Economics of the Family and Family Policies

ECONOMICS OF THE FAMILY AND FAMILY POLICIES

Economic analysis of the family is a recent, but already well-established area in economics. Economists have developed new methods to analyze decisions such as marriage, childbearing, divorce and the use of family resources. The economic approach has become crucial for design and understanding in many policy areas of current interest in modern societies, such as family, tax, social security and gender equality policies. Economics of the Family and Family Policies bears evidence to the lively and relevant research in the area. The first part provides a clear picture of the state of the art of economics of the family as it relates to economic theory and economic modeling, examining the developments from common preference family models to the more recent cooperative or non-cooperative bargaining models. The second part explores theoretical and empirical applications: the effect of the intrafamily distribution of income on family decisions; the interaction between marriage markets and labour markets; and the factors behind the rise of single-parent families. The final part of the book focuses on family policies and analyzes tax, public childcare and parental leave policies in terms of the incentives they create for labor supply, time allocation, human capital accumulation and the choice of how to organize childcare. The empirical studies in this section are mainly drawn from the Nordic countries, renowned for their experience with family and gender equality policies. This volume will be an invaluable, up-to-date resource for economists and those involved in the social sciences and gender studies, as well as policy-makers themselves. Inga Persson is Professor of Economics at Lund University, Sweden. She holds a chair in the Economics of Gender and has published on labor market policy, unemployment, the welfare state and the economic position of women. Her publications include Generating Equality in the Welfare State: The Swedish Experience (1990). Christina Jonung is a University Lecturer in Economics at Lund University. Her research has covered the economic position of women in Sweden and gender equality policies.

ROUTLEDGE RESEARCH IN GENDER AND SOCIETY 1. ECONOMICS OF THE FAMILY AND FAMILY POLICIES Edited by Inga Persson and Christina Jonung

ECONOMICS OF THE FAMILY AND FAMILY POLICIES Edited by Inga Persson and Christina Jonung A selection of papers from the 15th Arne Ryde Symposium on “Economics of Gender and the Family,” in honor of Anna Bugge and Knut Wicksell

London and New York

First published 1997 by Routledge 11 New Fetter Lane, London EC4P 4EE This edition published in the Taylor & Francis e-Library, 2005. “To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.” Simultaneously published in the USA and Canada by Routledge 29 West 35th Street, New York, NY 10001 © 1997 Inga Persson and Christina Jonung All rights reserved. No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data Arne Ryde Symposium (15th:1995) Economics of the family and family policies: a selection of papers from the 15th Arne Ryde Symposium…/edited by Inga Persson and Christina Jonung p. cm. —(Routledge research in gender and society) Includes bibliographical references and index. 1. Family—Economic aspects—Congresses. 2. Family policy—Economic aspects—Congresses. 3. Family policy—Economic aspects—Scandinavia— Congresses. I. Persson, Inga. II. Jonung, Christina, 1945– III. Title. IV. Series. HQ518.A76 1997 306.85–dc21 97–10253 ISBN 0-203-44133-8 Master e-book ISBN

ISBN 0-203-74957-X (Adobe eReader Format) ISBN 0-415-14902-9 (Print Edition)

CONTENTS

List of figures

vii

List of tables

viii

List of contributors Preface

x xii

ANNA AND KNUT Christina Jonung and Inga Persson

2

INTRODUCTION Inga Perssonand and Christina Jonung

8

Part I Where are we in the economics of the family? 1

BARGAINING AND DISTRIBUTION IN MARRIAGE Shelly Lundberg and Robert A.Pollak

17

2

BATTLES OF THE SEXES: NON-COOPERATIVE GAMES IN THE THEORY OF THE FAMILY Kjell Erik Lommerud

33

Part II Marriage and family formation 3

INTRAHOUSEHOLD DISTRIBUTION OF RESOURCES AND LABOR MARKET PARTICIPATION DECISIONS Daniela Del Boca

49

4

A FAMILY WITH ONE DOMINATING SPOUSE Kristian Bolin

65

5

WOMEN’S HOURS OF WORK AND MARRIAGE MARKET IMBALANCES Shoshana Grossbard-Shechtman and Matthew Neideffer

77

6

PREMARITAL COHABITATION, CHILDBEARING AND THE CREATION OF ONE-PARENT FAMILIES John Ermisch

92

Part III Family policies and household allocation of time 7

CHILDCARE, HUMAN CAPITAL AND ECONOMIC EFFICIENCY Siv S.Gustafsson and Frank P.Stafford

107

vi

8

THE CHOICE BETWEEN FULL-TIME AND PART-TIME WORK FOR NORWEGIAN AND SWEDISH MOTHERS Marit Rønsen and Marianne Sundström

123

9

PUBLIC POLICY AND CHILDCARE CHOICE Seija Ilmakunnas

139

TAXATION AND THE MARKET FOR DOMESTIC SERVICES Anne-Marie Pålsson

153

Index

171

10

FIGURES

Anna and Knut The Bugge-Wicksell marriage contract 1.1 The Nash bargaining solution 5.1 Markets for (a) Female spousal labor; (b) Male spousal labor; (c) Female labor; (d) Male labor. Primary effects of an increase in the relative number of men 6.1 First partnership rates, 1950–62 and post-1962 cohorts 6.2 Comparison of first partnership rates for two broad cohorts 6.3 Destinations of never-married women entering cohabitation, per 1000, 1950–62 cohorts 6.4 Destinations of never-married women entering cohabitation, per 1000, post-1962 cohorts 6.5 Destinations of women having children in first cohabitations, per 1000, all cohorts 7.1 Intersibling equity tax 7.2 Child development and the distribution of well-being over children and parents 10.1 The market for domestic labor (services) 10.2 Impact on GDP by allowing tax deductions

1 4 22 82 94 94 99 99 100 114 115 163 168

TABLES

3.1 3.2 3.3a 3.3b 3.4a

Descriptive statistics Effect of total family non-labor income on labor market participation Effect of male and female non-labor income on labor market participation Tests for the equality of income effects Effect of male and female non-labor income on labor market participation. Families with children under six 3.4b Tests for the equality of income effects 3.5 Maximum likelihood estimates. Bivariate probit. Effect of male and female non-labor income on labor market participation 5.1 Means and standard deviations 5.2 Regressions of labor force participation, predicted wages and hours of work, married white women ages 25–29, US census, 1990 6.1 Observed first partnerships of women, BHPS 6.2 Observed and simulated first “destinations” of women, BHPS 6.3 Cox model parameter estimates 6.4 Observed and simulated outcomes for never-married women in first cohabiting unions, BHPS 6.5 Simulated outcomes for two broad cohorts (percentages) 6.6 Relative risks of birth in cohabiting union 7.1 Work and childcare arrangements, 1900 and 2000 7.2 Equity/efficiency trade-offs in child development 8.1 Descriptive statistics for the variables used in the analyses 8.2 Relative risks of entry into full-time and part-time employment after first childbirth among Swedish and Norwegian women. Model with preferences and human capital variables 8.3 Relative risks of entry into full-time and part-time employment after first childbirth among Swedish and Norwegian women. Model with policy variables 8.4 Relative risks of entry into full-time and part-time employment after first childbirth among Swedish and Norwegian women. Model with interactions with calendar period of birth 9.1 Recipients of home care allowance (HCA) 1985–93, whole country 9.2 The childcare modes and their economic characteristics 9.3 Description of the data 9.4 The mixed model 9.5 The changes in estimated choice probabilities: a “base case” analysis 9.6 The effects of the mother’s wage and home care allowance on the choice probabilities (a “base case” analysis) 9.7 The effects of home care allowance on the choice probabilities of the whole sample 10.1a Time allocation for men, 1990–1, average hours and minutes per week 10.1b Time allocation for women, 1990–1, hours and minutes per week

55 57 58 59 60 60 61 87 88 93 95 96 97 101 102 109 110 127 132 133 135 141 142 145 147 148 148 149 154 155

ix

10.2 Time allocation in household work, men and women 20–64 years, Sweden 1990, average hours and minutes per week 10.3 The time input (number of hours) for the teacher and the carpenter and the tax income generated, SEK; four different solutions 10.4 Summary of the marginal analysis 10.5 First-order conditions for optimality

155 157 160 165

CONTRIBUTORS

Kristian Bolin has a Ph.D. in Economics from Lund University, Sweden. His main research interest is family economics and he has undertaken both theoretical and empirical work in this area. He is now working on a project which, using Swedish data, examines the effects of the risk of divorce on female labor force participation and on the probability of having children. Daniela Del Boca has a Ph.D. from the University of Wisconsin, USA. She is Associate Professor of Economics and teaches at the University of Turin, Italy, as well as at New York University, USA. Her main interests are labor economics and applied econometrics. She has published several books and articles in Italian and international journals. John Ermisch is Professor of Economic Demography at the ESRC Research Centre on Micro-social Change at the University of Essex, United Kingdom. He is a Fellow of the British Academy and former president (1989) of the European Society for Population Economics. His primary research field is in the economics of the family and household. Shoshana Grossbard-Shechtman is Professor of Economics at San Diego State University, USA, and is a specialist in the economics of marriage and the family. Her publications include On the Economics of Marriage, a Theory of Marriage, Labor and Divorce. Siv S.Gustafsson is Professor of Economics at the University of Amsterdam, The Netherlands. She specializes in comparative population and gender economics. Her publications include Separate Taxes and Married Women’s Labor Supply. A Comparison of Sweden and West Germany and Labor Force Transitions in Connection with Childbirth. A Comparison of Germany, Great Britain and Sweden. Seija Ilmakunnas is Senior Researcher at the Labour Institute for Economic Research, Helsinki, Finland. Her main research interests revolve around labor supply, household production and social security systems. She is a member of the Network of Experts on the Situation of Women in the Labor Market, European Commission. Christina Jonung is a University Lecturer at the Department of Economics at Lund University, Sweden. Her research has concerned the economic position of women in Sweden and gender equality policies. Kjell Erik Lommerud is Professor of Economics at the University of Bergen, Norway. His primary field of interest is labor economics, with emphasis on the economics of family and gender and the economics of education. He has also published articles in the areas of public economics and industrial organization. Shelly Lundberg is Professor of Economics at the University of Washington, USA, and specializes in labor and family economics. Matthew Neideffer was a graduate student in economics at San Diego State University, USA, and is currently a graduate student at Texas A&M University.

xi

Anne-Marie Pålsson is Associate Professor of Economics at Lund University, Sweden. Her primary research field is the economics of the family and household, ranging from personal finance such as wealth accumulation, risk-taking attitudes, etc. to household production, time allocation and taxes. Inga Persson is Professor of Economics at Lund University, Sweden. She holds a chair in Economics of Gender and her research interests are labor market policy, unemployment and the economic position of women. Robert A.Pollak is Hernreich Professor of Economics at Washington University in St Louis, USA. He is the author of The Theory of the Cost-of-Living Index and co-author of Demand System Specification and Estimation and From Parent to Child. Marit Rønsen is a Senior Executive Officer in the Division for Social and Demographic Research at Statistics, Oslo, Norway. Her main research interests include female labor supply and fertility, wage formation and income distribution. Frank P.Stafford is Professor of Economics at the University of Michigan, USA, and director of the Michigan Panel Study. His publications deal with time use, earnings, childcare, human capital and economic growth. His publications include Time Goods and Wellbeing and Divergence, Convergence and Gains to Trade. Marianne Sundström is Associate Professor of Economics at the Demography Unit, Stockholm University, Sweden. Her main research interest lies in female labor force participation and social policy.

PREFACE

This volume contains a selection of the papers presented at the 15th Arne Ryde Symposium on “Economics of Gender and the Family”, held on August 18–19, 1995, at Rungsted in Denmark. Another selection of the papers presented at the symposium is published in an accompanying volume entitled Women’s Work and Wages. During two hot summer days, about 100 economists met to discuss about 40 papers in this rapidly expanding area of international research. We want to thank all the participants in the symposium for their contributions to the lively discussions that took place in the various sessions. We (and the authors) are particularly grateful to the appointed discussants who by their comments and insights helped improve the papers. We also want to express our gratitude to the Arne Ryde Foundation for financing the symposium. Since 1973, the Foundation, established in memory of Arne Ryde, a promising young doctoral student in Economics at Lund University who died in a car accident, has generously supported international symposia and lectures as well as other professional activities arranged by the Department of Economics in Lund. This support has proved to be of great value for the economics profession in Sweden and, in particular, for the doctoral students and economists at the department in Lund. Professor Björn Thalberg, Chairman of the Board of the Arne Ryde Foundation, initiated the symposium and also, as a member of the organizing committee, saw it through from start to finish. We owe him many thanks for having contributed his vast experience. Other crucial members of the team behind the symposium and this volume have been Kristian Bolin, Carole Gillis, Keith Persson and Ann-Charlotte Sahlin. Kristian Bolin helped us in planning the symposium and also acted as our consultant when the intricacies of game theory etc. threatened to overwhelm us. Carole Gillis worked hard at improving the English. Keith Persson spent part of what was supposed to be his summer vacation at the copying machine producing the conference volumes. Ann-Charlotte Sahlin, in her calm and efficient manner, took care of all practical arrangements and later also of getting the manuscripts into shape for publication. The Arne Ryde Symposium on “Economics of Gender and the Family” was held in honor of Anna Bugge and Knut Wicksell. The reasons for dedicating the symposium to them are explained in our short tale of “Anna and Knut” opening this volume. In their own way they were forerunners both in gender relations and in family economics. Their life story provided a source of inspiration and gave us a sense of continuity through the generations in our work with this project. Inga Persson and Christina Jonung Lund, December 1996

xiii

ACKNOWLEDGMENTS We want to thank the Journal of Economic Perspectives for permission to reprint as Chapter 1 in this book the paper “Bargaining and Distribution in Marriage” by Shelly Lundberg and Robert A.Pollak, which appeared in Journal of Economic Perspectives, vol. 10, Fall 1996.

Anna and Knut

ANNA AND KNUT Christina Jonung and Inga Persson

The symposium on “Economics of Gender and the Family” in Rungsted, Denmark was dedicated to the world-famous Swedish economist Knut Wicksell (1851–1926) and his wife Anna Bugge (1862–1928). In this short contribution we wish to explain why we find they deserve such an acknowledgment by telling you the story of “Anna and Knut.” Among economists Knut Wicksell is best known for his theoretical work in economics which established him as Sweden’s leading economist at the turn of the century. Paul Samuelson even ranks him alongside Adam Smith, Walras and Keynes. Knut Wicksell was Professor of Economics at Lund University between 1901 and 1916. However, it is not in his capacity as a prominent economist or a professor at our university that he was honored at this symposium. Knut Wicksell is honored as a forerunner and radical in the area of gender and the family and Anna Bugge is honored for being, in her own right, “a woman before her time.” It may come as a surprise to many to hear that Knut Wicksell first became known to a wider public in Sweden through a fiercely feminist poem. At the Scandinavian student festivities at Uppsala University in 1878, he gave the traditional poetic “Address to Woman.” The poem, which in content departed radically from the traditional themes of women’s beauty and attractiveness, was widely published by Swedish newspapers, where it was highly commended, or accused of manifesting the “depraved spirit of the times.” Unfortunately the poem is only available in Swedish, but we will try to convey some of its ideas. At this point in time Knut was not yet an economist: he was studying mathematics and physics at Uppsala University. Nevertheless the poem contains several themes that could be found in the sessions at Rungsted. After a few of the usual verses acclaiming Woman’s charming and gracious nature, the poet lets his first critical thesis burst upon his listeners: “Wealth is Woman’s true ornament.” So unjustly is society constructed that without that attribute, she will never win a respected position. If she inherits nothing from her parents, she will probably become just one more poverty-stricken seamstress, working hard to buy food for the morrow and ignored by all honorable, wealthy admirers (Gårdlund 1996:39). We recognize here a clear forerunner to Becker’s theory of marriage! The next verse introduces Wicksell’s theory of gender wage differentials. He argues simply that since women have smaller appetites than men, men have wisely arranged things in such a way that the fruits of women’s labors “in just proportion also should be small.” As the sessions at the symposium illustrated, some further theories of gender wage differentials have been developed through time, but the smallness is still with us. Another verse eloquently illustrates how unequal access to human capital shapes men’s and women’s future. Eventually Wicksell ends in a quieter and more hopeful tone. He looks forward to the day when the achievement of greater influence for women in society will create a different legal and moral climate; “a

ANNA AND KNUT

3

spirit as gentle as Woman herself would inform the law.” The strong would then protect and the weak be protected. This theme is resounding among today’s essentialist feminists. Marriage, which according to Wicksell at that time often meant slavery and the subordination of women, would also become a free and tender union between equal citizens. (Gårdlund 1996:39) In the following decade Knut Wicksell became one of Sweden’s leading radical figures, through his neoMalthusian ideas and his writings and public lectures against prostitution and in support of birth control, which was illegal at the time, and his proposals of freer forms of marriage and marriage at a younger age. Knut Wicksell’s ideas were considered extremely provocative by his contemporaries. One young female student commented on his lectures in the following way: “His talk has caused a sensation, the like of which has not been seen for many years. He arouses admiration, astonishment, loathing, hate. He has stirred the passions of all” (Gårdlund 1996:58). Hjalmar Branting, who was to become Sweden’s first Social Democratic Prime Minister, said of him, “Together with Strindberg, Wicksell was a harbinger of revolution bringing the first tidings of change to the youth of the 1880s” (Gårdlund 1996:58). It was this controversial “harbinger of revolution” that 25-year-old Anna Bugge was to meet at a Scandinavian feminist meeting in Copenhagen in 1888. Knut had then reached the respectable age of 36 and had felt lonely and unhappy for many years. It should perhaps be added that Knut was a generally very mildmannered, friendly and courteous revolutionary. A year before their first personal encounter, Anna had heard Knut give a lecture in Oslo in which he had criticized marriage on the grounds that under existing law, the husband had legal authority over his wife and children. He proposed instead a common-law marriage—a cohabitation where neither party had any legal claims on the other. This was in fact what he offered Anna when they met for the second time, in the summer of 1889 in Oslo. But who was this young Norwegian woman who dared to flout all accepted social conventions and become the close associate of the infamous Knut Wicksell, free thinker, subversive and apostle of immorality?1 When they met, Anna was already a public figure in her home country, despite her young age. Along with a few female friends, she had founded a private “gymnasium” and became the fifth Norwegian girl to take her “studentexam” and thereby gain entrance to the university. In her and her friends’ view, knowledge brought with it responsibility and they set up a debating society in order to learn to use their newly won knowledge in lectures and debates. In 1885 the society became part of the Norwegian Feminist Association, which was subsequently chaired by Anna Bugge. A few years later, Anna took part in the setting-up of the Norwegian Women’s Suffrage Association. According to Anna herself: “There has never been a more fortunate group of individuals than the young people of the 1880s. This was the period when the great issues were under discussion and nothing barred our way” (Wicksell Nordqvist 1985). This belief in the future and the firm conviction that everything was possible provided that one worked for its achievement seems to have remained with Anna for the rest of her life. The idea of a common-law marriage between equal partners must have been appealing to Anna. However, her radicalism was of a more quiet kind than that favored by the more outspoken Knut. Anna preferred to avoid conflicts and to work for long-term changes. To a greater extent than Knut she undoubtedly also understood the costs that a common-law marriage would impose upon themselves as well as upon their families. However, a few weeks later Anna traveled to Paris in order to meet Knut and a week later she had moved into what became their joint home. Some time later, this event was announced in the Stockholm press under

