Abstract
Numerous studies find that married men earn more than single men. However, identifying whether and why marriage affects earnings is complicated by the fact that marriage market outcomes are jointly determined with potential earnings. As such, I exploit exogenous variation in marriage induced by the introduction of nofault divorce laws in the USA to estimate the effect of marriage on the earnings of men. I find a 38% causal increase of marriage on earnings of husbands. This increase in earnings is explained by a large increase in labor market work after marriage. My findings are robust to the possibility of unobserved heterogeneity in the effect of marriage on earnings across individuals.
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Notes
Chiappori et al. (2015) provide a theoretical argument under which couples may divorce or not depending on the prevailing divorce legislation. What is interesting is that counterintuitive results obtain depending on the realization of individual match qualities and consumption after divorce. For example, a couple may choose to divorce under mutual consent legislation but would choose to remain married under unilateral divorce. Since couples would then internalize the possibility of divorce at the time of marriage, shifting divorce legislation can affect the decision to marry.
Using the terminology common in the LATE literature, a defier is a man who would have married under the previous divorce regime but who decides not to marry after the passage of the nofault divorce legislation.
A complier is a man who married only because of the introduction of nofault divorce laws and would not have married otherwise. As de Chaisemartin (2017) notes, this subpopulation of compliers is the same size as the population of compliers under the standard LATE.
The states in white in Fig. 1 are Alaska and Oklahoma.
The states in black in Fig. 1 are Arkansas, Louisiana, Maryland, New Jersey, New York, North Carolina, South Carolina, Vermont, and Virginia.
Those collusive behaviors included alleging cruelty by the husband, as most cruelty cases went uncontested, or “collusive adultery” in which the couple presented staged evidence of adultery to the court.
He also finds that unilateral divorce increased selection into marriage, and potentially decreased divorce rates in the long run.
Under the hypothesis of marriage as commitment, lower divorce costs would also lead to lower propensity to divorce because only high match quality couples would marry in the first place.
The effect on divorce propensity is also the opposite, as the average match quality of couples would be lower, thereby increasing the propensity to divorce.
However, theoretically, this version of the Becker–Coase theorem holds only under strong conditions on the utility function of the partners, see Chiappori et al. (2015). Only couples that cannot reach a mutually profitable agreement under the new legislative regime would eventually divorce.
Note, however, that individuals can remain single for many periods after the passing of the nofault divorce legislation.
These individuals are the ones “at risk of marriage,” and therefore the ones to be potentially induced or discouraged into marriage by the divorce reforms.
“Appendix” contains an empirical check of the testable implications arising from the assumptions required for the identification of the LATE with defiers.
If there are no defiers in the population, then the estimated effects in this paper would have the interpretation of a standard LATE as in Imbens and Angrist (1994).
Miller (2008) uses the same approach in his study of suffrage rights for women and their effect on child survival.
These are “progressive” policies that could confound the effect of nofault divorce legislation.
The table also includes the Sanderson–Windmeijer \(\chi ^2\)test of under identification and Ftest of weak identification (Sanderson and Windmeijer 2016). The \(\chi ^2\)statistic is distributed \(\chi ^2(1)\) under the null hypothesis of underidentification of the endogenous regressor. The Fstatistic is distributed \(F(1, n  k)\) under the null of weak identification of the endogenous regressor, where k is the number of exogenous regressors.
With Assumptions 1, 2, and 3 in Sect. A.2, one can also derive nonparametrically partially identified worst case bounds for the LATE. Table 11 in “Appendix” shows that using that approach the treatment effect for comvivors is between − 1.3 and 1.6.
The data are captured through a survey, but it is unlikely that subjects misreport whether they are married, nor their age, so the only plausible sources for measurement error are experience and the outcomes (earnings, hours of work, and wages).
