children as collective goods and divorce settlements the failure of many divorced fathers to comply with court mandated child support awards has been identified as a major reason why a growing number of children live in poverty in female headed households this paper presents a model that seeks to explain why so many divorced fathers allow their children s welfare to suffer as a consequence of divorce the point of departure is the recognition that children are collective consumption goods from the point of view of the father and mother within marriage proximity and altruism serve to overcome the free rider problem associated with the provision of public goods however on divorce the noncustodial parent suffers a loss of control over the allocative decisions of the custodial parent and it is not feasible for the couple to achieve a pareto optimal allocation of their joint resources a model of optimal marriage contracts is constructed in which a couple decides on the allocation of resources within marriage and on the terms of a settlement in the event

female labour supply and marital status decisions a life cycle model this paper studies the interdependence between and the determinants of life cycle marital status and labour force participation decisions of women a dynamic utility maximization model is presented and estimated using longitudinal data on women from the panel study of income dynamics the mle method employed involves solving a dynamic programming problem further a minimum distance estimator is proposed which allows for the incorporation of wage data in a computationally simple way the estimates are used to predict changes in the life cycle patterns of employment marriage and divorce due to differences in education race the female s earnings and her potential husband s earnings the estimation results indicate that the utility gains to marriage are decreasing in the female s wage rate and increasing in her potential husband s earnings while the opposite is found for gains to working ignoring the endogeneity of marital status decisions is shown to lead to an underestimation of own and husband s wage effects on female labour supply

a diamond is forever and other fairy tales the relationship between wedding expenses and marriage duration in this study we evaluate the association between wedding spending and marriage duration using data from a survey of more than 3 000 ever married persons in the united states controlling for a number of demographic and relationship characteristics we find evidence that marriage duration is inversely associated with spending on the engagement ring and wedding ceremony jel j12 z1 d1

on the indeterminacy of capital accumulation paths abstract in neoclassical optimal growth models the stability of the accumulation paths depends on the discount parameter we prove that for discount factors small enough the policy function which describes an optimal path can be of any type the result is achieved using the notion of concavity we adopt a constructive approach given any twice differentiable map we show how to construct an optimal growth problem which produces that map as the optimal policy function a consequence is that chaos can appear in these models we also provide bounds on the values of the discount parameter for which indeterminacy is possible

a reanalyis of marital stability in the seattle denver income maintenance experiment this paper challenges the widely cited finding of groeneveld hannan and tuma that the seattle denver income maintenance experiment provides evidence that guaranteed income plans for poor husband wife families will increase marital dissolution relative to the existing program aid to families with dependent children the reanalysis of the experimental data distinguishes between the experimental treatment in the form of the pure negative income tax and the treatment plans that involved an experimental training program all the time periods of the experiment are used with allowance for the timing of the marital dissolution in the inferences and with allowance for attrition the conclusion of this paper is that the plans specifically the negative income tax plans in the experiment had no effect on the rate of marital dissolutions among the treatment couples relative to the control couples

wealth inequality preference heterogeneity and macroeconomic volatility in two sector economies we explore the link between wealth inequality preference heterogeneity and macroeconomic volatility in a two sector neoclassical growth model first we prove that if agents have homogeneous preferences when the absolute risk tolerance is a strictly convex concave function sufficiently high low levels of wealth inequality may lead to endogenous fluctuations in the neighborhood of the steady state second we consider the effects of preference heterogeneity when agents are homogeneous with respect to their wealth we show that when the utility function belongs to the hara class sufficiently high levels of preference heterogeneity may lead to endogenous fluctuations in the neighborhood of the steady state if the elasticity of intertemporal substitution in consumption is greater than one

female income and the divorce decision evidence from micro data escalating divorce rates during the 1960s and 1970s led to large numbers of academic investigations into the causes of divorce most of these studies concentrated on a significant increase in female income that resulted from rising female labour force participation rates the difficulty with quantifying these arguments is that it is possible to observe the income of married females or it is possible to observe the income of divorced females but it is not possible to observe both outcomes simultaneously this research attempts to resolve these difficulties by using sample selection techniques to correct for possible bias from simple observation of the income of married and divorced females

