Munich Personal RePEc Archive
The black-white gap in non marital fertility education and mates in
segmented marriage markets
Stone, Joe A.
2 January 2012
Online at https://mpra.ub.uni-muenchen.de/35763/
MPRA Paper No. 35763, posted 06 Jan 2012 02:48 UTC
Th e Bla ck-W h ite Ga p in N o n Ma rita l Fe rtility
Education an d Mates in Segm en ted Marriage Markets J oe A. Ston e
Departm ent of Econ om ics Un iversity of Oregon
J an uary 2, 20 12 Abs tra ct
This study is the first to fin d that m ate availability explain s m uch of the race gap in n on m arital fertility in the Un ited States. Both a gen eral an d an education -based m etric have stron g effects. The n ovel statistical power arises from differen ce-in - differen ces for blacks an d whites, m ultiple cohorts, periods, an d coefficien t restriction s con sisten t with both the data and m odels in which differen ces in m ate availability can in duce blacks an d whites to respon d in opposite direction s to changes in m ate availability. Results are robust to several altern ative specification s an d tests an d appear relevan t where m arriages are segm en ted alon g racial, religious, or other lin es.
J EL Categories A10 J 12 J 13.
Keywords race m arriage, fertility, education
Ove rvie w
Non m arital birth shares, the shares of n on m arital births in total births, are m uch higher for blacks than for whites in the U. S., but have in creased for both. Man y explan ation s—econ om ic, political, legal, biological, and cultural have been proposed, gen eratin g volum in ous eviden ce for the effects of various public policies on fem ale headship an d n on m arital fertility.1 There is m uch less direct eviden ce to explain the pron oun ced race differen tial in n on m arital fertility. Wilson (198 7), Willis (1999), Brien (1997), an d others em phasize m ate availability, relative resources, education , an d other factors, but our eviden ce is the first to con firm that m etrics of m ate availability explain m uch of the race differen ce in n on m arital birth shares (NBS). Brien (1997) suggests that prior weak results, as in South an d Lloyd (1992), arise from m easurem en t error in locale-specific data, as com pared to use of state-aggregate data, but state-aggregate estim ates can also have weak power, perhaps because variation s tend to be com m on ly shared, leavin g little between -state variation an d low power in estim ation . The stron gest eviden ce to date for the role of m ate availability in n on m arital fertility does n ot apply directly to the black-white gap an d is drawn from idiosyn cratic sources of variation , such as prison in carceration rates (Charles and Luoh, 20 0 6), WWI m ilitary deaths (Fran ce Abram itzky et. al., 20 10 ), an d sex ratios am on g secon d- an d third-generation im m igran ts in the Un ited States (An grist, 20 0 1).
H ere, we focus directly on the race gap in n on m arital fertility. The n ovel stren gth of our estim ates is largely due to a differen ce-in -differen ces specification for blacks an d whites, m ultiple birth cohorts an d periods, an d coefficien t restriction s con sisten t with both the data an d theory. We assess robustn ess in several ways, e.g. by usin g altern ative
1For example, Gray et al (2006) and Moffitt (2000)
age ran ges for cohort variables, in clusion of con trols for both fixed an d tim e-varyin g age effects, an d use of altern ative tests, in cludin g tests of Granger causality, which fail to reject the key regression results. Moreover, our n ull hypotheses require a specific set of restriction s in the pattern of effects for ch an ges in the m etrics of m ate availability am on g blacks an d whites—restriction s n ot rejected by the data an d groun ded in m odels of fertility an d m arriage in which blacks an d whites respon d in opposite direction s to chan ges in m ate availability due to their in itial differen ces in m ate availability. H en ce, odds that poten tial sources of bias would yield spurious results sim ultan eously
con sisten t with all n ull hypotheses in m ultiple estim ation m ethods appear rem ote.
