A Sexually Unbalanced Model of Current Account Imbalances

Transcription

1 University of Zurich Department of Economics Center for Institutions, Policy an Culture in the Development Process Working Paper Series Working Paper No. 105 A Sexually Unbalance Moel of Current Account Imbalances Qingyuan Du an Shang-Jin Wei March 010

2 A Sexually Unbalance Moel of Current Account Imbalances Qingyuan Du (Columbia University) an Shang-Jin Wei (Columbia University an NBER) y This version: November 3, 010 Abstract Large savings an current account surpluses by China an other countries are sai to be a contributor to the global current account imbalances. This paper proposes a theory of excess savings base on a major transformation in many of these societies, albeit one that is selomly emphasize by macroeconomists, namely, a steay increase in the surplus of men relative to women. We construct an OLG moel with two sexes an a esire to marry. We show conitions uner which an intensi e competition in the marriage market can inuce men to raise their savings rate, an prouce a rise in the aggregate savings an current account surplus. This e ect is economically signi cant if the biological esire to have a partner of the opposite sex is strong. A calibration of the moel suggests that this factor coul generate economically signi cant current account responses, or more than 1/ of the actual current account imbalances observe in the ata. Key wors: surplus men, trae surplus, global imbalances JEL coe: F3, F4, J1 an J7 Corresponing author: Shang-Jin Wei, Columbia University, Grauate School of Business, 619 Uris Hall, 30 Broaway, New York, NY [email protected]. y Acknowlegement: We thank Stefania Albanesi, V. Bhaskar, Pierre-Anre Chiappori, E Hopkins, Aloysius Siow, an especially Xiaobo Zhang, an seminar participants at the IMF, Worl Bank, University of California-Berkeley, Columbia University, University of Washington, Hong Kong University an Chinese University of Hong Kong for very helpful iscussions, an Joy Glazener for eitorial assistance. All errors are our responsibilities.

3 1 Introuction High savings rates in excess of omestic investment rates in many countries in East an Southeast Asia have prouce a massive current account surplus as a share of GDP, an are sai to be a major contributor to the global current account imbalances, to the unusually low long-term interest rates, an possibly to the onset of the global nancial crisis. As to theories of savings behavior, the existing literature has highlighte the roles of life-cycle consierations (Moigliani, 1970), precautionary savings (Kimball, 1990), habit formation (Carroll, Overlan, an Weil, 008), culture (Belton an Uwaifo Oyelere, 008), an nancial uner-evelopment (Caballero, Farhi, an Gourinchas, 008; Ju an Wei, 006, 008 an forthcoming; Menoza, Quarini an Rios-Rull 007). The aim of the current paper is to propose an alternative theory that gives prominence to a major, albeit insu ciently recognize by macroeconomists, social transformation in many economies, namely an increasing gap in the numbers of men an women in the marriage market. The basic thesis is that as competition intensi es in the marriage market, men or parents with sons raise their savings rates with the hope of improving their relative staning in the marriage market. Because the biological esire to have a partner of the opposite sex is strong, this e ect is quantitatively important enough to reveal itself in the aggregate savings rate an the current account balance. The irect inspiration for the theory is an empirical paper by Wei an Zhang (009), which stuies househol savings behavior in China. They provie both cross-regional an cross-househol evience that is consistent with the notion that a worsening prospect for men in the marriage market has motivate them an their parents to raise their savings rates substantially. They call this the "competitive saving motive." Chinese househol savings as a share of isposable income rose from 16% in 1990 to 30% in 007. Wei an Zhang suggest that the rise in the sex ratio imbalance coul account for half the total increase in the savings rate. Because their paper oes not have a formal theory, there is a nee to construct a moel to see if the hypothesis can work in a general equilibrium, an whether a calibration of the moel can prouce an e ect whose magnitue is economically signi cant. In this paper, we aim to ll these important vois. The core part of the paper is to analyze theoretically whether an how a sex ratio imbalance will in uence the economy-wie savings rate an the current account. We construct a simple overlapping generations (OLG) moel with two sexes an a esire to marry. To focus on the macroeconomic implications of sex ratio imbalances, we intentionally shut own channels such as the usual precautionary savings motive, habit formation, culture, an nancial evelopment. Because it is an OLG moel, there are still life-cycle consierations, which, however, o not lea to current account imbalances on their own. Uner reasonable conitions, we show that men respon to a rise in the sex ratio by raising their savings rates. Moreover, the increment in their savings is always enough to o set any ecrease in women s savings when it happens. As a result, the aggregate savings rises with the sex ratio. To check if the moel can eliver an e ect that is economically signi cant, we go to quantitative calibrations. In the benchmark case, for a small open economy, as sex ratio rises from 1 to 1.15, the economy-wie 1

4 savings rate an the current account will rise by more than 10%. We also consier the case of two large economies, whose relative sizes an income levels are calibrate to mimic China an the Unite States. The synthetic Unite States is assume to always have a balance sex ratio, while the synthetic China experiences a rise in the sex ratio from 1 (balance) to 1.5 (very unbalance). The rise in China s sex ratio prouces a rise in its current account surplus, an a corresponing rise in the current account e cit for the Unite States. The magnitues of the current account imbalances in the simulations (about 7.7% of GDP for China an -.6% of GDP for the Unite States) are such that they are more than one-half of the actual current account imbalances observe in the ata. While the sex ratio imbalance is not the sole reason for the global current account imbalances in recent years, it coul be one of the signi cant, an yet thus far unrecognize, factors. A esire to enhance one s prospect in the marriage market through a higher level of wealth coul be a motive for savings even in countries with a balance sex ratio. But such a motive is not as easy to etect when the competition is moest. When the sex ratio gets out of balance, obtaining a marriage partner becomes much less assure. A host of behaviors that are motivate by a esire to succee in the marriage market may become magni e. But sex ratio imbalances so far have not been investigate by macroeconomists. This may be a serious omission. A sex ratio imbalance at birth an in the marriage age cohort is a common emographic feature in many economies, especially in East, South, an Southeast Asia, such as Korea, Inia, Vietnam, Singapore, Taiwan an Hong Kong, in aition to China. In many economies, parents have a preference for a son over a aughter. This use to lea to large families, not necessarily an unbalance sex ratio. However, in the last three ecaes, as the technology to etect the gener of a fetus (Ultrasoun B) has become less expensive an more wiely available, many more parents engage in selective abortions in favor of a son, resulting in an increasing relative surplus of men. The strict family planning policy in China, introuce in the early 1980s, has inuce Chinese parents to engage in sex-selective abortions more aggressively than their counterparts in other countries. The sex ratio at birth in China rose from 106 boys per hunre girls in 1980 to 1 boys per hunre girls in 1997 (see Wei an Zhang, 009, for more etail). It may not be a coincience that the Chinese current account surplus starte to garner international attention aroun 003 just when the rst cohort born after the implementation of the strict family planning policy were entering the marriage market. Throughout the moel, we assume an exogenous sex ratio. While the sex ratio is enogenous in the long-run as parental preference shoul evolve, the assumption of an exogeous sex ratio can be efene on two grouns. First, the technology that enables the rapi rise in the sex ratio has only become inexpensive an wiely accessible in eveloping countries within the last 5 years or so. As a result, it is reasonable to think that the rising sex ratio a ects only the relatively young cohorts savings ecisions, but not those who have past half of their working careers. Secon, in terms of cross country experience, Korea is the only major economies whose sex ratio appeare to have starte to revert back from a very skewe level. Most other countries still exhibit a rising sex ratio. This suggests that the mean reversion process of the sex ratio is a very slow one. A systematic reversal of the sex ratio is unlikely to happen in most economies in the short run.

5 To see if the theoretical preicion has any support in the ata, we check if a country s private sector savings rate (e ne as current account minus government savings, ivie by GDP) is systematically linke to its sex ratio. After controlling for the e ects on the savings rate from income, the share of working age people in the population (i.e., a proxy for the life cycle theory), the ratio of private bank creit to GDP (a proxy for nancial evelopment), an social security expeniture as a share of GDP (a proxy for the precautionary savings motive), we n that a rise in the sex ratio from a balance level to 1.15 (the sex ratio in China) is associate with a higher current account (excluing government savings) by over 10% of GDP. There are three boies of work that are relate to the current paper. First, the literature on status goos, positional goos, an social norms (e.g., Cole, Mailath an Postlewaite, 199, Corneo an Jeanne, 1999, Hopkins an Kornienko, 004 an 009) has o ere many useful insights. One key point is that when wealth can improve one s social status (incluing improving one s staning in the marriage market), in aition to a oring a greater amount of consumption goos, there is an extra incentive to save. This element is in our moel as well. However, all existing theories on status goos feature a balance sex ratio. Yet, an unbalance sex ratio presents some non-trivial challenges. In particular, while a rise in the sex ratio is an unfavorable shock to men (or parents with sons), it is a favorable shock to women (or parents with aughters). Coul the latter group strategically reuce their savings so as to completely o set whatever increments in savings men or parents with sons may have? In other wors, the impact on aggregate savings from a rise in the sex ratio appears ambiguous. Our moel will aress this question. In any case, the literature on status goos has no iscernible impact in policy circles. For example, while there are voluminous ocuments prouce by the International Monetary Fun or speeches by U.S. o cials on China s high savings rate an large current account surplus, no single paper or speech thus far has pointe to a possible connection with its high sex ratio imbalance. A secon relate literature is the economics of family, which is too vast to be summarize here comprehensively. One interesting insight of this literature is that a marrie couple s consumption has a partial public goos feature (Browning, Bourguignon an Chiappori, 1994; Donni, 006). We make use of this feature in our moel as well. None of the papers in this literature explores the general equilibrium implications for aggregate savings from a change in the sex ratio. The thir literature examines empirically the causes of a rise in the sex ratio. The key insight is that the proximate cause responsible for a majority of the recent rise in the sex ratio imbalance is sex-selective abortions, which have been mae increasingly possible by the sprea of Ultrasoun B machines. There are two eeper causes for the parental willingness to isproportionately abort female fetuses. The rst is the parental preference for sons, which in part has to o with the relatively inferior economic status of women. When the economic status of women improves, sex-selective abortions appear to ecline (Qian, 008). The secon is either something that leas parents to voluntarily choose to have fewer chilren than the earlier generations, or a government policy that limits the number of chilren a couple can have. In regions of China where the family planning policy is less 3

6 strictly enforce, there is also less sex ratio imbalance (Wei an Zhang, 009). Bhaskar (009) examines parental sex selections an their welfare consequences. The rest of the paper is organize as follows: in Section, we present a benchmark moel with no intra-househol bargaining. In Section 3, we consier a number of extensions. One such extension allows for intra-househol bargaining, an show that the key propositions still hol. In Section 4, we calibrate the moel to see if the sex ratio imbalance can prouce changes in the aggregate savings rate an current account whose magnitues are economically signi cant. In Section 5, we provie some international evience that sex ratio may have signi cant impact on a country s current account. Finally, in section 6, we o er concluing remarks an iscusses possible future research. The Benchmark Moel We construct an overlapping generations moel with two sexes. Both men an women live two perios: young an ol. An iniviual (of either sex) receives an exogenous enowment in the rst perio an nothing in the secon perio. She or he consumes a part of the enowment in the rst perio an saves the rest for the secon perio. A marriage can only take place between a man an a women in the same generation an at the beginning of their secon perio. Once marrie, the husban an the wife pool their rst-perio savings together an consume an ientical amount in the secon perio. The secon perio consumption within a marriage has a partial public goo feature. In other wors, the husban an the wife can each consume more than half of their combine secon perio income - the exact proportion is an exogenous parameter to be explaine below. Everyone is enowe with an ability to give his/her spouse some emotional utility (or "love" or "happiness"). This emotional utility is a ranom variable in the rst perio with a common an known istribution across all members of the same sex, an its value is realize an becomes public information when the iniviual enters the marriage market. Each generation is characterize by an exogenous ratio of men to women (>= 1). All men are ientical ex ante, an all women are ientical ex ante. Men an women are symmetric in all aspects except that the sex ratio may be unbalance. We escribe the equilibrium in this economy in six steps. First, we start with a representative woman s optimization, followe by a representative man s optimization problem. Secon, we escribe how the marriage market works. Thir, we perform comparative statics, in particular, on how the savings rates change in response to a rise in the sex ratio. Fourth, we consier a small open economy with prouction an iscuss the current account response to a change in the sex ratio. Fifth, we solve for a two-country moel in which the global interest rate is enogenous. Sixth, we use numerical calibrations to see if the moel can eliver current account responses that are economically signi cant. 4

7 .1 A Representative Woman s Optimization Problem A representative woman makes her consumption/saving ecisions in her rst perio, taking as given the choices by men an all other women. If she is not marrie, her secon-perio consumption is c w;n = Rs w y w where R, y w an s w are the gross interest rate, her rst perio enowment, an savings rate, respectively. If she is marrie (at the beginning of the secon perio), her secon-perio consumption is c w = (Rs w y w + Rs m y m ) where y m an s m are her husban s rst perio enowment an savings rate, respectively. ( 1 =< =< 1) represents the notion that consumption within a marriage is a public goo with congestion. As an example, if a couple buys one car, both spouses can use it. When = 1 ; the husban an the wife only consume private goos. In contrast, when = 1, all the consumption is a public goo with no congestion 1. The representative woman chooses her savings rate to maximize the following objective function: subject to the buget constraints that V w = max s w u(c 1w) + E [u(c w ) + m ] c 1w = (1 ( s w )y w (.1) c w = (Rs w y w + Rs m y m ) if marrie Rs w y w otherwise (.) where V w is her value function, an E is the expectation operator. m is the emotional utility (or "love") she obtains from her husban, which is a ranom variable with a istribution function F m. The exact value of emotional utility is reveale at the beginning of the secon perio an becomes a common knowlege at that time. Bhaskar (009) also introuces a similar "love" variable.. A Representative Man s Optimization Problem 1 By assuming the same for the wife an the husban, we abstract from a iscussion of bargaining within a househol. In an extension later in the paper, we allow to be gener specifc, an be a function of the sex ratio an the relative wealth levels of the two spouses, along the line in Chiappori (1988 an 199) an Browning an Chiappori (1998). This tens to make the response of the aggregate savings stronger to a given rise in the sex ratio. 5