discounting and long run behavior global bifurcation analysis of a family of dynamical systems abstract this paper is concerned with the relationship between the discount rate and the nature of long run behavior in dynamic optimization models the theory is developed under two conditions the first is history independence which rules out multiple limit sets the second is a condition that avoids the reversion to a stable steady state as the discount factor is lowered once cycles have emerged these conditions appear to be the minimal restrictions that would allow analysis by a bifurcation diagram the results are illustrated by two well known examples in this literature due to sutherland and weitzman samuelson journal of economic literature classification numbers c61 d90 041

work and welfare as determinants of female poverty and household headship this paper formulates and estimates a model of the determinants of female household headship headship responds to variations in the levels of well being a woman can expect if she marries or if she heads her own household the authors measure the opportunity cost of female headship and the effects of welfare benefits and womens work in the market on female headship and poverty they find that if welfare benefits were reduced there would be small reductions in the proportion of women heading households for whites and nonwhites but a substantial increase in poverty for nonwhites they also find that wives work in the market reduces poverty and female headship for nonwhites and reduces poverty but increases headship for whites the study is based on 1975 u s data excerpt

wealth distribution and output fluctuations we explore the link between wealth inequality and output fluctuations in a general two sector neoclassical growth model with endogenous labor and heterogeneous agents when agents have homogeneous crra preferences and individual wealth is pareto distributed a sufficiently large rise in the gini index typically leads to an increase in endogenous fluctuations of output for general economies we show that under plausible conditions on the fundamentals wealth inequality is still a destabilizing factor

endogenous price fluctuations in an optimizing model of a monetary economy this paper demonstrates that an optimizing model of a monetary economy can produce perfect foresight equilibria in which the price level fluctuates forever cyclically or chaotically fluctuating equilibria are more likely to exist when the rate of money supply growth is high furthermore the set of equilibrium prices may have a complicated topological structure which poses a more serious problem concerning the validity of comparative statics method than any sort of indeterminacy previously discussed in the literature copyright 1991 by the econometric society

ramsey equilibrium in a two sector model with heterogeneous households abstract we prove an existence theorem for a stationary perfect foresight equilibrium under borrowing constraints in a two sector model with infinitely lived heterogeneous agents the most patient agent holds all the capital in this solution we also show that if the capital goods sector is capital intensive and capital income is increasing in the aggregate capital stock then the aggregate capital stock eventually is monotonic and converges to the steady state stock if the consumption goods sector is more capital intensive and capital income is increasing in aggregate capital we prove convergence to the steady state under more restrictive conditions periodic equilibria are shown to exist under weaker hypotheses journal of economic literature classification numbers d52 d90 e13

the role of capital depreciation in multi sectoral models abstract this study investigates the role of capital depreciation in economic fluctuations that may appear in multi sectoral models of optimal growth in the standard literature on non linear optimal dynamics it has been assumed that capital depreciates completely within a period this study in contrast deals with the case in which capital depreciates slowly more precisely only by a certain percentage we adopt the standard two sector model with cobb douglas production functions and characterize the dynamics around the stationary state we derive explicit conditions on parameter values under which cyclical optimal paths appear these conditions reveal the complexity that slow depreciation adds to multi sectoral optimal dynamics the economic interpretation of slow depreciation in multi sectoral models is also discussed

the economics of grief we study the short run and long run economic impact of one of the largest losses that an individual can face the death of a child we utilise unique registers on the entire swedish population combining information on the date and cause of death with parental outcomes we exploit the longitudinal dimension of the data and deal with several selection issues losing a child has adverse effects on labour income employment status marital status and hospitalisation the value of policy measures aimed at preventing mortal accidents of children is underestimated if it does not take bereavement effects on parents into account

child support and partnership dissolution this article studies the determinants of partnership dissolution and focuses on the role of child support we exploit the variation in child support liabilities and entitlements driven in part by the introduction of a new set of complex rules that determined child support liability in the uk and by their interaction with welfare rules our panel has the virtue that the post 1993 variation in child support liability for all couples in partnerships formed prior to 1993 is unanticipated we find strong evidence that the resulting large child support liabilities significantly reduced dissolution risks

