Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
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=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
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=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
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=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
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=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
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=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
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=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
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# The Fertility, Marriage, and Gender Equality Quandary

Authors: Anson Zhou  
Discussant: None  
Video: https://www.youtube.com/watch?v=0mE9GNhwdY8&t=2764s


## Talk (00:46:04 – 01:45:13)

[00:46:04] [applause] >> Wonderful. Thank you very much. Our next paper will be presented by Zo from the  
[00:46:17] University of Hong Kong. All right. Um, I would like to first  
[00:46:44] thank the organizers for including my paper in the program. I'm Anson from the University of Hong Kong and this paper is called the fertility marriage and gender equality quandry. I'm using the word quandry in the title to describe a difficult situation but different from the word trailemma quandry has a way  
[00:46:59] out. So the goal of the presentation is really just to describe what is the difficulty that I find between fertility, marriage and gender equality and also what is the way out that I identify. The paper is motivated by the fact that during the grand gender  
[00:47:12] convergence, we really see three important trends happening almost at the same time. We witnessed the dramatic drop of fertility and we also have seen the decline of marriage as a social institution and now many kids grow up  
[00:47:25] without both of their biological parents and also we have witnessed a dramatic or remarkable convergence of gender gaps not just income gap but also labor supply education and wealth and so on and sometimes even a reversal.  
[00:47:39] Interestingly, at the same time, there are many policies either they want to try to encourage or resist these changes. Importantly, we've seen policies trying to incentivize fertility for the reasons for related to pension  
[00:47:52] sustainability and many macroeconomists will say related to economic growth because people create ideas. We've also seen policies trying to promote dual parenthood either due to cultural or religious reasons or due to the many research that have shown that marriage  
[00:48:07] is so important for the outcomes of the kids. And we also have policies trying to advance gender equality not just for the redistribution purposes per se but also to reduce misallocation. Right?  
[00:48:20] Um existing research typically study these outcomes of fertility, marriage, gender equality and these policies in a isolated fashion or sometimes in a pair-wise uh way but it there lacks a unified framework to think about them  
[00:48:33] jointly and ask a question which I think is important. Suppose you are a government that wants to promote fertility. Suppose you want to preserve marriage as well and if you also want to encourage gender equality is that possible is it feasible or not? So that  
[00:48:48] is the question of the paper. So in the paper um first I'm going to document I think an interesting three-way trade-off which I'll just call quandry. The quandry is in the data simultaneously achieving high fertility, low single  
[00:49:03] parenthood and gender income equality arguably desirable to some extent is statistically very rare. And I'll define what high and low in a few slides. And this interesting statistical raress um  
[00:49:18] basically shows that there might be some deep dependency structures between these three indogenous outcomes. And more importantly, I think speaks to the potential policy boundaries. In other words, maybe you're a policy maker, but somehow there's a tension or a constraint that you cannot achieve all  
[00:49:32] three even though you want it. Then I developed a equilibrium model of marriage, fertility and female labor supply to understand why that is the case in the data and also to identify if there is a way out. I think the  
[00:49:45] surprising result is that level policies to improve fertility and marriage or gender equality per se can only improve at most two outcomes at expense of the third. However, there seems to be a magic bullet which is redistributing the  
[00:49:59] childcare obligations from the wives to the husbands. they can improve all three but under some circumstances it's not always true and a model will speak out two equations that you know tell you what exact are the conditions so that  
[00:50:13] it's a magic bullet then I'm going to conduct some quantitative analysis and also uh hopefully I'll have time to talk about a dynamic extension of the model so let me just jump right in into the  
[00:50:27] analysis and here is the my empirical analysis and I can I can wave my 10-minute kind of uh restriction without question. You can already start asking question if you want. So here's the empirical analysis. The first step is to  
[00:50:40] construct data. So I construct four data sets in which I can measure fertility, marriage and gender equality in a harmonized or consistent way. The first data is a OECD sample where I have 37 countries from 1970s to 2014. Oh, by the  
[00:50:54] way, I need to have four data sets because each of them come with some advantages and disadvantages so that I can have a bigger p more complete picture by having multiple data sets.  
