2.1 Data

For our analyses we use the two nationally representative datasets discussed above—(1) TUS of 1998 and (2) the NSS, Employment and Unemployment Schedule 1999. In keeping with our previous discussion, the sample is restricted to individuals who are currently married and living in urban areas. We focus on women in the age group of 20–45 years and their husbands in the corresponding age group of 20–60 years.Footnote ¹⁷ We generate a dataset where each observation gives the time spent at work (n _f and n _m), on home production (h _f and h _m), on leisure (l _f and l _m), and education levels (i and j) for each married couple along with their weights in the population.Footnote ¹⁸ Since educational attainment is not reported in years, we use six different education levels—illiterate, less than primary, Primary, middle, higher secondary, graduate and above. As the TUS does not contain data on wages, the wage returns to education are estimated using the NSS (1999). Corresponding to the sample used in the TUS dataset we restrict the NSS data as well and estimate the median wage for men (w _m) and women (w _f) corresponding to each education category separately. Our final dataset comprises of 3725 couples (see Appendix B).

Our couples dataset indicates that the average time spent on home production (domestic work) in the household (sum of husband and wife's time) is high, at nearly 8.5 hours per day, equivalent to a full day of market work. There is remarkably little variation in the total home production time by households’ monthly per capita expenditure (MPCE)—8.3 hours for the bottom relative to 8 for the top 10% of MPCE. Of the time spent on domestic work, nearly 1/8th (1.4 hours daily) of this time is spent on exclusive child care, again with barely any variation in child care time across households’ MPCE (Figure A.5 in Appendix A).Footnote ¹⁹ This suggests a social benchmark on the time spent on producing the home good of “child quality”—minimum level of human capital of the child.

Additionally, data on households’ education expenditures from the NSS, Consumption Schedule (1999) show that education is one of the largest components of child quality expenditures by households.Footnote ²⁰ Further, we find that child quality, measured by children's learning outcomes, increases with the level of education of their mothers. In the absence of data linking individuals to home-produced goods within the household in the TUS, we utilize the Indian Human Development Survey (IHDS) in 2004–05 to examine the relationship between mother's education and her child's learning. Conditional on a number of confounding factors (viz. household's economic status, father's education, and district of residence), a rise in mother's education is accompanied by higher reading, writing, and math attainment of her children (Table A.1 in Appendix A). This suggests that the productivity of more educated (married) women in home production activities may be higher than that of the less educated.

Based on the above observations, we build a theoretical model that focuses on three determinants of women's labor supply—returns to market, returns to home production, and a social norm represented by benchmarked minimum level of home good.

3.1 Household optimization

As mentioned above, households solve a joint utility maximization problem by choosing {$c_{f}^{i, j}$, $c_{m}^{i, j}$, $n_{f}^{i, j}$, $n_{m}^{i, j}$, $h_{f}^{i, j}$, $h_{m}^{i, j}$, $l_{f}^{i, j}$, $l_{m}^{i, j}$, q}. Precisely, household's utility maximization problem is given as follows:

(1)$$\max_{c_{\,f}^{i, j}, c_{m}^{i, j}, n_{\,f}^{i, j}, n_{m}^{i, j}, h_{\,f}^{i, j}, h_{m}^{i, j}, l_{\,f}^{i, j}, l_{m}^{i, j}, q} \; \theta^{i, j} U_{m}^{\,j} + ( 1-\theta^{i, j}) U_{\,f}^{i},\; $$

subject to,

$$\eqalign{& c_{\,f}^{i, j} + c_{m}^{i, j} + q = w_{\,f}^{i}n_{\,f}^{i, j} + w_{m}^{\,j}n_{m}^{i, j} \quad [ \rm{income\, constraint}] ,\; \cr & n_{\,f}^{i, j} + h_{\,f}^{i, j} + l_{\,f}^{i, j} = 1,\; \, n_{m}^{i, j} + h_{m}^{i, j} + l_{m}^{i, j} = 1 \quad [ \rm{time\, constraints}] ,\; \cr & H = q^{\delta}[ z_{\,f}( a_{\,f}^{i}h_{\,f}^{i, j}) ^{1-\rho} + z_{m}( a_{m}^{\,j}h_{m}^{i, j}) ^{1-\rho}] ^{( 1-\delta) /( 1-\rho) }\ \quad [ \rm{technology\, constraint}] ,\; \rm{and}\cr & c_{\,f}^{i, j},\; n_{\,f}^{i, j},\; h_{\,f}^{i, j},\; l_{\,f}^{i, j},\; c_{m}^{i, j},\; n_{m}^{i, j},\; h_{m}^{i, j},\; l_{m}^{i, j} \geq 0 \quad [ \rm{non {\hbox -} negativity\, constraints}] .}$$

