003 Jont Statstcal Meetngs - Secton on Srvey Research Methods Health Insrance Estmates for Contes 1 Robn Fsher and Joanna Trner U.S. Censs Brea, HHES-SAEB, FB 3 Room 146 Washngton, DC, 033 Phone: (301) 763-3193, emal: robn.c.fsher@censs.gov Key Words: Small Area Estmates; Health Insrance Coverage; ASEC 1. Introdcton There s broad pblc nterest n health nsrance coverage sses. The nmber of nnsred people n the Unted States ncreased by roghly 10 mllon n the 1990s, despte a strengthenng economy (Mlls, 00). Wth the falre of the proposal for nversal health nsrance coverage n the md 1990s, t became apparent that targeted polces wold be the path to follow for programs desgned to ncrease coverage n the poplaton. In order to determne how one wold best target certan poplatons that may have dsproportonate levels of non-coverage, polcy makers need to be able to accrately dentfy these grops. The U.S. Censs Brea Small Area Health Insrance Estmates (SAHIE) project of the Small Area Estmates Branch (SAEB) s researchng the feasblty of prodcng model-based estmates of the nmber of people not covered by health nsrance (.e. nnsred) for states and contes. Generally, health nsrance coverage statstcs are avalable only throgh natonal hosehold srveys, and the estmates from these srveys vary wdely for a nmber of well-docmented reasons (Lews et al, 1998). The Annal Socal and Economc Spplement (ASEC) to the Crrent Poplaton Srvey (CPS) s the most wdely cted sorce for health nsrance statstcs. It s annal, the data are released n a tmely manner, the sample sze s relatvely large, and t has a state-based desgn. Sample szes are not large enogh, however, that the srvey alone can prodce sffcently relable state estmates for many polcy prposes. Whle recent follow-p legslaton has provded the U.S. Censs Brea wth addtonal fndng n order to mprove these estmates, relance on srveys alone wll contne to prevent the se of drect estmators for sb-state levels of geography. Recent methodologcal developments, at both the U.S. Censs Brea and n the broader research commnty, offer new potental for developng estmates of varos nnsred poplatons n small areas. SAEB has played a sgnfcant role n ths feld, developng a program that prodces ncome and poverty estmates at the state, conty, and school dstrct levels. The Small Area Income and Poverty Estmates (SAIPE) program constrcts statstcal models that relate ncome and poverty to varos ndcators based on the followng data: Federal tax retrns Food stamp partcpaton Estmates from the Brea of Economc Analyss Estmates from the Socal Secrty Admnstraton Estmates from the U.S. Censs Brea s Poplaton Dvson Decennal censs. These are then combned wth drect estmates from the ASEC to provde estmates and standard errors for the geographc areas of nterest. The SAIPE estmates were evalated favorably by the Panel on Estmates of Poverty for Small Geographc Areas of the Natonal Academy of Scences (Natonal Research Concl, 000). They are sed n Ttle I fndng allocaton formlas of the No Chld Left Behnd Act of 001 by the Department of Edcaton, and 1 Ths paper reports the reslts of research and analyss ndertaken by the U.S. Censs Brea staff. It has ndergone a Censs Brea revew more lmted n scope than that gven to offcal Censs Brea pblcatons. Ths report s released to nform nterested partes of ongong research and to encorage dscsson of work n progress. The vews expressed are those of the athors and not necessarly those of the U.S. Censs Brea. 1467
003 Jont Statstcal Meetngs - Secton on Srvey Research Methods by the Department of Health and Hman Servces to gage the effcacy of welfare reform programs on chldren. Ths paper s part of an ongong effort to expand SAIPE knowledge and methodologes to the area of health nsrance coverage. The effort began wth Fsher and Campbell (00), who modeled the nmbers of chldren of nterest for the State Chldren s Health Insrance Program (SCHIP). Ths paper ses a Bayesan verson of the method sed n the SAIPE poverty models, wth some modfcatons, to estmate the nsrance coverage rate at the conty level, from whch the nmber of nnsred can be calclated. The paper proceeds as follows: Secton descrbes or data sorces; Secton 3 descrbes the model; Secton 4 dscsses the estmaton; prelmnary reslts are provded n Secton 5; we conclde and descrbe ftre plans n Secton 6.. Data We descrbe the varables we consdered, althogh not all were nclded n the model. a. CPS Log proporton nsred. Ths s the log of the rato of the total nsred to the