[00:51:03] So, the first one is a OECD data set, right? Where I collect TF total fertility rate out of wedlock birth rate. In other words, it's the share of children who are born without the parents being married. And then I have gender gap measured in earnings. The  
[00:51:17] advantage of the OECD data set is that it has a long horizon in the sense that I can observe many countries over 20 or 30 years. So I can know what the transition was, where they were and where they are now.  
[00:51:30] >> And the second yes, >> you want to take marriage seriously as a as the contract in a lot of countries, you know, especially.  
[00:51:38] >> Yeah, I'm about to talk about that. Exactly. That's why I need a sec two things. One is that that's why I need a second data set and the second reason is I will be very specific about what marriage is in a model. It will be a contract. So it's not like a legal piece of paper but rather an exchange  
[00:51:52] mechanism between men and women in a model. So in the data the second data set is a world data set. It's a much so it has a much larger coverage in terms of population and also deals with some of the measurement issues in the first  
[00:52:05] data set. uh the fertility is still the TFR but you know the second the dual parenthood I'm using the nice data by Bruno and Melennia on this uh uh um dual living arrangement of the kids where they use the IPMS international microolo  
[00:52:19] data to document what fraction of the kids are living with only one parent two parents or none of them the biological parents so I'm using their data sets here and the third is the income share which I'm using from the world inequality database because the relative  
[00:52:33] earnings gap is conditional on people working. So it doesn't really account for the extensive margin of what if they don't participate in labor force at all.  
[00:52:41] So the wording equality database they have a measure which I directly take what is called the women's share of the total labor income. So I think that kind of accounts for the extensive margin of labor supply. So that's the second the the the world data set and then I'm  
[00:52:55] having two US data sets across states or across commuting zones and the reason of having US data sets is that I'm comparing drastically different economies in the previous two data sets.  
[00:53:05] Right? You can be very rich or very poor in these data sets. But now I want to look for more homogeneous institutional setting to look for if that query is still there even within the United States where you know the institutions are much more similar. That's why I have  
[00:53:20] a US uh state and commuting zone data set. And after I construct the data sets, here's the empirical analysis that I do. Um I first construct dummies for each observation using sample medians.  
[00:53:33] I'm having high fertility called F, marriage or due parenthood labeled as M and gender equality labeled as G. So the way I construct it is the following. For each observation, if your fertility is higher than the sample median, I'm just  
[00:53:47] calling you a high fertility country. Otherwise you are low fertility country and the same for for marriage and gender equality and the reason I'm using sample median instead of some arbitrary level is that for example if I just call hey  
[00:53:59] if you have a 3.0 zero to total fertility rate then you're high fertility then none of the OUCD sample would be high fertility then I can rule out the trinity by assumption but if I'm using the sample median to construct high and low then I can use something  
[00:54:13] called a dartboard approach where the joint attainment and the statistical independence benchmark will be 50% 50% 50% which is 12.5%.  
[00:54:24] Then what I'm going to do is to use the vin diagram which is something many of us learned in middle school high school to visualize you know what fraction of these observations actually achieved all three together and compare that with the  
[00:54:38] random benchmark which is 1/8 ace 12.5%. So that is the empirical analysis that I do with using these four data sets.  
[00:54:48] So let me now if without any questions about what I do here let me just show you the empirical result.  
[00:54:54] Oops. Here it is. So, these are the three van diagrams. You don't need to kind of add up the numbers yourself, but you know, every circle in the van diagram within a circle is 50% of the observation and outside a circle is  
[00:55:08] another 50% of the observation. And the main point I want you to take out from these three figures of OECD, world, and United States is that the joint attainment in all cases is way less than  
[00:55:21] the 2.5% benchmark. for the OECD it's like 1/5 for the world it's like one/ird and for the United States it's more homogeneous institution so it's better but still it's less than half in other words even though many  
[00:55:35] countries in these sample actually try to have higher fertility gender equality and preserve marriage at the same time very few countries or very few observations in the data can actually achieve that and on top of that I want  
[00:55:48] to make uh three points the typical transition that I observe when use the OUCD data, you know, I I see which status each country have before and after. The very typical pattern is that many countries started off with high  
[00:56:03] fertility and high marriage which is your canonical kind of patriarchal society to begin with. Over time, they either get rid of high fertility or they get rid of marriage or they get rid of both and they always gain gender  
[00:56:16] equality. That is a very typical transition path when countries grow.  
