Chapter 69 Labor Supply Models: Unobserved Heterogeneity, Nonparticipation and Dynamics

In recent years, Congress has considered a variety of work-subsidy programs designed to encourage work among welfare recipients. Many of these programs would subsidize individuals only if they work some minimum number of hours. Commonly used techniques cannot give direct answers to relevant policy questions since a tied offer is involved, and hence the offer cannot be treated as a simple wage change. The essence of the problem involves utility comparisons between two or more discrete alternatives. Such comparisons inherently require information about consumer preferences in a way not easily obtained from ordinary labor-supply functions. To make such comparisons, I present a method for directly estimating consumer indifference surfaces between money income and nonmarket time. Once these surfaces are determined, they can be used to compare a variety of alternative programs to investigate whether or not there is scope for Pareto-optimal redistribution of income transfers and time, improving the general level of welfare of the community at large without reducing the welfare of individuals receiving income transfers. Knowledge of these indifference surfaces allows us to estimate reservation wages to estimate the value of nonworking-women's time (Gronau 1973), laborforce participation functions, hours-of-work functions, and welfare losses due to income tax programs (Harberger 1964). I demonstrate that direct estimation of indifference surfaces allows us, at least in principle, to relax

This paper discusses the properties of parallel preference structures and their potential usefulness in empirical research. The parallel structure can accommodate arbitrarily flexible substitution properties and linear or nonlinear income-consumption curves, with the linear form representing a special case of the Gorman polar form. The global properties are distinctive in that indifference loci are parallel surfaces, identical in shape and scale at all utility levels. These properties are potentially appropriate for models of family labor supply but are less suitable for applications to production over a wide range of output. Alternative parameterizations and estimation forms are discussed and the model is shown to provide a basis for interpretation of models of labor supply estimated by Professors Ashenfelter and Heckman. PARALLEL PREFERENCE STRUCTURES are characterized by indifference surfaces that are identical in shape and scale, each being a translation of a basic surface along parallel income-consumption curves. The purpose of this paper is to discuss the properties of parallel structures and their potential usefulness in models of labor supply and commodity demand. Limited applications in production analysis are also discussed but are not the primary focus of the paper. In their most tractable form, with linear income-consumption curves, parallel 2 structures are a special case of the Gorman polar form. A suitably parameterized cost or expenditure function for a linear parallel structure provides a second order point approximation to an arbitrary general cost or expenditure function. By that criterion, a variety of simple versions of the parallel structure are on roughly equal footing with other flexible functional forms employed in recent demand, produc

Models of the labor supply behavior of single persons predict that a negative income tax (NIT) will always reduce the labor supply and earnings of such persons. I consider three models of family labor supply; and find that in all three, a NIT might raise a given family member's labor supply and might also raise total family labor supply: in one, a NIT could even raise total family earnings. These models and recent empirical estimates (showing positive NIT effects on some family members' labor amply and on some families' earnings) suggest that the work disincentive effects and the cost of a NIT may be less than has previously been thought.

Work on estimating the labor supply effects of high marginal tax rates in welfare programs has been hindered by the difficulty of estimating the effects of participation in multiple welfare programs simultaneously. The authors solve this problem by applying methods of simulation estimation to a model of labor supply and multiple program participation. The results show asymmetric wage and tax rate effects, with fairly large wage elasticities of labor supply but very inelastic responses to moderate changes in cumulative marginal tax rates, implying that high welfare tax rates do not necessarily induce major reductions in work effort. Copyright 1998 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

This paper examines the effect of cash transfers and food stamp benefits on family labor supply and welfare participation among two-parent families. The Aid to Families with Dependent Children-Unemployed Parent Program has provided cash benefits to two-parent households since 1961. Despite recent expansions, little is known about the program's effect on labor supply and welfare participation. I develop a model of family labor supply in which hours of work for the husband and wife are chosen to maximize family utility subject to a family budget constraint accounting for AFDC-UP benefits and other tax and transfer programs. The husband's and wife's labor supply decisions are restricted to no work, part-time work, and full-time work. Maximum likelihood techniques are used to estimate parameters of the underlying hours of work and welfare participation equations. The estimates are used to determine the magnitude of the work disincentive effects of the AFDC-UP program, and to simulate the effects of changes in AFDC-UP benefit and eligibility rules on family labor supply and welfare participation. The results suggest that labor supply and welfare participation among two-parent families are highly responsive to changes in the benefit structure under the AFDC-UP program.