poplaton, measred by the ASEC; ths s a three-year average of the three ASEC drect estmates, centered on the year of nterest, weghted by the nmber of hoseholds n sample. The ASEC sample s reweghted so each conty s drect estmate s approxmately nbased for the nmber of nsred for that conty. Ths s denoted LINSHR for conty. Note that, for every conty wth sample, there are nsred people. Ths when the log proporton nsred s calclated, there are no contes for whch the response s ndefned. There are 1198 contes wth sample n at least one of the three years, wth an average of 13 hoseholds n sample. b. Internal Revene Servce (IRS) Ths s nformaton from ndvdal tax retrns aggregated by the U. S. Censs Brea to state and conty levels sng the street address on the retrn. The total nmber of exemptons attrbted to a retrn ncldes the fler, the spose of the fler, and the nmber of chld exemptons for the hosehold. For more detals see http://www.censs.gov/hhes/www/sape/techdoc/ npts/taxdata.html. Log IRS proporton between mltples of the Federal Poverty Threshold (FPT). Ths s the log of the fracton of exemptons on tax retrns lvng n hoseholds wth money ncome between two proportons of the FPT, say p 1 and p. Ths s denoted lpoorn (p 1, p ) for conty. Avalable vales for p k are 0%, 50%, 100%, 130%, 00%, 300%, and nfnty. Of partclar nterest s lpoorn (100%, 130%); these are low ncome people for whom the expense of health nsrance may be too hgh and who may not be covered by a program that targets the nnsred poor. An alternatve smmary to the proportons between mltples of the FPT follows. IRS moment of the log ratos of ndvdals famly ncome to ther Federal Poverty Threshold (FPT). Ths s N j ncj LIPR ( r) ln FPT j j = r =1,..., 4. FPT j s the Federal Poverty Threshold for the famly of person j n conty. Famly money ncome of that person s nc j. These moments contan nformaton abot the shape of the ncome dstrbton. There s evdence of a relatonshp between ncome relatve to the FPT and nsrance coverage at the state level (Fsher and Campbell, 00). c. Censs 000 Several varables tablated from Censs 000 were consdered as predctors, n partclar the log of the total poplaton (denoted lrpop ), log proportons n several age categores, log proporton Hspanc (denoted lhsprt ), and log proportons n varos race categores. d. Medcad The Balanced Bdget Act of 1997 reqres states, begnnng n fscal year 1999, to sbmt ther elgblty and clams data qarterly to the r, 1468
003 Jont Statstcal Meetngs - Secton on Srvey Research Methods Centers for Medcare and Medcad Servces 1 (CMS) throgh the Medcad Statstcal Informaton System (MSIS). Ths fle also contans the nmber of SCHIP recpents. States may mplement SCHIP wth a separate program, wth a Medcad expanson program, or wth a combnaton of the two. States report ther Medcad expanson program elgbles nto MSIS, bt not all states report ther separate SCHIP program elgbles. Snce 1999 was the frst year for reportng nder these rles, states were not reqred to follow them as strctly as n later years (Centers for Medcare and Medcad Servces, 00). These data can be expected to mprove for or prposes n sbseqent years. Log proporton elgble for Medcad by varos age and race/ethncty categores n second qarter of calendar year 1999. Grops of partclar nterest are chldren (denoted lpbaskd ), adlts ages 35 to 64 (denoted lpbasadlt ), and Hspancs (denoted lpbashsp ). An ndvdal s consdered elgble f they were covered by Medcad for at least one day drng the qarter. We conted an ndvdal as elgble f they receved fll benefts or receved benefts throgh a SCHIP expanson program. e. Conty Bsness Patterns (CBP) Ths s an annal seres of data, pblshed by the U.S. Censs Brea, that tracks economc actvty by ndstry. There are some lmtatons wth ths data for or prposes. Data are exclded on the self-employed, ralroad employees, agrcltral prodcton employees, and most government employees. De to the omsson of government employees, where there s a prevalence for health nsrance coverage, we are nvestgatng alternatve sorces of employment data for ftre work. For more detals on CBP data see http://www.censs.gov/epcd/cbp/vew/cbpvew.h tml. Employment s by far the leadng sorce of health nsrance coverage, wth nearly two-thrds of all people covered throgh an employer (Mlls, 00). Sze of the employer and ndstry are two key factors assocated wth a person s chances of havng health nsrance coverage. 