4

ANNA AND KNUT

the heading “United.” With the help of Karl Staff (Knut’s friend and a lawyer and future liberal Prime Minister), they drew up and signed a marriage contract that established their mutual financial obligations (Wicksell Nordqvist 1985:95). The content of the contract in English translation is reproduced here. It is quite a remarkable document; and not only for those interested in contract theories of marriage. It would be seven years before Anna was to visit Norway and her family again. At the start of their life together, Knut had still not become an economist. Although he had visited various European universities to study and attend lectures given by leading economists of the day, he had not yet produced any academic publications. The question may be asked whether there would have been as many, or indeed any at all, without Anna Bugge. Anna made numerous contributions to their life together. First, she provided the stimulus, peace of mind and security that Knut had lacked for so long and without which he had been unable to undertake any systematic academic research. Second, she continually tried to steer Knut’s efforts Whereas we the undersigned, N.N. (husband’s name) and N.N. (wife’s name), have freely entered into mutual union, we do hereby pledge and covenant as follows:

(1) (2)

(3) (4) (5)

(6)

Each of us hereby pledges to provide for the other, to the extent that our incomes and assets reasonably allow, such provision continuing as long as our union prevails. In the event that I, N.N. (wife’s name), should have children during our union or, should our union cease to exist, during such time when I, N.N. (husband’s name) could be the father, we jointly pledge to make provision for the proper support and upbringing of these children, in accordance with our respective incomes and assets, until such time as they are able to provide for themselves. Our union shall exist until such time as it is renounced by either of the undersigned. The obligation in clause 2 to make provision for our children will remain in force irrespective of a cessation of our union. The mutually agreed pledge in clause 1 to provide for the other will remain in force until such time as our union is dissolved as specified in clause 3. However, in the event of illness or any other reason that prevents either of the undersigned from being able to make adequate provision for him/herself and if he (she) is without his/her own assets, the other contracting party shall be bound to make provision for the first, without regard to the dissolution of the union. This obligation will remain in force as long as the need exists and will come into force whenever the need arises. This contract has been drawn up in duplicate, both parties receiving their own contract.

Paris, July 1889 (signatures) THE BUGGE-WICKSELL MARRIAGE CONTRACT

towards academic output and away from an overriding concern with contemporary political issues. She even went as far as trying to curtail his reading of fiction and mathematics in favor of articles on economics. Third, Anna also helped him in practical matters. This was not just a question of running a household and

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5

managing the family economy, an area in which Knut never had much success.2 She also played an important role as secretary, linguistic advisor and, not least, in planning his academic career. After a year in Paris, the Wicksell family moved to Stockholm. Anna was now expecting a child. In order to support himself and his family, Knut devoted the next few years to public lectures, political pamphlets and journalism. Anna had a share in this work as Knut’s assistant, but she also did work of her own. She held lectures and wrote polemic pamphlets on the rights of women (the legal standing of married women in the Scandinavian countries) and on world peace (efforts to establish international arbitration)— the two areas that were to preoccupy her for the rest of her life. It was not until 1900 when Knut Wicksell became an Associate Professor at the University of Lund that he secured his first regular source of income. For more than a decade, the family had often been fairly poor, living on temporary sources of income, irregular scholarships and loans from friends and relatives. Anna had continually tried to provide Knut with the opportunity to carry out the research that would enable him to gain a university position. Finally, Anna succeeded in persuading him to take the law degree required in order to be able to lecture in economics. Her concern with Knut’s career was not just a question of their perennial shortage of money. Her overriding desire to support Knut’s academic work reflected her belief that it was through such work that Knut’s radical views would reach a larger audience. Devotion, the demand for truth and his unswerving incorruptibility were undoubtedly among the qualities that Anna found most attractive in Knut. She also learned right from the start about his “all or nothing” moral code. However, living with Knut Wicksell cannot have been an easy matter. His regard for principles would seem to have been more important than the distress that he could inflict on his family and close friends as a result of his actions. He was even willing to put the family’s future at stake by refusing to sign his professorial application to the King with the words “most humbly.” The economic pressure eased once Knut had been appointed professor. But Anna had to continue to put up with what she called her “regular dose of torment per term” from Knut, as a result of, for example, the crisis in the union between Norway and Sweden, Knut’s pro-Russian views on defense and his period of imprisonment on a charge of blasphemy. The academic community in Lund turned up their noses at the unconventional ideas and lifestyle of the Wicksell family—the unmarried professorial couple, who were often seen walking hand in hand, who set up home out in the countryside, with the husband-professor doing the shopping in the market place and carrying his books around along with the vegetables in a discarded pram, who taught their children themselves at home and who demanded that the children should not receive religious instruction once they started school. It was in Lund that Anna finally found time to devote to the fulfillment of her own ambitions. Ever since her years in Norway, Anna had dreamed of becoming a lawyer. She had started legal studies during their year in Paris but the children, Knut’s career, the problems of supporting a family and illness had all intervened to delay her studies. It was not until 1911 that Anna, at the age of 48, took her final exam for her law degree. She was to specialize in international law. During the first two decades of this century, Swedish women campaigned actively for the right to vote. Anna had started this campaign 15 years earlier in Norway and was to become one of the movement’s leading figures in Sweden as well. If Knut’s strategy for change could be described as one of provocative action, Anna’s strategy was instead one of persistent, practical work. She formed associations, organized work on behalf of women’s suffrage, held lectures, wrote articles and political pamphlets, put forward legislative proposals, electioneered for the Liberals and regularly attended international conferences as a

6

ANNA AND KNUT

delegate for women’s suffrage. Her commitment to women’s right to vote was not just a question of justice or the belief that there would be a new outlook on political life once women were able to participate fully in the political process. It was also, she argued, a matter of social responsibility, which forms an essential part of each individual citizen’s development and maturity. Using the same methods as she had applied to feminist issues, Anna involved herself in the peace movement. The solution of international conflicts by means of international law was a question which had preoccupied her for a long time. During World War I, she acted as an expert advisor to the committee that was working on a Nordic proposal for an international legal system. On the formation of the League of Nations, Anna was appointed Swedish delegate and thereby became the country’s first female diplomat. From then on and until her death in 1928, she was to spend many weeks of the year in Geneva or traveling on feminist or peace business. Her travels made life lonely for Knut and he complained endlessly about a feeling of restlessness and an inability to get on with his academic work. His last major scholarly study was the second part of Lectures on Political Economy, which he began when Anna started her legal studies. The story of Anna and Knut is excellently told in the biography of Knut Wicksell written by Torsten Gårdlund, available in English (1996) as well as Swedish (1990). There, quite naturally, the focus is on Knut. Throughout their lives, Anna and Knut wrote to each other almost every day when they were apart. They also wrote frequently to friends—long, frank letters, full of ideas and thoughts about everyday life and work. This abundant and informative correspondence formed the basis for a biography of Anna Bugge by her granddaughter Liv Wicksell Nordqvist (1985) which provides unique insights into Anna’s and Knut’s life and thoughts. Most of the social reforms which Anna and Knut worked for are now in force, e.g. the right to vote for men and women alike, a more liberal matrimonial legislation, the access to birth control, increased social and economic equality, international agencies for the promotion of peace. In spite of all of these achievements, many of the changes that they had hoped to bring about still seem very far away today, such as the abolition of prostitution and the achievement of a lasting peace. Moreover, no matter which country we come from, we may also ask ourselves to what extent we have actually attained their overriding goal for a successful society—an open climate of public debate, characterized by a search for truth and reasoned argument. For example, do dissenting opinions, in this age of “political correctness,” meet with greater tolerance at our universities and in society at large than they did around the turn of the century? We hope we have now made it clear why we feel that Anna and Knut, through their life and their work, their dreams and their ideals, have been forerunners and may serve as examples in the work and the ambitions for equality between men and women. This is why this symposium was in their honor. ACKNOWLEDGMENTS We want to thank Liv Wicksell Nordqvist who most generously provided us with the photographs of her grandparents, Anna Bugge and Knut Wicksell. REFERENCES Gårdlund, T. (1990) Knut Wicksell, Rebell i det nya riket, Stockholm: SNS förlag (first published by Bonniers, 1956). —— (1996) The Life of Knut Wicksell, Cambridge: Edward Elgar (first published by Almqvist & Wiksell, 1958). Wicksell Nordqvist, L. (1985) Anna Bugge Wicksell. En kvinna före sin tid (Anna Bugge Wicksell. A Woman before Her Time), Lund: Liber.

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NOTES 1 Wicksell Nordqvist (1985) is a fascinating biography about Anna’s life. 2 Despite being a leading expert on Sweden’s system of taxation, Knut Wicksell was not able to complete his own tax returns (Gårdlund 1996:326).

INTRODUCTION Inga Persson and Christina Jonung

Economic models of the family and of family decision-making have by now become an important and wellestablished area of research within economics. The models have enabled economists to analyze a number of issues related to the family that previously were not amenable to economic analysis, such as marriage, fertility and divorce. Economic models of the family have also turned out to be crucial tools when it comes to policy design and policy evaluation in many of the areas that are of central importance in modern societies: policies concerning the family, taxes, social security and gender equity. Concomitantly, the increased availability of cross-sectional and longitudinal data about individuals and households has greatly enriched the possibilities for empirical tests and studies of the theories. Thus, economics of the family is definitely here to stay. That it is also a very lively and dynamic research area is witnessed by the contents of this book. The book is divided into three parts. Part I consists of two chapters which describe and discuss the current state of economic modeling of the family, the reasons behind the evolution of “second-generation” models of family decision-making and the differences in the results obtained from different models. Together the two contributions establish a clear picture of “the state of the art” within economics of the family. Part II contains four chapters with theoretical and/or empirical applications. The chapters analyze family labor supply and time allocation, the role of marriage markets, and family formation. The four chapters in Part III are devoted to issues related to family policies. They treat the equity/efficiency tradeoffs that exist between parents and children and the incentive effects for households that arise from tax policies and public childcare policies. PART I WHERE ARE WE IN THE ECONOMICS OF THE FAMILY? “First-generation” economic models of the family are “common preference” models which assume that the family maximizes a single utility function. Common preference models imply that family behavior is independent of who it is in the household that receives income or controls resources. The common preference model has proved to be a powerful analytical tool, but in recent years the approach has been seriously brought into question both from a theoretical and an empirical perspective. Shelly Lundberg and Robert A.Pollak take their starting-point in the common preference model and discuss how the common preference assumption has been rationalized either by a Samuelson consensus model or by a Becker altruist model. They describe the theoretical and empirical criticisms that have been leveled against common preference models and how “second-generation” game-theoretic models of the

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family have been developed as alternative analytical tools. The game-theoretic models permit independent agency of men and women in marriage and differ from the common preference models in their implications for distribution within marriage and for observed family behavior. These models are thus consistent with a growing amount of empirical evidence which indicates that income controlled by husbands has different effects on family behavior than that controlled by wives. The game-theoretic models of the family first developed in the literature were cooperative bargaining models. Lundberg and Pollak review the salient features of cooperative family models and the types of results such models generate. They also highlight and discuss the importance in such models of the assumptions made about what constitutes the threat point in marital bargaining. In common preference models and cooperative bargaining models of the family, family behavior is Pareto-optimal, i.e. no family member can be made better off without making another worse off. This is not necessarily the case in non-cooperative models of the family—the second strand of game-theoretic models of the family to have been developed. Non-cooperative models open up the possibility that family behavior might be inefficient, and consequently they allow economists to examine what conditions might enable families to sustain Pareto-optimal outcomes. Lundberg and Pollak show how this, in turn, tends to bring the role of family legislation, social norms and conventions, etc. into the picture. Such norms and conventions constitute a framework within which the bargaining in a particular marriage takes place and can influence the outcome of that bargaining. The authors also show the important role played by the marriage market and demonstrate that marriage market repercussions must be taken into account when evaluating the more longrun effects of family policy interventions and changes in family legislation. Kjell Erik Lommerud delves deeper into the insights that can be obtained from non-cooperative models of family decision-making. He focuses on fully non-cooperative family models and, within that category, on models where the family members have conflicting objectives. First he looks at situations where there are family-specific public goods (for example, care of children, a tidy home), and family members try to freeride on the public-good provision of others. Several interesting results can be derived from such models. One group of results concerns neutrality and crowding-out effects. For example, public provision of a close substitute to the family public good (e.g. public childcare) can be shown to crowd out private provision and thus might have no net effect on investments in children. On the other hand, in such models public provision might very well affect the distribution between the spouses in an equalizing direction. Another result from these models is that not only the comparative advantages (as in Becker-type models), but also the absolute advantages of the spouses will affect the family’s allocation of time between household work and market work. Lommerud then goes on to take a look at intergenerational games. He demonstrates the strong structural similarities that exist between various models of “battles of the generations” and private-provision-ofpublic-goods models of the nuclear family. He ends his chapter with an overall assessment of the contributions made so far and the future role and potential of game-theoretic modeling of the family. PART II MARRIAGE AND FAMILY FORMATION The traditional, common preference model of the family implies that the consumption of each family member is not dependent on which individuals in the household receive income or control economic resources but only on total household income. However, as discussed above, if family members differ in their preferences, household decision-making is more appropriately modeled as a (cooperative) bargaining game

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INTRODUCTION

in which each member’s ability to influence the distributional outcome is related to his or her own contribution to household income, for example to the non-labor income of the spouses. This is the startingpoint for the chapter by Daniela Del Boca in which she uses data about Italian families to test the hypothesis that households in Italy may be treated as if they pool all their income. Rejection of the incomepooling hypothesis, however, does not allow one to distinguish between different bargaining models but only to reject the common preference model. Del Boca uses two samples of married couples: one of all married Italian couples in the age range 21–58 years and one subsample of married couples where a child under six years of age is present. For these samples labor supply functions are estimated which permit income effects to vary depending on the family member to whom the income is attributed. It turns out that the equality of the effects of male and female non-labor incomes is rejected for the total family sample but not for the sample of families with small children. Thus the extent to which the intrafamily distribution of income influences labor supply and household consumption patterns may be related to the composition of the household and to the stage in the life cycle. Del Boca also shows that the “traditional family” model (which treats the labor supply of married men as independent of the behavior of their wives and the husband’s behavior in turn as exogenous with respect to the wife’s work decision) does not seem to be an adequate description of the behavior of Italian families with small children. Taken together her results suggest that families with young children tend to behave and interact in a different way from other families, pooling their resources to a greater extent and allowing their individual labor supply decisions to be mutually and significantly influenced by the characteristics and behavior of the other partner. In the next chapter Kristian Bolin proposes a new, additional explanation for the time allocation of spouses within marriage, namely that one of them (usually the husband) dominates. Dominance is defined as the husband having a first-mover advantage in the process which settles the household’s time allocation, i.e. the husband is allowed to make an irreversible decision about his time allocation before his wife decides upon hers, leaving her no choice but to do the best she can given his time allocation. The decision process in families with one dominating spouse is modeled by a specific non-cooperative game, namely the Stackelberg game. Bolin shows that in such families not only comparative advantages, but also dominance, will matter for time allocation and that the husband will supply more time to the market and the wife will supply more time to the household when the husband has a first-mover advantage than when that is not the case. This means, for example, that in a family where the husband dominates, even if the husband and the wife were identical with respect to their preferences and comparative advantages, the husband would supply more time to the market than would the wife. Furthermore, the existence of dominance can be shown to improve the husband’s utility and to lower the wife’s utility. Does the existence of dominance have implications for family policy? Bolin examines this by looking at the incentives for a government to supply a substitute for the time inputs of family members into a familyspecific public good (such as childcare) under the presence, or respectively the absence, of dominance. The result of his analysis is that the existence of dominance tends to increase the incentives for public provision, so that a government which would not choose to supply a substitute in the absence of dominance might choose to do so in the presence of dominance. Marriage markets and labor markets are likely to interact in ways that are usually ignored in studies of labor supply. The chapter by Shoshana Grossbard-Shechtman and Matthew Neideffer studies these interactions, theoretically and empirically. Based on earlier theoretical work by Grossbard-Shechtman, they expand the theoretical model of married women’s labor supply by incorporating a market for “spousal

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11

labor” and marriage decisions into the analysis. Their model of labor and marriage is put into perspective by comparisons with traditional labor supply theory, Becker’s theory of marriage, and household bargaining theory. A major benefit of using their theory of labor and marriage is that it leads to the consideration of a number of factors which can influence labor supply but which have been ignored by traditional labor supply theory, one such factor being marriage market conditions. The effects of marriage market imbalances on labor supply is also the subject of their empirical study. Earlier empirical studies that have tested for the effects of marriage market imbalances on labor supply have been based on aggregate level data. The study by Grossbard-Shechtman and Neideffer presented here uses micro-level data from the 1990 US census (for married, white women aged 25–29) and is the first to look at the effects of marriage market imbalances on individual labor supply. The hypothesis to be tested is the one that in marriage markets with high male/female sex-ratios, women will be getting more income from spousal labor and therefore will supply less labor outside the household. The sex-ratio turns out to have a negative and statistically significant effect on the amount of market labor a woman will supply. This provides empirical evidence for the existence of a sex-ratio or marriage squeeze effect, as predicted from their theoretical model of marriage market and labor market interactions. In the industrialized countries changing patterns of family formation and family dissolution have combined to create what is often considered a problematic family form—the one-parent family. In particular, concern is often expressed about the rapid rise in one-parent families headed by never-married mothers. In Britain the proportion of one-parent families headed by never-married mothers increased from about one-fifth in 1981 to about one-third in 1992. This has triggered a policy backlash and has led to proposals to reduce state benefits which might encourage young women to become single mothers. However, in reality little has been known about the factors behind the rise. John Ermisch disentangles the role of various demographic factors in creating more never-married, single mothers in Britain, using new data which allow the issue to be addressed for more than one cohort and consequently to trace changes over time. Based on the life histories collected in the British Household Panel Study in 1992, Ermisch compares the demographic experiences of two broad cohorts of women, those born during the period 1950–62 and those born after 1962. He finds that the increase in the number of one-parent families headed by never-married mothers reflects a combination of factors. Of prime importance is the fact that a much larger proportion of women are spending some time before marriage in cohabitational unions. While marriage was the dominant mode of entering a first partnership in the 1950–62 cohort, cohabitation had become the dominant mode in the post-1962 cohort. Women in the later cohort are also much more likely to bear a child while cohabiting. If and when such fertile cohabitational unions break up, and in the post-1962 cohort about one-half of them do dissolve, one-parent families of never-married mothers are created. In fact, Ermisch’s estimates suggest that among more recent cohorts of women, about two-fifths of the one-parent families headed by nevermarried mothers are created in this way as compared to one-fifth among the 1950–62 cohort. But of course such families are also created by first births outside of partnerships. About 5 percent of the women in the 1950–62 cohort had a birth before any partnership. The incidence of pre-partnership births is larger in the post-1962 cohort, but is still estimated to be only about 8 percent.