The first constraint is the income constraint of the household which ensures that the consumption of female and male agents and the expenditure toward market good for home production is equal to the total income of the household. Next, the time availability constraint, which holds for both females and males, guarantees that the total time on the three different activities adds up to one. The third constraint is the technology constraint for the household good production. The last constraint is the usual non-negativity constraint that will hold for both the agents. For notational simplicity, we do not put a superscript or subscript on H but it is denoted for the pair i, j. We introduce the parameter α^i,j  ∈ (0, 1) which represents the inverse of the responsiveness of home good production to a given social norm.Footnote ²⁶ In our specification, if all households face the same social benchmark $\bar {H}$, households that produce high H have low α^i,j .Footnote ²⁷

The optimization problem defined above guarantees unique interior solutions for the choice variables (see details in Appendix C). The solution to the above problem, using the first-order conditions, is given below:

(2)$$\eqalignno{c_{\,f}^{i, j} & = {( 1-\theta^{i, j}) ( w_{m}^{\,j} + w_{\,f}^{i}) \over ( 1 + \phi_L) + \frac{\phi_H}{1 - \alpha^{i, j}}};\; c_{m}^{i, j} = {\theta^{i, j} ( w_{m}^{\,j} + w_{\,f}^{i}) \over ( 1 + \phi_L) + \frac{\phi_H}{1 - \alpha^{i, j}}},\; \cr n_{\,f}^{i, j} & = 1- {\left(1 + \frac{w_{m}^{\,j}}{w_{\,f}^{i}} \right)( 1-\delta) \over \left(\frac{( 1 + \phi_L) ( 1-\alpha^{i, j}) }{\phi_H} + 1\right)( \Psi_{\,f}^{i, j} + 1) } - {\left(1 + \frac{w_{m}^{\,j}}{w_{\,f}^{i}} \right)( 1-\theta^{i, j}) \over \frac{( 1 + \phi_L) }{\phi_L} + \frac{\phi_H}{\phi_L( 1-\alpha^{i, j}) }},\; \cr & \quad \rm{where} \ \Psi_{\,f}^{i, j} = \left( \it {z_{m}\over \it z_{\,f}}\right)^{\it 1/\rho}\left( \it {w_{\,f}^{i}a_{m}^{\,j}\over w_{m}^{\,j} a_{\,f}^{i}}\right) ^{\! \! \!{\it 1-\rho\over \rho}},}$$

(3)$$\eqalignno{n_{m}^{i, j}& = 1- { \left(1 + \frac{w_{\,f}^{i}}{w_{m}^{\,j}} \right)( 1-\delta) \over \left(\frac{( 1 + \phi_L) ( 1-\alpha^{i, j}) }{\phi_H} + 1\right)( \Psi_{m}^{i, j} + 1) } - { \left(1 + \frac{w_{\,f}^{i}}{w_{m}^{\,j}}\right)\theta^{i, j}\over \frac{( 1 + \phi_L) }{\phi_L} + \frac{\phi_H}{\phi_L( 1-\alpha^{i, j}) }},\; \cr & \quad\rm{where } \ \Psi_{m}^{i, j} = 1/\Psi_{\,f}^{i, j},}$$

(4)$$h_{\,f}^{i, j} = {\left(1 + \frac{w_{m}^{\,j}}{w_{\,f}^{i}} \right)( 1-\delta) \over \left(\frac{( 1 + \phi_L) ( 1-\alpha^{i, j}) }{\phi_H} + 1\right)( \Psi_{\,f}^{i, j} + 1) },\; $$

