The purpose of this study is to reveal the importance of unobserved heterogeneity on marital status. The results for monozygotic (identical) and dizygotic twins indicate an important genetic component in marital status. Simply controlling for marital status could be misleadingmarriage; divorce; heterogeneity; selection; twins

Nilsson, William

English

Research Papers in Economics

 
Marital Status and Unobserved Heterogeneity  
- Do twins suggest a genetic inheritance? 
 
by William Nilsson
1 
Department of Economics, Umeå University, Sweden and 
Centre for Research on Welfare Economics (CREB), Barcelona, Spain  
 
 
 
Abstract 
The purpose of this study is to reveal the importance of unobserved heterogeneity 
on marital status. The results for monozygotic (identical) and dizygotic twins 
indicate an important genetic component in marital status. Simply controlling for 
marital status could be misleading. 
 
JEL: J12 
Keywords: marriage, divorce, heterogeneity, selection, twins 
 
Umeå Economic Studies 685, 2006 
 
 
 
 
 
 
                                                 
1 Financial support from the Swedish Council for Working Life and Social Research is gratefully 
acknowledged. (Grant number: 2005-1330). All data, except for the identification of the twin 
sample come from Statistics Sweden (SCB). The twin information comes from the Swedish Twin 
Registry (STR). The Swedish Twin Registry is supported by grants from the Swedish Research 
Council. To contact the author, write to william.nilsson@econ.umu.se.   2
1. Introduction 
An increasing amount of empirical literature studies the effects of marital status, such 
as marriage, divorce or living with a partner, on earnings, health status and labor supply. 
Marital status is, however, a choice variable and this should be considered in the 
econometrical specification. Otherwise, the results could be biased due to endogeneity. In 
addition to this, important unobserved heterogeneity could be left out which could lead to 
further bias, due to omitted variables. 
The purpose of this study is to use twin data to reveal the importance of (usually) 
omitted background variables, including genes, on marital status. Bivariate probit models 
are estimated separately for male and female monozygotic (identical) and dizygotic 
(fraternal) twin siblings' marital status. The models include variables that typically can be 
found in data sets used in the literature. The correlation of the error terms on the marital 
status equations for the twin siblings gives an omnibus measure of the importance of 
common unobserved heterogeneity. In addition, measures for the aggregate background 
effect on marital status are also estimated from the models. 
 
2. Model 
The latent propensity to be married, Msit
∗ , is assumed to be determined by 
 
) 2 (
) 1 (
2 2 2 2 2
1 1 1 1 1
it i it it
it i it it
M
M
ξ η
ξ η
+ + =
+ + =
′ ∗
′ ∗
x
x
β
β
 
T t N i s
M I M sit sit
,..., 1   and   , ,..., 1   , 2 , 1
) 0 (
= = =
> =
∗
 
 
Subindex  s  1 indicates the first group of twins, and s  2 indicates the second 
group of twins consisting of the sibling twins of s  1. The model, accordingly, consists of 
an equation for each twin sibling. Explanatory variables are included in xsit and s are 
vectors of parameters to be estimated. Subindex i refers to the pair of twins i = 1,…,N  and   3
t = 1,…,T refers to different periods. Individuals are either observed to be married 
(Msit  1), or not (Msit  0). IMsit
∗  0 is an indicator function which takes the value 1  
if the inequality is satisfied, and zero otherwise. The error term, vsit, includes an individual 
specific effect, si, and an orthogonal white noise, sit. The error term is assumed 
vs  N0,1. In addition, Covv1,v2  . The correlation between the error terms is 
interesting since it measure to what extent unobservables are correlated for twin siblings. 
Any factor that is shared by the twins and influences their marital status, apart from what is 
captured by the included variables, will contribute to the coefficient. In addition to this 
measure, it is also possible to estimate the Aggregate Background Effect,  
 
 
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
−
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
=
−
= = = =
∑
∑
∑
∑
= ∈ = ∈
) 1 (
) 0 | 1 Pr( ) 1 | 1 Pr(
1
2
2 1
) 0 2 (
2
2 1
) 1 2 (
it
i
it it
it M i
it
i
it it
it M i
M
M M
M
M M
ABE   
 
where the probabilities are calculated from the estimated bivariate probit model as 
indicated below; 
 
