2. Literature and institutional background

Our paper contributes to at least two strands of literature. The first deals with the literature on marital assortative matching. Second, we contribute to the literature on the role played by dowry as an equilibrating mechanism to compensate for the differences in the characteristics of the bride and the groom. Below we discuss the contributions of this study in the context of these two strands of literature.

There is divided opinion among economists regarding the existence of positive assortative mating in education in the marriage market. Dalmia and Lawrence (Reference Dalmia and Lawrence2001) find that similarity in education is the second most important predictor of marital matchmaking in India after age. Deolalikar and Rao (Reference Deolalikar and Rao1992) find a positive association between the traits of bride and groom in characteristics such as height, age at marriage, and schooling in rural south-central India. Lin et al. (Reference Lin, Desai and Chen2020) on the contrary find evidence of a decline in education hypergamy in India, women marrying men with higher education, and a rise in hypogamy, women married to men with fewer years of schooling.

Studies of education-based assortative matching in India are both unique and complex since marriages and spouse selection are governed by two important elements of the marriage market. First, most marriages are arranged by the families of the bride and groom and are governed by strong social and cultural norms [Schwartz (Reference Schwartz2013)]. These norms, and the resulting son preference, guide human capital investments with persistent gaps in the literacy levels of boys and girls in all age groups. Girls are more likely to drop out of schools to take care of younger children in the family, to support household work, or due to financial constraints [White et al. (Reference White, Ruther and Kahn2016)]. The socio-economic status of women in India has remained persistently poor relative to men, and women are less likely to participate in the wage market, own assets, migrate for work, or take part in decision-making within or outside the family [Agarwal Goel (Reference Agarwal Goel2021)].

Thus, contrary to the evidence from developed countries that explicitly attributes the rise in assortative mating in education to rise in wages and female work productivity, similar conclusions are hard to draw for India. Women are engaged in low productivity and low-paying jobs and there exists a significant gender wage gap in the labor market [Duraisamy and Duraisamy (Reference Duraisamy and Duraisamy2016)]. Grossbard-Schectman (Reference Grossbard-Schectman2019) suggest that changes in market-determined wages or quasi-wages for spousal work relative to market wages for labor work can alter decisions regarding labor supply by women. In this paper, we argue that gender-segregated roles and non-monetary benefits of education offer an alternative explanation for the existence of assortative mating in India.

Second, dowry transfers from the bride to the groom's family are common across Indian states [Anderson (Reference Anderson2003, Reference Anderson2007)]. Such inter-household transfers act as income insurance in low-income countries [Rosenzweig and Stark (Reference Rosenzweig and Stark1989)]. In economic theory, dowry in the marriage market is perceived as an equilibrating mechanism to compensate for the differences in the characteristics of the bride and the groom [Anderson (Reference Anderson2007)]. Larger is the difference in the distribution of traits of the groom relative to the bride, greater is the dowry that is exchanged as a compensation. In India, girls are usually married up, with grooms likely to be taller, better educated, and with higher earnings. Rao (Reference Rao1993) in estimating the rising groom prices in South-Central India shows that dowry transfers rise with the widening gap in bride and groom characteristics such as height, land ownership, and years of schooling. A positive shift in the potential brides' ability distribution and rise in female education should raise female bargaining in the marriage market [Sweeney and Cancian (Reference Sweeney and Cancian2004); Anderson (Reference Anderson2007)]. However, Edlund (Reference Edlund2000) suggests that attributes do not influence dowry symmetrically, i.e., dowry should be regressed on individual traits instead of differences in traits.

We contribute to the literature on assortative matching in education by studying, empirically and theoretically, assortative mating decisions in the presence of strong patriarchal social norms, low female labor force participation rates, and the institutional practice of dowry.

Empirically, we draw four important conclusions. First, there exists positive assortative matching in education levels of husbands and wives in India. Second, this association is weaker in dowry-prominent districts. This suggests that assortative mating in education is weakened by the existence of dowry and the groom's family is willing to substitute lower bride's education in return for higher dowry. Third, we directly test for the independent effects of gender-specific education levels and the joint effect of male and female education on dowry. The estimates show that dowry payments rise with additional years of male education but falls with female education. Fourth, we find that, the joint effect of male and female education on dowry is negative, indicating that dowry increases with male education but at a decreasing rate in response to rise in female education. Finally, we explain the heterogeneity in the empirical results as a trade-off between marginal benefits and costs associated with female education and dowry using a simple theoretical framework.