8 A representative man has a similar optimization problem as the representative woman. In particular, if he is not marrie, his secon-perio consumption is c m;n = Rs m y m If he is marrie, his secon-perio consumption is c m = (Rs w y w + Rs m y m ) He chooses his savings rate to maximize the following value function: subject to the buget constraints that V m = max s m u(c 1m) + E [u(c m ) + w ] c 1m = (1 ( s m )y m (.3) c m = (Rs w y w + Rs m y m ) if marrie Rs m y m otherwise (.4) where V m is his value function. w is the emotional utility he obtains from his wife, which is rawn from a istribution function F w. We assume w an m are inepenent..3 The Marriage Market In the marriage market, every woman (or man) ranks all members of the opposite sex by a combination of two criteria: (1) the level of wealth (which is etermine solely by the rst-perio savings), an () the size of "love" he/she can obtain from his/her spouse. The weights on the two criteria are implie by the utility functions speci e earlier. More precisely, woman i prefers a higher ranke man to a lower ranke one, where the rank on man j is given by u(c w;i;j )+ m j. Symmetrically, man j assigns a rank to woman i base on the utility he can obtain from her u(c m;j;i )+ w i. (To ensure that the preference is strict for men an women, when there is a tie in terms of the above criteria, we break the tie by assuming that a woman prefers j if j < j 0 an a man oes the same.) Note that "love" is not in the eyes of beholer in the sense that every woman (man) has the same ranking over men (women). The marriage market is assume to follow the Gale-Shapley algorithm, which prouces a unique an stable equilibrium of matching (Gale an Shapley, 196; an Roth an Sotomayor, 1990). The algorithm speci es the following: (1) Each man proposes in the rst roun to his most preferre choice We use the wor" market" informally here. The pairing of husbans an wives in this moel is in fact not one through prices. 6

9 of woman. Each woman hols the proposal from her most preferre suitor an rejects the rest. () Any man who is rejecte in roun k-1 makes a new proposal in roun k to his most preferre woman among those who have not have rejecte him. Each available women in roun k "hols" the proposal from her most preferre man an rejects the rest. (3) The proceure repeats itself until no further proposals are mae 3. With many women an men in the marriage market, all women (an all men) approximately form a continuum an each iniviual has a measure close to zero. Let I w an I m enote the continuum forme by women an men, respectively. We normalize I w an let I w = (0; 1). Since the sex ratio is, the set of men I m = (0; ). Men an women are orere in such a way that a higher value means a higher ranking by members of the opposite sex. In equilibrium, there exists a unique mapping ( w ) for women in the marriage market. w : I w! I m That is, woman i (i I w ) is mappe to man j (j I m ), given all the initial wealth an emotional utility raws. This implies a mapping from a combination (s w i, w i ) to another combination (sm j, m j ). In other wors, for woman i, given all her rivals (s w i, w i ) an all men s (sm, m ), the type of husban j she can marry epens on her (s w i, w i ). Before she enters the marriage market, she knows only the istribution of her own type but not the exact value. As a result, the type of her future husban (s m j, m j ) is also a ranom variable. Woman i s secon perio expecte utility is where w i = Z Z w i h max u (cw;i;j ) + m w ( ijs w i ;w i ;sw i ;w i ;sm ; m ) ; u (Rsw i yw i ) i F w ( w i ) h i u (c w;i;j ) + m w ( ijs w i ;w i ;sw i ;w i ;sm ; m ) F w ( w i ) + Z w i u (Rs w i y w i ) F w ( w i ) is her threshol ranking on men such that she is ini erent between marriage or not. Any lower-ranke man, or any man with w i < w i, won t be chosen by her. Since we assume there are (weakly) fewer women than men, we expan the set I w to I ew so that ei w = (0; ). In the expane set, women in the marriage market start from value 1 to. The measure for women in the marriage market remains to be one. In equilibrium, there exists an unique mapping for men in the marriage market: m : I m! e I w where m maps man j (j I m ) to woman i (i I w ). Those men who are matche with a low value i < 1 in set e I w will not be marrie. In that case, w m (j) = 0 an c m;j;i = Rs m j ym j. In general, 3 If only women can propose an men respon with efere acceptance, the same matching outcomes will emerge. What we have to rule out is that both men an women can propose, in which case, one cannot prove that the matching is unique. 7

10 man j s secon perio expecte utility is = Z Z h max u (cm;j;i ) + w m ( jjs m j ;m j ;sm j ;m j ;sw ; w ) ; h i u (c m;j;i ) + w m ( jjs m j ;m j ;sm j ;m j ;sw ; w ) F m u Rsm j ym j m j Z m j + i F m m j u Rs m j y m j F m m j m j where m j is his threshol ranking on all women. Any woman with a poorer rank, m j < m j be chosen by him., will not We assume that the ensity functions of m an w are continuously i erentiable. Since all men (women) in the marriage market have ientical problems, they make the same savings ecisions. In equilibrium, a positive assortative matching emerges for those men an women who are matche. In other wors, there exists a mapping M from w to m such that 1 F w ( w ) = (1 F m (M( w ))), M( w ) = (F m ) 1 F w ( w ) + 1 For simplicity, we assume that w an m are rawn from the same istribution, F w = F m = F. Furthermore, the lowest possible value of the emotional utility min is su ciently large that everyone esires to be marrie. We also assume that there exists a small an exogenous possibility p that a woman may not n a marriage partner ue to "natural" frictions in the marriage market that are not relate to the sex ratio. The last assumption plays no role in the analytical part of the moel but will simplify the quantitative calibrations later. In equilibrium, given all her rivals saving ecisions an w, woman i s secon perio utility is Z (1 p) u( (Rs w i y w + Rs m y m )) + M(~ w i ) F ~ (~ w i ) + pu(rs w y w ) min where ~ w i = u( (Rs w i yw + Rs m y m )) u( (Rs w y w + Rs m y m )) + w. Due to the symmetry, we rop the sub-inex i for women. For a woman who chooses to enter the marriage market, given men s savings ecisions, the rst orer conition to her optimization problem is u 0 1wy w + (1 p) " u 0 w R M (~ w ) F ~ # w (~ w w + pu 0 w;ny w = 0 (.5) R M (~ w ) ~ F (~ w w Z = u 0 wry w M 0 ( w )F ( w ) + M( min )f( min ) Similarly, for a man who ecies to enter the marriage market, given women s savings ecisions, 8

11 the rst orer conition to his optimization problem is (1 p) " ~ m j u Rs w y w + Rs m j y m Z + M 1 M( min ) ~ m j # h i F ~ (~ m j ) + (1 p)(1 ~ m j ) + p u(rs m j y m ) where ~ m j = u Rs w y w + Rs m j ym u( (Rs w y w + Rs m y m )) + m j an ~ m j is the probability he gets marrie ~ m j = Pr u(c w (j)) u(c w ) + m j M( min ) Rs w y w ; Rs m y m = 1 F M( min ) u(c w (j)) + u(c w ) (.6) If a man chooses to enter the marriage market, the rst orer conition for his optimization problem is u 0 1my m +(1 p) where Z " M( min ) m u + 1 (~ m ) m M( min F ~ m (~ m ) m +f M( min ) u u m m u m;n + 1 (~ m Z m F ~ m (~ m ) = u 0 wry m M( min ) # +[(1 m ) (1 p) + p] u 0 m;ny m = 0 M 1 0 ( m ) F ( m ) (.7).4 Equilibrium Savings Rates An equilibrium is e ne as a collecton of savings rates by men an women that solve their respective optimalization problems, taking all other men an women s ecisions as given. De nition 1 Equilibrium fs w ; s m j y w ; y m ; F w ; F m g satis es the following conitions: s w i = arg max Vi w j s w i; s m ; y w ; y m ; F w ; F m an s m j = arg max V m s w ; s m j; y w ; y m ; F w ; F m j where i an j stan for a representative woman an man, respectively, an i an j represent all women other than i an all men other than j, respectively. s w = s w i ; sw i an s m = s m j ; sm j are the sets of women s an men s savings rates respectively. We assume that population growth rate is zero, an women an men receive the same rst perio income (y w = y m = y). Before perio t, the economy has a balance sex ratio. In this case, s w = s m = s, an s can be obtaine from solving the set of rst orer conitions (.5) or (.7): u 0 1y + (1 p) [] + + pyu 0 9

12 where we use the fact that at = 1, M( min ) = min. We rewrite the rst orer conition as u (1 p)u 0 + M( min )f( min ) + pu 0 n = 0 (.8) an can solve for the optimal savings rates. The rst key proposition is about the e ect of a rise in the sex ratio on the aggregate savings rate. The thought experiment assumes that people in the ol cohort have mae their savings ecision when the sex ratio is balance. When the sex ratio rises, any change in the aggregate savings is riven by a change in the savings by the young cohort. This simplifying assumption is motivate by the reality: A rise in the sex ratio in almost all economies is a recent phenomenon, since large-scale sex-selective abortions are a recent phenomenon. More precisely, while the iagnostic sonography use for prenatal checkups was available in the 1960s, the proceure became graually more a orable to people in countries that currently have a high sex ratio only since the 1980s. (The strict version of the Chinese family planning policy, another contributor to the sprea of sex-selective abortions, was also put in place in the early 1980s.) For this reason, the savings pattern for the currently ol was largely ecie when there was no severe sex ratio imbalance. In what follows, whenever we say a man (or a woman), we mean a young man, or a young woman, unless otherwise speci e. We rst state the propostion formally, an then explain the intuition behin the key parts of the proposition. A etaile formal proof is provie in Appenix A. Proposition 1 As the sex ratio rises, a representative man weakly increases his savings rate while a representative woman weakly reuces her savings rate. However, the economy-wie savings rate increases unambiguously. Proof. See Appenix A. Three remarks are in orer. First, it is perhaps not surprising that the representative man raises his savings rate in response to a rise in the sex ratio because the nee to compete in the marriage market becomes greater. Why oes the representative woman reuce her savings rate? Because she anticipates that a higher sex ratio woul inuce a higher savings rate from her future husban. As a result, she oes not nee to sacri ce her rst-perio consumption as much as she otherwise woul have to. Secon, why oes the aggregate savings rate rise in response to a rise in the sex ratio? In other wors, why is the increment in men s savings greater than the ecline in women s savings? Intuitively, a representative man raises his savings rate for two reasons: in aition to improving his relative staning in the marriage market, he raises his savings rate to make up for the lower savings rate by his future wife. The more he anticipates his future wife to cut own her savings, the more he woul have to raise his own savings rate to compensate. This ensures that his incremental savings is more 10

13 than enough to o set any reuction in her future wife s savings. In aition, a rise in the sex ratio implies a change in the composition of the population - relatively more men with a higher savings rate than women with a lower savings rate, which woul also raise the aggregate savings rate. While both channels contribute to a rise in the aggregate savings rate, it is easy to verify that the rst channel (the incremental competitive savings by any given man) is more important than the secon e ect (a change in the composition of the population with i erent saving propensities). Thir, as the sex ratio rises, women experience a welfare gain while men have to enure a welfare loss. Women gain both because they can free rie on their future husbans higher savings rates, an because they now face an improve probability of marrying a man with a higher level of emotional utility. In comparision, men lose both because they face a lower probability of marriage, an because the reuctions in their rst-perio consumption o not in the en alter their probability of marriage in the aggregate. (The aggregate number of unmarrie men is inepenent of the savings ecision.) We will present an extension in which the ecision to enter or exit the marriage market is enogenous. We will also iscuss another extension in which women may not reuce their savings rate in response to a rise in the sex ratio, when their bargaining power within a marriage epens in part on their savings rate. In both cases, the aggregate savings rate rises in response to a rise in the sex ratio (uner some conitions)..5 A Prouction Economy To analyze how the sex ratio imbalance a ects a country s current account imbalance, we nee to compare economy-wie savings with investments. In this subsection, we introuce a prouction sector. We assume that both the nal goo market an the factor markets are perfectly competitive. The prouction function is Cobb-Douglas: Q t = Kt L 1 t (.9) where K t is the capital stock an L t is the labor input. is the share of capital input to total output an is the total factor prouctivity (TFP). Everyone in the economy inelastically supplies one unit of labor an earns the same income 4. A representative rm maximizes the pro t max Q t R t K t W t L t K t;l t 4 Allowing men an women to earn i erent wages (with a xe proportional gap) woul not change our results. 11

14 The capital return an the wage rate are etermine by R t 1 t 1 = t K t W t t = (1 ) K t (.11) where we normalize the aggregate labor supply in the economy to be 1, i.e., L t = 1. For simplicity, we assume no tax or government expeniture; then y t = W t where y t is the corresponing rst perio isposable income in the enownment economy. We also assume complete epreciation in each perio. The aggregate capital supply in perio t + 1 is preetermine by the aggregate savings in perio t K s t+1 = 1 + sm t W t sw t W t (.1).6 Current Account in a Small Open Economy In a small open economy, we assume that capital can ow freely among countries an the gross interest rate R is exogenously etermine by the rest of the worl. By (.10) an (.11), the wage rate is also a constant, an the aggregate investment in the economy is K t = Substituting (.10) an (.13) into the prouction function, we have W t (1 )R t (.13) Q t = W t 1 The current account in perio t equals the increase in net foreign assets, NF A t = Q t + (R 1) NF A t 1 C 1t C t K t+1 where (R 1) NF A t 1 is the factor income from abroa. C 1t an C t represent the aggregate consumptions by young an ol people respectively. Then NF A t = 1 + sm t W t sw t W t NF A t 1 K t+1 We e ne the economy-wie savings rate as the aggregate private savings to GDP ratio; then s P t = Q t + (R 1) NF A t 1 C 1t C t Q t (.14) 1