[00:56:22] And the second thing is I conduct something in information theory called a mutual information analysis. So mutual information anal analysis is a way to analyze whether the joint distribution of fertility, marriage and gender equality can be reduced to a pair-wise  
[00:56:36] combination by observing the pair-wise correlation. Can you summarize the relationship between all three? And the answer is no. The mutual information analysis shows something called synergy.  
[00:56:46] In other words, knowing one variable will tell you some information between the dependency structure of the two other variables. In other words, you want to know three all together and analyze them jointly at least from a statistical point of view. And third, these results are quite robust. I can  
[00:57:00] divide the samples by development levels, human capital levels or education levels and so on and the results are still there or can use different measures of what high and low means. The results are always there.  
[00:57:11] Yes. >> Why is looking above the median rather than absolutely no >> yeah I have that in the paper so I have used for example fertility can use the replacement level etc and the result holds >> but for everything  
[00:57:25] >> yes >> why you know world% >> that's a good very good point I think two things one is that using the sample  
[00:57:39] median has a very nice benchmark that you can compare with that's the 12.5% which makes it clear that somehow you know it's very much lower than that and second I think what I want you to drive home with is not really kind of uh the levels per se but rather I want to show  
[00:57:54] a negative correlation between the three things and this is kind of best visualization that I can come up with but I agree I can if you prefer any numbers and a policy targets I can use it here and see what fractional countries achieve all that  
[00:58:08] all right so the remaining questions that I want to answer in this paper is one what explain explains the three-way trade-off, right? You know, what kind of model do we need to write down to explain it? I mean, because after I show  
[00:58:21] it, I find itself quite intuitive, but you know, otherwise, I wouldn't have thought about it. And second, are there policies that it can resolve this trade-off? Suppose you are a government who actually want to achieve all three for some reason. Can you do it? And  
[00:58:35] third, what roles do technological progress play? Is this transition from having fertility and marriage to only having gender something driven by a genderneutral or gender biased technological change? So that's kind of why I need a model. I also want a model  
[00:58:49] to do welfare analysis, decompositions and predictions. I need to calibrate it.  
[00:58:53] That's kind of why I need to introduce you the structural framework.  
[00:58:58] So let me just jump right into the model. So here's the the Siri really kind of builds on the the classic >> I just want to ask one question. Yes, >> I I can build a model very simple model in which I would get all three.  
[00:59:12] >> Mhm. >> Okay. So, why don't I start with that and then ask which of the assumptions and I have just two assumptions that's all.  
[00:59:23] >> So, which of those assumptions doesn't hold >> rather than looking at your model which you're going to put a whole bunch of stuff in that's going to make certain that it doesn't hold.  
[00:59:37] Right. >> So I can come up with a really simple model >> in which I'll get all three >> Yeah. I never thought about that. Yeah.  
[00:59:46] >> Well, I mean why would you want to start that way? I mean there's many things that assumptions >> but there could be you know you have two assumptions and you get that but I could have another two assumptions and get that. So it may not be  
[01:00:01] >> I'm not certain that you can get it with an these are two extremely simple these are two very simple assumptions and one of them >> has to do with a lack of convexity  
[01:00:14] >> in pay per hour. So if I have linearity >> in pay per hour >> I'm going to get around a lot of the problems in terms of specialization.  
[01:00:26] >> Okay. The second one gets rid of the issue that we just heard before which we call we women call men's learned helplessness.  
[01:00:37] Okay. >> I I just have those two very simple.  
[01:00:43] >> I'll get all three. >> Yeah, I'm happy to talk to you later about it. But uh for now you have to stuck you stuck with with my version of the the world and uh see what what is wrong about that. I also have some simple assumptions about you know what's  
[01:00:56] going on but let's see yeah I'm very happy to talk to you later about it.  
[01:01:01] Yeah. All right. So let me just jump right into the model um if everyone is fine. So here's the model. The model is really a simple view that follows through the the Gary Becker's view of what marriage is and also how true and  
[01:01:13] sue models marriage markets. And I will have individuals with gender G. And I got tired of using the letter F and M.  
