Pierre André Chiappori (Columbia) "Family Economics" - Cemmap

More documents

Recommendations

Info

7 Matching on the Marriage Market: Theory Individuals in society have many potential partners. This situation creates competition over the potential gains from marriage. In modern societies, explicit price mechanisms are not observed. Nevertheless, the assignment of partners and the sharing of the gains from marriage can be analyzed within a market framework. The main insight of this approach is that the decision to form and maintain a particular union depends on the whole range of opportunities and not only on the merits of the specific match. However, the absence of explicit prices raises important informational issues. There are two main issues distinguishing the approaches used in the matching literature. The first issue concerns the information structure and the second relates to the extent of transferability of resources among agents with different attributes. Specifically, models based on frictionless matching assume that perfect and costless information about potential matches is available to all participants; the resulting choices exclusively reflect the interaction of individual preferences. Such models may belong to several classes, depending on whether or not compensating transfers are allowed to take place between individuals and, if so, at what ‘exchange rate’. Still, they all rely on a specific equilibrium concept, namely stability. Formally, we say that a matching is stable if: (i) There is no married person who would rather be single. (ii) There are no two (married or unmarried) persons who prefer to form a new union. The interest in stable marriage assignments arises from the presumption that in a frictionless world, a marriage structure which fails to satisfy (i) and (ii) either will not form or will not survive. Models based on frictionless matching are studied in the next three Sections. An alternative approach emphasizes the role of frictions in the matching process; in these models, based on search theory, information is limited and it takes time to find a suitable match. The corresponding framework will be discussed in the last Section. This is page 293 Printer: Opaque this
294 7. Matching on the Marriage Market: Theory 7.1 Stable Matching without transfers: the Gale-Shapley Algorithm We begin our analysis of the marriage market assuming that there are no frictions - that is, that each man and woman knows the potential gains from marrying any potential mate. Marriage can be viewed as a voluntary matching of males and females, allowing for the possibility of staying single. We consider here only monogamic marriages so that each person can have at most one spouse of the opposite sex. These assignments can be presented by matrices with 0/1 entries depending upon whether or not male i is married to female j. Since we consider only monogamic marriages, there is at most one nonzero entry in each column and row. An illustration of such a representation is shown in Example 7.1. In this example there are 4 men and 3 women, where man 1 is married to woman 3, man2 is married to woman 1, man3 is single and man 4 is married to woman 2: Example 7.1 1 2 3 1 0 0 1 2 1 0 0 3 0 0 0 4 0 1 0 We first study matching when agents cannot make transfers between each other. We thus assume that a marriage generates an outcome for each partner that is fully determined by the individual traits of the partners; this outcome cannot be modified by one partner compensating the other forhisorherdeficient traits. Although