1 CMS s the agency formerly named Health Care Fnancng Admnstraton (HCFA). Log proporton of employees by ndstry. Ths s the log of the proporton of adlts n varos sectors defned by the North Amercan Indstry Classfcaton System (NAICS). Log proporton of employees by frm sze. Ths s the log of the proporton of adlts n frms of varos szes. Indvdals who work for large frms are more lkely to have health coverage than workers n small frms. f. Food Stamp Program The food stamp program s a low-ncome assstance program that s nform n elgblty reqrements and beneft levels across states, wth the excepton of Alaska and Hawa. For more detals see http://www.censs.gov/hhes/www/sape/techdoc/ npts/foodstmp.html. Log nmber of recpents. By conty, ths s the log of the nmber of ndvdals partcpatng n the food stamp program n the month of Jly. 3. Model The model for log nsred rate for conty s LINSHR = X β + +, where X s the vector of covarates for that conty. The random effects term,, and the samplng error term,, have normal dstrbtons N 0, v ) and ( N( 0, v ), respectvely. Here, 1/ v = v / k, as n the SAIPE poverty model, and k s the ASEC sample sze. (We wll see that ths assmpton fts mperfectly n a followng secton.) For brevty we wll denote the parameters ( β, v, v ) as θ and X β + as µ. The nderlyng dscreteness of the ASEC sample, whch may be mportant when the proporton of nterest s close to zero or one and the sample sze s small, makes the normalty assmpton for the samplng error partclarly sspect. The SAIPE program, n ts program to estmate poverty for contes, ses a model wth two eqatons. One of the eqatons descrbes a model of the decennal censs log nmber n poverty as a lnear combnaton of the same predctors as the eqaton for the ASEC log nmber n poverty (U.S. Censs Brea, 003, 1469
003 Jont Statstcal Meetngs - Secton on Srvey Research Methods Fsher, 1997). The estmated random effects varance s then sed n the eqaton for the ASEC poverty, and estmaton proceeds as f the random effects varance were known. Ths confers some robstness to possble msspecfcatons of the varance model and some protecton aganst weakly dentfed varance parameters. In these health nsrance estmates, ths technqe s not avalable, snce the decennal censs had no qestons abot health nsrance. Unfortnately, jst becase the varance fncton can be decomposed nto two terms, one constant and one proportonal to the sqare root of the ASEC sample sze, there s no garantee that these components actally match the model error and samplng error, respectvely. Frther, there s no nformaton n the model abot the fnctonal forms of the error terms, except collectvely. It remans to specfy the pror dstrbtons. β n ~ N (0,100) v ~ Γ(0.1,1 ) v ~ Γ(0.1,1 ) The notaton Γ ( α, β ) denotes the gamma dstrbton wth mean α / β. 4. Model Ft and Estmaton Canddate models were chosen by examnng scatter plots and other exploratory methods. Other research has also shown the tlty of varos versons of the predctors we chose. (See Fsher and Campbell (00); Popoff, O Hara, and Jdson (00); Popoff, Jdson, and Fadal (001); Lazers et al (000); and Brown et al (001).) We rely on plots and posteror predctve p- vales (PPP-vales) to check the ft of the model. Gven a fncton of the data and θ, namely T ( y, θ), the PPP-vale s p( T ( y rep, θrep ) > T ( y obs, θrep ) ). Here the sbscrpt obs ndcates the actal observed vale whle the sbscrpt rep denotes a realzaton from the posteror dstrbton. (More detal s avalable n Gelfand (1998) and Gelman and Meng (1998).) Generally, PPP-vales near zero or one ndcate falres of the model to explan the data. We concentrate on PPP-vales based on the followng three defnng fnctons: T (, θ) = y 1 y T ( y, θ) = ( y µ ) ( y ) X β T3 ( y, θ) =. v + 1 / ( v / k ) The frst two fnctons gve ndcatons of the ft of the model wth respect to the expectaton and varance, respectvely, by conty. We also smmarze the resltng PPP-vales by takng the mean across the contes to measre the overall ft of the models wth respect to expectaton and varance. The thrd s a measre of the overall goodness of ft. Yo et al (000) se ths measre n ther small-area estmaton of nemployment. We se Markov chan Monte Carlo methods to sample from the posteror dstrbton of θ and the conty log nsred rate, and to evalate the model. The mplementaton s a Metropols algorthm wrtten n GNU Fortran 77 (Brown and Lovato, 1993). The tre conty log nsred rates were ntegrated ot and the parameters were ndvdally pdated. Then the conty log nsred rates, µ, were pdated n a Gbbs step. We chose the Metropols algorthm to preserve flexblty, snce t s not necessary to derve fll condtonal dstrbtons as t wold be for a Gbbs sampler. Ths, changes to the model wold reqre only a modfcaton of the fncton that comptes the lkelhood f ( y θ ). In ths paper we do not take advantage of ths featre. 5. Reslts and Dscsson The model we chose s LINSHR = lpbasadlt β 0 + β1lpbaskd + β 3lpbashsp β 4 +β + lhsprt +β lpoorn (1.0,1.3) 5 6lpoorn (.0,3.0) β 7lrpop +β + That s, the log nsred rate n a conty s a lnear fncton of: log proporton chldren, adlts ages 35-64, and Hspancs elgble for Medcad; log proporton Hspanc; log proporton between 100%-130% and 00%-300% of the FPT; and log of the total poplaton. The overall posteror. 1470