Chapter 27 Labor supply: A review of alternative approaches

This chapter surveys existing approaches to modeling labor supply and identifies important gaps in the literature that could be addressed in future research. The discussion begins with a look at recent policy reforms and labor market facts that motivate the study of labor supply. The analysis then presents a unifying framework that allows alternative empirical formulations of the labor supply model to be compared and their resulting elasticities to be interpreted. This is followed by critical reviews of alternative approaches to labor-supply modeling. The first review assesses the difference in-differences approach and its relationship to natural experiments. The second analyzes estimation with non-linear budget constraints and welfare-program participation. The third appraises developments of family labor-supply models including both the standard unitary and collective labor-supply formulations. The fourth briefly explores dynamic extensions of the labor supply model, characterizing how participation decisions, learning-by-doing, human capital accumulation and habit formation affect the analysis of the lifecycle model. At the end of each of the four broad reviews, we summarize a selection of the recent empirical findings. The concluding section asks whether the developments reviewed in this chapter place us in a better position to answer the policy-reform questions and to interpret the trends in participation and hours with which we began this review. q1999 Elsevier Science B.V. All rights reserved.

Over the period 1960 - 1983 the proportion of federal tax revenue raised by taxation of labor supply has risen from 57-77 percent. In this paper, we specify and estimate a model of family labor supply which treats both federal and state taxation. Husbands and wives labor supply are treated jointly rather than in aseparate manner as in previous research. A method to calculate the virtual wage for nonworking spouses is used within a utility maximizing framework to treat correctly the joint family labor supply decision. Joint family efforts are found to be important. The efficiency cost (deadweight loss) of labor taxation is estimated to be 29.6% of tax revenue raised. The effect of the new 10% deduction to ease the marriage tax for working spouses leads to a prediction of 3.8% increase in wives labor supply and a .9% decrease in husbands labor supply.Overall taxes paid are predicted to decrease by 3.4%.

The aim of this paper is to analyse the impact of unobserved preference heterogeneity in empirical applications of discrete choice models of labour supply. Typically, unobserved heterogeneity is estimated either with continuous or discrete mixture models. However, in order to avoid estimation difficulties, most of the empirical analysis assumes a relatively constrained mixture, standard examples being models where only few coefficients are allowed to vary with independent normal distributions or with discrete distributions with few mass points. We compare labour supply elasticities obtained with these typical specifications of unobserved heterogeneity with those from a more general model that we are able to estimate through an EM algorithm for the nonparametric estimation of mixed models. Results show that labour supply elasticities change significantly with respect to a basic model without unobserved heterogeneity only when the joint distribution of the varying tastes is left completely unspecified.

Macroeconomic calibrations imply much larger labor supply elasticities than microeconometric studies. One prominent explanation for this divergence is that indivisible labor generates extensive margin responses that are not captured in micro studies of hours choices. We evaluate whether existing calibrations of macro models are consistent with micro evidence on extensive margin responses using two approaches. First, we use a standard calibrated macro model to simulate the impacts of tax policy changes on labor supply. Second, we present a metaanalysis of quasi-experimental estimates of extensive margin elasticities. We find that micro estimates are consistent with macro evidence on the steady-state (Hicksian) elasticities relevant for cross-country comparisons. However, micro estimates of extensive-margin elasticities are an order of magnitude smaller than the values needed to explain business cycle fluctuations in aggregate hours. Hence, indivisible labor supply does not explain the large gap between micro and macro estimates of intertemporal substitution (Frisch) elasticities. Our synthesis of the micro evidence points to Hicksian elasticities of 0.3 on the intensive and 0.25 on the extensive margin and Frisch elasticities of 0.5 on the intensive and 0.25 on the extensive margin.