15 We assume that the country has a balance sex ratio in perio t 1, an the sex ratio in the young cohort in perio t, rises from one to (> 1). Then the ratio of the current account to GDP is where the secon equality hols because 5 ca t = Q t + (R 1) NF A t 1 C 1t C t Kt+1 (.15) Q t = (1 ) 1 + sm t sw t s t 1 NF A t 1 = s t 1 W t 1 K t where s t 1 is the savings rate by the cohort born in perio t 1: Since the sex ratio is balance at that time, both the women an the men will have the same savings rate. Since the wage rate is constant in the small open economy, we can show that a country s current account rises as its sex ratio rises (up to a point). Proposition The economy-wie savings rate an the current account in perio t are increasing in. Proof. See Appenix B. The assumption of an exogenous interest rate hols only for a small open economy. But some of the countries that motivate this stuy are large. An increase in the savings rate in such economies coul lower the worl interest rate, which coul alter investment an savings ecisions in all countries. We examine the large country case in the next subsection..7 Two Large Countries Consier a worl consisting of only two countries. The two countries are ientical in every respect except for their sex ratios in perio t (they both have balance sex ratios in perio t 1). Country 1 s sex ratio 1 is smaller than Country s sex ratio. There are no barriers to either goos trae or capital ows (although labor is not mobile internationally). We can show the following result: Proposition 3 Country 1 (with a more balance sex ratio) runs a current account e cit while country runs a current account surplus. Proof. See Appenix C. 5 In overlapping generations moels, net foreign asset is equal to the i erence between the savings by the young cohort an the omestic investment eman. 13

16 To see the intuition, let us x 1 = 1 (i.e., Country 1 has a balance sex ratio). If Country were to have a balance sex ratio, the current account must be zero for both countries since they are ientical in every respect. In other wors, within each country, the investment must be equal to the aggregate savings. However, the sex ratio imbalance in Country causes it to have a higher aggregate savings for a given worl interest rate. This epresses the worl interest rate. The lower interest rate raises the investment level in both economies (an reuces the savings rate a little bit). This must imply that the esire investment level in Country 1 is now greater than its esire savings rate. As a result, capital ows from Country to Country 1. That is, Country 1 runs a current account e cit, an Country a surplus..8 Welfare There are two sources of market failure in the moel economy. On one han, a part of the savings in the competitive equilibrium is motivate by a esire to out-save one s competitors in the marriage market. The increment in the savings, while iniviually rational, is not useful in the aggregate, since when everyone raises the savings rate by the same amount, the ultimate marriage market outcome is not a ecte by the increase in the savings. In this sense, the competitive equilibrium prouces too much savings. On the other han, because the savings contribute to a pubic goo in a marriage (an iniviual s savings raises the utility of his/her partner), but an iniviual in the rst perio oes not take this into account, he/she may uner-save relative to the social optimum. Note that these sources of market failure exist even with a balance sex ratio. They also have opposite e ects on the aggregate savings rate. (In the calibrations that will be reporte later, these two e ects cancel each other out when the sex ratio is balance.) As the sex ratio rises, the importance of the over-saving e ect also increases, which gives rise to our rst proposition. We now consier what a hypothetical welfare-maximizing central planner woul o. The central planner gives equal weight to each man an women. He assigns the marriage market matching outcome an optimally chooses women s an men s savings rates to maximize the following social welfare function, The rst orer conitions are u 0 1m + max U = U w U m u 0 1w + (1 p)u 0 w + pu 0 w;n = 0 (.16) (1 p) u 0 1 w + 1 (1 p) u 0 w;n = 0 (.17) Comparing (.16), (.17) to (A.1) an (A.), in general, it is not obvious whether women or men will save at a higher rate in a ecentralize equilibrium than that uner central planning ue to the two opposing sources of market failure. However, when = 1, since women an men have the same 14

17 optimization problem, by (.8), if f( min )M( min ) > 0, then women an men will save more in the competitive equilibrium. If f( min )M( min ) is su ciently small, the competitive equilibrium is very close to the central planner s economy. In calibrations with a log utility function, we show that men s welfare uner a ecentralize equilibrium relative to the central planner s economy eclines as the sex ratio increases. In comparision, women s relative welfare increases as the sex ratio goes up. The social welfare (a weighte average of men s an women s welfare) goes own as the sex ratio rises. 6 As a thought experiment, one may also consier what the central planner woul o if she can choose the sex ratio (in aition to the savings rates) to maximize the social welfare, the new rst orer conition with respect to is U m U w = 0 (.18) The only sex ratio that satis es (.18) is = 1. In other wors, the central planner woul have chosen a balance sex ratio. Deviations from a balance sex ratio represent welfare losses. 3 Extensions While the benchmark moel is simple with clear preictions, we now consier a series of extensions that woul a some more realisms to the moel. First, We consier enogenous ecisions to enter an exit the marriage market. This allows agents to choose to quit (or not enter) the marriage market. Secon, we iscuss potential intra-family bargaining between husban an wife, with their relative bargaining power epening in part on their relative savings rate. Thir, we incorporate parental savings in aition to agents own savings. An nally, we consier a setting in which each agent has 50 perios in his/her ault life, an has to make savings ecisions in multiple perios. 3.1 Marriage market with enogenous entries an exits In the rst extension, we allow both men an women to choose to enter or exit the marriage market together with the savings rates. For a representative woman, if she chooses to be single throughout her life, the optimization problem is V w n = maxu(c 1w;n ) + u(c w;n ) s w n where Vn w is the value function of a life-time spinster. We still use V w to enote her value function if she chooses to enter the marriage market. Agents can play a mixe strategy in terms of whether or not to enter the marriage market. More precisely, the representative woman chooses the probability of entering the marriage market w, a 6 The results are similar if we change the utility function to a CRRA form. 15

18 savings rate if she ecies to enter, an a (potentially) separate savings rate if she ecies to abstain from marriage. The optimization problem is max w ;s w ;s w n w V w + (1 w )V w n Obviously, she will choose w = 1 if an only if V w > V w n. For a representative man, similarly, if he chooses to be a life-time bachelor, his optimization problem is V m n = maxu(c 1m;n ) + u(c m;n ) s m n where Vn w is the corresponing value function. The representative man also chooses the probability of entering the marriage market m as well as two potentially separate savings rates. The optimization problem is max m ;s m ;s m n m V m + (1 m )V m n He ecies to enter the marriage market with probability one if an only if the expecte utility of oing so is greater than otherwise, or V m > V m n : We now e ne an equilibrium in this case. De nition 1 An equilibrium is a set of savings rates an probabilities of entering the marriage market, fs w ; w ; s m ; m j y w ; y m ; F w ; F m g that satis es the following conitions: (s w i ; w i ) = arg max Vi w j s w i; w i; s m ; m ; y w ; y m ; F w ; F m an s m j ; m j = arg max V m j s w ; w ; s m j; m j; y w ; y m ; F w ; F m where i an j stan for a representative woman an man, respectively, an i an j represent all women other than i an all men other than j, respectively. (s w ; w ) = s w i ; sw i ; w i ; w i an (s m ; m ) = s m j ; sm j ; m j ; m j are the sets of women s an men s choices, respectively. At = 1, i.e., when the sex ratio is balance, uner the assumption that the mean value of emotional utility is large enough, it is easy to verify that the ominant strategy for both women an men is to enter the marriage market. Moreoever, we can show the following proposition. Proposition 4 There exist two threshol values, 1 an, where 1 <, that satisfy V m = Vn m an U w = 0 respectively. For <, both women an men choose to enter the marriage market with probability one. In aition, (i) for any < 1, as the sex ratio rises, a representative man weakly increases his savings rate while a representative woman weakly reuces her savings rate. However, the economy-wie savings rate increases unambiguously; (ii) For 1 <, as the sex ratio rises, a 16

19 representative man keeps his (high) savings rate constant but a representative woman raises her savings rate. The aggregate savings rate increases. Proof. See Appenix D. A few remarks are in orer. First, the ominant strategy for both men an women is to enter the marriage market unless the sex ratio is extremely high. To see the intuition, we note rst that when the sex ratio is balance, both men an women strictly prefer to be marrie than to be single. As both the utility function an the ensity function of are assume to be continuously i erentiable, in the neighbourhoo of = 1, entering the marriage market must also be a ominant strategy for men an women. Secon, 1 is the threshol level of sex ratio at which the representative man is i erent between entering the marriage market or not, V m = V m n. The value of the threshol can be very high if a man s biological esire to be matche with a female is strong enough. In the calibrations that we will report later, the threshol is always higher than the highest sex ratio one observes in the ata. In other wors, the sex ratios in the real worl appear to be always below this threshol. Finally, beyon the rst threshol, 1 ; if the sex ratio continues to rise, up to another threshol ( ), men woul switch to a mixe strategy (that assigns some probability of not entering the marriage market) if women o nothing. Due to the bene ts associate with marriage, women woul not n it optimal to o nothing an let some goo men to skip the marriage market. By raising their own savings rate, women can succee in enticing men to come back to the marriage market. However, beyon the secon threshol, if the sex ratio continues to rise, the require sacri ce for women in terms of reuce rst-perio consumption becomes too large for them to continue to raise their savings rate. At that point, women woul keep their (high) savings rate constant, an let men play their mixe strategy. More formally, is the level of sex ratio at which U w = 0. In other wors, can be solve by equation y u 0 1w + (1 p)u 0 w + pu 0 s w w;n + E [] = 0 Since the sex ratios in the real worl are unlikely to reach the rst threshol 1, it is even less likely to reach the secon threshol : To summarize, as the sex ratio rises, as long as <, the aggregate savings rate rises unambiguously. Base on the same reasoning, we can show that all results in Propositions an 3 (uner the conition that < ) also hol in this extension. 3. Intra-househol Bargaining Chiappori (1988 an 199) an Browning an Chiappori (1998), among others in the literature on the economics of family, have consiere intra-househol bargainings, an emphasize that the relative 17

20 income between the husban an the wife matters for their respective bargaining power. In this section, we exten the benchmark moel by allowing the relative bargaining power to be a function of both the sex ratio an the relative wealth. We assume that everyone consumes two goos in the secon perio, a public goo (e.g., a house) an a private goo. The aggregate secon perio consumption inex is z i h1 c i = (1 ) 1 i = w; m where z w an z m are private goos consumption by women an men respectively. h is the public goo consumption. A representative househol maximizes the weighte sum of the utilities of the husban an the wife. Let enote the weight on the wife s utility, which represents her bargaining power in the family. Then the househol s optimization problem is max u(c w ) + (1 )u(c m ) h;z w;z m with the resource constraint z w + z m + h = Rs w y w + Rs m y m (3.1) If we assume u(c) = c1 1 1 ( 1), solving the househol s maximization problem, we have c w = c m = Rs w y w + Rs m y m Rs w y w + Rs m y m If = 1, this is the case in our benchmark moel an 1 < = < 1. More generally, similar to Browning et al (1994), we assume to be an increasing function in the sex ratio, the relative wealth, an w, a ecreasing function in m, then c w = w (Rs w y w + Rs m y m ) c m = m (Rs w y w + Rs m y m ) where w = m = " " # 1 + (3.) 1 # 1 + (3.3) 18

21 We enote the erivatives we will use as following: w 1 0, m 1 w w 0, Rsw y w = Rs m m w w 0, m 3 w m 0, m m w m Rsm y m Rs w y w 0 For simplicity, we assume that w = m, if = 1, Rs w y w = Rs m y m an w = m. We assume y w = y m = y. To simplify the iscussions, we make several aitional assumptions. Assumption j j i j u 0 i c i This means that the elasticity of the bargaining power for househol member i is small enough given the relative wealth between women an men. This assumption ensures that u( i (Rs w y w + Rs m y m )) + j is increasing in j, i.e., everyboy wants her/his spouse to have a higher. Therefore, in equilibrium, the mapping that results in an assortative matching M still hols. i Rs i y i Rs j y j Rs i y i i Rs j y j Rs j y j Rs i y i + Rs j y j This ensures that each person prefers a wealthy spouse even though this may reuce his/her bargaining power within the househol. Assumption E3: M( min ), u(c m ) + min = u(c m;n ). In the secon perio, for the man who enters the marriage market with type This implies that the marginal marrie man is ini erent between getting marrie an staying single. This assumption is reasonable because ex ante men o not know their type an make the same saving ecision. In the secon perio, the woman matche to the man of type M( min ) makes an intra-househol allocation o er that woul make the man slightly happier than being single. If he oes not accept the o er, the next ranke man may accept the o er, which woul have resulte in a welfare loss to the man of type M( min ). Hence, he accepts the o er. Assumption E4: i 1 is either positive or small in its absolute value, i = w; m. 19

22 Without this assumption, as a man s incentive to raise savings rate is so strong, the contribution of a woman s own savings to her bargaining power within the family woul be small. This woul not be very interesting as the result woul be similar to the benchmark moel. Proposition 5 Uner assumptions E1-E4, as the sex ratio rises, a representative man s savings rate rises, but the change in a woman s savings rate is ambiguous. However, the aggregate savings rate rises unambiguously. Proof. (See Appenix E). The ambiguity in a woman s response to a rise in the sex ratio comes from two opposing forces. On one han, she wishes to free rie on her future husban s higher savings rate by reucing her savings rate. On the other han, she oes not wish to see an erosion in her intra-househol bargaining power, an one way to protect her bargaining power is to raise her own savings rate. This ambiguity on the part of the women s savings oes not a ect the comparative statics on the aggregate savings. Even if the women o not raise their savings rate to preserve intra-househol bargaining power, we alreay know from Proposition 1 that in the aggregate, the increment in men s savings is always more than enough to o set any ecline in women s savings. Any increase in women s savings out of concern for intra-househol bargaining power can only further increase the response of the aggregate savings to a rise in the sex ratio. As for the aggregate savings rate, the qualitative results are similar to Proposition 1. As a result, it is easy to verify that all open-economy conclusions still hol with this extension. 3.3 Parental savings As ocumente in Wei an Zhang (009), parental savings for chilren are likely to be an important part of househol savings. To incorporate this feature, we consier an OLG moel in which every cohort lives three perio (young, mile-age, an ol). Everyone works an earns labor income in the rst two perios. If one gets marrie, the marriage takes place at the beginning of the secon perio, an the couple prouces a single chil right away. The chil is a boy with a probability of 1+, an a girl with a probability of If the chil ever gets marrie, the marriage takes place at the beginning of the chil s secon perio, which is also the beginning of the parents thir perio. They erive irect emotional utility from having a chil, although the value of this emotional utility coul epen on the gener of the chil. Parents are also altrustic towar their chil an can save for their chilren (in aition to for themselves). For simplicity, we assume that chilren o not make a reverse nancial transfer to their parents. With this setup, the optimization problem for a representative woman who enters the marriage 0

