Recommended reading

1. NY Times post on using game theory to design high school application system in the New York City. I also found an older article by Alvin Roth reviewing the theory of deferred acceptance and its applications.

2. Professor Marc Bellemare on how academic economists can use social media for research. I echo the following reason he has for using social media to talk about research:

I believe all of us should spend some time contributing to public goods by helping people think through social problems in your area. This is especially true for those of us whose research is publicly funded and whose isn’t? With more and more Americans questioning the value of a college education, we have a duty to show that universities play a much broader role, and to put knowledge in the service of society.

I also agree with him that it is important to keep the blog fresh by writing regularly and succinctly (obviously I haven’t done a good job in that regard, at least recently).

3. Yale job market candidate Alex Cohen on how imperfect factor markets dampen the positive impacts of relaxing credit constraints. I’m excited to see more structural approaches being used in development economics.

4. The Economist on whether the government should regulate digital monopolies. The internet is essentially a two-sided market which provides a platform for multiple parties (in this case, companies which advertise their products, and consumers) to make transactions more efficiently . To evaluate the welfare consequences of policies, we need to be more clear about whose welfare we want to maximize.

5. World Development Report 2015 focuses on understanding mind, society and behavior, questioning the fundamental rationality assumption in economics and suggesting alternative methods to analyze individual behavior.

The Effects of Taxes and Transfers (5): Status Quo of Life Cycle Labor Supply Models and Future Research

This post follows my previous two posts assessing the contributions and limitations of life cycle labor supply models.

Since its introduction in the early 1980s, life cycle labor supply models have taken on various forms in the economic literature on the effects of taxes and transfers, and the dynamic considerations for human capital acquisition. The literature has not reached a consensus on the magnitude of labor supply elasticities. While most studies find small elasticities for (prime working age) men, a few find large values that even exceed those in the macro literature. For women, most studies find large elasticities of labor supply, especially on the participation margin. In particular, Keane (2011a) finds that allowing for dynamic effects of wages on fertility, marriage, education and work experience leads to larger estimates for long-run elasticities.

More research remains to be done in the following areas. First, modeling human capital accumulation, labor force participation and progressive taxation jointly will allow us to assess how individuals make schooling and labor supply decisions under taxation. Second, modeling labor supply and consumption decisions within the family decision can shed light on how changes in taxes and welfare programs affect different household members differently. Third, the effects of transfer programs on the skill acquisition and occupation choice and marriage and fertility decisions of the low income population (especially women) need to be estimated more accurately. Such long term impacts are relevant to design a welfare system that provides work incentive as well as the skills required for work. Finally, the availability of longitudinal data on a greater array of individual responses, such as consumption and health (in PSID), makes it possible to assess the dynamic impact of tax and welfare programs on other fronts in addition to labor supply (Hokayem and Ziliak, 2014).

References are available upon request.

The Effects of Taxes and Transfers (4): Challenges and Concerns with Life Cycle Labor Supply Models

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.

The Effects of Taxes and Transfers (3): Contributions of Life Cycle Labor Supply Models

The past few weeks have been a bit overwhelming for me, and I wasn’t able to blog as much as I would like to. My class on the effects of taxes and transfers has come to an end (many thanks for Prof. Hotz and my classmates for the intellectual simulation!). In this post and the next two posts, I share my thoughts on the contributions and limitations of the life cycle labor supply models and potential areas for future research.

The main contribution of life cycle models is to expand the margins along which individuals can adjust their behaviors. The earliest models addressed the endogeneity of nonlabor incomes introduced by life time budget constraints while abstracting from endogenous human capital accumulation and uncertainty. Subsequent research has built on this framework and accounted for different sources of uncertainty that might affect individual behavior. Incorporating uncertainty in prices and interest rates into the life cycle model links microeconomics with macroeconomics literature on business cycles and intertemporal labor supply decisions. Models of human capital accumulation highlights the long lasting impact of current labor supply on life cycle earnings. Relaxing the nonseparability constraints on utility allows for habit formation and persistence in tastes for work. In particular, allowing for intertemporally nonseparable budget constraints enables us to jointly model nonlinear taxes on labor incomes and interest rates jointly. These advances allow us to estimate labor supply elasticities more accurately and evaluate the effects of taxes more realistically.

