Technical Report Panel Study of Income Dynamics Revised Longitudinal Weights June, 2008

Transcription

1 Technical Repor Panel Sudy of Income Dynamics Revised Longiudinal Weighs June, 2008 Elena Gouskova, Seven G. Heeringa, Kaherine McGonagle, and Rober F. Schoeni Survey Research Cener, Insiue for Social Research, Universiy of Michigan, Ann Arbor, MI 1. Inroducion This documen describes he consrucion of a revised se of Core/Immigran individual and family longiudinal sample weighs for he Panel Sudy of Income Dynamics (PSID). These weighs are a revised version of he longiudinal weighs currenly included in he PSID daa public use daa ses for hese years. The new approach described in his documen was also used o consruc he 2005 core/immigran longiudinal weighs. The principal difference beween he old and new weighs is found in he approach for assigning weighs o reappearers, i.e., persons who reurn o he sudy afer skipping one or more waves. PSID analyss who use he revised longiudinal weighs for cross-secional analysis of a single wave of daa will find increased case couns of sample persons wih posiive weighs. Researchers conducing longiudinal analyses such as sudies of simple change over ime, general linear mixed modeling (e.g. growh curves), laen variable modeling or even hisory analyses will also have increased case couns; however, hey will need o pay special aenion o he paern of missing daa over ime since he revised weighs assign non-zero values o a significan number of cases wih an incomplee daa series for he period Prior o 1993, he number of PSID sample persons who reappeared in he inerviewed sample afer one or more waves of nonresponse was very limied ypically around per year. Individual weigh values for hese reurning cases were se o 1

2 he weigh hey were assigned a he las wave in which hey had paricipaed. If he reappearer was a nonresponden in a wave a which PSID weighs were adjused for cumulaive panel ariion (i.e., 1969, 1974, 1979, 1984, and 1989), his procedure for carrying forward of he las recorded weigh could inroduce a small bias in he weighed populaion disribuion for he PSID responden sample. Wih such small numbers of prior wave nonrespondens reappearing in each wave, he poenial size of any bias ha resuled from his pracical approach o creaing a curren individual weigh for responding sample persons was very small. In 1992, 1993 and 1994, he PSID was funded o conduc a major follow-up of sample persons who had been los o nonresponse over he preceding decade. The nonresponse follow-up was very successful. From 1992 o 1994, PSID inerviewed approximaely 1800 persons who had no been inerviewed since The recovery of former nonrespondens in 1994 was even more successful, wih an addiional 2900 persons who had been nonrespondens since 1988 brough back ino he sudy. The success of he 1993 and 1994 reconac projec presened a difficul choice in he creaion of he 1993 and 1994 longiudinal weighs. One opion was o follow he convenional procedure of carrying forward he las available weigh (he reference weigh ) for reappearers / reconacs. Wih appropriae updaes o he correcion for panel ariion, his opion would maximize he case coun of sample persons for crosssecional analysis of each wave of PSID daa. However, a longiudinal weigh ha assigned a populaion weigh o reappearers / reconacs wih exended sequences of missing daa would be problemaic for analyss who wished o conduc rue longiudinal analysis. For example, an analys ineresed in measuring simple change beween 1992 and 1993 would choose he 1993 longiudinal weigh (he erminal poin weigh). However, he large numbers of posiively weighed reappearers / reconacs would have no daa for If defaul case-wise deleion was permied in he analysis, he weighed esimaes of simple change would very likely be biased. Analyss wih more advanced saisical background would have recognized his problem and possibly underaken heir own adjusmens (propensiy models, E-M ype algorihms) o address he missing daa problem bu i could no be assumed ha rouine users of he PSID public use daa would have access o he advanced saisical raining required o apply 2

3 hese approaches. To ensure ha he public use daa ses would suppor robus inference in boh cross-secional and longiudinal analysis, a rule was inroduced in he 1993 and 1994 weigh developmen ha assigned a zero individual weigh o a sample person who had been a nonresponden in 1989, which is he year of he las weigh adjusmen for panel ariion. The majoriy of sample persons who were assigned a value of zero for heir individual weigh under his rule had no daa for he period 1989 o 1992 hey had been PSID nonrespondens prior o So he decision was made o assign zero individual weighs o hose 1993 and 1994 reappearers/reconacs whose individual weigh was no adjused for ariion and moraliy in 1989 and who, for he mos par, had incomplee daa for he inerval. However, as he sudy coninued ino he 1990s, i became apparen ha as a resul of he 1993 and 1994 rule for handling he reappearers/reconacs, he number of sample persons wih zero-valued individual weighs was becoming increasingly large, and so was he number of families wih zero family weighs. This resuled in subsanial losses of usable cases for PSID analyss ineresed in single-wave cross-secional analyses for 1993 and following waves, or for shor-erm longiudinal analysis involving he pos-1992 waves of daa. To maximize he available case coun for sample persons a each wave, i was decided o revise he longiudinal weighs. Effecively, he new weigh variables conain a posiive weigh for each PSID sample person a each wave ( ) in which hey are associaed wih a responding family. The revised individual weighs make no exclusions of sample persons based on heir hisory of response/nonresponse in he PSID panel. Consequenly, researchers ineresed in rue longiudinal analysis are encouraged o carefully examine he paerns of missing daa across waves of ineres before proceeding wih heir longiudinal analysis. Wih he new, revised longiudinal weighs, he sample size available for weighed analysis has increased; in 2003 he sample of individuals wih posiive weighs has increased by abou 30% and he sample of families has increased by 19%. In addiion, he new weigh assignmen sraegy makes i easy o idenify sample persons wih non-zero daa, all of whom now carry a posiive individual weigh. This documen provides deails on he consrucion of he revised series of longiudinal weighs and is organized as follows. Firs, he PSID sample is described in 3

