Policy Brief - Recherche en IA spécialisée au MIT

Policy Brief

Aaron M. Antoine

(corresponding author)

Institute for Learning

University of Pittsburgh

Pittsburgh, Pennsylvanie 15260

aaronanthony@pitt.edu

Lindsay C. Page

Learning Research and

Development Center

University of Pittsburgh

Pittsburgh, Pennsylvanie 15260

lpage@pitt.edu

HOW BIG IS THE BALLPARK? ASSESSING

VARIATION IN GRANT AID AWARDS WITHIN

NET PRICE CALCULATOR STUDENT PROFILES

Abstrait
Net price calculators (NPCs) are online tools designed to increase
transparency in college pricing by presenting students with in-
dividualized estimates of net prices to attend a given postsec-
ondary institution. The federal template NPC predicts identical
aid awards for similarly proﬁled students attending the same in-
stitution. Using the 2012 National Postsecondary Student Aid
Survey, we use regression analysis to assess variation in actual
ﬁnancial aid awards among students predicted by the federal
template NPC to receive identical awards. We ﬁnd estimated aid,
derived from the federal template NPC, accounts for 70 pour cent
of the variation in actual grant aid received by students. We then
consider modiﬁcations to the federal template NPC that include
an additional upper-income bracket option and indicators of both
high school grade point average and Free Application for Fed-
eral Student Aid ﬁling time. These modiﬁcations explain an addi-
tional 16 percentage points, or more than half, of the unexplained
variation in actual grant aid awards across all institutional sec-
tors. These ﬁndings are especially relevant as legislators consider
policy eﬀorts to bring greater transparency to college cost and
pricing, including creating a universal NPC in which prospective
students can enter information once to receive net price estimates
at any institution.

https://doi.org/10.1162/edfp_a_00353

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Aaron M. Anthony and Lindsay C. Page

INTRODUCTION
College net prices—the out-of-pocket prices students and families pay for college af-
ter accounting for grant aid—are the best indicators of a postsecondary institution’s
aﬀordability. Cependant, net prices are stubbornly opaque and often remain so until af-
ter students have had to make important college choices, such as where to apply and
sometimes even where to enroll.

Financial aid can make higher education feasible for families who otherwise would
not be able to aﬀord it. Cependant, ﬁnancial aid also contributes to an unclear pricing sys-
tem in which inclusive sticker prices are often far higher and more visible than the net
prices students face after receiving grant aid. Lack of clarity in pricing can contribute to
inequalities in enrollment and persistence in higher education. Though a lower-income
family would likely be eligible for more need-based ﬁnancial aid than their wealthier
homologues, they are also less likely to successfully navigate complicated ﬁnancial aid
applications and accurately estimate college costs they would actually face (Avery and
Kane 2004; Grodsky et Jones 2007; Hoxby et Turner 2015).

In response, policy makers have introduced a variety of eﬀorts. Some, like re-
gional Promise programs, aim to reduce real costs of college with clearly articulated
“promises” of grant-based aid. Others, like Free Application for Federal Student Aid
(FAFSA) simpliﬁcation eﬀorts, aim to reduce the complexity in the process of access-
ing aid. And still others, like net price calculators (NPCs), aim to make the real costs of
college more transparent. NPCs are online tools to estimate the net price that a given
student would pay to attend a given school. Because they provide students with esti-
mates of net pricing prior to navigating complicated aid applications, NPCs are a pri-
mary way for colleges and universities to improve pricing transparency.

To be most useful to prospective students and their families, NPCs should be de-
signed with a focus on providing reasonably accurate grant aid estimates while min-
imizing complicated inputs from users. All NPCs must allow for an estimate of how
much a family would be expected to contribute toward the cost of college, or expected
family contribution (EFC).1 Cependant, colleges use diﬀerent NPCs, and these diﬀerent
NPCs vary in terms of how much information they request from users to form this es-
timate. Ici, we focus on the NPC template provided federally by the U.S. Department
of Education because it is among the most common NPCs and its limited data inputs
are relatively straightforward for student users to provide unassisted. Speciﬁcally, le
federal template draws on the student’s dependency status, approximate family income,
residency status, and college housing arrangements to produce net price estimates.