perfectly competitive models of endogenous business fluctuations the endogenous hypothesis is not new at a pre analytic level it is based on the simple intuition that market mechanisms are inherently dynamically unstable at least around their stationary positions in this note i want to stress the theoretical point that there is nothing in the working of a perfectly competitive market system that prevents it from displaying persistent and endogenous fluctuations and that moreover such fluctuations may have their origins in market fundamentals such as factor intensities factor substitutability degree of impatience and so forth nevertheless macroeconomic models of endogenous fluctuations still have to prove that apart from being very beautiful they can also be useful to understand the so called heal world hit sunt leones this article is not intended to be a survey of all that has been written in this area in the last decade i have no title whatsoever to talk about empirical studies chera sayers contribution in this same volume addresses that guestion scheinkman 1990 is a readily available survey of nonlinear statistical methods that are relevant to this debate as for the theory incompetence recommends that i avoid touching on sunspot equilibria olg models and more generally expectations driven cycles they are instead discussed in jean michel grandmont s article finally marketing awareness implies recommending boldrin and woodford 1990 as a reasonably complete survey of what the endogenous cycle research program has recently produced at a theoretical level

non linear dynamics in the infinite time horizon model there are two important reasons why economic growth theory became again a popular field during the last 15 years the first one is that recently developed growth theoretic models capture more aspects of economic growth than the models used in the fifties and sixties nowadays models of economic growth try to explain technological progress and innovations whereas the purpose of traditional models was mainly to describe the process of capital accumulation

lucky in life unlucky in love the effect of random income shocks on marriage and divorce abstract economists have long been interested in the extent to which economic resources affect decisions to marry and divorce however this issue has been difficult to address empirically due to a lack of exogenous income shocks we overcome this problem by exploiting the randomness of the florida lottery and comparing recipients of large prizes to those of small prizes results indicate that while positive income shocks of 25 000 to 50 000 do not cause statistically significant or economically meaningful changes in divorce rates single women are less likely to marry as a result of the additional income

household finances income shocks and family separation in britain we examine the effect of household financial indebtedness on the incidence of partnership dissolution using a large survey of families with children in britain we use detailed data on household finances to provide a robust statistical analysis of the relationship between indebtedness and partnership dissolution and to avoid the potential simultaneity of financial and psychological health responses that arise when using self reported data on the extent of household financial problems we examine whether the data provides any support for the economic models of divorce and separation developed by gary becker and his colleagues

on the minimum rate of impatience for complicated optimal growth paths the occurrence of complex dynamics in economic models has received wide attention by the economic profession during the last decade see boldrin and woodford 1990 for a recent survey one of the most interesting and surprising results obtained so far is the indeterminacy theorem of boldrin and montrucchio 1986b which implies that virtually every dynamical behavior is fully compatible with the standard assumptions of decreasing returns competitive markets and perfect foresight deneckere and pelikan 1986 have used a related approach to derive similar results for the special case of one dimensional dynamics whereas the analysis in boldrin and montrucchio 1986b and deneckere and pelikan 1986 is restricted to optimal growth models formulated in discrete time an analogous result holds also for the continuous time case see montrucchio 1988 and sorger 1990 all of these indeterminacy theorems have been proved by a constructive approach which requires a sufficiently high rate of impatience on the side of the decision maker in particular to construct optimal growth models exhibiting some well known chaotic maps like the logistic map or the henon map as optimal policy functions one needs time preference rates of more than 400

taxes and transfers their effects on the decision to end a marriage abstract the transfer system typically has large marriage disincentives while the income tax system is likely to subsidize marriage for many low income families in other words the tax system may offset an increase in transfer benefits associated with marital separation the interaction of the transfer system with the income tax system has largely been overlooked the income tax system has become more relevant for low income families with the recent expansion of the earned income tax credit which filers may be eligible for even if their tax liability is zero this paper uses family level measures of the change in transfer benefits and tax liability associated with a change in family structure to consider the effect of these financial incentives on separation decisions

competitive equilibrium cycles recently there has been a surge of interest in endogenous business cycles that arise in competitive laissez faire economies in the context of standard overlapping generations economies conditions for the existence of equilibrium cycles have been given by grandmont 1983 and by benhabib and day 1982 models of the economy with extrinsic uncertainty or sunspots that have been developed by shell 1977 and by cass and shell 1983 see also balasko 1983 can also lead to equilibrium cycles