4 Secion 2. Deails are provided on he PSID sample design, composiion, following rules and reconac effors. Secion 3 provides background on he sample design and following rules wih a focus on he period saring in 1990 when some changes were made o hese rules. Deails on he mehodological approaches in consrucion of he revised Core (Core/Immigran) longiudinal weighs are provided in Secion 4. Secion 5 describes he revised weighs series, , and presens he resuling weighs. Case couns and disribuional saisics for he consruced weighs are presened. Secion 5 also includes a comparison of weighed disribuions of some sample characerisics in he PSID wih hose of he Curren Populaion Survey (CPS). 2. The PSID Sample The PSID s dynamic sample design and following rules are he building blocks for he sraegy used in weigh consrucion, he assignmen of weighs, and he use of weighs in differen ypes of analysis. The following rules are imporan for undersanding how he weighs are consruced, who ges a posiive weigh and who does no, and how weighs should be used in differen ypes of analysis 1. The nex hree subsecions provide a brief overview of he PSID sample design and sample composiion. These secions also describe he PSID sample following rules during he period 1989 hrough The PSID sample design and composiion The PSID sared in 1968 wih 4,802 families. The sample was comprised of wo separae samples: an equal probabiliy naional sample of households seleced from he Survey Research Cener 1960 Naional Sample (SRC) and a subsample of families inerviewed in 1967 by he Bureau of he Census for he Office of Economic Opporuniy (SEO). The SEO sample included poor families wih income levels wice below he 1967 federal povery line. The resuling combined SRC and SEO sample, referred o here as he Core sample, is an unequal selecion probabiliy sample. Compensaory weighs were developed in 1968 o accoun for he differenial sampling raes used o selec he SEO 1 Weighing choice for differen ypes of saisical analyses using PSID daa is also discussed in Heeringa e. al. (2008) 4

5 and SRC componens of he PSID. (A descripion of hese weighs may be found a he PSID web sie (hp://psidonline.isr.umich.edu/daa/weighs/). The iniial PSID sample is no represenaive of individuals who immigraed o he US afer Two independen effors have been made o address his limiaion. Firs, in 1990 he PSID added 2,043 Laino households, represening he hree larges Laino groups in he counry: Mexican-, Puero Rican-, and Cuban-American- 2. Bu while his sample did include some major groups of immigrans, i missed ou on he full range of pos-1968 immigrans, and hose of Asian descen, in paricular. Because of his crucial shorcoming, and a lack of sufficien funding, he Laino sample was dropped afer Today, mos analyss using he panel aspecs of he PSID do no use he daa from he Laino supplemen. The second effor o incorporae pos-1968 immigrans was in survey years 1997 and 1999, when 511 in 1997 and 70 in immigran families were added o he PSID. The sample was obained by screening a represenaive sample o deermine if he family was headed by an individual who was neiher living in he U.S. in 1968 nor a U.S. ciizen or, if born since 1968, was he child of parens who were neiher U.S. ciizens nor living in he U.S. in If he head has a spouse or long-erm cohabier presen in he family, hen ha person mus also have me he crieria for immigran saus. In addiion, he individual or spouse/long-erm cohabier had o have resided in he U.S. since January 1 of wo calendar years prior. By 2005, he number of pos-1968 immigran families had increased o 572 because some family members had spli off ino heir own family unis. A second change ha occurred in 1997 was he reducion of he SEO sample in order o achieve cos savings. While many SEO families were eliminaed, 43%, or 1,714 families, remained in he acive sample. The reducions were achieved by dropping enire family rees, i.e., individuals wih he same 1968 ID. This approach preserved he maximum number of family rees for suppor of inergeneraional sudies. Through naural sample growh generaed by spli-offs since 1997, he SEO sample had grown o include 2,279 families as of For fuller descripion of he Laino sample refer o PSID documenaion for 1990 inerview year (hp://psidonline.isr.umich.edu/daa/documenaion/pdf_doc/psid90w23.pdf). 3 The 70 families were screened in 1997 bu had no been in he U.S. coninually for 2 years. 5

6 As of 2005 here was a oal of 8,041 PSID families. All of hese families are members of he Core or he Immigran samples, labels ha help o disinguish hem from he Laino sample families ha were inerviewed during inerview years. The longiudinal weighs described in his documen perain only o he Core and he Immigran samples and will be referred o as he Core longiudinal weighs for or he Core/Immigran weighs for survey years. 2.2 PSID following sraegies and he sample person concep Throughou his secion and he nex we will describe he PSID following rules and reconac effors, which are summarized in Table 1 for he period 1990 hrough 2005 during which some of he rules were changed. Afer he firs inerview, PSID sample members, including all hose leaving o esablish separae family unis, are racked and followed. The PSID rules for following household members were designed, wih weighs, o mainain a naionally represenaive sample of families a any poin in ime as well as across ime, absen immigraion. As described above, a sample of immigrans arriving in he US afer 1968 was added in 1997/1999. Children born o or adoped by an original sample person are classified as sample members and are eligible for racking as separae family unis when hey se up heir own households 4. These individuals, as well as any oher family uni (FU) members 4 A child who is born o or adoped by a paren who is a sample member becomes a sample person if he child was born afer he iniial inerview for he specific sample. For SRC and Census samples, his means ha he child was born afer he 1968 inerview; for Lainos, afer he 1990 inerview (sample saus for Laino sample cases added in 1992 was based on consideraions of who was living wih he argeed original sample family in 1990); and for Immigrans, afer he 1997 or 1999 inerview. Unlike he Lainos in 1992, sample membership for hose Immigrans who were added in 1999 was based on he 1999 family. In an adopive siuaion, he child mus have no prior blood or marriage kinship ies o he sample paren. For example, a sepchild who is adoped by a sample member does no qualify for sample membership. In oher words, he fac of an adopion by a blood or sep relaionship does no change a child's sample saus, whereas adopion by a nonrelaive does change i. A sample child who is adoped by unrelaed foser parens becomes nonsample; a nonsample child who is adoped by an unrelaed sample member becomes sample. 6