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INTRODUCTION

PART III FAMILY POLICIES AND HOUSEHOLD ALLOCATION OF TIME The family is often at the center of social policies. The goals as well as the means of family policies have shifted through time and differ between countries. The goals may be as varied as encouraging or discouraging fertility, achieving a more equal income distribution between families or between children growing up under varying circumstances, equalizing the human capital of children, fostering gender equality or simply supporting the family as an institution. The means utilized to achieve family policy goals are also manifold: tax and transfer policies, social security policy, childcare programs, educational policies and family legislation. The papers included in this part of the book analyze some of the policies directed at families in terms of the incentives they create for labor supply, time allocation, human capital accumulation and the choice of how to organize childcare. Economic analyses of childcare policies have generally focused on their effect on women’s labor force participation, and their economic efficiency has been evaluated in terms of whether the production value of women’s increased labor supply outweighs the costs. Siv S.Gustafsson and Frank P. Stafford want to put the focus instead on the role of childcare in the accumulation of human capital, and therefore on how it affects income distribution and long-term economic growth. The family is an important environment, and the parents’ time a valuable input in the building of children’s human capital. As women enter the labor market, some of this human capital production is transferred to the market. At the same time the importance of human capital as a generator of growth is increasing. According to Gustafsson and Stafford, family policy in the future must confront these issues and show a greater awareness of the efficiency and equity aspects of human capital investments involved in the choice of various policy approaches. Any family policy measure will give rise to efficiency as well as equity effects and often there are trade-offs between them. Gustafsson and Stafford provide an overview of the different equity/efficiency trade-offs that parents and policy-makers have to consider in their human capital investments, e.g. between siblings in a family, between children from families with unequal resources, between time for children and time for adults, and between husbands and wives. They then delve deeper into the problem of how to handle investments in children with different learning abilities. Another trade-off they elaborate upon is the intergenerational one between a parent and a child. As illustrated by examples of family policy approaches in The Netherlands, Sweden and the US, the conflict between the mother’s time use in market work, her time use for her own investments in human capital, and her time use for investments in the child’s human capital are approached quite differently in different countries. In view of the rising expenses for childcare programs as well as the increased importance attached to human capital and education in the process of economic growth in industrialized countries today, the equity/efficiency issues raised by the authors in this chapter are likely to receive much more attention in future debate and research. The Scandinavian countries are renowned for their extensive family policies such as generous parental leaves, childcare programs and other types of economic support to families with children. No doubt such policies have made it easier for women to combine work in the market with having children. Female employment in Scandinavia is characterized by very high employment rates for mothers of young children. For example, in 1988 the labor force participation rate among mothers with preschool children was 86 percent in Sweden and 72 percent in Norway. Another feature of Scandinavian female employment is the high prevalence of part-time work among working women. A question little studied is that of the relationship between the design of the family policies and the incidence of part-time work.

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The paper by Marit Rönsen and Marianne Sundström explores the impact of the parental leave programs and other factors on women’s choice between part-time and full-time work upon re-entry to the labor market after the birth of their first child. Through the use of two national data-sets that are very similar in design, they are also able to compare the policy effects between two countries, namely, Norway and Sweden, that are culturally close and have the same set of public policies, although with some country variations. Their findings indicate among other things that the right to a paid leave of absence makes women resume employment faster after childbirth and that the rates of part-time work as well as those of full-time work are affected. The impact is larger in Sweden, perhaps due to the longer entitlement period there, which makes it easier to reconcile work and motherhood and not drop out of the labor market. On the other hand, the “speed-premium” feature of the Swedish program, introduced in 1980 and enabling women to have a second child within 24 months (since 1986 within 30 months) and maintain their benefit level without returning to the labor market, seems to have delayed the return to both full-time and part-time work after giving birth. In the late 1980s the Finnish government introduced a new policy in the childcare area. The child home care allowance (HCA) is an income transfer paid to all families with children under the age of three who do not use public day-care services. It can be used to finance parental care or as a voucher for hired private childcare. The system is combined with a legal right for the mother or the father to be on leave from work until the child is three years old. Parents with small children may thus choose between a subsidized place in the public day-care system and a cash option. Seija Ilmakunnas analyzes the effects of this measure on the choice of childcare mode and women’s labor supply. In 1994 about three-quarters of the potential recipients chose the home care allowance. Out of those, only a small minority used it to finance private care. Thus parental care of small children has increased. As a result the labor force participation rate of women of childbearing age has dropped and the number of women in full-time household work has increased. Since 90 percent of those taking advantage of the allowance are women, the measure has encouraged a traditional division of labor by sex. An empirical study based on survey data about desired childcare modes illustrates how the use of the HCA varies according to family characteristics. As expected, having more and younger children encourages the use of HCA. There is a strong relationship between the mother’s opportunity wage in the market and the choice of childcare mode. As the mother’s time becomes more highly valued in the labor market, she is less likely to stay at home when her child is small. However, the level of the HCA plays an important role in the decisions. Simulation results indicate that the incidence of family care rises as the generosity of the allowance increases. Overall the study provides clear evidence that family policy and economic incentives play a distinct role in family decisions about the organization of care for small children. The paper by Anne-Marie Pålsson treats an issue that hitherto has received little attention in the literature: the market for employed domestic labor. In the Becker tradition the major focus has been on the household’s possibilities to substitute market goods for home time and on the substitution between the husband’s and the wife’s time within domestic production. Not much attention has been paid to the opportunity to substitute market time for home time and to the preconditions for a market for domestic services to develop. In a high-tax society, such a market will be virtually non-existent. By use of an example based on tax rates similar to the Swedish ones, Pålsson demonstrates that “do-it-yourself solutions” or illegal employment are always economically superior to legal market employment for domestic services in such an environment.

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INTRODUCTION

She then makes a concrete proposal for a revised tax system in order to expand the market for domestic services. Her suggestion is to make expenditures for such services tax deductible, combining this with transferring social security payments, and the corresponding benefits, from the buyer to the seller of domestic services. Taxes, just like tariffs in international trade, serve as a deterrent to trade between households. Reducing the tax wedges in the domestic sector will encourage specialization and trade in services directed to households. In a Gronau-type model which separates between market goods, domestic output and leisure, she demonstrates that such a tax change may increase overall economic efficiency and thereby total output in society. All households stand to gain. Households with high productivity on the market can supply more of their labor to the market and hire domestic services to substitute their own labor at home. Low-productivity households will gain access to an additional labor market. Households who continue to do their own household work will gain from the improved economic efficiency and the rise in total output in the economy. Since women are the ones who carry out the major share of domestic work, an additional benefit may be improved gender equality in the sense that women, through having access to domestic services, will be able to compete with men on more equal terms in the market. WHY ECONOMICS CANNOT DO WITHOUT ECONOMICS OF THE FAMILY The family is a basic social institution. For a long time the focus of economic analysis on market activities excluded decisions and activities within the family from the economists’ realm. However, the choices made within the family about time allocation, about the distribution of income and consumption, and about human capital accumulation in parents and children have important repercussions for what happens in the market and to the development of the economy. There are also several reasons why the interactions and the repercussions between the market sector and the household sector have grown in importance over time. One reason is the dramatic increase in women’s participation in market work and the less dramatic, but still increased participation of men in household work. This changing division of labor between the sexes means that a much larger share of the adult population today uses their time in both market and household work, rather than being specialized in one or the other. As long as women devoted their time mainly to the household sector, and men to the market sector, it was less misleading to disregard the repercussions for household production when making economic analyses of the market sector. The two sectors then solved their problems of time allocation and resource allocation more or less independently of each other. Today changes in wages, relative prices, taxes, social security programs, etc. are likely to have more direct and immediate effects on the time allocation and household production of households, effects which must not be ignored when evaluating such changes. A second reason for greater interdependence is that with the increase in women’s market work, a lot of production with close substitutes in household production (as exemplified by childcare, school meals, care of the elderly) has been transferred to the market. And the interdependence between the market sector and the household sector will be larger, the closer substitutes in consumption are the goods and services produced in the two sectors, and the smaller are the productivity differences between the two sectors in the production of such goods and services. A third reason is the growth in the number and size of public policies and programs which do not treat market work and non-market work in the same way. Examples are tax systems, social security systems, subsidized market-produced childcare and other family policies. Such policies and programs will introduce “tax and/or benefit wedges” between market and non-market work and between market-produced and household-produced goods and services. These wedges will affect household decisions and might give rise

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to economic inefficiencies in production and consumption. Awareness and consideration of this is needed when designing public policies and programs. In order to analyze the growing interactions between the household sector and the market sector, economists need the theories, models and empirical insights provided by the economics of the family. The development of this rapidly growing field and the contributions to this volume show that family decisions are indeed amenable to the use of the basic tools contained in the economist’s tool kit.

Part I WHERE ARE WE IN THE ECONOMICS OF THE FAMILY?

1 BARGAINING AND DISTRIBUTION IN MARRIAGE Shelly Lundberg and Robert A.Pollak

INTRODUCTION In the 1970s, a proposed change in social welfare policy in the United Kingdom excited considerable debate. The universal child allowance, which had consisted primarily of a reduction in the amount withheld for taxes from the father’s paycheck, was to be replaced by a cash payment to the mother. An excerpt from the parliamentary debate in Hansard (House of Commons, May 13, 1975) expresses a popular sentiment: [F]ar from a new deal for families, it will take money out of the husband’s pocket on the Friday and put it into the wife’s purse on the following Tuesday. Far from being a child benefit scheme, it looks like being a father disbenefit scheme. Popular discussions of family policies such as the UK child benefit often concern their presumed effects on distribution within the family—on the relative well-being of husbands, wives and children. The economist armed only with traditional models of the family must view these discussions as naive. Until very recently, the standard of the profession for both theoretical and empirical analysis was a “common preference” model of the family, which assumes that family members act as though they are maximizing a single utility function. A family’s common preference ordering may be the outcome of consensus among family members or the dominance of a single family member, but all such models imply that family expenditures are independent of which individuals in the family receive income or control resources. Common preference models imply that all income is “pooled” and then allocated to maximize a single objective function, so that family demand behavior depends on total family income, and not the incomes of individual members. This pooling of resources within the family implies that a change from child allowances paid to fathers to child allowances paid to mothers should arouse neither the ire of affected fathers nor the opposition of their parliamentary representatives. The United Nations World Population Conference, held in Cairo in September 1994, witnessed a continuation of a long-standing debate about how to reduce birth rates in developing countries. Population experts divided into two camps: one favoring continued emphasis on family planning services, the other favoring policies that improve the status of women. The latter group argues that greater access to education, business loans and development projects would give women more control over reproduction and that, as a result, birth rates would fall. Economists understand a link between fertility rates and the educational and earnings opportunities of women that operates through the value of women’s time and the time price of children, but the proponents

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SHELLY LUNDBERG AND ROBERT A.POLLAK

of women’s “empowerment” have emphasized the effect of women’s education and income on their decision-making authority within the household. Models that treat the family as a black box, with income flowing in and demands for goods, services, leisure and children flowing out, cannot deal with this argument, and so cannot address the intrafamily distribution issues that concern population and development agencies. If economists are to participate in this important debate (or at a minimum comprehend it), we must move beyond common preference models of family behavior. To this end, the theoretical challenge facing family economics is to develop models in which joint family decisions are derived from the sometimes divergent interests of husbands and wives, and in which the formation and dissolution of marriages provide a beginning and an end to the family allocation process. In recent years, a large number of game-theoretic models of marriage and the family have been developed, building on the seminal contributions of Manser and Brown (1980) and McElroy and Horney (1981). In general, these models impose fewer restrictions on observed family behavior than do common preference models, and recent theoretical contributions have been prompted, and supported, by a growing body of empirical evidence inconsistent with common preference models. The most provocative of this empirical work demonstrates a strong positive association between child well-being and the mother’s relative control over family resources, and has raised new questions about the potential effectiveness of policies “targeted” to specific family members. A current snapshot of family economics would show the traditional framework under siege on both theoretical and empirical fronts. The political potency of gender issues has given a certain urgency to the development of alternatives to common preference models. However, no new theoretical framework has gained general acceptance as a replacement for common preference models, and empirical studies have concentrated on debunking old models, rather than on discriminating among new ones. In this paper, we review a number of simple bargaining models that permit independent agency of men and women in marriage, discuss their implications for distribution within marriage and for observed family behavior, and present a sampling of the relevant empirical evidence.1 MODELS OF FAMILY BEHAVIOR Economic models of consumer demand and labor supply begin with an individual economic agent choosing actions that maximize his or her utility function subject to a budget constraint. How can we reconcile this individualistic theory of the consumer with the reality that people tend to live, eat, work and play in families?2 Application of a single-agent model to the household or family raises two distinct issues—the identity of the consumer and the identity of the decision-maker. The identity of the consumer is an issue because microdata on “consumption” usually report expenditures at the household level, seldom consumption at the individual level. The household purchases bread and refrigerators, ballet lessons and haircuts, but in general the data do not assign the consumption of these goods and services to individual household members. If the problem were fundamentally data-based, however, we could solve it by collecting better data on individual consumption, time allocation and income. There are two reasons why better data would be only a partial solution, and thus no solution at all. First, goods whose consumption is inherently joint are an important component of household consumption. With household public goods, better data cannot solve the assignment problem and, hence, cannot restore the integrity of the simple single-agent consumer model.3 Second, family members who are linked by love and duty have an interest in each other’s consumption. Even if we could assign direct consumption to individual family members, interdependent preferences would invalidate the single consumer assumption.

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Economists have dealt with the multiplicity of decision-makers in the family in two ways. The first approach, in ascendancy from the 1950s until the 1980s, was the common preference approach—treating the family as though it were a single decision-making agent, with a single pooled budget constraint and a single utility function that includes the consumption and leisure time of every family member. The second approach, pioneered by Manser-Brown and McElroy-Horney in the early 1980s, was to model family demands as the solution to a bargaining game. Most bargaining models of family behavior allow two decision-makers—the husband and the wife. Children are customarily excluded from the set of decisionmaking agents in the family, though they may be recognized as consumers of goods chosen and provided by loving or dutiful parents. The empirical implications of bargaining models of marriage depend upon their assumptions about the form of the bargaining game but, in general, these models widen the range of “rational” family behavior. COMMON PREFERENCE MODELS AND THE INCOME-POOLING ASSUMPTION Two models provide the theoretical underpinning of the common preference approach to family behavior: Samuelson’s (1956) consensus model and Backer’s (1974, 1981) altruist model. The consensus model was introduced by Samuelson to exhibit the conditions under which family behavior can be rationalized as the outcome of maximizing a single utility function. Consider a two-member family consisting of a husband and a wife. Each has an individual utility function that depends on his or her private consumption of goods but, by consensus, they agree to maximize a social welfare function of their individual utilities, subject to a joint budget constraint that pools the income received by the two family members. Then we can analyze their aggregate expenditure pattern as though the family were a single agent maximizing a utility function. This optimization problem generates family demands that depend only upon prices and total family income, and that have standard properties provided the utility functions are well-behaved.4 Thus, the comparative statics of traditional consumer demand theory apply directly to family behavior under the consensus model. Samuelson did not, however, purport to explain how the family achieves a consensus regarding the joint welfare function, or how this consensus is maintained. Becker’s altruist model (1974, 1981) addresses these questions, and also provides an account of how resources are distributed within the family. In Becker’s model, the family consists of a group of purely selfish but rational “kids” and one altruistic parent whose utility function reflects his concern for the wellbeing of other family members. Becker argues that the presence of an altruistic parent who makes positive transfers to each member of the family is sufficient to induce the selfish kids to act in an apparently unselfish way. The altruistic parent will adjust transfers so that each “rotten kid” finds it in his interest to choose actions that maximize family income. The resulting distribution is the one that maximizes the altruist’s utility function subject to the family’s resource constraint, so the implications of the altruist model for family demands coincide with those of the consensus model. Whether motivated by Samuelson’s family consensus story or Becker’s altruist story, the common preference framework is a simple, powerful mechanism for generating demand functions and establishing their comparative statics for use in applied problems. It remains the standard theoretical framework for analyzing consumption behavior and labor supply. Only serious deficiencies could justify replacing this approach with a more complicated alternative. In recent years, however, common preference models have been targets of an intense barrage of theoretical and empirical criticism.

