November 15 2004 GENDER AND SAY A Model of Household Behavior with Endogenously determined Balance of Power Kaushik Basu Department of Economics Cornell University Ithaca NY 14853 and Department of Economics Harvard University Cambridge MA 02138 Email kbasu fas harvard edu Abstract The evidence that the same total income can lead a household to choose different consumption vectors depending on who brings in how much of the income has led to an effort to replace the standard unitary model of the household with the collective model which recognizes that the husband and the wife may have different preferences and depending on the balance of power between them the household may choose differently One weakness of this new literature is that it fails to recognize that the household s choice could in turn influence the balance of power Once this two way relation between choice and power is recognized we are forced to confront some new questions concerning how to model the household This paper tries to answer these by defining a household equilibrium examining its game theoretic properties and drawing out its testable implications It is shown for instance that once we allow for dynamic interaction a household can exhibit inefficient behavior and that for a certain class of parameters children will be less likely to work in a household where power is evenly balanced than one in which all power is concentrated in the hands of either the father or the mother The paper also draws out the implications for female labor supply Keywords Gender Power Household behavior Female labor supply Child labor JEL classification numbers D13 J22 C70 Acknowledgements The author is grateful to Chris Barrett Alaka Basu Francois Bourguignon Nancy Chau Amanda J Felkey Dragan Filipovich Patrick Francois Karla Hoff Ravi Kanbur Rachel Kranton Valerie Lechene Dilip Mookherjee Omar Robles and Erik Thorbecke for useful discussions and to three anonymous referees for detailed comments and suggestions The paper has also benefited from seminar presentations at Columbia University M I T Cornell University University of Maryland at College Park Virginia Tech and Boston University GENDER AND SAY A Model of Household Behavior with Endogenously determined Balance of Power 1 Introduction The unitary model of the household which had served mainstream economics well for a long time has in recent times given way to a more fractious view of the household This has been an outcome of theoretical advances empirical investigations and anthropological insights 1 It is for instance clear that how much say a woman has in the household can vary across households in the same region and with the same total income and this could depend for example on how much income she contributes to the household s total income This recognition has enormous implications for the design of policy It means that how a certain amount of money is injected by government into households can influence the well being of individuals significantly Ten dollars given to the male head of the household and the same money given to his wife can have very different implications for not only the amount of tobacco and alcohol purchased by the household but on child labor education and health Kanbur and Haddad 1995 When a series of policy changes in the United Kingdom see Walker and Zhu 1999 for description from 1976 to 1979 caused the household allowance for children to be handed over to the women instead of men there was a rise in the expenditure on children s clothings 1 Manser and Brown 1980 McElroy and Horney 1981 Folbre 1986 Mencher 1988 Sen 1983 1990 Thomas 1990 Bourguignon and Chiappori 1994 Browning Bourguignon Chiappori and Lechene 1994 Moehling 1995 Udry 1996 Agarwal 1997 Riley 1997 Haddad Hoddinott and Alderman 1997 Basu 1999 Ligon Thomas and Worrall 2000 Haller 2000 2 Lundberg Pollak and Wales 1997 for related accounts see Hoddinott and Haddad 1995 and Quisumbing and Maluccio 1999 2 However to go from this broad recognition to the actual design of policy one needs to understand the relation between household balance of power and household behavior There is now a substantial literature on this some of which was cited in footnote 1 above It will be argued in this paper that there is one important lacuna in this new theoretical literature While this literature models successfully the impact of household power balance on household decision making it tends to ignore the opposite relation that is the effect of household decisions on the balance of power 3 Modeling both these relations simultaneously requires some theoretical inventiveness as we shall show presently This demonstration forms the core of this paper The next section recapitulates the received doctrine and develops the central idea of this paper Treating this as the core the paper goes on to allow for the realistic possibility that the decisions that a household takes may influence the household s balance of power with a certain time lag This is especially so because the story being told here is not one of negotiation and agreement but the natural and maybe even unwitting influence of certain decisions on one s power The decision taken by a traditional household to send the woman out to work would in all likelihood affect the woman s power but this 2 For a survey of how micro credit may have contributed to the empowerment of women in Bangladesh see Rahman 2000 3 There are a few recent exceptions to this such as Lundberg and Pollak 2003 Adam Hoddinott and Ligon 2003 and Iyigun 2002 These papers take up specific examples of decisions which have a feedback on the structure of power 3 happens gradually So section 3 goes on to adapt the basic model of the next section to one in which there are time lags involved The remaining sections are best viewed as corollaries they develop special cases draw out the implications of this approach for different areas of economics such as female labor supply and child labor and suggest new directions for empirical research It is shown for instance that one consequence of endogenizing power is that it can lead to multiple equilibria in female labor supply Two societal equilibria one in which women work and one in which they do not can arise from fundamentals for example preferences technology and wages which are identical 2 Household Decision Making The Main Model Consider a household with two adults There may or may not be children in the household In the standard unitary