[01:01:20] So I just found out these symbols very nicely in latte that this is female and this is female and that is male right and individuals yeah you see that in the restroom but yeah anyways so [laughter] so individuals have preferences uh over  
[01:01:35] consumption which I interpreted as a bundle infertility ucn and I'm modeling it as a ces utility function over consumption and fertility and a very important assumption that I will use in this paper is that the elasticity of substitution between consumption and  
[01:01:50] fertility which is row is bigger than one. I'm making this assumption for two reasons. The first obvious reason is that you know once you have row is bigger than one you can define what is the utility of a childlessness person right otherwise if row is equal to zero  
[01:02:05] or less than zero sorry if equal to one or less than one is negative infinity so that's kind of one practical reason and the second reason I'll explain to you in like two slides to focus on uh inequality between  
[01:02:18] genders instead of within genders I'm going to make a simplification where we have homogene homogeneous wage within gender So there's exogenous wage of the men and exogenous wage of the woman.  
[01:02:29] This is an assumption that I will relax in a dynamic model where the wages are indogenously determined. But for now in this static model you have exogenous wages. And the gender wage gap gamma w is basically the ratio between men's wage and women's wage. Gamma is a short  
[01:02:44] hand of of gap. And here is the economic environment.  
[01:02:49] The marriage and fertility decision of men is is really simple. It's just a discrete choice. If men stay single, they're going to work one unit of time and they're going to consume their labor income and they don't have kids. So these are bachelors. So you have the  
[01:03:03] value of a man being single uh which is a utility of consuming all your labor income.  
[01:03:09] Otherwise once married man needs to take a contract in which they going to transfer a share of their labor income to their wives but they gain access to fertility.  
[01:03:20] So NM is basically marto fertility. So there are two things I want to say. One is that you know you have this lambda which is a sync item for other reasons not related to fertility that people wants to get married. So this is everything else and second this pair of  
[01:03:34] alpha and nm which is how much you transfer to your wives and how how large the marital fertility is is determined in the equilibrium. So these is the price vector that clears the marriage market.  
[01:03:46] And also by the way you know I don't restrict alpha to be always positive. So you can use the model to think about dollaries as well because it can be negative.  
[01:03:55] So this is from a men's side. It's a very simple economic problem. Do you get married or you take the contract, you transfer and you get kids or do you stay single where you are the bachelor and eating your income?  
[01:04:07] For women, I'm going to show you the simplest fertility choice model you've ever seen as well. Single women were going to solve this classic problem of having the trade-off between consumption and fertility. So the more children they  
[01:04:19] have, it entails a time cost, right? So they work less, but they gain uh and they have lower uh earnings and lower consumption. So this is the fertility choice of women through the labor supply margin. Very plain vanilla. For married  
[01:04:34] women, things are almost the same except for two things. One is that they also get the lambda which is the psychic benefit of marriage and second they also gain the transfer from their husbands.  
[01:04:46] So now I can talk about a second reason why I want rows to be bigger than one.  
[01:04:51] You know what happens to fertility when female wage rises in this situation.  
[01:04:55] Well from econ 101 we know that a rising wage will have both income effect and substitution effect. Right? From income income effect point of view higher wage make me want to have more children because it's a normal good. But from a substitution point of view because  
[01:05:09] children takes time cost the rising opportunity cost will reduce fertility.  
[01:05:14] Right? because you know having a kids become more expensive. So row is bigger than one means that a substitution effect dominates. In other words, in this environment, a higher woman's wage will reduce fertility due to that assumption. On the other hand, what  
[01:05:28] happens to fertility when men's wage goes up? Well, men's wage goes into the fertility decision through a simple income effect from for the married woman. So a rising man's weight will raise fertility. So in other words in this very simple model you can get  
[01:05:42] asymmetric effect of the wage changes on fertility outcomes which is consistent with the recent empirical literature by people like hlo and so on and in this very simple model I'm assuming that oh yes that's a question  
[01:05:55] there's a question Johanna so my question is so typically when we  
[01:06:09] think of the the single parent fertility decision. It's not made assuming you will stay single. It's usually made assuming you are in the perhaps not married full contract situation, but you  
[01:06:22] are at least partnered at one point >> and perhaps assuming that that transfer will come from the man that you are assuming only comes in the marriage situation.  