indeterminacy and endogenous fluctuations in two sector growth models with externalities abstract this paper discusses the influence of technological externalities on the dynamic properties of accumulation paths in a two sector growth model in discrete time following the recent paper of boldrin and rustichini 1994 in which the authors study indeterminacy in a particular case we first provide some necessary and or sufficient conditions for the indeterminacy of equilibria in the general two sector model we also provide some conditions for the existence of period two cycles when equilibria are indeterminate we prove finally that depending on the nature of externality indeterminacy may lead to the existence of quasi periodic paths

the emergence of equilibrium cycles in a monetary economy with a separable utility function abstract this paper analyzes the dynamic properties of the monetary economy when money held during the period induces some utility it is shown that the price level and real money balances may have chaotic dynamic paths even if the utility function is separable in real money balances and consumption a crucial point is that a constraint on the utility of money yields the wealth effect that inflation will reduce the real value of assets hence as in the overlapping generations model the conflict between substitution and wealth effects may cause globally stable periodic orbits as well as the complicated dynamics

a reassessment of the effect of income maintenance on marital dissolution in the seattle denver experiment cain and wissoker claim that income maintenance treatment had no effect on marital dissolution in the seattle denver income maintenance experiment yet parametric and nonparametric analyses reveal that there was a significant increase in the dissolution rate for blacks and whites but not chicanos this conclusion holds for many different specifications including a number that allow free form time variation in response while cain and wissoker s analyses and results differ in many ways from that of groeneveld hannan and tuma consideration of the full set of estimates including both main effects and interaction effects and analyses of the complete samples reveal that their analyses agree that the income maintenance treatment increased rates of marital dissolution for blacks and whites

wealth inequality and dynamic stability abstract we explore the link between wealth inequality and stability in a two sector neoclassical growth model with heterogeneous agents we show that when the inverse of absolute risk aversion or risk tolerance is a strictly convex function wealth inequality is a factor that favors instability in the opposite case inequality favors stability our characterization also shows that whenever absolute risk tolerance is linear as when preferences exhibit hyperbolic absolute risk aversion hara wealth heterogeneity is neutral

marriage and divorce informational constraints and private contracting the relationship between divorce rates in the united states and laws regulating divorce are analyzed using data from a special current population survey undertaken in 1979 with particular reference to the adoption by many states of no fault divorce laws the author utilizes a contract theoretic framework to examine the impact of both legal and informational constraints on several aspects of the marriage relationship 1 the probability of divorce 2 compensation at divorce i e the terms of the divorce settlement 3 the probability of entering marriage and 4 incentives for investment in marriage specific capital two different models are developed the first assumes that ex post information about the value of each spouses opportunites at divorce is symmetric and that since divorce would only occur if the joint benefits outweigh the joint costs the law has no effect on the divorce rate the second model asserts that the existence of asymmetric information results in a fixed wage marriage contract and that divorce would be higher in states that allow unilateral divorce the evidence supports the first of these hypotheses excerpt

til death or taxes do us part the effect of income taxation on divorce there is now much empirical evidence that economic incentives affect the divorce decision via their impact on the flow of benefits of divorced vs married individuals however the effect of the individual income tax on divorce has been neglected in this work the income tax in the us is structured so that tax liability often changes with marriage some couples incur a marriage penalty in the form of higher taxes when they marry while others receive a marriage subsidy because their tax burden falls with marriage in this paper the authors examine the impact of the individual income tax on the likelihood of divorce in the us using data from the panel study on income dynamics they estimate a discrete time hazard model of the probability of divorce from the first marriage to test the hypothesis that the probability of divorce rises with the marriage penalty they also examine the role of other economic factors in the divorce decision the authors find that individuals respond to tax incentives in their decision to divorce although these responses are typically small and differ for men and women authors

effective tax rates and guarantees in the afdc program 1967 1982 estimates of effective tax rates on earned and unearned income and estimates of effective guarantees in the afdc program by state are provided for the period 1967 1982 the results indicate that effective real guarantees fell every year from 1967 to 1981 but stabilized in 1982 effective tax rates on unearned income rose steadily from 1967 to 1981 and took a particularly large additional jump in 1982 effective tax rates on earned income fell after 1967 but then gradually rose throughout the 1970s until 1982 when they took a much larger jump thus guarantees fell and tax rates rose over the 1970s as tight budgets forced states to restrict benefits and in the early 1980s tax rates were pushed even higher by federal legislation