(5)$$\eqalign{h_{m}^{i, j}& = { \left(1 + \frac{w_{\,f}^{i}}{w_{m}^{\,j}} \right)( 1-\delta) \over \left(\frac{( 1 + \phi_L) ( 1-\alpha^{i, j}) }{\phi_H} + 1\right)( \Psi_{m}^{i, j} + 1) },\; \cr l_{\,f}^{i, j} &= {\left(1 + \frac{w_{m}^{\,j}}{w_{\,f}^{i}} \right)( 1-\theta^{i, j}) \over \frac{( 1 + \phi_L) }{\phi_L} + \frac{\phi_H}{\phi_L( 1-\alpha^{i, j}) }};\; \quad l_{m}^{i, j} = { \left(1 + \frac{w_{\,f}^{i}}{w_{m}^{\,j}}\right)\theta^{i, j}\over \frac{( 1 + \phi_L) }{\phi_L} + \frac{\phi_H}{\phi_L( 1-\alpha^{i, j}) }},\; \quad \rm{and} \cr q &= {( w_{m}^{\,j} + w_{\,f}^{i}) \delta \phi_H\over ( 1 + \phi_L) ( 1-\alpha^{i, j}) + \phi_H}. }$$

Using the above expressions, it is straightforward to verify that in this proposed theoretical setup, all the endogenous variables are affected by the social norm. More precisely, for a given level of education i, j, if α^i,j is low, both members of the household provide lower labor time in home production and the level of leisure increases for both. However, the accompanying change in labor hours provided in the market remains ambiguous. Further, higher norm also results in higher expenditure on market input q required for home good production. The following two relationships are also, then, obvious from above:

(6)$${h_{\,f}^{i, j}\over h_{m}^{i, j}} = \left({w_{m}^{\,j}z_{\,f}( a_{\,f}^{i}) ^{1-\rho}\over z_{m}w_{\,f}^{i}( a_{m}^{\,j}) ^{1-\rho}}\right)^{1/\rho},\; \quad \rm{and}$$

(7)$${l_{\,f}^{i, j}\over l_{m}^{i, j}} = {( 1-\theta^{i, j}) w_{m}^{i}\over ( \theta^{i, j}) w_{\,f}^{\,j}}.$$

Note that while θ affects the ratio of relative market labor supply ($n_f^{i, j}/n_m^{i, j}$) as well as leisure ($l_f^{i, j}/l_m^{i, j}$), it does not affect the ratio of time provided for home good production ($h_f^{i, j}/h_m^{i, j}$) because of the public nature of the home good. Also, in this setup relative market labor supply is affected by the benchmark $\bar {H}$. This statement follows directly from equations (2) and (3) above. This is a crucial feature of the model, since not only do we want to capture the effect of norm on individual market labor supply (i.e., in absolute terms) but also the variation in the relative labor supply with the benchmark level of $\bar {H}$. This implies that the norm affects the market labor supply of both agents, however the effects are not symmetric and therefore the relative market labor supply is not independent of the parameter α^i,j .

3.1.1 Theoretical decomposition of effects

The following expression for the allocation of time to market work by a wife with education level i and husband's education level, j, is obtained in this model,

$$n_{\,f}^{i, j} = 1- {\left(1 + \frac{w_{m}^{\,j}}{w_{\,f}^{i}} \right)( 1-\delta) \over \left(\frac{( 1 + \phi_L) ( 1-\alpha^{i, j}) }{\phi_H} + 1\right)( \Psi_{\,f}^{i, j} + 1) } - {\left(1 + \frac{w_{m}^{\,j}}{w_{\,f}^{i}} \right)( 1-\theta^{i, j}) \over \frac{( 1 + \phi_L) }{\phi_L} + \frac{\phi_H}{\phi_L( 1-\alpha^{i, j}) }} ,\;$$

where $\Psi _{f}^{i, j} = ( {z_{m}\over z_{f}}) ^{1/\rho }( {w_{f}^{i}a_{m}^{j}\over w_{m}^{j} a_{f}^{i}}) ^{{1-\rho \over \rho }}$.

Note that Ψ_f falls with the relative home productivity ratio a _f/a _m but increases with the wage ratio w _f/w _m. Given that, the following three observations are clear from the above expression of $n_{f}^{i, j}$. First, keeping other factors constant, $n_{f}^{i, j}$ increases with the level of w _f/w _m, that is, a relative wage that favors women encourages FLFP. Second, $n_{f}^{i, j}$ decreases with the Pareto weight on men (1 − θ^i,j ), ceteris paribus. This implies that the higher the bargaining power of women in household decision-making, the lower is the supply of market work by them (at the same time, they enjoy more consumption and leisure).Footnote ²⁸

Third, $n_{f}^{i, j}$ decreases with the level of home productivity ratio a _f/a _m. As the home productivity of women relative to men increases, the supply of market work by women falls, holding other factors constant. Each of these three effects is for a given level of α^i,j . As we have mentioned above, the effect of α^i,j on $n_{f}^{i, j}$ is ambiguous.