Basu (2019) shows that the asymptotic bias (\(\varvec{\delta }^j \varvec{\gamma }\)) is equivalent to \(\Vert {\varvec{\delta }^j}\Vert \Vert {\varvec{\gamma }}\Vert \cos (\theta )\), where \(\varvec{\gamma }\) is a vector of the coefficients of omitted variables in the causal equation, \(\varvec{\delta }^j\) is a vector of the coefficients of projecting the omitted variable indexed by j onto the included regressors in the causal equation, and \(\theta \) is the angle between those two vectors in the Euclidean space. He notes that if \(\varvec{\delta }^j\) and \(\varvec{\gamma }\) are both nonzero but are neither orthogonal, nor lie in the same or in opposite orthants, then the direction of bias cannot be determined based on the signs of partial effects alone.
The results are robust to regressions with state trends. See Table 12 in “Appendix.”
See Chiappori and Mazzocco (2017) for a full discussion.
This does not imply, however, that women specialize in house work. Specialization of one spouse does not necessarily imply a specialization of the other spouse.
Partly due to a smaller sample size (see Sect. A.6 in “Appendix” for evidence that low statistical power can explain the low precision of the estimates).
This section uses the basic setup and notation from Chiappori (2017, Section 5.5).
See A.1.1 for details.
\(v^D\) will also depend on remarriage probabilities in the marriage market, but I am abstracting from that in this simple model.
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I thank Arvind Magesan, Pamela Campa, Eugene Choo, Atsuko Tanaka, Alan Woodland, and Arezou Zaresani for their comments and suggestions. I also thank seminar participants at the University of Calgary and the Canadian Economics Association Annual Meeting 2016. This research was supported by the Australian Research Council through its grant to the ARC Centre of Excellence in Population Ageing Research (CEPAR). Two anonymous referees provided helpful comments that greatly improved the paper.
A Appendix
A Appendix
1.1 A.1 A simple framework of marriage and divorce
This section provides a framework of marriage and divorce for analyzing the effect of divorce legislation on marriage decisions.^{Footnote 29} Consider individual utilities for partners 1 and 2:
where \(q_i\) is individual consumption, Q is public good consumption, and \(\theta _i\) is the quality of the match which is assumed to be independent between partners and independent of their incomes. Agents live for two periods. In the first period, agents marry and consume. The quality of the match is revealed at the end of the first period and agents decide whether to remain married or divorce. In the second period, couples who remained married consume as before, while members of couples who divorced consume as newly divorced singles. Under Pareto efficiency (in a collective model), the economic gain from marriage is
and the total gain from marriage is \(G(t) + \sum _i \theta _i\), where t is total income. In addition, let \(u^D_i(q_i, Q)\) denote utility when \(i=1,2\) is divorced. If and when agents divorce, they each maximize their respective divorce utilities subject to their respective budget constraints. To that end, let \(y_1\) and \(y_2\) denote their respective individual incomes. In the case of divorce, the woman gets \(d_1(y_1,y_2) = d(y_1,y_2)\), and the man gets \(d_2(y_1,y_2) = y_1+y_2  d(y_1,y_2)\). The indirect utility function is
In the second period, partners divorce if the total surplus is larger when divorced than when married, that is
and remain married otherwise.
From the above inequality, we can easily compute the probability of divorce as follows. Let F be the CDF of \(\theta _1 + \theta _2\), then
Notice that the probability of divorce depends on \(y_1\), \(y_2\), and d, so we can write \(\Pr (\text {divorce}) = \Pi (y_1, y_2, d, v^D)\), where \(v^D = (v^D_1, v^D_2)\).