Th e o re tic a l Co n te xt
Wilson (198 7), Willis (1999), an d others argue that blacks an d whites are likely to respon d differen tly to chan ges in m ate availability. Where eligible wom en exceed m en in a cohort, as for blacks, then with positive assortative m atin g, children ten d to be born outside m arriage to low-in com e/ education fathers and m others, at least when the in com es of the m others exceed a value critical to their decision to bear a child, so that in creases in the ratio of m en ’s to wom en ’s in com es/ education or in the ratio of m en to wom en decrease n on m arital birth rates when eligible wom en outn um ber m en , but where the ratio of eligible m en to wom en is above parity, as it is for whites, children ten d to be born within m arriage to high-in com e/ education m en an d wom en in positively assortative m atches.
M odel in tuition
In term s of m argin al effects, the Wilson -Willis approach yields the in tuitive result that a relative in crease in the short (lon g) side of m ate availability decreases (in creases) NBS. The overall ratio of m en to wom en has been below parity for blacks in recen t
decades but above parity for whites, so that m ales are the short (long) side of m ate availability for blacks (whites), a divergen ce due largely to higher death, in carceration , m ilitary en listm en t, an d in stitution alization rates am on g black m en . Tem poral variation s in these rates ten d to be widely shared, with stan dard deviation s well below the correspon din g m ean s. H en ce, between -locale variation typically yields weak estim ates.
D a ta a n d Va ria b le s
All data are publicly available an d refer to the civilian , n on institution alized population , ages 20 -44.2 We lim it the an alysis to birth cohorts for which full data are available, from 1972 through 20 0 2. The cohorts, their birth years, an d the years at which they are ages 20 -24 and 40 -44 are presen ted in Table 1. As with m any cohort analyses, we em ploy five-year age ran ges, a ran ge wide en ough to provide reliable m easures, but n arrow en ough to lim it tim e- an d age-varyin g heterogen eity within the cohort.
Robustn ess checks usin g altern ative age groupin gs suggest that the cohort data are align ed appropriately for gen der differen ces in age at first m arriage an d tem poral differen ces, as em phasized by Neelakan tan an d Tertilt (20 0 8 ).
Table 2 reports sum m ary statistics for all variables used in estim ation .3 The depen den t variable is the n on m arital birth share (NBS), the share of n on m arital births am on g all births. As expected, NBSB, the NBS for blacks, (at 43.4) is greater than
2Non marital births are from National Vital Statistics Reports (2000, 2002); Total births from Vital Statistics of the United States
3Data for sex ratio are from U.S. Bureau of the Census
NBSW, the NBS for whites (12.3), though both have risen over tim e, as reflected in the m in im um an d m axim um values.
Our prim ary, m ost gen eral m easure of m ate availability is SEXRATIO, the ratio of eligible m en to wom en when each cohort was 20 -24. This variable is calculated by dividin g the n um ber of m en in this age group for a given birth cohort by the n um ber of wom en an d m ultiplyin g by 10 0 to express the result in percen tage poin ts. The average sex ratio for whites, SEXRATIOW, is 10 2.5, ran gin g narrowly from 10 0 .9 for the oldest cohort to 10 7.0 for the m ost recen t cohort. By con trast, the average sex ratio for blacks SEXRATIOB is on ly 93.6, ran gin g from 8 8 .6 for the oldest cohort to 97.5 for the m ost recen t cohort an d un iform ly below un ity.
SEXRATIO values for whites an d blacks do n ot overlap, hen ce, estim ation by race or by whether the sex ratio is above or below parity are equivalen t. As an ticipated, stan dard deviation s for SEXRATIO relative to the correspon din g m ean s are larger than the relative variation typical for the locale-specific data shown to be subject to substan tial m easurem en t error.
Our qualitative m etric of m ate availability at the upper en d of potential m arriage pairs is POSTS, the ratio of m ale to fem ale school enrollm ents at ages 20 -24, which prim arily reflect post-secon dary school en rollm en ts. Use of relative wages in prior studies as an altern ative qualitative or resource m etric yields weak results, perhaps either because differen ces between average earn in gs for m en and wom en , especially am on g blacks are m uch sm aller than differen ces for post-secon dary schoolin g or because m easurem en t error dom in ates in locale-specific data.