To understand how the labor supply of a wife at an education level i + 1, matched with a husband of education level k, is different from that chosen by a wife with a lower education level i, matched with a husband of education level j, we can take the difference between $n_{f}^{i + 1, k}-n_{f}^{i, j}$ which can be written as,

(8)$$\eqalign{& n_{\,f}^{i + 1, k}-n_{\,f}^{i, j} = \underbrace{\left[{( 1 - \theta^{i, j}) \over \left(\frac{( 1 + \phi_L) }{\phi_L} + \frac{\phi_H}{\phi_L( 1 - \alpha^{i, j}) } \right)} - {( 1 - \theta^{i + 1, k}) \over \left(\frac{( 1 + \phi_L) }{\phi_L} + \frac{\phi_H}{\phi_L( 1 - \alpha^{i + 1, k}) }\right)} \right]}_{a} \cr & \quad + \underbrace{\left[{\frac{w_{m}^{\,j}}{w_{\,f}^{i}}( 1 - \theta^{i, j}) \over \left(\frac{1 + \phi_L}{\phi_L} + \frac{\phi_H}{\phi_L( 1 - \alpha^{i, j}) }\right)} - {\frac{w_{m}^{k}}{w_{\,f}^{i + 1}}( 1 - \theta^{i + 1, k}) \over \left(\frac{1 + \phi_L}{\phi_L} + \frac{\phi_H}{\phi_L( 1 - \alpha^{i + 1, k}) }\right)} \right]}_{b} \cr & \quad + ( 1 - \delta) \underbrace{ \left[{\left(1 + \frac{w_{m}^{\,j}}{w_{\,f}^{i}} \right)\over ( 1 + \Psi_{\,f}^{i, j}) \left(\frac{( 1 + \phi_L) ( 1 - \alpha_{i, j}) }{\phi_H} + 1 \right)} - {\left(1 + \frac{w_{m}^{k}}{w_{\,f}^{i + 1}}\right)\over ( 1 + \Psi_{\,f}^{i + 1, k}) \left(\frac{( 1 + \phi_L) ( 1 - \alpha_{i + 1, k}) }{\phi_H} + 1\right)}\right].}_{c}}$$

Equation (7) shows that the difference in the allocation of time to market work by a wife as her education level increases can be explained using the three components shown in the under-brackets. We first discuss the role of the three components, keeping α^i,j constant across education levels. The first component (a) is clearly the effect of a change in Pareto weights when the wife's education increases (now matched to a husband having a different education level). The second component (b) reflects a combined effect of the Pareto weights and relative female wage. The third component (c) reflects the combined effect of relative female wage and relative female home productivity. All three factors in these components—Pareto weights, relative female wage, and relative female home productivity—vary with the education level for a fixed α. The next paragraph sheds some light on the sign of the expression $n_{f}^{i + 1, k}-n_{f}^{i, j}$.

The effect of a change in Pareto weights through (a) on the marginal labor supply is straight forward: higher Pareto weights for women imply less time allocated by them in market work. To understand term (b) better, let us first assume that Pareto weights are invariant to education and equal 1 − θ. Then (b) can be written as $( 1-\theta ) ( {w_{m}^{j}\over w_{f}^{i}}-{w_{m}^{k}\over w_{f}^{i + 1}})$ which says that if the relative wage in the higher education category is greater than the relative wage in the previous education group, that is if $w_{m}^{k}/w_{f}^{i + 1}< w_{m}^{j}/{w_{f}^{i}}$ [or equivalently if $w_{f}^{i + 1}/{w_{f}^{i}}> w_{m}^{k}/w_{m}^{j}$, i.e., the relative gain in wage by a more educated woman is higher than the relative gain (or loss) in male wage], then this will increase the wife's labor supply. Thus, women's labor supply to market work will depend positively on a favorable movement of the gender wage ratio toward them. This inequality may not hold if (1 − θ) varies with education since $w_{m}^{k}/w_{f}^{i + 1}< w_{m}^{j}/{w_{f}^{i}}$ does not necessarily imply $( 1-\theta ^{i + 1, k}) w_{m}^{k}/w_{f}^{i + 1}< ( 1-\theta ^{i, j}) w_{m}^{j}/{w_{f}^{i}}$. To understand the term (c), we first assume that the home productivity ratios are constant, that is, ${a_{m}}/{a_{f}} = {a_{m}^{j}}/{a_{f}^{i}} = {a_{m}^{k}}/{a_{f}^{i + 1}}$. Given that, a favorable wage movement, which means an improvement in the relative female wage in a higher education category, guarantees an increase in her labor supply. However, in our model home productivity varies with education. Hence as the gender ratio of home productivity improves in favor of the wife with her education level, the wife's labor supply may fall due to (c).