003 Jont Statstcal Meetngs - Secton on Srvey Research Methods predctve p-vales for the model for contes wth sample n ASEC are presented n Table 1. There s no evdence n these overall PPP-vales that the model fals wth respect to ther defnng fnctons. Plots for the PPP-vales for the ndvdal contes for the frst two fnctons were plotted verss varos varables and examned, smlarly to resdal plots. Plots of the PPP-vales for the means, verss the predctor varables and varos demographc varables, faled to show any systematc tendency to over- or nder-estmate the nsred rate. The PPP-vales for the varance, plotted aganst sample sze, show a lower bond whch depends on the sample sze. Ths may ndcate that the model for the samplng varance cold be mproved. Table 1. PPP-vales for the model sng the measres n Secton Defnng Fncton PPP-Vale y 0.5 The mean, calclated across contes, of the posteror standard devatons of the LINSHR s 0.0085. The mean posteror coeffcent of varaton (CV) for the nnsred rate s abot 5.3 percent. The posteror means and standard devaton (SD) of v and v are presented n Table. The posteror dstrbtons have mch smaller varance than the pror dstrbtons; they are clearly domnated by the lkelhood. The average rato of the random-effects varance to the total varance s abot 0.6 percent. Table. Posteror Means and SD of the Varance Parameters Varance Parameter Posteror Mean Posteror SD v 0.00009 0.00041 ( ) y 0.45 µ ( y X β ) + v ( v 1/ k ) / 0.49 v 0.044 0.009 Recall one possblty n a model lke ths, wthot the se of a separate estmate of one of the varance parameters, s that the two components of varance are weakly dentfed. Examnaton of the scatterplot of the sample of the jont posteror dstrbton of the varance parameters, v and v, together wth the observaton that the prors have relatvely large varances, show that the lkelhood s well behaved and dentfcaton s not a problem. 6. Conclson We have formlated a Bayesan model relatng the fracton nsred to varos varables from admnstratve records and U.S. Censs Brea poplaton estmates. The model has no obvos bases wth respect to expectaton, thogh the varance model may stll be weak. By estmatng the nsred rate rather than the nnsred rate we are able to avod some of the problems we see n the poverty model, specfcally the staton where there s no nnsred n sample and the log of that s ndefned. The average CV of the estmates, abot 5.3 percent, seems sffcently precse for general se. Ths depends, of corse, on ftre research regardng the senstvty of the reslts to the pror dstrbtons. Althogh ths type of model wold work n a prodcton envronment, mch needs to be done to make ths procedre adeqate for the prodcton of relable estmates. Some of the varables n the data have problems (sch as those n the Medcad data.) Whle not severe enogh to prevent the exploraton of ther nclson n a model, these problems shold be solved before they are sed to make estmates wth the U.S. Censs Brea mprmatr. Also, a canon of tests has evolved for small area estmates as prodced by the SAIPE project (and nherted by the SAHIE project), whch are yet to be done. (See Natonal Research Concl (000).) More work s also approprate on the methodology. Whle the estmaton of the log nsred rate avods the problem of censorng contes wth no nnsred n sample, there s stll an sse, perhaps neglgble n the present problem, of the falre of the normalty assmpton for contes wth small sample and proportons of nterest close to zero or one. 1471
