Semiparametric Analysis of Wealth-Age Profiles

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2 Semparametrc Analyss of Wealth-Age Profles Joon W. Nahm Professor of Economcs, Sogang Unversty, S. Korea. Robert F. Schoen Research Assocate Professor, Insttute for Socal Research Assocate Professor of Economcs and Publc Polcy, Unversty of Mchgan May 2006 Populaton Studes Center Research Report

3 Semparametrc Analyss of Wealth-Age Profles Page 2 Abstract Gven the mportance of the shape of the wealth-age profle for the lfe cycle model, and the fact that the theory does not mply a specfc functonal form, we argue that a non-parametrc estmaton strategy s deal. Nonparametrc profles and semparametrc partal lnear models ndcate that typcal parametrc representatons can be msleadng. Moreover, we fnd that after accountng for year effects, there are strong and clear patterns of wealth accumulaton through the md-50s, flat wealth holdngs durng the late 50s and md-60s, followed by decumulaton durng the rest of the lfe cycle, whch s consstent wth predctons of the lfe cycle model.

4 Semparametrc Analyss of Wealth-Age Profles Page 3 1. Introducton Asset accumulaton and decumulaton are central to the lfe cycle theory of consumer behavor. A tenet of the lfe cycle model s that assets are accumulated durng the workng years to support consumpton n the retrement years, mplyng asset decumulaton n older ages. Despte the substantal amount of research devoted to establshng whether people actually decumulate assets and the exact shape of the wealth-age profle more generally no conclusve evdence has yet emerged (Hurd, 1990; Attanaso and Hoynes, 2000). The dspartes n fndngs may arse for several reasons, ncludng use of cross-sectonal versus pooled cross-sectonal versus panel data, dfferng tme perods of analyss that may be subject to dfferent perod effects that vary by age, and dfferng assumptons about the parameterzaton of the wealth-age profle (Hurd, 1990; Jappell, 1999). Our contrbuton s on ths last dmenson: allowng a general functonal form n the estmaton of the wealth-age profle. Economc theory does not gve strct gudance about the exact form of the wealth-age profle. And to date only parametrc frameworks have been used to estmate the profle. Whle Jappell (1999) consders quntc terms of age, most studes consder lnear or quadratc regresson specfcatons. For example, Mrer (1979) and Damond and Hausman (1984) consdered lnear functonal forms, Kng and Dcks-Mreaux (1982) consdered a lnear splne, and Burbdge and Robb (1985) specfed quadratc and cubc functonal forms. If the profle s nonlnear, whch prevous studes have shown to be the case, a poor approxmaton of the wealth-age profle by parametrc specfcaton may lead to napproprate conclusons about the extent of wealth accumulaton and decumulaton. We argue that a nonparametrc or semparametrc approach s most approprate snce t does not mpose a functonal form; t allows for a flexble analyss of the data. Usng wealth data collected n the Panel Study of Income Dynamcs startng n 1984, we apply nonparametrc estmaton technques based on kernel smoothng. In addton, a semparametrc partal lnear model s consdered comprsng a nonparametrc and a parametrc component, whch allows one to take nto account control varables. Because the ndvduals ntervewed n any cross-secton belong to dfferent brth cohorts wth dfferent preferences and productvty, we construct cohort data from fve waves of the PSID: 1984, 1989, 1994, 1999, and These data allow us to analyze wealth-age profles for brth cohorts and nvestgate whether the dfferences n profles across cohorts are due to dfferences n productvty or year effects, whle at the same tme contnung to allow for nonparametrc and semparametrc specfcatons of age. In ths paper, Secton 2 descrbes the modelng of the wealth-age profle; Secton 3 presents results from cross-secton data; Secton 4 constructs cohort data from repeated cross-sectonal data and analyzes wealth-age profles for cohorts; and Secton 5 summarzes fndngs. 2. Modelng Framework The basc household wealth model takes wealth as a functon of age and demographc factors. Theory provdes no gudance as to the approprate functonal form to use for estmaton. Moreover, flexble nonparametrc methods cannot be used to help specfy the entre model because there are numerous plausble demographc varables besdes age. Consequently, some modelng restrctons must be mposed.