Briefly, when all the three factors are allowed to vary, the final effect of a change in education on labor supply depends on the direction and relative magnitudes of the movements in (a), (b), and (c). While the previous literature has focused on the role of gender wage ratio and Pareto weights, our model shows that varying home productivity with the level of one's education is important for this analysis. The above discussion clearly shows that the model is capable of generating both a rise and a fall in market labor supply (U-shape) of married women as their education increases. For instance, for women with higher levels of education who may have a favorable gender wage ratio, this model can generate little increase (or in fact a fall) in market work if the rise in the home productivity ratio is much larger than the rise in wage ratio at that education level.

The discussion above is for a fixed level of α^i,j and α^i+1,k. However, note that H is a normal good with respect to household (total) income and therefore with an increase in the level of education (hence wages), the level of home good production increases. Since in our theoretical model we assume a universal social norm $\bar {H}$ that is constant across all education groups, given the multiplicative relationship between H and $\bar {H}$ (section 3.1 above), α is lower for the education group that produces a higher level of home good H. Thus a fall in α with increase in education reduces the market labor supply of the wife through the components (a) and (b). However, a fall in α through the component (c) results in an increase in her market labor supply. This means that keeping all else constant, when relative home productivity and its interaction with the relative market wage is taken into consideration, a decrease in α augments the market labor supply of the wife. Thus, the overall effect of a change in α due to a higher level of education of the wife suitably matched with a husband can be of either sign depending on the characteristics of the economy.Footnote ²⁹

Table 1 summarizes the theoretical predictions in the movement of the four factors in equation (7)—relative wages (column 2), relative home productivity (column 3), relative Pareto weights on men (column 4), and relative change in responsiveness to social norms on home production (column 5)—on changes in wife's labor supply. Row 1, columns (2)–(4) show the effect on wife's labor supply for each factor when these factors increase across education levels, i.e., the direction of change in them is > 1. For instance, following the above discussion, a relative increase in female to male wage ratio as wife's education level increases, leads to an increase in wife's labor supply across education levels (denoted by > 0 in column 2, row 1). Row 2 shows the predicted effect when these factors decrease across education levels, i.e., the direction of change in them is < 1. For instance, in row 2, a relative decrease in female to male wage ratio as wife's education level increases, decreases wife's labor supply across education levels (denoted by < 0 in column 2, row 2). The effects of change in home productivity, Pareto weights, and norm responsiveness on wife's labor supply can be read in similar manner following the discussion above.Footnote ³⁰ The last row shows that in the trivial case when none of the four factors change with wife's education (= 1), there is no change in her labor supply.

Table 1. Theoretical predictions of effects on wife's labor supply

Note: Column 1 shows the direction of change in each of these four variables—relative wages (column 2), home productivity (column 3), Pareto weight (column 4), and norm responsiveness (column 5). Each cell in columns 2–5 shows the predicted direction of change in wife's labor supply for a given change in the corresponding variable (column 1) when her education increases. The predictions follow the theoretical decomposition of changes in wife's labor supply derived from equation (7). For example, an increase (> 1, depicted in row 1 in column 1) in the relative wage ratio when wife's education level increases, raises her labor supply (> 0, row 1 in column 2).

We now turn to calibrating and simulating our model on agents’ time allocation to market work, home production, and leisure.