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Dissatisfaction with common preference models on theoretical grounds has been the product of serious study, by economists, of marriage and divorce. Models of marriage and divorce require a theoretical framework in which agents compare their expected utilities inside marriage with their expected utilities outside marriage. Common preference models cannot be used to examine these decisions, because the individual utilities of husband and wife cannot be recovered from the social welfare function that generates consumption, labor supply, fertility and other behavior within marriage. If the analysis of marriage and divorce is awkward, the analysis of marital decisions in the shadow of divorce is even more so. If unilateral divorce is possible, individual rationality implies that marital decisions cannot leave either husband or wife worse off than they would be outside the marriage. This individual rationality requirement, however, alters the comparative statics of the model, and destroys the correspondence between the behavior of a single rational agent and the behavior of a family. Recent empirical evidence suggests that the restrictions imposed on demand functions by common preference models are not well-supported. Rejections of the family income-pooling assumption have been most influential in weakening economists’ attachment to common preference models.5 Income-pooling implies a restriction on family demand functions that appears simple to test: if family members pool their income and allocate the total to maximize a single objective function, then only total income will affect demands. The fraction of income received or controlled by one family member should not influence demands, conditional on total family income. A large number of recent empirical studies have rejected pooling, finding that earned and unearned income received by the husband or wife significantly affect demand patterns when total income or expenditure is held constant. Many studies find that children appear to do better when their mothers control a larger fraction of family resources. Empirical tests of pooling, using data from a variety of countries, invariably show that income controlled by the husband and wife have significant and often substantially different effects on family behavior, whether measured by expenditure on categories of goods and services, or measured by outcomes such as child health.6 For example, increases in the wife’s income relative to the husband’s income have been shown to be associated with greater expenditures on restaurant meals, childcare and women’s clothing (Phipps and Burton 1992),7 and with reduced expenditures on alcohol and tobacco (Phipps and Burton 1992; Hoddinott and Haddad 1995). Increases in child health, nutrition and survival probabilities have also been associated with mothers’ control over family resources (Thomas 1990, 1994; Hoddinott and Haddad 1995; Rose 1994). Estimated differences in the effects of mothers’ and fathers’ resources on child outcomes are often large: Thomas (1990) finds that the effects of mothers’ unearned income on child survival probabilities in Brazilian data is almost 20 times that of fathers’ income. A test of the pooling hypothesis requires a measure of husband’s and wife’s relative control over resources. Relative earnings would seem to be an attractive candidate for this measure, since labor income is by far the largest component of family income, and earnings data are readily available and reliably measured. Also, the earnings of wives relative to husbands have increased dramatically in the US and many other countries, and we would like to assess the distributional consequences, if any, of this change. The difficulty with this approach is that earnings are clearly endogenous with respect to the household’s time allocation decisions, so that households with different ratios of wife’s earnings to husband’s earnings are likely to face different prices and may have different preferences. If we think of earned income as the product of hours worked and a fixed market wage rate, then the first factor, hours worked, is a standard choice variable in models of household behavior and is determined simultaneously with the expenditure patterns the pooling test examines. The second factor, the wage rate,

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measures the price of time for the husband or wife, and enters the household’s demand functions in common preference models and in bargaining models. Thus the interpretation of the separate effects of wife’s earnings and husband’s earnings is problematic. Consider the finding of Phipps and Burton (1992) that expenditures on restaurant meals are more elastic with respect to the wife’s earnings than the husband’s earnings. A bargaining interpretation of this result is that, as the wife’s earnings rise relative to the husband’s, she gains more influence over the household’s spending patterns and that increased expenditures on restaurant meals reflect her preferences. The common preference interpretation is that restaurant expenditures depend upon the cost of substitutes, and that the wife’s wage is an important component of the cost of home-prepared meals. Thus, the Phipps-Burton result can be interpreted as a price effect rather than as evidence against income-pooling. One might try to avoid these problems by testing the pooling of unearned income rather than earnings. Unearned income is not contaminated by price effects, but most unearned income sources are not entirely exogenous with respect to past or present household behavior. Furthermore, variations in unearned income over a cross-section are likely to be correlated with other (possibly unobservable) determinants of consumption.8 For example, property income reflects, to a considerable extent, accumulated savings and is therefore correlated with past labor supply and, if those who worked a lot in the past continue to do so, current labor supply. Public and private transfers may be responsive to household distress due to unemployment or bad health, and may be related to expenditures through the events that prompted them (Schultz 1990). Unexpected transfers such as lottery winnings, unexpected gifts or unexpected bequests will affect resources controlled by individuals without affecting prices, but are likely to be sporadic and unimportant for most families. The ideal test of the pooling hypothesis would be based on an experiment in which some husbands and some wives were randomly selected to receive an income transfer. A less-than-ideal test could be based on a “natural experiment” in which some husbands or some wives received an exogenous income change. Lundberg et al. (1997) examine the effects of such a natural experiment—the policy change in the UK that transferred a substantial child allowance from husbands to wives in the late 1970s. They find strong evidence that a shift towards relatively greater expenditures on women’s goods and children’s goods coincided with this income redistribution,9 and interpret this as a rejection of the pooling hypothesis. Rejecting the pooling hypothesis has important policy implications. Policy-makers sometimes want to target transfers or programs to particular classes of individuals within families, such as women or children. Common preference models imply that such policies are ineffective, beyond their influence on total family resources, because the equilibrium intrahousehold allocation is independent of the distribution of income among family members. Bargaining models, on the other hand, suggest that the government can affect distribution within marriage, either by changing the income of divorced men and women, or by transferring control over resources within the marriage from one spouse to the other. Some empirical work supports the potential effectiveness of such policies, but much more will be required to establish the nature of family equilibrium in different cultural and institutional contexts, and the extent to which it can be shifted by government policies. COOPERATIVE BARGAINING MODELS A viable alternative to common preference models of the family must relax the pooling assumption and must recognize, in a non-trivial fashion, the involvement of two or more agents with distinct preferences in

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Figure 1.1 The Nash bargaining solution

determining family consumption. Bargaining models from cooperative game theory satisfy these conditions. A typical cooperative bargaining model of marriage begins with a family that consists of only two members: a husband and a wife. Each has a utility function that depends on his or her consumption of private goods (Uh for the husband Uw and for the wife). If agreement is not reached, then the payoff received is represented by the “threat point,” (Th, Tw)—the utilities associated with a default outcome of divorce or, alternatively, a non-cooperative equilibrium within the marriage. The Nash bargaining model provides the leading solution concept in bargaining models of marriage.10 This solution can be illustrated by a diagram in utility space, where AB is the utility-possibility frontier (see Figure 1.1). Nash (1950) shows that a set of four axioms, including Pareto-optimality—which ensures that the solution lies on the utilitypossibility frontier—uniquely characterizes the Nash bargaining solution. The utility received by husband or wife in the Nash bargaining solution depends upon the threat point; the higher one’s utility at the threat point, the higher one’s utility in the Nash bargaining solution. This dependence is the critical empirical implication of Nash bargaining models: family demands depend, not only on prices and total family income, but also on determinants of the threat point. In divorce-threat bargaining models, the threat point is the maximal level of utility attainable outside the marriage. If divorcing partners maintain ownership of income received separately within marriage, the demands emerging from marital bargaining will depend not on total family income, but on the income received by the husband and the income received by the wife. The divorce threat point is also likely to depend on environmental factors (extrahousehold environmental parameters, or EEPs in McElroy’s (1990) terminology) that do not directly affect marital utility, such as conditions in the remarriage market and the income available to divorced men and women. The family demands that result from divorce-threat marital bargaining will therefore depend upon these parameters as well. As McElroy points out, the absence of pooling and the presence of extrahousehold parameters in family demands yield a model that can be tested

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against the common preference alternative. For example, changes in the welfare payments available to divorced mothers, or in laws defining marital property and regulating its division upon divorce, should affect distribution between men and women in two-parent families through their effect on the threat point. In the separate spheres bargaining model of Lundberg and Pollak (1993), the threat point is internal to the marriage, not external as in divorce-threat bargaining models. The husband and wife settle their differences by Nash bargaining, but the alternative to agreement is an inefficient non-cooperative equilibrium within marriage. In a non-cooperative equilibrium, each spouse voluntarily provides household public goods, choosing actions that are utility-maximizing, given the actions of their partner. This non-cooperative marriage may be better for both spouses than divorce. Divorce, the argument goes, may be the ultimate threat available to marital partners in disagreement, but a non-cooperative marriage in which the spouses receive some benefits due to joint consumption of public goods may be a more plausible threat in day-today marital bargaining. The introduction of this internal threat point has important implications, because separate spheres bargaining generates family demands that, under some circumstances, depend not on who receives income after divorce, but on who receives (or controls) income within the marriage. Control over resources within marriage need not affect the equilibrium: if both the husband and the wife make positive contributions to each public good in the non-cooperative equilibrium, then household allocation will not depend upon how income is distributed between the spouses.11 In the separate spheres model, however, a non-pooling outcome arises when gender specialization in the provision of household public goods ensures that only one spouse makes a positive contribution. The model assumes that socially recognized and sanctioned gender roles assign primary responsibility for certain activities to husbands and others to wives. In the absence of cooperation, one household public good, q1, will be provided by the husband out of his own resources and the other public good, q2, by the wife out of her own resources. Lundberg and Pollak assume that this allocation of marital responsibilities reflects social norms, rather than preference or productivity differences between husband and wife in a particular marriage. In a non-cooperative marriage, the husband treats the level of public good chosen by his wife as fixed and chooses quantities of his private good and his assigned public good so as to maximize his utility subject to his budget constraint. Similarly, the wife treats the quantity of the public good supplied by her husband as fixed and chooses utility-maximizing quantities of her private and public goods subject to her budget constraint. These decisions lead to a pair of reaction functions that determine a Cournot-Nash equilibrium in which the public goods contributions are inefficiently low. An important characteristic of this non-cooperative equilibrium, which serves as the threat point in the separate spheres model, is that the husband’s utility depends upon the resources of his wife through his consumption of “her” public good, and vice versa. Since the demand functions generated by cooperative bargaining depend upon the threat point, they will also be independently influenced by husband’s income and wife’s income. In the cooperative equilibrium, the husband’s and wife’s utilities will depend not on total family income but on the incomes controlled separately by each spouse.12 As the divorce-threat and separate spheres models show, cooperative bargaining does not necessarily imply income-pooling. Bargained outcomes depend upon the threat point, and the income controlled by husband and wife will affect family behavior (and the relative well-being of men and women within marriage) if this control influences the threat point. This dependence implies that public policy (e.g. taxes and transfers) need not be neutral in their effects on distribution within the family, although how they affect distribution depends upon how the alternative to agreement is specified. A divorce-threat bargaining model predicts that policies

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improving the status of divorced women will shift resources within marriage to wives; it also predicts that policies affecting the control of income within the marriage will have no effect on distribution within marriage if they have no effect on the incomes of divorced men and women. A separate spheres bargaining model predicts that policies reallocating income within marriage will change distribution within marriage and family demands, even if they do not affect the well-being of divorced men and women. Consider, for example, a change in child allowance policy from one that pays husbands to one that pays wives, but suppose that in the event of divorce, the mother is always the custodial parent and receives the child allowance. Divorce-threat models predict that this change will have no effect on distribution in two-parent families, while the separate spheres model predicts redistribution towards the wife. PARETO-OPTIMALITY AND NON-COOPERATIVE BARGAINING MODELS Most models of the family either assume or conclude that family behavior is Pareto-optimal. Common preference models ensure Pareto-optimality by assuming a family social welfare function that is an increasing function of the utilities of all family members: no member can be made better off without making another worse off. Cooperative bargaining models characterize the equilibrium distribution by means of a set of axioms, one of which is Pareto-optimality. Distributional issues remain important: as Lommerud has stressed in his paper in this book, “efficiency” does not imply “harmony.” However, the focus on models that restrict us to the utility-possibility frontier is striking. Two recent departures have been the development of empirical models that permit tests of Pareto-optimality, and applications of non-cooperative game theory to the family that allow us to examine what conditions might enable families to sustain Paretooptimal outcomes. Pareto-optimality is the defining property of the “collective model” of Chiappori (1988, 1992). Rather than applying a particular cooperative or non-cooperative bargaining model to the household allocation process, Chiappori assumes only that equilibrium allocations are Pareto-optimal, and so his collective model contains cooperative bargaining models and common preference models as special cases. He demonstrates that, given a set of assumptions including weak separability of public goods and the private consumption of each family member, Pareto-optimality implies, and is implied by, the existence of a “sharing rule.” Under a sharing rule, the family acts as though decisions were made in two stages, with total family income first divided between public goods and the private expenditures of each individual, and then each individual allocating his or her share among private goods. The collective framework thus imposes a set of testable restrictions on the observed demands of the household. In essence, the ratio of the marginal propensities to consume any two goods must be the same for all sources of income, because the independent incomes of husband and wife affect consumption only through the sharing rule. The pattern of consumption expenditures in Canadian and French households has been found to be consistent in this sense with Pareto-optimality (Bourguignon et al. 1993; Browning et al. 1994). Nevertheless, the prevalence of destructive or wasteful phenomena such as domestic violence and child abuse, as well as the demand for marriage counseling and family therapy, suggests that we consider the possibility that family behavior is sometimes inefficient. Other researchers have pointed to gender segmentation in the management of businesses or agricultural plots in many countries as evidence of an essentially non-cooperative, and possibly inefficient, family environment. A rare fragment of empirical evidence is provided by Udry (1996), who finds that the household allocation of resources to male- and female-controlled agricultural plots in Burkina Faso is inefficient.

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Cooperative game theory motivates the assumption of Pareto-optimality by assuming that information is relatively good (or at least not asymmetric) and that the players can make binding, costlessly enforceable agreements. Since legal institutions do not provide for external enforcement of contracts regarding consumption, labor supply and allocation within marriage, the binding agreement assumption is unappealing. Non-cooperative game theory, in contrast, does not assume that binding agreements enforce intrahousehold allocations, but focuses instead on self-enforcing equilibria. Pareto-optimal outcomes are possible in non-cooperative games, but not necessary. Without binding agreements, much of the motivation for assuming Pareto-optimality vanishes. It is possible, however, for non-cooperative bargaining to yield Pareto-optimal outcomes under certain conditions. For example, if the voluntary contribution game played by husbands and wives in the separate spheres model is played only once, it yields an inefficient equilibrium in which public goods are underprovided; but if the voluntary contribution game is played repeatedly, many other equilibria are possible.13 In general, repeated non-cooperative games have multiple equilibria, and Pareto-optimal equilibria can often be sustained by the threat of punishment. In essence, each spouse realizes that the one-period gain from deviating from an agreement will be less than the loss associated with being punished by their spouse in the periods that follow. Browning et al. motivate their assumption of Pareto-optimality with the claim that the marital environment possesses characteristics that would promote efficient outcomes in a repeated non-cooperative game—a long-term relationship, relatively good information and a stable bargaining environment. We prefer a different research strategy. One of the benefits of modeling distribution within marriage as a noncooperative game is the opportunity to treat efficiency as endogenous, potentially dependent upon the institutions and social context of marriage in a particular society and upon the characteristics of the marital partners. The corresponding costs include the need to specify fully the set of possible actions and the timing of moves. The existence of multiple equilibria in repeated non-cooperative games and the need to choose among them suggest how history and culture might affect distribution within marriage. Kreps (1990) points out that, in many games, there seems to be a “self-evident way to play” that corresponds to a particular equilibrium. He emphasizes that which equilibrium corresponds to the self-evident way to play cannot, in many cases, be identified solely from the formal description of the game: in realistic social contexts, conventional modes of behavior may suggest to the players a “focal point equilibrium,” thus reducing or eliminating the need for pre-play negotiations. In the case of marriage, social conventions regarding the rights and responsibilities of husbands and wives may indeed suggest to the spouses a particular equilibrium. For example, consider a model with two-household public goods in which the husband and wife make voluntary contributions. Suppose that specialization is desirable in the sense that the household is better off if the wife supplies one good and the husband supplies the other. This game may possess two Nash equilibria analogous to those in the “Battle of the Sexes” game— one in which the wife supplies good one and the husband good two, and another in which the provider roles are reversed.14 The husband and wife may prefer to provide one good rather than the other, but both will prefer a coordinated provision of public goods to the inefficient alternative in which both supply the same good. The choice between the two equilibria is likely to be sensitive to history and culture, which may generate a “self-evident” way to play. The separate spheres bargaining model provides an obvious example: if some household public goods are regarded as within the wife’s sphere and others as within the husband’s sphere, then the focal point equilibrium may involve complete gender specialization in the provision of household public goods

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corresponding to this conventional gender assignment of responsibilities. In this non-cooperative model, distribution within marriage will depend on the individual resources of husband and wife, due to the corner solution in public goods provision. Treating distribution within marriage as the outcome of a repeated non-cooperative game, we see the issue of Pareto-optimality through a different lens. The existence of multiple equilibria, some of which are Pareto-optimal and some of which are not, suggests that we consider factors omitted from the formal model to explain the patterns of marital behavior and gender allocations that develop in any particular society. The behavior of any particular couple may be directed towards a focal point equilibrium that conforms with the behavior of those around them and is consistent with socially sanctioned gender roles. Viewed as the outcome of a repeated game in a social context, the Pareto-optimality of distribution within marriage must be investigated and analyzed, not simply assumed. Like any microanalysis that appeals to focal points or social norms, our analysis inevitably raises macro questions—how do the social norms and gender roles that constrain a particular marriage arise and how are they maintained—and directs our attention to these larger issues. If the achievement of a Pareto-optimal outcome depends upon such factors as the stability of the marital environment and the quality of information possessed by husband and wife, then we may be able to analyze the role of marital and other societal institutions in promoting efficient marriage (as well as affecting distribution between husbands and wives), at least in the short run. These institutional factors could include the role of older generations in arranging marriages and regulating marital behavior, restrictions on the economic behavior of married women, the costs of leaving a marriage, and the social and legal treatment of domestic violence. If one takes seriously the notion that institutions and practices, norms and gender roles are endogenous, then the analysis of individual behavior, individual well-being and Pareto-optimality must be recast. England and Kilbourne (1990) and Sen (1990) develop analyses that depend crucially on this endogeneity. England and Kilbourne argue that women are socialized to be less willing than men to drive hard bargains with their spouses and, hence, that wives get less than they otherwise would. Sen carries the internalization argument a step further, arguing that “socialization”—he avoids the word— may prevent a woman from recognizing her true interests. Non-economists’ critiques of economists’ analyses of distribution between men and women often use words like “power” that are foreign to the vocabulary of economics. Pollak (1994) argues that, although the language is unfamiliar, the substance of these critiques is that economic models of distribution between men and women focus on the subgame of bargaining within a particular marriage and that the real action is elsewhere—in the prior game that determines social norms and gender roles. Although individual men and women take the outcome of this earlier game as given, economists should not, for it determines the institutions and norms that affect the play in a particular marriage. THE MARRIAGE MARKET Models that analyze bargaining within existing marriages can give only an incomplete picture of the determinants of the well-being of men and women. The marriage market, as Becker has emphasized (1991: 13–15), is an important determinant of distribution between men and women. At a minimum, the marriage market determines who marries, and who marries whom. The extent to which the marriage market also determines distribution within particular marriages depends crucially on whether prospective spouses can make binding agreements in the marriage market. At one extreme, if binding, fully contingent contracts regarding marital distribution can be made prior to marriage, then there is no scope for bargaining within marriage: distribution within marriage simply implements agreements previously made in the marriage

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market.15 At the other extreme, if binding agreements cannot be made in the marriage market, then husbands and wives bargain over the surplus generated by a particular marriage. The marriage market can also generate substantial differences between the short-run and long-run effects of tax, transfer and other redistributive policies. In Lundberg and Pollak (1993), we consider a model in which prospective spouses can agree on a transfer payment from (for example) husbands to wives that is uncontingent on the realized values of income later in the marriage. If policy-makers attempt to redistribute income by transferring the ownership of a child allowance payment from husbands to wives, some redistribution is likely to occur within marriages in existence at the time of the policy change. For the next generation of marriages, however, there will be a new equilibrium with the same pairing of men and women, but with the agreed transfer to wives reduced by the amount of the child allowance. With binding marital agreements, therefore, targeted policies that have redistributive effects in existing marriages may be “undone” by subsequent generations in the marriage market—a pure Ricardian equivalence result. Even without binding agreements, however, the long-run effects of a redistributive policy are likely to differ from the short-run effects on existing marriages. Prospective spouses understand that marriage commits them to playing a particular bargaining game with a particular partner. A policy that transfers income from husbands to wives will make marriage relatively more attractive to women and less attractive to men. Such a change in transfer policy can alter the equilibrium number of marriages contracted in subsequent marriage markets, as well as the equilibrium matching and distribution of marital surpluses (Lundberg and Pollak, 1993). The scope for bargaining within marriage also depends upon the alternatives available to the marital partners. In the marriage market, if there are close substitutes for each individual, then the next best marriage is nearly as good as the proposed one, and the surplus to be divided by bargaining is small. Over time, however, a sizable surplus may develop in an ongoing marriage, perhaps because of investments in marriage-specific human capital. In this situation, the possibility of divorce (perhaps followed by remarriage) defines the scope for bargaining ex post within marriage by placing bounds on the distributions that can emerge as equilibria. These “divorce bounds” depend upon the costs of divorce, including psychic costs, the resources available to divorced individuals, and conditions in the remarriage market. Individual rationality ensures that no individual will accept less than he or she would receive in the next best alternative and implies that the divorce bounds apply to all bargaining models, both cooperative and noncooperative.16 Just as there is little scope for bargaining in the marriage market when the next best marriage is almost as good as the proposed marriage, there is little scope for bargaining within marriage when the divorce bounds are tight. Bargaining models of marriage are motivated by the assumption that, in at least some marriages, surpluses are large enough that their distribution is worth modeling. The role of marriage markets in determining distribution within marriage provides another example of the importance of social norms and institutions. When matching models have multiple equilibria, as they often do, which equilibrium is selected or realized may depend upon institutions and practices not specified in the formal model. For example, it is well-known that in a marital matching model, the equilibrium realized when men propose to women is more favorable to men and less favorable to women than the equilibrium realized when women propose to men. Pollak (1994) argues that when the selection of one equilibrium rather than another has important distributional implications, institutions and practices (e.g. courting conventions) should be explicitly modeled.