Use of the broader spatial data for POSTS is con sisten t with the greater spatial m obility for m en an d wom en at higher levels of education an d skill. POSTS is favorable
on average for wom en of both races early in the sam ple period, but has becom e in creasin gly un favorable, especially for black wom en . Overall, the average for POSTSW is 1.64, ran gin g from over 4.0 for the oldest cohort to on ly .8 9 for the m ost recen t cohort. The average ratio for POSTSB is 1.25, ran ging from 1.78 for the oldest cohort down to only 0 .71 for the m ost recen t cohort. These shifts exhibit the n ow-fam iliar dom in an ce of school en rollm en ts for wom en over m en durin g these ages– particularly so for blacks, for whom in carceration rates of youn g m ales have in creased relative fem ale- m ale en rollm en ts for black wom en (Mechoulan , 20 0 6).
We fin d sim ilar results usin g altern ative age ran ges for school en rollm en t, e.g., either 18 -21 or 18 -24 years old. Con sisten t with the Wilson -Willis m odel, we expect the effect of an increase in SEXRATIOB on NBSB to be negative because m ales are ‘short’
am on g blacks, an d the effect of an in crease in SEXRATIOW on NBSW to be positive because wom en are short am on g whites, if on ly slightly.
By con trast, we expect the effect of POSTS on NBS to be positive for both whites an d blacks because un til on ly very recen tly, m ales outn um ber fem ales in both cases.
Based on fam iliar racial differences in the tim in g of non m arital births, the black-white differen ce in NBS should declin e with age, so we con trol for cohort age and subsequen tly, also for age-year in teraction s to accoun t for tem poral chan ges in racial differen ces in the tim in g of fertility.
Es tim a tio n Is s u e s
Specification
Our focus is directly on the black-white gap in NBS, an d our estim ation strategy is to use differen ces for blacks an d whites across birth cohorts, tim e an d age, to iden tify the effects of SEXRATIO an d POSTS. Of course, age, year, an d birth cohort are lin early
depen den t, so on ly two of these three effects are iden tified in lin ear form . Because values for SEXRATIO for blacks an d whites do n ot overlap, estim ation separately by race and separately by whether SEXRATIO is above or below un ity are equivalen t, so we begin by expressin g the black-white differen ce in NBS as a lin ear fun ction of fixed year in tercepts an d black-white differen ces in SEXRATIO an d POSTS, with all variables in log form , which m itigates differen ces in scale for blacks an d whites an d yields m ore robust results for cohort i, age j, an d year t:
[NBSWijt -NBSB ijt ]=
ct +bw1 SEXRATIOWijt-bB1 SEXRATIOBijt +bW2 POSTSW ijt -bB2 POSTSB ijt + b3 AGE + e ijt (1) Where cohort i, year t, age j, an d other effects com m on to blacks an d whites are elim in ated by differencin g by race, so that the age an d fixed year effects capture residual race differen ces.
For the two m etrics for m ate availability, SEXRATIO an d POSTS, the Wilson Willis m odels predict opposite, possibly equal, effects for blacks an d whites. That is, for equal but opposite effects to hold :
bw1+bB1 =bB2+bW2= 0 (2)
in which case, eq (1) reduces to eq (3) below:
[NBSWijt -NBSB ijt ]=
ct +b1 (SEXRATIOWijt -SEXRATIOBijt)+b2(POSTSW ijt -POSTSB ijt) +b3 AGE +e ijt (3) Where we expect b3<0 , an d b1 , b2 >0
En dogen eity
There is little reason to suspect en dogen eity bias for SEXRATIO because the cohort sex ratio at age 20 -24 is predeterm in ed an d in depen den t of NBS. H owever, POSTS is predeterm in ed on ly for subsequen t ages within a cohort an d strictly
exogenous on ly across cohorts. Even so, we can assess the im portan ce of endogeneity bias for POSTS in several ways, includin g tests of Gran ger causality an d exam in in g the sen sitivity of the estim ated effect of POSTS to usin g altern ative age ran ges for school en rollm en ts, Moreover, we expect the specific sign s and restriction s in eq. (2), so that the likelihood of an y bias sim ultan eously con sisten t with all the prediction s for blacks an d whites appears rem ote. In addition , we are also able to replicate key results with tests of Granger causality.