4.1 Calibration

The Pareto weights for each of the 36 combinations of spousal education are calibrated using the ratio of the first-order conditions. We have no a priori reason to assume that men and women have the same bargaining power within the household (θ = 0.5), and across education categories. Utilizing equation (6) from the model which relates the leisure ratio of men and women to θ^i,j and their wages, we have:

$${l_{m}^{i, j}\over l_{\,f}^{i, j}} = {\theta^{i, j} w_{\,f}^{i}\over ( 1-\theta^{i, j}) w_{m}^{\,j}}.$$

From the TUS couples data, we substitute for average values of time spent on leisure by a woman and a man, and for median wages received by a woman and a man, for each combination of education categories of spouses. This gives us 36 values of θs for each possible combination of spouses with different education levels.Footnote ³¹

Next, we discuss the calibration of the (inverse of) responsiveness to the social norm—the ratio of the benchmarked minimum home production to actual home production—for each spousal education group ($\alpha ^{i, j} = {\bar {H}\over H^{i, j}}$). As discussed earlier, the home production function in our setup measures the effective expenditure on the home good (expenditure adjusted for home productivity).Footnote ³² We use data on average household education expenditure per child in urban India [from NSS (1999)] as a proxy for effective expenditure on home good production.Footnote ³³ We then compute the extent to which each education group exceeds the norm on home good production, i.e., the ratio of the minimum expenditure on education per child that must be incurred ($\bar {H}$) to the actual education expenditure per child incurred by an education group (H). The first percentile value of education expenditure per child of the lowest spousal education group (e _f = Illiterate and e _m = Illiterate) denotes the benchmarked minimum level of home good production that must be incurred by all education groups, i.e., $\bar {H}$. We assume this minimum education expenditure, $\bar {H}$, to be fixed across all spousal education categories while the average household expenditure on education per child for each combination of spousal education (H) varies across spousal education groups. Using this procedure, we are able to calibrate the value of α for each of the 36 education groups.

The parameters of the home production function—home productivity ($a_{f}^{i}$, $a_{m}^{j}$) and share of female and male labor input into home production (z _f, z _m)—and the preference parameters (ϕ _L and ϕ _H) are estimated using the closed form solutions obtained in the model. The observed values of each couple's time spent in the market and in home production are fitted to the theoretical expressions in equations (2), (3), (4), and (5). This method gives the estimates for the 12 home productivity parameters (six each for men and women corresponding to each of the six education categories) and the three parameters—z _m, ϕ _L, and ϕ _H—which do not change across education categories. We are able to obtain a set of unique solutions for all the calibrated parameters using non-linear least squares.Footnote ³⁴

The calibrated parameters are shown in Table 2. For simplicity, the 36 calibrated Pareto weights (for each possible i, j education combination of wife and husband) are averaged for each education group of women in the table. The average household Pareto weight on wife's utility does not change significantly across lower education categories (on average it is 0.27 for illiterate—middle education women) but it increases drastically for women with more than higher secondary education (approximately 0.45). The change in bargaining power with wife's education is, therefore, unlikely to explain the initial decline in female LFPR and may reduce women's LFPR only at higher secondary education or above.

Table 2. Calibrated parameters

Note: To ease presentation the 36 calibrated Pareto weights and α values (for each possible i, j education combination of wife and husband) are averaged for each education group of women and men in this table.

As expected, α decreases as education increases since more educated women (men) produce a higher value of the home good (child quality) relative to the benchmarked minimum—in line with the theoretical analysis above. Thus α decreases from 0.018 (0.024) for illiterate women (men) to almost 0.008 (0.010) for primary-middle educated women (men) and further to 0.003 (0.002) for higher secondary and above educated women (men). Hence, on average women (men) in the highest education group produce almost 9 (12) times as much of the home good as illiterate women (men).

The estimated home productivity parameters show that home productivity increases with increase in education for both men and women, with the rate of increase being largest for the highest education categories. The increase is smaller and uneven, though, for lower levels of education. Across the disaggregated education levels, from less than primary to middle schooling, home productivity is very similar. It would then be more intuitive to look at the comparison across broad four categories of education—illiterate, women with some education (less than primary—middle classes), completed schooling, and graduate. Here, we do find an unambiguous increase in home productivity between illiterate women (0.02) and women with some education (0.034) by almost 70%.