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CONTRIBUTIONS OF BARGAINING APPROACHES TO MARRIAGE Common preference models of the family have proven to be too limited a framework for the analysis of family behavior. Though a rigorous and powerful tool for analyzing family expenditure patterns and labor supply, its assumption of a single family utility function and its implication of family income-pooling are problematic. Furthermore, common preference models rule out analysis of intrafamily distribution or of the connection between marriage markets and marital behavior. Game-theoretic approaches to family behavior provide new models, yield new results and provoke new questions. Novel questions and areas of inquiry are numerous, but three that seem particularly interesting to us are the effect of control of resources by husbands and wives on the well-being of children, the effect of social norms on marital bargaining, and the relationship between marital distribution and marriage markets. Policies that empower women have been supported not only by claims that they will increase the wellbeing of women and reduce birth rates, but also by claims that they will increase the well-being of children. The belief that “kids do better” when their mothers control a larger fraction of family resources, which was presumably part of the rationale for changing the UK child benefit program in the late 1970s, has now attained the status of conventional wisdom among development agencies. This belief entails two distinct propositions, both confidently maintained in a recent World Bank (1995) monograph on gender equality. First, we must reject income-pooling in favor of some alternative in which control over resources influences distribution within the family. As the World Bank (1995:59) puts it, “policies that specifically target women or girls can address the needs of this group more efficiently and with greater cost-effectiveness than general policy measures.” Second, we must accept the additional hypothesis that “[f]emale household members tend to allocate resources more directly to children, while men tend to allocate more resources to adults” (World Bank 1995:59). The kids-do-better hypothesis is widely accepted and has received extensive empirical support: Bruce et al. (1995) and Blumberg (1991) cite and summarize many of the relevant studies. Economists, many of whom have been skeptical on theoretical grounds that the kids-do-better results were caused by mothers’ control over resources, have found the possible endogeneity of income sources discussed earlier to be sufficient econometric grounds for discounting the empirical evidence that supports it. Though the evidence on this point is not conclusive, we think that the burden of proof has shifted to those who doubt that children benefit when their mothers control a larger fraction of family resources. The notion that control over resources matters focuses attention on the difficult issue of the meaning and measurement of “control.” Does the individual family member whose name is on the check maintain control over its disbursement? Are in-kind transfers more controllable by individual recipients than cash? To what extent are own earnings “owned” by the worker rather than pooled for household use? Work by sociologists on family budgeting suggests considerable heterogeneity among families in money management practices (Pahl 1983; Treas 1993; Zelizer 1989, 1994; and the literature they cite). Economists, however, are unlikely to find money management practices especially interesting as outcome variables or appropriate as explanatory variables. A more interesting focus for economists is the relationship between control over resources and the extramarital environment, on the one hand, and outcomes such as expenditure patterns, labor supply, and observable indicators of individual well-being such as morbidity and mortality, on the other. In particular, empirical studies that examine the effects of differences in tax and transfer policies that appear to establish different claims on resources within the household are likely to improve our understanding of intrahousehold allocation.

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Bargaining models of marriage suggest a number of mechanisms through which social norms and institutions can affect distribution between men and women. Most directly, social norms may affect the preferences of marital partners. In bargaining models, social norms affect outcomes indirectly, often through their effect on the threat point. In the divorce-threat bargaining model, custody and child support standards and the social position of divorced men and women will be among the extramarital environmental parameters that determine the threat point. In the context of this model, an increase in welfare “stigma” will be associated with a decline in the relative well-being of women and children in low-income families, as will reductions in the real value of welfare payments. If the threat point reflects the possibility of domestic violence, marital distribution may depend upon the expected reaction of neighbors and the behavior of police on domestic violence calls. Non-cooperative outcomes may be influenced by social norms in a different way; in models with multiple equilibria, social conventions may suggest a focal point equilibrium and a way of coordinating behavior without explicit bargaining. Norms regarding appropriate marital or parental behavior for men and women may be powerful in their ability to channel the behavior of marital partners to one equilibrium among many—raising the question of how such norms develop and are maintained. Bargaining models place distribution within marriage in a theoretical framework that is consistent with existing analyses of marriage and of divorce: two decision-makers with well-defined preferences choosing an action or strategy from a well-specified set of alternatives. Bargaining models thus provide an opportunity for integrating the analysis of distribution within marriage with a matching or search model of the marriage market. In a unified model, marital bargaining is conditional upon the match (and perhaps contract) agreed to in the marriage market, and agents in the marriage market anticipate the bargaining environment within marriage. We can expect outcomes in these two arenas for male—female contracting to be closely related. A change in the bargaining environment within marriage (e.g. a change in tax policy, relative wages or social norms) can not only affect distribution within existing marriages but can also alter subsequent marriage market equilibria; under some circumstances, these marriage market effects can entirely undo the effects of the initial redistribution. We are far from a unified model of marriage, divorce and marital behavior, but a model of distribution within marriage that recognizes the independent agency of men and women within marriage is a prerequisite to a unified model. ACKNOWLEDGMENTS This paper was published in Journal of Economic Perspectives, Fall 1996. We thank the Journal of Economic Perspectives for permission to reprint the paper here. An earlier version of the paper was presented at the Arne Ryde Symposium. The authors wish to thank participants at the symposium, Elaina Rose, Dick Startz and the editors of Journal of Economic Perspectives for comments. REFERENCES Becker, Gary (1974) “A Theory of Social Interactions,” Journal of Political Economy 82, 6:1063–94. —— (1981; enlarged edition 1991) A Treatise on the Family, Cambridge, Mass.: Harvard University Press. Behrman, Jere R. (1996) “Intrahousehold Distribution and the Family,” in Mark R. Rosenzweig and Oded Stark (eds) Handbook of Population and Family Economics, Amsterdam: North-Holland Publishing Company. Behrman, Jere R., Pollak, Robert A. and Taubman, Paul (1995) From Parent to Child: Inequality and Immobility in the United States, Chicago: University of Chicago Press.

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Bergstrom, Theodore C. (1996) “A Survey of Theories of the Family,” in Mark R. Rosenzweig and Oded Stark (eds) Handbook of Population and Family Economics, Amsterdam: North-Holland Publishing Company. Bergstrom, Theodore C., Blume, Lawrence and Varian, Hal (1986) “On the Private Provision of Public Goods,” Journal of Public Economics 29, 1:25–49. Blumberg, Rae Lesser (ed.) (1991) “Income Under Female Versus Male Control: Hypothesis from a Theory of Gender Stratification and Data from the Third World,” in Gender, Family, and Economy: The Triple Overlap, Newbury Park: Sage. Bourguignon, Francois, Browning, Martin, Chiappori, Pierre-André and Lechene, Valerie (1993) “Intra Household Allocation of Consumption: A Model and Some Evidence from French Data,” Annales d’Economie et de Statistique 29:138–56. Browning, Martin, Bourguignon, Francois, Chiappori, Pierre-André and Lechene, Valerie (1994) “Income and Outcomes: A Structural Model of Intrahousehold Allocution,” Journal of Political Economy 102, 6:1067–96. Bruce, Judith, Lloyd, Cynthia B. and Leonard, Ann (1995) Families in Focus: New Perspectives on Mothers, Fathers, and Children, New York: Population Council. Chiappori, Pierre-André (1988) “Rational Household Labor Supply,” Econometrica 56, 1:63–89. —— (1992) “Collective Labor Supply and Welfare,” Journal of Political Economy 100, 3:437–67. England, Paula and Stanek Kilbourne, Barbara (1990) “Markets, Marriages, and Other Mates: The Problem of Power,” in Roger Friedland and A.F.Robertson (eds) Beyond the Marketplace: Rethinking Economy and Society, New York: Aldine de Gruyter. Grossbard-Shechtman, Amyra Shoshana (1993) On the Economics of Marriage—A Theory of Marriage, Labor and Divorce, Boulder: Westview Press. Haddad, Lawrence and Kanbur, Ravi (1990) “How Serious is the Neglect of Intrahousehold Inequality?,” Economic Journal 100:866–81. Hoddinott, John and Haddad, Lawrence (1995) “Does Female Income Share Influence Household Expenditure? Evidence from Cote d’Ivoire,” Oxford Bulletin of Economics and Statistics 57, 1:77–95. House of Commons (1980) Hansard January. Kreps, David M. (1990) Game Theory and Economic Modelling, Oxford: Oxford University Press. Lundberg, Shelly and Pollak, Robert A. (1993) “Separate Spheres Bargaining and the Marriage Market,” Journal of Political Economy 101, 6:988–1010. Lundberg, Shelly and Pollak, Robert A. (1994) “Noncooperative Bargaining Models of Marriage,” American Economic Review Papers and Proceedings 84, 2:132–7. Lundberg, Shelly, Pollak, Robert A. and Wales, Terence J. (1997) “Do Husbands and Wives Pool Their Resources? Evidence from the U.K.Child Benefit,” Journal of Human Resources 32, 3, Summer: 463–80. McElroy, Marjorie B. (1981) “Appendix: Empirical Results from Estimates of Joint Labor Supply Functions of Husbands and Wives,” in R.G.Ehrenberg (ed.) Research in Labor Economics 4, Greenwich, Conn.: JAI Press. —— (1990) “The Empirical Content of Nash-Bargained Household Behavior Journal of Human Resources 25, 4: 559–83. McElroy, Marjorie B. and Homey, Mary Jean (1981) “Nash Bargained Household Decisions,” International Economic Review 22, 2:333–49. Manser, Marilyn and Brown, Murray (1980) “Marriage and Household Decision Making: A Bargaining Analysis,” International Economic Review 21, 1:31–44. Nash, John F. (1950) “The Bargaining Problem,” Econometrica 18, 1:155–62. Pahl, Jan (1983) “The Allocation of Money and the Structuring of Inequality within Marriage,” Sociological Review 31: 237–62. Phipps, Shelley and Burton, Peter (1992) “What’s Mine is Yours? The Influence of Male and Female Incomes on Patterns of Household Expenditure,” Working Paper 92–12, Department of Economics, Dalhousie University. Pollak, Robert A. (1994) “Taking Power Seriously,” mimeo, University of Washington. Rose, Elaina (1994) “Consumption Smoothing and Excess Female Mortality in Rural India,” mimeo, University of Washington.

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Samuelson, Paul A. (1956) “Social Indifference Curves,” Quarterly Journal of Economics 70, 1:1–22. Schultz, T.Paul (1990) “Testing the Neoclassical Model of Family Labor Supply and Fertility,” Journal of Human Resources 25, 4:599–634. Sen, Amartya K. (1990) “Gender and Cooperative Conflicts,” in Irene Tinker (ed.) Persistent Inequalities: Women and World Development, New York: Oxford University Press. Thomas, Duncan (1990) “Intra-Household Resource Allocation: An Inferential Approach,” Journal of Human Resources 25, 4:635–64. —— (1994) “Like Father, Like Son: Like Mother, Like Daughter: Parental Resources and Child Height,” Journal of Human Resources 29, 4:950–88. Treas, Judith (1993) “Money in the Bank: Transaction Costs and the Economic Organization of Marriage,” American Sociological Review 58:723–34. Udry, Christopher (1996) “Gender, Agricultural Production and the Theory of the Household,” Journal of Political Economy 104, 5:1010–46. Warr, Peter G. (1983) “The Private Provision of a Public Good Is Independent of the Distribution of Income,” Economic Letters 13, 2:207–11. Weiss, Yoram (1994; revised) “The Formation and Dissolution of Families: Why Marry? Who Marries Whom? And What Happens Upon Divorce?,” Working Paper 15–93, Foerder Institute for Economic Research, Tel-Aviv University. World Bank (1995) Toward Gender Equality: The Role of Public Policy, Washington DC: World Bank. Zelizer, Viviana A. (1989) “The Social Meaning of Money: ‘Special Monies’,” American Journal of Sociology 95, 2: 342–77. —— (1994) The Social Meaning of Money, New York: Basic Books.

NOTES 1 Those interested in a more technical review of theories of the family should refer to Bergstrom (1996). Weiss (1994) provides an extensive review of models of marriage and divorce and Behrman (1996) of the empirical literature on intra-household distribution. 2 For our present purposes, we interpret “families” broadly to encompass all types of multi-person households, though some of our discussions of bargaining models of marriage emphasize the legal institutions surrounding marriage and divorce. 3 The allocation of time provides a set of family demands that are more readily assigned to individuals than is the consumption of goods and services. If leisure is assumed to be the only alternative to market work, we can assume that it is privately consumed, and standard cross-section and panel data sources report the relevant prices and quantities. For many years, the analysis of male labor supply proceeded on the basis of a single-agent model with researchers expressing few qualms about ignoring household interdependencies. When serious study of female labor supply began in the 1960s, however, the limitations of this approach became apparent. In a model of the labor force participation of married women, both leisure and time spent in home production—cooking, cleaning, childcare— are alternatives to market work. Since home production yields a variety of goods that are consumed by others in the household, the interest of other family members in the time allocation of married women is difficult to ignore. 4 More explicitly, suppose that the husband, h, has an individual utility function that depends on his private consumption of m goods, and the wife, w, has an individual utility function . If they agree to maximize a consensus social welfare function of the form W[Uh, Uw], then we can analyze their aggregate expenditure pattern as though the family were a single agent maximizing a utility function of the form U(x1,…, xm) where , subject to the joint budget constraint

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5

6

7 8 9 10

11

12

13 14

15 16

that pools the income received by the two family members. This optimization problem generates family demands . If the utility functions are well-behaved, these demand functions are homogeneous of degree zero in prices and total family income, and the implied Slutsky matrix of compensated cross-price effects is symmetric and negative semi-definite. Another restriction implied by the common preference model is the symmetry of compensated cross-price effects. McElroy (1981) surveys the evidence provided by demand systems estimation, and concludes that it provides little support for such symmetry. Although more recent work has not altered this conclusion, statistical rejections of symmetry do not appear to have shaken anyone’s faith in common preference models: rejections of symmetry can always be attributed to functional form misspecification or improper aggregation of goods. Expenditures on a purely private good are not required to test pooling. If husband and wife have different preferences, some bargaining models suggest that the marginal propensity to spend the husband’s income on a public good may differ from the marginal propensity to spend the wife’s income on the same good. Increases in expenditure on women’s clothing are also found by Browning et al. (1994) and by Lundberg et al. (1997). Behrman et al. (1995) express reservations about interpreting the results of Thomas (1990) or Schultz (1990) as conclusive rejections of pooling on these grounds. Annual expenditures on children’s clothing rose about £50, and expenditures on women’s clothing about £30, in an average two-child family receiving a child allowance of £400. The Nash bargaining solution is the allocation that maximizes the product of the gains to cooperation, given by the function: subject to the constraint that the family’s joint income equal joint expenditure, . The control of resources among the potential contributors to a public good in a voluntary provision model affects neither the equilibrium level of the public good nor the equilibrium utility levels of the potential contributors, provided that each makes a strictly positive contribution. This neutrality result is well-known in public finance; see Warr (1983) and Bergstrom et al. (1986). More explicitly, the husband treats, , the level of public good chosen by his wife, as fixed and chooses quantities of his private good and his assigned public good so as to maximize his utility subject to his budget constraint . Similarly, the wife treats the quantity of the public good supplied by her husband as fixed and chooses utility-maximizing quantities of her private and public good subject to her budget constraint. The separate spheres threat point is determined by the husband’s and wife’s utilities in this noncooperative equilibrium, and can be written as: . Since the demand functions generated by cooperative bargaining will depend upon the threat point, they will be of the form: . Lundberg and Pollak (1994) analyze distribution within marriage as a repeated non-cooperative game. The canonical battle of the sexes story relies heavily on gender stereotypes. Both the husband and wife want to spend the evening together, but the husband wants to go to a sporting event (e.g. a prize fight) and the wife to a cultural event (e.g. a ballet). The story is used to motivate a non-cooperative non-zero sum game in which the Pareto-optimal outcomes correspond to successful coordination (i.e. both go to the prize fight or both go to the ballet) and are Nash equilibria. The formal structure of the game provides no way to choose between them. For example, Grossbard-Shechtman (1993) analyzes marital distribution assuming that the marriage market determines a “wage” for spousal labor that is binding during the marriage. The divorce-threat bargaining model goes beyond the notion of divorce bounds to make the cooperative equilibrium depend explicitly on the value of divorce.