In the first period, agents marry based on the expected surplus generated by marriage in both periods, but taking into consideration the probability of divorce. Let \(\theta = \theta _1 + \theta _2\), the total gains realized from marriage in both periods is
Since \(\theta \) is not observed prior to marriage, we can take the expectation of \(\bar{G}\) to obtain the expected gains from marriage (but prior to marriage):
We are interested in analyzing the effect of divorce legislation on marriage decisions. Marriage decisions are embodied in \({\mathbb {E}}[\bar{G}]\), the expected gains from marriage. Larger gains induce higher propensity for marriage. Divorce legislation is harder to pin in this general framework; however, we can think about divorce legislation affecting the utility of parters after divorce that is \(v^D_i\). In that regard, we can take the derivative of the expected marriage gains, which determine marriage decisions, with respect to utilities after divorce, which act as the channel through which divorce legislation affects marriage decisions and represents welfare after divorce. The total effect of \(v^D_i\) on \({\mathbb {E}}[\bar{G}(\cdot )]\) can be decomposed as
The derivative in the first term has a simple expression: \(\partial {{\mathbb {E}}[\bar{G}(\cdot )] }{\sum _i v^D_i(\cdot )} = \beta \Pi (\cdot )\).^{Footnote 30} Then we have:
Equation (A.9) says that the effect of divorce legislation on (the gains of) marriage depends on how the legislation changes total welfare after divorce, and that change should be weighted by the probability of divorce and discounted over time. The second term of Eq. (A.9) will depend on the particular divorce legislation under analysis. The change from mutual consent to nofault divorce clearly increases the postdivorce utility for the spouse that initially has less bargaining power, but the other spouse can experience a decrease in their postdivorce utility. In general, divorce legislation will make \(v^D_1(\cdot )\) and \(v^D_2(\cdot )\) interdependent, for example increasing one spouse’s utility at the expense of the other, which results in a nontrivial calculation of the derivative that could result in a positive or negative overall effect on the expected gains from marriage and therefore on the marriage decision.^{Footnote 31}
In particular, Chiappori et al. (2015) show that there are cases where mutual consent induces couples to divorce when nofault would sustain the marriage, and vice versa. We can then conclude that the effect of divorce on marriage depends on the utilities at divorce of both partners, and that effect can go in one direction or another. Moreover, since the only source of heterogeneity in this simple model is individual incomes, a richer model would induce different types of ambiguity in the effects of divorce on marriage.
1.1.1 A.1.1 Proof of equation (A.9)
We take the derivative of \({\mathbb {E}}[\bar{G}(\cdot )]\) with respect to \(\sum _i v^D_i(\cdot )\):
Let \(A(v^D) = \{ \theta : \theta \ge \sum _i v^D_i(\cdot )  G(\cdot ) \}\). Then the conditional expectation in equation (A.7) can be simplified.
Taking the derivative of the last expression, we obtain
Plugging that last expression into equation (A.10), we obtain
1.2 A.2 A local average treatment effect with defiers
This section sketches the main result in de Chaisemartin (2017), the estimation of a local average treatment effect under the presence of defiers. Consider a binary instrument Z, let \(D_z \in \{ 0, 1 \}\) be the treatment when the instrument takes a value \(Z=z\) and \(Y_{dz}\) denote the outcome when the instrument takes value z and treatment takes value \(d \in \{ 0, 1 \}\). Only Z, \(D \equiv D_Z\) and \(Y \equiv Y_{DZ}\) are observed. Four subpopulations are defined:

1.
Never takers (NT): individuals for whom \(D_0 = 0\) and \(D_1 = 0\).

2.
Always takers (AT): individuals for whom \(D_0 = 1\) and \(D_1 = 1\).

3.
Compliers (C): individuals for whom \(D_0 = 0\) and \(D_1 = 1\).

4.
Defiers (F): individuals for whom \(D_0 = 1\) and \(D_1 = 0\).
Now, under the assumptions that (1) the instrument is independent of the potential values of D and Y
and (2) Z does not enter the structural equation,
the Wald estimator W can be written as:
In addition, if either \(\Pr (F) = 0\) or \({\mathbb {E}}[Y_1  Y_0 \mid C] ={\mathbb {E}}[Y_1  Y_0 \mid F]\), W is the average causal effect of treatment on the compliers \({\mathbb {E}}[Y_1  Y_0 \mid C]\) and the coefficient of the first stage in a 2SLS framework is equal to the subpopulation of compliers \(FS = \Pr (C)\). de Chaisemartin (2017) relaxes these conditions to:
In words, it says that there exists a subpopulation of compliers (the compliers–defiers or “comfiers”) that has the same size as the subpopulation of defiers and that the average treatment effect for these two subpopulations is the same.