More complicated NPC alternatives are also common. An NPC that requests highly
detailed student and family ﬁnancial information may generate more accurate aid es-
timates, but requiring ﬁne-grained ﬁnancial information risks introducing complexity
and barriers to NPC use similar to those associated with federal aid applications (voir
Dynarski and Scott-Clayton 2013 and Dynarski and Wiederspan 2012). In contrast, un
simple NPC requires only basic inputs that most users are readily able to provide, mais
may trade accuracy for ease of use.

1. As part of the Consolidated Appropriations Act of 2021, EFC is set to be replaced with Student Aid Index (SAI)
beginning in July 2023. The SAI will serve a similar function to EFC, but at the time of writing, it is not yet
clear how the change from EFC to SAI will impact the formula for the federal template NPC; though a direct
substitution of SAI for EFC is practical and plausible.

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717

Variation in Aid within NPC Profiles

We study this simplicity and accuracy balance by measuring the variation in actual
ﬁnancial grant aid amounts among students predicted by the federal template NPC to
receive identical awards. We then explore modiﬁcations to the federal template NPC to
reduce unexplained variation in aid awards. We ﬁnd that estimated grant aid derived
from the simple inputs of the federal template NPC accounts for 70 percent of the vari-
ation in actual grant aid received by students overall. We consider modiﬁcations to the
federal template NPC, including further diﬀerentiation of household income categories
at the upper end of the distribution, incorporating an indicator of high school perfor-
mance, and including an indicator for the timing of ﬁnancial aid application. These
modiﬁcations explain more than half of the remaining variation in awards. Yet stu-
dents predicted to receive identical grant aid awards can still receive actual aid awards
that vary by thousands of dollars. Discrepancies between estimated and actual net prices
may lead families to deem certain postsecondary options to be more (ou moins) aﬀordable
than they actually are, potentially shifting students’ application choices. Information on
simple enhancements to NPCs is especially timely as Congress considers changes to
existing NPCs and the creation of a “Universal NPC,” a topic of legislation since 2013,
though such a bill has not yet been introduced in the current legislative session.

R E V I E W O F P R E V I O U S L I T E R AT U R E
Net price calculators are a product of the 2008 renewal of the Higher Education Oppor-
tunity Act and have been federally mandated to be included on postsecondary institu-
tions’ Web sites since October 2011. In an early review of NPCs, Cheng (2012) found the
calculators challenging to ﬁnd and use, inconsistently labeled, and diﬃcult to compare
across institutions. These critiques are the basis for many of the speciﬁc improvements
cited in Net Price Calculator Improvement Act legislation. Previous versions of legis-
lation would require postsecondary institutions to consistently and prominently label
their calculators as “Net Price Calculators” (as opposed to “Education Cost Calculator”
or “Tuition Calculator,” for example) and populate their calculators with data no more
than two years old. Such legislation would also allow the Secretary of Education to cre-
ate a universal NPC that would make it possible to complete one set of questions and
receive net price estimates for any institution.

A more recent review of NPCs at eighty public and private four-year institutions
found that about 40 percent of schools were using outdated data, and other schools used
NPCs that did not clearly diﬀerentiate loans from grants or scholarships (Perna, Wright-
Kim, and Jiang 2019). In addition to the enhancements listed in the previous NPC
improvement legislation, Perna and colleagues recommend the federal NPC template
list grant awards by source, variation in costs by major or academic discipline, et
groups for whom estimates do not apply (par exemple., non-U.S. citizens or part-time students).
A pilot study of NPC performance found that, on average, NPCs provide better es-
timates of out-of-pocket prices than sticker prices, yet actual grant aid awards may vary
substantially from NPC predictions (Antoine, Page, and Seldin 2016). Especially for
low-income families, even small disparities between predicted and actual aid may im-
pact college decisions (Pallais 2009; Castleman et Page 2016). An NPC that severely
overestimates grant aid may lead students to face unexpectedly large college net prices.
Inversement, an NPC that substantially underestimates grant aid could tilt a school’s

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Aaron M. Anthony and Lindsay C. Page

applicant pool in favor of those students who are ﬁnancially able to make up the pre-
dicted shortfall in grant aid, while less ﬁnancially secure students may consider the
school to be unaﬀordable and forgo even applying.