5 Semparametrc Analyss of Wealth-Age Profles Page 4 Because our prmary nterest s n the wealth-age profle, greatest flexblty s allowed n the effects of age. In partcular, we begn wth a partal lnear model that takes wealth as a general functon of age plus a lnear functon of the qualtatve varables. The semparametrc model s summarzed as: w = g( a ) + z β + ε (1) where w s wealth, a years of age, and ndvdual. We assume ( a, z ) = 0 z denotes the remanng demographc varables for E ε. The functon g a ) has the standard regresson nterpretaton, namely as the wealth-age profle holdng other demographc varables constant. Here, t s assumed that demographc varables have no effect on the shape of the profle, they only shft the profles 1. We estmate g (.) nonparametrcally and dsplay t graphcally. From the assumpton of E( ε a, z ) = 0, E ( w a ) = g a ) + E( z a )β ( (, (2) so that dfferencng equatons (1) and (2) yelds a lnear regresson: ( w a ) = [ z E( z a )] β + ε w E, (3) mplyng that β can be estmated n a two-step procedure as n Robnson (1988). That s, frst the unknown condtonal means, E ( w a ) and E ( z a ), are estmated usng a nonparametrc kernel estmaton technque. Here, because age s observed as dscrete, we estmate the two condtonal means dscretely, n partcular, n = 1 ( a = a) I w ˆ = 1 E( w a) = (4) n I ( a = a) where I (.) denotes an ndcator functon, that s, I ( A) = 1 f event A occurs and I ( A) = 0 otherwse. In ths case, the rate of convergence of kernel estmates to the true regresson curve s n, same as most of the parametrc estmates. Secondly, the nonparametrc estmates, ( ) w a Ê and Ê ( ) z a, are substtuted n place of the unknown functons n equaton (3) and OLS s used to estmate β. Recall that our prmary nterest s n the wealth-age structure, or g a ) n equaton (1). It can be estmated as ( ( w a ) ˆ E( z a )βˆ ˆ g( a ) = ˆ E. (5) 1 Whle fndngs from Hubbard et al. (1995) suggest that wealth accumulaton patterns dffer by educatonal attanment, Burbdge and Robb (1985) found that educaton affects only the heght but not the shape of the wealth-age profle.

6 Semparametrc Analyss of Wealth-Age Profles Page 5 3. PSID Data and Cross-Sectonal Wealth-Age Profles The PSID s deal for estmatng wealth-age profles because t ncludes households of all ages and t has collected wealth data for nearly two decades. Wealth was frst collected n 1984, wth subsequent collectons n 1989, 1994, 1999, and Data from all fve waves are analyzed. Famles are asked to report nformaton on a comprehensve lst of wealth factors. The defnton of net worth ncludes the market value of cash, deposts, bonds, stocks and shares, regstered savngs plans, other fnancal assets, vehcles, owner-occuped houses and other real estate, equty n a busness or farm, less debts of varous knds. It excludes socal securty and penson wealth, consumer durables other than cars, lfe nsurance polces, and other assets such as the expected value of future nhertances and support from relatves or chldren. Dependng on the year of the data, percent of famles have non-postve wealth. All nomnal values are adjusted for nflaton and reported n 2001 dollars (n thousands). PSID famly weghts are used n all analyses. We restrct our attenton to famles n whch the head s age s at least 25 and at most 85 at the tme of survey; samples outsde ths range are qute small. Table 1 shows the mean, standard devaton, and medan of net worth n 1984 by age, martal status, work status, educaton, and race. Patterns and dfferentals for 1984 are smlar to those observed n other years. The frst thng to note s that n the full sample there s substantal heterogenety n the holdngs of wealth n each age group. Standard devatons are large and the mean of net worth s well above the medan, ndcatng that the dstrbuton s substantally skewed to the rght. The data sets on wealth typcally nclude a few observatons wth very large amounts, hence the wealth dstrbuton has long tals and the mean s nosy. As a result, we also report estmates wth the upper and lower 5% of the wealth dstrbuton trmmed n each year. The wealth varable n the trmmed sample also exhbts substantal dsperson and skewness, however, the varance s substantally reduced. The sze and standard devatons of these changes suggest that t s mportant to rely on robust estmators when usng wealth data from mcro data sets. The wealth skewness and the presence of nfluental values suggest that untrmmed mean or OLS regressons may not adequately characterze the wealth-age profle. In vew of robustness crteron of Hampel (1971), the trmmed mean or trmmed LS regressons are more robust to extreme observatons 2. The strkng feature of Table 1 s that for both the full and the trmmed sample, there s clear evdence of a hump-shaped pattern n the mean value of wealth. Wealth accumulaton s rapd n the age range 30-40, reaches a plateau n the pre-retrement phase, and then decumulaton begns sometme n the 60s. The maxmum value of wealth s found n the age bracket There s a puzzlng dp n the mean of wealth for the group aged 60-64, and then wealth rses agan at age range There s a large dfference between the full sample and trmmed sample at ages In the full sample, wealth 2 Jappell(1999) also ponted out ths ssue n estmatng the wealth-age profle of Italan households, where he used quantle regressons.