3. Data

The empirical analysis uses household level data drawn from the India Human Development Survey (IHDS-II), 2011. IHDS-II is a nationally representative, multi-topic survey of 42,152 households across India for 2011–12. The survey gathers household and individual level details on variables related to health, education, employment status, marriage, and other components that are important indicators of economic and social well-being.

For our analysis, we map data at the level of household, individual (belonging to the given household), and eligible womenFootnote ¹ (of the household). The data set on eligible women provides variables on education of the married woman and the husband, mother-in-law's education, age, expectation of expenses borne during the marriage by the groom side and the bride side and other forms of gifts received from the community in marriage. These variables are used to study assortative mating in education and its relation to dowry. Factors such as household income and average education level in the household are mapped from the household data of IHDS-II. These variables are used as controls since they may play an important role in selection of bride. For example, a household with high average education would prefer educated brides. Further religious affiliation and caste categories are also taken from the household data.

Marriage expenditure net of expenses by the bride and groom's family provides for a close proxy for dowry. Marital expenditure by the groom's family was based on the following question from the head of the household, “At the time of the boy's marriage, how much money is usually spent by the boy's family?” Similarly, expenditure by the bride's family was based on the following question, “At the time of the girl's marriage, how much money is usually spent by the girl's family?” Dowry was calculated as the difference in average expenditure incurred by the bride and the groom's family. To avoid measurement bias due to differences in cost of living across states, the calculated dowry was weighted by consumer price index of each state in the year 2011.

We include dowry prominence status of a district as an explanatory variable to examine marital assortative mating. Marital expenditure however may not be a good measure for dowry prominence in a district. Marriage expenditure may be determined by other factors also such as ability to pay and preferences of individuals, besides the cultural norms regarding marital transfers. To compute a measure of dowry predominance in a district, we used the proportionate number of dowry deaths in a district in 2011 based on data provided by National Crime Records Bureau (NCRB). Dowry deaths provide a good proxy for the prominence of dowry in a district, since it is likely to be reported with a high probability and with greater accuracy. A district is defined as more tolerant toward the practice of dowry if the percentage of dowry deaths exceeds 1.5 (average percentage of dowry deaths).Footnote ² Finally, data for 10–16 age-specific sex ratio (males per 1000 females) at the district level is taken from the Indian Decennial Census 2011 and data for the number of high schools in a district is sourced from the Department of School Education and Literacy Statistics Division, MHRD, Government of India.

The descriptive statistics for the variables from IHDS-II, NCRB, and Census 2011 are presented in Table A.1 in Appendix A.3. The descriptive statistics suggest that, on average, husbands are more educated than the wives. The net expenses borne on wedding by the bride's family are positive, indicating positive groom price and marital transfers from the bride to the groom's family. The statistics are representative of sex ratio biased toward males, showing 1098 males as compared to females in the age group of 10–16 years old across India. Dowry deaths as a percentage of married females in a district range from 0 to 8.4%. On average, the districts in India witness approximately 1.5% of dowry deaths as a proportion of married girls.

Scatter plots of the education level of husband and wife in Figure 1 show a strong positive association between the two variables. Potential grooms and brides are likely to choose from their own education (ability) distribution.

Figure 1. Scatter plot for association between the education level of husband and wife in a household (IHDS-II).

Figure 2 provides an overview of state-wise average net expenditure incurred by the bride's family. The figure suggests large regional variation in the net marital expenditures borne by the bride side of the family. A closer look at the numbers is indicative of least dowry transfers in the north-eastern states of India including Nagaland, Assam, Mizoram, and Meghalaya. These states are also known for an above average level of women representation and independence. On the contrary, states from southern India such as Kerala, Tamil Nadu, and Karnataka, although possess highest standards of women literacy levels and women workforce participation, rank highest in dowry payments.

Figure 2. Average dowry expenditure across states of India (IHDS-II).

Region-wise and state-wise dot plot in Figure 3 provides an overview of the association between average dowry payments and years of schooling of the husband and wife. Dowry payments are seen to be higher in states with higher levels of husband's education and lower levels of wife's education.

Figure 3. Region-wise dot plot of average dowry across states and average schooling years of husband and wife.