Re s u lts
Colum n 1 of Table 3 presen ts the baselin e regression for eq. (3) The regression in cludes fixed year effects, which are join tly sign ifican t, but om itted for brevity. The differen ce-in -differen ces specification in eq. (3) pushes the data hard, leaving on ly 23 degrees of freedom , roughly the m in im um n eeded to rely on the sm all-sam ple properties of ordin ary least squares. H en ce, the power of the estim ates in colum n 1 rests n ot on large n um bers, but on the exten t to which cohort variation s in the data are sufficien tly large an d com m on en ough across locales to iden tify the effects of m ate availability, given the restriction s of eq. (2). Otherwise, with such lim ited degrees of freedom , stan dard errors will likely be large an d yield in sign ifican t coefficien ts even where sign ifican ce is expected. In fact, however, power does n ot appear to be a problem for the estim ates. The equation fit is stron g, with an R-squared of 0 .766, an d all coefficien ts are sign ifican t in the hypothesized direction . In addition , the coefficien t for AGE is sign ifican tly n egative, in dicatin g that n on m arital fertility falls relative to total fertility m ore rapidly with age for blacks as com pared to whites.4 The coefficien ts for
4 Gray and Stone (2010) examine factors determining black-white differences in the timing of both marital and nonmarital fertility.
SEXRATIO an d POSTS are sign ifican tly positive, as hypothesized an d in dicate in each case that an in crease in the short side of m ate availability for blacks or whites decreases the correspon din g NBS.
Ro b u s tn e s s a n d S p e cifica tio n Te s ts
Age-y ear in teraction s
Addition of an age-year in teraction in Colum n 2 dem on strates that estim ates for the m etrics of m ate availability are n ot sensitive to the sign ificant in teraction between cohort age an d year, an d in dicates that the age-NBS profile for the race gap in NBS becam e even m ore n egative later in the later years of the period.
R esidual diagn ostics
The J arque-Bera test of n orm ality does n ot reject the n ull hypothesis that the regression residuals follow a n orm al distribution (p=.0 38 3), an d The Q statistic for first- order autocorrelation fails to reject the n ull of zero autocorrelation , (p =0 .327), an d the Q-statistic for first-order autocorrelation fails to reject the n ull of zero autocorrelation , (p =0 .327). The absen ce of sign ifican t autocorrelation is con sisten t with the absen ce of sign ifican t specification error and len ds creden ce to relian ce on the recursive in ertia of predeterm in ed data at earlier ages of a cohort for iden tification . Results are n ot sen sitive to use of differen t, n eighborin g age ran ges for either SEXRATIO or POSTS, an d tests for Gran ger causality based on the regression residuals reject the null hypothesis of no Gran ger causality for each of the hypothesized lin ks in eq. (3), an d yet also fail to reject the n ull of n o reverse Gran ger causality from the race gap in NBS to either SEXRATIO or POSTS, so the tests raise n o sign ifican t con cerns regarding reverse causality or en dogen eity bias, at least in the Gran ger sen se.
Coefficien t restriction s
Despite the strong significance and power of the in dividual estim ates, a Wald test of the join t lin ear restriction s set out in eq. (2) an d im posed in colum n 1 (for equal, but opposite effects for blacks an d whites) fails to reject the restriction s (p= 0 .712).
Un restricted estim ates of eq. (3) are presen ted in Table 4. The separate variables by race for SEXRATIO an d POSTS en ter sign ifican tly as a set, but POSTSW is the on ly m etric for m ate availability to en ter sign ifican tly.