The complexity of the calculator is important because the very purpose of an NPC
is to increase transparency in college pricing and ﬁnancial aid. Substantial research
points to the complexity of the ﬁnancial aid application process as a primary cause of
low take-up rates of student aid (Dynarski and Scott-Clayton 2006, 2008, 2013; Bet-
tinger et al. 2012; Dynarski and Wiederspan 2012; Page and Scott-Clayton 2016). Overly
complex calculators risk becoming an additional barrier to clear price information if
the calculator tools themselves are too burdensome to use.

This study builds on prior research by Kane (1995), Stoll and Stedman (2004), et
Dynarski and Scott-Clayton (2006) on exploring the sensitivity of ﬁnancial aid calcu-
lations to manipulations in its independent components. Kane notes that most of the
variation in Pell grants can be explained using just a few variables. Stoll and Stedman
simulate the eﬀect of excluding items from the calculation of EFC. Dynarski and Scott-
Clayton show that federal need-based aid distribution can be reproduced using just a
fraction of the information that is now collected on the FAFSA.

We expand on this line of research in two key ways. D'abord, these prior studies focus
on means-tested federal grant aid. We focus on all sources of grant aid, including insti-
tutional grant aid, which tends to be more variable, especially for private institutions.
This is important to consider as more than 40 percent of all grant aid—the largest
portion from any source—comes from the postsecondary institutions themselves (Ma
et autres. 2017). Deuxième, the policy objective in these previous studies focused on strate-
gically reducing ﬁnancial aid data elements and maintaining aid distribution. Plutôt,
we consider the possibility of strategically increasing or modifying data components to
decrease variation in grant aid awards to similar students, while aiming to balance the
beneﬁt of decreased variation with the potential of increased complexity by requiring
students to input additional information.

N E W E M P I R I C A L E V I D E N C E
We use data from the 2012 National Postsecondary Student Aid Survey (NPSAS:12) et
ﬁxed-eﬀects regression analyses to assess the extent to which actual grant aid received
varies for students with identical NPC grant aid estimates. Ideally, our analysis would
consider two grant aid ﬁgures central to this study: the grant aid students actually re-
ceive and the grand aid students are predicted to receive based on information used in
the federal template NPC. If this data were available, we could estimate for what shares
of students NPC estimates were within x percent (or dollars) of their actual aid awards.
Cependant, because NPSAS:12 data include actual grant aid information but not NPC-
estimated grant aid, this approach is not possible. C'est, while NPSAS provides us
with information on actual aid received, we lack information on each student’s actual
aid estimate.

Although we do have the student- and institution-level information for estimating
grant aid within the federal template NPC, we cannot do so directly because the data
populating NPCs at the time of our analysis did not correspond to the year of our data.
For this reason, we use a ﬁxed-eﬀects approach through which we focus on variation

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Variation in Aid within NPC Profiles

in grant aid for students who would receive identical NPC estimates. Speciﬁcally, nous
generate a set of ﬁxed eﬀects for groups of students that the federal template NPC
would estimate at the same level of grant-based aid by virtue of attending the same
institution, and being identical on the full set of characteristics on which the federal
template NPC relies. We then examine the variation in actual aid awards within these
observationally similar groups of students (see Appendix A for sampling and methods
details, and ﬁgure A.1 for how the federal template NPC operates; appendix materials
are available in a separate online appendix that can be accessed on Education Finance
and Policy’s Web site at https://doi.org/10.1162/edfp_a_00353).

NPC estimates pertain to ﬁrst-time, full-time undergraduate students who applied
for federal ﬁnancial aid and enrolled in a single institution for the full year. We limit our
sample to include only these students. En outre, as our analysis relies on measuring
variation in grant aid awards for students with the same NPC proﬁle attending the same
institution, we exclude from the sample any student who has an NPC proﬁle diﬀerent
from all other students observed for their institution. About half of the remaining ob-
servations are instances of two (33 pour cent) or three (17 pour cent) observations within a
given institution-NPC proﬁle.

Suivant, we consider three modiﬁcations that might be incorporated into the federal
template NPC to decrease variation in aid awards for similar students attending the
same school.