23 market now becomes V w t = max s u(cw 1t) + E u(c w ;t+1) + m + E u(c w 3;t+) + m + E w " V m t+1 + s V # t+1 w where V m t+1 (V w t+1) is the life utility of the woman s son (aughter) if she gets marrie. s an are the emotional utility parents obtain from having a son an a aughter, respectively. is the parameter shows the egree of altruism. If her rst-perio savings rate is s w t, her rst-perio consumption is c w 1t = (1 s w t )y w t In the secon perio, if she fails to get marrie, she woul consume the same amount in the secon an the thir perios: c w;n ;t+1 = cw;n 3;t+ = R 1 + R (Rsw t yt w + yt w ) Parents can save for their chil, an that savings rate potentially epens on the gener of their chil. Let T i t+1 be the amount of parental savings for their chil, where i = w (a aughter) or m (a son). Parental savings augments a young person s rst-perio income. We represent this by assuming that a person s rst-perio income is a positive an concave function of his/her parents savings: y i = Y (T i ) an Y 0 > 0, Y 00 < 0, Y 0! 1 as T i! 0 an Y 0! 0 as T i! 1. 7 The representative woman s secon an thir perio consumptions are where i stans for the chil s gener. perios, c w;i ;t+1 = cw;i 3;t+ = R 1 + R Rsw t yt w + Rs m t yt m + yt w + yt m Tt+1 i If the representative woman ecies to be single, she will smooth her consumptions over three c w 1t = c w ;t+1 = c w 3;t+ = R + R 1 + R + R yw As in the benchmark moel, we assume a uniform istribution for i. The optimization conition for the representative woman is 3 u 0 1w + + R (1 p) R 4 1+R M(min )f( min ) 5 = 0 (3.4) + pu 0 w;n 1+ u0 w;m u0 w;w 7 We use this assumption to avoi the inequality contraint T i 0, which greatly simpli es the calculation. 1

24 an by the Benveniste an Scheinkman formula w w t = u 0 1t;wY 0 (T w t ) Similarly, for a representative man, the optimal conition is u 0 1m + + R " (1 p) R 1+R m + um+ max u m;n max min 1+ u0 w;m u0 w;w + ((1 m ) (1 p) + p) u 0 m;n # = 0 (3.5) m m t = u 0 1t;mY 0 (T m t ) Parents optimal savings for their chil in perio t satis es the following conitions: R (1 + ) 1 + R u0 t;w t w R (1 + ) 1 + R u0 t;m t m t = 0 (3.6) = 0 (3.7) We totally i erentiate (3.4), (3.5), (3.6) an (3.7). We assume E m an E w are su ciently large, so that marriage is strongly attractive. With these assumptions, we have the following proposition: Proposition 6 If utility function is of log form, an Y 00 Y 0 is close to being a constant, as the sex ratio rises, not only a representative man weakly increases his rst-perio savings rate, but parents with a son also increase their savings for their son. The savings responses by young women an by parents with a aughter are ambiguous. However, both the aggregate savings by the young cohort an the aggregate parental savings for chilren rise unambiguously. Proof. (see Appenix F) If a chil s income in log linear in his/her eucation level (which woul be consistent with the usual empirical speci cation of the Mincer equation that links log income with years of schooling), an if the level of a chil s eucation is linear in the level of parental investment, then Y 00 is a constant. This woul ensure that Proposition 6 hols. Here is the intuition. Parents save for their chil for two reasons: to increase their chil s ability (for instance, investing in chilren s eucation) an to make a transfer (brie price or owry) when their chil reaches the marriage stage. The transfer mae at the marriage is a linear term an will not contribute to Y 00 Y 0. In a prouction economy, we consier y i as representing the labor prouctivity, an normalize Y 0

25 the wage rate to be one. The economy-wie savings rate is s P t = 1 1 p 1 1+ cw 1t + 1+ cm 1t + + [(1 p) (c w t + c m t) + pc w t] 1 p [(1 p) (cw 3t + c m 3t) + pc n 3t] 1 p [ 1+ Y (T t m) Y (T t w )]+Y (Tt) 1 where c w 3t = c m 3t, c w 3t, c m 3t an c n 3t o not vary with a change in the sex ratio. In perio t, in response to a rise in the sex ratio, parental savings for their chil, Tt m an Tt w both rise, an c m t an c w t go 1 own. For the young cohort, their average savings rate rises an hence 1+ cw 1t + 1+ cm 1t ecreases. As a result, economy-wie savings rate goes up. Then we obtain the following proposition:! Proposition 7 As the sex ratio increases, both the economy-wie savings rate an the current account in perio t rise in response. 3.4 Muti-perio moel In this extension, we consier a multi-perio moel in which every cohort lives for 50 perios. Everyone works in the rst 30 perios, an retires in the last 0 perios. If one gets marrie, the marriage take place in the th perio. We have not been able to solve the problem that allow for parental savings for their chil in the 50-perio setup. As a result, we concentrate on a moel in which men an women save for themselves. However, as we recognize the quantitave importance of parental savings in the ata, we choose a value of su ciently large to mimic the typical age of parents when their chil gets marrie. In the benchmark multi-perio moel, we on t allow parents savings. Then for a woman who ecies to enter the marriage market, the optimization problem is " X 1 50 # X max t 1 u(c w t ) + E 1 t 1 (u(c w t ) + m ) t=1 t= For t <, when the woman is still single, the intertemporal buget constraint is A t+1 = R (A t + y w t c w t ) where A t is the wealth hel by the woman in the beginning of perio t. If the woman gets marrie in perio, then her family buget constaint now becomes ( A H R A H t + yt w c t t+1 = R A H t c w t if t 30 if t > 30 3

26 where A H t is the wealth hel by the family (wife an husban) in the beginning of perio t. c t is the public goo consumption by wife an husban, which takes the same form as in the two perio OLG moel. A representative man will have the similar problem. We will calibrate the moel to see whether a rise in the sex ratio can result in an economically signi cant change in the economy-wie savings rate an the current account. 4 Calibrations The analytical moel presents conitions uner which a rise in the sex ratio leas to an increase in a country s current account surplus. Are the actual sex ratios observe in the ata capable of generating a current account response whose magnitue is economically signi cant? We answer this question in this section by quantitative calibrations of the moel. We start with a small open economy, an move on to two cases of a large economy. 4.1 The Small Open Economy Assume that the utility function is of the log form u(c) = ln(c) In the calibrations for a small open economy, we x R = 1. (In the large country case, the interest rate is enogenously etermine.) The emotional utility nees to follow a continuously i erential istribution. In the benchmark calibration, we assume a truncate normal istribution which might be more realistic than a uniform istribution use in the analytical moel. We choose a stanar eviation that is relatively tight, = 0:01. This limits the extent of heterogeneity among women (or men) in the eye of the opposite sex. We truncate the istribution at the 1% in the left tail an at the 99% in the right tail. We choose the mean value of the emotional utility/love in the following way: holing all other factors constant, we compute the income compensation to a life-time bachelor that can makes him ini erent between marrie an being single. 1 1 u (1 + m)y = u y + E () where my is the compensation pai to a life-time bachelor for being single an 1 1+ (1+m)y is his secon perio consumption. We calculat the value of m base on Blanch ower an Oswal (004). Base on an econometrically estimate relationship between subjective well-being an income an marital 4

27 status (an other eterminants of happiness) in the Unite States uring , Blanch ower an Oswal (004) estimate that, on average, a lasting marriage is equivalent to augmenting one s income by $100,000 (in 1990 ollars) per year every year.since the average income per working person was about $48,000 uring that perio, a sustaine marriage is worth times the average income. We therefore choose m = as the benchmark. This implies that the mean value of the emotional utility/love is: 3y E () = u 1 + We will vary the value of m in the robustness checks. y u 1 + For other parameters, whenever possible, we assign values that are consistent with the stanar literature. Choice of Parameter Values Parameters Benchmark Source an robustness checks Discount factor = 0:45 Prescott (1986), iscount factor takes value 0.96 base on annual frequency. We take 0 years as one perio, then = 0:96 0 ' 0:45 Share of capital input = 0:35 Bernanke, Gertler an Gilchrist (1999) Congestion inex = 0:8 = 0:7; 0:9 in the robustness checks. Marriage market friction 8 p = 0:0 p = 0:05 in the robustness checks Love, stanar eviation = 0:01 = 0:05 in the robustness checks Love, mean m = m = 0:5 in the robustness checks Tables 3, 3a, 3b an 3c report the calibration results (when the sex ratio changes from 1 to ). Figure 3 plots the aggregate savings rate as a function of the sex ratio (which changes from 1 to 1.5). In our benchmark case, we assume that the share that each spouse can consume out of the combine secon-perio income is = 0:8, the mean of the love factor m =, the ispersion of the love factor is = 0:01, an the exogenous probability that a given person is roppe out of the marriage market (a measure of marriage market frictions that are not relate to the sex ratio imbalance) is p = 0:0. For a sensitivity analysis, we consier i erent combinations involving = 0:7; 0:8 an 0:9, m = an 0:5, = 0:01 an 0:05, an p = 0:0 an 0:05. In the benchmark moel calibration, when the sex ratio goes up from 1 to 1.15, the savings rate woul go up by 10.3 percentage points. This is within the 90% con ence interval of the empirical estimates. Accoring to the regression reporte in Table 1, the same increase in the sex ratio is associate with an increase in the savings rate between 5.7 an 31.9 percentage points. There are a few noteworthy patterns. First, generally speaking, the economy-wie savings rate always rises in response to a rise in the sex ratio. With all parameter combinations, as we raise the sex 8 p is the exogenous possibility that any iniviual (a women or a man) entering the marriage market is bumpe o the market inepenent of the sex ratio. 5

28 ratio from 1 to, we o not see a turning point in the savings response. In other wors, the theoretical values of 1 an in Proposition 1 must be greater than. Since no economy in the real worl has a sex ratio that excees 1.5, all real economies appear to satisfy the conitions uner which the savings rate (an the current account) rises as the sex ratio rises. Secon, as becomes larger, the economy-wie savings rate an the current account respon more strongly to a rise in the sex ratio. Intuitively, as becomes larger, consumption within a marriage acquires more public goos feature. Consequently, the esire to marry (an the nee to compete in the marriage market) also increase. However, the response of the aggregate savings is not very sensitive to small perturbations of this parameter. Thir, when the mean value of the love factor is higher (e.g., when m = compare to m = 0:5), the economy-wie savings rate an the current account respon more strongly to a rise in the sex ratio. This is intuitive since men have a stronger esire to compete for a marriage partner. Notice that in our empirical regressions, the coe cient of the variable sex ratio is aroun 15, which means that if the sex ratio rises from 1.05 to 1.15, the current account to GDP ratio will rise by about 1.5%, which is higher than all calibration results. This means that the mean value of the love factor we select in the paper is within a reasonable range. Fourth, when there are more frictions in the marriage market (unrelate to the sex ratio) (e.g., when p = 0:05 rather than 0:0), a women oes not reuce her savings by as much in response to a rise in the sex ratio. Because a spinster cannot free rie on the savings of her husban, with an increase probability that a woman coul stay single in her life, she woul not reuce her savings in response to a rise in the same sex as much as she otherwise woul. (However, the e ect on the aggregate savings rate is not very sensitive to p. If women are inuce to save more ue to a fear of singlehoo, men may save less. As a result, the net e ect on the aggregate savings is smaller than otherwise.) Fifth, as the ispersion for emotional utility becomes smaller, the economy-wie savings rate an the current account respon more strongly to a rise in the sex ratio. This is because, since all men are more similar in terms of the amount of "love" they can o er to women, the nee to compete on the basis of wealth also rises. Again, if we compare our calibration results to the estimation results, we n that the stanar eviation parameter we choose is within the reasonable range. 4. Two Large Countries We consier two cases of calibrations. In the rst case, we assume that the two countries are ientical in every respect except for their sex ratios. While Country 1 always has a balance sex ratio ( 1 = 1), we vary the sex ratio in country from 1 to. The interest rate R an the wage rate W are now enogenously etermine. All other parameter values are the same as in the small open economy case. Table 4 reports the calibration results. Figure 4 traces out the current account responses in both countries as Country s sex ratio increases. The most important result is that a rise in Country s sex ratio triggers a rise in its current account surplus an a rise in Country 1 s current account e cit. 6

29 Note that Country 1 s current account exhibits a bigger change than Country. This is because as Country s sex ratio rises, its economy-wie savings rate rises. As a result, it becomes a progressively larger country than Country 1. We have also one robustness checks by varying the values of ; m, p an. Base on the same reasoning as in the small open economy case, for larger, m, p or smaller, a given increase in Country s sex ratio results in a greater current account imbalance in the two countries. In the secon case, we attempt to let Countries 1 an mimic the Unite States an China, respectively. In particular, we assume that L 1 = 1=5 L to match the fact that the U.S. population is aroun 1=5 of that of China. In aition, we choose the TFP parameter in Country 1, 1 ; to match the fact that the U.S. per capita GDP was about 15 times the Chinese level aroun 1990 when the sex ratio in China for the marriage age cohort was not yet seriously out of balance. The remaining parameters are set to be the same as before. We let the sex ratio in the Unite States be always balance, an vary the Chinese sex ratio from 1 to. Tables 5a an 5b report the benchmark result an robustness checks. Figure 5 plots the calibration results. Qualitatively, they look similar to the rst large-country experiment. Quantitatively, Country s (China) current account response (as a share of GDP) becomes stronger. With China s sex ratio at 1.15 (an = 0:8), the Unite States runs a current account e cit of.6% of GDP, an China runs a surplus of 7.7% of GDP. This resembles the real worl pattern in which the U.S. e cit is about 4-6% of GDP, whereas the Chinese surplus is on the orer of 7-10% of GDP in recent years. In other wors, the rise in the Chinese sex ratio coul potentially generate an economically signi cant current account imbalance. To summarize, the calibrations suggest that a rise in the sex ratio coul prouce an economically signi cant increase in the aggregate savings rate that results in a current account surplus. If the country is large enough, this coul inuce other countries to run a current account e cit even if they have a balance sex ratio. 4.3 Welfare In the welfare calibrations, we compare the welfare uner a ecentralize equilibrium relative to the central planner s economy (Table 6). Figures 6, 6a an 6b trace out the savings rates for men (the upper left panel), women (the upper right panel), the economy as a whole (the lower left panel) an the welfare (the lower right panel). With a log-utility function, the optimal savings rates chosen for men an women chosen by the planner o not epen on the sex ratio an intra-househol bargaining powers. 9 When the sex ratio is balance, the savings rates by women, men an the economy as a whole are almost the same as those uner the planner s economy. With unbalance sex ratios, men s (ecentralize) savings rates overshoot the socially optimally level, an the extent of excessive savings rises with the sex ratio. Women s savings rates follow an opposite pattern. The economy-wie savings 9 This feature oes not hol when we use CRRA utility function. 7