On e can see from the larger stan dard errors an d weaker power for the other in dividual estim ates that the restriction s play an im portan t role in the power of the in dividual estim ates in colum n 1 of Table 3, despite the fact that the join t test of the restriction s fails to reject them . Note that the sign ifican tly positive effect of POSTSW is con sisten t with the Wilson -Willis approach, where a relative in crease (decrease) in the long side of m ate availability , in this case white m ales en rolled in school at ages 20 -24, in creases (decreases) NBS. The weak in dividual estim ates in Table 4 are in lin e with other sim ilarly weak prior estim ates, suggestin g that prior eviden ce m ay m ask the sign ifican t effects foun d here, perhaps because either the opposin g effects for blacks an d whites can cel to zero in pooled specification s for blacks an d whites or because the iden tifyin g power of differen cin g by race or cross-race restriction s is n ot exploited.
Exp la in in g th e Ra cia l Ga p
R egression v arian ce
The m odel expressed by eq. (3) explain s about 77% of the sam ple varian ce of the (log) race gap in n on m arital birth shares for blacks an d whites. Because this
explan atory power is n ot due solely to our two m etrics of m ate availability, we isolate their effects usin g the estim ates in Table 3 to sim ulate chan ges in the race gap.
M odel sim ulation
To use the estim ated m odel to sim ulate the proportion of the m axim um chan ge in the (log) race gap explain ed by SEXRATIO an d POSTS, we 1) calculate the m axim um chan ge for the race gap in the sam ple (i.e. from m in to m ax), an d 2) use the m odel coefficien ts alon g with the m axim um chan ge in each explan atory variable to sim ulate the chan ge in the race gap attributable to the two m etrics of m ate availability. The m axim um chan ge in the log race gap is 2.8 1, of which SEXRATIO explain s 0 .8 5, or 30 .2%, an d POSTS explain s .60 , or 21.4%. H en ce the two m etrics join tly accoun t for 51.6%, m ore than half of the m axim um chan ge in the race gap in NBS. AGE differen ces explain - .544, -19.4%, so the proportion of the chan ge in the race gap (n et of age effects) explain ed by m etrics of m ate availability is higher, roughly 64%.
Co n clu d in g Re m a rks
Our two m etrics of m ate availability reflect an d are heavily in fluen ced by education an d other public policies, especially the decades-long ‘war on drugs’ in the U.S, possibly at the loss of a gen eration of black m en to fam ilies they m ight have fathered with their children ’s m other. Results here com plem en t other recen t eviden ce on effects of in carceration rates in the U. S. an d WWI m ilitary deaths in Fran ce on n on m arital fertility, but in dicate broader effects for both a gen eral an d an education - based m etric for m ate availability directly on the black-white gap in n on m arital fertility.
Gen eral m ate availability is less a factor am on g whites, though the relative pools of college educated m en an d wom en are n ow rapidly chan gin g am on g both whites an d blacks. Our results m ay be relevan t where m arriages are segm en ted alon g racial, ethn ic,
or religious lin es, as for exam ple, am on g castes in In dia, ethn ic Malays an d Chin ese in Malaysia; or whites, South Asian s, an d blacks in the U. K. (Barthoud 20 11). Fin ally, the results here con firm theoretical con jectures that the direction of the effect of a chan ge in m ate availability depen ds on both the direction of the chan ge an d whether the chan ge com es from the lon g or short side of the m arriage m arket.
Re fe re n ce s
Abram itzky, R., Delavan do, A. an d Luis Vascon celos. 20 10 . “Marryin g Up: The Role of Sex Ratio in Assortative Matchin g.” Workin g paper Stan ford U.
Berthoud. 20 11. “Fam ily Form ation in M ulticultural Britain : Three pattern s of div ersity.” workin g paper In stitute for Social an d Econ om ic Research, U. Essex Brien , Michael J . 1997. "Racial Differen ces in Marriage an d the Role of Marriage Markets." Journ al of H um an R esources 32(4):741-78
Cen sus. 20 0 5. Fertility of Am erican W om en : 20 0 4. Washin gton : Com m erce Dept.