4. Identification strategy

To study the association between female education, marital sorting, and dowry prominence, we estimate the following specification for individual i in household h of district d:

(1)$$ \eqalign{ Edu\_Wife_{ihd} = \alpha & + \beta _1Edu\_Husband_{ihd} + \beta _2Dowry\_District_d \cr & + \beta _3Educ\_Husband_{ihd} \times Dowry\_District_d + \gamma _hX_h + \delta _{rh} + \delta _{ch} + \delta _s \cr & + \varepsilon _{ih}}$$

where $Edu\_Husband_{ihd}$ denotes the education level of husband (of the surveyed married female i) in household h of district d. A positive estimate of β ₁ would indicate positive assortative mating where a household finds it optimal to marry potential grooms and brides with similar education levels. β ₂ measures the difference in the education level of brides in districts with greater prominence of dowry.

β ₃ estimates the differential outcome on marital assortative decision of male education in districts with greater dowry prominence. This could be either positive or negative. Districts strongly driven by norms of dowry may exhibit a positive β ₃ that would suggest stronger assortative mating in marriage market in dowry prevalent districts. In this case, dowry and female education are complements, such that higher dowry is paid to seek a better educated groom for a bride with higher education. If dowry and female education are substitutes, β ₃ would be negative that indicates males with higher education find it desirable to substitute education of potential bride in compensation of dowry.

X _h includes household level controls for income, age difference between husband and wife, average education level of the household, and the urban or rural status of residence of the household. δ _rh, δ _ch, and δ _s are the fixed effect controls for religion and caste of a householdFootnote ³ and state fixed effects, respectively.

Ordinary least squares (OLS) estimates may pose potential endogeneity bias due to omitted unobserved factors that may together determine the education levels of husband and wife. To circumvent this problem, we use the IV strategy and instrument husband's years of schooling with the mother-in-laws years of schooling. Existing studies show that the education level of mothers is positively and significantly associated with the education level of children [Rihani (Reference Rihani2006); De Coulon et al. (Reference De Coulon, Meschi and Vignoles2008)]. Mother-in-laws schooling is derived from the “Eligible Woman” questionnaire for married females in the age group of 15–49 years. An eligible woman's response to mother-in-law's education is recorded from the question that asks, “How many standards/class your husband's parents completed?” (The response is recorded for mother and father separately.)

As discussed before, dowry transfers from the bride's family to the groom can have potentially offsetting effects on education homogamy. To examine this hypothesis, we estimate in equation (2) the direct relation between dowry and education levels of husband and wife, independently, and the joint effects of husband-and-wife education on dowry. The coefficient b ₃ in equation (2) directly tests for the joint association between husband-and-wife female education and the dowry exchanged:

(2)$$Log( {Dowry} ) _{ihd} = a + b_1Edu\_Husband_{ihd} + b_2Edu\_Wife_{ihd} + b_3Edu\_Husband_{ihd} \times Edu\_Wife_{ihd} + \gamma _hX_h + \gamma _dX_d + \delta _{rh} + \delta _{ch} + \delta _s + \varepsilon _{ih}$$

Here, b ₁ is expected to be positive as higher education of potential grooms would reflect greater ability and hence be more valued in the marriage market. b ₂, on the contrary, is expected to be negative. A rise in the education level of potential bride would raise her bargaining power in the marriage market and hence would lead to a fall in the transfers made to the groom's family at the time of marriage. b ₃ directly tests for whether dowry changes with an additional year of education of both the groom-and-bride. A positive estimate of b ₃ would suggest complementarity in education levels for dowry, such that the bride's parents are willing to pay a higher dowry to seek a better ability husband for their daughters with higher education. If b ₃ is negative, education levels of husband and wife are substitutes in dowry. With a positive b ₁, although dowry may rise with male education, but the marginal increase is smaller with rise in female education with a negative b ₃. The household is willing to substitute dowry for a bride with higher education. The conceptual framework shown in section 6 mathematically shows these relations in further details.

X _h includes household level controls for income, age difference between husband and wife, and urban or rural status of residence of the household. X _d includes district level control for sex ratio. δ _rh, δ _ch, and δ _s are the fixed effect controls for religion and caste of a household and state fixed effects, respectively.