003 Jont Statstcal Meetngs - Secton on Srvey Research Methods Fsher and Asher (000) propose one solton n the context of the estmaton of poverty, and Sld (000) proposes another. We wll also consder sng external estmates for the varance parameters as n Fay and Herrot (1979), Fsher (1997), or Bell (1999). There are other sorces of data that may be exploted, both as predctors and as responses. The Srvey of Income and Program Partcpaton measres nsrance coverage as well. Several athors have dscssed the dfferences between these measres and those prodced by the ASEC. The fttng and estmaton of a mltvarate model lke ths may allow s to make small area estmates for ether defnton of nsrance coverage and to make nferences abot the dfferences between them. Fnally, the form of the model tself may be mproved pon. Here the average of three years of ASEC s sed as the dependent varable. An alternatve s to form a mltvarate model wth the vector of the three years on the left-hand sde of the model, as n Yo et al (000) or n Fsher and Campbell (00). Then we can model the correlaton strctre of the random effects term and of the samplng error term. References Bell, Wllam. 1999. Accontng for Uncertanty abot Varances n Small Area Estmaton, Proceedngs of the Secton on Srvey Research Methods, Alexandra, VA: the Amercan Statstcal Assocaton. Brown, Barry W. and J. Lovato; 1993; RANLIB random nmber generaton lbrary; <http://www.netlb.org/random/ranlb.c.tar.gz>; (accessed: May 003). Brown, Rchard E., Yng-Yng Meng, Carolyn A. Mendez, and Hongjan Y. 001. Unnsred Calfornans n Assembly and Senate Dstrcts, 000, UCLA Center for Health Polcy Research, Los Angeles, CA. Centers for Medcare and Medcad Servces; 00; FY 1999 MSIS Caveats and Data Lmtatons; <http://cms.hhs.gov/medcad/mss/caveat99.asp >; (accessed: May 003). Fay, Robert E. and Roger A. Herrot. 1979. Estmates of Income for Small Places: An Applcaton of James-Sten Procedres to Censs Data, Jornal of the Amercan Statstcal Assocaton, Vol. 74, No. 366, pp. 69-77. Fsher, Robn. 1997. Methods Used for Small Area Poverty and Income Estmaton, 1997 Proceedngs of the Secton on Government and Socal Statstcs, Alexandra, VA: the Amercan Statstcal Assocaton. Fsher, Robn and Jana Asher; 000; Alternate CPS Samplng Varance Strctres for Constraned and Unconstraned Conty Models; released Jly 000; <http://www.censs.gov/hhes/www/sape/techre p/tech.report.1.revsed.pdf>. Fsher, Robn and Jennfer Campbell. 00. Health Insrance Estmates for States, 00 Proceedngs of the Secton on Government and Socal Statstcs, Alexandra, VA: the Amercan Statstcal Assocaton. Gelfand, Alan E. 1998. Model Determnaton Usng Samplng-Based Methods, In Markov Chan Monte Carlo n Practce, (eds W.R. Glks, et al), pp. 145-161. Gelman, A. and X. Meng. 1998. Model Checkng and Model Improvement, In Markov Chan Monte Carlo n Practce, (eds W.R. Glks, et al), pp. 189-01. Lazars, W., B. Fost, and B. Htt. 000. The Florda Health Insrance Stdy Volme 6: The Small Area Analyss, State of Florda, Agency for Health Care Admnstraton, Tallahassee, FL. Lews, Kmball, M. Ellwood, and J. Czajka. Jly 1998. Contng the Unnsred: A Revew of the Lteratre, The Urban Insttte, Assessng the New Federalsm: Occasonal Paper No. 8, Washngton, D.C. Mlls, Robert. 00. Health Insrance Coverage: 001. U.S. Censs Brea, Crrent Poplaton Reports, P60-0. Washngton, DC: U.S. Government Prntng Offce. Natonal Research Concl. 000. Small Area Estmates of School-Age Chldren n Poverty: Evalaton of Crrent Methodology, Panel on Estmates of Poverty for Small Geographc 147
003 Jont Statstcal Meetngs - Secton on Srvey Research Methods Areas, Constance F. Ctro and Graham Kalton, edtors. Commttee on Natonal Statstcs. Washngton, DC: Natonal Academy Press. Popoff, Carole, D.H. Jdson, and Betsy Fadal. 001. Measrng the Nmber of People wthot Health Insrance: A Test of a Synthetc Estmates Approach for Small Areas Usng SIPP Mcrodata, presented at the 001 Federal Commttee on Statstcal Methodology Conference. Popoff, Carole, B. O Hara, and D.H. Jdson. 00. Estmatng the Proporton of Unnsred Persons at the Conty Level: Explorng the Use of Addtonal Covarates n a Synthetc Estmates System, 00 Proceedngs of the Secton on Government and Socal Statstcs, Alexandra, VA: the Amercan Statstcal Assocaton. Sld, Erc; 000; Models for Smlaton & Comparson of SAIPE Analyses; released May 000; <http://www.censs.gov/hhes/www/sape/techre p/sapemod.pdf>. U.S. Censs Brea; 003; Small Area Income and Poverty Estmates Overall Estmaton Strategy; <http://www.censs.gov/hhes/www/sape/techdo c/strategy.html>; (accessed: May 003). Yo, Yong, J.N.K. Rao, and Jack Gambno. 000. Herarchcal Bayes Estmaton of Unemployment Rate for Sb-provncal Regons Usng Cross-sectonal and Tme Seres Data, 000 Proceedngs of the Secton on Government and Socal Statstcs, Alexandra, VA: the Amercan Statstcal Assocaton. 1473