Charles, Kerwin K. an d Min g Ching Luoh. 20 0 6. “Male In carceration , the Marriage Market, an d Fem ale outcom es,” NBER workin g paper
Gray, J o A., Stockard, J ean an d J oe A. Ston e. 20 0 6. “The Risin g Share of Non m arital Births: Fertility Choice or Marriage Behavior?” Dem ography 43:2, 241-53
Mechoulan Stéphan e. 20 0 6 “Extern al Effects of Black Male In carceration on Black Fem ales.” U. Toron to.
Moffitt, Robert. 20 0 0 . “Welfare an d Fem ale H eadship in U.S. Tim e Series.” Am erican Econ om ic R ev iew 90 :373-77
Neelakan tan, U. an d M. Tertilt. 20 0 8 . “A n ote on m arriage m arket clearin g.” Econ om ics Letters 10 1 (2): 103-105.
South, Scott J . an d Kim M. Lloyd. 1992. “Marriage Markets an d Non m arital Fertility in the Un ited States.” Dem ography 29: 247-64
Willis, Robert J . 1999. “A Theory of Out-of-Wedlock Childbearin g.” Journ al of Political Econ om y 10 7(6): S33-64.
Wilson , W. 198 7. The Truly disadv an taged: Chicago: U Chicago Press
Ta b le 1. Co h o rts a n d B irth Ye a rs ( 19 72 -2 0 0 7) , ( Age s 2 0 -2 4 )
Cohort # Age 20 -24 in Age 40 -44 in
1 1952 1972
2 1957 1977
3 1962 198 2
4 1967 198 7
5 1972 1992
6 1977 1997
7 198 2 20 0 2
8 198 7 9 1992 10 1997
11 20 0 2
Ta ble 2 . S u m m a ry s ta tis tics ( 19 72 -2 0 0 7) , ( Age s 2 0 -4 4 )
NBSB NBSW SEXRATIOB SEXRATIOW POSTSB POSTSW
Mean 43.42 12.28 93.64 10 2.49 124 165
Median 41.60 10 .54 93.42 10 2.11 125 130
Max 8 1.30 44.60 97.47 10 6.998 178 414
Min 23.0 8 2.71 8 8 .57 10 0 .94 71 8 9
Std.
Dev.
15.65 9.49 2.0 7 1.41 34 75
Obs. 35 Notes:
See text for sources of data.
All ratios in percen tage poin ts.
Bsuffix Blacks Wsuffix Whites
NBS Non marital births as a share of total births SEXRATIO Ratio of males to females
POSTS Ratio of males to females enrolled in school at ages 20-24 AGE Average cohort age (same for blacks and whites)
Ta ble 3 . Ra ce Ga p in N o n m a rita l Birth S h a re s ln ( w h ite / bla ck) , ( 19 72 - 2 0 0 7) , ( a ge s 2 0 -4 4 )
(Robust std. errors below coefficien ts)
(1) (2) Con stan t 1.468 2 46.8 0 2*
1.5473 5.445
lnSEXRATIO 14.238 1 7.68 6*
5.5743 1.775
ln POSTS 0 .6412* 0 .5473*
0 .20 68 0 .150 9
ln AGE -0 .544* -7.129*
0 .221 0 .774
Year effects Yes* Yes*
AGE x YEAR/ k No 0 .0 0 2*
R-squared 0 .766* 0 .937*
See n otes, Table 2.
* sign ifican t .0 5
Ta ble 4 . U n re s tricte d Es tim a te s , N o n m a rita l B irth S h a re ln ( w h ite / bla ck) , ( 19 72 -2 0 0 7) , ( Age s 2 0 -2 4 )
(Robust std. errors below coefficien ts)
Con stan t -0 .469 34.610
lnSEXRATIOW 3.268
5.8 57
ln SEXRATIOB -3.149
7.261
lnPOSTSW 1.564*
0 .40 8
ln POSTSB -0 .38 1
0 .527
ln AGE -1.20 3*
0 .374
Year Effects Yes
AGE x YEAR No
R-Squared 0 .8 0 9*
See n otes to Table 2 * sign ifican t .0 5