Theorem 2.1 in de Chaisemartin (2017) then applies:
That is, the Wald estimator identifies the treatment effect on the subpopulation of compliers that “survive” elimination with the defiers (these compliers–survivors are the “comvivors”). A sufficient condition for the last theorem to hold is
This last expression says that at any point of the distribution of treatment effects (\(Y_1  Y_0\)), there are more compliers than defiers. This condition is significantly stronger than the necessary conditions since it requires that the distribution of treatment effects for compliers and defiers to fully overlap.
1.3 A.3 Other potential threats to identification
To assess whether the relationship between the instrument and the marriage decisions is spurious, I regress the marriage decision on the instrument and dummies for up to 3 years before the introduction of the nofault divorce laws. The results are presented in Table 8. Globally, the dummy variables are indistinguishable from zero.
In addition, I explore whether other potential instruments induce the decision to marry. I restrict my search to variables that a priori may be correlated or be confounded with the introduction of nofault divorce or that can be thought of as instruments themselves. Table 9 shows the results of using different variables as instruments for marriage in a regression of total earnings in the lhs. None of the reported coefficients is significant.
Another potential threat to identification arises from different compositions in the population of men across different states. Specifically, I assess whether there are differences in the ages of single men in states that enacted nofault divorce laws early and states that enacted nofault divorce laws later. I regress age on a dummy that indicates early enactment (before 1973), while controlling for time fixed effects. The results are shown in Table 10. The coefficient on early is not statistically different from zero.
1.4 A.4 Testability of the identification assumptions
Here I check the validity of the implications of the assumptions necessary for the LATE with defiers. This represents a mathematically necessary condition for identification, as if the check is not satisfied then the assumptions in Sect. A.2 cannot hold, which renders invalid the identification of the treatment effect. Specifically, as de Chaisemartin (2017) points out, if Assumptions 1, 2, and 3 in Sect. A.2 are satisfied, then
where
\(p_d = \frac{FS}{\Pr (D = d \mid Z = d)}\), and \(U_{dz}\) is the rank of an observation in the distribution of \(Y(D = d, Z = z)\). The intuition is that the LATE W is also partially identified since \(C_V\) is also included in the population for whom \(\{ D = 0, Z = 0 \}\), and it accounts for \(p_0\)% of that population. Therefore, \({\mathbb {E}}[Y_0 \mid C_V]\) cannot be larger than the mean of \(Y_0\) for the \(p_0\)% with highest \(Y_0\). Also, it cannot be smaller than the mean of \(Y_0\) for the \(p_0\)% with lowest \(Y_0\). One can establish analogous bounds for \({\mathbb {E}}[Y_1 \mid C_V]\). When one combines those two results, one can arrive at worstcase bounds for the treatment effect of comvivors \({\mathbb {E}}[Y_1  Y_0 \mid C_V]\), which are \(\underline{L}\) and \(\overline{L}\). Then the pointidentified treatment effect W must lie within those bounds.
Using the data in this application, I compute all the components of condition (A.14). They are displayed in the Table 11. Condition (A.14) is satisfied.
1.5 A.5 Other regressions
1.5.1 A.5.1 Specifications with state trends
See Table 12.
1.5.2 A.5.2 Regressions for women
See Table 13, 14, 15, 16 and 17.
1.6 A.6 Power of estimates for hours of housework
Table 7 shows that after marriage, comvivors reduce their hours of housework by 24%. However, I fail to reject the null hypothesis that the effect of marriage is equal to zero. Note that the sample size in that table is smaller than the sample size in Tables 3, 4, and 5. The lack of statistical significance in Table 7 can be due to low power. To explore that possibility, I reestimate the regressions in column IV FE2 of Tables 3, 4, and 5 but keeping the same sample as in Table 7. Table 18 shows the results of such exercise; it illustrates the loss of power when using a smaller sample size.
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OlivoVillabrille, M. The marital earnings premium: an IV approach. Empir Econ 62, 709–747 (2022). https://doi.org/10.1007/s00181021020217
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DOI: https://doi.org/10.1007/s00181021020217