7 who separae from he reinerview family o esablish separae households, are referred o as spli-offs and racked o heir new family unis. This procedure replicaes he populaion s family-building aciviy and produces a dynamic sample of families each year. New PSID families form when children grow up and esablish separae households or when marriage parners go separae ways. Wih a high reinerview rae and a high success rae in adding spli-offs, sample growh occurs over ime in boh he number of family unis and he number of people residing wih a sample member a some ime during he sudy. For undersanding he PSID following sraegies he concep of he sample person is crucial. Through 1993, a sample person was defined as someone who is eiher an original sample individual or an offspring born o or adoped by a sample individual who a he ime was acively paricipaing in he sudy; he child had o appear in he sudy more or less a birh. In 1994 his definiion was expanded o include children born o or adoped by a sample person when he sample person was no paricipaing in he sudy; he child need no have moved ino a responding panel family a birh. The main PSID following rule, called base in Table 1, saes ha a sample person who responded in he previous wave is eligible o be followed. Through 1992, sample members under 18 years of age were never followed in heir own righ if hey lef he family unless: a) hey had se up heir own independen households or b) hey moved o he new home wih an adul sample member. In 1993 PSID relaxed is rules so ha hese younger persons were followed and an inerview wih an adul in he new family group was aemped. As a corollary o his aleraion of a long-esablished radiion, he family composiion rules changed. PSID families had always included a sample member as he Head or Wife/ Wife of he family uni, bu his became impossible in some cases where underage sample members moved wih a nonsample paren. Therefore, boh he Head and he Wife/ Wife may be nonsample persons beginning 1993 in order o coninue o follow he underage sample member. In wo insances he PSID argeed and inerviewed paricular groups of nonsample respondens o suppor specific research areas. Firs, nonsample elderly persons who were 65 or older were followed beween 1990 and Second, he 7

8 nonsample parens of young sample children were followed saring in 1994, bu his pracice was ended for he 2005 and succeeding waves (see Table 1). As a resul of his following of nonsample respondens, during he period some PSID families may no include a sample member. 2.3 The reconac effors Prior o 1990, PSID did no aemp o conac persons who had become nonrespondens in previous waves. Some of hese respondens, however, reappeared as respondens in a curren wave s daa collecion hrough ies o cooperaing families. The annual oals for hese reappearers were relaively small for he period In 1990, he PSID made he firs aemp o locae and inerview prior wave nonrespondens. As par of he supplemenal sudy of elderly, he PSID conaced abou 200 sample and nonsample individuals older han 65 who had been nonresponse since 1985 ( elderly reconac in Table 1). In 1995, as par of anoher supplemenal sudy, PSID aemped o conac nonsample parens of children under 18 who were nonresponse prior o 1995 ( nonsample paren reconac in Table 1). In 1992, 1993 and 1994, he PSID was funded o conduc a major follow-up of sample persons who had been los o nonresponse over he preceding decade ( primary reconac in Table1). During hese years abou 500, 1000, and 2000 prior nonrespondens were reinroduced in he sudy. Among hese reconaced persons he corresponding numbers of sample persons were abou 400, 700 and Saring in 1997, PSID also aemped o conac sample individuals who did no respond in he prior wave, bu responded in he wave before he prior wave. This group of respondens is called esablished reconac (see Table 1). 3. Overview of he Longiudinal Weighs and Sample Receiving Posiive Weighs The Core (Core/Immigran) longiudinal weighs are designed o enable unbiased esimaion of he descripive saisics for he U.S. individuals and families ha were 8

9 eligible for he PSID survey populaion. 5 Since he Laino sample was no included in he projec o reconsruc longiudinal weighs, he Laino sample members carry a zero value for he Core (Core/Immigran) longiudinal weigh. Sample persons Under he revised Core/Immigran longiudinal weigh compuaion algorihm, a non-zero posiive weigh value is assigned o each cooperaing PSID sample person. Each inerviewed family ha includes one or more sample persons receives a posiive, nonzero family weigh. Nonsample persons The PSID is designed o be a longiudinal sudy of individual and families. Each year, individual daa are colleced for nonsample persons who ener a PSID family hrough marriage or residency. Daa for nonsample persons presens a problem for longiudinal analysis since he ime series for hese individuals is lef censored a he dae a which hey enered he PSID family. Furhermore, i is no likely ha his lef censoring is random wih respec o he ypes of variables ha migh be considered in longiudinal analysis. Because of he lef censoring of heir daa series, nonsample persons in PSID families have hisorically been assigned a zero value selecion weigh facor and zero value for he PSID longiudinal weighs. The longiudinal weighs coninue his pracice: all nonsample persons inerviewed in have a zero value on he longiudinal weigh 6. Reappearers and reconac persons PSID assigns he las available posiive weigh, called he reference weigh, o sample persons who appear in he sudy afer being nonresponse in prior waves. A noe is 5 As noed, before he 1997 wave he eligible families excluded hose who immigraed ino he U.S. afer Addiion of he Immigran subsample in 1997 and 1999 allowed he pos-1968 immigran families in he pool of eligible families. 6 Noe ha he Core (Core/Immigran) cross-secional weighs available for survey years provide a posiive weigh for all individuals in he PSID, boh sample and nonsample members (see Heeringa e. al. (2008)) 9