7 Semparametrc Analyss of Wealth-Age Profles Page 6 holdngs rse n the last part of the lfe cycle. By contrast, n the trmmed sample, elderly n ths age range clearly dssave, hence wealth-age profles from the trmmed sample dsplay the hump-shaped pattern consstent wth lfe cycle predctons. Ths pattern s consstent wth the medan wealth holdngs both from the full sample and the trmmed sample. The dfference between mean holdngs from the full sample and trmmed sample strongly supports the use of the trmmed sample. Breakdowns of wealth holdngs by other demographc categores are also gven n Table 1. The table shows that mean wealth holdngs of marred couples s approxmately two tmes hgher than those of sngles. Wealth vares wdely across educaton groups. Famles n whch the head has a postcollege degree have 2-4 tmes greater total net worth than famles n whch the head s a hgh school drop out. Consstent wth pror lterature, the table shows that mean wealth holdngs of non-black famles are substantally hgher than those of black famles. The next step s to estmate the cross-sectonal wealth model gven by equaton (5). Table 2 reports the semparametrc estmates of β along wth two parametrc results. All of the coeffcents from the parametrc models and semparametrc model have the predcted sgns though not all are sgnfcantly dfferent from zero at conventonal levels n all specfcatons. We checked whether quadratc and cubc parameterzatons are consstent wth the semparametrc estmates usng the statstcs of Aït Sahala, Bckel, and Stoker (1998); the p-value was Consequently, we reject the two parametrc specfcatons aganst the semparametrc partal lnear model. Fgure 1 llustrates the wealth-age profles for each cross-secton: 1984, 1989, 1994, 1999, and In ths fgure, we present some prma face evdence concernng the valdty of a smple verson of lfe cycle hypothess. We examne the dstrbuton of wealth across the lfe cycle nonparametrcally by usng a kernel-smoothng estmator. 3 In partcular, we nvestgate one of the key predctons of ths model, namely, that households run down ther assets n old age. Panel (a) shows nonparametrc wealth-age profles for all sample years before controllng for the demographc varables,.e., the profles represented by Ê ( w a ), and panel (b) shows the profles after controllng for the demographc varables,.e., the profles represented by ˆ g ( a ) n equaton (5). In panel (b) of Fgure 1, n every profle, there exsts a moderately hump-shaped age profle. Whle the wealth-age profles for 1994, 1999, and 2001 have clear hump shapes, the profles for 1984 and 1989 show some plateaus n the range of ages Wealth holdngs at younger ages do not show much dfference across sample years; however the wealth-age profles show vertcal shfts at ages In Fgure 1, the hump-shaped pattern s clearly evdent beyond age 65. On the bass of ths, one mght be tempted to conclude that the elderly reduce ther wealth n order to fnance consumpton after retrement. However, t should be realzed that Fgure 1 s constructed takng nto account only the cross-sectonal aspect of the PSID. Consequently, cohort and age effects are not dsentangled n ths fgure. As underlned by Shorrocks (1975), ths pattern has no mplcatons for the shape of the lfetme profle of wealth ownershp We use a standard normal kernel and set the bandwdth to h = 1.5 SX n where S X denotes the standard devaton of age.

