The effects of taxes and transfers (1): from static to life cycle labor supply models

The second half of this semester I am taking a PhD module on the effects of taxes and transfers by Professor Joe Hotz. I have enjoyed it so much that I decided to write a series of reflective posts on it. This post is the first one. References to the papers are available upon request; I won’t post them here because of time constraint.

Taxes and transfer programs change individual behavior through various channels, among which labor supply is one of the most important and policy relevant. Knowledge about the responsiveness of labor supply towards tax changes allows us to better evaluate the distortionary effects of taxes and the magnitude of dead weight loss of different tax schedules (e.g. progressive vs. regressive).

The earliest models of labor supply assume individual decisions are made in a static setting (Heckman, 1974). Given exogenous wage and non labor income, individuals choose to their labor supply levels to maximize utility (which depends on their tastes). There is no dynamic concerns: “lifetime” is treated as the one and only period where the individual needs to make a decision.Tax changes figure into individual’s budget constraint through changing pre-tax wage rates. In more sophisticated models, taxes on wages and nonlabor income are modeled jointly.

Since labor supply decisions are made throughout the life cycle, static labor supply models yield incomprehensible estimates for labor supply elasticity that cannot be used for policy evaluation. Life cycle labor supply models are developed as a consequence. The simplest life cycle model (MaCurdy, 1980) assumes no uncertainty, i.e. wages, prices, and interest rates are all exogenous and known to the individual. From there we can derive the Frisch elasticity (holding the marginal utility of wealth constant) which measures the intertemporal substitution of labor supply. Frisch elasticities allow us to infer individual dynamic behavior along a given profile, but a structural model of individual effects needs to be estimated in order to derive compensated and uncompensated elasticities for cross-sectional comparisons.

Later models incorporate uncertainty into the evolution of wages, prices, and interest rates. In such settings, individuals maximize expected utility over their remaining life and adjust their labor supply/consumption choices after period-specific information is revealed. Using appropriate IVs that are not correlated with present-period “shocks”, we can still adopt the first-difference method used in the perfect certainty models to estimate intertemporal elasticity.

A few other papers relaxed the unrealistic assumptions that individual utility is separable contemporaneously between leisure and consumption and across periods. Ziliak and Kniesner (1999. 2005) found that contemporaneous consumption and leisure are complements, and ignoring this relationship can bias the estimates for labor supply elasticity.

The important takeaway is tax changes will affect people’s behavior along multiple margins. The significance of the earliest models lies in their simplicity. The subsequent development in the literature enriches the life cycle model and allow people to respond to foreseeable as well as unpredicted changes in wage rates and prices, to endogenously determine their wages (through human capital accumulation), to have preference for joint consumption of leisure and other goods, etc. I will write a post on human capital accumulation after tomorrow’s class.

For this course, each student is required to lead one class, where he/she has to write summary notes of the papers, do a presentation, and draft a few discussion questions. I found it’s harder than I thought to summarize a few related papers (to extract the “juice” out of them) and to explicitly point out how they complement each other or where the dispute is. You need to really digest the papers, think through about the fundamental modelling assumptions and empirical methodologies, and what are the pros and cons of each approach. It took me one and a half week to fully digest and to organize the four papers such that my classmates would spend the minimum time getting the essence out of them. But I felt really glad to receive positive feedback on my summary notes and presentation. It was also rewarding to see my questions generated a fair bit of insightful discussion. Keep it up!


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