Healthy, wealthy, and wise? Tests for direct causal paths...

Journal of Econometrics 112 (2003) 3ndash56wwwelseviercomlocateeconbase

Healthy wealthy and wise Tests fordirect causal paths between health and

socioeconomic statusPeter Adamsa Michael D Hurdb Daniel McFaddena lowast

Angela Merrillc Tiago Ribeiroa

aDepartment of Economics University of California Berkeley CA 94720-3880 USAbRAND Corporation USA

cMathematica USA

Abstract

This paper provides statistical methods that permit the association of socioeconomic statusand health to be partially unraveled in panel data by excluding some postulated causal paths ordelimiting their range of action These methods are applied to the Asset and Health Dynamicsof the Oldest Old (AHEAD) Panel to test for the absence of causal links from socioeconomicstatus (SES) to health innovations and mortality and from health conditions to innovations inwealth We conclude that in this elderly American population where Medicare covers mostacute care and pension income is not a2ected by ability to work the evidence supports thehypothesis of no direct causal link from SES to mortality and to incidence of most sudden onsethealth conditions (accidents and some acute conditions) once initial health conditions are con-trolled but there is some association of SES with incidence of gradual onset health conditions(mental conditions and some degenerative and chronic conditions) due either to causal linksor to persistent unobserved behavioral or genetic factors that have a common in4uence on bothSES and innovations in health There is mixed evidence for an association of health conditionsand innovations in wealth The death of a spouse appears to have a negative e2ect on the wealthof the survivor this is plausibly a direct causal e2ect There is evidence for some associationof health conditions with increased dissaving from liquid wealth for intact couples and singlesFrom these 7ndings we conclude that there is no evidence that SES-linked therapies for acutediseases induce mortality di2erentials The question of whether SES-linked preventative care in-4uences onset of chronic and mental diseases remains open The appendix to this paper containing

lowastCorresponding authorE-mail address mcfaddeneconberkeleyedu (D McFadden)URL httpelsaberkeleyedusimmcfadden

0304-407602$ - see front matter ccopy 2002 Elsevier Science BV All rights reservedPII S0304 -4076(02)00145 -8

4 P Adams et al Journal of Econometrics 112 (2003) 3ndash56

JEL classi4cation C3 C9 I0 I12 C33 C35

Keywords Health Wealth Causality Markov

1 Introduction

11 The issue

The links between health wealth and education have been studied in a number ofpopulations with the general 7nding that higher socioeconomic status (SES) is as-sociated with better health and longer life 1 In a survey of this literature Goldman(2001) notes that this association has been found in di2erent eras places genders andages and occurs over the whole range of SES levels so that it is not linked solely topoverty The association holds for a variety of health variables (most illnesses mortal-ity self-rated health status psychological well-being and biomarkers such as allostaticload) and alternative measures of SES (wealth education occupation income level ofsocial integration) 2 There has been considerable discussion of the causal mechanismsbehind this association but there have been relatively few natural experiments thatpermit causal paths to be de7nitively identi7ed 3 In this paper we test for the absenceof direct causal links in an elderly population by examining whether innovations inhealth and wealth in a panel are in4uenced by features of the historical stateFig 1 depicts possible causal paths for the health and SES innovations that occur

over a short period An individualrsquos life history is built from these period-by-period

1 Backlund et al (1999) Barsky et al (1997) Bosma et al (1997) Chandola (1998 2000) Davey-Smithet al (1994) Drever and Whitehead (1997) Ecob and Smith (1999) Elo and Preston (1996) Ettner (1996)Feinstein (1992) Fitzpatrick et al (1997) Fitzpatrick and Dollamore (1999) Fox et al (1985) Goldblatt(1990) Haynes (1991) Hertzman (1999) Humphries and van Doorslaer (2000) Hurd (1987) Hurd andWise (1989) Kaplan and Manuck (1999) Karasek et al (1988) Kitagawa and Hauser (1973) Lewis et al(1998) Leigh and Dhir (1997) Luft (1978) Marmot et al (1991 1995 1997) Martin and Preston (1994)Martin and Soldo (1997) McDonough et al (1997) Murray et al (1992) Power et al (1996) Power andMatthews (1998) Rodgers (1991) Ross and Mirowsky (2000) Schnall et al (1994) Seeman et al (2002)Shorrocks (1975) Stern (1983) Wadsworth (1991) Whitehead (1988) Wilkinson (1998) and Woodwardet al (1992)

2 The associations can become more complex when multiple health conditions and multiple SES measuresare studied Competing risks may mask the hazard for late-onset diseases eg elevated mortality risk fromcardiovascular diseases in low SES groups may induce an apparent reverse relationship between SES andlater-onset cancer in the surviving population (Adler and Ostrove 1999) Longer-run measures of SES suchas education occupation and wealth appear to have a stronger association with health status than currentincome (Fuchs 1993) Using carefully measured wealth we 7nd that it explains most of the associationwith health and education conditioned on wealth is not systematically correlated with health

3 Papers examining explicit causal mechanisms include Chapman and Hariharran (1994) Dohrenwend etal (1992) Evans (1978) Felitti et al (1998) Fox et al (1985) Goldman (1994) Kelley et al (1997) andMcEwen and Stellar (1993)

P Adams et al Journal of Econometrics 112 (2003) 3ndash56 5

Fig 1 Possible causal paths for SES and health

transitions First low SES may lead to failures to seek medical care and delay indetection of conditions reduced access to medical services or less e2ective treat-ment 4 Also increased risk of health problems may result from increased stress orfrustration or increased exposure to environmental hazards that are associated withlow SES 5 These factors could provide direct causal links from SES history to healthevents Second poor health may reduce the ability to work or look after oneself andincrease medical care expenditures leading to reduced income and less opportunity toaccumulate assets This could provide a direct causal link from health to changes inSESThere may also be hidden common factors that lead to ecological association of

health and SES For example unobserved genetic heterogeneity may in4uence both re-sistance to disease and ability to work Causal links may be reinforced or confoundedby behavioral response Behavioral factors such as childhood nutrition and stress exer-cise and smoking may in4uence both health and economic activity level For exampletastes for work and for ldquoclean livingrdquo whether genetic or learned may in4uence bothhealth and earnings Finally rational economic decision-making may induce robust con-sumers to accumulate in order to 7nance consumption over a long expected retirementor unhealthy individuals to spend down assets

4 There may be an important distinction between direct causal mechanisms in4uencing mortality condi-tioned on health status and direct causal mechanisms in4uencing onset of health conditions For mortalityan SES gradient could be due to di2erentially e2ective treatment of acute health conditions For morbidityan SES gradient could re4ect di2erentials in prevention and detection of health conditions These involvedi2erent parts of the health care delivery system and di2er substantially in the importance of individualawareness and discretion and allocation of costs between Medicare and the individual

5 For example industrial and traKc pollution and poor dwelling ventilation are risk factors for lungdisease and housing prices and household income are negatively correlated with air pollution levels incensus data (Chay and Greenstone 2000)

Preston and Taubman (1994) Smith and Kington (1997a b) and Smith (1998 1999)give detailed discussions of the various causal mechanisms that may be at work and therole of behavioral response from economic consumers The epidemiological literature(Goldman 2001) uses a di2erent terminology for the causal paths links from SES tohealth innovations are termed causal mechanisms while links from health to SES aretermed selection or reverse causation mechanisms Apparent association due to mea-surement errors such as overstatement of the SES of the healthy or under-detection ofillnesses among the poor are called artifactual mechanisms 6 This literature classi7esall common factors in terms of their implicit initial action as either causal or selectionmechanisms 7

12 This study

We study the population of elderly Americans aged 70 and older and in this pop-ulation test for the absence of direct causal paths from SES to innovations in healthand from health status to innovations in SES These hypotheses will in general beaccepted only if no causal link is present and there are no persistent hidden factorsthat in4uence both initial state and innovations Rejection of one of these hypothesesdoes not demonstrate a direct causal link since this may be the result of common hid-den factors However in an elderly population persistent hidden factors will often bemanifest in observed covariates so that once these covariates are controlled the resid-ual impact of the hidden factors on innovations will be small For example geneticfrailty that is causal to both health problems and low wages leading to low wealthmay be expressed through a health condition such as diabetes Then onset of newhealth conditions that are also linked to genetic frailty may be only weakly associatedwith low wealth once diabetic condition has been entered as a covariate Thus in thispopulation rejection of the hypotheses may provide useful diagnostics for likely causalpathsThe objectives and conclusions of this paper are limited We study only elderly

Americans for whom Medicare provides relatively homogeneous and comprehensivehealth care at limited out-of-pocket cost to the individual This population is retiredso that new health problems do not impact earnings Statements about the presence orabsence of direct causal mechanisms in this population given previous health and SESstatus say nothing about the structure of these mechanisms in a younger population

6 Consider phenomena such as under-estimation of the hazard of a disease due to competing risks fromother illnesses or death In an unfortunate discrepancy in terminology economists would call this a selectione2ect while epidemiologists would classify it as an artifactual mechanism rather than a selection mechanism

7 Usually one can argue that observed association must originate from some initial causal action so thatcommon factors originate from some initial direction of causation However there is no apparent initial causalaction for genetically linked conditions such as Downs syndrome which increase mortality risk and precludework Further as a practical matter it is often impossible to make observations at the high frequencies thatwould be required to identify causal chains when feedbacks are nearly instantaneous Then common factorswill appear at feasible levels of detection to operate simultaneously and their true causal structure will notbe identi7ed For these reasons there would be considerable merit in adding common mechanisms to theepidemiologistrsquos classi7cations

where associations of health and SES emerge as a result of some pattern of causationand operation of common factorsOur tests for the absence of causality do not address the question of how to identify

invariant models and causal links when these tests fail If a test for the absence of adirect causal path is rejected it may be possible through natural or designed exper-iments to separate causal and ecological e2ects see Angrist et al (1996) Heckman(2000 2001) Suppose a strictly exogenous variable is causal to SES and clearly notitself directly causal to health or causal to common factors Then an association ofthis variable with innovations in health conditions can only be through a direct causallink from SES to health A variable with these properties is termed an proper instru-ment or control variable for SES Proper instruments are hard to 7nd They can beobtained through designed experiments where random treatment assignment precludesthe possibility of confounding by common factors provided recruitment and retention ofexperimental subjects does not re-introduce confounding For example an experimentthat randomly assigned co-payment rates and coverage within Medicare for prescrip-tion drugs or assisted living could provide evidence on direct causal links from SESto health conditions provided attrition and compliance are not problems Occasionallynatural experiments may provide random treatment assignment Economic events thatimpact individuals di2erently and that are not related to their prior SES or health arepotentially proper instruments For example a tax change that a2ects wealth di2erentlyin di2erent States is arguably a proper instrument as is a change in mandated Medicaidcoverage that has a di2erential impact across States Individual events such as receiptof inheritances may be proper instruments although they would be confounded if theyare anticipated or if the probability of their occurrence is linked to health status seeMeer et al (2001) Weak association between SES and a proper instrument for itmakes it diKcult to obtain precise estimates of direct causal e2ects see Staiger andStock (1997)Section 2 of this paper discusses the foundation for econometric causality tests and

sets out the models for the dynamics of health and SES that will be used for ouranalysis Section 3 describes the panel study and data that we use Section 4 de-scribes the association of SES and prevalence of health conditions in the initial waveof the panel Section 5 analyzes incidence of new health conditions and presentstests for non-causality of SES for the incidence of health innovations Section 6tests for the absence of a causal link from health conditions to wealth accumula-tion and other SES indicators Section 7 uses our estimated models for prevalenceand incidence to simulate life histories for a current population aged 70 undercounterfactual (and unrealistically simplistic) interventions that assume a major healthhazard can be removed or SES shifted for the entire population This simulation ac-counts consistently for co-morbidities and competing hazards over the life course Thepurpose of this exercise is to demonstrate the feasibility of using our modeling ap-proach for policy applications when the models pass the causality tests described innext section Finally Section 8 gives conclusions and outlines topics for future re-search The appendix to this paper containing Tables A1ndashA8 with detailed estimationresults and the data and computer routines we use are posted on the internet athttpelsaberkeleyeduwphwwhww202html

2 Association and causality in panel data

21 Testing causality

The primary purpose of this study is to test for direct causal links between SES andhealth There is a large literature on the nature of causality and the interpretation ofldquocausality testsrdquo 8 Our analysis 7ts generally within the approach of Granger (1969)Sims (1972) and Hoover (2001) but our panel data structure permits some re7nementsthat are not available in a pure time series settingLet Yt denote a K-vector of demographic health and socioeconomic random vari-

ables for a household at date t and interpret a realization of these variables as anobservation in one wave of a panel survey Let Yt be the information set containingthe history of this vector through date t Let

f(Yt |Ytminus1)

equiv f1(Y1t |Ytminus1) middot f2(Y2t |Y1t Ytminus1) middot middot fK (YKt |Y1t YKminus1 t Ytminus1) (1)

denote a model of the conditional distribution of Yt given Ytminus1 Without loss of gen-erality we have written this model as a product of one-dimensional conditional distri-butions given history and given components of Yt determined previously Writing themodel in this way does not imply that the components of Yt form a causal chain asthey may be simultaneously determined or determined in some causal sequence otherthan the speci7ed sequence However the model structure simpli7es if the currentcomponents of Yt in the speci7ed order do form a causal chain or are conditionally in-dependent If one takes Woldrsquos view that causal action takes time then for suKcientlybrief time intervals fK (YKt |Y1t YKminus1 t Ytminus1) will not depend on contemporaneousvariables and what Granger calls ldquoinstantaneous causalityrdquo is ruled out In practicetime aggregation to observation intervals can introduce apparent simultaneous determi-nation Conversely in applications where time aggregation is an issue one can treatobserved variables as indicators for some latent causal chain structure de7ned for veryshort time intervalsWe shall focus on 7rst-order Markov processes specializations of (1) in which only

the most recent history conveys information

f(Yt |Ytminus1)equivf(Yt |Ytminus1)

equivf1(Y1t |Ytminus1) middot f2(Y2t |Y1t Ytminus1) middot middot fK (YKt |Y1t YKminus1 t Ytminus1)(2)

Note that if (1) is a higher-order Markov process then (2) can be obtained by ex-panding the variables in Yt to include higher-order lags Greater generality could beachieved via a hidden Markov structure in which the observed Yt are deterministic