10 warraned wih regard o his rule. Researchers should be aware of a possible bias ha may arise when he number of reappearers/reconac persons is large and heir preceding years of nonresponse happen o include a year in which a nonresponse adjusmen was performed 7. The weighs of heir counerpars, hose who responded coninuously, were adjused for he reappearers' nonresponse in previous waves. Alhough in years prior o 1993 he oal annual number of reappearers was relaively small wih a small associaed risk of bias, a considerable number of sample persons was reinroduced ino he sudy in 1993 and There is also a possibiliy of a bias in assuming ha each sample person assigned a posiive weigh a ime has he requisie daa o conduc a weighed longiudinal analysis for he muli-year inerval (-k,). Depending on he ime inerval of ineres, he reappearers/reconacs may no, in fac, have he required daa for he previous year(s). Researchers who are conducing longiudinal analysis of he PSID daa are encouraged o check how many cases are excluded from he analysis due o nonresponse for an enire wave or have iem missing daa for key variables. 4. Mehodological Approach o he Longiudinal Weigh Consrucion PSID longiudinal weighs are inverse probabiliy weighs. In each year weigh consrucion for he PSID family and individual weighs follows a wo-sep procedure. In he firs sage, individual longiudinal weighs are consruced for all individuals who ever paricipaed in he sudy. In he second sage, he family weigh is calculaed as he average of he individual weighs of all he family members boh sample and nonsample --- paricipaing in he sudy in ha year 8. Since derivaion of family weighs from he individual weighs is sraighforward, we focus on he consrucion approach used for he individual weighs. There are wo seps involved in he approach o he consrucion of he individual weighs. Firs, he sample is divided ino sraa according o a person s saus in wo consecuive waves. 7 Prior o 1993 he nonresponse adjusmens were performed in 1969, 1974,1979,1984, Prior o 1993, a family weigh was calculaed as he average of he head and wife/ wife weighs. The modificaion in family weigh calculaion was a resul of he change in he following rule described in secion 2.2. Saring in 1993following sample children regardless of age creaed a possibiliy of families wih neiher he head or he wife being a sample member. 10

11 Noe ha in he process of weigh consrucion we always consider wo waves, which we will refer o as he prior year and he curren year. In he following discussion, he curren year is also denoed as and he prior year as. In he second sep, each person 0 is given an individual weigh depending on he sraum o which he person belongs. The nex wo subsecions provide deails on hese wo seps. The las subsecion discusses he derivaion of he ariion adjusmen facor used in he weigh consrucion. 4.1 Sep1: The sample division ino sraa Each individual who has ever paricipaed in he sudy is assigned o one of en sraa depending on his/her saus ransiion beween and. These sraa can be generalized ino six main groups: 1) response, hose who responded in he previous and he curren waves; 2) recen exi, hose who lef he sudy beween he previous and he curren wave, 3) pas exi, hose who appeared in he sudy a some poin in ime bu lef i before he previous wave; 4) recen enry, hose who firs enered he sudy a he ime of he curren wave; 5) reenry/re-conac, hose who paricipaed in he sudy a some poin in ime, were nonresponse in he previous wave and volunarily re-enered he sudy or responded o re-conac during he curren wave; 6) fuure enry, hose who have no ye appeared in he sudy as of he ime of he curren wave bu will ener i in a laer wave. Each group consiss of one sraum, wih he excepion of wo: he recen enry and recen exi. Recen enry and recen exi groups are each comprised of muliple sraa. Table 2 repors numbers of persons in each sraum for seleced pairs of he curren and prior years. Recen enry Currenly, a person has one of four main enry roues ino he sudy. Firs is a child who mees he qualificaions above and is born ino a responding sample family. This group also includes very young adopees who are placed wih he adopive parens quie soon afer birh ( Sample born in in Table 2). Second is a child who oherwise mees he ess above bu is no born ino a responding sample family. Such a child may be born o or adoped by a sample person who has lef he panel while ha sample person is nonresponse. Also included here are older children who are adoped ino responding family unis. Before 1994, children who 0 11

12 had moved ino a PSID family more han a year/wave afer hey were born bu had a leas one sample paren were no considered sample individuals and herefore were no given posiive weighs. In 1994, he definiion of a sample member was changed o include such movers-in, and, henceforh, hese individuals received a posiive weigh ( Sample mover in in Table 2). The hird way one can ener he panel is by marriage or hrough cohabiaion wih a sample person. Such an individual is a nonsample member and receives a zero weigh ( Nonsample in Table 2). Finally, one can become a panel sample member by being par of a responding family uni in he wave in which a specific sample is iniiaed, e.g., he SRO or Census samples in 1968 or he samples of Immigrans in 1997 and Naurally, we have one addiional wis o his rule: he appearers. An appearer is a sample member who, hrough an error in he iniial family lising, is subsequenly discovered o have been presen in a family uni since he incepion of he sample. This siuaion arises very infrequenly and usually happens wihin a wave or wo of he original inerview ( Sample new / Sample appear in Table 2). Recen exi Recen exi is anoher complex group consising of wo subsraa. Exi from he panel occurs because of moraliy and nonresponse. The nonresponse group includes cases where a family or a sample person refuses o paricipae or canno be locaed or conaced. 4.2 Sep2: Assignmen crieria for he individual weigh Nex in he developmen of he individual weigh is assignmen and compuaion of weighs. The individual weigh assignmen occurs in wo phases. Firs, weighs are assigned o individuals in all sraa wih he excepion of he recen enry group. Then weighs are assigned o hose who enered he panel for he firs ime based on he individual weighs of he oher family members. 12