the effect of incomes wages and afdc benefits on marital disruption this paper uses a choice based model to estimate the effects of a broad set of economic factors including afdc benefit levels husband s earnings and a woman s wage rate on the probability of marital dissolution we find that the probability of divorce is lower for marriages in which the husband s labor income is higher we also find that while afdc income has a substantial effect on welfare receipt by a divorced woman it has a relatively small effect on the probability that a married woman will become divorced finally we find no support for the hypothesis that rising wages for women have increased marital instability

social assistance and conjugal union dissolution in canada a dynamic analysis using statistics canadas general social survey on family and friends carried out in 1990 we piece together the matrimonial and conjugal life history of a large sample of canadian men and women we then estimate duration models coxs proportional hazard models describing the evolutionary laws of marriages and unions which depend on various economic or socio demographic explanatory variables the empirical modelling focuses primarily on estimating the impact of couples earned incomes and of provincial welfare programs on the dissolution rate of first marriages and unions we find that welfare benefits do not have an impact on the hazard of union dissolution and that earned incomes have a positive effect on conjugal stability excerpt summary in fre

till death do us part or i get my pension wives pension holding and marital dissolution in the united states wives financial independence gained from their pension may increase the risk of marital dissolution especially when wives are approaching retirement age the older wives independence hypothesis applying single and simultaneous equations probit models to data from the panel study of income dynamics we investigate the effect of wives pension holding in 1984 on the risk of subsequent marital dissolution results from the single equation model appear to support the older wives independence hypothesis however results from the simultaneous equations model suggest that interpreting the single equation results as a sign of older wives economic independence may be misleading

sources of complex dynamics in two sector growth models this paper develops a tractable multisectoral dynamic equilibrium model and provides a fairly complete analysis of the dynamics that may arise along the intertemporal competitive equilibrium path despite the fact that the environment displays neither random nor deterministic variability the model may produce oscillations in aggregate variables such as output consumption and investment we show that these oscillations can be exactly periodic of any finite period i and even totally aperiodic chaotic we characterize the parameter values for which each of these cases occur but also provide some strong global asymptotic stability results

government consumption and growth i introduction interest in formulating and testing growth models has surged in recent years following the seminal articles of romer 1986 and lucas 1988 the theoretical growth literature has primarily sought to endogenize the trend growth rate which had been treated as an exogenous parameter in the earlier vintage of growth models formulated by solow 1956 and cass 1965 inter alia although the goal of endogenizing trend growth rates is surely desirable it is still important to test whether trend growth rates are indeed better characterized as exogenous or endogenous many papers have attempted to do so unfortunately virtually all of them have used ordinary least squares to fit cross sectional regressions relating the average growth rate of per capita output over some period to its initial value and other country characteristics 1 my 1996a paper shows that this method produces seriously biased estimates and unreliable inferences this paper makes two contributions first using a simple stochastic growth model that nests both exogenous and endogenous growth it shows that the growth rate of output per capita should be mean stationary if growth is exogenous and should be difference stationary if growth is endogenous and any difference stationary variable affects investment specifically if the share of output devoted to government consumption is difference stationary the growth rate should be mean stationary or difference stationary depending on whether growth is exogenous or endogenous furthermore the growth rate should be negatively related to the share of output devoted to exhaustive government consumption if and only if growth is endogenous the second contribution is to test whether growth is exogenous or endogenous data for 92 countries over the period 1960 to 1989 strongly support the mean stationarity of the growth rate of per capita output and are consistent with the difference stationarity of the share of output devoted to government consumption moreover the growth rate is not significantly related to the government share these two findings support the exogeneity of growth finally the relationship is precisely estimated to be weak if not nonexistent hence even if growth is endogenous the degree of endogeneity is likely to be small 2 the rest of the paper is organized as follows section ii formulates a simple stochastic growth model for demonstrating the basic theoretical results section iii investigates whether growth rates are mean stationary and whether shares of output devoted to government consumption are difference stationary section iv examines whether and how growth rates and government shares are related to each other finally section v summarizes the paper and offers a few conclusions ii theoretical discussion this section lays out a simple and tractable stochastic growth model that nests both exogenous and endogenous growth the model is special in many ways because several restrictive assumptions are made for the sake of tractability nevertheless results similar to the ones derived below should hold in a wide class of models consider a closed economy inhabited by a government and a household that lives in periods t 0 1 2 the sole activity of the government is exhaustively consuming g which is financed by a proportional tax on gross output y at the rate tau its budget constraint is therefore 1 g sub t tau sub t y sub t i assume that government consumption is set so that 2 g sub t ln 1 g sub t y sub t is a driftless difference stationary process the household is endowed with one unit of labor which it supplies completely inelastically each period a positive initial capital stock and a technology 3 mathematical expression omitted 0 less than alpha less than or equal to 1 t 0 1 2