8 Dawid (2000) Freedman (1985 2001) Granger (1969) Sims (1972) Zellner (1979) Swert (1979)Engle et al (1983) Geweke (1984) Gill and Robins (2001) Heckman (2000 2001) Holland (1986 1988)Pearl (2000) Robins (1999) Sobel (1997 2000) Hendry and Mizon (1999) and Woodward (1999)

functions of a latent 7rst-order Markov process 9 We leave this extension for futureresearchModel (2) is valid for a given history Ytminus1 if it is the true conditional distribution

of Yt given this history Term f a structural or causal model or a (probabilistic)law for Yt relative to a family of histories if it has the invariance property that itis valid for each history in the family Operationally this means that within speci7eddomains f has the transferability property that it is valid in di2erent populationswhere the marginal distribution of Ytminus1 changes and the predictability or invarianceunder treatments property that it remains valid following policy interventions thatalter the marginal distribution of Ytminus1 By including temporal or spatial variables inY it is possible to weaken invariance requirements to 7t almost any application Doneindiscriminately this creates a substantial risk of producing an ldquoover-7ttedrdquo model thatwill be invalid for any ldquoout-of-samplerdquo policy interventions Then proposed modelsshould be as generic as possible However it may be necessary in some applicationsto model ldquoregime shiftsrdquo that account for factors that are causal for some populationsor time periods and not for othersSuppose the vector Yt = (Ht St Xt) is composed of subvectors Ht St and Xt which

will later be interpreted as health conditions SES status and strictly exogenous vari-ables respectively We say that S is conditionally non-causal for H given X iff(Ht |Htminus1 Xtminus1) is a valid model ie given Htminus1 and Xtminus1 knowledge of Stminus1 isnot needed to achieve the invariance properties of a causal model Conversely iff(Ht |Htminus1 Stminus1 Xtminus1) equiv f(Ht |Htminus1 Xtminus1) then knowledge of Stminus1 contributes to thepredictability of Ht Note that either one or both conditional non-causality of S for Hand conditional non-causality of H for S may hold If either holds then H and S canbe arrayed in a (block) causal chain and if both hold then H and S are condition-ally independent Writing model (2) as a product of univariate conditional probabilitiesfi(Hit |H1t Himinus1 t Htminus1 Stminus1 Xtminus1) one can test for conditional non-causality of Sfor each component Hi It is possible to have a causal chain in which S is conditionallycausal to a previous component of H and this component is in turn ldquoinstantaneouslyrdquocausal to Hj yet there is no direct causal link from S to Hi Placing S after H in thevector Y we have conditional probabilities f(St |Ht Htminus1 Stminus1 Xtminus1) There may beinstantaneous conditional independence of H and S with the conditional distributionof St not depending on Ht or conditional non-causality of H for S with the conditionaldistribution not depending on Htminus1 or both The statement that X is strictly exoge-nous in a valid model (2) is equivalent to the condition that H and S are conditionallynon-causal for X in this model 10

The conventional de7nition of a causal model or probabilistic law requires that f bevalid for the universe of possible histories (except possibly those in a set that occurswith probability zero) see Pearl (2000) It is possible to reject statistically a proposed

9 Any discrete-time stationary stochastic process can be approximated (in distribution for restrictions to a7nite number of periods) by a 7rst-order hidden Markov model so there is no loss of generality in consideringonly models of this form see Kunsch et al (1995)10 Econometricians have traditionally used the term strictly exogenous to refer to properties of variables in

the true data generation process a stronger non-positivistic version of this condition

causal model by showing that it is highly improbable that an observed sample with agiven history was generated by this model It is far more diKcult using statistical anal-ysis to conclude inductively that a proposed model is valid for the universe of possiblehistories We have the far more limited objective of providing a foundation for policyanalysis where it is the invariance property under policy interventions that is crucial topredicting policy consequences We have de7ned validity and non-causality as prop-erties of a model and of the outcomes of a process of statistical testing that could inprinciple be conducted on this model Only within the domain where the model is validand invariance con7rms that the model is accurately describing the true data generationprocess can these limited positivistic model properties be related to the causal struc-ture embedded in the true data generation process Further we can choose the domainover which invariance will be tested to make the de7nition operational and relevantfor a speci7c analysis of policy interventions Similarly our de7nition of conditionalnon-causality is a positivistic construct in the spirit of the purely statistical treatmentof ldquocausalityrdquo by Granger (1969) and the test we will use is simply Grangerrsquos test forthe absence of causality augmented with invariance conditions Thus for example ifour analysis using this framework concludes that SES is not conditionally causal fornew health events within the domain where the Medicare system 7nances and delivershealth care then this 7nding would support the conclusion that policy interventions inthe Medicare system to increase access or reduce out-of-pocket medical expenses willnot alter the conditional probabilities of new health events given the health historiesof enrollees in this system It is unnecessary for this policy purpose to answer thequestion of whether the analysis has uncovered a causal structure in any deeper senseEconometric analysis is better matched to the modest task of testing invariance andnon-causality in limited domains than to the grander enterprise of discovering universalcausal laws However our emphasis on invariance properties of the model and on testsfor Granger causality within invariant families is consistent with the view of philoso-phers of science that causality is embedded in ldquolawsrdquo whose validity as a descriptionof the true data generation process is characterized by their invariance properties seePearl (2000) Feigl (1953) and Nozick (2001)

22 Some speci4c formulations

Starting from class (2) we consider operational models of the linear latent variableform

Y lowastit = Y1 t1i + middot middot middot+ Yiminus1 timinus1 i + Y prime

tminus113i + i minus iit (3)

with

Yit = i(Y lowastit Ytminus1) (4)

where Y lowast is a latent variable it is an unobserved disturbance that is standard normaland independent across i and t and is a partial observability mapping that dependson the latent variable and possibly on the lagged variables For example for a chronichealth condition such as diabetes Yit will indicate whether there has ever been a di-agnosis of the disease with Yit =maxY1 tminus1 1(Y lowast

it iquest 0) For an acute condition such

as a heart attack Yit = 1(Y lowastit iquest 0) indicates a new occurrence Components of Y may

be binomial or ordered discrete variables such as health status or continuous vari-ables such as household income In this model the primes 13 and are parametersrestrictions are imposed as necessary for identi7cation In (3) the linearity in vari-ables and parameters the 7rst-order Markov property and the triangular dependenceof Y lowast

it on previous components of Yt are not in themselves particularly restrictiveas one can approximate any continuous Markov model of form (2) by a form (3) inwhich Yt is expanded to include transformations and interactions to suKcient orderThe normality assumption is also not restrictive in principle A latent random vari-able with conditional CDF F(Y lowast

1t |Ytminus1) and the partial observability transformation(4) can be rede7ned using the standard normal CDF as Y lowastlowast

1t = minus1(F(Y lowast1t |Ytminus1))

and Y1t = 1(Fminus1((Y lowastlowast1t ) |Ytminus1) Y1 tminus1) this gives a version of models (3) and (4) in

which the disturbance is standard normal 11 The same construction can be applied tothe remaining components of Yt The causal chain assumption is innocuous when thetime interval is too short for most causal actions to operate and the components ofYt are conditionally independent However the causal chain assumption is much moresubstantive restriction when the time interval is long enough so that multiple eventshave time to occur as it rules out even the feedbacks that would appear in multipleiterations of a true causal chain Of course the generally non-restrictive approximationproperties of models (3) and (4) do not imply that a particular speci7cation chosen foran application is accurate and failures of tests for invariance can also be interpretedas diagnostics for inadequate speci7cationsIn models (3) and (4) a binomial component i of Yt with the partial observability

mapping maxYi tminus1 1(Y lowastit iquest 0) and the identifying restriction i = 1 satis7es Yit = 1

if Yi tminus1 = 1 and otherwise is one with the probit probability

fi(Yit = 1|Y1t Yiminus1 t Ytminus1) = (Y1 t1i + middot middot middot+ Yiminus1 timinus1 i + Y primetminus113i + i) (5)

Analogous expressions can be developed for ordered or continuous components

23 Measurement issues

A feature of the panel we use is that the waves are separated by several years andthe interviews within a wave are spread over many months with the months betweenwaves di2ering across households If model (2) applies to short intervals say monthsthen the transition from one wave in month t to another in month t + s is describedby the probability model

f(Yt+s|Yt) =sum

Yt+1 Yt+sminus1

f(Yt+1|Yt) middot middot f(Yt+s|Yt+sminus1) (6)

Direct computation of these probabilities will generally be intractable although analysisusing simulation methods is possible

11 For the CDF F of a random variable Y de7ne F(yminus)=supyprimeiexclyF(yprime) and Fminus1(p)=minxprime|F(xprime)iquestp

De7ne the random variable Z equiv h(Y ) = minus1(F(Yminus) + U [F(Y ) minus F(Yminus)]) where U is a uniform (0 1)random variable Then Z is as standard normal De7ne Ylowast = Fminus1((Z)) Then Ylowast = Y as so that Y isgiven as by a non-decreasing transformation of a standard normal random variable

A major additional complication in our panel is that interview timing appears tobe related to health status with household or proxy interviews delayed for individualswho have died or have serious health conditions This introduces a spurious correlationbetween apparent time at risk and health status that will bias estimation of structuralparameters To study empirical approximations to (6) and corrections for spuriouscorrelation we consider a simple model of interview delay Let p=(+ 13x) denotethe monthly survival probability for an individual who was alive at the previous waveinterview where x is a single time-invariant covariate that takes the value minus1 0 +1each with probability 13 Counting from the time of the previous wave interviewlet k denote the number of months this individual lives and c denote the monththat interviews begin for the current wave 12 There is a distribution of initial contacttimes let q denote the probability of a month passing without being contacted and letm denote the month of initial contact Assume that an individual who is living at thetime of initial contact is interviewed immediately but for individuals who have died bythe time of initial contact there is an interview delay with r denoting the probability ofan additional month passing without a completed interview with a household memberor proxy Let n denote the number of months of delay in this event Assume that m andn are not observed but the actual inter-wave interval t equal to m if the individual isalive at time of initial contact and equal to m+ n otherwise is observed The densityof k is pkminus1(1minus p) for kiquest 1 The density of m is qmminusc(1minus q) for miquest c Let d bean indicator for the event that the individual is dead at the time of initial contact Theprobability of t and d= 0 is h(0 t) = qtminusc(1minus q)pt the product of the probability ofcontact at t and the probability of being alive at t The probability of t and d = 1denoted h(1 t) is the sum of the probabilities that the individual is dead at an initialcontact month m with c6m6 t and the subsequent interview delay is n= t minusm or

h(1 t) =tsum

m=c

(1minus pm)qmminusc(1minus q)rtminusm(1minus r) (7)

If r iexclpq then h(1 t) = (1 minus q)(1 minus r)(qtminusc+1 minus rtminusc+1)=(q minus r) minus pc((pq)tminusc+1 minusrtminusc+1)=(pqminus r) Then the probability of an observed inter-wave interval t is h(t) =h(0 t)+h(1 t) and the conditional probability of d=1 given t is P(1|t)=h(1 t)=h(t)Absent interview delay the conditional probability of d = 1 given t would be simplyptminus1(1 minus p) The parameter values = minus247474 13 = 03 c = 22 q = 085 andr = 05 roughly match our panel For these values the median inter-wave interval is255 months and at t = 34 87 percent of the interviews have been completedFig 2 plots the inverse normal transformations of the true death rate ptminus1(1minusp) and

the apparent death rate P(1|t) against log(t) for each value of the covariate x The truerelationship is to a reasonable empirical approximation linear in x and in log(t) Thenin the absence of interview delay one could approximate p given x with reasonableaccuracy by estimating a probit model for death of the form ( + ampx + log(t))and then estimating p using the transformation p = (1 minus ( + ampx + log(t)))1=t for

12 It does not matter for the example if the previous wave interview month is 7xed or has a distributionprovided the relative inter-wave interval c is 7xed and current wave outcomes are independent of the timingof the previous wave interview

Fig 2 E2ect of interview delay (cumulative mortality hazard = minus1 (death probability))

the observed inter-wave interval t 13 However the 7gure shows that interview delayinduces a sharp gradient of apparent mortality hazard with inter-wave interval so that anestimated model will not extrapolate to realistic mortality hazards over shorter periodsA simple imputation of time at risk up to initial contact leads again to models that workwell with the procedure just outlined for estimation of p conditioned on x A simpleimputed time of initial contact for those who have died is the observed inter-waveinterval less the di2erence in the mean inter-wave interview times for dead and livingrespondents This imputation can be adjusted further so that the extrapolated annualdeath rate ( + log(12) + ampx) matches the sample average mortality rate We dothe additional adjustment for our panel with results that are almost identical to thesimple imputation of time of initial contactWe conducted a Monte Carlo calculation of the approximations above in a sample

of 50000 In this simulation the empirical approximation to observed mortality in theabsence of interview delay is (minus31053+05327x+0652 log(t)) With interview de-lay and the simple imputation described above (minus29900 + 05349x + 06174 log(t))is the empirical approximation 14 Table 1 gives the annual mortality rates implied bythese approximations From these results we conclude 7rst that in the absence of inter-view delay the probit model (+ log(t) + ampx) provides an adequate approximationto exact annual mortality rates as a function of time at risk across values of the co-variate x that substantially change relative risk and second that this remains true in

13 A BoxndashCox transformation of time at risk z = 4(t1=4 minus 1) gives a somewhat better approximation inthe probit model than log(t) but has no appreciable e2ect on the accuracy of estimated monthly transitionprobabilities14 The model estimated with interview delay and without imputation is (minus46639 + 05349x +

11178 log(t))

Table 1Approximation accuracy with interview delay

x Exact annual Approximate annual Error Approximate annual Errormortality rate mortality rate () mortality rate with ()() without interview interview delay and

delay () imputed contact time ()

0 771 790 241 793 279minus1 327 306 minus655 307 minus603+1 1641 1671 180 1675 205Avg 913 922 098 925 134

Note The approximate annual mortality rate is given by 1 minus (1 minus ( + ampx + log(t)))12=t where t isthe exact or imputed initial contact time and the model is estimated from the data generated by the MonteCarlo experiment

the presence of interview delay when one imputes the initial contact time for deadsubjectsThese conclusions on the accuracy of the approximation should extend to the exact

inter-wave transition probabilities (6) in our Markov model supporting use of theprobit approximation

fi(Yi t+s = 1|Y1t+s Yiminus1 t+s Yt)

=(Y1 t+s1i + middot middot middot+ Yiminus1 t+siminus1 i + Y primet 13i + i + i log(s)) (8)

where s=ti2minusti1 is the imputed months between initial contact for a wave and previouswave interview for estimation of incidence between waves For simulation of yearlytransitions we use the approximation

fi(Yi t+12 = 1|Y1t+12 Yiminus1 t+12 Yt)

= 1minus (1minus (Y1 t+11i + middot middot middot+ Yiminus1 t+1iminus1 i + Y primet 13i + i + i log(s)))12=s

asymp (Y1 t+11i + middot middot middot+ Yiminus1 t+1iminus1 i + Y primet 13i + i + i log(s))12=s (9)

where s is the median inter-wave interval and the 7nal approximation holds whenthe probability of a transition is small Formula (9) generalizes to any probability ofa transition from the status quo with the probability of remaining at the initial statede7ned so that all the transition probabilities sum to one We expect this formula toapproximate well the probabilities of no new health conditions in a sample populationover periods corresponding to the observed inter-wave intervalsEstimation of models based on (2)ndash(8) is straightforward Because of the inde-

pendence assumption on the disturbances and the absence of common parametersacross equations the estimation separates into a probit ordered probit or ordinaryleast-squares regression for each component of Y depending on whether the partialobservability mapping is binary ordered or linear Conventional likelihood ratio testscan be used for the signi7cance of explanatory variables

3 The AHEAD panel data

31 Sample characteristics

Our data come from the Asset and Health Dynamics among the Oldest-Old(AHEAD) study 15 This is a panel of individuals born in 1923 or earlier and theirspouses At baseline in 1993 the AHEAD panel contained 8222 individuals representa-tive of the non-institutionalized population except for over-samples of blacks Hispanicsand Floridians Of these subjects 7638 were over age 69 the remainder were youngerspouses There were 6052 households including individuals living alone or with oth-ers in the sample The wave 1 surveys took place between October 1993 and August1994 with half the total completed interviews 7nished before December 1993 Thewave 2 surveys took place approximately 24 months later between November 1995and June 1996 with half the total completed interviews 7nished by the beginning ofFebruary 1996 The wave 3 surveys took place approximately 27 months after thatbetween January 1998 and December 1998 with half the total completed interviews7nished near the beginning of March 1998 In each wave there was a long but thin tailof late interviews heavily weighted with subjects who had moved or required proxyinterviews due to death or institutionalization Subjects never interviewed directly orby proxy are excluded from the calculation of the distribution of interview monthsAHEAD is a continuing panel but it has now been absorbed into the larger Healthand Retirement Study (HRS) which is being interviewed on a 3-year cycleThe AHEAD panel has substantial attrition with death being the primary but not

the only cause A signi7cant e2ort has been made to track attritors and identify thosewho have died through the National Death Register Fig 3 describes outcomes for thefull age-eligible sample For subjects where a proxy interview was possible an ldquoexitinterviewrdquo gives information on whether decedents had a new occurrence of cancerheart attack or stroke since the previous wave From the 6743 age-eligible individualswho did not attrit prior to death we formed a working sample for analysis consist-ing of 6489 by excluding 254 additional individuals with critical missing informationFig 4 describes their outcomes In a few cases attritors in wave 2 rejoined the samplein wave 3 but we treat these as permanent attritors because the missing interviewmakes the observation unusableThe restriction of the AHEAD panel to the non-institutionalized elderly in wave 1

selects against those with the highest mortality risk particularly at the oldest ages butthe impact of this selection attenuates over time For white females Fig 5 compares theobserved annual mortality rate in the AHEAD panel with the expected annual mortalityrate from the 1997 Life Tables for the United States (US Census 1999) 16 Between