The share parameters in the home production function show that men's effective time spent in home production is about 35% and that by women is 65%. Though, on an average women's share of overall time in home production is almost 90%, adjusted for home productivity this falls to 65%. This could be driven by a higher average home productivity of men relative to women up to middle education levels, as shown in the panel above of Table 2. We also find that the ratio of ϕ _H and ϕ _L is 1.1, indicating that households place a greater weight on home production than leisure. Two behavioral parameter values are borrowed from the literature for the US—(1) the inverse of the elasticity of substitution, ρ is set at 0.4037 and (2) δ, which measures the relative share of market inputs to labor in home production is set at 0.29.Footnote ³⁵ Later we conduct sensitivity analyses to show that using different values of ρ or δ don't change the results significantly.

To summarize, our calibration results approximate the broad patterns observed in the Indian economy and also capture the household preferences in time allocation.

4.2 Simulation

In this section, we first verify the contribution of each channel toward the observed movements in wife's labor market time. To do this, we use data on wages and the calibrated parameters to calculate the movement of relative wages, home productivity, Pareto weights, and the (inverse of) responsiveness to the social norm (i.e., the extent to which the benchmarked minimum home production is lower than actual home production) across education levels. These are reported in Table 3 for changes across each consecutive education level in column (1), denoted by the following numeric codes: 0 − illiterate, 1 − less than primary, 2 − primary, 3 − middle, 4 − higher secondary, 5 − graduate and above.

Table 3. Estimated changes in factors affecting wife's time allocation

Source: Time Use Data and NSS. Note: Numeric education codes denote the following education levels. 0 − Illiterate, 1 − less than primary, 2 − primary, 3 − middle, 4 − higher secondary, 5 − graduate and above. Average relative wage, relative home productivity, Pareto weight, and norm responsiveness is estimated for each level of wife's education using the calibrated parameter values from time use data for 3725 couples. Changes in estimated ratios across successive education levels are reported in columns 2–5.

It can be seen that the relative female wage ratio in column (2) of Table 3 declines (or increases by less than one) for each consecutive level between illiterate and middle schooling. This observed fall in relative female wages contributes toward reducing wife's labor supply with an increase in her education up to middle schooling. Thereafter, the relative female wage ratio increases (or change by more than one) for education levels from middle—graduate and above, which would raise wife's labor supply between these education levels. These findings are in line with the theoretical predictions in Table 1, column (2), which shows that wife's relative labor supply is positively related with relative female wages. Similarly, an increase in relative female home productivity from illiterate to less than primary and middle to higher secondary [denoted by a change of more than one in column (3) of Table 3 for these education levels] would contribute toward reducing female labor supply across these education levels [Table 1, column (3)]. Column (4) shows that bargaining power of men does not change much when wife's education increases from illiterate to middle schooling while it falls when wife's education increases from middle to higher secondary schooling. As predicted in Table 1, column (4), this should contribute towarddecreasing the wife's labor supply from middle to higher secondary schooling, holding other factors constant. Lastly, column (5) shows that α decreases across successive levels of wife's education, which has an ambiguous effect on wife's labor supply, as discussed theoretically earlier.

Using the estimated wages and the calibrated parameters we predict the time spent in the labor market, home production, and leisure for individuals in each education group in urban India, accounting for all the four factors simultaneously. Figure 4 plots the model's predictions against the actual time allocations observed in the data for women and men by education groups. The model is successful in generating a U-shaped female labor supply with respect to their education level—women's time allocation to market work falls from 11% for the illiterate to 7% for those with less than primary or primary levels of schooling and further to 4% at middle education level. It then rises to 17% and 21% for the two highest education levels, respectively. For men, the simulations mimic the relatively stable allocation of time to market work at over 60% across the education groups, though it somewhat under predicts market work at lower education levels. Overall the model does well for the time allocation variables that we are focusing on in this analysis, including the large gender gap in time devoted to home good production.

Figure. 4. Simulations for time spent in labor market, home production, leisure. (a) Labor supply, (b) domestic work, (c) leisure. Note: Time spent in labor market, home production, and leisure is shown as a fraction of the total time endowment of one. See data appendix for details on time use data.

