In this paper we propose a modelling approach for labor supply and consumption decisions that is firmly grounded within a utility maximizing framework and allows for a role of such institutional constraints as limited access to borrowing and involuntary unemployment. We report estimations for a system of dynamic probit models with data from the Panel Study of Income Dynamics. These estimations test broad predictions of the theoretical model.
One of our models describes a household’s propensity to be liquidity constrained in a given period. The second is a dynamic ordered probit model for a labor constraint indicator describing qualitative aspects of the conditions of employment, that is whether the household head is involuntarily overemployed, voluntarily employed, or involuntarily underemployed or unemployed. These models are estimated separately as well as jointly. Our results provide strong support for the basic theory of constrained behavior and the interaction between liquidity constraints and exogenous constraints on labor supply.
This paper considers a dual approach to the problem of maximizing lifetime utility subject to liquidity constraints in a discrete time setting. These constraints prohibit the decision maker from borrowing against future endowment income. The dual approach allows us to exploit directly the supermartingale property of the marginal utility of expenditure and to establish existence and uniqueness of the optimal solution. The optimal solution is interpreted as deriving from a version of the problem that is subject to a single lifetime budget constraint, where expenditures and incomes are discounted to the beginning of the horizon by means of individualized Arrow-Debreu prices.