Marriage, Divorce, and Asymmetric Information

1. Marriage, Divorce, and Asymmetric Information Leora Friedberg Steven Stern University of Virginia University of Virginia March 2007

2. Model Uh, Uw = utility of husband, wife from being married h, w = component of U that is observable to spouse h, w= component of U that is private information p = side payment (p>0 if the husband makes a side payment to the wife)

3. Caring Preferences • Vh(Uh ,Uw) and Vw(Uh ,Uw) • Non-negative derivatives • Bounds on altruism

4. Perfect Information • With perfect information, the marriage continues iff Vh(Uh ,Uw) + Vw(Uh ,Uw) >0

5. Perfect information • If preferences are not caring, marriages continue as long as: • Suppose spouse j is unhappy (j+j<0) • Spouse i is willing to pay p to j so that j is happy (j+p+j>0) as long as spouse i remains happy enough (i-p+i>0)

6. Perfect Information • If preferences are caring, then there is a reservation value of εw • The probability of a divorce is Fw(εw*)

7. Partial Information

8. Partial Information • The husband chooses p*:

9. An Equilibrium Exists: • (monotonicity) • (reservation values) εw*, εh* • (effect of p on res val) • (comp statics for p) • (information in p) • (comp statics for div prob)

10. Proof sketch • Assume (temporarily) that

11. Proof Sketch • And show that • And then • And then • And then • And then • And then

12. Proof Sketch • And then • And then • And then Schauder fixed point theorem • And then comp stats for divorce probs

13. Partial Information wo/ Caring • Suppose the husband makes an offer p • As before, they fail to agree (and divorce) if p is such that: h-p+h< 0 or w+p+w< 0 • Now, this may occur inefficiently: • a higher p could preserve the marriage • a higher p won’t be offered because the wife is unobservably unhappier than the husband believes • If p is acceptable, the marriage continues

14. Partial Information wo/ Caring • The husband chooses his offer p* as follows: • he has beliefs about the density f(w)of his wife’s private information w • p* maximizes his expected utility from marriage, given those beliefs: E[Uh] = [h-p+h]*[1-F(-w-p)]  p* solves [h-p+h ]*[f(-w-p)]-[1-F(-w-p)] = 0

15. Partial information • p* is bigger if the husband is happier (unobservably or observably): dp*/dh> 0, dp*/dh>0 • p* is smaller if the wife is observably happier: dp*/dw< 0 • The probability that Uw 0 (so the marriage continues after the offer p*) is higher if the husband is observably happier: Pr[w+p+w 0]/h 0

16. Other results • We can compute utility from marriage, after the side payment • Expected utility from marriage • Loss in utility (or expected utility) due to asymmetric information

17. Government policy • Consider adding (or increasing) a divorce cost D • Husband pays D, wife pays (1-)D • Now, p* maximizes the husband’s expected utility from marriage minus expected divorce costs: E[Uh] = [h-p+h]*[1-F(-w-(1-)D-p)] - D*F(-w-(1- )D-p)

18. Impact of the divorce cost • Fewer divorces • p* may rise or fall • Expected utility from marriage may rise or fall

19. An example • Assume that i  iid N(0,1), i = h,w • Then the optimal payment p( hh) solves: • we can use this to compute p*, the divorce probability, total expected value E[Uh]+E[Uw], welfare effects • we can show how they vary with the husband’s happiness h+h and the wife’s observable happiness w

26. Empirical analysis • Data from the National Survey of Families and Households (NSFH) • The NSFH reports: • each spouse’s happiness in marriage • each spouse’s beliefs about the other’s happiness • We can estimate determinants of each spouse’s happiness, the correlation of their happiness • We can infer the magnitude of side payments

27. Selection • The NSFH sample is a random sample of 13008 households surveyed in 1987. • We excluded 6131 households because there was no married couple, 4 because racial information was missing, 796 because the husband was younger than 20 or older than 65, and 1835 because at least one of the dependent variables was missing. • This left a sample of 4242 married couples.

28. Selection • The NSFH sample is a random sample of 13008 households surveyed in 1987. • We excluded 6131 households (no married couple), 4 (racial information was missing), 796 (the husband was younger than 20 or older than 65), and 1835 (at least one of the dependent variables was missing). • This left a sample of 4242 married couples.

30. Dependent Variable • Responses by each spouse to the following questions: • Even though it may be very unlikely, think for a moment about how various areas of your life might be different if you separated. How do you think your overall happiness would change? [1-Much worse; 2-Worse; 3-Same; 4-Better; 5-Much better] • How about your partner? How do you think his/her overall happiness might be different if you separated? [same measurement scale]

38. Overheard Interviews and Bias

40. Estimation wo/ Caring • Dependent variables: each spouse’s utility from marriage before side payments p each spouse’s happiness: u*h = h+h , u*w = w+w • We assume the following: each spouse’s belief about the other spouse’s happiness: v*h = Eh[u*w] = w , v*w = Ew[u*h] = h observable happiness depends on observable control variables Xi: either h i = Xih, w = Xiw or h i = Xi, w = Xi • People actually report discrete values: uh, uw, vh, vw • We estimate , the variance  of (h,w), and the cutoff points determining how happiness u*,v* maps into discrete values u,v

41. Estimation • Log likelihood of each couple i:

45. Estimation w/ Caring • Specify • Impose restrictions:

46. Estimation w/ Caring • Objective function is log likelihood function with penalty for not matching divorce probabilities in CPS data

49. Specification Tests • Kids on divorce – no significant effect • Marriage duration on signal noise variance – t-statistic = -10.11 • New kid on signal noise variance – t-statistic = 2.20