## Summary:

The goal of this project is to analyze analytically, quantitatively, and empirically a framework where labor supply has three distinct roles. First, as usual, it increases contemporaneous earnings. Second, because of incomplete asset markets, it provides some partial insurance for idiosyncratic labor productivity shocks. And last, labor supply also works as investment in future earnings potential (human capital). In this sense, in our model wage dynamics is partially endogenous. The insurance effect of labor supply was (among others) studied by Pijoan-Mas (2006). The human capital investment dimension of labor supply was first introduced by Imai and Keane (2004) in a life-cycle environment without idiosyncratic shocks. In terms of modeling, our contribution to the literature is twofold. First, we develop a framework where both the additional insurance (incomplete markets) and investment (human capital accumulation through learning-by-doing) aspect of hours are present. Second, we allow the return from an additional hour to vary with the initial level of wages (human capital). Based upon my earlier work in Santos (2010) we show that this feature is particularly important: in both CPS and PSID data, the marginal effect of an hour on future wages is increasing significantly with current wages. This implies that learning-by-doing can provide a better 'technology' of generating wage growth (or avoiding a reduction in wages) for agents with higher initial wage (human capital).

We want to focus on three main issues using this framework. First of all, in this environment the monetary return of an additional hour is not equal to the current hourly wage as in the standard models of labor supply. Rather, it is augmented by the expected net present discounted value of all the earnings increases this hour's choice implies for the future. Consequently, labor supply does have an insurance role not only in the static sense but also in a dynamic precautionary perspective (ceteris paribus, higher labor supply decreases the chance of lower wages in the future). Given that this dynamic effect of labor supply is stronger for high wage earners, this implies that this mechanism amplifies contemporaneous cross-sectional inequality.

Second, the above observation has some strong implications on labor supply elasticity. As just noted, when the dynamic effect is considered the rewards of a marginal hour become more dispersed across agents with different current wages. This implies that to explain the fact that hours are relatively constant across wage groups, we need to have a smaller elasticity of labor supply. Early results show that indeed this is the case: when ignoring the endogeneity of the wage process we obtain 0.5 as a Frisch elasticity of labor supply. This is a standard estimate in the micro literature but it is lower than the 0.72 that Pijoan-Mas (2006) obtains in a similar macro model. However, he uses an exogenous and somewhat different wage process. When we estimate/calibrate this elasticity using our model allowing for the asymmetric investment role of labor supply we obtain an estimate of 0.25, which is significantly lower than what we have in the benchmark case. Hence, we show that ignoring the presence of the asymmetric investment effects of labor supply biases upward the estimate of the Frisch elasticity significantly (double it up).

Third, a low Frisch elasticity is usually bad news for macroeconomists, because fitting aggregate hours and wages data and/or matching the responses of aggregate labor supply (and hence aggregate output) to tax policy changes usually requires a high elasticity of labor supply of the representative agent (see Prescott (1986, 2004). However, in our framework we can have a low elasticity and yet expect significant responses of aggregate labor supply and human capital when the progressivity of the tax system is decreased. This is the case because, in our environment, progressivity does not only change the distribution of contemporaneous wages but also the dynamic gains associated with an additional hour.