However, OLS estimates may be biased due to unobserved factors that may simultaneously affect the education levels and dowry. The endogenous variables in this specification are: education level of husband and wife, and the interaction. Following Currie and Moretti (Reference Currie and Moretti2003) who use availability of colleges in a woman's county as an instrument for maternal education, years of schooling of the wife is instrumented with the number of high schools in the district. The number of schools in a district is unlikely to be correlated with dowry exchanged in the household. Unlike in equation (1), we cannot use mother-in-law's education as an instrument for husband's education due to the potential failure of the exclusion restriction. Jeyaseelan et al. (Reference Jeyaseelan, Kumar, Jeyaseelan, Shankar, Yadav and Bangdiwala2015) show that the socio-economic status of the mother-in-law affects dowry and dowry-inflicted violence on the bride. Instead, we proxy husband's education with that of his mother and instrument for female education with the number of high schools in a district as shown in equation (2a):

(2a)$$Log( {Dowry} ) _{ihd} = \mu + \psi _1Edu\_Husband\_Mother_{ihd} + \psi _2\widehat{{Edu\_Wife_{ihd}}} + \psi _3Edu\_Husband\_Mother_{ihd} \times \widehat{{Edu\_Wife}}_{ihd} + \gamma _hX_h + \gamma _dX_d + \delta _{rh} + \delta _{ch} + \delta _s + \varepsilon _{ih}$$

where $\widehat{{Edu\_Wife_{ihd}}}$ is the predicted education of wife from the first stage when instrumented with the number of high schools in the district.

5. Empirical assessment

Table 1 shows results for equation (1). Columns 1–3 show the OLS estimates. All regressions control for district and household-specific characteristics that may be correlated with the education level of the husband and the wife.

Table 1. Marital assortative mating in years of schooling and difference in dowry-prominent districts

Includes controls for urban/rural residence of the household, average education of the household, difference in age of the husband and wife, household income, religion, and caste.

Robust standard errors in parentheses.

***p < 0.01, **p < 0.05, *p < 0.1.

The OLS estimates are directionally consistent. The results suggest that there exists a positive association between the education levels of husband and wife which indicates positive assortative mating in education.

These results are consistent with the findings of Mare (Reference Mare1991) and Mancuso (Reference Mancuso1997) who show that it is unlikely for individuals with higher education levels to marry someone with a lower education. Similarly, Qian (Reference Qian1998) found that females with higher education were less likely to marry men with a lower education level.

In column 3, we include as an additional regressor the interaction variable between the dowry district and husband's education. Although the estimates suggest a positive and significant association between the education level of the husband and the wife, this association is weaker in the dowry prevalent districts as indicated by the negative significant effect of the interaction variable. The groom's family is willing to accept a bride with lower education for higher dowry. There exists substitution between bride's schooling years and dowry exchanged. Potential brides with lower education are able to secure a better educated groom by paying higher dowry and vice-versa.

As discussed in the empirical strategy, IV estimation addresses any potential endogeneity arising due to reverse causality or omitted variable. A female with higher education may choose to marry a male who is better educated and thus the causality may run in the reverse direction. Alternatively, husband and wife's education levels may be determined simultaneously by factors such as cultural norms, preferences, attitude, and perception of individuals toward education. Wu–Hausman's F-statistic to test for the endogeneity of education level of husband is 685.43 and rejects the null of the variable being exogenous. To address this, bride's mother-in-law's education is used as an IV for the years of schooling of the husband.

Table 2 shows the first-stage estimates. The estimates suggest that men with mothers of higher education have higher years of schooling. Husband's mother's education is significantly and positively associated with husband's education level and the overall model is significant with a high F-statistic.Footnote ⁴

Table 2. First stage: husband's mother's years of schooling as IV for husband's years of schooling

Includes controls for urban/rural residence of the household, average education of the household, difference in age of the husband and wife, household income, religion, and caste.

Robust standard errors in parentheses.

***p < 0.01, **p < 0.05, *p < 0.1.

In Table 1, columns 4–6 show the estimates with IV estimation. Comparing the OLS to IV estimates in Table 1, we find that OLS estimates are downward biased suggesting that omitted variables such as cultural beliefs that encourage investment in education of men may also discourage schooling among women.