somewhat extreme, this assumption captures situations where, because of public goods and social norms that regulate within family allocations, there is limited scope for transfers, so that the success of a marriage mainly depends on the attributes of the partners. However, an undesired marriage can be avoided or replaced by a better one. Although there is no scope for trade within marriage, there is margin for trade across couples. Let there be a given, finite number of men, M, andagiven,finite number of women, N. We designate a particular man by i and a particular woman by j. Assume that each man has a preference ranking over all women and each woman has a preference ordering over all men. Such preferences can be represented by a M ×N bi-matrix with a pair of utility payoffs, (uij,vij) in each cell. For a given j, theentriesvij describe the preference ordering of woman j over all feasible males, i =1, 2...M. Similarly, for a given i, the entries uij describe the preference ordering of man i over all feasible women j =1, 2...N. We may incorporate the ranking of the single state by adding a column and a row to the matrix, denoting the utility levels of single men and women by ui0 and v0j, respectively. The preferences of
Page 1:
Family Economics Martin Browning Pi
Page 4 and 5:
iv 3.2 Householdproduction ........
Page 6 and 7:
vi 6.4 IntertemporalBehavior ......
Page 8 and 9:
viii 11 Marriage, Divorce, Children
Page 11 and 12:
List of Figures 1.1 Marriage Rates
Page 13 and 14:
xiii 4.2 Apotentiallycompensatingva
Page 16 and 17:
Introduction The existence of a nuc
Page 18 and 19:
two distinct solution concepts; one
Page 20 and 21:
were affectedbytherisinginvestments
Page 22 and 23:
Murat Iyigun, Guy Lacroix, Valérie
Page 24:
Part I Models of Household Behavior
Page 27 and 28:
14 1. Facts there appear to be age,
Page 29 and 30:
16 1. Facts 1.1.4 Transitions The m
Page 31 and 32:
18 1. Facts sumption goods within h
Page 33 and 34:
20 1. Facts may not capture the ful
Page 35 and 36:
22 1. Facts This process is driven
Page 37 and 38:
24 1. Facts 1.4 Children Children a
Page 39 and 40:
26 1. Facts a major policy concern
Page 41 and 42:
28 1. Facts have means for, say, hi
Page 43 and 44:
30 1. Facts [21] Michael, Robert,
Page 45 and 46:
32 1. Facts Age group USA Denmark 1
Page 47 and 48:
34 1. Facts Birth cohort 1931-36 19
Page 49 and 50:
36 1. Facts USA Canada UK Norway Ye
Page 51 and 52:
38 1. Facts Country Male Participat
Page 53 and 54:
40 1. Facts Mother’s Age 20-30 31
Page 55 and 56:
42 1. Facts rate per 1000, 20+ 18 1
Page 57 and 58:
44 1. Facts Marriage rate per 1000
Page 59 and 60:
46 1. Facts percent entering first
Page 61 and 62:
48 1. Facts percent entering divorc
Page 63 and 64:
50 1. Facts 100% 90% 80% 70% 60% 50
Page 65 and 66:
52 1. Facts 1 0.8 0.6 0.4 0.2 0 23
Page 67 and 68:
54 1. Facts 0.8 0.6 0.4 0.2 0 23 25
Page 69 and 70:
56 1. Facts 0.8 0.6 0.4 0.2 0 1968
Page 71 and 72:
58 1. Facts 6.8 6.6 6.4 6.2 6 5.8 2
Page 73 and 74:
60 1. Facts 0.4 0.2 0 -0.2 -0.4 196
Page 75 and 76:
62 1. Facts 0.6 0.4 0.2 0 1968 1970
Page 77 and 78:
64 1. Facts FIGURE 1.23. Age Pyrami
Page 79 and 80:
66 1. Facts 0.6 0.4 0.2 0 1930 1933
Page 81 and 82:
68 1. Facts 100% 80% 60% 40% 20% 0%
Page 83 and 84:
70 1. Facts 0.35 0.3 0.25 0.2 0.15
Page 85 and 86:
72 1. Facts 100% 80% 60% 40% 20% 0%
Page 87 and 88:
74 1. Facts Average number of child
Page 89 and 90:
76 1. Facts Age 28 27 26 25 24 23 1
Page 91 and 92:
78 1. Facts FIGURE 1.37. Consumptio
Page 93 and 94:
80 1. Facts
Page 95 and 96:
82 2. The gains from marriage for o
