The following are some very good
articles related to regression discontinuity, difference-in- difference, and instrumental
variable applications in assessing the impact of financial aid on student
college enrollment decisions:
van der Klaauw (2002). Estimating
the effect of financial aid offers on college enrollment: A
regression-discontinuity approach. International Economic Review. 43(4),
1249–1287.
“An important problem faced
by colleges and universities, that of evaluating the effect of their financial
aid offers on student enrollment decisions, is complicated by the likely
endogeneity of the aid offer variable in a student enrollment equation. This
article shows how discontinuities in an East Coast college’s aid assignment
rule can be exploited to obtain credible estimates of the aid effect without
having to rely on arbitrary exclusion restrictions and functional form
assumptions. Semiparametric estimates based on a regression–discontinuity (RD)
approach affirm the importance of financial aid as an effective instrument in
competing with other colleges for students.”
Stephanie Riegg
Cellini. Causal Inference and Omitted Variable Bias in Financial Aid Research:
Assessing Solutions The Review of Higher
Education Spring
2008, Volume 31, No. 3, pp. 329–354
Discusses the shortfall of
multivariable regression estimates when used to estimate treatment effects in
the face of omitted variable and selection bias in the case of analyzing
treatment effects of financial aid offers on enrollment. Introduces
quasi-experimental methods such as instrumental variables, difference in
difference, and regression discontinuity approaches. This paper acknowledges
that these methods are the new standard (over multivariable regression) in
program evaluation in higher ed research and advocates the use of multiple
methods to assess the robustness of results in the face of these challenges.
Godman, J. Who
merits financial aid?: Massachusetts' Adams Scholarship. Journal of Public Economics. Volume 92, Issues 10–11, October
2008, Pages 2121–2131
This paper discusses the potential biases
involved in simply comparing scholarship recipients to losers. Consistent with
Cellini (2008) it uses multiple methods to addresses these issues including
difference-in-difference and regression discontinuity estimates. The DD estimates identify treatment effects
by comparing variation across time between groups that would have received the
scholarship in the past had it been implemented to winners in the present. The
RD methods (similar to van der Klaauw (2002)) by contrast utilize a single
contemporary cohort based on the identifying assumption that treatment
assignment near the cutoff is as good as random, providing an estimate of an
average treatment effect of scholarships.