A threat to the exclusion restriction is that the mother-in-law's socio-economic status, in particular education level, may be correlated with the bride's schooling level. For instance, more educated mother-in-law may have greater bargaining power in the household and consequentially in deciding the characteristics of potential brides including age at marriage and education. In our study, there is some survey evidence that this may not be the case. As part of the IHDS survey, ever-married women between the ages of 15 and 49 were asked a series of five questions about decision-making in the household. The respondent reported whether she, her husband, a senior male, a senior female, or someone else had a say in that decision. One of the questions asked was: “Please tell me who in your family decides: To whom your children should marry?”. Survey data revealed that in 74% of the cases, the decision is made mostly by the husband. The respondent herself has a larger role only in 11% of the cases. Since women are less likely to make a decision on the marital choices for their children, it would be valid to assume that husband's mother's education is exogenous to the years of schooling of wife.

However, survey data responses could be influenced by the experimenter demand effect. Thus, we conduct additional robustness checks to test for the validity of the instrument. We first estimate the model again by excluding from the sample households with a female household head who may be more likely to make marriage-related decisions.

The results in Table 3 in column 1 show that the findings on positive assortative mating in education are robust to exclusion of such households, where mother-in-law could have a significant role in determining the education levels of the bride. In columns 2 and 3, we exclude females “who have ever worked for pay/wages” and those with years of schooling more than 10 years, respectively. By restricting the sample to women who either do not have sufficient education levels or have never been employed, we focus on the sub-sample where female education offers pure non-monetary benefits to the household. The estimates are consistent with the main specification, which suggests positive marital assortative mating in education, with results being weaker in districts with greater dowry prominence.

Table 3. Validity of mother-in-laws schooling as an IV for husband's years of schooling

Robust standard errors in parentheses.

***p < 0.01, **p < 0.05, *p < 0.1.

Next, we study the association between dowry on the one hand and husband and wife's education level and their interaction on the other hand. OLS estimates in Table 4, columns 1 and 2, show a positive and significant relationship between education levels of both husband and wife and the amount of dowry exchanged. However, OLS estimates may be biased due to unobserved factors that may simultaneously affect the education levels and dowry. As discussed in the empirical strategy, in this case, we are wary of using mother-in-law's education as an instrument for husband's education due to the potential failure of the exclusion restriction. Instead, we proxy husband's education with that of his mother and instrument for female education with the number of high schools in a district.

Table 4. Association between dowry and years of schooling

Includes controls for urban/rural residence of the household, difference in age of the husband and wife, household income, religion, caste, and district sex ratio.

Standard errors in parentheses.

***p < 0.01, **p < 0.05, *p < 0.1.

First-stage estimates are presented in Table 5. The estimates show a strong positive association between the number of high schools in the district and wife's years of schooling. In case of higher district sex ratio with a greater number of males, females achieve fewer years of schooling. Estimates suggest that in households with urban residence and higher income, wives have higher education levels. Higher age difference between husband and wife is negatively correlated with wives' education level.Footnote ⁵ The overall F-statistic of first-stage model is 210.92 for wife's schooling and indicates the overall model being significant.

Table 5. First stage: number of high schools in the district as IV for wife's years of schooling

Standard errors in parentheses.

***p < 0.01, **p < 0.05, *p < 0.1.

In column 4 of Table 6, IV estimates suggest that an additional year of husband's schooling is associated with a rise in dowry by 1%. A rise in wife's schooling year on the contrary shows a fall in dowry by 0.21%. The estimates thus suggest that son's education offers positive returns to the household in terms of a higher dowry, whereas bride's education is associated with lower dowry exchanged. The coefficient for interaction between education levels of husband-and-wife tests for the joint marginal effect of additional years of schooling of the bride and groom on dowry. A negative estimate for the interaction term suggests that the marginal rise in dowry with male education is smaller with a rise in female years of schooling. Thus, there exists substitution between the education levels of bride and the dowry exchanged.

Table 6. Robustness validation IV estimates for the association between dowry payments and years of schooling

Robust standard errors in parentheses.

***p < 0.01, **p < 0.05, *p < 0.1.

These results provide credence to the assortative mating estimates in Table 1 that show that positive assortative mating result is weaker in dowry-prominent districts. Education of husband-and-wife is substitutes in dowry. Dowry falls with the education level of the bride for a given level of groom's education, and rises if the bride is less educated. In India, therefore, both education and transfers at the time of marriage are significant determinants of marital assortative mating.