) 3 (
) (
) ; , (
) 1 | 1 Pr(
2 2
2 2 1 1 2
2 1
it
it it
it it M M
x
x x
′
′ ′
Φ
Φ
= = =
β
β β ρ
 
) 4 (
) (
) ; , (
) 0 | 1 Pr(
2 2
2 2 1 1 2
2 1
it
it it
it it M M
x
x x
′
′ ′
− Φ
− − Φ
= = =
β
β β ρ
 
. and  (.) 2 Φ  are the cumulative density functions of univariate and bivariate 
standard normal distributions. The Aggregate Background Effect compares the average 
probability to be married for two different groups, i.e. depending on the marital status of 
the twin sibling. (Note that ABE2 can be estimated by conditioning on the first twin). If the 
background is important for the marital status, observing one twin as married Msit, 
divorced Dsit or having a spouse Ssit, will increase the probability of witnessing his 
twin sibling in the same marital status. If the background hardly influences the marital   4
status at all, the average probability will be similar for the different groups and the 
Aggregate Background Effect will be close to zero.  
 
3. Data 
This study uses information from the Swedish Twin Registry, (STR), and Statistics 
Sweden, (SCB). 1001 female and 851 male pairs of monozygotic twins that were born 
between 1949 and 1958 are available. In addition, 1361 female and 1421 male pairs of 
dizygotic twins are available. Monozygotic twins have identical genes, while dizygotic 
twins are no more genetically alike than ordinary siblings. It is therefore interesting to 
compare estimates for monozygotic and dizygotic twins. In addition to information about 
the twins, biological parents and social siblings are connected to the twins. Social siblings 
are observed in the Population and Housing Census for the years 1965, 1970 and 1975. To 
all individuals in the population information from the Income and Wealth Register is 
included for the years 1968, 1971, 1974, 1977, 1980 and 1983. Variables from the 
longitudinal database LOUISE are included for the years 1994-1999. During this period, 
i.e. when the twins were between 36 and 50, marital status is observed. In this study three 
different measures are used. Apart from being married or being divorced, the twins can 
also be identified as living with a spouse. A spouse is defined as a legal marriage or a twin 
living together with a partner, with whom he/she has at least one common child. For the 
female (male) monozygotic sample, about 62 (59) percent were married, 14 (10) percent 
divorced and 67 (66) percent were identified as living with a spouse.  
 
4. Results 
Results from the bivariate probit models for the female and male monozygotic 
samples are included in Table 1. Whether the biological father or mother was observed as 
divorced or not when the twins were between 20 and 22 years old seems to matter for the 
marital status. Note, however, that a significant coefficient does not reveal if it is the event, 
or a biologically genetic motive for a correlation. No marginal effects are calculated since 
the main interest is  and the measure of Aggregate Background Effect. These results are 
included in Table 2, together with the same measures for the dizygotic samples.   5
For the female monozygotic sample,  is large and significantly different from zero 
in all cases. The corresponding coefficients for the dizygotic sample are estimated to be 
smaller, and in fact, only significantly different from zero when the probability of being 
married is estimated. The results indicate an important role for genetics in determining 
marital status in adulthood for the female sample. The measures for Aggregate Background 
Effects are also substantially larger for the monozygotic sample. 
 is found to be significantly different from zero for both male monozygotic and 
dizygotic samples and when both marriage and spousal status are studied.  is also found 
to be positive when the bivariate probit models for divorce are estimated, but in these cases 
it is not significantly different from zero. The Aggregate Background Effects are again 
found to be quite large and this suggests that the background is important for studies of 
marital status. 
 in all cases is estimated to be larger for the monozygotic twins. It is, of course, 
difficult to ascribe all of the differences between the samples to the genes, since it cannot 
be ruled out that monozygotic twins, in general, are treated more alike. The conclusion that 
genetics play an important role seems, however, to be robust. The reason is that dizygotic 
twins also share genes, although to a lesser extent, and this also contributes to the 
correlation for the dizygotic sample.   
 