2 BATTLES OF THE SEXES: NON-COOPERATIVE GAMES IN THE THEORY OF THE FAMILY Kjell Erik Lommerud

INTRODUCTION Family economists commonly assume that decisions taken within a family are Pareto-efficient. For instance, in much of his seminal work on the family, Becker (1991) assumes that the family is able to reach efficient outcomes, and makes no attempt to describe the process through which this is achieved. Also Gronau’s (1973) well-known work on the time allocation in families is an efficiency model; a more recent example is Chiappori (1992). Some efficiency models of the family postulate that the family maximizes a joint welfare function over the family members’ utilities. This can be seen, though, as a trick to generate efficient outcomes, rather than as an attempt to describe actual family behavior. The efficiency assumption is sometimes referred to as an assumption of complete contracts: a sufficient condition for achieving efficiency is that there are no limitations whatsoever on the type of binding contract that can be written and enforced. One should be careful about interpreting efficiency models of the family as models of harmony. In an efficiency model the intrafamily distribution of resources may be very uneven, and this could be a source of conflict. Rather, the assumption of the efficiency models is not that there are no distributional fights within the family, but that such distributional conflicts do not prevent efficiency from being realized. Crudely put, an efficient family can be seen as one which first agrees on the division of labor that maximizes the resources available to the family, and then—perhaps—fights over the division of these resources.1 It should also be stressed that when one talks about efficient family decisions, one means that no inefficiency arises in the family decision process itself. If, for instance, wages in the outside labor market give incorrect signals about productivity, perhaps, for example, because there is discrimination against women, the division of labor decided upon within the family will be inefficient: this is a derived inefficiency, however, that does not have its primary cause inside the family. Around 1980 several authors argued that Nash bargaining models would be a way to introduce distribution concerns into economic models of the family. (Key references are Manser and Brown 1980 and McElroy and Horney 1981.) However, the difference between a Nash bargaining model and a welfare maximization model of a family is small. Nash bargaining models also assume that decisions will be efficient. The Nash maximand is a Cobb–Douglas welfare function over Von-Neumann–Morgenstern utilities. In the so-called generalized Nash bargaining solution, welfare-weight-like parameters are referred to as “bargaining power” parameters. Does this similarity between a welfare maximization model and a Nash bargaining model imply that the Nash bargaining model is empirically void? (See the exchange

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between Chiappori 1988, 1991 and McElroy and Horney 1990 and McElroy 1990.) One difference between a Nash bargaining model and a welfare maximization model is that under Nash bargaining the “threat points” of the parties influence the distribution of resources whereas this is not the case under welfare maximization. Here lies a possible route to distinguish the two models empirically—a point made by McElroy (1990). However, what should be treated as the threat point in a family bargain is quite ambiguous. In line with Binmore’s et al. (1986) non-cooperative gametheoretic underpinning of the Nash solution, it is often argued that the proper threat point is the utilities of the parties during a conflict when an agreement has not yet been struck. For example, in labor economics it has now become customary to use utility and profit during a strike as the threat point in models of labor disputes, rather than for example using the outside opportunity wage as the fall-back for workers. Correspondingly, when a family cannot reach agreement on a given decision, immediate divorce is not always the consequence. This casts doubt on the validity of using utilities as single as the threat point in family bargaining (as McElroy 1990 does). But what corresponds to a strike in a family? We will return to this question later in the paper. The use of efficiency models is extremely common in family economics. And since families are long-run projects and the members hopefully tend to be sympathetic towards each other, this is perhaps not a hopeless assumption. However, as a contrast to this ruling tradition, some authors have suggested that it might be worthwhile to use non-cooperative models in the study of the family: thus efficiency is not assumed from the start. As a by-product, of considerable value in itself, non-cooperative game theory also forces the modeler to specify, for example, the timing of events, the action spaces and the possibilities to enter into contracts, in a more rigorous way than has been usual in the received literature. Family economists in the Becker tradition wage war on many fronts. Some, both inside and outside economics, accuse family economists of placing too much reliance on the assumption of rationality, thus giving a too cynical picture of how families function. Others maintain that family economists tend to give a too consensus-oriented description of family life. Non-cooperative family models meet the latter criticism— these types of models can be set up, for example, to allow for women being oppressed in the family. However, models of non-cooperation arguably draw even more heavily on the assumption that individuals are rational —to be “rational” means that individuals will calculate more complicated strategies than in simpler efficiency models. Nelson (1995) calls both Becker-type models and subsequent game-theoretic formulations in family economics “something of a double-edged sword to feminists.” I agree with this statement. According to Bergmann (1987) the Becker type of family model “explains, justifies, and even glorifies role differentiation by sex.” This type of criticism is harder to apply to non-cooperative models. Broadly speaking, game-theoretic models of the family can be divided into two categories. First we have models of “incomplete contracts” or “transactions costs.” These models postulate that the family in many respects can make binding agreements—but that these possibilities are not complete. One then imposes some exogenous limit on the type of family agreement which can be entered into. One example of this approach is Lommerud (1989). There it is assumed that love and altruism bind spouses in an implicit family agreement as long as they remain married; after a divorce, non-cooperative behavior follows. A seminal contribution in transaction-cost family economics is Pollak (1985). Other references include King (1982), Cohen (1987) and Allen (1990). Incomplete contracts models of the family can be accused of being ad hoc in the sense that the assumption about which contracts can be entered into, and which not, is quite arbitrary. An alternative model strategy is to assume full non-cooperation in the family. This at least brings out the clearest contrast to the efficiency models and can also be a benchmark for future research in the incomplete contracts vein.

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For the most part this paper will focus on fully non-cooperative models. It should be stressed that such models, at the best, picture life in families who are on or beyond the brink of divorce—but I hope that they can provide a fruitful starting-point for later research that combines cooperative and non-cooperative elements. There are a few non-cooperative family models in the literature. In this paper we will in no way try to give a full overview of these models. I should admit at once that I emphasize my own work in a quite biased way. Gametheoretic models of behavior in organizations—with the family as one example of an organization—fall broadly into two categories. First, there are models of conflicting objectives. Second, there are situations where goals do not necessarily conflict, but where the parties when operating noncooperatively have problems in coordinating their actions. In this paper we concentrate on the first class of models. First we will look at situations where there are family public goods, and family members try to free-ride on the public-good provision of others. This type of game is a simultaneous moves game, often used to study behavior in a non-cooperative nuclear family. Alternatively, one can operate with the Stackelberg assumption that players choose their actions in a prespecified order. Free-rider problems then translate into incentive problems: one player tries to steer the actions of another. This type of structure is often used to study relationships between family members of different generations. Coordination-problems models are potentially very interesting in family economics. There are large potential benefits if married couples can coordinate their career choices, but this is difficult to do. This means we can have self-fulfilling expectations—where women are expected to bear the main responsibility for the children, which discourages investments in career development both by the female herself and by employers, which in turn implies that it is rational that the female actually does bear the main responsibility for children. We will not discuss this class of models in this paper, primarily because this type of family economic theory is still not very well developed. Some starting-points can be found in Coate and Loury (1993) and Lommerud and Vagstad (1996). Since the title of this paper is “Battles of the Sexes,” we note that the original Battle-of-the-Sexes game is indeed a game of coordination. The paper is organized as follows. First we look at private-provision-of-public-goods games. These games share an assumption that family members non-cooperatively use their resources either to acquire a private good or a family-specific good. What exactly constitutes the “private good” and the “public good” will be seen to vary from model to model. The next section suggests that the type of non-cooperative model presented earlier can be used to reformulate the Nash bargaining theory of the household. Then we take a brief look at intergenerational games. These games, known under buzzwords as “the rotten kid theorem,” “the Samaritan’s dilemma” and “the strategic bequest motive,” are doubtless the best-known examples of non-cooperative game models in family theory. The emphasis will be on the close structural links between this type of intergenerational models and the private-provision-of-public-goods models. PRIVATE PROVISION OF PUBLIC GOODS—IN THE FAMILY In the field of public economics a fast-growing body of research looks at individual incentives to provide public goods. Among the seminal references are Warr (1982, 1983) and Bergstrom et al. (1986). An important point in this literature is that even though free-rider problems usually lead to the underprovision of a public good, this only means that agents’ incentives to provide a public good are weak, not non-existent, which previously was a standard assumption in public economics. Especially in small groups the voluntary contribution of a group member towards the public good might be quite substantial. This literature focuses on investigating the effects of public policies that aim at redistribution between the members of the group

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and at increasing the total provision of the public good. As we shall see, a typical result is that public policies tend to be powerless, since changes in private provisions to the public good will counteract the effect of policy. The family seems to be a natural example of a small group setting where private provision of public goods actually takes place even in the absence of binding contracts. A small amount of literature on noncooperative provision of public goods within the family does exist. To some extent this literature draws on findings in public economics, but it has also arrived at results that are novel relative to the public economics literature. These models of non-cooperative families share the description of family members as allocating their resources between a private good and a family public good. Definitions of what exactly constitutes the private and the public good vary considerably, however. For the most part we will concentrate on a set of models that, in one way or the other, assumes that agents can use their time either to work in the labor market to produce private benefits (for example private money) or to work at home to produce a family-specific public good (care of children, a tidy home, a beautiful garden). The presentation follows Konrad and Lommerud (1995). Other work will be commented on later. The Konrad-Lommerud model We study a model that is fully non-cooperative. Each spouse determines independently and simultaneously his or her time allocation, and there is no transfer of money between the parties. Time can be used either to work in the outside labor market or to produce a family-specific good, for example childcare. Money earned in the labor market is seen as a pure private good, the home-produced good is seen as a pure public good. In reality most goods consumed in a family are more or less impure public goods. The present “sharp” assumption is made to reach sharper conclusions. Both spouses have a utility function u(xi, G), where xi denotes quantity of the private good, and G denotes total quantity of the public good.2 Further, wi is the wage rate in the labor market and hi is the productivity at home (number of units produced per period of time), with subscript i referring either to individual a or b. Under some assumptions it can be shown that a unique Nash equilibrium in time allocations exists, and that an interior private provision equilibrium is characterized by (2.1) Subscripts G and x denote partial derivatives. These conditions simply say that any agent will choose his or her allocation of time—taking the allocation of time of the other as given—such that the marginal rate of substitution between the two goods in question equals something which can be interpreted as the relative price of the two goods. More precisely, wi/hi can be interpreted as the forgone earnings cost of producing one unit of the public good. The difference between this model and the standard voluntary contributions model of Warr (1982, 1983) and Bergstrom et al. (1986) is that in those models one assumes that the contribution productivity (here: wi/ hi) is equal for all, but that agents differ by having different levels of monetary wealth. In that framework some well-known results follow. With identical and interpersonally comparable utility functions, and when the equilibrium is and remains an interior one, the richer you are, the more you contribute to the public good. In fact, in an interior equilibrium people will contribute to the extent that their remaining private income is equalized. Public good consumption is by necessity the same. We therefore see that participation in private-provision-of-public-goods games is strongly redistributing, in spite of no actual redistribution of

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money among individuals taking place. Transfers of money among members of the contributing group are neutral in the sense that if a gives $ 1 to b this will only lead b to contribute $ 1 more to the public good, and a will contribute $ 1 less. Both total contributions and both parties’ remaining income therefore are unchanged. We will refer to this result as Warr neutrality. A closely related result states that public provision of the public good crowds out private contribution in a 1:1 ratio if the public provision is financed by lump-sum taxes levied on the contributing parties. Let us assume that a government taxes $ 1 away from individual a in a non-distortionary manner. The proceeds from the tax are used to provide $ 1 worth of public good. If a now contributes $ 1 less, he can in fact choose to return to the situation before government intervention. His income after contribution to the public good will be unchanged, as will be the total amount of the public good. If the pre-intervention adaptation was privately optimal, it will be optimal to restore the same situation. This crowding-out result is a variant of Warr neutrality. The government can be seen as one of the contributors in a provision-of-a-public-good game, and transfers among the contributing parties, including transfers from an individual to the state, will then be neutral. Let us return to our specified family model. It differs from the standard model in that it allows contribution productivities to differ. This extension is quite natural for a family economist, since for decades a key focus in family economics has been the effect of comparative advantages on the allocation of time between household work and market work. A family’s allocation of time, as characterized by (2.1), will be determined both by comparative advantage and absolute advantage. Assume first that the male (a) is relatively more productive in the labor market, and the female (b) in household production, but in a way where the total value of their abilities is the “same.”3 There will then be specialization according to comparative advantage, as in an efficiency model, but the specialization will be less pronounced. In Nash equilibrium the female contributes more than the male to the public good, simply because provision is cheaper for her. However, specialization occurs at her own expense in the sense that when she works more at home, it is her own wage income that suffers. She is not compensated for this through transfers of income from the male. If one is willing to assume that the common utility function is interpersonally comparable, the distribution in the marriage can be seen to be uneven: the wife enjoys—by necessity —the same amount of the public good, but has lower wage income, and therefore lower utility. In a model such as this, as opposed to an efficiency model, absolute advantages also help determine the allocation of time. Assume now that the female is more able both in market work and in household production, but in such a way that wi/hi is the same for both spouses (i.e. there are no comparative advantages). Also in such a situation the female will contribute more towards the public good. This reflects the standard result that in voluntary contributions games the richer party contributes more, and one way to be rich is simply to be very productive overall. Family policy Let us now investigate how some common family policy measures work in this framework. We will look at the public provision of a perfect substitute to the family public good, at redistribution within marriage from the male to the female, and also at the effect of income taxation. Naturally, the results will be related to Warr neutrality, but the neutrality results obtained in a model with equal contribution productivities do not hold strictly when contribution productivities differ.

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Government provision of a close substitute to a family public good, with public provision of childcare as a prime example, is often thought of as an allocative policy, in the sense that it is meant to correct for some inefficiency. Here, however, there will be a strong tendency for such government provision free of charge, combined with lump-sum taxation of the contributing parties, to crowd out private contributions. Whether the crowding out is more than, less than or exactly equal to 100 percent, depends on how the contribution productivity of the government compares with that of the party who bears the tax. Government provision will increase the total amount of the public good only if the government has a cost advantage in providing the good, or if the arrangement means that the family is subsidized by other groups in society, such as singles and the elderly, or if government provision is taken beyond the point where private contributions are already crowded out. The driving force behind the crowding-out result is the unobservability of the contributions of family members.4 Had these contributions been observable, the government could have made its own contribution contingent on private contributions not being reduced. The most important family public good is probably childcare. Childcare has a quantity-quality aspect: under-provision of childcare can mean having too few children or spending too little time and resources on a given number of children. The unobservability assumption fits the quality dimension, but hardly the quantity aspect. If one wants to increase the number of children people have, a per child subsidy can indeed do the job. However, if a government cares both about the number of children and the amount of time spent on each child, it should be noted that a policy that encourages people along the observable dimension (they have more children) can have disadvantageous effects along the unobservable one (they spend less time on each child). It should be noted that government provision of the family public good may have beneficial distribution effects. Assume for the sake of illustration that the government has the same contribution productivity as the woman, whom we assume to be the least-cost provider within the family. But even though the female provides childcare more efficiently than her husband, we assume that she has the same outside wage opportunity as the husband. Assume further that government provision of day care is so extensive that it exactly crowds out private contributions, and that the lump-sum tax to finance the contribution is split evenly between the spouses. Distribution in marriage then becomes equal. Remember that in the equilibrium without government provision the wife, because she is more productive in providing childcare, is the one who worked more at home—and since she is not compensated for her forfeited earnings, she suffers from a distribution point of view. In this particular example, it can be shown that the total provision of the public good increases somewhat.5,6 Next, let us turn to policies explicitly aimed at changing the distribution in the family to the female’s benefit. For example, in several countries child allowances are paid to mothers, and not to families as entities. We represent such a policy by studying a lump-sum redistribution from b to a. For the case with equal contribution productivities and where the equilibrium is and remains an interior one, Warr’s neutrality result will apply. But what happens when contribution productivities are allowed to differ? In such a case, it is still true that such a transfer is a bad instrument for redistribution. The fact that the man gets poorer and the woman richer will tend to make the man contribute less and the woman more to the public good, which undoes the redistribution effect of the transfer. However, the transfer constitutes a Pareto improvement, since the provision of the public good is shifted to the individual with the higher productivity. And this time the transfer means that the woman is compensated for her increased public-good provision. In fact, our result implies that transfers should at least be taken to a point where the equilibrium ceases to be an interior one.

