Research paperHow much does schooling disutility matter?☆
Introduction
Many structural models include a utility cost when an agent attends school, largely for the purpose of matching observed patterns in education choices.1 The theoretical implications and consequent implicit structural limitations imposed by introducing a disutility of education term to agents’ decision problems, are largely unknown, especially in a framework with uncertainty and inequality.2 We aim to fill this gap by creating a simple two-period decision model to investigate how the disutility term links wealth, risk, and education choices.3
The primary message of this paper is that including disutility of education in a dynamic model breaks the direct association between financial return and utility return to education, allowing risk and precautionary saving motive to impact education choice. Education serves as a saving/insurance device that transfers current wealth into human capital for future earnings. A heightened future consumption risk further increases the expected consumption utility in addition to any increase in lifetime income. If going to school yields a greater financial return than other saving vehicles, an increase in consumption risk implies an increase in the utility return to education if a disutility term is present. The agent is more likely to go to school. Without a disutility term, this increase in the utility return of education does not matter because the agent will just choose whichever education option maximizes her lifetime budget constraint.
We investigate two forces affecting education decisions in an environment of uncertainty: risk aversion reduces the appeal of the option with higher relative risk, while a rise in precautionary saving increases the importance of a higher financial return. If, for example, the variance of consumption is higher after schooling instead of working in the first period, schooling will be less attractive than if it had the same risk as working. However, if both schooling and working experience an increase in risk, but to different degrees, agents will increase their precautionary saving differently for the different options. Focusing on the case where schooling has a positive financial return, if working becomes riskier relative to schooling , then both forces compound and the utility return to education increases further. If the relative risk of schooling increases, but only moderately, the precautionary saving motive dominates the effects of risk aversion and attending school still becomes more appealing despite the increase in relative risk. Even if the increase in risk after schooling is sufficiently large so that the risk aversion factor is dominant, its influence will be partially counteracted by the precautionary saving motive.
Our results build on Belley and Lochner (2007), who show that concave consumption utility implies that the utility returns to education decrease in wealth. The absolute difference between consumption with and without education is constant, but the proportional difference in consumption is smaller with higher base wealth. Consequently, holding human capital constant, a wealthier individual who faces disutility of education will be less inclined to go to school than one currently holding no assets because of the smaller increase in utility. Similarly, if education provides positive utility then a wealthy agent will be more likely to attend school than one with no initial endowment if doing so provides a negative financial return.
The above results demonstrate that adding a disutility term in a structural education model embeds these connections between wealth, risk, and education into any counterfactual simulations. Causal inference requires an identification of which results are assumed and which come from the data. The literature is often less than totally cautious in considering the inclusion and estimation of the disutility term. If disutility exists in the data, omitting the disutility term in a model may underestimate the impact of wealth and risk on education choices.4 Similarly, projects which include a disutility term but who do not discipline the term with wealth and risk related data create an inconsistency between the assumptions used to estimate the disutility term and the implicit assumptions in the model used to analyze its implications.
In addition to their methodological significance, the above connections from risk and wealth to human capital investment through disutility provide an alternative explanation for intermittent schooling choices documented by the recent empirical literature (e.g. Arcidiacono, Aucejo, Maurel, Ransom, 2016, Dynarski, 1999, Jepsen, Montgomery, 2012, Johnson, 2013, Light, 1995, Light, 1995, Monks, 1997, Seftor, Turner, 2002, Yang). Changing wealth/human capital conditions, the relative disutility of schooling, and relative risk between work and education can induce agents to enter or exit school. Our results can also be extended to a variety of choices. For example, in college major choices, a larger financial return is required to induce an agent to choose a major with higher risk or larger disutility. This adds a new angle to the literature on the Roy Model of college major choice by suggesting sorting based on differential risks and disutilities across choices and agents as well as financial return.
We investigate the impact of risk aversion and precautionary savings motives on human capital investment choices. Belley and Lochner (2007) has the most relevance to our work. They provide a first order investigation detailing the direct impact that the financial return of education choice needs to overcome its utility loss. In addition to our different focus in risk aversion and precautionary savings, we relax a number of simplifying assumptions from Belley and Lochner (2007) (e.g., assuming that the product of the discount rate and one plus the interest rate is 1), which allows us to explore the comparative statics of the model in richer detail. They impose these assumptions because their main focus is on the impact of credit constraints. We are interested in exploring the relationship between the disutility of schooling and schooling decisions. Most importantly, Belley and Lochner (2007)’s model does not include risk, and we show that the variance of future consumption has a significant impact on education decisions if a disutility term is present.
Levhari and Weiss (1974) and Bilkic et al. (2012) examine the relationship between risk and education choices, but without differentiating the utility cost from the other costs. Our results demonstrate that disutility of schooling connects wealth and precautionary saving motives to education choices, providing some guidance for the construction of structural models embedding the disutility term.
