Economc Research Servce. Relly, J.J., Wlson, J., Durnn, J.V.G.A., Determnaton of body composton from sknfold thckness: a valdaton study. Archves of Dsease n Chldhood 73, School Nutrton Assocaton, School lunch prces rse. Schanzenbach, D., Does the federal school lunch program contrbute to chldhood obesty? Journal of Human Resources 44 (3), Slaughter, M.H., Lohman, T.G., Boleau, R.A., Sknfold equatons for estmaton of body fatness n chldren and youth. Human Bology 60, U.S. Department of Agrculture, Nutrton Standards n the Natonal School Lunch and School Breakfast Programs; Proposed Rule 76 (9). 13 January

29 U.S. Department of Health and Human Servces, Chldhood obesty. Avalable onlne: 28

30 Table 1. Varables Varable Measures of Obesty BMI Body Fat WtH Rato Indvdual Characterstcs NSLP Age Gender Race Health Indcators Brth Weght Daly Televson Use Daly Computer use Household Demographcs Educaton Income/Poverty Martal Status Survey Year Indvdual Body Mass Index (BMI) s greater than age/gender specfc cutoff for obese (Yes or No) Indvdual percent body fat s greater than 30% for obese (Yes or No) Indvdual wast to heght rato s greater than.50 for obese (Yes or No) Indvdual partcpates n Natonal School Lunch Program (NSLP) fve days per week (Yes or No) Indvdual's age (years) Indvdual's gender (Male or Female) Indvdual's race (Non-Hspanc Whte, Non-Hspanc Black, Mexcan Amercan, and Other) Indvdual s weght at brth (lbs) Average hours per day ndvdual spends watchng TV (Less than 1, 1, 2, 3, 4, 5, 5+ hours) Average hours per day ndvdual spends usng the computer (Less than 1, 1, 2, 3, 4, 5, 5+ hours) Educaton level of female household reference (Less than hgh school, hgh school dploma or GED, some college, college graduate or above) Rato of household ncome to federal poverty lne (e.g. 1 = household ncome s at poverty lne) Martal status of household reference (Marred, dvorced or separated, other) Year of questonnare and medcal examnaton ( , , , ) 29