15 The AHEAD survey is conducted by the University of Michigan Survey Research Center for the NationalInstitute on Aging see Soldo et al (1997)16 The AMR for the AHEAD sample is the actual death rate between waves for each 5-year segment of

ages in the initial wave annualized using the median 255 month interval between the waves The AMRfrom the life tables is obtained by applying life table death rates by month to the actual months at riskfor each individual in the 5-year segment of ages in the initial wave to calculate expected deaths betweenwaves This is annualized For these calculations the distribution of months at risk for decedents is assumedto be the same as that for survivors

Fig 3 Age-eligible sample outcomes

Fig 4 Working sample outcomes

Fig 5 Mortality hazard for AHEAD white females

waves 1 and 2 the AHEAD mortality risk is substantially below the life table for agesabove 75 re4ecting the selection e2ect of non-institutionalization Between waves 2and 3 this e2ect has essentially disappeared There is a persistent divergence of themortality risks above age 90 In this range the AHEAD data is sparse so the curveis imprecisely determined However the life tables derived from historical mortalityexperience may overstate current mortality risk at advanced ages Fig 6 makes the samemortality experience comparisons for the full AHEAD working sample and draws thesame conclusions 17

32 Descriptive statistics

The AHEAD survey provides data on health and socioeconomic status as well asbackground demographics A list of the health conditions we study with summary

17 The construction mimics Fig 5 with life table rates applied using the age sex and race of each subject

Fig 6 Mortality hazard for AHEAD working sample

statistics is given in Table 2 A list of the socioeconomic conditions and demographicvariables we use is given in Table 3 Appendix Table A1 lists the variable transforma-tions used in our statistical analysis 18 In setting up causality tests using the frameworkset out in Section 2 we will use the health conditions followed by the socioeconomicconditions in the order given in these tables We list cancer heart disease and stroke7rst because they may be instantaneously causal for death and because we have infor-mation from decedentrsquos exit interviews on new occurrence of these diseases We groupthe remaining health conditions by degenerative and chronic conditions then accidentsthen mental conditions since if there is any contemporaneous causality it will plausi-bly 4ow in this order Similarly if there is contemporaneous causality between healthand socioeconomic conditions it plausibly 4ows from the former to the latter

18 All appendices can be found at httpelsaberkeleyeduwphwwhww202html

P Adams et al Journal of Econometrics 112 (2003) 3ndash56 19Table

2Health

cond

ition

variablesin

AHEAD

Label

Wave1

Wave2

Wave3

Variable

NMean

Std

dev

Variable

NMean

Std

dev

Variable

NMean

Std

dev

Healthconditionprevalence

Doc

ever

told

hadcancer

CANCER1

6489

013

7034

4CANCER2

6432

017

6038

1CANCER3

5685

018

8039

1Doc

ever

told

heartattackdisease

HEART1

6489

031

7046

5HEART2

6432

036

4048

1HEART3

5685

032

1046

7Doc

ever

told

hadstroke

STROKE1

6489

008

9028

5ST

ROKE2

6432

012

3032

9ST

ROKE3

5685

014

3035

0Doc

ever

told

hadlung

disease

LUNG1

6489

011

5031

8LUNG2

6432

012

4033

0LUNG3

5685

012

7033

3Doc

ever

told

haddiabetes

DIA

BET1

6489

013

4034

0DIA

BET2

5741

014

7035

4DIA

BET3

4867

015

8036

5Doc

ever

told

hadhigh

bloo

dpressure

HIG

HBP1

6489

050

2050

0HIG

HBP2

5741

052

5049

9HIG

HBP3

4867

055

3049

7Se

enDoc

forarthritis

inlast

12m

ARTHRT1

6489

026

7044

2ARTHRT2

5741

027

8044

8ARTHRT3

4867

027

9044

8Incontinence

last

12m

INCONT1

6489

020

2040

2IN

CONT2

5741

030

1045

9IN

CONT3

4867

037

1048

3Fa

llin

last

12m

requ

iretreatm

ent

FALL1

6489

008

0027

1FA

LL2

6432

018

0038

4FA

LL3

5685

026

7044

3Everfracturedhip

HIPFR

C1

6489

005

0021

9HIPFR

C2

6432

006

8025

2HIPFR

C3

5685

008

4027

8Prox

yinterview

PROXYW1

6489

010

4030

6PR

OXYW2

5741

013

2033

9PR

OXYW3

4867

015

4036

1Age-edu

cadjust

cogn

itive

impairment

COGIM

164

89025

7043

7COGIM

257

41034

9047

7COGIM

348

67040

3049

1Everseen

Doc

forpsychprob

PS

YCH1

6489

010

9031

2PS

YCH2

5741

012

8033

4PS

YCH3

4867

014

3035

0Depressed

(cesd8

iquest4)

DEPR

ES1

6488

009

9029

9DEPR

ES2

5741

008

6028

0DEPR

ES3

4862

010

8031

0Bod

ymassindex(Q

uetelet)

BMI1

6475

254

45

BMI2

5740

251

46

BMI3

4866

250

46

Low

BMIsplin

e=

max(020minus

bmi)

LOBMI1

6475

015

5065

4LOBMI2

5740

019

8076

3LOBMBI3

4866

022

3081

0HighBMIsplin

e=

max(0bmiminus

25)

HIB

MI1

6475

188

9316

4HIB

MI2

5740

180

8314

3HIB

MI3

4866

174

0303

7Current

smok

er

SMOKNOW1

6489

010

2030

3SM

OKNOW2

5741

007

8026

7SM

OKNOW3

4867

006

6024

9of

ADLs(needs

helpdiK

cult)

NUMADL1

6489

072

5139

1NUMADL2

6432

088

2165

2NUMADL3

5444

103

5177

4of

IADLs(needs

helpdiK

cult)

NUMIA

DL1

6489

061

8116

6NUMIA

DL2

6432

058

2120

4NUMIA

DL3

5685

071

1125

3Po

orfairself-reportedhealth

DHLTH1

6483

037

3048

4DHLTH2

5739

036

8048

2DHLTH3

4859

043

4049

6

Healthconditionincidence

Cancera

JCANCER2

6432

005

0021

8JC

ANCER3

5685

006

1023

9Heart

attackcon

ditio

naJH

EART2

6432

008

7028

1JH

EART3

5685

015

4036

1Stroke

aJSTROKE2

6432

005

0021

9JSTROKE3

5685

006

9025

4Diedsincelast

wave

TDIED2

6489

011

5031

9TDIED3

5741

015

2035

9Lun

gdiseasea

ILUNG2

6432

002

4015

4ILUNG3

5685

003

2017

7Diabetesa

IDIA

BET2

5741

002

4015

3ID

IABET3

4867

002

5015

6

Table

2(continued)

Label

Wave1

Wave2

Wave3

Variable

NMean

Std

dev

Variable

NMean

Std

dev

Variable

NMean

Std

dev

Highbloo

dpressure

(HBP)

aIH

IGHBP2

5741

005

3022

5IH

IGHBP3

4867

005

5022

9Arthritisa

IARTHRT2

5741

011

2031

6IA

RTHRT3

4867

011

7032

1Incontinence

inlast12

months

JINCONT2

5741

023

3042

3JINCONT3

4867

025

8043

8Fa

llrequ

iringtreatm

enta

JFALL2

6432

012

8033

5JFALL3

5240

016

503

71Hip

fracture

aJH

IPFR

C2

6432

002

015

0JH

IPFR

C3

5681

003

3017

8Prox

yinterview

PROXYW2

5741

013

2033

9PR

OXYW3

4867

015

4036

1Cog

nitiv

eim

pairment

ICOGIM

257

41012

1032

6IC

OGIM

348

67010

0030

0Psychiatricprob

lemsa

IPSY

CH2

5741

004

6021

0IPSY

CH3

4867

004

0019

6Depression

IDEPR

ES2

5741

005

1022

0ID

EPR

ES3

4862

007

2025

9BMIbette

rindicator

BMIB

T2

5740

019

7039

7BMIB

T3

4866

019

0039

2BMIworse

indicator

BMIW

S257

40016

7037

3BMIW

S348

66018

8039

1

a AHEAD

Waves

2and3

ldquoSince

thelast

interview

rdquo

Table

3SE

Sanddemog

raph

icvariablesin

AHEAD

Label

Wave1

Wave2

Wave3

Variable

NMean

Std

dev

Variable

NMean

Std

dev

Variable

NMean

Std

dev

SESvariables

Wealth

97Dol

(V2)(000

)C

2W1

6489

1766

2978

C2W

257

4123

75

5273

C2W

348

6724

77

7362

Non

-liquidwealth

(000

)C

2N1

6489

1120

1918

C2N

257

4112

12

3121

C2N

348

6711

92

4007

Liquidwealth

(000

)C

2L1

6489

647

1852

C2L

257

4111

63

3096

C2L3

4867

1286

5606

Income97

Dol

(V2)(000

)C

2I1

6489

238

288

C2I2

5741

245

586

1stqu

artilewealth

indicator

Q1W

B1

6489

026

1065

4Q1W

B2

5741

022

8041

9Q1W

B3

4867

025

5043

64thqu

artilewealth

indicator

Q4W

B1

6489

021

6041

2Q4W

B2

5741

027

3044

6Q4W

B3

4867

026

8044

31stqu

artileincomeindicator

Q1IB1

6489

026

0043

9Q1IB2

5741

024

6043

14thqu

Q4IB1

6489

024

7043

1Q4IB2

5741

024

6043

1Chang

eresidence

NMOVED2

5642

006

8025

1MOVED3

4867

010

2030

3Ownresidence

DNHOUS1

6489

073

2044

3DNHOUS2

5741

072

1044

9DNHOUS3

4867

070

7045

5Neigh

borhoo

dsafety

poorfair

HOODPF

164

89014

7035

4HOODPF

257

41010

7030

9HOODPF

348

67010

1030

1Hou

second

ition

poorfair

CONDPF

164

89014

6035

4CONDPF

257

41010

9031

2CONDPF

348

67012

3032

8

Dem

ographicvariables

Widow

WID

OW1

6489

041

6049

3WID

OW2

5741

044

3049

7WID

OW3

4867

043

4049

6Divorcedseparated

DIV

SEP1

6489

005

4022

6DIV

SEP2

5741

005

4022

6DIV

SEP3

4867

005

5022

8Married

MARRIED1

6489

049

8050

0MARRIED2

5741

046

5049

9MARRIED3

4867

047

7050

0Never

married

NEVMARR1

6489

003

2017

6NEVMARR2

5741

003

5017

2NEVMARR3

4867

003

1017

2Age

atinterview

inmon

ths

AGEM1

6489

9392

720

AGEM2

6432

9629

719

AGEM3

5741

9848

687

Motherrsquosdeathage

MAGEDIE1

6489

739

174

Fatherrsquos

deathage

PAGEDIE1

6489

715

151

Eversm

oke

SMOKEV

6489

052

6049

9Edu

catio

n(years)

EDUC

6489

107

38

Edu

ciquest

10yearsindicator

HS

6489

060

5048

9Edu

ciquest

14yearsindicator

COLL

6489

014

3035

0

33 Constructed variables

The collection and processing of some of the variables requires comment AHEADhas an extensive battery of questions about health conditions including mental healthMost health conditions are asked for in the form ldquoHas a doctor ever told you thatyou had rdquo However for cancer heart disease and stroke subjects are also askedif there was a new occurrence since the previous interview and for some conditionssuch as arthritis incontinence and falls the questions in wave 1 ask for an occurrencein the past 12 months We note that there are some major groups of health conditionsthat were not investigated in AHEAD degenerative neurological diseases kidney andliver diseases immunological disorders other than arthritis sight and hearing prob-lems back problems and accidents other than falls The BMI index is calculated fromself-reported height and weight Information is collected on the number of ADL lim-itations for six activities of daily living and on the number of IADL limitations for7ve instrumental activities of daily living A high ADL limitation count indicates thatthe individual has diKculty with personal self-care while a high IADL limitation countindicates diKculty in household management The study collects data on self-assessedhealth status where the subject is asked to rate his or her health as excellent verygood good fair or poor We use an indicator for a poorfair response No referenceis made to other groups such as ldquopeople your agerdquo The study contains the CESDbattery of questions measuring general mood and from this we form an indicator fordepressionAHEAD is linked to Medicare records There is insuKcient detail to permit recon-

ciliation of self-reports on objective health conditions against diagnoses in the medicalrecords but errors in self-reports are an issue We 7nd small but signi7cant inconsis-tencies across waves of AHEAD in reported chronic conditions A study of Canadiandata for a younger population 7nds substantial discrepancies between self-reported con-ditions and diagnoses from medical records particularly for chronic conditions such asarthritis see Baker et al (2001) These authors also 7nd support for a ldquoself-justi7cationrdquohypothesis that non-workers are more likely to make false positive claims for healthconditions If this reporting behavior carries into old age then the reduction in SESas a consequence of spotty employment would induce an artifactual association ofself-reported health conditions and SESThe study measures cognition using a battery of questions which test several do-

mains (Herzog and Wallace 1997) learning and memory are assessed by immediateand delayed recall from a list of 10 words that were read to the subject reasoningorientation and attention are assessed from Serial 7rsquos counting backwards by 1 andthe naming of public 7gures dates and objects 19 This score re4ects both long-termnative ability and health-related impairments due to health events We carry out thefollowing statistical analysis to reduce the e2ect of native ability so that we can con-centrate on health-related loss of cognitive function First we analyze a ldquonon-impairedrdquo

19 Serial 7rsquos asks the subject to subtract 7 from 100 and then to continue subtracting from each successivedi2erence for a total of 7ve subtractions

sample of younger individuals born between 1942 and 1947 who were adminis-tered the same cognitive battery in the 1998 Health and Retirement Study as werethe AHEAD subjects For these younger individuals where health-related impairmentof cognitive function is rare we carry out a LAD regression of the cognitive scoreon education level sex and race We use this 7tted regression to predict a ldquobase-linerdquo non-impaired cognitive score for each member of the AHEAD sample An ad-ditional adjustment is required because average education levels were rising rapidlyearly in the Twentieth Century due to changes in child labor laws and introductionof compulsory education We assign each AHEAD subject a ldquo1923 cohort equiva-lentrdquo education level by 7rst regressing education on sex race and birth cohort us-ing a speci7cation search to 7nd interactions and non-linearities and then adding totheir actual years of education the di2erence in the mean years of education for theirsexndashrace cohort and the corresponding 1923 sexndashrace cohort We then calculate foreach AHEAD sample member the deviation of their cognitive score from this ad-justed baseline As a normalization we assign a threshold such that 15 percent ofAHEAD subjects aged 70ndash74 in wave 1 fall below the threshold We then use thesame threshold in other age groups and other waves to de7ne an indicator for cognitiveimpairment 20