It may be argued that the IV estimates derived in Table 4, that estimate the joint association of husband-and-wife's years of schooling on dowry, may be driven by certain factors specific to individuals, household, or the districts themselves. Validation tests are presented in Table 6. Models 1 and 2 exclude women from analysis who belonged to a different town or city before marriage. Since we use the “number of high schools in the district” as an instrument for wife's education level, this robustness check ensures that we have correctly mapped high-school data to each eligible woman. The IHDS-II data do not provide information on the district of residence of females before marriage, therefore we are assuming here that the spouses belong to the same district. But, the survey asks the eligible women “What is your childhood place of residence.” There are approximately 2,000 observations where the natal district of the wife is not same as the husband's. Our results are robust to excluding these observations.

Models 3 and 4 exclude the outlier districts in dowry deaths to ensure that the results are not driven by extreme values. Excluding the districts that either have a history of almost negligible dowry deaths or a large percentage of dowry deaths, we exclude any biasedness in the results that may be caused due to strong cultural norms or social beliefs. The estimates from the validation tests are consistent, significant, and close to the main model.

6. Model to explain empirical findings

Our empirical results suggest that there exists education homogamy in India; however, this association is weaker in dowry-prominent districts. This section explains the empirical findings through a theoretical model of household utility maximization based on Becker's (Reference Becker1991) “Assortative Marriage Market” model. We derive and discuss the conditions under which positive or negative assortative mating would be optimal in education levels. Dowry is considered to be a one-time income augmenting transfer payment from the bride's family to the groom's family. Since dowry is an equilibrating factor for the differences in the traits of the husband and wife, we model dowry to be a function of education levels of groom and bride [Anderson (Reference Anderson2007)].

The household utility function of the groom is a function of m market goods and services x _i, and leisure t _j for each male j. We assume that only males participate in the wage market so that there is no division of time by females between leisure and labor work. This assumption is driven by the data that indicate low female participation in the labor market in India.

Household production function:

(3)$$Z = f( {x_1, \;\ldots , \;x_m; \;t_1, \;\ldots , \;t_j} ) $$

where x _i is the market goods and services i = 1…..m and t _j is the leisure hours of male members j = 1…..n.

Budget constraint: The household budget constraint ensures that the total expenditure on consumption goods and services, x _i, with price vector p cannot exceed the sum of income from labor l _j at a wage rate w _j for each male individual j in the household; property income v (given and constant); and dowry, D. Dowry is assumed to be a one-time inter-household transfer and adds to the income of the post marital household (groom's household). Dowry is a function of male and female education in the post-marital household, S _m and S _f respectivelyFootnote ⁶ (Goli et al., Reference Goli, Singh and Sekher2013). In the marriage market, households choose a bride with a given level of education among potential brides (with different education levels). We assume that further investment in the education of girl after marriage is not taken into consideration at the time of match making or for fixing the dowry amount:

(4)$$\mathop \sum \limits_{i = 1}^m p_ix_i = \mathop \sum \limits_{\,j = 1}^n w_jl_j + v + D( {S_m, \;S_f} ) ; \;\;\;\;\;\;\;\;\;\;\;\;$$

where p _i is the price of market goods and services; w _j is the wages of male j; l _j is the work hours of male j; v is the property income; D is the dowry; S _f is the education of female, bride; and S _m is the education of male, groom

Time constraint:

(5)$$l_j + t_j = T, \;\;\;\;\;\;\;\forall j$$

Substituting equation (5) in (4), the goods market and time constraints can be represented as a full income constraint:

(6)$$\mathop \sum \limits_{i = 1}^m p_ix_i + \sum w_jt_j = \sum w_jT + v + D( {S_m, \;S_f} ) = I$$

where I stands for full income achievable with w _j as given in a perfectly competitive labor market.

In developing nations characterized by low female workforce participation and poor returns to female education, there exists division of work roles between males and females. Males take up larger roles in the labor market and females in household activities. We thus assume that S _m increases both monetary and non-monetary returns in the household production and males face competitive wages across labor markets such that, w _j = w. Female education, S _f, on the other hand, is a non-monetary trait. This is consistent with Afridi et al. (Reference Afridi, Dinkelman and Mahajan2018) who find evidence of declining labor force participation in rural India among married and educated women. They further argue that relatively higher returns from education from engaging in domestic work, than from labor force, may explain the declining trends.