The central hypothesis of the "new micro-economics of fertility" was examined, i.e., because children are female-time intensive, fertility is inversely related to the mother's wage. A theoretical model of lifetime family labor supply and completed fertility which forms the basis for the subsequent empirical investigation is presented. Empirical estimates of the model are provided using 1971 Canadian census data. The 1-period model of completed family size and lifetime labor supply indicates that fertility and labor supply behavior of families where the wife participates in the labor market will differ from that of families with never-participating wives. The systematic differences arise because families with nonworking wives face the additional binding constraint of an inflexible supply of wife's time to the home. A comparison of these 2 regimes allows inferences concerning the female-time intensity of children and the substitutability of husband's and wife's time. In the context of the 1-period model, the relevant criterion for separating families into the 2 regimes is the lifetime rather than current participation status. The evidence suggests that when this procedure is followed, much doubt is cast on the conventional wisdom that children are female-time intensive. The usual inverse relation found between wife's wage or education and completed family size appears to be the result of a complex interaction between wage rates, lifetime labor force participation, and fertility. Some support is found for complementarity between the home time of the husband and wife, but the evidence is not totally consistent. Results of the female participation equation strongly suggest complementarity; proxies for the husband's lifetime labor supply suggest weak or zero complementarity. When the sample is split by current participation of the wife rather than lifetime participation, then the results support conventional wisdom concerning the female-time intensity of children and replicate Kneisner's finding of complementarity between husband and wife's time. Reconciling these differences within the framework of the 1-period model is difficult since it yields no predictions concerning current variables. Yet, since the wife's lifetime participation is the correct criterion for allocating families to the 2 regimes under the 1-period model, doubt must remain concerning the female-time intensity of children until the current lifetime results are reconciled.

This paper deals with family labour supply under nonlinear income taxation in a life-cycle consistent framework. A major purpose of the paper is, therefore, to bring together previous research on how to model joint supply decisions, life-cycle consistency and piecewise linear taxation, and then perform an econometric application using Swedish cross-section data. The paper starts by constructing an intertemporal model of household behaviour, which is used to derive optimal hours of work for the husband and the wife, respectively. Then, given the appropriate theoretical framework, the model is specified in a way suitable for econometric analysis. Regarding the estimation results, we find that both male and female labour supply are sensitive not only to changes in the own marginal wage rate and the virtual nonlabour income, but also to changes in the marginal wage rate of the spouse. The latter means that cross-wage effects are important when it comes to interpret the consequences of income taxation.

This paper develops a unified model of dual and unitary job holding based on a Stone-Geary utility function. The model incorporates both constrained and unconstrained labor supply. Panel data methods are adapted to accommodate unobserved heterogeneity and multinomial selection into six mutually exclusive labor supply regimes. We estimate the wage and income elasticities arising from selection and unobserved heterogeneity as well as from the Stone-Geary Slutsky equations. The labor supply model is estimated with data from the British Household Panel Survey 1991–2008. Among dual job holders, our study finds that the Stone-Geary income and wage elasticities are much larger for labor supply to the second job compared with the main job. When the effects of selection and unobserved heterogeneity are taken account of, the magnitudes of these elasticities on the second job tend to be significantly reduced.

The McElroy-Horney Nash-bargaining model of family demand behavior relaxes the restriction that nonearned income of husband and wife has the identical effect on family labor supply and commodity demands. This restriction of the neoclassical model offamily behavior is tested for the determination of husband and wife labor supply andfertility based on the 1981 Socioeconomic Survey of Thailand. The neoclassical restriction is rejected for female labor supply andfertility. Another unexplored limitation offamily demand studies, due to the sample self selection of intact marriages, is empirically treated through alternative estimation strategies. In this case, a more sharply focused theory of marital behavior is needed to identify family demand models.

Consumption inequality across heterogeneous families