Triangles: The Effects of Educational Differences on Wellbeing

Recent decades have seen a surge of empirical work estimating causal determinants of education. In my own work, I have used natural experiments to examine causal determinants of education and income, as is common in impact evaluation.  Much of this literature, including my own papers, uses years of schooling as a central outcome, although this is often combined with longer-term follow-ups on income and/or health.

An open question is what these findings mean in terms of well-being (or ‘welfare’ in economists’ parlance), which should be the ultimate benchmark for measuring the benefit of interventions. A common, yet ad hoc approach employs Jacob Mincer’s (1958) returns to schooling, which are estimates of the proportional increase in adult earnings associated with each additional year of schooling. Mincer himself showed that this measure is not a true rate of return, but rather a footprint of a decision problem solved earlier in life.  Specifically, these so-called returns to schooling are not adjusted for costs incurred, such as tuition and foregone wages, during childhood. Therefore they cannot be directly compared with financial rates of return, nor are they, as such, directly relevant for thinking about well-being. A more recent approach (e.g., Dhaliwal et al., 2011) is ‘cost effectiveness,’ which normalizes increased time in school per dollar spent in an intervention. Such exercises are, however, imperfectly related to how much a program influences welfare (Alderman and Bleakley, 2013; Canning, 2013). For example, an intervention that increases the marginal quantity of school (e.g., a tuition subsidy) is quite different from one that increases the quality of schooling and thereby induces an increase in quantity of schooling as a side effect. These two interventions might appear equally cost effective, but the former is less beneficial than the latter. (If they have the same cost-effectiveness score, then they increase quantity the same amount per dollar spent. But the former has lagniappe of improving quality as well.) What is missing is an approach that permits applied welfare analysis of educational interventions, to complement these existing, ad hoc approaches.

My long-term goal is to bring time-honored tools—rectangles and triangles—to the analysis of educational interventions. These have a long history of use for analysis of taxes or monopolies in economics, but have not been widely employed in educational questions. These concepts measure the change in well-being caused by a change in the underlying environment (e.g., from an intervention). These are polygons because they appear in the graphical analysis of an optimization problem (for example, for optimal years of schooling). The rectangle refers to the change in well-being if choices are held fixed, while the triangle measures the additional gain realized upon re-optimization. (They are, respectively, the first- and second-order approximations to the change in welfare, and their sum is total change in welfare.)  An example is seen in Figure 1, in which the MC curve is the marginal cost of going to school and the MB curves measure the marginal benefits of time in school. If marginal benefits were MB, it would be optimal to finish s0 years of school. If an intervention shifts marginal benefits from MB to MB’, the person gains R without changing anything else, and then an additional T by staying in school until s1, instead of stopping at s0.  The rectangles-and-triangles approach, in contrast to the tools mentioned above, is explicitly designed to account for costs by evaluating gains and losses local to optimal years of school, at which point marginal benefits and costs are equal.

Other works cited:

Alderman, Harold, and Hoyt Bleakley. 2013. “Child Health and Educational Outcomes.” In Education Policy in Developing Countries. , ed. Paul Glewwe, Chapter 4.  Chicago, IL:University of Chicago Press.

Canning, David. 2013. “Axiomatic Foundations for Cost-Effectiveness Analysis.” Health Economics, 22(12): 1405–1416.

Dhaliwal, Iqbal, Esther Duflo, Rachel Glennerster, and Caitlin Tulloch. 2011. “Comparative Cost-Effectiveness Analysis to Inform Policy in Developing Countries: A General Framework with Applications for Education.” Abdul Latif Jameel Poverty Action Lab (J-PAL), MIT.

Mincer, Jacob. 1958. “Investment in Human Capital and Personal Income Distribution.”  Journal of Political Economy, 66(4): 281–302.