30 rate follows a pattern that is qualitatively similar to the men s savings rate. In particular, the economy in a ecentralize equilibrium tens to save too much relative to the social optimum, an the excess savings rises with the sex ratio. In the lower right panel, we can see that welfare levels for both men an the economy as a whole ecline as the sex ratio increases, while the welfare for women rises with the sex ratio. 4.4 Enogenous Intra-househol Bargaining One problem in the benchmark calibration is that, as the sex ratio rises, women s savings rates ecline very quickly. As we have note earlier, if the analytical moel allows for intra-househol bargaining, then the e ect of a rise in the sex ratio on the change in women s savings rates is ambiguous. As men start to save more, women o not wish to reuce their bargaining power in a marriage if the relative size of the savings rates is a eterminant of the bargaining power. We use calibrations to emonstrate this e ect. For simplicity, we assume that the intra-househol bargaining power epens only on the relative wealth of househol members. In particular, we assume that the wife s bargaining power within a family is an the husban s bargaining power is 1 = (s w ) " (s w ) " + (s m ) ". " (0; 1) is the parameter that governs the sensitivity of bargaining power to relative wealth. A larger " means that househol bargaining power will respon to the relative wealth more strongly. The log-utility function implies = 1 in (3.) an (3.3), then w = an m = (1 ) where is the share of private expeniture in the secon perio consumption inex. We take the same values for other parameters as in the benchmark. Table 7 reports the calibration results, an Figures 7a an 7b plot the saving rates. Relative to the case of no intra-househol bargaining, women now reuce their savings rates more slowly as the sex ratio rises. For " = 0:7 or = 0:7, women may even raise their savings rates by a small amount when the sex ratio is moest ( 1:05). Since there is no big change in men s response to the rise in the sex ratio, the economy-wie savings rate respons more strongly to a rise in the sex ratio than the benchmark case. For " = 0:5 an = 0:5, as the sex ratio rises from 1 to 1.15, the current account to GDP ratio rises by 15.3%. This calibration result is within the 90% con ence interval of the empirical estimates from Table 1 an Table. In Table 8, we re-calibrate the case of two otherwise ientical countries except for the sex ratio. In Table 9, we re-calibrate the case of the Unite States versus China. Figures 8 an 9 plot the current account responses an the welfare changes. In both cases, the only i erence relative to the benchmark moel is the allowance for the enogenous bargaining power with a family. The qualitative results on 8

31 the aggregate savings an the current account are similar to before. However, the savings response by women becomes more realistic. For " = 0:5 an = 0:5, we can n in Table 9 that as the sex ratio in China rises from 1 to 1.15, this can generate a 11.5% current account suplus in China an 3.8% e cit in the U.S. The calibration result can completely account for the current account surplus in China an more than half of the e cit in the U.S. In the right panel in both Figures 8 an 9, we trace out the economy-wie welfare in a ecentralize equilibrium for a given sex ratio relative to the welfare in a ecentralize equilibrium but with a balance sex ratio. The country that experiences a rise in the sex ratio (e.g., China) clearly su ers from an ever-eteriorating welfare. Interestingly, the country with a balance sex ratio (e.g., the Unite States) coul enjoy a small welfare gain as China s sex ratio starts to be imbalance. Intuitively, a rise in the Chinese sex ratio epresses the global interest rate, but this prouces two e ects of opposite signs on the Unite States. On the one han, the lower cost of capital boosts the real wage in the Unite States, which is positive for the U.S. On the other han, the lower interest rate also implies a lower interest income for a given amount of savings, which is negative for the U.S. For a moerately unbalance sex ratio in China, the positive e ect for the Unite States ominates. As the Chinese sex ratio becomes seriously out of balance, the welfare levels in both countries coul go own. We note, however, that the quantitative e ect of a rise in the Chinese sex ratio on the U.S. welfare is small. The Chinese lose the most from a rise in the sex ratio. As an illustration, base on the right panel of Figure, if the Chinese sex ratio reaches 1.15, the U.S. enjoys a gain of utility that is equivalent to an increase in consumption by 1.%. In contrast, China su ers a welfare loss that is equivalent to a ecline in consumption by 36.5%. 4.5 Multi-perio moel calibration In this section, we calibrate the multi-perio moel to see whether our results i er from the twoperio moel. We change some parameters here. As in the stanar literature, we will take R = 1:04 for an annual calibration. Then the subjective iscount factor now takes value = 1=R. We take = 5 an 10 in the two experiments. All other parameters are the same as in the benchmark OLG moel. The results are showe in Figure 10 an Figure 11. If marriage takes place in the 5th perio, as sex ratio rises from 1 to 1.1, the economy-wie savings rate an current account can rise by 3 percent. If marriage takes place in the 10th perio, as sex ratio rises from 1 to 1.1, the economy-wie savings rate an current account can rise by almost 4 percent. 5 Some Empirical Evience 9

32 We iscuss two types of empirical approaches that allow us to check for plausibility an empirical importance of the theory. First we provie some cross-country evience on the relationship between a country s sex ratio an its non-government part of the current account. Secon, we review househollevel evience from China on the association between sex ratios an savings rates. 5.1 Cross country ata patterns We e ne a country s non-governmental part of the current account as its current account balance minus its government savings (or government revenue minus expeniture), ivie by its GDP. We exclue government savings because our theory is about private sector savings. In Figure 1a, we plot the ratio of the non-governmental part of the current account to GDP in 006 against the sex ratio for chilren of age 0-15 for all countries for which we can obtain ata on all relevant variables. The year 006 is chosen for current account information because it is relatively recent (when the global current account imbalances have become a policy issue), an the ata are available for a large section of countries. The age group 0-15 is chosen for the sex ratio to maximize country coverage. There is a visible positive correlation between the two variables. The slope coe cient of the tte line is statistically signi cant at the one percent level, with a point estimate of 15.5 an a stanar error of In other wors, those countries with a higher sex ratio also ten to have a higher private-sector current account to GDP ratio. Economic theories suggest that other factors can a ect a country s current account. We run a multivariate regression of the ratio of non-governmental current account to GDP on sex ratio an other control variables. To be precise, the speci cation equation is the following: cagp i = sex ratio i + Z i + " i where cagp i is the ratio of current account minus government saving to country i s GDP. Sex ratio is e ne as the male to female ratio for the age group Our choice of the control variables are guie by the life-cycle theory, precautionary saving theory, an nancial evelopment theory. We therefore inclue variables in Z i log per capita GDP, the share of working age people in the population (a proxy for life-cycle theory), social security expeniture as a share of GDP (a proxy for the precautionary saving theory), private creit to GDP ratio (a proxy for nancial evelopment), an continental ummies (a proxy for possible cultural factors). Current account, GDP, the share of working age in the population an private creit to GDP ratio can be obtaine from the Worl Bank s WDI atabase. The sex ratio ata is obtaine from the Worl Factbook. Social security expeniture as a share of GDP ata is obtaine from the International Labor Organization (ILO) atabase. A series of regression results are reporte in Table 1a, where the set of control variables is progressively enlarge. In each regression, we have a positive an statistically 30

33 signi cant coe cient on the sex ratio: as sex ratio becomes more unbalance, the current account balance tens to go up. This result still hols after we exclue potential outliers (in particular, Kuwait, which has a very large current account surplus in 006). From Table 1a, as sex ratio rises from 1.05 (normal biological level without sex selection) to 1.15 (China s sex ratio), base on the last column, current account will rise by aroun 1.5 percent. In Table 1a, we can n that the nancial evelopment inex has signi cant negative signs as the theory preicts. This means that a country with a well evelope nancial market tens to have a current account e cit. The age pro le of populations an the social security expeniture inex prouce some puzzling patterns. In contrast to the life-cycle theory an precautionary saving theory, the share of working age population has a negative coe cient an social security expeniture as a share of GDP has a positive coe cient. The coe cients mean that ol-age househols an househols with chilren save more than o househols in between, an people save more even though they may get more social security bene ts. However, those coe cients are not signi cant in several regressions which means that life-cycle theory an precautionary saving theory are not capable of explaining the global current account imbalances. The intertemporal theory preicts that a country s current account shoul be very sensitive to temporary shocks. To minimize the in uence of year-to-year uctuations in the current account ue to temporary shocks, we also conuct a robustness check whereby the epenent variable is the average ratio of non-governmental current account to GDP over a ve-year perio ( ). The bilateral relationship between the average non-government current account/gdp ratio an the sex ratio is presente in Figure 1b. A strong positive association is still clearly visible. Inee, the relative positions of iniviual countries on t change very much between the two graphs. In Table 1b, we report a similar set of regressions where the set of controls is expane progressively. Again, the positive relationship between the local sex ratio an the local non-governmental current account is robustly positively. We also stuy the relationship between a country s sex ratio an its savings rate (% of GDP). Table a an b provie the regression results. The coe cients on the sex ratio in all the regressions are positive an signi cant which means that as a country s sex ratio rises, aggregate savings rate will increase. Figure a an b plot the country s aggregate savings rate against the sex ratio. We can n strong positive correlations between the two variables. There are many caveats with the empirical patterns. First, in spite of our best e ort, there may still be potential control variables that are missing from our list. Secon, because the sex ratio ata are not available for most countries in the earlier years, we are not able to conuct a panel regression. In any case, the sex ratio ata are likely to be strongly serially correlate, which woul have require a long time series to successfully ientify the parameters. Thir, the sex ratio can be enogenous an/or measure with errors. This woul normally call for an instrumental variable approach. At this point, we are not able to come up with convincing instrumental variables in a cross-country context. For these reasons, it is important to review some micro-evience from within China. 31

34 5. Cross-househol an cross-region evience from China to be ae 6 Concluing Remarks an Future Research This paper buils a theoretical moel to analyze whether an how a rise in the sex ratio may trigger a competitive race in the savings rate by men (or househols with sons). Generally speaking, men raise their savings rate in orer to improve their relative staning in the marriage market. If we on t consier intra-househol bargaining, women may respon to a rise in the sex ratio by reucing their savings rate because they may free rie on the increase savings from their husbans. If we consier intra-househol bargaining, then women s response becomes ambiguous because they also have an incentive to raise their savings rate in orer to protect their bargaining power within a family. In any case, the aggregate savings always rises unambiguously in response to a rise in the sex ratio, as long as the sex ratio is below some threshol. We argue conceptually an through calibrations that the sex ratios in real economies are unlikely to excee the threshol. When the country with an unbalance sex ratio is large, this coul have global rami cations. In particular, when the sex ratio rises, the worl interest rate becomes lower. Other countries with a balance sex ratio coul be inuce to run a current account e cit. Calibration results suggest that the sex ratio e ect coul potentially explain more than 1/ of China s current account surplus an the U.S. current account e cit. In other wors, the e ect is economically signi cant. The theory can be extene in a number of irections. First, the sex ratio coul enogenously respon to the economic buren of raising a son (as in Bhaskar, 009). As a result, there may be forces that will eventually inuce a correction in the trajectory of a country s sex ratio. It will be a useful extension to enogenize the sex ratio in the moel. This will help us unerstan better the future trajectories of the global current account imbalances. Secon, while the moel focuses on the responses of the savings an current account to a rise in the sex ratio, one may exten it to stuy entrepreneurship an growth e ects. Thir, while we have provie some cross country evience on the connection between a country s sex ratio an its non-governmental part of the current account, the evience is base on OLS regressions. It will be useful to n instrumental variables to prove the causality more forcefully. These will be useful topics for future research. References [1] Becker, G. S. (1973). A Theory of Marriage: Part I. Journal of Political Economy 81(4):

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37 [33] Moigliani, Franco, 1970, The Life Cycle Hypothesis of Saving an Intercountry Di erences in the Saving Ratio, Introuction, Growth an Trae, Essays in Honor of Sir Roy Harro, W.A. Elits, M.F. Scott, an J.N. Wolfe, es. Oxfor University Press. [34] Moigliani, Franco, an Shi Larry Cao, 004, The Chinese Saving Puzzle an the Life Cycle Hypothesis, Journal of Economic Literature, 4: [35] Peters, M., an A. Siow, 00, Competing Pre-marital Investments Journal of Political Economy 113, [36] Qian, Nancy, 008, Missing Women an the Price of Tea in China: The E ect of Sexspeci c Earnings on Sex Imbalance, Quarterly Journal of Economics, 13(3): [37] Roth, A. E. (1984). The evolution of the labor market for meical interns an resients: A case stuy in game theory. Journal of Political Economy, 9, [38] Roth, A. E., an Sotomayor, M. A. O. (1990). Two-sie matching: A stuy in game-theoretic moeling an analysis. Cambrige University Press. [39] Wei, Shang-Jin, an Xiaobo Zhang, 009, The Competitive Saving Motive: Evience from Rising Sex Ratios an Savings Rates in China, NBER working paper 15093, June. [40] Wei, Shang-Jin, an Xiaobo Zhang, 009, "The Sexual Founations of Economic Growth: Evience from China", working paper 35