[01:06:33] So there's no timing here and I know you said this is static and won't be going dynamic but how do you think about you're essentially assuming that the single women are solving a problem assuming they will get no transfers from a male partner when the reality is  
[01:06:46] >> the reality is something like a quarter of them actually do. Yeah I guess >> no I mean that they are they are making the decision about fertility under an expectation of receiving a transfer and then that transfer potentially being  
[01:06:59] withdrawn when the couple breaks up. And so like there's no contracting is some of what I'm asking about.  
[01:07:05] >> Agree. I mean this is highly stylized in the sense that you know I'm assuming this kind of commitment in the marriage market where they exactly know what they're getting into without any uncertainty and misbelief but I think you are thinking of a broader framework where they might assume they will have  
[01:07:19] something but later they actually won't but you know I think that's not in the model here. Yeah. But I think that's a good point in the data how much of that drives the results but yeah.  
[01:07:28] >> Yeah. >> [laughter] >> Thanks.  
[01:07:45] When when you initially you said that that you were going to introduce dynamics, right? I thought what you >> Oh, that's OG. That's kind of across generations, but not but not within the generation. Yeah. No, but because there is a and I think Joanna was pointing to that there is an important dynamic that  
[01:07:58] you might have at least I mean in quite a few countries if you think about life cycle dynamic.  
[01:08:04] >> Yes, true. You might have a child outside of wedlock but eventually >> with an SCS gradient you get married. So that you know it's if you're thinking in a macro model to the average person >> right  
[01:08:19] >> the average person you know transition state then you become married so you spend a certain I don't know 80% of your life cycle when you have a child you're in a couple even if you had a child so  
[01:08:32] >> I'm not sure uh if that would matter >> right that's a good question >> when you when you bring this back to your uh >> that's a good question I think at least to some extent I can try to deal with the problem in the data by looking at the living arrangement of the kids when  
[01:08:46] you know for example when the kid is young and how what fraction of the kids age is only with one parent instead of you know really transitional phase where they actually get end up marrying so that's something maybe I can do in a data but in a model for now I don't have  
[01:08:58] anything like that yeah thank you all right um yes >> yeah I I understand you're trying to keep things simple I it's hard for me to think about this without thinking about  
[01:09:13] human capital investment. Can I understand that can you sort of agree say a word about that?  
[01:09:21] >> No, no. I mean here the way I'm interpreting it is that consumption is a huge bundle which might include potential human capital investments of the kids and where the substitutability parameter row is capturing in a very reduced form way the quantity quarter the trade-off but you know I can make  
[01:09:34] the model more complicated by having another good which is the human capital of the kid and that enters the budget in some way but I don't think the the main intuition will will change much. Yeah.  
[01:09:46] >> Yeah. Please, [clears throat] >> can I ask one more question? And just if we're thinking about a hypothetical world where we might be able to solve these three things, why are we starting >> assuming things are the way they are between men and women? That is, if you look at the previous slide,  
[01:10:00] >> yeah, >> with men's choices, >> why is it why couldn't it be the case, for example, that if they choose to become fathers, they could immediately withdraw and there was a trade-off between their their time. in in the  
[01:10:15] model here there are two fundamental asymmetries that are going to build in like one is the biological asymmetry in the sense that you can have single women with kids but not like single dads with kids that's kind of one thing that I bake in which I think you know is to some extent not always true we we do  
[01:10:30] have single fathers so that's not not here and the second asymmetry is that in the baseline model I'm assuming wives bear older child care and the results will all go through as long as woman is doing more and I'm going to change that assumption later and that is actually  
[01:10:43] the magic bullet. So there will be fundamental symmetries but one is biological which I'm not going to do much about it but the second I'm going to do something about in a policy. Yeah.  
