This is a continuation of my last post.

The life cycle labor supply framework expands the margins of individual dynamic responses, but its flexibility leads to extensive requirements about data and challenges in modeling and estimation. In the following I attempt to describe some of the major challenges and concerns.

I. Prioritizing Margins

Life cycle labor supply models allow for a variety of margins that individuals can respond to, but specific margins need to be chosen (and others ignored) according to the research question. In particular, the results of labor supply elasticity and the predicted effects of taxes seem to be sensitive to functional assumptions.

There are two main sets of assumptions. The first set concerns the form of the individual utility function and the budget constraint. The intertemporal separability assumption facilitates the use of two-stage budgeting approach where information outside the period can be conveniently summarized by the marginal utility of wealth. However, this assumption rules out persistence across time and complementarity between work and consumption within a period. The separability assumptions seem to drive some of the estimation results, but it is unclear whether they are of first order importance, especially given that the analysis would usually become significantly more complicated when they are relaxed. It should also be noted that the separability assumptions reflect the researcher’s beliefs about individual behavior and need more justification.

The second set of assumptions concerns the process governing prices, wages, and savings and asset incomes. These assumptions determine to what extent individuals can control the state they are in. For example, the human capital accumulation assumption yields very large labor supply elasticities, but it is unclear whether this factor is taken into account in policy discussions about optimal tax policy (Saez 2001).

II. Household versus Individual Decision

Life cycle models do not have a systematic approach for joint treatment of labor supply of members within the household. In most papers, individuals are the units of observation. When the decisions of the husband and the wife are modeled jointly, different studies take different stances on the underlying decision process in the household. It is often assumed that a household operate like a unified decision maker with a household utility function subject to a joint budget constraint that accounts for every household member’s incomes. However, some studies on female labor supply (e.g. Altonji 1986) assume the incomes of the husband are exogenous nonlabor incomes for women. Such treatment completely rules out sorting in household formation and bargaining within the household. Allowing household formation and joint labor supply decisions to be endogenous and to depend on the bargaining between household members will complicate the analysis significantly but will have important implications for the joint tax treatment of married couples.

III. Data and Estimation

The multiple margins that the life cycle models allow for imposes extensive requirements on the data.

Estimating the full labor supply responses to permanent wage changes (“parametric changes” as in MaCurdy 1981) requires first estimating the individual fixed effects and then specifying a functional form of them to recover the structural parameters. Without data on subjective expectations, researchers need to specify the exact functional forms of expectation (MaCurdy 1980) which might lack justification. As an exception, Pistaferri (2003) uses information on subjective expectations about wages and prices and estimates the effects of life cycle wage growth through three channels: anticipated wage growth, unanticipated wage growth, and risk in wages (measured by the dispersion in the conditional distribution of future wages). Assuming all unanticipated wage changes are viewed as permanent, he uses expected and expected wage changes to estimate the intertemporal elasticity effect and the permanent effect respectively. This approach avoids the problem of finding instruments for wage growth that are uncorrelated with unexpected wage changes. However, in this study the expected wage changes are calculated from expected earnings changes which are affected by shifts in tastes and are therefore endogenous.

Another challenge is present in models with uninsurable uncertainty and aggregate shocks. In such models, estimation of the parameters characterizing intertemporal allocations requires sufficiently long time series because the GMM moment conditions relating forecast errors to marginal utilities of wealth do not hold in the cross section (Atlug and Miller, 1998).

Accounting for labor force participation decisions complicates the analysis significantly and requires more sophisticated treatment in estimation. Under perfect certainty, first differences will eliminate the individual fixed effects. But the instrumental variables, such as hours and wages lagged two periods, need to be strong instruments for future growth in wages. If labor force participation decisions are accounted for (Heckman and MaCurdy, 1980), the model will become nonlinear, and individual fixed effects cannot be consistently estimated by within-group estimators because of the incidental parameters problem. Heckman and MaCurdy (1980) provide Monte Carlo evidence that this problem will not generate a big bias in the estimates for moderate number of time periods, but this is not a general result. In models with time nonseparable endogenous variables, the bias could be substantial (Blundell et al, 2007). Time nonseparable endogeneity of wages could be induced by intertemporal nonseparable preference, intertemporal nonseparable budget constraint, or human capital accumulation. An alternative approach is joint Maximum Likelihood estimation (MLE) as in Heckman and MaCurdy (1980), but this approach imposes restrictive assumptions including intratemporal separability of preferences, perfect certainty, and perfect foresight.

It is also widely acknowledged that estimates of labor supply elasticities are sensitive to the specific approach taken and the choice of instrumental variables. MaCurdy (1983) uses two methods to estimate the labor supply elasticities. The first is to specify a form of the marginal rate of substitution between consumption and leisure and to estimate the optimality condition using instruments for wages, hours, and consumption. This method is intuitive but requires many instruments, all of which need to be uncorrelated with tastes for work. The second approach is to use an augmented “virtual income” measure which accounts for savings across periods and to estimate a labor supply regression model that is consistent with the life cycle model. The first method generates much larger estimates for intertemporal elasticity (6.25 at mean) than previous studies. One weakness of the paper is that age and education are used as instruments for wages, but these variables are likely to be correlated with tastes for work. Based on this criticism, Altonji (1986) adopts two other instruments for changes in wages: directed reported hourly wages, and “permanent incomes” which are based on regressing observed wages on individual characteristics and fixed effects. The resulting Frisch elasticity estimate is 0.17, much smaller than MaCurdy’s. Because these two papers make different assumptions of the information individuals have and use different data, measures of wages and consumption and instruments, the reason for the discrepancies is unclear.

IV. From Elasticities to Policy Design

Labor supply elasticity with respect to wage changes are useful for policy evaluation. Higher labor supply elasticities often imply lower optimal tax rates because of the larger efficiency loss resulted from tax increases.

There is still little agreement on whether the compensated wage elasticity is positive and whether the Slutsky matrix conditions hold empirically (Ziliak and Kniesner, 1999). A positive compensated wage elasticity suggests that a flatter tax schedule increases working hours and reduces deadweight loss, while a negative compensated wage elasticity suggests the opposite. Certain behavioral assumptions are involved in choosing the specific assumption. For example, Saez (2001) showed that for a given compensated elasticity, the optimal tax rates for the high income population depend on the relative magnitudes of the income effects and uncompensated rate effects. However, there is little consensus in the magnitude of these elasticities, with some estimates close to zero and others exceeding one (Gruber and Saez, 2002).

The optimal design of welfare transfer programs also depends critically on the labor supply responses of the low income population. Saez (2002) showed that a classical Negative Income Tax (NIT) is optimal if responses are concentrated along the intensive margin while a system similar to the Earned Income Tax Credit (EITC) is optimal is responses are primarily along the extensive margin.

Another approach to estimate the aggregate effects of tax changes on labor supply decisions is to use “natural experiments” (Eissa, 1995; Gruber and Saez, 2002). This method avoids many of the econometric challenges posed by a structural model but does not directly account for life cycle considerations and the results have limited external validity.

References are available upon request.