Gender bias, sex ratios, and sex selection. Why is there son preference in some countries (e.g. India and China)?

Transcription

1 Gender bias, sex ratios, and sex selection Why is there son preference in some countries (e.g. India and China)? Sex ratio imbalances, aggravated with ultrasound + sex selective abortions Should parents be allowed to choose the sex of the child? What are the implications for countries like the UK?

2 Outline of lectures 1) Biological model of the equilibrium sex ratio (Fisher) 2) Economic model of sex ratio.

3 Sex ratio (males/females), 2003 At birth under over 65 in population UK China India S. Africa Brazil Germany Source: World Factbook, 2003 Sex ratio 1.05 )Proportion of males 0:51

4 Taiwan: 109 S. Korea: 108 Sex ratio close to 1, but not quite. Sex ratio at birth somewhat biased towards boys boys per 100 girls is considered normal Boys have higher infant/child mortality, which leads to a decline in the sex ratio in the early childhood

5 Economic development and improvements in health and nutrition, reduce infant mortality and still-births. This disproportionately helps the weaker sex (boys), so that development is associated with a rise in the sex ratio Auent societies have a higher child sex ratio, ratio also rises with the process of development India & China have somewhat higher sex ratio than others countries

6 Table 1: Boys per 100 girls, years 0-6 boys/100girls, age Maharashtra Gujarat Haryana Himachal Delhi Punjab Rajasthan India

7 South and East India show normal sex ratios, with increase that is consistent with development. North and West show "abnormally" high sex ratios in 1961, and s signicant increases in the recently Child sex ratios 115 to 125 are clearly extreme and cannot be attributable to normal biological processes.

8 Biological models of equilibrium sex ratio Fisher (1930), Genetical Theory of Natural Selection Each female can have m children. Each man can have many more From reproductive point of view of species, enough to have few men relative to women Let r be the ratio of women to men

9 r can be very large small { no need to have it close to 1 Darwinian model: each individual tries to maximize individual tness Equilibrium sex ratio will be 1 (under some conditions) Homogeneous population: all boys are similar, as are all girls Matching : dierent possibilities: a) Monogamy: if r 6= 1; all members of minority sex are matched, but some of the majority sex are left unmatched. b) Polygamy: if r > 1; each male is matched with r females

10 c) Polyandry: if r < 1; each female is matched with 1 r males Polygyny { polygamy or polyandry Sequential polygyny { having second partner after rst dies. similar (analytically) in reproductive terms

11 Fundamental asymmetry between males and females under polygyny Females are the scarce factor in reproduction Each female can have m children need one male (or even less) for this having more males doesnt help Each male can have large number of children, constraint is number of females available Suppose population is size N

12 # children # males = m[r=(1 + r)]n [1=(1 + r)n = mr expected number of children of a male is mr: Suppose mother can choose the sex of the child The payo U is the expected number of grandchildren from a boy U(r) = mr: where r is now the ratio of girls to boys in the next generation

13 Let V denote payo from having a girl. V (r) = m If the mother chooses the probability of having a boy p; V (p) = pu(r) + (1 p)v (r). If U(r) > V (.) optimal to choose boy with prob. 1 If U(r) < V (.)optimal to choose girl with prob. 1

14 But the decision is same for each mother (and for each child of each mother) Equilibrium is a value r is such that each mother is indierent U(r ) = V (r ): mr = m ) r = 1 If population sex ratio is r ; any mother is indierent between boy and girl Willing to choose p = 1=2; so r = 1

15 Infant and child mortality rate of boys exceeds that of girls Girls may have greater mortality later in life Let i ; i 2 fb; gg be the infant mortality of boys and girls, b > g : Bringing up one child imposes a cost, that may preclude bringing up another If the rst child dies in infancy, a part of the resources can be used to bring up another child. Let be probability of having another child if you lose rst. < 1; since the sunk parental investment in the rst child is irrevocably lost.

16 > 0 since infant mortality takes place before the entire investment is incurred. x is the sex ratio at conception, of girls relative to boys. The ratio of girls to boys at adulthood is y y = 1 g x: 1 b y is the sex ratio in the marriage market. Polygamous matching: every woman will be able to nd a partner to father her children, even if y > 1:

17 U(x) = (1 b )ym + b U(x): U(x) = x 1 g m: 1 b V (x) = (1 g )m + g V (x): V (x) = 1 g m: 1 g

18 Solve U(x ) = V (x ); which yields: x = 1 b : 1 g y = 1 b 1 g : 1 g 1 b If b > g ; x < 1 Higher infant mortality of boys ) sex ratio at birth biased towards boys. Adult mortality: = 0 ) x not aected by dierences in

19 No gender bias { boys and girls equally good from parents' point of view. What can explain gender preference or bias? Trivers-Willard { amongst animals, males have more unequal distribution of partners than females All females can mate & get children, regardless of size Large males mate with many females; small males unable to mate at all. Human context { wealthy males can support many females, poor ones may support only one or none.

20 If the child is going to be large (or if you are wealthy) { better to have a boy If the child is small (or if you are poor) { better to have a girl Class specic gender preferences: rich prefer boys, poor prefer girls No systematic gender bias

21 Why gender bias? Technological change { agriculture { has changed payos Boserup (1970) { women better in hoe cultivation (Sub Saharan Africa) than plough (Asia) Bardhan (1974) { women better in rice (South & East India) than wheat (North & West) Questions parents may prefer boys but also want grandchildren

22 are unbalanced sex ratios consistent with rationality? is sex selection a good thing? in developed societies, should sex selection be permitted for family balancing reasons?