34 Measurement of wealth

AHEAD individuals and couples are asked for a complete inventory of assets anddebts and about income sources Subjects are asked 7rst if they have any assets ina speci7ed category and if so they are asked for the amount A non-response to theamount is followed by unfolding bracket questions to bound the quantity in questionand this may result in complete or incomplete bracket responses Through the use ofunfolding brackets full non-response to asset values was reduced to levels usually lessthan 5 percent much lower than would be found in a typical household survey Gener-ally median responses among full respondents for an asset category are comparable toother economic surveys such as the Survey of Consumer Finance However changesin reported assets between waves contain outliers that suggest signi7cant responseerrors between waves For couples where both members are asked the questions onassets there is also substantial inter-subject response variation It is possible that theserepeated reports could be used to control statistically for response error in couplesHowever there are systematic di2erences between respondents and we use the assetresponses only from the individual that a couple says manages the household 7nancesThere may also be an issue of bias in responses recovered by unfolding brackets Hurdet al (1998b) used experimental variation in the bracket sequences for two 7nancialquestions on wave 2 of AHEAD and found that anchoring to the bracket quantitieswas signi7cant

20 When an interview was done with a proxy the cognitive battery was not given but the intervieweewas asked if the respondent was cognitively impaired In our analysis we treat proxy interview status as acomponent of the state that appears as a contemporaneous explanation of cognitive impairment the coeKcienton this variable compensates for di2erences in the de7nitions of cognitive impairment

For complete or incomplete bracket responses in an asset category we impute con-tinuous quantities using hot deck methods In wave 1 if information on ownershipof an asset is missing for a subject but this subject does give ownership status inwave 2 then we impute wave 1 ownership by drawing from the conditional empiricaldistribution of those who have the same response in wave 2 and give a response inwave 1 For subjects missing ownership in both waves 1 and 2 we draw an owner-ship pair from the empirical distribution of ownership pairs for those giving responsesGiven ownership and complete or incomplete bracket information we draw from theempirical distribution of wave 1 continuous responses that are consistent with the sub-jectrsquos bracket In later waves we have adopted a 7rst-order Markov cross-wave hotdeck imputation procedure that assigns a continuous quantity within the given responsebracket First missing ownership is imputed by choosing randomly from respondentsconditional on ownership in the previous wave Then given ownership we impute aquantitative change in the item from the previous wave by drawing from the empiricaldistribution of subjects with complete responses that fall in the corresponding bracketsin the current and the previous wave This assures that imputed changes will havethe same empirical distribution as observed changes given the conditioning informa-tion available This procedure does not revise previous wave imputations so analysesbased on earlier waves are not a2ected We have experimented with cross-item impu-tation methods where bracket information on some asset categories would be used tore7ne the conditioning used in the imputation of other asset categories We have foundthat this has very little e2ect on the imputed variables or on the results obtained fromanalyses that use these variables Therefore we carry out all imputations one item ata timeMeasured wealth is accumulated over 11 asset categories including imputed items

We distinguish liquid wealth composed of IRA balances stocks bonds checking ac-counts certi7cates of deposit less debt and non-liquid wealth composed of net home-owner equity other real estate vehicles and other transportation equipment businessesand other assets The variation in reported wealth of AHEAD households by asset cat-egory is substantial from wave to wave suggesting that in addition to real volatilityand reallocation of wealth portfolios there are serious reporting problems with assetsValues of businesses owned and real estate are problematic items since current marketvaluations may be unavailable to respondents and subjective valuations may be unre-liable Suppose that Wt is measured wealth of household in wave t in 1997 dollarsand that Wt = W lowast

t + t where W lowastt is true wealth and t is reporting error To mini-

mize the impact of extreme outliers in wealth and wealth changes which we believeare a particular problem due to gross reporting errors our statistical analysis will usebounded transformations of measured wealthThe equations of motion for real wealth satisfy dW lowast

i =dt= rW lowasti +Si where i=T N L

indexes total wealth or its non-liquid and liquid components r is the instantaneous realrate of return including unrealized capital gains and Si is the 4ow of savings to thewealth component Make the logistic transformation Zi=1=(1+exp(minusciWi+di)) whereci and di are chosen so that in AHEAD wave 1 the median and the semi-interquartilerange of Zi are one-half Then Zi is a monotone transformation of measured wealththat is less sensitive to extremes The equation of motion for Zi is dZi=dt minus rZi

(1minus Zi)(log(Zi=(1minus Zi)) + di) = ciZi(1minus Zi)Si + ciZi(1minus Zi)(d=dt minus r) We assumethat over an inter-wave interval this equation of motion can be approximated by

Zit minus Zi tminus1 minus Rtminus1Zi tminus1(1minus Zi tminus1)(log(Zi tminus1=(1minus Zi tminus1)) + di)mt

=Sit + 0it (10)

where t indexes the wave mt is the interval in months between waves t minus 1 and tRt is the SampP real rate of return over the given interval S

it is the measured part ofciZi tminus1(1minus Zi tminus1)Si tminus1 attenuated at extreme values of Zi tminus1 and the disturbance 0itincludes the measurement error ciZi tminus1(1minus Zi tminus1)((it minus i tminus1)=mtminus1 minus rtminus1) and theunmeasured part of ciZi tminus1(1 minus Zi tminus1)Si tminus1 We assume 0 is homoskedastic This isconsistent with a measurement error in observed wealth that is heteroskedastic withgross measurement errors more likely when true wealth is near its extremes 21 Thedisturbance in (10) may be serially correlated however we have not incorporatedthis into our analysis The e2ect of the transformation is to substantially reduce thein4uence of outliers in the distribution of changes in measured wealth In applicationwe specify S

it to be a linear function of transformed nonliquid and liquid wealthZT tminus1(1minusZT tminus1) log(ZN tminus1=(1minusZN tminus1)) and ZT tminus1(1minusZT tminus1) log(ZL tminus1=(1minusZL tminus1))and of other SES demographic and health variables scaled by ZT tminus1(1minus ZT tminus1)

35 Mortality and observed wealth change

A problem with the analysis of wealth changes is that terminal wealth is not ob-served following the death of a single or the death of both members of a householdintroducing a selection e2ect A second problem is that a household death may have adirect impact on the wealth of a survivor due to the expenses associated with a deathand the disposition of the estate There are also severe wealth measurement problemsfollowing a household death since a death typically requires a valuation of assets andin many cases changes the 7nancially responsible respondent For this reason we willanalyze separately wealth changes for singles and for couples allow a regime shiftfollowing the death of one member of a couple and account for the selection thatoccurs when there are no survivorsFor a single female we adopt a bivariate selection model

Y lowastft = Yf tminus113f + yft = 1(Y lowast

ft iquest 0) Ywt = Yw tminus113w + Y primew tampw + + 2

Ywt observed if yft = 1 (11)

where the 7rst latent equation determines survival yft =1 the second equation corre-sponds to the transformed wealth change equation (10) with dependence on the previousstate Yw tminus1 and the previously determined components Y prime

w t of the current state with

21 Heteroskedasticity in (10) will arise from selection e2ects described later as well as possibly from afailure of the transformation to fully control the e2ects of gross reporting errors When working with thismodel we use standard error estimates that are robust with respect to heteroskedasticity of unknown formand do not attempt direct tests of the implicit error speci7cation underlying transformation (10)

the wealth change observed for survivors The disturbance f has mean zero varianceone and a density f() The disturbance is independent of and has mean zero andvariance one The correlation of the disturbances in the selection and wealth changeequations is 3 = =(2 + 22)1=2 and the unconditional variance of the wealth changeequation is 2 = 2 + 22 When and are standard normal this is the conventionalbivariate normal selection model However speci7cation tests for normality fail andfor robustness we adopt a more 4exible speci7cation approximating the density f()by an Edgeworth expansion

f() =Jsum

j=0

ampjHj()5() (12)

where the ampj are parameters and Hj() are Hermite orthogonal polynomials see Neweyet al (1990) Let 6jk(a) =

intinfina kHj()5() d Then the polynomials Hj() and the

partial moment functions 6jk(a) can be constructed using the recursions

H0() = 1 H1() = and Hj() = Hjminus1()minus(jminus1)Hjminus2() for jiquest 1

600(a) = (minusa) 601(a) = 5(a) and

60k(a) = akminus15(a) + (k minus 1)60 kminus2(a) for k iquest 1

6j0(a) =Hjminus1(a)5(a) and 6jk(a) = akHjminus1(a)5(a) + k6jminus1 kminus1(a)

for k iquest 0 for jiquest 0 (13)

Appendix Table A1 derives these results and gives the leading terms for Hj and 6jk We require that f integrate to one and have unconditional mean zero and varianceone this forces amp0 = 1 amp1 = 0 and amp2 = 0 The free parameters ampj for jiquest 2 determinehigher-order moments of For example skewness and kurtosis are determined byE3 = 6amp3 and E4 = 3 + 24amp4 With these restrictions we have 7nally

E(|iquesta) =rsquo(a) +

sumjj=3 ampj6j1(a)

(minusa) +sumJ

j=3 ampj6j0(a)and

E(2|iquesta) =(minusa) + arsquo(a) +

sumjj=3 ampj6j2(a)

(minusa) +sumj

j=3 ampj6j0(a) (14)

We use the Edgeworth approximation and these conditional expectations with J = 4We then have

E(Y lowastwt |iquestminus Yf tminus113f)

=Yw tminus113w + Y primew tampw +

rsquo(Yf tminus113f) +sum4

j=3 ampj6j1(minusYf tminus113f)

(Yf tminus113f) +sum4

j=3 ampj6j0(minusYf tminus113f) (15)

We estimate this conditional expectation in a two-step procedure First the parameters13f of the selection equation are estimated by maximum likelihood and substituted

into expression (15) for the expectation of the wealth change equation 22 Then theparameters in this conditional expectation are estimated using non-linear least squaresThe disturbance 9= + 2minus E(|iquestminus Yf tminus113f) has mean zero and variance

E(92|iquestminus Yf tminus113f)

=22 + 2

sumJ

j=0 ampj6j2(minusYf tminus113f)sumJj=0 ampj6j0(minusYf tminus113f)

minus[sumJ

]2 (16)

We regress the squared residuals from the estimation of (15) on the right-hand-sidevariables in (16) to obtain an estimate of 22 Finally we estimate the covariance matrixfor the parameter estimates using the generalized method of moments ldquosandwichrdquo for-mula with the EickerndashWhite procedure used for robustness against heteroskedasticityof unknown form and the delta method used to incorporate the e2ects of variance inthe 7rst-stage selection parameter estimatesNext consider the e2ects of death and selection on couples We adopt a trivariate

selection model with selection equations

Y lowastft = Yf tminus113f + f Y lowast

mt = Ymtminus113m + m yft = 1(Y lowastft iquest 0)

ymt = 1(Y lowastmt iquest 0) (17)

for the female and male members of the couple respectively where f and m areassumed to be independent with zero mean and unit variance and densities gf(f)and gm(m) The independence assumption could fail if there are hidden common fac-tors in mortality risk for both household members eg indirect e2ects of smokingHowever the frequency of multiple deaths in a household between waves is suK-ciently rare in the AHEAD data so that mortality risk interactions are empiricallynot identi7ed We distinguish three regimes (yf ym) in which wealth change is ob-served intact couples where both members survive (11) the female survives the deathher spouse (10) and the male survives the death of his spouse (01) We will letY 0t =[Yhtminus1Yftminus1Ymtminus1yftlowastY prime

ftymtlowastY primemt] denote the vector of variables that explain wealth

change where Yhtminus1 Yftminus1 and Ymtminus1 are respectively previous wave common fe-male and male variables Y prime

ft are previously determined components of the currentstate for females observed only for survivors and hence zeroed out for non-survivorsand Y prime

mt are the analogous previously determined components of the current state formales again observed only for survivors We assume that in an observed regime jkthe wealth change model takes the form

Ywt = Y 0t 13wjk + (f minus f1(j + k = 1))f + (m minus m1(j + k = 1))m + 2jk (18)

where is independent of f and m with zero mean and unit variance For intactcouples unobserved dependence of wealth change on selection is re4ected in the para-meters f and m a direct extension of the bivariate selection model to the trivariate

22 We 7nd that the coeKcients of the index in the mortality model are not sensitive to the Edgeworthgeneralization and in estimation of the model for wealth change use the 7rst-stage probit models for mortalityestimated earlier with invariance imposed to obtain the indices that appear in the selection e2ects

case with two independent selection e2ects For intact couples the correlations of thedisturbances in the selection and wealth change equations are 3f=f=(22

11+2f+2m)1=2

and 3m = m=(2211 + 2f + 2m)

1=2 The coeKcients 13jk and the standard deviation 2jk

are allowed to vary by regime to capture the observed and unobserved economice2ects of a death on valuation and reporting of assets In addition the selection e2ectsare allowed to shift from f to f minus f for the female selection disturbance andfrom m to m minus m for the male selection disturbance We incorporate these e2ects toaccommodate an apparent interaction in which unexpected survival of a couple (eg fand m large positive) increases dissaving perhaps due to additional medical and livingexpenses linked to overcoming high mortality hazards but the unexpected death of aspouse (eg f large negative) also increases dissaving perhaps because revaluationsof assets tend to be more drastic in circumstances where mortality hazard is lowWe adopt the Edgeworth approximation (12) for each of the densities gf(f) and

gm(m) In regime jk with j + k iquest 0 letting sf = 2yf minus 1 and sm = 2ym minus 1 one has

E(Ywt |jk) = Y 0t 13wjk+sf(fminusyff)

rsquo(Yf tminus113f)+sum4

j=3 ampj6j1(minusYftminus113f)

(sfYf tminus113f)+sfsum4

+ sm(m minus Ymm)5(Ymtminus113m) +

sum4j=3 ampj6j1(minusYmtminus113m)

(smYm tminus113m) + smsum4

j=3 ampj6j0(minusYmtminus113m)

(19)

As in the case of singles we estimate the conditional expectation (19) by nonlinear leastsquares after plugging in estimates of 13f and 13m from the earlier mortality models A7nal stage analogous to (16) regresses the squared residuals from (19) for each regimeon an intercept E(2f|sf)minus (E(f|sf))2 and E(2m|sm)minus (E(m|sm))2 the coeKcient onthe intercept is an estimate of 22

jk Because the number of deaths among couples isrelatively small we impose the constraints 13w10 = 13w01 for empirical identi7cation

Household income in AHEAD is also susceptible to measurement error and to min-imize its e2ect we use income quartiles as explanatory variables These are obtainedby converting all incomes to 1997 dollars determining the quartiles for the pooled in-comes of all subjects in all waves and using the thresholds thus established to classifyeach observed subject income AHEAD respondents rate the safety of their neighbor-hood and the condition of their dwelling on a 7ve-point scale from poor to excellentwe use indicators for poor or fair responses

4 SES and prevalence of health conditions

We 7rst give some descriptive statistics on the prevalence of health conditions inthe AHEAD population Table 4 shows prevalence rates in the AHEAD sample inwave 1 classi7ed by age and sex for the health conditions listed in Table 2 Generallyprevalence of health conditions does not show a strong age gradient indicating broadly

Table 4Prevalence of health conditions by age and sex

Condition White females White males

Age 70ndash74 75ndash79 80ndash84 85ndash89 90+ 70ndash74 75ndash79 80ndash84 85ndash89 90+