Modification 1: Additional Upper-Income Boundaries
The federal NPC template uses income brackets ranging from “less than $30,000” to “$99,999” in $10,000 increments, and “above $100,000” to classify students’ house-
hold income. This binning process means, Par exemple, that a family earning $100,000 annually is categorically identical to a family earning ten times that amount. Twenty per- cent of families in our sample are clustered into the uppermost of nine income brackets. We add a new uppermost income bracket, such that the resulting income levels include the original “less than $30,000” to “99,999,” plus “$100,000 to $150,000” and “above
$150,000.” Modification 2: Indicator of Academic Merit Many institutions distribute merit aid based on predictable and widely used merit2 met- rics (par exemple., SAT or ACT scores or high school grade point average [HSGPA]). We consider whether adding a threshold indicator for relatively high versus low GPA explains addi- tional variation in aid received. We consider three potential GPA threshold values: 2.5, 3.0, et 3.5. Modification 3: FAFSA Filing Timing Certain types of ﬁnancial aid are awarded on a ﬁrst-come, ﬁrst-served basis3 (McKin- ney and Novak 2015). Par conséquent, grant aid awards may be determined not only by what 2. We use categorical variables for indicators of academic merit to be in line with the federal template NPC, which requires institutions to enter their data in terms of categorical variables. 3. We use categorical variables for indicators of FAFSA ﬁling time to be in line with the federal template NPC, which requires institutions to enter their data in terms of categorical variables. 720 l Téléchargé à partir du site Web : / / direct . m je t . / F / e du e d p a r t i c e – pdlf / / / / 1 6 4 7 1 6 1 9 6 5 2 5 0 e d p _ a _ 0 0 3 5 3 pd / F . f par invité 0 7 Septembre 2 0 2 3 Aaron M. Anthony and Lindsay C. Page information the student provides on the FAFSA itself, but also by when the student completes the FAFSA. As more than 60 percent of students in our sample ﬁled within the ﬁrst three months of the ﬁling window, we use monthly intervals within this time- frame to test thresholds for early FAFSA ﬁlers. We consider three potential timeframes, measured in months from the opening of the FAFSA application ﬁling window: within one month, within two months, and within three months.4 R E S U LT S Our results focus on two key metrics derived from our regression models: R2 and root mean square error (RMSE). R2 communicates the share of variation in a given outcome that a model explains. An R2 of 0, Par exemple, indicates that a model does not predict any of the variation in the outcome, while an R2 of 1 indicates that a model fully explains all of the variation in the outcome. In our context, R2 shows how much variation in actual award packages is explained by information requested by the federal template NPC. RMSE is a measure of the distance between actual data points and the model’s predictions. For our NPC models, the RMSE is the typical distance between actual aid awards and average awards for observationally identical students. An RMSE of 0 (or an R2 of 1) is likely not possible with any amount of information because of modest noise intentionally introduced in the NPSAS data to preserve conﬁdentiality. En plus, we note that we only know ﬁnancial aid information for the aid oﬀers students actually accept. It is possible that there are grants a student could not or would not accept. In ﬁgure 1, we present the model modiﬁcations with the best performance. We ﬁrst show the R2 statistic associated with the current federal template NPC (“Basic model”) compared to the most eﬀective (“Best model”) of the proposed NPC modiﬁcations. Be- neath the ﬁgure, we specify the most eﬀective HSGPA and FAFSA ﬁling thresholds for each sector, along with the percentage point improvement in R2 between the basic and “best” modiﬁcation model. First consider the R2 value of 0.70 (ﬁgure 1, leftmost bar). This tells us the data ele- ments gathered by the current federal template NPC explain 70 percent of the variation in actual grant aid awards. Continuing with the darker gray bars showing R2 values as- sociated with the current federal template, or “basic” model, we see these rates diﬀer somewhat by institutional sector: The federal template NPC data explain about 70 par- cent of variation in aid awards at public four-year institutions, 60 percent in private four-year and public two-year institutions, et 55 percent in for-proﬁt institutions. The lighter bars show the most eﬀective modiﬁcations to the federal template NPC model. Within each institutional sector, the modiﬁcations explain more than half of the variation in grant aid awards that the current federal template NPC left unex- plained. Each model includes additional upper income brackets, but optimal HSGPA and FAFSA ﬁling thresholds vary by institutional sector. The combination of a 1 Febru- ary FAFSA ﬁling threshold and HSGPA indicator of 3.5 most eﬀectively improves the federal template NPC’s explanatory potential overall, increasing the R2 from 0.70 à 0.86. By sector, the best model combinations include a 3.0 (public two-year and 4. Dans 2012, when data for this study were collected, the FAFSA application window began on 1 Janvier. It has since been moved to 1 Octobre. For this reason, we discuss relative time periods (c'est à dire., “within one month”) rather than speciﬁc dates and months. l Téléchargé à partir du site Web : / / direct . m je t . / F / e du e d p a r t i c e – pdlf / / / / 1 6 4 7 1 6 1 9 6 5 2 5 0 e d p _ a _ 0 0 3 5 3 pdf . / f par invité 0 7 Septembre 2 0 2 3 721 Variation in Aid within NPC Profiles l D o w n o a d e d f r o m h t t p : / / direct . m je t . / / f edu ed p a r t i c e – pdlf / / / / 1 6 4 7 1 6 1 9 6 5 2 5 0 e d p _ a _ 0 0 3 5 3 pd / F . f par invité 0 7 Septembre 2 0 2 3 Remarques: Overall results, comparing federal template Net Price Calculator (NPC) R2 and root mean square error (RMSE) values to those of the best (c'est à dire., highest R2) NPC model. Modifications include additional upper-income brackets and indicators of high school grade point average (HSGPA) and Free Application for Federal Student Aid (FAFSA) filing time. The corresponding “best model” combinations of HSGPA and FAFSA filing dates along with the percentage point difference in R2 are listed below each institutional sector. RMSE indicates the typical dollar difference between actual awards and the amount anticipated by the federal template NPC. N = 7,560. Chiffre 1. Overall Results for-proﬁt) ou 3.5 (public and private four-year) HSGPA, and a 1 Février (private four- année) ou 1 Mars (public four-year, two-year, and for-proﬁt) FAFSA ﬁling date. With improvements in R2 statistics ranging from 20 à 26 percentage points within sec- tors, the proposed modiﬁcations represent a sizeable increase in NPC explanatory po- tential over the current federal template model by adding easily reportable and simple metrics. Suivant, we focus on the RMSE (shown in parentheses beneath the R2 statistic). We see that 1 standard deviation in actual aid awards from what current NPC inputs anticipate is $5,670. Autrement dit, a typical student received an actual ﬁnancial aid package that
was nearly $5,700 plus (ou moins) than what the NPC model would estimate. Because we do not have actual NPC estimates, we were not able to assess if the estimates were over- or under-predicted. Cependant, residual analyses reveal a narrower residual distribution for those from households with up to $30,000 in annual income and a wider distribu-
tion above that level. This suggests a greater potential for inaccuracy for middle- et
upper-income households. The RMSE may be a useful measure for prospective stu-
dents to approximate high and low estimates of their expected grant awards.