8 Semparametrc Analyss of Wealth-Age Profles Page 7 4. Wealth Profles from Cohorts 4.1. Results for Cohorts For most of the nterestng questons about wealth and the lfe-cycle, t s necessary to track ndvduals or cohorts of households over tme and to observe changes n wealth holdng as people age. The models above confound the age and cohort effects, and t s possble that older cohorts are smply poorer or rcher than younger ones. Thus, n cross-sectonal data, one cannot dentfy both age and cohort effects. In ths secton we track brth cohorts. For each year of data, we track the sample from the same cohort n the subsequent survey. In ths way, we can examne cohort wealth holdngs as the cohort ages. Analyss s restrcted to the trmmed sample, and households headed by persons born before 1920 and after 1959 are excluded because of small sample szes. The fnal sample covers 19,282 households. We dvde the whole sample nto four cohorts; pre-depressoner, depressoner, WWII, and baby boomer. Table 3 reports the year of brth ntervals and the numbers of households n each of these four cohorts. The frst two columns n Table 3 defne each cohort by the year of brth and the next fve columns report the range over whch the age of each cohort s observed n each sample year. Table 4 reports the summary statstcs of wealth for each cohort across age groups. All cohorts hold a substantal amount of wealth. The mean and medan wealth holdngs of depressoner, WWII, and baby boomer cohorts are steadly ncreasng as they age. For the pre-depressoner cohort, wealth holdngs peak at ages and then declne, demonstratng the typcal lfe-cycle pattern, wth the excepton beng the very oldest ages, ages To separate the cohort effect from age effect, equaton (1) can be estmated usng cohort data by regressng the wealth holdngs of households aganst age, demographc varables, and brth cohort dummes. Most studes regardng cohort effects, for example Deaton and Paxson (1994) among others, assume the shapes of wealth-age profles are the same across dfferent cohorts. However, the savng behavor of households may be dfferent across the cohorts. Indeed, the assumpton of common age effects across cohorts was rejected n our sample, therefore we allow cohorts to have dfferent wealthage profles. Therefore, for each cohort, the result after controllng demographc varables can be gven an explct lfe-cycle nterpretaton by estmatng equaton (3), and the results are gven n Table 5. 6 Although the szes are somewhat dfferent across cohorts, each cohort has the same expected sgns of coeffcents on the control varables. Fgure 2, panels (a) and (b), show nonparametrc wealth-age profles across cohorts before and after controllng for the demographc varables, respectvely. In panel (b), the profles for each cohort are shown to have smlar shapes, wth the profle for the pre-depressoners havng the smaller ntercept and maxmum wealth holdngs attaned at around age 73. All cohorts have smlar rates of growth n wealth untl age 73. The lesson from Fgure 2 s that the wealth-age profle has a clear hump-shaped pattern whch supports the standard lfe-cycle hypotheses. Wealth s accumulated throughout the lfe and then decumulated after roughly age Agan, we conduct tests for quadratc and cubc models and reject the two parametrc specfcatons aganst the semparametrc one. Heren, we do not report the results for parametrc models; the results are avalable from the authors upon request.