Cancera 0122 0137 0168 0141 0127 0132 0185 0202 0187 0093Heart diseasea 0244 0275 0361 0339 0370 0361 0390 0423 0368 0296Strokea 0051 0069 0104 0121 0133 0066 012 0102 0130 0148Lung diseasea 0109 0123 0108 0082 0055 0151 0171 0173 0093 0056Diabetesa 0121 0097 0107 0088 0055 0133 0145 0112 0104 0074High blood pressurea 0481 0510 0537 0582 0448 0433 0477 0418 0321 0167Arthritisb 0222 0285 0267 0328 0254 0167 0205 0196 0161 0167Incontinenceb 0228 0263 0266 0331 0365 0085 0138 0145 0161 0259Fallb 0082 0096 0116 0138 0133 0044 0046 0048 0088 0056Hip fracturea 0032 0052 0079 0127 0138 0020 0031 0041 0067 0056Cognitive impairment 0120 0149 0338 0452 0635 0137 0173 0291 0446 0500Psychiatric diseasea 0149 0137 0105 0082 0044 0094 0092 0071 0036 0056Depression 0070 0117 0131 0099 0116 0048 0050 0071 0083 0093Smoker 0133 0095 0058 0040 0017 0142 0123 0082 0041 0093ADL impairmentc 0375 0544 0829 1266 216 0285 0499 0691 1114 1444IADL impairmentc 0293 0340 0662 1099 2011 0304 0422 0658 0964 1426Self-reported health 0273 0348 0387 0393 042 0263 0364 0437 0332 0296

aAHEAD 1993 (wave 1) question ldquoHas a doctor ever told you =Do you have =Have you ever rdquobAHEAD 1993 (wave 1) question ldquoDuring the last 12 months have you rdquocAverage number max(ADL) = 6 max(IADL) = 5

that morbidity rates among survivors do not increase much with age Selection e2ectsfrom initial non-institutionalization and from mortality may be responsible The majorexception is cognitive impairment which rises as age increases The prevalence ofacute and degenerative conditions among survivors fall after about age 80 re4ectingthe e2ect of selection due to deaths from these conditions Males have higher prevalenceof acute and degenerative diseases than do females but females have higher prevalenceof mental and chronic conditions and accidentsFig 7 shows the age gradients of wealth income and education in wave 1 of the

AHEAD sample These gradients re4ect substantial cohort e2ects as well as life-cycleand composition e2ects Work income and asset accumulation patterns of the AHEADpopulation were impacted by World War II and those over age 80 experienced theGreat Depression during their prime working years The US was substantially ruralwhen the AHEAD population was born and education was truncated for work formany members of this population In addition to cohort e2ects the curve for assetsre4ects life-cycle decumulation of assets through the retirement years and the curve forincome re4ects the rising proportion of widows in the survivors to older ages Thereis an additional compositional e2ect from the association of SES and mortality higherSES is selected preferentially among survivors However in aggregate cross-sectionthe life cycle and cohort e2ects dominate the compositional e2ects

Fig 7 Cohort gradients (education wealth and income)

42 Models of association

To examine the association of SES and health conditions we estimate a series ofbinomial probit models of the form

P(Yit = 1|Y1t Yiminus1 t Wt Xt) (20)

where the Yit are indicators for the prevalence of various health conditions Wt denotesa vector of SES conditions and Xt denotes other demographic variables The healthconditions appear in the same sequence as in Table 2 with previous conditions in(20) providing information on association among health conditions Included in Wt areindicators for the top and bottom quartiles of wealth and income indicators for 10 ormore years of education (high school) and for 14 or more years of education (college)and indicators for poor or fair neighborhood safety and dwelling conditionThe detailed estimation results are given for whites in Appendix Table A2 Sample

sizes are not adequate for comparable models for non-whites We 7nd the expectedpatterns of co-morbidity with a strong association of heart disease stroke lung diseaseand arthritis and a strong association of diabetes heart disease and high blood pres-sure Incontinence is associated with cancer and stroke and for women with diabeteshigh blood pressure and arthritis Falls hip fractures and strokes are associated Psy-chiatric diseases and depression are associated with arthritis and falls BMI is positivelyassociated with diabetes high blood pressure and arthritis and negatively associatedwith lung disease Current smokers have lower BMI are less likely to have diabetesand are more likely to be depressed Numbers of ADLs and IADLs are positively as-sociated with most acute diseases arthritis falls hip fractures cognitive impairmentand psychiatric disease A poor or fair self-reported health status is associated withmost acute and chronic diseases with ADLs and IADLs and with depressionSome covariates are associated with health conditions and may be risk factors

for these conditions Widowhood is associated with increased cancer and heart

Table 5Summary of associations of SES and health conditions AHEAD wave 1

SES association White females White males

1 percent level Heart disease stroke lung disease di-abetes cognitive impairment depressionBMI IADL impairment self-reportedhealth status

Lung disease cognitive impairment BMIcurrent smoker ADL impairment IADLimpairment self-reported health status

5 percent level Cancer HBP Arthritis HBP depressionNot signi7cant Incontinence fall hip fracture psychiatric

condition current smoker ADL impair-ment

Cancer heart disease stroke diabetesarthritis incontinence fall hip fracturepsychiatric condition

Note HBP = high blood pressure BMI = body mass index (high or low) ADL = activities of dailyliving (impairment requiring assistance with personal care) IADL = instrumental activities of daily living(impairment requiring assistance with household management)

disease for women increased psychiatric disease for men and increased lung dis-ease and depression for both men and women For women fatherrsquos age at death isassociated with heart disease and motherrsquos age at death is associated with high bloodpressure For men fatherrsquos age at death is associated with high blood pressure andarthritisWe generally 7nd a statistically signi7cant association of SES and prevalence of

health conditions as summarized in Table 5 It is noteworthy that for males the preva-lence of the acute diseases cancer heart disease and stroke are not strongly associatedwith SES contrary to literature 7ndings for younger populations This may be the re-sult of early onset of these diseases particularly among the poor and among smokersthat selects out of the AHEAD population those males most at risk for these dis-eases Overall wealth is the SES component most commonly associated with healthconditions Education neighborhood rating and dwelling rating are occasionally sig-ni7cant and income is almost never signi7cant Table 6 summarizes the SES compo-nents that are individually signi7cant in their association with various health conditionsand indicates the sign of the correlation For a number of these conditions preva-lence rates are insuKcient to detect the e2ects of SES components with satisfactorypower However for heart disease high blood pressure arthritis cognitive impair-ment and self-rated health status sample sizes should guarantee reliable indicators ofassociation

43 Relative risk

To provide an indication of the direction and magnitude of the association of healthconditions and SES we calculate relative risk for low SES versus high SES wherethe de7nition of low SES is bottom quartiles for income and wealth less than a highschool education and a poorfair neighborhood and dwelling and the de7nition of highSES is top quartiles for income and wealth a college education and a good or betterneighborhood and dwelling Relative risk is de7ned as the AHEAD sample average of

Table 6Signi7cant associations of SES components and health conditionsa

Condition Wealth Income Educ Unsafe Nbd Dwelling PF

F M F M F M F M F M

Cancer Heart disease Stroke Lung disease Diabetes HBP Arthritis Incontinence Fall Hip fractureCognitive impairment Psychiatric condition Depression BMI Current smoker ADL impairment IADL impairment PF self-rated health Note The table summarizes 180 two-tailed signi7cance tests so that if the tests were independent one

would expect about 9 of the 41 signi7cant coeKcients at the 5 percent level by chance and about 2 of the23 signi7cant coeKcients at the 1 percent level by chance

a = positive at 5 level = positive at 1 level = negative at 5 level = negative at1 level

Table 7Relative risk of high vs low SES for various health conditionsa

Condition Relative risk Condition Relative risk Condition Relative risk

F M F M F M

Cancer 197 098 HBP 076 065 Cognitive imp 053 017Heart disease 046 075 Arthritis 080 060 Psychiatric 114 064Stroke 061 043 Incontinence 083 071 Depression 034 021Lung disease 030 033 Fall 068 044 Smoke now 027 023Diabetes 019 065 Hip fracture 082 083 Health poorfair 031 034

Note High SES is de7ned as top quartile in wealth and income college education and good neighborhoodand dwelling low SES is de7ned as bottom quartile in wealth and income less than a high school educationand poor neighborhood and dwelling Relative risks that are signi7cantly di2erent from one at the 5 percentlevel are denoted by lsquorsquo

aAssociations in AHEAD wave 1

the ratio of the two probabilities all other variables remaining at the observed levelsfor the subjects Table 7 summarizes the relative risks for the various health conditionsNote that the prevalence models are describing only association not causation so that

relative risk numbers cannot be interpreted causally With the statistically insigni7cantexception of cancer and psychiatric conditions for females high SES is associated withlower prevalence Thus we con7rm in the AHEAD population the literature 7ndingsof a systematic association of SES with mortality and morbidity risk and show thatthis association extends across a variety of acute degenerative chronic and mentalhealth impairments

5 Incidence of health conditions and tests for causality in the AHEAD panel

51 Models of incidence

Following the format described in Section 2 we use the incidence of new healthproblems (or recurrence of cancer heart disease stroke incontinence falls and hipfractures) conditioned on initial demographic health and SES status to test for theabsence of direct causal pathways We de7ne incidence for a group of health conditionsto be the occurrence of a condition that was not previously reported or a recordedreoccurrence in the case of an acute condition (cancer heart disease stroke) Thedescriptive statistics in Table 2 provide information on rates of incidence of theseconditions between waves 23

We estimate models for incidence of each health condition conditioned on previouslyconsidered incidences of health conditions the prevalence of health conditions in theprevious wave of the panel and on SES and demographic variables in the previouswave The models are binomial probit except for BMI which is 7tted with a linearmodel using OLS and numbers of ADL and IADL impairments which are 7tted asordered probits The estimates are given in Appendix Table A3 for whites Againthe data do not permit the same analysis of non-whites The models are estimated bystacking the data for wave 1 to wave 2 transitions above the data for wave 2 to wave 3transitions Table 8 summarizes the health conditions and covariates that are signi7cantrisk factors for the incidence of health conditions The associations re4ect a numberof known co-morbidities but show relatively few associations of SES components andincidence of health conditions

52 Causality tests

Fig 8 gives the structure of the invariance and causality tests we report We testonly whether the model parameters are invariant between the wave 1 to 2 transitionsand the wave 2 to 3 transitions We exclude intercepts age splines and log of timeat risk terms from the invariance test The reason for doing so is that these terms willcapture variations in survey recontact procedure across waves However we 7nd inmost cases that there is no signi7cant di2erence in the age spline coeKcients across

23 The incidence rates in Table 2 can be converted to crude annual rates via the formula 04706lowastlog(1+rate)These rates are uncorrected for population composition e2ects

34 P Adams et al Journal of Econometrics 112 (2003) 3ndash56Table

8Statistic

ally

sign

i7cant

risk

factorsforincidenceof

health

cond

ition

sa

Incidence

Health

cond

ition

sandco-m

orbiditie

sSE

Scovariates

Female

Male

Female

Male

Cancer

Cancer(

)BMI(

)Eversm

oke(

)

Heart

disease

Lun

gdisease(

)diabetes

()PFself-rated

health

()

Diabetes(

)PFself-rated

health

()

Stroke

()

new

heart(

)Stroke

()

HBP(

)psychiatric(

)new

heart(

)Income(

)

Mortality

Cancer(

)HBP

()

arthritis

()

cogn

i-tiv

eim

pairment(

)BMI(

)ADL

()

PF

self-rated

health

()

new

cancer

()

new

heart(

)new

stroke

()

Cancer

()

lung

()

diabetes

()

in-

continence

()

cogn

itive

impairment(

)BMI()ADL(

)PFself-rated

health

()

new

cancer

()

new

heart(

)new

stroke

()

Motherrsquos

deathage

()

Lun

gdisease

Heart(

)currentsm

oker

()

PFself-rated

health

()

PFself-rated

health

()

Wealth

()

Diabetes

BMI(

)Lun

gdisease(

)BMI(

)Eversm

oke(

)Edu

catio

n(

)

HBP

BMI(

)new

heart(

)new

stroke

()

new

diabetes

()

Heart(

)arthritis

()

new

heart(

)new

stroke

()

Arthritis

Lun

g(

)depression

()

BMI(

)ADL

()

PFself-rated

health

()

HBP(

)BMI(

)Edu

catio

n(

)motherrsquosdeathage

()

Incontinence

Arthritis

()

incontinence

()

fall

()

BMI(

)ADL

()

IADL

()

new

heart

()

new

stroke

()

new

arthritis

()

Lun

g(

)incontinence

()IA

DL(

)new

stroke

()

P Adams et al Journal of Econometrics 112 (2003) 3ndash56 35Fa

llFa

ll(

)hip

fracture

()

cogn

itive

impair-

ment(

)psychiatric(

)new

incontinence

()

Fall

()

new

stroke

()

new

incontinence

()

Hip

fracture

Fall(

)hipfracture

()

new

fall(

)Hip

fracture

()

new

incontinence

()

Cog

nitiv

eim

-pairment

New

stroke

()

new

hipfracture

()

HBP(

)IA

DL

()

Edu

catio

n(

)

Psychiatric

Heart

()

hipfracture

()

cogn

itive

impair-

ment(

)depression

()

new

incontinence

()

new

cogn

itive

impairment(

)

Arthritis(

)BMI(

)new

HBP

()

new

incontinence

()

Income

()

widow

()

divo

rcedsep

()

Depression

Cancer(

)heart(

)PF

self-rated

health

()

newarthritis

()

newincontinence

()

new

psychiatric(

)

Lun

g(

)new

incontinence

()

Eversm

oke(

)

Self-rated

health

Heart

()

lung

()

diabetes

()

arthri-

tis(

)cogn

itive

impairment(

)depression

()PFself-rated

health

()newcancer

()

new

heart(

)new

stroke

()

new

lung

()

new

arthritis

()

new

depression

()

new

ADL

()

Heart(

)lung

()

HBP(

)PFself-rated

health

()

new

cancer

()

new

heart(

)new

stroke

()

new

lung

()

new

cogn

itive

impairment(

)new

psychiatric(

)new

de-

pression

()

new

BMI()

new

ADL

()

Dwellin

gPF(

)

Notes()indicatesanychange

inBMIup

ordo

wn

lowersself-rated

healthThe

tablesummarizes

approx

imately10

00testsof

individu

alcoeK

cientsso

that

ifthey

wereindepend

enton

ewou

ldexpect

approx

imately10

ofthelistedassociations

re4ect

type

Ierrors

a One

percentsign

i7cancelevel

Fig 8 Invariance and causality tests Note LL denotes log likelihood for speci7ed condition an unconditionalinvariance test is denoted by ldquoIrdquo a conditional test for no direct SES causality given invariance is denotedby ldquoS|Irdquo and a joint test of invariance and no direct SES causality is denoted by ldquoSampIrdquo

the di2erent transitions The models are estimated unconstrained and with the imposi-tion of invariance non-causality of SES or both Likelihood ratio tests are conductedfor invariance with and without non-causality imposed and for non-causality condi-tioned on invariance Since the invariance test without non-causality of SES imposedand the non-causality test conditioned on invariance are nested they should give thesame conclusion at compatible signi7cance levels as a joint test of invariance andnon-causality In accordance with Section 2 we take acceptance of the joint hypothe-sis as evidence that there is not a direct causal path from SES to incidence of the givenhealth condition and take this as support for the proposition that di2erential access tomedical care and SES-linked environmental hazards are not causing incidence rates tovary with SESThe test results are given in Table 9 The columns of numbers in these tables are

respectively signi7cance levels for the invariance test with SES variables includedthe invariance test with SES variables excluded the non-causality test conditioned oninvariance and the joint test of invariance and non-causality The 7nal columns inthe table give the relative risk for high versus low SES (see Section 43) and thesigni7cance level of a T -test of the null hypothesis that the relative risk is oneIn a majority of cases our test for invariance is accepted For cancer and heart disease

incidence it is necessary to separate models for those with and without a previousoccurrence of the condition For females exceptions where invariance is rejected atthe 1 percent level are mortality and ADL count Exceptions for males are cancer witha previous occurrence mortality ADL count BMI and IADL count The failure ofthe mortality models to satisfy invariance may be related to the initial selection of anon-institutionalized population in wave 1 of the AHEAD panel Of course in additionto the question of the power of our test to detect invariance failures our single test ofinvariance across waves falls considerably short of the battery of invariance tests that