I. Effects of Taxes on Work Incentive

Life cycle labor supply models allow us to estimate intertemporal (Frisch) elasticity, Marshallian compensated elasticity, and Hicksian uncompensated labor supply elasticity more accurately, which has critical implications for optimal tax policies. In a static setting, taxes only changes the relative prices of labor supply to consumption in the current period. In the life cycle setting, however, current tax changes can have a long lasting effect on future periods depending on individual expectations about their future wage profiles and whether the changes in taxes are permanent. The tax changes also affect people on different segments on the tax schedule differently. Progressive taxation introduces disincentive for work because workers receive relative lower after-tax wage rates as they move up the income ladder.

II. Retirement Decisions

One of the key assumptions in the life cycle model is that individuals are forward-looking and have rational expectations. In the earlier models, the length of working periods is taken as exogenous, but retirement decisions are likely to be endogenous. This can affect life cycle human capital investment decisions as the horizon over which the returns will be realized are changing endogenously.

One of the earliest investigation on this issue is Rust (1989). He outlines a dynamic programming problem where individuals maximize expected utility in their remaining life by choosing consumption and the degree of labor force participation (part-time, full-time, non participation). This model highlights the sequential nature of the retirement decision problem and accounts for uncertainty in the state variables including health, marital status, employment, earnings, assets, etc. More recently, French (2005) estimates a life cycle model of retirement behavior where health, wealth, and wages are uncertain and individuals face borrowing constraints. He finds that the tax structures of the Social Security incomes and the pension incomes are key determinants of retirement behavior while Social Security benefit levels, health, and borrowing constraints are less important. Consistent with previous research, he finds little life-cycle variation for prime-age working men and large declines in labor force participation and hours worked among older men near retirement age.

III. Incentives to Invest in Human Capital

The literature has mainly explored two channels of human capital accumulation: schooling or on-the-job training (OJT), and learning-by-doing (LBD). In the former scenario, an individual’s time is allocated between human capital investment, work, and leisure. Learning is rivalrous with working but will increase future wages. In the latter scenario, skills are acquired as a byproduct of working. Without the nonlinearity in budget constraint (introduced by progressive taxes and welfare transfers), lower taxes discourages human capital investment in the OJT scenario but encourages human capital investment in the LBD scenario (as individuals will have a stronger incentive to work). When the budget constraint is nonlinear, however, the effects on human capital investment are more subtle. Heckman (2002) shows that changes in EITC rates will affect different individuals differently depending on the income segment they are located and the the magnitude of the increase in wages brought by human capital investment.

The life cycle perspective is useful for characterizing a broader set of forces that drive the human capital accumulation process. For instance, taxes that privilege certain types of incomes over others creates varying incentives to investment in skills among sub populations with different social-economic status. The fact that interest rates paid on educational loans are not tax deductible while mortgage interests are creates a privilege towards the skilled and the wealthy who are more likely to own homes and can finance their children’s education by taking mortgages. In the long term, this unbalanced treatment might aggravate the income inequality in the US (Heckman, 2000).

IV. Welfare Dependence

The life cycle framework suggests the possibility that welfare recipients might “bank” their benefits, i.e. participate in welfare programs in economic downturns to mitigate negative income shocks. Bitler et al (2014) find evidence that the EITC is stronger counter cyclical for married couples with children.

Participation in welfare programs also affects the future earnings ability and work incentive of welfare recipients. If the goal of the welfare system is to provide a safety net for those in need but to introduce them job-relevant skills, optimal design of the welfare system needs to account for the dynamic considerations in individual decisions of welfare participation. Keane and Wolpin (2002a, 2002b) investigate the long term effects of welfare benefits on economic and demographic behaviors including welfare participation, marriage and fertility, and work and schooling. Approximating decision rules from dynamic optimization, they find that welfare benefit as measured by the current realization of the benefit rule parameters and by their “permanent” means are jointly significant determinants of all the choices they consider.

Another branch of the literature investigates the effectiveness of different training programs on encouraging welfare recipients to work. For example, Hotz et al (2006) highlight the importance of the interactions between labor market conditions after the random treatment of welfare programs and the estimated effects of labor force attachment (LFA) versus human capital development (HCD) training components. They account for differences in the mix and assignment of LFA and HCD programs using non experimental regression adjustment, and find a bigger impact of HCD programs (relative to LFA) on labor force participation and hours worked in the long run.

