The Determinants of Educational Attainment: Modeling and Estimating the Human Capital Model and Education Production Functions.

• Author: Wilson, Kathryn

Kathryn Wilson [*]

This paper develops and estimates a theoretical model of an individual's high school graduation choice. The model incorporates the idea of a utility-maximizing youth responding to the economic incentives associated with incremental education, as posited by the human capital literature. However, it also allows for family, neighborhood, and school characteristics to affect the process of being educated, as posited by the education production function literature. Estimation of the model, using the Panel Study of Income Dynamics (PSID) supplemented with neighborhood and school data, indicates that indeed students respond to economic incentives in making education choices; however, most of the effects of background characteristics are working through the education process rather than affecting returns to schooling.

1. Introduction

   Despite the important role of education in our society, there are still many unknowns about the process of educational attainment and an individual's decision regarding how much education to obtain. This study develops and estimates a theoretical model of an individual's high school graduation decision within the framework of utility maximization. The model posits that an individual makes this education decision in response to the expected economic returns associated with the incremental human capital accumulation and allows background characteristics and circumstances to affect both the returns to education and the schooling process. In addition, the study broadens the scope of past research on educational attainment by examining both neighborhood and school characteristics in the same study.

   The model and its estimation address three questions that are informative and also have policy implications: Do youths respond to economic incentives? [1] Is youth behavior better explained by the human capital model or the education production function model? Does school spending affect either the education level of students directly or the future income students will receive? Answering these questions not only gives us insights into the decision-making process but also suggests what policy instruments may be most effective at increasing both educational attainment and the income returns to this education.

   Historically, there have been three rather different ways of conceptualizing educational attainment in economics. The human capital literature models individuals as choosing to acquire human capital in response to the expected returns to education. In this view, education is an investment good, and the individual chooses the level of education consistent with these returns. Studies that focus on the empirical effect of school characteristics on educational attainment model education production functions in which the output (education) is a function of the inputs (school and family characteristics); changing an input will result in a change in the output. Therefore, educational attainment in these models is determined by the inputs and the technology rather than being a choice of the individual. The final method, used by most empirical studies of family and neighborhood characteristics, is to estimate reduced-form equations of educational attainment where there is no attempt to understand the mechanism through which the independent variables are affecting educational attainment but that rather simply examine the relationships that are present.

   This study combines both the idea of family, school, and neighborhood characteristics being inputs in the production of educational attainment and that of an individual who makes decisions in response to the expected returns to high school graduation. The structural model recognizes that youths make decisions about educational attainment on the basis of their perceptions of the expected returns to education. By explicitly modeling the expected returns to high school graduation for each individual, I am able to separate the nonincome effects of family, neighborhood, and school characteristics on educational attainment (the education production process) from the linkages through which those characteristics influence the youth's expected returns to education and hence attainment. [2]

   Section 2 of this paper provides a more thorough discussion of the previous literature on educational attainment. Section 3 contains the structural model where utility-maximizing youths choose an education level on the basis of expected future income and the nonpecuniary benefits and costs of education. Following a description of the data in section 4, section 5 contains a discussion of methodology and issues involved in estimating the structural model, and the results of the estimation are reported in section 6. Section 7 discusses the policy implications of the paper and the conclusions.

2. Literature Review of Educational Attainment

   A review of the primary findings of previous literature provides a context for understanding the contributions of this model and data. Given the vastness of the literature on educational attainment and returns to education, the review focuses on providing a general overview of the strategies employed, the findings, and a discussion of the shortcomings of these studies. The literature review is divided into those studies that use the human capital theory, the education production function, and reduced-form models.

   Human Capital Literature

   Becker's (1964) famous work Human Capital develops a model of the individual's investment in education. An individual is modeled as choosing between current work or forgoing this work to acquire human capital that will have higher rates of return in the future. The key factor in the model is the notion that education is an investment of time and forgone earnings for future pay. This marked the first work where education is an investment good. An empirical body of literature has focused on the investment model of the decision to pursue education by using time-series data. [3] These types of studies, summarized in Freeman (1986), generally find that the estimated elasticity of supply of higher-educated persons to changes in salaries falls in the range of one to two.

   Willis and Rosen (1979) is the first study to examine education as an investment good at an individual level. They present a structural model of the demand for postsecondary schooling in which individuals make their education decision in response to the incomes associated with the two education levels. They estimate that expected lifetime earnings gains associated with incremental schooling influence the decision to attend college; they find an estimated elasticity of enrollment to earnings of about two.

   These studies assume that returns to human capital affect the amount of education an individual will choose to receive, but they ignore other factors that may directly affect the education process. For example, if an individual is attending a very poor quality school, this may affect her expected returns to education and thus how much education she receives. However, if attending a poor-quality school reduces the utility she receives from the process of going to school, perhaps because the school is unsafe or other students are unruly, this direct utility from school is not allowed to influence her decision conditional on returns to schooling. The importance of this shortcoming will be more evident when contrasted with the discussion of the education production function literature, which takes the opposite position that her schooling environment will directly affect how much education she receives but which does not consider the returns to education.

   A related vein of literature on the returns to education, particularly relevant for this study, examines the relationship between education, earnings, and measures of school quality. Card and Krueger (1992) use state-level data to estimate the effect of school quality on the rate of return to education for men born between 1920 and 1949. They find that men educated in states with lower student/teacher ratios, longer average term length, and higher-paid teachers have higher rates of return to education but that men educated in states where parents are more educated or have higher income do not have statistically significantly different rates of return to education. Altonji and Dunn (1995) use individual-level data in estimating the effect of parental education and school quality on returns to education. They find mixed evidence regarding the effect of parental education, but in most of the specifications, including their preferred specification, having a more educated parent is associated with a higher rate o f return to education. School expenditures per student, however, while increasing the level of income at all education levels, does not have a positive effect on the rate of return to education.

   Education Production Function Literature

   Studies that focus on the effects of school characteristics on educational attainment have done so primarily within the context of an education production function. School quality and family characteristics are viewed as inputs in the production of children's educational attainment. The measurement of the school inputs and the outputs of interest vary from study to study, but most measure inputs as expenditures per student, student/teacher ratios, teacher salaries, and class size. For about two-thirds of the studies, the output of educational attainment is measured by test scores. The other one-third focus on quantity of schooling achieved, such as high school graduation, college attendance, or years of education.

   The most well known and cited article on the school quality literature is Hanushek's (1986) article "The Economics of Schooling: Production and Efficiency in Public Schools." [4] In this article, Hanushek reviews 147 regressions, taken from 33 separate published articles, of the effects of school characteristics on educational...