Table 9Health innovations tests for invariance and causality

Health Condition Sex Signi7cance levels Relative riskcondition occurred

previously Invariance Invariance No SES Joint High SES vs Signi7cancewith SES wo SES causality invariance low SESvariables variables given and no SES

invariance causality

CancerAll F 0056 0023 0311 0057 1260 0568No F 0856 0865 0315 0777 1234 0633Yes F 0133 0335 0949 0313 3729 0608All M 0000 0000 0225 0000 0569 0045No M 0122 0071 0059 0044 0467 0008Yes M 0002 0046 0021 0000 14731 0645

HeartAll F 0000 0000 0812 0000 0889 0617No F 0214 0075 0447 0240 0814 0480Yes F 0690 0832 0623 0744 0963 0927All M 0017 0020 0290 0018 1321 0412No M 0802 0571 0007 0240 1698 0350Yes M 0472 0601 0250 0382 1225 0710

StrokeAll F 0068 0034 0056 0023 0765 0410No F 0371 0239 0104 0205 0748 0413Yes F NC 0529 0597 NC 1999 0755All M 0086 0042 0290 0080 1179 0717No M 0248 0162 0641 0336 0874 0756Yes M NC 0002 0200 NC 8300 0584

Mortality F 0010 0006 0812 0030 0680 0122M 0021 0032 0228 0018 1196 0664

Lung disease F 0493 0479 0381 0470 0341 0000M 0603 0620 0013 0174 0225 0000

Diabetes F 0110 0177 0246 0091 0847 0778M 0243 0199 0043 0085 2649 0941

HBP F 0004 0009 0777 0012 1109 0779M 0220 0121 0668 0310 0886 0809

Arthritis F 0041 0017 0042 0012 1126 0623M 0187 0276 0145 0116 0415 0000

Incontinence F 0357 0329 0080 0183 0867 0324M 0161 0486 0237 0129 0980 0943

Fall F 0864 0763 0515 0861 1016 0940M 0402 0383 0507 0438 0944 0871

Hip fracture F 0604 0470 0275 0520 0413 0048M 0056 0051 0305 0055 0198 0003

Proxy F 0345 0442 0250 0283 0414 0000M 0424 0326 0019 0131 0447 0001

Table 9 (continued)

Cognitive F 0020 0007 0001 0000 0759 0162M 0429 0245 0022 0140 0522 0003

Psychiatric F 0075 0031 0012 0012 0342 0000M 0194 0546 0110 0108 0102 0000

Depression F 0299 0347 0078 0151 0411 0000M 0767 0856 0302 0695 0352 0001

BMI F 0419 0330 0738 0531M 0010 0002 0249 0009

Smoke now F 0509 0242 0838 0650 0649 0530M 0366 0146 0064 0182 6448 0841

ADL F 0010 0018 0818 0027M 0004 0044 0370 0005

IADL F 0673 0514 0368 0636M 0016 0003 0006 0002

Self-rated health F 0151 0111 0001 0009 0670 0000M 0581 0570 0034 0282 0656 0000

would be desirable to establish that the model system has the stability and sensitivityrequired for policy applicationsFor females the tests for non-causality of the SES variables conditioned on a main-

tained hypothesis of invariance are rejected for arthritis and psychiatric disease at the5 percent level and for cognitive impairment and self-rated health at the one percentlevel Notably these are all chronic or mental conditions where Medicare coverage islimited and the cost of drugs or assistance may be substantial For males this test fornon-causality is rejected for cancer with a previous occurrence heart disease with noprevious occurrence lung disease diabetes cognitive impairment and self-rated healthat the 5 percent level and for IADL count at the one percent level The results ofthe joint test for invariance and non-causality are roughly consistent with the separatetests For conditions such as cancer with a previous occurrence and IADL count formales cognitive impairment for females and mortality for both females and males thenon-causality test results may be confounded by the failure of invarianceThe relative risks in Table 9 should not be interpreted causally since again the

cases where non-causality is rejected and the relative risks are substantially di2erentfrom one may be due to a common unobserved e2ect rather than a direct causal linkThe pattern of 15 relative risks exceeding one and 18 less than one suggests no broadlinkage between SES and health changes given prior health and the direct links thatmay be indicated from the signi7cance levels (lung disease and hip fractures for malesand females some cancers and arthritis for males) appear to be related to speci7cfeatures of poverty such as smoking history and poor dwelling environment Thereare a few cases where the relative risk for high versus low SES is substantially lessthan one irrespective of statistical signi7cance indicating an unproven link of suKcientmagnitude to warrant further investigation lung disease hip fracture and the mental

diseases for females and lung disease diabetes arthritis and the mental diseases formales Large deviations in relative risk from one that are not statistically signi7cantsuggest that acceptance of the joint hypothesis of invariance and non-causality couldbe due to low power Notably death shows no relation to SES once previous healthstate is controlled and the relative risks are insigni7cantly di2erent from one Thisindicates that there are no strong direct causal links from SES to mortality which atthe level of resolution of this study rules out di2erential access to medical treatment forlife-threatening illness Thus the association of SES and mortality among the elderlyappears to come primarily from variation in the prevalence of health conditions withSES and more weakly from indirect causal links from SES to incidence of healthconditions that increase mortality riskThe pattern of failures of the non-causality test for mental diseases suggests the

possibility of a direct causal link related to di2erential access Medicare limits thescope of care for mental conditions so ability to pay may indeed be an importantfactor in eKcacy of treatments that prevent or control these conditions

6 Tests for non-causality from health status to asset accumulation

Health may in4uence asset accumulation of elderly households because of the costof medical treatment and related services Medicare covers acute conditions with lim-ited copayments but there is the possibility of direct e2ects from uncovered costs ofdrugs and living assistance Also health conditions may limit the consumption of othergoods and because health status is an indicator of longevity an individual planningconsumption and precautionary reserves over remaining life may adjust target wealthbased on altered perceptions of longevity and anticipated medical costs see Alessieet al (2000) Attanasio and Hoynes (1995) Hurd (1987) Hurd and Wise (1989)Hurd and McGarry (1997) Hurd et al (1998a) These e2ects could induce an associ-ation of SES and health status even if there were no causal links from SES to healthIn the elderly AHEAD population we will not observe the most likely direct causallink from health status to accumulation among workers the e2ect of health on currentlabor market participation and productivityWe analyze transitions in wealth from wave to wave using the framework of Section

2 and model (11) for singles and (17) and (18) for couples with demographicsprevious wave health conditions and current wave incidence of new health conditionsas explanatory variables Statistically signi7cant selection coeKcients are consistent witha direct causal link from death to a change in household wealth but also consistentwith ecological factors that induce an association of mortality risk and SES Totalnon-liquid and liquid wealth are analyzed separately with transformation (10) appliedto each componentAppendix Table A4 gives the detailed incidence models for total non-liquid and liq-

uid wealth change As in previous studies of savings we 7nd that most of the variancein wealth changes over the population is not explained by observed economic variables

This remains true after introduction of health conditions We 7nd dissaving rates outof liquid wealth before realization of returns calculated from the SampP 500 that are53 percent for couples 48 percent for singles and 60 percent for survivors whosespouses have died The dissaving rates from non-liquid wealth again before realizationof returns are respectively 69 percent 63 percent and 80 percent for intact couplessingles and survivors The higher dissaving rates from non-liquid assets indicates thatthe wealth portfolios of the elderly are rebalanced to become more liquid as they ageThese dissaving rates can be compared to an average rate of dissaving of 83 percent ofremaining wealth in an age 70+ population with life table survival probabilities whoconsume the expected annuitized value of their wealth 24 Then observed dissavingrates out of wealth are not grossly lower than would be expected with pure life cy-cle consumption averaging over retirement and full pooling of mortality risk We 7ndthat low income couples and individuals have signi7cantly higher dissaving rates thantheir high income counterparts but the di2erences are not quantitatively large Homeownership is associated with signi7cantly less dissaving for intact couplesThe models for both singles and couples show signi7cant departures from normality

in the selection equations The Edgeworth expansion parameters show positive skew-ness and smaller than normal kurtosis for female singles negative skewness and in-signi7cantly di2erent from normal kurtosis for male singles For couples both malesand females have negative skewness and larger than normal kurtosis We also 7ndsigni7cant selection e2ects with 3f = minus049 for couples and minus021 for singles and3m = minus051 for couples and minus089 for singles These imply that households that sur-vive despite unfavorable mortality risks have increased dissaving either because ofincreased cost of overcoming health problems or because households at elevated riskspend down more rapidly Eq (18) includes shift parameters that modify the depen-dence of the wealth change disturbance on the unobserved selection e2ects in regimeswhere a spouse dies These are statistically signi7cant and suKciently large to reversethe direction of the intact couple selection e2ectsTable 10 summarizes the health conditions and other covariates that are individually

signi7cant in explaining changes in wealth For intact couples we 7nd some acuteconditions increase saving perhaps because they restrict consumption or perhaps be-cause couples conserve assets for a potential surviving spouse For the conditions thatare associated with increased dissaving (cognitive impairment and stroke for single fe-males) costs of maintenance associated with these conditions may be directly causalto wealth changes

62 Causality tests

Table 11 summarizes our tests for invariance and absence of direct causal linksWe test for common parameters in the wealth change models between waves 1ndash2and waves 2ndash3 excepting intercepts and age e2ects to allow for the e2ects of sampletiming Invariance is convincingly rejected for each demographic group and wealth

24 This calculation is made from the 1996 life tables and assumes the historical SampP rate of return from1993 to 1997 and a 7 percent real rate of return on assets after 1997

Table 10Statistically signi7cant risk factors for wealth changesa

Component Health conditions Covariates

Intact coupleTotal wealth M self-rated health PF () M new

heart ()Non-liquid wealth () liquid wealth() income () homeowner ()

M new hip fracture () F new cancer()

Non-liquidwealth

Non-liquid wealth () liquid wealth() homeowner ()

Liquid wealth M new heart () M BMIworse ()

Non-liquid wealth () liquid wealth() income () dwelling PF ()

Spouse diedTotal wealth Non-liquid wealth () liquid wealth

() income ()Non-liquidwealth

Non-liquid wealth ()

Liquid wealth F new stroke () Non-liquid wealth () liquid wealth() Income ()

SingleTotal wealth M new cancer () F new cancer

() F newMndashF non-liquid wealth () MndashF liq-uid wealth () MndashF income ()

depression ()Non-liquidwealth

Mhip fracture ()M new cancer ()M new

MndashF non-liquid wealth () M liquidwealth () F income ()

heart () F homeowner ()Liquid wealth F cognitive impairment () F new

stroke ()MndashF non-liquid wealth () MndashF liq-uid wealth () MndashF income ()

F new cognitive impairment () F dwelling PF ()

Note M = male F = female new = incidence since last wave PF = poor or fairaOne percent signi7cance level indicates increased saving indicates decreased saving

category indicating that our model fails to capture the structural determinants of wealthchange As a consequence our non-causality tests to follow may produce rejectionsdue to model misspeci7cation confounding the detection of direct causal links Adeconstruction of the invariance failures detailed in Appendix Table A5 shows that fornon-liquid and liquid wealth invariance passes for demographic and health prevalenceand incidence variables but fails for female SES variables and for all male variablesincluding SES taken together Thus there was an unexplained regime shift before andafter wave 2 of AHEAD Possible explanations for this are an interaction betweenthe criterion of non-institutionalization in the initial panel recruitment and economicbehavioral response a wealth-linked interaction in panel retention problems in themeasurement of wealth in the AHEAD population which exhibits unexplained meanreversion or a true behavioral shift with age in a single cohort that is not capturedaccurately by a model that pools wealth change observations across cohorts

Table 11Wealth changes tests for invariance and causality

Demographic group Signi7cance levelswealth component

Invariance Non-causality

Previous health Current health All healthconditions conditions conditions

Intact coupleTotal wealth 0000 0036 0001 0000Non-liquid wealth 0000 0014 0028 0001Liquid wealth 0000 0006 0012 0000

Spouse diedTotal wealth 0000 0811 0776 0074Non-liquid wealth 0000 0071 0814 0037Liquid wealth 0000 0676 0456 0023

SingleTotal wealth 0000 0004 0022 0001Non-liquid wealth 0000 0100 0347 0235Liquid wealth 0000 0000 0028 0000

We expect that terminal medical and burial expenses estate taxes and other estatesettlement costs insurance payments and bequests will have a substantial impact on thesize of a decedentrsquos estate and surviving spousersquos reported wealth We easily reject thehypothesis that the model coeKcients for intact couples and for surviving spouses arethe same but note that measurement problems associated with a change in 7nanciallyresponsible respondent could also produce this rejectionThe hypothesis of no direct causality of health conditions for total wealth changes is

rejected at the 1 percent level for intact couples and singles For non-liquid wealth thehypothesis is rejected for intact couples and for liquid wealth the hypothesis is rejectedfor all demographic groups The failure of the invariance tests and the possibility ofconfounding by persistent common factors and selection suggest that conclusions onthe health to wealth link be interpreted with caution Appendix Table A6 deconstructsthe causality tests and identi7es the health conditions and genders responsible for re-jections The pattern of results suggest that if there is indeed a direct causal link thenit is most likely to involve liquid wealth and health conditions that require assistedlivingAppendix Table A7 estimates models of income change given health conditions

and other covariates One would not expect health status to have a signi7cant impacton the incomes of retirees conditioned on previous wealth and the empirical resultsare generally consistent with this expectation We have not done formal tests of in-variance or causality for income Also included in the state vector Yt that describesindividuals are changes in home ownership status and dwelling and neighborhood con-ditions We estimate incidence models for these components results are in AppendixTable A8

7 Simulation of life courses under counterfactual conditions

71 The simulation experiment

For policy analysis of interventions that alter delivery or cost of medical servicesor retirement 7nancing one would like to trace through the direct and indirect causallinks between wealth health and mortality If Markov models of the sort developedin Sections 2ndash6 satisfy the required invariance properties then they can be used tosimulate the impacts of these interventions on the life courses of a synthetic populationIn this section we develop such a simulation analysis and apply it to illustrativeinterventions Because we have not uniformly accepted invariance and in a numberof cases 7nd associations that may be either direct causal links or hidden commonfactors this simulation analysis assumes more than our estimates support It should beinterpreted only as an exercise that shows how a model of this general structure mightbe used in a policy application to unravel the dynamics of co-morbidities and forecastcondition-speci7c morbidity and mortality and life expectancyWe simulate the life courses of a synthetic population in which heads of household

are initially age 70ndash74 To synthesize this population we start from the 1612 house-holds in AHEAD wave 1 whose heads are white and age 70ndash74 Using the SES anddemographic variables for each household in this subsample we make 10 Monte Carlodraws from the prevalence models in Section 4 to create synthetic initial health pro7lesfor the household head and spouse if present This gives an initial synthetic sample of16 120 households We then create life courses for the members of each household bydrawing recursively from the Markov incidence models in Sections 5 and 6 adjusted toannual transitions using (9) to approximate the probabilities of moving to new statesWe 7rst consider a base scenario (S0) in which initial prevalence and incidence

transitions are given by our models estimated on the AHEAD data We note that thesimulation outcomes can be expected to di2er to some degree from the cross-cohortpatterns found in AHEAD because the distribution of conditions at ages 70ndash74 willdi2er from the distributions of prevalence that actually prevailed for older individualsin AHEAD when they were ages 70ndash74 They should also di2er to some degree fromthe actual experience that the age 70ndash74 cohort in AHEAD will have through theremainder of their lives because the simulation cannot anticipate the realized futuredistribution of exogenous variables and because our models do not allow for drift indisease incidence or condition-speci7c mortality hazards that will result from changes inmedical care Historically these drifts have been very signi7cant reducing morbiditiesand increasing life expectancies If these trends continue then the baseline simulationswill underestimate actual survival experienceWe next consider two stylized policy interventions The 7rst alternative scenario