38 A Proof of Proposition 1 Proof. Since 1 1, at = 1 (Rs m y + Rs w y) > max (Rs w y, Rs m y) Then within the neighbourhoo of = 1, we have u 0 m < u 0 m;n. 1. If for all [1; 1 ), we have u 0 m < u 0 m;n The rst orer conitions for a woman an a man, respectively, are: u 0 1w + (1 p)u 0 m M(min )f( min ) + pu 0 w;n = 0 (A.1) u 0 1m + (1 p) m u 0 m + u 0 um + max u m;n w + [(1 m ) (1 p) + p] u 0 m;n = 0 (A.) max min Totally i erentiating the system, we obtain s = z (A.3) where = h i A (1 p) Ryu 00 w M(min )f( min ) D B!, s = s w s m! an = 0 E! where A = y B = y 4 u 00 1w + (1 p) Ru 00 w + Ru 00 w u 00 1m + R m u 00 um u m;n+ min max min D = (1 p) m um + 1) + E = (u0 m(n) u 0 m) < M(min )f( min ) m + u 00 mr + Ru 0 w( u0 m u0 m;n u m;n + min max min max min ) yu 00 mr + + pru 00 w;n 3 < [p + (1 p)(1 m )] Ryu 00 m;n < 0 u0 wu 0 m max min It is easy to show that et() > 0 36

39 an s w s m = = h i Ryu 00 w M(min )f( min ) E AE et() > 0 et() < 0 The aggregate savings rate of the young cohort is s y = 1 + sm sw an we can show that s y = sm s w (1 + ) + 1 s m s m sw = sm s w (1 + ) + 1 s m yu 00 1wE 1 + et() Obviously, the secon an the thir term on the right han sie are postive. When = 1, women an men have the same savings rates. As the sex ratio rises, we have showe that men raise their savings while women reuce their savings. Then s m > s w, which implies that the rst term on the right han sie is positive. Therefore, the aggregate savings rate of the young cohort increases as the sex ratio rises. Since the (is-)savings rate of the ol cohort is xe (their sex ratio is balance), an increase in the savings rate by the young cohort translates into an increase in the economy-wie savings rate. The impact of a rise in the sex ratio on the social welfare w = y u 0 1w + (1 p)u 0 w + pu 0 s w w;n s > (1 p) yu 0 m w + sw + E [] > 0 + (1 p) yu 0 s m w + E [] (A.4) = y u 0 1m + (1 p)u 0 m + [(1 p) + (1 )] u 0 s m m;n + (1 s w p)yu0 w R +(1 u m u m;n + M( + min ) M 3 1 ( m )F ( m ) 5 < (1 p) yu 0 s w w u m u m;n + min E [] < 0 where the rst inequality in (A.4) hols because u 0 1w + (1 p)u 0 w + pu 0 w;n = (1 p)u 0 m 1 + M(min )f( min ) < 0 37

40 an the rst inequality in (A.5) hols because u 0 1m + (1 p)(1 + )u 0 m + p(1 )u 0 m;n = (1 p)u 0 um + min w max u m;n min < 0. If there exists a 3 (< 1 ) at which u 0 m = u 0 m;n In this case, we still have V m > V m n, i.e., no man will choose to be single an at 3. Substituting the equation u 0 m = u 0 m;n into (A.3), we can easily show that s m = sw = 0 For any slightly greater than 3, men an women will not change their saving ecisions. Since we have shown that for 3, a man has a higher savings rate than a woman. Therefore, as the sex ratio becomes more unbalance, the aggregate savings rate of the young cohort rises unambiguously since men represent a larger share in the total population. For any aitional increase in the sex ratio beyon 3, both women an men will keep their savings rates as constants. An since men save at a higher rate than women, the aggregate savings rate of the young cohort increases as the sex ratio rises. If the (is-)savings of the ol cohort are xe, the economy-wie savings rate rises unambiguously as the sex ratio becomes more unbalance. In this proof, we use the assumption of the uniform istribution of i (i = w; m). In fact, there exist many other istributions that can give us the same results. Two su cient conitions R f(m( w )) 0 h R i 1 f( w ) f(m( w )) F (w ) + M( min )f( min ) The rst su cient conition is equivalent to an the secon one is equivalent to 1 Z f( w ) f(m( w )) Z max min f 0 (M( w )) f(m( w )) 1 F ( w ) w 0 f( min ) f(m( min F ( w ) + 1 Z max f( w )f 0 (M( w )) 1 F ( w ) )) f 3 (M( w )) min w 0 Distributions that are similar to normal istributions (i.e., symmetric aroun the mean an f( min ) is small) may satisfy the two conitions. 38

41 B Proof of Proposition Proof. We rewrite the the economy-wie savings rate as following s P t = (1 ) 1 + sm t sw t s y t 1 1+ sm t R As we have shown in Proposition 1, 1+ sw t strictly increases in since men will save at a higher rate than women. s P then is an increasing function of. By the expression of the current account to GDP ratio, this is also the conition that the current account is an increasing function of the sex ratio. Therefore, the economy-wie savings rate an the current account rise as the sex ratio becomes more unbalance. C Proof of Proposition 3 Proof. Since capital can ow freely between countries, the interest rates R are equal in both countries. By (.10) an (.11), the wage rates are also equal in the two countries. Given the same wage rates, the househols in the two countries have the same rst perio enowment. By Proposition 1, country will have a higher savings rate than country 1. On the other han, in equilibrium, given a constant R, the investments in both countries are the same, an the worl capital market always clears. Therefore, country runs a current account surplus an country 1 runs a current account e cit. D Proof of Proposition 4 Proof. We have shown that when = 1, entering the marriage market is a ominant strategy for both women an men. Then if is close to one, we still have V i > Vn i (i = w; m), all women an men choose to enter the marriage market in the secon perio. Since 1 1, (Rs m y + Rs w y) > max (Rs w y, Rs m y) which means that within the neighbourhoo of = 1, we have u 0 m < u 0 m;n. 1. If for all [1; 1 ), we have u 0 m < u 0 m;n We can obtain the same results as in Proposition 1 for < 1. For 1, if women o not change their rst perio consumption/saving ecisions, some men begin to quit from the marriage market. One equilibrium in the economy is that, all women enter the marriage market with the same savings rate. With probability 1 =, men will enter the 39

42 marriage market with the same savings rate at = 1. For the rest of men, they choose to be single. However, women o not achieve their highest welfare in this equilibrium. We can show in the following that, if women can show a signal (raising their savings) before men s ecisions, they can achieve higher welfare in another equilibrium. Lemma 1 For slightly above 1, the women increase their savings rate. Suppose the sex ratio rises just above 1, if women o not raise their savings rates, men woul choose a mixe strategy: with probability 1, they enter the marriage market an with probability 1 they opt to be out of the marriage market. However, women 1 woul not choose to o nothing, because they strictly prefer to be marrie an have the men with the highest values of the emotional utility staying in the marriage pool. By raising her savings rate by a small amount, she won t experience a rst-orer welfare loss. At the same time, by raising her secon-perio wealth, men will be inuce to go back to always entering the marriage market. Woman i will have a welfare gain because she will have a higher probability to marry a man with a higher m. Therefore, if rises beyon 1, women will optimally show a signal to all men by increasing their savings rates to inuce all men to enter the marriage market. A woman s savings ecision must satisfy the following equation: max s m u(c 1m) + " (1 p) m u(c m ) + (1 p)e( w j s m ; s w ; ) + (p + (1 p)(1 m )) u(c m (n)) # R = (1 + )u 1 + R y (D.1) where we have use the fact that the optimal savings rate of a life-time bachelor equals 1 1+R. Totally i erentiating (D.1) an (A.), we obtain s = where = (1 p)u 0 my 0 D B!, s = s w s m! an = I E! where an Then I = (1 p) um u m;n + min + E ( w ) > 0 et() = (1 p)u 0 my B < 0 s w = I B et() > 0 40

43 Since (D.1) hols, we have an = 0 s m = (1 p) u0 my s w u m u m;n + min E [] y u 0 1m + (1 + ) u0 m y + (1 )u0 m;n = (1 p) I u m u m;n + min E [] y u 0 1m + (1 + ) u0 m y + (1 )u0 m;n = 0 Therefore, if 1, as the sex ratio rises, a representative man s savings rate stays constant an a representative woman s savings rate increases. However, by (A.4), as the sex ratio becomes su ciently high (over another threshol), raising the savings rate further by the representative woman may lea to a welfare loss for her. Therefore, at a certain point, the representative woman stops responing to any aitional increase in the sex ratio by raising her savings rate. We use to enote this threshol value, an satis es the conition that U w = 0, which means that y u 0 1w + (1 p)u 0 w + pu 0 s w w;n + E [] = 0 (D.) Lastly, we will show that the aggregate savings rate of the young cohort rises as the sex ratio rises. Consier the case =, substituting the expression of sw we have Since u m u 0 1w + (1 p)u 0 m + (1 p)e [] [u m u m;n + min + E ( w )] u0 m + pu 0 w;n = 0 u m;n + min > 0, u 0 m;n > u 0 m, an u w = u m, then u 0 1m + (1 p) m u 0 m + u 0 um + max w which means that s w < s m. max u m;n min into (D.), + [(1 m ) (1 p) + p] u 0 m(n) > 0 Therefore, the aggregate savings rate of the young cohort will rise because (1) the women raise their savings rates; () the men o not reuce their savings rates, an (3) the men (with a higher savings rate than women) represent a larger share in the population. The economy-wie savings rate will also rise if we assume the (is-)savings of the ol people are xe. In any case, entering the marriage market is a ominant strategy for both sexes. Starting from a high enough sex ratio that excees the threshol, >, any aitional increase in the sex ratio woul not inuce the women to cut own their consumption 41

44 further, an woul inuce some men to quit the marriage market. The aggregate savings rate of the young cohort eclines since a life-time bachelor s savings rate is now lower than a wife-seeker s savings rate.. If there exists a 3 (< 1 ) at which u 0 m = u 0 m;n We obtain the same results for < 1 as in Proposition 1. If the sex ratio keeps rising, similar to the analysis in part 1, there exists a threshol value 1 at which the representative man becomes ini erent between entering the marriage market an remaining single. The rest of the iscussions in the analysis of part 1 is applicable here in terms of how a rise in the sex ratio a ects the savings rates. E Proof of Proposition 5 Proof. For 1, we can rewrite the rst orer conitions for women an men, respectively, u 0 1w + (1 p) u 0 1m + (1 p) 4 + R M( min ) u0 w " R u 0 w w + sw +s m + R u 0 m RM( min ) u0 m m + sw +s m s w m m (s w +s m )s m s m w w (s w +s m )s w (s m ) w (s w ) m F ( m ) F ( w ) F ( m ) F ( w ) We totally i erentiate the system an enote the outcome by 3 # + pu 0 w;n = 0 (E.1) 5 + (1 m (1 p))u 0 m;n = 0 (E.) s = z where = A 0 Q 0 D 0 B 0!, s = s w s m! an = V 0 E 0! where A 0 = Ry(1 p) 4 R 1 u 00 1w + R u 00 w w + sw +s m s w m F ( w ) + R 3 u 0 s m +s w w w s m s F ( w ) m + R u 00 m m (s w +s m )s m m (s w ) F ( w ) + R 5 + pryu 00 u 0 (s w +s m )(s m ) m m (s w ) F ( w w;n ) 4 B 0 = R(1 p)y 4 R 1 u 00 1m + R M( min ) u00 m m + sw +s m s m w F ( m ) + R M( min ) u0 s w +s m m m s w s F ( m ) w + R u 00 w w (s w +s m )s w w (s m ) F ( w ) + R u 0 (s w +s m )(s w ) w w (s m ) F ( w ) 4 + [p + (1 m )(1 p)] u 00 m(n)ryu 00 m;n 3 5 4

45 D 0 = R(1 p)y 6 4 Q 0 = R(1 p)y 6 4 R R m + sw +s m M( min ) u00 m s w m M( min ) u0 s w +s m s m m s m w (s w ) + R u 0 w R u 00 + R u 0 w w w + sw +s m s w m w (s m ) 3 + (sw +s m )(s w ) (s w ) + R u 00 m m F ( m ) + R u 00 w s w w (s m ) + (sw +s m )s w w (s m ) 3 w w (s m ) 4 m (s w +s m )s m (s w ) m (s w +s m )s m m (s w ) w (s w +s m )s w (s w +s m )s w w (s m ) F ( w ) + R u 0 m 3 F ( m ) w (s m ) F ( w ) 7 5 F ( w ) 3 F ( w ) s w +s m s w m + sw +s m s w m s m m (s w ) F ( w ) F ( w ) 7 5 Z E 0 = (1 p) u 0 m m 1 + M( min ) Z (1 p)r(s m + s w )y Z (1 p)r(s m + s w )y Z (1 p) u 0 w M( min ) M( min ) M( min ) m 4 ( max min ) + sw + s m s w m 1 m + sw + s m u 00 m s w m u 00 w w (s w + s m ) s w (s m ) w m 1 + w 1 w 4 (s w + s m ) s w w 1 max min (s m ) F ( m ) m 4 F ( m ) ( max min )! w 1 w 4 max! F ( m ) min F ( m ) Z V 0 = (1 p) u 0 w 1 w 4 s w + s m w 1 w max min s m Z (1 p)r(s m + s w )y w + sw + s m Z (1 p) u 0 m m 1 + Z (1 p)r(s m + s w )y u 00 w m 4 ( max min ) s m w F ( w ) w 1 w 4 max! (s w + s m ) s m u 00 m m (sw + s m ) s m (s w ) m (s w ) m 1! m 1 + min F ( w ) F ( w ) m 4 F ( w ) ( max min ) Uner Assumptions E1 to E3, we can show that et() > 0 an A 0 < 0, B 0 < 0, D 0 < 0, Q 0 < 0 At = 1, both men an women have the symmetric problem, m 1 = w 1, then Z E 0 = R(1 p)(s m + s w )y Z V 0 = (1 p) The sign of V 0 is ambiguous: M( min ) s u 00 w + s m m s w m m 1 + u 0 s w + s m w 1 w s m F (w ) + R(1 p)(s m + s w )y m 4 ( max min ) Z u 00 s w + s m w s m w F ( m ) < 0 w 1 + w 4 max min F ( w ) 43