[01:10:53] So okay that is the decision problem. That's kind of roughly the model. Men they make a discrete choice marry or single. Women they also decide marry or single. And also the woman who chooses how many kids to have. And to smooth things up of course I mean having  
[01:11:07] discrete choice I need some idiosyncratic lotus shocks. So people draw these idiosyncratic taste shocks for marriage and then they decide oh do I pick this contract of not having kids and with keeping my income or do I pick to get married and transfer my income to  
[01:11:21] my wife's so in the end of the day marriage rates from the men's side the supply of marriage or demand of marriage whatever you call it depends on a relative depends on the gains of marriage which is the relative values of being married and single in the  
[01:11:36] equilibrium marriage market clearing condition would just be the share of men who wants to get married is the same as the share of women who get one married.  
[01:11:44] Essentially, this is a very plain vanilla marriage market model where I just have a two-dimensional vector, right? Alpha, which is the within family transfer, and NM, which is the marital fertility that clears the marriage market.  
[01:11:57] And the first proposition of the paper is that for the wage pair, you can show that there exists a unique equilibrium, you know, under some mild conditions.  
[01:12:05] Essentially, it's the best response functions of men to woman and woman to men. You show there's only one intersection and that is equilibrium.  
[01:12:13] And second, you can characterize what is the gains of marriage and hence the share of people getting married in a very simple reduced form way. The gains of marriage I'm writing it for female can be written as a product of lambda  
[01:12:27] which is intuitive that is the residual the sync item the u to the psychic benefit of marriage multiply by 1 plus alpha gamma w alpha gamma w has a very nice economic interpretation because from woman's point of view in this model  
[01:12:41] the gains from marriage is purely economical right what matters to her is how much income transfer she's going to receive relative to her own income in other words how much marriage actually expends your budget set and that depends only on the product of how rich the man  
[01:12:56] relatively is, how high his income potential and what fraction of that additional income potential is he willing to transfer to me. That's why it's the product of alpha and gamma w instead put the idiosyncratic taste  
[01:13:13] shock to children to my desire to have children >> or enjoy children rather than on marriage. the algebra was will be way more uglier. So in other words, I think you're thinking about the thing in the inside of utility function the weight on  
[01:13:27] fertility people have shocks there. It will be complicated. I tried. Yeah. You won't have nice things like that. Yeah.  
[01:13:34] Okay. So now the model basically reduces to three equations which are all intuitive. One of them is or two of them are actually just accounting. The first equation basically says that marriage depends on the gains of marriage in an increasing fashion. And the second is it  
[01:13:49] says gender income gap. The gamma y is how much the income of the man is relative to woman depends on the gender wage gap which I take as exogenous. It also depends on female labor supply. And third equation is also accounting.  
[01:14:02] Female labor supply depends negatively on fertility because I'm assuming women do childare not men.  
[01:14:07] So the intuition of why we have the quandry in the data according to my model not not your model claudia for now is that if we want to have high fertility okay then it reduces relative labor supply of women because women do  
[01:14:20] childare with lower relative labor supply of women you can still achieve gender income equality if women's wage are high but in the model if women's wage are high what's the point of marrying men that's essentially the  
[01:14:33] economic logic of the And you can do conactuals by by these comparative statics. Yes.  
[01:14:47] >> Sorry. Just before you go on, um I'm there's nothing about bargaining power here and I'm worried I'm I'm thinking about like an alternative model where there is some bargaining power and so having a higher wage Yeah. potentially generates more  
[01:15:01] allows women to have more surplus in the marriage potentially can seek out more time.  
[01:15:06] >> I'm very sympathetic to that equality and so so does it does it still go through if you think about that seriously >> I'm very sympathetic to that you know very sympathetic overall to the kingdom and match and kingdom and their their framework of a limited commitment and  
[01:15:20] then you have the timing of whether having a kid first or later but we can talk about that later. Yeah.  
[01:15:26] So this is not in the model. I'm sympathetic to that idea but uh I don't have that here. Yeah.  
[01:15:31] All right. So you can do comparative statics of thinking about traditional policies like you know you can improve uh uh marriage by raising lambda. You can improve women's wage by increasing wage of the female. You can also reduce the cost of the kids and none of them  
[01:15:45] can actually achieve all three because of two fundamental frictions in a sense that I built in. One is that wives is doing the child care. So if you want high fertility then necess necessarily reduces female labor supply and gender  
[01:16:00] wage gap can come in and help but only rescue one of gender income equality and marriage. You cannot get both that's baked in. And second exchange motive in other words marriage is an institution where uh the money is exchanged for fertility really links marriage and  
[01:16:14] fertility through a composition effect because marital fertility is higher due to a simple income effect. Yes. Are both men both men and women better off in your model as uh wages say exogenously  
[01:16:29] increase through technological progress? Say >> I think so. I think yes. I think the answer is yes.  