5. Concluding remarks 
The results in this study underline that controlling for unobserved heterogeneity in 
studies that estimate the causal effects of marital status is indeed, very important. The 
results indicate an important role for genes. The social background, including the genes, is 
likely to affect health, labor supply and labor income in adulthood and the risk for omitted 
variables is evident. While the social background and the genes are fixed over the life-time, 
it is important to note that a fixed-effect model that uses variation over time, can still fail to 
control for unobserved heterogeneity. Bergstrom & Bagnoli (1993) suggest in a theoretical 
model that "males who regard their prospects as unusually good choose to wait until their 
economic success is revealed before choosing a bride". Comparing the income before and 
after marriage would, accordingly, be misleading as an estimate for the causal effect of   6
marriage. It is possible that a fixed-effect method would rather capture unobserved ability 
that has different returns on the labor market and the marriage market at different ages. 
Further, a fixed-effect model cannot handle reverse causality, i.e. a good situation on the 
labor market can increase the chance of becoming married. 
Instrumental variables (IV) methods that uses exogenous variation in marital status 
can also fail to measure the causal effect of marriage. First, it is in general, difficult to find 
valid instruments. It is also possible that the exogenous information only affects a small 
share of the population. In that case the interpretation of the causal effect could be limited 
to that specific group. If the effect of marital status varies among individuals and 
individuals are aware of this when deciding to marry or not, IV could give misleading 
results (Heckman, 1997). It is not unreasonable that this is the case. 
The results in this study suggest that empirical studies of the effects of marital status 
should deal with unobserved heterogeneity. The degree of unobserved heterogeneity found 
by comparing twins is of course specific to the sample. It would, accordingly, be 
informative to see results for different ages and different countries. 
 
References 
Bergstrom, T. C. and M. Bagnoli, 1993, Courtship as a Waiting Game, Journal of Political 
Economy 101(1), 185-202. 
Heckman J. J., 1997, Instrumental Variables: A Study of Implicit Behavioral Assumptions 
in One Widely Used Estimator, Journal of Human Resources 32(3), 441-462.  Notes: Estimated coefficients are found in the first line for each variable and second row includes t-ratios. 
The standard errors are corrected for repeated observations from the same twins over the years. * p < 0.10, ** 
p < 0.05, *** p < 0.01. a) Parameters for variables are constrained to be the same for both sets of twins, i.e. β1 
= β2.  b) Numbers in parenthesis are χ
2(d.f.=1). c) The incomes are relative to the average income among 30-
60 years old in municipality. The average refers to up to three observations during the period. d) The 
reference case for the twins’ age is 36-40 years old. e) The reference case for education is compulsory school. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Table 1 – Estimates from bivariate probit models for monozygotic twins.   
     
  Female sample  Male sample 
 Divorced  Married  Divorced  Married 
 D st = 1  Mst = 1  Dst = 1  Mst = 1 
Variable
  (β1 = β2)
a ( β1 = β2)
a ( β1 = β2)
a ( β1 = β2)
a 
Biological father or mother was divorced, when 
twin observed between age 20 and 22. 
0.1556 
(1.35) 
-0.3154*** 
(-3.06) 
0.2744** 
(2.09) 
-0.1567 
(-1.36) 
Biological father not identified or dead before 
twin turned 25 
0.2151 
(1.59) 
-0.0761 
(-0.54) 
-0.1046 
(-0.49) 
0.1656 
(0.94) 
Biological mother not identified or dead before 
twin turned 25 
-0.0096 
(-0.04) 
0.0697 
(0.30) 
0.2416 
(0.92) 
0.1665 
(0.66) 
Relative averaged income for biological father 
when twin was 17-25
 c  
-0.1481*** 
(-2.85) 
0.0587 
(1.37) 
0.0204 
(0.45) 
0.1469*** 
(3.16) 
Twin’s oldest sibling was an older social sister, 
when observed between 12 and 16 years old. 
-0.1003 
(-1.02) 
0.0862 
(1.02) 
-0.0339 
(-0.33) 
0.1335 
(1.54) 
Twin 41-45 years old
 d  
 