9 Semparametrc Analyss of Wealth-Age Profles Page 8 To evaluate whether there s a dsparty between parametrc methods and the semparametrc method, the semparametrcally estmated wealth-age profles for each cohort are presented together wth 95% confdence bands and two parametrc curves n Fgure 3. The parametrc curves provde an adequate representaton of the wealth-age relatonshp for the baby boomer cohort. However, for the other cohorts, the approxmatons are poor. Especally for pre-depressoner, the parametrc curve does not capture the hump-shaped pattern that exsts between the late 60 s and late 70 s. In general, the wealth-age relatonshp becomes hghly non-lnear at older ages, and parametrc representatons msrepresent ths relatonshp. For example, for the predepressoners, the quadratc profles mply that wealth contnues to be accumulated at least through age 80, whle the semparametrc estmates show clear evdence of decumulaton begnnng around age The Next Generatons: Rcher or Poorer? Table 4 provdes estmates of the age-adjusted rankng of the wealth holdngs across cohorts at the same age level. For most age groups, the pre-depressoner cohort has the lowest holdngs, followed by the depressoner cohort, wth the WWII cohort the rchest among these three cohorts. Ths may be due to the fact that subsequent generatons have been more productve than ther predecessors, so that, at the same age, the profles of younger generatons le above the profles of older generatons. At the same tme, the baby-boomer cohort does not appear to be wealther than earler cohorts. Ths rankng s clearer f we look at profles dsplayed n Fgure 2. In Fgure 2, the vertcal shfts of one curve to the other curves are due to cohort effects, and the general shape of the curves represents the process of wealth accumulaton/decumulaton as people age. From Fgure 2, both before and after controllng for the demographc varables, we confrm the above stylzed facts. In Fgure 2 (a) and (b), the vertcal shft of wealth profles from pre-depressoner cohort to the other cohorts s due to the productvty effect; that s, younger cohorts are rcher n lfetme wealth than the older cohort. The ncreasng wealth shows up n the profles as a pronounced vertcal shft, or cohort effect, as we move from one cohort to the next. Another feature of Fgure 2, partcularly panel (b), s that there are no clear dfferences n vertcal ntercepts among the profles of the three most recent cohorts: depressoner, WWII, and baby boomer cohorts. Ths pattern s consstent wth no dfferental productvty across cohorts. However, the lack of dfference could also be drven by dfferences n year effects across cohorts. If a certan year or perod experenced a boom n the stock market, and certan brth cohorts have fortunate tmng n wealth prolferaton, then the year effect may pck up cohort and age effects. To control for the year effect, we add year dummes to the model (Table 6). Here, the predepressoner cohort has the strongest year effects among the four groups and the recent sample year has the strongest year effects n all groups. The ˆ( g a ) profles from these models are drawn n Fgure 4. When we control for year effects n addton to demographc effects, all the profles shft downward and the slopes are much flatter, especally at the older ages. In partcular, the profle for the pre-depressoner cohort has a negatve slope after about age 63, wth a clear pattern of dssavng after age 63. The other feature of Fgure 4 s that the profles for three of the cohorts depressoner, WWII, and baby boomer le on top of each other, wth a clear vertcal shft between the pre-depressoner cohort

10 Semparametrc Analyss of Wealth-Age Profles Page 9 and the three remanng cohorts. 7 The general shape of profles n Fgure 4 shows the hump-shaped pattern. 5. Summary and Concluson The goal of ths paper s to assess the valdty of the lfe-cycle model of wealth by estmatng the wealth-age profle. To avod a pror judgments on whether the elderly actually save or dssave, we employed a nonparametrc estmaton method. Snce t does not mpose a functonal form, ths method allows flexblty n the wealth-age profle throughout the lfe course. We fnd that the added flexblty s qute mportant. Conclusons about the extent of accumulaton and decumulaton as well as the age at whch decumulaton begns, depend to a large degree on functonal form assumptons. In cross-secton studes, the wealth-age profles have a clear hump-shaped pattern, wth an excepton at the very oldest ages. Because the ndvduals n any cross-secton belong to dfferent cohorts, the estmated cross-sectonal wealth-age profles may be msleadng to the actual wealth-age profles. Constructng cohort data, the pattern of wealth accumulaton conforms reasonably well to the predctons of the lfe-cycle model. The hump-shaped pattern s clear, wth most wealth accumulaton occurrng by young and the mddle-age famles; the wealth profle has a peak at around 73, and then at the last stage of lfe assets are decumulated. The oldest cohort - the predepressoners - experenced partcularly large gans n the 1990s through Ignorng these unque gans would lead to erroneous conclusons about the lfe cycle profle of wealth holdngs. That s, after accountng for year effects n the semparametrc models, there are strong and clear patterns of wealth accumulaton through the md-50s, flat wealth holdngs durng the late 50s and md-60s, followed by decumulaton durng the rest of the lfe cycle. Ths pattern s consstent wth predctons of the lfe cycle model. Despte unque lfetme economc, socal, and demographc experences across brth cohorts, the data ndcate that three of the cohorts depressoners, WWII, and baby boomers have almost dentcal lfe cycle wealth holdngs, at least through the common lfe cycle stages covered by the PSID. It s only the predepressoners who dverged; ths cohort had lower wealth, and ths gap perssted wth controls for demographc and year effects. 7 In a recent unpublshed paper, Gottschalk and Muynh (2005) shows that economc growth led to hgher mean earnngs for recent cohorts but the dstrbuton of yearly earnngs became less equal. As a result, the average worker had hgher long-run earnngs than members of prevous cohorts. However, f the gans from growth were more than offset by the ncrease n nequalty of earnngs durng 1980s, those at bottom of the dstrbuton of long-run earnngs mght actually have had lower accumulated earnngs than prevous cohorts.