6.1 Market goods for home production

In low or middle-income countries, limited supply of market goods can constrain women's time allocated to market work. This may be especially true for the more educated women, who are also more likely to belong to higher income households, and can afford to purchase market goods for home production. Hence the lack of or limited supply of market goods and services could be an alternative explanation of both low levels of women's time allocated to labor market and the muted response of women at higher levels of education to market wages.

Note that in our setup, households choose optimal amount of market good in home production. To test for the possible mechanism described above we constrain the usage of market goods in the model by imposing a restriction that q is same across education levels and that $q \leq \bar {q}$. Here $\bar {q}$ is defined to be strictly less than the minimum of the optimal q obtained across all education levels in the main model. This modification reduces wife's labor supply at higher education levels, in comparison to our model, but by a negligible amount. Since in our original setup q is chosen optimally, households respond to a constant amount of q (which is also lower relative to the optimal) by reducing the total H produced at higher education levels, while H still exceeds the minimum benchmark of $\bar {H}$ for high education groups. Thus, even though the total H produced by the household rises with education, the level of H is now lower due to the constraint on the market good. Hence, instead of increasing time spent on home production by the wife and consequently reducing her labor supply, restricting q primarily results in lower production of the home produced good. Thus, the absence or low supply of market goods may not explain the observed levels of women's time spent on market work in India.Footnote ³⁷

6.2 Household wealth

Another possible channel that could impact women's labor supply is household wealth. As female education levels increase, households are more likely to be wealthier, inducing a wealth effect which could lower women's LFP. We, therefore, incorporate exogenous increases in household wealth over the distribution of education using the 2003 National Sample Survey on Household Assets (NSS-HA) which collected information on assets owned by households. Appendix Figure A.6 plots the simulations for labor supply, domestic work, and leisure after incorporating the wealth effect. We do observe some reduction in labor supply but not substantially over and above our model's predictions. Overall, the estimated household wealth from land or residential property is too small to predict the muted allocation of time to market work by highly educated women.Footnote ³⁸

7.1 Sensitivity analyses

We conduct sensitivity analyses of the predicted paths of labor supply, home production, and leisure for the parameters which could not be calibrated and were taken from the existing literature on the US—the inverse of the degree of substitutability between men and women (ρ) and the share of market inputs in home production (δ). Under the assumption that men and women are imperfect substitutes in home production (i.e., 0 < ρ ≤ 1), we calibrate our model taking different values of ρ ∈ [0.2, 0.6] around the benchmark value of 0.4037 in the literature.Footnote ³⁹ The predicted paths do not change much because the share of men's time in home production is smaller than women's. Similarly, we calibrate the model with δ ∈ (0, 0.29). The benchmark value of δ taken from the US data is 0.29 (an average across various studies). The calibrated value of δ for the US depends on whether housing is included as a market good or not. In the Indian context, since the share of market goods is likely to be smaller than that for a developed country, for sensitivity checks we take values less than 0.29. The predicted paths again do not change much. The results for these sensitivity checks are available on request.

7.2 Variation of social norm across education groups

Recall that our theoretical model assumes a single $\bar {H}$ for society, i.e., the minimum benchmark for the home good is the same for all education groups. However, it is possible that $\bar {H}$ varies by education—higher education groups may desire higher minimum level of child quality. Notably, we calibrate the value of α, which represents the ratio of $\bar {H}$, to actual H. When higher education groups have a higher benchmarked level of home good, the ratio of the two (${\bar {H}\over H}$) may not vary significantly across education groups, since they also produce higher levels of H.Footnote ⁴⁰

We check the robustness of our results to calibrating α using the first percentile value of education expenditure per child for each education group as the $\bar {H}$ for that group. Indeed, Appendix Table A.2 shows that α does not vary much across education of women and men, except for the highest education group, when we allow $\bar {H}$ to vary by education groups. Appendix Figure A.7 plots the simulations for labor supply, domestic work, and leisure using this alternative model. We do not find much difference from our previous predictions when $\bar {H}$ is constant across education groups.Footnote ⁴¹

7.3 Recent employment data

We conduct our analysis by approximating individuals’ time allocations using the most recent, comparable employment data from the NSS 2011. The details of our assumptions for the approximation of time-allocation and the simulation results using the NSS 2011 are discussed in Appendix A and Figure A.8. Specifically, Appendix Figure A.9 shows that the labor supply simulation results for our model predicts well the U-shaped labor supply of women across education categories in 2011 as well.