labor supply and marital separation panel data are used to estimate the effect of marital separation on labor supply female labor supply increases substantially and male labor supply declines marginally lending support to the theory of specialization within the household the most interesting finding is that women began to increase their labor supply well before the actualsplit occurs suggesting either that shocks to labor supply change divorce probabilities or that women with a higher likelihood of divorcework more this argument is pursued by constructing and estimating a simultaneous model of labor supply and divorce risk copyright 1986 by american economic association

the effect of the u s welfare system on marital status abstract an issue of long standing importance in the u s welfare system has been its lack of neutrality with respect to family composition which generally provides payments only to female headed families that is families with no able bodied male present using data from 1969 to 1985 to examine the issue this study finds that 1 the simple cross sectional correlations between marital status and welfare benefits are almost always in the expected direction but are generally weak in significance 2 that the magnitude and significance of the correlations have nevertheless grown over time and 3 that the correlations for men are no weaker and usually stronger especially for blacks than those for women

trends in the well being of american women 1970 1995 this paper examines the trends in the well being of american women over the last 25 years a time of significant changes in the relative economic status of women and in the labor market as a whole a broad range of indicators are considered to capture changes in women s well being in the family as well as in the labor market for virtually all age and education groups substantial evidence is obtained of rising gender equality in labor market outcomes notably labor force participation wages and occupational distributions broad evidence is also found of greater gender parity within married couple families as the housework time of husbands increased relative to wives and the relative wages of wives rose compared to their husbands however parallel to the recent evidence of the declining labor market position of lower skilled men there has been a similar deterioration in the economic status of less educated women especially high school dropouts their labor force participation rates and wages have risen at a much slower pace than those of more highly educated women while their incidence of single headship has increased much more rapidly these findings for less educated women serve to underscore the widening gap between more and less skilled americans of both sexes as well as to emphasize its broad dimensions

unilateral divorce versus child custody and child support in the u s this paper explores the response of the divorce rate to law reforms introducing unilateral divorce after controlling for law reforms concerning the aftermath of divorce which are omitted from most previous studies we introduce two main policy changes that have swept the us since the late 1970s the approval of the joint custody regime and the child support enforcement program because those reforms affect divorce decisions by counteracting the reallocation of property rights generated by the unilateral divorce procedure and by increasing the expected financial costs of divorce it is arguable that their omissions might obscure the impact of unilateral divorce reforms on divorce rates after allowing for changes in laws concerning the aftermath of divorce we find that the positive impact of unilateral divorce reforms on divorce rates does not vanish over time suggesting that the coase theorem may not apply to changes in divorce laws supplemental analysis developed to examine the frequency of permanent shocks in us divorce rates indicates that the positive permanent changes in divorce rates can be associated with the implementation of unilateral divorce reforms and that the negative permanent changes can be related to the law reforms concerning living arrangements in the aftermath of divorce this seems to confirm the important role of these policies in the evolution of divorce rates

durable capital and chaos in competitive business cycles abstract this study constructs an example of chaotic optimal accumulation that results from the existence of the limitation of capital depreciation an example is an extension of the model developed by weitzman

female earnings and the divorce rate a simultaneous equations model economists have contributed a great deal of research both theoretical and empirical to the study of marital formation and dissolution many empirical examinations of marriage and divorce rates exist based on becker s seminal contributions to the literature all of these divorce studies are single equation models with female earnings assumed exogenous as discussed by becker 1981 however causality may run in the opposite direction as well the divorce rate may influence female earnings this paper estimates a simultaneous equations model in which divorce rates and female earnings are the jointly endogenous variables data are by state for 1960 1970 1980 and 1990 the state wide divorce rate equation is an extension of waters and ressler 1999 and the specification of a state wide earnings equation follows standard human capital theory the specification of joint endogeneity between female earnings and the divorce rate allows valid inferences to be made regarding the effect of female earnings on