[01:16:35] >> Okay. Men as well. >> Men as well. Men as well because they can they're free to choose their alpha to clear the market. So I don't think they would be worse off. Okay. Exactly.  
[01:16:43] >> I didn't realize they were free to choose alpha >> at in the equipium. in the equilibrium.  
[01:16:47] Yes. But the key thing is what if the allocation of the child care itself is a policy lever. What if I resolve this kind of fundamental friction because as many paper including the previous one has acknowledged many times this thing is like not is not a feature. It's a bug  
[01:17:02] right in the sense that uh it's dictated by outside things like social norm.  
[01:17:06] Maybe you want to increase ma men's child care but somehow the society doesn't really allow it to do. So there's inefficiencies in other words.  
[01:17:13] So to think about that policy level I need to extend the model a little bit to having you know child care time of the fathers of the husbands and also childare time of the of the wives. Um in so I think I'm regarding social norm as a reason why I'm setting this thing as  
[01:17:27] exogenous right as you see it doesn't really vary too much with you know the wife the wage of the woman and the man data. Um so the wife's effective childare cost basically becomes a combination of the husband's wage and the wife's own wage because now the  
[01:17:41] husband also needs to chime in for child care. All the previous results go through as long as woman is doing more childare. But now let's think of a very simple policy maybe something like a mandated paternity leave or somehow the government is having a propaganda as  
[01:17:54] fathers you guys need to do more. Suppose that is successful in redistributing a lambda or a delta share of childare from wives to husbands.  
[01:18:03] Let's do that compared to static. So the key theoretical result of the paper is redistribution can improve all three.  
[01:18:10] That's a magic bullet only under two conditions. The first condition reading in plain language is that women are happy. Her disposable income is going to be needs to be increasing after the distribution occurs. So that is true  
[01:18:25] when her wage is high or the husband is not the only bread winner of the household. They needs to be having a larger budget set instead of smaller budget set. If the husbands are required to work more for child care, the woman needs to be happy which I don't think is a very difficult constraint to satisfy  
[01:18:40] especially when you have technologies working in women's favor when when the economy develops. The second condition which I think is a way harder constraint to satisfy is that men needs to be happy. So if you are men in the economy, you are transferring some share of your  
[01:18:54] income to the wives to support raising kids and now the government wants you to do more child care. How could you be happy about that? And in a model you you're happy about that only if the fertility increase from that policy is  
[01:19:07] large enough to offset your lost income. So this is what this condition this equation is essentially saying is men needs to be compensated with the marital fertility enough so that they're happy to do the childare and this condition is more likely to  
[01:19:22] hold if their preference on fertility beta is large. If initial men's childcare burden is not too big and also the fertility responses needs to be strong which depends on the structural parameters that's why I need to calibrate a model and to test if that  
[01:19:36] condition is true or not in a baseline economy >> the what there's a commitment problem I agree I agree so that's where kind of the earlier question about commitment comes along >> sure it's it's a combination of  
[01:19:53] different things and Yeah. Yeah.  
[01:19:58] >> Exactly. >> But there might be a problem. Yeah.  
[01:20:03] >> Yeah. So, so I think like the theoretical point I want you guys to take away here is that if you view fertility, marriage and gender equality as an equilibrium outcome, you need to not just think about oh only woman is the the bottleneck or only men is the bottleneck rather you need we need to  
[01:20:18] think about how they interact. In my setting, it's a simple marriage market, but you can think about like commitment problem, other things. And you need to make both sides happy for a policy to be successful. That's kind of the point.  
[01:20:29] All right. With my remaining time, um I will do some quantitative analysis. Um and here I'm I'm doing it for Mexico.  