Looking across institutional sectors, we also see that typical deviations from NPC-
predicted awards vary substantially by institutional sector. Par exemple, within the

722

Aaron M. Anthony and Lindsay C. Page

sample of private four-year institutions, where students receive relatively more grant
aide, on average, the standard deviation between estimated and actual awards is nearly
$11,000. Par contre, a typical community college student receives an award that is only $2,400 diﬀerent from what the federal template NPC estimates. See table B.1 (in online
Appendix B) for complete results of the eﬀects of the diﬀerent modiﬁcation combina-
tion, and ﬁgure B.1 for a chart summarizing changes in R2 from introducing one, deux,
and three additional NPC elements.

D I S C U S S I O N O F P O L I C Y A LT E R N AT I V E S
We demonstrate that with relatively simple modiﬁcations, the federal template NPC can
explain up to 90 percent of the variation in actual grant aid awards, but that remaining
variation in actual awards among similar students can remain quite large, especially
within postsecondary sectors with higher sticker prices and more generous ﬁnancial aid
packages. Whether the remaining share of unexplained variation warrants the added
complexity of alternative calculators is a subjective matter, which may vary depending
on the student and the institution in question.

As the layout of the federal template NPC requires institutions to enter their data
in terms of categorical variables, it is important for NPC developers to consider exactly
what thresholds constitute “high” or “low” high school GPAs or “early” or “late” FAFSA
ﬁling. A one-size-ﬁts-all model might adopt the thresholds that were most eﬀective in
our overall analysis—that is, 3.5 HSGPA and comparatively early FAFSA ﬁling. A more
targeted approach, cependant, would likely be more eﬀective. One strategy is to allow
for institutions to use HSGPA and FAFSA ﬁling information best-suited to their own
levels and methods of awarding ﬁnancial aid. The front-facing end of the NPC would
look the same but operational thresholds of high/low HSGPA and early/late FAFSA
could be speciﬁc to individual institutions. Par exemple, an institution can select a GPA
threshold in line with the merit aid they provide or a FAFSA timing threshold in line
with relevant priority deadlines for FAFSA ﬁling.