11 Semparametrc Analyss of Wealth-Age Profles Page 10 References Aït-Sahala, Y., P. Bckel and T. Stoker (1998), Goodness-of-Ft Tests for Regresson Usng Kernel Methods, MIT Sloan School of Management Workng Paper No Attanaso, O. and H. Hoynes (2000), Dfferental Mortalty and Wealth Accumulaton, Journal of Human Resources 35(1), Burbdge, J. and A. Robb (1985), Evdence on Wealth-Age Profles n Canadan Cross-Secton Data, Canadan Journal of Economcs 18(4), Daves, J. (1981), Uncertan Lfetme, Consumpton and Dssavng n Retrement, Journal of Poltcal Economy 89, Deaton, A. and C. Paxson (1994), Savng, Growth, and Agng n Tawan, n Studes n the Economcs of Agng, ed. by Davd Wse: NBER, Damond, P. and J. Hausman (1984), Indvdual Retrement and Savngs Behavor, Journal of Publc Economcs 23, Gottschalk, P. and M. Huynh (2005), Changes n the Dstrbuton of Long-Run Earnngs and Retrement Incomes-Have Recent Cohort Fallen Behnd? CRP WP Gouskova, E., F. Juster and F. Stafford (2003), Trends and Turbulence: Allocatons and Dynamcs of Amercan Famly Portfolos, , Paper for Presentaton at the Levy Insttute Conference. Hampel, F. (1971), A General Qualtatve Defnton of Robustness, Annals of Mathematcal Statstcs, Härdle, W. and T. Stoker (1989), Investgatng Smooth Multple Regresson by the Method of Average Dervatves, Journal of Amercan Statstcal Assocaton, 84, Hubbard, R., J. Sknner and S. Zeldes (1995), Precautonary Savng and Socal Insurance, Journal of Poltcal Economy 103(2), Hurd, M. (1987), Savngs of the Elderly and Desred Bequests, Amercan Economc Revews 77(3), Hurd, M. (1990), Research on the Elderly: Economc Status, Retrement, and Consumpton and Savng, Journal of Economc Lterature 28(2), Hurst, E., M. Luoh, F. Stafford, and W. Gale (1998), The Wealth Dynamcs of Amercan Famles, , Brookngs Papers on Economc Actvty, Jappell, T. (1999), The Age-Wealth Profle and the Lfe-Cycle Hypothess: A Cohort Analyss wth a Tme Seres of Cross-Sectons of Italan Households, Revew of Income and Wealth 45(1), Kng, M. and Dcks-Mreaux, L. (1982), Asset Holdng and the Lfe Cycle, Economc Journal 92, Lupton, J. and F. Stafford (2000), Fve Years Older: Much Rcher or Deeper n Debt? Manuscrpt. Mrer, T. (1979), The Wealth-Age Relaton among the Aged, Amercan Economc Revew 69(3), Robnson, P. (1988), Root-N-Consstent Semparametrc Regresson, Econometrca, 56, Shorrocks, A. (1975), The Age-Wealth Relatonshp: A Cross-Secton and Cohort Analyss, Revew of Economcs and Statstcs 57,

12 Semparametrc Analyss of Wealth-Age Profles Page 11 Fgure 1. Semparametrc Estmaton of Cross-Secton Wealth-Age Profles

13 Semparametrc Analyss of Wealth-Age Profles Page 12 Fgure 2. Wealth-Age Profles: Cohort Analyss

14 Semparametrc Analyss of Wealth-Age Profles Page 13 Fgure 3. Estmated Wealth-Age Profles wth 95% Confdence Bands for Each Cohort

15 Semparametrc Analyss of Wealth-Age Profles Page 14 Fgure 4. Wealth-Age Profles: After Controllng Demographc and Year Effects

16 Semparametrc Analyss of Wealth-Age Profles Page 15 Table 1. Dstrbuton of Wealth, 1984 (Thousands of 2001 dollars) Full sample Trmmed sample % n Sample (weghted) Mean Std. Dev. Medan Mean Std. Dev. Medan Total , Age of head 25 to to , to , to , to , to , to , to , to , to , to , to , Martal status Marred couple , Sngle male Sngle female Work Work for others , Work for self , Educaton of head Hgh school Dropout Hgh sch. degree , College degree , Post col. degree , Race of head Black Non-black , Total observatons 6,088 5,480