46 (i) If i 1 > 0, then V 0 > 0. an At = 1 s m = A0 E 0 D 0 V 0 > 0 et() s w = B0 V 0 D 0 E 0 < 0 et() The aggregate savings rate of the young cohort is s y, s y = sm s w (1 + ) + 1 s m s m + sw We have shown in this case that men increase their savings rate as the sex ratio rises while women reuce their savings. Then s m > s w. Plugging the expressions of A 0 ; B 0 ; D 0 ; E 0 an V 0, we can also show that sm + sw sy > 0. Therefore, > 0. If the (is-)savings of the ol cohort are xe, the economy-wie savings rate rises as the sex ratio becomes more unbalance. (ii) If i 1 < 0, the sign of V 0 is ambiguous. However, if we assume that i 1 is small enough in its absolute value, then we still have sm A 0 an D 0. The sign of sw If sw is ambiguous. > 0 by substituting the expressions of > 0, then the aggregate savings rate of the young cohort an the economy-wie savings rate rise as the sex ratio becomes more unbalance. Even if sw show that s m + sw = (A0 Q 0 ) E 0 + (B 0 D 0 ) V 0 > 0 et() 0, we still can By the same logic in (1), the aggregate savings rate of the young cohort an the economywie savings rate rise as the sex ratio becomes more unbalance. Since all functions in the moel are continuously i erentiable, then for moerately unbalance sex ratios (i.e., within the neighbourhoo of = 1), we have similar results: as the sex ratio rises, a representative man raises his savings rate, but the response by a representative woman is ambiguous. Nonetheless, the economy-wie savings rate rises unambiguously. 44

47 We can rewrite E 0 an V 0 as following: Z E 0 ' ( 1) (1 p) u 0 m m m M( min ) ( max min ) Z + (sw + s m ) s w (1 p) Z V 0 ' ( 1) (1 p) M( min ) (s w + s m Z ) s w (1 p) 4 u0 w w s w M( min ) +u 0 m m u 0 m m u0 w w s w M( min ) +u 0 m m If i is large enough, E 0 < 0 an V 0 > 0. Then it is easy to show that w s m m 1 + m 4 ( max min ) w s m 1 m 1 + u 0 w 1 + w 4 max min m 4 ( max min ) u 0 w + w 4 max min m 4 ( max min ) w 1 + w 4 max 3 5 F ( m ) w 1 + w 4 max 3 5 F ( m ) min min F ( m ) F ( m ) s m > 0, sw < 0, an sy > 0 As the sex ratio rises, a representative man s savings rate rises while a representative woman s savings rate eclines. The economy-wie savings rate rises. The impacts of a rise in the sex ratio on women an men s welfare are, w Z = y u 0 1w + (1 p) u 0 w w + sw + s m s s m w F ( w ) + pu 0 w w;n " Z! # +(1 p) y u 0 w w (s w + s m ) s w (s m ) w F ( w ) sm + E [] > 0 u 0 1m + (1 p) R! M( = y min ) u0 m m + sw +s m s m w F ( m ) s m + ((1 m ) (1 p) + p) u 0 m;n +(1 p) 4 y R 3 M( min ) u0 m m (s w +s m )s m m (s w ) F ( m ) sw R 5 M( min) M 1 ( m )F ( ) " Z! # < (1 p) y u 0 m m (sw + s m ) s m (s w ) m F ( m ) sw E [] < 0 M( min ) 45

48 F Proof of Proposition 6 Proof. We totally i erentiate the system s = z where 0 s = s w s m T w T m 1 C A 0 an = z 1 z z 3 z 4 1 C A where 11 = y w + R 4 u00 1w + (1 p) 1+ u00 1 = y m + R R (1 p) 1 + R 13 = 8 < 1 + u00 w;m u00 w;w : (1 sw t )u 00 1w + + R s w t 14 = + R s w t 4 (1 p) R 1+R R 1+R M(min )f( min ) + pu 00 w;n w;m u00 w;w M(min )f( min ) M(min )f( min ) + pu 00 w;n R 1+R 1+ u00 w;m u00 w;w 4 (1 p) M(min )f( min ) 1+ u00 w;m u00 w;w 3 5 Y = 5 ; Y 0 46

49 1 = y w + (1 p) R 6 4 = y m + R 6 4 +(1 p) 3 = + (1 p) R s w 6 t 4 4 = 8 >< >: R 1+R + R 1+R m + 1+ uw;m uw;w+max u m;n max min 1+ u00 w;m u00 w;w 1+ u0 w;m u0 w;w u 00 1w + pu 00 w;n + R 1+R R 1+R R 1+R + R 1+R (1 s m t )u 00 1m + + R s m t 1+ u0 w;m u0 w;w R 1+R( 1+ u0 w;m u0 w;w) u 0 m;n max min 3 1+ u0 w;m + 1 R 1+R( 1+ u0 1+ u0 w;m u0 w;w) u 0 m;n w;w max min m 1+ + uw;m uw;w+max u 7 m;n 5 max min 1+ u00 w;m u00 w;w m 1+ + uw;m uw;w+max u 3 m;n max min 1+ u00 w;m u00 w;w 7 5 Y (1 p) R 1+R R 1+R( 1+ u0 w;m u0 w;w) u 0 m;n m + 1+ u00 + R 1+R 1+ u0 w;m u0 w;w max min 1+ uw;m uw;w+max u m;n max min + pu 00 m;n R 1+R( 1+ u0 w;m u0 w;w) u 0 m;n max min w;m u00 w;w >= 7 5 >; Y 0 31 = y w t Y 0 u 00 1w;t 3 = 0 33 = (1 + ) 34 = 0 R u 00 t;w + u R 1t;wY 00 (Tt w ) + (1 s w t )u 00 1t;wY 0 (Tt w ) 41 = 0 4 = y m t Y 0 u 00 1m;t 43 = 0 44 = (1 + ) R u 00 t;m + u R 1t;mY 00 (Tt m ) + (1 s m t )u 00 1t;mY 0 (Tt m ) an z 1 = z = z 3 = 0 z 4 = 0 + R R (1 p) (1 + ) 1 + R + R 6 (1 p) 4 (1 + ) R 1+R M(min )f( min m + u 0 m(n) 1+ uw;m+ 1 u 0 w;m u 0 w;w < 0 R 1+R 1+ u0 w;m u0 w;w 1+ uw;w+max u m;n max u 0 min w;m u 0 w;w < 0 47

50 If utility function is log form, then 13 = 3 = 14 = 4 = 0, the eterminant of matrix is et () = ( ) Similar to the proof of Proposition 1, for very small, we have u 0 m(n) > R 1+R 1+ u0 w;m u0 w;w, then s m t s w t = (z 11 z 1 1 ) et () = (z 1 z 1 ) et () = z 11 z > 0 = z 1 z It is ambiguous that whether z 1 z 1 > 0 or not. The intuition is that women will concern the case that they may have a male chil in the future an hence they probably will increase their savings as the sex ratio rises. The aggregate savings rate in the young cohort rises unambiguously since s y t s w t = sm t (1 + ) + s m t + sw t m st ( 1) 1 + an s m t + sw t = z 1 ( 1 ) + z ( 11 1 ) > 0 As for the investment on chilren, T m t T w t = = 4 (z 11 z 1 1 ) > 0 ( ) (z 1 z 1 ) ( ) 33 The e ect of the rising sex ratio on the investment on a aughter is ambiguous. Here is the intuition. As sex ratio rises, parents with a aughter may expect a welfare improvement to their aughter since she can free rie on her future husban, which may lea to a reuction in the investment on the aughter. However, on the other han, once their aughter gets marrie, she may have a son. Due to the rise in the sex ratio, she an her husban will make higher investment on their son, which leas to a welfare loss to her. The aughters parents are also aware of such a situation an then may increase their investment on their aughter. The net e ect on the investment on aughters is ambiguous. We now show that T m t + T w t > 0 48

51 Notice that = (1 + ) R 1+R u 00 t;w u 00 1w;t yw t Y + 0 h u 0 1t;w u 00 1w;t i Y 00 yt wy + (1 s w 0 t ) Y 0 (Tt w) yt w Uner the assumption of log utility, we have an similarly = 4 44 = 1 (1 s w t ) Y 00 Y s w t 1 (1 s m t ) Y 00 Y s m t Y 0 (T w t ) y w t Y 0 (T m t ) y m t If Y 00 Y 0 is close to a constant, then we can easily show that 4 44 > > 0 then hols. T m t + T w t > 0 since Then the aggregate investment on chilren by parents increases as the sex ratio rises T w t T = T t m (1 + ) + T m t + T w t m Tt ( 1) 1 + As the sex ratio keeps rising, men will increase their savings much an it might be possible that u 0 m(n) becomes smaller than R 1+R 1+ u0 w;m u0 w;w, then the sign of s m t may reverse. We will show here that this cannot never happen. Suppose there exist a threshol 3 of the sex ratio such that at 3, sm t have 1 z = z 1 11 Substitute the equation into the expression of sw t, we have s w t = z1 11 ( ) > > 0 = 0 an for > 3, sm t 0. Then we 49

52 For slightly greater than 3, u 0 m(n) > u 0 m(n) which means that then R 1 + R 1 + u0 w;m w;w u0 R 1 + R 1 + u0 w;m w;w u0 z j >3 < z j =3 < 0 s m t > 0 >3 > 3 = 3 Contraiction! Therefore, for < 1, we always have s m t > 0, T m t > 0 an sy t > 0, T > 0 Similar to the proof of Proposition 1, the e ect of a rise in the sex ratio on the young cohort s welfare w > + m < +(1 1 (1 +(1 an on parents welfare y m R 1 + R 1 + u0 w;m + 1 s m 1 + u0 w;w + 1 E [] p) V t+1 m + s Vt+1 w (1 + ) p) + R 1 + u w;m u w;w u m;n + min p) V m t+1 + s V w t+1 (1 + ) + E w = = R T 1 + R u0 t w t;w t+1 R T 1 + R u0 t m t;m t+1 Uner the assumption that emotional utility from marriage is large, w > 0, < 0 < 0 the welfare impact on parents with a aughter is ambiguous. 50

53 Figures an Tables SGP CHE BOL NLD LBN EGYDEU ISR LUX BHRPHL MAC CIV AUT ZMB FRA POL UGA HUN BGD CAN MAR DNK LKA RUS FIN CZE PRY UKR ITA IND KEN COL SVN PER GBR BEL SLV NOR KOR MLI CYP SVK CHL KHM USA GTMTHA TUN URY PAK MLT DOM KAZ ARM CPV HND GHA PRT ZAF BEN CRI MUS BLR MNGHRV IRL JOR JAM TUR AUS ROM GRC KGZ BIH LTU TGO LSO NER ESP NIC MDA NZL GEO KNA FJI LVA SYC EST BGR MDV ISL Sex ratio KWT CHN Non-governmental CA/GDP Fitte values Figure 1a: (CA-Gov Saving)/GDP vs Sex ratio, year MAC SGP BOL VEN CHE NLD DEU LUX EGY PHL ISR NPLAUT SLE CIV ARG UGA IDN UKR FRA LKA BHR COLCAN POL MAR BGD NOR ITA IND HUNDNK RUS PER GBR FIN BEL CZE ZMB KEN DOM LBN PRY USA PAK KOR ZAF SVK CHL TJK GTM MUS CYP LAO KAZ THA TUN URY SVN MLT SLV KHM CRI PRT JOR JAMLI CPV MDG BEN BLR ARM IRL COG TUR KGZ HND HRVGRC GHA AUS ROMLTUALB LSO NER MNG ESP NZL MDA TGO FJI LVA NICGEO BIH KNA EST ISL SYC BGR MDV Sex ratio KWT CHN Average non-governmental CA/GDP, Fitte values Figure 1b: (CA-Gov Saving)/GDP vs Sex ratio, average

54 BWA DZA AZE COG UZB BOLVEN MNG AGONAM IRNNOR GAB VNM PNG MAR PHL ARM IND RUS KAZ LSO SVN CPV TCD ARG BLR KNAJPN NPL NLD MRT CHL MEX BGDSWE ZMB DNK ECU HND PRY THA CAN FIN GHA TUN MKD MUS SVK AUS CZE BEL PER UKR PAK LKA DEU SYR MDAEST AUT IRL SEN LAO PAN HRVESP CMR GMB HUN ITA LVA CRI BRAFRA POL LTU MDG ETHTUR KENKHM JOR CIV MLI ZAF DOM GEO URY ALB GBR GNB UGA RWA USA NZL SLE NIC SLV BGR MOZTZA KGZ BIH PRT SDN TJK GIN ROM GRC ISL CAFZARSWZ BFA SYC MWI BDI LBN LBR FJI sex ratio KOR CHN Savings (% of GDP, year 006) Fitte values Figure a: Savings (% of GDP) vs Sex ratio, year BWA DZA GAB IRN UZB VEN AZE MNGNOR COG VNM PNG IND CHE AGO MDV MAR BOL RUSPHL NAM KAZ LSOTKMNIC BLR NPL ARM SVN CPV JPN GNB ARG DNK HND NLD THA ECU CHL MEX EGYBGD FINSWE CAN ETH TCD MUS SVK GHA KNA UKR AUS COLTUN CZE BEL PERDEU PAK ZMB MDA LVAGTM HUN SYR ITA MKD POL EST AUT IRL LKA PRY HRVESP SEN CMR LTU MLIGMB TUR KEN LAO PAN DOM RWA GEO CRI BRAFRA URY ALB ZAF SWZ ROM NZL MDG NER CIV UGA SDN KHMGBR MRTBGR PRT KGZ TJK USA SLE SLV JOR MOZTZA ISL LBR BEN GRC GIN MWI BFA BIH TGO CAFZAR BDI SYC ZWE LBN FJI sex ratio AFG KOR CHN Savings (% of GDP, averge ) Fitte values Figure b: Savings (% of GDP) vs Sex ratio, average

55 Economy-wie savings rate Economy-wie savings rate Economy-wie savings rate kappa= sex ratio kappa= m=, st ev=0.05, p= sex ratio kappa= m=, st ev=0.01, p=0.0 m=0.5, st ev=0.01, p=0.0 m=, st ev=0.01, p=0.05 x=, st ev=0.01, p=0.0 x=0.5, st ev=0.01, p= x=, st ev=0.01, p=0.05 x=, st ev=0.05, p= sex ratio Figure 3: Economy-wie saving rate vs sex ratio