13 The weigh assignmen follows he same rule for individuals in he same sraa. Individuals in groups ha are nonresponse in he curren-wave daa, for reasons including pas exi, fuure enry, and recen exi, ge assigned a zero weigh. The reenry/reconac group, i.e. hose who were nonresponse in he previous wave, are given a weigh equal o heir las available non-zero weigh, i.e., he reference weigh. The weigh assignmen rule for hose in he recen enry group varies by sraum. A new nonsample individual is given an individual weigh equal o 0. Born in and mover in sample individual weighs are equal o an average of head and wife/ wife individual weighs. The new sample individuals in he las sraum, new sample individuals/reappearers, receive a weigh equal o he inverse of selecion probabiliy. If he case is a reappearer, hen he weigh is he average of individual weighs among he sample members of he family. Two approaches are generally used in PSID o consruc individual weighs for he response group. In boh cases he curren-wave weighs are based on he prior period s individual weighs. The difference is ha in one case he adjusmen is made o accoun for ariion and moraliy beween he waves, while in he oher insance, no such adjusmen is made. We refer o he weighs obained wih he former approach as he adjused weighs and o he weighs obained wih he laer approach as he carry-over weighs. In he carry-over weighs he individual weigh in he curren wave is aken o be he same as he weigh in he previous wave. For adjused weighs, he individual weigh is a produc of he previous wave weigh and he ariion adjusmen facor. The deails on he derivaion of he facor are given in he nex subsecion. Table 3 summarizes he weigh assignmen rules for adjused weigh and carryover weighs. 4.3 Ariion adjusmen facor This subsecion provides heoreical jusificaion for he way he ariion adjusmen is made. I also describes he approach used o calculae he ariion adjusmen parameer in he PSID. The discussion in his subsecion considers only hose who were respondens in he prior period and in he curren period are eiher in he response group or in he recen exi group. 13

14 The main sources of ariion among he respondens who paricipaed in he sudy in previous years include: nonresponse of living panel members; loss o follow-up where he deah of he sample person is unknown; and known deahs o panel members. The able below shows he paern of vial saus among hose who responded a condiional on he inerview oucome a. The vial saus is denoed by A, and inerview saus is denoed by S. Noe ha when he inerview saus is response, S = 1, or he inerview saus is known dead, S = 2, hen he vial saus is known. However, when he saus is nonresponse, S = 1, we have no informaion wheher he person is living or dead. Vial saus Inerview oucome A = 0 (dead) A = 1(alive) S = 1(response) 0 X S = 2 (known dead) X 0 S = 3 (nonresponse: refusal or los o follow up) X ( exac number is no known) X ( exac number is no known) To undersand our adjusmens, i is useful o noe ha he probabiliy of he inersecion of S and A can be decomposed ino a produc of wo oher probabiliies as follows: Pr( S, A ) = Pr( A ) * Pr( S A ) When he purpose of he weigh is o represen he populaion, he condiional probabiliy, Pr( S A ), should be he basis of he weigh, no Pr( S, A ). Only hose surviving o are sill in he populaion a ha ime, and we wan o know jus how many people each surviving person who responds represens in he populaion a ime. Pr( S A ) ells us wha he probabiliy of an individual responding in was, given ha person was indeed among hose who survived unil. Thus, his is he probabiliy ha we wan o incorporae ino our weigh adjusmen. The reciprocal of he condiional 14

15 1 [ = probabiliy, Pr( S 1 A = 1) ] nonresponse and moraliy., is he facor we use o adjus he weigh for differenial Noing ha he probabiliy of response, Pr( S = 1), is he same as probabiliy of response and survival, Pr( S 1, A = 1), we ge = Pr( S = 1 A = 1) = Pr( S = 1, A Pr( A = 1) = 1) = Pr( S Pr( A = 1) = 1) Thus, condiional on being alive, he probabiliy of responding is a raio of he probabiliy of response, Pr( S = 1), and he probabiliy of being alive, Pr( A = 1). The probabiliy of being alive can be rewrien as: Pr( A Pr( S = 1) = Pr( A 3 j= 1 = 1) + Pr( A = 1 S = 1 S = j) Pr( S = 3) Pr( S = 3) = j) = The second line follows because Pr( A 1 S = 2) = 0 and Pr( A 1 S = 1) = 1. = = Denoe Pr( S = j) as q j, hen he expression for he condiional probabiliy becomes Pr( S q 1 = 1 A = 1) = (1) q1 + Pr( A = 1 S = 3) q3 q j, where j {1,2,3}, can be esimaed direcly from he daa. However, he condiional probabiliy of being alive, Pr( A 1 S = 3), is no possible o esimae from he daa, = and so one needs o have addiional informaion or o make an assumpion. Prior o 1993 in he weigh consrucion process, he numeraor and denominaor of he raio (1) were esimaed separaely. The numeraor was esimaed from he daa using he weighing cell approach. The denominaor was obained wih he use of he naional esimaes of moraliy raes. This approach was based on he assumpion ha moraliy raes in he sample are he same as he moraliy raes in he populaion. The 15