An alternative approach is to provide NPC options for students to use according to
the information and time they have available. Some examples of this approach include
the college search site College Raptor (collegeraptor.com) and the MyinTuition NPC
(see myintuition.org). The college search function on College Raptor allows a user to
indicate the amount of ﬁnancial data they are prepared to provide—options include
“no ﬁnancial data,” “I know my EFC,” “limited family and ﬁnancial data,” and “full
family and ﬁnancial data”—and the extent of ﬁnancial information requested adjusts
accordingly.

The MyinTuition NPC requests more detailed information, including remaining
mortgage balance and assets in retirement and nonretirement accounts, which may
pose challenges for some users but is still simpler than many popular NPC alternatives.
The MyinTuition NPC also provides a range of net price estimates (labeled “low,” “best,»
and “high”), along with a graphic illustration of grant and loan sources (as opposed to
the single line-item federal NPC estimate).

A modiﬁed federal template NPC may adopt a similar feature to present users with
a prediction interval within which grant aid estimates are likely to vary. Even though

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723

Variation in Aid within NPC Profiles

we decrease the share of unexplained variation in grant aid awards, the typical diﬀer-
ence between estimated and actual awards still exceeds $5,000 overall and approaches $11,000 within private four-year institutions. Providing an institution-speciﬁc estimated
range of likely grant aid, in addition to a speciﬁc dollar estimate, may help students
make more informed college enrollment decisions.

R E C O M M E N DAT I O N
Minimizing complexity in user-provided data is a key motivator in our NPC design rec-
ommendation. Our suggested modiﬁcations would require relatively simple changes
to both the front- and back-facing sides of the federal template NPC. On the user-facing
side, we suggest adding options for household income of “$100,000 to $150,000” and
“Above $150,000” to better distinguish upper-middle and upper-income households.
We also suggest introducing two questions to assess HSGPA and expected FAFSA ﬁl-
ing time. Users could report their unweighted HSGPA on a scale of 1 à 4, and their
expected FAFSA ﬁling time as a speciﬁc date on a calendar. On the back end, ces
HSGPA and FAFSA ﬁling time measures would be translated into relatively high and
low GPA values and relatively early and late FAFSA ﬁling dates.

These limited data inputs could operate as a framework for designing a “Universal
Net Price Calculator” as outlined in the Net Price Calculator Improvement Act, lequel
had been introduced in Congress since 2013, but has not yet been introduced in the
current legislative session. Additional data elements such as college-speciﬁc savings
accounts, parents’ retirement savings, or remaining mortgage balances may be espe-
cially helpful for narrowing variation in aid among similar students attending schools
where aid is relatively more plentiful—such as four-year private nonproﬁt schools—or
where pricing varies substantially by ﬁeld of study or academic major (as recommended
by Perna, Wright-Kim, and Jiang 2019).

D I S C U S S I O N O F T H E I M P L I C AT I O N F O R P O L I C Y A N D P R AC T I C E
Previous policy recommendations for NPCs centered on their usefulness and usability
(see Cheng 2012 and Perna, Wright-Kim, and Jiang 2019). With recommendations on
consistent labeling of aid terminology, improved prominence on Web sites, and sug-
gested additional helpful information such as diﬀering costs by academic major or for
whom the estimates do not apply, these reviews emphasize improvements for many spe-
ciﬁc facets of NPCs. They do not, cependant, assess how NPCs use the information they
request to estimate aid. Our study diﬀers because it is an assessment of potential ad-
ditional data elements that are straightforward for students to provide and eﬀective for
improving college net price estimates. These recommendations represent an additional
dimension of NPC improvement potentially allowing policy makers and institutions to
improve the form and function of their NPCs. The Consolidated Appropriations Act of
2021 included changes to simplify the FAFSA and make aid predictable, but did not cre-
ate a Universal Net Price Calculator. Cependant, postsecondary institutions do not need
to wait for federal legislation to make such improvements to their NPCs and overall
price transparency.

724

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Aaron M. Anthony and Lindsay C. Page

REMERCIEMENTS
Funding for this brief was provided by a grant from the American Educational Research Associ-
ation, which receives funds for its AERA Grants Program from the National Science Foundation
under grant number DRL-091014.

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