Recent empirical studies explain varying educational choices using heterogeneous risk aversion and risk levels for individuals with different demographic backgrounds (Belzil, Leonardi, 2007, Brodaty, Gary-Bobo, Prieto, 2014, Chen, 2008, Hartog, Diaz-Serrano, 2015, Heckman, Montalto, 2018, Jung, 2015, Mazza, Ophem, 2018, Mazza, van Ophem, Hartog, 2013, Schweri, Hartog, Wolter, 2011). We show that, when a disutility term is present, heterogeneity in wealth alone can create a difference in education choices. Studies estimating risk aversion and education choices may be vulnerable to omitted variable bias if they specify the utility function without a disutility term.
Additionally, almost all of this previous work has focused on the implications of risk aversion for education decisions without considering the implications of the third derivative of the utility function. Our discussion of Leland (1978)’s precautionary saving motive is new. It allows us to make more specific predictions for the interaction between risk and education choices than theoretical models which consider risk aversion alone.
Section snippets
Model
We create an individual decision model rather than a general equilibrium model in order to focus on the implications of schooling disutility for education decisions. The decision maker is an agent with a two-period lifetime. She is endowed with a certain amount of human capital () and initial wealth (). At the start of the model (), she decides whether to work or to attend school in addition to optimally choosing consumption () and savings () facing consumption price 1 and interest
Risk aversion, precautionary saving and education
Given each education choice, consumption/saving decisions will be the solution to an Euler equation derived from the first order conditions of the utility maximization problem. Consider the agent’s Euler equation for saving if she chooses to attend school:
Since is concave, saving must decrease as increases. This is because human capital acts as a substitute for monetary saving via higher future income. In an empirical setting, this could mean
Discussion
In this section, we discuss the implications of our results in relevant literature studying the relationship between human capital investment and lifecycle inequality, the decision to enter and leave a school, and decisions among multiple choices.
Any study which includes a disutility term should keep the implicit assumptions that follow from doing so in mind when interpreting their results. If, for example, a researcher using this setting were to find an increase in school attendance after
Conclusion
We present a two-period model where a decision maker decides between schooling and working in the first period in addition to optimizing her consumption/saving choices across periods. The utility return is decreasing in wealth. When there is a precautionary saving motive, it is increasing in the variance of future consumption, meaning that introducing a disutility term makes education choices much more sensitive to the parameters of the model. When the increase in risk is heterogeneous across
Declaration of Competing Interest
Guanyi Yang and Ben Casner declare that they have no relevant or material financial interests that relate to the research described in this paper.
References (48)
- et al.
Can risk aversion explain schooling attainments? Evidence from italy
Labour Econ.
(2007) - et al.
Stay in school or start working?—The human capital investment decision under uncertainty and irreversibility
Labour Econ.
(2012) - et al.
Do risk aversion and wages explain educational choices?
J. Public Econ.
(2014) - et al.
Career choice and the risk premium in the labor market
Rev. Econ. Dyn.
(2017) - et al.
Interpreting the evidence on life cycle skill formation
Handb. Econ. Edu.
(2006) - et al.
Factors affecting college attainment and student ability in the us since 1900
Rev. Econ. Dyn.
(2019) - et al.
Exposure to academic fields and college major choice
Econ. Edu. Rev.
(2018) - et al.
Inequality in human capital and endogenous credit constraints
Rev. Econ. Dyn.
(2017) - et al.
Back to school: an application of human capital theory for mature workers
Econ. Edu. Rev.
(2012) - et al.
The effect of risk on the investment in human capital
Am. Econ. Rev.
(1974)
Unobserved heterogeneity and risk in wage variance: does more schooling reduce earnings risk?
Labour Econ.
Increasing risk: I. A definition
J. Econ. Theory
Do students expect compensation for wage risk?
Econ. Edu. Rev.
Back to school: federal student aid policy and adult college enrollment
J. Hum. Resour.
Education policy and intergenerational transfers in equilibrium
J. Polit. Econ.
Heterogeneity in human capital investments: high school curriculum, college major, and careers
Annu. Rev. Econ.
College attrition and the dynamics of information revelation
Technical Report
The changing role of family income and ability in determining educational achievement
J. Hum. Capital
Female labor supply, human capital, and welfare reform
Econometrica
Earnings, schooling, and ability revisited
Technical Report
Estimating the return to schooling: progress on some persistent econometric problems
Econometrica
Estimating the variance of wages in the presence of selection and unobserved heterogeneity
Rev. Econ. Stat.
Cited by (0)
- ☆
Previous versions of this paper have circulated as “The Relationship Between Disutility of Education, Wealth, and Schooling Decisions”. We would like to thank Cynthia Bansak, Peter Nencka, Audrey Light, Yaron Azreli, PJ Healy, Xuan Jiang, Abolfazl Setayesh, Jaroslav Horvath, and many others for their useful comments. All mistakes are our own.
- †
This work was completed while Dr. Ben Casner was affiliated with the Ohio State University.