(S1) examines the impact on life courses of the introduction of a hypothetical medicaltreatment that cures diabetes for example by stem cell and immune system therapythat rejuvenates the pancreas for both type I and type II diabetics In this scenario weassume that prevalence of diabetes at the start of the simulated panel drops to zero andthat there is zero incidence of this condition as the cohort ages We do not alter thehistorical prevalence of conditions associated with diabetes Thus we assume that the

historical impact on individuals of type I diabetes notably increased prevalence of heartdisease and stroke at age 70ndash74 is not altered The second alternative scenario (S2)examines the impact on life courses of reducing the entire population from their currentsocioeconomic status to our de7nition of a low-SES individual bottom quartile forwealth and income less than a high school education and a poor or fair neighborhoodand dwelling This alternative is obviously hypothetical and is not even a stylizedapproximation to any real policy alternative However it provides an extreme in whichthe interactions of health and SES are permitted maximum play giving an upper boundon the e2ect that SES could possibly have on health outcomes and providing a 7ngerexercise that tests the plausibility of our model system

72 Baseline simulation

Table 12 summarizes the survival probabilities and prevalence of health conditionsamong survivors in the simulated cohort as it ages under the baseline scenario (S0)the no-diabetes scenario (S1) and the low-SES scenario (S2) Keeping in mind thatwe expect the simulation model to di2er from the historical cross-cohort record inAHEAD the success of this model in plausibly mimicking observed conditions in theAHEAD population can be judged by comparing the results for scenario S0 with lifetable survival probabilities Life expectancy for a cohort of white females aged 70ndash74is 1315 years from the 1996 Life Tables and 1436 years in our baseline simulationThe life table probability of survival for 15 years for the aged 70ndash74 cohort is 0535while the corresponding survival probability in the simulation model is 0500 Forwhite males the life expectancy at age 70 is 1131 years from the Life Tables and1081 years from the S0 simulation The 15-year survival probability is 0381 fromthe life tables and 0279 from the simulation model Thus relative to the life tablesthe simulation model under-predicts female mortality and over-predicts male mortalityThe comparison of annual mortality rates for white females given in Fig 5 indicates thatactual AHEAD mortality experience was more favorable than the life tables betweenwaves 1 and 2 presumably due to selection in panel recruitment and very close to thelife tables between waves 2 and 3 Then the baseline simulation appears to reproducerelatively accurately the cross-cohort survival experience in AHEAD This provides areality check for the simulation model but also suggests that if the survival experienceof a current cohort di2ers from the historical cross-cohort pattern then the simulationmodel will miss the drift in mortality hazards that a single cohort will face in thefutureA comparison of prevalence rates for various health conditions among survivors of

various ages can be made between AHEAD at wave 1 given in Table 4 and thebaseline simulation in Table 12 There are issues of comparability in the de7nitionof prevalence for some conditions but the pattern that emerges is that the simulatedprevalences are systematically higher than the historical prevalences and increasingly soat older ages For example for white females aged 80ndash84 the historical and simulatedprevalence rates are 0168 versus 0219 for cancer 0361 versus 0442 for heart diseaseand 0338 versus 0437 for cognitive impairment One possible explanation for thisis that the links from morbidity to mortality are stronger than the mortality model

Table 12Simulation outcomesa

Age

70 75 80 85 90 95

White femalesSurvival probability (a) S0 1000 0905 0743 0500 0240 0079

S1 1000 0906 0757 0517 0257 0087S2 1000 0884 0662 0359 0125 0027

Cancer (b) S0 0112 0174 0219 0245 0257 0262S1 0112 0169 0217 0243 0258 0252S2 0112 0208 0273 0298 0302 0336

Heart disease (b) S0 0224 0322 0442 0538 0588 0594S1 0224 0321 0429 0515 0569 0608S2 0224 0344 0495 0608 0663 0679

Stroke (b) S0 0042 0105 0191 0272 0326 0341S1 0042 0104 0186 0260 0317 0351S2 0042 0105 0196 0274 0320 0366

Lung disease (b) S0 0105 0151 0179 0190 0168 0143S1 0105 0150 0183 0190 0175 0154S2 0105 0193 0258 0278 0276 0286

Diabetes (b) S0 0114 0161 0198 0199 0170 0157S1 0114 0000 0000 0000 0000 0000S2 0114 0181 0231 0233 0207 0231

HBP (b) S0 0467 0583 0678 0738 0761 0778S1 0467 0585 0678 0742 0783 0804S2 0467 0597 0701 0764 0786 0810

Arthritis (b) S0 0232 0501 0677 0791 0857 0901S1 0232 0501 0670 0784 0856 0905S2 0232 0567 0769 0876 0925 0965

Incontinence (b) S0 0232 0416 0601 0751 0843 0891S1 0232 0427 0611 0749 0844 0906S2 0232 0444 0664 0814 0891 0917

Fall (b) S0 0071 0271 0464 0635 0759 0837S1 0071 0268 0456 0628 0754 0846S2 0071 0260 0460 0640 0759 0822

Hip fracture (b) S0 0030 0046 0070 0109 0153 0215S1 0030 0043 0069 0109 0156 0190S2 0030 0056 0104 0160 0224 0258

Proxy interview S0 0038 0056 0103 0163 0230 0294S1 0038 0063 0095 0155 0222 0271S2 0038 0103 0211 0316 0409 0521

Cognitive impairment (b) S0 0104 0253 0437 0609 0736 0818S1 0104 0251 0435 0602 0722 0803S2 0104 0405 0669 0838 0910 0952

Table 12 (continued)

Age

70 75 80 85 90 95

Psychiatric disease (b) S0 0154 0215 0307 0376 0421 0434S1 0154 0219 0305 0379 0416 0426S2 0154 0316 0508 0634 0704 0762

Depression (b) S0 0068 0183 0305 0429 0515 0575S1 0068 0179 0305 0424 0521 0596S2 0068 0247 0434 0574 0665 0749

BMI (c) S0 257 247 236 223 210 205S1 257 247 236 223 211 203S2 257 247 234 222 212 208

Current smoker (b) S0 0128 0088 0063 0043 0027 0017S1 0128 0091 0063 0048 0031 0016S2 0128 0109 0084 0056 0039 0020

ADL limits (c) S0 031 027 066 118 168 214S1 031 026 059 108 163 199S2 031 045 121 208 277 333

IADL limits (c) S0 025 011 029 058 085 114S1 025 010 027 053 081 104S2 025 025 073 134 184 230

PF self-rated health (b) S0 0254 0305 0441 0540 0585 0613S1 0254 0293 0416 0501 0574 0582S2 0254 0507 0711 0811 0841 0860

White MalesSurvival probability (a) S0 1000 0828 0558 0279 0091 0019

S1 1000 0844 0586 0304 0105 0025S2 1000 0827 0485 0170 0032 0004

Cancer (b) S0 0145 0242 0320 0400 0478 0514S1 0145 0248 0321 0395 0482 0546S2 0145 0281 0391 0479 0555 0596

Heart (b) S0 0352 0490 0611 0709 0774 0733S1 0352 0488 0626 0701 0752 0766S2 0352 0443 0554 0627 0632 0681

Stroke (b) S0 0075 0140 0213 0282 0317 0310S1 0075 0142 0213 0287 0323 0351S2 0075 0190 0317 0423 0517 0596

Diabetes (b) S0 0135 0171 0183 0190 0177 0171S1 0135 0000 0000 0000 0000 0000S2 0135 0135 0119 0095 0085 0128

HBP (b) S0 0443 0553 0636 0699 0719 0743S1 0443 0551 0637 0702 0740 0784S2 0443 0565 0643 0689 0692 0638

Age

70 75 80 85 90 95

Arthritis (b) S0 0175 0405 0582 0718 0801 0848S1 0175 0419 0602 0719 0792 0865S2 0175 0581 0806 0913 0948 0915

Fall (b) S0 0041 0162 0300 0435 0547 0667S1 0041 0163 0292 0440 0559 0681S2 0041 0214 0410 0588 0728 0809

Proxy Interview S0 0111 0110 0114 0125 0155 0157S1 0111 0109 0120 0147 0170 0170S2 0111 0223 0303 0382 0429 0468

Depression (b) S0 0038 0105 0184 0233 0262 0281S1 0038 0110 0196 0259 0263 0344S2 0038 0199 0344 0421 0445 0404

BMI (c) S0 261 255 249 246 244 244S1 261 256 250 247 246 241S2 261 246 236 232 232 229

ADL limits (c) S0 033 036 075 133 184 245S1 033 038 079 137 188 246S2 033 094 211 324 415 451

IADL limits (c) S0 034 016 033 063 094 124S1 034 015 034 064 095 123S2 034 052 122 200 265 285

Notes (a) Proportion of age 70 population surviving to the speci7ed age (b) Proportion of survivingpopulation at speci7ed age who ever had condition (c) Mean in surviving population

aScenarios S0 = Baseline S1 = no diabetes S2 = all low SES

detects perhaps because of under-reporting of health conditions that arise prior todeath so that the simulation model underestimates the selection e2ect of mortalitythat reduces prevalence among survivors A second possible explanation is that thereis strong unobserved heterogeneity in susceptibility to various health conditions sothat cumulative prevalence is overestimated by our 7rst-order Markov models whichdescribe prevalence for most conditions as the result of one or more positives in aseries of Bernoulli trials It is possible to test for persistent unobserved heterogeneityby asking whether the frequency of a negative for a condition between waves 1 and 3of AHEAD is the product of the frequencies of a negative between successive wavesWhen we do this we do not 7nd persistent unobserved heterogeneity However thepower of the test is modest and it is possible that even a limited degree of persistentunobserved heterogeneity is enough to explain the di2erences in AHEAD and thesimulationA comparison is given in Table 13 between median wealth and income by age in the

AHEAD panel and in the baseline simulation The historical cross-cohort data showssharply declining wealth and income with age and a less liquid portfolio with agere4ecting strong cohort e2ects as well as life cycle and selection e2ects The simulationresults which exclude cohort e2ects nevertheless show even more sharply decliningwealth with age and a strong shift toward a more liquid portfolio mix If the simulationis correctly describing portfolio balance of a single cohort over its life course then thereis a strong cross-cohort e2ect with older cohorts starting from retirement portfolios thatare more heavily invested in housing equity and other nonliquid forms The simulatedsemi-interquartile range is narrower than its historical counterpart particularly for olderhouseholds In the simulation variability (de7ned as the ratio of the semi-interquartilerange divided by the median) falls with age whereas in the historical cross-cohortdata variability rises with age This suggests that in addition to cross-cohort e2ectsthat there may be persistent heterogeneity in savings behavior that is not captured inour model

73 Alternative scenarios

Table 12 gives the survival probabilities and prevalences of various health condi-tions under our alternative no-diabetes scenario (S1) and the low-SES scenario (S2)In the no-diabetes simulation the direct mortality risk from diabetes and the incidenceof co-morbidities with diabetes are eliminated although our simulated population willdisplay elevated prevalence of heart disease and stroke at age 70 among former di-abetics Life expectancy at age 70 under this scenario increases from 1436 to 1469years for females and from 1081 to 1126 years for males These rates imply in turnthat a former diabeticrsquos life expectancy increases by 272 years for females and 332years for males Other health condition prevalences that fall in the absence of dia-betes are heart disease stroke cognitive impairment ADL and IADL impairment andpoorfair self-rated health While reduction in mortality risk from one source must as amatter of accounting eventually lead to more deaths from competing risks there areno substantial movements in prevalences of the remaining health conditions

Table 13Wealth and income in AHEAD and in the baseline scenario

Age 70ndash74 75ndash79 80ndash84 85ndash89 90+

AHEAD cross-cohort dataTotal wealth (000)

1st quartile 6438 4692 3276 1405 217Median 14404 11276 9435 7134 40133rd quartile 31427 24268 20320 18591 11793

Non-liquid wealth (000)1st quartile 4772 2820 1081 086 000Median 9494 8048 6201 4419 5443rd quartile 17896 15168 11388 10912 6547

Liquid wealth (000)1st quartile 218 131 054 033 000Median 2619 1597 1189 973 5403rd quartile 9821 7093 7093 5531 3783

Income (000)1st quartile 1415 1197 976 868 674Median 2278 1959 1526 1377 9763rd quartile 3492 3165 2806 2510 1529

Baseline simulation dataTotal wealth (000)

Non-liquid wealth (000)1st quartile 4272 3739 1756 297 minus377Median 9153 7434 4713 2917 21213rd quartile 17134 11809 7890 5544 4507

The alternative low-SES scenario reduces our entire age 70 simulated population tothe bottom quartile for wealth and income gives them less than a high school edu-cation and places them in a dwelling in poor condition in an unsafe neighborhoodThey are kept in this low-SES status for the remainder of their lives ie there is noopportunity in this simulation for households to escape low SES by a lucky changein wealth or income However our population displays the patterns of prevalence ofhealth conditions established in their earlier lives with their historical SES status Thisscenario is quite arti7cial but it demonstrates the holistic e2ect on the broad spectrumof health conditions of low SES Life expectancies at age 70 in this scenario dropdramatically from 1436 to 1227 years for females and from 1081 to 956 years

for males Prevalences of cancer heart disease lung disease diabetes arthritis in-continence hip fractures cognitive impairment psychiatric disease and depression allincrease sharply as do the number of ADL and IADL impairments Conditions whoseprevalence is not a2ected substantially by low SES are stroke high blood pressureand falls These results indicate that if the associations of SES and incidence of healthconditions that we 7nd in AHEAD were entirely the result of direct causal links fromwealth to health then the protective e2ect of the prevailing pattern of higher SESis 126ndash208 years of added life expectancy Thus our 7ndings that for most healthconditions the evidence is against direct causal links from SES to incidence do notappear to rule out a substantial cumulative e2ect of SES over conditions and time thatinduce a noticeable SES gradient in mortality Given our speci7c 7ndings against directcausal links from SES to incidence of acute conditions and mortality the most obviouspossible source for this gradient are SES-linked di2erences in genetic susceptibilityand behaviorWe have emphasized that our stylized hypothetical policy intervention and the

changes in health they produce over the life course are strictly illustrative and shouldbe interpreted with great caution These 7nger exercises cannot be used to draw conclu-sions about any real policy initiatives This is particularly true since we have includedwithin our model system components that fail the invariance tests that we have em-phasized must be met by a valid policy model and because in many cases our modelsdisplay some wealth or income gradients for incidence that we cannot with our sta-tistical methods identify as the sole result of direct causal links While most of thesee2ects are not statistically signi7cant it is possible that in a larger or longer panel withgreater statistical power they will prove to be signi7cant Then it is essential to turnto the more advanced statistical methods of Heckman (2001) and others to identify thedirect causal components in these incidence associations and improve the models toachieve invariance Only after this is done and realistically detailed policy scenariosare considered could policy makers take our model system seriously as a policy toolHowever we believe that our results do demonstrate that it would be useful for healthpolicy analysis to utilize a system of invariant models with a causal chain structureto simulate policy impacts in a framework that takes into account indirect impactscompeting hazards and direct causal links between SES and health We believe thatanalysis of the broad sweep of co-morbidities and wealth e2ects over the life courseis an important complement to the disease-centric orientation of many medical andepidemiological studies of health outcomes

