Structural Labor Supply Models when Budget Constraints are Nonlinear

 Structural labor supply methods are generally needed to separate out income and substitution effects, to calculate deadweight losses, and to study policies that make budget constraints highly nonlinear. However, the relationship between the economic assumptions, implicit restrictions, and biases in various estimation methods is not well understood. This situation leaves researchers in a quandary about what approach they should use. As a result, many recent papers cite papers by MaCurdy and co-authors as a justification for avoiding structural methods, and instead using simple estimation methods such as differences in differences. This paper examines the role of economic assumptions in structural labor supply methods and how some of the assumptions may be relaxed. We first show the sources of inconsistency in the local linearization method. We then examine the standard approach generally attributed to Hausman, and show that this approach relies on the convexity of preferences in the construction of the likelihood function. We show that the criticisms of MaCurdy can be reinterpreted as showing where in the estimation method the assumption of convexity is enforced. We provide a formal argument that if observed preferences are nonconvex, but the estimation method does not allow for nonconvexity, then estimated parameters may not satisfy the Slutsky restrictions, as has often been found. Finally, we show that the standard methods in the literature do not permit estimation of parameters consistent with nonconvex preferences, and describe methods that allow for less restrictive assumptions