16 naional esimaes of moraliy raes given in Vial Saisics, U.S. Census Bureau, were used o consruc age-gender-race-specific probabiliies of survival, which served as esimaes of Pr( A = 1). From 1993 forward he condiional probabiliy (1) was esimaed simulaneously wih he use of a saisical modeling approach. In his approach we assumed a value for Pr( A 1 S = 3) = from he [0,1] inerval. In paricular we assumed ha he condiional probabiliy is 1, which would mean ha all nonrespondens are living. While his is a srong assumpion, i appears o be a reasonable approximaion in he PSID case. The same assumpion is made in he analysis of ariion in Healh and Reiremen Sudy (HRS) by Kapeyn, Michaud, Smih, van Soes (2006). The mulinomial logisic model (Maddala, 1983) was used o esimae probabiliies of hree saes ( j = 1,2,3). The probabiliy of being in sae j by q j household i ha responded in he previous wave is given by P( S i, exp( β j ' xi ) 0 = j xi ) =, (2) 0 3 exp( β ' x ) j= 1 k i 0 where x i0 is a vecor of observaions on a se of characerisics a he previous wave and β j is a vecor of coefficiens. Idenificaion requires ha some consrain be imposed on he β vecors. We employ he following consrain: β = 0 (3) 1 The model is esimaed on he subse comprised of he response and he recen exi groups, i.e., hose for whom daa were colleced in he previous wave. 4.4 Scaling The revised PSID family and individuals weighs are scaled o arbirary oal couns ha were esablished when he iniial weighs were creaed for he 1968 Wave I probabiliy sample. Wih he obvious excepion of weighed esimaion of populaion oals, saisics esimaed from he PSID daa should be invarian o any linear scaling (muliplicaion or division by a consan) of he family or individual weighs. Analyss 16

17 may wish o rescale he weigh values o sui heir individual preference for requiremens of heir seleced sofware sysems or programs. One common procedure is o simply rescale he weighs o he appropriae U.S. Census populaion couns/esimaes or Curren Populaion Survey (CPS) esimaes of he size of he arge populaion in he year of ineres: W pop ipop, i n where : i pop ipop, = W N i= 1 W i W = he revised PSID weigh value for uni i (family, individual); N W = he U.S. Census or CPS value for he arge populaion oal; = he rescaled PSID "populaion weigh", n i= 1 W = N i, pop pop. A second procedure commonly seen in public use daa ses is o normalize he weighs or rescale he weighs so ha hey sum o he nominal sample size for he se of observaions included in he analysis: W i, norm i n where : i i, norm = W n i= 1 W i W = he revised PSID weigh value for uni i (family, individual); n = he coun of PSID sample families or persons included in he analysis; W = he rescaled PSID "normalized weigh", W = n. n i= 1 i, norm In pas decades, he pracice of normalizing he weighs was ofen a necessiy since saisical sofware sysems employed he case weighs as frequency couns of 17

18 observaions (e.g., a weigh of 100 was reaed as 100 duplicae cases) resuling in biased esimaes of variances, covariances and pseudo likelihood funcions ha are required in he compuaion of sandard errors and inferenial saisics for simple saisics such as means or more complex saisics such as mulivariae regression coefficiens. In oday s saisical sofware sysems, i should no be necessary for researchers o normalize weigh values prior o conducing analysis; however, a few of he older programs such as SAS Proc Logisic sill require he user o specify an opion o normalize he weighs prior o analysis. Analyss are encouraged o review he documenaion for heir chosen sofware sysem o deermine how weighs are applied in he programs ha hey will use for analysis of PSID daa. 5 The Core (Core/ Immigran) Longiudinal Weighs, 1993 hrough Descripion The specific mehods used in he consrucion of he Core (Core/Immigran) longiudinal 1993 hrough 2005 weighs in each year are summarized in Table 4. The 1993 longiudinal weighs are ariion-adjused weighs consruced o accoun for losses beween 1989 and Table 5 repors he resul of he mulinomial logisic regression. The weighs in he following hree years, 1994, 1995 and 1996, are carry-over weighs. As described above, 1997 is marked by he reducion of a porion of he SEO sample and by he addiion he Immigran sample. To accoun for he parial reducion of he Core sample, a weighing cell process was used. All PSID Core individuals were assigned o one of he 24 cells based on age (age<=25, 25<age<=40, 40<age<=60, age>60), gender (male, female) and race of head (whie, black, oher). For each cell, he weighs of sample individuals who responded in 1997 were increased o compensae for loss of individuals who responded in 1996 bu did no respond in The 1997 PSID Immigran Supplemen sample families were iniially seleced wih equal probabiliy. During he field period, sample replicaes of area segmens wih higher expeced prevalence of immigran households were oversampled o increase he efficiency of he household screening. Each of he inerviewed families in he 1997 Immigran Supplemen was assigned an iniial base weigh value ha refleced he probabiliy of selecion and screening for he area segmen in which hey resided. 18