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To sum up so far, we are left with the somewhat paradoxical conclusion that an “efficiency tool” such as government provision of day care seems to have its limitations as a means to correct an undersupply of family public goods, but that this policy can be very advantageous from an intrafamily distribution point of view. On the other hand, a “distribution tool” such as the transfer of money from the man to the woman does little to improve the intrafamily distribution, but does, in fact, improve efficiency. Since we work within a framework with comparative advantages, improving efficiency here means that the person with comparative advantage in household production will be led by the transfers to take over a larger share of the household production. As long as transfers are Pareto-improving, this means that a husband voluntarily and with no binding contract would be willing to transfer money to his wife, just because he knows how this will affect her equilibrium behavior as regards the provision of family public goods. However, if staying away from the labor market is a long-term decision, this means that the husband should transfer quite a substantial amount to the wife at the outset of marriage. Liquidity constraints may keep him from doing this. The state, though, is more likely to be able to commit itself to transferring a given sum from the male to the female each year. Liquidity constraints would thus play less of a part, explaining why we have concentrated on a transfer system implemented by the government. We will also mention briefly that the normal system of income taxation can be evaluated within a framework like the present one. It is a standard claim that progressive income taxation leads to inefficiencies in agents’ use of time. Here the crucial inefficiency is that people try to escape household production, with market work as an important alternative use of time. “Distortionary” income taxation can therefore improve efficiency—and it can be shown that under some assumptions a marginal increase in the degree of progressivity can lead at the same time to increased production of the public good, increased activity by the male in household production, and more female market work. This is, however, a typical second-best result: driving the husband back to family production is a Pareto improvement, but the global optimum is reached only when the female (with comparative advantage in household work) specializes in household production and is properly compensated for it. Other family models of private-provision-of-public-goods So far we have followed the presentation of Konrad and Lommerud (1995). Lundberg and Pollak’s (1993) work is a parallel contribution.7 One difference is that Lundberg and Pollak exogenously impose a “separate spheres” assumption, meaning that the male provides only one type of family public good and the female another. This seems unnecessarily restrictive, but the assumption is made because (as is well-known) Warr neutrality ceases to hold in corner solutions. Our paper also puts more emphasis on family policy. Bragstad (1991) looks at a situation where the spouses are different because they care differently about the public good. This is of course parallel to having different contribution productivities. Weiss and Willis (1985) tailor their model to fit a divorced couple.8 One of the parties has custody, the other does not. The non-custodian parent must decide whether or not to transfer money to the parent who has custody. The custodian parent decides independently the amount of resources to devote to the child. In a way, this is an extreme case of different contribution productivities, since the parent not living with the child cannot contribute directly to the child’s welfare at all. We should also mention that there are “voluntary contributions”-type models with a different specification of what constitutes the private and the public good. The seminal contribution is Leuthold (1968). Her focus is on public transfers to the poor and their effect on labor supply. Each family member

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chooses independently his or her own labor supply. Leisure is a private good, but money is seen as a family public good. Kooreman and Kapteyn (1990) suggest that a Leuthold-type model can be used as fall-back in household bargaining, and use this idea in empirical work. In their empirical application Kooreman and Kapteyn associate “leisure” with all time spent outside the labor market. It then becomes clear that the Leuthold model in a way is the Konrad-Lommerud model turned upside-down: here it is production at home that is the private good and market activity that produces the public good. The fact that Dutch women tend to have a loose attachment to the labor market is thus interpreted as their having a strong bargaining position. Ulph (1988) and Woolley (1988) study a family’s demand for goods when some goods are private for one family member, and other goods in varying degrees are public goods. An issue of interest also in such a framework is how earmarked transfers to one of the spouses alter the demand composition. THE BARGAINING FAMILY REVISITED Several writers on non-cooperative families claim that even if one does not believe in the fully noncooperative model as a true description of family behavior, non-cooperation is a natural threat in bargaining.9 This means that a better picture of non-cooperative behavior within the family is needed even for those who believe that a family is best depicted as an efficiently bargaining unit. The alternative to using non-cooperation as a bargaining lever is to use utilities as single, as for example in McElroy (1990). As mentioned in my introduction, this alternative has been criticized, and the utilities under non-cooperation intuitively seem better suited to represent “utilities during conflict.” Konrad and Lommerud (1996a) suggest a model with the following characteristics. The model is a twostage one. In the first stage, long-run, irreversible educational decisions are made. We assume that these choices are non-cooperative. In the second stage, the day-to-day allocation of time between market work and household production is decided upon. These decisions are assumed to be arrived at through Nash bargaining—but with non-cooperative behavior as the fall-back in bargaining. We should mention that in this model we work with a more specialized assumption about utility functions, namely that utility takes the form . The convex cost functions a(.) and b(.) are the costs of providing the public good and of acquiring education, respectively; gi is individual i’s contribution to the public good. A first result within this model, which combines cooperative and non-cooperative elements, is that the inefficiency may be even worse than in a fully non-cooperative model, where stage two decisions are also taken non-cooperatively. But the finding that we will focus on here is that using utilities under noncooperation as fall-back in bargaining is not very different from using utilities as single. For example, in both cases a key determinant of the distribution of resources within the family is the outside wage of the man and the woman, respectively. This warrants some intuitive explanation. Non-cooperative behavior, as we have described it, can be regarded as “internal divorce.” Transfers of money and coordination of time use cease. The parties are still linked, though, through the mutual concern for family public goods, such as children, but this is most likely also the case after a real divorce. The difference between “internal divorce” and a real divorce is that in the latter case the spouses stop living together —and this may change their valuation of the public goods. If living together or not does not change the value of the public good—people continue to love their children regardless of living arrangements—then at this level of abstraction it is difficult to spot any differences between non-cooperation and divorce at all. It should then come as no surprise that both under non-cooperation and divorce, one’s individual utility is higher the higher one’s outside wage—and consequently, the better one’s bargaining position is. If divorce

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implies an even greater reduction in time spent in household production than does non-cooperation, there will be a difference in degree between the two cases: the outside wage will influence the distribution of resources even more when utilities as single rather than non-cooperative utilities are used as the threat. It can be argued that when family bargainers cannot reach agreement, the result will be partial rather than full non-cooperation. Some rudimentary contracts, perhaps about the sharing of financial resources, will still be honored. This may very well be true, but we still conjecture that the difference between noncooperation and divorce is one of degree rather than a qualitative one: thus, empirical work that investigates the impact of the outside wage on the allocation of resources within the family will continue to have a theoretical justification. INTERGENERATIONAL ISSUES Many of the most famous attempts to use game-theoretical formulations in family economics fall within the heading “intergenerational issues.” In spite of the title of this article, which suggests that we will concentrate on the economics of the nuclear family, we will briefly mention here some examples of “battles of the generations.” There are important structural similarities between game situations in the nuclear family and intergenerational games. Models of parent–child relationships often include an assumption about altruism within the family—but probably altruism should be included in all types of family models. Specific to the intergenerational setting is the frequent assumption that altruism is one-sided: the parent cares for the child, the child is selfish. Another difference between models of marriage and models of parent–child relationships is that in models of married couples it is most often assumed that actions occur simultaneously. In intergenerational games, the structure is often a Stackelberg one, where the parties make their moves in a prespecified order. The rotten kid theorem The “rotten kid theorem” comes from Becker (1974). Later research includes Bergstrom (1989) and Bruce and Waldman (1990). The term “rotten kid” refers to the mentioned assumption that altruism in the family is one-sided. Becker’s finding is that if a family has a head who “cares sufficiently about all other members to transfer general resources to them, then redistribution of income among members [of the household] would not affect the consumption of any member, as long as the head continues to contribute to all” (Becker 1974:1076). He continues, “The major, and somewhat unexpected, conclusion is that if a head exists, other members also are motivated to maximize family income and consumption, even if their welfare depends on their own consumption alone” (Becker 1974:1080). Here Becker does not start by assuming efficiency, but shows that for a given decision procedure efficiency is nevertheless achieved. Although the result in the rotten kid theorem is rather surprising, it is not difficult to understand. The altruistic head has a preference ordering of the consumption levels of all family members. He is rich enough so that on top of the income of each family member he always adds an additional grant that determines the member’s final income. So if one of the “kids” manages to get hold of additional resources, the head can always confiscate these by reducing his grant correspondingly, and then redistribute this additional income among family members as he pleases. Each kid’s consumption is uniquely determined by the amount of total resources the head has for distribution, so the best the selfish kid can do is to maximize family income. The rotten kid theorem is a neutrality result closely related to many other neutrality results. Let us start by looking at its relationship to Warr neutrality. Altruism makes the utility of the kid a public good for the kid

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and the head. If the kid manages to transfer $ 1 from the head to himself, the head, content with the original amount of public good (here: the kid’s utility level), reduces his contribution equally much, and nothing will be changed. Whether this story is an example of Warr neutrality or of the rotten kid theorem at play is hard to determine. The rotten kid theorem, and therefore also Warr neutrality, is very close to Barro’s (1974) concept of Ricardian equivalence. Ricardian equivalence means that a government policy of giving an altruistic family head tax relief financed by debt which in the end must be paid by the “kids” of this family head, will have no effect. The government policy is just an attempt to redistribute within the altruistic family. The head can undo the transfer by saving the tax reduction, and handing the money over to the generation which in the end will have to pay the bill. The relationship to the two above concepts should be immediate. The rotten kid theorem, if it is generally correct, is a very striking result. It means that under certain circumstances all non-altruistic “kids” will automatically behave in a way which maximizes the welfare function used by the head, without the head in any way using incentive schemes or thinking strategically. All team problems go away if the head is sufficiently altruistic and rich. We now turn to discussing the socalled Samaritan’s dilemma. The Samaritan’s dilemma also deals with how one-sided altruism affects the need for incentive schemes—and reaches a conclusion more or less totally opposite to the rotten kid theorem. A comparison of the assumptions underlying the two results implicitly provides a discussion of how general the rotten kid theorem is. The Samaritan’s dilemma The term “the Samaritan’s dilemma” was coined by Buchanan (1975). It refers to the fact that when an altruist wants to help somebody, this aid can result in negative incentive effects: the recipient places himself in a more impoverished state than he would otherwise have done, just to get more help. Poverty can result from either the lack of savings or the lack of work effort, or both. Buchanan’s result emphasizes that one-sided altruism allows the altruist to be manipulated; the best strategy for the altruist is to commit to some incentive scheme, rather than yielding to his altruistic impulses. Becker’s result, as we have seen, is that the altruist should follow his altruistic impulses; as an effect of this, the object of this altruism contributes to the common good. What differences in assumptions lie behind the dramatic differences in conclusions? Bergstrom (1989) has investigated under what assumptions the rotten kid theorem would hold. Becker operated under the assumption that there is only one good in the economy. Bergstrom shows that the rotten kid theorem generalizes to a multi-good setting only under special assumptions. The Samaritan’s dilemma illustrates why the move to a two-good economy matters. Assume there are two goods, consumption today and consumption tomorrow. Assume that the transfer can take place tomorrow only. By not saving, one will have low consumption tomorrow and high marginal utility of money. Even if the Samaritan understands what is happening, his optimal choice can still be to give a high transfer. One way of viewing this is that the Samaritan is a victim of having too few transfer instruments; he cannot transfer utility directly, only money in the second period. In the version of the model where the two goods are lack of work effort and consumption, the Samaritan’s problem arises because he is limited to transferring consumption rather than utility.

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The strategic bequest motive Strategic bequest behavior to elicit higher filial attention (Bernheim et al. 1985) is a further example of an altruistic family head who thinks strategically about incentives. The parent is altruistic towards the children, so he or she wants to leave his or her monetary wealth to them, but he or she also wants them to exert disutility of effort and come to pay a visit. The issue in Bernheim et al.’s paper is to what extent a threat to disinherit a child, in order to elicit more filial attention, is a credible one. Their initial assumption is that with only one child present, such commitment is difficult: the parent is altruistic and loves his or her child, so giving the money to strangers does not seem a credible alternative. However, it is argued, the situation is different with two or more children: the alternative to giving the inheritance to one loved child is then to give it to another, equally loved child. The parent therefore pits the two children against each other in an “auction.” This auction is most naturally seen as an all-pay auction, where the participants all pay their bidded amount regardless of who wins the auction. The children bid for the inheritance by offering amounts of attention they are willing to spend to get it. It is well-known from auction theory that having two rather than one bidder can tilt the outcome in favor of the owner of the object to be auctioned away quite dramatically. However, as Bernheim et al. perhaps do not underline sufficiently, it is also well-known from auction theory that even with two bidders there are circumstances where the “bids” become rather low. The commitment assumptions underlying the Bernheim et al. model are strong: the parent can state how much of the wealth the children are going to inherit in total, and also present an inheritance rule that specifies how more filial attention is to be rewarded. The children, on the other hand, cannot enter binding contracts between themselves, for instance promising not to pay any attention to the parent at all, and then dividing the inheritance afterwards. Another problem is that if the children were sufficiently asymmetric, for example as regards popularity with their parent or in “contribution productivity” in filial attention, the equilibrium outcome could easily be that one child gave up and the other secured the inheritance with a minimum of effort. Finally, it is not obvious that a parent who loves his or her children equally is indifferent to the distribution of money among them: if the parent is not, threatening to give all the money to a better-behaved brother or sister may again not be credible.10 WHAT’S LOVE GOT TO DO WITH IT? There is little talk of love in the economic theory of the family. Most economic models of the family can be changed into models of labor-managed firms or partnerships by slightly changing the interpretation of the variables. Can an elusive concept like “love” be introduced in family economics? Can one understand the concept of family at all without including that of love? Economics is defined as a field by referring either to topics that are fit to be studied by an economist or to the methodology used. As family economics is concerned with topics that until recently were thought to lie outside economics, it is tempting to agree with Gary Becker that economics should be distinguished from related social sciences by its methodology. The economic methodology centers around rigorous analysis of optimizing behavior. In my view, though, it is not an integral element of the economic methodology that the maximand of the optimizing agents is one’s own consumption of material goods. One can for instance introduce altruism into the analysis and still associate oneself with economics. In recent years it has not been uncommon to introduce elements such as altruism, envy, status-seeking and the like into utility functions. The argument is sometimes raised that by “fooling around with utility functions,” one can in reality “assume” oneself into obtaining any result one wants from the analysis. There is some element of truth in this. However, I believe that assuming that individuals are not altruistic, do not

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care for status, and so on, is as equally ad hoc as the opposite assumptions. If it is true that any and all conclusions can be reached by varying the assumptions about the utility function, let us then systematically investigate how predictions and policy conclusions are affected by different assumptions. Even if one allows non-traditional utility functions, it is not clear how love should be introduced into the analysis. In his recent book, Stark (1995) works with two different notions of altruism. One is the standard concept that one’s utility depends positively on the utility level of others. This is the assumption of many intergenerational games, and should perhaps also be used more in models of the nuclear family. But altruism and love surely mean more than this: for example, you may care about your own actions towards the object of love per se by keeping promises regardless of the utility consequences of not doing so. This is Stark’s second concept of altruism. In both descriptions of “altruism,” or “love,” it would appear that the scope for opportunism and free-riding is reduced. Models like the voluntary contributions games would therefore exaggerate the tendency to inefficient decision-making within the family. But it is a far step to assume that love solves all free-riding problems. And as Bernheim and Stark (1988) point out, one cannot even be sure that the degree of inefficiency in the family always decreases with the degree of altruism. One point made by these authors is that an altruist can have trouble in sufficiently punishing a less altruistic group member who deviates from the terms of an implicit contract. This is, of course, a continuation of the theme from the Samaritan’s dilemma literature. However, if one wants to work with mathematical models of optimizing behavior, I am afraid that the psychological picture of homo economicus must remain quite simplistic, with or without altruism included. Also in other economic models of small organizations—like a partnership—a broader description of human motivations could be needed. This means that even with altruism included, the economic theory of the family will continue closely to resemble a model of two dentists sharing office space. But it is not only a disadvantage to operate at a level of abstraction where the similarities between apparently disparate phenomena catch the eye more easily. For example, it may be enlightening to notice that the dilemma of a divorced father who wants to give his child something but can do so only via the mother indeed has something in common with the problem facing a donor of development aid who wants to reach the poor in a given country but can do so only by transferring resources through a local government dominated by the rich. CONCLUSIONS In this paper I have tried to review some models that introduce game-theoretical modeling to the economic theory of the family. Apart from the string of literature that deals with the relationship between an altruistic parent and a not-so-altruistic child, this is still a small and little noticed area. My personal belief is that we shall see more of these types of models in the years to come. One reason is simply that for young economists game theory has almost become another word for microeconomics—so game-theoretical formulations will naturally be used to attack any social phenomenon, including the family. Family economists will then undoubtedly encounter a phenomenon that is much discussed in contemporary industrial organization theory. Industrial organization was one of the applied subfields of economics that first utilized modern game theory. Initially this led to an explosion of interest in the field, with new results and confirmations of older hypotheses pouring forth. However, after some time a sense of saturation could be sensed, and a common criticism against game-theoretical modeling became that “everything could be explained” simply by slightly changing the timing of events or altering some other assumption.

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When game-theoretical family economics matures, the same argument that “everything can be explained” will certainly appear here as well. Of course everything can be explained by the right choice of assumptions; to me the idea that some results should be very robust over all assumptions about timing of events, commitment possibilities and so on, seems very strange. For family economists, as for researchers in industrial organization before them, the conclusion must be that the true value of a game-theoretical model will only be realized when both assumptions and predictions meet empirical scrutiny. But since empirical work has its limitations as well, developing a whole array of models that span the different possible assumptions which can be made will at least give the modeler a good understanding of how different assumptions interact to produce given results. REFERENCES Allen, D. (1990) “An Inquiry into the State’s Role in Marriage,” Journal of Economic Behavior and Organization 13: 171–90. Barro, R. (1974) “Are Government Bonds Net Wealth?,” Journal of Political Economy 82:1095–117. Becker, G. (1974) “A Theory of Social Interactions,” Journal of Political Economy 82: 1063–93. —— (1991; enlarged edition) A Treatise on the Family, Cambridge, Mass.: Harvard University Press. Bergmann, B.R. (1987) “The Task of a Feminist Economics: A More Equitable Future,” in Christie Farman (ed.) The Impact of Feminist Research in the Academy, Bloomington: Indiana University Press. Bergstrom, T.C. (1989) “A Fresh Look at the Rotten Kid Theorem,” Journal of Political Economy 97:1138–59. Bergstrom, T.C., Blume, L. and Varian, H. (1986) “On the Private Provision of Public Goods,” Journal of Public Economics 29:25–49. Bernheim, D., Shleifer, A. and Summers, L. (1985) “The Strategic Bequest Motive,” Journal of Political Economy 85: 1045–76. Bernheim, D. and Stark, O. (1988) “Altruism within the Family Reconsidered: Do Nice Guys Finish Last?,” American Economic Review 78, 1034–45. Binmore, K., Rubinstein, A. and Wolinsky, A. (1986) “The Nash Bargaining Solution in Economic Modelling,” Rand Journal of Economics 17:176–88. Bragstad, T. (1991) “Private Provision of a Public Good—The Significance of Thresholds,” manuscript, University of Oslo. Bruce, N. and Waldman, M. (1990) “The Rotten Kid Theorem Meets the Samaritan’s Dilemma,” Quarterly Journal of Economics 105:155–65. Buchanan, J.M. (1975) “The Samaritan’s Dilemma,” in Edmund S.Phelps (ed.) Altruism, Morality and Economic Theory, New York: Russel Sage Foundation. Chiappori, P.-A. (1988) “Nash-bargained Household Decisions: A Comment,” International Economic Review 29: 791–6. —— (1991) “Nash-bargained Households: A Rejoinder,” International Economic Review 32:761–2. —— (1992) “Collective Labor Supply and Welfare,” Journal of Political Economy 100:437–67. Coate, S. and Loury, G.C. (1993) “Will Affirmative-action Policies Eliminate Negative Stereotypes?,” American Economic Review 83:1220–40. Cohen, L. (1987) “Marriage, Divorce and Quasi-rents; Or ‘I Gave Him the Best Years of My Life’,” Journal of Legal Studies 16:267–303. Gronau, R. (1973) “The Intrafamily Allocation of Time,” American Economic Review 63:634–51. King, A.G. (1982) “Human Capital and the Risk of Divorce: An Asset in Search of a Property Right,” Southern Economic Journal 49:536–41. Konrad, K.A. and Lommerud, K.E. (1995) “Family Policy with Non-cooperative Families,” Scandinavian Journal of Economics 97:581–601.