[01:20:36] Not just not because Mexico is anything any special but rather it's a very typical case of a developing country where as their economy develops you can see fertility the first one fertility is falling and you see the dual parenthood  
[01:20:49] uh is falling almost entirely driven by the increasing share of single motherhood and you see the female income share rises dramatically from like less than a quarter to something like a third. you have GDP per capita rising dramatically and you also see a human  
[01:21:03] capital or a schooling reversal. It used to be that men has a higher uh years of schooling than woman and now it's completely opposite. So I'm going to calibrate the model period by period assuming that only the TFPS of men and  
[01:21:17] women and also the human capitals of of the men and the women are exogenous drivers. In other words, I'm going to keep all the other parameters fixed.  
[01:21:24] That's the assumption of what is driving this. So in other words, I'm going to decompose the wages in the data into three sources. This is just accounting.  
[01:21:32] Okay, there's no calibration yet. This is just accounting. I'm going to have 80 TFP, which is the genderneutral TFP. I'm going to have a gender gap in human capital, which is directly calculated from the years of schooling. I'm using a  
[01:21:45] very standard macro style meaneran transformation, right? using the skill premium multiply by the number of years and the residual how much I cannot explain with the human the schooling reversal I'm just calling that gender bias TFP change these are just  
[01:22:00] accounting and if you do this accounting you will see that the TFP gender neutral a increases uh and the gender bias technology also biases favoring women and you have a human capital gap that is closing and actually reverses towards  
[01:22:14] the end of the sample then what I'm going to do is basically to feed in these data into the model and calibrate it period by period by picking four parameters. So as a as a macroeconomist I'm picking I'm doing calibration so  
[01:22:28] without standard errors so it's my apology. [snorts] So I'm I'm picking this cost of kids from the literature. I'm picking some numbers for this kai. Then essentially I'm just picking four parameters to fit two s time series. One is the fertility  
[01:22:43] time series, the level and the slope and also the dual parenthood time series.  
[01:22:47] The level and the slope. And the fit is reasonable.  
[01:22:50] >> Yeah. Can I go back to what I was? >> Yes.  
[01:22:55] [laughter] >> The mic.  
[01:22:56] >> Can I go back to what I worry about just in terms of calibration?  
[01:23:01] uh is that and and I think Mexico might be one of those but I don't know 100%.  
[01:23:06] Is that that there's been a huge increase uh in cohabitation.  
[01:23:10] >> So I'm um I think what do you think about you know how do you define single mother rate? Is it just that you're not married or is just or is that you I have a kid but you're not because in that case >> for this part I rely hugely on on what  
[01:23:25] we know and millennial was doing is like they document the living arrangement of the kids and taking that literally in the sense that I'm assuming this single this kind of a share of due parenthood at a share of households that the kids are born where this marital contract is  
[01:23:39] effective. >> I don't care about whether they have a piece of paper or not. But I'm just assuming that if in the data you see them living having both parents there I'm assuming they're transacting with the alpha. Yeah.  
[01:23:51] All right. So with this calibrated model in hand I'm going to do show you three quantitative results. First is that um the alpha how much the imputed alpha how much the husbands is imputed to transfer to the wives is actually quite stable  
[01:24:05] despite a dramatic fall in fertility. So fertility has been falling a lot in Mexico. I think it's from 3 to two but the imputed alpha stays roughly constant around 14% or to 13%. I mean the reason is just that the woman's weight has  
[01:24:18] risen so much. So to keep even to get this declining fertility man needs to keep up with the transfers and this implies that the the gains of marriage for men is declining. So the relative utility between the single man and  
[01:24:32] married man in this model is declining uh is increasing uh in Mexico. That's kind of the first result. And the second I can do some decomposition. I can turn these TFPs on and off. Right? I'm showing that only having the  
[01:24:46] genderneutral TFP A, you can already explain roughly half of the decline in fertility and also half of the declining in marriage. And the reason for the left figure is that I'm assuming fertility and consumption as substitutes. So the  
[01:25:01] rising uh uh gender neutral TFP raises opportunity cost of kids for everybody and that reduces fertility. So that is by assumption but the figure on the right is like what the model gives me because fertility is something that a  
[01:25:13] marriage is for for these men. So when the fertility is falling that's why marriage is falling. So they're deeply intertwined in a marriage Good.  
[01:25:56] and a circle. Everybody  
[01:44:52] turns. Sorry.