19 To combine he weighs from he Core and he Immigran samples, he Immigran sample weighs were scaled so ha he proporion of he Immigran sample in he combined sample is 7%, which is an esimae of he proporion of he households ha had immigraed o he Unied Saes by 1997, since Similar o 1997, he 1999 weighs are consruced separaely for he Core and he Immigran samples and hen combined using he 93:7 raio. The Core sample weighs are carry-over weighs. In 2001 he Immigran and Core samples are reaed he same way, wih weighs for boh being carried over from he previous wave. The 2003 weighs are ariion-adjused weighs. They accoun for he ariion beween 1999 and 2003 among 1999 sudy paricipans from he Core and he Immigran samples. Table 6 repors he resul of he mulinomial logisic regression. Finally, he 2005 weighs are consruced by using he carryover approach summarized in Table 3. The resuling longiudinal weighs are sored in he PSID daa archive under names provided in Table Esimaes For each PSID wave from 1989 hrough 2005, Tables 7 and 8 repor he oal number of cases where he revised longiudinal weighs are posiive, zero, or missing for individuals and families, respecively. Table 7 also provides informaion on he oal number of individuals in he sudy and he number of sample and nonsample persons. Table 8 shows he oal number of families in he sudy each year, and how many families have no sample person. Informaion is given separaely for he Core/Immigran sample and he Laino sample. Table 7 shows ha, saring in 1993, all sample persons from he Core/Immigran sample are assigned a posiive individual longiudinal weigh and nonsample persons are assigned a zero weigh. Members of he Laino sample families are also assigned a zero individual longiudinal weigh. Table 8 shows ha he Core/Immigran longiudinal family weigh can be zero in only wo insances: when he family belongs o he Laino sample or when he 9 Based on daa from he 1997 CPS, an esimaed 7.5 percen of U.S. households have immigraed o he Unied Saes afer

20 family has no sample person associaed wih i. (Recall from he discussion above ha prior o 2005 he following rules were such ha some families could conain no sample members.) In all oher cases he family weigh is a posiive number. 10 Tables 9 and 10 repor summary saisics for he longiudinal individual and family weighs, respecively. The mos imporan paern is he increase in he mean and variance in 1997 resuling from he eliminaion of some of he SEO sample and addiion of he immigran sample. Tables 11 hrough 15 compare disribuions of seleced characerisics, including age, gender, race, and family income in he PSID daa obained wih and wihou he longiudinal weighs o hose in he Curren Populaion Survey (CPS) beween survey years 1990 and These ables are useful for examining hree feaures of he PSID daa: consisency of unweighed and weighed esimaes across years, effec of he longiudinal weighs on he disribuions of he characerisics, and, finally, he closeness of he PSID esimaes wih hose obained wih he CPS daa 11. The ables show ha consisency across years of weighed disribuions is comparable o he consisency of unweighed disribuions. An excepion is for race and income beween 1996 and 1997; he changes in he sample (i.e., eliminaion of par of he SEO sample and addiion of he immigran sample) led o a one-ime change beween 1996 and 1997 in he unweighed racial and income disribuions. Comparison of he unweighed and weighed PSID disribuions wih he CPS disribuions reveals ha weighed esimaes in a majoriy of cases are closer o CPS esimaes han are he esimaes obained wihou weighs. In addiion, he PSID and CPS align fairly closely in mos cases. An excepion is for he racial disribuion, and his arises for a leas wo reasons. Prior o 1997 he PSID sample did no include pos-1968 immigrans, he 10 Noe ha for a handful of cases families have no sample members bu hey have posiive weighs. This mos likely arose because here were individuals in hese families who a he ime of inerview were believed o be sample members, bu a some laer wave were redefined as nonsample based on addiional informaion. 11 Noe, ha some characerisics are no sricly comparable beween he wo surveys. For example, in he PSID race is no asked for everybody while in he CPS i is. To calculae proporions of black and nonblack individuals in he PSID daa, individual race was approximaed wih he race of he family head. Second, measures of educaional aainmen differ beween he surveys because of how hese quesions are formulaed and because of changes in he quesion sequences ha occurred over he years. Finally, he family income measure in he PSID is no direcly comparable o he CPS household income measure due o he difference in definiion of family uni in PSID and household uni in CPS. 20

21 majoriy of whom would be classified as whie. In addiion, since PSID weighs were never benchmarked o he CPS or anoher federal source such as a pos-1968 Census, we believe ha he original 1968 compuaions for he SEO/SRC join probabiliies and subsequen ariion adjusmens in 1969, 1974, 1979, 1984 and 1989 may have led o a small posiive bias in he weighed represenaion for black families and individuals. 21

22 References Heeringa S., E. Gouskova and K. McGonagle, Cross-secional Analysis of PSID daa and Cross-secional weighs , echnical repor, Survey Research Cener, Insiue for Social Research, Universiy of Michigan. Kapeyn A., P. Michaud,J. Smih and A. van Soes, 2006."Effecs of Ariion and Non- Response in he Healh and Reiremen Sudy," IZA Discussion Papers 2246, Insiue for he Sudy of Labor (IZA). Maddala, G.S Limied Dependen and Qualiaive Variables Economerics. Cambridge: Cambridge Universiy Press 22

23 Table 1: Following Sraegies Who is followed base non-sample paren S, R in S, R in 1990, S, R in 1989, or 1991, 18 S, R in S, R in S, R in S, R in S, R in S, R in S, R in S, R in S, R in or older older or older NS paren, R in 1993, has a S child who is 18 or younger NS paren, R in 1994, has a S child who is 18 or younger NS paren, R in 1995, has a S child who is 18 or younger NS paren, R in 1996, has a S child who is 18 or younger NS paren, R in 1997, has a S child who is 18 or younger NS paren, R in 1999, has a S child who is 25 or younger NS paren, R in 2001, has a S child who is 25 or younger non-sample elderly Who is excluded from being followed New sample added Reconac esablished reconac primary reconac non-sample paren reconac NS, R in 1989, 65 or older Laino sample (2,043 families) NS, R in 1990, 65 or older NS, R in 1991, 65 or older Laino sample (265 families) S, NR by 1990 NS, R in 1992, 65 or older S, NR by 1992 NS, R in 1993, 65 or older S, NR by 1992 NS, paren, has a S child who is 18 or younger NS, R in 1994, 65 or older Laino sample is dropped A par of SEO is dropped Immigrans sample (441 families) S,NR in 1996, R in 1995 Immigrans sample (70 families) S, NR in 1997, R in 1996 S, NR in 1999, R in 1997 S, NR in 2001, R in 1999 S, NR in 2003, R in 2001 elderly reconac S and NS, NR in ,65 or older Noes: 1) S=sample, 2) NS=nonsample, 3) R=response, 4) NR=nonresponse 23