56 0.1 kappa= CA/GDP country 's sex ratio 0.1 kappa=0.8 CA/GDP country 1 country country 's sex ratio kappa=0.9 CA/GDP country 's sex ratio Figure 4: Two large countries, iffering only in sex ratio

57 0.15 kappa= CA/GDP country 's sex ratio kappa=0.8 CA/GDP country 1 country country 's sex ratio kappa=0.9 CA/GDP country 's sex ratio Figure 5: Two large countries, (GDP per capita) 1 =15*(GDP per capita)

58 1 Men's savings rate, kappa= Women's savings rate, kappa= Savings rate Planner economy Decentralize economy Savings rate Planner economy Decentralize economy sex ratio sex ratio 0.35 Economy-wie savings rate, kappa=0.8 1 Welfare, kappa=0.8 Savings rate Planner economy Decentralize economy Welfare Men Women Social welfare sex ratio sex ratio Figure 6: Planner s economy vs ecentralize economy, Κ=0.8 1 Men's savings rate, kappa= Women's savings rate, kappa= Savings rate Planner economy Decentralize economy Savings rate Planner economy Decentralize economy sex ratio sex ratio 0.35 Economy-wie savings rate, kappa=0.7 1 Welfare, kappa=0.7 Savings rate Planner economy Decentralize economy Welfare Men Women Social welfare sex ratio sex ratio Figure 6a: Planner s economy vs ecentralize economy, Κ=0.7

59 1 Men's savings rate, kappa= Women's savings rate, kappa= Savings rate Planner economy Decentralize economy Savings rate Planner economy Decentralize economy sex ratio sex ratio 0.35 Economy-wie savings rate, kappa=0.9 1 Welfare, kappa=0.9 Savings rate Planner economy Decentralize economy Welfare Men Women Social welfare sex ratio sex ratio Figure 6b: Planner s economy vs ecentralize economy, Κ=0.9 1 Men's savings rate, gamma= Women's savings rate, gamma= Savings rate e=0.5 e=0.3 e=0.7 Savings rate e=0.5 e=0.3 e= sex ratio sex ratio 0.4 Economy-wie savings rate, gamma=0.5 0 Welfare, gamma=0.5 Savings rate e=0.5 e=0.3 e=0.7 Welfare e=0.5 e=0.3 e= sex ratio sex ratio Figure 7a: Saving rate vs sex ratio, enogenous intra-househol bargaining, γ=0.5

60 1 Men's savings rate, e= Women's savings rate, e= Savings rate gamma=0.5 gamma=0.3 gamma=0.7 Savings rate gamma=0.5 gamma=0.3 gamma= sex ratio sex ratio 0.4 Economy-wie savings rate, e=0.5 0 Welfare, e=0.5 Savings rate gamma=0.5 gamma=0.3 gamma=0.7 Welfare gamma=0.5 gamma=0.3 gamma= sex ratio sex ratio Figure 7b: Saving rate vs sex ratio, enogenous intra-househol bargaining, ε= e=0.5, gamma= e=0.5, gamma= CA/GDP 0 country 1 country Welfare country 1 country country 's sex ratio country 's sex ratio Figure 8: Two large countries, iffering in sex ratio, enogenous bargaining power, welfare loss in units of consumption goos relative to the case of Φ=1

61 0.3 e=0.5, gamma= e=0.5, gamma= CA/GDP country 1 country Welfare country 1 country country 's sex ratio country 's sex ratio Figure 9: Two large countries, enogenous bargaining power, welfare loss in units of consumption goos relative to the case of Φ=1, (GDP per capita) 1 =15*(GDP per capita) 0.6 Aggregate savings rate 0.05 Non-governmental CA savings rate phi=1.1 phi=1.3 phi=1.5 CA/GDP phi=1.1 phi=1.3 phi= time Figure 10: Multi-perio calibration, τ= time 0.8 Aggregate savings rate 0.07 Non-governmental CA savings rate phi=1.1 phi=1.3 phi= time CA/GDP phi= phi=1.3 phi= time Figure 11: Multi-perio calibration, τ=10

62 Table 1a: Current account vs sex ratio, year 006 (6.11) (5.881) (5.484) (5.301) (5.76) (5.081) (5.819) (5.591) (6.565) (6.330) (1) () (3) (4) (5) (6) (7) sex ratio 15.5*** 16.6*** 134.3** 166.3*** 171.6*** 131.1** 15.1** (44.94) (44.31) (54.60) (55.71) (55.14) (55.41) (53.7) ln(real GDP per capita) * ** -0.58* (0.664) (6.846) (1.088) (1.075) (1.418) (1.437) (10.590) social security expeniture/gdp ** 0.434* (0.179) (0.179) (0.177) (0.9) (0.1) working age population * ** (0.77) (0.76) (0.73) (0.94) private creit/gdp * ** *** (0.06) (0.05) (0.06) Africa 17.89*** 17.3*** Asia 16.98*** 15.58*** Europe North America 11.03* 11.48** Oceania 16.74** 18.09*** ln(real GDP per capita) square 0.793* 1.444** (0.417) (0.636) Observations R-square Stanar errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1

63 Table 1b: Current account vs sex ratio, average (5.084) (4.848) (4.631) (4.440) (4.45) (4.54) (4.941) (4.710) (5.566) (5.36) (1) () (3) (4) (5) (6) (7) sex ratio 110.0*** 11.0*** 107.** 14.3*** 144.8*** 109.4** 107.5** (38.73) (37.8) (44.37) (45.07) (45.35) (46.11) (43.94) ln(real GDP per capita) ** ** ** (0.558) (5.514) (0.891) (0.876) (1.170) (1.03) (8.135) social security expeniture/gdp * 0.30* (0.151) (0.149) (0.150) (0.19) (0.183) working age population -0.54** ** ** (0.3) (0.7) (0.6) (0.47) private creit/gdp * *** (0.0) (0.01) (0.01) Africa 13.71*** 13.0*** Asia 14.55*** 13.1*** Europe North America 8.337* 8.95* Oceania 14.00** 15.35*** ln(real GDP per capita) square 0.83** 1.41** (0.341) (0.49) Observations R-square Stanar errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1

64 Table a: Savings (% of GDP) vs sex ratio, year 006 (6.063) (6.078) (5.36) (5.431) (5.17) (5.8) (6.67) (6.30) (6.316) (6.37) (1) () (3) (4) (5) (6) (7) sex ratio 144.1*** 10.9** 18.7*** 169.5*** 165.9*** 113.5* 11.8** (50.57) (50.) (54.7) (57.69) (56.31) (56.63) (57.41) ln(real GDP per capita) *** (0.688) (5.850) (1.085) (1.113) (1.590) (1.634) (11.90) social security expeniture/gdp (0.190) (0.193) (0.193) (0.59) (0.70) working age population * (0.78) (0.78) (0.84) (0.356) private creit/gdp (0.08) (0.07) (0.030) Africa 1.00* 11.75* Asia 16.05*** 15.10*** Europe North America Oceania 18.17*** 18.88*** ln(real GDP per capita) square -1.19*** (0.371) (0.736) Observations R-square Stanar errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1

65 Table b: Savings (% of GDP) vs sex ratio, average (5.53) (5.64) (4.87) (4.908) (4.64) (4.635) (5.91) (5.300) (5.709) (5.741) (1) () (3) (4) (5) (6) (7) sex ratio 17.8*** 10.5** 180.5*** 159.3*** 157.5*** 118.6** 14.6** (43.18) (4.94) (47.47) (49.1) (48.07) (49.74) (50.5) ln(real GDP per capita) *** (0.589) (4.898) (0.939) (0.944) (1.338) (1.439) (9.788) social security expeniture/gdp (0.163) (0.166) (0.165) (0.18) (0.5) working age population * 0.41* 0.553* (0.9) (0.7) (0.35) (0.81) private creit/gdp (0.04) (0.04) (0.07) Africa 10.07* 9.96* Asia 13.4*** 1.65** Europe North America Oceania 1.73** 13.19** ln(real GDP per capita) square *** 0.55 (0.311) (0.603) Observations R-square Stanar errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1

66 Κ=0.8 σ=0.01, m=, p=0.0 σ =0.01, m=0.5, p=0.0 σ =0.01, m=, p=0.05 σ =0.05, m=, p=0.0 (sm, sw, st, ca) (sm, sw, st, ca) (sm, sw, st, ca) (sm, sw, st, ca) Table 3a: Saving rate vs sex ratio, small country (not for publication) sm men s saving rate, sw women s saving rate, st economy-wie saving rate, ca current account to GDP ratio

67 Κ=0.7 σ=0.01, m=, p=0.0 σ =0.01, m=0.5, p=0.0 σ =0.01, m=, p=0.05 σ =0.05, m=, p=0.0 (sm, sw, st, ca) (sm, sw, st, ca) (sm, sw, st, ca) (sm, sw, st, ca) Table 3b: Saving rate vs sex ratio, small country (not for publication) sm men s saving rate, sw women s saving rate, st economy-wie saving rate, ca current account to GDP ratio

68 Κ=0.9 σ=0.01, m=, p=0.0 σ =0.01, m=0.5, p=0.0 σ =0.01, m=, p=0.05 σ =0.05, m=, p=0.0 (sm, sw, st, ca) (sm, sw, st, ca) (sm, sw, st, ca) (sm, sw, st, ca) Table 3c: Saving rate vs sex ratio, small country (not for publication) sm men s saving rate, sw women s saving rate, st economy-wie saving rate, ca current account to GDP ratio

69 Table 4: CA/GDP vs country s sex ratio, two large countries, iffering in sex ratio (not for publication) Κ=0.8 σ=0.01, m=, p=0.0 σ =0.01, m=0.5, p=0.0 σ =0.01, m=, p=0.05 σ =0.05, m=, p=0.0 (s1, s, ca1, ca) (s1, s, ca1, ca) (s1, s, ca1, ca) (s1, s, ca1, ca) s1 country 1 s economy-wie saving rate, s country s economy-wie saving rate, ca1 country 1 s current account to GDP ratio, ca country s current account to GDP ratio

70 Table 5a: CA/GDP vs country s sex ratio, two large countries: US an China (not for publication) Κ=0.8 σ=0.01, m=, p=0.0 σ =0.01, m=0.5, p=0.0 σ =0.01, m=, p=0.05 σ =0.05, m=, p=0.0 (s1, s, ca1, ca) (s1, s, ca1, ca) (s1, s, ca1, ca) (s1, s, ca1, ca) s1 country 1 s economy-wie saving rate, s country s economy-wie saving rate, ca1 country 1 s current account to GDP ratio, ca country s current account to GDP ratio

71 Table 5b: CA/GDP vs country s sex ratio, two large countries: US an China (not for publication) Κ=0.7 σ=0.01, m=, p=0.0 σ =0.01, m=0.5, p=0.0 σ =0.01, m=, p=0.05 σ =0.05, m=, p=0.0 (s1, s, ca1, ca) (s1, s, ca1, ca) (s1, s, ca1, ca) (s1, s, ca1, ca) Κ=0.9 σ=0.01, m=, p=0.0 σ =0.01, m=0.5, p=0.0 σ =0.01, m=, p=0.05 σ =0.05, m=, p=0.0 (s1, s, ca1, ca) (s1, s, ca1, ca) (s1, s, ca1, ca) (s1, s, ca1, ca) s1 country 1 s economy-wie saving rate, s country s economy-wie saving rate, ca1 country 1 s current account to GDP ratio, ca country s current account to GDP ratio

72 planner's economy Κ =0.7 Κ =0.8 Κ =0.9 (sm, sw, st) (sm, Δw(m), sw, Δw(w), st, Δw) (sm, Δw(m), sw, Δw(w), st, Δw) (sm, Δw(m), sw, Δw(w), st, Δw) sm men s saving rate, sw women s saving rate, st economy-wie saving rate, Δw(m) men s welfare gain uner the ecentralize economy compare to that uner the planner s economy, Δw(w) women s welfare gain uner the ecentralize economy compare to that uner the planner s economy, Δw social welfare gain uner the ecentralize economy compare to that uner the planner s economy Table 6: Planner s economy vs competitive equilibrium, small country (not for publication)

73 Table 7: Saving rate vs sex ratio, enogenous intra-househol bargaining, small country (not for publication) γ=0.5 ε=0.5 ε =0.3 ε =0.7 (sm, sw, st, ca) (sm, sw, st, ca) (sm, sw, st, ca) ε =0.5 γ =0.5 γ =0.3 γ =0.7 (sm, sw, st, ca) (sm, sw, st, ca) (sm, sw, st, ca) sm men s saving rate, sw women s saving rate, st economy-wie saving rate, ca current account to GDP ratio

74 Table 8: CA/GDP vs country s sex ratio, enogenous intra-househol bargaining, two large countries, iffering in sex ratio (not for publication) γ=0.5 ε=0.5 ε =0.3 ε =0.7 (s1, s, ca1, ca, w1, w) (s1, s, ca1, ca, w1, w) (s1, s, ca1, ca, w1, w) ε=0.5 γ=0.5 γ =0.3 γ =0.7 (s1, s, ca1, ca, w1, w) (s1, s, ca1, ca, w1, w) (s1, s, ca1, ca, w1, w) s1 country 1 s economy-wie saving rate, s country s economy-wie saving rate, ca1 country 1 s current account to GDP ratio, ca country s current account to GDP ratio, w1 welfare change in country 1 in units of consumption goos relative to the case Φ=1, w1 welfare change in country in units of consumption goos relative to the case Φ=1

75 Table 9: CA/GDP vs country s sex ratio, enogenous intra-househol bargaining, two large countries, US vs China (not for publication) γ=0.5 ε=0.5 ε =0.3 ε =0.7 (s1, s, ca1, ca, w1, w) (s1, s, ca1, ca, w1, w) (s1, s, ca1, ca, w1, w) ε=0.5 γ=0.5 γ =0.3 γ =0.7 (s1, s, ca1, ca, w1, w) (s1, s, ca1, ca, w1, w) (s1, s, ca1, ca, w1, w) s1 country 1 s economy-wie saving rate, s country s economy-wie saving rate, ca1 country 1 s current account to GDP ratio, ca country s current account to GDP ratio, w1 welfare change in country 1 in units of consumption goos relative to the case Φ=1, w1 welfare change in country in units of consumption goos relative to the case Φ=1