Page 97 and 98:
84 2. The gains from marriage Q 2 y
Page 99 and 100:
86 2. The gains from marriage this
Page 101 and 102:
88 2. The gains from marriage as wh
Page 103 and 104:
90 2. The gains from marriage ing a
Page 105 and 106:
92 2. The gains from marriage absen
Page 107 and 108:
94 2. The gains from marriage 2.5 C
Page 109 and 110:
96 2. The gains from marriage 2.5.3
Page 111 and 112:
98 2. The gains from marriage This
Page 113 and 114:
100 2. The gains from marriage [14]
Page 115 and 116:
102 2. The gains from marriage
Page 117 and 118:
104 3. Preferences and decision mak
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
Page 141 and 142:
Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
Page 163 and 164:
Page 165 and 166:
Page 167 and 168:
Page 169 and 170:
Page 171 and 172:
158 4. The collective model: a form
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
Page 187 and 188:
Page 189 and 190:
Page 191 and 192:
Page 193 and 194:
Page 195 and 196:
Page 197 and 198:
Page 199 and 200:
Page 201 and 202:
Page 203 and 204:
Page 205 and 206:
Page 207 and 208:
Page 209 and 210:
Page 211 and 212:
Page 213 and 214:
200 5. Empirical issues for the col
Page 215 and 216:
Page 217 and 218:
Page 219 and 220:
Page 221 and 222:
Page 223 and 224:
Page 225 and 226:
Page 227 and 228:
Page 229 and 230:
Page 231 and 232:
Page 233 and 234:
Page 235 and 236:
Page 237 and 238:
Page 239 and 240:
Page 241 and 242:
Page 243 and 244:
Page 245 and 246:
Page 247 and 248:
Page 249 and 250:
Page 251 and 252:
Page 253 and 254:
Page 255 and 256: 242 5. Empirical issues for the col
Page 257 and 258: 244 6. Uncertainty and Dynamics in
Page 305: 292
Page 309 and 310: 296 7. Matching on the Marriage Mar
Page 347 and 348: 334 8. Sharing the gains from marri
Page 357 and 358:
344 8. Sharing the gains from marri
Page 359 and 360:
Page 361 and 362:
Page 363 and 364:
Page 365 and 366:
Page 367 and 368:
Page 369 and 370:
Page 371 and 372:
Page 373 and 374:
Page 375 and 376:
Page 377 and 378:
Page 379 and 380:
Page 381 and 382:
Page 383 and 384:
Page 385 and 386:
Page 387 and 388:
Page 389 and 390:
Page 391 and 392:
Page 393 and 394:
Page 395 and 396:
Page 397 and 398:
Page 399 and 400:
Page 401 and 402:
Page 403 and 404:
Page 405 and 406:
392 9. Investment in Schooling and
Page 407 and 408:
Page 409 and 410:
Page 411 and 412:
Page 413 and 414:
Page 415 and 416:
Page 417 and 418:
Page 419 and 420:
Page 421 and 422:
Page 423 and 424:
Page 425 and 426:
Page 427 and 428:
Page 429 and 430:
Page 431 and 432:
Page 433 and 434:
Page 435 and 436:
Page 437 and 438:
Page 439 and 440:
Page 441 and 442:
Page 443 and 444:
Page 445 and 446:
Page 447 and 448:
Page 449 and 450:
436 10. An equilibrium model of mar
Page 451 and 452:
Page 453 and 454:
Page 455 and 456:
Page 457 and 458:
Page 459 and 460:
Page 461 and 462:
Page 463 and 464:
Page 465 and 466:
Page 467 and 468:
Page 469 and 470:
Page 471 and 472:
Page 473 and 474:
460 11. Marriage, Divorce, Children
Page 475 and 476:
Page 477 and 478:
Page 479 and 480:
Page 481 and 482:
Page 483 and 484:
Page 485 and 486:
Page 487 and 488:
Page 489 and 490:
Page 491 and 492:
Page 493 and 494:
Page 495 and 496:
Page 497 and 498:
Page 499 and 500:
Page 501 and 502:
Page 503 and 504:
Page 505 and 506:
Page 507 and 508:
Page 509 and 510:
Page 511 and 512:
Page 513 and 514:
Page 515 and 516:
Page 517 and 518:
Page 519 and 520:
Page 521 and 522:
Page 523 and 524:
Page 525:
show all

Pierre André Chiappori (Columbia) "Family Economics" - Cemmap

Create successful ePaper yourself

Delete template?

Save as template?