24 Table 2: Number of Individuals in Each Group/Sraa 0=1989 0=1993 0=1994 0=1995 0=1996 0=1999 0=1968 Group Sraum =1993 =1994 =1995 =1996 =1997 =2003 =2003 Pas Exi Fuure Enry Sample born in Recen Enry Sample mover in Nonsample Sample new/ Sample appear Reenry/reconac Recen Exi Response Died beween he prior and he curren wave Responded in he prior wave and nonresponse in he curren wave Responded in he prior and he curren wave Toal Laino sample is excluded from he analysis repored in his able. 24

25 Table3: Adjused and Carry Over Weigh Assignmen Rules Adjused weighs Carry over weighs Group Sraum Daa colleced a 0? Daa colleced a? Sep 1 Sep 2 Sep 1 Sep 2 Pas Exi No No Zero Zero Fuure Enry No No Zero Zero Sample born in No Yes Average of head's and wife's weighs if here are head and wife in he family and 1/2 of head's weigh if here is no wife in he family. Average of head's and wife's weighs if here are head and wife in he family and 1/2 of head's weigh if here is no wife in he family. Recen Enry Sample mover in No Yes Average of head's and wife's weighs if here are head and wife in he family and 1/2 of head's weigh if here is no wife in he family. Nonsample No Yes Zero Zero Average of head's and wife's weighs if here are head and wife in he family and 1/2 of head's weigh if here is no wife in he family. Reenry/reconac Recen Exi Response Sample new/ Sample appearer No Yes No Yes Reference weigh a) If a member of a newly added sample hen he weigh is inverse probabiliy of selecion; b) If a sample appear hen he weigh is equal o an average of sample family members individual weighs Reference weigh Died beween he prior and he curren wave Yes No Zero Zero Responded in he prior wave and nonresponse in he curren wave Yes No Zero Zero Responded in he prior and he curren wave Yes Yes weigh a 0 *ariion adjusmen weigh a 0 a) If a member of a newly added sample hen he weigh is inverse probabiliy of selecion; b) If a sample appear hen he weigh is equal o an average of sample family members individual weighs 25

26 Table 4: Core (Core/Immigran) Longiudinal Weigh Consrucion Approach 1993: 1994: 1995: 1996: 1997: 1999: 2001: 2003: 2005: 0=1989 0=1993 0=1994 0=1995 0=1996 0=1997 0=1999 0=1999 0=2003 Sample =1993 =1994 =1995 =1996 =1997 =1999 =2001 =2003 =2005 Core Adjused Carry over Carry over Carry over Immigran Core/Immigran Adjused wih he weighing cell process Carry over Weighs are inverse prob. of selecion Core and Immigran weighs are combined wih he 93:7 raio Carry over and inverse prob. of selecion Core and Immigran weighs are combined wih he 93:7 raio Carry over Adjused Carry over 26

27 Table 5: Mulinomial Logisic Regression, = , = (Omied Caegory is Response. ) Dead Nonresponse Variable Coefficien SE Coefficien SE Inercep *** *** s income percenile *** Log of income *** *** h income percenile Age * Age squared ** Norh Cenral Souh Wes * Male *** SEO sample ** SEO sample*1 s income percenile * SEO sample*log income *** SEO*Age SEO*Age squared * SEO*Norh Cenral *** SEO*Souh *** SEO*Wes *** SEO*Male Summary saisics: Number of observaions Response profile: Dead 359 Nonresponse 1437 Response Likelihood Raio: Chi-squared DF 36 27

28 Table 6: Mulinomial Logisic Regression, = 1999, = 2003 (Omied Caegory is Response. ) 0 Dead Nonresponse Variable Coefficien SE Coefficien SE Inercep ** *** s income percenile *** log of income *** h income percenile Age *** Age squared ** Norh Cenral Souh Wes Male *** * SEO sample * SEO sample*1 s income percenile SEO sample*log income *** ** SEO*Age * SEO*Age squared * ** SEO*Norh Cenral SEO*Souh SEO*Wes SEO*Male * Immigran sample *** *** Summary saisics Number of observaions Response profile: Dead 366 Nonresponse 842 Response Likelihood Raio: Chi-squared DF 38 28

29 Table 7: he Core (Core/Immigran) Longiudinal Individual Weighs coun Core sample (SRC, SEO) and Immigran sample Laino sample Year Toal number of individuals in he sudy Toal number of individuals Toal number of sample individuals Toal number of nonsample individuals Number of cases wih posiive individual weigh Number of Number of cases wih cases wih zero missing individual individual weigh weigh Toal number of individuals Toal number of sample individuals Toal number of non-sample individuals Number of cases wih posiive individual weigh Number of cases wih zero individual weigh Number of cases wih missing individual weigh

30 Table 8: he Core (Core/Immigran) Longiudinal Family Weighs coun Core sample (SRC, SEO) and Immigran sample Laino sample YEAR Toal number of families Number of Number of Number of Number of families wih Toal number of families wih no families wih families wih missing families sample person posiive weigh zero weigh weigh Toal number of families Number of families wih no sample person Number of families wih posiive weigh Number of families wih zero weigh Number of families wih missing weigh 30