23 Parents prefer boys to girls, conditional on marital status being same Prefer married girl to single boy Let u B be the base payo to parents from single boy, Let u B + be total payo from married boy u G is the payo to the parents from having a single girl { additional payo in the event that this girl nds a partner. Let r be the ratio of girls to boys in the population.

24 Every member of the scarcer sex gets a partner. Every member of the more abundant sex has an equal chance of getting a partner. Expected payo to the parents from a boy: U(r) = u B + min fr; 1g : Payo from having a girl: V (r) = u G + min 1 r ; 1 :

25 Parental choice { child is a girl or a boy with equal probability. On observing the sex of foetus/ child, parents can pay a cost c and try again. u B > u G ; boys are more desired than girls, abstracting from reproductive value. Assume u B < u G + : Married girl is preferable to a boy who will remain single. If c is suciently small, r = 1 cannot be an equilibrium. At an interior equilibrium, r 2 (0; 1), parent is indierent between accepting a girl child and trying again

26 1 2 fu(r ) + V (r )g c = V (r ): U(r ) V (r ) = 2c: r = 1 (u B u G ) 2c : If c < u B u G 2 ; equilibrium sex ratio is biased against girls. Analysis formally identical for ex ante selection (e.g. in vitro fertilization or sperm sorting)

27 Welfare implications Moral (non welfarist) considerations: if abortion is okay, what is wrong with sex selective abortion? With new technologies (in vitro fertilization)... Non-paternalistic welfare evaluation. All parents are ex ante identical (before the realization of the sex of their child) Welfare criterion { expected ex ante utility of a typical parent

28 W (r) = r U(r) + r r V (r) c1 1 + r 1 + r : Proportion 1 1+r of parents have boys, and get utility U(r); Proportion r 1+r have girls and utility V (r): third term is expected cost direct cost of achieving sex ratio r Equilibrium is inecient: if a parent who aborts a girl and gets a boys stops this, no eect on own payo

29 but benet of 2 in the aggregate Welfare optimal level of r is 1; i.e. when the sexes are balanced. Intuition: suppose a single girl is converted to a boy when r 1 direct payo gain is (u B u G 2c), but two boys are left unmatched for sure in aggregate social cost is 2 eect on welfare is u B u G 2c 2 < 0 Cost is shared amongst all the boys

30 Not just boys of parents who have exercised choice. Congestion externality in the marriage market

31 Technological progress { ultrasound, in vitro fertilization { reduces c What is the eect on equilibrium welfare In equilibrium, expected utility of parent is W (c) = W (r (c)) = 0:5V (r (c)) + 0:5U(r (c)) = 0:5V (r ) + 0:5fV (r ) + 2cg Since V (r ) does not vary with r (c); W (:) increases linearly with c So technological progress reduces welfare

32 Walrasian Markets Assume that ex-post marriage market is Walrasian Let t denote the transfer from boys to girls, i.e. bride price: In a Walrasian market, t = if r < 1 and t = t 2 [ ; ] is a market clearing price. if r > 1:If r = 1; then any Focus on a rational expectations equilibrium Parents make choices on gender, anticipating a bride price

33 Bride price Walrasian Market? 1 r (sex ratio)?

34 Equals the realized bride price. sex ratio cannot be unbalanced in a rational expectations equilibrium. If r < 1; so that t = ; strictly better to have a girl r = 1 is unique rational expectations allocation continuum of equilibrium prices t such that choice is not exercised Outcome is socially ecient

35 Frictional Matching Walrasian model: equilibrium price moves discontinuously with sex ratio r Decentralized matching, with bride-price as outcome of bargaining If r is equal to 1, t = 0; t will be small is r is close to 1. Results

36 Bride price? 1 r (sex ratio)?

37 With frictional matching, r < 1 and t > 0 both price and quantity adjust to equilibrate the market Equilibrium sex ratio r ineciently low { x < x o Socially optimal sex ratio x o < 1 Improvement in selection technology reduces welfare Qualitatively, results similar to model without prices

38 In societies without large gender bias, parents still have gender related preferences In vitro fertilization permits sex selection with low nancial/psychological costs UK: Human Fertilization and Embryology Authority recommended against allowing selection for "social reasons" such as family balancing. Allowing choice { increases welfare directly but may cause gender imbalance { if parents more likely to exercise selection when they have girls than when they have boys Angrist & Evans (1998){ evidence of family balancing concerns in US

39 Table 1: Prob. of having 3rd child, US 1st two children GB BB or GG Dierence GG BB Dierence Dahl and Moretti (2007): some evidence that US parents (esp men) prefer boys

40 Preferences for gender balancing direct utility from pair of children u GB > u BB ; u GB > u GG also u BB > u GG : utility from matching: i ; if i children match 2 1 > 2 > 1

41 If either preferences are asymmetric or technology is asymmetric, then equilibrium sex ratio may be unbalanced. This is socially inecient due to congestion externality Social optimality: balanced sex ratio where either everyone exercises choice for second child If (u BB u BG 2c) + (u GG u BG 2c) > 0; optimal allocation has everyone selecting. Subsidy to the parents of one boy paid for by a tax on the parents of one girl If (u BB u BG 2c) + (u GG u BG 2c) < 0; optimal allocation has no-one selecting

42 One-child policy in China what is the eect of the one-child policy upon the sex ratio? not clear that policy is responsible for adverse sex ratio parents with two children, where the rst is a girl have greater incentives for sex selection than parents of single child a girl ensures a grandchild, and "diminishing marginal utility" for girls

43 Conclusion unbalanced sex ratios can be explained as an equilibrium phenomenon Parents not stupid (take into account imbalance) Congestion externality implies that selection is inecient Prices partially oset but need not overcome problem Family balancing concerns: selection can improve welfare, but measures may need to be taken to prevent imbalance