17 Semparametrc Analyss of Wealth-Age Profles Page 16 Table 2. Wealth-Age Profle Estmates: Cross Secton for 1984 Varable Quadratc Cubc Semparametrc Constant ** (0.051) ** (0.053) Sngle male ** (4.795) ** (5.013) ** (4.906) Sngle female ** (3.460) ** (3.525) ** (3.422) Work-self ** (4.997) ** (4.913) ** (4.868) Hgh school dploma ** (3.523) ** (3.565) ** (3.517) College degree ** (5.225) ** (5.252) ** (5.206) Post-college degree ** (6.919) ** (6.839) ** (6.758) Black ** (5.189) ** (5.124) ** (3.769) # of chldren ** (1.560) (1.618) (1.658) Age 2.945** (0.249) ** (0.574) Age squared * (0.003) 0.225** (0.017) Age cubc ** (0.000) 2 R Standard errors n parentheses. * Sgnfcant n 10% sgnfcance level. ** Sgnfcant n 5% sgnfcance level.

18 Semparametrc Analyss of Wealth-Age Profles Page 17 Table 3. Desgn of Trmmed Cohort Sample Age of Year of brth cohort n 1984 Predepressoner (719) Depressoner (724) WWII (1145) Baby boomer (2094) Age of cohort n (650) (669) (1039) (1994) Age of cohort n (595) (607) (999) (1844) Age of cohort n (412) (442) (766) (1328) Age of cohort n (400) (457) (809) (1589) Total (2776) (2899) (4758) (8849) Number of observatons reported n parentheses n each cell.

19 Semparametrc Analyss of Wealth-Age Profles Page 18 Table 4. Wealth Dstrbuton of Cohorts (Thousands of 2001 dollars) Pre-depressoner Depressoner WWII Baby boomer Year of brth Mean S.D. Medan Mean S.D. Medan Mean S.D. Medan Mean S.D. Medan Age of head 25 to to to to to to , to , to , , , to , , to , , to , to , Total , ,

20 Semparametrc Analyss of Wealth-Age Profles Page 19 Table 5. Semparametrc Estmaton of Wealth-Age Profle for Cohorts Varable Predepressoner Depressoner WWII Baby boomer Sngle male ** (15.592) ** (14.271) ** (7.640) ** (3.059) Sngle female ** (9.041) ** (9.353) ** (6.238)) ** (2.617) Work-self ** (15.828) ** (11.879) ** (6.982) ** (3.584) Hgh school dploma ** (9.151) ** (9.390) ** (6.733) ** (3.038) College degree ** (15.758) ** (14.945) ** (8.333) ** (3.753) Post-college degree ** (16.971) ** (14.473) ** (8.814) ** (4.647) Black ** (12.142) ** (11.141) ** (7.092) ** (2.519) # of chldren (11.119) ** (6.699) ** (2.686) * (0.975) 2 R Standard errors n parentheses. * Sgnfcant n 10% sgnfcance level. ** Sgnfcant n 5% sgnfcance level.

21 Semparametrc Analyss of Wealth-Age Profles Page 20 Table 6. Semparametrc Estmaton wth Year Effect Varable Predepressoner Depressoner WWII Baby boomer Sngle male ** (15.328) ** (14.247) ** (7.638) ** (3.060) Sngle female ** (8.899) ** (9.343) ** (6.238)) ** (2.622) Work-self ** (15.649) ** (11.853) ** (6.982) ** (3.587) Hgh School dploma ** (8.997) ** (9.372) ** (6.744) ** (3.042) College degree ** (15.518) ** (14.920) ** (8.366) ** (3.760) Post-college degree ** (16.746) ** (14.446) ** (8.844) ** (4.652) Black ** (11.935) ** (11.122) ** (7.092) ** (2.522) # of chldren (10.935) ** (6.681) (2.688) (0.975) Year ** (16.061) (16.374) (10.596) (4.408) Year ** (23.232) (23.263) (14.772) (6.234) Year ** (29.391) ** (29.087) (18.336) (7.755) Year ** (30.782) ** (30.193) (18.988) 1.239* (8.051) 2 R Standard errors n parentheses. * Sgnfcant n 10% sgnfcance level. ** Sgnfcant n 5% sgnfcance level.

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