6.1 Household cost of production

Household production necessitates the employment of inputs in the production process. The household output is the amount of goods and services it could consume, assets it could raise, and the quality of children it could rear. Children are considered consumption goods that generate positive utility with inputs required in terms of time and effort. Costs would involve time, effort, and human capital required in the process of production. Cost of household production is a function of prices of consumption goods and education levels of household members. Rise in prices makes consumption expensive, raising the opportunity cost of leisure, and cost of household production:

(7)$$C = C( {\,p, \;S_m, \;\;S_f} ) $$

Researchers have shown that the children of better educated mothers spend more time studying and exhibit better health outcomes compared to mothers with lower schooling [Glewwe (Reference Glewwe1999); Cui et al. (Reference Cui, Liu and Zhao2019)]. Thus, education raises individual efficiency through increased marginal productivity in production and affects outcomes such as health and child education positively leading to lower costs of household production. Due to improved efficiency with education, marginal cost of the household is assumed to be decreasing in the education of both male and female such that:

$$\displaystyle{{\partial C} \over {\partial S_m}}\equiv C_m < 0$$

$$\displaystyle{{\partial C} \over {\partial S_f}}\equiv C_f < 0$$

The household production could be represented as a proportion of household production to costs:

$$\eqalign{Z = & \displaystyle{{Full\;Income} \over {Average\;Cost\;of\;Production}} = \displaystyle{{\sum w_jT + v + D( {S_m, \;S_f} ) } \over {C( {\;p, \;S_m, \;\;S_f} ) }} \cr = & \;\displaystyle{I \over {C( {\;p, \;S_m, \;\;S_f} ) }}} $$

As is evident from the household income per unit of cost, the education of the potential groom (S _m) and bride (S _f) impacts household production function both via a change in dowry income and a fall in the cost of household production.

A rise in male education raises the groom-price in the market with a corresponding increase in dowry transfers. Higher male education simultaneously brings down the cost of household production. The total effect of increase in male education is thus positive on household production per unit of cost. However, a rise in female education increases bargaining power in the marriage market and leads to fall in dowry transfers. This causes countering effects on the production to cost ratio. On the one hand, the groom's household would see a fall in dowry with rise in female education, reducing the post-marital income. On the other hand, an educated bride would lead to a fall in cost. The net effect of female education on household production per unit of cost is thus ambiguous. Mathematical explanations for the same are provided in the following sub-sections and Appendix A.1 shows the derivations.

6.4 Model propositions

In the given framework, there exists four conditions/propositions under which positive or negative assortative mating in education may be optimal.

Proposition 1: Reinforcing household cost and offsetting dowry in education of husband-and-wife, such that C _m.f < 0 and D _m.f < 0 .

For positive assortative mating to be an optimal outcome, the decline in costs −both direct (C _m and C _f) and joint (C _m.f) −should be stronger to overcome the fall in dowry with a rise in female education (D _f) and the corresponding offsetting effects (D _m.f).

Proposition 2: Offsetting effects on household cost and dowry in education of husband-and-wife, C _m.f > 0 and D _m.f < 0.

In this case, the marriage market can still achieve positive sorting where the likes get sorted in equilibrium if the direct effects of fall in cost and rise in dowry with male education are stronger than the offsetting effects. This would be true if the individual efficiencies in cost achieved with higher education are stronger than the offsetting effects on both cost and dowry. If the bride individually is able to bring down the household costs to an extent that it compensates both for the loss in dowry and any substitutions in the cost reductions, positive assortative mating would be ideal even with offsetting education effects on costs and dowry.

Proposition 3: Offsetting household costs and reinforcing dowry effects in education of male and female, C _m.f > 0 and D _m.f > 0.

The result on positive assortative mating gets strengthened, in comparison with proposition 2. Dowry effect may be reinforcing, i.e., dowry increases with the education of husband-and-wife together, with the willingness to marry an educated daughter to a higher educated groom. The household would achieve higher output with an increase in education levels of both the groom-and-bride if the individual cost reducing effects and reinforcing dowry effects are stronger than the joint offsetting cost effects.

Proposition 4: Reinforcing effects of education of husband-and-wife together in both household costs and dowry, C _m.f < 0 and D _m.f > 0.

With reinforcing dowry effects, the parents of the bride may be willing to pay a higher dowry for a better, higher educated groom. Bride with higher education would thus add to the groom's household production, both by reduction in cost and a rise in dowry. This would make positive assortative mating an optimal outcome.