0.2590*** 
(4.38) 
0.0879* 
(1.82) 
0.0322 
(0.47) 
0.1780*** 
(3.50) 
Twin 46-50 years old
 d 
 
0.4091*** 
(4.85) 
0.1359* 
(1.84) 
0.1818* 
(1.99) 
0.2889*** 
(3.60) 
Education, B (1=upper secondary school)
 e 
  
-0.0494 
(-0.50) 
-0.0198 
(-0.22) 
0.0863 
(0.82) 
0.0792 
(0.95) 
Education, C (1=post secondary school and post 
graduate education)
 e 
-0.1825 
(-1.64) 
0.1115 
(1.16) 
-0.0749 
(-0.59) 
0.4053*** 
(3.94) 
Relative averaged income for twin when twin 
was 17-25 years old
 c 
-0.6670*** 
(-4.33) 
0.2838** 
(2.26) 
-0.1024 
(-0.70) 
0.3141** 
(2.35) 
Constant 
 
-0.7551*** 
(-4.97) 
-0.0029 
(-0.02) 
-1.3998*** 
(-8.53) 
-0.5163*** 
(-3.49) 
ρ 
  
0.3155*** 
(21.5337)
 b 
.4433*** 
(79.1846)
 b 
0.1273 
(2.1217)
 b 
0.4325 *** 
(67.5171)
 b 
Number of observations  5445  5445  4686  4686 
Log pseudo-likelihood  -4095.77 -6922.09  -2839.13 -5863.30 Table 2 - Measures for  and Aggregate Background Effects on marital status 
 
  Female samples    Male samples 
  Monozygotic Dizygotic Monozygotic    Dizygotic 
Measure  Twin 1  Twin 2 Twin 1 Twin 2 Twin 1 Twin 2    Twin 1  Twin 2
Divorce               
Aggregate Background 
Effect  
0.1792 
 
0.1769
 
0.0563
 
0.0490
 
0.0535
 
0.0473 
  
0.0325 
 
0.0356
 
Marginal probability, 
P(Ds = 1) 
0.1344 
 
0.1355
 
0.1289
 
0.1278
 
0.0917
 
0.0915 
   
0.1020 
 
0.1018
 
ρ 
 
0.3155*** 
(0.0634) 
0.0852 
(0.0628) 
0.1273 
(0.0865)   
0.0746 
(0.0672) 
Marriage               
Aggregate Background 
Effect 
0.3001 
 
0.2940
 
0.1187
 
0.1174
 
0.3013
 
0.3015 
  
0.1663 
 
0.1762
 
Marginal probability, 
P(Ms = 1) 
0.6206 
 
0.6194
 
0.5979
 
0.5987
 
0.5892
 
0.5916 
   
0.5625 
 
0.5627
 
ρ  
 
0.4433*** 
(0.0430) 
0.1760*** 
(0.0421) 
0.4325*** 
(0.0458)   
0.2457*** 
(0.0397) 
Spouse               
Aggregate Background 
Effect 
0.2750 
 
0.2708
 
0.0403
 
0.0377
 
0.2361
 
0.2377 
  
0.1231 
 
0.1294
 
Marginal probability, 
P(Ss = 1) 
0.6859 
 
0.6852
 
0.6866
 
0.6877
 
0.6694
  
0.6715 
  
0.6485 
 
0.6487
 
ρ  
 
0.4176*** 
(0.0443) 
0.0563 
(0.0447) 
0.3525*** 
(0.0481)   
0.1953*** 
(0.0405) 
Note: Regression results for the dizygotic samples, and when spouse is used as dependent variable, are 
available from the author on request. The measures for ρ are marked * p < 0.10, ** p < 0.05 and *** p < 
0.01. Standard errors are included in parenthesis. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Courtship as a Waiting Game,

Instrumental Variables: A Study of Implicit Behavioral Assumptions in One Widely Used Estimator,

Marital Status and Unobserved Heterogeneity - Do twins suggest a genetic inheritance?

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Marital Status and Unobserved Heterogeneity - Do twins suggest a genetic inheritance?

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