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—— (1996a) “The Bargaining Family Revisited,” CEPR Discussion Paper No. 1312. —— (1996b) “Fertility Choices in a Non-cooperative Family,” manuscript, University of Bergen. Kooreman, P. and Kapteyn, A. (1990) “On the Empirical Implementation of Some Game Theoretic Models of Household Labor Supply,” Journal of Human Resources 25:584–98. Leuthold, J. (1968) “An Empirical Study of Formula Income Transfers and the Work Decisions of the Poor,” Journal of Human Resources 3:312–23. Lommerud, K.E. (1989) “Marital Division of Labor with Risk of Divorce: The Role of ‘Voice’ Enforcement of Contracts,” Journal of Labor Economics 7:113–27. Lommerud, K.E. and Vagstad, S. (1996) “Mommy Tracks and Public Policy,” manuscript, University of Bergen. Lundberg, S. and Pollak, R.A. (1993) “Separate Spheres Bargaining and the Marriage Market,” Journal of Political Economy 101:988–1010. —— (1994) “Noncooperative Bargaining Models of Marriage,” American Economic Review, Papers and Proceedings 84:132–7. McElroy, M.B. (1990) “The Empirical Content of Nash-bargained Household Behavior,” Journal of Human Resources 25:559–83. McElroy, M.B. and Horney, M.B. (1981) “Nash-bargained Household Decisions: Towards a Generalization of the Theory of Demand,” International Economic Review 22:333–49. —— (1990) “Nash-bargained Household Decisions: Reply,” International Economic Review 31:237–2. Manser, M. and Brown, M. (1980) “Marriage and Household Decision Making: A Bargaining Analysis,” International Economic Review 21:31–44. Nelson, J.A. (1995) “Feminism and Economics,” Journal of Economic Perspectives 9: 131–48. Pollak, R.A. (1985) “A Transaction Cost Approach to Families and Household,” Journal of Economic Literature 23: 581–608. Stark, O. (1995) Altruism and Beyond, Cambridge: Cambridge University Press. Ulph, D. (1988) “A General Noncooperative Nash Model of Household Behaviour,” manuscript, University of Bristol. Warr, P. (1982) “Pareto Optimal Redistribution and Charity,” Journal of Public Economics 19:131–8. —— (1983) “The Private Provision of a Public Good is Independent of the Distribution of Income,” Economics Letters 13:207–11. Weiss, Y. and Willis, R.J. (1985) “Children as Collective Goods and Divorce Settlements,” Journal of Labor Economics 3:268–92. —— (1993) “Transfers among Divorced Couples: Evidence and Interpretation,” Journal of Labor Economics 11: 629–78. Woolley, F. (1988) “A Non-cooperative Model of Family Decision Making,” Discussion paper no. TIDI 125, London School of Economics.

NOTES 1 This strict separation between efficiency and distribution applies only when utility is transferable between the parties. 2 Konrad and Lommerud (1995) do not limit their analysis to the case of identical utility functions. 3 For a more precise definition, see Konrad and Lommerud (1995). 4 To be precise, the real issue is whether or not these contributions can be observed in a verifiable way. 5 First, the crowding out of the male’s contribution by the state will mean that a contributor with higher contribution productivity crowds out one with a lower. Second, after the male’s contribution is fully crowded out, additional government contribution crowds out only the contribution of the female. As the cost of government provision is borne by both spouses, it is as if the female is subsidized by an outside party, so this too implies that total provision increases.

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6 Konrad and Lommerud (1996b) stress that policy measures that tilt the distribution in marriage in favor of women can help to increase the number of children. If both parents can veto having a child, one reason for the female to exercise this right is that she fears that she will have to bear the bulk of the responsibility for rearing the children in a later non-cooperative phase in family life. Policy measures that ensure that the female does not suffer too much in such a situation can therefore make much sense. 7 See also Lundberg and Pollak (1994). 8 See also Weiss and Willis (1993). 9 See the already mentioned articles by Ulph (1988), Woolley (1988), Lundberg and Pollak (1993) and Konrad and Lommerud (1995). 10 One also wonders if attention based on the threat of disinheritance is equally valuable for the parent as attention given freely out of love.

Part II MARRIAGE AND FAMILY FORMATION

3 INTRAHOUSEHOLD DISTRIBUTION OF RESOURCES AND LABOR MARKET PARTICIPATION DECISIONS Daniela Del Boca

INTRODUCTION AND BACKGROUND Within the traditional neoclassical model of household behavior, the household is assumed to have a unified preference function concerning outcomes for each of the household members. Such a preference function is consistent with a situation where there is a dictator (Becker’s altruistic model) as well as a situation in which every member of the family has the same preferences defined over the consumption of all household members (Samuelson’s consensus model).1 This traditional neoclassical model of the family has however come into question both on empirical and theoretical grounds.2 Recently attention has been devoted to the intrahousehold distributional implications of family policies: for example, policies directed toward increasing female labor supply, especially when related to the care or custody of children. However, traditional neoclassical models of household behavior which assume a single utility function neglect the effect of the intrahousehold distribution of resources on the distribution of welfare in the household. Both Samuelson’s consensus model and Becker’s altruistic model imply that an increase in family resources would have the same effect on family welfare regardless of which family member receives this increase. Because the incomes of individual family members are pooled in a joint household budget, it does not matter which family member receives them: the effect of lump-sum payments (property income or transfers) will be the same. Recent empirical studies have shown that data fail to support the restrictions embodied in the single utility function models (Schultz 1990; Thomas 1990). Alternative models take into account the intrahousehold distribution of resources and make it possible to understand the separate effects of price and income and the distributional implications of various policies within the family (McElroy and Horney 1981; Manser and Brown 1980; Chiappori 1988). As discussed in chapters 1 and 2 of this book, game-theoretical bargaining models which allow heterogeneity in preferences provide an appropriate way to consider interactions within the family. Recently researchers have thus attempted to investigate alternative hypotheses about household decisionmaking, testing them against each other on the basis of the restrictions they may imply for the household demand. McElroy and Horney (1981) and Manser and Brown (1980) propose a cooperative Nash bargaining model of household behavior. In the Nash bargaining models each household member has a utility function and a threat point (maximal utility level if agreement is not reached). The greater the threat point, the more strongly that member’s relative valuation of goods is reflected in the household demands. An important element of these models is the existence of threat points that relate to the possibility of an individual “not agreeing.” The definition of the threat point is still an open question. In McElroy (1990) the

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threat point is the threat of divorce and is determined by the options outside the family and therefore by the wife’s/husband’s assets, while in the “separate spheres” model of Lundberg and Pollak (1993), the threat point is the utility associated with the non-cooperative outcome. If the members of the family do not agree, they will change to a non-cooperative type of behavior in which each spouse takes the other spouse’s strategy as given.3 The household bargaining model shifts the attention from resource-pooling to the control of resources. Resources are not an indistinguishable income, but are attributable to each spouse: therefore, the two partners may want to allocate a different share of resources to their consumption, possibly making the effect of the husband’s income different from that of the wife’s income. Equality of the income effects is a necessary condition in order for the traditional approach to be supported and is sufficient to reject the bargaining model (see Ott 1992 for a discussion). The issue of the intrahousehold allocation is very important for welfare considerations. Traditional household models are based on the assumption that only the distribution of income across households is relevant while the allocation within the household is not. Analyses which take into account intrahousehold distribution of resources may significantly modify a number of normative recommendations provided by the traditional approach. Various aspects of this issue have been examined. For example, Apps and Rees (1988) analyze the effects of the system of taxation on family decisions. More recently, Lundberg and Pollak (1993) compare the distributional effects of child allowances under alternative household models. This paper attempts to test the hypothesis that households in Italy may be treated as if they pool all their income. Labor supply functions are estimated which permit income effects to vary depending on the family member to whom the income is attributed. We test whether income accruing to the husband has the same effect on his leisure demand as that accruing to wives. Rejection of equality does not allow us to distinguish among the bargaining models discussed so far, but only to reject the income-pooling hypothesis of the single utility function model. Following McElroy we also test for the significance of the extrahousehold environmental parameters which affect the threat points or reservation utility that each member could achieve outside the household. The difference from the single decision-maker’s model is that here the opportunity cost of family membership is of importance for the intrafamily distribution of income and therefore for the household demands. This analysis also allows us to test the hypothesis of the “traditional family decision model” widely used in labor supply literature, which treats the labor supply decision of married men as independent of the behavior of their wives and the labor supply decision of married women as conditional on their husbands’ behavior. The paper is structured in the following way. First the neoclassical single utility model of family decisions is discussed and compared with models derived from the two-person cooperative game theory. The next section describes some of the most relevant results of the recent research on income-pooling. Then the data and the econometric models used in the analysis are described. The following section reports the results, and finally the conclusions are summarized. TESTING FAMILY DECISION MODELS In the single decision-maker model, the household is assumed to have a unified preference function concerning outcomes for each of the household members. Such a preference function is consistent with a situation where there is a dictator as well as a situation in which every member of the family has the same preferences defined over the consumption of all household members (Becker 1981).

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In the model characterized by a single decision-maker, the husband and the wife (h, w) maximize utility by purchasing market goods Xw, Xh and allocating leisure l, under the full income budget constraint. (3.1) where Li is the labor supply and will be a function of price P, wages Ww and Wh, and non-labor income Y, —that is, the total non-labor income of the family. Unearned income has an identical where effect on household demands and labor supplies regardless of the recipient of the non-earned income. (3.2) In models characterized by multiple decision-makers, husbands and wives are usually assumed to bargain over allocation, subject to the restriction that outcomes be Pareto-efficient. One example is the Nash bargaining model (McElroy and Horney 1981), where the partners maximize the product of their individual gains from marriage, i.e. the product of the difference between U, the utility level each partner achieves within the marriage, and V, the threat point or reservation utility each of them would achieve outside the family. (3.3) subject to the full household expenditures being equal to full household income: (3.4) The threat point in McElroy and Horney (1981) is the husband’s/wife’s maximized indirect utility outside the marriage and depends on the prices of each partner’s goods, wage rate, non-wage income and extrahousehold parameters. The greater the threat point, the more strongly that member’s relative valuation of goods will be reflected in the household demands. The vectors Ew and Eh represent non-price characteristics of the environment each partner would face outside the marriage such as conditions in the local marriage market as well as in the local labor market, family laws, welfare transfers that in case of separation or divorce would go to one of the spouses, etc. In the Nash bargaining model of household behavior, Yw and Yh are assumed to be resources that the wife or the husband could take with her/him when leaving the household. The solution to the maximization of (3. 3) subject to (3.4) is a system of demand equations where the arguments of the Nash demand system include all prices, separate measures of non-labor income for the partners (w, h) and the extrahousehold parameters. (3.5) Since the Nash bargaining model is a generalization and the neoclassical family demand is a special case, statistical tests can be used to determine whether the data on family behavior satisfy the restrictions implied by the neoclassical model. One testable restriction is the income-pooling hypothesis according to which nonlabor incomes of husbands and wives enter the labor supply functions (as well as the family demand functions) separately. The second restriction on (3.5) consists in the inclusion of the extrahousehold environmental parameters, since in the neoclassical demand system the opportunity costs of being married are not relevant. These tests are based on the fact that the neoclassical models are more restrictive and therefore the empirical evidence would not lead to acceptance of the Nash bargaining model, but only to rejection of the neoclassical restrictions.

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We also conduct tests of the “traditional” family model using the same econometric framework. In this conceptualization of family behavior, the husband is assumed to make his labor supply choice first; then the wife makes her labor supply choice conditional on her husband’s. One way to model this situation formally is as follows. Say there exists a unitary family utility function, U(Xw, Xh, lw). Let the husband “move” first and behave as though his wife would not work [i.e. lw=T]; let him also ignore any non-labor income his wife has when making his allocation decisions. He would select his labor supply and his and his wife’s private consumption, according to the following program:

(3.6) Denote the optimal labor supply decision associated with this problem by Lh (wh, Yh). The wife maximizes the same objective function as the husband, but she conditions on the husband’s labor supply choice and considers also her own non-labor income when making her decision. Thus her problem is given by (3.7) The wife’s labor supply function thus is given by This model is quite restrictive: the only reasonable interpretation is that men decide upon their labor supply when they are young and single and seldom change during their life time. Therefore male labor supply depends on the man’s own characteristics, but not on the characteristics of other family members. This model could be appropriate to describe a situation where the wife has no non-labor income and is not employed (a situation which has been quite common in the past). The implicit assumption is a joint household utility function, given that the labor supply of the spouses is treated as a twostep decision of the household. Some recent studies have tried to test alternative hypotheses of family allocative behavior (McElroy and Horney 1981; Bourgignon et al. 1994; Kooreman and Kapteyn 1990). Most of them have attempted to verify empirically whether the single utility model is consistent with the data. An implication of the traditional household utility model is the income-pooling hypothesis. If households maximize a single utility function under a budget constraint, then only total non-labor income should matter and the various recipients of the non-labor income should be irrelevant for the analysis of consumption behavior. EMPIRICAL EVIDENCE SUPPORTING THE INCOME-POOLING HYPOTHESIS Most empirical tests of household allocation have focused on leisure demand (or labor supply). In most household surveys, in fact, with the exception of leisure, data on consumption and non-labor income are collected at the household rather than at the individual level. As Kooreman and Kapteyn (1990:366) have recently pointed out, there is a need to collect more specific data on each of the players of the family unit. “In other words, not only the theorist should stop considering the family as an homogeneous unit, but also the data collector should do the same thing.”

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Because of the lack of appropriate data, only a few studies have tested the income hypothesis using consumption data. Thomas (1990, 1993), using survey data on family health in Brazil, finds that the distribution of income among men and women within the household significantly affects demand patterns. His results show that income controlled by a mother has a greater effect on her family’s health, human capital (household services, education) and also leisure (recreation activities) than does income under the control of a father. The strongest result emerges for child survival probabilities: a mother’s unearned income has almost 20 times the effect of a father’s unearned income. Bourgignon et al. (1994) investigate whether the income-pooling hypothesis can be accepted for consumption data from France. They consider a subsample of couples where both husband and wife work full time, so that they can assume that labor supply is not a choice variable, but is determined by labor demand. A consequence is that earnings (as the product of wages times the constrained number of hours) are exogenous. For a given amount of total income, the respective shares of each other’s earnings and nonlabor incomes can be treated as distribution factors. They find that income-pooling is rejected and that for a given level of total income, the share of husband’s and wife’s own income significantly affects the structure of consumption: the intrahousehold distribution of income seems to influence household behavior even when total income is fixed. In their study an empirical test of the cooperative hypothesis (that is, of a Paretoefficient collective decision-making) is also proposed. Their results reject the approach of income-pooling and seem consistent with the cooperative hypothesis. Most studies have focused on leisure demand, on which data for each member of the family are more likely to be collected. McElroy and Horney (1981) and Manser and Brown (1980) used National Longitudinal Survey data to analyze family labor supply decisions. McElroy and Horney’s results indicate equality of income effects only for the husbands’ labor supply equation, while Manser and Brown’s results reject the hypothesis that non-labor income received by the husband, the wife and other members of the household has the same effect on male and female labor supply. Schultz (1990) used the Socioeconomic Survey of Thailand to test the pooling hypothesis for both the female labor supply and the fertility demands of Thai families. The results reject the pooling restriction and imply that women with more bargaining power prefer to increase their own consumption of leisure or time in non-market activities and prefer to have more children. A woman’s non-labor income has a larger negative effect on the probability that she enters the wage labor force than does her husband’s unearned income. The opposite is true for men, while fertility is not influenced by the husband’s non-wage income. Alternative tests of the pooling hypothesis are based on natural experiments. Lundberg, Pollak and Wales (1995), using UK data, show that the policy change that transferred a substantial child allowance to wives has implied a shift towards larger expenditures on women’s and children’s goods. Other studies have tested the second restriction—that is, the relevance of the opportunity costs of being married. Carlin (1991) analyzed the effects of extrahousehold environmental variables on women’s spending patterns. According to his empirical results, women in states characterized by legal structures that allow generous divorce settlements spend more on investing in their human capital. Recent research on unmarried couples shows supporting results and points to the importance of considering the interactions between partners. A comparison between married and cohabiting families shows that among cohabiting couples a higher proportion of individuals do not share their income (van der Klaauw 1994). Similar tests of the effect of income composition on family consumption patterns have been produced for divorced households, using US Consumer Expenditure Survey data (Del Boca and Flinn 1994; Del Boca 1994). They test for the equality

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of the income of the exspouses on the demands for child-specific goods and for leisure demands by separated mothers.4 The empirical results they report concerning the income composition effect show that the income equality restriction could be rejected in the cases of both consumption of child-specific goods and leisure demands of mothers. These results appear to be at odds with the implications of the standard neoclassical utility-based models as well as with non-cooperative household models in which no role is allowed for the composition of income in determining demand allocations across goods, including leisure. THE DATA Our empirical analysis utilizes the data of the Bank of Italy’s Survey of Household Income and Wealth (1993). This survey is conducted every two years by the Central Bank of Italy and contains detailed information on the incomes and wealth of family members as well as several characteristics of the workplace (wages, hours of work) and socio-demographic characteristics of the households (age of the members of the family, number of children, marital status). Family structure in Italy has undergone substantial changes over the last two decades. The extended family which dominated in the southern regions was disrupted by the massive migration to the northern regions during the 1950s and 1960s. Women’s labor force participation rate has increased (even if it is still among the lowest in Europe), while women’s hourly wages have come closer to men’s hourly wages. Over these years, as an effect of these trends, there has been a remarkable decline in fertility rates: Italy now ranks lowest of all countries. In spite of the increase in the participation of women in the labor market, other changes have been slower. The percentage of part-time jobs is still extremely low in comparison with other countries and has not significantly increased in the last few years. Time budget studies show that men’s household labor has not been very responsive to women’s market work. Men married to working women spend about the same number of hours in household activities per week as men married to non-working women. The supply of subsidized childcare services increased during the 1970s and 1980s, but is characterized by extreme rigidity in the weekly hours as well as great variability across regions. The availability of public childcare services for children between 0 and 5 years of age is about 30 percent in the northern regions and only 1–2 percent in the southern regions (number of places available to the population 0–5 years of age). Profound differences remain in demographic as well as labor market aspects between the northern and central areas of the country and the southern regions, where female employment rates are much lower than in the northern regions and the availability of formal childcare services is very limited while the structure of the family is still characterized by very traditional relationships. Especially in these areas of the country, we would expect that a “traditional” model of household decision-making should perform well. Descriptive statistics of the variables used in the empirical analysis are presented in Table 3.1. The labor incomes measured by the survey are net of social security contributions and of the contributions paid by the employers toward personal income tax. We restrict our sample to married couples. Married couples with income from self-employment have been excluded from the sample. The exclusion of these families is justified since we do not observe hours worked for the self-employed. Age is restricted to the 21–58 year range. The sample size after the selection is 4074 households. Women work in 40 percent of the cases, while men work in 90 percent of the cases. Women work much less and therefore have on the average lower yearly incomes than men. However, when they work, their weekly hours of work and hourly wages are not

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very different from those of men (36 hours a week as opposed to 40 for men and an income of about 11,000 liras versus 12,000 liras). The distribution of hours for both men and women is highly concentrated, around Table 3.1 Descriptive statistics Variables Husbands Hours of work (positive values) Hourly wages (positive values) Non-labor income (positive values) Age No. children0 and that k