8 Summary and speculations for further research

This paper has used innovations in health conditions and in wealth in the AHEADpanel to carry out tests for the absence of direct causal links from SES to health andfrom health conditions to wealth By advancing beyond the detection of associationto a framework in which there is some possibility of detecting the absence of causallinks this paper provides a methodology that may be useful in winnowing the listof possible direct causal mechanisms or delimiting their domain of action For the

AHEAD sample a panel of US elderly age 70 and older in 1993 we concludegenerally that for mortality and for acute sudden-onset diseases the hypothesis of nocausal link from SES is accepted and for incidence of mental problems the hypothesisis rejected The results for chronic and degenerative diseases are mixed We generallyreject the hypothesis of no direct causal link from health conditions to total wealthchanges but cannot rule out confounding of the test by invariance failuresThe pattern of results suggests that incidence of acute sudden onset health con-

ditions conditioned on existing health conditions does not exhibit a signi7cant SESgradient while incidence of some mental chronic and degenerative conditions appearto have an association to SES due to some combination of direct causal links andcommon unobserved behavioral or genetic factors The results suggest that there maybe an SES gradient in seeking treatment for the second class of conditions whichmay in4uence detection or for maintaining preventative regimens that may maintainsome conditions below the reporting thresholds Our 7ndings are not inconsistent withthe possibility that for mental and chronic illnesses where the acute care procedurescovered by Medicare are often inapplicable ability to pay may be a causal factor inseeking and receiving treatment We do not 7nd systematic persuasive associations ofhealth conditions and changes in total wealth except for surviving spouses Problemsin measuring and modeling wealth changes suggest caution in concluding from theseresults that there is generally no direct causal link from health conditions to wealthchangesWe emphasize that our results apply only to elderly individuals in the US where

Medicare and Medicaid programs limit out-of-pocket medical costs particularly foracute care and where retired status eliminates a possible direct causal link from healthstatus to ability to work Further in an elderly population common factors may bemanifest in prior health conditions and economic status so they have little impact onceincidence is conditioned on prior state Our results provide no evidence on the natureof the causal links at younger ages during the stages of life where association of healthand wealth is emerging as a consequence of some causal structureFuture waves of the AHEAD (HRS) panel will allow the hypotheses of invariance

and non-causality to be tested with greater power This will particularly be the casewhen full tracking of decedents and determination of cause of death from medicalrecords become part of the data It seems likely that some of the associations we havefound between changes in health and wealth will survive more detailed analysis andthat suitably de7ned natural or designed experiments are likely to be needed to fullyunravel the causal structure underlying these associationsThe modeling structure used in this paper is parametric and the high dimensionality

of the vector of possible explanatory variables and the relatively limited informationcontained in binomial outcomes in the AHEAD panel make it diKcult to move to amore robust non-parametric analysis However we have been 4exible in specifying thevariable transformations that appear in our models and we interpret our analysis asconforming in spirit if hardly in fact to a method of sieves approach to non-parametricanalysis One of the major limitations of our models which would be likely to leadthem to fail invariance tests in situations where a sharp test is possible is that theydo not account adequately for the multiple risk structure of health conditions and its

implications for the duration patterns that can emerge particularly over the relativelylong intervals between waves Some outcomes such as mortality and non-fatal heartdisease are competing risks while others like diabetes and heart conditions are com-plementary risks For future research we are investigating hidden Markov modelsin which a latent vector of propensities for all health and SES conditions followsa 7rst-order Markov process conditioned on demographic state and all possible causallinks across the components of this latent vector appear in the model Given thresh-olds that trigger observed states this model provides a consistent but computationallydemanding data generation process for the vector of Markov states month-by-monthWithin this model it is possible to carry out joint tests for the absence of classes ofcausal links The next wave of this research incorporating wave 4 of AHEAD willinclude full development of 4exible multiple-risk duration models

Acknowledgements

We gratefully acknowledge 7nancial support from the National Institute on Agingthrough a grant to the NBER Program Project on the Economics of Aging TiagoRibeiro acknowledges support from scholarship PRAXIS XXIBD1601498 from thePortuguese Funda[cao para a Ciencia e a Tecnologia We thank Laura Chioda VictorFuchs Rosa Matzkin James Poterba and Jim Powell for useful comments

References

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Alessie R Lusardi A Kapteyn A 2000 Savings after retirement evidence from three di2erent surveysLabour Economics 6 (2) 277ndash310

Angrist J Imbens G Rubin D 1996 Identi7cation of causal e2ects using instrumental variables Journalof the American Statistical Association 91 444ndash472

Attanasio O Hoynes H 1995 Di2erential mortality and wealth accumulation National Bureau ofEconomic Research Working Paper No 5126

Backlund E Sorlie P Johnson N 1999 A comparison of the relationships of education and income withmortality the national longitudinal mortality study Social Science and Medicine 49 1373ndash1384

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Barsky R Juster T Kimball M Shapiro M 1997 Preference parameters and behavioral heterogeneityan experimental approach in the health and retirement survey Quarterly Journal of Economics 112537ndash579

Bosma H Marmot MG Hemingway H Nicholson AC Brunner E Stansfeld SA 1997 Low jobcontrol and risk of coronary hear disease in Whitehall II (prospective cohort) study British MedicalJournal 314 558ndash565

Chandola T 1998 Social inequality in coronary heart disease a comparison of occupational classi7cationsSocial Science and Medicine 47 525ndash533

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Chapman K Hariharran G 1994 Controlling for causality in the link from income to mortality Journalof Risk and Uncertainty 8 (1) 85ndash93

Chay K Greenstone M 2000 Does air quality matter Evidence from the housing market Journal ofPolitical Economy forthcoming

Davey-Smith G Blane D Bartley M 1994 Explanations for socio-economic di2erentials in mortalityevidence from Britain and elsewhere European Journal of Public Health 4 131ndash144

Dawid A 2000 Causal inference without counterfactuals Journal of the American Statistical Association95 407ndash448

Dohrenwend B et al 1992 Socioeconomic status and psychiatric disorders the causationndashselection issueScience 255 946ndash952

Drever F Whitehead M 1997 Health Inequalities ONS LondonEcob R Smith G 1999 Income and health what is the nature of the relationship Social Science and

Medicine 48 693ndash705Elo I Preston S 1996 Educational di2erentials in mortality United States 1979ndash85 Social Science and

Medicine 42 (1) 47ndash57Engle R Hendry D Richard J 1983 Exogeneity Econometrica 51 277ndash304Ettner S 1996 New evidence on the relationship between income and wealth Journal of Health Economics

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Socio-Economic Classi7cation Health Statistics Quarterly 2 33ndash40Fitzpatrick R Bartley M Dodgeon B Firth D Lynch K 1997 Social variations in health relationship

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Freedman D 2001 On specifying graphical models for causation and the identi7cation problem WorkingPaper Department of Statistics University of California Berkeley

Fuchs V 1993 Poverty and health asking the right questions In Rogers D Ginzberg E (Eds) MedicalCare and the Health of the Poor Westview press Boulder pp 9ndash20

Geweke J 1984 Inference and causality in economic time series models In Griliches Z Intriligator M(Eds) Handbook of Econometrics Vol 2 North-Holland Amsterdam pp 1101ndash1144

Gill R Robins J 2001 Causal inference of complex longitudinal data the continuous case Annals ofStatistics forthcoming

Goldblatt PO 1990 Longitudinal study Mortality and Social Organization HMSO LondonGoldman N 1994 Social factors and health the causationndashselection issue revisited Proceedings of the

National Academy of Science 91 1251ndash1255Goldman N 2001 Social inequalities in health disentangling the underlying mechanisms In Weinstein

M Hermalin A (Eds) Strengthening the Dialogue between Epidemiology and Demography Annals ofthe New York Academy of Sciences

Granger C 1969 Investigating causal relations by econometric models and cross-spectral methodsEconometrica 37 424ndash438

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Hendry D Mizon G 1999 The pervasiveness of Granger causality in econometrics In Engle R WhiteH (Eds) Cointegration Causality and Forecasting Oxford University Press Oxford

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Herzog R Wallace R 1997 Measures of cognitive functioning in the AHEAD study Journal ofGerontology Series B 52B 37ndash48

Holland P 1986 Statistics and causal inference Journal of the American Statistical Association 81945ndash960

Holland P 1988 Causal inference path analysis and recursive structural equation models In Clogg C(Ed) Sociological Methodology American Sociological Association Washington (Chapter 14)

Hoover K 2001 Causality in Macroeconomics Cambridge University Press CambridgeHumphries K van Doorslaer E 2000 Income related health inequality in Canada Social Science and

Medicine 50 (5) 663ndash671Hurd M 1987 Savings of the elderly and desired bequests American Economic Review 77 298ndash312Hurd M McGarry K 1997 Evaluation of the subjective probabilities of survival in the health and

retirement survey Journal of Human Resources 30 S268ndashS292Hurd M Wise D 1989 Wealth depletion and life cycle consumption by the elderly In Wise D (Ed)

Topics in the Economics of Aging University of Chicago Press ChicagoHurd M McFadden D Gan L 1998a Subjective survival curves and life cycle behavior In Wise D

(Ed) Inquiries in the Economics of Aging University of Chicago Press ChicagoHurd M McFadden D Gan L Merrill A Roberts M 1998b Consumption and savings balances of the

elderly experimental evidence on survey response bias In Wise D (Ed) Frontiers in the Economicsof Aging University of Chicago Press Chicago pp 353ndash387

Kaplan J Manuck S 1999 Status stress and arteriosclerosis the role of environment and individualbehaviour In Adler N et al (Eds) Socioeconomic Status and Health in Industrialized Nations Annalsof the New York Academy of Science 896 145ndash161

Karasek RA Theorell T Schwartz J Schnell P Peiper C Michela J 1988 Job characteristics inrelation to the prevalence of myocardial infarction in the US Health Examination Survey (HES) and theHealth and Nutrition Examination Survey (NHANES) American Journal of Public Health 78 910ndash918

Kelley S Hertzman C Daniels M 1997 Searching for the biological pathways between stress and healthAnnual Review of Public Health 18 437ndash462

Kitagawa E Hauser P 1973 Di2erential mortality in the United States a study In SocioeconomicEpidemiology Harvard University Press Cambridge MA

Kunsch H Geman S Kehagias A 1995 Hidden Markov random 7elds Annals of Applied Probability5 577ndash602

Lewis G Bebbington P Brugha T Farell M Gill B Jenkins R Meltzer H 1998 Socioeconomicstatus standard of living and neurotic disorder Lancet 352 605ndash609

Marmot M et al 1991 Health inequalities among British civil servants the Whitehall II study Lancet337 1387ndash1393

Marmot M Bobak M Davey-Smith G 1995 Explanations for social inequalities in health In AmickB et al (Ed) Society and Health Oxford University Press Oxford

Marmot M Bosma H Hemingway H Brunner E Stansfeld S 1997 Contribution of job control andother risk factors to social variations in coronary heart disease incidence Lancet 350 235ndash239

McDonough P Duncan G Williams D House J 1997 Income dynamics and adult mortality in theUnited States American Journal of Public Health 87 1476ndash1483

Meer J Miller D Rosen H 2001 Exploring the healthndashwealth nexus Princeton University WorkingPaper

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Pearl J 2000 Causality Models Reasoning and Inference Cambridge University Press Cambridge MAPower C Matthews S 1998 Accumulation of health risks across social groups in a national longitudinal

study In Strickland S Shetty P (Eds) Human Biology and Social Inequality Cambridge UniversityPress Cambridge

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Preston S Taubman P 1994 Socioeconomic di2erences in adult mortality and health status InMartin L Preston S (Eds) Demography of Aging National Academy Press Washingtonpp 279ndash318

Robins J 1999 Association causation and marginal structural models Synthese 121 151ndash179Rodgers B 1991 Socio-economic status employment and neurosis Social Psychiatry and Psychiatric

Epidemiology 26 104ndash114Ross C Mirowsky J 2000 Does medical insurance contribute to socioeconomic di2erentials in health

The Millbank Quarterly 78 291ndash321Schnall P Landsbergis P Baker D 1994 Job strain and cardiovascular disease Annual Review of Public

Health 15 381ndash411Seeman T Singer B Love G Levy-Storms L 2002 Social relationships gender and allostatic load

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and Statistics 57 155ndash163Sims C 1972 Money income and causality American Economic Review 62 540ndash552Smith J 1998 Socioeconomic status and health American Economic Review 88 192ndash196Smith J 1999 Healthy bodies and thick wallets the dual relation between health and economic status

Journal of Economic Perspectives 13 145ndash166Smith J Kington R 1997a Race socioeconomic status and health in late life In Martin L Soldo

B (Eds) Racial and Ethnic Di2erences in the Health of Older Americans National Academy PressWashington pp 106ndash162

Smith J Kington R 1997b Demographic and economic correlates of health in old age Demography 34(1) 159ndash170

Sobel M 1997 Measurement causation and local independence in latent variable models In Berkane M(Ed) Latent Variable Modeling and Applications to Causality Springer Berlin

Sobel M 2000 Causal inference in the social sciences Journal of the American Statistical Association 95647ndash651

Soldo B Hurd M Rodgers W Wallace R 1997 Asset and health dynamics among the oldest old anoverview of the AHEAD study Journal of Gerontology Series B 52B 1ndash20

Staiger D Stock J 1997 Instrumental variables regression with weak instruments Econometrica 64556ndash586

Stern J 1983 Social mobility and the interpretation of social class mortality di2erentials Journal of SocialPolicy 12 27ndash49

Swert W 1979 Tests of causality In Brunner K Meltzer A (Eds) Three Aspects of Policy andPolicymaking North-Holland Amsterdam pp 55ndash96

US Census 1999 National Vital Statistics Reports United States Life Tables 1997 Vol 47 (28)Wadsworth M 1991 The Imprint of Time Childhood History and Adult Life Clarendon Press Oxford

Whitehead M 1988 The Health Divide Penguin LondonWilkinson R 1998 Equity social cohesion and health In Strickland S Shetty P (Eds) Human Biology

and Social Inequality Cambridge University Press CambridgeWoodward J 1999 Causal interpretation in systems of equations Synthese 212 199ndash247Woodward M Shewry M Smith C Tunstall-Pedoe H 1992 Social status and coronary heart disease

results from the Scottish Heart Health Study Preventive Medicine 21 136ndash148Zellner A 1979 Causality and econometrics In Brunner K Meltzer A (Eds) Three Aspects of the

Policy and Policymaking North-Holland Amsterdam pp 9ndash54

Healthy wealthy and wise Tests fordirect causal paths between health andsocioeconomic status
- Introduction
- - The issue
  - This study
  - - Association and causality in panel data
    - - Testing causality
      - Some specific formulations
      - Measurement issues
      - The AHEAD panel data
        
        Sample characteristics
        
        Descriptive statistics
        
        Constructed variables
        
        Measurement of wealth
        
        Mortality and observed wealth change
        
        SES and prevalence of health conditions
        
        
        Models of association
        
        Relative risk
        
        Incidence of health conditions and tests for causality in the AHEAD panel
        
        Models of incidence
        
        Causality tests
        
        Tests for non-causality from health status to asset accumulation
        
        Models of incidence
        
        Causality tests
        
        Simulation of life courses under counterfactual conditions
        
        The simulation experiment
        
        Baseline simulation
        
        Alternative scenarios
        
        Summary and speculations for further research
        
        Acknowledgements
        
        References

Page 2: Healthy, wealthy, and wise? Tests for direct causal paths ...people.tamu.edu/~ganli/publicecon/adams03.pdf · Journal of Econometrics 112 (2003) 3–56 Healthy, wealthy, and wise?