References are available upon request.

Challenges of a PhD

The economic graduate student council organized a sharing session among PhD students on the challenges of doing a PhD. A few upper year students and job market candidates shared their experiences going through the PhD process. The following is some useful advice:

1. Manage your time well. Develop a regular schedule and stick to it. This will help you develop a rhythm and improve productivity.

2. When you feel there are too many things to do, list the tasks with the approximate time needed to finish them, and bundle big, time consuming ones with small, trivial ones.

3. Talk with people. Talk with your peers about research ideas, problems encountered in your work, and voice out your stress. Also, talk with your advisor(s) regularly and keep them posted about where you are. Even if you have not made a lot of progress, it is worth telling them what you have tried and failed doing.

4. Start preparing for the job market early. This includes simple things like starting your website and uploading materials. It also includes building up your ability to talk about your research in front of a broader audience. An upper year student specializing in IO also mentioned that people outside the economics department (business school, public policy, etc) can be good mentors and friends as well.

I still need to figure a lot of things out, but I’m lucky enough to be at a truly friendly and collaborative department.

Assorted Links

1. Eva Vivalt at NYU looks at how much do impact evaluations generalize in her job market paper. Her guest post at the World Bank Development Impact blog summarizes the paper well. The following paragraph caught my attention:

In the greater paper, I also find that when academics or NGOs implement a project, the project tends to yield higher effect sizes than when a government implements it; worrisome if the smaller, academic/NGO-implemented projects are intended to estimate the effects of the program were the government to implement it on a larger scale.

The generalizability of impact evaluation is very important for policy implementation, and more work needs to be done on this.

2. Brookings report on the rationale of encouraging higher education in STEM fields to meet the demand of employers. This made me wonder what forces are driving the location decision of different types of firms and how local policies interact with those. Sounds like there’s some spatial equilibrium there.

3. New York Times interview with executive women on finding and owning their voice. The whole article is worth reading. but these two pieces of advice stand out:

One of the things I see sometimes is that women mistake words for voice. They feel that because they have a seat at the table and they say something, that’s good. But it’s important for women to know that having a voice really means having a track record of success and accomplishments, so that people want to listen to what you have to say, because you’re saying something of value. So use your voice, but use it strategically.

Sometimes when you’re the only woman in a meeting, or one of just a few women in the group, you can feel like you almost have to say something. I think there are women who just want to make sure that they present at a meeting and that people are hearing them. But I think it’s just as important that you listen, because when you listen you get more out of the meeting. Sometimes you’re waiting to talk, and then you’re not listening. You have to balance listening and speaking. Then it becomes more natural.

The effects of taxes and transfers (2): incorporating human capital accumulation in life cycle labor supply models

Following our last class on simple models of life cycle labor supply, we discussed about incorporating human capital accumulation into the individual decision-making process. Now the wages are no longer exogenous. Instead, current wage depends on the amount of labor supplied in the last period, which is a proxy of human capital accumulation. Everything else stays the same. If this model is a more realistic description of the world (which is likely), the traditional estimation of Frisch elasticity (intertemporal substitution elasticity) will be biased downwards. To see this, note that over time wage rates are rising as a result of human capital accumulation, but the returns to “learning by doing” is decreasing (as the individual gets nearer to retirement). The total marginal return on labor supply estimated by Frisch elasticity combines these two effects and understates the true intertemporal substitution effect.

These models are nice, but here are two questions worth considering:

The first question is due to my classmate DS: How should we perceive the process of human capital accumulation?

The model presented above assumes that human capital accumulation happens through working more hours, which implies labor supply and human capital are complements. But they might well be substitutes: think about workers who have accumulated a body of knowledge and can work more efficiently with shorter hours. In this case, the Frisch elasticity might not be downward biased.

The second question is due to my classmate MZ:

Suppose you are at a cocktail party and two people start arguing over the effect of raising or lowering taxes on the incomes of wealthy people. Someone mentions that you are a budding young economist, so the two parties temporarily stop arguing to hear your words of wisdom. What do you say?

After our discussion, I think a fair answer would be that tax changes affect people’s behavior along multiple margins. The more margins we allow people to respond to in our analysis, the more distortionary effects we are likely to find. Obviously, economists rarely agree and even if they agree, it takes a long time for them to channel through policy making and have a real-world impact.